TSTP Solution File: ITP026^1 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ITP026^1 : TPTP v7.5.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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
% DateTime : Sun Mar 21 13:23:58 EDT 2021
% Result : Unknown 0.73s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ITP026^1 : TPTP v7.5.0. Released v7.5.0.
% 0.00/0.10 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.29 % Computer : n015.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % DateTime : Fri Mar 19 04:36:25 EDT 2021
% 0.10/0.29 % CPUTime :
% 0.10/0.30 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.16/0.31 Python 2.7.5
% 0.16/0.57 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.16/0.57 FOF formula (<kernel.Constant object at 0x1432d40>, <kernel.Type object at 0x14325a8>) of role type named ty_n_t__Algebra1__Ocarrier__Ocarrier____ext_I_062_Itf__e_Mtf__e_J_Mt__Algebra4__OaGroup__OaGroup____ext_I_062_Itf__e_Mtf__e_J_Mt__Algebra7__OModule__OModule____ext_I_062_Itf__e_Mtf__e_J_Mtf__b_Mt__Product____Type__Ounit_J_J_J
% 0.16/0.57 Using role type
% 0.16/0.57 Declaring carrie377329159t_unit:Type
% 0.16/0.57 FOF formula (<kernel.Constant object at 0x14593f8>, <kernel.Type object at 0x1432ab8>) of role type named ty_n_t__Algebra1__Ocarrier__Ocarrier____ext_I_062_Itf__e_Mtf__a_J_Mt__Algebra4__OaGroup__OaGroup____ext_I_062_Itf__e_Mtf__a_J_Mt__Algebra7__OModule__OModule____ext_I_062_Itf__e_Mtf__a_J_Mtf__b_Mt__Product____Type__Ounit_J_J_J
% 0.16/0.57 Using role type
% 0.16/0.57 Declaring carrie292259835t_unit:Type
% 0.16/0.57 FOF formula (<kernel.Constant object at 0x1432b90>, <kernel.Type object at 0x1432d88>) of role type named ty_n_t__Algebra1__Ocarrier__Ocarrier____ext_I_062_Itf__a_Mtf__e_J_Mt__Algebra4__OaGroup__OaGroup____ext_I_062_Itf__a_Mtf__e_J_Mt__Algebra7__OModule__OModule____ext_I_062_Itf__a_Mtf__e_J_Mtf__b_Mt__Product____Type__Ounit_J_J_J
% 0.16/0.57 Using role type
% 0.16/0.57 Declaring carrie1065537299t_unit:Type
% 0.16/0.57 FOF formula (<kernel.Constant object at 0x14325a8>, <kernel.Type object at 0x1432b00>) of role type named ty_n_t__Algebra1__Ocarrier__Ocarrier____ext_I_062_Itf__a_Mtf__a_J_Mt__Algebra4__OaGroup__OaGroup____ext_I_062_Itf__a_Mtf__a_J_Mt__Algebra7__OModule__OModule____ext_I_062_Itf__a_Mtf__a_J_Mtf__b_Mt__Product____Type__Ounit_J_J_J
% 0.16/0.57 Using role type
% 0.16/0.57 Declaring carrie980467975t_unit:Type
% 0.16/0.57 FOF formula (<kernel.Constant object at 0x1432ab8>, <kernel.Type object at 0x1432d88>) of role type named ty_n_t__Algebra1__Ocarrier__Ocarrier____ext_Itf__a_Mt__Algebra4__OaGroup__OaGroup____ext_Itf__a_Mt__Algebra7__OModule__OModule____ext_Itf__a_Mtf__b_Mt__Product____Type__Ounit_J_J_J
% 0.16/0.57 Using role type
% 0.16/0.57 Declaring carrie1963041556t_unit:Type
% 0.16/0.57 FOF formula (<kernel.Constant object at 0x1432a28>, <kernel.Type object at 0x2b92e793aea8>) of role type named ty_n_t__Algebra1__Ocarrier__Ocarrier____ext_Itf__e_Mt__Algebra4__OaGroup__OaGroup____ext_Itf__e_Mt__Algebra7__OModule__OModule____ext_Itf__e_Mtf__b_Mtf__f_J_J_J
% 0.16/0.57 Using role type
% 0.16/0.57 Declaring carrie1821755406_e_b_f:Type
% 0.16/0.57 FOF formula (<kernel.Constant object at 0x1432b00>, <kernel.Type object at 0x2b92e793aea8>) of role type named ty_n_t__Algebra1__Ocarrier__Ocarrier____ext_Itf__a_Mt__Algebra4__OaGroup__OaGroup____ext_Itf__a_Mt__Algebra7__OModule__OModule____ext_Itf__a_Mtf__b_Mtf__c_J_J_J
% 0.16/0.57 Using role type
% 0.16/0.57 Declaring carrie722926983_a_b_c:Type
% 0.16/0.57 FOF formula (<kernel.Constant object at 0x1432d88>, <kernel.Type object at 0x2b92e793ae60>) of role type named ty_n_t__Algebra1__Ocarrier__Ocarrier____ext_Itf__b_Mt__Algebra4__OaGroup__OaGroup____ext_Itf__b_Mt__Algebra4__ORing__ORing____ext_Itf__b_Mtf__d_J_J_J
% 0.16/0.57 Using role type
% 0.16/0.57 Declaring carrie1950868226xt_b_d:Type
% 0.16/0.57 FOF formula (<kernel.Constant object at 0x1432c20>, <kernel.Type object at 0x2b92e793a128>) of role type named ty_n_t__Set__Oset_I_062_It__Nat__Onat_Mtf__e_J_J
% 0.16/0.57 Using role type
% 0.16/0.57 Declaring set_nat_e:Type
% 0.16/0.57 FOF formula (<kernel.Constant object at 0x1432d88>, <kernel.Type object at 0x2b92e793ae60>) of role type named ty_n_t__Set__Oset_I_062_It__Nat__Onat_Mtf__b_J_J
% 0.16/0.57 Using role type
% 0.16/0.57 Declaring set_nat_b:Type
% 0.16/0.57 FOF formula (<kernel.Constant object at 0x1432b00>, <kernel.Type object at 0x2b92e7918a70>) of role type named ty_n_t__Set__Oset_I_062_It__Nat__Onat_Mtf__a_J_J
% 0.16/0.57 Using role type
% 0.16/0.57 Declaring set_nat_a:Type
% 0.16/0.57 FOF formula (<kernel.Constant object at 0x1432b00>, <kernel.Type object at 0x2b92e7918758>) of role type named ty_n_t__Set__Oset_It__Nat__Onat_J
% 0.16/0.57 Using role type
% 0.16/0.57 Declaring set_nat:Type
% 0.16/0.57 FOF formula (<kernel.Constant object at 0x1432b00>, <kernel.Type object at 0x2b92e7918cf8>) of role type named ty_n_t__Set__Oset_Itf__e_J
% 0.16/0.57 Using role type
% 0.16/0.57 Declaring set_e:Type
% 0.16/0.57 FOF formula (<kernel.Constant object at 0x2b92e793aea8>, <kernel.Type object at 0x2b92e7918998>) of role type named ty_n_t__Set__Oset_Itf__b_J
% 0.16/0.57 Using role type
% 0.16/0.58 Declaring set_b:Type
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e793a128>, <kernel.Type object at 0x2b92e7937488>) of role type named ty_n_t__Set__Oset_Itf__a_J
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring set_a:Type
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e793a2d8>, <kernel.Type object at 0x2b92e7937488>) of role type named ty_n_t__Nat__Onat
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring nat:Type
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e793a128>, <kernel.Type object at 0x2b92e79378c0>) of role type named ty_n_tf__e
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring e:Type
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e793a128>, <kernel.Type object at 0x2b92e7937290>) of role type named ty_n_tf__b
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring b:Type
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e7918998>, <kernel.Type object at 0x2b92e79373b0>) of role type named ty_n_tf__a
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring a:Type
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e7918998>, <kernel.DependentProduct object at 0x2b92e79377a0>) of role type named sy_c_Algebra1_Ocarrier_Ocarrier_001tf__a_001t__Algebra4__OaGroup__OaGroup____ext_Itf__a_Mt__Algebra7__OModule__OModule____ext_Itf__a_Mtf__b_Mt__Product____Type__Ounit_J_J
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring carrie1074654371t_unit:(carrie1963041556t_unit->set_a)
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e7918998>, <kernel.DependentProduct object at 0x2b92e7937bd8>) of role type named sy_c_Algebra1_Ocarrier_Ocarrier_001tf__a_001t__Algebra4__OaGroup__OaGroup____ext_Itf__a_Mt__Algebra7__OModule__OModule____ext_Itf__a_Mtf__b_Mtf__c_J_J
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring carrie2021454486_a_b_c:(carrie722926983_a_b_c->set_a)
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e7937b90>, <kernel.DependentProduct object at 0x2b92e7937f38>) of role type named sy_c_Algebra1_Ocarrier_Ocarrier_001tf__b_001t__Algebra4__OaGroup__OaGroup____ext_Itf__b_Mt__Algebra4__ORing__ORing____ext_Itf__b_Mtf__d_J_J
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring carrie2079586589xt_b_d:(carrie1950868226xt_b_d->set_b)
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e79377a0>, <kernel.DependentProduct object at 0x2b92e7937170>) of role type named sy_c_Algebra1_Ocarrier_Ocarrier_001tf__e_001t__Algebra4__OaGroup__OaGroup____ext_Itf__e_Mt__Algebra7__OModule__OModule____ext_Itf__e_Mtf__b_Mtf__f_J_J
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring carrie730238621_e_b_f:(carrie1821755406_e_b_f->set_e)
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e7937bd8>, <kernel.DependentProduct object at 0x2b92e7937290>) of role type named sy_c_Algebra4_ORing_001tf__b_001tf__d
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring ring_b_d:(carrie1950868226xt_b_d->Prop)
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e7937f38>, <kernel.DependentProduct object at 0x2b92e7937f80>) of role type named sy_c_Algebra4_OaGroup_Ozero_001tf__a_001t__Algebra7__OModule__OModule____ext_Itf__a_Mtf__b_Mtf__c_J
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring zero_a1261444626_a_b_c:(carrie722926983_a_b_c->a)
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e7937170>, <kernel.DependentProduct object at 0x2b92e79377a0>) of role type named sy_c_Algebra4_Oideal_001tf__b_001tf__d
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring ideal_b_d:(carrie1950868226xt_b_d->(set_b->Prop))
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e7937290>, <kernel.DependentProduct object at 0x2b92e79375a8>) of role type named sy_c_Algebra7_OAnnihilator_001tf__b_001tf__d_001tf__a_001t__Product____Type__Ounit
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring annihi259882159t_unit:(carrie1950868226xt_b_d->(carrie1963041556t_unit->set_b))
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e7937f80>, <kernel.DependentProduct object at 0x2b92e7937ea8>) of role type named sy_c_Algebra7_OAnnihilator_001tf__b_001tf__d_001tf__a_001tf__c
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring annihilator_b_d_a_c:(carrie1950868226xt_b_d->(carrie722926983_a_b_c->set_b))
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e7937440>, <kernel.DependentProduct object at 0x2b92e7937758>) of role type named sy_c_Algebra7_OAnnihilator_001tf__b_001tf__d_001tf__e_001tf__f
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring annihilator_b_d_e_f:(carrie1950868226xt_b_d->(carrie1821755406_e_b_f->set_b))
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e7937a70>, <kernel.DependentProduct object at 0x2b92e7937f38>) of role type named sy_c_Algebra7_OHOM_001tf__b_001tf__d_001tf__a_001t__Product____Type__Ounit_001tf__a_001t__Product____Type__Ounit
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring hOM_b_1103679019t_unit:(carrie1950868226xt_b_d->(carrie1963041556t_unit->(carrie1963041556t_unit->carrie980467975t_unit)))
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92dfe41518>, <kernel.DependentProduct object at 0x2b92e7937290>) of role type named sy_c_Algebra7_OHOM_001tf__b_001tf__d_001tf__a_001t__Product____Type__Ounit_001tf__a_001tf__c
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring hOM_b_796081438it_a_c:(carrie1950868226xt_b_d->(carrie1963041556t_unit->(carrie722926983_a_b_c->carrie980467975t_unit)))
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e7937ef0>, <kernel.DependentProduct object at 0x2b92e7937128>) of role type named sy_c_Algebra7_OHOM_001tf__b_001tf__d_001tf__a_001t__Product____Type__Ounit_001tf__e_001tf__f
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring hOM_b_1959675421it_e_f:(carrie1950868226xt_b_d->(carrie1963041556t_unit->(carrie1821755406_e_b_f->carrie1065537299t_unit)))
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e7937f38>, <kernel.DependentProduct object at 0x144fc20>) of role type named sy_c_Algebra7_OHOM_001tf__b_001tf__d_001tf__a_001tf__c_001tf__a_001t__Product____Type__Ounit
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring hOM_b_717364638t_unit:(carrie1950868226xt_b_d->(carrie722926983_a_b_c->(carrie1963041556t_unit->carrie980467975t_unit)))
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x144f200>, <kernel.DependentProduct object at 0x2b92e7937128>) of role type named sy_c_Algebra7_OHOM_001tf__b_001tf__d_001tf__a_001tf__c_001tf__a_001tf__c
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring hOM_b_d_a_c_a_c:(carrie1950868226xt_b_d->(carrie722926983_a_b_c->(carrie722926983_a_b_c->carrie980467975t_unit)))
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x144fc20>, <kernel.DependentProduct object at 0x2b92e7937170>) of role type named sy_c_Algebra7_OHOM_001tf__b_001tf__d_001tf__a_001tf__c_001tf__e_001tf__f
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring hOM_b_d_a_c_e_f:(carrie1950868226xt_b_d->(carrie722926983_a_b_c->(carrie1821755406_e_b_f->carrie1065537299t_unit)))
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x144ff80>, <kernel.DependentProduct object at 0x2b92e7937e60>) of role type named sy_c_Algebra7_OHOM_001tf__b_001tf__d_001tf__e_001tf__f_001tf__a_001t__Product____Type__Ounit
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring hOM_b_1375846429t_unit:(carrie1950868226xt_b_d->(carrie1821755406_e_b_f->(carrie1963041556t_unit->carrie292259835t_unit)))
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x144ff80>, <kernel.DependentProduct object at 0x2b92e7937f38>) of role type named sy_c_Algebra7_OHOM_001tf__b_001tf__d_001tf__e_001tf__f_001tf__a_001tf__c
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring hOM_b_d_e_f_a_c:(carrie1950868226xt_b_d->(carrie1821755406_e_b_f->(carrie722926983_a_b_c->carrie292259835t_unit)))
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e7937170>, <kernel.DependentProduct object at 0x2b92e7937a70>) of role type named sy_c_Algebra7_OHOM_001tf__b_001tf__d_001tf__e_001tf__f_001tf__e_001tf__f
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring hOM_b_d_e_f_e_f:(carrie1950868226xt_b_d->(carrie1821755406_e_b_f->(carrie1821755406_e_b_f->carrie377329159t_unit)))
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e7937e60>, <kernel.DependentProduct object at 0x16f68c0>) of role type named sy_c_Algebra7_OModule_001_062_Itf__a_Mtf__a_J_001tf__b_001t__Product____Type__Ounit_001tf__d
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring module589927589unit_d:(carrie980467975t_unit->(carrie1950868226xt_b_d->Prop))
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e7937f38>, <kernel.DependentProduct object at 0x16f6878>) of role type named sy_c_Algebra7_OModule_001_062_Itf__a_Mtf__e_J_001tf__b_001t__Product____Type__Ounit_001tf__d
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring module1648870817unit_d:(carrie1065537299t_unit->(carrie1950868226xt_b_d->Prop))
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e7937440>, <kernel.DependentProduct object at 0x16f6b90>) of role type named sy_c_Algebra7_OModule_001_062_Itf__e_Mtf__a_J_001tf__b_001t__Product____Type__Ounit_001tf__d
% 0.16/0.58 Using role type
% 0.16/0.58 Declaring module1330273449unit_d:(carrie292259835t_unit->(carrie1950868226xt_b_d->Prop))
% 0.16/0.58 FOF formula (<kernel.Constant object at 0x2b92e7937e60>, <kernel.DependentProduct object at 0x16f6a70>) of role type named sy_c_Algebra7_OModule_001_062_Itf__e_Mtf__e_J_001tf__b_001t__Product____Type__Ounit_001tf__d
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring module241733029unit_d:(carrie377329159t_unit->(carrie1950868226xt_b_d->Prop))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x2b92e7937f38>, <kernel.DependentProduct object at 0x16f6bd8>) of role type named sy_c_Algebra7_OModule_001tf__a_001tf__b_001t__Product____Type__Ounit_001tf__d
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring module1821517916unit_d:(carrie1963041556t_unit->(carrie1950868226xt_b_d->Prop))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x2b92e7937e60>, <kernel.DependentProduct object at 0x16f6908>) of role type named sy_c_Algebra7_OModule_001tf__a_001tf__b_001tf__c_001tf__d
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring module_a_b_c_d:(carrie722926983_a_b_c->(carrie1950868226xt_b_d->Prop))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x2b92e7937f38>, <kernel.DependentProduct object at 0x16f6b90>) of role type named sy_c_Algebra7_OModule_001tf__e_001tf__b_001tf__f_001tf__d
