TSTP Solution File: ITP002_2 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP002_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 07:46:28 EDT 2024
% Result : Theorem 123.63s 37.36s
% Output : Refutation 124.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 70
% Syntax : Number of formulae : 385 ( 138 unt; 34 typ; 0 def)
% Number of atoms : 952 ( 519 equ; 0 cnn)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 4809 ( 466 ~; 401 |; 31 &;3822 @)
% ( 13 <=>; 76 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 14 con; 0-4 aty)
% Number of variables : 376 ( 0 ^ 375 !; 1 ?; 376 :)
% 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(k_type,type,
k: del > $i > $i ).
thf(i_type,type,
i: del > $i ).
thf(p_type,type,
p: $i > $o ).
thf(tp__o_type,type,
tp__o: $tType ).
thf(inj__o_type,type,
inj__o: tp__o > $i ).
thf(surj__o_type,type,
surj__o: $i > tp__o ).
thf(c_2Ebool_2EF_type,type,
c_2Ebool_2EF: $i ).
thf(fo__c_2Ebool_2EF_type,type,
fo__c_2Ebool_2EF: tp__o ).
thf(c_2Ebool_2ET_type,type,
c_2Ebool_2ET: $i ).
thf(fo__c_2Ebool_2ET_type,type,
fo__c_2Ebool_2ET: tp__o ).
thf(ty_2Eoption_2Eoption_type,type,
ty_2Eoption_2Eoption: del > del ).
thf(c_2Eoption_2ENONE_type,type,
c_2Eoption_2ENONE: del > $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_2Eoption_2EIS__SOME_type,type,
c_2Eoption_2EIS__SOME: del > $i ).
thf(c_2Ebool_2E_2F_5C_type,type,
c_2Ebool_2E_2F_5C: $i ).
thf(fo__c_2Ebool_2E_2F_5C_type,type,
fo__c_2Ebool_2E_2F_5C: tp__o > tp__o > tp__o ).
thf(c_2Ebool_2ECOND_type,type,
c_2Ebool_2ECOND: del > $i ).
thf(c_2Eoption_2EOPTION__MAP2_type,type,
c_2Eoption_2EOPTION__MAP2: del > 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: del ).
thf(sk3_type,type,
sk3: del ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $i > $i > del > del > $i ).
thf(sk8_type,type,
sk8: $i > del > $i ).
thf(13,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(65,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)],[13]) ).
thf(67,plain,
! [D: $i,C: $i,B: del,A: del] :
( ~ ( mem @ C @ ( arr @ A @ B ) )
| ~ ( mem @ D @ ( arr @ A @ B ) )
| ( ( ap @ C @ ( sk7 @ D @ C @ B @ A ) )
!= ( ap @ D @ ( sk7 @ D @ C @ B @ A ) ) )
| ( C = D ) ),
inference(cnf,[status(esa)],[65]) ).
thf(69,plain,
! [D: $i,C: $i,B: del,A: del] :
( ( ( ap @ C @ ( sk7 @ D @ C @ B @ A ) )
!= ( ap @ D @ ( sk7 @ D @ C @ B @ A ) ) )
| ( C = D )
| ~ ( mem @ C @ ( arr @ A @ B ) )
| ~ ( mem @ D @ ( arr @ A @ B ) ) ),
inference(lifteq,[status(thm)],[67]) ).
thf(24,axiom,
! [A: del] : ( mem @ ( c_2Ebool_2ECOND @ A ) @ ( arr @ bool @ ( arr @ A @ ( arr @ A @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2ECOND) ).
thf(101,plain,
! [A: del] : ( mem @ ( c_2Ebool_2ECOND @ A ) @ ( arr @ bool @ ( arr @ A @ ( arr @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(30,axiom,
mem @ c_2Ebool_2ET @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).
thf(119,plain,
mem @ c_2Ebool_2ET @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(20,axiom,
! [A: del,B: $i] :
( ( mem @ B @ A )
=> ( ( ap @ ( c_2Eoption_2ETHE @ A ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Eoption_2ETHE__DEF) ).
thf(84,plain,
! [A: del,B: $i] :
( ( mem @ B @ A )
=> ( ( ap @ ( c_2Eoption_2ETHE @ A ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(85,plain,
! [B: $i,A: del] :
( ~ ( mem @ B @ A )
| ( ( ap @ ( c_2Eoption_2ETHE @ A ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ B ) )
= B ) ),
inference(cnf,[status(esa)],[84]) ).
thf(86,plain,
! [B: $i,A: del] :
( ( ( ap @ ( c_2Eoption_2ETHE @ A ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ B ) )
= B )
| ~ ( mem @ B @ A ) ),
inference(lifteq,[status(thm)],[85]) ).
thf(6316,plain,
! [B: $i,A: del] :
( ( ( ap @ ( c_2Eoption_2ETHE @ A ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ B ) )
= B )
| ( ( mem @ c_2Ebool_2ET @ bool )
!= ( mem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[119,86]) ).
thf(6317,plain,
( ( ap @ ( c_2Eoption_2ETHE @ bool ) @ ( ap @ ( c_2Eoption_2ESOME @ bool ) @ c_2Ebool_2ET ) )
= c_2Ebool_2ET ),
inference(pattern_uni,[status(thm)],[6316:[bind(A,$thf( bool )),bind(B,$thf( c_2Ebool_2ET ))]]) ).
thf(22,axiom,
! [A: del,B: $i,C: $i] :
( ( mem @ C @ A )
=> ( ( ap @ ( k @ A @ B ) @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kbeta) ).
thf(89,plain,
! [A: del,B: $i,C: $i] :
( ( mem @ C @ A )
=> ( ( ap @ ( k @ A @ B ) @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(90,plain,
! [C: $i,B: $i,A: del] :
( ~ ( mem @ C @ A )
| ( ( ap @ ( k @ A @ B ) @ C )
= B ) ),
inference(cnf,[status(esa)],[89]) ).
thf(91,plain,
! [C: $i,B: $i,A: del] :
( ( ( ap @ ( k @ A @ B ) @ C )
= B )
| ~ ( mem @ C @ A ) ),
inference(lifteq,[status(thm)],[90]) ).
thf(9903,plain,
! [C: $i,B: $i,A: del] :
( ( ( ap @ ( k @ A @ B ) @ C )
= B )
| ( ( mem @ c_2Ebool_2ET @ bool )
!= ( mem @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[119,91]) ).
thf(9904,plain,
! [A: $i] :
( ( ap @ ( k @ bool @ A ) @ c_2Ebool_2ET )
= A ),
inference(pattern_uni,[status(thm)],[9903:[bind(A,$thf( bool )),bind(B,$thf( B )),bind(C,$thf( c_2Ebool_2ET ))]]) ).
thf(10476,plain,
! [A: $i] :
( ( ap @ ( k @ bool @ A ) @ c_2Ebool_2ET )
= A ),
inference(simp,[status(thm)],[9904]) ).
thf(7,axiom,
p @ c_2Ebool_2ET,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_true_p) ).
thf(53,plain,
p @ c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
! [A: del,B: del,C: del,D: $i] :
( ( mem @ D @ ( arr @ B @ ( arr @ C @ A ) ) )
=> ! [E: $i] :
( ( mem @ E @ B )
=> ! [F: $i] :
( ( mem @ F @ C )
=> ( ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A @ B @ C ) @ D ) @ ( ap @ ( c_2Eoption_2ESOME @ B ) @ E ) ) @ ( ap @ ( c_2Eoption_2ESOME @ C ) @ F ) )
= ( ap @ ( c_2Eoption_2ESOME @ A ) @ ( ap @ ( ap @ D @ E ) @ F ) ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A @ B @ C ) @ D ) @ ( ap @ ( c_2Eoption_2ESOME @ B ) @ E ) ) @ ( c_2Eoption_2ENONE @ C ) )
= ( c_2Eoption_2ENONE @ A ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A @ B @ C ) @ D ) @ ( c_2Eoption_2ENONE @ B ) ) @ ( ap @ ( c_2Eoption_2ESOME @ C ) @ F ) )
= ( c_2Eoption_2ENONE @ A ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A @ B @ C ) @ D ) @ ( c_2Eoption_2ENONE @ B ) ) @ ( c_2Eoption_2ENONE @ C ) )
= ( c_2Eoption_2ENONE @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eoption_2EOPTION__MAP2__THM) ).
thf(2,negated_conjecture,
~ ! [A: del,B: del,C: del,D: $i] :
( ( mem @ D @ ( arr @ B @ ( arr @ C @ A ) ) )
=> ! [E: $i] :
( ( mem @ E @ B )
=> ! [F: $i] :
( ( mem @ F @ C )
=> ( ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A @ B @ C ) @ D ) @ ( ap @ ( c_2Eoption_2ESOME @ B ) @ E ) ) @ ( ap @ ( c_2Eoption_2ESOME @ C ) @ F ) )
= ( ap @ ( c_2Eoption_2ESOME @ A ) @ ( ap @ ( ap @ D @ E ) @ F ) ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A @ B @ C ) @ D ) @ ( ap @ ( c_2Eoption_2ESOME @ B ) @ E ) ) @ ( c_2Eoption_2ENONE @ C ) )
= ( c_2Eoption_2ENONE @ A ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A @ B @ C ) @ D ) @ ( c_2Eoption_2ENONE @ B ) ) @ ( ap @ ( c_2Eoption_2ESOME @ C ) @ F ) )
= ( c_2Eoption_2ENONE @ A ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A @ B @ C ) @ D ) @ ( c_2Eoption_2ENONE @ B ) ) @ ( c_2Eoption_2ENONE @ C ) )
= ( c_2Eoption_2ENONE @ A ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(38,plain,
~ ! [A: del,B: del,C: del,D: $i] :
( ( mem @ D @ ( arr @ B @ ( arr @ C @ A ) ) )
=> ! [E: $i] :
( ( mem @ E @ B )
=> ! [F: $i] :
( ( mem @ F @ C )
=> ( ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A @ B @ C ) @ D ) @ ( ap @ ( c_2Eoption_2ESOME @ B ) @ E ) ) @ ( ap @ ( c_2Eoption_2ESOME @ C ) @ F ) )
= ( ap @ ( c_2Eoption_2ESOME @ A ) @ ( ap @ ( ap @ D @ E ) @ F ) ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A @ B @ C ) @ D ) @ ( ap @ ( c_2Eoption_2ESOME @ B ) @ E ) ) @ ( c_2Eoption_2ENONE @ C ) )
= ( c_2Eoption_2ENONE @ A ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A @ B @ C ) @ D ) @ ( c_2Eoption_2ENONE @ B ) ) @ ( ap @ ( c_2Eoption_2ESOME @ C ) @ F ) )
= ( c_2Eoption_2ENONE @ A ) )
& ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A @ B @ C ) @ D ) @ ( c_2Eoption_2ENONE @ B ) ) @ ( c_2Eoption_2ENONE @ C ) )
= ( c_2Eoption_2ENONE @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(41,plain,
mem @ sk5 @ sk2,
inference(cnf,[status(esa)],[38]) ).
