TSTP Solution File: ITP003^3 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : ITP003^3 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:27:02 EDT 2024
% Result : Theorem 155.28s 22.61s
% Output : Refutation 155.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 35
% Syntax : Number of formulae : 140 ( 71 unt; 20 typ; 0 def)
% Number of atoms : 280 ( 148 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 1010 ( 90 ~; 66 |; 5 &; 840 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 8 con; 0-4 aty)
% Number of variables : 184 ( 0 ^ 167 !; 16 ?; 184 :)
% ( 1 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Enum_2Enum_type,type,
tyop_2Enum_2Enum: $tType ).
thf(c_2Earithmetic_2E_2A_type,type,
c_2Earithmetic_2E_2A: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2E_2B_type,type,
c_2Earithmetic_2E_2B: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Enum_2E0_type,type,
c_2Enum_2E0: tyop_2Enum_2Enum ).
thf(c_2Eprim__rec_2E_3C_type,type,
c_2Eprim__rec_2E_3C: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Earithmetic_2EBIT1_type,type,
c_2Earithmetic_2EBIT1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EBIT2_type,type,
c_2Earithmetic_2EBIT2: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebool_2ECOND_type,type,
c_2Ebool_2ECOND:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(c_2Earithmetic_2EEVEN_type,type,
c_2Earithmetic_2EEVEN: tyop_2Enum_2Enum > $o ).
thf(c_2Ebool_2EF_type,type,
c_2Ebool_2EF: $o ).
thf(c_2Earithmetic_2EMOD_type,type,
c_2Earithmetic_2EMOD: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2ENUMERAL_type,type,
c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2EODD_type,type,
c_2Earithmetic_2EODD: tyop_2Enum_2Enum > $o ).
thf(c_2Enum_2ESUC_type,type,
c_2Enum_2ESUC: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebool_2ET_type,type,
c_2Ebool_2ET: $o ).
thf(c_2Earithmetic_2EZERO_type,type,
c_2Earithmetic_2EZERO: tyop_2Enum_2Enum ).
thf(sk1_type,type,
sk1: tyop_2Enum_2Enum ).
thf(sk2_type,type,
sk2: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(sk16_type,type,
sk16: tyop_2Enum_2Enum ).
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/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EODD__EXISTS) ).
thf(141,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EODD @ A )
= ( ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(142,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EODD @ A )
= ( ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ) ),
inference(cnf,[status(esa)],[141]) ).
thf(143,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EODD @ A )
= ( ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ) ),
inference(lifteq,[status(thm)],[142]) ).
thf(28,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EODD @ A )
= ( ~ ( c_2Earithmetic_2EEVEN @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EODD__EVEN) ).
thf(153,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EODD @ A )
= ( ~ ( c_2Earithmetic_2EEVEN @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(154,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EODD @ A )
= ( ~ ( c_2Earithmetic_2EEVEN @ A ) ) ),
inference(cnf,[status(esa)],[153]) ).
thf(155,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EODD @ A )
= ( ~ ( c_2Earithmetic_2EEVEN @ A ) ) ),
inference(lifteq,[status(thm)],[154]) ).
thf(567,plain,
! [A: tyop_2Enum_2Enum] :
( ( ~ ( c_2Earithmetic_2EEVEN @ A ) )
= ( ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ) ),
inference(rewrite,[status(thm)],[143,155]) ).
thf(568,plain,
! [A: tyop_2Enum_2Enum] :
( ~ ~ ( c_2Earithmetic_2EEVEN @ A )
| ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ),
inference(bool_ext,[status(thm)],[567]) ).
thf(572,plain,
! [A: tyop_2Enum_2Enum] :
( ( A
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( sk2 @ A ) ) ) )
| ( c_2Earithmetic_2EEVEN @ A ) ),
inference(cnf,[status(esa)],[568]) ).
thf(573,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( sk2 @ A ) ) )
= A )
| ( c_2Earithmetic_2EEVEN @ A ) ),
inference(lifteq,[status(thm)],[572]) ).
