TSTP Solution File: ITP211^3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP211^3 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:19:50 EDT 2023
% Result : Timeout 300.03s 300.37s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.26/2.31 % Problem : ITP211^3 : TPTP v8.1.2. Released v8.1.0.
% 2.26/2.31 % Command : do_cvc5 %s %d
% 2.31/2.52 % Computer : n022.cluster.edu
% 2.31/2.52 % Model : x86_64 x86_64
% 2.31/2.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 2.31/2.52 % Memory : 8042.1875MB
% 2.31/2.52 % OS : Linux 3.10.0-693.el7.x86_64
% 2.31/2.52 % CPULimit : 300
% 2.31/2.52 % WCLimit : 300
% 2.31/2.52 % DateTime : Sun Aug 27 15:08:26 EDT 2023
% 2.31/2.53 % CPUTime :
% 4.60/4.86 %----Proving TH0
% 4.69/4.86 %------------------------------------------------------------------------------
% 4.69/4.86 % File : ITP211^3 : TPTP v8.1.2. Released v8.1.0.
% 4.69/4.86 % Domain : Interactive Theorem Proving
% 4.69/4.86 % Problem : Sledgehammer problem Assertions 00607_017823
% 4.69/4.86 % Version : [Des22] axioms.
% 4.69/4.86 % English :
% 4.69/4.86
% 4.69/4.86 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 4.69/4.86 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 4.69/4.86 % Source : [Des22]
% 4.69/4.86 % Names : 0024_Assertions_00607_017823 [Des22]
% 4.69/4.86
% 4.69/4.86 % Status : Theorem
% 4.69/4.86 % Rating : 0.85 v8.1.0
% 4.69/4.86 % Syntax : Number of formulae : 9705 (3210 unt;1879 typ; 0 def)
% 4.69/4.86 % Number of atoms : 24722 (9168 equ; 0 cnn)
% 4.69/4.86 % Maximal formula atoms : 17 ( 3 avg)
% 4.69/4.86 % Number of connectives : 84528 (3128 ~; 291 |;1450 &;67800 @)
% 4.69/4.86 % ( 0 <=>;11859 =>; 0 <=; 0 <~>)
% 4.69/4.86 % Maximal formula depth : 22 ( 7 avg)
% 4.69/4.86 % Number of types : 160 ( 159 usr)
% 4.69/4.86 % Number of type conns : 8578 (8578 >; 0 *; 0 +; 0 <<)
% 4.69/4.86 % Number of symbols : 1723 (1720 usr; 85 con; 0-8 aty)
% 4.69/4.86 % Number of variables : 22195 ( 759 ^;20824 !; 612 ?;22195 :)
% 4.69/4.86 % SPC : TH0_THM_EQU_NAR
% 4.69/4.86
% 4.69/4.86 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 4.69/4.86 % from the van Emde Boas Trees session in the Archive of Formal
% 4.69/4.86 % proofs -
% 4.69/4.86 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 4.69/4.86 % 2022-02-17 14:51:40.090
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% 4.69/4.87 bNF_re5228765855967844073nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001_Eo,type,
% 4.69/4.87 bNF_re8699439704749558557nt_o_o: ( product_prod_int_int > product_prod_int_int > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.69/4.87 bNF_re7145576690424134365nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 4.69/4.87 bNF_re7627151682743391978at_rat: ( product_prod_int_int > rat > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( rat > rat > rat ) > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001_Eo_001_Eo,type,
% 4.69/4.87 bNF_re1494630372529172596at_o_o: ( product_prod_int_int > rat > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( rat > $o ) > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 4.69/4.87 bNF_re8279943556446156061nt_rat: ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.69/4.87 bNF_re7408651293131936558nt_int: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 4.69/4.87 bNF_re7400052026677387805at_int: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 4.69/4.87 bNF_re3099431351363272937at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.69/4.87 bNF_re2241393799969408733at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Def_OsndOp_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.69/4.87 bNF_sn4039337771197282234et_nat: ( heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o ) > ( heap_e7401611519738050253t_unit > set_nat > $o ) > produc3658429121746597890et_nat > produc3658429121746597890et_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Def_OsndOp_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 4.69/4.87 bNF_sn1062102010912252026nt_int: ( int > int > $o ) > ( int > int > $o ) > product_prod_int_int > product_prod_int_int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Wellorder__Constructions_Obsqr_001t__Int__Oint,type,
% 4.69/4.87 bNF_We1730399552001240015qr_int: set_Pr958786334691620121nt_int > set_Pr2560585780119916871nt_int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Wellorder__Constructions_Obsqr_001t__Nat__Onat,type,
% 4.69/4.87 bNF_We1732890022510290291qr_nat: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
% 4.69/4.87 bNF_We740377018556551609_nat_o: set_Pr2161125870931222855_nat_o > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_001_Eo,type,
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% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_001t__Int__Oint,type,
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% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_001t__Nat__Onat,type,
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% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_001t__Product____Type__Ounit,type,
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% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_OisMinim_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
% 4.69/4.87 bNF_We5608535359669600131_nat_o: set_Pr2161125870931222855_nat_o > set_Pr4532377907799695533_nat_o > ( produc3658429121746597890et_nat > $o ) > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_OisMinim_001_Eo,type,
% 4.69/4.87 bNF_We4647864369647134286inim_o: set_Product_prod_o_o > set_o > $o > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_OisMinim_001t__Int__Oint,type,
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% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_OisMinim_001t__Nat__Onat,type,
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% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_OisMinim_001t__Product____Type__Ounit,type,
% 4.69/4.87 bNF_We909621271159000003t_unit: set_Pr5094982260447487303t_unit > set_Product_unit > product_unit > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Omax2_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
% 4.69/4.87 bNF_We6400040844883348763_nat_o: set_Pr2161125870931222855_nat_o > ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Omax2_001_Eo,type,
% 4.69/4.87 bNF_We3104086342435940326max2_o: set_Product_prod_o_o > $o > $o > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Omax2_001t__Int__Oint,type,
% 4.69/4.87 bNF_We2378448595015613790x2_int: set_Pr958786334691620121nt_int > int > int > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Omax2_001t__Nat__Onat,type,
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% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Omax2_001t__Product____Type__Ounit,type,
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% 4.69/4.87 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Ominim_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
% 4.69/4.87 bNF_We8236795211600914329_nat_o: set_Pr2161125870931222855_nat_o > set_Pr4532377907799695533_nat_o > produc3658429121746597890et_nat > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Ominim_001_Eo,type,
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% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Ominim_001t__Int__Oint,type,
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% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Ominim_001t__Nat__Onat,type,
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% 4.69/4.87
% 4.69/4.87 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_Ominim_001t__Product____Type__Ounit,type,
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% 4.69/4.87
% 4.69/4.87 thf(sy_c_Basic__BNF__LFPs_Oprod_Osize__prod_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.69/4.87 basic_5567952622663070111et_nat: ( heap_e7401611519738050253t_unit > nat ) > ( set_nat > nat ) > produc3658429121746597890et_nat > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Basic__BNF__LFPs_Oprod_Osize__prod_001t__Int__Oint_001t__Int__Oint,type,
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% 4.69/4.87 thf(sy_c_Basic__BNFs_Ofsts_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
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% 4.69/4.87
% 4.69/4.87 thf(sy_c_Basic__BNFs_Ofsts_001t__Int__Oint_001t__Int__Oint,type,
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% 4.69/4.87 thf(sy_c_Basic__BNFs_Ofsts_001t__Nat__Onat_001t__Nat__Onat,type,
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% 4.69/4.87
% 4.69/4.87 thf(sy_c_Finite__Set_Ofold_001t__Set__Oset_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J_001t__Set__Oset_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
% 4.69/4.87 finite8456856254070787592_nat_o: ( set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o ) > set_Pr4532377907799695533_nat_o > set_se1353816476878259085_nat_o > set_Pr4532377907799695533_nat_o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Finite__Set_Ofold_001t__Set__Oset_I_Eo_J_001t__Set__Oset_I_Eo_J,type,
% 4.69/4.87 finite4337638375924247368_set_o: ( set_o > set_o > set_o ) > set_o > set_set_o > set_o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Finite__Set_Ofold_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J,type,
% 4.69/4.87 finite2508883933289561102et_int: ( set_int > set_int > set_int ) > set_int > set_set_int > set_int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Finite__Set_Ofold_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.69/4.87 finite677925301803182934et_nat: ( set_nat > set_nat > set_nat ) > set_nat > set_set_nat > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Finite__Set_Ofold_001t__Set__Oset_It__Product____Type__Ounit_J_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 4.69/4.87 finite4243028863286625800t_unit: ( set_Product_unit > set_Product_unit > set_Product_unit ) > set_Product_unit > set_set_Product_unit > set_Product_unit ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_C5076291335850163704nteger: ( ( code_integer > code_integer ) > code_integer ) > ( code_integer > code_integer > code_integer ) > code_integer > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Set__Oset_It__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_P4885729792186999034nteger: ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > set_Code_integer ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > set_Code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Set__Oset_It__Nat__Onat_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_P8262219321096090349nteger: ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > set_nat ) > ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_I_Eo_J_Mt__Assertions__Oassn_J_001_062_It__Set__Oset_It__Set__Oset_I_Eo_J_J_Mt__Assertions__Oassn_J_001_062_I_Eo_Mt__Assertions__Oassn_J,type,
% 4.69/4.87 comp_s518380907012905326o_assn: ( ( set_o > assn ) > set_set_o > assn ) > ( ( $o > assn ) > set_o > assn ) > ( $o > assn ) > set_set_o > assn ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_I_Eo_J_Mt__Nat__Onat_J_001_062_It__Set__Oset_It__Set__Oset_I_Eo_J_J_Mt__Nat__Onat_J_001_062_I_Eo_Mt__Nat__Onat_J,type,
% 4.69/4.87 comp_s6084864194472624150_o_nat: ( ( set_o > nat ) > set_set_o > nat ) > ( ( $o > nat ) > set_o > nat ) > ( $o > nat ) > set_set_o > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Assertions__Oassn_J_001_062_It__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_Mt__Assertions__Oassn_J_001_062_It__Code____Numeral__Ointeger_Mt__Assertions__Oassn_J,type,
% 4.69/4.87 comp_s3531641609786562035r_assn: ( ( set_Code_integer > assn ) > set_set_Code_integer > assn ) > ( ( code_integer > assn ) > set_Code_integer > assn ) > ( code_integer > assn ) > set_set_Code_integer > assn ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Nat__Onat_J_001_062_It__Set__Oset_It__Set__Oset_It__Code____Numeral__Ointeger_J_J_Mt__Nat__Onat_J_001_062_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J,type,
% 4.69/4.87 comp_s8759123648413916139er_nat: ( ( set_Code_integer > nat ) > set_set_Code_integer > nat ) > ( ( code_integer > nat ) > set_Code_integer > nat ) > ( code_integer > nat ) > set_set_Code_integer > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Assertions__Oassn_J_001_062_It__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_Mt__Assertions__Oassn_J_001_062_It__Int__Oint_Mt__Assertions__Oassn_J,type,
% 4.69/4.87 comp_s4595925057662634336t_assn: ( ( set_int > assn ) > set_set_int > assn ) > ( ( int > assn ) > set_int > assn ) > ( int > assn ) > set_set_int > assn ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Int__Oint_J_001_062_It__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.69/4.87 comp_s9098231955081793132nt_int: ( ( set_int > int ) > set_set_int > int ) > ( ( int > int ) > set_int > int ) > ( int > int ) > set_set_int > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Nat__Onat_J_001_062_It__Set__Oset_It__Set__Oset_It__Int__Oint_J_J_Mt__Nat__Onat_J_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
% 4.69/4.87 comp_s3237642481825588056nt_nat: ( ( set_int > nat ) > set_set_int > nat ) > ( ( int > nat ) > set_int > nat ) > ( int > nat ) > set_set_int > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_It__Nat__Onat_J_Mt__Assertions__Oassn_J_001_062_It__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J_Mt__Assertions__Oassn_J_001_062_It__Nat__Onat_Mt__Assertions__Oassn_J,type,
% 4.69/4.87 comp_s2451231738238893644t_assn: ( ( set_nat > assn ) > set_set_nat > assn ) > ( ( nat > assn ) > set_nat > assn ) > ( nat > assn ) > set_set_nat > assn ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_It__Nat__Onat_J_Mt__Nat__Onat_J_001_062_It__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.69/4.87 comp_s5456809700045850692at_nat: ( ( set_nat > nat ) > set_set_nat > nat ) > ( ( nat > nat ) > set_nat > nat ) > ( nat > nat ) > set_set_nat > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_It__Product____Type__Ounit_J_Mt__Assertions__Oassn_J_001_062_It__Set__Oset_It__Set__Oset_It__Product____Type__Ounit_J_J_Mt__Assertions__Oassn_J_001_062_It__Product____Type__Ounit_Mt__Assertions__Oassn_J,type,
% 4.69/4.87 comp_s8247530669214396195t_assn: ( ( set_Product_unit > assn ) > set_set_Product_unit > assn ) > ( ( product_unit > assn ) > set_Product_unit > assn ) > ( product_unit > assn ) > set_set_Product_unit > assn ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_062_It__Set__Oset_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_001_062_It__Set__Oset_It__Set__Oset_It__Product____Type__Ounit_J_J_Mt__Nat__Onat_J_001_062_It__Product____Type__Ounit_Mt__Nat__Onat_J,type,
% 4.69/4.87 comp_s8928436226432208331it_nat: ( ( set_Product_unit > nat ) > set_set_Product_unit > nat ) > ( ( product_unit > nat ) > set_Product_unit > nat ) > ( product_unit > nat ) > set_set_Product_unit > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_Eo_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_o8922910837708301817nteger: ( $o > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > $o ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_Eo_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Product____Type__Ounit,type,
% 4.69/4.87 comp_o6961622296474427249t_unit: ( $o > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( product_unit > $o ) > product_unit > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_Eo_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_o1085144040659434033nteger: ( $o > code_integer ) > ( code_integer > $o ) > code_integer > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_Eo_001t__Code____Numeral__Ointeger_001t__Product____Type__Ounit,type,
% 4.69/4.87 comp_o780160699970281785t_unit: ( $o > code_integer ) > ( product_unit > $o ) > product_unit > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_Eo_001t__Code____Numeral__Onatural_001t__Product____Type__Ounit,type,
% 4.69/4.87 comp_o2643362028263920430t_unit: ( $o > code_natural ) > ( product_unit > $o ) > product_unit > code_natural ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_Eo_001t__Int__Oint_001t__Int__Oint,type,
% 4.69/4.87 comp_o_int_int: ( $o > int ) > ( int > $o ) > int > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_Eo_001t__Product____Type__Ounit_001_Eo,type,
% 4.69/4.87 comp_o3916225744453444672unit_o: ( $o > product_unit ) > ( $o > $o ) > $o > product_unit ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_Eo_001t__Product____Type__Ounit_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_o6635994240230588853nteger: ( $o > product_unit ) > ( code_integer > $o ) > code_integer > product_unit ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_Eo_001t__Product____Type__Ounit_001t__Int__Oint,type,
% 4.69/4.87 comp_o7049022088938261380it_int: ( $o > product_unit ) > ( int > $o ) > int > product_unit ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_Eo_001t__Product____Type__Ounit_001t__Nat__Onat,type,
% 4.69/4.87 comp_o7051512559447311656it_nat: ( $o > product_unit ) > ( nat > $o ) > nat > product_unit ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_Eo_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
% 4.69/4.87 comp_o7724735231917782709t_unit: ( $o > product_unit ) > ( product_unit > $o ) > product_unit > product_unit ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_Eo_001t__Set__Oset_I_Eo_J_001t__Product____Type__Ounit,type,
% 4.69/4.87 comp_o6895741221744486154t_unit: ( $o > set_o ) > ( product_unit > $o ) > product_unit > set_o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_Eo_001t__Set__Oset_It__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 4.69/4.87 comp_o7929101295636871983nteger: ( $o > set_Code_integer ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > set_Code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_Eo_001t__Set__Oset_It__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_o4291842030903409511nteger: ( $o > set_Code_integer ) > ( code_integer > $o ) > code_integer > set_Code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_Eo_001t__Set__Oset_It__Int__Oint_J_001t__Product____Type__Ounit,type,
% 4.69/4.87 comp_o1521574261646630388t_unit: ( $o > set_int ) > ( product_unit > $o ) > product_unit > set_int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_Eo_001t__Set__Oset_It__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 4.69/4.87 comp_o1289984117834210338nteger: ( $o > set_nat ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_Eo_001t__Set__Oset_It__Nat__Onat_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_o172754640513974618nteger: ( $o > set_nat ) > ( code_integer > $o ) > code_integer > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_Eo_001t__Set__Oset_It__Nat__Onat_J_001t__Product____Type__Ounit,type,
% 4.69/4.87 comp_o9190160103024335696t_unit: ( $o > set_nat ) > ( product_unit > $o ) > product_unit > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001_Eo_001t__Set__Oset_It__Product____Type__Ounit_J_001t__Product____Type__Ounit,type,
% 4.69/4.87 comp_o2086126948152544725t_unit: ( $o > set_Product_unit ) > ( product_unit > $o ) > product_unit > set_Product_unit ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_C2931745410781319416nteger: ( code_integer > code_integer > code_integer ) > ( code_integer > code_integer ) > code_integer > code_integer > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 4.69/4.87 comp_C95226695241045696nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( ( code_integer > code_integer ) > code_integer ) > ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001_Eo,type,
% 4.69/4.87 comp_C5733264393235242609eger_o: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( $o > code_integer ) > $o > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Int__Oint,type,
% 4.69/4.87 comp_C834242911430131603er_int: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( int > code_integer ) > int > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Nat__Onat,type,
% 4.69/4.87 comp_C836733381939181879er_nat: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( nat > code_integer ) > nat > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Product____Type__Ounit,type,
% 4.69/4.87 comp_C5854136495726678886t_unit: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( product_unit > code_integer ) > product_unit > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_C3026223900822616519nteger: ( code_integer > assn ) > ( code_integer > code_integer ) > code_integer > assn ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Assertions__Oassn_001t__Nat__Onat,type,
% 4.69/4.87 comp_C8462447471145125178sn_nat: ( code_integer > assn ) > ( nat > code_integer ) > nat > assn ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_C7449957260575251196nteger: ( code_integer > code_integer ) > ( code_integer > code_integer ) > code_integer > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Onatural,type,
% 4.69/4.87 comp_C6273552412331968711atural: ( code_integer > code_integer ) > ( code_natural > code_integer ) > code_natural > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 4.69/4.87 comp_C6974050283906349679er_nat: ( code_integer > code_integer ) > ( nat > code_integer ) > nat > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 4.69/4.87 comp_C1043215000170864188nteger: ( code_integer > code_integer ) > ( produc8923325533196201883nteger > code_integer ) > produc8923325533196201883nteger > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Ounit,type,
% 4.69/4.87 comp_C2290379119555921966t_unit: ( code_integer > code_integer ) > ( product_unit > code_integer ) > product_unit > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Onatural_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_C1891057325546811591nteger: ( code_integer > code_natural ) > ( code_integer > code_integer ) > code_integer > code_natural ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Onatural_001t__Code____Numeral__Onatural,type,
% 4.69/4.87 comp_C714652477303529106atural: ( code_integer > code_natural ) > ( code_natural > code_integer ) > code_natural > code_natural ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Onatural_001t__Product____Type__Ounit,type,
% 4.69/4.87 comp_C4153580447849560611t_unit: ( code_integer > code_natural ) > ( product_unit > code_integer ) > product_unit > code_natural ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_C7610259292922237131nteger: ( code_integer > int ) > ( code_integer > code_integer ) > code_integer > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Nat__Onat,type,
% 4.69/4.87 comp_C5048910307564104766nt_nat: ( code_integer > int ) > ( nat > code_integer ) > nat > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_C7238605732685392495nteger: ( code_integer > nat ) > ( code_integer > code_integer ) > code_integer > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Product____Type__Ounit_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_C8146212659816229034nteger: ( code_integer > product_unit ) > ( code_integer > code_integer ) > code_integer > product_unit ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Product____Type__Ounit_001t__Code____Numeral__Onatural,type,
% 4.69/4.87 comp_C6969807811572946549atural: ( code_integer > product_unit ) > ( code_natural > code_integer ) > code_natural > product_unit ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
% 4.69/4.87 comp_C2408090164605745152t_unit: ( code_integer > product_unit ) > ( product_unit > code_integer ) > product_unit > product_unit ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Set__Oset_It__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 4.69/4.87 comp_C6344129587964912378nteger: ( code_integer > set_Code_integer ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > set_Code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Set__Oset_It__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_C8186931911283765298nteger: ( code_integer > set_Code_integer ) > ( code_integer > code_integer ) > code_integer > set_Code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Set__Oset_It__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 4.69/4.87 comp_C3184339336801759213nteger: ( code_integer > set_nat ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Set__Oset_It__Nat__Onat_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_C6537567860429791781nteger: ( code_integer > set_nat ) > ( code_integer > code_integer ) > code_integer > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Onatural_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_C456341964420721295nteger: ( code_natural > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_natural ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_i2874689474467862163nteger: ( int > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > int ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001_Eo_001_Eo,type,
% 4.69/4.87 comp_int_o_o: ( int > $o ) > ( $o > int ) > $o > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001_Eo_001t__Int__Oint,type,
% 4.69/4.87 comp_int_o_int: ( int > $o ) > ( int > int ) > int > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001_Eo_001t__Nat__Onat,type,
% 4.69/4.87 comp_int_o_nat: ( int > $o ) > ( nat > int ) > nat > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Code____Numeral__Ointeger_001_Eo,type,
% 4.69/4.87 comp_i5286552343147518890eger_o: ( int > code_integer ) > ( $o > int ) > $o > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_i6014793192326455499nteger: ( int > code_integer ) > ( code_integer > int ) > code_integer > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 4.69/4.87 comp_i1585864551200866970er_int: ( int > code_integer ) > ( int > int ) > int > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 4.69/4.87 comp_i1588355021709917246er_nat: ( int > code_integer ) > ( nat > int ) > nat > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Code____Numeral__Onatural_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_i455893257298015894nteger: ( int > code_natural ) > ( code_integer > int ) > code_integer > code_natural ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 4.69/4.87 comp_int_int_o: ( int > int ) > ( $o > int ) > $o > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 4.69/4.87 comp_int_int_int: ( int > int ) > ( int > int ) > int > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat,type,
% 4.69/4.87 comp_int_int_nat: ( int > int ) > ( nat > int ) > nat > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.69/4.87 comp_i4330622015127193916nt_int: ( int > int ) > ( product_prod_int_int > int ) > product_prod_int_int > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001_Eo,type,
% 4.69/4.87 comp_int_nat_o: ( int > nat ) > ( $o > int ) > $o > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
% 4.69/4.87 comp_int_nat_int: ( int > nat ) > ( int > int ) > int > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.69/4.87 comp_int_nat_nat: ( int > nat ) > ( nat > int ) > nat > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Product____Type__Ounit_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_i8439899303502915483nteger: ( int > product_unit ) > ( code_integer > int ) > code_integer > product_unit ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Set__Oset_I_Eo_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_i5479505385629679622nteger: ( int > set_o ) > ( code_integer > int ) > code_integer > set_o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Set__Oset_It__Int__Oint_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_i1887841406321795152nteger: ( int > set_int ) > ( code_integer > int ) > code_integer > set_int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Set__Oset_It__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.69/4.87 comp_i5103216804979976198nt_int: ( int > set_int ) > ( product_prod_int_int > int ) > product_prod_int_int > set_int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Set__Oset_It__Nat__Onat_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_i5102403792180996084nteger: ( int > set_nat ) > ( code_integer > int ) > code_integer > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Set__Oset_It__Nat__Onat_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.69/4.87 comp_i6200299785623974754nt_int: ( int > set_nat ) > ( product_prod_int_int > int ) > product_prod_int_int > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Set__Oset_It__Product____Type__Ounit_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_i3319814986458681467nteger: ( int > set_Product_unit ) > ( code_integer > int ) > code_integer > set_Product_unit ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 4.69/4.87 comp_nat_nat_nat_nat: ( nat > nat > nat ) > ( nat > nat ) > nat > nat > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_n2033352843805742135nteger: ( nat > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > nat ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Onatural,type,
% 4.69/4.87 comp_n856947995562459650atural: ( nat > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_natural > nat ) > code_natural > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Assertions__Oassn_001t__Nat__Onat,type,
% 4.69/4.87 comp_nat_assn_nat: ( nat > assn ) > ( nat > nat ) > nat > assn ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_n6876073255676942959nteger: ( nat > code_integer ) > ( code_integer > nat ) > code_integer > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Onatural,type,
% 4.69/4.87 comp_n5699668407433660474atural: ( nat > code_integer ) > ( code_natural > nat ) > code_natural > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 4.69/4.87 comp_n3898172953802868194er_nat: ( nat > code_integer ) > ( nat > nat ) > nat > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Code____Numeral__Onatural_001_Eo,type,
% 4.69/4.87 comp_n2857367870785791611ural_o: ( nat > code_natural ) > ( $o > nat ) > $o > code_natural ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Code____Numeral__Onatural_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_n1317173320648503354nteger: ( nat > code_natural ) > ( code_integer > nat ) > code_integer > code_natural ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Code____Numeral__Onatural_001t__Code____Numeral__Onatural,type,
% 4.69/4.87 comp_n140768472405220869atural: ( nat > code_natural ) > ( code_natural > nat ) > code_natural > code_natural ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Code____Numeral__Onatural_001t__Int__Oint,type,
% 4.69/4.87 comp_n9160511493981425161al_int: ( nat > code_natural ) > ( int > nat ) > int > code_natural ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Code____Numeral__Onatural_001t__Nat__Onat,type,
% 4.69/4.87 comp_n9163001964490475437al_nat: ( nat > code_natural ) > ( nat > nat ) > nat > code_natural ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat,type,
% 4.69/4.87 comp_nat_int_nat: ( nat > int ) > ( nat > nat ) > nat > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Product____Type__Ounit_001t__Code____Numeral__Onatural,type,
% 4.69/4.87 comp_n8360577435903631554atural: ( nat > product_unit ) > ( code_natural > nat ) > code_natural > product_unit ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Set__Oset_It__Int__Oint_J_001t__Code____Numeral__Onatural,type,
% 4.69/4.87 comp_n1572716621429000127atural: ( nat > set_int ) > ( code_natural > nat ) > code_natural > set_int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 4.69/4.87 comp_n3623798160786426464nteger: ( nat > set_nat ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > nat ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_n5963683855531483544nteger: ( nat > set_nat ) > ( code_integer > nat ) > code_integer > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J_001t__Code____Numeral__Onatural,type,
% 4.69/4.87 comp_n4787279007288201059atural: ( nat > set_nat ) > ( code_natural > nat ) > code_natural > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_M_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 4.69/4.87 comp_P5544053077415136032nteger: ( produc723880050079548563nteger > produc101387210554329899nteger ) > ( produc8923325533196201883nteger > produc723880050079548563nteger ) > produc8923325533196201883nteger > produc101387210554329899nteger ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_I_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_M_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 4.69/4.87 comp_P1414880308642389412nteger: ( produc2221115339011613079nteger > produc101387210554329899nteger ) > ( produc8923325533196201883nteger > produc2221115339011613079nteger ) > produc8923325533196201883nteger > produc101387210554329899nteger ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_M_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 4.69/4.87 comp_P6312383820422015140nteger: ( produc1397831737260518551nteger > produc101387210554329899nteger ) > ( produc8923325533196201883nteger > produc1397831737260518551nteger ) > produc8923325533196201883nteger > produc101387210554329899nteger ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_P7111796090210262324nteger: ( produc8923325533196201883nteger > code_integer ) > ( code_integer > produc8923325533196201883nteger ) > code_integer > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 4.69/4.87 comp_P3428181540658402820nteger: ( produc8923325533196201883nteger > code_integer ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc8923325533196201883nteger > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Product____Type__Ounit,type,
% 4.69/4.87 comp_P659088277599099894t_unit: ( produc8923325533196201883nteger > code_integer ) > ( product_unit > produc8923325533196201883nteger ) > product_unit > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_M_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 4.69/4.87 comp_P234064951390806312nteger: ( produc8923325533196201883nteger > produc101387210554329899nteger ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc101387210554329899nteger ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_P7101464685127059239nteger: ( produc6433947425880249742er_nat > code_integer ) > ( code_integer > produc6433947425880249742er_nat ) > code_integer > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_001t__Code____Numeral__Ointeger_001t__Product____Type__Ounit,type,
% 4.69/4.87 comp_P7581484221039074243t_unit: ( produc6433947425880249742er_nat > code_integer ) > ( product_unit > produc6433947425880249742er_nat ) > product_unit > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_P5964733648194011802nteger: ( produc6433947425880249742er_nat > nat ) > ( code_integer > produc6433947425880249742er_nat ) > code_integer > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Product____Type__Ounit,type,
% 4.69/4.87 comp_P6821003776282389008t_unit: ( produc6433947425880249742er_nat > nat ) > ( product_unit > produc6433947425880249742er_nat ) > product_unit > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_It__Nat__Onat_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 4.69/4.87 comp_P2930521774885306735et_nat: ( produc3658429121746597890et_nat > set_nat ) > ( produc3658429121746597890et_nat > produc3658429121746597890et_nat ) > produc3658429121746597890et_nat > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_It__Nat__Onat_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.69/4.87 comp_P8606889026643445772nt_int: ( produc3658429121746597890et_nat > set_nat ) > ( product_prod_int_int > produc3658429121746597890et_nat ) > product_prod_int_int > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 4.69/4.87 comp_P8308861049717174982et_nat: ( product_prod_int_int > int ) > ( produc3658429121746597890et_nat > product_prod_int_int ) > produc3658429121746597890et_nat > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.69/4.87 comp_P5356232565778667509nt_int: ( product_prod_int_int > int ) > ( product_prod_int_int > product_prod_int_int ) > product_prod_int_int > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Int__Oint_001t__Product____Type__Ounit,type,
% 4.69/4.87 comp_P6796073005956588617t_unit: ( product_prod_int_int > int ) > ( product_unit > product_prod_int_int ) > product_unit > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001_Eo,type,
% 4.69/4.87 comp_P7177471617286032590eger_o: ( produc2591615631378489102nteger > code_integer ) > ( $o > produc2591615631378489102nteger ) > $o > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_P6122662217367900327nteger: ( produc2591615631378489102nteger > code_integer ) > ( code_integer > produc2591615631378489102nteger ) > code_integer > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Product____Type__Ounit,type,
% 4.69/4.87 comp_P7320554561093743171t_unit: ( produc2591615631378489102nteger > code_integer ) > ( product_unit > produc2591615631378489102nteger ) > product_unit > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__Nat__Onat_001_Eo,type,
% 4.69/4.87 comp_P7179991235626930843_nat_o: ( produc2591615631378489102nteger > nat ) > ( $o > produc2591615631378489102nteger ) > $o > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_P5725896914063526938nteger: ( produc2591615631378489102nteger > nat ) > ( code_integer > produc2591615631378489102nteger ) > code_integer > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Code____Numeral__Ointeger_J_001t__Nat__Onat_001t__Product____Type__Ounit,type,
% 4.69/4.87 comp_P7621350044865347728t_unit: ( produc2591615631378489102nteger > nat ) > ( product_unit > produc2591615631378489102nteger ) > product_unit > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001_Eo,type,
% 4.69/4.87 comp_P4394204175247225320_nat_o: ( product_prod_nat_nat > nat ) > ( $o > product_prod_nat_nat ) > $o > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Product____Type__Ounit,type,
% 4.69/4.87 comp_P2980510830910040157t_unit: ( product_prod_nat_nat > nat ) > ( product_unit > product_prod_nat_nat ) > product_unit > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_P4511551582283981294nteger: ( product_unit > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > product_unit ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001_062_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_P4558236313141964142nteger: ( product_unit > product_unit > product_unit ) > ( code_integer > product_unit ) > code_integer > product_unit > product_unit ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001_062_It__Product____Type__Ounit_Mt__Product____Type__Ounit_J_001t__Nat__Onat,type,
