TSTP Solution File: ITP011_1 by Leo-III---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP011_1 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:21:32 EDT 2024
% Result : Theorem 56.01s 23.31s
% Output : Refutation 56.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 122
% Syntax : Number of formulae : 252 ( 86 unt; 68 typ; 0 def)
% Number of atoms : 620 ( 314 equ; 0 cnn)
% Maximal formula atoms : 33 ( 3 avg)
% Number of connectives : 6557 ( 166 ~; 121 |; 157 &;5969 @)
% ( 36 <=>; 108 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 62 usr; 36 con; 0-3 aty)
% Number of variables : 429 ( 0 ^ 415 !; 14 ?; 429 :)
% Comments :
%------------------------------------------------------------------------------
thf(u_type,type,
u: $tType ).
thf(d_type,type,
d: $tType ).
thf(du_type,type,
du: $tType ).
thf(mono_2Etyop_2Emin_2Ebool_type,type,
mono_2Etyop_2Emin_2Ebool: $tType ).
thf(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_type,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: $tType ).
thf(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_type,type,
mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: $tType ).
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: d ).
thf(tyop_2Emin_2Efun_type,type,
tyop_2Emin_2Efun: d > d > d ).
thf(tyop_2Eoption_2Eoption_type,type,
tyop_2Eoption_2Eoption: d > d ).
thf(s_type,type,
s: d > u > du ).
thf(app_2E2_type,type,
app_2E2: du > du > u ).
thf(p_type,type,
p: mono_2Etyop_2Emin_2Ebool > $o ).
thf(combin_i_2E0_type,type,
combin_i_2E0: u ).
thf(combin_k_2E0_type,type,
combin_k_2E0: u ).
thf(combin_s_2E0_type,type,
combin_s_2E0: u ).
thf(c_2Ebool_2E_21_2E0_type,type,
c_2Ebool_2E_21_2E0: u ).
thf(c_2Ebool_2E_21_2E1_type,type,
c_2Ebool_2E_21_2E1: du > u ).
thf(c_2Emin_2E_3D_2E0_type,type,
c_2Emin_2E_3D_2E0: u ).
thf(c_2Emin_2E_3D_2E2_type,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(c_2Ebool_2E_3F_2E0_type,type,
c_2Ebool_2E_3F_2E0: u ).
thf(c_2Ebool_2E_3F_2E1_type,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(c_2Eoption_2EIS__NONE_2E0_type,type,
c_2Eoption_2EIS__NONE_2E0: u ).
thf(c_2Eoption_2EIS__NONE_2E1_type,type,
c_2Eoption_2EIS__NONE_2E1: du > u ).
thf(c_2Eoption_2EIS__SOME_2E0_type,type,
c_2Eoption_2EIS__SOME_2E0: u ).
thf(c_2Eoption_2EIS__SOME_2E1_type,type,
c_2Eoption_2EIS__SOME_2E1: du > u ).
thf(c_2Eoption_2ENONE_2E0_type,type,
c_2Eoption_2ENONE_2E0: u ).
thf(c_2Eoption_2EOPTION__JOIN_2E0_type,type,
c_2Eoption_2EOPTION__JOIN_2E0: u ).
thf(c_2Eoption_2EOPTION__JOIN_2E1_type,type,
c_2Eoption_2EOPTION__JOIN_2E1: du > u ).
thf(c_2Eoption_2EOPTION__MAP_2E0_type,type,
c_2Eoption_2EOPTION__MAP_2E0: u ).
thf(c_2Eoption_2EOPTION__MAP_2E2_type,type,
c_2Eoption_2EOPTION__MAP_2E2: du > du > u ).
thf(c_2Eoption_2EOPTREL_2E0_type,type,
c_2Eoption_2EOPTREL_2E0: u ).
thf(c_2Eoption_2EOPTREL_2E3_type,type,
c_2Eoption_2EOPTREL_2E3: du > du > du > u ).
thf(c_2Eoption_2ESOME_2E0_type,type,
c_2Eoption_2ESOME_2E0: u ).
thf(c_2Eoption_2ESOME_2E1_type,type,
c_2Eoption_2ESOME_2E1: du > u ).
thf(c_2Eoption_2ETHE_2E0_type,type,
c_2Eoption_2ETHE_2E0: u ).
thf(c_2Eoption_2ETHE_2E1_type,type,
c_2Eoption_2ETHE_2E1: du > u ).
thf(c_2Eoption_2Eoption__CASE_2E0_type,type,
c_2Eoption_2Eoption__CASE_2E0: u ).
thf(c_2Eoption_2Eoption__CASE_2E3_type,type,
c_2Eoption_2Eoption__CASE_2E3: du > du > du > u ).
thf(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool_type,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 > mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).
thf(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_type,type,
mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 > mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
thf(mono_2Ec_2Ebool_2E_2F_5C_2E0_type,type,
mono_2Ec_2Ebool_2E_2F_5C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
thf(mono_2Ec_2Ebool_2E_2F_5C_2E2_type,type,
mono_2Ec_2Ebool_2E_2F_5C_2E2: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).
thf(mono_2Ec_2Emin_2E_3D_3D_3E_2E0_type,type,
mono_2Ec_2Emin_2E_3D_3D_3E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
thf(mono_2Ec_2Emin_2E_3D_3D_3E_2E2_type,type,
mono_2Ec_2Emin_2E_3D_3D_3E_2E2: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).
thf(mono_2Ec_2Ebool_2EF_2E0_type,type,
mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).
thf(mono_2Ec_2Ebool_2ET_2E0_type,type,
mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).
thf(mono_2Ec_2Ebool_2E_5C_2F_2E0_type,type,
mono_2Ec_2Ebool_2E_5C_2F_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
thf(mono_2Ec_2Ebool_2E_5C_2F_2E2_type,type,
mono_2Ec_2Ebool_2E_5C_2F_2E2: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).
thf(mono_2Ec_2Ebool_2E_7E_2E0_type,type,
mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
thf(mono_2Ec_2Ebool_2E_7E_2E1_type,type,
mono_2Ec_2Ebool_2E_7E_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).
