TSTP Solution File: ITP011+1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP011+1 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:46:44 EDT 2024
% Result : Theorem 83.54s 28.05s
% Output : Refutation 83.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 101
% Syntax : Number of formulae : 227 ( 76 unt; 55 typ; 0 def)
% Number of atoms : 607 ( 310 equ; 0 cnn)
% Maximal formula atoms : 33 ( 3 avg)
% Number of connectives : 6960 ( 177 ~; 116 |; 163 &;6356 @)
% ( 36 <=>; 112 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 55 usr; 36 con; 0-3 aty)
% Number of variables : 446 ( 0 ^ 430 !; 16 ?; 446 :)
% Comments :
%------------------------------------------------------------------------------
thf(s_type,type,
s: $i > $i > $i ).
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $i ).
thf(c_2Eoption_2EOPTREL_2E3_type,type,
c_2Eoption_2EOPTREL_2E3: $i > $i > $i > $i ).
thf(tyop_2Emin_2Efun_type,type,
tyop_2Emin_2Efun: $i > $i > $i ).
thf(tyop_2Eoption_2Eoption_type,type,
tyop_2Eoption_2Eoption: $i > $i ).
thf(c_2Eoption_2ENONE_2E0_type,type,
c_2Eoption_2ENONE_2E0: $i ).
thf(c_2Ebool_2ET_2E0_type,type,
c_2Ebool_2ET_2E0: $i ).
thf(c_2Eoption_2ESOME_2E1_type,type,
c_2Eoption_2ESOME_2E1: $i > $i ).
thf(c_2Ebool_2EF_2E0_type,type,
c_2Ebool_2EF_2E0: $i ).
thf(app_2E2_type,type,
app_2E2: $i > $i > $i ).
thf(p_type,type,
p: $i > $o ).
thf(c_2Ebool_2E_3F_2E1_type,type,
c_2Ebool_2E_3F_2E1: $i > $i ).
thf(c_2Ebool_2E_7E_2E0_type,type,
c_2Ebool_2E_7E_2E0: $i ).
thf(c_2Ebool_2E_7E_2E1_type,type,
c_2Ebool_2E_7E_2E1: $i > $i ).
thf(c_2Eoption_2Eoption__CASE_2E3_type,type,
c_2Eoption_2Eoption__CASE_2E3: $i > $i > $i > $i ).
thf(c_2Eoption_2Eoption__CASE_2E0_type,type,
c_2Eoption_2Eoption__CASE_2E0: $i ).
thf(c_2Emin_2E_3D_3D_3E_2E0_type,type,
c_2Emin_2E_3D_3D_3E_2E0: $i ).
thf(c_2Ebool_2E_5C_2F_2E0_type,type,
c_2Ebool_2E_5C_2F_2E0: $i ).
thf(c_2Eoption_2EOPTION__JOIN_2E1_type,type,
c_2Eoption_2EOPTION__JOIN_2E1: $i > $i ).
thf(c_2Eoption_2EOPTION__JOIN_2E0_type,type,
c_2Eoption_2EOPTION__JOIN_2E0: $i ).
thf(c_2Eoption_2EIS__NONE_2E1_type,type,
c_2Eoption_2EIS__NONE_2E1: $i > $i ).
thf(c_2Eoption_2EIS__NONE_2E0_type,type,
c_2Eoption_2EIS__NONE_2E0: $i ).
thf(c_2Eoption_2EOPTREL_2E0_type,type,
c_2Eoption_2EOPTREL_2E0: $i ).
thf(c_2Eoption_2ESOME_2E0_type,type,
c_2Eoption_2ESOME_2E0: $i ).
thf(c_2Ebool_2E_2F_5C_2E2_type,type,
c_2Ebool_2E_2F_5C_2E2: $i > $i > $i ).
thf(c_2Ebool_2E_5C_2F_2E2_type,type,
c_2Ebool_2E_5C_2F_2E2: $i > $i > $i ).
thf(combin_k_2E0_type,type,
combin_k_2E0: $i ).
thf(combin_s_2E0_type,type,
combin_s_2E0: $i ).
thf(c_2Ebool_2E_21_2E1_type,type,
c_2Ebool_2E_21_2E1: $i > $i ).
thf(c_2Ebool_2E_21_2E0_type,type,
c_2Ebool_2E_21_2E0: $i ).
thf(c_2Eoption_2EOPTION__MAP_2E2_type,type,
c_2Eoption_2EOPTION__MAP_2E2: $i > $i > $i ).