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/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EMULT__COMM) ).
thf(123,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ B )
= ( c_2Earithmetic_2E_2A @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(124,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ B )
= ( c_2Earithmetic_2E_2A @ B @ A ) ),
inference(cnf,[status(esa)],[123]) ).
thf(125,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ B )
= ( c_2Earithmetic_2E_2A @ B @ A ) ),
inference(lifteq,[status(thm)],[124]) ).
thf(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/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CLAUSES) ).
thf(158,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A )
& ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(159,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ),
inference(cnf,[status(esa)],[158]) ).
thf(161,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ),
inference(lifteq,[status(thm)],[159]) ).
thf(3,axiom,
! [A: $o] :
( ( A
=> c_2Ebool_2EF )
=> ~ A ),
file('/export/starexec/sandbox2/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(328,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ $false @ A @ B )
= B ),
inference(rewrite,[status(thm)],[161,39]) ).
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/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EMOD__UNIQUE) ).
thf(129,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ? [D: tyop_2Enum_2Enum] :
( ( B
= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ A ) @ C ) )
& ( c_2Eprim__rec_2E_3C @ C @ A ) )
=> ( ( c_2Earithmetic_2EMOD @ B @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(130,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum] :
( ( ? [D: tyop_2Enum_2Enum] :
( B
= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ A ) @ C ) )
& ( c_2Eprim__rec_2E_3C @ C @ A ) )
=> ( ( c_2Earithmetic_2EMOD @ B @ A )
= C ) ),
inference(miniscope,[status(thm)],[129]) ).
thf(131,plain,
! [D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( B
!= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ A ) @ C ) )
| ~ ( c_2Eprim__rec_2E_3C @ C @ A )
| ( ( c_2Earithmetic_2EMOD @ B @ A )
= C ) ),
inference(cnf,[status(esa)],[130]) ).
thf(132,plain,
! [D: tyop_2Enum_2Enum,C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( B
!= ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ D @ A ) @ C ) )
| ( ( c_2Earithmetic_2EMOD @ B @ A )
= C )
| ~ ( c_2Eprim__rec_2E_3C @ C @ A ) ),
inference(lifteq,[status(thm)],[131]) ).
thf(133,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ A ) @ B ) @ A )
= B )
| ~ ( c_2Eprim__rec_2E_3C @ B @ A ) ),
inference(simp,[status(thm)],[132]) ).
thf(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/sandbox2/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(370,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ B @ A )
| ( B
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
| ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ A ) @ B ) @ A )
!= ( c_2Earithmetic_2EMOD @ sk1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[133,36]) ).
thf(378,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ A )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ B @ A ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( A
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[370]) ).
thf(390,plain,
! [A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ) ),
inference(simp,[status(thm)],[378]) ).
thf(474,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ $false @ A @ B )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[328,390]) ).
thf(497,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( c_2Earithmetic_2EEVEN @ sk1 )
| ( A != c_2Enum_2E0 )
| ( B
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[474]) ).
thf(510,plain,
! [A: tyop_2Enum_2Enum] :
( ~ ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( c_2Earithmetic_2EEVEN @ sk1 ) ),
inference(simp,[status(thm)],[497]) ).
thf(23,axiom,
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
= ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EONE) ).
thf(139,plain,
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) )
= ( c_2Enum_2ESUC @ c_2Enum_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(140,plain,
( ( c_2Enum_2ESUC @ c_2Enum_2E0 )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ),
inference(lifteq,[status(thm)],[139]) ).
thf(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/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2ETWO) ).
thf(156,plain,
( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(157,plain,
( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ),
inference(lifteq,[status(thm)],[156]) ).
thf(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/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2ELESS__MONO__EQ) ).
thf(126,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Enum_2ESUC @ B ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(127,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Enum_2ESUC @ B ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) ),
inference(cnf,[status(esa)],[126]) ).
thf(128,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Enum_2ESUC @ B ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) ),
inference(lifteq,[status(thm)],[127]) ).