thf(i_mono_2Etyop_2Emin_2Ebool_type,type,
i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_type,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_type,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 > u ).
thf(j_mono_2Etyop_2Emin_2Ebool_type,type,
j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_type,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_type,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).
thf(sk1_type,type,
sk1: d ).
thf(sk2_type,type,
sk2: u ).
thf(sk3_type,type,
sk3: d ).
thf(sk4_type,type,
sk4: u ).
thf(sk5_type,type,
sk5: u ).
thf(sk6_type,type,
sk6: d ).
thf(sk7_type,type,
sk7: u ).
thf(sk8_type,type,
sk8: u ).
thf(sk9_type,type,
sk9: d ).
thf(sk10_type,type,
sk10: u ).
thf(sk11_type,type,
sk11: u ).
thf(sk12_type,type,
sk12: u ).
thf(1,conjecture,
! [A: d,B: u,C: u,D: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
= mono_2Ec_2Ebool_2ET_2E0 )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
= mono_2Ec_2Ebool_2EF_2E0 )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
= mono_2Ec_2Ebool_2EF_2E0 )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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/sandbox2/benchmark/theBenchmark.p',thm_2Equotient__option_2EOPTION__REL__def) ).
thf(2,negated_conjecture,
~ ! [A: d,B: u,C: u,D: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
= mono_2Ec_2Ebool_2ET_2E0 )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
= mono_2Ec_2Ebool_2EF_2E0 )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
= mono_2Ec_2Ebool_2EF_2E0 )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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(56,plain,
~ ! [A: d,B: u,C: u,D: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
= mono_2Ec_2Ebool_2ET_2E0 )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
= mono_2Ec_2Ebool_2EF_2E0 )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
= mono_2Ec_2Ebool_2EF_2E0 )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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(5,axiom,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( p @ ( mono_2Ec_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) )
<=> ( ( p @ A )
=> ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D_3D_3E) ).
thf(74,plain,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( p @ ( mono_2Ec_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) )
=> ( ( p @ A )
=> ( p @ B ) ) )
& ( ( ( p @ A )
=> ( p @ B ) )
=> ( p @ ( mono_2Ec_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(75,plain,
( ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( p @ ( mono_2Ec_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) )
=> ( ( p @ A )
=> ( p @ B ) ) )
& ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ B ) )
=> ( p @ ( mono_2Ec_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) ) ) ),
inference(miniscope,[status(thm)],[74]) ).
thf(78,plain,
! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
( ~ ( p @ ( mono_2Ec_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) )
| ~ ( p @ A )
| ( p @ B ) ),
inference(cnf,[status(esa)],[75]) ).
thf(51,axiom,
! [A: u] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Ebool) ).
thf(386,plain,
! [A: u] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(387,plain,
! [A: u] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ A ) ),
inference(cnf,[status(esa)],[386]) ).
thf(388,plain,
! [A: u] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ A ) ),
inference(lifteq,[status(thm)],[387]) ).
thf(26,axiom,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ A ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Ebool) ).
thf(246,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ A ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(247,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ A ) ) )
= A ),
inference(cnf,[status(esa)],[246]) ).
thf(248,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ A ) ) )
= A ),
inference(lifteq,[status(thm)],[247]) ).
thf(57,plain,
~ ( ! [A: d,B: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
= mono_2Ec_2Ebool_2ET_2E0 )
& ! [A: d,B: u,C: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
= mono_2Ec_2Ebool_2EF_2E0 )
& ! [A: d,B: u,C: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
= mono_2Ec_2Ebool_2EF_2E0 )
& ! [A: d,B: u,C: u,D: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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)],[56]) ).
thf(58,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
!= mono_2Ec_2Ebool_2ET_2E0 )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
!= mono_2Ec_2Ebool_2EF_2E0 )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
!= mono_2Ec_2Ebool_2EF_2E0 )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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)],[57]) ).
thf(59,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
!= mono_2Ec_2Ebool_2ET_2E0 )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
!= mono_2Ec_2Ebool_2EF_2E0 )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
!= mono_2Ec_2Ebool_2EF_2E0 )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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)],[58]) ).
thf(408,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
!= mono_2Ec_2Ebool_2ET_2E0 )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
!= mono_2Ec_2Ebool_2EF_2E0 )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
!= mono_2Ec_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)],[59]) ).
thf(426,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A != mono_2Ec_2Ebool_2ET_2E0 )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
!= mono_2Ec_2Ebool_2EF_2E0 )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
!= mono_2Ec_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 ) ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ A ) ) )
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[248,408]) ).
thf(452,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
!= mono_2Ec_2Ebool_2EF_2E0 )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
!= mono_2Ec_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 ) ) )
| ( ( 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 @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET_2E0 ) ) ) ),
inference(simp,[status(thm)],[426]) ).
thf(460,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
!= mono_2Ec_2Ebool_2EF_2E0 )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
!= mono_2Ec_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 @ ( 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 @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET_2E0 ) ) ) ),
inference(simp,[status(thm)],[452]) ).
thf(496,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A != mono_2Ec_2Ebool_2EF_2E0 )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
!= mono_2Ec_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 @ ( 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 @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET_2E0 ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ A ) ) )
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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)],[248,460]) ).
thf(502,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
!= mono_2Ec_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 ) ) )
| ( 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 ) )
!= ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_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 @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) ) ) ),
inference(simp,[status(thm)],[496]) ).
thf(513,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
!= mono_2Ec_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 ) ) )
| ( ( 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 ) )
!= ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_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 @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) ) ) ),
inference(simp,[status(thm)],[502]) ).
thf(695,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A != mono_2Ec_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 ) ) )
| ( ( 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 ) )
!= ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_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 @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ A ) ) )
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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)],[248,513]) ).
thf(702,plain,
( ( ( 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 ) ) )
| ( ( 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 ) )
!= ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_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 ) )
!= ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_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 @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) ) ) ),
inference(simp,[status(thm)],[695]) ).
