TSTP Solution File: ITP011^2 by Leo-III---1.7.10
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP011^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:46:44 EDT 2024
% Result : Theorem 104.49s 20.43s
% Output : Refutation 104.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 77
% Syntax : Number of formulae : 166 ( 75 unt; 31 typ; 0 def)
% Number of atoms : 563 ( 146 equ; 0 cnn)
% Maximal formula atoms : 50 ( 4 avg)
% Number of connectives : 2032 ( 72 ~; 39 |; 81 &;1698 @)
% ( 0 <=>; 142 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 30 usr; 13 con; 0-2 aty)
% Number of variables : 229 ( 0 ^ 221 !; 8 ?; 229 :)
% Comments :
%------------------------------------------------------------------------------
thf(del_type,type,
del: $tType ).
thf(bool_type,type,
bool: del ).
thf(arr_type,type,
arr: del > del > del ).
thf(mem_type,type,
mem: $i > del > $o ).
thf(ap_type,type,
ap: $i > $i > $i ).
thf(lam_type,type,
lam: del > ( $i > $i ) > $i ).
thf(p_type,type,
p: $i > $o ).
thf(inj__o_type,type,
inj__o: $o > $i ).
thf(ty_2Eoption_2Eoption_type,type,
ty_2Eoption_2Eoption: del > del ).
thf(c_2Eoption_2EOPTION__JOIN_type,type,
c_2Eoption_2EOPTION__JOIN: del > $i ).
thf(c_2Eoption_2EOPTION__MAP_type,type,
c_2Eoption_2EOPTION__MAP: del > del > $i ).
thf(c_2Eoption_2Eoption__CASE_type,type,
c_2Eoption_2Eoption__CASE: del > del > $i ).
thf(c_2Emin_2E_3D_3D_3E_type,type,
c_2Emin_2E_3D_3D_3E: $i ).
thf(c_2Eoption_2EIS__NONE_type,type,
c_2Eoption_2EIS__NONE: del > $i ).
thf(c_2Ebool_2EF_type,type,
c_2Ebool_2EF: $i ).
thf(c_2Ebool_2ET_type,type,
c_2Ebool_2ET: $i ).
thf(c_2Eoption_2EIS__SOME_type,type,
c_2Eoption_2EIS__SOME: del > $i ).
thf(c_2Ebool_2E_7E_type,type,
c_2Ebool_2E_7E: $i ).
thf(c_2Eoption_2ETHE_type,type,
c_2Eoption_2ETHE: del > $i ).
thf(c_2Eoption_2ESOME_type,type,
c_2Eoption_2ESOME: del > $i ).
thf(c_2Ebool_2E_3F_type,type,
c_2Ebool_2E_3F: del > $i ).
thf(c_2Eoption_2ENONE_type,type,
c_2Eoption_2ENONE: del > $i ).
thf(c_2Ebool_2E_2F_5C_type,type,
c_2Ebool_2E_2F_5C: $i ).
thf(c_2Ebool_2E_5C_2F_type,type,
c_2Ebool_2E_5C_2F: $i ).
thf(c_2Eoption_2EOPTREL_type,type,
c_2Eoption_2EOPTREL: del > del > $i ).
thf(c_2Emin_2E_3D_type,type,
c_2Emin_2E_3D: del > $i ).
thf(c_2Ebool_2E_21_type,type,
c_2Ebool_2E_21: del > $i ).
thf(sk1_type,type,
sk1: del ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(43,axiom,
p @ c_2Ebool_2ET,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_true_p) ).
thf(202,plain,
p @ c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(10,axiom,
~ ( p @ c_2Ebool_2EF ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_false_p) ).
thf(65,plain,
~ ( p @ c_2Ebool_2EF ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(66,plain,
~ ( p @ c_2Ebool_2EF ),
inference(polarity_switch,[status(thm)],[65]) ).
thf(210,plain,
( ( p @ c_2Ebool_2ET )
!= ( p @ c_2Ebool_2EF ) ),
inference(paramod_ordered,[status(thm)],[202,66]) ).
thf(211,plain,
c_2Ebool_2ET != c_2Ebool_2EF,
inference(simp,[status(thm)],[210]) ).
thf(8,axiom,
! [A: del] : ( mem @ ( c_2Ebool_2E_3F @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_3F) ).
thf(60,plain,
! [A: del] : ( mem @ ( c_2Ebool_2E_3F @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(39,axiom,
! [A: $o] :
( ( p @ ( inj__o @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_o) ).
thf(189,plain,
! [A: $o] :
( ( p @ ( inj__o @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(192,plain,
( ( p @ ( inj__o @ $false ) )
= $false ),
inference(instance,[status(thm)],[189]) ).
thf(193,plain,
~ ( p @ ( inj__o @ $false ) ),
inference(simp,[status(thm)],[192]) ).
thf(16,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ A ) @ B ) )
= ( ( p @ A )
| ( p @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_or_p) ).
thf(129,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ A ) @ B ) )
= ( ( p @ A )
| ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(19,axiom,
! [A: $o] : ( mem @ ( inj__o @ A ) @ bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_o) ).
thf(134,plain,
! [A: $o] : ( mem @ ( inj__o @ A ) @ bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(135,plain,
mem @ ( inj__o @ $true ) @ bool,
inference(instance,[status(thm)],[134]) ).
thf(4,axiom,
! [A: del,B: $i] :
( ( mem @ B @ A )
=> ( ( B = B )
= $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EREFL__CLAUSE) ).
thf(55,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(190,plain,
( ( p @ ( inj__o @ $true ) )
= $true ),
inference(instance,[status(thm)],[189]) ).
thf(191,plain,
p @ ( inj__o @ $true ),
inference(simp,[status(thm)],[190]) ).