thf(286,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ A @ B ) )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Enum_2ESUC @ B ) ) ),
inference(paramod_ordered,[status(thm)],[157,128]) ).
thf(287,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( c_2Enum_2ESUC @ A ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pattern_uni,[status(thm)],[286:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ))]]) ).
thf(3926,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
| ( ( c_2Enum_2ESUC @ c_2Enum_2E0 )
!= ( c_2Enum_2ESUC @ A ) ) ),
inference(paramod_ordered,[status(thm)],[140,287]) ).
thf(3927,plain,
( ( c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pattern_uni,[status(thm)],[3926:[bind(A,$thf( c_2Enum_2E0 ))]]) ).
thf(21,axiom,
! [A: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Enum_2ESUC @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eprim__rec_2ELESS__0) ).
thf(134,plain,
! [A: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Enum_2ESUC @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(135,plain,
! [A: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Enum_2ESUC @ A ) ),
inference(cnf,[status(esa)],[134]) ).
thf(257,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Enum_2ESUC @ c_2Enum_2E0 )
!= ( c_2Enum_2ESUC @ A ) ) ),
inference(paramod_ordered,[status(thm)],[140,135]) ).
thf(258,plain,
c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ),
inference(pattern_uni,[status(thm)],[257:[bind(A,$thf( c_2Enum_2E0 ))]]) ).
thf(4104,plain,
c_2Eprim__rec_2E_3C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ),
inference(rewrite,[status(thm)],[3927,258]) ).
thf(15501,plain,
! [A: tyop_2Enum_2Enum] :
( ~ $true
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( c_2Earithmetic_2EEVEN @ sk1 ) ),
inference(rewrite,[status(thm)],[510,4104]) ).
thf(15502,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 )
| ( c_2Earithmetic_2EEVEN @ sk1 ) ),
inference(simp,[status(thm)],[15501]) ).
thf(15525,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ B )
!= sk1 )
| ( c_2Earithmetic_2EEVEN @ sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ $false @ A @ B )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[328,15502]) ).
thf(15549,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ sk1 )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ B )
!= sk1 )
| ( c_2Earithmetic_2EEVEN @ sk1 )
| ( A != c_2Enum_2E0 )
| ( B
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[15525]) ).
thf(15593,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ sk1 )
| ( ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 ) ),
inference(simp,[status(thm)],[15549]) ).
thf(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/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EADD1) ).
thf(144,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Enum_2ESUC @ A )
= ( c_2Earithmetic_2E_2B @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(145,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Enum_2ESUC @ A )
= ( c_2Earithmetic_2E_2B @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(cnf,[status(esa)],[144]) ).
thf(146,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2B @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
= ( c_2Enum_2ESUC @ A ) ),
inference(lifteq,[status(thm)],[145]) ).
thf(18385,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ sk1 )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= sk1 ) ),
inference(rewrite,[status(thm)],[15593,146]) ).
thf(18386,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ sk1 )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ B @ A ) )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ A @ B )
!= ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[125,18385]) ).
thf(18387,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ sk1 )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[18386:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).
thf(21900,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ A )
| ( c_2Earithmetic_2EEVEN @ sk1 )
| ( A != sk1 )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ ( sk2 @ A ) ) )
!= ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[573,18387]) ).
thf(21901,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ A )
| ( c_2Earithmetic_2EEVEN @ sk1 )
| ( A != sk1 ) ),
inference(pattern_uni,[status(thm)],[21900:[bind(A,$thf( C )),bind(B,$thf( sk2 @ C ))]]) ).
thf(21951,plain,
( ( c_2Earithmetic_2EEVEN @ sk1 )
| ( c_2Earithmetic_2EEVEN @ sk1 ) ),
inference(simp,[status(thm)],[21901]) ).
thf(22060,plain,
c_2Earithmetic_2EEVEN @ sk1,
inference(simp,[status(thm)],[21951]) ).