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring module_e_b_f_d:(carrie1821755406_e_b_f->(carrie1950868226xt_b_d->Prop))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x2b92e7937440>, <kernel.DependentProduct object at 0x16f68c0>) of role type named sy_c_Algebra7_Ofree__generator_001tf__b_001tf__d_001tf__a_001t__Product____Type__Ounit
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring free_g637607517t_unit:(carrie1950868226xt_b_d->(carrie1963041556t_unit->(set_a->Prop)))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x2b92e7937440>, <kernel.DependentProduct object at 0x16f6a70>) of role type named sy_c_Algebra7_Ofree__generator_001tf__b_001tf__d_001tf__a_001tf__c
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring free_g1087686480_d_a_c:(carrie1950868226xt_b_d->(carrie722926983_a_b_c->(set_a->Prop)))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x2b92e7937440>, <kernel.DependentProduct object at 0x16f6a28>) of role type named sy_c_Algebra7_Ofree__generator_001tf__b_001tf__d_001tf__e_001tf__f
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring free_g103796815_d_e_f:(carrie1950868226xt_b_d->(carrie1821755406_e_b_f->(set_e->Prop)))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x16f68c0>, <kernel.DependentProduct object at 0x16f6b90>) of role type named sy_c_Algebra7_Ogenerator_001tf__b_001tf__d_001tf__a_001t__Product____Type__Ounit
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring genera1692266857t_unit:(carrie1950868226xt_b_d->(carrie1963041556t_unit->(set_a->Prop)))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x16f6a70>, <kernel.DependentProduct object at 0x16f6b48>) of role type named sy_c_Algebra7_Ogenerator_001tf__b_001tf__d_001tf__a_001tf__c
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring generator_b_d_a_c:(carrie1950868226xt_b_d->(carrie722926983_a_b_c->(set_a->Prop)))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x16f6a28>, <kernel.DependentProduct object at 0x14551b8>) of role type named sy_c_Algebra7_Ogenerator_001tf__b_001tf__d_001tf__e_001tf__f
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring generator_b_d_e_f:(carrie1950868226xt_b_d->(carrie1821755406_e_b_f->(set_e->Prop)))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x16f6b90>, <kernel.DependentProduct object at 0x1455440>) of role type named sy_c_Algebra7_Ol__comb_001tf__b_001tf__d_001tf__a_001t__Product____Type__Ounit
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring l_comb1138968323t_unit:(carrie1950868226xt_b_d->(carrie1963041556t_unit->(nat->((nat->b)->((nat->a)->a)))))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x16f6a70>, <kernel.DependentProduct object at 0x14552d8>) of role type named sy_c_Algebra7_Ol__comb_001tf__b_001tf__d_001tf__a_001tf__c
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring l_comb_b_d_a_c:(carrie1950868226xt_b_d->(carrie722926983_a_b_c->(nat->((nat->b)->((nat->a)->a)))))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x16f6a28>, <kernel.DependentProduct object at 0x1455440>) of role type named sy_c_Algebra7_Ol__comb_001tf__b_001tf__d_001tf__e_001tf__f
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring l_comb_b_d_e_f:(carrie1950868226xt_b_d->(carrie1821755406_e_b_f->(nat->((nat->b)->((nat->e)->e)))))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x16f6a70>, <kernel.DependentProduct object at 0x14552d8>) of role type named sy_c_Algebra7_Olinear__span_001tf__b_001tf__d_001tf__a_001tf__c
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring linear_span_b_d_a_c:(carrie1950868226xt_b_d->(carrie722926983_a_b_c->(set_b->(set_a->set_a))))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x16f6a28>, <kernel.DependentProduct object at 0x1455908>) of role type named sy_c_Algebra7_Omdl_001tf__a_001tf__b_001tf__c
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring mdl_a_b_c:(carrie722926983_a_b_c->(set_a->carrie1963041556t_unit))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x16f6b90>, <kernel.DependentProduct object at 0x1455998>) of role type named sy_c_Algebra7_Omisomorphic_001tf__b_001tf__d_001tf__a_001t__Product____Type__Ounit_001tf__a_001t__Product____Type__Ounit
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring misomo493403663t_unit:(carrie1950868226xt_b_d->(carrie1963041556t_unit->(carrie1963041556t_unit->Prop)))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x16f6b90>, <kernel.DependentProduct object at 0x14551b8>) of role type named sy_c_Algebra7_Omisomorphic_001tf__b_001tf__d_001tf__a_001t__Product____Type__Ounit_001tf__a_001tf__c
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring misomo1935876354it_a_c:(carrie1950868226xt_b_d->(carrie1963041556t_unit->(carrie722926983_a_b_c->Prop)))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x1455a70>, <kernel.DependentProduct object at 0x1455440>) of role type named sy_c_Algebra7_Omisomorphic_001tf__b_001tf__d_001tf__a_001t__Product____Type__Ounit_001tf__e_001tf__f
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring misomo951986689it_e_f:(carrie1950868226xt_b_d->(carrie1963041556t_unit->(carrie1821755406_e_b_f->Prop)))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x1455ef0>, <kernel.DependentProduct object at 0x1455488>) of role type named sy_c_Algebra7_Omisomorphic_001tf__b_001tf__d_001tf__a_001tf__c_001tf__a_001t__Product____Type__Ounit
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring misomo1857159554t_unit:(carrie1950868226xt_b_d->(carrie722926983_a_b_c->(carrie1963041556t_unit->Prop)))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x1455908>, <kernel.DependentProduct object at 0x1455290>) of role type named sy_c_Algebra7_Omisomorphic_001tf__b_001tf__d_001tf__a_001tf__c_001tf__a_001tf__c
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring misomo1282343797_c_a_c:(carrie1950868226xt_b_d->(carrie722926983_a_b_c->(carrie722926983_a_b_c->Prop)))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x1455998>, <kernel.DependentProduct object at 0x1455488>) of role type named sy_c_Algebra7_Omisomorphic_001tf__b_001tf__d_001tf__a_001tf__c_001tf__e_001tf__f
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring misomo298454132_c_e_f:(carrie1950868226xt_b_d->(carrie722926983_a_b_c->(carrie1821755406_e_b_f->Prop)))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x1455440>, <kernel.DependentProduct object at 0x1454320>) of role type named sy_c_Algebra7_Omisomorphic_001tf__b_001tf__d_001tf__e_001tf__f_001tf__a_001t__Product____Type__Ounit
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring misomo368157697t_unit:(carrie1950868226xt_b_d->(carrie1821755406_e_b_f->(carrie1963041556t_unit->Prop)))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x1455290>, <kernel.DependentProduct object at 0x1454830>) of role type named sy_c_Algebra7_Omisomorphic_001tf__b_001tf__d_001tf__e_001tf__f_001tf__a_001tf__c
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring misomo1752826100_f_a_c:(carrie1950868226xt_b_d->(carrie1821755406_e_b_f->(carrie722926983_a_b_c->Prop)))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x1455998>, <kernel.DependentProduct object at 0x1454950>) of role type named sy_c_Algebra7_Omisomorphic_001tf__b_001tf__d_001tf__e_001tf__f_001tf__e_001tf__f
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring misomo768936435_f_e_f:(carrie1950868226xt_b_d->(carrie1821755406_e_b_f->(carrie1821755406_e_b_f->Prop)))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x1455440>, <kernel.DependentProduct object at 0x1454830>) of role type named sy_c_Algebra7_Oquotient__of__submodules_001tf__b_001tf__d_001tf__a_001t__Product____Type__Ounit
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring quotie1196826005t_unit:(carrie1950868226xt_b_d->(carrie1963041556t_unit->(set_a->(set_a->set_b))))
% 0.16/0.59 FOF formula (<kernel.Constant object at 0x1455998>, <kernel.DependentProduct object at 0x1454950>) of role type named sy_c_Algebra7_Oquotient__of__submodules_001tf__b_001tf__d_001tf__a_001tf__c
% 0.16/0.59 Using role type
% 0.16/0.59 Declaring quotie1153752712_d_a_c:(carrie1950868226xt_b_d->(carrie722926983_a_b_c->(set_a->(set_a->set_b))))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1455440>, <kernel.DependentProduct object at 0x1454dd0>) of role type named sy_c_Algebra7_Oquotient__of__submodules_001tf__b_001tf__d_001tf__e_001tf__f
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring quotie169863047_d_e_f:(carrie1950868226xt_b_d->(carrie1821755406_e_b_f->(set_e->(set_e->set_b))))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1455290>, <kernel.DependentProduct object at 0x14543b0>) of role type named sy_c_Algebra7_Osmodule__ideal__coeff_001tf__b_001tf__d_001tf__a_001t__Product____Type__Ounit
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring smodul132175289t_unit:(carrie1950868226xt_b_d->(carrie1963041556t_unit->(set_b->set_a)))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1455290>, <kernel.DependentProduct object at 0x1454830>) of role type named sy_c_Algebra7_Osmodule__ideal__coeff_001tf__b_001tf__d_001tf__a_001tf__c
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring smodul818989740_d_a_c:(carrie1950868226xt_b_d->(carrie722926983_a_b_c->(set_b->set_a)))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454dd0>, <kernel.DependentProduct object at 0x1454710>) of role type named sy_c_Algebra7_Osmodule__ideal__coeff_001tf__b_001tf__d_001tf__e_001tf__f
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring smodul1982583723_d_e_f:(carrie1950868226xt_b_d->(carrie1821755406_e_b_f->(set_b->set_e)))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x14543b0>, <kernel.DependentProduct object at 0x1454d40>) of role type named sy_c_Algebra7_Osubmodule_001tf__b_001tf__d_001tf__a_001t__Product____Type__Ounit
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring submod903911234t_unit:(carrie1950868226xt_b_d->(carrie1963041556t_unit->(set_a->Prop)))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454830>, <kernel.DependentProduct object at 0x1454050>) of role type named sy_c_Algebra7_Osubmodule_001tf__b_001tf__d_001tf__a_001tf__c
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring submodule_b_d_a_c:(carrie1950868226xt_b_d->(carrie722926983_a_b_c->(set_a->Prop)))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454710>, <kernel.DependentProduct object at 0x1454d88>) of role type named sy_c_Algebra7_Osubmodule_001tf__b_001tf__d_001tf__e_001tf__f
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring submodule_b_d_e_f:(carrie1950868226xt_b_d->(carrie1821755406_e_b_f->(set_e->Prop)))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454d40>, <kernel.DependentProduct object at 0x1454680>) of role type named sy_c_Algebra8__Mirabelle__tltoludslr_Ofgs_001tf__b_001tf__d_001tf__a_001t__Product____Type__Ounit
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring algebr1039611956t_unit:(carrie1950868226xt_b_d->(carrie1963041556t_unit->(set_a->set_a)))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454050>, <kernel.DependentProduct object at 0x1454f38>) of role type named sy_c_Algebra8__Mirabelle__tltoludslr_Ofgs_001tf__b_001tf__d_001tf__a_001tf__c
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring algebr1152250919_d_a_c:(carrie1950868226xt_b_d->(carrie722926983_a_b_c->(set_a->set_a)))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454d88>, <kernel.DependentProduct object at 0x1454cf8>) of role type named sy_c_Algebra8__Mirabelle__tltoludslr_Ofgs_001tf__b_001tf__d_001tf__e_001tf__f
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring algebr168361254_d_e_f:(carrie1950868226xt_b_d->(carrie1821755406_e_b_f->(set_e->set_e)))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454680>, <kernel.DependentProduct object at 0x1454f80>) of role type named sy_c_FuncSet_OPi_001t__Nat__Onat_001tf__a
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring pi_nat_a:(set_nat->((nat->set_a)->set_nat_a))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454f38>, <kernel.DependentProduct object at 0x14549e0>) of role type named sy_c_FuncSet_OPi_001t__Nat__Onat_001tf__b
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring pi_nat_b:(set_nat->((nat->set_b)->set_nat_b))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454cf8>, <kernel.DependentProduct object at 0x1454bd8>) of role type named sy_c_FuncSet_OPi_001t__Nat__Onat_001tf__e
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring pi_nat_e:(set_nat->((nat->set_e)->set_nat_e))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454f80>, <kernel.DependentProduct object at 0x1454ef0>) of role type named sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring minus_minus_nat:(nat->(nat->nat))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x14549e0>, <kernel.DependentProduct object at 0x1454b48>) of role type named sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_I_062_It__Nat__Onat_Mtf__a_J_J
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring minus_1788767276_nat_a:(set_nat_a->(set_nat_a->set_nat_a))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454bd8>, <kernel.DependentProduct object at 0x1454e60>) of role type named sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_I_062_It__Nat__Onat_Mtf__b_J_J
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring minus_780847917_nat_b:(set_nat_b->(set_nat_b->set_nat_b))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454ef0>, <kernel.DependentProduct object at 0x1454f38>) of role type named sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__a_J
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring minus_minus_set_a:(set_a->(set_a->set_a))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454b48>, <kernel.Constant object at 0x1454f38>) of role type named sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring zero_zero_nat:nat
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454bd8>, <kernel.DependentProduct object at 0x14549e0>) of role type named sy_c_Nat_OSuc
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring suc:(nat->nat)
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454320>, <kernel.Constant object at 0x14549e0>) of role type named sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_I_062_It__Nat__Onat_Mtf__a_J_J
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring bot_bot_set_nat_a:set_nat_a
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454b48>, <kernel.Constant object at 0x14549e0>) of role type named sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_I_062_It__Nat__Onat_Mtf__b_J_J
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring bot_bot_set_nat_b:set_nat_b
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454bd8>, <kernel.Constant object at 0x14549e0>) of role type named sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring bot_bot_set_nat:set_nat
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454320>, <kernel.Constant object at 0x14549e0>) of role type named sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring bot_bot_set_a:set_a
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454b48>, <kernel.Constant object at 0x14549e0>) of role type named sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__e_J
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring bot_bot_set_e:set_e
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454bd8>, <kernel.DependentProduct object at 0x2b92dfe67200>) of role type named sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring ord_less_nat:(nat->(nat->Prop))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x14545f0>, <kernel.DependentProduct object at 0x2b92dfe67170>) of role type named sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_Itf__a_J