thf(226,plain,
( ( p @ ( inj__o @ $true ) )
!= ( p @ c_2Ebool_2EF ) ),
inference(paramod_ordered,[status(thm)],[191,66]) ).
thf(232,plain,
( ( inj__o @ $true )
!= c_2Ebool_2EF ),
inference(simp,[status(thm)],[226]) ).
thf(5,axiom,
! [A: del,B: del] : ( mem @ ( c_2Eoption_2EOPTION__MAP @ A @ B ) @ ( arr @ ( arr @ A @ B ) @ ( arr @ ( ty_2Eoption_2Eoption @ A ) @ ( ty_2Eoption_2Eoption @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2EOPTION__MAP) ).
thf(56,plain,
! [A: del,B: del] : ( mem @ ( c_2Eoption_2EOPTION__MAP @ A @ B ) @ ( arr @ ( arr @ A @ B ) @ ( arr @ ( ty_2Eoption_2Eoption @ A ) @ ( ty_2Eoption_2Eoption @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,axiom,
! [A: del] : ( mem @ ( c_2Eoption_2ENONE @ A ) @ ( ty_2Eoption_2Eoption @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2ENONE) ).
thf(70,plain,
! [A: del] : ( mem @ ( c_2Eoption_2ENONE @ A ) @ ( ty_2Eoption_2Eoption @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(71,plain,
! [A: del] : ( mem @ ( c_2Eoption_2ENONE @ A ) @ ( ty_2Eoption_2Eoption @ A ) ),
inference(cnf,[status(esa)],[70]) ).
thf(1,conjecture,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ ( arr @ A @ bool ) ) )
=> ! [C: $i] :
( ( mem @ C @ A )
=> ! [D: $i] :
( ( mem @ D @ A )
=> ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A @ A ) @ B ) @ ( c_2Eoption_2ENONE @ A ) ) @ ( c_2Eoption_2ENONE @ A ) ) )
= $true )
& ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A @ A ) @ B ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ C ) ) @ ( c_2Eoption_2ENONE @ A ) ) )
= $false )
& ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A @ A ) @ B ) @ ( c_2Eoption_2ENONE @ A ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ D ) ) )
= $false )
& ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A @ A ) @ B ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ C ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ D ) ) )
= ( p @ ( ap @ ( ap @ B @ C ) @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Equotient__option_2EOPTION__REL__def) ).
thf(2,negated_conjecture,
~ ! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ ( arr @ A @ bool ) ) )
=> ! [C: $i] :
( ( mem @ C @ A )
=> ! [D: $i] :
( ( mem @ D @ A )
=> ( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A @ A ) @ B ) @ ( c_2Eoption_2ENONE @ A ) ) @ ( c_2Eoption_2ENONE @ A ) ) )
= $true )
& ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A @ A ) @ B ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ C ) ) @ ( c_2Eoption_2ENONE @ A ) ) )
= $false )
& ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A @ A ) @ B ) @ ( c_2Eoption_2ENONE @ A ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ D ) ) )
= $false )
& ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A @ A ) @ B ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ C ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ D ) ) )
= ( p @ ( ap @ ( ap @ B @ C ) @ D ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(48,plain,
~ ! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ ( arr @ A @ bool ) ) )
=> ! [C: $i] :
( ( mem @ C @ A )
=> ! [D: $i] :
( ( mem @ D @ A )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A @ A ) @ B ) @ ( c_2Eoption_2ENONE @ A ) ) @ ( c_2Eoption_2ENONE @ A ) ) )
& ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A @ A ) @ B ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ C ) ) @ ( c_2Eoption_2ENONE @ A ) ) )
& ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A @ A ) @ B ) @ ( c_2Eoption_2ENONE @ A ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ D ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A @ A ) @ B ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ C ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ D ) ) )
= ( p @ ( ap @ ( ap @ B @ C ) @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(52,plain,
mem @ sk2 @ ( arr @ sk1 @ ( arr @ sk1 @ bool ) ),
inference(cnf,[status(esa)],[48]) ).
thf(14,axiom,
! [A: del,B: del,C: $i] :
( ( mem @ C @ B )
=> ! [D: $i] :
( ( mem @ D @ ( arr @ A @ B ) )
=> ! [E: $i] :
( ( mem @ E @ ( ty_2Eoption_2Eoption @ A ) )
=> ( ! [F: $i] :
( ( mem @ F @ A )
=> ! [G: $i] :
( ( mem @ G @ A )
=> ( ( ( ap @ ( c_2Eoption_2ESOME @ A ) @ F )
= ( ap @ ( c_2Eoption_2ESOME @ A ) @ G ) )
= ( F = G ) ) ) )
& ! [F: $i] :
( ( mem @ F @ A )
=> ( ( ap @ ( c_2Eoption_2ETHE @ A ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ F ) )
= F ) )
& ! [F: $i] :
( ( mem @ F @ A )
=> ( ( c_2Eoption_2ENONE @ A )
!= ( ap @ ( c_2Eoption_2ESOME @ A ) @ F ) ) )