thf(709,plain,
( ( ( 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 ) ) )
| ( ( 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 ) )
!= ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_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 ) )
!= ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_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 @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) ) ) ),
inference(simp,[status(thm)],[702]) ).
thf(983,plain,
( ( ( 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 ) ) )
| ( ( 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 ) )
!= ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_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 ) )
!= ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_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 ) ) ) )
!= ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) ) ),
inference(simp,[status(thm)],[709]) ).
thf(984,plain,
( ( ( 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 ) ) )
| ( ( 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 ) )
!= ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_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 ) )
!= ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_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 ) ) ) )
!= ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) ) ),
inference(simp,[status(thm)],[983]) ).
thf(16,axiom,
! [A: d,B: d,C: u,D: u,E: u] :
( ! [F: u,G: u] :
( ( ( 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: u] :
( ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) ) )
= ( s @ A @ F ) )
& ! [F: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) )
& ! [F: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
& ! [F: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) ) ) )
= mono_2Ec_2Ebool_2ET_2E0 )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
= mono_2Ec_2Ebool_2EF_2E0 )
& ! [F: u] :
( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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: u] :
( ~ ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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: u] :
( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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: u] :
( ( 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: u] :
( ( 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: u] :
( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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: u] :
( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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: u] :
( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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: u,G: u] :
( ( 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: u,G: u,H: u] :
( ( 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: u,G: u] :
( ( 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: u] :
( ( 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: u] :
( ( 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/sandbox2/benchmark/theBenchmark.p',thm_2Eoption_2Eoption__CLAUSES) ).
thf(134,plain,
! [A: d,B: d,C: u,D: u,E: u] :
( ! [F: u,G: u] :
( ( ( ( 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: u] :
( ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) ) )
= ( s @ A @ F ) )
& ! [F: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 )
!= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) )
& ! [F: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) )
!= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
& ! [F: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ F ) ) ) ) ) )
= mono_2Ec_2Ebool_2ET_2E0 )
& ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
= mono_2Ec_2Ebool_2EF_2E0 )
& ! [F: u] :
( ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) ) ) )
& ! [F: u] :
( ( ~ ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ F ) ) ) ) ) ) )
& ! [F: u] :
( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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: u] :
( ( 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: u] :
( ( 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: u] :
( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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: u] :
( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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: u] :
( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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: u,G: u] :
( ( 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: u,G: u,H: u] :
( ( 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: u,G: u] :
( ( 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: u] :
( ( 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: u] :
( ( 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)],[16]) ).
thf(135,plain,
( ! [A: d,B: u,C: u] :
( ( ( 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: d,B: u,C: u] :
( ( ( 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: d,B: u] :
( ( s @ A @ ( c_2Eoption_2ETHE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) )
= ( s @ A @ B ) )
& ~ ? [A: d,B: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) )
& ~ ? [A: d,B: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
& ! [A: d,B: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) ) )
= mono_2Ec_2Ebool_2ET_2E0 )
& ! [A: d] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
= mono_2Ec_2Ebool_2EF_2E0 )
& ! [A: d,B: u] :
( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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: d,B: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
=> ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ) ) )
& ! [A: d,B: u] :
( ~ ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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: d,B: u] :
( ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) )
=> ~ ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) ) ) )
& ! [A: d,B: u] :
( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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: d,B: u] :
( ( 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: d,B: u] :
( ( 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: d,B: d,C: u,D: u,E: u] :
( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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: d,B: d,C: u,D: u,E: u] :
( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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: d,B: u,C: u] :
( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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: d,B: d,C: u,D: u] :
( ( 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: d,B: d,C: u,D: u,E: u] :
( ( 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: d,B: d,C: u,D: u] :
( ( 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: d,B: d,C: u] :
( ( 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: d] :
( ( 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: d,B: u] :
( ( 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)],[134]) ).
thf(148,plain,
! [A: d] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
= mono_2Ec_2Ebool_2EF_2E0 ),
inference(cnf,[status(esa)],[135]) ).
thf(185,plain,
! [A: d] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
= mono_2Ec_2Ebool_2EF_2E0 ),
inference(lifteq,[status(thm)],[148]) ).
thf(186,plain,
! [A: d] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
= mono_2Ec_2Ebool_2EF_2E0 ),
inference(simp,[status(thm)],[185]) ).
thf(39,axiom,
! [A: d,B: u,C: u,D: u] :
( ( 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/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29) ).
thf(333,plain,
! [A: d,B: u,C: u,D: u] :
( ( 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)],[39]) ).
thf(27,axiom,
! [A: d,B: u] :
( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) )
<=> ? [C: u] : ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Equant_2E_3F) ).
thf(249,plain,
! [A: d,B: u] :
( ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) )
=> ? [C: u] : ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ) )
& ( ? [C: u] : ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) )
=> ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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)],[27]) ).
thf(34,axiom,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( ( mono_2Ec_2Ebool_2ET_2E0 = A )
<=> ( p @ A ) )
& ( ( A = mono_2Ec_2Ebool_2ET_2E0 )
<=> ( p @ A ) )
& ( ( mono_2Ec_2Ebool_2EF_2E0 = A )
<=> ~ ( p @ A ) )
& ( ( A = mono_2Ec_2Ebool_2EF_2E0 )
<=> ~ ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
thf(276,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( ( mono_2Ec_2Ebool_2ET_2E0 = A )
=> ( p @ A ) )
& ( ( p @ A )
=> ( mono_2Ec_2Ebool_2ET_2E0 = A ) )
& ( ( A = mono_2Ec_2Ebool_2ET_2E0 )
=> ( p @ A ) )
& ( ( p @ A )
=> ( A = mono_2Ec_2Ebool_2ET_2E0 ) )
& ( ( mono_2Ec_2Ebool_2EF_2E0 = A )
=> ~ ( p @ A ) )
& ( ~ ( p @ A )
=> ( mono_2Ec_2Ebool_2EF_2E0 = A ) )
& ( ( A = mono_2Ec_2Ebool_2EF_2E0 )
=> ~ ( p @ A ) )
& ( ~ ( p @ A )
=> ( A = mono_2Ec_2Ebool_2EF_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(12,axiom,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( p @ A )
& ( p @ B ) )
<=> ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2E_2F_5C_2E0 @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) ).