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/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EEVEN__EXISTS) ).
thf(150,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ A )
= ( ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(151,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ A )
= ( ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ),
inference(cnf,[status(esa)],[150]) ).
thf(152,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ A )
= ( ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ) ),
inference(lifteq,[status(thm)],[151]) ).
thf(22076,plain,
! [A: tyop_2Enum_2Enum] :
( ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) )
| ( ( c_2Earithmetic_2EEVEN @ sk1 )
!= ( c_2Earithmetic_2EEVEN @ A ) ) ),
inference(paramod_ordered,[status(thm)],[22060,152]) ).
thf(22077,plain,
? [A: tyop_2Enum_2Enum] :
( sk1
= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) ),
inference(pattern_uni,[status(thm)],[22076:[bind(A,$thf( sk1 ))]]) ).
thf(22137,plain,
( sk1
= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ sk16 ) ),
inference(cnf,[status(esa)],[22077]) ).
thf(22138,plain,
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ sk16 )
= sk1 ),
inference(lifteq,[status(thm)],[22137]) ).
thf(938,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ A )
| ~ ? [B: tyop_2Enum_2Enum] :
( A
= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) ) ),
inference(bool_ext,[status(thm)],[152]) ).
thf(983,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( A
!= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) )
| ( c_2Earithmetic_2EEVEN @ A ) ),
inference(cnf,[status(esa)],[938]) ).
thf(984,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( A
!= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ B ) )
| ( c_2Earithmetic_2EEVEN @ A ) ),
inference(lifteq,[status(thm)],[983]) ).
thf(985,plain,
! [A: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A ) ),
inference(simp,[status(thm)],[984]) ).
thf(1013,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ A @ B ) )
| ( ( c_2Earithmetic_2E_2A @ B @ A )
!= ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[125,985]) ).
thf(1014,plain,
! [A: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(pattern_uni,[status(thm)],[1013:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).
thf(160,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A ),
inference(cnf,[status(esa)],[158]) ).
thf(162,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A ),
inference(lifteq,[status(thm)],[160]) ).
thf(6,axiom,
! [TA: $tType,A: TA] :
( ( A = A )
= c_2Ebool_2ET ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EREFL__CLAUSE) ).
thf(52,plain,
c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(413,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ $true @ A @ B )
= A ),
inference(rewrite,[status(thm)],[162,52]) ).
thf(261,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
| ( ( c_2Enum_2ESUC @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Enum_2ESUC @ A ) ) ),
inference(paramod_ordered,[status(thm)],[157,135]) ).
thf(262,plain,
c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ),
inference(pattern_uni,[status(thm)],[261:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ))]]) ).
thf(375,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ C @ A ) @ B ) @ A )
= B )
| ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Eprim__rec_2E_3C @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[262,133]) ).
thf(376,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= c_2Enum_2E0 ),
inference(pattern_uni,[status(thm)],[375:[bind(A,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(B,$thf( c_2Enum_2E0 )),bind(C,$thf( C ))]]) ).
thf(388,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ c_2Enum_2E0 ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= c_2Enum_2E0 ),
inference(simp,[status(thm)],[376]) ).
thf(32,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2B @ A @ c_2Enum_2E0 )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Earithmetic_2EADD__0) ).
thf(166,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2B @ A @ c_2Enum_2E0 )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(167,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2B @ A @ c_2Enum_2E0 )
= A ),
inference(cnf,[status(esa)],[166]) ).
thf(168,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2B @ A @ c_2Enum_2E0 )
= A ),
inference(lifteq,[status(thm)],[167]) ).
thf(6248,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
= c_2Enum_2E0 ),
inference(rewrite,[status(thm)],[388,168]) ).
thf(6279,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2EMOD @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Earithmetic_2EMOD @ sk1 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6248,36]) ).
thf(6290,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ( ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[6279]) ).
thf(6303,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) )
!= c_2Enum_2E0 )
| ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 ) ),
inference(simp,[status(thm)],[6290]) ).