& ! [F: $i] :
( ( mem @ F @ A )
=> ( ( ap @ ( c_2Eoption_2ESOME @ A ) @ F )
!= ( c_2Eoption_2ENONE @ A ) ) )
& ! [F: $i] :
( ( mem @ F @ A )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ F ) ) )
= $true ) )
& ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ ( c_2Eoption_2ENONE @ A ) ) )
= $false )
& ! [F: $i] :
( ( mem @ F @ ( ty_2Eoption_2Eoption @ A ) )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__NONE @ A ) @ F ) )
= ( F
= ( c_2Eoption_2ENONE @ A ) ) ) )
& ! [F: $i] :
( ( mem @ F @ ( ty_2Eoption_2Eoption @ A ) )
=> ( ( ~ ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ F ) ) )
= ( F
= ( c_2Eoption_2ENONE @ A ) ) ) )
& ! [F: $i] :
( ( mem @ F @ ( ty_2Eoption_2Eoption @ A ) )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ F ) )
=> ( ( ap @ ( c_2Eoption_2ESOME @ A ) @ ( ap @ ( c_2Eoption_2ETHE @ A ) @ F ) )
= F ) ) )
& ! [F: $i] :
( ( mem @ F @ ( ty_2Eoption_2Eoption @ A ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A @ ( ty_2Eoption_2Eoption @ A ) ) @ F ) @ ( c_2Eoption_2ENONE @ A ) ) @ ( c_2Eoption_2ESOME @ A ) )
= F ) )
& ! [F: $i] :
( ( mem @ F @ ( ty_2Eoption_2Eoption @ A ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A @ ( ty_2Eoption_2Eoption @ A ) ) @ F ) @ F ) @ ( c_2Eoption_2ESOME @ A ) )
= F ) )
& ! [F: $i] :
( ( mem @ F @ ( ty_2Eoption_2Eoption @ A ) )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__NONE @ A ) @ F ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A @ B ) @ F ) @ C ) @ D )
= C ) ) )
& ! [F: $i] :
( ( mem @ F @ ( ty_2Eoption_2Eoption @ A ) )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ F ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A @ B ) @ F ) @ C ) @ D )
= ( ap @ D @ ( ap @ ( c_2Eoption_2ETHE @ A ) @ F ) ) ) ) )
& ! [F: $i] :
( ( mem @ F @ ( ty_2Eoption_2Eoption @ A ) )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ F ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A @ ( ty_2Eoption_2Eoption @ A ) ) @ F ) @ E ) @ ( c_2Eoption_2ESOME @ A ) )
= F ) ) )
& ! [F: $i] :
( ( mem @ F @ B )
=> ! [G: $i] :
( ( mem @ G @ ( arr @ A @ B ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A @ B ) @ ( c_2Eoption_2ENONE @ A ) ) @ F ) @ G )
= F ) ) )
& ! [F: $i] :
( ( mem @ F @ A )
=> ! [G: $i] :
( ( mem @ G @ B )
=> ! [H: $i] :
( ( mem @ H @ ( arr @ A @ B ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A @ B ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ F ) ) @ G ) @ H )
= ( ap @ H @ F ) ) ) ) )
& ! [F: $i] :
( ( mem @ F @ ( arr @ A @ B ) )
=> ! [G: $i] :
( ( mem @ G @ A )
=> ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A @ B ) @ F ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ G ) )
= ( ap @ ( c_2Eoption_2ESOME @ B ) @ ( ap @ F @ G ) ) ) ) )
& ! [F: $i] :
( ( mem @ F @ ( arr @ A @ B ) )
=> ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A @ B ) @ F ) @ ( c_2Eoption_2ENONE @ A ) )
= ( c_2Eoption_2ENONE @ B ) ) )
& ( ( ap @ ( c_2Eoption_2EOPTION__JOIN @ A ) @ ( c_2Eoption_2ENONE @ ( ty_2Eoption_2Eoption @ A ) ) )
= ( c_2Eoption_2ENONE @ A ) )
& ! [F: $i] :
( ( mem @ F @ ( ty_2Eoption_2Eoption @ A ) )
=> ( ( ap @ ( c_2Eoption_2EOPTION__JOIN @ A ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Eoption_2Eoption @ A ) ) @ F ) )
= F ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eoption_2Eoption__CLAUSES) ).
thf(72,plain,
! [A: del,B: del,C: $i] :
( ( mem @ C @ B )
=> ! [D: $i] :
( ( mem @ D @ ( arr @ A @ B ) )
=> ! [E: $i] :
( ( mem @ E @ ( ty_2Eoption_2Eoption @ A ) )
=> ( ! [F: $i] :
( ( mem @ F @ A )
=> ! [G: $i] :
( ( mem @ G @ A )
=> ( ( ( ap @ ( c_2Eoption_2ESOME @ A ) @ F )
= ( ap @ ( c_2Eoption_2ESOME @ A ) @ G ) )
= ( F = G ) ) ) )
& ! [F: $i] :
( ( mem @ F @ A )
=> ( ( ap @ ( c_2Eoption_2ETHE @ A ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ F ) )
= F ) )
& ! [F: $i] :
( ( mem @ F @ A )
=> ( ( c_2Eoption_2ENONE @ A )
!= ( ap @ ( c_2Eoption_2ESOME @ A ) @ F ) ) )
& ! [F: $i] :
( ( mem @ F @ A )
=> ( ( ap @ ( c_2Eoption_2ESOME @ A ) @ F )
!= ( c_2Eoption_2ENONE @ A ) ) )
& ! [F: $i] :
( ( mem @ F @ A )
=> ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ F ) ) ) )
& ~ ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ ( c_2Eoption_2ENONE @ A ) ) )
& ! [F: $i] :
( ( mem @ F @ ( ty_2Eoption_2Eoption @ A ) )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__NONE @ A ) @ F ) )
= ( F
= ( c_2Eoption_2ENONE @ A ) ) ) )
& ! [F: $i] :
( ( mem @ F @ ( ty_2Eoption_2Eoption @ A ) )
=> ( ( ~ ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ F ) ) )
= ( F