% 4.69/4.87 comp_P6204500334276302049it_nat: ( product_unit > product_unit > product_unit ) > ( nat > product_unit ) > nat > product_unit > product_unit ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_P6790823133229852966nteger: ( product_unit > code_integer ) > ( code_integer > product_unit ) > code_integer > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001t__Set__Oset_It__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 4.69/4.87 comp_P4635212033913086756nteger: ( product_unit > set_Code_integer ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > product_unit ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > set_Code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001t__Set__Oset_It__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_P4767411901762164316nteger: ( product_unit > set_Code_integer ) > ( code_integer > product_unit ) > code_integer > set_Code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001t__Set__Oset_It__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 4.69/4.87 comp_P6101996899264665623nteger: ( product_unit > set_nat ) > ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > product_unit ) > ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Product____Type__Ounit_001t__Set__Oset_It__Nat__Onat_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_P5878433733084393551nteger: ( product_unit > set_nat ) > ( code_integer > product_unit ) > code_integer > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Set__Oset_I_Eo_J_001_062_It__Set__Oset_I_Eo_J_Mt__Set__Oset_I_Eo_J_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_s90868338361139993nteger: ( set_o > set_o > set_o ) > ( code_integer > set_o ) > code_integer > set_o > set_o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Set__Oset_I_Eo_J_001_062_It__Set__Oset_I_Eo_J_Mt__Set__Oset_I_Eo_J_J_001t__Nat__Onat,type,
% 4.69/4.87 comp_s4424444925706540684_o_nat: ( set_o > set_o > set_o ) > ( nat > set_o ) > nat > set_o > set_o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_s956550612328592744nteger: ( set_Code_integer > set_Code_integer ) > ( code_integer > set_Code_integer ) > code_integer > set_Code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Int__Oint_J_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Set__Oset_It__Int__Oint_J_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_s3634918272309710215nteger: ( set_int > set_int > set_int ) > ( code_integer > set_int ) > code_integer > set_int > set_int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Int__Oint_J_001_062_It__Set__Oset_It__Int__Oint_J_Mt__Set__Oset_It__Int__Oint_J_J_001t__Nat__Onat,type,
% 4.69/4.87 comp_s6689493721604790522nt_nat: ( set_int > set_int > set_int ) > ( nat > set_int ) > nat > set_int > set_int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001_062_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_s3169385134670675059nteger: ( set_nat > set_nat > set_nat ) > ( code_integer > set_nat ) > code_integer > set_nat > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001_062_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Nat__Onat,type,
% 4.69/4.87 comp_s2351873599094224870at_nat: ( set_nat > set_nat > set_nat ) > ( nat > set_nat ) > nat > set_nat > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 4.69/4.87 comp_s1601710177542341017et_nat: ( set_nat > int ) > ( produc3658429121746597890et_nat > set_nat ) > produc3658429121746597890et_nat > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_s8292494440407567195nteger: ( set_nat > set_Code_integer ) > ( code_integer > set_nat ) > code_integer > set_Code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_s4605850120322998606nteger: ( set_nat > set_nat ) > ( code_integer > set_nat ) > code_integer > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 4.69/4.87 comp_s5696514601250091763et_nat: ( set_nat > set_nat ) > ( produc3658429121746597890et_nat > set_nat ) > produc3658429121746597890et_nat > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Product____Type__Ounit_J_001_062_It__Set__Oset_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Product____Type__Ounit_J_J_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 comp_s3199726385246003790nteger: ( set_Product_unit > set_Product_unit > set_Product_unit ) > ( code_integer > set_Product_unit ) > code_integer > set_Product_unit > set_Product_unit ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ocomp_001t__Set__Oset_It__Product____Type__Ounit_J_001_062_It__Set__Oset_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Product____Type__Ounit_J_J_001t__Nat__Onat,type,
% 4.69/4.87 comp_s6943286182646368705it_nat: ( set_Product_unit > set_Product_unit > set_Product_unit ) > ( nat > set_Product_unit ) > nat > set_Product_unit > set_Product_unit ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001_Eo_001_Eo,type,
% 4.69/4.87 fun_upd_o_o: ( $o > $o ) > $o > $o > $o > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001_Eo_001t__Int__Oint,type,
% 4.69/4.87 fun_upd_o_int: ( $o > int ) > $o > int > $o > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001_Eo_001t__Nat__Onat,type,
% 4.69/4.87 fun_upd_o_nat: ( $o > nat ) > $o > nat > $o > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001_Eo_001t__Product____Type__Ounit,type,
% 4.69/4.87 fun_up846054379331416818t_unit: ( $o > product_unit ) > $o > product_unit > $o > product_unit ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001_Eo_001t__Set__Oset_I_Eo_J,type,
% 4.69/4.87 fun_upd_o_set_o: ( $o > set_o ) > $o > set_o > $o > set_o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001_Eo_001t__Set__Oset_It__Int__Oint_J,type,
% 4.69/4.87 fun_upd_o_set_int: ( $o > set_int ) > $o > set_int > $o > set_int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001_Eo_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.69/4.87 fun_upd_o_set_nat: ( $o > set_nat ) > $o > set_nat > $o > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001_Eo_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 4.69/4.87 fun_up4718931970374059986t_unit: ( $o > set_Product_unit ) > $o > set_Product_unit > $o > set_Product_unit ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 fun_up8355007323143964473nteger: ( code_integer > code_integer ) > code_integer > code_integer > code_integer > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Nat__Onat,type,
% 4.69/4.87 fun_upd_int_nat: ( int > nat ) > int > nat > int > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Set__Oset_I_Eo_J,type,
% 4.69/4.87 fun_upd_int_set_o: ( int > set_o ) > int > set_o > int > set_o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001t__Int__Oint_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 4.69/4.87 fun_up5054257004045450754t_unit: ( int > set_Product_unit ) > int > set_Product_unit > int > set_Product_unit ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 fun_up3904115110581602988nteger: ( nat > code_integer ) > nat > code_integer > nat > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.69/4.87 fun_upd_nat_nat: ( nat > nat ) > nat > nat > nat > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.69/4.87 fun_upd_nat_set_nat: ( nat > set_nat ) > nat > set_nat > nat > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Ounit_001_Eo,type,
% 4.69/4.87 fun_up5432024876597553480unit_o: ( product_unit > $o ) > product_unit > $o > product_unit > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Ounit_001t__Int__Oint,type,
% 4.69/4.87 fun_up6470560416331323516it_int: ( product_unit > int ) > product_unit > int > product_unit > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Ounit_001t__Nat__Onat,type,
% 4.69/4.87 fun_up6473050886840373792it_nat: ( product_unit > nat ) > product_unit > nat > product_unit > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
% 4.69/4.87 fun_up6875000483049295805t_unit: ( product_unit > product_unit ) > product_unit > product_unit > product_unit > product_unit ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Ounit_001t__Set__Oset_I_Eo_J,type,
% 4.69/4.87 fun_up1762901246852280360_set_o: ( product_unit > set_o ) > product_unit > set_o > product_unit > set_o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Ounit_001t__Set__Oset_It__Int__Oint_J,type,
% 4.69/4.87 fun_up391983181201004082et_int: ( product_unit > set_int ) > product_unit > set_int > product_unit > set_int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Ounit_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.69/4.87 fun_up4569834200710200790et_nat: ( product_unit > set_nat ) > product_unit > set_nat > product_unit > set_nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Ofun__upd_001t__Product____Type__Ounit_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 4.69/4.87 fun_up488859312337516701t_unit: ( product_unit > set_Product_unit ) > product_unit > set_Product_unit > product_unit > set_Product_unit ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oid_001_Eo,type,
% 4.69/4.87 id_o: $o > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Nat__Onat,type,
% 4.69/4.87 inj_on5271586719803267564_o_nat: ( ( produc3658429121746597890et_nat > $o ) > nat ) > set_Pr4532377907799695533_nat_o > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001_Eo_001_Eo,type,
% 4.69/4.87 inj_on_o_o: ( $o > $o ) > set_o > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001_Eo_001t__Int__Oint,type,
% 4.69/4.87 inj_on_o_int: ( $o > int ) > set_o > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001_Eo_001t__Nat__Onat,type,
% 4.69/4.87 inj_on_o_nat: ( $o > nat ) > set_o > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001_Eo_001t__Product____Type__Ounit,type,
% 4.69/4.87 inj_on4268752236855399398t_unit: ( $o > product_unit ) > set_o > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 inj_on1158064722259180589nteger: ( code_integer > code_integer ) > set_Code_integer > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 4.69/4.87 inj_on1981279154655846304er_nat: ( code_integer > nat ) > set_Code_integer > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001t__Int__Oint_001t__Int__Oint,type,
% 4.69/4.87 inj_on_int_int: ( int > int ) > set_int > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001t__Int__Oint_001t__Nat__Onat,type,
% 4.69/4.87 inj_on_int_nat: ( int > nat ) > set_int > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
% 4.69/4.87 inj_on7779444506608719434_nat_o: ( nat > produc3658429121746597890et_nat > $o ) > set_nat > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001_Eo,type,
% 4.69/4.87 inj_on_nat_o: ( nat > $o ) > set_nat > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 inj_on2245834603434889120nteger: ( nat > code_integer ) > set_nat > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Int__Oint,type,
% 4.69/4.87 inj_on_nat_int: ( nat > int ) > set_nat > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.69/4.87 inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Product____Type__Ounit,type,
% 4.69/4.87 inj_on7061601236592826506t_unit: ( nat > product_unit ) > set_nat > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.69/4.87 inj_on_nat_set_nat: ( nat > set_nat ) > set_nat > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 4.69/4.87 inj_on20428373856169009nteger: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > set_Pr4811707699266497531nteger > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Ounit_001_Eo,type,
% 4.69/4.87 inj_on8854722734121536060unit_o: ( product_unit > $o ) > set_Product_unit > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Ounit_001t__Int__Oint,type,
% 4.69/4.87 inj_on8427948621271784584it_int: ( product_unit > int ) > set_Product_unit > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Ounit_001t__Nat__Onat,type,
% 4.69/4.87 inj_on8430439091780834860it_nat: ( product_unit > nat ) > set_Product_unit > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
% 4.69/4.87 inj_on8151373323710067377t_unit: ( product_unit > product_unit ) > set_Product_unit > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001t__Rat__Orat_001t__Rat__Orat,type,
% 4.69/4.87 inj_on_rat_rat: ( rat > rat ) > set_rat > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Oinj__on_001t__Set__Oset_It__Nat__Onat_J_001t__Nat__Onat,type,
% 4.69/4.87 inj_on_set_nat_nat: ( set_nat > nat ) > set_set_nat > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 4.69/4.87 map_fu8272188784021352819nteger: ( code_integer > int ) > ( ( int > int ) > code_integer > code_integer ) > ( int > int > int ) > code_integer > code_integer > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 map_fu2599414010547811884nteger: ( code_integer > int ) > ( int > code_integer ) > ( int > int ) > code_integer > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J,type,
% 4.69/4.87 map_fu6549440983881763648atural: ( code_natural > nat ) > ( ( nat > nat ) > code_natural > code_natural ) > ( nat > nat > nat ) > code_natural > code_natural > code_natural ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001t__Nat__Onat_001t__Code____Numeral__Onatural,type,
% 4.69/4.87 map_fu1239815594074539274atural: ( code_natural > nat ) > ( nat > code_natural ) > ( nat > nat ) > code_natural > code_natural ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.69/4.87 map_fu4960017516451851995nt_int: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > int > int > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 4.69/4.87 map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Omap__fun_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 4.69/4.87 map_fu4333342158222067775at_rat: ( rat > product_prod_int_int ) > ( ( product_prod_int_int > product_prod_int_int ) > rat > rat ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > rat > rat > rat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Omap__fun_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001_Eo,type,
% 4.69/4.87 map_fu898904425404107465nt_o_o: ( rat > product_prod_int_int ) > ( $o > $o ) > ( product_prod_int_int > $o ) > rat > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Fun_Omap__fun_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 4.69/4.87 map_fu5673905371560938248nt_rat: ( rat > product_prod_int_int ) > ( product_prod_int_int > rat ) > ( product_prod_int_int > product_prod_int_int ) > rat > rat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_GCD_OGcd__class_OGcd_001t__Int__Oint,type,
% 4.69/4.87 gcd_Gcd_int: set_int > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_GCD_OGcd__class_OGcd_001t__Nat__Onat,type,
% 4.69/4.87 gcd_Gcd_nat: set_nat > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_GCD_OGcd__class_OLcm_001t__Nat__Onat,type,
% 4.69/4.87 gcd_Lcm_nat: set_nat > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_GCD_Obezw,type,
% 4.69/4.87 bezw: nat > nat > product_prod_int_int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_GCD_Obezw__rel,type,
% 4.69/4.87 bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 gcd_gcd_Code_integer: code_integer > code_integer > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Int__Oint,type,
% 4.69/4.87 gcd_gcd_int: int > int > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Nat__Onat,type,
% 4.69/4.87 gcd_gcd_nat: nat > nat > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_GCD_Ogcd__class_Olcm_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 gcd_lcm_Code_integer: code_integer > code_integer > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_GCD_Ogcd__class_Olcm_001t__Int__Oint,type,
% 4.69/4.87 gcd_lcm_int: int > int > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_GCD_Ogcd__class_Olcm_001t__Nat__Onat,type,
% 4.69/4.87 gcd_lcm_nat: nat > nat > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_GCD_Osemiring__gcd__class_OGcd__fin_001t__Int__Oint,type,
% 4.69/4.87 semiri4256215615220890538in_int: set_int > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_GCD_Osemiring__gcd__class_OGcd__fin_001t__Nat__Onat,type,
% 4.69/4.87 semiri4258706085729940814in_nat: set_nat > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Groups_Oabs__class_Oabs_001t__Code____Numeral__Ointeger,type,
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% 4.69/4.87
% 4.69/4.87 thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint,type,
% 4.69/4.87 abs_abs_int: int > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Groups_Ominus__class_Ominus_001t__Assertions__Oassn,type,
% 4.69/4.87 minus_minus_assn: assn > assn > assn ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Groups_Ominus__class_Ominus_001t__Code____Numeral__Ointeger,type,
% 4.69/4.87 minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint,type,
% 4.69/4.87 minus_minus_int: int > int > int ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 4.69/4.87 minus_minus_nat: nat > nat > nat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Groups_Ominus__class_Ominus_001t__Rat__Orat,type,
% 4.69/4.87 minus_minus_rat: rat > rat > rat ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
% 4.69/4.87 minus_1801376950450012436_nat_o: set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_I_Eo_J,type,
% 4.69/4.87 minus_minus_set_o: set_o > set_o > set_o ).
% 4.69/4.87
% 4.69/4.87 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Assertions__Oassn_J,type,
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% 4.69/4.87
% 4.69/4.87 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
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% 4.69/4.87
% 4.69/4.87 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Int__Oint_J,type,
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% 4.69/4.88
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% 4.69/4.88
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% 4.69/4.88
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% 4.69/4.88 produc3447581998352395295_nat_o: ( int > produc3658429121746597890et_nat ) > produc3776562785724475560_o_int > produc3925858234332021118et_nat ).
% 4.69/4.88
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% 4.69/4.88
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% 4.69/4.88 produc2122153897363312795t_unit: ( int > set_nat ) > produc2475246329834808232it_int > produc3658429121746597890et_nat ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Product__Type_Oapsnd_001t__Int__Oint_001t__Set__Oset_It__Nat__Onat_J_001t__Int__Oint,type,
% 4.69/4.88 produc1253519502038700766at_int: ( int > set_nat ) > product_prod_int_int > produc2771989624626745363et_nat ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Product__Type_Oapsnd_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.69/4.88 produc3094765310956027504at_nat: ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 4.69/4.88
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% 4.69/4.88
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% 4.69/4.88 produc1515462096303866701_nat_o: ( produc3925858234332021118et_nat > produc3658429121746597890et_nat ) > produc2732055786443039994et_nat > produc3925858234332021118et_nat ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Product__Type_Oapsnd_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
% 4.69/4.88 produc7714581247149323085_nat_o: ( produc3658429121746597890et_nat > produc3925858234332021118et_nat ) > produc3925858234332021118et_nat > produc2732055786443039994et_nat ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Product__Type_Oapsnd_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
% 4.69/4.88 produc8750854537940449737_nat_o: ( produc3658429121746597890et_nat > produc3658429121746597890et_nat ) > produc3925858234332021118et_nat > produc3925858234332021118et_nat ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Product__Type_Oapsnd_001t__Set__Oset_It__Nat__Onat_J_001t__Int__Oint_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 4.69/4.88 produc7345612820240450715t_unit: ( set_nat > int ) > produc3658429121746597890et_nat > produc2475246329834808232it_int ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Product__Type_Oapsnd_001t__Set__Oset_It__Nat__Onat_J_001t__Int__Oint_001t__Int__Oint,type,
% 4.69/4.88 produc2744032961877892830nt_int: ( set_nat > int ) > produc2771989624626745363et_nat > product_prod_int_int ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Product__Type_Oapsnd_001t__Set__Oset_It__Nat__Onat_J_001t__Nat__Onat_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Product__Type_Oapsnd_001t__Set__Oset_It__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.69/4.88 produc1747169720485888550at_nat: ( set_nat > nat ) > produc2400336064389900727et_nat > product_prod_nat_nat ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Product__Type_Oapsnd_001t__Set__Oset_It__Nat__Onat_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Product__Type_Oapsnd_001t__Set__Oset_It__Nat__Onat_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Product__Type_Oapsnd_001t__Set__Oset_It__Nat__Onat_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Product__Type_Oapsnd_001t__Set__Oset_It__Nat__Onat_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 4.69/4.88 produc7441988914112407621t_unit: ( set_nat > produc3658429121746597890et_nat ) > produc3658429121746597890et_nat > produc5697189838369619070et_nat ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Product__Type_Oapsnd_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J,type,
% 4.69/4.88 produc3286488329990770625t_unit: ( set_nat > set_nat ) > produc3658429121746597890et_nat > produc3658429121746597890et_nat ).
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% 4.69/4.88
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Product__Type_Ocurry_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 4.69/4.88 produc175634133007206835_int_o: ( product_prod_int_int > $o ) > int > int > $o ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Product__Type_Ocurry_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 4.69/4.88 produc1310100445399344235_nat_o: ( product_prod_nat_nat > $o ) > nat > nat > $o ).
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% 4.69/4.88
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% 4.69/4.88
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% 4.69/4.88 thf(sy_c_Product__Type_Omap__prod_001t__Code____Numeral__Ointeger_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 4.69/4.88 produc3789967387199524714nteger: ( code_integer > code_integer > code_integer ) > ( code_integer > code_integer ) > produc8923325533196201883nteger > produc2221115339011613079nteger ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Product__Type_Omap__prod_001t__Code____Numeral__Ointeger_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
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% 4.69/4.88
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% 4.69/4.88
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% 4.69/4.88 produc1084426483498010290er_o_o: ( code_integer > code_integer ) > ( $o > $o ) > produc6271795597528267376eger_o > produc6271795597528267376eger_o ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Product__Type_Omap__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001_Eo_001t__Int__Oint,type,
% 4.69/4.88 produc7547902865030867346_o_int: ( code_integer > code_integer ) > ( $o > int ) > produc6271795597528267376eger_o > produc2256096406371053034er_int ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Product__Type_Omap__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001_Eo_001t__Nat__Onat,type,
% 4.69/4.88 produc7550393335539917622_o_nat: ( code_integer > code_integer ) > ( $o > nat ) > produc6271795597528267376eger_o > produc6433947425880249742er_nat ).
% 4.69/4.88
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% 4.69/4.88
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Oconverse_001_Eo_001_Eo,type,
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% 4.69/4.88
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Oconverse_001t__Nat__Onat_001t__Nat__Onat,type,
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% 4.69/4.88
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Oinv__image_001_Eo_001_Eo,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Oinv__image_001_Eo_001t__Nat__Onat,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Oinv__image_001t__Int__Oint_001_Eo,type,
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% 4.69/4.88 thf(sy_c_Relation_Oinv__image_001t__Int__Oint_001t__Int__Oint,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Oinv__image_001t__Int__Oint_001t__Nat__Onat,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Oinv__image_001t__Nat__Onat_001_Eo,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Oinv__image_001t__Nat__Onat_001t__Int__Oint,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Oinv__image_001t__Nat__Onat_001t__Nat__Onat,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Oinv__image_001t__Product____Type__Ounit_001_Eo,type,
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% 4.69/4.88 thf(sy_c_Relation_Oinv__image_001t__Product____Type__Ounit_001t__Nat__Onat,type,
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% 4.69/4.88 thf(sy_c_Relation_Oinv__image_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
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% 4.69/4.88 thf(sy_c_Relation_Orefl__on_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Orefl__on_001_Eo,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Orefl__on_001t__Int__Oint,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Orefl__on_001t__Nat__Onat,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Orefl__on_001t__Product____Type__Ounit,type,
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% 4.69/4.88 thf(sy_c_Relation_Orelcomp_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
% 4.69/4.88 relcom6251035627269349452_nat_o: set_Pr2161125870931222855_nat_o > set_Pr2161125870931222855_nat_o > set_Pr2161125870931222855_nat_o ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Orelcomp_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 4.69/4.88 relcom2608444778321954367et_nat: set_Pr2161125870931222855_nat_o > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Orelcomp_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 4.69/4.88 relcom6619595054755144899et_nat: set_Pr2161125870931222855_nat_o > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Orelcomp_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 4.69/4.88 relcom8303140135939483018et_nat: set_Pr8536935166611901872et_nat > set_Pr7928877670098842301et_nat > set_Pr8536935166611901872et_nat ).
% 4.69/4.88
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% 4.69/4.88 relcom430014394250001422et_nat: set_Pr8536935166611901872et_nat > set_Pr3721596426557623617et_nat > set_Pr3286484037609594932et_nat ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Orelcomp_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 4.69/4.88 relcom8031709186682293262et_nat: set_Pr3286484037609594932et_nat > set_Pr8807100098903490369et_nat > set_Pr8536935166611901872et_nat ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Orelcomp_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 4.69/4.88 relcom5975814107203797650et_nat: set_Pr3286484037609594932et_nat > set_Pr719794911490849221et_nat > set_Pr3286484037609594932et_nat ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Orelcomp_001_Eo_001_Eo_001_Eo,type,
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% 4.69/4.88
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% 4.69/4.88
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% 4.69/4.88 relcom8881708762719574682et_nat: set_Pr3948176798113811640et_nat > set_Pr5488025237498180813et_nat > set_Pr3948176798113811640et_nat ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Orelcomp_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 4.69/4.88 relcomp_int_int_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Orelcomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Orelcomp_001t__Product____Type__Ounit_001t__Product____Type__Ounit_001t__Product____Type__Ounit,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Orelcomp_001t__Set__Oset_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J_001t__Set__Oset_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J_001t__Set__Oset_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
% 4.69/4.88 relcom7236094467932586796_nat_o: set_Pr3813038829465207111_nat_o > set_Pr3813038829465207111_nat_o > set_Pr3813038829465207111_nat_o ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Orelcomp_001t__Set__Oset_I_Eo_J_001t__Set__Oset_I_Eo_J_001t__Set__Oset_I_Eo_J,type,
% 4.69/4.88 relcom7534720040753365047_set_o: set_Pr4577759397028426247_set_o > set_Pr4577759397028426247_set_o > set_Pr4577759397028426247_set_o ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Relation_Orelcomp_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J,type,
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% 4.69/4.88 thf(sy_c_Set_Oinsert_001_Eo,type,
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% 4.69/4.88
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% 4.69/4.88
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% 4.69/4.88
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% 4.69/4.88
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 4.69/4.88 thf(sy_c_Set_Oinsert_001t__Rat__Orat,type,
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% 4.69/4.88 thf(sy_c_Typedef_Otype__definition_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Nat__Onat,type,
% 4.69/4.88 type_d6278479724763174947er_nat: ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > nat ) > ( nat > produc8923325533196201883nteger > produc8923325533196201883nteger ) > set_nat > $o ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Typedef_Otype__definition_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Product____Type__Ounit,type,
% 4.69/4.88 type_d6996789741066924922t_unit: ( ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > product_unit ) > ( product_unit > produc8923325533196201883nteger > produc8923325533196201883nteger ) > set_Product_unit > $o ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Typedef_Otype__definition_001t__Assertions__Oassn_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
% 4.69/4.88 type_d3909072315231072503_nat_o: ( assn > produc3658429121746597890et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > assn ) > set_Pr4532377907799695533_nat_o > $o ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Typedef_Otype__definition_001t__Code____Numeral__Ointeger_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 4.69/4.88 type_d669523880323286244nteger: ( code_integer > code_integer > code_integer ) > ( ( code_integer > code_integer ) > code_integer ) > set_Co726186806682698383nteger > $o ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Typedef_Otype__definition_001t__Code____Numeral__Ointeger_001_Eo,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Typedef_Otype__definition_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Typedef_Otype__definition_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Typedef_Otype__definition_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Typedef_Otype__definition_001t__Code____Numeral__Ointeger_001t__Product____Type__Ounit,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Typedef_Otype__definition_001t__Code____Numeral__Onatural_001t__Nat__Onat,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Typedef_Otype__definition_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Typedef_Otype__definition_001t__Nat__Onat_001t__Nat__Onat,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Typedef_Otype__definition_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.69/4.88 type_d3768499744764857476et_nat: ( nat > set_nat ) > ( set_nat > nat ) > set_set_nat > $o ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Typedef_Otype__definition_001t__Product____Type__Ounit_001_Eo,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Typedef_Otype__definition_001t__Set__Oset_It__Nat__Onat_J_001t__Nat__Onat,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 4.69/4.88 accp_P4507279754199951662nt_int: ( produc5030937667867769463nt_int > produc5030937667867769463nt_int > $o ) > produc5030937667867769463nt_int > $o ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 4.69/4.88 accp_P5604362734843950218nt_int: ( produc6128020648511768019nt_int > produc6128020648511768019nt_int > $o ) > produc6128020648511768019nt_int > $o ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 4.69/4.88 accp_P3050404660685545426at_nat: ( produc3574062574353363227at_nat > produc3574062574353363227at_nat > $o ) > produc3574062574353363227at_nat > $o ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 4.69/4.88 accp_P4147487641329543982at_nat: ( produc4671145554997361783at_nat > produc4671145554997361783at_nat > $o ) > produc4671145554997361783at_nat > $o ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
% 4.69/4.88 accp_P1862375125659990705et_nat: ( produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ) > produc2732055786443039994et_nat > $o ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_Eo_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 4.69/4.88 accp_P8458817951426537472et_nat: ( produc6197004810343482825et_nat > produc6197004810343482825et_nat > $o ) > produc6197004810343482825et_nat > $o ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 4.69/4.88 accp_P5801069581201407417et_nat: ( produc3658429121746597890et_nat > produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.69/4.88 accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.69/4.88 accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Olex__prod_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 4.69/4.88 lex_pr4722427456421979612et_nat: set_Pr2161125870931222855_nat_o > set_Pr7928877670098842301et_nat > set_Pr3444600963470892981et_nat ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Olex__prod_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 4.69/4.88 lex_pr5340572901959109728et_nat: set_Pr2161125870931222855_nat_o > set_Pr719794911490849221et_nat > set_Pr7928877670098842301et_nat ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Olex__prod_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.69/4.88 lex_pr538634069021852900et_nat: set_Pr1776176089890104647t_unit > set_Pr5488025237498180813et_nat > set_Pr719794911490849221et_nat ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Olex__prod_001t__Int__Oint_001t__Int__Oint,type,
% 4.69/4.88 lex_prod_int_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr2560585780119916871nt_int ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Olex__prod_001t__Int__Oint_001t__Nat__Onat,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Olex__prod_001t__Nat__Onat_001t__Int__Oint,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Olex__prod_001t__Nat__Onat_001t__Nat__Onat,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Omax__ext_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Omax__ext_001_Eo,type,
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% 4.69/4.88 thf(sy_c_Wellfounded_Omax__ext_001t__Code____Numeral__Ointeger,type,
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% 4.69/4.88 thf(sy_c_Wellfounded_Omax__ext_001t__Int__Oint,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Omax__ext_001t__Nat__Onat,type,
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% 4.69/4.88 thf(sy_c_Wellfounded_Omax__ext_001t__Product____Type__Ounit,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Omeasure_001t__Int__Oint,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Omeasure_001t__Nat__Onat,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Omin__ext_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Omin__ext_001_Eo,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Omin__ext_001t__Int__Oint,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Omin__ext_001t__Nat__Onat,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Omin__ext_001t__Product____Type__Ounit,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Owf_001_Eo,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Owf_001t__Int__Oint,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Wellfounded_Owf_001t__Product____Type__Ounit,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Zorn_OChains_001t__Int__Oint,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Zorn_OChains_001t__Nat__Onat,type,
% 4.69/4.88 chains_nat: set_Pr1261947904930325089at_nat > set_set_nat ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Zorn_Ochains_001t__Nat__Onat,type,
% 4.69/4.88 chains_nat2: set_set_nat > set_set_set_nat ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Zorn_Opred__on_Ochain_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
% 4.69/4.88 pred_c177362287423414904_nat_o: set_Pr4532377907799695533_nat_o > ( ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o ) > set_Pr4532377907799695533_nat_o > $o ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_Zorn_Opred__on_Ochain_001_Eo,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Zorn_Opred__on_Ochain_001t__Int__Oint,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Zorn_Opred__on_Ochain_001t__Nat__Onat,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_Zorn_Opred__on_Ochain_001t__Product____Type__Ounit,type,
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% 4.69/4.88 thf(sy_c_Zorn_Opred__on_Ochain_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
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% 4.69/4.88 thf(sy_c_Zorn_Opred__on_Ochain_001t__Set__Oset_It__Nat__Onat_J,type,
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% 4.69/4.88 thf(sy_c_member_001_Eo,type,
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% 4.69/4.88 thf(sy_c_member_001t__Filter__Ofilter_It__Nat__Onat_J,type,
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% 4.69/4.88
% 4.69/4.88 thf(sy_c_member_001t__Int__Oint,type,
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% 4.69/4.88
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% 4.69/4.88 member5877623283571906838t_unit: set_Product_unit > set_set_Product_unit > $o ).
% 4.69/4.88
% 4.69/4.88 thf(sy_c_member_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 4.69/4.88 member_set_set_nat: set_set_nat > set_set_set_nat > $o ).
% 4.69/4.88
% 4.69/4.88 thf(sy_v_h,type,
% 4.69/4.88 h: produc3658429121746597890et_nat ).
% 4.69/4.88
% 4.69/4.88 % Relevant facts (7796)
% 4.69/4.88 thf(fact_0_Rep__assn__inject,axiom,
% 4.69/4.88 ! [X: assn,Y: assn] :
% 4.69/4.88 ( ( ( rep_assn @ X )
% 4.69/4.88 = ( rep_assn @ Y ) )
% 4.69/4.88 = ( X = Y ) ) ).
% 4.69/4.88
% 4.69/4.88 % Rep_assn_inject
% 4.69/4.88 thf(fact_1_Rep__assn__inverse,axiom,
% 4.69/4.88 ! [X: assn] :
% 4.69/4.88 ( ( abs_assn @ ( rep_assn @ X ) )
% 4.69/4.88 = X ) ).
% 4.69/4.88
% 4.69/4.88 % Rep_assn_inverse
% 4.69/4.88 thf(fact_2_Abs__assn__eqI_I2_J,axiom,
% 4.69/4.88 ! [P: produc3658429121746597890et_nat > $o,Pr: assn] :
% 4.69/4.88 ( ! [H: produc3658429121746597890et_nat] :
% 4.69/4.88 ( ( P @ H )
% 4.69/4.88 = ( rep_assn @ Pr @ H ) )
% 4.69/4.88 => ( Pr
% 4.69/4.88 = ( abs_assn @ P ) ) ) ).
% 4.69/4.88
% 4.69/4.88 % Abs_assn_eqI(2)
% 4.69/4.88 thf(fact_3_Abs__assn__eqI_I1_J,axiom,
% 4.69/4.88 ! [P: produc3658429121746597890et_nat > $o,Pr: assn] :
% 4.69/4.88 ( ! [H: produc3658429121746597890et_nat] :
% 4.69/4.88 ( ( P @ H )
% 4.69/4.88 = ( rep_assn @ Pr @ H ) )
% 4.69/4.88 => ( ( abs_assn @ P )
% 4.69/4.88 = Pr ) ) ).
% 4.69/4.88
% 4.69/4.88 % Abs_assn_eqI(1)
% 4.69/4.88 thf(fact_4_empty__iff,axiom,
% 4.69/4.88 ! [C: produc3658429121746597890et_nat > $o] :
% 4.69/4.88 ~ ( member6576561426505652726_nat_o @ C @ bot_bo7824918357723582233_nat_o ) ).
% 4.69/4.88
% 4.69/4.88 % empty_iff
% 4.69/4.88 thf(fact_5_empty__iff,axiom,
% 4.69/4.88 ! [C: product_unit] :
% 4.69/4.88 ~ ( member_Product_unit @ C @ bot_bo3957492148770167129t_unit ) ).
% 4.69/4.88
% 4.69/4.88 % empty_iff
% 4.69/4.88 thf(fact_6_empty__iff,axiom,
% 4.69/4.88 ! [C: $o] :
% 4.69/4.88 ~ ( member_o @ C @ bot_bot_set_o ) ).
% 4.69/4.88
% 4.69/4.88 % empty_iff
% 4.69/4.88 thf(fact_7_empty__iff,axiom,
% 4.69/4.88 ! [C: nat] :
% 4.69/4.88 ~ ( member_nat @ C @ bot_bot_set_nat ) ).
% 4.69/4.88
% 4.69/4.88 % empty_iff
% 4.69/4.88 thf(fact_8_empty__iff,axiom,
% 4.69/4.88 ! [C: int] :
% 4.69/4.88 ~ ( member_int @ C @ bot_bot_set_int ) ).