thf(10,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(56,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 ) ) )
& ( ( ( p @ A )
& ( p @ B ) )
=> ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ~ ( mem @ A @ bool )
| ~ ( mem @ B @ bool )
| ~ ( p @ A )
| ~ ( p @ B )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ A ) @ B ) ) ),
inference(cnf,[status(esa)],[56]) ).
thf(236,plain,
! [B: $i,A: $i] :
( ~ ( mem @ A @ bool )
| ~ ( p @ A )
| ~ ( p @ B )
| ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ A ) @ B ) )
| ( ( mem @ sk5 @ sk2 )
!= ( mem @ B @ bool ) ) ),
inference(paramod_ordered,[status(thm)],[41,57]) ).
thf(268,plain,
! [B: $i,A: $i] :
( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ A ) @ B ) )
| ~ ( mem @ A @ bool )
| ~ ( p @ A )
| ~ ( p @ B )
| ( sk5 != B )
| ( sk2 != bool ) ),
inference(simp,[status(thm)],[236]) ).
thf(286,plain,
! [A: $i] :
( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ A ) @ sk5 ) )
| ~ ( mem @ A @ bool )
| ~ ( p @ A )
| ~ ( p @ sk5 )
| ( sk2 != bool ) ),
inference(simp,[status(thm)],[268]) ).
thf(710,plain,
! [A: $i] :
( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ A ) @ sk5 ) )
| ~ ( p @ A )
| ~ ( p @ sk5 )
| ( sk2 != bool )
| ( ( mem @ sk5 @ sk2 )
!= ( mem @ A @ bool ) ) ),
inference(paramod_ordered,[status(thm)],[41,286]) ).
thf(742,plain,
! [A: $i] :
( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ A ) @ sk5 ) )
| ~ ( p @ A )
| ~ ( p @ sk5 )
| ( sk2 != bool )
| ( sk5 != A )
| ( sk2 != bool ) ),
inference(simp,[status(thm)],[710]) ).
thf(764,plain,
( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ sk5 ) @ sk5 ) )
| ~ ( p @ sk5 )
| ~ ( p @ sk5 )
| ( sk2 != bool ) ),
inference(simp,[status(thm)],[742]) ).
thf(1294,plain,
( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ sk5 ) @ sk5 ) )
| ~ ( p @ sk5 )
| ( sk2 != bool ) ),
inference(simp,[status(thm)],[764]) ).
thf(5,axiom,
~ ( p @ c_2Ebool_2EF ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_false_p) ).
thf(49,plain,
~ ( p @ c_2Ebool_2EF ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(50,plain,
~ ( p @ c_2Ebool_2EF ),
inference(polarity_switch,[status(thm)],[49]) ).
thf(1295,plain,
( ~ ( p @ sk5 )
| ( sk2 != bool )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ sk5 ) @ sk5 ) )
!= ( p @ c_2Ebool_2EF ) ) ),
inference(paramod_ordered,[status(thm)],[1294,50]) ).
thf(1318,plain,
( ~ ( p @ sk5 )
| ( sk2 != bool )
| ( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ sk5 ) @ sk5 )
!= c_2Ebool_2EF ) ),
inference(simp,[status(thm)],[1295]) ).
thf(1335,plain,
( ( sk2 != bool )
| ( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ sk5 ) @ sk5 )
!= c_2Ebool_2EF )
| ( ( p @ sk5 )
!= ( p @ c_2Ebool_2ET ) ) ),
inference(paramod_ordered,[status(thm)],[53,1318]) ).
thf(1347,plain,
( ( sk2 != bool )
| ( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ sk5 ) @ sk5 )
!= c_2Ebool_2EF )
| ( sk5 != c_2Ebool_2ET ) ),
inference(simp,[status(thm)],[1335]) ).
thf(13057,plain,
! [A: $i] :
( ( sk2 != bool )
| ( A != c_2Ebool_2EF )
| ( sk5 != c_2Ebool_2ET )
| ( ( ap @ ( k @ bool @ A ) @ c_2Ebool_2ET )
!= ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ sk5 ) @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[10476,1347]) ).
thf(13589,plain,
( ( sk2 != bool )
| ( sk5 != c_2Ebool_2ET )
| ( ( k @ bool @ c_2Ebool_2EF )
!= ( ap @ c_2Ebool_2E_2F_5C @ sk5 ) )
| ( sk5 != c_2Ebool_2ET ) ),
inference(simp,[status(thm)],[13057]) ).
thf(13768,plain,
( ( sk2 != bool )
| ( sk5 != c_2Ebool_2ET )
| ( ( k @ bool @ c_2Ebool_2EF )
!= ( ap @ c_2Ebool_2E_2F_5C @ sk5 ) ) ),
inference(simp,[status(thm)],[13589]) ).
thf(21,axiom,
! [A: tp__o] : ( mem @ ( inj__o @ A ) @ bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_mem_o) ).
thf(87,plain,
! [A: tp__o] : ( mem @ ( inj__o @ A ) @ bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(88,plain,
! [A: tp__o] : ( mem @ ( inj__o @ A ) @ bool ),
inference(cnf,[status(esa)],[87]) ).
thf(39,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk1 ) @ ( ap @ ( ap @ sk4 @ sk5 ) @ sk6 ) ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) ) @ ( c_2Eoption_2ENONE @ sk3 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( c_2Eoption_2ENONE @ sk3 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(43,plain,
( ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk1 ) @ ( ap @ ( ap @ sk4 @ sk5 ) @ sk6 ) ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) ) @ ( c_2Eoption_2ENONE @ sk3 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( c_2Eoption_2ENONE @ sk3 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(146,plain,
( ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) )
!= ( c_2Eoption_2ESOME @ sk1 ) )
| ( ( ap @ ( ap @ sk4 @ sk5 ) @ sk6 )
!= ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) ) @ ( c_2Eoption_2ENONE @ sk3 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( c_2Eoption_2ENONE @ sk3 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) ) ),
inference(simp,[status(thm)],[43]) ).
thf(155,plain,
( ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) )
!= ( c_2Eoption_2ESOME @ sk1 ) )
| ( ( ap @ sk4 @ sk5 )
!= ( c_2Eoption_2ESOME @ sk3 ) )
| ( sk6 != sk6 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) ) @ ( c_2Eoption_2ENONE @ sk3 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( c_2Eoption_2ENONE @ sk3 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) ) ),
inference(simp,[status(thm)],[146]) ).
thf(170,plain,
( ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) )
!= ( c_2Eoption_2ESOME @ sk1 ) )
| ( ( ap @ sk4 @ sk5 )
!= ( c_2Eoption_2ESOME @ sk3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) ) @ ( c_2Eoption_2ENONE @ sk3 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( c_2Eoption_2ENONE @ sk3 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) ) ),
inference(simp,[status(thm)],[155]) ).
thf(31,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(120,plain,
! [A: del] : ( mem @ ( c_2Emin_2E_3D @ A ) @ ( arr @ A @ ( arr @ A @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(37,axiom,
! [A: tp__o,B: tp__o] :
( ( inj__o @ ( fo__c_2Ebool_2E_2F_5C @ A @ B ) )
= ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ A ) ) @ ( inj__o @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Ebool_2E_2F_5C) ).
thf(139,plain,
! [A: tp__o,B: tp__o] :
( ( inj__o @ ( fo__c_2Ebool_2E_2F_5C @ A @ B ) )
= ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ A ) ) @ ( inj__o @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(140,plain,
! [B: tp__o,A: tp__o] :
( ( inj__o @ ( fo__c_2Ebool_2E_2F_5C @ A @ B ) )
= ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ A ) ) @ ( inj__o @ B ) ) ),
inference(cnf,[status(esa)],[139]) ).
thf(141,plain,
! [B: tp__o,A: tp__o] :
( ( inj__o @ ( fo__c_2Ebool_2E_2F_5C @ A @ B ) )
= ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ A ) ) @ ( inj__o @ B ) ) ),
inference(lifteq,[status(thm)],[140]) ).
thf(330,plain,
! [C: tp__o,B: tp__o,A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ A ) ) @ ( inj__o @ B ) ) @ bool )
| ( ( inj__o @ ( fo__c_2Ebool_2E_2F_5C @ A @ B ) )
!= ( inj__o @ C ) ) ),
inference(paramod_ordered,[status(thm)],[141,88]) ).
thf(331,plain,
! [B: tp__o,A: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ A ) ) @ ( inj__o @ B ) ) @ bool ),
inference(pattern_uni,[status(thm)],[330:[bind(A,$thf( D )),bind(B,$thf( E )),bind(C,$thf( fo__c_2Ebool_2E_2F_5C @ D @ E ))]]) ).
thf(677,plain,
! [B: tp__o,A: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ A ) ) @ ( inj__o @ B ) ) @ bool ),
inference(simp,[status(thm)],[331]) ).
thf(6,axiom,
( ( inj__o @ fo__c_2Ebool_2EF )
= c_2Ebool_2EF ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Ebool_2EF) ).
thf(51,plain,
( ( inj__o @ fo__c_2Ebool_2EF )
= c_2Ebool_2EF ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(52,plain,
( ( inj__o @ fo__c_2Ebool_2EF )
= c_2Ebool_2EF ),
inference(lifteq,[status(thm)],[51]) ).
thf(3,axiom,
( ( inj__o @ fo__c_2Ebool_2ET )
= c_2Ebool_2ET ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_eq_fo_c_2Ebool_2ET) ).
thf(44,plain,
( ( inj__o @ fo__c_2Ebool_2ET )
= c_2Ebool_2ET ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(45,plain,
( ( inj__o @ fo__c_2Ebool_2ET )
= c_2Ebool_2ET ),
inference(lifteq,[status(thm)],[44]) ).
thf(903,plain,
! [B: tp__o,A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ A ) ) @ c_2Ebool_2ET ) @ bool )
| ( ( inj__o @ fo__c_2Ebool_2ET )
!= ( inj__o @ B ) ) ),
inference(paramod_ordered,[status(thm)],[45,677]) ).
thf(904,plain,
! [A: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ A ) ) @ c_2Ebool_2ET ) @ bool ),
inference(pattern_uni,[status(thm)],[903:[bind(A,$thf( A )),bind(B,$thf( fo__c_2Ebool_2ET ))]]) ).
thf(1008,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) @ bool )
| ( ( inj__o @ fo__c_2Ebool_2EF )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[52,904]) ).
thf(1009,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) @ bool,
inference(pattern_uni,[status(thm)],[1008:[bind(A,$thf( fo__c_2Ebool_2EF ))]]) ).
thf(12,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ( A
= ( inj__o @ ( surj__o @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_iso_mem_o) ).
thf(62,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ( A
= ( inj__o @ ( surj__o @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(63,plain,
! [A: $i] :
( ~ ( mem @ A @ bool )
| ( A
= ( inj__o @ ( surj__o @ A ) ) ) ),
inference(cnf,[status(esa)],[62]) ).
thf(64,plain,
! [A: $i] :
( ( ( inj__o @ ( surj__o @ A ) )
= A )
| ~ ( mem @ A @ bool ) ),
inference(lifteq,[status(thm)],[63]) ).