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring ord_less_set_a:(set_a->(set_a->Prop))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454320>, <kernel.DependentProduct object at 0x2b92dfe671b8>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring ord_less_eq_nat:(nat->(nat->Prop))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454bd8>, <kernel.DependentProduct object at 0x2b92dfe670e0>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_062_It__Nat__Onat_Mtf__a_J_J
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring ord_le157368549_nat_a:(set_nat_a->(set_nat_a->Prop))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x14545f0>, <kernel.DependentProduct object at 0x2b92dfe67128>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_062_It__Nat__Onat_Mtf__b_J_J
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring ord_le1296932838_nat_b:(set_nat_b->(set_nat_b->Prop))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454bd8>, <kernel.DependentProduct object at 0x2b92dfe67050>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring ord_less_eq_set_a:(set_a->(set_a->Prop))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x14545f0>, <kernel.DependentProduct object at 0x2b92dfe67200>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__e_J
% 0.16/0.60 Using role type
% 0.16/0.60 Declaring ord_less_eq_set_e:(set_e->(set_e->Prop))
% 0.16/0.60 FOF formula (<kernel.Constant object at 0x1454320>, <kernel.DependentProduct object at 0x2b92dfe671b8>) of role type named sy_c_Set_OCollect_001_062_It__Nat__Onat_Mtf__a_J
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring collect_nat_a:(((nat->a)->Prop)->set_nat_a)
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x1454320>, <kernel.DependentProduct object at 0x2b92dfe67098>) of role type named sy_c_Set_OCollect_001_062_It__Nat__Onat_Mtf__b_J
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring collect_nat_b:(((nat->b)->Prop)->set_nat_b)
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x2b92dfe67248>, <kernel.DependentProduct object at 0x2b92dfe673b0>) of role type named sy_c_Set_OCollect_001t__Nat__Onat
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring collect_nat:((nat->Prop)->set_nat)
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x2b92dfe671b8>, <kernel.DependentProduct object at 0x2b92dfe67200>) of role type named sy_c_Set_OCollect_001tf__a
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring collect_a:((a->Prop)->set_a)
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x2b92dfe67098>, <kernel.DependentProduct object at 0x2b92dfe67170>) of role type named sy_c_Set_Oinsert_001_062_It__Nat__Onat_Mtf__a_J
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring insert_nat_a:((nat->a)->(set_nat_a->set_nat_a))
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x2b92dfe67128>, <kernel.DependentProduct object at 0x2b92dfe671b8>) of role type named sy_c_Set_Oinsert_001_062_It__Nat__Onat_Mtf__b_J
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring insert_nat_b:((nat->b)->(set_nat_b->set_nat_b))
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x2b92dfe673f8>, <kernel.DependentProduct object at 0x2b92dfe673b0>) of role type named sy_c_Set_Oinsert_001tf__a
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring insert_a:(a->(set_a->set_a))
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x2b92dfe67440>, <kernel.DependentProduct object at 0x2b92dfe67128>) of role type named sy_c_member_001_062_It__Nat__Onat_Mtf__a_J
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring member_nat_a:((nat->a)->(set_nat_a->Prop))
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x2b92dfe671b8>, <kernel.DependentProduct object at 0x2b92dfe673f8>) of role type named sy_c_member_001_062_It__Nat__Onat_Mtf__b_J
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring member_nat_b:((nat->b)->(set_nat_b->Prop))
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x2b92dfe67200>, <kernel.DependentProduct object at 0x2b92dfe67440>) of role type named sy_c_member_001_062_It__Nat__Onat_Mtf__e_J
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring member_nat_e:((nat->e)->(set_nat_e->Prop))
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x2b92dfe67368>, <kernel.DependentProduct object at 0x2b92dfe673f8>) of role type named sy_c_member_001t__Nat__Onat
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring member_nat:(nat->(set_nat->Prop))
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x2b92dfe673b0>, <kernel.DependentProduct object at 0x2b92dfe67170>) of role type named sy_c_member_001tf__a
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring member_a:(a->(set_a->Prop))
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x2b92dfe67440>, <kernel.DependentProduct object at 0x2b92dfe671b8>) of role type named sy_c_member_001tf__e
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring member_e:(e->(set_e->Prop))
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x2b92dfe673f8>, <kernel.Constant object at 0x2b92dfe671b8>) of role type named sy_v_H
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring h:set_a
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x2b92dfe673b0>, <kernel.Constant object at 0x2b92dfe671b8>) of role type named sy_v_H1
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring h1:set_a
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x2b92dfe67440>, <kernel.Constant object at 0x2b92dfe671b8>) of role type named sy_v_M
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring m:carrie722926983_a_b_c
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x2b92dfe673f8>, <kernel.Constant object at 0x2b92dfe671b8>) of role type named sy_v_N
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring n:carrie1821755406_e_b_f
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x2b92dfe673b0>, <kernel.Constant object at 0x2b92dfe671b8>) of role type named sy_v_R
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring r:carrie1950868226xt_b_d
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x2b92dfe67440>, <kernel.DependentProduct object at 0x2b92dfe677e8>) of role type named sy_v_g
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring g:(nat->a)
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x2b92dfe67710>, <kernel.Constant object at 0x2b92dfe677e8>) of role type named sy_v_h
% 0.44/0.61 Using role type
% 0.44/0.62 Declaring h2:a
% 0.44/0.62 FOF formula (<kernel.Constant object at 0x2b92dfe673b0>, <kernel.Constant object at 0x2b92dfe677e8>) of role type named sy_v_m
% 0.44/0.62 Using role type
% 0.44/0.62 Declaring m2:nat
% 0.44/0.62 FOF formula (<kernel.Constant object at 0x2b92dfe67440>, <kernel.DependentProduct object at 0x2b92dfe678c0>) of role type named sy_v_t
% 0.44/0.62 Using role type
% 0.44/0.62 Declaring t:(nat->b)
% 0.44/0.62 FOF formula (<kernel.Constant object at 0x2b92dfe676c8>, <kernel.Constant object at 0x2b92dfe678c0>) of role type named sy_v_x
% 0.44/0.62 Using role type
% 0.44/0.62 Declaring x:a
% 0.44/0.62 FOF formula (<kernel.Constant object at 0x2b92dfe673b0>, <kernel.Constant object at 0x2b92dfe678c0>) of role type named sy_v_xa
% 0.44/0.62 Using role type
% 0.44/0.62 Declaring xa:nat
% 0.44/0.62 FOF formula (ring_b_d r) of role axiom named fact_0_sc__Ring
% 0.44/0.62 A new axiom: (ring_b_d r)
% 0.44/0.62 FOF formula (forall (H:set_a) (H2:a), ((((submodule_b_d_a_c r) m) H)->(((member_a H2) H)->((member_a H2) (carrie2021454486_a_b_c m))))) of role axiom named fact_1_submodule__subset1
% 0.44/0.62 A new axiom: (forall (H:set_a) (H2:a), ((((submodule_b_d_a_c r) m) H)->(((member_a H2) H)->((member_a H2) (carrie2021454486_a_b_c m)))))
% 0.44/0.62 FOF formula (((submodule_b_d_a_c r) m) (carrie2021454486_a_b_c m)) of role axiom named fact_2_submodule__whole
% 0.44/0.62 A new axiom: (((submodule_b_d_a_c r) m) (carrie2021454486_a_b_c m))
% 0.44/0.62 FOF formula (forall (H:set_a), ((((submodule_b_d_a_c r) m) H)->((ord_less_eq_set_a H) (carrie2021454486_a_b_c m)))) of role axiom named fact_3_submodule__subset
% 0.44/0.62 A new axiom: (forall (H:set_a), ((((submodule_b_d_a_c r) m) H)->((ord_less_eq_set_a H) (carrie2021454486_a_b_c m))))
% 0.44/0.62 FOF formula (forall (H:set_a), ((((free_g1087686480_d_a_c r) m) H)->((ord_less_eq_set_a H) (carrie2021454486_a_b_c m)))) of role axiom named fact_4_free__generator__sub
% 0.44/0.62 A new axiom: (forall (H:set_a), ((((free_g1087686480_d_a_c r) m) H)->((ord_less_eq_set_a H) (carrie2021454486_a_b_c m))))
% 0.44/0.62 FOF formula (forall (A:set_a) (X:a), (((ord_less_eq_set_a A) (carrie2021454486_a_b_c m))->(((member_a X) A)->((member_a X) (((algebr1152250919_d_a_c r) m) A))))) of role axiom named fact_5_elem__fgs
% 0.44/0.62 A new axiom: (forall (A:set_a) (X:a), (((ord_less_eq_set_a A) (carrie2021454486_a_b_c m))->(((member_a X) A)->((member_a X) (((algebr1152250919_d_a_c r) m) A)))))
% 0.44/0.62 FOF formula (forall (A:set_a), (((ord_less_eq_set_a A) (carrie2021454486_a_b_c m))->((ord_less_eq_set_a (((algebr1152250919_d_a_c r) m) A)) (carrie2021454486_a_b_c m)))) of role axiom named fact_6_fgs__sub__carrier
% 0.44/0.62 A new axiom: (forall (A:set_a), (((ord_less_eq_set_a A) (carrie2021454486_a_b_c m))->((ord_less_eq_set_a (((algebr1152250919_d_a_c r) m) A)) (carrie2021454486_a_b_c m))))
% 0.44/0.62 FOF formula (forall (H:set_a) (J:set_a) (K:set_a), ((((free_g1087686480_d_a_c r) m) H)->(((ord_less_eq_set_a J) K)->(((ord_less_eq_set_a K) H)->((ord_less_eq_set_a (((algebr1152250919_d_a_c r) m) J)) (((algebr1152250919_d_a_c r) m) K)))))) of role axiom named fact_7_fgs__mono
% 0.44/0.62 A new axiom: (forall (H:set_a) (J:set_a) (K:set_a), ((((free_g1087686480_d_a_c r) m) H)->(((ord_less_eq_set_a J) K)->(((ord_less_eq_set_a K) H)->((ord_less_eq_set_a (((algebr1152250919_d_a_c r) m) J)) (((algebr1152250919_d_a_c r) m) K))))))
% 0.44/0.62 FOF formula (forall (A:set_a), (((ord_less_eq_set_a A) (carrie2021454486_a_b_c m))->(((submodule_b_d_a_c r) m) (((algebr1152250919_d_a_c r) m) A)))) of role axiom named fact_8_fgs__submodule
% 0.44/0.62 A new axiom: (forall (A:set_a), (((ord_less_eq_set_a A) (carrie2021454486_a_b_c m))->(((submodule_b_d_a_c r) m) (((algebr1152250919_d_a_c r) m) A))))
% 0.44/0.62 FOF formula (forall (H:set_a) (S:(nat->b)) (N:nat) (F:(nat->a)) (G:(nat->a)), (((ord_less_eq_set_a H) (carrie2021454486_a_b_c m))->(((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d r))))->(((member_nat_a F) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->(((member_nat_a G) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->((forall (X2:nat), (((member_nat X2) (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N))))->(((eq a) (F X2)) (G X2))))->(((eq a) (((((l_comb_b_d_a_c r) m) N) S) F)) (((((l_comb_b_d_a_c r) m) N) S) G)))))))) of role axiom named fact_9_linear__comb__eq
% 0.47/0.64 A new axiom: (forall (H:set_a) (S:(nat->b)) (N:nat) (F:(nat->a)) (G:(nat->a)), (((ord_less_eq_set_a H) (carrie2021454486_a_b_c m))->(((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d r))))->(((member_nat_a F) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->(((member_nat_a G) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->((forall (X2:nat), (((member_nat X2) (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N))))->(((eq a) (F X2)) (G X2))))->(((eq a) (((((l_comb_b_d_a_c r) m) N) S) F)) (((((l_comb_b_d_a_c r) m) N) S) G))))))))
% 0.47/0.64 FOF formula (forall (H:set_a) (S:(nat->b)) (N:nat) (F:(nat->a)) (G:(nat->a)), (((ord_less_eq_set_a H) (carrie2021454486_a_b_c m))->(((and ((and ((and ((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d r))))) ((member_nat_a F) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))) ((member_nat_a G) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))) (forall (X2:nat), (((member_nat X2) (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N))))->(((eq a) (F X2)) (G X2)))))->(((eq a) (((((l_comb_b_d_a_c r) m) N) S) F)) (((((l_comb_b_d_a_c r) m) N) S) G))))) of role axiom named fact_10_linear__comb__eqTr
% 0.47/0.64 A new axiom: (forall (H:set_a) (S:(nat->b)) (N:nat) (F:(nat->a)) (G:(nat->a)), (((ord_less_eq_set_a H) (carrie2021454486_a_b_c m))->(((and ((and ((and ((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d r))))) ((member_nat_a F) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))) ((member_nat_a G) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))) (forall (X2:nat), (((member_nat X2) (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N))))->(((eq a) (F X2)) (G X2)))))->(((eq a) (((((l_comb_b_d_a_c r) m) N) S) F)) (((((l_comb_b_d_a_c r) m) N) S) G)))))
% 0.47/0.64 FOF formula (forall (A2:set_b) (H:set_a) (S:(nat->b)) (N:nat) (M:(nat->a)), (((ideal_b_d r) A2)->(((ord_less_eq_set_a H) (carrie2021454486_a_b_c m))->(((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> A2)))->(((member_nat_a M) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->((member_a (((((l_comb_b_d_a_c r) m) N) S) M)) (carrie2021454486_a_b_c m))))))) of role axiom named fact_11_l__comb__mem
% 0.47/0.64 A new axiom: (forall (A2:set_b) (H:set_a) (S:(nat->b)) (N:nat) (M:(nat->a)), (((ideal_b_d r) A2)->(((ord_less_eq_set_a H) (carrie2021454486_a_b_c m))->(((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> A2)))->(((member_nat_a M) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->((member_a (((((l_comb_b_d_a_c r) m) N) S) M)) (carrie2021454486_a_b_c m)))))))
% 0.47/0.64 FOF formula (forall (A2:set_b) (H:set_a) (N:nat), (((ideal_b_d r) A2)->(((ord_less_eq_set_a H) (carrie2021454486_a_b_c m))->(forall (S2:(nat->b)) (M2:(nat->a)), (((and ((member_nat_b S2) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> A2)))) ((member_nat_a M2) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))->((member_a (((((l_comb_b_d_a_c r) m) N) S2) M2)) (carrie2021454486_a_b_c m))))))) of role axiom named fact_12_liear__comb__memTr
% 0.47/0.64 A new axiom: (forall (A2:set_b) (H:set_a) (N:nat), (((ideal_b_d r) A2)->(((ord_less_eq_set_a H) (carrie2021454486_a_b_c m))->(forall (S2:(nat->b)) (M2:(nat->a)), (((and ((member_nat_b S2) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> A2)))) ((member_nat_a M2) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))->((member_a (((((l_comb_b_d_a_c r) m) N) S2) M2)) (carrie2021454486_a_b_c m)))))))
% 0.47/0.65 FOF formula ((ideal_b_d r) ((annihilator_b_d_a_c r) m)) of role axiom named fact_13_Ann__is__ideal
% 0.47/0.65 A new axiom: ((ideal_b_d r) ((annihilator_b_d_a_c r) m))
% 0.47/0.65 FOF formula (forall (K:set_a) (X:a), ((not (((eq set_a) K) bot_bot_set_a))->(((ord_less_eq_set_a K) (carrie2021454486_a_b_c m))->(((member_a X) (((algebr1152250919_d_a_c r) m) K))->((ex nat) (fun (N2:nat)=> ((ex (nat->a)) (fun (X2:(nat->a))=> ((and ((member_nat_a X2) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N2)))) (fun (Uu:nat)=> K)))) ((ex (nat->b)) (fun (Xa:(nat->b))=> ((and ((member_nat_b Xa) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N2)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d r))))) (((eq a) X) (((((l_comb_b_d_a_c r) m) N2) Xa) X2)))))))))))))) of role axiom named fact_14_mem__fgs__l__comb
% 0.47/0.65 A new axiom: (forall (K:set_a) (X:a), ((not (((eq set_a) K) bot_bot_set_a))->(((ord_less_eq_set_a K) (carrie2021454486_a_b_c m))->(((member_a X) (((algebr1152250919_d_a_c r) m) K))->((ex nat) (fun (N2:nat)=> ((ex (nat->a)) (fun (X2:(nat->a))=> ((and ((member_nat_a X2) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N2)))) (fun (Uu:nat)=> K)))) ((ex (nat->b)) (fun (Xa:(nat->b))=> ((and ((member_nat_b Xa) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N2)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d r))))) (((eq a) X) (((((l_comb_b_d_a_c r) m) N2) Xa) X2))))))))))))))
% 0.47/0.65 FOF formula ((module_a_b_c_d m) r) of role axiom named fact_15_Module__axioms
% 0.47/0.65 A new axiom: ((module_a_b_c_d m) r)
% 0.47/0.65 FOF formula (forall (P:set_a) (Q:set_a), ((((submodule_b_d_a_c r) m) P)->((((submodule_b_d_a_c r) m) Q)->((ideal_b_d r) ((((quotie1153752712_d_a_c r) m) P) Q))))) of role axiom named fact_16_quotient__of__submodules__is__ideal