% 4.69/4.88
% 4.69/4.88 % empty_iff
% 4.69/4.88 thf(fact_9_all__not__in__conv,axiom,
% 4.69/4.88 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.88 ( ( ! [X2: produc3658429121746597890et_nat > $o] :
% 4.69/4.88 ~ ( member6576561426505652726_nat_o @ X2 @ A ) )
% 4.69/4.88 = ( A = bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.88
% 4.69/4.88 % all_not_in_conv
% 4.69/4.88 thf(fact_10_all__not__in__conv,axiom,
% 4.69/4.88 ! [A: set_Product_unit] :
% 4.69/4.88 ( ( ! [X2: product_unit] :
% 4.69/4.88 ~ ( member_Product_unit @ X2 @ A ) )
% 4.69/4.88 = ( A = bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.88
% 4.69/4.88 % all_not_in_conv
% 4.69/4.88 thf(fact_11_all__not__in__conv,axiom,
% 4.69/4.88 ! [A: set_o] :
% 4.69/4.88 ( ( ! [X2: $o] :
% 4.69/4.88 ~ ( member_o @ X2 @ A ) )
% 4.69/4.88 = ( A = bot_bot_set_o ) ) ).
% 4.69/4.88
% 4.69/4.88 % all_not_in_conv
% 4.69/4.88 thf(fact_12_all__not__in__conv,axiom,
% 4.69/4.88 ! [A: set_nat] :
% 4.69/4.88 ( ( ! [X2: nat] :
% 4.69/4.88 ~ ( member_nat @ X2 @ A ) )
% 4.69/4.88 = ( A = bot_bot_set_nat ) ) ).
% 4.69/4.88
% 4.69/4.88 % all_not_in_conv
% 4.69/4.88 thf(fact_13_all__not__in__conv,axiom,
% 4.69/4.88 ! [A: set_int] :
% 4.69/4.88 ( ( ! [X2: int] :
% 4.69/4.88 ~ ( member_int @ X2 @ A ) )
% 4.69/4.88 = ( A = bot_bot_set_int ) ) ).
% 4.69/4.88
% 4.69/4.88 % all_not_in_conv
% 4.69/4.88 thf(fact_14_Collect__empty__eq,axiom,
% 4.69/4.88 ! [P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 4.69/4.88 ( ( ( collec939566748876313656_nat_o @ P )
% 4.69/4.88 = bot_bo7824918357723582233_nat_o )
% 4.69/4.88 = ( ! [X2: produc3658429121746597890et_nat > $o] :
% 4.69/4.88 ~ ( P @ X2 ) ) ) ).
% 4.69/4.88
% 4.69/4.88 % Collect_empty_eq
% 4.69/4.88 thf(fact_15_Collect__empty__eq,axiom,
% 4.69/4.88 ! [P: product_unit > $o] :
% 4.69/4.88 ( ( ( collect_Product_unit @ P )
% 4.69/4.88 = bot_bo3957492148770167129t_unit )
% 4.69/4.88 = ( ! [X2: product_unit] :
% 4.69/4.88 ~ ( P @ X2 ) ) ) ).
% 4.69/4.88
% 4.69/4.88 % Collect_empty_eq
% 4.69/4.88 thf(fact_16_Collect__empty__eq,axiom,
% 4.69/4.88 ! [P: $o > $o] :
% 4.69/4.88 ( ( ( collect_o @ P )
% 4.69/4.88 = bot_bot_set_o )
% 4.69/4.88 = ( ! [X2: $o] :
% 4.69/4.88 ~ ( P @ X2 ) ) ) ).
% 4.69/4.88
% 4.69/4.88 % Collect_empty_eq
% 4.69/4.88 thf(fact_17_Collect__empty__eq,axiom,
% 4.69/4.88 ! [P: nat > $o] :
% 4.69/4.88 ( ( ( collect_nat @ P )
% 4.69/4.88 = bot_bot_set_nat )
% 4.69/4.88 = ( ! [X2: nat] :
% 4.69/4.88 ~ ( P @ X2 ) ) ) ).
% 4.69/4.88
% 4.69/4.88 % Collect_empty_eq
% 4.69/4.88 thf(fact_18_Collect__empty__eq,axiom,
% 4.69/4.88 ! [P: int > $o] :
% 4.69/4.88 ( ( ( collect_int @ P )
% 4.69/4.88 = bot_bot_set_int )
% 4.69/4.88 = ( ! [X2: int] :
% 4.69/4.88 ~ ( P @ X2 ) ) ) ).
% 4.69/4.88
% 4.69/4.88 % Collect_empty_eq
% 4.69/4.88 thf(fact_19_empty__Collect__eq,axiom,
% 4.69/4.88 ! [P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 4.69/4.88 ( ( bot_bo7824918357723582233_nat_o
% 4.69/4.88 = ( collec939566748876313656_nat_o @ P ) )
% 4.69/4.88 = ( ! [X2: produc3658429121746597890et_nat > $o] :
% 4.69/4.88 ~ ( P @ X2 ) ) ) ).
% 4.69/4.88
% 4.69/4.88 % empty_Collect_eq
% 4.69/4.88 thf(fact_20_empty__Collect__eq,axiom,
% 4.69/4.88 ! [P: product_unit > $o] :
% 4.69/4.88 ( ( bot_bo3957492148770167129t_unit
% 4.69/4.88 = ( collect_Product_unit @ P ) )
% 4.69/4.88 = ( ! [X2: product_unit] :
% 4.69/4.88 ~ ( P @ X2 ) ) ) ).
% 4.69/4.88
% 4.69/4.88 % empty_Collect_eq
% 4.69/4.88 thf(fact_21_empty__Collect__eq,axiom,
% 4.69/4.88 ! [P: $o > $o] :
% 4.69/4.88 ( ( bot_bot_set_o
% 4.69/4.88 = ( collect_o @ P ) )
% 4.69/4.88 = ( ! [X2: $o] :
% 4.69/4.88 ~ ( P @ X2 ) ) ) ).
% 4.69/4.88
% 4.69/4.88 % empty_Collect_eq
% 4.69/4.88 thf(fact_22_empty__Collect__eq,axiom,
% 4.69/4.88 ! [P: nat > $o] :
% 4.69/4.88 ( ( bot_bot_set_nat
% 4.69/4.88 = ( collect_nat @ P ) )
% 4.69/4.88 = ( ! [X2: nat] :
% 4.69/4.88 ~ ( P @ X2 ) ) ) ).
% 4.69/4.88
% 4.69/4.88 % empty_Collect_eq
% 4.69/4.88 thf(fact_23_empty__Collect__eq,axiom,
% 4.69/4.88 ! [P: int > $o] :
% 4.69/4.88 ( ( bot_bot_set_int
% 4.69/4.88 = ( collect_int @ P ) )
% 4.69/4.88 = ( ! [X2: int] :
% 4.69/4.88 ~ ( P @ X2 ) ) ) ).
% 4.69/4.88
% 4.69/4.88 % empty_Collect_eq
% 4.69/4.88 thf(fact_24_emptyE,axiom,
% 4.69/4.88 ! [A2: produc3658429121746597890et_nat > $o] :
% 4.69/4.88 ~ ( member6576561426505652726_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ).
% 4.69/4.88
% 4.69/4.88 % emptyE
% 4.69/4.88 thf(fact_25_emptyE,axiom,
% 4.69/4.88 ! [A2: product_unit] :
% 4.69/4.88 ~ ( member_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ).
% 4.69/4.88
% 4.69/4.88 % emptyE
% 4.69/4.88 thf(fact_26_emptyE,axiom,
% 4.69/4.88 ! [A2: $o] :
% 4.69/4.88 ~ ( member_o @ A2 @ bot_bot_set_o ) ).
% 4.69/4.88
% 4.69/4.88 % emptyE
% 4.69/4.88 thf(fact_27_emptyE,axiom,
% 4.69/4.88 ! [A2: nat] :
% 4.69/4.88 ~ ( member_nat @ A2 @ bot_bot_set_nat ) ).
% 4.69/4.88
% 4.69/4.88 % emptyE
% 4.69/4.88 thf(fact_28_emptyE,axiom,
% 4.69/4.88 ! [A2: int] :
% 4.69/4.88 ~ ( member_int @ A2 @ bot_bot_set_int ) ).
% 4.69/4.88
% 4.69/4.88 % emptyE
% 4.69/4.88 thf(fact_29_equals0D,axiom,
% 4.69/4.88 ! [A: set_Product_unit,A2: product_unit] :
% 4.69/4.88 ( ( A = bot_bo3957492148770167129t_unit )
% 4.69/4.88 => ~ ( member_Product_unit @ A2 @ A ) ) ).
% 4.69/4.88
% 4.69/4.88 % equals0D
% 4.69/4.88 thf(fact_30_equals0D,axiom,
% 4.69/4.88 ! [A: set_o,A2: $o] :
% 4.69/4.88 ( ( A = bot_bot_set_o )
% 4.69/4.88 => ~ ( member_o @ A2 @ A ) ) ).
% 4.69/4.88
% 4.69/4.88 % equals0D
% 4.69/4.88 thf(fact_31_equals0D,axiom,
% 4.69/4.88 ! [A: set_nat,A2: nat] :
% 4.69/4.88 ( ( A = bot_bot_set_nat )
% 4.69/4.88 => ~ ( member_nat @ A2 @ A ) ) ).
% 4.69/4.88
% 4.69/4.88 % equals0D
% 4.69/4.88 thf(fact_32_equals0D,axiom,
% 4.69/4.88 ! [A: set_int,A2: int] :
% 4.69/4.88 ( ( A = bot_bot_set_int )
% 4.69/4.88 => ~ ( member_int @ A2 @ A ) ) ).
% 4.69/4.88
% 4.69/4.88 % equals0D
% 4.69/4.88 thf(fact_33_equals0D,axiom,
% 4.69/4.88 ! [A: set_Pr4532377907799695533_nat_o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/4.88 ( ( A = bot_bo7824918357723582233_nat_o )
% 4.69/4.88 => ~ ( member6576561426505652726_nat_o @ A2 @ A ) ) ).
% 4.69/4.88
% 4.69/4.88 % equals0D
% 4.69/4.88 thf(fact_34_equals0I,axiom,
% 4.69/4.88 ! [A: set_Product_unit] :
% 4.69/4.88 ( ! [Y2: product_unit] :
% 4.69/4.88 ~ ( member_Product_unit @ Y2 @ A )
% 4.69/4.88 => ( A = bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.88
% 4.69/4.88 % equals0I
% 4.69/4.88 thf(fact_35_equals0I,axiom,
% 4.69/4.88 ! [A: set_o] :
% 4.69/4.88 ( ! [Y2: $o] :
% 4.69/4.88 ~ ( member_o @ Y2 @ A )
% 4.69/4.88 => ( A = bot_bot_set_o ) ) ).
% 4.69/4.88
% 4.69/4.88 % equals0I
% 4.69/4.88 thf(fact_36_equals0I,axiom,
% 4.69/4.88 ! [A: set_nat] :
% 4.69/4.88 ( ! [Y2: nat] :
% 4.69/4.88 ~ ( member_nat @ Y2 @ A )
% 4.69/4.88 => ( A = bot_bot_set_nat ) ) ).
% 4.69/4.88
% 4.69/4.88 % equals0I
% 4.69/4.88 thf(fact_37_equals0I,axiom,
% 4.69/4.88 ! [A: set_int] :
% 4.69/4.88 ( ! [Y2: int] :
% 4.69/4.89 ~ ( member_int @ Y2 @ A )
% 4.69/4.89 => ( A = bot_bot_set_int ) ) ).
% 4.69/4.89
% 4.69/4.89 % equals0I
% 4.69/4.89 thf(fact_38_equals0I,axiom,
% 4.69/4.89 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.89 ( ! [Y2: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ~ ( member6576561426505652726_nat_o @ Y2 @ A )
% 4.69/4.89 => ( A = bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % equals0I
% 4.69/4.89 thf(fact_39_ex__in__conv,axiom,
% 4.69/4.89 ! [A: set_Product_unit] :
% 4.69/4.89 ( ( ? [X2: product_unit] : ( member_Product_unit @ X2 @ A ) )
% 4.69/4.89 = ( A != bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.89
% 4.69/4.89 % ex_in_conv
% 4.69/4.89 thf(fact_40_ex__in__conv,axiom,
% 4.69/4.89 ! [A: set_o] :
% 4.69/4.89 ( ( ? [X2: $o] : ( member_o @ X2 @ A ) )
% 4.69/4.89 = ( A != bot_bot_set_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % ex_in_conv
% 4.69/4.89 thf(fact_41_ex__in__conv,axiom,
% 4.69/4.89 ! [A: set_nat] :
% 4.69/4.89 ( ( ? [X2: nat] : ( member_nat @ X2 @ A ) )
% 4.69/4.89 = ( A != bot_bot_set_nat ) ) ).
% 4.69/4.89
% 4.69/4.89 % ex_in_conv
% 4.69/4.89 thf(fact_42_ex__in__conv,axiom,
% 4.69/4.89 ! [A: set_int] :
% 4.69/4.89 ( ( ? [X2: int] : ( member_int @ X2 @ A ) )
% 4.69/4.89 = ( A != bot_bot_set_int ) ) ).
% 4.69/4.89
% 4.69/4.89 % ex_in_conv
% 4.69/4.89 thf(fact_43_ex__in__conv,axiom,
% 4.69/4.89 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.89 ( ( ? [X2: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X2 @ A ) )
% 4.69/4.89 = ( A != bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % ex_in_conv
% 4.69/4.89 thf(fact_44_set__notEmptyE,axiom,
% 4.69/4.89 ! [S: set_Product_unit] :
% 4.69/4.89 ( ( S != bot_bo3957492148770167129t_unit )
% 4.69/4.89 => ~ ! [X3: product_unit] :
% 4.69/4.89 ~ ( member_Product_unit @ X3 @ S ) ) ).
% 4.69/4.89
% 4.69/4.89 % set_notEmptyE
% 4.69/4.89 thf(fact_45_set__notEmptyE,axiom,
% 4.69/4.89 ! [S: set_o] :
% 4.69/4.89 ( ( S != bot_bot_set_o )
% 4.69/4.89 => ~ ! [X3: $o] :
% 4.69/4.89 ~ ( member_o @ X3 @ S ) ) ).
% 4.69/4.89
% 4.69/4.89 % set_notEmptyE
% 4.69/4.89 thf(fact_46_set__notEmptyE,axiom,
% 4.69/4.89 ! [S: set_nat] :
% 4.69/4.89 ( ( S != bot_bot_set_nat )
% 4.69/4.89 => ~ ! [X3: nat] :
% 4.69/4.89 ~ ( member_nat @ X3 @ S ) ) ).
% 4.69/4.89
% 4.69/4.89 % set_notEmptyE
% 4.69/4.89 thf(fact_47_set__notEmptyE,axiom,
% 4.69/4.89 ! [S: set_int] :
% 4.69/4.89 ( ( S != bot_bot_set_int )
% 4.69/4.89 => ~ ! [X3: int] :
% 4.69/4.89 ~ ( member_int @ X3 @ S ) ) ).
% 4.69/4.89
% 4.69/4.89 % set_notEmptyE
% 4.69/4.89 thf(fact_48_set__notEmptyE,axiom,
% 4.69/4.89 ! [S: set_Pr4532377907799695533_nat_o] :
% 4.69/4.89 ( ( S != bot_bo7824918357723582233_nat_o )
% 4.69/4.89 => ~ ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ~ ( member6576561426505652726_nat_o @ X3 @ S ) ) ).
% 4.69/4.89
% 4.69/4.89 % set_notEmptyE
% 4.69/4.89 thf(fact_49_memb__imp__not__empty,axiom,
% 4.69/4.89 ! [X: product_unit,S: set_Product_unit] :
% 4.69/4.89 ( ( member_Product_unit @ X @ S )
% 4.69/4.89 => ( S != bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.89
% 4.69/4.89 % memb_imp_not_empty
% 4.69/4.89 thf(fact_50_memb__imp__not__empty,axiom,
% 4.69/4.89 ! [X: $o,S: set_o] :
% 4.69/4.89 ( ( member_o @ X @ S )
% 4.69/4.89 => ( S != bot_bot_set_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % memb_imp_not_empty
% 4.69/4.89 thf(fact_51_memb__imp__not__empty,axiom,
% 4.69/4.89 ! [X: nat,S: set_nat] :
% 4.69/4.89 ( ( member_nat @ X @ S )
% 4.69/4.89 => ( S != bot_bot_set_nat ) ) ).
% 4.69/4.89
% 4.69/4.89 % memb_imp_not_empty
% 4.69/4.89 thf(fact_52_memb__imp__not__empty,axiom,
% 4.69/4.89 ! [X: int,S: set_int] :
% 4.69/4.89 ( ( member_int @ X @ S )
% 4.69/4.89 => ( S != bot_bot_set_int ) ) ).
% 4.69/4.89
% 4.69/4.89 % memb_imp_not_empty
% 4.69/4.89 thf(fact_53_memb__imp__not__empty,axiom,
% 4.69/4.89 ! [X: produc3658429121746597890et_nat > $o,S: set_Pr4532377907799695533_nat_o] :
% 4.69/4.89 ( ( member6576561426505652726_nat_o @ X @ S )
% 4.69/4.89 => ( S != bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % memb_imp_not_empty
% 4.69/4.89 thf(fact_54_bot__set__def,axiom,
% 4.69/4.89 ( bot_bo3957492148770167129t_unit
% 4.69/4.89 = ( collect_Product_unit @ bot_bo4642748612307482820unit_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % bot_set_def
% 4.69/4.89 thf(fact_55_bot__set__def,axiom,
% 4.69/4.89 ( bot_bot_set_o
% 4.69/4.89 = ( collect_o @ bot_bot_o_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % bot_set_def
% 4.69/4.89 thf(fact_56_bot__set__def,axiom,
% 4.69/4.89 ( bot_bot_set_nat
% 4.69/4.89 = ( collect_nat @ bot_bot_nat_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % bot_set_def
% 4.69/4.89 thf(fact_57_bot__set__def,axiom,
% 4.69/4.89 ( bot_bot_set_int
% 4.69/4.89 = ( collect_int @ bot_bot_int_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % bot_set_def
% 4.69/4.89 thf(fact_58_bot__set__def,axiom,
% 4.69/4.89 ( bot_bo7824918357723582233_nat_o
% 4.69/4.89 = ( collec939566748876313656_nat_o @ bot_bo7963750851167320836at_o_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % bot_set_def
% 4.69/4.89 thf(fact_59_mod__false,axiom,
% 4.69/4.89 ! [H2: produc3658429121746597890et_nat] :
% 4.69/4.89 ~ ( rep_assn @ bot_bot_assn @ H2 ) ).
% 4.69/4.89
% 4.69/4.89 % mod_false
% 4.69/4.89 thf(fact_60_Set_Ois__empty__def,axiom,
% 4.69/4.89 ( is_emp5529367068699929823t_unit
% 4.69/4.89 = ( ^ [A3: set_Product_unit] : ( A3 = bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Set.is_empty_def
% 4.69/4.89 thf(fact_61_Set_Ois__empty__def,axiom,
% 4.69/4.89 ( is_empty_o
% 4.69/4.89 = ( ^ [A3: set_o] : ( A3 = bot_bot_set_o ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Set.is_empty_def
% 4.69/4.89 thf(fact_62_Set_Ois__empty__def,axiom,
% 4.69/4.89 ( is_empty_nat
% 4.69/4.89 = ( ^ [A3: set_nat] : ( A3 = bot_bot_set_nat ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Set.is_empty_def
% 4.69/4.89 thf(fact_63_Set_Ois__empty__def,axiom,
% 4.69/4.89 ( is_empty_int
% 4.69/4.89 = ( ^ [A3: set_int] : ( A3 = bot_bot_set_int ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Set.is_empty_def
% 4.69/4.89 thf(fact_64_Set_Ois__empty__def,axiom,
% 4.69/4.89 ( is_emp6650082560925436063_nat_o
% 4.69/4.89 = ( ^ [A3: set_Pr4532377907799695533_nat_o] : ( A3 = bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Set.is_empty_def
% 4.69/4.89 thf(fact_65_Collect__empty__eq__bot,axiom,
% 4.69/4.89 ! [P: product_unit > $o] :
% 4.69/4.89 ( ( ( collect_Product_unit @ P )
% 4.69/4.89 = bot_bo3957492148770167129t_unit )
% 4.69/4.89 = ( P = bot_bo4642748612307482820unit_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % Collect_empty_eq_bot
% 4.69/4.89 thf(fact_66_Collect__empty__eq__bot,axiom,
% 4.69/4.89 ! [P: $o > $o] :
% 4.69/4.89 ( ( ( collect_o @ P )
% 4.69/4.89 = bot_bot_set_o )
% 4.69/4.89 = ( P = bot_bot_o_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % Collect_empty_eq_bot
% 4.69/4.89 thf(fact_67_Collect__empty__eq__bot,axiom,
% 4.69/4.89 ! [P: nat > $o] :
% 4.69/4.89 ( ( ( collect_nat @ P )
% 4.69/4.89 = bot_bot_set_nat )
% 4.69/4.89 = ( P = bot_bot_nat_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % Collect_empty_eq_bot
% 4.69/4.89 thf(fact_68_Collect__empty__eq__bot,axiom,
% 4.69/4.89 ! [P: int > $o] :
% 4.69/4.89 ( ( ( collect_int @ P )
% 4.69/4.89 = bot_bot_set_int )
% 4.69/4.89 = ( P = bot_bot_int_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % Collect_empty_eq_bot
% 4.69/4.89 thf(fact_69_Collect__empty__eq__bot,axiom,
% 4.69/4.89 ! [P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 4.69/4.89 ( ( ( collec939566748876313656_nat_o @ P )
% 4.69/4.89 = bot_bo7824918357723582233_nat_o )
% 4.69/4.89 = ( P = bot_bo7963750851167320836at_o_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % Collect_empty_eq_bot
% 4.69/4.89 thf(fact_70_bot__empty__eq,axiom,
% 4.69/4.89 ( bot_bo4642748612307482820unit_o
% 4.69/4.89 = ( ^ [X2: product_unit] : ( member_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % bot_empty_eq
% 4.69/4.89 thf(fact_71_bot__empty__eq,axiom,
% 4.69/4.89 ( bot_bot_o_o
% 4.69/4.89 = ( ^ [X2: $o] : ( member_o @ X2 @ bot_bot_set_o ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % bot_empty_eq
% 4.69/4.89 thf(fact_72_bot__empty__eq,axiom,
% 4.69/4.89 ( bot_bot_nat_o
% 4.69/4.89 = ( ^ [X2: nat] : ( member_nat @ X2 @ bot_bot_set_nat ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % bot_empty_eq
% 4.69/4.89 thf(fact_73_bot__empty__eq,axiom,
% 4.69/4.89 ( bot_bot_int_o
% 4.69/4.89 = ( ^ [X2: int] : ( member_int @ X2 @ bot_bot_set_int ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % bot_empty_eq
% 4.69/4.89 thf(fact_74_bot__empty__eq,axiom,
% 4.69/4.89 ( bot_bo7963750851167320836at_o_o
% 4.69/4.89 = ( ^ [X2: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X2 @ bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % bot_empty_eq
% 4.69/4.89 thf(fact_75_wand__assn__def,axiom,
% 4.69/4.89 ( wand_assn
% 4.69/4.89 = ( ^ [P2: assn,Q: assn] : ( abs_assn @ ( wand_raw @ ( rep_assn @ P2 ) @ ( rep_assn @ Q ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % wand_assn_def
% 4.69/4.89 thf(fact_76_one__assn__def,axiom,
% 4.69/4.89 ( one_one_assn
% 4.69/4.89 = ( abs_assn @ one_assn_raw ) ) ).
% 4.69/4.89
% 4.69/4.89 % one_assn_def
% 4.69/4.89 thf(fact_77_Abs__assn__inverse,axiom,
% 4.69/4.89 ! [Y: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( member6576561426505652726_nat_o @ Y @ ( collec939566748876313656_nat_o @ proper ) )
% 4.69/4.89 => ( ( rep_assn @ ( abs_assn @ Y ) )
% 4.69/4.89 = Y ) ) ).
% 4.69/4.89
% 4.69/4.89 % Abs_assn_inverse
% 4.69/4.89 thf(fact_78_one__assn__raw_Osimps,axiom,
% 4.69/4.89 ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 4.69/4.89 ( ( one_assn_raw @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 4.69/4.89 = ( As = bot_bot_set_nat ) ) ).
% 4.69/4.89
% 4.69/4.89 % one_assn_raw.simps
% 4.69/4.89 thf(fact_79_one__assn__raw_Oelims_I1_J,axiom,
% 4.69/4.89 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 4.69/4.89 ( ( ( one_assn_raw @ X )
% 4.69/4.89 = Y )
% 4.69/4.89 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.89 ( ( X
% 4.69/4.89 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.89 => ( Y
% 4.69/4.89 = ( As2 != bot_bot_set_nat ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % one_assn_raw.elims(1)
% 4.69/4.89 thf(fact_80_one__assn__raw_Oelims_I2_J,axiom,
% 4.69/4.89 ! [X: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ( one_assn_raw @ X )
% 4.69/4.89 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.89 ( ( X
% 4.69/4.89 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.89 => ( As2 != bot_bot_set_nat ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % one_assn_raw.elims(2)
% 4.69/4.89 thf(fact_81_one__assn__raw_Oelims_I3_J,axiom,
% 4.69/4.89 ! [X: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ~ ( one_assn_raw @ X )
% 4.69/4.89 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.89 ( ( X
% 4.69/4.89 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.89 => ( As2 = bot_bot_set_nat ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % one_assn_raw.elims(3)
% 4.69/4.89 thf(fact_82_is__singletonI_H,axiom,
% 4.69/4.89 ! [A: set_Product_unit] :
% 4.69/4.89 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.89 => ( ! [X3: product_unit,Y2: product_unit] :
% 4.69/4.89 ( ( member_Product_unit @ X3 @ A )
% 4.69/4.89 => ( ( member_Product_unit @ Y2 @ A )
% 4.69/4.89 => ( X3 = Y2 ) ) )
% 4.69/4.89 => ( is_sin2160648248035936513t_unit @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singletonI'
% 4.69/4.89 thf(fact_83_is__singletonI_H,axiom,
% 4.69/4.89 ! [A: set_o] :
% 4.69/4.89 ( ( A != bot_bot_set_o )
% 4.69/4.89 => ( ! [X3: $o,Y2: $o] :
% 4.69/4.89 ( ( member_o @ X3 @ A )
% 4.69/4.89 => ( ( member_o @ Y2 @ A )
% 4.69/4.89 => ( X3 = Y2 ) ) )
% 4.69/4.89 => ( is_singleton_o @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singletonI'
% 4.69/4.89 thf(fact_84_is__singletonI_H,axiom,
% 4.69/4.89 ! [A: set_nat] :
% 4.69/4.89 ( ( A != bot_bot_set_nat )
% 4.69/4.89 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.89 ( ( member_nat @ X3 @ A )
% 4.69/4.89 => ( ( member_nat @ Y2 @ A )
% 4.69/4.89 => ( X3 = Y2 ) ) )
% 4.69/4.89 => ( is_singleton_nat @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singletonI'
% 4.69/4.89 thf(fact_85_is__singletonI_H,axiom,
% 4.69/4.89 ! [A: set_int] :
% 4.69/4.89 ( ( A != bot_bot_set_int )
% 4.69/4.89 => ( ! [X3: int,Y2: int] :
% 4.69/4.89 ( ( member_int @ X3 @ A )
% 4.69/4.89 => ( ( member_int @ Y2 @ A )
% 4.69/4.89 => ( X3 = Y2 ) ) )
% 4.69/4.89 => ( is_singleton_int @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singletonI'
% 4.69/4.89 thf(fact_86_is__singletonI_H,axiom,
% 4.69/4.89 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.89 ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.89 => ( ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( member6576561426505652726_nat_o @ X3 @ A )
% 4.69/4.89 => ( ( member6576561426505652726_nat_o @ Y2 @ A )
% 4.69/4.89 => ( X3 = Y2 ) ) )
% 4.69/4.89 => ( is_sin5180296473474724033_nat_o @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singletonI'
% 4.69/4.89 thf(fact_87_wand__proper,axiom,
% 4.69/4.89 ! [P: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o] : ( proper @ ( wand_raw @ P @ Q2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % wand_proper
% 4.69/4.89 thf(fact_88_one__assn__proper,axiom,
% 4.69/4.89 proper @ one_assn_raw ).
% 4.69/4.89
% 4.69/4.89 % one_assn_proper
% 4.69/4.89 thf(fact_89_assn__basic__inequalities_I3_J,axiom,
% 4.69/4.89 bot_bot_assn != one_one_assn ).
% 4.69/4.89
% 4.69/4.89 % assn_basic_inequalities(3)
% 4.69/4.89 thf(fact_90_bex2I,axiom,
% 4.69/4.89 ! [A2: heap_e7401611519738050253t_unit,B: set_nat,S: set_Pr3948176798113811640et_nat,P: heap_e7401611519738050253t_unit > set_nat > $o] :
% 4.69/4.89 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ B ) @ S )
% 4.69/4.89 => ( ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ B ) @ S )
% 4.69/4.89 => ( P @ A2 @ B ) )
% 4.69/4.89 => ? [A4: heap_e7401611519738050253t_unit,B2: set_nat] :
% 4.69/4.89 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A4 @ B2 ) @ S )
% 4.69/4.89 & ( P @ A4 @ B2 ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % bex2I
% 4.69/4.89 thf(fact_91_bex2I,axiom,
% 4.69/4.89 ! [A2: nat,B: nat,S: set_Pr1261947904930325089at_nat,P: nat > nat > $o] :
% 4.69/4.89 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ S )
% 4.69/4.89 => ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ S )
% 4.69/4.89 => ( P @ A2 @ B ) )
% 4.69/4.89 => ? [A4: nat,B2: nat] :
% 4.69/4.89 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A4 @ B2 ) @ S )
% 4.69/4.89 & ( P @ A4 @ B2 ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % bex2I
% 4.69/4.89 thf(fact_92_bex2I,axiom,
% 4.69/4.89 ! [A2: int,B: int,S: set_Pr958786334691620121nt_int,P: int > int > $o] :
% 4.69/4.89 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ S )
% 4.69/4.89 => ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ S )
% 4.69/4.89 => ( P @ A2 @ B ) )
% 4.69/4.89 => ? [A4: int,B2: int] :
% 4.69/4.89 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A4 @ B2 ) @ S )
% 4.69/4.89 & ( P @ A4 @ B2 ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % bex2I
% 4.69/4.89 thf(fact_93_bex2I,axiom,
% 4.69/4.89 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,S: set_Pr3286484037609594932et_nat,P: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ B ) @ S )
% 4.69/4.89 => ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ B ) @ S )
% 4.69/4.89 => ( P @ A2 @ B ) )
% 4.69/4.89 => ? [A4: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A4 @ B2 ) @ S )
% 4.69/4.89 & ( P @ A4 @ B2 ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % bex2I
% 4.69/4.89 thf(fact_94_bex2I,axiom,
% 4.69/4.89 ! [A2: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,S: set_Pr8536935166611901872et_nat,P: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 4.69/4.89 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ B ) @ S )
% 4.69/4.89 => ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ B ) @ S )
% 4.69/4.89 => ( P @ A2 @ B ) )
% 4.69/4.89 => ? [A4: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 4.69/4.89 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A4 @ B2 ) @ S )
% 4.69/4.89 & ( P @ A4 @ B2 ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % bex2I
% 4.69/4.89 thf(fact_95_one__assn__raw_Ocases,axiom,
% 4.69/4.89 ! [X: produc3658429121746597890et_nat] :
% 4.69/4.89 ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.89 ( X
% 4.69/4.89 != ( produc7507926704131184380et_nat @ H @ As2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % one_assn_raw.cases
% 4.69/4.89 thf(fact_96_sndE,axiom,
% 4.69/4.89 ! [X: product_prod_nat_nat,A2: nat,B: nat,P: nat > $o] :
% 4.69/4.89 ( ( X
% 4.69/4.89 = ( product_Pair_nat_nat @ A2 @ B ) )
% 4.69/4.89 => ( ( P @ ( product_snd_nat_nat @ X ) )
% 4.69/4.89 => ( P @ B ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % sndE
% 4.69/4.89 thf(fact_97_sndE,axiom,
% 4.69/4.89 ! [X: produc3925858234332021118et_nat,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,P: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( X
% 4.69/4.89 = ( produc5001842942810119800et_nat @ A2 @ B ) )
% 4.69/4.89 => ( ( P @ ( produc4011572625026189258et_nat @ X ) )
% 4.69/4.89 => ( P @ B ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % sndE
% 4.69/4.89 thf(fact_98_sndE,axiom,
% 4.69/4.89 ! [X: produc2732055786443039994et_nat,A2: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,P: produc3925858234332021118et_nat > $o] :
% 4.69/4.89 ( ( X
% 4.69/4.89 = ( produc2245416461498447860et_nat @ A2 @ B ) )
% 4.69/4.89 => ( ( P @ ( produc5374455773327741254et_nat @ X ) )
% 4.69/4.89 => ( P @ B ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % sndE
% 4.69/4.89 thf(fact_99_sndE,axiom,
% 4.69/4.89 ! [X: produc3658429121746597890et_nat,A2: heap_e7401611519738050253t_unit,B: set_nat,P: set_nat > $o] :
% 4.69/4.89 ( ( X
% 4.69/4.89 = ( produc7507926704131184380et_nat @ A2 @ B ) )
% 4.69/4.89 => ( ( P @ ( produc8586169260539613262et_nat @ X ) )
% 4.69/4.89 => ( P @ B ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % sndE
% 4.69/4.89 thf(fact_100_sndE,axiom,
% 4.69/4.89 ! [X: product_prod_int_int,A2: int,B: int,P: int > $o] :
% 4.69/4.89 ( ( X
% 4.69/4.89 = ( product_Pair_int_int @ A2 @ B ) )
% 4.69/4.89 => ( ( P @ ( product_snd_int_int @ X ) )
% 4.69/4.89 => ( P @ B ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % sndE
% 4.69/4.89 thf(fact_101_Rep__assn,axiom,
% 4.69/4.89 ! [X: assn] : ( member6576561426505652726_nat_o @ ( rep_assn @ X ) @ ( collec939566748876313656_nat_o @ proper ) ) ).