thf(1413,plain,
! [A: $i] :
( ( ( inj__o @ ( surj__o @ A ) )
= A )
| ( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) @ bool )
!= ( mem @ A @ bool ) ) ),
inference(paramod_ordered,[status(thm)],[1009,64]) ).
thf(1414,plain,
( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ) )
= ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ),
inference(pattern_uni,[status(thm)],[1413:[bind(A,$thf( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ))]]) ).
thf(5813,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ) @ c_2Ebool_2ET ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1414,904]) ).
thf(5814,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ) @ c_2Ebool_2ET ) @ bool,
inference(pattern_uni,[status(thm)],[5813:[bind(A,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ))]]) ).
thf(1010,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) @ bool )
| ( ( inj__o @ fo__c_2Ebool_2ET )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45,904]) ).
thf(1011,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) @ bool,
inference(pattern_uni,[status(thm)],[1010:[bind(A,$thf( fo__c_2Ebool_2ET ))]]) ).
thf(1403,plain,
! [A: $i] :
( ( ( inj__o @ ( surj__o @ A ) )
= A )
| ( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) @ bool )
!= ( mem @ A @ bool ) ) ),
inference(paramod_ordered,[status(thm)],[1011,64]) ).
thf(1404,plain,
( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) )
= ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ),
inference(pattern_uni,[status(thm)],[1403:[bind(A,$thf( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ))]]) ).
thf(899,plain,
! [B: tp__o,A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ A ) ) @ c_2Ebool_2EF ) @ bool )
| ( ( inj__o @ fo__c_2Ebool_2EF )
!= ( inj__o @ B ) ) ),
inference(paramod_ordered,[status(thm)],[52,677]) ).
thf(900,plain,
! [A: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ A ) ) @ c_2Ebool_2EF ) @ bool ),
inference(pattern_uni,[status(thm)],[899:[bind(A,$thf( A )),bind(B,$thf( fo__c_2Ebool_2EF ))]]) ).
thf(936,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) @ bool )
| ( ( inj__o @ fo__c_2Ebool_2ET )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45,900]) ).
thf(937,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) @ bool,
inference(pattern_uni,[status(thm)],[936:[bind(A,$thf( fo__c_2Ebool_2ET ))]]) ).
thf(1374,plain,
! [A: $i] :
( ( ( inj__o @ ( surj__o @ A ) )
= A )
| ( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) @ bool )
!= ( mem @ A @ bool ) ) ),
inference(paramod_ordered,[status(thm)],[937,64]) ).
thf(1375,plain,
( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) )
= ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ),
inference(pattern_uni,[status(thm)],[1374:[bind(A,$thf( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ))]]) ).
thf(1469,plain,
! [B: tp__o,A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ A ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) )
!= ( inj__o @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1375,677]) ).
thf(1470,plain,
! [A: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ A ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ bool ),
inference(pattern_uni,[status(thm)],[1469:[bind(A,$thf( A )),bind(B,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ))]]) ).
thf(18799,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1404,1470]) ).
thf(18800,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ bool,
inference(pattern_uni,[status(thm)],[18799:[bind(A,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ))]]) ).
thf(1471,plain,
! [B: tp__o,A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ ( inj__o @ B ) ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1375,677]) ).
thf(1472,plain,
! [A: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ ( inj__o @ A ) ) @ bool ),
inference(pattern_uni,[status(thm)],[1471:[bind(A,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) )),bind(B,$thf( B ))]]) ).
thf(1507,plain,
! [A: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ ( inj__o @ A ) ) @ bool ),
inference(simp,[status(thm)],[1472]) ).
thf(42,plain,
mem @ sk4 @ ( arr @ sk2 @ ( arr @ sk3 @ sk1 ) ),
inference(cnf,[status(esa)],[38]) ).
thf(1388,plain,
! [A: $i] :
( ( ( inj__o @ ( surj__o @ A ) )
= A )
| ( ( mem @ sk5 @ sk2 )
!= ( mem @ A @ bool ) ) ),
inference(paramod_ordered,[status(thm)],[41,64]) ).
thf(1417,plain,
! [A: $i] :
( ( ( inj__o @ ( surj__o @ A ) )
= A )
| ( sk5 != A )
| ( sk2 != bool ) ),
inference(simp,[status(thm)],[1388]) ).
thf(1434,plain,
( ( ( inj__o @ ( surj__o @ sk5 ) )
= sk5 )
| ( sk2 != bool ) ),
inference(simp,[status(thm)],[1417]) ).
thf(1564,plain,
( ( sk2 != bool )
| ( sk5 = c_2Ebool_2ET )
| ( ( inj__o @ ( surj__o @ sk5 ) )
!= ( inj__o @ fo__c_2Ebool_2ET ) ) ),
inference(paramod_ordered,[status(thm)],[1434,45]) ).
thf(1576,plain,
( ( sk5 = c_2Ebool_2ET )
| ( sk2 != bool )
| ( ( surj__o @ sk5 )
!= fo__c_2Ebool_2ET ) ),
inference(simp,[status(thm)],[1564]) ).
thf(40,plain,
mem @ sk6 @ sk3,
inference(cnf,[status(esa)],[38]) ).
thf(1363,plain,
! [A: $i] :
( ( ( inj__o @ ( surj__o @ A ) )
= A )
| ( ( mem @ sk6 @ sk3 )
!= ( mem @ A @ bool ) ) ),
inference(paramod_ordered,[status(thm)],[40,64]) ).
thf(1429,plain,
! [A: $i] :
( ( ( inj__o @ ( surj__o @ A ) )
= A )
| ( sk6 != A )
| ( sk3 != bool ) ),
inference(simp,[status(thm)],[1363]) ).
thf(1441,plain,
( ( ( inj__o @ ( surj__o @ sk6 ) )
= sk6 )
| ( sk3 != bool ) ),
inference(simp,[status(thm)],[1429]) ).
thf(16,axiom,
mem @ c_2Ebool_2EF @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).
thf(78,plain,
mem @ c_2Ebool_2EF @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6111,plain,
! [B: $i,A: del] :
( ( ( ap @ ( c_2Eoption_2ETHE @ A ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ B ) )
= B )
| ( ( mem @ c_2Ebool_2EF @ bool )
!= ( mem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[78,86]) ).
thf(6112,plain,
( ( ap @ ( c_2Eoption_2ETHE @ bool ) @ ( ap @ ( c_2Eoption_2ESOME @ bool ) @ c_2Ebool_2EF ) )
= c_2Ebool_2EF ),
inference(pattern_uni,[status(thm)],[6111:[bind(A,$thf( bool )),bind(B,$thf( c_2Ebool_2EF ))]]) ).
thf(719,plain,
! [A: $i] :
( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ A ) @ sk5 ) )
| ~ ( p @ A )
| ~ ( p @ sk5 )
| ( sk2 != bool )
| ( ( mem @ c_2Ebool_2ET @ bool )
!= ( mem @ A @ bool ) ) ),
inference(paramod_ordered,[status(thm)],[119,286]) ).
thf(720,plain,
( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ sk5 ) )
| ~ ( p @ c_2Ebool_2ET )
| ~ ( p @ sk5 )
| ( sk2 != bool ) ),
inference(pattern_uni,[status(thm)],[719:[bind(A,$thf( c_2Ebool_2ET ))]]) ).
thf(773,plain,
( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ sk5 ) )
| ~ $true
| ~ ( p @ sk5 )
| ( sk2 != bool ) ),
inference(rewrite,[status(thm)],[720,53]) ).
thf(774,plain,
( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ sk5 ) )
| ~ ( p @ sk5 )
| ( sk2 != bool ) ),
inference(simp,[status(thm)],[773]) ).
thf(779,plain,
( ~ ( p @ sk5 )
| ( sk2 != bool )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ sk5 ) )
!= ( p @ c_2Ebool_2EF ) ) ),
inference(paramod_ordered,[status(thm)],[774,50]) ).
thf(793,plain,
( ~ ( p @ sk5 )
| ( sk2 != bool )
| ( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ sk5 )
!= c_2Ebool_2EF ) ),
inference(simp,[status(thm)],[779]) ).
thf(7508,plain,
( ~ ( p @ sk5 )
| ( sk2 != bool )
| ( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ sk5 )
!= ( ap @ ( c_2Eoption_2ETHE @ bool ) @ ( ap @ ( c_2Eoption_2ESOME @ bool ) @ c_2Ebool_2EF ) ) ) ),
inference(paramod_ordered,[status(thm)],[6112,793]) ).
thf(7822,plain,
( ~ ( p @ sk5 )
| ( sk2 != bool )
| ( ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET )
!= ( c_2Eoption_2ETHE @ bool ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ bool ) @ c_2Ebool_2EF )
!= sk5 ) ),
inference(simp,[status(thm)],[7508]) ).
thf(28,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(109,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 ) ) ) )
& ( ! [C: $i] :
( ( mem @ C @ A )
=> ( p @ ( ap @ B @ C ) ) )
=> ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(110,plain,
! [C: $i,B: $i,A: del] :
( ~ ( mem @ B @ ( arr @ A @ bool ) )
| ~ ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ B ) )
| ~ ( mem @ C @ A )
| ( p @ ( ap @ B @ C ) ) ),
inference(cnf,[status(esa)],[109]) ).
thf(17,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(79,plain,
mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(26,axiom,
! [A: del,B: $i] :
( ( mem @ B @ A )
=> ( ( ap @ ( i @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ibeta) ).
thf(105,plain,
! [A: del,B: $i] :
( ( mem @ B @ A )
=> ( ( ap @ ( i @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(106,plain,
! [B: $i,A: del] :
( ~ ( mem @ B @ A )
| ( ( ap @ ( i @ A ) @ B )
= B ) ),
inference(cnf,[status(esa)],[105]) ).
thf(107,plain,
! [B: $i,A: del] :
( ( ( ap @ ( i @ A ) @ B )
= B )
| ~ ( mem @ B @ A ) ),
inference(lifteq,[status(thm)],[106]) ).
thf(25658,plain,
! [B: $i,A: del] :
( ( ( ap @ ( i @ A ) @ B )
= B )
| ( ( mem @ c_2Ebool_2E_2F_5C @ ( arr @ bool @ ( arr @ bool @ bool ) ) )
!= ( mem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[79,107]) ).
thf(25659,plain,
( ( ap @ ( i @ ( arr @ bool @ ( arr @ bool @ bool ) ) ) @ c_2Ebool_2E_2F_5C )
= c_2Ebool_2E_2F_5C ),
inference(pattern_uni,[status(thm)],[25658:[bind(A,$thf( arr @ bool @ ( arr @ bool @ bool ) )),bind(B,$thf( c_2Ebool_2E_2F_5C ))]]) ).
thf(4193,plain,
! [A: tp__o] :
( ( sk3 != bool )
| ( mem @ sk6 @ bool )
| ( ( inj__o @ ( surj__o @ sk6 ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1441,88]) ).