% 0.47/0.65 A new axiom: (forall (P:set_a) (Q:set_a), ((((submodule_b_d_a_c r) m) P)->((((submodule_b_d_a_c r) m) Q)->((ideal_b_d r) ((((quotie1153752712_d_a_c r) m) P) Q)))))
% 0.47/0.65 FOF formula (forall (A2:set_b), (((ideal_b_d r) A2)->(((submodule_b_d_a_c r) m) (((smodul818989740_d_a_c r) m) A2)))) of role axiom named fact_17_smodule__ideal__coeff__is__Submodule
% 0.47/0.65 A new axiom: (forall (A2:set_b), (((ideal_b_d r) A2)->(((submodule_b_d_a_c r) m) (((smodul818989740_d_a_c r) m) A2))))
% 0.47/0.65 FOF formula (forall (A2:set_b) (X:a), (((ideal_b_d r) A2)->(((member_a X) (((smodul818989740_d_a_c r) m) A2))->((ex nat) (fun (N2:nat)=> ((ex (nat->b)) (fun (X2:(nat->b))=> ((and ((member_nat_b X2) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N2)))) (fun (Uu:nat)=> A2)))) ((ex (nat->a)) (fun (Xa:(nat->a))=> ((and ((member_nat_a Xa) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N2)))) (fun (Uu:nat)=> (carrie2021454486_a_b_c m))))) (((eq a) X) (((((l_comb_b_d_a_c r) m) N2) X2) Xa))))))))))))) of role axiom named fact_18_mem__smodule__ideal__coeff
% 0.47/0.65 A new axiom: (forall (A2:set_b) (X:a), (((ideal_b_d r) A2)->(((member_a X) (((smodul818989740_d_a_c r) m) A2))->((ex nat) (fun (N2:nat)=> ((ex (nat->b)) (fun (X2:(nat->b))=> ((and ((member_nat_b X2) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N2)))) (fun (Uu:nat)=> A2)))) ((ex (nat->a)) (fun (Xa:(nat->a))=> ((and ((member_nat_a Xa) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N2)))) (fun (Uu:nat)=> (carrie2021454486_a_b_c m))))) (((eq a) X) (((((l_comb_b_d_a_c r) m) N2) X2) Xa)))))))))))))
% 0.47/0.65 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (A:set_e) (X:e), (((module_e_b_f_d M3) R)->(((ord_less_eq_set_e A) (carrie730238621_e_b_f M3))->(((member_e X) A)->((member_e X) (((algebr168361254_d_e_f R) M3) A)))))) of role axiom named fact_19_Module_Oelem__fgs
% 0.47/0.65 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (A:set_e) (X:e), (((module_e_b_f_d M3) R)->(((ord_less_eq_set_e A) (carrie730238621_e_b_f M3))->(((member_e X) A)->((member_e X) (((algebr168361254_d_e_f R) M3) A))))))
% 0.47/0.65 FOF formula (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (A:set_a) (X:a), (((module1821517916unit_d M3) R)->(((ord_less_eq_set_a A) (carrie1074654371t_unit M3))->(((member_a X) A)->((member_a X) (((algebr1039611956t_unit R) M3) A)))))) of role axiom named fact_20_Module_Oelem__fgs
% 0.47/0.66 A new axiom: (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (A:set_a) (X:a), (((module1821517916unit_d M3) R)->(((ord_less_eq_set_a A) (carrie1074654371t_unit M3))->(((member_a X) A)->((member_a X) (((algebr1039611956t_unit R) M3) A))))))
% 0.47/0.66 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (A:set_a) (X:a), (((module_a_b_c_d M3) R)->(((ord_less_eq_set_a A) (carrie2021454486_a_b_c M3))->(((member_a X) A)->((member_a X) (((algebr1152250919_d_a_c R) M3) A)))))) of role axiom named fact_21_Module_Oelem__fgs
% 0.47/0.66 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (A:set_a) (X:a), (((module_a_b_c_d M3) R)->(((ord_less_eq_set_a A) (carrie2021454486_a_b_c M3))->(((member_a X) A)->((member_a X) (((algebr1152250919_d_a_c R) M3) A))))))
% 0.47/0.66 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (H:set_e) (J:set_e) (K:set_e), (((module_e_b_f_d M3) R)->((((free_g103796815_d_e_f R) M3) H)->(((ord_less_eq_set_e J) K)->(((ord_less_eq_set_e K) H)->((ord_less_eq_set_e (((algebr168361254_d_e_f R) M3) J)) (((algebr168361254_d_e_f R) M3) K))))))) of role axiom named fact_22_Module_Ofgs__mono
% 0.47/0.66 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (H:set_e) (J:set_e) (K:set_e), (((module_e_b_f_d M3) R)->((((free_g103796815_d_e_f R) M3) H)->(((ord_less_eq_set_e J) K)->(((ord_less_eq_set_e K) H)->((ord_less_eq_set_e (((algebr168361254_d_e_f R) M3) J)) (((algebr168361254_d_e_f R) M3) K)))))))
% 0.47/0.66 FOF formula (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (H:set_a) (J:set_a) (K:set_a), (((module1821517916unit_d M3) R)->((((free_g637607517t_unit R) M3) H)->(((ord_less_eq_set_a J) K)->(((ord_less_eq_set_a K) H)->((ord_less_eq_set_a (((algebr1039611956t_unit R) M3) J)) (((algebr1039611956t_unit R) M3) K))))))) of role axiom named fact_23_Module_Ofgs__mono
% 0.47/0.66 A new axiom: (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (H:set_a) (J:set_a) (K:set_a), (((module1821517916unit_d M3) R)->((((free_g637607517t_unit R) M3) H)->(((ord_less_eq_set_a J) K)->(((ord_less_eq_set_a K) H)->((ord_less_eq_set_a (((algebr1039611956t_unit R) M3) J)) (((algebr1039611956t_unit R) M3) K)))))))
% 0.47/0.66 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (H:set_a) (J:set_a) (K:set_a), (((module_a_b_c_d M3) R)->((((free_g1087686480_d_a_c R) M3) H)->(((ord_less_eq_set_a J) K)->(((ord_less_eq_set_a K) H)->((ord_less_eq_set_a (((algebr1152250919_d_a_c R) M3) J)) (((algebr1152250919_d_a_c R) M3) K))))))) of role axiom named fact_24_Module_Ofgs__mono
% 0.47/0.66 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (H:set_a) (J:set_a) (K:set_a), (((module_a_b_c_d M3) R)->((((free_g1087686480_d_a_c R) M3) H)->(((ord_less_eq_set_a J) K)->(((ord_less_eq_set_a K) H)->((ord_less_eq_set_a (((algebr1152250919_d_a_c R) M3) J)) (((algebr1152250919_d_a_c R) M3) K)))))))
% 0.47/0.66 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (A:set_e), (((module_e_b_f_d M3) R)->(((ord_less_eq_set_e A) (carrie730238621_e_b_f M3))->(((submodule_b_d_e_f R) M3) (((algebr168361254_d_e_f R) M3) A))))) of role axiom named fact_25_Module_Ofgs__submodule
% 0.47/0.66 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (A:set_e), (((module_e_b_f_d M3) R)->(((ord_less_eq_set_e A) (carrie730238621_e_b_f M3))->(((submodule_b_d_e_f R) M3) (((algebr168361254_d_e_f R) M3) A)))))
% 0.47/0.66 FOF formula (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (A:set_a), (((module1821517916unit_d M3) R)->(((ord_less_eq_set_a A) (carrie1074654371t_unit M3))->(((submod903911234t_unit R) M3) (((algebr1039611956t_unit R) M3) A))))) of role axiom named fact_26_Module_Ofgs__submodule
% 0.47/0.66 A new axiom: (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (A:set_a), (((module1821517916unit_d M3) R)->(((ord_less_eq_set_a A) (carrie1074654371t_unit M3))->(((submod903911234t_unit R) M3) (((algebr1039611956t_unit R) M3) A)))))
% 0.47/0.66 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (A:set_a), (((module_a_b_c_d M3) R)->(((ord_less_eq_set_a A) (carrie2021454486_a_b_c M3))->(((submodule_b_d_a_c R) M3) (((algebr1152250919_d_a_c R) M3) A))))) of role axiom named fact_27_Module_Ofgs__submodule
% 0.47/0.68 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (A:set_a), (((module_a_b_c_d M3) R)->(((ord_less_eq_set_a A) (carrie2021454486_a_b_c M3))->(((submodule_b_d_a_c R) M3) (((algebr1152250919_d_a_c R) M3) A)))))
% 0.47/0.68 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (K:set_e) (X:e), (((module_e_b_f_d M3) R)->((not (((eq set_e) K) bot_bot_set_e))->(((ord_less_eq_set_e K) (carrie730238621_e_b_f M3))->(((member_e X) (((algebr168361254_d_e_f R) M3) K))->((ex nat) (fun (N2:nat)=> ((ex (nat->e)) (fun (X2:(nat->e))=> ((and ((member_nat_e X2) ((pi_nat_e (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N2)))) (fun (Uu:nat)=> K)))) ((ex (nat->b)) (fun (Xa:(nat->b))=> ((and ((member_nat_b Xa) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N2)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d R))))) (((eq e) X) (((((l_comb_b_d_e_f R) M3) N2) Xa) X2))))))))))))))) of role axiom named fact_28_Module_Omem__fgs__l__comb
% 0.47/0.68 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (K:set_e) (X:e), (((module_e_b_f_d M3) R)->((not (((eq set_e) K) bot_bot_set_e))->(((ord_less_eq_set_e K) (carrie730238621_e_b_f M3))->(((member_e X) (((algebr168361254_d_e_f R) M3) K))->((ex nat) (fun (N2:nat)=> ((ex (nat->e)) (fun (X2:(nat->e))=> ((and ((member_nat_e X2) ((pi_nat_e (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N2)))) (fun (Uu:nat)=> K)))) ((ex (nat->b)) (fun (Xa:(nat->b))=> ((and ((member_nat_b Xa) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N2)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d R))))) (((eq e) X) (((((l_comb_b_d_e_f R) M3) N2) Xa) X2)))))))))))))))
% 0.47/0.68 FOF formula (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (K:set_a) (X:a), (((module1821517916unit_d M3) R)->((not (((eq set_a) K) bot_bot_set_a))->(((ord_less_eq_set_a K) (carrie1074654371t_unit M3))->(((member_a X) (((algebr1039611956t_unit R) M3) K))->((ex nat) (fun (N2:nat)=> ((ex (nat->a)) (fun (X2:(nat->a))=> ((and ((member_nat_a X2) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N2)))) (fun (Uu:nat)=> K)))) ((ex (nat->b)) (fun (Xa:(nat->b))=> ((and ((member_nat_b Xa) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N2)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d R))))) (((eq a) X) (((((l_comb1138968323t_unit R) M3) N2) Xa) X2))))))))))))))) of role axiom named fact_29_Module_Omem__fgs__l__comb
% 0.47/0.68 A new axiom: (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (K:set_a) (X:a), (((module1821517916unit_d M3) R)->((not (((eq set_a) K) bot_bot_set_a))->(((ord_less_eq_set_a K) (carrie1074654371t_unit M3))->(((member_a X) (((algebr1039611956t_unit R) M3) K))->((ex nat) (fun (N2:nat)=> ((ex (nat->a)) (fun (X2:(nat->a))=> ((and ((member_nat_a X2) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N2)))) (fun (Uu:nat)=> K)))) ((ex (nat->b)) (fun (Xa:(nat->b))=> ((and ((member_nat_b Xa) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N2)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d R))))) (((eq a) X) (((((l_comb1138968323t_unit R) M3) N2) Xa) X2)))))))))))))))
% 0.47/0.68 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (K:set_a) (X:a), (((module_a_b_c_d M3) R)->((not (((eq set_a) K) bot_bot_set_a))->(((ord_less_eq_set_a K) (carrie2021454486_a_b_c M3))->(((member_a X) (((algebr1152250919_d_a_c R) M3) K))->((ex nat) (fun (N2:nat)=> ((ex (nat->a)) (fun (X2:(nat->a))=> ((and ((member_nat_a X2) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N2)))) (fun (Uu:nat)=> K)))) ((ex (nat->b)) (fun (Xa:(nat->b))=> ((and ((member_nat_b Xa) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N2)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d R))))) (((eq a) X) (((((l_comb_b_d_a_c R) M3) N2) Xa) X2))))))))))))))) of role axiom named fact_30_Module_Omem__fgs__l__comb
% 0.47/0.69 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (K:set_a) (X:a), (((module_a_b_c_d M3) R)->((not (((eq set_a) K) bot_bot_set_a))->(((ord_less_eq_set_a K) (carrie2021454486_a_b_c M3))->(((member_a X) (((algebr1152250919_d_a_c R) M3) K))->((ex nat) (fun (N2:nat)=> ((ex (nat->a)) (fun (X2:(nat->a))=> ((and ((member_nat_a X2) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N2)))) (fun (Uu:nat)=> K)))) ((ex (nat->b)) (fun (Xa:(nat->b))=> ((and ((member_nat_b Xa) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N2)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d R))))) (((eq a) X) (((((l_comb_b_d_a_c R) M3) N2) Xa) X2)))))))))))))))
% 0.47/0.69 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (A:set_e), (((module_e_b_f_d M3) R)->(((ord_less_eq_set_e A) (carrie730238621_e_b_f M3))->((ord_less_eq_set_e (((algebr168361254_d_e_f R) M3) A)) (carrie730238621_e_b_f M3))))) of role axiom named fact_31_Module_Ofgs__sub__carrier
% 0.47/0.69 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (A:set_e), (((module_e_b_f_d M3) R)->(((ord_less_eq_set_e A) (carrie730238621_e_b_f M3))->((ord_less_eq_set_e (((algebr168361254_d_e_f R) M3) A)) (carrie730238621_e_b_f M3)))))
% 0.47/0.69 FOF formula (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (A:set_a), (((module1821517916unit_d M3) R)->(((ord_less_eq_set_a A) (carrie1074654371t_unit M3))->((ord_less_eq_set_a (((algebr1039611956t_unit R) M3) A)) (carrie1074654371t_unit M3))))) of role axiom named fact_32_Module_Ofgs__sub__carrier
% 0.47/0.69 A new axiom: (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (A:set_a), (((module1821517916unit_d M3) R)->(((ord_less_eq_set_a A) (carrie1074654371t_unit M3))->((ord_less_eq_set_a (((algebr1039611956t_unit R) M3) A)) (carrie1074654371t_unit M3)))))
% 0.47/0.69 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (A:set_a), (((module_a_b_c_d M3) R)->(((ord_less_eq_set_a A) (carrie2021454486_a_b_c M3))->((ord_less_eq_set_a (((algebr1152250919_d_a_c R) M3) A)) (carrie2021454486_a_b_c M3))))) of role axiom named fact_33_Module_Ofgs__sub__carrier
% 0.47/0.69 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (A:set_a), (((module_a_b_c_d M3) R)->(((ord_less_eq_set_a A) (carrie2021454486_a_b_c M3))->((ord_less_eq_set_a (((algebr1152250919_d_a_c R) M3) A)) (carrie2021454486_a_b_c M3)))))
% 0.47/0.69 FOF formula (((misomo1282343797_c_a_c r) m) m) of role axiom named fact_34_misom__self
% 0.47/0.69 A new axiom: (((misomo1282343797_c_a_c r) m) m)
% 0.47/0.69 FOF formula (forall (N3:carrie1821755406_e_b_f), (((module_e_b_f_d N3) r)->((module1648870817unit_d (((hOM_b_d_a_c_e_f r) m) N3)) r))) of role axiom named fact_35_HOM__is__module
% 0.47/0.69 A new axiom: (forall (N3:carrie1821755406_e_b_f), (((module_e_b_f_d N3) r)->((module1648870817unit_d (((hOM_b_d_a_c_e_f r) m) N3)) r)))
% 0.47/0.69 FOF formula (forall (N3:carrie722926983_a_b_c), (((module_a_b_c_d N3) r)->((module589927589unit_d (((hOM_b_d_a_c_a_c r) m) N3)) r))) of role axiom named fact_36_HOM__is__module
% 0.47/0.69 A new axiom: (forall (N3:carrie722926983_a_b_c), (((module_a_b_c_d N3) r)->((module589927589unit_d (((hOM_b_d_a_c_a_c r) m) N3)) r)))
% 0.47/0.69 FOF formula (forall (N3:carrie1963041556t_unit), (((module1821517916unit_d N3) r)->((module589927589unit_d (((hOM_b_717364638t_unit r) m) N3)) r))) of role axiom named fact_37_HOM__is__module
% 0.47/0.69 A new axiom: (forall (N3:carrie1963041556t_unit), (((module1821517916unit_d N3) r)->((module589927589unit_d (((hOM_b_717364638t_unit r) m) N3)) r)))
% 0.47/0.69 FOF formula (forall (N:nat), (((ord_less_nat zero_zero_nat) N)->(((eq nat) (suc ((minus_minus_nat N) (suc zero_zero_nat)))) N))) of role axiom named fact_38_Suc__pred
% 0.47/0.69 A new axiom: (forall (N:nat), (((ord_less_nat zero_zero_nat) N)->(((eq nat) (suc ((minus_minus_nat N) (suc zero_zero_nat)))) N)))
% 0.47/0.69 FOF formula (forall (H:set_a), ((((generator_b_d_a_c r) m) H)->((ord_less_eq_set_a H) (carrie2021454486_a_b_c m)))) of role axiom named fact_39_generator__sub__carrier
% 0.47/0.69 A new axiom: (forall (H:set_a), ((((generator_b_d_a_c r) m) H)->((ord_less_eq_set_a H) (carrie2021454486_a_b_c m))))
% 0.47/0.69 FOF formula (forall (H:set_a), ((((free_g1087686480_d_a_c r) m) H)->(((generator_b_d_a_c r) m) H))) of role axiom named fact_40_free__generator__generator
% 0.55/0.71 A new axiom: (forall (H:set_a), ((((free_g1087686480_d_a_c r) m) H)->(((generator_b_d_a_c r) m) H)))
% 0.55/0.71 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (A2:set_b) (H:set_e) (S:(nat->b)) (N:nat) (M:(nat->e)), (((module_e_b_f_d M3) R)->(((ideal_b_d R) A2)->(((ord_less_eq_set_e H) (carrie730238621_e_b_f M3))->(((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> A2)))->(((member_nat_e M) ((pi_nat_e (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->((member_e (((((l_comb_b_d_e_f R) M3) N) S) M)) (carrie730238621_e_b_f M3)))))))) of role axiom named fact_41_Module_Ol__comb__mem
% 0.55/0.71 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (A2:set_b) (H:set_e) (S:(nat->b)) (N:nat) (M:(nat->e)), (((module_e_b_f_d M3) R)->(((ideal_b_d R) A2)->(((ord_less_eq_set_e H) (carrie730238621_e_b_f M3))->(((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> A2)))->(((member_nat_e M) ((pi_nat_e (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->((member_e (((((l_comb_b_d_e_f R) M3) N) S) M)) (carrie730238621_e_b_f M3))))))))