% 4.69/4.89
% 4.69/4.89 % Rep_assn
% 4.69/4.89 thf(fact_102_mem__Collect__eq,axiom,
% 4.69/4.89 ! [A2: produc3658429121746597890et_nat > $o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 4.69/4.89 ( ( member6576561426505652726_nat_o @ A2 @ ( collec939566748876313656_nat_o @ P ) )
% 4.69/4.89 = ( P @ A2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % mem_Collect_eq
% 4.69/4.89 thf(fact_103_mem__Collect__eq,axiom,
% 4.69/4.89 ! [A2: nat,P: nat > $o] :
% 4.69/4.89 ( ( member_nat @ A2 @ ( collect_nat @ P ) )
% 4.69/4.89 = ( P @ A2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % mem_Collect_eq
% 4.69/4.89 thf(fact_104_mem__Collect__eq,axiom,
% 4.69/4.89 ! [A2: int,P: int > $o] :
% 4.69/4.89 ( ( member_int @ A2 @ ( collect_int @ P ) )
% 4.69/4.89 = ( P @ A2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % mem_Collect_eq
% 4.69/4.89 thf(fact_105_mem__Collect__eq,axiom,
% 4.69/4.89 ! [A2: $o,P: $o > $o] :
% 4.69/4.89 ( ( member_o @ A2 @ ( collect_o @ P ) )
% 4.69/4.89 = ( P @ A2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % mem_Collect_eq
% 4.69/4.89 thf(fact_106_mem__Collect__eq,axiom,
% 4.69/4.89 ! [A2: product_unit,P: product_unit > $o] :
% 4.69/4.89 ( ( member_Product_unit @ A2 @ ( collect_Product_unit @ P ) )
% 4.69/4.89 = ( P @ A2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % mem_Collect_eq
% 4.69/4.89 thf(fact_107_Collect__mem__eq,axiom,
% 4.69/4.89 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.89 ( ( collec939566748876313656_nat_o
% 4.69/4.89 @ ^ [X2: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X2 @ A ) )
% 4.69/4.89 = A ) ).
% 4.69/4.89
% 4.69/4.89 % Collect_mem_eq
% 4.69/4.89 thf(fact_108_Collect__mem__eq,axiom,
% 4.69/4.89 ! [A: set_nat] :
% 4.69/4.89 ( ( collect_nat
% 4.69/4.89 @ ^ [X2: nat] : ( member_nat @ X2 @ A ) )
% 4.69/4.89 = A ) ).
% 4.69/4.89
% 4.69/4.89 % Collect_mem_eq
% 4.69/4.89 thf(fact_109_Collect__mem__eq,axiom,
% 4.69/4.89 ! [A: set_int] :
% 4.69/4.89 ( ( collect_int
% 4.69/4.89 @ ^ [X2: int] : ( member_int @ X2 @ A ) )
% 4.69/4.89 = A ) ).
% 4.69/4.89
% 4.69/4.89 % Collect_mem_eq
% 4.69/4.89 thf(fact_110_Collect__mem__eq,axiom,
% 4.69/4.89 ! [A: set_o] :
% 4.69/4.89 ( ( collect_o
% 4.69/4.89 @ ^ [X2: $o] : ( member_o @ X2 @ A ) )
% 4.69/4.89 = A ) ).
% 4.69/4.89
% 4.69/4.89 % Collect_mem_eq
% 4.69/4.89 thf(fact_111_Collect__mem__eq,axiom,
% 4.69/4.89 ! [A: set_Product_unit] :
% 4.69/4.89 ( ( collect_Product_unit
% 4.69/4.89 @ ^ [X2: product_unit] : ( member_Product_unit @ X2 @ A ) )
% 4.69/4.89 = A ) ).
% 4.69/4.89
% 4.69/4.89 % Collect_mem_eq
% 4.69/4.89 thf(fact_112_Collect__cong,axiom,
% 4.69/4.89 ! [P: ( produc3658429121746597890et_nat > $o ) > $o,Q2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 4.69/4.89 ( ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( P @ X3 )
% 4.69/4.89 = ( Q2 @ X3 ) )
% 4.69/4.89 => ( ( collec939566748876313656_nat_o @ P )
% 4.69/4.89 = ( collec939566748876313656_nat_o @ Q2 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Collect_cong
% 4.69/4.89 thf(fact_113_Collect__cong,axiom,
% 4.69/4.89 ! [P: nat > $o,Q2: nat > $o] :
% 4.69/4.89 ( ! [X3: nat] :
% 4.69/4.89 ( ( P @ X3 )
% 4.69/4.89 = ( Q2 @ X3 ) )
% 4.69/4.89 => ( ( collect_nat @ P )
% 4.69/4.89 = ( collect_nat @ Q2 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Collect_cong
% 4.69/4.89 thf(fact_114_Collect__cong,axiom,
% 4.69/4.89 ! [P: int > $o,Q2: int > $o] :
% 4.69/4.89 ( ! [X3: int] :
% 4.69/4.89 ( ( P @ X3 )
% 4.69/4.89 = ( Q2 @ X3 ) )
% 4.69/4.89 => ( ( collect_int @ P )
% 4.69/4.89 = ( collect_int @ Q2 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Collect_cong
% 4.69/4.89 thf(fact_115_Collect__cong,axiom,
% 4.69/4.89 ! [P: $o > $o,Q2: $o > $o] :
% 4.69/4.89 ( ! [X3: $o] :
% 4.69/4.89 ( ( P @ X3 )
% 4.69/4.89 = ( Q2 @ X3 ) )
% 4.69/4.89 => ( ( collect_o @ P )
% 4.69/4.89 = ( collect_o @ Q2 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Collect_cong
% 4.69/4.89 thf(fact_116_Collect__cong,axiom,
% 4.69/4.89 ! [P: product_unit > $o,Q2: product_unit > $o] :
% 4.69/4.89 ( ! [X3: product_unit] :
% 4.69/4.89 ( ( P @ X3 )
% 4.69/4.89 = ( Q2 @ X3 ) )
% 4.69/4.89 => ( ( collect_Product_unit @ P )
% 4.69/4.89 = ( collect_Product_unit @ Q2 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Collect_cong
% 4.69/4.89 thf(fact_117_Rep__assn__cases,axiom,
% 4.69/4.89 ! [Y: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( member6576561426505652726_nat_o @ Y @ ( collec939566748876313656_nat_o @ proper ) )
% 4.69/4.89 => ~ ! [X3: assn] :
% 4.69/4.89 ( Y
% 4.69/4.89 != ( rep_assn @ X3 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Rep_assn_cases
% 4.69/4.89 thf(fact_118_Rep__assn__induct,axiom,
% 4.69/4.89 ! [Y: produc3658429121746597890et_nat > $o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 4.69/4.89 ( ( member6576561426505652726_nat_o @ Y @ ( collec939566748876313656_nat_o @ proper ) )
% 4.69/4.89 => ( ! [X3: assn] : ( P @ ( rep_assn @ X3 ) )
% 4.69/4.89 => ( P @ Y ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Rep_assn_induct
% 4.69/4.89 thf(fact_119_Abs__assn__cases,axiom,
% 4.69/4.89 ! [X: assn] :
% 4.69/4.89 ~ ! [Y2: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( X
% 4.69/4.89 = ( abs_assn @ Y2 ) )
% 4.69/4.89 => ~ ( member6576561426505652726_nat_o @ Y2 @ ( collec939566748876313656_nat_o @ proper ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Abs_assn_cases
% 4.69/4.89 thf(fact_120_Abs__assn__induct,axiom,
% 4.69/4.89 ! [P: assn > $o,X: assn] :
% 4.69/4.89 ( ! [Y2: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( member6576561426505652726_nat_o @ Y2 @ ( collec939566748876313656_nat_o @ proper ) )
% 4.69/4.89 => ( P @ ( abs_assn @ Y2 ) ) )
% 4.69/4.89 => ( P @ X ) ) ).
% 4.69/4.89
% 4.69/4.89 % Abs_assn_induct
% 4.69/4.89 thf(fact_121_Abs__assn__inject,axiom,
% 4.69/4.89 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( member6576561426505652726_nat_o @ X @ ( collec939566748876313656_nat_o @ proper ) )
% 4.69/4.89 => ( ( member6576561426505652726_nat_o @ Y @ ( collec939566748876313656_nat_o @ proper ) )
% 4.69/4.89 => ( ( ( abs_assn @ X )
% 4.69/4.89 = ( abs_assn @ Y ) )
% 4.69/4.89 = ( X = Y ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Abs_assn_inject
% 4.69/4.89 thf(fact_122_mod__h__bot__indep,axiom,
% 4.69/4.89 ! [P: assn,H2: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit] :
% 4.69/4.89 ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 4.69/4.89 = ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % mod_h_bot_indep
% 4.69/4.89 thf(fact_123_old_Oprod_Oinject,axiom,
% 4.69/4.89 ! [A2: heap_e7401611519738050253t_unit,B: set_nat,A5: heap_e7401611519738050253t_unit,B3: set_nat] :
% 4.69/4.89 ( ( ( produc7507926704131184380et_nat @ A2 @ B )
% 4.69/4.89 = ( produc7507926704131184380et_nat @ A5 @ B3 ) )
% 4.69/4.89 = ( ( A2 = A5 )
% 4.69/4.89 & ( B = B3 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % old.prod.inject
% 4.69/4.89 thf(fact_124_old_Oprod_Oinject,axiom,
% 4.69/4.89 ! [A2: nat,B: nat,A5: nat,B3: nat] :
% 4.69/4.89 ( ( ( product_Pair_nat_nat @ A2 @ B )
% 4.69/4.89 = ( product_Pair_nat_nat @ A5 @ B3 ) )
% 4.69/4.89 = ( ( A2 = A5 )
% 4.69/4.89 & ( B = B3 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % old.prod.inject
% 4.69/4.89 thf(fact_125_old_Oprod_Oinject,axiom,
% 4.69/4.89 ! [A2: int,B: int,A5: int,B3: int] :
% 4.69/4.89 ( ( ( product_Pair_int_int @ A2 @ B )
% 4.69/4.89 = ( product_Pair_int_int @ A5 @ B3 ) )
% 4.69/4.89 = ( ( A2 = A5 )
% 4.69/4.89 & ( B = B3 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % old.prod.inject
% 4.69/4.89 thf(fact_126_old_Oprod_Oinject,axiom,
% 4.69/4.89 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A5: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ( ( produc5001842942810119800et_nat @ A2 @ B )
% 4.69/4.89 = ( produc5001842942810119800et_nat @ A5 @ B3 ) )
% 4.69/4.89 = ( ( A2 = A5 )
% 4.69/4.89 & ( B = B3 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % old.prod.inject
% 4.69/4.89 thf(fact_127_old_Oprod_Oinject,axiom,
% 4.69/4.89 ! [A2: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A5: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat] :
% 4.69/4.89 ( ( ( produc2245416461498447860et_nat @ A2 @ B )
% 4.69/4.89 = ( produc2245416461498447860et_nat @ A5 @ B3 ) )
% 4.69/4.89 = ( ( A2 = A5 )
% 4.69/4.89 & ( B = B3 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % old.prod.inject
% 4.69/4.89 thf(fact_128_prod_Oinject,axiom,
% 4.69/4.89 ! [X1: heap_e7401611519738050253t_unit,X22: set_nat,Y1: heap_e7401611519738050253t_unit,Y22: set_nat] :
% 4.69/4.89 ( ( ( produc7507926704131184380et_nat @ X1 @ X22 )
% 4.69/4.89 = ( produc7507926704131184380et_nat @ Y1 @ Y22 ) )
% 4.69/4.89 = ( ( X1 = Y1 )
% 4.69/4.89 & ( X22 = Y22 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % prod.inject
% 4.69/4.89 thf(fact_129_prod_Oinject,axiom,
% 4.69/4.89 ! [X1: nat,X22: nat,Y1: nat,Y22: nat] :
% 4.69/4.89 ( ( ( product_Pair_nat_nat @ X1 @ X22 )
% 4.69/4.89 = ( product_Pair_nat_nat @ Y1 @ Y22 ) )
% 4.69/4.89 = ( ( X1 = Y1 )
% 4.69/4.89 & ( X22 = Y22 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % prod.inject
% 4.69/4.89 thf(fact_130_prod_Oinject,axiom,
% 4.69/4.89 ! [X1: int,X22: int,Y1: int,Y22: int] :
% 4.69/4.89 ( ( ( product_Pair_int_int @ X1 @ X22 )
% 4.69/4.89 = ( product_Pair_int_int @ Y1 @ Y22 ) )
% 4.69/4.89 = ( ( X1 = Y1 )
% 4.69/4.89 & ( X22 = Y22 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % prod.inject
% 4.69/4.89 thf(fact_131_prod_Oinject,axiom,
% 4.69/4.89 ! [X1: produc3658429121746597890et_nat > $o,X22: produc3658429121746597890et_nat,Y1: produc3658429121746597890et_nat > $o,Y22: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ( ( produc5001842942810119800et_nat @ X1 @ X22 )
% 4.69/4.89 = ( produc5001842942810119800et_nat @ Y1 @ Y22 ) )
% 4.69/4.89 = ( ( X1 = Y1 )
% 4.69/4.89 & ( X22 = Y22 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % prod.inject
% 4.69/4.89 thf(fact_132_prod_Oinject,axiom,
% 4.69/4.89 ! [X1: produc3658429121746597890et_nat > $o,X22: produc3925858234332021118et_nat,Y1: produc3658429121746597890et_nat > $o,Y22: produc3925858234332021118et_nat] :
% 4.69/4.89 ( ( ( produc2245416461498447860et_nat @ X1 @ X22 )
% 4.69/4.89 = ( produc2245416461498447860et_nat @ Y1 @ Y22 ) )
% 4.69/4.89 = ( ( X1 = Y1 )
% 4.69/4.89 & ( X22 = Y22 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % prod.inject
% 4.69/4.89 thf(fact_133_sndI,axiom,
% 4.69/4.89 ! [X: product_prod_nat_nat,Y: nat,Z: nat] :
% 4.69/4.89 ( ( X
% 4.69/4.89 = ( product_Pair_nat_nat @ Y @ Z ) )
% 4.69/4.89 => ( ( product_snd_nat_nat @ X )
% 4.69/4.89 = Z ) ) ).
% 4.69/4.89
% 4.69/4.89 % sndI
% 4.69/4.89 thf(fact_134_sndI,axiom,
% 4.69/4.89 ! [X: produc3925858234332021118et_nat,Y: produc3658429121746597890et_nat > $o,Z: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ( X
% 4.69/4.89 = ( produc5001842942810119800et_nat @ Y @ Z ) )
% 4.69/4.89 => ( ( produc4011572625026189258et_nat @ X )
% 4.69/4.89 = Z ) ) ).
% 4.69/4.89
% 4.69/4.89 % sndI
% 4.69/4.89 thf(fact_135_sndI,axiom,
% 4.69/4.89 ! [X: produc2732055786443039994et_nat,Y: produc3658429121746597890et_nat > $o,Z: produc3925858234332021118et_nat] :
% 4.69/4.89 ( ( X
% 4.69/4.89 = ( produc2245416461498447860et_nat @ Y @ Z ) )
% 4.69/4.89 => ( ( produc5374455773327741254et_nat @ X )
% 4.69/4.89 = Z ) ) ).
% 4.69/4.89
% 4.69/4.89 % sndI
% 4.69/4.89 thf(fact_136_sndI,axiom,
% 4.69/4.89 ! [X: produc3658429121746597890et_nat,Y: heap_e7401611519738050253t_unit,Z: set_nat] :
% 4.69/4.89 ( ( X
% 4.69/4.89 = ( produc7507926704131184380et_nat @ Y @ Z ) )
% 4.69/4.89 => ( ( produc8586169260539613262et_nat @ X )
% 4.69/4.89 = Z ) ) ).
% 4.69/4.89
% 4.69/4.89 % sndI
% 4.69/4.89 thf(fact_137_sndI,axiom,
% 4.69/4.89 ! [X: product_prod_int_int,Y: int,Z: int] :
% 4.69/4.89 ( ( X
% 4.69/4.89 = ( product_Pair_int_int @ Y @ Z ) )
% 4.69/4.89 => ( ( product_snd_int_int @ X )
% 4.69/4.89 = Z ) ) ).
% 4.69/4.89
% 4.69/4.89 % sndI
% 4.69/4.89 thf(fact_138_snd__eqD,axiom,
% 4.69/4.89 ! [X: nat,Y: nat,A2: nat] :
% 4.69/4.89 ( ( ( product_snd_nat_nat @ ( product_Pair_nat_nat @ X @ Y ) )
% 4.69/4.89 = A2 )
% 4.69/4.89 => ( Y = A2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % snd_eqD
% 4.69/4.89 thf(fact_139_snd__eqD,axiom,
% 4.69/4.89 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat,A2: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ( ( produc4011572625026189258et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 4.69/4.89 = A2 )
% 4.69/4.89 => ( Y = A2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % snd_eqD
% 4.69/4.89 thf(fact_140_snd__eqD,axiom,
% 4.69/4.89 ! [X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat,A2: produc3925858234332021118et_nat] :
% 4.69/4.89 ( ( ( produc5374455773327741254et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 4.69/4.89 = A2 )
% 4.69/4.89 => ( Y = A2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % snd_eqD
% 4.69/4.89 thf(fact_141_snd__eqD,axiom,
% 4.69/4.89 ! [X: heap_e7401611519738050253t_unit,Y: set_nat,A2: set_nat] :
% 4.69/4.89 ( ( ( produc8586169260539613262et_nat @ ( produc7507926704131184380et_nat @ X @ Y ) )
% 4.69/4.89 = A2 )
% 4.69/4.89 => ( Y = A2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % snd_eqD
% 4.69/4.89 thf(fact_142_snd__eqD,axiom,
% 4.69/4.89 ! [X: int,Y: int,A2: int] :
% 4.69/4.89 ( ( ( product_snd_int_int @ ( product_Pair_int_int @ X @ Y ) )
% 4.69/4.89 = A2 )
% 4.69/4.89 => ( Y = A2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % snd_eqD
% 4.69/4.89 thf(fact_143_snd__conv,axiom,
% 4.69/4.89 ! [X1: nat,X22: nat] :
% 4.69/4.89 ( ( product_snd_nat_nat @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 4.69/4.89 = X22 ) ).
% 4.69/4.89
% 4.69/4.89 % snd_conv
% 4.69/4.89 thf(fact_144_snd__conv,axiom,
% 4.69/4.89 ! [X1: produc3658429121746597890et_nat > $o,X22: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ( produc4011572625026189258et_nat @ ( produc5001842942810119800et_nat @ X1 @ X22 ) )
% 4.69/4.89 = X22 ) ).
% 4.69/4.89
% 4.69/4.89 % snd_conv
% 4.69/4.89 thf(fact_145_snd__conv,axiom,
% 4.69/4.89 ! [X1: produc3658429121746597890et_nat > $o,X22: produc3925858234332021118et_nat] :
% 4.69/4.89 ( ( produc5374455773327741254et_nat @ ( produc2245416461498447860et_nat @ X1 @ X22 ) )
% 4.69/4.89 = X22 ) ).
% 4.69/4.89
% 4.69/4.89 % snd_conv
% 4.69/4.89 thf(fact_146_snd__conv,axiom,
% 4.69/4.89 ! [X1: heap_e7401611519738050253t_unit,X22: set_nat] :
% 4.69/4.89 ( ( produc8586169260539613262et_nat @ ( produc7507926704131184380et_nat @ X1 @ X22 ) )
% 4.69/4.89 = X22 ) ).
% 4.69/4.89
% 4.69/4.89 % snd_conv
% 4.69/4.89 thf(fact_147_snd__conv,axiom,
% 4.69/4.89 ! [X1: int,X22: int] :
% 4.69/4.89 ( ( product_snd_int_int @ ( product_Pair_int_int @ X1 @ X22 ) )
% 4.69/4.89 = X22 ) ).
% 4.69/4.89
% 4.69/4.89 % snd_conv
% 4.69/4.89 thf(fact_148_eq__snd__iff,axiom,
% 4.69/4.89 ! [B: nat,P3: product_prod_nat_nat] :
% 4.69/4.89 ( ( B
% 4.69/4.89 = ( product_snd_nat_nat @ P3 ) )
% 4.69/4.89 = ( ? [A6: nat] :
% 4.69/4.89 ( P3
% 4.69/4.89 = ( product_Pair_nat_nat @ A6 @ B ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % eq_snd_iff
% 4.69/4.89 thf(fact_149_eq__snd__iff,axiom,
% 4.69/4.89 ! [B: produc3658429121746597890et_nat,P3: produc3925858234332021118et_nat] :
% 4.69/4.89 ( ( B
% 4.69/4.89 = ( produc4011572625026189258et_nat @ P3 ) )
% 4.69/4.89 = ( ? [A6: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( P3
% 4.69/4.89 = ( produc5001842942810119800et_nat @ A6 @ B ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % eq_snd_iff
% 4.69/4.89 thf(fact_150_eq__snd__iff,axiom,
% 4.69/4.89 ! [B: produc3925858234332021118et_nat,P3: produc2732055786443039994et_nat] :
% 4.69/4.89 ( ( B
% 4.69/4.89 = ( produc5374455773327741254et_nat @ P3 ) )
% 4.69/4.89 = ( ? [A6: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( P3
% 4.69/4.89 = ( produc2245416461498447860et_nat @ A6 @ B ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % eq_snd_iff
% 4.69/4.89 thf(fact_151_eq__snd__iff,axiom,
% 4.69/4.89 ! [B: set_nat,P3: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ( B
% 4.69/4.89 = ( produc8586169260539613262et_nat @ P3 ) )
% 4.69/4.89 = ( ? [A6: heap_e7401611519738050253t_unit] :
% 4.69/4.89 ( P3
% 4.69/4.89 = ( produc7507926704131184380et_nat @ A6 @ B ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % eq_snd_iff
% 4.69/4.89 thf(fact_152_eq__snd__iff,axiom,
% 4.69/4.89 ! [B: int,P3: product_prod_int_int] :
% 4.69/4.89 ( ( B
% 4.69/4.89 = ( product_snd_int_int @ P3 ) )
% 4.69/4.89 = ( ? [A6: int] :
% 4.69/4.89 ( P3
% 4.69/4.89 = ( product_Pair_int_int @ A6 @ B ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % eq_snd_iff
% 4.69/4.89 thf(fact_153_pure__assn__raw_Oelims_I3_J,axiom,
% 4.69/4.89 ! [X: $o,Xa: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ~ ( pure_a825153325127701367it_nat @ X @ Xa )
% 4.69/4.89 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.89 ( ( Xa
% 4.69/4.89 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.89 => ( ( As2 = bot_bot_set_nat )
% 4.69/4.89 & X ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % pure_assn_raw.elims(3)
% 4.69/4.89 thf(fact_154_pure__assn__raw_Oelims_I2_J,axiom,
% 4.69/4.89 ! [X: $o,Xa: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ( pure_a825153325127701367it_nat @ X @ Xa )
% 4.69/4.89 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.89 ( ( Xa
% 4.69/4.89 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.89 => ~ ( ( As2 = bot_bot_set_nat )
% 4.69/4.89 & X ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % pure_assn_raw.elims(2)
% 4.69/4.89 thf(fact_155_pure__assn__raw_Oelims_I1_J,axiom,
% 4.69/4.89 ! [X: $o,Xa: produc3658429121746597890et_nat,Y: $o] :
% 4.69/4.89 ( ( ( pure_a825153325127701367it_nat @ X @ Xa )
% 4.69/4.89 = Y )
% 4.69/4.89 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.89 ( ( Xa
% 4.69/4.89 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.89 => ( Y
% 4.69/4.89 = ( ~ ( ( As2 = bot_bot_set_nat )
% 4.69/4.89 & X ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % pure_assn_raw.elims(1)
% 4.69/4.89 thf(fact_156_pure__assn__raw_Osimps,axiom,
% 4.69/4.89 ! [B: $o,H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 4.69/4.89 ( ( pure_a825153325127701367it_nat @ B @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 4.69/4.89 = ( ( As = bot_bot_set_nat )
% 4.69/4.89 & B ) ) ).
% 4.69/4.89
% 4.69/4.89 % pure_assn_raw.simps
% 4.69/4.89 thf(fact_157_pure__assn__proper,axiom,
% 4.69/4.89 ! [B: $o] : ( proper @ ( pure_a825153325127701367it_nat @ B ) ) ).
% 4.69/4.89
% 4.69/4.89 % pure_assn_proper
% 4.69/4.89 thf(fact_158_times__assn__raw_Ocases,axiom,
% 4.69/4.89 ! [X: produc2732055786443039994et_nat] :
% 4.69/4.89 ~ ! [P4: produc3658429121746597890et_nat > $o,Q3: produc3658429121746597890et_nat > $o,H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.89 ( X
% 4.69/4.89 != ( produc2245416461498447860et_nat @ P4 @ ( produc5001842942810119800et_nat @ Q3 @ ( produc7507926704131184380et_nat @ H @ As2 ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % times_assn_raw.cases
% 4.69/4.89 thf(fact_159_pure__assn__raw_Ocases,axiom,
% 4.69/4.89 ! [X: produc6197004810343482825et_nat] :
% 4.69/4.89 ~ ! [B2: $o,H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.89 ( X
% 4.69/4.89 != ( produc3762353314782720579et_nat @ B2 @ ( produc7507926704131184380et_nat @ H @ As2 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % pure_assn_raw.cases
% 4.69/4.89 thf(fact_160_old_Oprod_Oexhaust,axiom,
% 4.69/4.89 ! [Y: produc3658429121746597890et_nat] :
% 4.69/4.89 ~ ! [A4: heap_e7401611519738050253t_unit,B2: set_nat] :
% 4.69/4.89 ( Y
% 4.69/4.89 != ( produc7507926704131184380et_nat @ A4 @ B2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % old.prod.exhaust
% 4.69/4.89 thf(fact_161_old_Oprod_Oexhaust,axiom,
% 4.69/4.89 ! [Y: product_prod_nat_nat] :
% 4.69/4.89 ~ ! [A4: nat,B2: nat] :
% 4.69/4.89 ( Y
% 4.69/4.89 != ( product_Pair_nat_nat @ A4 @ B2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % old.prod.exhaust
% 4.69/4.89 thf(fact_162_old_Oprod_Oexhaust,axiom,
% 4.69/4.89 ! [Y: product_prod_int_int] :
% 4.69/4.89 ~ ! [A4: int,B2: int] :
% 4.69/4.89 ( Y
% 4.69/4.89 != ( product_Pair_int_int @ A4 @ B2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % old.prod.exhaust
% 4.69/4.89 thf(fact_163_old_Oprod_Oexhaust,axiom,
% 4.69/4.89 ! [Y: produc3925858234332021118et_nat] :
% 4.69/4.89 ~ ! [A4: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 4.69/4.89 ( Y
% 4.69/4.89 != ( produc5001842942810119800et_nat @ A4 @ B2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % old.prod.exhaust
% 4.69/4.89 thf(fact_164_old_Oprod_Oexhaust,axiom,
% 4.69/4.89 ! [Y: produc2732055786443039994et_nat] :
% 4.69/4.89 ~ ! [A4: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 4.69/4.89 ( Y
% 4.69/4.89 != ( produc2245416461498447860et_nat @ A4 @ B2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % old.prod.exhaust
% 4.69/4.89 thf(fact_165_surj__pair,axiom,
% 4.69/4.89 ! [P3: produc3658429121746597890et_nat] :
% 4.69/4.89 ? [X3: heap_e7401611519738050253t_unit,Y2: set_nat] :
% 4.69/4.89 ( P3
% 4.69/4.89 = ( produc7507926704131184380et_nat @ X3 @ Y2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % surj_pair
% 4.69/4.89 thf(fact_166_surj__pair,axiom,
% 4.69/4.89 ! [P3: product_prod_nat_nat] :
% 4.69/4.89 ? [X3: nat,Y2: nat] :
% 4.69/4.89 ( P3
% 4.69/4.89 = ( product_Pair_nat_nat @ X3 @ Y2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % surj_pair
% 4.69/4.89 thf(fact_167_surj__pair,axiom,
% 4.69/4.89 ! [P3: product_prod_int_int] :
% 4.69/4.89 ? [X3: int,Y2: int] :
% 4.69/4.89 ( P3
% 4.69/4.89 = ( product_Pair_int_int @ X3 @ Y2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % surj_pair
% 4.69/4.89 thf(fact_168_surj__pair,axiom,
% 4.69/4.89 ! [P3: produc3925858234332021118et_nat] :
% 4.69/4.89 ? [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 4.69/4.89 ( P3
% 4.69/4.89 = ( produc5001842942810119800et_nat @ X3 @ Y2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % surj_pair
% 4.69/4.89 thf(fact_169_surj__pair,axiom,
% 4.69/4.89 ! [P3: produc2732055786443039994et_nat] :
% 4.69/4.89 ? [X3: produc3658429121746597890et_nat > $o,Y2: produc3925858234332021118et_nat] :
% 4.69/4.89 ( P3
% 4.69/4.89 = ( produc2245416461498447860et_nat @ X3 @ Y2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % surj_pair
% 4.69/4.89 thf(fact_170_prod__cases,axiom,
% 4.69/4.89 ! [P: produc3658429121746597890et_nat > $o,P3: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ! [A4: heap_e7401611519738050253t_unit,B2: set_nat] : ( P @ ( produc7507926704131184380et_nat @ A4 @ B2 ) )
% 4.69/4.89 => ( P @ P3 ) ) ).
% 4.69/4.89
% 4.69/4.89 % prod_cases
% 4.69/4.89 thf(fact_171_prod__cases,axiom,
% 4.69/4.89 ! [P: product_prod_nat_nat > $o,P3: product_prod_nat_nat] :
% 4.69/4.89 ( ! [A4: nat,B2: nat] : ( P @ ( product_Pair_nat_nat @ A4 @ B2 ) )
% 4.69/4.89 => ( P @ P3 ) ) ).
% 4.69/4.89
% 4.69/4.89 % prod_cases
% 4.69/4.89 thf(fact_172_prod__cases,axiom,
% 4.69/4.89 ! [P: product_prod_int_int > $o,P3: product_prod_int_int] :
% 4.69/4.89 ( ! [A4: int,B2: int] : ( P @ ( product_Pair_int_int @ A4 @ B2 ) )
% 4.69/4.89 => ( P @ P3 ) ) ).
% 4.69/4.89
% 4.69/4.89 % prod_cases
% 4.69/4.89 thf(fact_173_prod__cases,axiom,
% 4.69/4.89 ! [P: produc3925858234332021118et_nat > $o,P3: produc3925858234332021118et_nat] :
% 4.69/4.89 ( ! [A4: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] : ( P @ ( produc5001842942810119800et_nat @ A4 @ B2 ) )
% 4.69/4.89 => ( P @ P3 ) ) ).
% 4.69/4.89
% 4.69/4.89 % prod_cases
% 4.69/4.89 thf(fact_174_prod__cases,axiom,
% 4.69/4.89 ! [P: produc2732055786443039994et_nat > $o,P3: produc2732055786443039994et_nat] :
% 4.69/4.89 ( ! [A4: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] : ( P @ ( produc2245416461498447860et_nat @ A4 @ B2 ) )
% 4.69/4.89 => ( P @ P3 ) ) ).