thf(4194,plain,
( ( sk3 != bool )
| ( mem @ sk6 @ bool ) ),
inference(pattern_uni,[status(thm)],[4193:[bind(A,$thf( surj__o @ sk6 ))]]) ).
thf(4,axiom,
! [A: tp__o] :
( ( surj__o @ ( inj__o @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stp_inj_surj_o) ).
thf(46,plain,
! [A: tp__o] :
( ( surj__o @ ( inj__o @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(901,plain,
! [B: tp__o,A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ ( inj__o @ B ) ) @ bool )
| ( ( inj__o @ fo__c_2Ebool_2EF )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[52,677]) ).
thf(902,plain,
! [A: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ ( inj__o @ A ) ) @ bool ),
inference(pattern_uni,[status(thm)],[901:[bind(A,$thf( fo__c_2Ebool_2EF ))]]) ).
thf(925,plain,
! [A: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ ( inj__o @ A ) ) @ bool ),
inference(simp,[status(thm)],[902]) ).
thf(5791,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1414,925]) ).
thf(5792,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ) @ bool,
inference(pattern_uni,[status(thm)],[5791:[bind(A,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ))]]) ).
thf(1493,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ c_2Ebool_2EF ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1375,900]) ).
thf(1494,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ c_2Ebool_2EF ) @ bool,
inference(pattern_uni,[status(thm)],[1493:[bind(A,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ))]]) ).
thf(25344,plain,
! [B: $i,A: del] :
( ( ( ap @ ( i @ A ) @ B )
= B )
| ( ( mem @ sk4 @ ( arr @ sk2 @ ( arr @ sk3 @ sk1 ) ) )
!= ( mem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[42,107]) ).
thf(25345,plain,
( ( ap @ ( i @ ( arr @ sk2 @ ( arr @ sk3 @ sk1 ) ) ) @ sk4 )
= sk4 ),
inference(pattern_uni,[status(thm)],[25344:[bind(A,$thf( arr @ sk2 @ ( arr @ sk3 @ sk1 ) )),bind(B,$thf( sk4 ))]]) ).
thf(121,plain,
! [A: del] : ( mem @ ( c_2Emin_2E_3D @ A ) @ ( arr @ A @ ( arr @ A @ bool ) ) ),
inference(cnf,[status(esa)],[120]) ).
thf(11,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(60,plain,
! [A: del] : ( mem @ ( c_2Eoption_2ETHE @ A ) @ ( arr @ ( ty_2Eoption_2Eoption @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(61,plain,
! [A: del] : ( mem @ ( c_2Eoption_2ETHE @ A ) @ ( arr @ ( ty_2Eoption_2Eoption @ A ) @ A ) ),
inference(cnf,[status(esa)],[60]) ).
thf(34,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(132,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)],[34]) ).
thf(33,axiom,
! [A: del] :
( ! [B: $i] :
( ( mem @ B @ A )
=> ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ B ) ) )
<=> $true ) )
& ( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ ( c_2Eoption_2ENONE @ A ) ) )
<=> $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Eoption_2EIS__SOME__DEF) ).
thf(127,plain,
! [A: del] :
( ! [B: $i] :
( ( mem @ B @ A )
=> ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ B ) ) ) )
& ~ ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ ( c_2Eoption_2ENONE @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(128,plain,
( ! [A: del,B: $i] :
( ( mem @ B @ A )
=> ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ B ) ) ) )
& ~ ? [A: del] : ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ ( c_2Eoption_2ENONE @ A ) ) ) ),
inference(miniscope,[status(thm)],[127]) ).
thf(129,plain,
! [A: del] :
~ ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ ( c_2Eoption_2ENONE @ A ) ) ),
inference(cnf,[status(esa)],[128]) ).
thf(131,plain,
! [A: del] :
~ ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ ( c_2Eoption_2ENONE @ A ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(789,plain,
! [A: del] :
( ~ ( p @ sk5 )
| ( sk2 != bool )
| ( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ sk5 ) )
!= ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ ( c_2Eoption_2ENONE @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[774,131]) ).
thf(792,plain,
! [A: del] :
( ~ ( p @ sk5 )
| ( sk2 != bool )
| ( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ sk5 )
!= ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ ( c_2Eoption_2ENONE @ A ) ) ) ),
inference(simp,[status(thm)],[789]) ).
thf(5057,plain,
! [A: del] :
( ( sk2 != bool )
| ( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ sk5 )
!= ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ ( c_2Eoption_2ENONE @ A ) ) )
| ( ( p @ sk5 )
!= ( p @ c_2Ebool_2ET ) ) ),
inference(paramod_ordered,[status(thm)],[53,792]) ).
thf(5117,plain,
! [A: del] :
( ( sk2 != bool )
| ( ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET )
!= ( c_2Eoption_2EIS__SOME @ A ) )
| ( ( c_2Eoption_2ENONE @ A )
!= sk5 )
| ( sk5 != c_2Ebool_2ET ) ),
inference(simp,[status(thm)],[5057]) ).
thf(102,plain,
! [A: del] : ( mem @ ( c_2Ebool_2ECOND @ A ) @ ( arr @ bool @ ( arr @ A @ ( arr @ A @ A ) ) ) ),
inference(cnf,[status(esa)],[101]) ).
thf(25504,plain,
! [B: $i,A: del] :
( ( ( ap @ ( i @ A ) @ B )
= B )
| ( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) @ bool )
!= ( mem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1011,107]) ).
thf(25505,plain,
( ( ap @ ( i @ bool ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) )
= ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ),
inference(pattern_uni,[status(thm)],[25504:[bind(A,$thf( bool )),bind(B,$thf( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ))]]) ).
thf(786,plain,
( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ sk5 ) )
| ( sk2 != bool )
| ( ( p @ sk5 )
!= ( p @ c_2Ebool_2ET ) ) ),
inference(paramod_ordered,[status(thm)],[53,774]) ).
thf(798,plain,
( ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ sk5 ) )
| ( sk2 != bool )
| ( sk5 != c_2Ebool_2ET ) ),
inference(simp,[status(thm)],[786]) ).
thf(6078,plain,
! [B: $i,A: del] :
( ( ( ap @ ( c_2Eoption_2ETHE @ A ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ B ) )
= B )
| ( ( mem @ sk6 @ sk3 )
!= ( mem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[40,86]) ).
thf(6079,plain,
( ( ap @ ( c_2Eoption_2ETHE @ sk3 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 ) )
= sk6 ),
inference(pattern_uni,[status(thm)],[6078:[bind(A,$thf( sk3 )),bind(B,$thf( sk6 ))]]) ).
thf(14,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(70,plain,
! [A: del] : ( mem @ ( c_2Eoption_2ESOME @ A ) @ ( arr @ A @ ( ty_2Eoption_2Eoption @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9649,plain,
! [C: $i,B: $i,A: del] :
( ( ( ap @ ( k @ A @ B ) @ C )
= B )
| ( ( mem @ sk6 @ sk3 )
!= ( mem @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[40,91]) ).
thf(9650,plain,
! [A: $i] :
( ( ap @ ( k @ sk3 @ A ) @ sk6 )
= A ),
inference(pattern_uni,[status(thm)],[9649:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk6 ))]]) ).
thf(10441,plain,
! [A: $i] :
( ( ap @ ( k @ sk3 @ A ) @ sk6 )
= A ),
inference(simp,[status(thm)],[9650]) ).
thf(23,axiom,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( p @ A )
<=> ( p @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boolext) ).
thf(92,plain,
! [A: $i] :
( ( mem @ A @ bool )
=> ! [B: $i] :
( ( mem @ B @ bool )
=> ( ( ( ( p @ A )
=> ( p @ B ) )
& ( ( p @ B )
=> ( p @ A ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(9779,plain,
! [C: $i,B: $i,A: del] :
( ( ( ap @ ( k @ A @ B ) @ C )
= B )
| ( ( mem @ sk5 @ sk2 )
!= ( mem @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,91]) ).
thf(9780,plain,
! [A: $i] :
( ( ap @ ( k @ sk2 @ A ) @ sk5 )
= A ),
inference(pattern_uni,[status(thm)],[9779:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( sk5 ))]]) ).
thf(10460,plain,
! [A: $i] :
( ( ap @ ( k @ sk2 @ A ) @ sk5 )
= A ),
inference(simp,[status(thm)],[9780]) ).
thf(12299,plain,
! [A: $i] :
( ~ ( p @ sk5 )
| ( sk2 != bool )
| ( A != c_2Ebool_2EF )
| ( ( ap @ ( k @ sk2 @ A ) @ sk5 )
!= ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[10460,793]) ).
thf(12531,plain,
( ~ ( p @ sk5 )
| ( sk2 != bool )
| ( ( k @ sk2 @ c_2Ebool_2EF )
!= ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[12299]) ).
thf(12910,plain,
( ~ ( p @ sk5 )
| ( sk2 != bool )
| ( ( k @ sk2 @ c_2Ebool_2EF )
!= ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) ) ),
inference(simp,[status(thm)],[12531]) ).
thf(905,plain,
! [B: tp__o,A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ ( inj__o @ B ) ) @ bool )
| ( ( inj__o @ fo__c_2Ebool_2ET )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45,677]) ).
thf(906,plain,
! [A: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ ( inj__o @ A ) ) @ bool ),
inference(pattern_uni,[status(thm)],[905:[bind(A,$thf( fo__c_2Ebool_2ET ))]]) ).
thf(926,plain,
! [A: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ ( inj__o @ A ) ) @ bool ),
inference(simp,[status(thm)],[906]) ).
thf(4052,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1404,926]) ).
thf(4053,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) @ bool,
inference(pattern_uni,[status(thm)],[4052:[bind(A,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ))]]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ~ ( mem @ A @ bool )
| ~ ( mem @ B @ bool )
| ~ ( p @ B )
| ~ ( p @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[92]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( mem @ A @ bool )
| ~ ( mem @ B @ bool )
| ~ ( p @ B )
| ~ ( p @ A ) ),
inference(lifteq,[status(thm)],[93]) ).
thf(4062,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) @ c_2Ebool_2EF ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1404,900]) ).
thf(4063,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) @ c_2Ebool_2EF ) @ bool,
inference(pattern_uni,[status(thm)],[4062:[bind(A,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ))]]) ).
thf(1540,plain,
! [A: tp__o] :
( ( sk2 != bool )
| ( mem @ sk5 @ bool )
| ( ( inj__o @ ( surj__o @ sk5 ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1434,88]) ).
thf(1541,plain,
( ( sk2 != bool )
| ( mem @ sk5 @ bool ) ),
inference(pattern_uni,[status(thm)],[1540:[bind(A,$thf( surj__o @ sk5 ))]]) ).
thf(5053,plain,
! [A: del] :
( ~ ( p @ sk5 )
| ( sk2 != bool )
| ( ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET )
!= ( c_2Eoption_2EIS__SOME @ A ) )
| ( ( c_2Eoption_2ENONE @ A )
!= sk5 ) ),
inference(simp,[status(thm)],[792]) ).