thf(6328,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( A != c_2Enum_2E0 )
| ( ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ $true @ A @ B )
!= ( c_2Ebool_2ECOND @ tyop_2Enum_2Enum @ ( c_2Earithmetic_2EEVEN @ sk1 ) @ c_2Enum_2E0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[413,6303]) ).
thf(6337,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ~ ( c_2Earithmetic_2EEVEN @ sk1 )
| ( c_2Enum_2E0 != c_2Enum_2E0 )
| ( A
!= ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ),
inference(simp,[status(thm)],[6328]) ).
thf(6355,plain,
! [A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ~ ( c_2Earithmetic_2EEVEN @ sk1 ) ),
inference(simp,[status(thm)],[6337]) ).
thf(6455,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ( ( c_2Earithmetic_2EEVEN @ ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
!= ( c_2Earithmetic_2EEVEN @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1014,6355]) ).
thf(6457,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 ) ),
inference(simp,[status(thm)],[6455]) ).
thf(9795,plain,
! [B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= ( c_2Earithmetic_2E_2A @ B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) )
| ( sk1 != sk1 ) ),
inference(eqfactor_ordered,[status(thm)],[6457]) ).
thf(9804,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) )
!= sk1 ),
inference(pattern_uni,[status(thm)],[9795:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(9817,plain,
! [C: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum,A: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_2A @ B @ A )
!= sk1 )
| ( ( c_2Earithmetic_2E_2A @ A @ B )
!= ( c_2Earithmetic_2E_2A @ C @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[125,9804]) ).
thf(9818,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_2A @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) ) @ A )
!= sk1 ),
inference(pattern_uni,[status(thm)],[9817:[bind(A,$thf( A )),bind(B,$thf( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT2 @ c_2Earithmetic_2EZERO ) )),bind(C,$thf( A ))]]) ).
thf(22247,plain,
$false,
inference(simplifyReflect,[status(thm)],[22138,9818]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : ITP003^3 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.11/0.16 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n023.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Sat May 18 17:32:54 EDT 2024
% 0.17/0.38 % CPUTime :
% 0.97/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.40/1.07 % [INFO] Parsing done (170ms).
% 1.40/1.08 % [INFO] Running in sequential loop mode.
% 2.06/1.32 % [INFO] nitpick registered as external prover.
% 2.06/1.33 % [INFO] Scanning for conjecture ...
% 2.11/1.40 % [INFO] Found a conjecture (or negated_conjecture) and 64 axioms. Running axiom selection ...
% 2.32/1.46 % [INFO] Axiom selection finished. Selected 31 axioms (removed 33 axioms).
% 2.56/1.50 % [INFO] Problem is higher-order (TPTP THF).
% 2.56/1.50 % [INFO] Type checking passed.
% 2.56/1.51 % [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 ...
% 155.00/22.59 % [INFO] Killing All external provers ...
% 155.28/22.60 % Time passed: 22048ms (effective reasoning time: 21505ms)
% 155.28/22.60 % 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)>
% 155.28/22.60 % Axioms used in derivation (14): thm_2Ebool_2EREFL__CLAUSE, thm_2Earithmetic_2EEVEN__EXISTS, thm_2Ebool_2ECOND__CLAUSES, thm_2Earithmetic_2EODD__EVEN, thm_2Earithmetic_2ETWO, thm_2Earithmetic_2EADD__0, thm_2Earithmetic_2ELESS__MONO__EQ, thm_2Ebool_2EIMP__F, thm_2Earithmetic_2EODD__EXISTS, thm_2Eprim__rec_2ELESS__0, thm_2Earithmetic_2EONE, thm_2Earithmetic_2EMOD__UNIQUE, thm_2Earithmetic_2EMULT__COMM, thm_2Earithmetic_2EADD1
% 155.28/22.60 % No. of inferences in proof: 120
% 155.28/22.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 22048 ms resp. 21505 ms w/o parsing
% 155.30/22.68 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 155.30/22.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------