% 0.55/0.71 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (A2:set_b) (H:set_a) (S:(nat->b)) (N:nat) (M:(nat->a)), (((module_a_b_c_d M3) R)->(((ideal_b_d R) A2)->(((ord_less_eq_set_a H) (carrie2021454486_a_b_c M3))->(((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> A2)))->(((member_nat_a M) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->((member_a (((((l_comb_b_d_a_c R) M3) N) S) M)) (carrie2021454486_a_b_c M3)))))))) of role axiom named fact_42_Module_Ol__comb__mem
% 0.55/0.71 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (A2:set_b) (H:set_a) (S:(nat->b)) (N:nat) (M:(nat->a)), (((module_a_b_c_d M3) R)->(((ideal_b_d R) A2)->(((ord_less_eq_set_a H) (carrie2021454486_a_b_c M3))->(((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> A2)))->(((member_nat_a M) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->((member_a (((((l_comb_b_d_a_c R) M3) N) S) M)) (carrie2021454486_a_b_c M3))))))))
% 0.55/0.71 FOF formula (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (A2:set_b) (H:set_a) (S:(nat->b)) (N:nat) (M:(nat->a)), (((module1821517916unit_d M3) R)->(((ideal_b_d R) A2)->(((ord_less_eq_set_a H) (carrie1074654371t_unit M3))->(((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> A2)))->(((member_nat_a M) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->((member_a (((((l_comb1138968323t_unit R) M3) N) S) M)) (carrie1074654371t_unit M3)))))))) of role axiom named fact_43_Module_Ol__comb__mem
% 0.55/0.71 A new axiom: (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (A2:set_b) (H:set_a) (S:(nat->b)) (N:nat) (M:(nat->a)), (((module1821517916unit_d M3) R)->(((ideal_b_d R) A2)->(((ord_less_eq_set_a H) (carrie1074654371t_unit M3))->(((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> A2)))->(((member_nat_a M) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->((member_a (((((l_comb1138968323t_unit R) M3) N) S) M)) (carrie1074654371t_unit M3))))))))
% 0.55/0.71 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (A2:set_b) (H:set_e) (N:nat), (((module_e_b_f_d M3) R)->(((ideal_b_d R) A2)->(((ord_less_eq_set_e H) (carrie730238621_e_b_f M3))->(forall (S2:(nat->b)) (M2:(nat->e)), (((and ((member_nat_b S2) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> A2)))) ((member_nat_e M2) ((pi_nat_e (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))->((member_e (((((l_comb_b_d_e_f R) M3) N) S2) M2)) (carrie730238621_e_b_f M3)))))))) of role axiom named fact_44_Module_Oliear__comb__memTr
% 0.55/0.72 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (A2:set_b) (H:set_e) (N:nat), (((module_e_b_f_d M3) R)->(((ideal_b_d R) A2)->(((ord_less_eq_set_e H) (carrie730238621_e_b_f M3))->(forall (S2:(nat->b)) (M2:(nat->e)), (((and ((member_nat_b S2) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> A2)))) ((member_nat_e M2) ((pi_nat_e (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))->((member_e (((((l_comb_b_d_e_f R) M3) N) S2) M2)) (carrie730238621_e_b_f M3))))))))
% 0.55/0.72 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (A2:set_b) (H:set_a) (N:nat), (((module_a_b_c_d M3) R)->(((ideal_b_d R) A2)->(((ord_less_eq_set_a H) (carrie2021454486_a_b_c M3))->(forall (S2:(nat->b)) (M2:(nat->a)), (((and ((member_nat_b S2) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> A2)))) ((member_nat_a M2) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))->((member_a (((((l_comb_b_d_a_c R) M3) N) S2) M2)) (carrie2021454486_a_b_c M3)))))))) of role axiom named fact_45_Module_Oliear__comb__memTr
% 0.55/0.72 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (A2:set_b) (H:set_a) (N:nat), (((module_a_b_c_d M3) R)->(((ideal_b_d R) A2)->(((ord_less_eq_set_a H) (carrie2021454486_a_b_c M3))->(forall (S2:(nat->b)) (M2:(nat->a)), (((and ((member_nat_b S2) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> A2)))) ((member_nat_a M2) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))->((member_a (((((l_comb_b_d_a_c R) M3) N) S2) M2)) (carrie2021454486_a_b_c M3))))))))
% 0.55/0.72 FOF formula (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (A2:set_b) (H:set_a) (N:nat), (((module1821517916unit_d M3) R)->(((ideal_b_d R) A2)->(((ord_less_eq_set_a H) (carrie1074654371t_unit M3))->(forall (S2:(nat->b)) (M2:(nat->a)), (((and ((member_nat_b S2) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> A2)))) ((member_nat_a M2) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))->((member_a (((((l_comb1138968323t_unit R) M3) N) S2) M2)) (carrie1074654371t_unit M3)))))))) of role axiom named fact_46_Module_Oliear__comb__memTr
% 0.55/0.72 A new axiom: (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (A2:set_b) (H:set_a) (N:nat), (((module1821517916unit_d M3) R)->(((ideal_b_d R) A2)->(((ord_less_eq_set_a H) (carrie1074654371t_unit M3))->(forall (S2:(nat->b)) (M2:(nat->a)), (((and ((member_nat_b S2) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> A2)))) ((member_nat_a M2) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))->((member_a (((((l_comb1138968323t_unit R) M3) N) S2) M2)) (carrie1074654371t_unit M3))))))))
% 0.55/0.72 FOF formula (forall (N:nat) (M:nat), (((eq Prop) ((ord_less_nat zero_zero_nat) ((minus_minus_nat N) M))) ((ord_less_nat M) N))) of role axiom named fact_47_zero__less__diff
% 0.55/0.72 A new axiom: (forall (N:nat) (M:nat), (((eq Prop) ((ord_less_nat zero_zero_nat) ((minus_minus_nat N) M))) ((ord_less_nat M) N)))
% 0.55/0.72 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (H:set_e) (S:(nat->b)) (N:nat) (F:(nat->e)) (G:(nat->e)), (((module_e_b_f_d M3) R)->(((ord_less_eq_set_e H) (carrie730238621_e_b_f M3))->(((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d R))))->(((member_nat_e F) ((pi_nat_e (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->(((member_nat_e G) ((pi_nat_e (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->((forall (X2:nat), (((member_nat X2) (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N))))->(((eq e) (F X2)) (G X2))))->(((eq e) (((((l_comb_b_d_e_f R) M3) N) S) F)) (((((l_comb_b_d_e_f R) M3) N) S) G))))))))) of role axiom named fact_48_Module_Olinear__comb__eq
% 0.55/0.74 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (H:set_e) (S:(nat->b)) (N:nat) (F:(nat->e)) (G:(nat->e)), (((module_e_b_f_d M3) R)->(((ord_less_eq_set_e H) (carrie730238621_e_b_f M3))->(((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d R))))->(((member_nat_e F) ((pi_nat_e (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->(((member_nat_e G) ((pi_nat_e (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->((forall (X2:nat), (((member_nat X2) (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N))))->(((eq e) (F X2)) (G X2))))->(((eq e) (((((l_comb_b_d_e_f R) M3) N) S) F)) (((((l_comb_b_d_e_f R) M3) N) S) G)))))))))
% 0.55/0.74 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (H:set_a) (S:(nat->b)) (N:nat) (F:(nat->a)) (G:(nat->a)), (((module_a_b_c_d M3) R)->(((ord_less_eq_set_a H) (carrie2021454486_a_b_c M3))->(((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d R))))->(((member_nat_a F) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->(((member_nat_a G) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->((forall (X2:nat), (((member_nat X2) (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N))))->(((eq a) (F X2)) (G X2))))->(((eq a) (((((l_comb_b_d_a_c R) M3) N) S) F)) (((((l_comb_b_d_a_c R) M3) N) S) G))))))))) of role axiom named fact_49_Module_Olinear__comb__eq
% 0.55/0.74 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (H:set_a) (S:(nat->b)) (N:nat) (F:(nat->a)) (G:(nat->a)), (((module_a_b_c_d M3) R)->(((ord_less_eq_set_a H) (carrie2021454486_a_b_c M3))->(((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d R))))->(((member_nat_a F) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->(((member_nat_a G) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->((forall (X2:nat), (((member_nat X2) (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N))))->(((eq a) (F X2)) (G X2))))->(((eq a) (((((l_comb_b_d_a_c R) M3) N) S) F)) (((((l_comb_b_d_a_c R) M3) N) S) G)))))))))
% 0.55/0.74 FOF formula (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (H:set_a) (S:(nat->b)) (N:nat) (F:(nat->a)) (G:(nat->a)), (((module1821517916unit_d M3) R)->(((ord_less_eq_set_a H) (carrie1074654371t_unit M3))->(((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d R))))->(((member_nat_a F) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->(((member_nat_a G) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->((forall (X2:nat), (((member_nat X2) (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N))))->(((eq a) (F X2)) (G X2))))->(((eq a) (((((l_comb1138968323t_unit R) M3) N) S) F)) (((((l_comb1138968323t_unit R) M3) N) S) G))))))))) of role axiom named fact_50_Module_Olinear__comb__eq
% 0.55/0.74 A new axiom: (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (H:set_a) (S:(nat->b)) (N:nat) (F:(nat->a)) (G:(nat->a)), (((module1821517916unit_d M3) R)->(((ord_less_eq_set_a H) (carrie1074654371t_unit M3))->(((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d R))))->(((member_nat_a F) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->(((member_nat_a G) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H)))->((forall (X2:nat), (((member_nat X2) (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N))))->(((eq a) (F X2)) (G X2))))->(((eq a) (((((l_comb1138968323t_unit R) M3) N) S) F)) (((((l_comb1138968323t_unit R) M3) N) S) G)))))))))
% 0.55/0.76 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (H:set_e) (S:(nat->b)) (N:nat) (F:(nat->e)) (G:(nat->e)), (((module_e_b_f_d M3) R)->(((ord_less_eq_set_e H) (carrie730238621_e_b_f M3))->(((and ((and ((and ((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d R))))) ((member_nat_e F) ((pi_nat_e (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))) ((member_nat_e G) ((pi_nat_e (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))) (forall (X2:nat), (((member_nat X2) (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N))))->(((eq e) (F X2)) (G X2)))))->(((eq e) (((((l_comb_b_d_e_f R) M3) N) S) F)) (((((l_comb_b_d_e_f R) M3) N) S) G)))))) of role axiom named fact_51_Module_Olinear__comb__eqTr
% 0.55/0.76 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (H:set_e) (S:(nat->b)) (N:nat) (F:(nat->e)) (G:(nat->e)), (((module_e_b_f_d M3) R)->(((ord_less_eq_set_e H) (carrie730238621_e_b_f M3))->(((and ((and ((and ((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d R))))) ((member_nat_e F) ((pi_nat_e (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))) ((member_nat_e G) ((pi_nat_e (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))) (forall (X2:nat), (((member_nat X2) (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N))))->(((eq e) (F X2)) (G X2)))))->(((eq e) (((((l_comb_b_d_e_f R) M3) N) S) F)) (((((l_comb_b_d_e_f R) M3) N) S) G))))))
% 0.55/0.76 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (H:set_a) (S:(nat->b)) (N:nat) (F:(nat->a)) (G:(nat->a)), (((module_a_b_c_d M3) R)->(((ord_less_eq_set_a H) (carrie2021454486_a_b_c M3))->(((and ((and ((and ((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d R))))) ((member_nat_a F) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))) ((member_nat_a G) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))) (forall (X2:nat), (((member_nat X2) (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N))))->(((eq a) (F X2)) (G X2)))))->(((eq a) (((((l_comb_b_d_a_c R) M3) N) S) F)) (((((l_comb_b_d_a_c R) M3) N) S) G)))))) of role axiom named fact_52_Module_Olinear__comb__eqTr
% 0.55/0.76 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (H:set_a) (S:(nat->b)) (N:nat) (F:(nat->a)) (G:(nat->a)), (((module_a_b_c_d M3) R)->(((ord_less_eq_set_a H) (carrie2021454486_a_b_c M3))->(((and ((and ((and ((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d R))))) ((member_nat_a F) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))) ((member_nat_a G) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))) (forall (X2:nat), (((member_nat X2) (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N))))->(((eq a) (F X2)) (G X2)))))->(((eq a) (((((l_comb_b_d_a_c R) M3) N) S) F)) (((((l_comb_b_d_a_c R) M3) N) S) G))))))
% 0.55/0.76 FOF formula (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (H:set_a) (S:(nat->b)) (N:nat) (F:(nat->a)) (G:(nat->a)), (((module1821517916unit_d M3) R)->(((ord_less_eq_set_a H) (carrie1074654371t_unit M3))->(((and ((and ((and ((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d R))))) ((member_nat_a F) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))) ((member_nat_a G) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))) (forall (X2:nat), (((member_nat X2) (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N))))->(((eq a) (F X2)) (G X2)))))->(((eq a) (((((l_comb1138968323t_unit R) M3) N) S) F)) (((((l_comb1138968323t_unit R) M3) N) S) G)))))) of role axiom named fact_53_Module_Olinear__comb__eqTr
% 0.61/0.77 A new axiom: (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (H:set_a) (S:(nat->b)) (N:nat) (F:(nat->a)) (G:(nat->a)), (((module1821517916unit_d M3) R)->(((ord_less_eq_set_a H) (carrie1074654371t_unit M3))->(((and ((and ((and ((member_nat_b S) ((pi_nat_b (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> (carrie2079586589xt_b_d R))))) ((member_nat_a F) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))) ((member_nat_a G) ((pi_nat_a (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N)))) (fun (Uu:nat)=> H))))) (forall (X2:nat), (((member_nat X2) (collect_nat (fun (J2:nat)=> ((ord_less_eq_nat J2) N))))->(((eq a) (F X2)) (G X2)))))->(((eq a) (((((l_comb1138968323t_unit R) M3) N) S) F)) (((((l_comb1138968323t_unit R) M3) N) S) G))))))
% 0.61/0.77 FOF formula (forall (M:nat) (N:nat), (((eq Prop) (((eq nat) ((minus_minus_nat M) N)) zero_zero_nat)) ((ord_less_eq_nat M) N))) of role axiom named fact_54_diff__is__0__eq
% 0.61/0.77 A new axiom: (forall (M:nat) (N:nat), (((eq Prop) (((eq nat) ((minus_minus_nat M) N)) zero_zero_nat)) ((ord_less_eq_nat M) N)))
% 0.61/0.77 FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((eq nat) ((minus_minus_nat M) N)) zero_zero_nat))) of role axiom named fact_55_diff__is__0__eq_H
% 0.61/0.77 A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((eq nat) ((minus_minus_nat M) N)) zero_zero_nat)))
% 0.61/0.77 FOF formula (forall (Nat:nat) (Nat2:nat), (((eq Prop) (((eq nat) (suc Nat)) (suc Nat2))) (((eq nat) Nat) Nat2))) of role axiom named fact_56_old_Onat_Oinject
% 0.61/0.77 A new axiom: (forall (Nat:nat) (Nat2:nat), (((eq Prop) (((eq nat) (suc Nat)) (suc Nat2))) (((eq nat) Nat) Nat2)))
% 0.61/0.77 FOF formula (forall (X22:nat) (Y2:nat), (((eq Prop) (((eq nat) (suc X22)) (suc Y2))) (((eq nat) X22) Y2))) of role axiom named fact_57_nat_Oinject
% 0.61/0.77 A new axiom: (forall (X22:nat) (Y2:nat), (((eq Prop) (((eq nat) (suc X22)) (suc Y2))) (((eq nat) X22) Y2)))
% 0.61/0.77 FOF formula (forall (N3:carrie1821755406_e_b_f), (((module_e_b_f_d N3) r)->((((misomo298454132_c_e_f r) m) N3)->(((misomo1752826100_f_a_c r) N3) m)))) of role axiom named fact_58_misom__sym
% 0.61/0.77 A new axiom: (forall (N3:carrie1821755406_e_b_f), (((module_e_b_f_d N3) r)->((((misomo298454132_c_e_f r) m) N3)->(((misomo1752826100_f_a_c r) N3) m))))
% 0.61/0.77 FOF formula (forall (N3:carrie1963041556t_unit), (((module1821517916unit_d N3) r)->((((misomo1857159554t_unit r) m) N3)->(((misomo1935876354it_a_c r) N3) m)))) of role axiom named fact_59_misom__sym
% 0.61/0.77 A new axiom: (forall (N3:carrie1963041556t_unit), (((module1821517916unit_d N3) r)->((((misomo1857159554t_unit r) m) N3)->(((misomo1935876354it_a_c r) N3) m))))
% 0.61/0.77 FOF formula (forall (N3:carrie722926983_a_b_c), (((module_a_b_c_d N3) r)->((((misomo1282343797_c_a_c r) m) N3)->(((misomo1282343797_c_a_c r) N3) m)))) of role axiom named fact_60_misom__sym