thf(c_2Eoption_2EOPTION__MAP_2E0_type,type,
c_2Eoption_2EOPTION__MAP_2E0: $i ).
thf(c_2Eoption_2ETHE_2E1_type,type,
c_2Eoption_2ETHE_2E1: $i > $i ).
thf(c_2Eoption_2EIS__SOME_2E1_type,type,
c_2Eoption_2EIS__SOME_2E1: $i > $i ).
thf(combin_i_2E0_type,type,
combin_i_2E0: $i ).
thf(c_2Eoption_2ETHE_2E0_type,type,
c_2Eoption_2ETHE_2E0: $i ).
thf(c_2Emin_2E_3D_2E2_type,type,
c_2Emin_2E_3D_2E2: $i > $i > $i ).
thf(c_2Ebool_2E_3F_2E0_type,type,
c_2Ebool_2E_3F_2E0: $i ).
thf(c_2Eoption_2EIS__SOME_2E0_type,type,
c_2Eoption_2EIS__SOME_2E0: $i ).
thf(c_2Emin_2E_3D_3D_3E_2E2_type,type,
c_2Emin_2E_3D_3D_3E_2E2: $i > $i > $i ).
thf(c_2Ebool_2E_2F_5C_2E0_type,type,
c_2Ebool_2E_2F_5C_2E0: $i ).
thf(c_2Emin_2E_3D_2E0_type,type,
c_2Emin_2E_3D_2E0: $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $i ).
thf(sk8_type,type,
sk8: $i ).
thf(sk9_type,type,
sk9: $i ).
thf(sk10_type,type,
sk10: $i ).
thf(sk11_type,type,
sk11: $i ).
thf(sk12_type,type,
sk12: $i ).
thf(sk13_type,type,
sk13: $i > $i > $i ).
thf(14,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ B ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEXISTS__SIMP) ).
thf(120,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [A: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).
thf(57,plain,
! [A: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(58,plain,
( ! [A: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) ) )
& ! [A: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) ),
inference(miniscope,[status(thm)],[57]) ).
thf(60,plain,
! [A: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i,G: $i] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ G ) ) ) )
<=> ( ( s @ A @ F )
= ( s @ A @ G ) ) )
& ! [F: $i] :
( ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) ) )
= ( s @ A @ F ) )
& ! [F: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) )
& ! [F: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
& ! [F: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
& ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
& ! [F: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) )
<=> ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
& ! [F: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) )
<=> ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
& ! [F: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) )
& ! [F: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) )
& ! [F: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) )
& ! [F: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) )
=> ( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ B @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) ) )
= ( s @ B @ E ) ) )
& ! [F: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) )
=> ( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ B @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) ) )
= ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) ) ) )
& ! [F: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) )
& ! [F: $i,G: $i] :
( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ B @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ G ) ) )
= ( s @ B @ F ) )
& ! [F: $i,G: $i,H: $i] :
( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) @ ( s @ B @ G ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ H ) ) )
= ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ H ) @ ( s @ A @ F ) ) ) )
& ! [F: $i,G: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ G ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) @ ( s @ A @ G ) ) ) ) ) )
& ! [F: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ B ) @ c_2Eoption_2ENONE_2E0 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
& ! [F: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2Eoption__CLAUSES) ).
thf(214,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i,G: $i] :
( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ G ) ) ) )
=> ( ( s @ A @ F )
= ( s @ A @ G ) ) )
& ( ( ( s @ A @ F )
= ( s @ A @ G ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ G ) ) ) ) ) )
& ! [F: $i] :
( ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) ) )
= ( s @ A @ F ) )
& ! [F: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) )
& ! [F: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
& ! [F: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
& ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
& ! [F: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) ) )
& ! [F: $i] :
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
& ( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) ) )
& ! [F: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) )
& ! [F: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) )
& ! [F: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) )
& ! [F: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) )
=> ( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ B @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) ) )
= ( s @ B @ E ) ) )
& ! [F: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) )
=> ( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ B @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) ) )
= ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) ) ) )
& ! [F: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) )
& ! [F: $i,G: $i] :
( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ B @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ G ) ) )
= ( s @ B @ F ) )
& ! [F: $i,G: $i,H: $i] :
( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) @ ( s @ B @ G ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ H ) ) )
= ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ H ) @ ( s @ A @ F ) ) ) )
& ! [F: $i,G: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ G ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) @ ( s @ A @ G ) ) ) ) ) )
& ! [F: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ B ) @ c_2Eoption_2ENONE_2E0 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
& ! [F: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(215,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ C ) ) ) )
=> ( ( s @ A @ B )
= ( s @ A @ C ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( s @ A @ B )
= ( s @ A @ C ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ C ) ) ) ) )
& ! [A: $i,B: $i] :
( ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) )
= ( s @ A @ B ) )
& ~ ? [A: $i,B: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) )
& ~ ? [A: $i,B: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
& ! [A: $i,B: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
& ! [A: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
& ! [A: $i,B: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
& ! [A: $i,B: $i] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ) )
& ! [A: $i,B: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
& ! [A: $i,B: $i] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ) )
& ! [A: $i,B: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) )
& ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ E ) ) ) )
=> ( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ E ) @ ( s @ B @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) ) )
= ( s @ B @ D ) ) )
& ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ E ) ) ) )
=> ( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ E ) @ ( s @ B @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) ) )
= ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ E ) ) ) ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) ) ) )
=> ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) ) )
& ! [A: $i,B: $i,C: $i,D: $i] :
( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ B @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) )
= ( s @ B @ C ) )
& ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) )
= ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ C ) ) ) )
& ! [A: $i,B: $i,C: $i,D: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ D ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ D ) ) ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ B ) @ c_2Eoption_2ENONE_2E0 ) )
& ! [A: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
& ! [A: $i,B: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ),
inference(miniscope,[status(thm)],[214]) ).