% 4.69/4.89
% 4.69/4.89 % prod_cases
% 4.69/4.89 thf(fact_175_Pair__inject,axiom,
% 4.69/4.89 ! [A2: heap_e7401611519738050253t_unit,B: set_nat,A5: heap_e7401611519738050253t_unit,B3: set_nat] :
% 4.69/4.89 ( ( ( produc7507926704131184380et_nat @ A2 @ B )
% 4.69/4.89 = ( produc7507926704131184380et_nat @ A5 @ B3 ) )
% 4.69/4.89 => ~ ( ( A2 = A5 )
% 4.69/4.89 => ( B != B3 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Pair_inject
% 4.69/4.89 thf(fact_176_Pair__inject,axiom,
% 4.69/4.89 ! [A2: nat,B: nat,A5: nat,B3: nat] :
% 4.69/4.89 ( ( ( product_Pair_nat_nat @ A2 @ B )
% 4.69/4.89 = ( product_Pair_nat_nat @ A5 @ B3 ) )
% 4.69/4.89 => ~ ( ( A2 = A5 )
% 4.69/4.89 => ( B != B3 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Pair_inject
% 4.69/4.89 thf(fact_177_Pair__inject,axiom,
% 4.69/4.89 ! [A2: int,B: int,A5: int,B3: int] :
% 4.69/4.89 ( ( ( product_Pair_int_int @ A2 @ B )
% 4.69/4.89 = ( product_Pair_int_int @ A5 @ B3 ) )
% 4.69/4.89 => ~ ( ( A2 = A5 )
% 4.69/4.89 => ( B != B3 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Pair_inject
% 4.69/4.89 thf(fact_178_Pair__inject,axiom,
% 4.69/4.89 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A5: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ( ( produc5001842942810119800et_nat @ A2 @ B )
% 4.69/4.89 = ( produc5001842942810119800et_nat @ A5 @ B3 ) )
% 4.69/4.89 => ~ ( ( A2 = A5 )
% 4.69/4.89 => ( B != B3 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Pair_inject
% 4.69/4.89 thf(fact_179_Pair__inject,axiom,
% 4.69/4.89 ! [A2: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A5: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat] :
% 4.69/4.89 ( ( ( produc2245416461498447860et_nat @ A2 @ B )
% 4.69/4.89 = ( produc2245416461498447860et_nat @ A5 @ B3 ) )
% 4.69/4.89 => ~ ( ( A2 = A5 )
% 4.69/4.89 => ( B != B3 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Pair_inject
% 4.69/4.89 thf(fact_180_prod__cases3,axiom,
% 4.69/4.89 ! [Y: produc3925858234332021118et_nat] :
% 4.69/4.89 ~ ! [A4: produc3658429121746597890et_nat > $o,B2: heap_e7401611519738050253t_unit,C2: set_nat] :
% 4.69/4.89 ( Y
% 4.69/4.89 != ( produc5001842942810119800et_nat @ A4 @ ( produc7507926704131184380et_nat @ B2 @ C2 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % prod_cases3
% 4.69/4.89 thf(fact_181_prod__cases3,axiom,
% 4.69/4.89 ! [Y: produc2732055786443039994et_nat] :
% 4.69/4.89 ~ ! [A4: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat > $o,C2: produc3658429121746597890et_nat] :
% 4.69/4.89 ( Y
% 4.69/4.89 != ( produc2245416461498447860et_nat @ A4 @ ( produc5001842942810119800et_nat @ B2 @ C2 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % prod_cases3
% 4.69/4.89 thf(fact_182_prod__cases4,axiom,
% 4.69/4.89 ! [Y: produc2732055786443039994et_nat] :
% 4.69/4.89 ~ ! [A4: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat > $o,C2: heap_e7401611519738050253t_unit,D: set_nat] :
% 4.69/4.89 ( Y
% 4.69/4.89 != ( produc2245416461498447860et_nat @ A4 @ ( produc5001842942810119800et_nat @ B2 @ ( produc7507926704131184380et_nat @ C2 @ D ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % prod_cases4
% 4.69/4.89 thf(fact_183_prod__induct3,axiom,
% 4.69/4.89 ! [P: produc3925858234332021118et_nat > $o,X: produc3925858234332021118et_nat] :
% 4.69/4.89 ( ! [A4: produc3658429121746597890et_nat > $o,B2: heap_e7401611519738050253t_unit,C2: set_nat] : ( P @ ( produc5001842942810119800et_nat @ A4 @ ( produc7507926704131184380et_nat @ B2 @ C2 ) ) )
% 4.69/4.89 => ( P @ X ) ) ).
% 4.69/4.89
% 4.69/4.89 % prod_induct3
% 4.69/4.89 thf(fact_184_prod__induct3,axiom,
% 4.69/4.89 ! [P: produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 4.69/4.89 ( ! [A4: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat > $o,C2: produc3658429121746597890et_nat] : ( P @ ( produc2245416461498447860et_nat @ A4 @ ( produc5001842942810119800et_nat @ B2 @ C2 ) ) )
% 4.69/4.89 => ( P @ X ) ) ).
% 4.69/4.89
% 4.69/4.89 % prod_induct3
% 4.69/4.89 thf(fact_185_prod__induct4,axiom,
% 4.69/4.89 ! [P: produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 4.69/4.89 ( ! [A4: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat > $o,C2: heap_e7401611519738050253t_unit,D: set_nat] : ( P @ ( produc2245416461498447860et_nat @ A4 @ ( produc5001842942810119800et_nat @ B2 @ ( produc7507926704131184380et_nat @ C2 @ D ) ) ) )
% 4.69/4.89 => ( P @ X ) ) ).
% 4.69/4.89
% 4.69/4.89 % prod_induct4
% 4.69/4.89 thf(fact_186_one__reorient,axiom,
% 4.69/4.89 ! [X: assn] :
% 4.69/4.89 ( ( one_one_assn = X )
% 4.69/4.89 = ( X = one_one_assn ) ) ).
% 4.69/4.89
% 4.69/4.89 % one_reorient
% 4.69/4.89 thf(fact_187_one__reorient,axiom,
% 4.69/4.89 ! [X: nat] :
% 4.69/4.89 ( ( one_one_nat = X )
% 4.69/4.89 = ( X = one_one_nat ) ) ).
% 4.69/4.89
% 4.69/4.89 % one_reorient
% 4.69/4.89 thf(fact_188_one__reorient,axiom,
% 4.69/4.89 ! [X: int] :
% 4.69/4.89 ( ( one_one_int = X )
% 4.69/4.89 = ( X = one_one_int ) ) ).
% 4.69/4.89
% 4.69/4.89 % one_reorient
% 4.69/4.89 thf(fact_189_one__reorient,axiom,
% 4.69/4.89 ! [X: code_integer] :
% 4.69/4.89 ( ( one_one_Code_integer = X )
% 4.69/4.89 = ( X = one_one_Code_integer ) ) ).
% 4.69/4.89
% 4.69/4.89 % one_reorient
% 4.69/4.89 thf(fact_190_one__reorient,axiom,
% 4.69/4.89 ! [X: code_natural] :
% 4.69/4.89 ( ( one_one_Code_natural = X )
% 4.69/4.89 = ( X = one_one_Code_natural ) ) ).
% 4.69/4.89
% 4.69/4.89 % one_reorient
% 4.69/4.89 thf(fact_191_type__definition__assn,axiom,
% 4.69/4.89 type_d3909072315231072503_nat_o @ rep_assn @ abs_assn @ ( collec939566748876313656_nat_o @ proper ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition_assn
% 4.69/4.89 thf(fact_192_times__assn__proper,axiom,
% 4.69/4.89 ! [P: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( proper @ P )
% 4.69/4.89 => ( ( proper @ Q2 )
% 4.69/4.89 => ( proper @ ( times_assn_raw @ P @ Q2 ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % times_assn_proper
% 4.69/4.89 thf(fact_193_is__pure__assn__basic__simps_I2_J,axiom,
% 4.69/4.89 is_pure_assn @ one_one_assn ).
% 4.69/4.89
% 4.69/4.89 % is_pure_assn_basic_simps(2)
% 4.69/4.89 thf(fact_194_bijective__def,axiom,
% 4.69/4.89 ( biject2219996528949639174et_nat
% 4.69/4.89 = ( ^ [R: set_Pr3948176798113811640et_nat] :
% 4.69/4.89 ( ! [X2: heap_e7401611519738050253t_unit,Y3: set_nat,Z2: set_nat] :
% 4.69/4.89 ( ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X2 @ Y3 ) @ R )
% 4.69/4.89 & ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X2 @ Z2 ) @ R ) )
% 4.69/4.89 => ( Y3 = Z2 ) )
% 4.69/4.89 & ! [X2: heap_e7401611519738050253t_unit,Y3: heap_e7401611519738050253t_unit,Z2: set_nat] :
% 4.69/4.89 ( ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X2 @ Z2 ) @ R )
% 4.69/4.89 & ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ Y3 @ Z2 ) @ R ) )
% 4.69/4.89 => ( X2 = Y3 ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % bijective_def
% 4.69/4.89 thf(fact_195_bijective__def,axiom,
% 4.69/4.89 ( bijective_nat_nat
% 4.69/4.89 = ( ^ [R: set_Pr1261947904930325089at_nat] :
% 4.69/4.89 ( ! [X2: nat,Y3: nat,Z2: nat] :
% 4.69/4.89 ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ R )
% 4.69/4.89 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Z2 ) @ R ) )
% 4.69/4.89 => ( Y3 = Z2 ) )
% 4.69/4.89 & ! [X2: nat,Y3: nat,Z2: nat] :
% 4.69/4.89 ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Z2 ) @ R )
% 4.69/4.89 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ Z2 ) @ R ) )
% 4.69/4.89 => ( X2 = Y3 ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % bijective_def
% 4.69/4.89 thf(fact_196_bijective__def,axiom,
% 4.69/4.89 ( bijective_int_int
% 4.69/4.89 = ( ^ [R: set_Pr958786334691620121nt_int] :
% 4.69/4.89 ( ! [X2: int,Y3: int,Z2: int] :
% 4.69/4.89 ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ R )
% 4.69/4.89 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Z2 ) @ R ) )
% 4.69/4.89 => ( Y3 = Z2 ) )
% 4.69/4.89 & ! [X2: int,Y3: int,Z2: int] :
% 4.69/4.89 ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Z2 ) @ R )
% 4.69/4.89 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ Z2 ) @ R ) )
% 4.69/4.89 => ( X2 = Y3 ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % bijective_def
% 4.69/4.89 thf(fact_197_bijective__def,axiom,
% 4.69/4.89 ( biject2615096655818420098et_nat
% 4.69/4.89 = ( ^ [R: set_Pr3286484037609594932et_nat] :
% 4.69/4.89 ( ! [X2: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat,Z2: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X2 @ Y3 ) @ R )
% 4.69/4.89 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X2 @ Z2 ) @ R ) )
% 4.69/4.89 => ( Y3 = Z2 ) )
% 4.69/4.89 & ! [X2: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat > $o,Z2: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X2 @ Z2 ) @ R )
% 4.69/4.89 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ Y3 @ Z2 ) @ R ) )
% 4.69/4.89 => ( X2 = Y3 ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % bijective_def
% 4.69/4.89 thf(fact_198_bijective__def,axiom,
% 4.69/4.89 ( biject1468766312547416318et_nat
% 4.69/4.89 = ( ^ [R: set_Pr8536935166611901872et_nat] :
% 4.69/4.89 ( ! [X2: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat,Z2: produc3925858234332021118et_nat] :
% 4.69/4.89 ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X2 @ Y3 ) @ R )
% 4.69/4.89 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X2 @ Z2 ) @ R ) )
% 4.69/4.89 => ( Y3 = Z2 ) )
% 4.69/4.89 & ! [X2: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat > $o,Z2: produc3925858234332021118et_nat] :
% 4.69/4.89 ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X2 @ Z2 ) @ R )
% 4.69/4.89 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ Y3 @ Z2 ) @ R ) )
% 4.69/4.89 => ( X2 = Y3 ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % bijective_def
% 4.69/4.89 thf(fact_199_ssubst__Pair__rhs,axiom,
% 4.69/4.89 ! [R2: heap_e7401611519738050253t_unit,S2: set_nat,R3: set_Pr3948176798113811640et_nat,S3: set_nat] :
% 4.69/4.89 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ R2 @ S2 ) @ R3 )
% 4.69/4.89 => ( ( S3 = S2 )
% 4.69/4.89 => ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ R2 @ S3 ) @ R3 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % ssubst_Pair_rhs
% 4.69/4.89 thf(fact_200_ssubst__Pair__rhs,axiom,
% 4.69/4.89 ! [R2: nat,S2: nat,R3: set_Pr1261947904930325089at_nat,S3: nat] :
% 4.69/4.89 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ R2 @ S2 ) @ R3 )
% 4.69/4.89 => ( ( S3 = S2 )
% 4.69/4.89 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ R2 @ S3 ) @ R3 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % ssubst_Pair_rhs
% 4.69/4.89 thf(fact_201_ssubst__Pair__rhs,axiom,
% 4.69/4.89 ! [R2: int,S2: int,R3: set_Pr958786334691620121nt_int,S3: int] :
% 4.69/4.89 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ R2 @ S2 ) @ R3 )
% 4.69/4.89 => ( ( S3 = S2 )
% 4.69/4.89 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ R2 @ S3 ) @ R3 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % ssubst_Pair_rhs
% 4.69/4.89 thf(fact_202_ssubst__Pair__rhs,axiom,
% 4.69/4.89 ! [R2: produc3658429121746597890et_nat > $o,S2: produc3658429121746597890et_nat,R3: set_Pr3286484037609594932et_nat,S3: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ R2 @ S2 ) @ R3 )
% 4.69/4.89 => ( ( S3 = S2 )
% 4.69/4.89 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ R2 @ S3 ) @ R3 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % ssubst_Pair_rhs
% 4.69/4.89 thf(fact_203_ssubst__Pair__rhs,axiom,
% 4.69/4.89 ! [R2: produc3658429121746597890et_nat > $o,S2: produc3925858234332021118et_nat,R3: set_Pr8536935166611901872et_nat,S3: produc3925858234332021118et_nat] :
% 4.69/4.89 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ R2 @ S2 ) @ R3 )
% 4.69/4.89 => ( ( S3 = S2 )
% 4.69/4.89 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ R2 @ S3 ) @ R3 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % ssubst_Pair_rhs
% 4.69/4.89 thf(fact_204_is__singletonI,axiom,
% 4.69/4.89 ! [X: product_unit] : ( is_sin2160648248035936513t_unit @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singletonI
% 4.69/4.89 thf(fact_205_is__singletonI,axiom,
% 4.69/4.89 ! [X: $o] : ( is_singleton_o @ ( insert_o @ X @ bot_bot_set_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singletonI
% 4.69/4.89 thf(fact_206_is__singletonI,axiom,
% 4.69/4.89 ! [X: nat] : ( is_singleton_nat @ ( insert_nat @ X @ bot_bot_set_nat ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singletonI
% 4.69/4.89 thf(fact_207_is__singletonI,axiom,
% 4.69/4.89 ! [X: int] : ( is_singleton_int @ ( insert_int @ X @ bot_bot_set_int ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singletonI
% 4.69/4.89 thf(fact_208_is__singletonI,axiom,
% 4.69/4.89 ! [X: produc3658429121746597890et_nat > $o] : ( is_sin5180296473474724033_nat_o @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singletonI
% 4.69/4.89 thf(fact_209_curryI,axiom,
% 4.69/4.89 ! [F: produc3658429121746597890et_nat > $o,A2: heap_e7401611519738050253t_unit,B: set_nat] :
% 4.69/4.89 ( ( F @ ( produc7507926704131184380et_nat @ A2 @ B ) )
% 4.69/4.89 => ( produc1807123492089482958_nat_o @ F @ A2 @ B ) ) ).
% 4.69/4.89
% 4.69/4.89 % curryI
% 4.69/4.89 thf(fact_210_curryI,axiom,
% 4.69/4.89 ! [F: product_prod_nat_nat > $o,A2: nat,B: nat] :
% 4.69/4.89 ( ( F @ ( product_Pair_nat_nat @ A2 @ B ) )
% 4.69/4.89 => ( produc1310100445399344235_nat_o @ F @ A2 @ B ) ) ).
% 4.69/4.89
% 4.69/4.89 % curryI
% 4.69/4.89 thf(fact_211_curryI,axiom,
% 4.69/4.89 ! [F: product_prod_int_int > $o,A2: int,B: int] :
% 4.69/4.89 ( ( F @ ( product_Pair_int_int @ A2 @ B ) )
% 4.69/4.89 => ( produc175634133007206835_int_o @ F @ A2 @ B ) ) ).
% 4.69/4.89
% 4.69/4.89 % curryI
% 4.69/4.89 thf(fact_212_curryI,axiom,
% 4.69/4.89 ! [F: produc3925858234332021118et_nat > $o,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ( F @ ( produc5001842942810119800et_nat @ A2 @ B ) )
% 4.69/4.89 => ( produc6216949301066131538_nat_o @ F @ A2 @ B ) ) ).
% 4.69/4.89
% 4.69/4.89 % curryI
% 4.69/4.89 thf(fact_213_curryI,axiom,
% 4.69/4.89 ! [F: produc2732055786443039994et_nat > $o,A2: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 4.69/4.89 ( ( F @ ( produc2245416461498447860et_nat @ A2 @ B ) )
% 4.69/4.89 => ( produc5101573711933517782_nat_o @ F @ A2 @ B ) ) ).
% 4.69/4.89
% 4.69/4.89 % curryI
% 4.69/4.89 thf(fact_214_insertCI,axiom,
% 4.69/4.89 ! [A2: produc3658429121746597890et_nat > $o,B4: set_Pr4532377907799695533_nat_o,B: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( ~ ( member6576561426505652726_nat_o @ A2 @ B4 )
% 4.69/4.89 => ( A2 = B ) )
% 4.69/4.89 => ( member6576561426505652726_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ B @ B4 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insertCI
% 4.69/4.89 thf(fact_215_insertCI,axiom,
% 4.69/4.89 ! [A2: nat,B4: set_nat,B: nat] :
% 4.69/4.89 ( ( ~ ( member_nat @ A2 @ B4 )
% 4.69/4.89 => ( A2 = B ) )
% 4.69/4.89 => ( member_nat @ A2 @ ( insert_nat @ B @ B4 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insertCI
% 4.69/4.89 thf(fact_216_insertCI,axiom,
% 4.69/4.89 ! [A2: int,B4: set_int,B: int] :
% 4.69/4.89 ( ( ~ ( member_int @ A2 @ B4 )
% 4.69/4.89 => ( A2 = B ) )
% 4.69/4.89 => ( member_int @ A2 @ ( insert_int @ B @ B4 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insertCI
% 4.69/4.89 thf(fact_217_insertCI,axiom,
% 4.69/4.89 ! [A2: $o,B4: set_o,B: $o] :
% 4.69/4.89 ( ( ~ ( member_o @ A2 @ B4 )
% 4.69/4.89 => ( A2 = B ) )
% 4.69/4.89 => ( member_o @ A2 @ ( insert_o @ B @ B4 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insertCI
% 4.69/4.89 thf(fact_218_insertCI,axiom,
% 4.69/4.89 ! [A2: product_unit,B4: set_Product_unit,B: product_unit] :
% 4.69/4.89 ( ( ~ ( member_Product_unit @ A2 @ B4 )
% 4.69/4.89 => ( A2 = B ) )
% 4.69/4.89 => ( member_Product_unit @ A2 @ ( insert_Product_unit @ B @ B4 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insertCI
% 4.69/4.89 thf(fact_219_insert__iff,axiom,
% 4.69/4.89 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.89 ( ( member6576561426505652726_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ B @ A ) )
% 4.69/4.89 = ( ( A2 = B )
% 4.69/4.89 | ( member6576561426505652726_nat_o @ A2 @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_iff
% 4.69/4.89 thf(fact_220_insert__iff,axiom,
% 4.69/4.89 ! [A2: nat,B: nat,A: set_nat] :
% 4.69/4.89 ( ( member_nat @ A2 @ ( insert_nat @ B @ A ) )
% 4.69/4.89 = ( ( A2 = B )
% 4.69/4.89 | ( member_nat @ A2 @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_iff
% 4.69/4.89 thf(fact_221_insert__iff,axiom,
% 4.69/4.89 ! [A2: int,B: int,A: set_int] :
% 4.69/4.89 ( ( member_int @ A2 @ ( insert_int @ B @ A ) )
% 4.69/4.89 = ( ( A2 = B )
% 4.69/4.89 | ( member_int @ A2 @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_iff
% 4.69/4.89 thf(fact_222_insert__iff,axiom,
% 4.69/4.89 ! [A2: $o,B: $o,A: set_o] :
% 4.69/4.89 ( ( member_o @ A2 @ ( insert_o @ B @ A ) )
% 4.69/4.89 = ( ( A2 = B )
% 4.69/4.89 | ( member_o @ A2 @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_iff
% 4.69/4.89 thf(fact_223_insert__iff,axiom,
% 4.69/4.89 ! [A2: product_unit,B: product_unit,A: set_Product_unit] :
% 4.69/4.89 ( ( member_Product_unit @ A2 @ ( insert_Product_unit @ B @ A ) )
% 4.69/4.89 = ( ( A2 = B )
% 4.69/4.89 | ( member_Product_unit @ A2 @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_iff
% 4.69/4.89 thf(fact_224_insert__absorb2,axiom,
% 4.69/4.89 ! [X: nat,A: set_nat] :
% 4.69/4.89 ( ( insert_nat @ X @ ( insert_nat @ X @ A ) )
% 4.69/4.89 = ( insert_nat @ X @ A ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_absorb2
% 4.69/4.89 thf(fact_225_insert__absorb2,axiom,
% 4.69/4.89 ! [X: int,A: set_int] :
% 4.69/4.89 ( ( insert_int @ X @ ( insert_int @ X @ A ) )
% 4.69/4.89 = ( insert_int @ X @ A ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_absorb2
% 4.69/4.89 thf(fact_226_insert__absorb2,axiom,
% 4.69/4.89 ! [X: $o,A: set_o] :
% 4.69/4.89 ( ( insert_o @ X @ ( insert_o @ X @ A ) )
% 4.69/4.89 = ( insert_o @ X @ A ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_absorb2
% 4.69/4.89 thf(fact_227_insert__absorb2,axiom,
% 4.69/4.89 ! [X: product_unit,A: set_Product_unit] :
% 4.69/4.89 ( ( insert_Product_unit @ X @ ( insert_Product_unit @ X @ A ) )
% 4.69/4.89 = ( insert_Product_unit @ X @ A ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_absorb2
% 4.69/4.89 thf(fact_228_singletonI,axiom,
% 4.69/4.89 ! [A2: product_unit] : ( member_Product_unit @ A2 @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.89
% 4.69/4.89 % singletonI
% 4.69/4.89 thf(fact_229_singletonI,axiom,
% 4.69/4.89 ! [A2: $o] : ( member_o @ A2 @ ( insert_o @ A2 @ bot_bot_set_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % singletonI
% 4.69/4.89 thf(fact_230_singletonI,axiom,
% 4.69/4.89 ! [A2: nat] : ( member_nat @ A2 @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) ).
% 4.69/4.89
% 4.69/4.89 % singletonI
% 4.69/4.89 thf(fact_231_singletonI,axiom,
% 4.69/4.89 ! [A2: int] : ( member_int @ A2 @ ( insert_int @ A2 @ bot_bot_set_int ) ) ).
% 4.69/4.89
% 4.69/4.89 % singletonI
% 4.69/4.89 thf(fact_232_singletonI,axiom,
% 4.69/4.89 ! [A2: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % singletonI
% 4.69/4.89 thf(fact_233_insertE,axiom,
% 4.69/4.89 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.89 ( ( member6576561426505652726_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ B @ A ) )
% 4.69/4.89 => ( ( A2 != B )
% 4.69/4.89 => ( member6576561426505652726_nat_o @ A2 @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insertE
% 4.69/4.89 thf(fact_234_insertE,axiom,
% 4.69/4.89 ! [A2: nat,B: nat,A: set_nat] :
% 4.69/4.89 ( ( member_nat @ A2 @ ( insert_nat @ B @ A ) )
% 4.69/4.89 => ( ( A2 != B )
% 4.69/4.89 => ( member_nat @ A2 @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insertE
% 4.69/4.89 thf(fact_235_insertE,axiom,
% 4.69/4.89 ! [A2: int,B: int,A: set_int] :
% 4.69/4.89 ( ( member_int @ A2 @ ( insert_int @ B @ A ) )
% 4.69/4.89 => ( ( A2 != B )
% 4.69/4.89 => ( member_int @ A2 @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insertE
% 4.69/4.89 thf(fact_236_insertE,axiom,
% 4.69/4.89 ! [A2: $o,B: $o,A: set_o] :
% 4.69/4.89 ( ( member_o @ A2 @ ( insert_o @ B @ A ) )
% 4.69/4.89 => ( ( A2 = ~ B )
% 4.69/4.89 => ( member_o @ A2 @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insertE
% 4.69/4.89 thf(fact_237_insertE,axiom,
% 4.69/4.89 ! [A2: product_unit,B: product_unit,A: set_Product_unit] :
% 4.69/4.89 ( ( member_Product_unit @ A2 @ ( insert_Product_unit @ B @ A ) )
% 4.69/4.89 => ( ( A2 != B )
% 4.69/4.89 => ( member_Product_unit @ A2 @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insertE
% 4.69/4.89 thf(fact_238_insertI1,axiom,
% 4.69/4.89 ! [A2: produc3658429121746597890et_nat > $o,B4: set_Pr4532377907799695533_nat_o] : ( member6576561426505652726_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ A2 @ B4 ) ) ).
% 4.69/4.89
% 4.69/4.89 % insertI1
% 4.69/4.89 thf(fact_239_insertI1,axiom,
% 4.69/4.89 ! [A2: nat,B4: set_nat] : ( member_nat @ A2 @ ( insert_nat @ A2 @ B4 ) ) ).
% 4.69/4.89
% 4.69/4.89 % insertI1
% 4.69/4.89 thf(fact_240_insertI1,axiom,
% 4.69/4.89 ! [A2: int,B4: set_int] : ( member_int @ A2 @ ( insert_int @ A2 @ B4 ) ) ).
% 4.69/4.89
% 4.69/4.89 % insertI1
% 4.69/4.89 thf(fact_241_insertI1,axiom,
% 4.69/4.89 ! [A2: $o,B4: set_o] : ( member_o @ A2 @ ( insert_o @ A2 @ B4 ) ) ).
% 4.69/4.89
% 4.69/4.89 % insertI1
% 4.69/4.89 thf(fact_242_insertI1,axiom,
% 4.69/4.89 ! [A2: product_unit,B4: set_Product_unit] : ( member_Product_unit @ A2 @ ( insert_Product_unit @ A2 @ B4 ) ) ).