thf(120,plain,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( ( p @ A )
& ( p @ B ) )
=> ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2E_2F_5C_2E0 @ A ) @ B ) ) )
& ( ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2E_2F_5C_2E0 @ A ) @ B ) )
=> ( ( p @ A )
& ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(48,axiom,
p @ mono_2Ec_2Ebool_2ET_2E0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Etruth) ).
thf(379,plain,
p @ mono_2Ec_2Ebool_2ET_2E0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(495,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
!= mono_2Ec_2Ebool_2EF_2E0 )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
!= mono_2Ec_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 ) ) )
| ( 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 ) )
!= ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET_2E0 ) ) ),
inference(simp,[status(thm)],[460]) ).
thf(511,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
!= mono_2Ec_2Ebool_2EF_2E0 )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
!= mono_2Ec_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 ) ) )
| ( ( 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 ) )
!= ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2ET_2E0 ) ) ),
inference(simp,[status(thm)],[495]) ).
thf(29,axiom,
! [A: d,B: u,C: u] :
( ( ( s @ A @ B )
= ( s @ A @ C ) )
<=> ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) ).
thf(257,plain,
! [A: d,B: u,C: u] :
( ( ( ( s @ A @ B )
= ( s @ A @ C ) )
=> ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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)],[29]) ).
thf(52,axiom,
! [A: d,B: u] :
( ( 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/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29) ).
thf(389,plain,
! [A: d,B: u] :
( ( 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)],[52]) ).
thf(21,axiom,
! [A: d,B: u] :
( ( ( s @ A @ B )
= ( s @ A @ B ) )
<=> ( p @ mono_2Ec_2Ebool_2ET_2E0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EREFL__CLAUSE) ).
thf(230,plain,
p @ mono_2Ec_2Ebool_2ET_2E0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(6,axiom,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( p @ ( mono_2Ec_2Ebool_2E_7E_2E1 @ A ) )
<=> ~ ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_7E) ).
thf(81,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( ( p @ ( mono_2Ec_2Ebool_2E_7E_2E1 @ A ) )
=> ~ ( p @ A ) )
& ( ~ ( p @ A )
=> ( p @ ( mono_2Ec_2Ebool_2E_7E_2E1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(82,plain,
( ! [A: mono_2Etyop_2Emin_2Ebool] :
( ( p @ ( mono_2Ec_2Ebool_2E_7E_2E1 @ A ) )
=> ~ ( p @ A ) )
& ! [A: mono_2Etyop_2Emin_2Ebool] :
( ~ ( p @ A )
=> ( p @ ( mono_2Ec_2Ebool_2E_7E_2E1 @ A ) ) ) ),
inference(miniscope,[status(thm)],[81]) ).
thf(84,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ~ ( p @ ( mono_2Ec_2Ebool_2E_7E_2E1 @ A ) )
| ~ ( p @ A ) ),
inference(cnf,[status(esa)],[82]) ).
thf(465,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ~ ( p @ A )
| ( ( p @ ( mono_2Ec_2Ebool_2E_7E_2E1 @ A ) )
!= ( p @ mono_2Ec_2Ebool_2ET_2E0 ) ) ),
inference(paramod_ordered,[status(thm)],[230,84]) ).
thf(475,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ~ ( p @ A )
| ( ( mono_2Ec_2Ebool_2E_7E_2E1 @ A )
!= mono_2Ec_2Ebool_2ET_2E0 ) ),
inference(simp,[status(thm)],[465]) ).
thf(23,axiom,
! [A: d,B: d,C: u,D: u] :
( ( 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/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b) ).
thf(238,plain,
! [A: d,B: d,C: u,D: u] :
( ( 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)],[23]) ).
thf(25,axiom,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ A ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29) ).
thf(243,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ A ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(32,axiom,
! [A: d,B: d,C: u,D: u,E: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27b) ).
thf(270,plain,
! [A: d,B: d,C: u,D: u,E: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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)],[32]) ).
thf(3,axiom,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ~ ( p @ A )
<=> ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).
thf(60,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( ~ ( p @ A )
=> ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ A ) ) )
& ( ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ A ) )
=> ~ ( p @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(49,axiom,
! [A: d,B: u,C: u,D: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27a) ).
thf(380,plain,
! [A: d,B: u,C: u,D: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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)],[49]) ).
thf(35,axiom,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
| ( p @ A ) )
<=> ( p @ mono_2Ec_2Ebool_2ET_2E0 ) )
& ( ( ( p @ A )
| ( p @ mono_2Ec_2Ebool_2ET_2E0 ) )
<=> ( p @ mono_2Ec_2Ebool_2ET_2E0 ) )
& ( ( ( p @ mono_2Ec_2Ebool_2EF_2E0 )
| ( p @ A ) )
<=> ( p @ A ) )
& ( ( ( p @ A )
| ( p @ mono_2Ec_2Ebool_2EF_2E0 ) )
<=> ( p @ A ) )
& ( ( ( p @ A )
| ( p @ A ) )
<=> ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EOR__CLAUSES) ).
thf(302,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
| ( p @ A ) )
=> ( p @ mono_2Ec_2Ebool_2ET_2E0 ) )
& ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
=> ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
| ( p @ A ) ) )
& ( ( ( p @ A )
| ( p @ mono_2Ec_2Ebool_2ET_2E0 ) )
=> ( p @ mono_2Ec_2Ebool_2ET_2E0 ) )
& ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
=> ( ( p @ A )
| ( p @ mono_2Ec_2Ebool_2ET_2E0 ) ) )
& ( ( ( p @ mono_2Ec_2Ebool_2EF_2E0 )
| ( p @ A ) )
=> ( p @ A ) )
& ( ( p @ A )
=> ( ( p @ mono_2Ec_2Ebool_2EF_2E0 )
| ( p @ A ) ) )
& ( ( ( p @ A )
| ( p @ mono_2Ec_2Ebool_2EF_2E0 ) )
=> ( p @ A ) )
& ( ( p @ A )
=> ( ( p @ A )
| ( p @ mono_2Ec_2Ebool_2EF_2E0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(53,axiom,
! [A: d,B: d,C: u,D: u] :
( ! [E: u] :
( ( 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/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Eeq__ext) ).