thf(218,plain,
! [B: $i,A: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ),
inference(cnf,[status(esa)],[215]) ).
thf(277,plain,
! [B: $i,A: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ),
inference(lifteq,[status(thm)],[218]) ).
thf(278,plain,
! [B: $i,A: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ),
inference(simp,[status(thm)],[277]) ).
thf(221,plain,
! [B: $i,A: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ),
inference(cnf,[status(esa)],[215]) ).
thf(245,plain,
! [B: $i,A: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ),
inference(lifteq,[status(thm)],[221]) ).
thf(246,plain,
! [B: $i,A: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ),
inference(simp,[status(thm)],[245]) ).
thf(8983,plain,
! [B: $i,A: $i] :
( ( ( tyop_2Eoption_2Eoption @ A )
!= ( tyop_2Eoption_2Eoption @ A ) )
| ( ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) )
!= c_2Eoption_2ENONE_2E0 ) ),
inference(simp,[status(thm)],[246]) ).
thf(9023,plain,
! [B: $i,A: $i] :
( ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) )
!= c_2Eoption_2ENONE_2E0 ),
inference(simp,[status(thm)],[8983]) ).
thf(9030,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_2Eoption_2ESOME_2E1 @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
!= c_2Eoption_2ENONE_2E0 )
| ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) )
!= ( s @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[278,9023]) ).
thf(9031,plain,
( ( c_2Eoption_2ESOME_2E1 @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
!= c_2Eoption_2ENONE_2E0 ),
inference(pattern_uni,[status(thm)],[9030:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( tyop_2Emin_2Ebool )),bind(D,$thf( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ J ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ J @ K ) ) ) ))]]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( s @ A @ B )
= ( s @ A @ C ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) ).
thf(361,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( s @ A @ B )
= ( s @ A @ C ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ A @ C ) ) ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ A @ C ) ) ) )
=> ( ( s @ A @ B )
= ( s @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(8994,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ C ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ C ) @ c_2Eoption_2ENONE_2E0 ) )
| ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) )
!= ( s @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[278,246]) ).
thf(8995,plain,
( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Emin_2Ebool ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Emin_2Ebool ) @ c_2Eoption_2ENONE_2E0 ) ),
inference(pattern_uni,[status(thm)],[8994:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( tyop_2Emin_2Ebool )),bind(D,$thf( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ J ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ J @ K ) ) ) ))]]) ).
thf(39,axiom,
! [A: $i] :
( ( ( ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 )
= ( s @ tyop_2Emin_2Ebool @ A ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ( ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ( ( ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 )
= ( s @ tyop_2Emin_2Ebool @ A ) )
<=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ( ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
<=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
thf(311,plain,
! [A: $i] :
( ( ( ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 )
= ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 )
= ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ( ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
& ( ( ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 )
= ( s @ tyop_2Emin_2Ebool @ A ) )
=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 )
= ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ( ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b) ).
thf(166,plain,
! [A: $i,B: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( s @ A @ B )
= ( s @ A @ B ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EREFL__CLAUSE) ).
thf(67,plain,
p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,axiom,
~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).
thf(130,plain,
~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(131,plain,
~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ),
inference(polarity_switch,[status(thm)],[130]) ).
thf(368,plain,
( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
!= ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) ),
inference(paramod_ordered,[status(thm)],[67,131]) ).
