%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP003^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:16 AM UTC 2026
% Result : Theorem 86.30s 18.33s
% Output : Refutation 73.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 33
% Syntax : Number of formulae : 612 ( 261 unt; 0 typ; 1 def)
% Number of atoms : 1508 ( 798 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 7209 ( 724 ~; 443 |; 51 &;5941 @)
% ( 0 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 230 ( 230 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 7 con; 0-4 aty)
% Number of variables : 1602 ( 138 ^;1445 !; 18 ?;1602 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% 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_decl,type,
c_2Earithmetic_2E_2A: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2E_2B_decl,type,
c_2Earithmetic_2E_2B: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Enum_2E0_decl,type,
c_2Enum_2E0: tyop_2Enum_2Enum ).
thf(c_2Eprim__rec_2E_3C_decl,type,
c_2Eprim__rec_2E_3C: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Earithmetic_2EBIT1_decl,type,
c_2Earithmetic_2EBIT1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EBIT2_decl,type,
c_2Earithmetic_2EBIT2: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebool_2ECOND_decl,type,
c_2Ebool_2ECOND:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(c_2Earithmetic_2EEVEN_decl,type,
c_2Earithmetic_2EEVEN: tyop_2Enum_2Enum > $o ).
thf(c_2Ebool_2EF_decl,type,
c_2Ebool_2EF: $o ).
thf(c_2Earithmetic_2EMOD_decl,type,
c_2Earithmetic_2EMOD: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2ENUMERAL_decl,type,
c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EODD_decl,type,
c_2Earithmetic_2EODD: tyop_2Enum_2Enum > $o ).
thf(c_2Enum_2ESUC_decl,type,
c_2Enum_2ESUC: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebool_2ET_decl,type,
c_2Ebool_2ET: $o ).
thf(c_2Earithmetic_2EZERO_decl,type,
c_2Earithmetic_2EZERO: tyop_2Enum_2Enum ).
thf(sk1_decl,type,
sk1: tyop_2Enum_2Enum ).
thf(sk1_def,definition,
( sk1
= ( @+[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 ) ) ) ) ) ) ).
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(149,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(150,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)],[149]) ).
thf(151,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)],[150]) ).
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(134,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(135,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)],[134]) ).
thf(136,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)],[135]) ).
thf(137,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)],[136]) ).
thf(138,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)],[137]) ).
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(406,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)],[138,36]) ).
thf(408,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)],[406]) ).
thf(420,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)],[408]) ).
thf(530,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)],[151,420]) ).
thf(535,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)],[530]) ).
thf(549,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)],[535]) ).
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(144,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(145,plain,
( ( c_2Enum_2ESUC @ c_2Enum_2E0 )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(lifteq,[status(thm)],[144]) ).
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(169,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(170,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)],[169]) ).
thf(171,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)],[170]) ).
thf(1586,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)],[145,171]) ).
thf(1675,plain,
! [A: $o] :
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Enum_2ESUC @ c_2Enum_2E0 ) @ ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ) ),
inference(pre_uni,[status(thm)],[1586:[bind(A,$thf( ^ [E: TA] : ( c_2Enum_2ESUC @ c_2Enum_2E0 ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(2083,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)],[1675]) ).
thf(3456,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)],[2083,145]) ).
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(155,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(156,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)],[155]) ).
thf(157,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)],[156]) ).
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(128,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(129,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)],[128]) ).
thf(130,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)],[129]) ).
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(163,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(164,plain,
! [TA: $tType,B: TA,A: TA] :
( ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A )
& ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ) ),
inference(cnf,[status(esa)],[163]) ).
thf(165,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A ),
inference(cnfConj,[status(thm)],[164]) ).
thf(167,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A ),
inference(lifteq,[status(thm)],[165]) ).
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(353,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ $true @ A @ B )
= A ),
inference(rewrite,[status(thm)],[167,52]) ).
thf(29,axiom,
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Earithmetic_2ETWO) ).
thf(161,plain,
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(162,plain,
( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(lifteq,[status(thm)],[161]) ).
thf(21,axiom,
! [A: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Enum_2ESUC @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2ELESS__0) ).
thf(139,plain,
! [A: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Enum_2ESUC @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(140,plain,
! [A: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Enum_2ESUC @ A ) ),
inference(cnf,[status(esa)],[139]) ).
thf(281,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Enum_2ESUC @ A ) ) ),
inference(paramod_ordered,[status(thm)],[162,140]) ).
thf(282,plain,
c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ),
inference(pattern_uni,[status(thm)],[281:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ))]]) ).
thf(394,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 )
| ~ $true
| ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Eprim__rec_2E_3C @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[282,138]) ).
thf(395,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ A ) @ B ) @ A )
= B )
| ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Eprim__rec_2E_3C @ B @ A ) ) ),
inference(simp,[status(thm)],[394]) ).
thf(396,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= c_2Enum_2E0 ),
inference(pattern_uni,[status(thm)],[395:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( c_2Enum_2E0 )),bind(C,$thf( C ))]]) ).
thf(414,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)],[396]) ).
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(172,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2B @ A @ c_2Enum_2E0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(173,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2B @ A @ c_2Enum_2E0 )
= A ),
inference(cnf,[status(esa)],[172]) ).
thf(174,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2B @ A @ c_2Enum_2E0 )
= A ),
inference(lifteq,[status(thm)],[173]) ).
thf(555,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)],[414,174]) ).
thf(567,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)],[555,36]) ).
thf(570,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)],[567]) ).
thf(575,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)],[570]) ).
thf(583,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 @ $true @ A @ B )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[353,575]) ).
thf(586,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ~ ( c_2Earithmetic_2EEVEN @ sk1 )
| ( c_2Enum_2E0 != c_2Enum_2E0 )
| ( A
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[583]) ).
thf(592,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ~ ( c_2Earithmetic_2EEVEN @ sk1 ) ),
inference(simp,[status(thm)],[586]) ).
thf(597,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ A )
!= sk1 )
| ~ ( c_2Earithmetic_2EEVEN @ sk1 )
| ( ( c_2Earithmetic_2E_2A @ A @ B )
!= ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[130,592]) ).
thf(598,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A )
!= sk1 )
| ~ ( c_2Earithmetic_2EEVEN @ sk1 ) ),
inference(pattern_uni,[status(thm)],[597:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).
thf(1034,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B )
!= sk1 )
| ~ ? [C: tyop_2Enum_2Enum] :
( A
= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ C ) )
| ( ( c_2Earithmetic_2EEVEN @ A )
!= ( c_2Earithmetic_2EEVEN @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[157,598]) ).
thf(1035,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A )
!= sk1 )
| ~ ? [B: tyop_2Enum_2Enum] :
( sk1
= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ),
inference(pattern_uni,[status(thm)],[1034:[bind(A,$thf( sk1 ))]]) ).
thf(1059,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A )
!= sk1 )
| ( sk1
!= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ),
inference(cnf,[status(esa)],[1035]) ).
thf(1060,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A )
!= sk1 ) ),
inference(lifteq,[status(thm)],[1059]) ).
thf(1061,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[1060]) ).
thf(7250,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A )
!= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) )
| ( sk1 != sk1 ) ),
inference(eqfactor_ordered,[status(thm)],[1061]) ).
thf(7253,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A )
!= sk1 ),
inference(pattern_uni,[status(thm)],[7250:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(7278,plain,
! [TA: $tType,E: tyop_2Enum_2Enum,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( A @ D ) ) @ E )
!= sk1 )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(paramod_ordered,[status(thm)],[171,7253]) ).
thf(7284,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
( ( c_2Earithmetic_2E_2A @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ B )
!= sk1 ),
inference(pre_uni,[status(thm)],[7278:[bind(A,$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(7288,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
( ( c_2Earithmetic_2E_2A @ ( 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 ) ) ) @ B )
!= sk1 ),
inference(simp,[status(thm)],[7284]) ).
thf(9891,plain,
! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ ( 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_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3456,7288]) ).
thf(9915,plain,
! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ C )
!= 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)],[9891]) ).
thf(9929,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(simp,[status(thm)],[9915]) ).
thf(1015,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)],[157]) ).
thf(1077,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ A )
| ( A
!= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ),
inference(cnf,[status(esa)],[1015]) ).
thf(1078,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)],[1077]) ).
thf(1079,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)],[1078]) ).
thf(1435,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)],[171,1079]) ).
thf(1921,plain,
! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ B ) ),
inference(pre_uni,[status(thm)],[1435:[bind(A,$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(2306,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)],[1921]) ).
thf(1432,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)],[171,1079]) ).
thf(1951,plain,
! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ B ) ),
inference(pre_uni,[status(thm)],[1432:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(2336,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)],[1951]) ).
thf(338,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)],[151,174]) ).
thf(341,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)],[338]) ).
thf(343,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)],[341]) ).
thf(283,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)],[162,145]) ).
thf(285,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)],[283]) ).