% 4.69/4.89
% 4.69/4.89 % insertI1
% 4.69/4.89 thf(fact_243_insertI2,axiom,
% 4.69/4.89 ! [A2: produc3658429121746597890et_nat > $o,B4: set_Pr4532377907799695533_nat_o,B: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( member6576561426505652726_nat_o @ A2 @ B4 )
% 4.69/4.89 => ( member6576561426505652726_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ B @ B4 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insertI2
% 4.69/4.89 thf(fact_244_insertI2,axiom,
% 4.69/4.89 ! [A2: nat,B4: set_nat,B: nat] :
% 4.69/4.89 ( ( member_nat @ A2 @ B4 )
% 4.69/4.89 => ( member_nat @ A2 @ ( insert_nat @ B @ B4 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insertI2
% 4.69/4.89 thf(fact_245_insertI2,axiom,
% 4.69/4.89 ! [A2: int,B4: set_int,B: int] :
% 4.69/4.89 ( ( member_int @ A2 @ B4 )
% 4.69/4.89 => ( member_int @ A2 @ ( insert_int @ B @ B4 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insertI2
% 4.69/4.89 thf(fact_246_insertI2,axiom,
% 4.69/4.89 ! [A2: $o,B4: set_o,B: $o] :
% 4.69/4.89 ( ( member_o @ A2 @ B4 )
% 4.69/4.89 => ( member_o @ A2 @ ( insert_o @ B @ B4 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insertI2
% 4.69/4.89 thf(fact_247_insertI2,axiom,
% 4.69/4.89 ! [A2: product_unit,B4: set_Product_unit,B: product_unit] :
% 4.69/4.89 ( ( member_Product_unit @ A2 @ B4 )
% 4.69/4.89 => ( member_Product_unit @ A2 @ ( insert_Product_unit @ B @ B4 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insertI2
% 4.69/4.89 thf(fact_248_Set_Oset__insert,axiom,
% 4.69/4.89 ! [X: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.89 ( ( member6576561426505652726_nat_o @ X @ A )
% 4.69/4.89 => ~ ! [B5: set_Pr4532377907799695533_nat_o] :
% 4.69/4.89 ( ( A
% 4.69/4.89 = ( insert5175938949040314269_nat_o @ X @ B5 ) )
% 4.69/4.89 => ( member6576561426505652726_nat_o @ X @ B5 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Set.set_insert
% 4.69/4.89 thf(fact_249_Set_Oset__insert,axiom,
% 4.69/4.89 ! [X: nat,A: set_nat] :
% 4.69/4.89 ( ( member_nat @ X @ A )
% 4.69/4.89 => ~ ! [B5: set_nat] :
% 4.69/4.89 ( ( A
% 4.69/4.89 = ( insert_nat @ X @ B5 ) )
% 4.69/4.89 => ( member_nat @ X @ B5 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Set.set_insert
% 4.69/4.89 thf(fact_250_Set_Oset__insert,axiom,
% 4.69/4.89 ! [X: int,A: set_int] :
% 4.69/4.89 ( ( member_int @ X @ A )
% 4.69/4.89 => ~ ! [B5: set_int] :
% 4.69/4.89 ( ( A
% 4.69/4.89 = ( insert_int @ X @ B5 ) )
% 4.69/4.89 => ( member_int @ X @ B5 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Set.set_insert
% 4.69/4.89 thf(fact_251_Set_Oset__insert,axiom,
% 4.69/4.89 ! [X: $o,A: set_o] :
% 4.69/4.89 ( ( member_o @ X @ A )
% 4.69/4.89 => ~ ! [B5: set_o] :
% 4.69/4.89 ( ( A
% 4.69/4.89 = ( insert_o @ X @ B5 ) )
% 4.69/4.89 => ( member_o @ X @ B5 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Set.set_insert
% 4.69/4.89 thf(fact_252_Set_Oset__insert,axiom,
% 4.69/4.89 ! [X: product_unit,A: set_Product_unit] :
% 4.69/4.89 ( ( member_Product_unit @ X @ A )
% 4.69/4.89 => ~ ! [B5: set_Product_unit] :
% 4.69/4.89 ( ( A
% 4.69/4.89 = ( insert_Product_unit @ X @ B5 ) )
% 4.69/4.89 => ( member_Product_unit @ X @ B5 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % Set.set_insert
% 4.69/4.89 thf(fact_253_insert__ident,axiom,
% 4.69/4.89 ! [X: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.89 ( ~ ( member6576561426505652726_nat_o @ X @ A )
% 4.69/4.89 => ( ~ ( member6576561426505652726_nat_o @ X @ B4 )
% 4.69/4.89 => ( ( ( insert5175938949040314269_nat_o @ X @ A )
% 4.69/4.89 = ( insert5175938949040314269_nat_o @ X @ B4 ) )
% 4.69/4.89 = ( A = B4 ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_ident
% 4.69/4.89 thf(fact_254_insert__ident,axiom,
% 4.69/4.89 ! [X: nat,A: set_nat,B4: set_nat] :
% 4.69/4.89 ( ~ ( member_nat @ X @ A )
% 4.69/4.89 => ( ~ ( member_nat @ X @ B4 )
% 4.69/4.89 => ( ( ( insert_nat @ X @ A )
% 4.69/4.89 = ( insert_nat @ X @ B4 ) )
% 4.69/4.89 = ( A = B4 ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_ident
% 4.69/4.89 thf(fact_255_insert__ident,axiom,
% 4.69/4.89 ! [X: int,A: set_int,B4: set_int] :
% 4.69/4.89 ( ~ ( member_int @ X @ A )
% 4.69/4.89 => ( ~ ( member_int @ X @ B4 )
% 4.69/4.89 => ( ( ( insert_int @ X @ A )
% 4.69/4.89 = ( insert_int @ X @ B4 ) )
% 4.69/4.89 = ( A = B4 ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_ident
% 4.69/4.89 thf(fact_256_insert__ident,axiom,
% 4.69/4.89 ! [X: $o,A: set_o,B4: set_o] :
% 4.69/4.89 ( ~ ( member_o @ X @ A )
% 4.69/4.89 => ( ~ ( member_o @ X @ B4 )
% 4.69/4.89 => ( ( ( insert_o @ X @ A )
% 4.69/4.89 = ( insert_o @ X @ B4 ) )
% 4.69/4.89 = ( A = B4 ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_ident
% 4.69/4.89 thf(fact_257_insert__ident,axiom,
% 4.69/4.89 ! [X: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.89 ( ~ ( member_Product_unit @ X @ A )
% 4.69/4.89 => ( ~ ( member_Product_unit @ X @ B4 )
% 4.69/4.89 => ( ( ( insert_Product_unit @ X @ A )
% 4.69/4.89 = ( insert_Product_unit @ X @ B4 ) )
% 4.69/4.89 = ( A = B4 ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_ident
% 4.69/4.89 thf(fact_258_insert__absorb,axiom,
% 4.69/4.89 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.89 ( ( member6576561426505652726_nat_o @ A2 @ A )
% 4.69/4.89 => ( ( insert5175938949040314269_nat_o @ A2 @ A )
% 4.69/4.89 = A ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_absorb
% 4.69/4.89 thf(fact_259_insert__absorb,axiom,
% 4.69/4.89 ! [A2: nat,A: set_nat] :
% 4.69/4.89 ( ( member_nat @ A2 @ A )
% 4.69/4.89 => ( ( insert_nat @ A2 @ A )
% 4.69/4.89 = A ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_absorb
% 4.69/4.89 thf(fact_260_insert__absorb,axiom,
% 4.69/4.89 ! [A2: int,A: set_int] :
% 4.69/4.89 ( ( member_int @ A2 @ A )
% 4.69/4.89 => ( ( insert_int @ A2 @ A )
% 4.69/4.89 = A ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_absorb
% 4.69/4.89 thf(fact_261_insert__absorb,axiom,
% 4.69/4.89 ! [A2: $o,A: set_o] :
% 4.69/4.89 ( ( member_o @ A2 @ A )
% 4.69/4.89 => ( ( insert_o @ A2 @ A )
% 4.69/4.89 = A ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_absorb
% 4.69/4.89 thf(fact_262_insert__absorb,axiom,
% 4.69/4.89 ! [A2: product_unit,A: set_Product_unit] :
% 4.69/4.89 ( ( member_Product_unit @ A2 @ A )
% 4.69/4.89 => ( ( insert_Product_unit @ A2 @ A )
% 4.69/4.89 = A ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_absorb
% 4.69/4.89 thf(fact_263_insert__eq__iff,axiom,
% 4.69/4.89 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: produc3658429121746597890et_nat > $o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.89 ( ~ ( member6576561426505652726_nat_o @ A2 @ A )
% 4.69/4.89 => ( ~ ( member6576561426505652726_nat_o @ B @ B4 )
% 4.69/4.89 => ( ( ( insert5175938949040314269_nat_o @ A2 @ A )
% 4.69/4.89 = ( insert5175938949040314269_nat_o @ B @ B4 ) )
% 4.69/4.89 = ( ( ( A2 = B )
% 4.69/4.89 => ( A = B4 ) )
% 4.69/4.89 & ( ( A2 != B )
% 4.69/4.89 => ? [C3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.89 ( ( A
% 4.69/4.89 = ( insert5175938949040314269_nat_o @ B @ C3 ) )
% 4.69/4.89 & ~ ( member6576561426505652726_nat_o @ B @ C3 )
% 4.69/4.89 & ( B4
% 4.69/4.89 = ( insert5175938949040314269_nat_o @ A2 @ C3 ) )
% 4.69/4.89 & ~ ( member6576561426505652726_nat_o @ A2 @ C3 ) ) ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_eq_iff
% 4.69/4.89 thf(fact_264_insert__eq__iff,axiom,
% 4.69/4.89 ! [A2: nat,A: set_nat,B: nat,B4: set_nat] :
% 4.69/4.89 ( ~ ( member_nat @ A2 @ A )
% 4.69/4.89 => ( ~ ( member_nat @ B @ B4 )
% 4.69/4.89 => ( ( ( insert_nat @ A2 @ A )
% 4.69/4.89 = ( insert_nat @ B @ B4 ) )
% 4.69/4.89 = ( ( ( A2 = B )
% 4.69/4.89 => ( A = B4 ) )
% 4.69/4.89 & ( ( A2 != B )
% 4.69/4.89 => ? [C3: set_nat] :
% 4.69/4.89 ( ( A
% 4.69/4.89 = ( insert_nat @ B @ C3 ) )
% 4.69/4.89 & ~ ( member_nat @ B @ C3 )
% 4.69/4.89 & ( B4
% 4.69/4.89 = ( insert_nat @ A2 @ C3 ) )
% 4.69/4.89 & ~ ( member_nat @ A2 @ C3 ) ) ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_eq_iff
% 4.69/4.89 thf(fact_265_insert__eq__iff,axiom,
% 4.69/4.89 ! [A2: int,A: set_int,B: int,B4: set_int] :
% 4.69/4.89 ( ~ ( member_int @ A2 @ A )
% 4.69/4.89 => ( ~ ( member_int @ B @ B4 )
% 4.69/4.89 => ( ( ( insert_int @ A2 @ A )
% 4.69/4.89 = ( insert_int @ B @ B4 ) )
% 4.69/4.89 = ( ( ( A2 = B )
% 4.69/4.89 => ( A = B4 ) )
% 4.69/4.89 & ( ( A2 != B )
% 4.69/4.89 => ? [C3: set_int] :
% 4.69/4.89 ( ( A
% 4.69/4.89 = ( insert_int @ B @ C3 ) )
% 4.69/4.89 & ~ ( member_int @ B @ C3 )
% 4.69/4.89 & ( B4
% 4.69/4.89 = ( insert_int @ A2 @ C3 ) )
% 4.69/4.89 & ~ ( member_int @ A2 @ C3 ) ) ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_eq_iff
% 4.69/4.89 thf(fact_266_insert__eq__iff,axiom,
% 4.69/4.89 ! [A2: $o,A: set_o,B: $o,B4: set_o] :
% 4.69/4.89 ( ~ ( member_o @ A2 @ A )
% 4.69/4.89 => ( ~ ( member_o @ B @ B4 )
% 4.69/4.89 => ( ( ( insert_o @ A2 @ A )
% 4.69/4.89 = ( insert_o @ B @ B4 ) )
% 4.69/4.89 = ( ( ( A2 = B )
% 4.69/4.89 => ( A = B4 ) )
% 4.69/4.89 & ( ( A2 = ~ B )
% 4.69/4.89 => ? [C3: set_o] :
% 4.69/4.89 ( ( A
% 4.69/4.89 = ( insert_o @ B @ C3 ) )
% 4.69/4.89 & ~ ( member_o @ B @ C3 )
% 4.69/4.89 & ( B4
% 4.69/4.89 = ( insert_o @ A2 @ C3 ) )
% 4.69/4.89 & ~ ( member_o @ A2 @ C3 ) ) ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_eq_iff
% 4.69/4.89 thf(fact_267_insert__eq__iff,axiom,
% 4.69/4.89 ! [A2: product_unit,A: set_Product_unit,B: product_unit,B4: set_Product_unit] :
% 4.69/4.89 ( ~ ( member_Product_unit @ A2 @ A )
% 4.69/4.89 => ( ~ ( member_Product_unit @ B @ B4 )
% 4.69/4.89 => ( ( ( insert_Product_unit @ A2 @ A )
% 4.69/4.89 = ( insert_Product_unit @ B @ B4 ) )
% 4.69/4.89 = ( ( ( A2 = B )
% 4.69/4.89 => ( A = B4 ) )
% 4.69/4.89 & ( ( A2 != B )
% 4.69/4.89 => ? [C3: set_Product_unit] :
% 4.69/4.89 ( ( A
% 4.69/4.89 = ( insert_Product_unit @ B @ C3 ) )
% 4.69/4.89 & ~ ( member_Product_unit @ B @ C3 )
% 4.69/4.89 & ( B4
% 4.69/4.89 = ( insert_Product_unit @ A2 @ C3 ) )
% 4.69/4.89 & ~ ( member_Product_unit @ A2 @ C3 ) ) ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_eq_iff
% 4.69/4.89 thf(fact_268_insert__commute,axiom,
% 4.69/4.89 ! [X: nat,Y: nat,A: set_nat] :
% 4.69/4.89 ( ( insert_nat @ X @ ( insert_nat @ Y @ A ) )
% 4.69/4.89 = ( insert_nat @ Y @ ( insert_nat @ X @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_commute
% 4.69/4.89 thf(fact_269_insert__commute,axiom,
% 4.69/4.89 ! [X: int,Y: int,A: set_int] :
% 4.69/4.89 ( ( insert_int @ X @ ( insert_int @ Y @ A ) )
% 4.69/4.89 = ( insert_int @ Y @ ( insert_int @ X @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_commute
% 4.69/4.89 thf(fact_270_insert__commute,axiom,
% 4.69/4.89 ! [X: $o,Y: $o,A: set_o] :
% 4.69/4.89 ( ( insert_o @ X @ ( insert_o @ Y @ A ) )
% 4.69/4.89 = ( insert_o @ Y @ ( insert_o @ X @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_commute
% 4.69/4.89 thf(fact_271_insert__commute,axiom,
% 4.69/4.89 ! [X: product_unit,Y: product_unit,A: set_Product_unit] :
% 4.69/4.89 ( ( insert_Product_unit @ X @ ( insert_Product_unit @ Y @ A ) )
% 4.69/4.89 = ( insert_Product_unit @ Y @ ( insert_Product_unit @ X @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % insert_commute
% 4.69/4.89 thf(fact_272_mk__disjoint__insert,axiom,
% 4.69/4.89 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.89 ( ( member6576561426505652726_nat_o @ A2 @ A )
% 4.69/4.89 => ? [B5: set_Pr4532377907799695533_nat_o] :
% 4.69/4.89 ( ( A
% 4.69/4.89 = ( insert5175938949040314269_nat_o @ A2 @ B5 ) )
% 4.69/4.89 & ~ ( member6576561426505652726_nat_o @ A2 @ B5 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % mk_disjoint_insert
% 4.69/4.89 thf(fact_273_mk__disjoint__insert,axiom,
% 4.69/4.89 ! [A2: nat,A: set_nat] :
% 4.69/4.89 ( ( member_nat @ A2 @ A )
% 4.69/4.89 => ? [B5: set_nat] :
% 4.69/4.89 ( ( A
% 4.69/4.89 = ( insert_nat @ A2 @ B5 ) )
% 4.69/4.89 & ~ ( member_nat @ A2 @ B5 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % mk_disjoint_insert
% 4.69/4.89 thf(fact_274_mk__disjoint__insert,axiom,
% 4.69/4.89 ! [A2: int,A: set_int] :
% 4.69/4.89 ( ( member_int @ A2 @ A )
% 4.69/4.89 => ? [B5: set_int] :
% 4.69/4.89 ( ( A
% 4.69/4.89 = ( insert_int @ A2 @ B5 ) )
% 4.69/4.89 & ~ ( member_int @ A2 @ B5 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % mk_disjoint_insert
% 4.69/4.89 thf(fact_275_mk__disjoint__insert,axiom,
% 4.69/4.89 ! [A2: $o,A: set_o] :
% 4.69/4.89 ( ( member_o @ A2 @ A )
% 4.69/4.89 => ? [B5: set_o] :
% 4.69/4.89 ( ( A
% 4.69/4.89 = ( insert_o @ A2 @ B5 ) )
% 4.69/4.89 & ~ ( member_o @ A2 @ B5 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % mk_disjoint_insert
% 4.69/4.89 thf(fact_276_mk__disjoint__insert,axiom,
% 4.69/4.89 ! [A2: product_unit,A: set_Product_unit] :
% 4.69/4.89 ( ( member_Product_unit @ A2 @ A )
% 4.69/4.89 => ? [B5: set_Product_unit] :
% 4.69/4.89 ( ( A
% 4.69/4.89 = ( insert_Product_unit @ A2 @ B5 ) )
% 4.69/4.89 & ~ ( member_Product_unit @ A2 @ B5 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % mk_disjoint_insert
% 4.69/4.89 thf(fact_277_singletonD,axiom,
% 4.69/4.89 ! [B: product_unit,A2: product_unit] :
% 4.69/4.89 ( ( member_Product_unit @ B @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.89 => ( B = A2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % singletonD
% 4.69/4.89 thf(fact_278_singletonD,axiom,
% 4.69/4.89 ! [B: $o,A2: $o] :
% 4.69/4.89 ( ( member_o @ B @ ( insert_o @ A2 @ bot_bot_set_o ) )
% 4.69/4.89 => ( B = A2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % singletonD
% 4.69/4.89 thf(fact_279_singletonD,axiom,
% 4.69/4.89 ! [B: nat,A2: nat] :
% 4.69/4.89 ( ( member_nat @ B @ ( insert_nat @ A2 @ bot_bot_set_nat ) )
% 4.69/4.89 => ( B = A2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % singletonD
% 4.69/4.89 thf(fact_280_singletonD,axiom,
% 4.69/4.89 ! [B: int,A2: int] :
% 4.69/4.89 ( ( member_int @ B @ ( insert_int @ A2 @ bot_bot_set_int ) )
% 4.69/4.89 => ( B = A2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % singletonD
% 4.69/4.89 thf(fact_281_singletonD,axiom,
% 4.69/4.89 ! [B: produc3658429121746597890et_nat > $o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( member6576561426505652726_nat_o @ B @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.89 => ( B = A2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % singletonD
% 4.69/4.89 thf(fact_282_singleton__iff,axiom,
% 4.69/4.89 ! [B: product_unit,A2: product_unit] :
% 4.69/4.89 ( ( member_Product_unit @ B @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.89 = ( B = A2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % singleton_iff
% 4.69/4.89 thf(fact_283_singleton__iff,axiom,
% 4.69/4.89 ! [B: $o,A2: $o] :
% 4.69/4.89 ( ( member_o @ B @ ( insert_o @ A2 @ bot_bot_set_o ) )
% 4.69/4.89 = ( B = A2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % singleton_iff
% 4.69/4.89 thf(fact_284_singleton__iff,axiom,
% 4.69/4.89 ! [B: nat,A2: nat] :
% 4.69/4.89 ( ( member_nat @ B @ ( insert_nat @ A2 @ bot_bot_set_nat ) )
% 4.69/4.89 = ( B = A2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % singleton_iff
% 4.69/4.89 thf(fact_285_singleton__iff,axiom,
% 4.69/4.89 ! [B: int,A2: int] :
% 4.69/4.89 ( ( member_int @ B @ ( insert_int @ A2 @ bot_bot_set_int ) )
% 4.69/4.89 = ( B = A2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % singleton_iff
% 4.69/4.89 thf(fact_286_singleton__iff,axiom,
% 4.69/4.89 ! [B: produc3658429121746597890et_nat > $o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( member6576561426505652726_nat_o @ B @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.89 = ( B = A2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % singleton_iff
% 4.69/4.89 thf(fact_287_doubleton__eq__iff,axiom,
% 4.69/4.89 ! [A2: product_unit,B: product_unit,C: product_unit,D2: product_unit] :
% 4.69/4.89 ( ( ( insert_Product_unit @ A2 @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.89 = ( insert_Product_unit @ C @ ( insert_Product_unit @ D2 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.89 = ( ( ( A2 = C )
% 4.69/4.89 & ( B = D2 ) )
% 4.69/4.89 | ( ( A2 = D2 )
% 4.69/4.89 & ( B = C ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % doubleton_eq_iff
% 4.69/4.89 thf(fact_288_doubleton__eq__iff,axiom,
% 4.69/4.89 ! [A2: $o,B: $o,C: $o,D2: $o] :
% 4.69/4.89 ( ( ( insert_o @ A2 @ ( insert_o @ B @ bot_bot_set_o ) )
% 4.69/4.89 = ( insert_o @ C @ ( insert_o @ D2 @ bot_bot_set_o ) ) )
% 4.69/4.89 = ( ( ( A2 = C )
% 4.69/4.89 & ( B = D2 ) )
% 4.69/4.89 | ( ( A2 = D2 )
% 4.69/4.89 & ( B = C ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % doubleton_eq_iff
% 4.69/4.89 thf(fact_289_doubleton__eq__iff,axiom,
% 4.69/4.89 ! [A2: nat,B: nat,C: nat,D2: nat] :
% 4.69/4.89 ( ( ( insert_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) )
% 4.69/4.89 = ( insert_nat @ C @ ( insert_nat @ D2 @ bot_bot_set_nat ) ) )
% 4.69/4.89 = ( ( ( A2 = C )
% 4.69/4.89 & ( B = D2 ) )
% 4.69/4.89 | ( ( A2 = D2 )
% 4.69/4.89 & ( B = C ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % doubleton_eq_iff
% 4.69/4.89 thf(fact_290_doubleton__eq__iff,axiom,
% 4.69/4.89 ! [A2: int,B: int,C: int,D2: int] :
% 4.69/4.89 ( ( ( insert_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) )
% 4.69/4.89 = ( insert_int @ C @ ( insert_int @ D2 @ bot_bot_set_int ) ) )
% 4.69/4.89 = ( ( ( A2 = C )
% 4.69/4.89 & ( B = D2 ) )
% 4.69/4.89 | ( ( A2 = D2 )
% 4.69/4.89 & ( B = C ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % doubleton_eq_iff
% 4.69/4.89 thf(fact_291_doubleton__eq__iff,axiom,
% 4.69/4.89 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o,C: produc3658429121746597890et_nat > $o,D2: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( ( insert5175938949040314269_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.89 = ( insert5175938949040314269_nat_o @ C @ ( insert5175938949040314269_nat_o @ D2 @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/4.89 = ( ( ( A2 = C )
% 4.69/4.89 & ( B = D2 ) )
% 4.69/4.89 | ( ( A2 = D2 )
% 4.69/4.89 & ( B = C ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % doubleton_eq_iff
% 4.69/4.89 thf(fact_292_insert__not__empty,axiom,
% 4.69/4.89 ! [A2: product_unit,A: set_Product_unit] :
% 4.69/4.89 ( ( insert_Product_unit @ A2 @ A )
% 4.69/4.89 != bot_bo3957492148770167129t_unit ) ).
% 4.69/4.89
% 4.69/4.89 % insert_not_empty
% 4.69/4.89 thf(fact_293_insert__not__empty,axiom,
% 4.69/4.89 ! [A2: $o,A: set_o] :
% 4.69/4.89 ( ( insert_o @ A2 @ A )
% 4.69/4.89 != bot_bot_set_o ) ).
% 4.69/4.89
% 4.69/4.89 % insert_not_empty
% 4.69/4.89 thf(fact_294_insert__not__empty,axiom,
% 4.69/4.89 ! [A2: nat,A: set_nat] :
% 4.69/4.89 ( ( insert_nat @ A2 @ A )
% 4.69/4.89 != bot_bot_set_nat ) ).
% 4.69/4.89
% 4.69/4.89 % insert_not_empty
% 4.69/4.89 thf(fact_295_insert__not__empty,axiom,
% 4.69/4.89 ! [A2: int,A: set_int] :
% 4.69/4.89 ( ( insert_int @ A2 @ A )
% 4.69/4.89 != bot_bot_set_int ) ).
% 4.69/4.89
% 4.69/4.89 % insert_not_empty
% 4.69/4.89 thf(fact_296_insert__not__empty,axiom,
% 4.69/4.89 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.89 ( ( insert5175938949040314269_nat_o @ A2 @ A )
% 4.69/4.89 != bot_bo7824918357723582233_nat_o ) ).
% 4.69/4.89
% 4.69/4.89 % insert_not_empty
% 4.69/4.89 thf(fact_297_singleton__inject,axiom,
% 4.69/4.89 ! [A2: product_unit,B: product_unit] :
% 4.69/4.89 ( ( ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit )
% 4.69/4.89 = ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.89 => ( A2 = B ) ) ).
% 4.69/4.89
% 4.69/4.89 % singleton_inject
% 4.69/4.89 thf(fact_298_singleton__inject,axiom,
% 4.69/4.89 ! [A2: $o,B: $o] :
% 4.69/4.89 ( ( ( insert_o @ A2 @ bot_bot_set_o )
% 4.69/4.89 = ( insert_o @ B @ bot_bot_set_o ) )
% 4.69/4.89 => ( A2 = B ) ) ).
% 4.69/4.89
% 4.69/4.89 % singleton_inject
% 4.69/4.89 thf(fact_299_singleton__inject,axiom,
% 4.69/4.89 ! [A2: nat,B: nat] :
% 4.69/4.89 ( ( ( insert_nat @ A2 @ bot_bot_set_nat )
% 4.69/4.89 = ( insert_nat @ B @ bot_bot_set_nat ) )
% 4.69/4.89 => ( A2 = B ) ) ).
% 4.69/4.89
% 4.69/4.89 % singleton_inject
% 4.69/4.89 thf(fact_300_singleton__inject,axiom,
% 4.69/4.89 ! [A2: int,B: int] :
% 4.69/4.89 ( ( ( insert_int @ A2 @ bot_bot_set_int )
% 4.69/4.89 = ( insert_int @ B @ bot_bot_set_int ) )
% 4.69/4.89 => ( A2 = B ) ) ).
% 4.69/4.89
% 4.69/4.89 % singleton_inject
% 4.69/4.89 thf(fact_301_singleton__inject,axiom,
% 4.69/4.89 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o )
% 4.69/4.89 = ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.89 => ( A2 = B ) ) ).
% 4.69/4.89
% 4.69/4.89 % singleton_inject
% 4.69/4.89 thf(fact_302_curryE,axiom,
% 4.69/4.89 ! [F: produc3658429121746597890et_nat > $o,A2: heap_e7401611519738050253t_unit,B: set_nat] :
% 4.69/4.89 ( ( produc1807123492089482958_nat_o @ F @ A2 @ B )
% 4.69/4.89 => ( F @ ( produc7507926704131184380et_nat @ A2 @ B ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % curryE
% 4.69/4.89 thf(fact_303_curryE,axiom,
% 4.69/4.89 ! [F: product_prod_nat_nat > $o,A2: nat,B: nat] :
% 4.69/4.89 ( ( produc1310100445399344235_nat_o @ F @ A2 @ B )
% 4.69/4.89 => ( F @ ( product_Pair_nat_nat @ A2 @ B ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % curryE
% 4.69/4.89 thf(fact_304_curryE,axiom,
% 4.69/4.89 ! [F: product_prod_int_int > $o,A2: int,B: int] :
% 4.69/4.89 ( ( produc175634133007206835_int_o @ F @ A2 @ B )
% 4.69/4.89 => ( F @ ( product_Pair_int_int @ A2 @ B ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % curryE
% 4.69/4.89 thf(fact_305_curryE,axiom,
% 4.69/4.89 ! [F: produc3925858234332021118et_nat > $o,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ( produc6216949301066131538_nat_o @ F @ A2 @ B )
% 4.69/4.89 => ( F @ ( produc5001842942810119800et_nat @ A2 @ B ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % curryE
% 4.69/4.89 thf(fact_306_curryE,axiom,
% 4.69/4.89 ! [F: produc2732055786443039994et_nat > $o,A2: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 4.69/4.89 ( ( produc5101573711933517782_nat_o @ F @ A2 @ B )
% 4.69/4.89 => ( F @ ( produc2245416461498447860et_nat @ A2 @ B ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % curryE
% 4.69/4.89 thf(fact_307_curryD,axiom,
% 4.69/4.89 ! [F: produc3658429121746597890et_nat > $o,A2: heap_e7401611519738050253t_unit,B: set_nat] :
% 4.69/4.89 ( ( produc1807123492089482958_nat_o @ F @ A2 @ B )
% 4.69/4.89 => ( F @ ( produc7507926704131184380et_nat @ A2 @ B ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % curryD
% 4.69/4.89 thf(fact_308_curryD,axiom,
% 4.69/4.89 ! [F: product_prod_nat_nat > $o,A2: nat,B: nat] :
% 4.69/4.89 ( ( produc1310100445399344235_nat_o @ F @ A2 @ B )
% 4.69/4.89 => ( F @ ( product_Pair_nat_nat @ A2 @ B ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % curryD
% 4.69/4.89 thf(fact_309_curryD,axiom,
% 4.69/4.89 ! [F: product_prod_int_int > $o,A2: int,B: int] :
% 4.69/4.89 ( ( produc175634133007206835_int_o @ F @ A2 @ B )
% 4.69/4.89 => ( F @ ( product_Pair_int_int @ A2 @ B ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % curryD
% 4.69/4.89 thf(fact_310_curryD,axiom,
% 4.69/4.89 ! [F: produc3925858234332021118et_nat > $o,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ( produc6216949301066131538_nat_o @ F @ A2 @ B )
% 4.69/4.89 => ( F @ ( produc5001842942810119800et_nat @ A2 @ B ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % curryD
% 4.69/4.89 thf(fact_311_curryD,axiom,
% 4.69/4.89 ! [F: produc2732055786443039994et_nat > $o,A2: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 4.69/4.89 ( ( produc5101573711933517782_nat_o @ F @ A2 @ B )
% 4.69/4.89 => ( F @ ( produc2245416461498447860et_nat @ A2 @ B ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % curryD
% 4.69/4.89 thf(fact_312_is__singleton__def,axiom,
% 4.69/4.89 ( is_sin2160648248035936513t_unit
% 4.69/4.89 = ( ^ [A3: set_Product_unit] :
% 4.69/4.89 ? [X2: product_unit] :
% 4.69/4.89 ( A3
% 4.69/4.89 = ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singleton_def
% 4.69/4.89 thf(fact_313_is__singleton__def,axiom,
% 4.69/4.89 ( is_singleton_o
% 4.69/4.89 = ( ^ [A3: set_o] :
% 4.69/4.89 ? [X2: $o] :
% 4.69/4.89 ( A3
% 4.69/4.89 = ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singleton_def
% 4.69/4.89 thf(fact_314_is__singleton__def,axiom,
% 4.69/4.89 ( is_singleton_nat
% 4.69/4.89 = ( ^ [A3: set_nat] :
% 4.69/4.89 ? [X2: nat] :
% 4.69/4.89 ( A3
% 4.69/4.89 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singleton_def
% 4.69/4.89 thf(fact_315_is__singleton__def,axiom,
% 4.69/4.89 ( is_singleton_int
% 4.69/4.89 = ( ^ [A3: set_int] :
% 4.69/4.89 ? [X2: int] :
% 4.69/4.89 ( A3
% 4.69/4.89 = ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singleton_def
% 4.69/4.89 thf(fact_316_is__singleton__def,axiom,
% 4.69/4.89 ( is_sin5180296473474724033_nat_o
% 4.69/4.89 = ( ^ [A3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.89 ? [X2: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( A3
% 4.69/4.89 = ( insert5175938949040314269_nat_o @ X2 @ bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singleton_def
% 4.69/4.89 thf(fact_317_is__singletonE,axiom,
% 4.69/4.89 ! [A: set_Product_unit] :
% 4.69/4.89 ( ( is_sin2160648248035936513t_unit @ A )
% 4.69/4.89 => ~ ! [X3: product_unit] :
% 4.69/4.89 ( A
% 4.69/4.89 != ( insert_Product_unit @ X3 @ bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singletonE
% 4.69/4.89 thf(fact_318_is__singletonE,axiom,
% 4.69/4.89 ! [A: set_o] :
% 4.69/4.89 ( ( is_singleton_o @ A )
% 4.69/4.89 => ~ ! [X3: $o] :
% 4.69/4.89 ( A
% 4.69/4.89 != ( insert_o @ X3 @ bot_bot_set_o ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singletonE
% 4.69/4.89 thf(fact_319_is__singletonE,axiom,
% 4.69/4.89 ! [A: set_nat] :
% 4.69/4.89 ( ( is_singleton_nat @ A )
% 4.69/4.89 => ~ ! [X3: nat] :
% 4.69/4.89 ( A
% 4.69/4.89 != ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singletonE
% 4.69/4.89 thf(fact_320_is__singletonE,axiom,
% 4.69/4.89 ! [A: set_int] :
% 4.69/4.89 ( ( is_singleton_int @ A )
% 4.69/4.89 => ~ ! [X3: int] :
% 4.69/4.89 ( A
% 4.69/4.89 != ( insert_int @ X3 @ bot_bot_set_int ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singletonE
% 4.69/4.89 thf(fact_321_is__singletonE,axiom,
% 4.69/4.89 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.89 ( ( is_sin5180296473474724033_nat_o @ A )
% 4.69/4.89 => ~ ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( A
% 4.69/4.89 != ( insert5175938949040314269_nat_o @ X3 @ bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singletonE
% 4.69/4.89 thf(fact_322_is__pure__assn__basic__simps_I1_J,axiom,
% 4.69/4.89 is_pure_assn @ bot_bot_assn ).
% 4.69/4.89
% 4.69/4.89 % is_pure_assn_basic_simps(1)
% 4.69/4.89 thf(fact_323_is__singleton__the__elem,axiom,
% 4.69/4.89 ( is_sin2160648248035936513t_unit
% 4.69/4.89 = ( ^ [A3: set_Product_unit] :
% 4.69/4.89 ( A3
% 4.69/4.89 = ( insert_Product_unit @ ( the_el608902216710161154t_unit @ A3 ) @ bot_bo3957492148770167129t_unit ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singleton_the_elem
% 4.69/4.89 thf(fact_324_is__singleton__the__elem,axiom,
% 4.69/4.89 ( is_singleton_o
% 4.69/4.89 = ( ^ [A3: set_o] :
% 4.69/4.89 ( A3
% 4.69/4.89 = ( insert_o @ ( the_elem_o @ A3 ) @ bot_bot_set_o ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singleton_the_elem
% 4.69/4.89 thf(fact_325_is__singleton__the__elem,axiom,
% 4.69/4.89 ( is_singleton_nat
% 4.69/4.89 = ( ^ [A3: set_nat] :
% 4.69/4.89 ( A3
% 4.69/4.89 = ( insert_nat @ ( the_elem_nat @ A3 ) @ bot_bot_set_nat ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singleton_the_elem
% 4.69/4.89 thf(fact_326_is__singleton__the__elem,axiom,
% 4.69/4.89 ( is_singleton_int
% 4.69/4.89 = ( ^ [A3: set_int] :
% 4.69/4.89 ( A3
% 4.69/4.89 = ( insert_int @ ( the_elem_int @ A3 ) @ bot_bot_set_int ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singleton_the_elem
% 4.69/4.89 thf(fact_327_is__singleton__the__elem,axiom,
% 4.69/4.89 ( is_sin5180296473474724033_nat_o
% 4.69/4.89 = ( ^ [A3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.89 ( A3
% 4.69/4.89 = ( insert5175938949040314269_nat_o @ ( the_el5959152443890766018_nat_o @ A3 ) @ bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_singleton_the_elem
% 4.69/4.89 thf(fact_328_the__elem__eq,axiom,
% 4.69/4.89 ! [X: product_unit] :
% 4.69/4.89 ( ( the_el608902216710161154t_unit @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.89 = X ) ).
% 4.69/4.89
% 4.69/4.89 % the_elem_eq
% 4.69/4.89 thf(fact_329_the__elem__eq,axiom,
% 4.69/4.89 ! [X: $o] :
% 4.69/4.89 ( ( the_elem_o @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.89 = X ) ).
% 4.69/4.89
% 4.69/4.89 % the_elem_eq
% 4.69/4.89 thf(fact_330_the__elem__eq,axiom,
% 4.69/4.89 ! [X: nat] :
% 4.69/4.89 ( ( the_elem_nat @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.89 = X ) ).
% 4.69/4.89
% 4.69/4.89 % the_elem_eq
% 4.69/4.89 thf(fact_331_the__elem__eq,axiom,
% 4.69/4.89 ! [X: int] :
% 4.69/4.89 ( ( the_elem_int @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.89 = X ) ).
% 4.69/4.89
% 4.69/4.89 % the_elem_eq
% 4.69/4.89 thf(fact_332_the__elem__eq,axiom,
% 4.69/4.89 ! [X: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( the_el5959152443890766018_nat_o @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.89 = X ) ).