thf(157,plain,
( ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) )
!= ( c_2Eoption_2ESOME @ sk1 ) )
| ( ( ap @ ( ap @ sk4 @ sk5 ) @ sk6 )
!= ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( c_2Eoption_2ENONE @ sk3 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) ) @ ( c_2Eoption_2ENONE @ sk3 ) )
!= ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( c_2Eoption_2ENONE @ sk3 ) ) )
| ( ( c_2Eoption_2ENONE @ sk1 )
!= ( c_2Eoption_2ENONE @ sk1 ) ) ),
inference(eqfactor_ordered,[status(thm)],[146]) ).
thf(165,plain,
( ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) )
!= ( c_2Eoption_2ESOME @ sk1 ) )
| ( ( ap @ sk4 @ sk5 )
!= ( c_2Eoption_2ESOME @ sk3 ) )
| ( sk6 != sk6 )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( c_2Eoption_2ENONE @ sk3 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) )
| ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) )
!= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) )
| ( ( c_2Eoption_2ENONE @ sk3 )
!= ( c_2Eoption_2ENONE @ sk3 ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(169,plain,
( ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) )
!= ( c_2Eoption_2ESOME @ sk1 ) )
| ( ( ap @ sk4 @ sk5 )
!= ( c_2Eoption_2ESOME @ sk3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( c_2Eoption_2ENONE @ sk3 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) )
| ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) )
!= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(180,plain,
( ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) )
!= ( c_2Eoption_2ESOME @ sk1 ) )
| ( ( ap @ sk4 @ sk5 )
!= ( c_2Eoption_2ESOME @ sk3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( c_2Eoption_2ENONE @ sk3 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) )
| ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) )
!= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 ) )
!= ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( c_2Eoption_2ENONE @ sk3 ) ) )
| ( ( c_2Eoption_2ENONE @ sk1 )
!= ( c_2Eoption_2ENONE @ sk1 ) ) ),
inference(eqfactor_ordered,[status(thm)],[169]) ).
thf(184,plain,
( ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) )
!= ( c_2Eoption_2ESOME @ sk1 ) )
| ( ( ap @ sk4 @ sk5 )
!= ( c_2Eoption_2ESOME @ sk3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( c_2Eoption_2ENONE @ sk3 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) )
| ( ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 )
!= ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 )
!= ( c_2Eoption_2ENONE @ sk2 ) )
| ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) )
!= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 )
!= ( c_2Eoption_2ENONE @ sk3 ) ) ),
inference(simp,[status(thm)],[180]) ).
thf(188,plain,
( ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) )
!= ( c_2Eoption_2ESOME @ sk1 ) )
| ( ( ap @ sk4 @ sk5 )
!= ( c_2Eoption_2ESOME @ sk3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( c_2Eoption_2ENONE @ sk3 ) )
!= ( c_2Eoption_2ENONE @ sk1 ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 )
!= ( c_2Eoption_2ENONE @ sk2 ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 )
!= ( c_2Eoption_2ENONE @ sk3 ) ) ),
inference(simp,[status(thm)],[184]) ).
thf(9660,plain,
! [D: $i,C: $i,B: del,A: tp__o] :
( ( ( ap @ ( k @ B @ C ) @ D )
= C )
| ( ( mem @ ( inj__o @ A ) @ bool )
!= ( mem @ D @ B ) ) ),
inference(paramod_ordered,[status(thm)],[88,91]) ).
thf(9661,plain,
! [B: tp__o,A: $i] :
( ( ap @ ( k @ bool @ A ) @ ( inj__o @ B ) )
= A ),
inference(pattern_uni,[status(thm)],[9660:[bind(A,$thf( E )),bind(B,$thf( bool )),bind(C,$thf( C )),bind(D,$thf( inj__o @ E ))]]) ).
thf(10445,plain,
! [B: tp__o,A: $i] :
( ( ap @ ( k @ bool @ A ) @ ( inj__o @ B ) )
= A ),
inference(simp,[status(thm)],[9661]) ).
thf(995,plain,
( ( sk2 != bool )
| ( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ sk5 )
!= c_2Ebool_2EF )
| ( ( p @ sk5 )
!= ( p @ c_2Ebool_2ET ) ) ),
inference(paramod_ordered,[status(thm)],[53,793]) ).
thf(1002,plain,
( ( sk2 != bool )
| ( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ sk5 )
!= c_2Ebool_2EF )
| ( sk5 != c_2Ebool_2ET ) ),
inference(simp,[status(thm)],[995]) ).
thf(13130,plain,
! [A: $i] :
( ( sk2 != bool )
| ( A != c_2Ebool_2EF )
| ( sk5 != c_2Ebool_2ET )
| ( ( ap @ ( k @ bool @ A ) @ c_2Ebool_2ET )
!= ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[10476,1002]) ).
thf(13324,plain,
( ( sk2 != bool )
| ( sk5 != c_2Ebool_2ET )
| ( ( k @ bool @ c_2Ebool_2EF )
!= ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) )
| ( sk5 != c_2Ebool_2ET ) ),
inference(simp,[status(thm)],[13130]) ).
thf(13676,plain,
( ( sk2 != bool )
| ( sk5 != c_2Ebool_2ET )
| ( ( k @ bool @ c_2Ebool_2EF )
!= ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) ) ),
inference(simp,[status(thm)],[13324]) ).
thf(189,plain,
( ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) )
!= ( c_2Eoption_2ESOME @ sk1 ) )
| ( ( ap @ sk4 @ sk5 )
!= ( c_2Eoption_2ESOME @ sk3 ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 )
!= ( c_2Eoption_2ENONE @ sk2 ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 )
!= ( c_2Eoption_2ENONE @ sk3 ) )
| ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) @ ( c_2Eoption_2ENONE @ sk3 ) )
!= ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) )
| ( ( c_2Eoption_2ENONE @ sk2 )
!= ( c_2Eoption_2ENONE @ sk1 ) ) ),
inference(eqfactor_ordered,[status(thm)],[188]) ).
thf(193,plain,
( ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) )
!= ( c_2Eoption_2ESOME @ sk1 ) )
| ( ( ap @ sk4 @ sk5 )
!= ( c_2Eoption_2ESOME @ sk3 ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 )
!= ( c_2Eoption_2ENONE @ sk2 ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 )
!= ( c_2Eoption_2ENONE @ sk3 ) )
| ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) )
!= ( c_2Eoption_2ESOME @ sk2 ) )
| ( ( c_2Eoption_2ENONE @ sk3 )
!= sk5 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[189]) ).
thf(214,plain,
( ( ( ap @ sk4 @ sk5 )
!= ( c_2Eoption_2ESOME @ sk3 ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 )
!= ( c_2Eoption_2ENONE @ sk2 ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 )
!= ( c_2Eoption_2ENONE @ sk3 ) )
| ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) )
!= ( c_2Eoption_2ESOME @ sk2 ) )
| ( ( c_2Eoption_2ENONE @ sk3 )
!= sk5 )
| ( sk2 != sk1 )
| ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) )
!= ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) ) )
| ( ( c_2Eoption_2ESOME @ sk2 )
!= ( c_2Eoption_2ESOME @ sk1 ) ) ),
inference(eqfactor_ordered,[status(thm)],[193]) ).
thf(220,plain,
( ( ( ap @ sk4 @ sk5 )
!= ( c_2Eoption_2ESOME @ sk3 ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 )
!= ( c_2Eoption_2ENONE @ sk2 ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 )
!= ( c_2Eoption_2ENONE @ sk3 ) )
| ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) )
!= ( c_2Eoption_2ESOME @ sk2 ) )
| ( ( c_2Eoption_2ENONE @ sk3 )
!= sk5 )
| ( sk2 != sk1 )
| ( ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 )
!= ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 )
!= ( c_2Eoption_2ENONE @ sk2 ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[214]) ).
thf(223,plain,
( ( ( ap @ sk4 @ sk5 )
!= ( c_2Eoption_2ESOME @ sk3 ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 )
!= ( c_2Eoption_2ENONE @ sk2 ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 )
!= ( c_2Eoption_2ENONE @ sk3 ) )
| ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) )
!= ( c_2Eoption_2ESOME @ sk2 ) )
| ( ( c_2Eoption_2ENONE @ sk3 )
!= sk5 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[220]) ).
thf(224,plain,
( ( ( ap @ sk4 @ sk5 )
!= ( c_2Eoption_2ESOME @ sk3 ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 )
!= ( c_2Eoption_2ENONE @ sk2 ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 )
!= ( c_2Eoption_2ENONE @ sk3 ) )
| ( ( c_2Eoption_2ENONE @ sk3 )
!= sk5 )
| ( sk2 != sk1 )
| ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) )
!= ( ap @ sk4 @ sk5 ) )
| ( ( c_2Eoption_2ESOME @ sk3 )
!= ( c_2Eoption_2ESOME @ sk2 ) ) ),
inference(eqfactor_ordered,[status(thm)],[223]) ).
thf(225,plain,
( ( ( ap @ sk4 @ sk5 )
!= ( c_2Eoption_2ESOME @ sk3 ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 )
!= ( c_2Eoption_2ENONE @ sk2 ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 )
!= ( c_2Eoption_2ENONE @ sk3 ) )
| ( ( c_2Eoption_2ENONE @ sk3 )
!= sk5 )
| ( sk2 != sk1 )
| ( ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 )
!= sk4 )
| ( ( c_2Eoption_2ENONE @ sk2 )
!= sk5 )
| ( ( c_2Eoption_2ESOME @ sk3 )
!= ( c_2Eoption_2ESOME @ sk2 ) ) ),
inference(simp,[status(thm)],[224]) ).
thf(15,axiom,
! [A: del,B: $i] :
( ( mem @ B @ A )
=> ! [C: $i] :
( ( mem @ C @ A )
=> ( ( ( ap @ ( c_2Eoption_2ESOME @ A ) @ B )
= ( ap @ ( c_2Eoption_2ESOME @ A ) @ C ) )
<=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eoption_2ESOME__11) ).
thf(72,plain,
! [A: del,B: $i] :
( ( mem @ B @ A )
=> ! [C: $i] :
( ( mem @ C @ A )
=> ( ( ( ( ap @ ( c_2Eoption_2ESOME @ A ) @ B )
= ( ap @ ( c_2Eoption_2ESOME @ A ) @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( ap @ ( c_2Eoption_2ESOME @ A ) @ B )
= ( ap @ ( c_2Eoption_2ESOME @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(74,plain,
! [C: $i,B: $i,A: del] :
( ~ ( mem @ B @ A )
| ~ ( mem @ C @ A )
| ( ( ap @ ( c_2Eoption_2ESOME @ A ) @ B )
!= ( ap @ ( c_2Eoption_2ESOME @ A ) @ C ) )
| ( B = C ) ),
inference(cnf,[status(esa)],[72]) ).
thf(77,plain,
! [C: $i,B: $i,A: del] :
( ( ( ap @ ( c_2Eoption_2ESOME @ A ) @ B )
!= ( ap @ ( c_2Eoption_2ESOME @ A ) @ C ) )
| ( B = C )
| ~ ( mem @ B @ A )
| ~ ( mem @ C @ A ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(5785,plain,
! [B: tp__o,A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ A ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ) )
!= ( inj__o @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1414,677]) ).