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(146,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(147,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)],[146]) ).
thf(148,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)],[147]) ).
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(158,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EODD @ A )
= ( ~ ( c_2Earithmetic_2EEVEN @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(159,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EODD @ A )
= ( ~ ( c_2Earithmetic_2EEVEN @ A ) ) ),
inference(cnf,[status(esa)],[158]) ).
thf(160,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EODD @ A )
= ( ~ ( c_2Earithmetic_2EEVEN @ A ) ) ),
inference(lifteq,[status(thm)],[159]) ).
thf(602,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)],[148,160]) ).
thf(604,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)],[602]) ).
thf(609,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Earithmetic_2EEVEN @ A )
| ( A
!= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ),
inference(cnf,[status(esa)],[604]) ).
thf(610,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)],[609]) ).
thf(611,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)],[610]) ).
thf(616,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)],[130,611]) ).
thf(617,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)],[616:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).
thf(623,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)],[285,617]) ).
thf(624,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)],[623:[]]) ).
thf(7361,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Enum_2E0 )
| ( ( 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)],[343,624]) ).
thf(7362,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(simp,[status(thm)],[7361]) ).
thf(7363,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)],[7362:[bind(A,$thf( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )),bind(B,$thf( C ))]]) ).
thf(7378,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)],[7363]) ).
thf(7660,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Enum_2E0 )
| ~ $true
| ( ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) )
!= ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1079,7378]) ).
thf(7661,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) )
!= ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ),
inference(simp,[status(thm)],[7660]) ).
thf(7662,plain,
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Enum_2E0 ),
inference(pattern_uni,[status(thm)],[7661:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ))]]) ).
thf(7706,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)],[171,7662]) ).
thf(7709,plain,
! [A: $o] :
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 ),
inference(pre_uni,[status(thm)],[7706:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(7712,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)],[7709]) ).
thf(7846,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)],[3456,7712]) ).
thf(7861,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)],[7846]) ).
thf(7868,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)],[7861]) ).
thf(7905,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)],[171,7868]) ).
thf(7913,plain,
! [A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(pre_uni,[status(thm)],[7905:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(7922,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)],[7913]) ).
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(152,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(153,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)],[152]) ).
thf(154,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)],[153]) ).
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(38,plain,
( ( $true
=> c_2Ebool_2EF )
=> ~ $true ),
inference(instance,[status(thm)],[37]) ).
thf(39,plain,
~ c_2Ebool_2EF,
inference(simp,[status(thm)],[38]) ).
thf(1279,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)],[171,39]) ).
thf(1733,plain,
! [A: $o] :
~ ( c_2Ebool_2ECOND @ $o @ A @ c_2Ebool_2EF @ c_2Ebool_2EF ),
inference(pre_uni,[status(thm)],[1279:[bind(A,$thf( ^ [E: TA] : c_2Ebool_2EF ))]]) ).
thf(2136,plain,
! [A: $o] :
~ ( c_2Ebool_2ECOND @ $o @ A @ c_2Ebool_2EF @ c_2Ebool_2EF ),
inference(simp,[status(thm)],[1733]) ).
thf(2428,plain,
! [A: $o] :
~ ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false ),
inference(rewrite,[status(thm)],[2136,39]) ).
thf(2432,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)],[154,2428]) ).
thf(2449,plain,
! [TA: $tType,B: $o,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ B
@ ^ [C: TA] : $false
@ ^ [C: TA] : $false
@ A ),
inference(pre_uni,[status(thm)],[2432:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : $false )),bind(C,$thf( ^ [F: TA] : $false ))]]) ).
thf(2456,plain,
! [TA: $tType,B: $o,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ B
@ ^ [C: TA] : $false
@ ^ [C: TA] : $false
@ A ),
inference(simp,[status(thm)],[2449]) ).
thf(3036,plain,
! [TA: $tType,TC: $tType,F: $o,E: TC,D: TA,C: TA,B: $o,A: TA > $o] :
( ~ ( c_2Ebool_2ECOND @ ( TC > $o ) @ F
@ ^ [G: TC] : $false
@ ^ [G: TC] : ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) )
@ E )
| ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,2456]) ).
thf(3041,plain,
! [TC: $tType,C: $o,B: TC,A: $o] :
~ ( c_2Ebool_2ECOND @ ( TC > $o ) @ C
@ ^ [D: TC] : $false
@ ^ [D: TC] : ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false )
@ B ),
inference(pre_uni,[status(thm)],[3036:[bind(A,$thf( ^ [G: TA] : $false ))]]) ).
thf(3048,plain,
! [TA: $tType,C: $o,B: TA,A: $o] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ C
@ ^ [D: TA] : $false
@ ^ [D: TA] : ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false )
@ B ),
inference(simp,[status(thm)],[3041]) ).
thf(2437,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)],[171,2428]) ).
thf(2451,plain,
! [B: $o,A: $o] :
~ ( c_2Ebool_2ECOND @ $o @ B @ $false @ ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false ) ),
inference(pre_uni,[status(thm)],[2437:[bind(A,$thf( ^ [F: TA] : $false ))]]) ).
thf(2457,plain,
! [B: $o,A: $o] :
~ ( c_2Ebool_2ECOND @ $o @ B @ $false @ ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false ) ),
inference(simp,[status(thm)],[2451]) ).
thf(4341,plain,
! [A: $o] :
~ ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false ),
inference(rewrite,[status(thm)],[2457,2428]) ).
thf(15361,plain,
! [TA: $tType,B: $o,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ B
@ ^ [C: TA] : $false
@ ^ [C: TA] : $false
@ A ),
inference(rewrite,[status(thm)],[3048,4341]) ).
thf(1541,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)],[171,140]) ).
thf(1807,plain,
! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) @ ( c_2Enum_2ESUC @ B ) ),
inference(pre_uni,[status(thm)],[1541:[bind(A,$thf( ^ [F: TA] : c_2Enum_2E0 ))]]) ).
thf(2201,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)],[1807]) ).
thf(3953,plain,
! [TA: $tType,F: tyop_2Enum_2Enum,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_2Enum_2ESUC @ F ) )
| ( ( 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)],[154,2201]) ).
thf(3974,plain,
! [TA: $tType,C: tyop_2Enum_2Enum,B: $o,A: TA] :
( c_2Eprim__rec_2E_3C
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [D: TA] : c_2Enum_2E0
@ ^ [D: TA] : c_2Enum_2E0
@ A )
@ ( c_2Enum_2ESUC @ C ) ),
inference(pre_uni,[status(thm)],[3953:[bind(A,$thf( E )),bind(B,$thf( ^ [G: TA] : c_2Enum_2E0 )),bind(C,$thf( ^ [G: TA] : c_2Enum_2E0 ))]]) ).
thf(3990,plain,
! [TA: $tType,C: tyop_2Enum_2Enum,B: $o,A: TA] :
( c_2Eprim__rec_2E_3C
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [D: TA] : c_2Enum_2E0
@ ^ [D: TA] : c_2Enum_2E0
@ A )
@ ( c_2Enum_2ESUC @ C ) ),
inference(simp,[status(thm)],[3974]) ).
thf(166,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ),
inference(cnfConj,[status(thm)],[164]) ).
thf(168,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ),
inference(lifteq,[status(thm)],[166]) ).
thf(447,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ $false @ A @ B )
= B ),
inference(rewrite,[status(thm)],[168,39]) ).
thf(531,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)],[447,420]) ).
thf(544,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)],[531]) ).
thf(546,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)],[544]) ).