= ( c_2Eoption_2ENONE @ A ) ) ) )
& ! [F: $i] :
( ( mem @ F @ ( ty_2Eoption_2Eoption @ A ) )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ F ) )
=> ( ( ap @ ( c_2Eoption_2ESOME @ A ) @ ( ap @ ( c_2Eoption_2ETHE @ A ) @ F ) )
= F ) ) )
& ! [F: $i] :
( ( mem @ F @ ( ty_2Eoption_2Eoption @ A ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A @ ( ty_2Eoption_2Eoption @ A ) ) @ F ) @ ( c_2Eoption_2ENONE @ A ) ) @ ( c_2Eoption_2ESOME @ A ) )
= F ) )
& ! [F: $i] :
( ( mem @ F @ ( ty_2Eoption_2Eoption @ A ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A @ ( ty_2Eoption_2Eoption @ A ) ) @ F ) @ F ) @ ( c_2Eoption_2ESOME @ A ) )
= F ) )
& ! [F: $i] :
( ( mem @ F @ ( ty_2Eoption_2Eoption @ A ) )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__NONE @ A ) @ F ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A @ B ) @ F ) @ C ) @ D )
= C ) ) )
& ! [F: $i] :
( ( mem @ F @ ( ty_2Eoption_2Eoption @ A ) )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ F ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A @ B ) @ F ) @ C ) @ D )
= ( ap @ D @ ( ap @ ( c_2Eoption_2ETHE @ A ) @ F ) ) ) ) )
& ! [F: $i] :
( ( mem @ F @ ( ty_2Eoption_2Eoption @ A ) )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ F ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A @ ( ty_2Eoption_2Eoption @ A ) ) @ F ) @ E ) @ ( c_2Eoption_2ESOME @ A ) )
= F ) ) )
& ! [F: $i] :
( ( mem @ F @ B )
=> ! [G: $i] :
( ( mem @ G @ ( arr @ A @ B ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A @ B ) @ ( c_2Eoption_2ENONE @ A ) ) @ F ) @ G )
= F ) ) )
& ! [F: $i] :
( ( mem @ F @ A )
=> ! [G: $i] :
( ( mem @ G @ B )
=> ! [H: $i] :
( ( mem @ H @ ( arr @ A @ B ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2Eoption__CASE @ A @ B ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ F ) ) @ G ) @ H )
= ( ap @ H @ F ) ) ) ) )
& ! [F: $i] :
( ( mem @ F @ ( arr @ A @ B ) )
=> ! [G: $i] :
( ( mem @ G @ A )
=> ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A @ B ) @ F ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ G ) )
= ( ap @ ( c_2Eoption_2ESOME @ B ) @ ( ap @ F @ G ) ) ) ) )
& ! [F: $i] :
( ( mem @ F @ ( arr @ A @ B ) )
=> ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP @ A @ B ) @ F ) @ ( c_2Eoption_2ENONE @ A ) )
= ( c_2Eoption_2ENONE @ B ) ) )
& ( ( ap @ ( c_2Eoption_2EOPTION__JOIN @ A ) @ ( c_2Eoption_2ENONE @ ( ty_2Eoption_2Eoption @ A ) ) )
= ( c_2Eoption_2ENONE @ A ) )
& ! [F: $i] :
( ( mem @ F @ ( ty_2Eoption_2Eoption @ A ) )
=> ( ( ap @ ( c_2Eoption_2EOPTION__JOIN @ A ) @ ( ap @ ( c_2Eoption_2ESOME @ ( ty_2Eoption_2Eoption @ A ) ) @ F ) )
= F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(79,plain,
! [E: $i,D: $i,C: $i,B: del,A: del] :
( ~ ( mem @ C @ B )
| ~ ( mem @ D @ ( arr @ A @ B ) )
| ~ ( mem @ E @ ( ty_2Eoption_2Eoption @ A ) )
| ~ ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ ( c_2Eoption_2ENONE @ A ) ) ) ),
inference(cnf,[status(esa)],[72]) ).
thf(237,plain,
! [E: $i,D: $i,C: $i,B: del,A: del] :
( ~ ( mem @ C @ B )
| ~ ( mem @ E @ ( ty_2Eoption_2Eoption @ A ) )
| ~ ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ ( c_2Eoption_2ENONE @ A ) ) )
| ( ( mem @ sk2 @ ( arr @ sk1 @ ( arr @ sk1 @ bool ) ) )
!= ( mem @ D @ ( arr @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[52,79]) ).
thf(238,plain,
! [B: $i,A: $i] :
( ~ ( mem @ A @ ( arr @ sk1 @ bool ) )
| ~ ( mem @ B @ ( ty_2Eoption_2Eoption @ sk1 ) )
| ~ ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk1 ) @ ( c_2Eoption_2ENONE @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[237:[bind(A,$thf( sk1 )),bind(B,$thf( arr @ sk1 @ bool )),bind(C,$thf( C )),bind(D,$thf( sk2 )),bind(E,$thf( E ))]]) ).
thf(297,plain,
! [B: $i,A: $i] :
( ~ ( mem @ A @ ( arr @ sk1 @ bool ) )
| ~ ( mem @ B @ ( ty_2Eoption_2Eoption @ sk1 ) )
| ~ ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk1 ) @ ( c_2Eoption_2ENONE @ sk1 ) ) ) ),
inference(simp,[status(thm)],[238]) ).
thf(320,plain,
! [B: $i,A: $i] :
( ~ ( mem @ B @ ( ty_2Eoption_2Eoption @ sk1 ) )
| ~ ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk1 ) @ ( c_2Eoption_2ENONE @ sk1 ) ) )
| ( ( mem @ ( inj__o @ $true ) @ bool )
!= ( mem @ A @ ( arr @ sk1 @ bool ) ) ) ),
inference(paramod_ordered,[status(thm)],[135,297]) ).
thf(329,plain,
! [B: $i,A: $i] :
( ~ ( mem @ B @ ( ty_2Eoption_2Eoption @ sk1 ) )
| ~ ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk1 ) @ ( c_2Eoption_2ENONE @ sk1 ) ) )
| ( ( inj__o @ $true )
!= A )
| ( ( arr @ sk1 @ bool )
!= bool ) ),
inference(simp,[status(thm)],[320]) ).