% 0.61/0.77 A new axiom: (forall (N3:carrie722926983_a_b_c), (((module_a_b_c_d N3) r)->((((misomo1282343797_c_a_c r) m) N3)->(((misomo1282343797_c_a_c r) N3) m))))
% 0.61/0.77 FOF formula (forall (N:nat) (M:nat), (((eq Prop) ((ord_less_eq_nat (suc N)) (suc M))) ((ord_less_eq_nat N) M))) of role axiom named fact_61_Suc__le__mono
% 0.61/0.77 A new axiom: (forall (N:nat) (M:nat), (((eq Prop) ((ord_less_eq_nat (suc N)) (suc M))) ((ord_less_eq_nat N) M)))
% 0.61/0.77 FOF formula (forall (A:nat), ((ord_less_eq_nat zero_zero_nat) A)) of role axiom named fact_62_bot__nat__0_Oextremum
% 0.61/0.77 A new axiom: (forall (A:nat), ((ord_less_eq_nat zero_zero_nat) A))
% 0.61/0.77 FOF formula (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)) of role axiom named fact_63_le0
% 0.61/0.77 A new axiom: (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N))
% 0.61/0.77 FOF formula (forall (M:nat) (N:nat), (((eq Prop) ((ord_less_nat (suc M)) (suc N))) ((ord_less_nat M) N))) of role axiom named fact_64_Suc__less__eq
% 0.61/0.77 A new axiom: (forall (M:nat) (N:nat), (((eq Prop) ((ord_less_nat (suc M)) (suc N))) ((ord_less_nat M) N)))
% 0.61/0.77 FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_nat (suc M)) (suc N)))) of role axiom named fact_65_Suc__mono
% 0.61/0.77 A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_nat (suc M)) (suc N))))
% 0.61/0.78 FOF formula (forall (A:(nat->a)) (P:((nat->a)->Prop)), (((eq Prop) ((member_nat_a A) (collect_nat_a P))) (P A))) of role axiom named fact_66_mem__Collect__eq
% 0.61/0.78 A new axiom: (forall (A:(nat->a)) (P:((nat->a)->Prop)), (((eq Prop) ((member_nat_a A) (collect_nat_a P))) (P A)))
% 0.61/0.78 FOF formula (forall (A:(nat->b)) (P:((nat->b)->Prop)), (((eq Prop) ((member_nat_b A) (collect_nat_b P))) (P A))) of role axiom named fact_67_mem__Collect__eq
% 0.61/0.78 A new axiom: (forall (A:(nat->b)) (P:((nat->b)->Prop)), (((eq Prop) ((member_nat_b A) (collect_nat_b P))) (P A)))
% 0.61/0.78 FOF formula (forall (A:a) (P:(a->Prop)), (((eq Prop) ((member_a A) (collect_a P))) (P A))) of role axiom named fact_68_mem__Collect__eq
% 0.61/0.78 A new axiom: (forall (A:a) (P:(a->Prop)), (((eq Prop) ((member_a A) (collect_a P))) (P A)))
% 0.61/0.78 FOF formula (forall (A:nat) (P:(nat->Prop)), (((eq Prop) ((member_nat A) (collect_nat P))) (P A))) of role axiom named fact_69_mem__Collect__eq
% 0.61/0.78 A new axiom: (forall (A:nat) (P:(nat->Prop)), (((eq Prop) ((member_nat A) (collect_nat P))) (P A)))
% 0.61/0.78 FOF formula (forall (A2:set_nat_a), (((eq set_nat_a) (collect_nat_a (fun (X3:(nat->a))=> ((member_nat_a X3) A2)))) A2)) of role axiom named fact_70_Collect__mem__eq
% 0.61/0.78 A new axiom: (forall (A2:set_nat_a), (((eq set_nat_a) (collect_nat_a (fun (X3:(nat->a))=> ((member_nat_a X3) A2)))) A2))
% 0.61/0.78 FOF formula (forall (A2:set_nat_b), (((eq set_nat_b) (collect_nat_b (fun (X3:(nat->b))=> ((member_nat_b X3) A2)))) A2)) of role axiom named fact_71_Collect__mem__eq
% 0.61/0.78 A new axiom: (forall (A2:set_nat_b), (((eq set_nat_b) (collect_nat_b (fun (X3:(nat->b))=> ((member_nat_b X3) A2)))) A2))
% 0.61/0.78 FOF formula (forall (A2:set_a), (((eq set_a) (collect_a (fun (X3:a)=> ((member_a X3) A2)))) A2)) of role axiom named fact_72_Collect__mem__eq
% 0.61/0.78 A new axiom: (forall (A2:set_a), (((eq set_a) (collect_a (fun (X3:a)=> ((member_a X3) A2)))) A2))
% 0.61/0.78 FOF formula (forall (A2:set_nat), (((eq set_nat) (collect_nat (fun (X3:nat)=> ((member_nat X3) A2)))) A2)) of role axiom named fact_73_Collect__mem__eq
% 0.61/0.78 A new axiom: (forall (A2:set_nat), (((eq set_nat) (collect_nat (fun (X3:nat)=> ((member_nat X3) A2)))) A2))
% 0.61/0.78 FOF formula (forall (P:(nat->Prop)) (Q:(nat->Prop)), ((forall (X2:nat), (((eq Prop) (P X2)) (Q X2)))->(((eq set_nat) (collect_nat P)) (collect_nat Q)))) of role axiom named fact_74_Collect__cong
% 0.61/0.78 A new axiom: (forall (P:(nat->Prop)) (Q:(nat->Prop)), ((forall (X2:nat), (((eq Prop) (P X2)) (Q X2)))->(((eq set_nat) (collect_nat P)) (collect_nat Q))))
% 0.61/0.78 FOF formula (forall (A:nat), (((eq Prop) (not (((eq nat) A) zero_zero_nat))) ((ord_less_nat zero_zero_nat) A))) of role axiom named fact_75_bot__nat__0_Onot__eq__extremum
% 0.61/0.78 A new axiom: (forall (A:nat), (((eq Prop) (not (((eq nat) A) zero_zero_nat))) ((ord_less_nat zero_zero_nat) A)))
% 0.61/0.78 FOF formula (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) of role axiom named fact_76_less__nat__zero__code
% 0.61/0.78 A new axiom: (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False))
% 0.61/0.78 FOF formula (forall (N:nat), (((eq Prop) (not (((eq nat) N) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N))) of role axiom named fact_77_neq0__conv
% 0.61/0.78 A new axiom: (forall (N:nat), (((eq Prop) (not (((eq nat) N) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N)))
% 0.61/0.78 FOF formula (forall (_TPTP_I:nat) (N:nat), (((ord_less_eq_nat _TPTP_I) N)->(((eq nat) ((minus_minus_nat N) ((minus_minus_nat N) _TPTP_I))) _TPTP_I))) of role axiom named fact_78_diff__diff__cancel
% 0.61/0.78 A new axiom: (forall (_TPTP_I:nat) (N:nat), (((ord_less_eq_nat _TPTP_I) N)->(((eq nat) ((minus_minus_nat N) ((minus_minus_nat N) _TPTP_I))) _TPTP_I)))
% 0.61/0.78 FOF formula (forall (M:nat) (N:nat) (K2:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat (suc M)) N)) (suc K2))) ((minus_minus_nat ((minus_minus_nat M) N)) K2))) of role axiom named fact_79_Suc__diff__diff
% 0.61/0.78 A new axiom: (forall (M:nat) (N:nat) (K2:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat (suc M)) N)) (suc K2))) ((minus_minus_nat ((minus_minus_nat M) N)) K2)))
% 0.61/0.78 FOF formula (forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat (suc M)) (suc N))) ((minus_minus_nat M) N))) of role axiom named fact_80_diff__Suc__Suc
% 0.61/0.79 A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat (suc M)) (suc N))) ((minus_minus_nat M) N)))
% 0.61/0.79 FOF formula (forall (M:nat), (((eq nat) ((minus_minus_nat M) M)) zero_zero_nat)) of role axiom named fact_81_diff__self__eq__0
% 0.61/0.79 A new axiom: (forall (M:nat), (((eq nat) ((minus_minus_nat M) M)) zero_zero_nat))
% 0.61/0.79 FOF formula (forall (N:nat), (((eq nat) ((minus_minus_nat zero_zero_nat) N)) zero_zero_nat)) of role axiom named fact_82_diff__0__eq__0
% 0.61/0.79 A new axiom: (forall (N:nat), (((eq nat) ((minus_minus_nat zero_zero_nat) N)) zero_zero_nat))
% 0.61/0.79 FOF formula (forall (L:carrie1821755406_e_b_f) (N3:carrie1821755406_e_b_f), (((module_e_b_f_d L) r)->(((module_e_b_f_d N3) r)->((((misomo1752826100_f_a_c r) L) m)->((((misomo298454132_c_e_f r) m) N3)->(((misomo768936435_f_e_f r) L) N3)))))) of role axiom named fact_83_misom__trans
% 0.61/0.79 A new axiom: (forall (L:carrie1821755406_e_b_f) (N3:carrie1821755406_e_b_f), (((module_e_b_f_d L) r)->(((module_e_b_f_d N3) r)->((((misomo1752826100_f_a_c r) L) m)->((((misomo298454132_c_e_f r) m) N3)->(((misomo768936435_f_e_f r) L) N3))))))
% 0.61/0.79 FOF formula (forall (L:carrie1821755406_e_b_f) (N3:carrie1963041556t_unit), (((module_e_b_f_d L) r)->(((module1821517916unit_d N3) r)->((((misomo1752826100_f_a_c r) L) m)->((((misomo1857159554t_unit r) m) N3)->(((misomo368157697t_unit r) L) N3)))))) of role axiom named fact_84_misom__trans
% 0.61/0.79 A new axiom: (forall (L:carrie1821755406_e_b_f) (N3:carrie1963041556t_unit), (((module_e_b_f_d L) r)->(((module1821517916unit_d N3) r)->((((misomo1752826100_f_a_c r) L) m)->((((misomo1857159554t_unit r) m) N3)->(((misomo368157697t_unit r) L) N3))))))
% 0.61/0.79 FOF formula (forall (L:carrie1963041556t_unit) (N3:carrie1821755406_e_b_f), (((module1821517916unit_d L) r)->(((module_e_b_f_d N3) r)->((((misomo1935876354it_a_c r) L) m)->((((misomo298454132_c_e_f r) m) N3)->(((misomo951986689it_e_f r) L) N3)))))) of role axiom named fact_85_misom__trans
% 0.61/0.79 A new axiom: (forall (L:carrie1963041556t_unit) (N3:carrie1821755406_e_b_f), (((module1821517916unit_d L) r)->(((module_e_b_f_d N3) r)->((((misomo1935876354it_a_c r) L) m)->((((misomo298454132_c_e_f r) m) N3)->(((misomo951986689it_e_f r) L) N3))))))
% 0.61/0.79 FOF formula (forall (L:carrie1963041556t_unit) (N3:carrie1963041556t_unit), (((module1821517916unit_d L) r)->(((module1821517916unit_d N3) r)->((((misomo1935876354it_a_c r) L) m)->((((misomo1857159554t_unit r) m) N3)->(((misomo493403663t_unit r) L) N3)))))) of role axiom named fact_86_misom__trans
% 0.61/0.79 A new axiom: (forall (L:carrie1963041556t_unit) (N3:carrie1963041556t_unit), (((module1821517916unit_d L) r)->(((module1821517916unit_d N3) r)->((((misomo1935876354it_a_c r) L) m)->((((misomo1857159554t_unit r) m) N3)->(((misomo493403663t_unit r) L) N3))))))
% 0.61/0.79 FOF formula (forall (L:carrie1821755406_e_b_f) (N3:carrie722926983_a_b_c), (((module_e_b_f_d L) r)->(((module_a_b_c_d N3) r)->((((misomo1752826100_f_a_c r) L) m)->((((misomo1282343797_c_a_c r) m) N3)->(((misomo1752826100_f_a_c r) L) N3)))))) of role axiom named fact_87_misom__trans
% 0.61/0.79 A new axiom: (forall (L:carrie1821755406_e_b_f) (N3:carrie722926983_a_b_c), (((module_e_b_f_d L) r)->(((module_a_b_c_d N3) r)->((((misomo1752826100_f_a_c r) L) m)->((((misomo1282343797_c_a_c r) m) N3)->(((misomo1752826100_f_a_c r) L) N3))))))
% 0.61/0.79 FOF formula (forall (L:carrie1963041556t_unit) (N3:carrie722926983_a_b_c), (((module1821517916unit_d L) r)->(((module_a_b_c_d N3) r)->((((misomo1935876354it_a_c r) L) m)->((((misomo1282343797_c_a_c r) m) N3)->(((misomo1935876354it_a_c r) L) N3)))))) of role axiom named fact_88_misom__trans
% 0.61/0.79 A new axiom: (forall (L:carrie1963041556t_unit) (N3:carrie722926983_a_b_c), (((module1821517916unit_d L) r)->(((module_a_b_c_d N3) r)->((((misomo1935876354it_a_c r) L) m)->((((misomo1282343797_c_a_c r) m) N3)->(((misomo1935876354it_a_c r) L) N3))))))
% 0.61/0.79 FOF formula (forall (L:carrie722926983_a_b_c) (N3:carrie1821755406_e_b_f), (((module_a_b_c_d L) r)->(((module_e_b_f_d N3) r)->((((misomo1282343797_c_a_c r) L) m)->((((misomo298454132_c_e_f r) m) N3)->(((misomo298454132_c_e_f r) L) N3)))))) of role axiom named fact_89_misom__trans
% 0.61/0.79 A new axiom: (forall (L:carrie722926983_a_b_c) (N3:carrie1821755406_e_b_f), (((module_a_b_c_d L) r)->(((module_e_b_f_d N3) r)->((((misomo1282343797_c_a_c r) L) m)->((((misomo298454132_c_e_f r) m) N3)->(((misomo298454132_c_e_f r) L) N3))))))
% 0.61/0.81 FOF formula (forall (L:carrie722926983_a_b_c) (N3:carrie1963041556t_unit), (((module_a_b_c_d L) r)->(((module1821517916unit_d N3) r)->((((misomo1282343797_c_a_c r) L) m)->((((misomo1857159554t_unit r) m) N3)->(((misomo1857159554t_unit r) L) N3)))))) of role axiom named fact_90_misom__trans
% 0.61/0.81 A new axiom: (forall (L:carrie722926983_a_b_c) (N3:carrie1963041556t_unit), (((module_a_b_c_d L) r)->(((module1821517916unit_d N3) r)->((((misomo1282343797_c_a_c r) L) m)->((((misomo1857159554t_unit r) m) N3)->(((misomo1857159554t_unit r) L) N3))))))
% 0.61/0.81 FOF formula (forall (L:carrie722926983_a_b_c) (N3:carrie722926983_a_b_c), (((module_a_b_c_d L) r)->(((module_a_b_c_d N3) r)->((((misomo1282343797_c_a_c r) L) m)->((((misomo1282343797_c_a_c r) m) N3)->(((misomo1282343797_c_a_c r) L) N3)))))) of role axiom named fact_91_misom__trans
% 0.61/0.81 A new axiom: (forall (L:carrie722926983_a_b_c) (N3:carrie722926983_a_b_c), (((module_a_b_c_d L) r)->(((module_a_b_c_d N3) r)->((((misomo1282343797_c_a_c r) L) m)->((((misomo1282343797_c_a_c r) m) N3)->(((misomo1282343797_c_a_c r) L) N3))))))
% 0.61/0.81 FOF formula (forall (N:nat), ((ord_less_nat zero_zero_nat) (suc N))) of role axiom named fact_92_zero__less__Suc
% 0.61/0.81 A new axiom: (forall (N:nat), ((ord_less_nat zero_zero_nat) (suc N)))
% 0.61/0.81 FOF formula (forall (N:nat), (((eq Prop) ((ord_less_nat N) (suc zero_zero_nat))) (((eq nat) N) zero_zero_nat))) of role axiom named fact_93_less__Suc0
% 0.61/0.81 A new axiom: (forall (N:nat), (((eq Prop) ((ord_less_nat N) (suc zero_zero_nat))) (((eq nat) N) zero_zero_nat)))
% 0.61/0.81 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (N3:carrie1821755406_e_b_f), (((module_e_b_f_d M3) R)->(((module_e_b_f_d N3) R)->((module241733029unit_d (((hOM_b_d_e_f_e_f R) M3) N3)) R)))) of role axiom named fact_94_Module_OHOM__is__module
% 0.61/0.81 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (N3:carrie1821755406_e_b_f), (((module_e_b_f_d M3) R)->(((module_e_b_f_d N3) R)->((module241733029unit_d (((hOM_b_d_e_f_e_f R) M3) N3)) R))))
% 0.61/0.81 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (N3:carrie722926983_a_b_c), (((module_e_b_f_d M3) R)->(((module_a_b_c_d N3) R)->((module1330273449unit_d (((hOM_b_d_e_f_a_c R) M3) N3)) R)))) of role axiom named fact_95_Module_OHOM__is__module
% 0.61/0.81 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (N3:carrie722926983_a_b_c), (((module_e_b_f_d M3) R)->(((module_a_b_c_d N3) R)->((module1330273449unit_d (((hOM_b_d_e_f_a_c R) M3) N3)) R))))
% 0.61/0.81 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (N3:carrie1963041556t_unit), (((module_e_b_f_d M3) R)->(((module1821517916unit_d N3) R)->((module1330273449unit_d (((hOM_b_1375846429t_unit R) M3) N3)) R)))) of role axiom named fact_96_Module_OHOM__is__module
% 0.61/0.81 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (N3:carrie1963041556t_unit), (((module_e_b_f_d M3) R)->(((module1821517916unit_d N3) R)->((module1330273449unit_d (((hOM_b_1375846429t_unit R) M3) N3)) R))))
% 0.61/0.81 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (N3:carrie1821755406_e_b_f), (((module_a_b_c_d M3) R)->(((module_e_b_f_d N3) R)->((module1648870817unit_d (((hOM_b_d_a_c_e_f R) M3) N3)) R)))) of role axiom named fact_97_Module_OHOM__is__module
% 0.61/0.81 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (N3:carrie1821755406_e_b_f), (((module_a_b_c_d M3) R)->(((module_e_b_f_d N3) R)->((module1648870817unit_d (((hOM_b_d_a_c_e_f R) M3) N3)) R))))
% 0.61/0.81 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (N3:carrie722926983_a_b_c), (((module_a_b_c_d M3) R)->(((module_a_b_c_d N3) R)->((module589927589unit_d (((hOM_b_d_a_c_a_c R) M3) N3)) R)))) of role axiom named fact_98_Module_OHOM__is__module
% 0.61/0.81 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (N3:carrie722926983_a_b_c), (((module_a_b_c_d M3) R)->(((module_a_b_c_d N3) R)->((module589927589unit_d (((hOM_b_d_a_c_a_c R) M3) N3)) R))))
% 0.61/0.81 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (N3:carrie1963041556t_unit), (((module_a_b_c_d M3) R)->(((module1821517916unit_d N3) R)->((module589927589unit_d (((hOM_b_717364638t_unit R) M3) N3)) R)))) of role axiom named fact_99_Module_OHOM__is__module
% 0.61/0.81 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (N3:carrie1963041556t_unit), (((module_a_b_c_d M3) R)->(((module1821517916unit_d N3) R)->((module589927589unit_d (((hOM_b_717364638t_unit R) M3) N3)) R))))
% 0.61/0.81 FOF formula (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (N3:carrie1821755406_e_b_f), (((module1821517916unit_d M3) R)->(((module_e_b_f_d N3) R)->((module1648870817unit_d (((hOM_b_1959675421it_e_f R) M3) N3)) R)))) of role axiom named fact_100_Module_OHOM__is__module
% 0.61/0.81 A new axiom: (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (N3:carrie1821755406_e_b_f), (((module1821517916unit_d M3) R)->(((module_e_b_f_d N3) R)->((module1648870817unit_d (((hOM_b_1959675421it_e_f R) M3) N3)) R))))
% 0.61/0.81 FOF formula (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (N3:carrie722926983_a_b_c), (((module1821517916unit_d M3) R)->(((module_a_b_c_d N3) R)->((module589927589unit_d (((hOM_b_796081438it_a_c R) M3) N3)) R)))) of role axiom named fact_101_Module_OHOM__is__module
% 0.61/0.81 A new axiom: (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (N3:carrie722926983_a_b_c), (((module1821517916unit_d M3) R)->(((module_a_b_c_d N3) R)->((module589927589unit_d (((hOM_b_796081438it_a_c R) M3) N3)) R))))