thf(369,plain,
( ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 )
!= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ),
inference(simp,[status(thm)],[368]) ).
thf(3390,plain,
! [B: $i,A: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) )
!= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ),
inference(paramod_ordered,[status(thm)],[278,369]) ).
thf(3703,plain,
! [B: $i,A: $i] :
( ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
| ( ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) )
!= c_2Ebool_2EF_2E0 ) ),
inference(simp,[status(thm)],[3390]) ).
thf(4319,plain,
! [B: $i,A: $i] :
( ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) )
!= c_2Ebool_2EF_2E0 ),
inference(simp,[status(thm)],[3703]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
& ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
& ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
& ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ C ) ) ) @ ( s @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Equotient__option_2EOPTION__REL__def) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
& ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
& ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
& ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ C ) ) ) @ ( s @ A @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(48,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
& ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
& ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
& ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ C ) ) ) @ ( s @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(40,axiom,
p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Etruth) ).
thf(336,plain,
p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
<=> ? [C: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Equant_2E_3F) ).
thf(52,plain,
! [A: $i,B: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
=> ? [C: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) )
& ( ? [C: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(53,plain,
( ! [A: $i,B: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
=> ? [C: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) )
& ! [A: $i,B: $i] :
( ? [C: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ),
inference(miniscope,[status(thm)],[52]) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ),
inference(cnf,[status(esa)],[53]) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(8933,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ C ) ) ) )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
!= ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ B @ D ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[60,56]) ).
thf(8934,plain,
! [A: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[8933:[bind(A,$thf( A )),bind(B,$thf( tyop_2Emin_2Ebool )),bind(C,$thf( c_2Ebool_2E_7E_2E0 )),bind(D,$thf( A ))]]) ).
thf(9098,plain,
! [A: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) ) ) )
!= ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[8934]) ).
thf(9110,plain,
p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) ) ),
inference(pattern_uni,[status(thm)],[9098:[bind(A,$thf( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) ))]]) ).
thf(9871,plain,
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) ) ) )
!= ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) ),
inference(paramod_ordered,[status(thm)],[9110,131]) ).
thf(9876,plain,
( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) ) )
!= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ),
inference(simp,[status(thm)],[9871]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
<=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_2F_5C) ).
thf(138,plain,
! [A: $i,B: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
& ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_2F_5C_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) ).
thf(347,plain,
! [A: $i,B: $i] :
( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_2F_5C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(49,plain,
~ ( ! [A: $i,B: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
& ! [A: $i,B: $i,C: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
& ! [A: $i,B: $i,C: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
& ! [A: $i,B: $i,C: $i,D: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ C ) ) ) @ ( s @ A @ B ) ) ) ) ),
inference(miniscope,[status(thm)],[48]) ).
thf(50,plain,
( ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) ) )
!= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) ) )
!= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
| ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) )
!= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
| ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) ) )
!= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) ) ) ),
inference(cnf,[status(esa)],[49]) ).
thf(51,plain,
( ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) ) )
!= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) ) )
!= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
| ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) )
!= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
| ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) ) )
!= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) ) ) ),
inference(lifteq,[status(thm)],[50]) ).
thf(388,plain,
( ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Ebool_2ET_2E0 )
| ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) ) )
!= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) )
!= c_2Ebool_2EF_2E0 )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
!= ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(666,plain,
( ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Ebool_2ET_2E0 )
| ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) ) )
!= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) )
!= c_2Ebool_2EF_2E0 )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
!= ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) ) ),
inference(simp,[status(thm)],[388]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
<=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D_3D_3E) ).
thf(340,plain,
! [A: $i,B: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
& ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_3D_3E_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(45,axiom,
p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(357,plain,
p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(5288,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ C ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) ) )
!= c_2Ebool_2EF_2E0 )
| ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) )
!= ( s @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[278,4319]) ).
thf(5289,plain,
( ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Emin_2Ebool ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) ) )
!= c_2Ebool_2EF_2E0 ),
inference(pattern_uni,[status(thm)],[5288:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( tyop_2Emin_2Ebool )),bind(D,$thf( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ J ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ J @ K ) ) ) ))]]) ).
thf(32,axiom,
( ! [A: $i] :
( ~ ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) )
& ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__CLAUSES) ).
thf(284,plain,
( ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
& ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
=> ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Eboolext) ).
thf(179,plain,
! [A: $i,B: $i] :
( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ B ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
=> ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ B ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b) ).
thf(211,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2EOPTION__MAP_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ B ) ) ) @ c_2Eoption_2EOPTION__MAP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(15,axiom,
! [A: $i] :
( ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Ebool__cases__ax) ).