thf(347,plain,
! [A: $i] :
( ~ ( mem @ A @ ( ty_2Eoption_2Eoption @ sk1 ) )
| ~ ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk1 ) @ ( c_2Eoption_2ENONE @ sk1 ) ) )
| ( ( arr @ sk1 @ bool )
!= bool ) ),
inference(simp,[status(thm)],[329]) ).
thf(481,plain,
! [B: $i,A: del] :
( ~ ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk1 ) @ ( c_2Eoption_2ENONE @ sk1 ) ) )
| ( ( arr @ sk1 @ bool )
!= bool )
| ( ( mem @ ( c_2Eoption_2ENONE @ A ) @ ( ty_2Eoption_2Eoption @ A ) )
!= ( mem @ B @ ( ty_2Eoption_2Eoption @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[71,347]) ).
thf(482,plain,
( ~ ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk1 ) @ ( c_2Eoption_2ENONE @ sk1 ) ) )
| ( ( arr @ sk1 @ bool )
!= bool ) ),
inference(pattern_uni,[status(thm)],[481:[bind(A,$thf( sk1 )),bind(B,$thf( c_2Eoption_2ENONE @ sk1 ))]]) ).
thf(498,plain,
( ( ( arr @ sk1 @ bool )
!= bool )
| ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk1 ) @ ( c_2Eoption_2ENONE @ sk1 ) ) )
!= ( p @ c_2Ebool_2ET ) ) ),
inference(paramod_ordered,[status(thm)],[202,482]) ).
thf(500,plain,
( ( ( arr @ sk1 @ bool )
!= bool )
| ( ( ap @ ( c_2Eoption_2EIS__SOME @ sk1 ) @ ( c_2Eoption_2ENONE @ sk1 ) )
!= c_2Ebool_2ET ) ),
inference(simp,[status(thm)],[498]) ).
thf(28,axiom,
! [A: del,B: $i] :
( ( mem @ B @ bool )
=> ( ( ? [C: $i] :
( ( mem @ C @ A )
& ( p @ B ) ) )
= ( p @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EEXISTS__SIMP) ).
thf(153,plain,
! [A: del,B: $i] :
( ( mem @ B @ bool )
=> ( ( ? [C: $i] :
( ( mem @ C @ A )
& ( p @ B ) ) )
= ( p @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(38,axiom,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ B ) )
=> ! [D: $i] :
( ( mem @ D @ ( arr @ A @ B ) )
=> ( ! [E: $i] :
( ( mem @ E @ A )
=> ( ( ap @ C @ E )
= ( ap @ D @ E ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(184,plain,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ B ) )
=> ! [D: $i] :
( ( mem @ D @ ( arr @ A @ B ) )
=> ( ! [E: $i] :
( ( mem @ E @ A )
=> ( ( ap @ C @ E )
= ( ap @ D @ E ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(41,axiom,
! [A: del,B: $i] :
( ( mem @ B @ A )
=> ! [C: $i] :
( ( mem @ C @ A )
=> ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ B ) @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_eq_p) ).
thf(196,plain,
! [A: del,B: $i] :
( ( mem @ B @ A )
=> ! [C: $i] :
( ( mem @ C @ A )
=> ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ B ) @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(27,axiom,
! [A: del] : ( mem @ ( c_2Eoption_2ESOME @ A ) @ ( arr @ A @ ( ty_2Eoption_2Eoption @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2ESOME) ).
thf(151,plain,
! [A: del] : ( mem @ ( c_2Eoption_2ESOME @ A ) @ ( arr @ A @ ( ty_2Eoption_2Eoption @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(152,plain,
! [A: del] : ( mem @ ( c_2Eoption_2ESOME @ A ) @ ( arr @ A @ ( ty_2Eoption_2Eoption @ A ) ) ),
inference(cnf,[status(esa)],[151]) ).
thf(57,plain,
! [B: del,A: del] : ( mem @ ( c_2Eoption_2EOPTION__MAP @ A @ B ) @ ( arr @ ( arr @ A @ B ) @ ( arr @ ( ty_2Eoption_2Eoption @ A ) @ ( ty_2Eoption_2Eoption @ B ) ) ) ),
inference(cnf,[status(esa)],[56]) ).
thf(61,plain,
! [A: del] : ( mem @ ( c_2Ebool_2E_3F @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
inference(cnf,[status(esa)],[60]) ).
thf(17,axiom,
mem @ c_2Ebool_2EF @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).
thf(132,plain,
mem @ c_2Ebool_2EF @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(18,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( $false
=> ( p @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EFALSITY) ).
thf(133,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(45,axiom,
! [A: del] : ( mem @ ( c_2Eoption_2EIS__SOME @ A ) @ ( arr @ ( ty_2Eoption_2Eoption @ A ) @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2EIS__SOME) ).
thf(205,plain,
! [A: del] : ( mem @ ( c_2Eoption_2EIS__SOME @ A ) @ ( arr @ ( ty_2Eoption_2Eoption @ A ) @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(206,plain,
! [A: del] : ( mem @ ( c_2Eoption_2EIS__SOME @ A ) @ ( arr @ ( ty_2Eoption_2Eoption @ A ) @ bool ) ),
inference(cnf,[status(esa)],[205]) ).
thf(30,axiom,
! [A: del] : ( mem @ ( c_2Eoption_2EIS__NONE @ A ) @ ( arr @ ( ty_2Eoption_2Eoption @ A ) @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2EIS__NONE) ).
thf(159,plain,
! [A: del] : ( mem @ ( c_2Eoption_2EIS__NONE @ A ) @ ( arr @ ( ty_2Eoption_2Eoption @ A ) @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(160,plain,
! [A: del] : ( mem @ ( c_2Eoption_2EIS__NONE @ A ) @ ( arr @ ( ty_2Eoption_2Eoption @ A ) @ bool ) ),
inference(cnf,[status(esa)],[159]) ).