thf(5786,plain,
! [A: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ A ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ) @ bool ),
inference(pattern_uni,[status(thm)],[5785:[bind(A,$thf( A )),bind(B,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ))]]) ).
thf(35,axiom,
! [A: del,B: del,C: del] : ( mem @ ( c_2Eoption_2EOPTION__MAP2 @ A @ B @ C ) @ ( arr @ ( arr @ B @ ( arr @ C @ A ) ) @ ( arr @ ( ty_2Eoption_2Eoption @ B ) @ ( arr @ ( ty_2Eoption_2Eoption @ C ) @ ( ty_2Eoption_2Eoption @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2EOPTION__MAP2) ).
thf(134,plain,
! [A: del,B: del,C: del] : ( mem @ ( c_2Eoption_2EOPTION__MAP2 @ A @ B @ C ) @ ( arr @ ( arr @ B @ ( arr @ C @ A ) ) @ ( arr @ ( ty_2Eoption_2Eoption @ B ) @ ( arr @ ( ty_2Eoption_2Eoption @ C ) @ ( ty_2Eoption_2Eoption @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(12356,plain,
! [A: $i] :
( ( sk2 != bool )
| ( A != c_2Ebool_2EF )
| ( sk5 != c_2Ebool_2ET )
| ( ( ap @ ( k @ sk2 @ A ) @ sk5 )
!= ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[10460,1002]) ).
thf(12541,plain,
( ( sk2 != bool )
| ( sk5 != c_2Ebool_2ET )
| ( ( k @ sk2 @ c_2Ebool_2EF )
!= ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[12356]) ).
thf(12913,plain,
( ( sk2 != bool )
| ( sk5 != c_2Ebool_2ET )
| ( ( k @ sk2 @ c_2Ebool_2EF )
!= ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) ) ),
inference(simp,[status(thm)],[12541]) ).
thf(934,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) @ bool )
| ( ( inj__o @ fo__c_2Ebool_2EF )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[52,900]) ).
thf(935,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) @ bool,
inference(pattern_uni,[status(thm)],[934:[bind(A,$thf( fo__c_2Ebool_2EF ))]]) ).
thf(1411,plain,
! [A: $i] :
( ( ( inj__o @ ( surj__o @ A ) )
= A )
| ( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) @ bool )
!= ( mem @ A @ bool ) ) ),
inference(paramod_ordered,[status(thm)],[935,64]) ).
thf(1412,plain,
( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) )
= ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ),
inference(pattern_uni,[status(thm)],[1411:[bind(A,$thf( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ))]]) ).
thf(4994,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) @ c_2Ebool_2EF ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1412,900]) ).
thf(4995,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) @ c_2Ebool_2EF ) @ bool,
inference(pattern_uni,[status(thm)],[4994:[bind(A,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ))]]) ).
thf(25302,plain,
! [B: $i,A: del] :
( ( ( ap @ ( i @ A ) @ B )
= B )
| ( ( mem @ sk6 @ sk3 )
!= ( mem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[40,107]) ).
thf(25303,plain,
( ( ap @ ( i @ sk3 ) @ sk6 )
= sk6 ),
inference(pattern_uni,[status(thm)],[25302:[bind(A,$thf( sk3 )),bind(B,$thf( sk6 ))]]) ).
thf(25352,plain,
! [B: $i,A: del] :
( ( ( ap @ ( i @ A ) @ B )
= B )
| ( ( mem @ c_2Ebool_2EF @ bool )
!= ( mem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[78,107]) ).
thf(25353,plain,
( ( ap @ ( i @ bool ) @ c_2Ebool_2EF )
= c_2Ebool_2EF ),
inference(pattern_uni,[status(thm)],[25352:[bind(A,$thf( bool )),bind(B,$thf( c_2Ebool_2EF ))]]) ).
thf(27335,plain,
( ( sk2 != bool )
| ( sk5 != c_2Ebool_2ET )
| ( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ sk5 ) @ sk5 )
!= ( ap @ ( i @ bool ) @ c_2Ebool_2EF ) ) ),
inference(paramod_ordered,[status(thm)],[25353,1347]) ).
thf(27896,plain,
( ( sk2 != bool )
| ( sk5 != c_2Ebool_2ET )
| ( ( ap @ c_2Ebool_2E_2F_5C @ sk5 )
!= ( i @ bool ) )
| ( sk5 != c_2Ebool_2EF ) ),
inference(simp,[status(thm)],[27335]) ).
thf(12358,plain,
! [A: $i] :
( ~ ( p @ sk5 )
| ( sk2 != bool )
| ( A != c_2Ebool_2EF )
| ( ( ap @ ( k @ sk2 @ A ) @ sk5 )
!= ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ sk5 ) @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[10460,1318]) ).
thf(12750,plain,
( ~ ( p @ sk5 )
| ( sk2 != bool )
| ( ( k @ sk2 @ c_2Ebool_2EF )
!= ( ap @ c_2Ebool_2E_2F_5C @ sk5 ) )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[12358]) ).
thf(12982,plain,
( ~ ( p @ sk5 )
| ( sk2 != bool )
| ( ( k @ sk2 @ c_2Ebool_2EF )
!= ( ap @ c_2Ebool_2E_2F_5C @ sk5 ) ) ),
inference(simp,[status(thm)],[12750]) ).
thf(6202,plain,
! [B: $i,A: del] :
( ( ( ap @ ( c_2Eoption_2ETHE @ A ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ B ) )
= B )
| ( ( mem @ sk5 @ sk2 )
!= ( mem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,86]) ).
thf(6203,plain,
( ( ap @ ( c_2Eoption_2ETHE @ sk2 ) @ ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 ) )
= sk5 ),
inference(pattern_uni,[status(thm)],[6202:[bind(A,$thf( sk2 )),bind(B,$thf( sk5 ))]]) ).
thf(7492,plain,
( ( sk2 != bool )
| ( sk5 != c_2Ebool_2ET )
| ( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ sk5 ) @ sk5 )
!= ( ap @ ( c_2Eoption_2ETHE @ bool ) @ ( ap @ ( c_2Eoption_2ESOME @ bool ) @ c_2Ebool_2EF ) ) ) ),
inference(paramod_ordered,[status(thm)],[6112,1347]) ).
thf(7753,plain,
( ( sk2 != bool )
| ( sk5 != c_2Ebool_2ET )
| ( ( ap @ c_2Ebool_2E_2F_5C @ sk5 )
!= ( c_2Eoption_2ETHE @ bool ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ bool ) @ c_2Ebool_2EF )
!= sk5 ) ),
inference(simp,[status(thm)],[7492]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ ( mem @ A @ bool )
| ~ ( mem @ B @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ A ) @ B ) )
| ( p @ B ) ),
inference(cnf,[status(esa)],[56]) ).
thf(25463,plain,
! [B: $i,A: del] :
( ( ( ap @ ( i @ A ) @ B )
= B )
| ( ( mem @ sk5 @ sk2 )
!= ( mem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[41,107]) ).
thf(25464,plain,
( ( ap @ ( i @ sk2 ) @ sk5 )
= sk5 ),
inference(pattern_uni,[status(thm)],[25463:[bind(A,$thf( sk2 )),bind(B,$thf( sk5 ))]]) ).
thf(12283,plain,
! [A: $i] :
( ( sk2 != bool )
| ( A != c_2Ebool_2EF )
| ( sk5 != c_2Ebool_2ET )
| ( ( ap @ ( k @ sk2 @ A ) @ sk5 )
!= ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ sk5 ) @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[10460,1347]) ).
thf(12766,plain,
( ( sk2 != bool )
| ( sk5 != c_2Ebool_2ET )
| ( ( k @ sk2 @ c_2Ebool_2EF )
!= ( ap @ c_2Ebool_2E_2F_5C @ sk5 ) )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[12283]) ).
thf(12986,plain,
( ( sk2 != bool )
| ( sk5 != c_2Ebool_2ET )
| ( ( k @ sk2 @ c_2Ebool_2EF )
!= ( ap @ c_2Ebool_2E_2F_5C @ sk5 ) ) ),
inference(simp,[status(thm)],[12766]) ).
thf(71,plain,
! [A: del] : ( mem @ ( c_2Eoption_2ESOME @ A ) @ ( arr @ A @ ( ty_2Eoption_2Eoption @ A ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(8,axiom,
! [A: tp__o] :
( ( ( $true
& ( p @ ( inj__o @ A ) ) )
<=> ( p @ ( inj__o @ A ) ) )
& ( ( ( p @ ( inj__o @ A ) )
& $true )
<=> ( p @ ( inj__o @ A ) ) )
& ( ( $false
& ( p @ ( inj__o @ A ) ) )
<=> $false )
& ( ( ( p @ ( inj__o @ A ) )
& $false )
<=> $false )
& ( ( ( p @ ( inj__o @ A ) )
& ( p @ ( inj__o @ A ) ) )
<=> ( p @ ( inj__o @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EAND__CLAUSES) ).
thf(54,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(29,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(113,plain,
! [A: del,B: $i] :
( ( mem @ B @ A )
=> ! [C: $i] :
( ( mem @ C @ A )
=> ( ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ B ) @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ B ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(18,axiom,
! [A: del] : ( mem @ ( c_2Ebool_2E_21 @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_21) ).
thf(80,plain,
! [A: del] : ( mem @ ( c_2Ebool_2E_21 @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(81,plain,
! [A: del] : ( mem @ ( c_2Ebool_2E_21 @ A ) @ ( arr @ ( arr @ A @ bool ) @ bool ) ),
inference(cnf,[status(esa)],[80]) ).
thf(1491,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ c_2Ebool_2ET ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1375,904]) ).
thf(1492,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ c_2Ebool_2ET ) @ bool,
inference(pattern_uni,[status(thm)],[1491:[bind(A,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ))]]) ).
thf(4036,plain,
! [B: tp__o,A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) @ ( inj__o @ B ) ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1404,677]) ).
thf(4037,plain,
! [A: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) @ ( inj__o @ A ) ) @ bool ),
inference(pattern_uni,[status(thm)],[4036:[bind(A,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) )),bind(B,$thf( B ))]]) ).
thf(4107,plain,
! [A: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) @ ( inj__o @ A ) ) @ bool ),
inference(simp,[status(thm)],[4037]) ).
thf(5815,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ) @ c_2Ebool_2EF ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1414,900]) ).
thf(5816,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ) @ c_2Ebool_2EF ) @ bool,
inference(pattern_uni,[status(thm)],[5815:[bind(A,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ))]]) ).
thf(25,axiom,
! [A: del] : ( mem @ ( c_2Eoption_2ENONE @ A ) @ ( ty_2Eoption_2Eoption @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2ENONE) ).
thf(103,plain,
! [A: del] : ( mem @ ( c_2Eoption_2ENONE @ A ) @ ( ty_2Eoption_2Eoption @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(4984,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1412,926]) ).
thf(4985,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) @ bool,
inference(pattern_uni,[status(thm)],[4984:[bind(A,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ))]]) ).
thf(4992,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) @ c_2Ebool_2ET ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1412,904]) ).