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(131,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(132,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)],[131]) ).
thf(133,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)],[132]) ).
thf(311,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)],[162,133]) ).
thf(312,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)],[311:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ))]]) ).
thf(3716,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
| ( ( c_2Enum_2ESUC @ c_2Enum_2E0 )
!= ( c_2Enum_2ESUC @ A ) ) ),
inference(paramod_ordered,[status(thm)],[145,312]) ).
thf(3717,plain,
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pattern_uni,[status(thm)],[3716:[bind(A,$thf( c_2Enum_2E0 ))]]) ).
thf(279,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)],[145,140]) ).
thf(280,plain,
c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ),
inference(pattern_uni,[status(thm)],[279:[bind(A,$thf( c_2Enum_2E0 ))]]) ).
thf(4036,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)],[3717,280]) ).
thf(13087,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)],[546,4036]) ).
thf(13088,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)],[13087]) ).
thf(1574,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)],[171,162]) ).
thf(1897,plain,
! [A: $o] :
( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[1574:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(2282,plain,
! [A: $o] :
( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[1897]) ).
thf(7276,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ A @ B )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ B @ A )
!= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[130,7253]) ).
thf(7277,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 ),
inference(pattern_uni,[status(thm)],[7276:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).
thf(7415,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)],[171,7277]) ).
thf(7420,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ),
inference(pre_uni,[status(thm)],[7415:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(7425,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)],[7420]) ).
thf(7551,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)],[154,7425]) ).
thf(7563,plain,
! [TA: $tType,C: tyop_2Enum_2Enum,B: $o,A: TA] :
( ( c_2Earithmetic_2E_2A @ C
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ A ) ) ) )
!= sk1 ),
inference(pre_uni,[status(thm)],[7551:[bind(A,$thf( E )),bind(B,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO )),bind(C,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(7573,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)],[7563]) ).
thf(1413,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > $o] :
( ( ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ $true )
= ( 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 @ D ) ) ),
inference(paramod_ordered,[status(thm)],[280,171]) ).
thf(1928,plain,
! [A: $o] :
( ( c_2Ebool_2ECOND @ $o @ A @ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ $true )
= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pre_uni,[status(thm)],[1413:[bind(A,$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(2313,plain,
! [A: $o] :
( ( c_2Ebool_2ECOND @ $o @ A @ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ $true )
= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[1928]) ).
thf(15086,plain,
! [A: $o] : ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ),
inference(rewrite,[status(thm)],[2313,280]) ).
thf(15122,plain,
! [TA: $tType,E: $o,D: TA,C: TA,B: $o,A: TA > $o] :
( ( c_2Ebool_2ECOND @ $o @ E @ $true @ ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) ) )
| ~ ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,15086]) ).
thf(15136,plain,
! [B: $o,A: $o] : ( c_2Ebool_2ECOND @ $o @ B @ $true @ ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ) ),
inference(pre_uni,[status(thm)],[15122:[bind(A,$thf( ^ [F: TA] : $true ))]]) ).
thf(15143,plain,
! [B: $o,A: $o] : ( c_2Ebool_2ECOND @ $o @ B @ $true @ ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ) ),
inference(simp,[status(thm)],[15136]) ).
thf(15158,plain,
! [A: $o] : ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ),
inference(rewrite,[status(thm)],[15143,15086]) ).
thf(1576,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( A @ C ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( A @ D ) ) ),
inference(paramod_ordered,[status(thm)],[162,171]) ).
thf(1712,plain,
! [A: $o] :
( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pre_uni,[status(thm)],[1576:[bind(A,$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(2116,plain,
! [A: $o] :
( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[1712]) ).
thf(12479,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)],[2116,162]) ).
thf(7912,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)],[171,7868]) ).
thf(7920,plain,
! [A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )
!= c_2Earithmetic_2EZERO ) ),
inference(pre_uni,[status(thm)],[7912:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(7921,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)],[7920]) ).
thf(15231,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)],[12479,7921]) ).
thf(15252,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)],[15231]) ).
thf(15266,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)],[15252]) ).
thf(15290,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)],[15266]) ).
thf(15299,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)],[15290]) ).
thf(7848,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)],[154,7712]) ).
thf(7864,plain,
! [TA: $tType,B: $o,A: TA] :
( ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT1
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : c_2Earithmetic_2EZERO
@ ^ [C: TA] : c_2Earithmetic_2EZERO
@ A ) ) )
!= c_2Enum_2E0 ),
inference(pre_uni,[status(thm)],[7848:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO )),bind(C,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(7871,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)],[7864]) ).
thf(1585,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)],[171,145]) ).
thf(1968,plain,
! [A: $o] :
( ( c_2Enum_2ESUC @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[1585:[bind(A,$thf( ^ [E: TA] : c_2Enum_2E0 ))]]) ).
thf(2352,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)],[1968]) ).
thf(3309,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)],[154,2352]) ).
thf(3328,plain,
! [TA: $tType,B: $o,A: TA] :
( ( c_2Enum_2ESUC
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : c_2Enum_2E0
@ ^ [C: TA] : c_2Enum_2E0
@ A ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[3309:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : c_2Enum_2E0 )),bind(C,$thf( ^ [F: TA] : c_2Enum_2E0 ))]]) ).
thf(3335,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)],[3328]) ).
thf(1284,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)],[171,282]) ).
thf(1964,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pre_uni,[status(thm)],[1284:[bind(A,$thf( ^ [E: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(2348,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)],[1964]) ).
thf(4,axiom,
! [A: $o] :
( c_2Ebool_2EF
=> A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EFALSITY) ).
thf(42,plain,
! [A: $o] :
( c_2Ebool_2EF
=> A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(402,plain,
! [E: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ E @ C ) @ D ) @ C )
= D )
| ~ ( c_2Eprim__rec_2E_3C @ A @ B )
| ( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Enum_2ESUC @ B ) )
!= ( c_2Eprim__rec_2E_3C @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[133,138]) ).
thf(403,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Enum_2ESUC @ C ) ) @ ( c_2Enum_2ESUC @ B ) ) @ ( c_2Enum_2ESUC @ C ) )
= ( c_2Enum_2ESUC @ B ) )
| ~ ( c_2Eprim__rec_2E_3C @ B @ C ) ),
inference(pattern_uni,[status(thm)],[402:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( c_2Enum_2ESUC @ G )),bind(D,$thf( c_2Enum_2ESUC @ F ))]]) ).
thf(417,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)],[403]) ).
thf(1347,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_2ET ) ),
inference(paramod_ordered,[status(thm)],[171,52]) ).
thf(1746,plain,
! [A: $o] : ( c_2Ebool_2ECOND @ $o @ A @ c_2Ebool_2ET @ c_2Ebool_2ET ),
inference(pre_uni,[status(thm)],[1347:[bind(A,$thf( ^ [E: TA] : c_2Ebool_2ET ))]]) ).
thf(2147,plain,
! [A: $o] : ( c_2Ebool_2ECOND @ $o @ A @ c_2Ebool_2ET @ c_2Ebool_2ET ),
inference(simp,[status(thm)],[1746]) ).
thf(2460,plain,
! [A: $o] : ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ),
inference(rewrite,[status(thm)],[2147,52]) ).
thf(2468,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 @ $true @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[154,2460]) ).
thf(2505,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Ebool_2ECOND @ ( TA > $o ) @ B
@ ^ [C: TA] : $true
@ ^ [C: TA] : $true
@ A ),
inference(pre_uni,[status(thm)],[2468:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : $true )),bind(C,$thf( ^ [F: TA] : $true ))]]) ).
thf(2519,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Ebool_2ECOND @ ( TA > $o ) @ B
@ ^ [C: TA] : $true
@ ^ [C: TA] : $true
@ A ),
inference(simp,[status(thm)],[2505]) ).
thf(3261,plain,
! [TA: $tType,TC: $tType,F: $o,E: TC,D: TA,C: TA,B: $o,A: TA > TC > $o] :
( ( c_2Ebool_2ECOND @ ( TC > $o ) @ F @ ( c_2Ebool_2ECOND @ ( TC > $o ) @ B @ ( A @ C ) @ ( A @ D ) )
@ ^ [G: TC] : $true
@ E )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= ( ^ [G: TC] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[171,2519]) ).
thf(3270,plain,
! [TC: $tType,C: $o,B: TC,A: $o] :
( c_2Ebool_2ECOND @ ( TC > $o ) @ C
@ ( c_2Ebool_2ECOND @ ( TC > $o ) @ A
@ ^ [D: TC] : $true
@ ^ [D: TC] : $true )
@ ^ [D: TC] : $true
@ B ),
inference(pre_uni,[status(thm)],[3261:[bind(A,$thf( ^ [G: TA] : ^ [H: TC] : $true ))]]) ).
thf(3280,plain,
! [TA: $tType,C: $o,B: TA,A: $o] :
( c_2Ebool_2ECOND @ ( TA > $o ) @ C
@ ( c_2Ebool_2ECOND @ ( TA > $o ) @ A
@ ^ [D: TA] : $true
@ ^ [D: TA] : $true )
@ ^ [D: TA] : $true
@ B ),
inference(simp,[status(thm)],[3270]) ).
thf(16118,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Ebool_2ECOND @ ( TA > $o ) @ B
@ ^ [C: TA] : $true
@ ^ [C: TA] : $true
@ A ),
inference(rewrite,[status(thm)],[3280,2519]) ).
thf(10999,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ A )
!= sk1 )
| ( ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(simp,[status(thm)],[9929]) ).
thf(1028,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ~ ? [C: tyop_2Enum_2Enum] :
( A
= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ C ) )
| ( ( c_2Earithmetic_2EEVEN @ A )
!= ( c_2Earithmetic_2EEVEN @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[157,592]) ).