thf(20,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ A ) @ B ) )
= ( ( p @ A )
& ( p @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_and_p) ).
thf(137,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ A ) @ B ) )
= ( ( p @ A )
& ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(33,axiom,
( ! [A: $i] :
( ( mem @ A @ bool )
=> ( ( ~ ~ ( p @ A ) )
= ( p @ A ) ) )
& ( ~ $true = $false )
& ( ~ $false = $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ENOT__CLAUSES) ).
thf(165,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(29,axiom,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ B ) )
= ( ! [C: $i] :
( ( mem @ C @ A )
=> ( p @ ( ap @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_all_p) ).
thf(156,plain,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ B ) )
= ( ! [C: $i] :
( ( mem @ C @ A )
=> ( p @ ( ap @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(49,plain,
( ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ sk1 @ sk1 ) @ sk2 ) @ ( c_2Eoption_2ENONE @ sk1 ) ) @ ( c_2Eoption_2ENONE @ sk1 ) ) )
| ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ sk1 @ sk1 ) @ sk2 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk1 ) @ sk3 ) ) @ ( c_2Eoption_2ENONE @ sk1 ) ) )
| ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ sk1 @ sk1 ) @ sk2 ) @ ( c_2Eoption_2ENONE @ sk1 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk1 ) @ sk4 ) ) )
| ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ sk1 @ sk1 ) @ sk2 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk1 ) @ sk3 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk1 ) @ sk4 ) ) )
!= ( p @ ( ap @ ( ap @ sk2 @ sk3 ) @ sk4 ) ) ) ),
inference(cnf,[status(esa)],[48]) ).
thf(53,plain,
( ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ sk1 @ sk1 ) @ sk2 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk1 ) @ sk3 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk1 ) @ sk4 ) ) )
!= ( p @ ( ap @ ( ap @ sk2 @ sk3 ) @ sk4 ) ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ sk1 @ sk1 ) @ sk2 ) @ ( c_2Eoption_2ENONE @ sk1 ) ) @ ( c_2Eoption_2ENONE @ sk1 ) ) )
| ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ sk1 @ sk1 ) @ sk2 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk1 ) @ sk3 ) ) @ ( c_2Eoption_2ENONE @ sk1 ) ) )
| ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ sk1 @ sk1 ) @ sk2 ) @ ( c_2Eoption_2ENONE @ sk1 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk1 ) @ sk4 ) ) ) ),
inference(lifteq,[status(thm)],[49]) ).
thf(22,axiom,
! [A: del] : ( mem @ ( c_2Emin_2E_3D @ A ) @ ( arr @ A @ ( arr @ A @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D) ).
thf(141,plain,
! [A: del] : ( mem @ ( c_2Emin_2E_3D @ A ) @ ( arr @ A @ ( arr @ A @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(15,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( ( $true
= ( p @ A ) )
= ( p @ A ) )
& ( ( ( p @ A )
= $true )
= ( p @ A ) )
& ( ( $false
= ( p @ A ) )
= ( ~ ( p @ A ) ) )
& ( ( ( p @ A )
= $false )
= ( ~ ( p @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EEQ__CLAUSES) ).
thf(128,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(34,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( p @ A )
=> ( p @ B ) )
=> ( ( ( p @ B )
=> ( p @ A ) )
=> ( ( p @ A )
= ( p @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EIMP__ANTISYM__AX) ).
thf(166,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( p @ A )
=> ( p @ B ) )
=> ( ( ( p @ B )
=> ( p @ A ) )
=> ( ( p @ A )
= ( p @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(25,axiom,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ B ) )
=> ! [D: $i] :
( ( mem @ D @ A )
=> ( mem @ ( ap @ C @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_tp) ).
thf(148,plain,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ B ) )
=> ! [D: $i] :
( ( mem @ D @ A )
=> ( mem @ ( ap @ C @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(31,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ETRUTH) ).
thf(161,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(7,axiom,
mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_2F_5C) ).
thf(59,plain,
mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(44,axiom,
! [A: del] : ( mem @ ( c_2Ebool_2E_21 @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_21) ).
thf(203,plain,
! [A: del] : ( mem @ ( c_2Ebool_2E_21 @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(204,plain,
! [A: del] : ( mem @ ( c_2Ebool_2E_21 @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
inference(cnf,[status(esa)],[203]) ).
thf(3,axiom,
mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D_3D_3E) ).
thf(54,plain,
mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(37,axiom,
! [A: del,B: $i > $i,C: $i] :
( ( mem @ C @ A )
=> ( ( ap @ ( lam @ A @ B ) @ C )
= ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta) ).
thf(181,plain,
! [A: del,B: $i > $i,C: $i] :
( ( mem @ C @ A )
=> ( ( ap @ ( lam @ A @ B ) @ C )
= ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(21,axiom,
mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_7E) ).
thf(140,plain,
mem @ c_2Ebool_2E_7E @ ( arr @ bool @ bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(212,plain,
( ( p @ ( inj__o @ $false ) )
!= ( p @ c_2Ebool_2ET ) ),
inference(paramod_ordered,[status(thm)],[202,193]) ).
thf(213,plain,
( ( inj__o @ $false )
!= c_2Ebool_2ET ),
inference(simp,[status(thm)],[212]) ).
thf(32,axiom,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ A ) @ B ) )
= ( ? [C: $i] :
( ( mem @ C @ A )
& ( p @ ( ap @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_ex_p) ).