thf(4993,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) @ c_2Ebool_2ET ) @ bool,
inference(pattern_uni,[status(thm)],[4992:[bind(A,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ))]]) ).
thf(47,plain,
! [A: tp__o] :
( ( surj__o @ ( inj__o @ A ) )
= A ),
inference(cnf,[status(esa)],[46]) ).
thf(48,plain,
! [A: tp__o] :
( ( surj__o @ ( inj__o @ A ) )
= A ),
inference(lifteq,[status(thm)],[47]) ).
thf(197,plain,
! [A: tp__o] :
( ( ( surj__o @ c_2Ebool_2EF )
= A )
| ( ( inj__o @ fo__c_2Ebool_2EF )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[52,48]) ).
thf(198,plain,
( ( surj__o @ c_2Ebool_2EF )
= fo__c_2Ebool_2EF ),
inference(pattern_uni,[status(thm)],[197:[bind(A,$thf( fo__c_2Ebool_2EF ))]]) ).
thf(27,axiom,
! [A: del,B: $i] :
( ( mem @ B @ A )
=> ( ( B = B )
<=> $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EREFL__CLAUSE) ).
thf(108,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(1473,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1375,925]) ).
thf(1474,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ bool,
inference(pattern_uni,[status(thm)],[1473:[bind(A,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ))]]) ).
thf(25311,plain,
! [C: $i,B: del,A: tp__o] :
( ( ( ap @ ( i @ B ) @ C )
= C )
| ( ( mem @ ( inj__o @ A ) @ bool )
!= ( mem @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[88,107]) ).
thf(25312,plain,
! [A: tp__o] :
( ( ap @ ( i @ bool ) @ ( inj__o @ A ) )
= ( inj__o @ A ) ),
inference(pattern_uni,[status(thm)],[25311:[bind(A,$thf( D )),bind(B,$thf( bool )),bind(C,$thf( inj__o @ D ))]]) ).
thf(26480,plain,
! [A: tp__o] :
( ( ap @ ( i @ bool ) @ ( inj__o @ A ) )
= ( inj__o @ A ) ),
inference(simp,[status(thm)],[25312]) ).
thf(226,plain,
( ( ( ap @ sk4 @ sk5 )
!= ( c_2Eoption_2ESOME @ sk3 ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 )
!= ( c_2Eoption_2ENONE @ sk2 ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 )
!= ( c_2Eoption_2ENONE @ sk3 ) )
| ( ( c_2Eoption_2ENONE @ sk3 )
!= sk5 )
| ( sk2 != sk1 )
| ( ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 ) @ ( c_2Eoption_2ENONE @ sk2 ) )
!= ( ap @ sk4 @ sk5 ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[224]) ).
thf(25703,plain,
! [B: $i,A: del] :
( ( ( ap @ ( i @ A ) @ B )
= B )
| ( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) @ bool )
!= ( mem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[935,107]) ).
thf(25704,plain,
( ( ap @ ( i @ bool ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) )
= ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ),
inference(pattern_uni,[status(thm)],[25703:[bind(A,$thf( bool )),bind(B,$thf( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ))]]) ).
thf(4964,plain,
! [B: tp__o,A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ A ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) )
!= ( inj__o @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1412,677]) ).
thf(4965,plain,
! [A: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ A ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) @ bool ),
inference(pattern_uni,[status(thm)],[4964:[bind(A,$thf( A )),bind(B,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ))]]) ).
thf(9689,plain,
! [C: $i,B: $i,A: del] :
( ( ( ap @ ( k @ A @ B ) @ C )
= B )
| ( ( mem @ c_2Ebool_2EF @ bool )
!= ( mem @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[78,91]) ).
thf(9690,plain,
! [A: $i] :
( ( ap @ ( k @ bool @ A ) @ c_2Ebool_2EF )
= A ),
inference(pattern_uni,[status(thm)],[9689:[bind(A,$thf( bool )),bind(B,$thf( B )),bind(C,$thf( c_2Ebool_2EF ))]]) ).
thf(10449,plain,
! [A: $i] :
( ( ap @ ( k @ bool @ A ) @ c_2Ebool_2EF )
= A ),
inference(simp,[status(thm)],[9690]) ).
thf(112,plain,
! [B: $i,A: del] :
( ~ ( mem @ B @ ( arr @ A @ bool ) )
| ( mem @ ( sk8 @ B @ A ) @ A )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ B ) ) ),
inference(cnf,[status(esa)],[109]) ).
thf(144,plain,
! [A: del] :
( ( p @ ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ ( c_2Eoption_2ENONE @ A ) ) )
!= ( p @ c_2Ebool_2ET ) ),
inference(paramod_ordered,[status(thm)],[53,131]) ).
thf(145,plain,
! [A: del] :
( ( ap @ ( c_2Eoption_2EIS__SOME @ A ) @ ( c_2Eoption_2ENONE @ A ) )
!= c_2Ebool_2ET ),
inference(simp,[status(thm)],[144]) ).
thf(4034,plain,
! [B: tp__o,A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ A ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) )
!= ( inj__o @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1404,677]) ).
thf(4035,plain,
! [A: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( inj__o @ A ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) @ bool ),
inference(pattern_uni,[status(thm)],[4034:[bind(A,$thf( A )),bind(B,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ))]]) ).
thf(4970,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1412,925]) ).
thf(4971,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) @ bool,
inference(pattern_uni,[status(thm)],[4970:[bind(A,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ))]]) ).
thf(1483,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1375,926]) ).
thf(1484,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ bool,
inference(pattern_uni,[status(thm)],[1483:[bind(A,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ))]]) ).
thf(18755,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1414,1470]) ).
thf(18756,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ bool,
inference(pattern_uni,[status(thm)],[18755:[bind(A,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ))]]) ).
thf(1543,plain,
( ( sk5 = c_2Ebool_2EF )
| ( sk2 != bool )
| ( ( inj__o @ ( surj__o @ sk5 ) )
!= ( inj__o @ fo__c_2Ebool_2EF ) ) ),
inference(paramod_ordered,[status(thm)],[52,1434]) ).
thf(1579,plain,
( ( sk5 = c_2Ebool_2EF )
| ( sk2 != bool )
| ( ( surj__o @ sk5 )
!= fo__c_2Ebool_2EF ) ),
inference(simp,[status(thm)],[1543]) ).
thf(4216,plain,
( ( sk3 != bool )
| ( sk6 = c_2Ebool_2ET )
| ( ( inj__o @ ( surj__o @ sk6 ) )
!= ( inj__o @ fo__c_2Ebool_2ET ) ) ),
inference(paramod_ordered,[status(thm)],[1441,45]) ).
thf(4246,plain,
( ( sk6 = c_2Ebool_2ET )
| ( sk3 != bool )
| ( ( surj__o @ sk6 )
!= fo__c_2Ebool_2ET ) ),
inference(simp,[status(thm)],[4216]) ).
thf(142,plain,
( ( p @ c_2Ebool_2ET )
!= ( p @ c_2Ebool_2EF ) ),
inference(paramod_ordered,[status(thm)],[53,50]) ).
thf(143,plain,
c_2Ebool_2ET != c_2Ebool_2EF,
inference(simp,[status(thm)],[142]) ).
thf(25372,plain,
! [B: $i,A: del] :
( ( ( ap @ ( i @ A ) @ B )
= B )
| ( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) @ bool )
!= ( mem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[937,107]) ).
thf(25373,plain,
( ( ap @ ( i @ bool ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) )
= ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ),
inference(pattern_uni,[status(thm)],[25372:[bind(A,$thf( bool )),bind(B,$thf( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ))]]) ).
thf(104,plain,
! [A: del] : ( mem @ ( c_2Eoption_2ENONE @ A ) @ ( ty_2Eoption_2Eoption @ A ) ),
inference(cnf,[status(esa)],[103]) ).
thf(4060,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) @ c_2Ebool_2ET ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1404,904]) ).
thf(4061,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) @ c_2Ebool_2ET ) @ bool,
inference(pattern_uni,[status(thm)],[4060:[bind(A,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ))]]) ).
thf(25626,plain,
! [B: $i,A: del] :
( ( ( ap @ ( i @ A ) @ B )
= B )
| ( ( mem @ c_2Ebool_2ET @ bool )
!= ( mem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[119,107]) ).
thf(25627,plain,
( ( ap @ ( i @ bool ) @ c_2Ebool_2ET )
= c_2Ebool_2ET ),
inference(pattern_uni,[status(thm)],[25626:[bind(A,$thf( bool )),bind(B,$thf( c_2Ebool_2ET ))]]) ).
thf(27351,plain,
( ~ ( p @ sk5 )
| ( sk2 != bool )
| ( ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ sk5 )
!= ( ap @ ( i @ bool ) @ c_2Ebool_2EF ) ) ),
inference(paramod_ordered,[status(thm)],[25353,793]) ).
thf(27825,plain,
( ~ ( p @ sk5 )
| ( sk2 != bool )
| ( ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET )
!= ( i @ bool ) )
| ( sk5 != c_2Ebool_2EF ) ),
inference(simp,[status(thm)],[27351]) ).
thf(9,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ETRUTH) ).
thf(55,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(25707,plain,
! [B: $i,A: del] :
( ( ( ap @ ( i @ A ) @ B )
= B )
| ( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) @ bool )
!= ( mem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1009,107]) ).
thf(25708,plain,
( ( ap @ ( i @ bool ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) )
= ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ),
inference(pattern_uni,[status(thm)],[25707:[bind(A,$thf( bool )),bind(B,$thf( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ))]]) ).
thf(19,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(82,plain,
! [A: del] : ( mem @ ( c_2Eoption_2EIS__SOME @ A ) @ ( arr @ ( ty_2Eoption_2Eoption @ A ) @ bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ~ ( mem @ A @ bool )
| ~ ( mem @ B @ bool )
| ~ ( p @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ A ) @ B ) )
| ( p @ A ) ),
inference(cnf,[status(esa)],[56]) ).
thf(4966,plain,
! [B: tp__o,A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) @ ( inj__o @ B ) ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1412,677]) ).
thf(4967,plain,
! [A: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) @ ( inj__o @ A ) ) @ bool ),
inference(pattern_uni,[status(thm)],[4966:[bind(A,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) )),bind(B,$thf( B ))]]) ).
thf(5051,plain,
! [A: tp__o] : ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2EF ) ) @ ( inj__o @ A ) ) @ bool ),
inference(simp,[status(thm)],[4967]) ).
thf(4038,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1404,925]) ).
thf(4039,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ) @ bool,
inference(pattern_uni,[status(thm)],[4038:[bind(A,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2ET ) ))]]) ).
thf(25348,plain,
! [B: $i,A: del] :
( ( sk3 != bool )
| ( ( ap @ ( i @ A ) @ B )
= B )
| ( ( mem @ sk6 @ bool )
!= ( mem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4194,107]) ).
thf(25349,plain,
( ( sk3 != bool )
| ( ( ap @ ( i @ bool ) @ sk6 )
= sk6 ) ),
inference(pattern_uni,[status(thm)],[25348:[bind(A,$thf( bool )),bind(B,$thf( sk6 ))]]) ).