thf(121,plain,
! [A: $i] :
( ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(59,plain,
! [A: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(61,plain,
! [A: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
| ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A @ B ) @ ( s @ A @ C ) ) ) )
<=> ( ( s @ A @ B )
= ( s @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D) ).
thf(293,plain,
! [A: $i,B: $i,C: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A @ B ) @ ( s @ A @ C ) ) ) )
=> ( ( s @ A @ B )
= ( s @ A @ C ) ) )
& ( ( ( s @ A @ B )
= ( s @ A @ C ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A @ B ) @ ( s @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eoption_2EOPTREL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27a) ).
thf(132,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eoption_2EOPTREL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(223,plain,
! [A: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ),
inference(cnf,[status(esa)],[215]) ).
thf(271,plain,
! [A: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ),
inference(lifteq,[status(thm)],[223]) ).
thf(272,plain,
! [A: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ),
inference(simp,[status(thm)],[271]) ).
thf(5291,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
!= c_2Ebool_2EF_2E0 )
| ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
!= ( s @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[272,4319]) ).
thf(5292,plain,
! [A: $i] :
( ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
!= c_2Ebool_2EF_2E0 ),
inference(pattern_uni,[status(thm)],[5291:[bind(A,$thf( I )),bind(B,$thf( tyop_2Eoption_2Eoption @ I )),bind(C,$thf( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ I ) ) @ c_2Eoption_2ENONE_2E0 ) ))]]) ).
thf(5296,plain,
! [A: $i] :
( ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
!= c_2Ebool_2EF_2E0 ),
inference(simp,[status(thm)],[5292]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
=> ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ B ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
=> ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__ANTISYM__AX) ).
thf(89,plain,
! [A: $i,B: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
=> ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ B ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
=> ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(382,plain,
( ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Ebool_2ET_2E0 )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Ebool_2EF_2E0 )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) )
!= c_2Ebool_2EF_2E0 )
| ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) ) )
!= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(660,plain,
( ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Ebool_2ET_2E0 )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Ebool_2EF_2E0 )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) )
!= c_2Ebool_2EF_2E0 )
| ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) ) )
!= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) ) ) ),
inference(simp,[status(thm)],[382]) ).
thf(226,plain,
! [A: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ),
inference(cnf,[status(esa)],[215]) ).
thf(273,plain,
! [A: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ),
inference(lifteq,[status(thm)],[226]) ).
thf(274,plain,
! [A: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ),
inference(simp,[status(thm)],[273]) ).
thf(8991,plain,
! [C: $i,B: $i,A: $i] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ B ) @ c_2Eoption_2ENONE_2E0 ) )
| ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
!= ( s @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[274,246]) ).
thf(8992,plain,
( ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Emin_2Ebool ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Emin_2Ebool ) @ c_2Eoption_2ENONE_2E0 ) ),
inference(pattern_uni,[status(thm)],[8991:[bind(A,$thf( G )),bind(B,$thf( tyop_2Emin_2Ebool )),bind(C,$thf( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ G ) @ c_2Eoption_2ENONE_2E0 ) ))]]) ).
thf(312,plain,
( ! [A: $i] :
( ( ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 )
= ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ! [A: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 )
= ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ! [A: $i] :
( ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ! [A: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
& ! [A: $i] :
( ( ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 )
= ( s @ tyop_2Emin_2Ebool @ A ) )
=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ! [A: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 )
= ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ! [A: $i] :
( ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ! [A: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( ( s @ tyop_2Emin_2Ebool @ A )
= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) ) ),
inference(miniscope,[status(thm)],[311]) ).
thf(313,plain,
! [A: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 )
= ( s @ tyop_2Emin_2Ebool @ A ) ) ),
inference(cnf,[status(esa)],[312]) ).
thf(327,plain,
! [A: $i] :
( ( ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 )
= ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ),
inference(lifteq,[status(thm)],[313]) ).
thf(328,plain,
! [A: $i] :
( ( ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 )
= ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ),
inference(simp,[status(thm)],[327]) ).
thf(8434,plain,
! [A: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Ebool_2ET_2E0 )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) )
!= c_2Ebool_2EF_2E0 )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
!= ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) )
| ( ( s @ tyop_2Emin_2Ebool @ A )
!= ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[328,666]) ).
thf(8435,plain,
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Ebool_2ET_2E0 )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) )
!= c_2Ebool_2EF_2E0 )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
!= ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) ) ),
inference(pattern_uni,[status(thm)],[8434:[bind(A,$thf( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) ))]]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ C ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) ) @ ( s @ A @ F ) ) )
= ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ A @ F ) ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ F ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Es__thm) ).