thf(1029,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ~ ? [B: tyop_2Enum_2Enum] :
( sk1
= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ),
inference(pattern_uni,[status(thm)],[1028:[bind(A,$thf( sk1 ))]]) ).
thf(1056,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ( sk1
!= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ),
inference(cnf,[status(esa)],[1029]) ).
thf(1057,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 ) ),
inference(lifteq,[status(thm)],[1056]) ).
thf(1058,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 ) ),
inference(simp,[status(thm)],[1057]) ).
thf(5834,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) )
| ( sk1 != sk1 ) ),
inference(eqfactor_ordered,[status(thm)],[1058]) ).
thf(5836,plain,
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 ),
inference(pattern_uni,[status(thm)],[5834:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ))]]) ).
thf(387,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 )
| ~ $true
| ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Enum_2ESUC @ A ) )
!= ( c_2Eprim__rec_2E_3C @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[140,138]) ).
thf(388,plain,
! [D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ B ) @ C ) @ B )
= C )
| ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Enum_2ESUC @ A ) )
!= ( c_2Eprim__rec_2E_3C @ C @ B ) ) ),
inference(simp,[status(thm)],[387]) ).
thf(389,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Enum_2ESUC @ B ) ) @ c_2Enum_2E0 ) @ ( c_2Enum_2ESUC @ B ) )
= c_2Enum_2E0 ),
inference(pattern_uni,[status(thm)],[388:[bind(A,$thf( E )),bind(B,$thf( c_2Enum_2ESUC @ E )),bind(C,$thf( c_2Enum_2E0 ))]]) ).
thf(411,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)],[389]) ).
thf(7754,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)],[411,174]) ).
thf(7705,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)],[171,7662]) ).
thf(7708,plain,
! [A: $o] :
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 ),
inference(pre_uni,[status(thm)],[7705:[bind(A,$thf( ^ [E: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(7711,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)],[7708]) ).
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(175,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(188,plain,
( ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $true )
= ( ( ~ $true
| $false )
& ( $true
| $true ) ) ),
inference(instance,[status(thm)],[175]) ).
thf(189,plain,
~ ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $true ),
inference(simp,[status(thm)],[188]) ).
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(93,plain,
! [A: $o] :
( ( ( c_2Ebool_2ET
| A )
= c_2Ebool_2ET )
& ( ( A
| c_2Ebool_2ET )
= c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
| A )
= A )
& ( ( A
| c_2Ebool_2EF )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(313,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ B ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Enum_2ESUC @ A ) ) ),
inference(paramod_ordered,[status(thm)],[162,133]) ).
thf(314,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ A ) )
= ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[313:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B ))]]) ).
thf(325,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ A ) )
= ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ A ) ),
inference(simp,[status(thm)],[314]) ).
thf(315,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) )
| ( ( c_2Enum_2ESUC @ c_2Enum_2E0 )
!= ( c_2Enum_2ESUC @ B ) ) ),
inference(paramod_ordered,[status(thm)],[145,133]) ).
thf(316,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ A @ c_2Enum_2E0 ) ),
inference(pattern_uni,[status(thm)],[315:[bind(A,$thf( A )),bind(B,$thf( c_2Enum_2E0 ))]]) ).
thf(3714,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Enum_2ESUC @ A ) ) ),
inference(paramod_ordered,[status(thm)],[162,312]) ).
thf(3715,plain,
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pattern_uni,[status(thm)],[3714:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ))]]) ).
thf(4159,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)],[145,316]) ).
thf(4160,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)],[4159:[bind(A,$thf( c_2Enum_2E0 ))]]) ).
thf(5264,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)],[3715,4160]) ).
thf(13121,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)],[447,13088]) ).
thf(13144,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)],[13121]) ).
thf(13167,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)],[13144]) ).
thf(14613,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)],[13167,151]) ).
thf(14617,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)],[130,14613]) ).
thf(14618,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)],[14617:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).
thf(14874,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ sk1 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= sk1 )
| ( ( 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)],[145,14618]) ).
thf(14881,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ sk1 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A )
!= c_2Enum_2E0 ) ),
inference(simp,[status(thm)],[14874]) ).
thf(7417,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)],[171,7277]) ).
thf(7418,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ),
inference(pre_uni,[status(thm)],[7417:[bind(A,$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(7423,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)],[7418]) ).
thf(306,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)],[140,133]) ).
thf(321,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)],[306]) ).
thf(566,plain,
! [D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ B @ A )
| ( B = c_2Enum_2E0 )
| ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ A ) @ B ) @ A )
!= ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[138,555]) ).
thf(569,plain,
! [D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( B = c_2Enum_2E0 )
| ~ ( c_2Eprim__rec_2E_3C @ B @ A )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ A ) @ B )
!= ( c_2Earithmetic_2E_2A @ D @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
| ( A
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[566]) ).
thf(574,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( A = c_2Enum_2E0 )
| ~ ( c_2Eprim__rec_2E_3C @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ A )
!= ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(simp,[status(thm)],[569]) ).
thf(1411,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)],[171,280]) ).
thf(1665,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pre_uni,[status(thm)],[1411:[bind(A,$thf( ^ [E: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(2073,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)],[1665]) ).
thf(7876,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)],[154,7711]) ).
thf(7892,plain,
! [TA: $tType,B: $o,A: TA] :
( ( c_2Earithmetic_2ENUMERAL
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO )
@ ^ [C: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO )
@ A ) )
!= c_2Enum_2E0 ),
inference(pre_uni,[status(thm)],[7876:[bind(A,$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(7899,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)],[7892]) ).
thf(1282,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)],[171,282]) ).
thf(1896,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[1282:[bind(A,$thf( ^ [E: TA] : c_2Enum_2E0 ))]]) ).
thf(2281,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)],[1896]) ).
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(4056,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)],[171,4036]) ).
thf(4072,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pre_uni,[status(thm)],[4056:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(4087,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)],[4072]) ).
thf(4060,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)],[171,4036]) ).
thf(4068,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pre_uni,[status(thm)],[4060:[bind(A,$thf( ^ [E: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(4082,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)],[4068]) ).
thf(448,plain,
! [B: $o,A: $o] :
( ~ B
| ( ( c_2Ebool_2ECOND @ $o @ $false @ A @ B )
!= ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[447,189]) ).
thf(467,plain,
! [A: $o] :
( ( c_2Ebool_2ECOND @ $o @ $false @ A @ $true )
!= ( c_2Ebool_2ECOND @ $o @ $true @ $false @ $true ) ),
inference(simp,[status(thm)],[448]) ).
thf(480,plain,
! [A: $o] : ( c_2Ebool_2ECOND @ $o @ $false @ A @ $true ),
inference(rewrite,[status(thm)],[467,189]) ).
thf(725,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)],[154,480]) ).
thf(792,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( c_2Ebool_2ECOND @ ( TA > $o ) @ $false @ A
@ ^ [C: TA] : $true
@ B ),
inference(pre_uni,[status(thm)],[725:[bind(A,$thf( $false )),bind(B,$thf( B )),bind(C,$thf( ^ [F: TA] : $true )),bind(D,$thf( D )),bind(E,$thf( B @ D ))]]) ).
thf(851,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( c_2Ebool_2ECOND @ ( TA > $o ) @ $false @ A
@ ^ [C: TA] : $true
@ B ),
inference(simp,[status(thm)],[792]) ).
thf(1564,plain,
! [TA: $tType,TC: $tType,F: TC,E: TC > $o,D: TA,C: TA,B: $o,A: TA > TC > $o] :
( ( c_2Ebool_2ECOND @ ( TC > $o ) @ $false @ E @ ( c_2Ebool_2ECOND @ ( TC > $o ) @ B @ ( A @ C ) @ ( A @ D ) ) @ F )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= ( ^ [G: TC] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[171,851]) ).
thf(1769,plain,
! [TC: $tType,C: TC,B: TC > $o,A: $o] :
( c_2Ebool_2ECOND @ ( TC > $o ) @ $false @ B
@ ( c_2Ebool_2ECOND @ ( TC > $o ) @ A
@ ^ [D: TC] : $true
@ ^ [D: TC] : $true )
@ C ),
inference(pre_uni,[status(thm)],[1564:[bind(A,$thf( ^ [G: TA] : ^ [H: TC] : $true ))]]) ).
thf(2167,plain,
! [TA: $tType,C: TA,B: TA > $o,A: $o] :
( c_2Ebool_2ECOND @ ( TA > $o ) @ $false @ B
@ ( c_2Ebool_2ECOND @ ( TA > $o ) @ A
@ ^ [D: TA] : $true
@ ^ [D: TA] : $true )
@ C ),
inference(simp,[status(thm)],[1769]) ).