thf(392,plain,
! [A: d,B: d,C: u,D: u] :
( ! [E: u] :
( ( 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)],[53]) ).
thf(4,axiom,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( p @ A )
<=> ( p @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Eboolext) ).
thf(65,plain,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ( p @ B ) )
& ( ( p @ B )
=> ( p @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(66,plain,
! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
( ~ ( p @ B )
| ~ ( p @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[65]) ).
thf(70,plain,
! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
( ( A = B )
| ~ ( p @ B )
| ~ ( p @ A ) ),
inference(lifteq,[status(thm)],[66]) ).
thf(8,axiom,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( p @ ( mono_2Ec_2Ebool_2E_5C_2F_2E2 @ A @ B ) )
<=> ( ( p @ A )
| ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_5C_2F) ).
thf(92,plain,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( p @ ( mono_2Ec_2Ebool_2E_5C_2F_2E2 @ A @ B ) )
=> ( ( p @ A )
| ( p @ B ) ) )
& ( ( ( p @ A )
| ( p @ B ) )
=> ( p @ ( mono_2Ec_2Ebool_2E_5C_2F_2E2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(36,axiom,
! [A: d,B: d,C: d,D: u,E: u,F: u] :
( ( 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/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Es__thm) ).
thf(324,plain,
! [A: d,B: d,C: d,D: u,E: u,F: u] :
( ( 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)],[36]) ).
thf(19,axiom,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A = mono_2Ec_2Ebool_2ET_2E0 )
| ( A = mono_2Ec_2Ebool_2EF_2E0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Ebool__cases__ax) ).
thf(224,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A = mono_2Ec_2Ebool_2ET_2E0 )
| ( A = mono_2Ec_2Ebool_2EF_2E0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(28,axiom,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ A ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29) ).
thf(254,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ A ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(255,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ A ) ) )
= A ),
inference(cnf,[status(esa)],[254]) ).
thf(256,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ A ) ) )
= A ),
inference(lifteq,[status(thm)],[255]) ).
thf(41,axiom,
! [A: d,B: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2EIS__NONE_2E1_2Emono_2EA_27a) ).
thf(339,plain,
! [A: d,B: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__NONE_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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)],[41]) ).
thf(61,plain,
( ! [A: mono_2Etyop_2Emin_2Ebool] :
( ~ ( p @ A )
=> ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ A ) ) )
& ! [A: mono_2Etyop_2Emin_2Ebool] :
( ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ A ) )
=> ~ ( p @ A ) ) ),
inference(miniscope,[status(thm)],[60]) ).
thf(62,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ~ ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ A ) )
| ~ ( p @ A ) ),
inference(cnf,[status(esa)],[61]) ).
thf(64,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ~ ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ A ) )
| ~ ( p @ A ) ),
inference(simp,[status(thm)],[62]) ).
thf(518,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ~ ( p @ A )
| ( ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ A ) )
!= ( p @ mono_2Ec_2Ebool_2ET_2E0 ) ) ),
inference(paramod_ordered,[status(thm)],[230,64]) ).
thf(526,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ~ ( p @ A )
| ( ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ A )
!= mono_2Ec_2Ebool_2ET_2E0 ) ),
inference(simp,[status(thm)],[518]) ).
thf(69,plain,
! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
( ( p @ A )
| ( p @ B )
| ( A = B ) ),
inference(cnf,[status(esa)],[65]) ).
thf(73,plain,
! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
( ( A = B )
| ( p @ A )
| ( p @ B ) ),
inference(lifteq,[status(thm)],[69]) ).
thf(14,axiom,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,B: mono_2Etyop_2Emin_2Ebool] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ A @ B ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ A ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool) ).
thf(128,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,B: mono_2Etyop_2Emin_2Ebool] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ A @ B ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ A ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( p @ ( mono_2Ec_2Ebool_2E_2F_5C_2E2 @ A @ B ) )
<=> ( ( p @ A )
& ( p @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_2F_5C) ).
thf(105,plain,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( p @ ( mono_2Ec_2Ebool_2E_2F_5C_2E2 @ A @ B ) )
=> ( ( p @ A )
& ( p @ B ) ) )
& ( ( ( p @ A )
& ( p @ B ) )
=> ( p @ ( mono_2Ec_2Ebool_2E_2F_5C_2E2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(55,axiom,
! [A: d,B: u] :
( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ combin_i_2E0 ) @ ( s @ A @ B ) ) )
= ( s @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Ei__thm) ).
thf(398,plain,
! [A: d,B: u] :
( ( 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)],[55]) ).
thf(30,axiom,
! [A: d,B: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27a) ).
thf(264,plain,
! [A: d,B: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ B ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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)],[30]) ).
thf(24,axiom,
~ ( p @ mono_2Ec_2Ebool_2EF_2E0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).
thf(241,plain,
~ ( p @ mono_2Ec_2Ebool_2EF_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(242,plain,
~ ( p @ mono_2Ec_2Ebool_2EF_2E0 ),
inference(polarity_switch,[status(thm)],[241]) ).
thf(401,plain,
( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
!= ( p @ mono_2Ec_2Ebool_2EF_2E0 ) ),
inference(paramod_ordered,[status(thm)],[230,242]) ).
thf(402,plain,
mono_2Ec_2Ebool_2ET_2E0 != mono_2Ec_2Ebool_2EF_2E0,
inference(simp,[status(thm)],[401]) ).
thf(17,axiom,
! [A: d,B: u] :
( ( 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/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a) ).
thf(204,plain,
! [A: d,B: u] :
( ( 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)],[17]) ).