thf(188,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ C ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) ) @ ( s @ A @ F ) ) )
= ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ A @ F ) ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
<=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_5C_2F) ).
thf(169,plain,
! [A: $i,B: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
& ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_5C_2F_2E2 @ ( s @ tyop_2Emin_2Ebool @ A ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) )
= ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ E ) ) ) )
=> ( ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C )
= ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Eeq__ext) ).
thf(124,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) )
= ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ E ) ) ) )
=> ( ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C )
= ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ D ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29) ).
thf(77,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ D ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ A ) ) @ combin_k_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) )
= ( s @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Ek__thm) ).
thf(176,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ A ) ) @ combin_k_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) )
= ( s @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E ) ) ) )
<=> ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E )
= ( s @ ( tyop_2Eoption_2Eoption @ B ) @ c_2Eoption_2ENONE_2E0 ) ) )
| ? [F: $i,G: $i] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E )
= ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ B @ G ) ) ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ B @ G ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2EOPTREL__def) ).
thf(191,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E ) ) ) )
=> ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E )
= ( s @ ( tyop_2Eoption_2Eoption @ B ) @ c_2Eoption_2ENONE_2E0 ) ) )
| ? [F: $i,G: $i] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E )
= ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ B @ G ) ) ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ B @ G ) ) ) ) ) ) )
& ( ( ( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E )
= ( s @ ( tyop_2Eoption_2Eoption @ B ) @ c_2Eoption_2ENONE_2E0 ) ) )
| ? [F: $i,G: $i] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) )
& ( ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E )
= ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ B @ G ) ) ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ B @ G ) ) ) ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) ).
thf(71,plain,
! [A: $i,B: $i] :
( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_3D_3E_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(22,axiom,
! [A: $i] :
( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
& ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
& ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EOR__CLAUSES) ).
thf(144,plain,
! [A: $i] :
( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
& ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) ) )
& ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
& ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ B ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2EOPTION__JOIN_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2EOPTION__JOIN_2E1_2Emono_2EA_27a) ).
thf(86,plain,
! [A: $i,B: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ B ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2EOPTION__JOIN_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(10000,plain,
( ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
| ( ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) )
!= c_2Ebool_2EF_2E0 ) ),
inference(simp,[status(thm)],[9876]) ).
thf(10037,plain,
( ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_7E_2E0 ) )
!= c_2Ebool_2EF_2E0 ),
inference(simp,[status(thm)],[10000]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) ).
thf(208,plain,
! [A: $i,B: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(13,axiom,
! [A: $i] :
( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) )
& ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) )
& ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EAND__CLAUSES) ).
thf(98,plain,
! [A: $i] :
( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
& ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) ) ) )
& ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
& ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
& ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ c_2Eoption_2EIS__SOME_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27a) ).
thf(303,plain,
! [A: $i,B: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ c_2Eoption_2EIS__SOME_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(5285,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ B ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) ) )
!= c_2Ebool_2EF_2E0 )
| ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
!= ( s @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[274,4319]) ).
thf(5286,plain,
( ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ tyop_2Emin_2Ebool ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) ) ) )
!= c_2Ebool_2EF_2E0 ),
inference(pattern_uni,[status(thm)],[5285:[bind(A,$thf( G )),bind(B,$thf( tyop_2Emin_2Ebool )),bind(C,$thf( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ G ) @ c_2Eoption_2ENONE_2E0 ) ))]]) ).
thf(390,plain,
( ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Ebool_2ET_2E0 )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Ebool_2EF_2E0 )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) )
!= c_2Ebool_2EF_2E0 )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
!= ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(668,plain,
( ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Ebool_2ET_2E0 )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Ebool_2EF_2E0 )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) )
!= c_2Ebool_2EF_2E0 )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
!= ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) ) ),
inference(simp,[status(thm)],[390]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
<=> ! [C: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Equant_2E_21) ).
thf(306,plain,
! [A: $i,B: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
=> ! [C: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) )
& ( ! [C: $i] : ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29) ).
thf(135,plain,
! [A: $i,B: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
<=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) ).
thf(80,plain,
! [A: $i,B: $i] :
( ( ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) )
& ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2E_5C_2F_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) )
=> ( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ c_2Eoption_2EIS__NONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2EIS__NONE_2E1_2Emono_2EA_27a) ).
thf(127,plain,
! [A: $i,B: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ c_2Eoption_2EIS__NONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(9028,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_2Eoption_2ESOME_2E1 @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
!= c_2Eoption_2ENONE_2E0 )
| ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) )
!= ( s @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[274,9023]) ).