thf(15023,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( c_2Ebool_2ECOND @ ( TA > $o ) @ $false @ A
@ ^ [C: TA] : $true
@ B ),
inference(rewrite,[status(thm)],[2167,2519]) ).
thf(7279,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)],[171,7253]) ).
thf(7283,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ B )
!= sk1 ),
inference(pre_uni,[status(thm)],[7279:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(7287,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)],[7283]) ).
thf(7503,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)],[3456,7287]) ).
thf(7526,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)],[7503]) ).
thf(7535,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)],[7526]) ).
thf(182,plain,
( ( c_2Ebool_2ECOND @ $o @ $false @ $false @ $false )
= ( ( ~ $false
| $false )
& ( $false
| $false ) ) ),
inference(instance,[status(thm)],[175]) ).
thf(183,plain,
~ ( c_2Ebool_2ECOND @ $o @ $false @ $false @ $false ),
inference(simp,[status(thm)],[182]) ).
thf(371,plain,
! [B: $o,A: $o] :
( ~ A
| ( ( c_2Ebool_2ECOND @ $o @ $true @ A @ B )
!= ( c_2Ebool_2ECOND @ $o @ $false @ $false @ $false ) ) ),
inference(paramod_ordered,[status(thm)],[353,183]) ).
thf(372,plain,
! [A: $o] :
( ( c_2Ebool_2ECOND @ $o @ $true @ $true @ A )
!= ( c_2Ebool_2ECOND @ $o @ $false @ $false @ $false ) ),
inference(simp,[status(thm)],[371]) ).
thf(380,plain,
! [A: $o] :
( ( c_2Ebool_2ECOND @ $o @ $true @ $true @ A )
!= ( c_2Ebool_2ECOND @ $o @ $false @ $false @ $false ) ),
inference(simp,[status(thm)],[372]) ).
thf(423,plain,
! [A: $o] : ( c_2Ebool_2ECOND @ $o @ $true @ $true @ A ),
inference(rewrite,[status(thm)],[380,183]) ).
thf(1494,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)],[171,423]) ).
thf(1742,plain,
! [B: $o,A: $o] : ( c_2Ebool_2ECOND @ $o @ $true @ ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ) @ B ),
inference(pre_uni,[status(thm)],[1494:[bind(A,$thf( ^ [F: TA] : $true ))]]) ).
thf(2144,plain,
! [B: $o,A: $o] : ( c_2Ebool_2ECOND @ $o @ $true @ ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ) @ B ),
inference(simp,[status(thm)],[1742]) ).
thf(3857,plain,
! [A: $o] : ( c_2Ebool_2ECOND @ $o @ $true @ $true @ A ),
inference(rewrite,[status(thm)],[2144,2460]) ).
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(117,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(7281,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)],[171,7253]) ).
thf(7282,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ B )
!= sk1 ),
inference(pre_uni,[status(thm)],[7281:[bind(A,$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(7286,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)],[7282]) ).
thf(697,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)],[154,189]) ).
thf(791,plain,
! [TA: $tType,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
@ ^ [B: TA] : $false
@ ^ [B: TA] : $true
@ A ),
inference(pre_uni,[status(thm)],[697:[bind(A,$thf( $true )),bind(B,$thf( ^ [E: TA] : $false )),bind(C,$thf( ^ [E: TA] : $true ))]]) ).
thf(850,plain,
! [TA: $tType,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
@ ^ [B: TA] : $false
@ ^ [B: TA] : $true
@ A ),
inference(simp,[status(thm)],[791]) ).
thf(1644,plain,
! [TA: $tType,TC: $tType,E: TC,D: TA,C: TA,B: $o,A: TA > TC > $o] :
( ~ ( c_2Ebool_2ECOND @ ( TC > $o ) @ $true @ ( c_2Ebool_2ECOND @ ( TC > $o ) @ B @ ( A @ C ) @ ( A @ D ) )
@ ^ [F: TC] : $true
@ E )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= ( ^ [F: TC] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[171,850]) ).
thf(1833,plain,
! [TC: $tType,B: TC,A: $o] :
~ ( c_2Ebool_2ECOND @ ( TC > $o ) @ $true
@ ( c_2Ebool_2ECOND @ ( TC > $o ) @ A
@ ^ [C: TC] : $false
@ ^ [C: TC] : $false )
@ ^ [C: TC] : $true
@ B ),
inference(pre_uni,[status(thm)],[1644:[bind(A,$thf( ^ [F: TA] : ^ [G: TC] : $false ))]]) ).
thf(2223,plain,
! [TA: $tType,B: TA,A: $o] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
@ ( c_2Ebool_2ECOND @ ( TA > $o ) @ A
@ ^ [C: TA] : $false
@ ^ [C: TA] : $false )
@ ^ [C: TA] : $true
@ B ),
inference(simp,[status(thm)],[1833]) ).
thf(6307,plain,
! [TA: $tType,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
@ ^ [B: TA] : $false
@ ^ [B: TA] : $true
@ A ),
inference(rewrite,[status(thm)],[2223,2456]) ).
thf(1117,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ A @ B ) )
| ( ( c_2Earithmetic_2E_2A @ B @ A )
!= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[130,1079]) ).
thf(1118,plain,
! [A: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pattern_uni,[status(thm)],[1117:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).
thf(1477,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)],[171,1118]) ).
thf(1922,plain,
! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(pre_uni,[status(thm)],[1477:[bind(A,$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(2307,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)],[1922]) ).
thf(746,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)],[423,154]) ).
thf(786,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
@ ^ [C: TA] : $true
@ A
@ B ),
inference(pre_uni,[status(thm)],[746:[bind(A,$thf( D @ E )),bind(B,$thf( $true )),bind(C,$thf( ^ [F: TA] : $true ))]]) ).
thf(845,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
@ ^ [C: TA] : $true
@ A
@ B ),
inference(simp,[status(thm)],[786]) ).
thf(1315,plain,
! [TA: $tType,TC: $tType,F: TC,E: TC > $o,D: TA,C: TA,B: $o,A: TA > $o] :
( ( c_2Ebool_2ECOND @ ( TC > $o ) @ $true
@ ^ [G: TC] : ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) )
@ E
@ F )
| ~ ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,845]) ).
thf(1671,plain,
! [TC: $tType,C: TC,B: TC > $o,A: $o] :
( c_2Ebool_2ECOND @ ( TC > $o ) @ $true
@ ^ [D: TC] : ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true )
@ B
@ C ),
inference(pre_uni,[status(thm)],[1315:[bind(A,$thf( ^ [G: TA] : $true ))]]) ).
thf(2079,plain,
! [TA: $tType,C: TA,B: TA > $o,A: $o] :
( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
@ ^ [D: TA] : ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true )
@ B
@ C ),
inference(simp,[status(thm)],[1671]) ).
thf(1286,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > $o] :
( ( ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ $true )
= ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) )
| ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( A @ D ) ) ),
inference(paramod_ordered,[status(thm)],[282,171]) ).
thf(1860,plain,
! [A: $o] :
( ( c_2Ebool_2ECOND @ $o @ A @ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ $true )
= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pre_uni,[status(thm)],[1286:[bind(A,$thf( ^ [E: TA] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(2246,plain,
! [A: $o] :
( ( c_2Ebool_2ECOND @ $o @ A @ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ $true )
= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[1860]) ).
thf(14542,plain,
! [A: $o] : ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ),
inference(rewrite,[status(thm)],[2246,282]) ).
thf(14578,plain,
! [TA: $tType,E: $o,D: TA,C: TA,B: $o,A: TA > $o] :
( ( c_2Ebool_2ECOND @ $o @ E @ $true @ ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) ) )
| ~ ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,14542]) ).
thf(14597,plain,
! [B: $o,A: $o] : ( c_2Ebool_2ECOND @ $o @ B @ $true @ ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ) ),
inference(pre_uni,[status(thm)],[14578:[bind(A,$thf( ^ [F: TA] : $true ))]]) ).
thf(14602,plain,
! [B: $o,A: $o] : ( c_2Ebool_2ECOND @ $o @ B @ $true @ ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ) ),
inference(simp,[status(thm)],[14597]) ).
thf(14792,plain,
! [A: $o] : ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ),
inference(rewrite,[status(thm)],[14602,14542]) ).
thf(14958,plain,
! [TA: $tType,B: TA,A: TA > $o] :
( c_2Ebool_2ECOND @ ( TA > $o ) @ $true
@ ^ [C: TA] : $true
@ A
@ B ),
inference(rewrite,[status(thm)],[2079,14792]) ).
thf(5986,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( 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)],[171,5836]) ).