% 0.61/0.81 FOF formula (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (N3:carrie1963041556t_unit), (((module1821517916unit_d M3) R)->(((module1821517916unit_d N3) R)->((module589927589unit_d (((hOM_b_1103679019t_unit R) M3) N3)) R)))) of role axiom named fact_102_Module_OHOM__is__module
% 0.61/0.81 A new axiom: (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (N3:carrie1963041556t_unit), (((module1821517916unit_d M3) R)->(((module1821517916unit_d N3) R)->((module589927589unit_d (((hOM_b_1103679019t_unit R) M3) N3)) R))))
% 0.61/0.81 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (L:carrie1821755406_e_b_f) (N3:carrie1821755406_e_b_f), (((module_e_b_f_d M3) R)->(((module_e_b_f_d L) R)->(((module_e_b_f_d N3) R)->((((misomo768936435_f_e_f R) L) M3)->((((misomo768936435_f_e_f R) M3) N3)->(((misomo768936435_f_e_f R) L) N3))))))) of role axiom named fact_103_Module_Omisom__trans
% 0.61/0.81 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (L:carrie1821755406_e_b_f) (N3:carrie1821755406_e_b_f), (((module_e_b_f_d M3) R)->(((module_e_b_f_d L) R)->(((module_e_b_f_d N3) R)->((((misomo768936435_f_e_f R) L) M3)->((((misomo768936435_f_e_f R) M3) N3)->(((misomo768936435_f_e_f R) L) N3)))))))
% 0.61/0.81 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (L:carrie1821755406_e_b_f) (N3:carrie722926983_a_b_c), (((module_e_b_f_d M3) R)->(((module_e_b_f_d L) R)->(((module_a_b_c_d N3) R)->((((misomo768936435_f_e_f R) L) M3)->((((misomo1752826100_f_a_c R) M3) N3)->(((misomo1752826100_f_a_c R) L) N3))))))) of role axiom named fact_104_Module_Omisom__trans
% 0.61/0.81 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (L:carrie1821755406_e_b_f) (N3:carrie722926983_a_b_c), (((module_e_b_f_d M3) R)->(((module_e_b_f_d L) R)->(((module_a_b_c_d N3) R)->((((misomo768936435_f_e_f R) L) M3)->((((misomo1752826100_f_a_c R) M3) N3)->(((misomo1752826100_f_a_c R) L) N3)))))))
% 0.61/0.81 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (L:carrie1821755406_e_b_f) (N3:carrie1963041556t_unit), (((module_e_b_f_d M3) R)->(((module_e_b_f_d L) R)->(((module1821517916unit_d N3) R)->((((misomo768936435_f_e_f R) L) M3)->((((misomo368157697t_unit R) M3) N3)->(((misomo368157697t_unit R) L) N3))))))) of role axiom named fact_105_Module_Omisom__trans
% 0.61/0.81 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (L:carrie1821755406_e_b_f) (N3:carrie1963041556t_unit), (((module_e_b_f_d M3) R)->(((module_e_b_f_d L) R)->(((module1821517916unit_d N3) R)->((((misomo768936435_f_e_f R) L) M3)->((((misomo368157697t_unit R) M3) N3)->(((misomo368157697t_unit R) L) N3)))))))
% 0.61/0.82 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (L:carrie722926983_a_b_c) (N3:carrie1821755406_e_b_f), (((module_e_b_f_d M3) R)->(((module_a_b_c_d L) R)->(((module_e_b_f_d N3) R)->((((misomo298454132_c_e_f R) L) M3)->((((misomo768936435_f_e_f R) M3) N3)->(((misomo298454132_c_e_f R) L) N3))))))) of role axiom named fact_106_Module_Omisom__trans
% 0.61/0.82 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (L:carrie722926983_a_b_c) (N3:carrie1821755406_e_b_f), (((module_e_b_f_d M3) R)->(((module_a_b_c_d L) R)->(((module_e_b_f_d N3) R)->((((misomo298454132_c_e_f R) L) M3)->((((misomo768936435_f_e_f R) M3) N3)->(((misomo298454132_c_e_f R) L) N3)))))))
% 0.61/0.82 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (L:carrie722926983_a_b_c) (N3:carrie1963041556t_unit), (((module_e_b_f_d M3) R)->(((module_a_b_c_d L) R)->(((module1821517916unit_d N3) R)->((((misomo298454132_c_e_f R) L) M3)->((((misomo368157697t_unit R) M3) N3)->(((misomo1857159554t_unit R) L) N3))))))) of role axiom named fact_107_Module_Omisom__trans
% 0.61/0.83 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (L:carrie722926983_a_b_c) (N3:carrie1963041556t_unit), (((module_e_b_f_d M3) R)->(((module_a_b_c_d L) R)->(((module1821517916unit_d N3) R)->((((misomo298454132_c_e_f R) L) M3)->((((misomo368157697t_unit R) M3) N3)->(((misomo1857159554t_unit R) L) N3)))))))
% 0.61/0.83 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (L:carrie1963041556t_unit) (N3:carrie1821755406_e_b_f), (((module_e_b_f_d M3) R)->(((module1821517916unit_d L) R)->(((module_e_b_f_d N3) R)->((((misomo951986689it_e_f R) L) M3)->((((misomo768936435_f_e_f R) M3) N3)->(((misomo951986689it_e_f R) L) N3))))))) of role axiom named fact_108_Module_Omisom__trans
% 0.61/0.83 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (L:carrie1963041556t_unit) (N3:carrie1821755406_e_b_f), (((module_e_b_f_d M3) R)->(((module1821517916unit_d L) R)->(((module_e_b_f_d N3) R)->((((misomo951986689it_e_f R) L) M3)->((((misomo768936435_f_e_f R) M3) N3)->(((misomo951986689it_e_f R) L) N3)))))))
% 0.61/0.83 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (L:carrie1963041556t_unit) (N3:carrie722926983_a_b_c), (((module_e_b_f_d M3) R)->(((module1821517916unit_d L) R)->(((module_a_b_c_d N3) R)->((((misomo951986689it_e_f R) L) M3)->((((misomo1752826100_f_a_c R) M3) N3)->(((misomo1935876354it_a_c R) L) N3))))))) of role axiom named fact_109_Module_Omisom__trans
% 0.61/0.83 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (L:carrie1963041556t_unit) (N3:carrie722926983_a_b_c), (((module_e_b_f_d M3) R)->(((module1821517916unit_d L) R)->(((module_a_b_c_d N3) R)->((((misomo951986689it_e_f R) L) M3)->((((misomo1752826100_f_a_c R) M3) N3)->(((misomo1935876354it_a_c R) L) N3)))))))
% 0.61/0.83 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (L:carrie1963041556t_unit) (N3:carrie1963041556t_unit), (((module_e_b_f_d M3) R)->(((module1821517916unit_d L) R)->(((module1821517916unit_d N3) R)->((((misomo951986689it_e_f R) L) M3)->((((misomo368157697t_unit R) M3) N3)->(((misomo493403663t_unit R) L) N3))))))) of role axiom named fact_110_Module_Omisom__trans
% 0.61/0.83 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (L:carrie1963041556t_unit) (N3:carrie1963041556t_unit), (((module_e_b_f_d M3) R)->(((module1821517916unit_d L) R)->(((module1821517916unit_d N3) R)->((((misomo951986689it_e_f R) L) M3)->((((misomo368157697t_unit R) M3) N3)->(((misomo493403663t_unit R) L) N3)))))))
% 0.61/0.83 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (L:carrie1821755406_e_b_f) (N3:carrie1821755406_e_b_f), (((module_a_b_c_d M3) R)->(((module_e_b_f_d L) R)->(((module_e_b_f_d N3) R)->((((misomo1752826100_f_a_c R) L) M3)->((((misomo298454132_c_e_f R) M3) N3)->(((misomo768936435_f_e_f R) L) N3))))))) of role axiom named fact_111_Module_Omisom__trans
% 0.61/0.83 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (L:carrie1821755406_e_b_f) (N3:carrie1821755406_e_b_f), (((module_a_b_c_d M3) R)->(((module_e_b_f_d L) R)->(((module_e_b_f_d N3) R)->((((misomo1752826100_f_a_c R) L) M3)->((((misomo298454132_c_e_f R) M3) N3)->(((misomo768936435_f_e_f R) L) N3)))))))
% 0.61/0.83 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (L:carrie1821755406_e_b_f) (N3:carrie1963041556t_unit), (((module_a_b_c_d M3) R)->(((module_e_b_f_d L) R)->(((module1821517916unit_d N3) R)->((((misomo1752826100_f_a_c R) L) M3)->((((misomo1857159554t_unit R) M3) N3)->(((misomo368157697t_unit R) L) N3))))))) of role axiom named fact_112_Module_Omisom__trans
% 0.61/0.83 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (L:carrie1821755406_e_b_f) (N3:carrie1963041556t_unit), (((module_a_b_c_d M3) R)->(((module_e_b_f_d L) R)->(((module1821517916unit_d N3) R)->((((misomo1752826100_f_a_c R) L) M3)->((((misomo1857159554t_unit R) M3) N3)->(((misomo368157697t_unit R) L) N3)))))))
% 0.61/0.83 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d), (((module_e_b_f_d M3) R)->(((misomo768936435_f_e_f R) M3) M3))) of role axiom named fact_113_Module_Omisom__self
% 0.61/0.83 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d), (((module_e_b_f_d M3) R)->(((misomo768936435_f_e_f R) M3) M3)))
% 0.61/0.83 FOF formula (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d), (((module1821517916unit_d M3) R)->(((misomo493403663t_unit R) M3) M3))) of role axiom named fact_114_Module_Omisom__self
% 0.61/0.83 A new axiom: (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d), (((module1821517916unit_d M3) R)->(((misomo493403663t_unit R) M3) M3)))
% 0.61/0.83 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d), (((module_a_b_c_d M3) R)->(((misomo1282343797_c_a_c R) M3) M3))) of role axiom named fact_115_Module_Omisom__self
% 0.61/0.83 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d), (((module_a_b_c_d M3) R)->(((misomo1282343797_c_a_c R) M3) M3)))
% 0.61/0.83 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (N3:carrie1821755406_e_b_f), (((module_e_b_f_d M3) R)->(((module_e_b_f_d N3) R)->((((misomo768936435_f_e_f R) M3) N3)->(((misomo768936435_f_e_f R) N3) M3))))) of role axiom named fact_116_Module_Omisom__sym
% 0.61/0.83 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (N3:carrie1821755406_e_b_f), (((module_e_b_f_d M3) R)->(((module_e_b_f_d N3) R)->((((misomo768936435_f_e_f R) M3) N3)->(((misomo768936435_f_e_f R) N3) M3)))))
% 0.61/0.83 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (N3:carrie722926983_a_b_c), (((module_e_b_f_d M3) R)->(((module_a_b_c_d N3) R)->((((misomo1752826100_f_a_c R) M3) N3)->(((misomo298454132_c_e_f R) N3) M3))))) of role axiom named fact_117_Module_Omisom__sym
% 0.61/0.83 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (N3:carrie722926983_a_b_c), (((module_e_b_f_d M3) R)->(((module_a_b_c_d N3) R)->((((misomo1752826100_f_a_c R) M3) N3)->(((misomo298454132_c_e_f R) N3) M3)))))
% 0.61/0.83 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (N3:carrie1963041556t_unit), (((module_e_b_f_d M3) R)->(((module1821517916unit_d N3) R)->((((misomo368157697t_unit R) M3) N3)->(((misomo951986689it_e_f R) N3) M3))))) of role axiom named fact_118_Module_Omisom__sym
% 0.61/0.83 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (N3:carrie1963041556t_unit), (((module_e_b_f_d M3) R)->(((module1821517916unit_d N3) R)->((((misomo368157697t_unit R) M3) N3)->(((misomo951986689it_e_f R) N3) M3)))))
% 0.61/0.83 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (N3:carrie1821755406_e_b_f), (((module_a_b_c_d M3) R)->(((module_e_b_f_d N3) R)->((((misomo298454132_c_e_f R) M3) N3)->(((misomo1752826100_f_a_c R) N3) M3))))) of role axiom named fact_119_Module_Omisom__sym
% 0.61/0.83 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (N3:carrie1821755406_e_b_f), (((module_a_b_c_d M3) R)->(((module_e_b_f_d N3) R)->((((misomo298454132_c_e_f R) M3) N3)->(((misomo1752826100_f_a_c R) N3) M3)))))
% 0.61/0.84 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (N3:carrie1963041556t_unit), (((module_a_b_c_d M3) R)->(((module1821517916unit_d N3) R)->((((misomo1857159554t_unit R) M3) N3)->(((misomo1935876354it_a_c R) N3) M3))))) of role axiom named fact_120_Module_Omisom__sym
% 0.61/0.84 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (N3:carrie1963041556t_unit), (((module_a_b_c_d M3) R)->(((module1821517916unit_d N3) R)->((((misomo1857159554t_unit R) M3) N3)->(((misomo1935876354it_a_c R) N3) M3)))))
% 0.61/0.84 FOF formula (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (N3:carrie1821755406_e_b_f), (((module1821517916unit_d M3) R)->(((module_e_b_f_d N3) R)->((((misomo951986689it_e_f R) M3) N3)->(((misomo368157697t_unit R) N3) M3))))) of role axiom named fact_121_Module_Omisom__sym
% 0.61/0.84 A new axiom: (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (N3:carrie1821755406_e_b_f), (((module1821517916unit_d M3) R)->(((module_e_b_f_d N3) R)->((((misomo951986689it_e_f R) M3) N3)->(((misomo368157697t_unit R) N3) M3)))))
% 0.61/0.84 FOF formula (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (N3:carrie722926983_a_b_c), (((module1821517916unit_d M3) R)->(((module_a_b_c_d N3) R)->((((misomo1935876354it_a_c R) M3) N3)->(((misomo1857159554t_unit R) N3) M3))))) of role axiom named fact_122_Module_Omisom__sym
% 0.61/0.84 A new axiom: (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (N3:carrie722926983_a_b_c), (((module1821517916unit_d M3) R)->(((module_a_b_c_d N3) R)->((((misomo1935876354it_a_c R) M3) N3)->(((misomo1857159554t_unit R) N3) M3)))))
% 0.61/0.84 FOF formula (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (N3:carrie1963041556t_unit), (((module1821517916unit_d M3) R)->(((module1821517916unit_d N3) R)->((((misomo493403663t_unit R) M3) N3)->(((misomo493403663t_unit R) N3) M3))))) of role axiom named fact_123_Module_Omisom__sym
% 0.61/0.84 A new axiom: (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (N3:carrie1963041556t_unit), (((module1821517916unit_d M3) R)->(((module1821517916unit_d N3) R)->((((misomo493403663t_unit R) M3) N3)->(((misomo493403663t_unit R) N3) M3)))))
% 0.61/0.84 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (N3:carrie722926983_a_b_c), (((module_a_b_c_d M3) R)->(((module_a_b_c_d N3) R)->((((misomo1282343797_c_a_c R) M3) N3)->(((misomo1282343797_c_a_c R) N3) M3))))) of role axiom named fact_124_Module_Omisom__sym
% 0.61/0.84 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (N3:carrie722926983_a_b_c), (((module_a_b_c_d M3) R)->(((module_a_b_c_d N3) R)->((((misomo1282343797_c_a_c R) M3) N3)->(((misomo1282343797_c_a_c R) N3) M3)))))
% 0.61/0.84 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (H:set_e), (((module_e_b_f_d M3) R)->((((free_g103796815_d_e_f R) M3) H)->(((generator_b_d_e_f R) M3) H)))) of role axiom named fact_125_Module_Ofree__generator__generator
% 0.61/0.84 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (H:set_e), (((module_e_b_f_d M3) R)->((((free_g103796815_d_e_f R) M3) H)->(((generator_b_d_e_f R) M3) H))))
% 0.61/0.84 FOF formula (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (H:set_a), (((module1821517916unit_d M3) R)->((((free_g637607517t_unit R) M3) H)->(((genera1692266857t_unit R) M3) H)))) of role axiom named fact_126_Module_Ofree__generator__generator
% 0.61/0.84 A new axiom: (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (H:set_a), (((module1821517916unit_d M3) R)->((((free_g637607517t_unit R) M3) H)->(((genera1692266857t_unit R) M3) H))))
% 0.61/0.84 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (H:set_a), (((module_a_b_c_d M3) R)->((((free_g1087686480_d_a_c R) M3) H)->(((generator_b_d_a_c R) M3) H)))) of role axiom named fact_127_Module_Ofree__generator__generator
% 0.61/0.84 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (H:set_a), (((module_a_b_c_d M3) R)->((((free_g1087686480_d_a_c R) M3) H)->(((generator_b_d_a_c R) M3) H))))
% 0.61/0.84 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (H:set_e), (((module_e_b_f_d M3) R)->((((generator_b_d_e_f R) M3) H)->((ord_less_eq_set_e H) (carrie730238621_e_b_f M3))))) of role axiom named fact_128_Module_Ogenerator__sub__carrier
% 0.61/0.85 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (H:set_e), (((module_e_b_f_d M3) R)->((((generator_b_d_e_f R) M3) H)->((ord_less_eq_set_e H) (carrie730238621_e_b_f M3)))))
% 0.61/0.85 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (H:set_a), (((module_a_b_c_d M3) R)->((((generator_b_d_a_c R) M3) H)->((ord_less_eq_set_a H) (carrie2021454486_a_b_c M3))))) of role axiom named fact_129_Module_Ogenerator__sub__carrier
% 0.61/0.85 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (H:set_a), (((module_a_b_c_d M3) R)->((((generator_b_d_a_c R) M3) H)->((ord_less_eq_set_a H) (carrie2021454486_a_b_c M3)))))
% 0.61/0.85 FOF formula (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (H:set_a), (((module1821517916unit_d M3) R)->((((genera1692266857t_unit R) M3) H)->((ord_less_eq_set_a H) (carrie1074654371t_unit M3))))) of role axiom named fact_130_Module_Ogenerator__sub__carrier
% 0.61/0.85 A new axiom: (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (H:set_a), (((module1821517916unit_d M3) R)->((((genera1692266857t_unit R) M3) H)->((ord_less_eq_set_a H) (carrie1074654371t_unit M3)))))