thf(36,axiom,
! [A: del,B: del,C: del,D: $i] :
( ( mem @ D @ ( arr @ B @ ( arr @ C @ A ) ) )
=> ! [E: $i] :
( ( mem @ E @ ( ty_2Eoption_2Eoption @ B ) )
=> ! [F: $i] :
( ( mem @ F @ ( ty_2Eoption_2Eoption @ C ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A @ B @ C ) @ D ) @ E ) @ F )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ B ) @ E ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ C ) @ F ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ ( ap @ ( ap @ D @ ( ap @ ( c_2Eoption_2ETHE @ B ) @ E ) ) @ ( ap @ ( c_2Eoption_2ETHE @ C ) @ F ) ) ) ) @ ( c_2Eoption_2ENONE @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Eoption_2EOPTION__MAP2__DEF) ).
thf(136,plain,
! [A: del,B: del,C: del,D: $i] :
( ( mem @ D @ ( arr @ B @ ( arr @ C @ A ) ) )
=> ! [E: $i] :
( ( mem @ E @ ( ty_2Eoption_2Eoption @ B ) )
=> ! [F: $i] :
( ( mem @ F @ ( ty_2Eoption_2Eoption @ C ) )
=> ( ( ap @ ( ap @ ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ A @ B @ C ) @ D ) @ E ) @ F )
= ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ ( ty_2Eoption_2Eoption @ A ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( c_2Eoption_2EIS__SOME @ B ) @ E ) ) @ ( ap @ ( c_2Eoption_2EIS__SOME @ C ) @ F ) ) ) @ ( ap @ ( c_2Eoption_2ESOME @ A ) @ ( ap @ ( ap @ D @ ( ap @ ( c_2Eoption_2ETHE @ B ) @ E ) ) @ ( ap @ ( c_2Eoption_2ETHE @ C ) @ F ) ) ) ) @ ( c_2Eoption_2ENONE @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(18739,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1375,1470]) ).
thf(18740,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ) @ bool,
inference(pattern_uni,[status(thm)],[18739:[bind(A,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ c_2Ebool_2EF ) ))]]) ).
thf(4196,plain,
( ( sk6 = c_2Ebool_2EF )
| ( sk3 != bool )
| ( ( inj__o @ ( surj__o @ sk6 ) )
!= ( inj__o @ fo__c_2Ebool_2EF ) ) ),
inference(paramod_ordered,[status(thm)],[52,1441]) ).
thf(4242,plain,
( ( sk6 = c_2Ebool_2EF )
| ( sk3 != bool )
| ( ( surj__o @ sk6 )
!= fo__c_2Ebool_2EF ) ),
inference(simp,[status(thm)],[4196]) ).
thf(5805,plain,
! [A: tp__o] :
( ( mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ) @ bool )
| ( ( inj__o @ ( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ) )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1414,926]) ).
thf(5806,plain,
mem @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2ET ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ) @ bool,
inference(pattern_uni,[status(thm)],[5805:[bind(A,$thf( surj__o @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ c_2Ebool_2EF ) @ c_2Ebool_2ET ) ))]]) ).
thf(199,plain,
! [A: tp__o] :
( ( ( surj__o @ c_2Ebool_2ET )
= A )
| ( ( inj__o @ fo__c_2Ebool_2ET )
!= ( inj__o @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45,48]) ).
thf(200,plain,
( ( surj__o @ c_2Ebool_2ET )
= fo__c_2Ebool_2ET ),
inference(pattern_uni,[status(thm)],[199:[bind(A,$thf( fo__c_2Ebool_2ET ))]]) ).
thf(66,plain,
! [D: $i,C: $i,B: del,A: del] :
( ~ ( mem @ C @ ( arr @ A @ B ) )
| ~ ( mem @ D @ ( arr @ A @ B ) )
| ( mem @ ( sk7 @ D @ C @ B @ A ) @ A )
| ( C = D ) ),
inference(cnf,[status(esa)],[65]) ).
thf(68,plain,
! [D: $i,C: $i,B: del,A: del] :
( ( C = D )
| ~ ( mem @ C @ ( arr @ A @ B ) )
| ~ ( mem @ D @ ( arr @ A @ B ) )
| ( mem @ ( sk7 @ D @ C @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[66]) ).
thf(111,plain,
! [B: $i,A: del] :
( ~ ( mem @ B @ ( arr @ A @ bool ) )
| ~ ( p @ ( ap @ B @ ( sk8 @ B @ A ) ) )
| ( p @ ( ap @ ( c_2Ebool_2E_21 @ A ) @ B ) ) ),
inference(cnf,[status(esa)],[109]) ).
thf(227,plain,
( ( ( ap @ sk4 @ sk5 )
!= ( c_2Eoption_2ESOME @ sk3 ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk2 ) @ sk5 )
!= ( c_2Eoption_2ENONE @ sk2 ) )
| ( ( ap @ ( c_2Eoption_2ESOME @ sk3 ) @ sk6 )
!= ( c_2Eoption_2ENONE @ sk3 ) )
| ( ( c_2Eoption_2ENONE @ sk3 )
!= sk5 )
| ( sk2 != sk1 )
| ( ( ap @ ( c_2Eoption_2EOPTION__MAP2 @ sk1 @ sk2 @ sk3 ) @ sk4 )
!= sk4 )
| ( ( c_2Eoption_2ENONE @ sk2 )
!= sk5 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[224]) ).
thf(32,axiom,
! [A: del,B: $i] :
( ( mem @ B @ A )
=> ! [C: $i] :
( ( mem @ C @ A )
=> ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A ) @ ( inj__o @ fo__c_2Ebool_2ET ) ) @ B ) @ C )
= B )
& ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A ) @ ( inj__o @ fo__c_2Ebool_2EF ) ) @ B ) @ C )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2ECOND__CLAUSES) ).
thf(122,plain,
! [A: del,B: $i] :
( ( mem @ B @ A )
=> ! [C: $i] :
( ( mem @ C @ A )
=> ( ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A ) @ ( inj__o @ fo__c_2Ebool_2ET ) ) @ B ) @ C )
= B )
& ( ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ A ) @ ( inj__o @ fo__c_2Ebool_2EF ) ) @ B ) @ C )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(83,plain,
! [A: del] : ( mem @ ( c_2Eoption_2EIS__SOME @ A ) @ ( arr @ ( ty_2Eoption_2Eoption @ A ) @ bool ) ),
inference(cnf,[status(esa)],[82]) ).
thf(25420,plain,
! [B: $i,A: del] :
( ( sk2 != bool )
| ( ( ap @ ( i @ A ) @ B )
= B )
| ( ( mem @ sk5 @ bool )
!= ( mem @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1541,107]) ).
thf(25421,plain,
( ( sk2 != bool )
| ( ( ap @ ( i @ bool ) @ sk5 )
= sk5 ) ),
inference(pattern_uni,[status(thm)],[25420:[bind(A,$thf( bool )),bind(B,$thf( sk5 ))]]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ~ ( mem @ A @ bool )
| ~ ( mem @ B @ bool )
| ( p @ A )
| ( p @ B )
| ( A = B ) ),
inference(cnf,[status(esa)],[92]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( mem @ A @ bool )
| ~ ( mem @ B @ bool )
| ( p @ A )
| ( p @ B ) ),
inference(lifteq,[status(thm)],[96]) ).
thf(99657,plain,
$false,
inference(cvc4,[status(thm)],[69,101,6317,13768,88,170,120,677,5814,56,18800,1507,42,1576,1441,52,7822,110,25659,4194,46,1347,78,5792,1494,57,25345,121,937,84,61,89,132,774,60,793,925,5117,1470,102,25505,798,6079,38,70,10441,92,65,12910,4053,97,4063,1541,5053,1375,188,53,10445,169,13676,141,109,225,77,5786,1414,1002,41,134,1434,105,792,12913,4995,926,1318,25303,27896,12982,6203,7753,45,64,286,59,25464,904,12986,44,71,54,49,86,900,113,1011,81,6112,1492,4107,5816,103,4985,91,25353,4993,198,108,1474,26480,223,226,25704,80,4965,10449,112,145,48,4035,10476,4971,1484,50,18756,127,1579,1404,4246,72,143,43,25373,87,1412,104,4061,25627,40,27825,55,25708,139,1294,82,119,58,5051,4039,25349,146,51,107,136,79,18740,4242,5806,131,200,68,62,111,227,122,10460,83,25421,100,935,1009]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : ITP002_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.11/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n010.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 6 14:23:24 EDT 2024
% 0.15/0.37 % CPUTime :
% 1.00/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/1.06 % [INFO] Parsing done (154ms).
% 1.24/1.07 % [INFO] Running in sequential loop mode.
% 1.87/1.28 % [INFO] eprover registered as external prover.
% 1.87/1.28 % [INFO] cvc4 registered as external prover.
% 1.87/1.29 % [INFO] Scanning for conjecture ...
% 2.09/1.38 % [INFO] Found a conjecture and 35 axioms. Running axiom selection ...
% 2.29/1.44 % [INFO] Axiom selection finished. Selected 35 axioms (removed 0 axioms).
% 2.58/1.48 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.61/1.48 % [INFO] Type checking passed.
% 2.61/1.49 % [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 ...
% 123.63/37.36 % External prover 'cvc4' found a proof!
% 123.63/37.36 % [INFO] Killing All external provers ...
% 123.63/37.36 % Time passed: 36829ms (effective reasoning time: 36286ms)
% 123.63/37.36 % 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)>
% 123.63/37.36 % Axioms used in derivation (35): ax_eq_p, mem_c_2Eoption_2ETHE, mem_c_2Ebool_2E_21, ax_thm_2Eoption_2ETHE__DEF, ax_and_p, mem_c_2Emin_2E_3D, ax_thm_2Eoption_2EOPTION__MAP2__DEF, mem_c_2Ebool_2EF, conj_thm_2Ebool_2ETRUTH, ax_all_p, mem_c_2Eoption_2ESOME, ap_tp, boolext, stp_iso_mem_o, conj_thm_2Ebool_2EREFL__CLAUSE, mem_c_2Ebool_2E_2F_5C, stp_inj_surj_o, ibeta, mem_c_2Eoption_2EOPTION__MAP2, stp_eq_fo_c_2Ebool_2E_2F_5C, kbeta, mem_c_2Eoption_2ENONE, funcext, conj_thm_2Ebool_2EAND__CLAUSES, ax_true_p, mem_c_2Ebool_2ECOND, ax_thm_2Eoption_2EIS__SOME__DEF, mem_c_2Eoption_2EIS__SOME, conj_thm_2Eoption_2ESOME__11, ax_false_p, conj_thm_2Ebool_2ECOND__CLAUSES, stp_eq_fo_c_2Ebool_2EF, mem_c_2Ebool_2ET, stp_inj_mem_o, stp_eq_fo_c_2Ebool_2ET
% 123.63/37.36 % No. of inferences in proof: 351
% 123.63/37.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 36829 ms resp. 36286 ms w/o parsing
% 124.06/37.45 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 124.06/37.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------