thf(9029,plain,
( ( c_2Eoption_2ESOME_2E1 @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
!= c_2Eoption_2ENONE_2E0 ),
inference(pattern_uni,[status(thm)],[9028:[bind(A,$thf( G )),bind(B,$thf( tyop_2Emin_2Ebool )),bind(C,$thf( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ G ) @ c_2Eoption_2ENONE_2E0 ) ))]]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
| ( p @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ ( sk13 @ B @ A ) ) ) ) ) ),
inference(cnf,[status(esa)],[53]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) )
= ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ A ) @ c_2Eoption_2ETHE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a) ).
thf(290,plain,
! [A: $i,B: $i] :
( ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) )
= ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ A ) @ c_2Eoption_2ETHE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(389,plain,
( ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) ) )
!= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Ebool_2EF_2E0 )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) )
!= c_2Ebool_2EF_2E0 )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
!= ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(667,plain,
( ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) ) )
!= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2ET_2E0 ) )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Ebool_2EF_2E0 )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) )
!= c_2Ebool_2EF_2E0 )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
!= ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) ) ),
inference(simp,[status(thm)],[389]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ combin_i_2E0 ) @ ( s @ A @ B ) ) )
= ( s @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Ei__thm) ).
thf(287,plain,
! [A: $i,B: $i] :
( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ combin_i_2E0 ) @ ( s @ A @ B ) ) )
= ( s @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) ).
thf(300,plain,
! [A: $i,B: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(9032,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Eoption_2ENONE_2E0 )
| ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ENONE_2E0 ) ) )
!= ( s @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[272,9023]) ).
thf(9033,plain,
! [A: $i] :
( ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Eoption_2ENONE_2E0 ),
inference(pattern_uni,[status(thm)],[9032:[bind(A,$thf( I )),bind(B,$thf( tyop_2Eoption_2Eoption @ I )),bind(C,$thf( c_2Eoption_2EOPTION__JOIN_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Eoption_2Eoption @ I ) ) @ c_2Eoption_2ENONE_2E0 ) ))]]) ).
thf(9034,plain,
! [A: $i] :
( ( c_2Eoption_2ESOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Eoption_2ENONE_2E0 ),
inference(simp,[status(thm)],[9033]) ).
thf(372,plain,
( ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
| ( c_2Ebool_2EF_2E0 != c_2Ebool_2ET_2E0 ) ),
inference(simp,[status(thm)],[369]) ).
thf(373,plain,
c_2Ebool_2EF_2E0 != c_2Ebool_2ET_2E0,
inference(simp,[status(thm)],[372]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eoption_2EOPTREL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27b) ).
thf(358,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) @ ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Eoption_2EOPTREL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ D ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ B ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(386,plain,
( ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Ebool_2ET_2E0 )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Ebool_2EF_2E0 )
| ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) )
!= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
| ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
!= ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(664,plain,
( ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Ebool_2ET_2E0 )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Ebool_2EF_2E0 )
| ( ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) )
!= ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
!= ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) ) ),
inference(simp,[status(thm)],[386]) ).
thf(5440,plain,
! [A: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Ebool_2ET_2E0 )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Ebool_2EF_2E0 )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
!= ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) )
| ( ( s @ tyop_2Emin_2Ebool @ A )
!= ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[328,664]) ).
thf(5441,plain,
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ) ) )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk1 @ ( tyop_2Emin_2Efun @ sk1 @ tyop_2Emin_2Ebool ) ) @ sk2 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk1 ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Ebool_2ET_2E0 )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk3 @ ( tyop_2Emin_2Efun @ sk3 @ tyop_2Emin_2Ebool ) ) @ sk5 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk3 @ sk4 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk3 ) @ c_2Eoption_2ENONE_2E0 ) )
!= c_2Ebool_2EF_2E0 )
| ( ( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk9 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk9 @ sk10 ) ) ) )
!= ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ sk9 @ ( tyop_2Emin_2Efun @ sk9 @ tyop_2Emin_2Ebool ) ) @ sk12 ) @ ( s @ sk9 @ sk11 ) ) ) @ ( s @ sk9 @ sk10 ) ) ) ),
inference(pattern_uni,[status(thm)],[5440:[bind(A,$thf( c_2Eoption_2EOPTREL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ sk6 @ ( tyop_2Emin_2Efun @ sk6 @ tyop_2Emin_2Ebool ) ) @ sk8 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ c_2Eoption_2ENONE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ sk6 ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ sk6 @ sk7 ) ) ) ))]]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) @ ( s @ B @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) )
= ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ B ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) ) ) @ ( s @ B @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b) ).