thf(5993,plain,
! [A: $o] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ),
inference(pre_uni,[status(thm)],[5986:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(6000,plain,
! [A: $o] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ),
inference(simp,[status(thm)],[5993]) ).
thf(8376,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)],[130,7286]) ).
thf(8377,plain,
! [B: $o,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ),
inference(pattern_uni,[status(thm)],[8376:[bind(A,$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(8414,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)],[8377]) ).
thf(12511,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)],[12479,8414]) ).
thf(12582,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)],[12511]) ).
thf(12650,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)],[12582]) ).
thf(7874,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)],[3456,7711]) ).
thf(7889,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)],[7874]) ).
thf(7896,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)],[7889]) ).
thf(7935,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)],[171,7896]) ).
thf(7936,plain,
! [A: $o] :
( ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[7935:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(7943,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)],[7936]) ).
thf(16216,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)],[12479,7943]) ).
thf(16234,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)],[16216]) ).
thf(16247,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)],[16234]) ).
thf(523,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_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)],[282,420]) ).
thf(524,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(simp,[status(thm)],[523]) ).
thf(538,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)],[524]) ).
thf(551,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)],[538]) ).
thf(8419,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)],[130,7423]) ).
thf(8420,plain,
! [B: $o,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ A )
!= sk1 ),
inference(pattern_uni,[status(thm)],[8419:[bind(A,$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(8446,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)],[8420]) ).
thf(4163,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
( ( ( 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 @ B @ c_2Enum_2E0 ) )
| ( ( c_2Enum_2ESUC @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) )
!= ( c_2Enum_2ESUC @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2352,316]) ).
thf(4164,plain,
! [A: $o] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) @ c_2Enum_2E0 ) ),
inference(pattern_uni,[status(thm)],[4163:[bind(A,$thf( C )),bind(B,$thf( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ C @ c_2Enum_2E0 @ c_2Enum_2E0 ))]]) ).
thf(4213,plain,
! [A: $o] :
( ( 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_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) @ c_2Enum_2E0 ) ),
inference(simp,[status(thm)],[4164]) ).
thf(15481,plain,
! [A: $o] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) @ c_2Enum_2E0 )
= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ c_2Enum_2E0 ) ),
inference(rewrite,[status(thm)],[4213,4160]) ).
thf(3069,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)],[154,2281]) ).
thf(3086,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Eprim__rec_2E_3C
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : c_2Enum_2E0
@ ^ [C: TA] : c_2Enum_2E0
@ A )
@ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[3069:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : c_2Enum_2E0 )),bind(C,$thf( ^ [F: TA] : c_2Enum_2E0 ))]]) ).
thf(3102,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)],[3086]) ).
thf(8418,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)],[3456,7423]) ).
thf(8437,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)],[8418]) ).
thf(8451,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)],[8437]) ).
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(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(141,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ A )
= ( ~ ( c_2Earithmetic_2EODD @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1573,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)],[171,162]) ).
thf(1802,plain,
! [A: $o] :
( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[1573:[bind(A,$thf( ^ [E: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(2196,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)],[1802]) ).
thf(1409,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)],[171,280]) ).
thf(1721,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[1409:[bind(A,$thf( ^ [E: TA] : c_2Enum_2E0 ))]]) ).
thf(2125,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)],[1721]) ).
thf(15405,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)],[12479,7922]) ).
thf(15428,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)],[15405]) ).
thf(15442,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)],[15428]) ).
thf(7504,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)],[130,7287]) ).
thf(7505,plain,
! [B: $o,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ),
inference(pattern_uni,[status(thm)],[7504:[bind(A,$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(7538,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)],[7505]) ).
thf(7722,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)],[154,7538]) ).
thf(7736,plain,
! [TA: $tType,C: $o,B: tyop_2Enum_2Enum,A: TA] :
( ( c_2Earithmetic_2E_2A @ B
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ C
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ A ) ) ) )
!= sk1 ),
inference(pre_uni,[status(thm)],[7722:[bind(A,$thf( F )),bind(B,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO )),bind(C,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(7749,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)],[7736]) ).
thf(399,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 )
| ~ $true
| ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Eprim__rec_2E_3C @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[280,138]) ).
thf(400,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ A ) @ B ) @ A )
= B )
| ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Eprim__rec_2E_3C @ B @ A ) ) ),
inference(simp,[status(thm)],[399]) ).
thf(401,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= c_2Enum_2E0 ),
inference(pattern_uni,[status(thm)],[400:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( c_2Enum_2E0 )),bind(C,$thf( C ))]]) ).
thf(416,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)],[401]) ).
thf(7020,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)],[416,174]) ).
thf(390,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)],[130,138]) ).
thf(391,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)],[390:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( D )),bind(E,$thf( A ))]]) ).
thf(412,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)],[391]) ).
thf(5983,plain,
! [TA: $tType,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 ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(paramod_ordered,[status(thm)],[171,5836]) ).
thf(5989,plain,
! [A: $o] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 ),
inference(pre_uni,[status(thm)],[5983:[bind(A,$thf( ^ [E: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(5996,plain,
! [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 ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 ),
inference(simp,[status(thm)],[5989]) ).
thf(7546,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)],[130,7425]) ).
thf(7547,plain,
! [B: $o,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ A )
!= sk1 ),
inference(pattern_uni,[status(thm)],[7546:[bind(A,$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(7582,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)],[7547]) ).
thf(7849,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)],[171,7712]) ).
thf(7859,plain,
! [B: $o,A: $o] :
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 ),
inference(pre_uni,[status(thm)],[7849:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(7866,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)],[7859]) ).
thf(12565,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)],[12479,7538]) ).
thf(12586,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)],[12565]) ).
thf(12654,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)],[12586]) ).
thf(565,plain,
! [D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Enum_2E0 = C )
| ~ ( c_2Eprim__rec_2E_3C @ C @ B )
| ( ( 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 @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ B ) @ C ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[555,138]) ).
thf(568,plain,
! [D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Enum_2E0 = C )
| ~ ( c_2Eprim__rec_2E_3C @ C @ B )
| ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ B ) @ C ) )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= B ) ),
inference(simp,[status(thm)],[565]) ).
thf(573,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Enum_2E0 = B )
| ~ ( c_2Eprim__rec_2E_3C @ B @ ( 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_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ B ) ) ),
inference(simp,[status(thm)],[568]) ).
thf(180,plain,
( ( c_2Ebool_2ECOND @ $o @ $false @ $true @ $false )
= ( ( ~ $false
| $true )
& ( $false
| $false ) ) ),
inference(instance,[status(thm)],[175]) ).
thf(181,plain,
~ ( c_2Ebool_2ECOND @ $o @ $false @ $true @ $false ),
inference(simp,[status(thm)],[180]) ).
thf(751,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)],[154,181]) ).
thf(780,plain,
! [TA: $tType,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $false
@ ^ [B: TA] : $true
@ ^ [B: TA] : $false
@ A ),
inference(pre_uni,[status(thm)],[751:[bind(A,$thf( $false )),bind(B,$thf( ^ [E: TA] : $true )),bind(C,$thf( ^ [E: TA] : $false ))]]) ).
thf(840,plain,
! [TA: $tType,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $false
@ ^ [B: TA] : $true
@ ^ [B: TA] : $false
@ A ),
inference(simp,[status(thm)],[780]) ).
thf(1290,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)],[171,840]) ).
thf(1677,plain,
! [TC: $tType,B: TC,A: $o] :
~ ( c_2Ebool_2ECOND @ ( TC > $o ) @ ( c_2Ebool_2ECOND @ $o @ A @ $false @ $false )
@ ^ [C: TC] : $true
@ ^ [C: TC] : $false
@ B ),
inference(pre_uni,[status(thm)],[1290:[bind(A,$thf( ^ [F: TA] : $false ))]]) ).
thf(2084,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)],[1677]) ).
thf(6001,plain,
! [TA: $tType,A: TA] :
~ ( c_2Ebool_2ECOND @ ( TA > $o ) @ $false
@ ^ [B: TA] : $true
@ ^ [B: TA] : $false
@ A ),
inference(rewrite,[status(thm)],[2084,4341]) ).
thf(561,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ B @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2E_2A @ A @ B )
!= ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[130,555]) ).
thf(562,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= c_2Enum_2E0 ),
inference(pattern_uni,[status(thm)],[561:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).
thf(12563,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)],[12479,7712]) ).
thf(12619,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)],[12563]) ).
thf(12688,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)],[12619]) ).
thf(12518,plain,
! [C: $o,B: tyop_2Enum_2Enum,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) @ B )
!= 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)],[12479,7582]) ).
thf(12595,plain,
! [C: $o,B: tyop_2Enum_2Enum,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) @ B )
!= sk1 )
| ( A != C )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[12518]) ).
thf(12663,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) @ A )
!= sk1 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= c_2Earithmetic_2EZERO ) ),
inference(simp,[status(thm)],[12595]) ).
thf(392,plain,
! [E: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ B ) @ D ) @ C )
= D )
| ~ ( c_2Eprim__rec_2E_3C @ D @ C )
| ( ( c_2Earithmetic_2E_2A @ B @ A )
!= ( c_2Earithmetic_2E_2A @ E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[130,138]) ).
thf(393,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ B ) @ C ) @ A )
= C )
| ~ ( c_2Eprim__rec_2E_3C @ C @ A ) ),
inference(pattern_uni,[status(thm)],[392:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( B ))]]) ).
thf(413,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)],[393]) ).
thf(1407,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)],[171,280]) ).
thf(1799,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pre_uni,[status(thm)],[1407:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(2193,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)],[1799]) ).