thf(162,plain,
! [A: del,B: $i] :
( ( mem @ B @ ( arr @ A @ bool ) )
=> ( ( p @ ( ap @ ( c_2Ebool_2E_3F @ A ) @ B ) )
= ( ? [C: $i] :
( ( mem @ C @ A )
& ( p @ ( ap @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(47,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( ( $true
& ( p @ A ) )
= ( p @ A ) )
& ( ( ( p @ A )
& $true )
= ( p @ A ) )
& ( ( $false
& ( p @ A ) )
= $false )
& ( ( ( p @ A )
& $false )
= $false )
& ( ( ( p @ A )
& ( p @ A ) )
= ( p @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EAND__CLAUSES) ).
thf(209,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(40,axiom,
! [A: del] : ( mem @ ( c_2Eoption_2ETHE @ A ) @ ( arr @ ( ty_2Eoption_2Eoption @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2ETHE) ).
thf(194,plain,
! [A: del] : ( mem @ ( c_2Eoption_2ETHE @ A ) @ ( arr @ ( ty_2Eoption_2Eoption @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(26,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( ( $true
| ( p @ A ) )
= $true )
& ( ( ( p @ A )
| $true )
= $true )
& ( ( $false
| ( p @ A ) )
= ( p @ A ) )
& ( ( ( p @ A )
| $false )
= ( p @ A ) )
& ( ( ( p @ A )
| ( p @ A ) )
= ( p @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EOR__CLAUSES) ).
thf(150,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(50,plain,
mem @ sk4 @ sk1,
inference(cnf,[status(esa)],[48]) ).
thf(11,axiom,
mem @ c_2Ebool_2ET @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).
thf(67,plain,
mem @ c_2Ebool_2ET @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(42,axiom,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ ( arr @ B @ bool ) ) )
=> ! [D: $i] :
( ( mem @ D @ ( ty_2Eoption_2Eoption @ A ) )
=> ! [E: $i] :
( ( mem @ E @ ( ty_2Eoption_2Eoption @ B ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A @ B ) @ C ) @ D ) @ E ) )
= ( ( ( D
= ( c_2Eoption_2ENONE @ A ) )
& ( E
= ( c_2Eoption_2ENONE @ B ) ) )
| ? [F: $i] :
( ( mem @ F @ A )
& ? [G: $i] :
( ( mem @ G @ B )
& ( D
= ( ap @ ( c_2Eoption_2ESOME @ A ) @ F ) )
& ( E
= ( ap @ ( c_2Eoption_2ESOME @ B ) @ G ) )
& ( p @ ( ap @ ( ap @ C @ F ) @ G ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Eoption_2EOPTREL__def) ).
thf(199,plain,
! [A: del,B: del,C: $i] :
( ( mem @ C @ ( arr @ A @ ( arr @ B @ bool ) ) )
=> ! [D: $i] :
( ( mem @ D @ ( ty_2Eoption_2Eoption @ A ) )
=> ! [E: $i] :
( ( mem @ E @ ( ty_2Eoption_2Eoption @ B ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTREL @ A @ B ) @ C ) @ D ) @ E ) )
= ( ( ( D
= ( c_2Eoption_2ENONE @ A ) )
& ( E
= ( c_2Eoption_2ENONE @ B ) ) )
| ? [F: $i] :
( ( mem @ F @ A )
& ? [G: $i] :
( ( mem @ G @ B )
& ( D
= ( ap @ ( c_2Eoption_2ESOME @ A ) @ F ) )
& ( E
= ( ap @ ( c_2Eoption_2ESOME @ B ) @ G ) )
& ( p @ ( ap @ ( ap @ C @ F ) @ G ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(35,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ A ) @ B ) )
= ( ( p @ A )
=> ( p @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_imp_p) ).
thf(175,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ A ) @ B ) )
= ( ( p @ A )
=> ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(23,axiom,
! [A: del,B: del,C: $i > $i] :
( ! [D: $i] :
( ( mem @ D @ A )
=> ( mem @ ( C @ D ) @ B ) )
=> ( mem @ ( lam @ A @ C ) @ ( arr @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam_tp) ).
thf(143,plain,
! [A: del,B: del,C: $i > $i] :
( ! [D: $i] :
( ( mem @ D @ A )
=> ( mem @ ( C @ D ) @ B ) )
=> ( mem @ ( lam @ A @ C ) @ ( arr @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(225,plain,
( ( p @ ( inj__o @ $false ) )
!= ( p @ ( inj__o @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[191,193]) ).
thf(231,plain,
( ( inj__o @ $false )
!= ( inj__o @ $true ) ),
inference(simp,[status(thm)],[225]) ).
thf(6,axiom,
mem @ c_2Ebool_2E_5C_2F @ ( arr @ bool @ ( arr @ bool @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_5C_2F) ).
thf(58,plain,
mem @ c_2Ebool_2E_5C_2F @ ( arr @ bool @ ( arr @ bool @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(46,axiom,
! [A: del,B: del] : ( mem @ ( c_2Eoption_2Eoption__CASE @ A @ B ) @ ( arr @ ( ty_2Eoption_2Eoption @ A ) @ ( arr @ B @ ( arr @ ( arr @ A @ B ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2Eoption__CASE) ).
thf(207,plain,
! [A: del,B: del] : ( mem @ ( c_2Eoption_2Eoption__CASE @ A @ B ) @ ( arr @ ( ty_2Eoption_2Eoption @ A ) @ ( arr @ B @ ( arr @ ( arr @ A @ B ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(24,axiom,
! [A: del] : ( mem @ ( c_2Eoption_2EOPTION__JOIN @ A ) @ ( arr @ ( ty_2Eoption_2Eoption @ ( ty_2Eoption_2Eoption @ A ) ) @ ( ty_2Eoption_2Eoption @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2EOPTION__JOIN) ).
thf(146,plain,
! [A: del] : ( mem @ ( c_2Eoption_2EOPTION__JOIN @ A ) @ ( arr @ ( ty_2Eoption_2Eoption @ ( ty_2Eoption_2Eoption @ A ) ) @ ( ty_2Eoption_2Eoption @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(51,plain,
mem @ sk3 @ sk1,
inference(cnf,[status(esa)],[48]) ).