% 0.61/0.85 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d), (((module_e_b_f_d M3) R)->((ideal_b_d R) ((annihilator_b_d_e_f R) M3)))) of role axiom named fact_131_Module_OAnn__is__ideal
% 0.61/0.85 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d), (((module_e_b_f_d M3) R)->((ideal_b_d R) ((annihilator_b_d_e_f R) M3))))
% 0.61/0.85 FOF formula (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d), (((module1821517916unit_d M3) R)->((ideal_b_d R) ((annihi259882159t_unit R) M3)))) of role axiom named fact_132_Module_OAnn__is__ideal
% 0.61/0.85 A new axiom: (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d), (((module1821517916unit_d M3) R)->((ideal_b_d R) ((annihi259882159t_unit R) M3))))
% 0.61/0.85 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d), (((module_a_b_c_d M3) R)->((ideal_b_d R) ((annihilator_b_d_a_c R) M3)))) of role axiom named fact_133_Module_OAnn__is__ideal
% 0.61/0.85 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d), (((module_a_b_c_d M3) R)->((ideal_b_d R) ((annihilator_b_d_a_c R) M3))))
% 0.61/0.85 FOF formula (forall (P:(nat->Prop)) (K2:nat) (B:nat), ((P K2)->((forall (Y:nat), ((P Y)->((ord_less_eq_nat Y) B)))->((ex nat) (fun (X2:nat)=> ((and (P X2)) (forall (Y3:nat), ((P Y3)->((ord_less_eq_nat Y3) X2))))))))) of role axiom named fact_134_Nat_Oex__has__greatest__nat
% 0.61/0.85 A new axiom: (forall (P:(nat->Prop)) (K2:nat) (B:nat), ((P K2)->((forall (Y:nat), ((P Y)->((ord_less_eq_nat Y) B)))->((ex nat) (fun (X2:nat)=> ((and (P X2)) (forall (Y3:nat), ((P Y3)->((ord_less_eq_nat Y3) X2)))))))))
% 0.61/0.85 FOF formula (forall (M:nat) (N:nat), ((or ((ord_less_eq_nat M) N)) ((ord_less_eq_nat N) M))) of role axiom named fact_135_nat__le__linear
% 0.61/0.85 A new axiom: (forall (M:nat) (N:nat), ((or ((ord_less_eq_nat M) N)) ((ord_less_eq_nat N) M)))
% 0.61/0.85 FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((ord_less_eq_nat N) M)->(((eq nat) M) N)))) of role axiom named fact_136_le__antisym
% 0.61/0.85 A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((ord_less_eq_nat N) M)->(((eq nat) M) N))))
% 0.61/0.85 FOF formula (forall (_TPTP_I:nat) (J3:nat) (K2:nat), (((ord_less_eq_nat _TPTP_I) J3)->(((ord_less_eq_nat J3) K2)->((ord_less_eq_nat _TPTP_I) K2)))) of role axiom named fact_137_le__trans
% 0.61/0.85 A new axiom: (forall (_TPTP_I:nat) (J3:nat) (K2:nat), (((ord_less_eq_nat _TPTP_I) J3)->(((ord_less_eq_nat J3) K2)->((ord_less_eq_nat _TPTP_I) K2))))
% 0.61/0.85 FOF formula (forall (N:nat), (not (((eq nat) N) (suc N)))) of role axiom named fact_138_n__not__Suc__n
% 0.61/0.85 A new axiom: (forall (N:nat), (not (((eq nat) N) (suc N))))
% 0.61/0.85 FOF formula (forall (X:nat) (Y4:nat), ((((eq nat) (suc X)) (suc Y4))->(((eq nat) X) Y4))) of role axiom named fact_139_Suc__inject
% 0.61/0.85 A new axiom: (forall (X:nat) (Y4:nat), ((((eq nat) (suc X)) (suc Y4))->(((eq nat) X) Y4)))
% 0.70/0.87 FOF formula (forall (X:nat) (Y4:nat), ((not (((eq nat) X) Y4))->((((ord_less_nat X) Y4)->False)->((ord_less_nat Y4) X)))) of role axiom named fact_140_linorder__neqE__nat
% 0.70/0.87 A new axiom: (forall (X:nat) (Y4:nat), ((not (((eq nat) X) Y4))->((((ord_less_nat X) Y4)->False)->((ord_less_nat Y4) X))))
% 0.70/0.87 FOF formula (forall (P:(nat->Prop)) (N:nat), ((forall (N2:nat), (((P N2)->False)->((ex nat) (fun (M2:nat)=> ((and ((ord_less_nat M2) N2)) ((P M2)->False))))))->(P N))) of role axiom named fact_141_infinite__descent
% 0.70/0.87 A new axiom: (forall (P:(nat->Prop)) (N:nat), ((forall (N2:nat), (((P N2)->False)->((ex nat) (fun (M2:nat)=> ((and ((ord_less_nat M2) N2)) ((P M2)->False))))))->(P N)))
% 0.70/0.87 FOF formula (forall (P:(nat->Prop)) (N:nat), ((forall (N2:nat), ((forall (M2:nat), (((ord_less_nat M2) N2)->(P M2)))->(P N2)))->(P N))) of role axiom named fact_142_nat__less__induct
% 0.70/0.87 A new axiom: (forall (P:(nat->Prop)) (N:nat), ((forall (N2:nat), ((forall (M2:nat), (((ord_less_nat M2) N2)->(P M2)))->(P N2)))->(P N)))
% 0.70/0.87 FOF formula (forall (N:nat), (((ord_less_nat N) N)->False)) of role axiom named fact_143_less__irrefl__nat
% 0.70/0.87 A new axiom: (forall (N:nat), (((ord_less_nat N) N)->False))
% 0.70/0.87 FOF formula (forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T)))) of role axiom named fact_144_less__not__refl3
% 0.70/0.87 A new axiom: (forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T))))
% 0.70/0.87 FOF formula (forall (N:nat) (M:nat), (((ord_less_nat N) M)->(not (((eq nat) M) N)))) of role axiom named fact_145_less__not__refl2
% 0.70/0.87 A new axiom: (forall (N:nat) (M:nat), (((ord_less_nat N) M)->(not (((eq nat) M) N))))
% 0.70/0.87 FOF formula (forall (N:nat), (((ord_less_nat N) N)->False)) of role axiom named fact_146_less__not__refl
% 0.70/0.87 A new axiom: (forall (N:nat), (((ord_less_nat N) N)->False))
% 0.70/0.87 FOF formula (forall (M:nat) (N:nat), (((eq Prop) (not (((eq nat) M) N))) ((or ((ord_less_nat M) N)) ((ord_less_nat N) M)))) of role axiom named fact_147_nat__neq__iff
% 0.70/0.87 A new axiom: (forall (M:nat) (N:nat), (((eq Prop) (not (((eq nat) M) N))) ((or ((ord_less_nat M) N)) ((ord_less_nat N) M))))
% 0.70/0.87 FOF formula (forall (_TPTP_I:nat) (J3:nat) (K2:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat _TPTP_I) J3)) K2)) ((minus_minus_nat ((minus_minus_nat _TPTP_I) K2)) J3))) of role axiom named fact_148_diff__commute
% 0.70/0.87 A new axiom: (forall (_TPTP_I:nat) (J3:nat) (K2:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat _TPTP_I) J3)) K2)) ((minus_minus_nat ((minus_minus_nat _TPTP_I) K2)) J3)))
% 0.70/0.87 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (A2:set_b), (((module_e_b_f_d M3) R)->(((ideal_b_d R) A2)->(((submodule_b_d_e_f R) M3) (((smodul1982583723_d_e_f R) M3) A2))))) of role axiom named fact_149_Module_Osmodule__ideal__coeff__is__Submodule
% 0.70/0.87 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (A2:set_b), (((module_e_b_f_d M3) R)->(((ideal_b_d R) A2)->(((submodule_b_d_e_f R) M3) (((smodul1982583723_d_e_f R) M3) A2)))))
% 0.70/0.87 FOF formula (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (A2:set_b), (((module1821517916unit_d M3) R)->(((ideal_b_d R) A2)->(((submod903911234t_unit R) M3) (((smodul132175289t_unit R) M3) A2))))) of role axiom named fact_150_Module_Osmodule__ideal__coeff__is__Submodule
% 0.70/0.87 A new axiom: (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (A2:set_b), (((module1821517916unit_d M3) R)->(((ideal_b_d R) A2)->(((submod903911234t_unit R) M3) (((smodul132175289t_unit R) M3) A2)))))
% 0.70/0.87 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (A2:set_b), (((module_a_b_c_d M3) R)->(((ideal_b_d R) A2)->(((submodule_b_d_a_c R) M3) (((smodul818989740_d_a_c R) M3) A2))))) of role axiom named fact_151_Module_Osmodule__ideal__coeff__is__Submodule
% 0.70/0.87 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (A2:set_b), (((module_a_b_c_d M3) R)->(((ideal_b_d R) A2)->(((submodule_b_d_a_c R) M3) (((smodul818989740_d_a_c R) M3) A2)))))
% 0.70/0.87 FOF formula (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (P:set_e) (Q:set_e), (((module_e_b_f_d M3) R)->((((submodule_b_d_e_f R) M3) P)->((((submodule_b_d_e_f R) M3) Q)->((ideal_b_d R) ((((quotie169863047_d_e_f R) M3) P) Q)))))) of role axiom named fact_152_Module_Oquotient__of__submodules__is__ideal
% 0.70/0.88 A new axiom: (forall (M3:carrie1821755406_e_b_f) (R:carrie1950868226xt_b_d) (P:set_e) (Q:set_e), (((module_e_b_f_d M3) R)->((((submodule_b_d_e_f R) M3) P)->((((submodule_b_d_e_f R) M3) Q)->((ideal_b_d R) ((((quotie169863047_d_e_f R) M3) P) Q))))))
% 0.70/0.88 FOF formula (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (P:set_a) (Q:set_a), (((module1821517916unit_d M3) R)->((((submod903911234t_unit R) M3) P)->((((submod903911234t_unit R) M3) Q)->((ideal_b_d R) ((((quotie1196826005t_unit R) M3) P) Q)))))) of role axiom named fact_153_Module_Oquotient__of__submodules__is__ideal
% 0.70/0.88 A new axiom: (forall (M3:carrie1963041556t_unit) (R:carrie1950868226xt_b_d) (P:set_a) (Q:set_a), (((module1821517916unit_d M3) R)->((((submod903911234t_unit R) M3) P)->((((submod903911234t_unit R) M3) Q)->((ideal_b_d R) ((((quotie1196826005t_unit R) M3) P) Q))))))
% 0.70/0.88 FOF formula (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (P:set_a) (Q:set_a), (((module_a_b_c_d M3) R)->((((submodule_b_d_a_c R) M3) P)->((((submodule_b_d_a_c R) M3) Q)->((ideal_b_d R) ((((quotie1153752712_d_a_c R) M3) P) Q)))))) of role axiom named fact_154_Module_Oquotient__of__submodules__is__ideal
% 0.70/0.88 A new axiom: (forall (M3:carrie722926983_a_b_c) (R:carrie1950868226xt_b_d) (P:set_a) (Q:set_a), (((module_a_b_c_d M3) R)->((((submodule_b_d_a_c R) M3) P)->((((submodule_b_d_a_c R) M3) Q)->((ideal_b_d R) ((((quotie1153752712_d_a_c R) M3) P) Q))))))
% 0.70/0.88 FOF formula (forall (M:nat) (N:nat) (R:(nat->(nat->Prop))), (((ord_less_eq_nat M) N)->((forall (X2:nat), ((R X2) X2))->((forall (X2:nat) (Y:nat) (Z:nat), (((R X2) Y)->(((R Y) Z)->((R X2) Z))))->((forall (N2:nat), ((R N2) (suc N2)))->((R M) N)))))) of role axiom named fact_155_transitive__stepwise__le
% 0.70/0.88 A new axiom: (forall (M:nat) (N:nat) (R:(nat->(nat->Prop))), (((ord_less_eq_nat M) N)->((forall (X2:nat), ((R X2) X2))->((forall (X2:nat) (Y:nat) (Z:nat), (((R X2) Y)->(((R Y) Z)->((R X2) Z))))->((forall (N2:nat), ((R N2) (suc N2)))->((R M) N))))))
% 0.70/0.88 FOF formula (forall (M:nat) (N:nat) (P:(nat->Prop)), (((ord_less_eq_nat M) N)->((P M)->((forall (N2:nat), (((ord_less_eq_nat M) N2)->((P N2)->(P (suc N2)))))->(P N))))) of role axiom named fact_156_nat__induct__at__least
% 0.70/0.88 A new axiom: (forall (M:nat) (N:nat) (P:(nat->Prop)), (((ord_less_eq_nat M) N)->((P M)->((forall (N2:nat), (((ord_less_eq_nat M) N2)->((P N2)->(P (suc N2)))))->(P N)))))
% 0.70/0.88 FOF formula (forall (P:(nat->Prop)) (N:nat), ((forall (N2:nat), ((forall (M2:nat), (((ord_less_eq_nat (suc M2)) N2)->(P M2)))->(P N2)))->(P N))) of role axiom named fact_157_full__nat__induct
% 0.70/0.88 A new axiom: (forall (P:(nat->Prop)) (N:nat), ((forall (N2:nat), ((forall (M2:nat), (((ord_less_eq_nat (suc M2)) N2)->(P M2)))->(P N2)))->(P N)))
% 0.70/0.88 FOF formula (forall (M:nat) (N:nat), (((eq Prop) (((ord_less_eq_nat M) N)->False)) ((ord_less_eq_nat (suc N)) M))) of role axiom named fact_158_not__less__eq__eq
% 0.70/0.88 A new axiom: (forall (M:nat) (N:nat), (((eq Prop) (((ord_less_eq_nat M) N)->False)) ((ord_less_eq_nat (suc N)) M)))
% 0.70/0.88 FOF formula (forall (N:nat), (((ord_less_eq_nat (suc N)) N)->False)) of role axiom named fact_159_Suc__n__not__le__n
% 0.70/0.88 A new axiom: (forall (N:nat), (((ord_less_eq_nat (suc N)) N)->False))
% 0.70/0.88 FOF formula (forall (M:nat) (N:nat), (((eq Prop) ((ord_less_eq_nat M) (suc N))) ((or ((ord_less_eq_nat M) N)) (((eq nat) M) (suc N))))) of role axiom named fact_160_le__Suc__eq
% 0.70/0.88 A new axiom: (forall (M:nat) (N:nat), (((eq Prop) ((ord_less_eq_nat M) (suc N))) ((or ((ord_less_eq_nat M) N)) (((eq nat) M) (suc N)))))
% 0.70/0.88 FOF formula (forall (N:nat) (M4:nat), (((ord_less_eq_nat (suc N)) M4)->((ex nat) (fun (M5:nat)=> (((eq nat) M4) (suc M5)))))) of role axiom named fact_161_Suc__le__D
% 0.70/0.88 A new axiom: (forall (N:nat) (M4:nat), (((ord_less_eq_nat (suc N)) M4)->((ex nat) (fun (M5:nat)=> (((eq nat) M4) (suc M5))))))
% 0.70/0.88 FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_eq_nat M) (suc N)))) of role axiom named fact_162_le__SucI
% 0.70/0.88 A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_eq_nat M) (suc N))))
% 0.70/0.88 FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) (suc N))->((((ord_less_eq_nat M) N)->False)->(((eq nat) M) (suc N))))) of role axiom named fact_163_le__SucE
% 0.70/0.88 A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) (suc N))->((((ord_less_eq_nat M) N)->False)->(((eq nat) M) (suc N)))))
% 0.70/0.88 FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat (suc M)) N)->((ord_less_eq_nat M) N))) of role axiom named fact_164_Suc__leD
% 0.70/0.88 A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat (suc M)) N)->((ord_less_eq_nat M) N)))
% 0.70/0.88 FOF formula (forall (A:nat), (((ord_less_eq_nat A) zero_zero_nat)->(((eq nat) A) zero_zero_nat))) of role axiom named fact_165_bot__nat__0_Oextremum__uniqueI
% 0.70/0.88 A new axiom: (forall (A:nat), (((ord_less_eq_nat A) zero_zero_nat)->(((eq nat) A) zero_zero_nat)))
% 0.70/0.88 FOF formula (forall (A:nat), (((eq Prop) ((ord_less_eq_nat A) zero_zero_nat)) (((eq nat) A) zero_zero_nat))) of role axiom named fact_166_bot__nat__0_Oextremum__unique
% 0.70/0.88 A new axiom: (forall (A:nat), (((eq Prop) ((ord_less_eq_nat A) zero_zero_nat)) (((eq nat) A) zero_zero_nat)))
% 0.70/0.88 FOF formula (forall (N:nat), (((eq Prop) ((ord_less_eq_nat N) zero_zero_nat)) (((eq nat) N) zero_zero_nat))) of role axiom named fact_167_le__0__eq
% 0.70/0.88 A new axiom: (forall (N:nat), (((eq Prop) ((ord_less_eq_nat N) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))
% 0.70/0.88 FOF formula (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)) of role axiom named fact_168_less__eq__nat_Osimps_I1_J
% 0.70/0.88 A new axiom: (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N))
% 0.70/0.88 FOF formula (forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ex nat) (fun (M5:nat)=> (((eq nat) N) (suc M5)))))) of role axiom named fact_169_not0__implies__Suc
% 0.70/0.88 A new axiom: (forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ex nat) (fun (M5:nat)=> (((eq nat) N) (suc M5))))))
% 0.70/0.88 FOF formula (forall (P:(nat->Prop)) (Nat:nat), ((P zero_zero_nat)->((forall (Nat3:nat), ((P Nat3)->(P (suc Nat3))))->(P Nat)))) of role axiom named fact_170_old_Onat_Oinducts
% 0.70/0.88 A new axiom: (forall (P:(nat->Prop)) (Nat:nat), ((P zero_zero_nat)->((forall (Nat3:nat), ((P Nat3)->(P (suc Nat3))))->(P Nat))))
% 0.70/0.88 <<<71_old_Onat_Oexhaust,axiom,(
% 0.70/0.88 ! [Y4: nat] :
% 0.70/0.88 ( ( Y4 != zero_zero_nat )
% 0.70/0.88 => ~ !>>>!!!<<< [Nat3: nat] :
% 0.70/0.88 ( Y4
% 0.70/0.88 != ( suc @ Nat3 ) ) ) )).
% 0.70/0.88
% 0.70/0.88 % old.nat.exhaust
% 0.70/0.88 th>>>
% 0.70/0.88 statestack=[0, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 11, 22, 30, 36, 43, 50, 99, 113, 185, 229, 265, 285, 300, 221, 120, 187, 124]
% 0.70/0.88 symstack=[$end, TPTP_file_pre, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, 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LexToken(THF,'thf',1,82034), LexToken(LPAR,'(',1,82037), name, LexToken(COMMA,',',1,82064), formula_role, LexToken(COMMA,',',1,82070), LexToken(LPAR,'(',1,82071), thf_quantified_formula_PRE, thf_quantifier, LexToken(LBRACKET,'[',1,82079), thf_variable_list, LexToken(RBRACKET,']',1,82087), LexToken(COLON,':',1,82089), LexToken(LPAR,'(',1,82097), thf_unitary_formula, thf_pair_connective, unary_connective]
% 0.70/0.88 Unexpected exception Syntax error at '!':BANG
% 0.70/0.88 Traceback (most recent call last):
% 0.70/0.88 File "CASC.py", line 79, in <module>
% 0.70/0.88 problem=TPTP.TPTPproblem(env=environment,debug=1,file=file)
% 0.70/0.88 File "/export/starexec/sandbox2/solver/bin/TPTP.py", line 38, in __init__
% 0.70/0.88 parser.parse(file.read(),debug=0,lexer=lexer)
% 0.70/0.88 File "/export/starexec/sandbox2/solver/bin/ply/yacc.py", line 265, in parse
% 0.70/0.88 return self.parseopt_notrack(input,lexer,debug,tracking,tokenfunc)
% 0.70/0.88 File "/export/starexec/sandbox2/solver/bin/ply/yacc.py", line 1047, in parseopt_notrack
% 0.70/0.88 tok = self.errorfunc(errtoken)
% 0.70/0.88 File "/export/starexec/sandbox2/solver/bin/TPTPparser.py", line 2099, in p_error
% 0.70/0.88 raise TPTPParsingError("Syntax error at '%s':%s" % (t.value,t.type))
% 0.70/0.88 TPTPparser.TPTPParsingError: Syntax error at '!':BANG
%------------------------------------------------------------------------------