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(3586,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)],[154,2348]) ).
thf(3606,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Eprim__rec_2E_3C @ c_2Enum_2E0
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO )
@ ^ [C: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO )
@ A ) ) ),
inference(pre_uni,[status(thm)],[3586:[bind(A,$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(3619,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)],[3606]) ).
thf(5984,plain,
! [TA: $tType,D: TA,C: TA,B: $o,A: TA > tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( 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)],[171,5836]) ).
thf(5990,plain,
! [A: $o] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ),
inference(pre_uni,[status(thm)],[5984:[bind(A,$thf( ^ [E: TA] : ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(5997,plain,
! [A: $o] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ 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 ) ) ) )
!= sk1 ),
inference(simp,[status(thm)],[5990]) ).
thf(7545,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)],[3456,7425]) ).
thf(7569,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)],[7545]) ).
thf(7579,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)],[7569]) ).
thf(7850,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)],[171,7712]) ).
thf(7858,plain,
! [B: $o,A: $o] :
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ B @ c_2Earithmetic_2EZERO @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) )
!= c_2Enum_2E0 ),
inference(pre_uni,[status(thm)],[7850:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(7865,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)],[7858]) ).
thf(7509,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)],[154,7287]) ).
thf(7520,plain,
! [TA: $tType,C: tyop_2Enum_2Enum,B: $o,A: TA] :
( ( c_2Earithmetic_2E_2A
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ A ) ) )
@ C )
!= sk1 ),
inference(pre_uni,[status(thm)],[7509:[bind(A,$thf( E )),bind(B,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO )),bind(C,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(7529,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)],[7520]) ).
thf(407,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)],[406]) ).
thf(419,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)],[407]) ).
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(81,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(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(98,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(1281,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)],[171,282]) ).
thf(1800,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pre_uni,[status(thm)],[1281:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(2194,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)],[1800]) ).
thf(2865,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)],[154,2194]) ).
thf(2873,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Eprim__rec_2E_3C @ c_2Enum_2E0
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : c_2Earithmetic_2EZERO
@ ^ [C: TA] : c_2Earithmetic_2EZERO
@ A ) ) ) ),
inference(pre_uni,[status(thm)],[2865:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO )),bind(C,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(2896,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)],[2873]) ).
thf(630,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)],[145,617]) ).
thf(631,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)],[630]) ).
thf(15408,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)],[3456,7922]) ).
thf(15424,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)],[15408]) ).
thf(15438,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)],[15424]) ).
thf(2583,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)],[154,2125]) ).
thf(2624,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Eprim__rec_2E_3C
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : c_2Enum_2E0
@ ^ [C: TA] : c_2Enum_2E0
@ A )
@ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[2583:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : c_2Enum_2E0 )),bind(C,$thf( ^ [F: TA] : c_2Enum_2E0 ))]]) ).
thf(2625,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)],[2624]) ).
thf(305,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)],[133,140]) ).
thf(323,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)],[305]) ).
thf(618,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)],[162,611]) ).
thf(621,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)],[618]) ).
thf(519,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)],[130,420]) ).
thf(520,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)],[519:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).
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(12497,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)],[12479,7711]) ).
thf(12612,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)],[12497]) ).
thf(12680,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)],[12612]) ).
thf(12510,plain,
! [C: $o,B: tyop_2Enum_2Enum,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ B )
!= 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)],[12479,8446]) ).
thf(12587,plain,
! [C: $o,B: tyop_2Enum_2Enum,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ B )
!= 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)],[12510]) ).
thf(12655,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)],[12587]) ).
thf(1474,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)],[171,1118]) ).
thf(1918,plain,
! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(pre_uni,[status(thm)],[1474:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(2303,plain,
! [B: tyop_2Enum_2Enum,A: $o] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(simp,[status(thm)],[1918]) ).
thf(4157,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ A @ c_2Enum_2E0 ) )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Enum_2ESUC @ A ) ) ),
inference(paramod_ordered,[status(thm)],[162,316]) ).
thf(4158,plain,
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ c_2Enum_2E0 ) ),
inference(pattern_uni,[status(thm)],[4157:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ))]]) ).
thf(11029,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ A @ B )
!= sk1 )
| ( ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO )
!= ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
| ( ( c_2Earithmetic_2E_2A @ B @ A )
!= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[130,10999]) ).
thf(11030,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(pattern_uni,[status(thm)],[11029:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).
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(112,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(8375,plain,
! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( 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_2EBIT2 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(paramod_ordered,[status(thm)],[3456,7286]) ).
thf(8398,plain,
! [C: tyop_2Enum_2Enum,B: $o,A: $o] :
( ( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ C )
!= 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)],[8375]) ).
thf(8409,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(simp,[status(thm)],[8398]) ).
thf(10201,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)],[130,7573]) ).
thf(10202,plain,
! [TA: $tType,C: TA,B: $o,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ C ) ) )
@ A )
!= sk1 ),
inference(pattern_uni,[status(thm)],[10201:[bind(A,$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(10228,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)],[10202]) ).
thf(1508,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)],[171,611]) ).
thf(1993,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ B ) ) ),
inference(pre_uni,[status(thm)],[1508:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(2375,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)],[1993]) ).
thf(16219,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)],[3456,7943]) ).
thf(16236,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)],[16219]) ).
thf(16249,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)],[16236]) ).
thf(5985,plain,
! [TA: $tType,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 ) ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ( ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) )
!= c_2Earithmetic_2EZERO ) ),
inference(paramod_ordered,[status(thm)],[171,5836]) ).
thf(5988,plain,
! [A: $o] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 ),
inference(pre_uni,[status(thm)],[5985:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(5995,plain,
! [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 ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 ),
inference(simp,[status(thm)],[5988]) ).
thf(525,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)],[353,420]) ).
thf(537,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)],[525]) ).
thf(550,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)],[537]) ).
thf(14420,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)],[550,282]) ).
thf(14421,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)],[14420]) ).
thf(14622,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ sk1 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= sk1 )
| ( ( 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)],[145,14613]) ).
thf(14631,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ sk1 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 ) ),
inference(simp,[status(thm)],[14622]) ).
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(72,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(4058,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)],[171,4036]) ).
thf(4062,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[4058:[bind(A,$thf( ^ [E: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(4093,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)],[4062]) ).
thf(3362,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)],[154,2073]) ).
thf(3389,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Eprim__rec_2E_3C @ c_2Enum_2E0
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO )
@ ^ [C: TA] : ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO )
@ A ) ) ),
inference(pre_uni,[status(thm)],[3362:[bind(A,$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(3398,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)],[3389]) ).
thf(10056,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)],[130,7529]) ).
thf(10057,plain,
! [TA: $tType,C: TA,B: $o,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ C ) ) ) )
!= sk1 ),
inference(pattern_uni,[status(thm)],[10056:[bind(A,$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(10082,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)],[10057]) ).
thf(1258,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)],[171,174]) ).
thf(1889,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
( ( c_2Earithmetic_2E_2B @ B @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Enum_2E0 @ c_2Enum_2E0 ) )
= B ),
inference(pre_uni,[status(thm)],[1258:[bind(A,$thf( ^ [F: TA] : c_2Enum_2E0 ))]]) ).
thf(2273,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)],[1889]) ).
thf(308,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)],[282,133]) ).
thf(319,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)],[308]) ).
thf(629,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)],[162,617]) ).
thf(632,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)],[629]) ).
thf(404,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)],[151,138]) ).
thf(405,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)],[404:[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(418,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)],[405]) ).
thf(1386,plain,
! [TA: $tType,E: $o,D: TA,C: TA,B: $o,A: TA > $o] :
( ( c_2Ebool_2ECOND @ $o @ $false @ E @ ( c_2Ebool_2ECOND @ $o @ B @ ( A @ C ) @ ( A @ D ) ) )
| ~ ( A @ ( c_2Ebool_2ECOND @ TA @ B @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[171,480]) ).