thf(136,plain,
mem @ ( inj__o @ $false ) @ bool,
inference(instance,[status(thm)],[134]) ).
thf(195,plain,
! [A: del] : ( mem @ ( c_2Eoption_2ETHE @ A ) @ ( arr @ ( ty_2Eoption_2Eoption @ A ) @ A ) ),
inference(cnf,[status(esa)],[194]) ).
thf(12,axiom,
! [A: del,B: del] : ( mem @ ( c_2Eoption_2EOPTREL @ A @ B ) @ ( arr @ ( arr @ A @ ( arr @ B @ bool ) ) @ ( arr @ ( ty_2Eoption_2Eoption @ A ) @ ( arr @ ( ty_2Eoption_2Eoption @ B ) @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2EOPTREL) ).
thf(68,plain,
! [A: del,B: del] : ( mem @ ( c_2Eoption_2EOPTREL @ A @ B ) @ ( arr @ ( arr @ A @ ( arr @ B @ bool ) ) @ ( arr @ ( ty_2Eoption_2Eoption @ A ) @ ( arr @ ( ty_2Eoption_2Eoption @ B ) @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( A
= ( inj__o @ ( p @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_o) ).
thf(62,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ( A
= ( inj__o @ ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(36,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( p @ ( ap @ c_2Ebool_2E_7E @ A ) )
= ( ~ ( p @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_neg_p) ).
thf(178,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ( ( p @ ( ap @ c_2Ebool_2E_7E @ A ) )
= ( ~ ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(499,plain,
( ( ( arr @ sk1 @ bool )
!= bool )
| ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ sk1 ) @ ( c_2Eoption_2ENONE @ sk1 ) ) )
!= ( p @ ( inj__o @ $true ) ) ) ),
inference(paramod_ordered,[status(thm)],[191,482]) ).
thf(501,plain,
( ( ( arr @ sk1 @ bool )
!= bool )
| ( ( ap @ ( c_2Eoption_2EIS__SOME @ sk1 ) @ ( c_2Eoption_2ENONE @ sk1 ) )
!= ( inj__o @ $true ) ) ),
inference(simp,[status(thm)],[499]) ).
thf(38334,plain,
$false,
inference(cvc4,[status(thm)],[202,211,60,65,193,129,135,55,232,56,500,153,52,184,196,189,152,57,61,132,133,206,160,137,165,297,70,156,53,141,134,128,205,166,148,161,191,59,204,71,54,181,159,140,213,66,162,209,194,48,150,50,67,199,72,175,143,231,482,203,58,207,151,146,51,136,79,195,68,62,178,501]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP011^2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n016.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 6 14:26:54 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.83/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.49/1.02 % [INFO] Parsing done (171ms).
% 1.49/1.03 % [INFO] Running in sequential loop mode.
% 1.92/1.28 % [INFO] eprover registered as external prover.
% 1.92/1.29 % [INFO] cvc4 registered as external prover.
% 1.92/1.29 % [INFO] Scanning for conjecture ...
% 2.14/1.39 % [INFO] Found a conjecture and 45 axioms. Running axiom selection ...
% 2.54/1.46 % [INFO] Axiom selection finished. Selected 45 axioms (removed 0 axioms).
% 2.80/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.80/1.57 % [INFO] Type checking passed.
% 2.80/1.57 % [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 ...
% 104.49/20.42 % External prover 'cvc4' found a proof!
% 104.49/20.42 % [INFO] Killing All external provers ...
% 104.49/20.43 % Time passed: 19903ms (effective reasoning time: 19389ms)
% 104.49/20.43 % 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)>
% 104.49/20.43 % Axioms used in derivation (45): mem_c_2Ebool_2E_21, mem_c_2Ebool_2E_7E, mem_c_2Ebool_2EF, conj_thm_2Ebool_2ETRUTH, mem_c_2Eoption_2ESOME, mem_c_2Eoption_2Eoption__CASE, conj_thm_2Ebool_2EREFL__CLAUSE, mem_c_2Ebool_2ET, mem_c_2Ebool_2E_3F, ax_neg_p, mem_c_2Ebool_2E_2F_5C, stp_inj_surj_o, mem_c_2Eoption_2EIS__NONE, conj_thm_2Ebool_2EEQ__CLAUSES, ax_imp_p, ax_eq_p, mem_c_2Eoption_2ENONE, funcext, conj_thm_2Ebool_2EOR__CLAUSES, mem_c_2Eoption_2ETHE, conj_thm_2Ebool_2EAND__CLAUSES, ax_true_p, ax_and_p, conj_thm_2Ebool_2ENOT__CLAUSES, mem_c_2Emin_2E_3D, mem_c_2Eoption_2EOPTION__JOIN, ax_or_p, ax_all_p, ax_ex_p, conj_thm_2Ebool_2EFALSITY, ap_tp, conj_thm_2Eoption_2Eoption__CLAUSES, beta, mem_c_2Eoption_2EOPTION__MAP, mem_c_2Eoption_2EIS__SOME, ax_false_p, ax_thm_2Eoption_2EOPTREL__def, conj_thm_2Ebool_2EEXISTS__SIMP, mem_c_2Ebool_2E_5C_2F, stp_iso_mem_o, mem_c_2Emin_2E_3D_3D_3E, lam_tp, mem_c_2Eoption_2EOPTREL, stp_inj_mem_o, conj_thm_2Ebool_2EIMP__ANTISYM__AX
% 104.49/20.43 % No. of inferences in proof: 135
% 104.49/20.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 19903 ms resp. 19389 ms w/o parsing
% 104.49/20.54 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 104.49/20.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------