% 4.69/4.89
% 4.69/4.89 % the_elem_eq
% 4.69/4.89 thf(fact_333_pure__assn__def,axiom,
% 4.69/4.89 ( pure_assn
% 4.69/4.89 = ( ^ [B6: $o] : ( abs_assn @ ( pure_a825153325127701367it_nat @ B6 ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % pure_assn_def
% 4.69/4.89 thf(fact_334_times__assn__def,axiom,
% 4.69/4.89 ( times_times_assn
% 4.69/4.89 = ( ^ [P2: assn,Q: assn] : ( abs_assn @ ( times_assn_raw @ ( rep_assn @ P2 ) @ ( rep_assn @ Q ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % times_assn_def
% 4.69/4.89 thf(fact_335_type__definition__def,axiom,
% 4.69/4.89 ( type_d3909072315231072503_nat_o
% 4.69/4.89 = ( ^ [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,A3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.89 ( ! [X2: assn] : ( member6576561426505652726_nat_o @ ( Rep @ X2 ) @ A3 )
% 4.69/4.89 & ! [X2: assn] :
% 4.69/4.89 ( ( Abs @ ( Rep @ X2 ) )
% 4.69/4.89 = X2 )
% 4.69/4.89 & ! [Y3: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( member6576561426505652726_nat_o @ Y3 @ A3 )
% 4.69/4.89 => ( ( Rep @ ( Abs @ Y3 ) )
% 4.69/4.89 = Y3 ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition_def
% 4.69/4.89 thf(fact_336_type__definition__def,axiom,
% 4.69/4.89 ( type_d8366093980585677751er_int
% 4.69/4.89 = ( ^ [Rep: code_integer > int,Abs: int > code_integer,A3: set_int] :
% 4.69/4.89 ( ! [X2: code_integer] : ( member_int @ ( Rep @ X2 ) @ A3 )
% 4.69/4.89 & ! [X2: code_integer] :
% 4.69/4.89 ( ( Abs @ ( Rep @ X2 ) )
% 4.69/4.89 = X2 )
% 4.69/4.89 & ! [Y3: int] :
% 4.69/4.89 ( ( member_int @ Y3 @ A3 )
% 4.69/4.89 => ( ( Rep @ ( Abs @ Y3 ) )
% 4.69/4.89 = Y3 ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition_def
% 4.69/4.89 thf(fact_337_type__definition__def,axiom,
% 4.69/4.89 ( type_d6188575255521822967unit_o
% 4.69/4.89 = ( ^ [Rep: product_unit > $o,Abs: $o > product_unit,A3: set_o] :
% 4.69/4.89 ( ! [X2: product_unit] : ( member_o @ ( Rep @ X2 ) @ A3 )
% 4.69/4.89 & ! [X2: product_unit] :
% 4.69/4.89 ( ( Abs @ ( Rep @ X2 ) )
% 4.69/4.89 = X2 )
% 4.69/4.89 & ! [Y3: $o] :
% 4.69/4.89 ( ( member_o @ Y3 @ A3 )
% 4.69/4.89 => ( ( Rep @ ( Abs @ Y3 ) )
% 4.69/4.89 = Y3 ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition_def
% 4.69/4.89 thf(fact_338_type__definition__def,axiom,
% 4.69/4.89 ( type_d4410041424927559462al_nat
% 4.69/4.89 = ( ^ [Rep: code_natural > nat,Abs: nat > code_natural,A3: set_nat] :
% 4.69/4.89 ( ! [X2: code_natural] : ( member_nat @ ( Rep @ X2 ) @ A3 )
% 4.69/4.89 & ! [X2: code_natural] :
% 4.69/4.89 ( ( Abs @ ( Rep @ X2 ) )
% 4.69/4.89 = X2 )
% 4.69/4.89 & ! [Y3: nat] :
% 4.69/4.89 ( ( member_nat @ Y3 @ A3 )
% 4.69/4.89 => ( ( Rep @ ( Abs @ Y3 ) )
% 4.69/4.89 = Y3 ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition_def
% 4.69/4.89 thf(fact_339_type__definition_ORep__inverse,axiom,
% 4.69/4.89 ! [Rep2: assn > produc3658429121746597890et_nat > $o,Abs2: ( produc3658429121746597890et_nat > $o ) > assn,A: set_Pr4532377907799695533_nat_o,X: assn] :
% 4.69/4.89 ( ( type_d3909072315231072503_nat_o @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( Abs2 @ ( Rep2 @ X ) )
% 4.69/4.89 = X ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Rep_inverse
% 4.69/4.89 thf(fact_340_type__definition_ORep__inverse,axiom,
% 4.69/4.89 ! [Rep2: code_integer > int,Abs2: int > code_integer,A: set_int,X: code_integer] :
% 4.69/4.89 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( Abs2 @ ( Rep2 @ X ) )
% 4.69/4.89 = X ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Rep_inverse
% 4.69/4.89 thf(fact_341_type__definition_ORep__inverse,axiom,
% 4.69/4.89 ! [Rep2: product_unit > $o,Abs2: $o > product_unit,A: set_o,X: product_unit] :
% 4.69/4.89 ( ( type_d6188575255521822967unit_o @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( Abs2 @ ( Rep2 @ X ) )
% 4.69/4.89 = X ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Rep_inverse
% 4.69/4.89 thf(fact_342_type__definition_ORep__inverse,axiom,
% 4.69/4.89 ! [Rep2: code_natural > nat,Abs2: nat > code_natural,A: set_nat,X: code_natural] :
% 4.69/4.89 ( ( type_d4410041424927559462al_nat @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( Abs2 @ ( Rep2 @ X ) )
% 4.69/4.89 = X ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Rep_inverse
% 4.69/4.89 thf(fact_343_type__definition_OAbs__inverse,axiom,
% 4.69/4.89 ! [Rep2: assn > produc3658429121746597890et_nat > $o,Abs2: ( produc3658429121746597890et_nat > $o ) > assn,A: set_Pr4532377907799695533_nat_o,Y: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( type_d3909072315231072503_nat_o @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( member6576561426505652726_nat_o @ Y @ A )
% 4.69/4.89 => ( ( Rep2 @ ( Abs2 @ Y ) )
% 4.69/4.89 = Y ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Abs_inverse
% 4.69/4.89 thf(fact_344_type__definition_OAbs__inverse,axiom,
% 4.69/4.89 ! [Rep2: code_integer > int,Abs2: int > code_integer,A: set_int,Y: int] :
% 4.69/4.89 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( member_int @ Y @ A )
% 4.69/4.89 => ( ( Rep2 @ ( Abs2 @ Y ) )
% 4.69/4.89 = Y ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Abs_inverse
% 4.69/4.89 thf(fact_345_type__definition_OAbs__inverse,axiom,
% 4.69/4.89 ! [Rep2: product_unit > $o,Abs2: $o > product_unit,A: set_o,Y: $o] :
% 4.69/4.89 ( ( type_d6188575255521822967unit_o @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( member_o @ Y @ A )
% 4.69/4.89 => ( ( Rep2 @ ( Abs2 @ Y ) )
% 4.69/4.89 = Y ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Abs_inverse
% 4.69/4.89 thf(fact_346_type__definition_OAbs__inverse,axiom,
% 4.69/4.89 ! [Rep2: code_natural > nat,Abs2: nat > code_natural,A: set_nat,Y: nat] :
% 4.69/4.89 ( ( type_d4410041424927559462al_nat @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( member_nat @ Y @ A )
% 4.69/4.89 => ( ( Rep2 @ ( Abs2 @ Y ) )
% 4.69/4.89 = Y ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Abs_inverse
% 4.69/4.89 thf(fact_347_type__definition_ORep__inject,axiom,
% 4.69/4.89 ! [Rep2: assn > produc3658429121746597890et_nat > $o,Abs2: ( produc3658429121746597890et_nat > $o ) > assn,A: set_Pr4532377907799695533_nat_o,X: assn,Y: assn] :
% 4.69/4.89 ( ( type_d3909072315231072503_nat_o @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( ( Rep2 @ X )
% 4.69/4.89 = ( Rep2 @ Y ) )
% 4.69/4.89 = ( X = Y ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Rep_inject
% 4.69/4.89 thf(fact_348_type__definition_ORep__inject,axiom,
% 4.69/4.89 ! [Rep2: code_integer > int,Abs2: int > code_integer,A: set_int,X: code_integer,Y: code_integer] :
% 4.69/4.89 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( ( Rep2 @ X )
% 4.69/4.89 = ( Rep2 @ Y ) )
% 4.69/4.89 = ( X = Y ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Rep_inject
% 4.69/4.89 thf(fact_349_type__definition_ORep__inject,axiom,
% 4.69/4.89 ! [Rep2: product_unit > $o,Abs2: $o > product_unit,A: set_o,X: product_unit,Y: product_unit] :
% 4.69/4.89 ( ( type_d6188575255521822967unit_o @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( ( Rep2 @ X )
% 4.69/4.89 = ( Rep2 @ Y ) )
% 4.69/4.89 = ( X = Y ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Rep_inject
% 4.69/4.89 thf(fact_350_type__definition_ORep__inject,axiom,
% 4.69/4.89 ! [Rep2: code_natural > nat,Abs2: nat > code_natural,A: set_nat,X: code_natural,Y: code_natural] :
% 4.69/4.89 ( ( type_d4410041424927559462al_nat @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( ( Rep2 @ X )
% 4.69/4.89 = ( Rep2 @ Y ) )
% 4.69/4.89 = ( X = Y ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Rep_inject
% 4.69/4.89 thf(fact_351_type__definition_ORep__induct,axiom,
% 4.69/4.89 ! [Rep2: assn > produc3658429121746597890et_nat > $o,Abs2: ( produc3658429121746597890et_nat > $o ) > assn,A: set_Pr4532377907799695533_nat_o,Y: produc3658429121746597890et_nat > $o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 4.69/4.89 ( ( type_d3909072315231072503_nat_o @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( member6576561426505652726_nat_o @ Y @ A )
% 4.69/4.89 => ( ! [X3: assn] : ( P @ ( Rep2 @ X3 ) )
% 4.69/4.89 => ( P @ Y ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Rep_induct
% 4.69/4.89 thf(fact_352_type__definition_ORep__induct,axiom,
% 4.69/4.89 ! [Rep2: code_integer > int,Abs2: int > code_integer,A: set_int,Y: int,P: int > $o] :
% 4.69/4.89 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( member_int @ Y @ A )
% 4.69/4.89 => ( ! [X3: code_integer] : ( P @ ( Rep2 @ X3 ) )
% 4.69/4.89 => ( P @ Y ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Rep_induct
% 4.69/4.89 thf(fact_353_type__definition_ORep__induct,axiom,
% 4.69/4.89 ! [Rep2: product_unit > $o,Abs2: $o > product_unit,A: set_o,Y: $o,P: $o > $o] :
% 4.69/4.89 ( ( type_d6188575255521822967unit_o @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( member_o @ Y @ A )
% 4.69/4.89 => ( ! [X3: product_unit] : ( P @ ( Rep2 @ X3 ) )
% 4.69/4.89 => ( P @ Y ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Rep_induct
% 4.69/4.89 thf(fact_354_type__definition_ORep__induct,axiom,
% 4.69/4.89 ! [Rep2: code_natural > nat,Abs2: nat > code_natural,A: set_nat,Y: nat,P: nat > $o] :
% 4.69/4.89 ( ( type_d4410041424927559462al_nat @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( member_nat @ Y @ A )
% 4.69/4.89 => ( ! [X3: code_natural] : ( P @ ( Rep2 @ X3 ) )
% 4.69/4.89 => ( P @ Y ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Rep_induct
% 4.69/4.89 thf(fact_355_type__definition_OAbs__inject,axiom,
% 4.69/4.89 ! [Rep2: assn > produc3658429121746597890et_nat > $o,Abs2: ( produc3658429121746597890et_nat > $o ) > assn,A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( type_d3909072315231072503_nat_o @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( member6576561426505652726_nat_o @ X @ A )
% 4.69/4.89 => ( ( member6576561426505652726_nat_o @ Y @ A )
% 4.69/4.89 => ( ( ( Abs2 @ X )
% 4.69/4.89 = ( Abs2 @ Y ) )
% 4.69/4.89 = ( X = Y ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Abs_inject
% 4.69/4.89 thf(fact_356_type__definition_OAbs__inject,axiom,
% 4.69/4.89 ! [Rep2: code_integer > int,Abs2: int > code_integer,A: set_int,X: int,Y: int] :
% 4.69/4.89 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( member_int @ X @ A )
% 4.69/4.89 => ( ( member_int @ Y @ A )
% 4.69/4.89 => ( ( ( Abs2 @ X )
% 4.69/4.89 = ( Abs2 @ Y ) )
% 4.69/4.89 = ( X = Y ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Abs_inject
% 4.69/4.89 thf(fact_357_type__definition_OAbs__inject,axiom,
% 4.69/4.89 ! [Rep2: product_unit > $o,Abs2: $o > product_unit,A: set_o,X: $o,Y: $o] :
% 4.69/4.89 ( ( type_d6188575255521822967unit_o @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( member_o @ X @ A )
% 4.69/4.89 => ( ( member_o @ Y @ A )
% 4.69/4.89 => ( ( ( Abs2 @ X )
% 4.69/4.89 = ( Abs2 @ Y ) )
% 4.69/4.89 = ( X = Y ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Abs_inject
% 4.69/4.89 thf(fact_358_type__definition_OAbs__inject,axiom,
% 4.69/4.89 ! [Rep2: code_natural > nat,Abs2: nat > code_natural,A: set_nat,X: nat,Y: nat] :
% 4.69/4.89 ( ( type_d4410041424927559462al_nat @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( member_nat @ X @ A )
% 4.69/4.89 => ( ( member_nat @ Y @ A )
% 4.69/4.89 => ( ( ( Abs2 @ X )
% 4.69/4.89 = ( Abs2 @ Y ) )
% 4.69/4.89 = ( X = Y ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Abs_inject
% 4.69/4.89 thf(fact_359_pure__assn__eq__conv,axiom,
% 4.69/4.89 ! [P: $o,Q2: $o] :
% 4.69/4.89 ( ( ( pure_assn @ P )
% 4.69/4.89 = ( pure_assn @ Q2 ) )
% 4.69/4.89 = ( P = Q2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % pure_assn_eq_conv
% 4.69/4.89 thf(fact_360_mult_Oright__neutral,axiom,
% 4.69/4.89 ! [A2: code_integer] :
% 4.69/4.89 ( ( times_3573771949741848930nteger @ A2 @ one_one_Code_integer )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % mult.right_neutral
% 4.69/4.89 thf(fact_361_mult_Oright__neutral,axiom,
% 4.69/4.89 ! [A2: code_natural] :
% 4.69/4.89 ( ( times_2397367101498566445atural @ A2 @ one_one_Code_natural )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % mult.right_neutral
% 4.69/4.89 thf(fact_362_mult_Oright__neutral,axiom,
% 4.69/4.89 ! [A2: assn] :
% 4.69/4.89 ( ( times_times_assn @ A2 @ one_one_assn )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % mult.right_neutral
% 4.69/4.89 thf(fact_363_mult_Oright__neutral,axiom,
% 4.69/4.89 ! [A2: rat] :
% 4.69/4.89 ( ( times_times_rat @ A2 @ one_one_rat )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % mult.right_neutral
% 4.69/4.89 thf(fact_364_mult_Oright__neutral,axiom,
% 4.69/4.89 ! [A2: nat] :
% 4.69/4.89 ( ( times_times_nat @ A2 @ one_one_nat )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % mult.right_neutral
% 4.69/4.89 thf(fact_365_mult_Oright__neutral,axiom,
% 4.69/4.89 ! [A2: int] :
% 4.69/4.89 ( ( times_times_int @ A2 @ one_one_int )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % mult.right_neutral
% 4.69/4.89 thf(fact_366_mult__1,axiom,
% 4.69/4.89 ! [A2: code_integer] :
% 4.69/4.89 ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A2 )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % mult_1
% 4.69/4.89 thf(fact_367_mult__1,axiom,
% 4.69/4.89 ! [A2: code_natural] :
% 4.69/4.89 ( ( times_2397367101498566445atural @ one_one_Code_natural @ A2 )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % mult_1
% 4.69/4.89 thf(fact_368_mult__1,axiom,
% 4.69/4.89 ! [A2: assn] :
% 4.69/4.89 ( ( times_times_assn @ one_one_assn @ A2 )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % mult_1
% 4.69/4.89 thf(fact_369_mult__1,axiom,
% 4.69/4.89 ! [A2: rat] :
% 4.69/4.89 ( ( times_times_rat @ one_one_rat @ A2 )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % mult_1
% 4.69/4.89 thf(fact_370_mult__1,axiom,
% 4.69/4.89 ! [A2: nat] :
% 4.69/4.89 ( ( times_times_nat @ one_one_nat @ A2 )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % mult_1
% 4.69/4.89 thf(fact_371_mult__1,axiom,
% 4.69/4.89 ! [A2: int] :
% 4.69/4.89 ( ( times_times_int @ one_one_int @ A2 )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % mult_1
% 4.69/4.89 thf(fact_372_merge__pure__star,axiom,
% 4.69/4.89 ! [A2: $o,B: $o] :
% 4.69/4.89 ( ( times_times_assn @ ( pure_assn @ A2 ) @ ( pure_assn @ B ) )
% 4.69/4.89 = ( pure_assn
% 4.69/4.89 @ ( A2
% 4.69/4.89 & B ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % merge_pure_star
% 4.69/4.89 thf(fact_373_star__false__right,axiom,
% 4.69/4.89 ! [P: assn] :
% 4.69/4.89 ( ( times_times_assn @ P @ bot_bot_assn )
% 4.69/4.89 = bot_bot_assn ) ).
% 4.69/4.89
% 4.69/4.89 % star_false_right
% 4.69/4.89 thf(fact_374_star__false__left,axiom,
% 4.69/4.89 ! [P: assn] :
% 4.69/4.89 ( ( times_times_assn @ bot_bot_assn @ P )
% 4.69/4.89 = bot_bot_assn ) ).
% 4.69/4.89
% 4.69/4.89 % star_false_left
% 4.69/4.89 thf(fact_375_pure__false,axiom,
% 4.69/4.89 ( ( pure_assn @ $false )
% 4.69/4.89 = bot_bot_assn ) ).
% 4.69/4.89
% 4.69/4.89 % pure_false
% 4.69/4.89 thf(fact_376_pure__assn__eq__false__iff,axiom,
% 4.69/4.89 ! [P: $o] :
% 4.69/4.89 ( ( ( pure_assn @ P )
% 4.69/4.89 = bot_bot_assn )
% 4.69/4.89 = ~ P ) ).
% 4.69/4.89
% 4.69/4.89 % pure_assn_eq_false_iff
% 4.69/4.89 thf(fact_377_is__pure__assn__starI,axiom,
% 4.69/4.89 ! [A2: assn,B: assn] :
% 4.69/4.89 ( ( is_pure_assn @ A2 )
% 4.69/4.89 => ( ( is_pure_assn @ B )
% 4.69/4.89 => ( is_pure_assn @ ( times_times_assn @ A2 @ B ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_pure_assn_starI
% 4.69/4.89 thf(fact_378_is__pure__assn__pure,axiom,
% 4.69/4.89 ! [P: $o] : ( is_pure_assn @ ( pure_assn @ P ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_pure_assn_pure
% 4.69/4.89 thf(fact_379_pure__true,axiom,
% 4.69/4.89 ( ( pure_assn @ $true )
% 4.69/4.89 = one_one_assn ) ).
% 4.69/4.89
% 4.69/4.89 % pure_true
% 4.69/4.89 thf(fact_380_pure__assn__eq__emp__iff,axiom,
% 4.69/4.89 ! [P: $o] :
% 4.69/4.89 ( ( ( pure_assn @ P )
% 4.69/4.89 = one_one_assn )
% 4.69/4.89 = P ) ).
% 4.69/4.89
% 4.69/4.89 % pure_assn_eq_emp_iff
% 4.69/4.89 thf(fact_381_assn__times__comm,axiom,
% 4.69/4.89 ( times_times_assn
% 4.69/4.89 = ( ^ [P2: assn,Q: assn] : ( times_times_assn @ Q @ P2 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % assn_times_comm
% 4.69/4.89 thf(fact_382_assn__times__assoc,axiom,
% 4.69/4.89 ! [P: assn,Q2: assn,R3: assn] :
% 4.69/4.89 ( ( times_times_assn @ ( times_times_assn @ P @ Q2 ) @ R3 )
% 4.69/4.89 = ( times_times_assn @ P @ ( times_times_assn @ Q2 @ R3 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % assn_times_assoc
% 4.69/4.89 thf(fact_383_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 4.69/4.89 ! [B: assn,A2: assn,C: assn] :
% 4.69/4.89 ( ( times_times_assn @ B @ ( times_times_assn @ A2 @ C ) )
% 4.69/4.89 = ( times_times_assn @ A2 @ ( times_times_assn @ B @ C ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % ab_semigroup_mult_class.mult.left_commute
% 4.69/4.89 thf(fact_384_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 4.69/4.89 ! [B: rat,A2: rat,C: rat] :
% 4.69/4.89 ( ( times_times_rat @ B @ ( times_times_rat @ A2 @ C ) )
% 4.69/4.89 = ( times_times_rat @ A2 @ ( times_times_rat @ B @ C ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % ab_semigroup_mult_class.mult.left_commute
% 4.69/4.89 thf(fact_385_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 4.69/4.89 ! [B: nat,A2: nat,C: nat] :
% 4.69/4.89 ( ( times_times_nat @ B @ ( times_times_nat @ A2 @ C ) )
% 4.69/4.89 = ( times_times_nat @ A2 @ ( times_times_nat @ B @ C ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % ab_semigroup_mult_class.mult.left_commute
% 4.69/4.89 thf(fact_386_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 4.69/4.89 ! [B: int,A2: int,C: int] :
% 4.69/4.89 ( ( times_times_int @ B @ ( times_times_int @ A2 @ C ) )
% 4.69/4.89 = ( times_times_int @ A2 @ ( times_times_int @ B @ C ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % ab_semigroup_mult_class.mult.left_commute
% 4.69/4.89 thf(fact_387_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 4.69/4.89 ( times_times_assn
% 4.69/4.89 = ( ^ [A6: assn,B6: assn] : ( times_times_assn @ B6 @ A6 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % ab_semigroup_mult_class.mult.commute
% 4.69/4.89 thf(fact_388_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 4.69/4.89 ( times_times_rat
% 4.69/4.89 = ( ^ [A6: rat,B6: rat] : ( times_times_rat @ B6 @ A6 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % ab_semigroup_mult_class.mult.commute
% 4.69/4.89 thf(fact_389_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 4.69/4.89 ( times_times_nat
% 4.69/4.89 = ( ^ [A6: nat,B6: nat] : ( times_times_nat @ B6 @ A6 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % ab_semigroup_mult_class.mult.commute
% 4.69/4.89 thf(fact_390_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 4.69/4.89 ( times_times_int
% 4.69/4.89 = ( ^ [A6: int,B6: int] : ( times_times_int @ B6 @ A6 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % ab_semigroup_mult_class.mult.commute
% 4.69/4.89 thf(fact_391_mult_Oassoc,axiom,
% 4.69/4.89 ! [A2: assn,B: assn,C: assn] :
% 4.69/4.89 ( ( times_times_assn @ ( times_times_assn @ A2 @ B ) @ C )
% 4.69/4.89 = ( times_times_assn @ A2 @ ( times_times_assn @ B @ C ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % mult.assoc
% 4.69/4.89 thf(fact_392_mult_Oassoc,axiom,
% 4.69/4.89 ! [A2: rat,B: rat,C: rat] :
% 4.69/4.89 ( ( times_times_rat @ ( times_times_rat @ A2 @ B ) @ C )
% 4.69/4.89 = ( times_times_rat @ A2 @ ( times_times_rat @ B @ C ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % mult.assoc
% 4.69/4.89 thf(fact_393_mult_Oassoc,axiom,
% 4.69/4.89 ! [A2: nat,B: nat,C: nat] :
% 4.69/4.89 ( ( times_times_nat @ ( times_times_nat @ A2 @ B ) @ C )
% 4.69/4.89 = ( times_times_nat @ A2 @ ( times_times_nat @ B @ C ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % mult.assoc
% 4.69/4.89 thf(fact_394_mult_Oassoc,axiom,
% 4.69/4.89 ! [A2: int,B: int,C: int] :
% 4.69/4.89 ( ( times_times_int @ ( times_times_int @ A2 @ B ) @ C )
% 4.69/4.89 = ( times_times_int @ A2 @ ( times_times_int @ B @ C ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % mult.assoc
% 4.69/4.89 thf(fact_395_comm__monoid__mult__class_Omult__1,axiom,
% 4.69/4.89 ! [A2: code_integer] :
% 4.69/4.89 ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A2 )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % comm_monoid_mult_class.mult_1
% 4.69/4.89 thf(fact_396_comm__monoid__mult__class_Omult__1,axiom,
% 4.69/4.89 ! [A2: code_natural] :
% 4.69/4.89 ( ( times_2397367101498566445atural @ one_one_Code_natural @ A2 )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % comm_monoid_mult_class.mult_1
% 4.69/4.89 thf(fact_397_comm__monoid__mult__class_Omult__1,axiom,
% 4.69/4.89 ! [A2: assn] :
% 4.69/4.89 ( ( times_times_assn @ one_one_assn @ A2 )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % comm_monoid_mult_class.mult_1
% 4.69/4.89 thf(fact_398_comm__monoid__mult__class_Omult__1,axiom,
% 4.69/4.89 ! [A2: rat] :
% 4.69/4.89 ( ( times_times_rat @ one_one_rat @ A2 )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % comm_monoid_mult_class.mult_1
% 4.69/4.89 thf(fact_399_comm__monoid__mult__class_Omult__1,axiom,
% 4.69/4.89 ! [A2: nat] :
% 4.69/4.89 ( ( times_times_nat @ one_one_nat @ A2 )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % comm_monoid_mult_class.mult_1
% 4.69/4.89 thf(fact_400_comm__monoid__mult__class_Omult__1,axiom,
% 4.69/4.89 ! [A2: int] :
% 4.69/4.89 ( ( times_times_int @ one_one_int @ A2 )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % comm_monoid_mult_class.mult_1
% 4.69/4.89 thf(fact_401_mult_Ocomm__neutral,axiom,
% 4.69/4.89 ! [A2: code_integer] :
% 4.69/4.89 ( ( times_3573771949741848930nteger @ A2 @ one_one_Code_integer )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % mult.comm_neutral
% 4.69/4.89 thf(fact_402_mult_Ocomm__neutral,axiom,
% 4.69/4.89 ! [A2: code_natural] :
% 4.69/4.89 ( ( times_2397367101498566445atural @ A2 @ one_one_Code_natural )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % mult.comm_neutral
% 4.69/4.89 thf(fact_403_mult_Ocomm__neutral,axiom,
% 4.69/4.89 ! [A2: assn] :
% 4.69/4.89 ( ( times_times_assn @ A2 @ one_one_assn )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % mult.comm_neutral
% 4.69/4.89 thf(fact_404_mult_Ocomm__neutral,axiom,
% 4.69/4.89 ! [A2: rat] :
% 4.69/4.89 ( ( times_times_rat @ A2 @ one_one_rat )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % mult.comm_neutral
% 4.69/4.89 thf(fact_405_mult_Ocomm__neutral,axiom,
% 4.69/4.89 ! [A2: nat] :
% 4.69/4.89 ( ( times_times_nat @ A2 @ one_one_nat )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % mult.comm_neutral
% 4.69/4.89 thf(fact_406_mult_Ocomm__neutral,axiom,
% 4.69/4.89 ! [A2: int] :
% 4.69/4.89 ( ( times_times_int @ A2 @ one_one_int )
% 4.69/4.89 = A2 ) ).
% 4.69/4.89
% 4.69/4.89 % mult.comm_neutral
% 4.69/4.89 thf(fact_407_mod__starE,axiom,
% 4.69/4.89 ! [A2: assn,B: assn,H2: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ( rep_assn @ ( times_times_assn @ A2 @ B ) @ H2 )
% 4.69/4.89 => ~ ( ? [X_1: produc3658429121746597890et_nat] : ( rep_assn @ A2 @ X_1 )
% 4.69/4.89 => ! [H_2: produc3658429121746597890et_nat] :
% 4.69/4.89 ~ ( rep_assn @ B @ H_2 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % mod_starE
% 4.69/4.89 thf(fact_408_mod__starD,axiom,
% 4.69/4.89 ! [A: assn,B4: assn,H2: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ( rep_assn @ ( times_times_assn @ A @ B4 ) @ H2 )
% 4.69/4.89 => ? [H1: produc3658429121746597890et_nat,H22: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ( rep_assn @ A @ H1 )
% 4.69/4.89 & ( rep_assn @ B4 @ H22 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % mod_starD
% 4.69/4.89 thf(fact_409_assn__one__left,axiom,
% 4.69/4.89 ! [P: assn] :
% 4.69/4.89 ( ( times_times_assn @ one_one_assn @ P )
% 4.69/4.89 = P ) ).
% 4.69/4.89
% 4.69/4.89 % assn_one_left
% 4.69/4.89 thf(fact_410_is__pure__assnE,axiom,
% 4.69/4.89 ! [A2: assn] :
% 4.69/4.89 ( ( is_pure_assn @ A2 )
% 4.69/4.89 => ~ ! [P4: $o] :
% 4.69/4.89 ( A2
% 4.69/4.89 != ( pure_assn @ P4 ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_pure_assnE
% 4.69/4.89 thf(fact_411_is__pure__assn__def,axiom,
% 4.69/4.89 ( is_pure_assn
% 4.69/4.89 = ( ^ [A6: assn] :
% 4.69/4.89 ? [P2: $o] :
% 4.69/4.89 ( A6
% 4.69/4.89 = ( pure_assn @ P2 ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % is_pure_assn_def
% 4.69/4.89 thf(fact_412_type__definition_ORep,axiom,
% 4.69/4.89 ! [Rep2: assn > produc3658429121746597890et_nat > $o,Abs2: ( produc3658429121746597890et_nat > $o ) > assn,A: set_Pr4532377907799695533_nat_o,X: assn] :
% 4.69/4.89 ( ( type_d3909072315231072503_nat_o @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( member6576561426505652726_nat_o @ ( Rep2 @ X ) @ A ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Rep
% 4.69/4.89 thf(fact_413_type__definition_ORep,axiom,
% 4.69/4.89 ! [Rep2: code_integer > int,Abs2: int > code_integer,A: set_int,X: code_integer] :
% 4.69/4.89 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( member_int @ ( Rep2 @ X ) @ A ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Rep
% 4.69/4.89 thf(fact_414_type__definition_ORep,axiom,
% 4.69/4.89 ! [Rep2: product_unit > $o,Abs2: $o > product_unit,A: set_o,X: product_unit] :
% 4.69/4.89 ( ( type_d6188575255521822967unit_o @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( member_o @ ( Rep2 @ X ) @ A ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Rep
% 4.69/4.89 thf(fact_415_type__definition_ORep,axiom,
% 4.69/4.89 ! [Rep2: code_natural > nat,Abs2: nat > code_natural,A: set_nat,X: code_natural] :
% 4.69/4.89 ( ( type_d4410041424927559462al_nat @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( member_nat @ ( Rep2 @ X ) @ A ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Rep
% 4.69/4.89 thf(fact_416_type__definition_Ointro,axiom,
% 4.69/4.89 ! [Rep2: assn > produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,Abs2: ( produc3658429121746597890et_nat > $o ) > assn] :
% 4.69/4.89 ( ! [X3: assn] : ( member6576561426505652726_nat_o @ ( Rep2 @ X3 ) @ A )
% 4.69/4.89 => ( ! [X3: assn] :
% 4.69/4.89 ( ( Abs2 @ ( Rep2 @ X3 ) )
% 4.69/4.89 = X3 )
% 4.69/4.89 => ( ! [Y2: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( member6576561426505652726_nat_o @ Y2 @ A )
% 4.69/4.89 => ( ( Rep2 @ ( Abs2 @ Y2 ) )
% 4.69/4.89 = Y2 ) )
% 4.69/4.89 => ( type_d3909072315231072503_nat_o @ Rep2 @ Abs2 @ A ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.intro
% 4.69/4.89 thf(fact_417_type__definition_Ointro,axiom,
% 4.69/4.89 ! [Rep2: code_integer > int,A: set_int,Abs2: int > code_integer] :
% 4.69/4.89 ( ! [X3: code_integer] : ( member_int @ ( Rep2 @ X3 ) @ A )
% 4.69/4.89 => ( ! [X3: code_integer] :
% 4.69/4.89 ( ( Abs2 @ ( Rep2 @ X3 ) )
% 4.69/4.89 = X3 )
% 4.69/4.89 => ( ! [Y2: int] :
% 4.69/4.89 ( ( member_int @ Y2 @ A )
% 4.69/4.89 => ( ( Rep2 @ ( Abs2 @ Y2 ) )
% 4.69/4.89 = Y2 ) )
% 4.69/4.89 => ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ A ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.intro
% 4.69/4.89 thf(fact_418_type__definition_Ointro,axiom,
% 4.69/4.89 ! [Rep2: product_unit > $o,A: set_o,Abs2: $o > product_unit] :
% 4.69/4.89 ( ! [X3: product_unit] : ( member_o @ ( Rep2 @ X3 ) @ A )
% 4.69/4.89 => ( ! [X3: product_unit] :
% 4.69/4.89 ( ( Abs2 @ ( Rep2 @ X3 ) )
% 4.69/4.89 = X3 )
% 4.69/4.89 => ( ! [Y2: $o] :
% 4.69/4.89 ( ( member_o @ Y2 @ A )
% 4.69/4.89 => ( ( Rep2 @ ( Abs2 @ Y2 ) )
% 4.69/4.89 = Y2 ) )
% 4.69/4.89 => ( type_d6188575255521822967unit_o @ Rep2 @ Abs2 @ A ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.intro
% 4.69/4.89 thf(fact_419_type__definition_Ointro,axiom,
% 4.69/4.89 ! [Rep2: code_natural > nat,A: set_nat,Abs2: nat > code_natural] :
% 4.69/4.89 ( ! [X3: code_natural] : ( member_nat @ ( Rep2 @ X3 ) @ A )
% 4.69/4.89 => ( ! [X3: code_natural] :
% 4.69/4.89 ( ( Abs2 @ ( Rep2 @ X3 ) )
% 4.69/4.89 = X3 )
% 4.69/4.89 => ( ! [Y2: nat] :
% 4.69/4.89 ( ( member_nat @ Y2 @ A )
% 4.69/4.89 => ( ( Rep2 @ ( Abs2 @ Y2 ) )
% 4.69/4.89 = Y2 ) )
% 4.69/4.89 => ( type_d4410041424927559462al_nat @ Rep2 @ Abs2 @ A ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.intro
% 4.69/4.89 thf(fact_420_type__definition_OAbs__cases,axiom,
% 4.69/4.89 ! [Rep2: assn > produc3658429121746597890et_nat > $o,Abs2: ( produc3658429121746597890et_nat > $o ) > assn,A: set_Pr4532377907799695533_nat_o,X: assn] :
% 4.69/4.89 ( ( type_d3909072315231072503_nat_o @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ~ ! [Y2: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( X
% 4.69/4.89 = ( Abs2 @ Y2 ) )
% 4.69/4.89 => ~ ( member6576561426505652726_nat_o @ Y2 @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Abs_cases
% 4.69/4.89 thf(fact_421_type__definition_OAbs__cases,axiom,
% 4.69/4.89 ! [Rep2: code_integer > int,Abs2: int > code_integer,A: set_int,X: code_integer] :
% 4.69/4.89 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ~ ! [Y2: int] :
% 4.69/4.89 ( ( X
% 4.69/4.89 = ( Abs2 @ Y2 ) )
% 4.69/4.89 => ~ ( member_int @ Y2 @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Abs_cases
% 4.69/4.89 thf(fact_422_type__definition_OAbs__cases,axiom,
% 4.69/4.89 ! [Rep2: product_unit > $o,Abs2: $o > product_unit,A: set_o,X: product_unit] :
% 4.69/4.89 ( ( type_d6188575255521822967unit_o @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ~ ! [Y2: $o] :
% 4.69/4.89 ( ( X
% 4.69/4.89 = ( Abs2 @ Y2 ) )
% 4.69/4.89 => ~ ( member_o @ Y2 @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Abs_cases
% 4.69/4.89 thf(fact_423_type__definition_OAbs__cases,axiom,
% 4.69/4.89 ! [Rep2: code_natural > nat,Abs2: nat > code_natural,A: set_nat,X: code_natural] :
% 4.69/4.89 ( ( type_d4410041424927559462al_nat @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ~ ! [Y2: nat] :
% 4.69/4.89 ( ( X
% 4.69/4.89 = ( Abs2 @ Y2 ) )
% 4.69/4.89 => ~ ( member_nat @ Y2 @ A ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Abs_cases
% 4.69/4.89 thf(fact_424_type__definition_ORep__cases,axiom,
% 4.69/4.89 ! [Rep2: assn > produc3658429121746597890et_nat > $o,Abs2: ( produc3658429121746597890et_nat > $o ) > assn,A: set_Pr4532377907799695533_nat_o,Y: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( type_d3909072315231072503_nat_o @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( member6576561426505652726_nat_o @ Y @ A )
% 4.69/4.89 => ~ ! [X3: assn] :
% 4.69/4.89 ( Y
% 4.69/4.89 != ( Rep2 @ X3 ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Rep_cases
% 4.69/4.89 thf(fact_425_type__definition_ORep__cases,axiom,
% 4.69/4.89 ! [Rep2: code_integer > int,Abs2: int > code_integer,A: set_int,Y: int] :
% 4.69/4.89 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( member_int @ Y @ A )
% 4.69/4.89 => ~ ! [X3: code_integer] :
% 4.69/4.89 ( Y
% 4.69/4.89 != ( Rep2 @ X3 ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Rep_cases
% 4.69/4.89 thf(fact_426_type__definition_ORep__cases,axiom,
% 4.69/4.89 ! [Rep2: product_unit > $o,Abs2: $o > product_unit,A: set_o,Y: $o] :
% 4.69/4.89 ( ( type_d6188575255521822967unit_o @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( member_o @ Y @ A )
% 4.69/4.89 => ~ ! [X3: product_unit] :
% 4.69/4.89 ( Y
% 4.69/4.89 = ( ~ ( Rep2 @ X3 ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Rep_cases
% 4.69/4.89 thf(fact_427_type__definition_ORep__cases,axiom,
% 4.69/4.89 ! [Rep2: code_natural > nat,Abs2: nat > code_natural,A: set_nat,Y: nat] :
% 4.69/4.89 ( ( type_d4410041424927559462al_nat @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ( member_nat @ Y @ A )
% 4.69/4.89 => ~ ! [X3: code_natural] :
% 4.69/4.89 ( Y
% 4.69/4.89 != ( Rep2 @ X3 ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Rep_cases
% 4.69/4.89 thf(fact_428_type__definition_OAbs__induct,axiom,
% 4.69/4.89 ! [Rep2: assn > produc3658429121746597890et_nat > $o,Abs2: ( produc3658429121746597890et_nat > $o ) > assn,A: set_Pr4532377907799695533_nat_o,P: assn > $o,X: assn] :
% 4.69/4.89 ( ( type_d3909072315231072503_nat_o @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ! [Y2: produc3658429121746597890et_nat > $o] :
% 4.69/4.89 ( ( member6576561426505652726_nat_o @ Y2 @ A )
% 4.69/4.89 => ( P @ ( Abs2 @ Y2 ) ) )
% 4.69/4.89 => ( P @ X ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Abs_induct
% 4.69/4.89 thf(fact_429_type__definition_OAbs__induct,axiom,
% 4.69/4.89 ! [Rep2: code_integer > int,Abs2: int > code_integer,A: set_int,P: code_integer > $o,X: code_integer] :
% 4.69/4.89 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ! [Y2: int] :
% 4.69/4.89 ( ( member_int @ Y2 @ A )
% 4.69/4.89 => ( P @ ( Abs2 @ Y2 ) ) )
% 4.69/4.89 => ( P @ X ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Abs_induct
% 4.69/4.89 thf(fact_430_type__definition_OAbs__induct,axiom,
% 4.69/4.89 ! [Rep2: product_unit > $o,Abs2: $o > product_unit,A: set_o,P: product_unit > $o,X: product_unit] :
% 4.69/4.89 ( ( type_d6188575255521822967unit_o @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ! [Y2: $o] :
% 4.69/4.89 ( ( member_o @ Y2 @ A )
% 4.69/4.89 => ( P @ ( Abs2 @ Y2 ) ) )
% 4.69/4.89 => ( P @ X ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Abs_induct
% 4.69/4.89 thf(fact_431_type__definition_OAbs__induct,axiom,
% 4.69/4.89 ! [Rep2: code_natural > nat,Abs2: nat > code_natural,A: set_nat,P: code_natural > $o,X: code_natural] :
% 4.69/4.89 ( ( type_d4410041424927559462al_nat @ Rep2 @ Abs2 @ A )
% 4.69/4.89 => ( ! [Y2: nat] :
% 4.69/4.89 ( ( member_nat @ Y2 @ A )
% 4.69/4.89 => ( P @ ( Abs2 @ Y2 ) ) )
% 4.69/4.89 => ( P @ X ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % type_definition.Abs_induct
% 4.69/4.89 thf(fact_432_total__on__singleton,axiom,
% 4.69/4.89 ! [X: product_unit] : ( total_5665700600833547665t_unit @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) @ ( insert4616891024742550839t_unit @ ( produc5692694829384537815t_unit @ X @ X ) @ bot_bo1654022762305692595t_unit ) ) ).