thf(1715,plain,
! [B: $o,A: $o] : ( c_2Ebool_2ECOND @ $o @ $false @ B @ ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ) ),
inference(pre_uni,[status(thm)],[1386:[bind(A,$thf( ^ [F: TA] : $true ))]]) ).
thf(2119,plain,
! [B: $o,A: $o] : ( c_2Ebool_2ECOND @ $o @ $false @ B @ ( c_2Ebool_2ECOND @ $o @ A @ $true @ $true ) ),
inference(simp,[status(thm)],[1715]) ).
thf(3780,plain,
! [A: $o] : ( c_2Ebool_2ECOND @ $o @ $false @ A @ $true ),
inference(rewrite,[status(thm)],[2119,2460]) ).
thf(2742,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)],[154,2193]) ).
thf(2753,plain,
! [TA: $tType,B: $o,A: TA] :
( c_2Eprim__rec_2E_3C @ c_2Enum_2E0
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT1
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : c_2Earithmetic_2EZERO
@ ^ [C: TA] : c_2Earithmetic_2EZERO
@ A ) ) ) ),
inference(pre_uni,[status(thm)],[2742:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO )),bind(C,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(2764,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)],[2753]) ).
thf(619,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)],[145,611]) ).
thf(620,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)],[619]) ).
thf(15559,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_2Enum_2E0 )
= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ c_2Enum_2E0 ) )
| ( ( 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)],[154,15481]) ).
thf(15617,plain,
! [TA: $tType,B: $o,A: TA] :
( ( c_2Eprim__rec_2E_3C
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ B
@ ^ [C: TA] : c_2Enum_2E0
@ ^ [C: TA] : c_2Enum_2E0
@ A )
@ c_2Enum_2E0 )
= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ c_2Enum_2E0 ) ),
inference(pre_uni,[status(thm)],[15559:[bind(A,$thf( E )),bind(B,$thf( ^ [F: TA] : c_2Enum_2E0 )),bind(C,$thf( ^ [F: TA] : c_2Enum_2E0 ))]]) ).
thf(15673,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_2Enum_2E0 )
= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ c_2Enum_2E0 ) ),
inference(simp,[status(thm)],[15617]) ).
thf(1579,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)],[171,617]) ).
thf(1955,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[1579:[bind(A,$thf( ^ [F: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(2340,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
~ ( c_2Earithmetic_2EEVEN @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) ) ) ),
inference(simp,[status(thm)],[1955]) ).
thf(397,plain,
! [D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ A @ B )
= C )
| ~ ( c_2Eprim__rec_2E_3C @ C @ B )
| ( ( c_2Earithmetic_2E_2B @ A @ c_2Enum_2E0 )
!= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[174,138]) ).
thf(398,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ B ) @ B )
= c_2Enum_2E0 )
| ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B ) ),
inference(pattern_uni,[status(thm)],[397:[bind(A,$thf( c_2Earithmetic_2E_2A @ E @ F )),bind(B,$thf( F )),bind(C,$thf( c_2Enum_2E0 )),bind(D,$thf( E ))]]) ).
thf(415,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ B ) @ B )
= c_2Enum_2E0 )
| ~ ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ B ) ),
inference(simp,[status(thm)],[398]) ).
thf(317,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ B ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) )
| ( ( c_2Enum_2ESUC @ c_2Enum_2E0 )
!= ( c_2Enum_2ESUC @ A ) ) ),
inference(paramod_ordered,[status(thm)],[145,133]) ).
thf(318,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Enum_2ESUC @ A ) )
= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ A ) ),
inference(pattern_uni,[status(thm)],[317:[bind(A,$thf( c_2Enum_2E0 ))]]) ).
thf(326,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)],[318]) ).
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(107,plain,
! [A: $o] :
( ( ~ A
=> c_2Ebool_2EF )
=> ( ( A
=> c_2Ebool_2EF )
=> c_2Ebool_2EF ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7959,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)],[154,7582]) ).
thf(7977,plain,
! [TA: $tType,C: $o,B: tyop_2Enum_2Enum,A: TA] :
( ( c_2Earithmetic_2E_2A
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ C
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ A ) ) )
@ B )
!= sk1 ),
inference(pre_uni,[status(thm)],[7959:[bind(A,$thf( F )),bind(B,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO )),bind(C,$thf( ^ [G: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(7987,plain,
! [TA: $tType,C: $o,B: tyop_2Enum_2Enum,A: TA] :
( ( c_2Earithmetic_2E_2A
@ ( c_2Earithmetic_2ENUMERAL
@ ( c_2Earithmetic_2EBIT2
@ ( c_2Ebool_2ECOND @ ( TA > tyop_2Enum_2Enum ) @ C
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ ^ [D: TA] : c_2Earithmetic_2EZERO
@ A ) ) )
@ B )
!= sk1 ),
inference(simp,[status(thm)],[7977]) ).
thf(7034,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ B @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2E_2A @ A @ B )
!= ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[130,7020]) ).
thf(7035,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= c_2Enum_2E0 ),
inference(pattern_uni,[status(thm)],[7034:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).
thf(7414,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)],[171,7277]) ).
thf(7419,plain,
! [B: tyop_2Enum_2Enum,A: $o] :
( ( c_2Earithmetic_2E_2A @ B @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ),
inference(pre_uni,[status(thm)],[7414:[bind(A,$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(7424,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)],[7419]) ).
thf(9935,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)],[3456,7424]) ).
thf(9958,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)],[9935]) ).
thf(9969,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)],[9958]) ).
thf(4055,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)],[171,4036]) ).
thf(4073,plain,
! [A: $o] : ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ A @ c_2Earithmetic_2EZERO @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(pre_uni,[status(thm)],[4055:[bind(A,$thf( ^ [E: TA] : c_2Earithmetic_2EZERO ))]]) ).
thf(4088,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)],[4073]) ).
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(310,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)],[280,133]) ).
thf(322,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)],[310]) ).
thf(529,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)],[133,420]) ).
thf(543,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)],[529]) ).
thf(18812,plain,
$false,
inference(e,[status(thm)],[549,9929,138,2306,2336,7922,555,15361,3990,13088,7253,2282,7573,15158,12479,15299,7871,174,3335,2348,42,417,37,16118,52,7277,10999,5836,157,7754,7711,189,93,325,152,316,5264,14881,7423,321,574,353,2073,7899,280,2281,61,4087,133,312,4082,602,15023,7535,3857,117,7286,6307,2307,14958,6000,160,12650,4160,16247,1079,551,15266,8446,15481,8414,3102,8451,53,169,141,420,1118,14613,2196,2125,15442,7749,134,4036,128,7020,412,5996,7582,7866,34,12654,573,149,161,6001,562,7287,4341,12688,12663,413,2193,7425,54,611,144,3619,181,5997,7579,7865,7529,172,419,81,39,98,2896,3456,631,15438,2625,323,140,621,155,520,66,12680,130,12655,2303,4158,7896,162,11030,112,617,8409,145,10228,282,2375,16249,7662,5995,14421,7921,154,14631,72,175,4093,3398,2352,10082,2194,2273,319,158,14618,632,171,418,3780,139,2764,151,620,447,7868,36,146,7712,2201,15673,7943,2340,415,326,107,7538,7987,7035,9969,163,4088,131,47,322,543]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP003^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.22 % Computer : n020.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 19:21:04 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.66/1.05 % [INFO] Parsing done (259ms).
% 1.66/1.06 % [INFO] Running in sequential loop mode.
% 2.56/1.47 % [INFO] eprover registered as external prover.
% 2.56/1.48 % [INFO] Scanning for conjecture ...
% 2.81/1.59 % [INFO] Found a conjecture (or negated_conjecture) and 64 axioms. Running axiom selection ...
% 2.98/1.67 % [INFO] Axiom selection finished. Selected 31 axioms (removed 33 axioms).
% 3.20/1.73 % [INFO] Problem is higher-order (TPTP THF).
% 3.20/1.74 % [INFO] Type checking passed.
% 3.20/1.74 % [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 ...
% 86.30/18.32 % External prover 'e' found a proof!
% 86.30/18.32 % [INFO] Killing All external provers ...
% 86.30/18.32 % Time passed: 17967ms (effective reasoning time: 17252ms)
% 86.30/18.32 % 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)>
% 86.30/18.33 % 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
% 86.30/18.33 % No. of inferences in proof: 611
% 86.30/18.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 17967 ms resp. 17252 ms w/o parsing
% 73.73/18.77 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 73.73/18.77 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------