thf(225,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A = mono_2Ec_2Ebool_2ET_2E0 )
| ( A = mono_2Ec_2Ebool_2EF_2E0 ) ),
inference(cnf,[status(esa)],[224]) ).
thf(226,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A = mono_2Ec_2Ebool_2ET_2E0 )
| ( A = mono_2Ec_2Ebool_2EF_2E0 ) ),
inference(lifteq,[status(thm)],[225]) ).
thf(519,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ~ ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ A ) )
| ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
!= ( p @ A ) ) ),
inference(paramod_ordered,[status(thm)],[230,64]) ).
thf(520,plain,
~ ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ mono_2Ec_2Ebool_2ET_2E0 ) ),
inference(pattern_uni,[status(thm)],[519:[bind(A,$thf( mono_2Ec_2Ebool_2ET_2E0 ))]]) ).
thf(530,plain,
( ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ mono_2Ec_2Ebool_2ET_2E0 ) )
!= ( p @ mono_2Ec_2Ebool_2ET_2E0 ) ),
inference(paramod_ordered,[status(thm)],[230,520]) ).
thf(533,plain,
( ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ mono_2Ec_2Ebool_2ET_2E0 )
!= mono_2Ec_2Ebool_2ET_2E0 ),
inference(simp,[status(thm)],[530]) ).
thf(610,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A = mono_2Ec_2Ebool_2EF_2E0 )
| ( A
!= ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ mono_2Ec_2Ebool_2ET_2E0 ) ) ),
inference(paramod_ordered,[status(thm)],[226,533]) ).
thf(611,plain,
( ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ mono_2Ec_2Ebool_2ET_2E0 )
= mono_2Ec_2Ebool_2EF_2E0 ),
inference(pattern_uni,[status(thm)],[610:[bind(A,$thf( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ mono_2Ec_2Ebool_2ET_2E0 ))]]) ).
thf(7,axiom,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( p @ A )
| ( p @ B ) )
<=> ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2E_5C_2F_2E0 @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) ).
thf(86,plain,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( ( p @ A )
| ( p @ B ) )
=> ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2E_5C_2F_2E0 @ A ) @ B ) ) )
& ( ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2E_5C_2F_2E0 @ A ) @ B ) )
=> ( ( p @ A )
| ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(244,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ A ) ) )
= A ),
inference(cnf,[status(esa)],[243]) ).
thf(245,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ A ) ) )
= A ),
inference(lifteq,[status(thm)],[244]) ).
thf(466,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ~ ( p @ ( mono_2Ec_2Ebool_2E_7E_2E1 @ A ) )
| ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
!= ( p @ A ) ) ),
inference(paramod_ordered,[status(thm)],[230,84]) ).
thf(467,plain,
~ ( p @ ( mono_2Ec_2Ebool_2E_7E_2E1 @ mono_2Ec_2Ebool_2ET_2E0 ) ),
inference(pattern_uni,[status(thm)],[466:[bind(A,$thf( mono_2Ec_2Ebool_2ET_2E0 ))]]) ).
thf(477,plain,
( ( p @ ( mono_2Ec_2Ebool_2E_7E_2E1 @ mono_2Ec_2Ebool_2ET_2E0 ) )
!= ( p @ mono_2Ec_2Ebool_2ET_2E0 ) ),
inference(paramod_ordered,[status(thm)],[230,467]) ).
thf(479,plain,
( ( mono_2Ec_2Ebool_2E_7E_2E1 @ mono_2Ec_2Ebool_2ET_2E0 )
!= mono_2Ec_2Ebool_2ET_2E0 ),
inference(simp,[status(thm)],[477]) ).
thf(598,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( A = mono_2Ec_2Ebool_2EF_2E0 )
| ( A
!= ( mono_2Ec_2Ebool_2E_7E_2E1 @ mono_2Ec_2Ebool_2ET_2E0 ) ) ),
inference(paramod_ordered,[status(thm)],[226,479]) ).
thf(599,plain,
( ( mono_2Ec_2Ebool_2E_7E_2E1 @ mono_2Ec_2Ebool_2ET_2E0 )
= mono_2Ec_2Ebool_2EF_2E0 ),
inference(pattern_uni,[status(thm)],[598:[bind(A,$thf( mono_2Ec_2Ebool_2E_7E_2E1 @ mono_2Ec_2Ebool_2ET_2E0 ))]]) ).
thf(38,axiom,
! [A: d,B: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b) ).
thf(330,plain,
! [A: d,B: u] :
( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) )
= ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ c_2Eoption_2ESOME_2E0 ) @ ( s @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(1260,plain,
! [B: u,A: d] :
( ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) )
= ( s @ tyop_2Emin_2Ebool @ B ) )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) )
!= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[186,388]) ).
thf(1261,plain,
! [A: d] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) ),
inference(pattern_uni,[status(thm)],[1260:[bind(A,$thf( F )),bind(B,$thf( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ F ) @ c_2Eoption_2ENONE_2E0 ) ))]]) ).
thf(1820,plain,
! [A: d] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ c_2Eoption_2ENONE_2E0 ) ) ) ),
inference(simp,[status(thm)],[1261]) ).
thf(43,axiom,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
& ( p @ A ) )
<=> ( p @ A ) )
& ( ( ( p @ A )
& ( p @ mono_2Ec_2Ebool_2ET_2E0 ) )
<=> ( p @ A ) )
& ( ( ( p @ mono_2Ec_2Ebool_2EF_2E0 )
& ( p @ A ) )
<=> ( p @ mono_2Ec_2Ebool_2EF_2E0 ) )
& ( ( ( p @ A )
& ( p @ mono_2Ec_2Ebool_2EF_2E0 ) )
<=> ( p @ mono_2Ec_2Ebool_2EF_2E0 ) )
& ( ( ( p @ A )
& ( p @ A ) )
<=> ( p @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EAND__CLAUSES) ).