thf(68,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( s @ B @ ( c_2Eoption_2Eoption__CASE_2E3 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) @ ( s @ B @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) )
= ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ B ) ) ) @ c_2Eoption_2Eoption__CASE_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) ) ) @ ( s @ B @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
<=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_7E) ).
thf(62,plain,
! [A: $i] :
( ( ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
=> ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) )
& ( ~ ( p @ ( s @ tyop_2Emin_2Ebool @ A ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_7E_2E1 @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(41,axiom,
! [A: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EFALSITY) ).
thf(337,plain,
! [A: $i] :
( ( p @ ( s @ tyop_2Emin_2Ebool @ c_2Ebool_2EF_2E0 ) )
=> ( p @ ( s @ tyop_2Emin_2Ebool @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a) ).
thf(354,plain,
! [A: $i,B: $i] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(27839,plain,
$false,
inference(cvc4,[status(thm)],[120,60,9031,361,8995,311,166,4319,48,336,9876,138,347,666,56,340,52,357,5289,284,57,179,211,121,61,293,132,5296,89,660,8992,8435,188,169,328,124,77,176,191,71,144,86,274,10037,208,98,303,5286,668,130,278,306,135,80,67,127,9029,55,290,246,667,272,214,287,300,9034,51,373,358,5441,664,9023,9110,131,68,62,369,337,354]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP011+1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n022.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 14:21:09 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.97/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.46/1.04 % [INFO] Parsing done (169ms).
% 1.46/1.05 % [INFO] Running in sequential loop mode.
% 1.96/1.24 % [INFO] eprover registered as external prover.
% 1.96/1.24 % [INFO] cvc4 registered as external prover.
% 1.96/1.25 % [INFO] Scanning for conjecture ...
% 2.16/1.34 % [INFO] Found a conjecture and 45 axioms. Running axiom selection ...
% 2.35/1.40 % [INFO] Axiom selection finished. Selected 45 axioms (removed 0 axioms).
% 2.71/1.49 % [INFO] Problem is first-order (TPTP FOF).
% 2.80/1.50 % [INFO] Type checking passed.
% 2.80/1.50 % [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 ...
% 83.54/28.05 % External prover 'cvc4' found a proof!
% 83.54/28.05 % [INFO] Killing All external provers ...
% 83.54/28.05 % Time passed: 27505ms (effective reasoning time: 26997ms)
% 83.54/28.05 % 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)>
% 83.54/28.05 % Axioms used in derivation (45): arityeq1_2Ec_2Eoption_2EIS__NONE_2E1_2Emono_2EA_27a, thm_2Ebool_2ENOT__CLAUSES, arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a, reserved_2Eho_2Enotfalse, thm_2Ebool_2EREFL__CLAUSE, arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b, thm_2Eoption_2Eoption__CLAUSES, arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27b, arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29, arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29, reserved_2Eho_2Ebool__cases__ax, thm_2Ebool_2EOR__CLAUSES, arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a, reserved_2Elogic_2E_5C_2F, reserved_2Equant_2E_21, thm_2Ebool_2EEQ__CLAUSES, thm_2Ebool_2EIMP__ANTISYM__AX, arityeq2_2Ec_2Ebool_2E_2F_5C_2E2, arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2, arityeq1_2Ec_2Eoption_2EOPTION__JOIN_2E1_2Emono_2EA_27a, arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a, arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b, reserved_2Equant_2E_3F, thm_2Eoption_2EOPTREL__def, reserved_2Eho_2Etruth, reserved_2Elogic_2E_2F_5C, reserved_2Eho_2Ei__thm, reserved_2Eho_2Es__thm, thm_2Ebool_2EFALSITY, reserved_2Elogic_2E_3D, arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, thm_2Ebool_2ETRUTH, reserved_2Eho_2Ek__thm, arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a, reserved_2Elogic_2E_7E, reserved_2Eho_2Eboolext, arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27a, reserved_2Eho_2Eeq__ext, reserved_2Elogic_2E_3D_3D_3E, arityeq1_2Ec_2Ebool_2E_7E_2E1, arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, thm_2Ebool_2EEXISTS__SIMP, arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27a, arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b, thm_2Ebool_2EAND__CLAUSES
% 83.54/28.05 % No. of inferences in proof: 172
% 83.54/28.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 27505 ms resp. 26997 ms w/o parsing
% 83.90/28.16 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 83.90/28.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------