thf(345,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
& ( p @ A ) )
=> ( p @ A ) )
& ( ( p @ A )
=> ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
& ( p @ A ) ) )
& ( ( ( p @ A )
& ( p @ mono_2Ec_2Ebool_2ET_2E0 ) )
=> ( p @ A ) )
& ( ( p @ A )
=> ( ( p @ A )
& ( p @ mono_2Ec_2Ebool_2ET_2E0 ) ) )
& ( ( ( p @ mono_2Ec_2Ebool_2EF_2E0 )
& ( p @ A ) )
=> ( p @ mono_2Ec_2Ebool_2EF_2E0 ) )
& ( ( p @ mono_2Ec_2Ebool_2EF_2E0 )
=> ( ( p @ mono_2Ec_2Ebool_2EF_2E0 )
& ( p @ A ) ) )
& ( ( ( p @ A )
& ( p @ mono_2Ec_2Ebool_2EF_2E0 ) )
=> ( p @ mono_2Ec_2Ebool_2EF_2E0 ) )
& ( ( p @ mono_2Ec_2Ebool_2EF_2E0 )
=> ( ( p @ A )
& ( p @ mono_2Ec_2Ebool_2EF_2E0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(44,axiom,
! [A: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ A ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29) ).
thf(367,plain,
! [A: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ A ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(31,axiom,
! [A: d,B: d,C: u,D: u] :
( ( 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/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Ek__thm) ).
thf(267,plain,
! [A: d,B: d,C: u,D: u] :
( ( 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)],[31]) ).
thf(47,axiom,
! [A: d,B: u] :
( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) )
<=> ! [C: u] : ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Equant_2E_21) ).
thf(374,plain,
! [A: d,B: u] :
( ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) )
=> ! [C: u] : ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ) )
& ( ! [C: u] : ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) )
=> ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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)],[47]) ).
thf(42,axiom,
! [A: d,B: d,C: u,D: u,E: u] :
( ( 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/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b) ).
thf(342,plain,
! [A: d,B: d,C: u,D: u,E: u] :
( ( 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)],[42]) ).
thf(63,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( p @ A )
| ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2E_7E_2E0 @ A ) ) ),
inference(cnf,[status(esa)],[61]) ).
thf(694,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
!= mono_2Ec_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 ) ) )
| ( ( 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 ) )
!= ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_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 ) )
!= ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) ) ),
inference(simp,[status(thm)],[513]) ).
thf(707,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
!= mono_2Ec_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 ) ) )
| ( ( 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 ) )
!= ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_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 ) )
!= ( i_mono_2Etyop_2Emin_2Ebool @ mono_2Ec_2Ebool_2EF_2E0 ) ) ),
inference(simp,[status(thm)],[694]) ).
thf(37,axiom,
! [A: d,B: u] :
( ( 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/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2EOPTION__JOIN_2E1_2Emono_2EA_27a) ).
thf(327,plain,
! [A: d,B: u] :
( ( 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)],[37]) ).
thf(45,axiom,
! [A: d,B: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) ).
thf(370,plain,
! [A: d,B: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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)],[45]) ).
thf(13,axiom,
! [A: d,B: mono_2Etyop_2Emin_2Ebool] :
( ? [C: u] : ( p @ B )
<=> ( p @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEXISTS__SIMP) ).
thf(127,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(40,axiom,
! [A: d,B: u] :
( ( 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/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a) ).
thf(336,plain,
! [A: d,B: u] :
( ( 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)],[40]) ).
thf(22,axiom,
! [A: d,B: u,C: u] :
( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A @ B ) @ ( s @ A @ C ) ) ) ) )
<=> ( ( s @ A @ B )
= ( s @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D) ).
thf(231,plain,
! [A: d,B: u,C: u] :
( ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A @ B ) @ ( s @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(9,axiom,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ B ) )
<=> ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Emin_2E_3D_3D_3E_2E0 @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) ).
thf(99,plain,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( ( p @ A )
=> ( p @ B ) )
=> ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Emin_2E_3D_3D_3E_2E0 @ A ) @ B ) ) )
& ( ( p @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Emin_2E_3D_3D_3E_2E0 @ A ) @ B ) )
=> ( ( p @ A )
=> ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(18,axiom,
! [A: d,B: d,C: u,D: u,E: u] :
( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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: u,G: u] :
( ( ( 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 @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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/sandbox2/benchmark/theBenchmark.p',thm_2Eoption_2EOPTREL__def) ).
thf(207,plain,
! [A: d,B: d,C: u,D: u,E: u] :
( ( ( p @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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: u,G: u] :
( ( ( 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 @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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: u,G: u] :
( ( ( 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 @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 @ ( j_mono_2Etyop_2Emin_2Ebool @ ( 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)],[18]) ).
thf(50,axiom,
! [A: d,B: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) ).
thf(383,plain,
! [A: d,B: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( 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)],[50]) ).
thf(33,axiom,
! [A: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ A ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29) ).
thf(273,plain,
! [A: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ A ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(46,axiom,
p @ mono_2Ec_2Ebool_2ET_2E0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(373,plain,
p @ mono_2Ec_2Ebool_2ET_2E0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(76,plain,
! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
( ( p @ A )
| ( p @ ( mono_2Ec_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) ) ),
inference(cnf,[status(esa)],[75]) ).
thf(79,plain,
! [B: mono_2Etyop_2Emin_2Ebool,A: mono_2Etyop_2Emin_2Ebool] :
( ( p @ A )
| ( p @ ( mono_2Ec_2Emin_2E_3D_3D_3E_2E2 @ A @ B ) ) ),
inference(simp,[status(thm)],[76]) ).
thf(143,plain,
! [B: u,A: d] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) ) )
= mono_2Ec_2Ebool_2ET_2E0 ),
inference(cnf,[status(esa)],[135]) ).
thf(194,plain,
! [B: u,A: d] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) ) )
= mono_2Ec_2Ebool_2ET_2E0 ),
inference(lifteq,[status(thm)],[143]) ).
thf(195,plain,
! [B: u,A: d] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eoption_2EIS__SOME_2E1 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Eoption_2ESOME_2E1 @ ( s @ A @ B ) ) ) ) ) )
= mono_2Ec_2Ebool_2ET_2E0 ),
inference(simp,[status(thm)],[194]) ).
thf(409,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
!= mono_2Ec_2Ebool_2ET_2E0 )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
!= mono_2Ec_2Ebool_2EF_2E0 )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
!= mono_2Ec_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)],[408]) ).
thf(415,plain,
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
!= mono_2Ec_2Ebool_2ET_2E0 )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) )
!= mono_2Ec_2Ebool_2EF_2E0 )
| ( ( j_mono_2Etyop_2Emin_2Ebool @ ( 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 ) ) ) ) ) )
!= mono_2Ec_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)],[409]) ).
thf(54,axiom,
( ! [A: mono_2Etyop_2Emin_2Ebool] :
( ~ ~ ( p @ A )
<=> ( p @ A ) )
& ( ~ ( p @ mono_2Ec_2Ebool_2ET_2E0 )
<=> ( p @ mono_2Ec_2Ebool_2EF_2E0 ) )
& ( ~ ( p @ mono_2Ec_2Ebool_2EF_2E0 )
<=> ( p @ mono_2Ec_2Ebool_2ET_2E0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__CLAUSES) ).
thf(395,plain,
( ( ~ ( p @ mono_2Ec_2Ebool_2ET_2E0 )
=> ( p @ mono_2Ec_2Ebool_2EF_2E0 ) )
& ( ( p @ mono_2Ec_2Ebool_2EF_2E0 )
=> ~ ( p @ mono_2Ec_2Ebool_2ET_2E0 ) )
& ( ~ ( p @ mono_2Ec_2Ebool_2EF_2E0 )
=> ( p @ mono_2Ec_2Ebool_2ET_2E0 ) )
& ( ( p @ mono_2Ec_2Ebool_2ET_2E0 )
=> ~ ( p @ mono_2Ec_2Ebool_2EF_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(15,axiom,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,B: mono_2Etyop_2Emin_2Ebool] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ A @ B ) ) )
= ( 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 ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ A ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29) ).
thf(131,plain,
! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,B: mono_2Etyop_2Emin_2Ebool] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ A @ B ) ) )
= ( 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 ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ A ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(11,axiom,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ B ) )
=> ( ( ( p @ B )
=> ( p @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__ANTISYM__AX) ).
thf(111,plain,
! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
( ( ( p @ A )
=> ( p @ B ) )
=> ( ( ( p @ B )
=> ( p @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(20,axiom,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( p @ mono_2Ec_2Ebool_2EF_2E0 )
=> ( p @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EFALSITY) ).
thf(227,plain,
! [A: mono_2Etyop_2Emin_2Ebool] :
( ( p @ mono_2Ec_2Ebool_2EF_2E0 )
=> ( p @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(32704,plain,
$false,
inference(cvc4,[status(thm)],[56,78,388,984,186,333,249,408,276,120,379,511,709,257,389,460,475,238,84,243,74,248,270,60,380,302,392,70,92,65,324,224,256,339,526,134,73,128,105,398,513,264,64,402,59,204,611,86,81,230,245,599,330,1820,345,367,226,267,241,374,342,63,707,327,370,127,336,386,231,99,246,207,383,273,373,242,79,195,415,395,131,111,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : ITP011_1 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.15/0.17 % Command : run_Leo-III %s %d
% 0.17/0.39 % Computer : n019.cluster.edu
% 0.17/0.39 % Model : x86_64 x86_64
% 0.17/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39 % Memory : 8042.1875MB
% 0.17/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39 % CPULimit : 300
% 0.17/0.39 % WCLimit : 300
% 0.17/0.39 % DateTime : Sat May 18 18:18:24 EDT 2024
% 0.17/0.39 % CPUTime :
% 0.95/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.61/1.07 % [INFO] Parsing done (167ms).
% 1.61/1.08 % [INFO] Running in sequential loop mode.
% 2.02/1.32 % [INFO] eprover registered as external prover.
% 2.02/1.32 % [INFO] cvc4 registered as external prover.
% 2.02/1.32 % [INFO] Scanning for conjecture ...
% 2.39/1.45 % [INFO] Found a conjecture (or negated_conjecture) and 53 axioms. Running axiom selection ...
% 2.54/1.52 % [INFO] Axiom selection finished. Selected 53 axioms (removed 0 axioms).
% 3.01/1.63 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.01/1.64 % [INFO] Type checking passed.
% 3.01/1.64 % [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 ...
% 5.02/2.18 % [INFO] [Domain constraints] Detected constraint on mono_2Etyop_2Emin_2Ebool
% 5.02/2.18 % [INFO] [Domain constraints] dom(mono_2Etyop_2Emin_2Ebool) ⊆ {mono_2Ec_2Ebool_2ET_2E0,mono_2Ec_2Ebool_2EF_2E0}
% 56.01/23.31 % External prover 'cvc4' found a proof!
% 56.01/23.31 % [INFO] Killing All external provers ...
% 56.01/23.31 % Time passed: 22758ms (effective reasoning time: 22225ms)
% 56.01/23.31 % 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)>
% 56.01/23.31 % Axioms used in derivation (53): arityeq1_2Ec_2Eoption_2EIS__NONE_2E1_2Emono_2EA_27a, thm_2Ebool_2ENOT__CLAUSES, 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, reserved_2Eho_2Ebool__cases__ax, thm_2Ebool_2EOR__CLAUSES, arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a, arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a, ji_2Emono_2Etyop_2Emin_2Ebool, 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, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, 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, arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29, 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, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, reserved_2Elogic_2E_7E, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29, 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, ij_2Emono_2Etyop_2Emin_2Ebool, thm_2Ebool_2EAND__CLAUSES, reserved_2Elogic_2E_5C_2F, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool
% 56.01/23.31 % No. of inferences in proof: 184
% 56.01/23.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 22758 ms resp. 22225 ms w/o parsing
% 56.36/23.43 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 56.36/23.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------