% 4.69/4.89
% 4.69/4.89 % total_on_singleton
% 4.69/4.89 thf(fact_433_total__on__singleton,axiom,
% 4.69/4.89 ! [X: $o] : ( total_on_o @ ( insert_o @ X @ bot_bot_set_o ) @ ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ X @ X ) @ bot_bo7073875226086086771od_o_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % total_on_singleton
% 4.69/4.89 thf(fact_434_total__on__singleton,axiom,
% 4.69/4.89 ! [X: nat] : ( total_on_nat @ ( insert_nat @ X @ bot_bot_set_nat ) @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X @ X ) @ bot_bo2099793752762293965at_nat ) ) ).
% 4.69/4.89
% 4.69/4.89 % total_on_singleton
% 4.69/4.89 thf(fact_435_total__on__singleton,axiom,
% 4.69/4.89 ! [X: int] : ( total_on_int @ ( insert_int @ X @ bot_bot_set_int ) @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ X @ X ) @ bot_bo1796632182523588997nt_int ) ) ).
% 4.69/4.89
% 4.69/4.89 % total_on_singleton
% 4.69/4.89 thf(fact_436_total__on__singleton,axiom,
% 4.69/4.89 ! [X: produc3658429121746597890et_nat > $o] : ( total_7429123086324524369_nat_o @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) @ ( insert5309882203591314743_nat_o @ ( produc7368190662567826135_nat_o @ X @ X ) @ bot_bo3657187498359500723_nat_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % total_on_singleton
% 4.69/4.89 thf(fact_437_refl__on__singleton,axiom,
% 4.69/4.89 ! [X: product_unit] : ( refl_on_Product_unit @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) @ ( insert4616891024742550839t_unit @ ( produc5692694829384537815t_unit @ X @ X ) @ bot_bo1654022762305692595t_unit ) ) ).
% 4.69/4.89
% 4.69/4.89 % refl_on_singleton
% 4.69/4.89 thf(fact_438_refl__on__singleton,axiom,
% 4.69/4.89 ! [X: $o] : ( refl_on_o @ ( insert_o @ X @ bot_bot_set_o ) @ ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ X @ X ) @ bot_bo7073875226086086771od_o_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % refl_on_singleton
% 4.69/4.89 thf(fact_439_refl__on__singleton,axiom,
% 4.69/4.89 ! [X: nat] : ( refl_on_nat @ ( insert_nat @ X @ bot_bot_set_nat ) @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X @ X ) @ bot_bo2099793752762293965at_nat ) ) ).
% 4.69/4.89
% 4.69/4.89 % refl_on_singleton
% 4.69/4.89 thf(fact_440_refl__on__singleton,axiom,
% 4.69/4.89 ! [X: int] : ( refl_on_int @ ( insert_int @ X @ bot_bot_set_int ) @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ X @ X ) @ bot_bo1796632182523588997nt_int ) ) ).
% 4.69/4.89
% 4.69/4.89 % refl_on_singleton
% 4.69/4.89 thf(fact_441_refl__on__singleton,axiom,
% 4.69/4.89 ! [X: produc3658429121746597890et_nat > $o] : ( refl_o1075864025857821388_nat_o @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) @ ( insert5309882203591314743_nat_o @ ( produc7368190662567826135_nat_o @ X @ X ) @ bot_bo3657187498359500723_nat_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % refl_on_singleton
% 4.69/4.89 thf(fact_442_Id__on__empty,axiom,
% 4.69/4.89 ( ( id_on_Product_unit @ bot_bo3957492148770167129t_unit )
% 4.69/4.89 = bot_bo1654022762305692595t_unit ) ).
% 4.69/4.89
% 4.69/4.89 % Id_on_empty
% 4.69/4.89 thf(fact_443_Id__on__empty,axiom,
% 4.69/4.89 ( ( id_on_o @ bot_bot_set_o )
% 4.69/4.89 = bot_bo7073875226086086771od_o_o ) ).
% 4.69/4.89
% 4.69/4.89 % Id_on_empty
% 4.69/4.89 thf(fact_444_Id__on__empty,axiom,
% 4.69/4.89 ( ( id_on_nat @ bot_bot_set_nat )
% 4.69/4.89 = bot_bo2099793752762293965at_nat ) ).
% 4.69/4.89
% 4.69/4.89 % Id_on_empty
% 4.69/4.89 thf(fact_445_Id__on__empty,axiom,
% 4.69/4.89 ( ( id_on_int @ bot_bot_set_int )
% 4.69/4.89 = bot_bo1796632182523588997nt_int ) ).
% 4.69/4.89
% 4.69/4.89 % Id_on_empty
% 4.69/4.89 thf(fact_446_Id__on__empty,axiom,
% 4.69/4.89 ( ( id_on_7438695062414216554_nat_o @ bot_bo7824918357723582233_nat_o )
% 4.69/4.89 = bot_bo3657187498359500723_nat_o ) ).
% 4.69/4.89
% 4.69/4.89 % Id_on_empty
% 4.69/4.89 thf(fact_447_linear__order__on__singleton,axiom,
% 4.69/4.89 ! [X: product_unit] : ( order_888282469287196226t_unit @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) @ ( insert4616891024742550839t_unit @ ( produc5692694829384537815t_unit @ X @ X ) @ bot_bo1654022762305692595t_unit ) ) ).
% 4.69/4.89
% 4.69/4.89 % linear_order_on_singleton
% 4.69/4.89 thf(fact_448_linear__order__on__singleton,axiom,
% 4.69/4.89 ! [X: $o] : ( order_6238756238976269133r_on_o @ ( insert_o @ X @ bot_bot_set_o ) @ ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ X @ X ) @ bot_bo7073875226086086771od_o_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % linear_order_on_singleton
% 4.69/4.89 thf(fact_449_linear__order__on__singleton,axiom,
% 4.69/4.89 ! [X: nat] : ( order_4473980167227706203on_nat @ ( insert_nat @ X @ bot_bot_set_nat ) @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X @ X ) @ bot_bo2099793752762293965at_nat ) ) ).
% 4.69/4.89
% 4.69/4.89 % linear_order_on_singleton
% 4.69/4.89 thf(fact_450_linear__order__on__singleton,axiom,
% 4.69/4.89 ! [X: int] : ( order_4471489696718655927on_int @ ( insert_int @ X @ bot_bot_set_int ) @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ X @ X ) @ bot_bo1796632182523588997nt_int ) ) ).
% 4.69/4.89
% 4.69/4.89 % linear_order_on_singleton
% 4.69/4.89 thf(fact_451_linear__order__on__singleton,axiom,
% 4.69/4.89 ! [X: produc3658429121746597890et_nat > $o] : ( order_1145710701291701250_nat_o @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) @ ( insert5309882203591314743_nat_o @ ( produc7368190662567826135_nat_o @ X @ X ) @ bot_bo3657187498359500723_nat_o ) ) ).
% 4.69/4.89
% 4.69/4.89 % linear_order_on_singleton
% 4.69/4.89 thf(fact_452_pure__assn__raw_Opelims_I1_J,axiom,
% 4.69/4.89 ! [X: $o,Xa: produc3658429121746597890et_nat,Y: $o] :
% 4.69/4.89 ( ( ( pure_a825153325127701367it_nat @ X @ Xa )
% 4.69/4.89 = Y )
% 4.69/4.89 => ( ( accp_P8458817951426537472et_nat @ pure_a6022498039421069578it_nat @ ( produc3762353314782720579et_nat @ X @ Xa ) )
% 4.69/4.89 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.89 ( ( Xa
% 4.69/4.89 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.89 => ( ( Y
% 4.69/4.89 = ( ( As2 = bot_bot_set_nat )
% 4.69/4.89 & X ) )
% 4.69/4.89 => ~ ( accp_P8458817951426537472et_nat @ pure_a6022498039421069578it_nat @ ( produc3762353314782720579et_nat @ X @ ( produc7507926704131184380et_nat @ H @ As2 ) ) ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % pure_assn_raw.pelims(1)
% 4.69/4.89 thf(fact_453_pure__assn__raw_Opelims_I2_J,axiom,
% 4.69/4.89 ! [X: $o,Xa: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ( pure_a825153325127701367it_nat @ X @ Xa )
% 4.69/4.89 => ( ( accp_P8458817951426537472et_nat @ pure_a6022498039421069578it_nat @ ( produc3762353314782720579et_nat @ X @ Xa ) )
% 4.69/4.89 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.89 ( ( Xa
% 4.69/4.89 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.89 => ( ( accp_P8458817951426537472et_nat @ pure_a6022498039421069578it_nat @ ( produc3762353314782720579et_nat @ X @ ( produc7507926704131184380et_nat @ H @ As2 ) ) )
% 4.69/4.89 => ~ ( ( As2 = bot_bot_set_nat )
% 4.69/4.89 & X ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % pure_assn_raw.pelims(2)
% 4.69/4.89 thf(fact_454_pure__assn__raw_Opelims_I3_J,axiom,
% 4.69/4.89 ! [X: $o,Xa: produc3658429121746597890et_nat] :
% 4.69/4.89 ( ~ ( pure_a825153325127701367it_nat @ X @ Xa )
% 4.69/4.89 => ( ( accp_P8458817951426537472et_nat @ pure_a6022498039421069578it_nat @ ( produc3762353314782720579et_nat @ X @ Xa ) )
% 4.69/4.89 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.89 ( ( Xa
% 4.69/4.89 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.89 => ( ( accp_P8458817951426537472et_nat @ pure_a6022498039421069578it_nat @ ( produc3762353314782720579et_nat @ X @ ( produc7507926704131184380et_nat @ H @ As2 ) ) )
% 4.69/4.89 => ( ( As2 = bot_bot_set_nat )
% 4.69/4.89 & X ) ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % pure_assn_raw.pelims(3)
% 4.69/4.89 thf(fact_455_Image__singleton__iff,axiom,
% 4.69/4.89 ! [B: nat,R2: set_Pr1763845938948868674it_nat,A2: product_unit] :
% 4.69/4.89 ( ( member_nat @ B @ ( image_5657742817519485770it_nat @ R2 @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.89 = ( member423003724879500579it_nat @ ( produc4803288329813530246it_nat @ A2 @ B ) @ R2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % Image_singleton_iff
% 4.69/4.89 thf(fact_456_Image__singleton__iff,axiom,
% 4.69/4.89 ! [B: int,R2: set_Pr8497134830871917726it_int,A2: product_unit] :
% 4.69/4.89 ( ( member_int @ B @ ( image_5655252347010435494it_int @ R2 @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.89 = ( member5468524742225079679it_int @ ( produc4800797859304479970it_int @ A2 @ B ) @ R2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % Image_singleton_iff
% 4.69/4.89 thf(fact_457_Image__singleton__iff,axiom,
% 4.69/4.89 ! [B: $o,R2: set_Pr5464989305201766866unit_o,A2: product_unit] :
% 4.69/4.89 ( ( member_o @ B @ ( image_Product_unit_o @ R2 @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.89 = ( member3689400097658526619unit_o @ ( produc8487917018914037602unit_o @ A2 @ B ) @ R2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % Image_singleton_iff
% 4.69/4.89 thf(fact_458_Image__singleton__iff,axiom,
% 4.69/4.89 ! [B: product_unit,R2: set_Pr5094982260447487303t_unit,A2: product_unit] :
% 4.69/4.89 ( ( member_Product_unit @ B @ ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.89 = ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A2 @ B ) @ R2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % Image_singleton_iff
% 4.69/4.89 thf(fact_459_Image__singleton__iff,axiom,
% 4.69/4.89 ! [B: nat,R2: set_Pr2101469702781467981_o_nat,A2: $o] :
% 4.69/4.89 ( ( member_nat @ B @ ( image_o_nat @ R2 @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 4.69/4.89 = ( member2802428098988154798_o_nat @ ( product_Pair_o_nat @ A2 @ B ) @ R2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % Image_singleton_iff
% 4.69/4.89 thf(fact_460_Image__singleton__iff,axiom,
% 4.69/4.89 ! [B: int,R2: set_Pr8834758594704517033_o_int,A2: $o] :
% 4.69/4.89 ( ( member_int @ B @ ( image_o_int @ R2 @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 4.69/4.89 = ( member7847949116333733898_o_int @ ( product_Pair_o_int @ A2 @ B ) @ R2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % Image_singleton_iff
% 4.69/4.89 thf(fact_461_Image__singleton__iff,axiom,
% 4.69/4.89 ! [B: $o,R2: set_Product_prod_o_o,A2: $o] :
% 4.69/4.89 ( ( member_o @ B @ ( image_o_o @ R2 @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 4.69/4.89 = ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ B ) @ R2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % Image_singleton_iff
% 4.69/4.89 thf(fact_462_Image__singleton__iff,axiom,
% 4.69/4.89 ! [B: product_unit,R2: set_Pr6671815714118170108t_unit,A2: $o] :
% 4.69/4.89 ( ( member_Product_unit @ B @ ( image_o_Product_unit @ R2 @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 4.69/4.89 = ( member9215336023991391429t_unit @ ( produc3901946521647900940t_unit @ A2 @ B ) @ R2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % Image_singleton_iff
% 4.69/4.89 thf(fact_463_Image__singleton__iff,axiom,
% 4.69/4.89 ! [B: int,R2: set_Pr7995236796853374141at_int,A2: nat] :
% 4.69/4.89 ( ( member_int @ B @ ( image_nat_int @ R2 @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 4.69/4.89 = ( member4262671552274231302at_int @ ( product_Pair_nat_int @ A2 @ B ) @ R2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % Image_singleton_iff
% 4.69/4.89 thf(fact_464_Image__singleton__iff,axiom,
% 4.69/4.89 ! [B: $o,R2: set_Pr3149072824959771635_nat_o,A2: nat] :
% 4.69/4.89 ( ( member_o @ B @ ( image_nat_o @ R2 @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 4.69/4.89 = ( member6310962623043647828_nat_o @ ( product_Pair_nat_o @ A2 @ B ) @ R2 ) ) ).
% 4.69/4.89
% 4.69/4.89 % Image_singleton_iff
% 4.69/4.89 thf(fact_465_mult_Oright__assoc,axiom,
% 4.69/4.89 ! [A2: assn,B: assn,C: assn] :
% 4.69/4.89 ( ( times_times_assn @ ( times_times_assn @ A2 @ B ) @ C )
% 4.69/4.89 = ( times_times_assn @ A2 @ ( times_times_assn @ B @ C ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % mult.right_assoc
% 4.69/4.89 thf(fact_466_mult_Oright__assoc,axiom,
% 4.69/4.89 ! [A2: rat,B: rat,C: rat] :
% 4.69/4.89 ( ( times_times_rat @ ( times_times_rat @ A2 @ B ) @ C )
% 4.69/4.89 = ( times_times_rat @ A2 @ ( times_times_rat @ B @ C ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % mult.right_assoc
% 4.69/4.89 thf(fact_467_mult_Oright__assoc,axiom,
% 4.69/4.89 ! [A2: nat,B: nat,C: nat] :
% 4.69/4.89 ( ( times_times_nat @ ( times_times_nat @ A2 @ B ) @ C )
% 4.69/4.89 = ( times_times_nat @ A2 @ ( times_times_nat @ B @ C ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % mult.right_assoc
% 4.69/4.89 thf(fact_468_mult_Oright__assoc,axiom,
% 4.69/4.89 ! [A2: int,B: int,C: int] :
% 4.69/4.89 ( ( times_times_int @ ( times_times_int @ A2 @ B ) @ C )
% 4.69/4.89 = ( times_times_int @ A2 @ ( times_times_int @ B @ C ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % mult.right_assoc
% 4.69/4.89 thf(fact_469_mult_Oright__commute,axiom,
% 4.69/4.89 ! [A2: assn,B: assn,C: assn] :
% 4.69/4.89 ( ( times_times_assn @ ( times_times_assn @ A2 @ B ) @ C )
% 4.69/4.89 = ( times_times_assn @ ( times_times_assn @ A2 @ C ) @ B ) ) ).
% 4.69/4.89
% 4.69/4.89 % mult.right_commute
% 4.69/4.89 thf(fact_470_mult_Oright__commute,axiom,
% 4.69/4.89 ! [A2: rat,B: rat,C: rat] :
% 4.69/4.89 ( ( times_times_rat @ ( times_times_rat @ A2 @ B ) @ C )
% 4.69/4.89 = ( times_times_rat @ ( times_times_rat @ A2 @ C ) @ B ) ) ).
% 4.69/4.89
% 4.69/4.89 % mult.right_commute
% 4.69/4.89 thf(fact_471_mult_Oright__commute,axiom,
% 4.69/4.89 ! [A2: nat,B: nat,C: nat] :
% 4.69/4.89 ( ( times_times_nat @ ( times_times_nat @ A2 @ B ) @ C )
% 4.69/4.89 = ( times_times_nat @ ( times_times_nat @ A2 @ C ) @ B ) ) ).
% 4.69/4.89
% 4.69/4.89 % mult.right_commute
% 4.69/4.89 thf(fact_472_mult_Oright__commute,axiom,
% 4.69/4.89 ! [A2: int,B: int,C: int] :
% 4.69/4.89 ( ( times_times_int @ ( times_times_int @ A2 @ B ) @ C )
% 4.69/4.89 = ( times_times_int @ ( times_times_int @ A2 @ C ) @ B ) ) ).
% 4.69/4.89
% 4.69/4.89 % mult.right_commute
% 4.69/4.89 thf(fact_473_in__range__empty,axiom,
% 4.69/4.89 ! [H2: heap_e7401611519738050253t_unit] : ( in_range @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ).
% 4.69/4.89
% 4.69/4.89 % in_range_empty
% 4.69/4.89 thf(fact_474_ImageI,axiom,
% 4.69/4.89 ! [A2: nat,B: int,R2: set_Pr7995236796853374141at_int,A: set_nat] :
% 4.69/4.89 ( ( member4262671552274231302at_int @ ( product_Pair_nat_int @ A2 @ B ) @ R2 )
% 4.69/4.89 => ( ( member_nat @ A2 @ A )
% 4.69/4.89 => ( member_int @ B @ ( image_nat_int @ R2 @ A ) ) ) ) ).
% 4.69/4.89
% 4.69/4.89 % ImageI
% 4.69/4.89 thf(fact_475_ImageI,axiom,
% 4.69/4.90 ! [A2: nat,B: $o,R2: set_Pr3149072824959771635_nat_o,A: set_nat] :
% 4.69/4.90 ( ( member6310962623043647828_nat_o @ ( product_Pair_nat_o @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( ( member_nat @ A2 @ A )
% 4.69/4.90 => ( member_o @ B @ ( image_nat_o @ R2 @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % ImageI
% 4.69/4.90 thf(fact_476_ImageI,axiom,
% 4.69/4.90 ! [A2: nat,B: product_unit,R2: set_Pr4334478416066269672t_unit,A: set_nat] :
% 4.69/4.90 ( ( member348563419383025609t_unit @ ( produc3434450474625521892t_unit @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( ( member_nat @ A2 @ A )
% 4.69/4.90 => ( member_Product_unit @ B @ ( image_4288904962331477416t_unit @ R2 @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % ImageI
% 4.69/4.90 thf(fact_477_ImageI,axiom,
% 4.69/4.90 ! [A2: int,B: nat,R2: set_Pr3448869479623346877nt_nat,A: set_int] :
% 4.69/4.90 ( ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( ( member_int @ A2 @ A )
% 4.69/4.90 => ( member_nat @ B @ ( image_int_nat @ R2 @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % ImageI
% 4.69/4.90 thf(fact_478_ImageI,axiom,
% 4.69/4.90 ! [A2: int,B: $o,R2: set_Pr903927857289325719_int_o,A: set_int] :
% 4.69/4.90 ( ( member4489920277610959864_int_o @ ( product_Pair_int_o @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( ( member_int @ A2 @ A )
% 4.69/4.90 => ( member_o @ B @ ( image_int_o @ R2 @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % ImageI
% 4.69/4.90 thf(fact_479_ImageI,axiom,
% 4.69/4.90 ! [A2: int,B: product_unit,R2: set_Pr5889264611543340172t_unit,A: set_int] :
% 4.69/4.90 ( ( member6688357403439981677t_unit @ ( produc550872421827702152t_unit @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( ( member_int @ A2 @ A )
% 4.69/4.90 => ( member_Product_unit @ B @ ( image_1405326909533657676t_unit @ R2 @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % ImageI
% 4.69/4.90 thf(fact_480_ImageI,axiom,
% 4.69/4.90 ! [A2: $o,B: nat,R2: set_Pr2101469702781467981_o_nat,A: set_o] :
% 4.69/4.90 ( ( member2802428098988154798_o_nat @ ( product_Pair_o_nat @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( ( member_o @ A2 @ A )
% 4.69/4.90 => ( member_nat @ B @ ( image_o_nat @ R2 @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % ImageI
% 4.69/4.90 thf(fact_481_ImageI,axiom,
% 4.69/4.90 ! [A2: $o,B: int,R2: set_Pr8834758594704517033_o_int,A: set_o] :
% 4.69/4.90 ( ( member7847949116333733898_o_int @ ( product_Pair_o_int @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( ( member_o @ A2 @ A )
% 4.69/4.90 => ( member_int @ B @ ( image_o_int @ R2 @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % ImageI
% 4.69/4.90 thf(fact_482_ImageI,axiom,
% 4.69/4.90 ! [A2: $o,B: $o,R2: set_Product_prod_o_o,A: set_o] :
% 4.69/4.90 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( ( member_o @ A2 @ A )
% 4.69/4.90 => ( member_o @ B @ ( image_o_o @ R2 @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % ImageI
% 4.69/4.90 thf(fact_483_ImageI,axiom,
% 4.69/4.90 ! [A2: $o,B: product_unit,R2: set_Pr6671815714118170108t_unit,A: set_o] :
% 4.69/4.90 ( ( member9215336023991391429t_unit @ ( produc3901946521647900940t_unit @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( ( member_o @ A2 @ A )
% 4.69/4.90 => ( member_Product_unit @ B @ ( image_o_Product_unit @ R2 @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % ImageI
% 4.69/4.90 thf(fact_484_Image__empty2,axiom,
% 4.69/4.90 ! [R3: set_Pr5094982260447487303t_unit] :
% 4.69/4.90 ( ( image_8431784415008483091t_unit @ R3 @ bot_bo3957492148770167129t_unit )
% 4.69/4.90 = bot_bo3957492148770167129t_unit ) ).
% 4.69/4.90
% 4.69/4.90 % Image_empty2
% 4.69/4.90 thf(fact_485_Image__empty2,axiom,
% 4.69/4.90 ! [R3: set_Pr5464989305201766866unit_o] :
% 4.69/4.90 ( ( image_Product_unit_o @ R3 @ bot_bo3957492148770167129t_unit )
% 4.69/4.90 = bot_bot_set_o ) ).
% 4.69/4.90
% 4.69/4.90 % Image_empty2
% 4.69/4.90 thf(fact_486_Image__empty2,axiom,
% 4.69/4.90 ! [R3: set_Pr1763845938948868674it_nat] :
% 4.69/4.90 ( ( image_5657742817519485770it_nat @ R3 @ bot_bo3957492148770167129t_unit )
% 4.69/4.90 = bot_bot_set_nat ) ).
% 4.69/4.90
% 4.69/4.90 % Image_empty2
% 4.69/4.90 thf(fact_487_Image__empty2,axiom,
% 4.69/4.90 ! [R3: set_Pr8497134830871917726it_int] :
% 4.69/4.90 ( ( image_5655252347010435494it_int @ R3 @ bot_bo3957492148770167129t_unit )
% 4.69/4.90 = bot_bot_set_int ) ).
% 4.69/4.90
% 4.69/4.90 % Image_empty2
% 4.69/4.90 thf(fact_488_Image__empty2,axiom,
% 4.69/4.90 ! [R3: set_Pr6671815714118170108t_unit] :
% 4.69/4.90 ( ( image_o_Product_unit @ R3 @ bot_bot_set_o )
% 4.69/4.90 = bot_bo3957492148770167129t_unit ) ).
% 4.69/4.90
% 4.69/4.90 % Image_empty2
% 4.69/4.90 thf(fact_489_Image__empty2,axiom,
% 4.69/4.90 ! [R3: set_Product_prod_o_o] :
% 4.69/4.90 ( ( image_o_o @ R3 @ bot_bot_set_o )
% 4.69/4.90 = bot_bot_set_o ) ).
% 4.69/4.90
% 4.69/4.90 % Image_empty2
% 4.69/4.90 thf(fact_490_Image__empty2,axiom,
% 4.69/4.90 ! [R3: set_Pr2101469702781467981_o_nat] :
% 4.69/4.90 ( ( image_o_nat @ R3 @ bot_bot_set_o )
% 4.69/4.90 = bot_bot_set_nat ) ).
% 4.69/4.90
% 4.69/4.90 % Image_empty2
% 4.69/4.90 thf(fact_491_Image__empty2,axiom,
% 4.69/4.90 ! [R3: set_Pr8834758594704517033_o_int] :
% 4.69/4.90 ( ( image_o_int @ R3 @ bot_bot_set_o )
% 4.69/4.90 = bot_bot_set_int ) ).
% 4.69/4.90
% 4.69/4.90 % Image_empty2
% 4.69/4.90 thf(fact_492_Image__empty2,axiom,
% 4.69/4.90 ! [R3: set_Pr4334478416066269672t_unit] :
% 4.69/4.90 ( ( image_4288904962331477416t_unit @ R3 @ bot_bot_set_nat )
% 4.69/4.90 = bot_bo3957492148770167129t_unit ) ).
% 4.69/4.90
% 4.69/4.90 % Image_empty2
% 4.69/4.90 thf(fact_493_Image__empty2,axiom,
% 4.69/4.90 ! [R3: set_Pr3149072824959771635_nat_o] :
% 4.69/4.90 ( ( image_nat_o @ R3 @ bot_bot_set_nat )
% 4.69/4.90 = bot_bot_set_o ) ).
% 4.69/4.90
% 4.69/4.90 % Image_empty2
% 4.69/4.90 thf(fact_494_Id__onI,axiom,
% 4.69/4.90 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.90 ( ( member6576561426505652726_nat_o @ A2 @ A )
% 4.69/4.90 => ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ A2 ) @ ( id_on_7438695062414216554_nat_o @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Id_onI
% 4.69/4.90 thf(fact_495_Id__onI,axiom,
% 4.69/4.90 ! [A2: $o,A: set_o] :
% 4.69/4.90 ( ( member_o @ A2 @ A )
% 4.69/4.90 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ A2 ) @ ( id_on_o @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Id_onI
% 4.69/4.90 thf(fact_496_Id__onI,axiom,
% 4.69/4.90 ! [A2: product_unit,A: set_Product_unit] :
% 4.69/4.90 ( ( member_Product_unit @ A2 @ A )
% 4.69/4.90 => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A2 @ A2 ) @ ( id_on_Product_unit @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Id_onI
% 4.69/4.90 thf(fact_497_Id__onI,axiom,
% 4.69/4.90 ! [A2: nat,A: set_nat] :
% 4.69/4.90 ( ( member_nat @ A2 @ A )
% 4.69/4.90 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ A2 ) @ ( id_on_nat @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Id_onI
% 4.69/4.90 thf(fact_498_Id__onI,axiom,
% 4.69/4.90 ! [A2: int,A: set_int] :
% 4.69/4.90 ( ( member_int @ A2 @ A )
% 4.69/4.90 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ A2 ) @ ( id_on_int @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Id_onI
% 4.69/4.90 thf(fact_499_bool__assn__proper_I1_J,axiom,
% 4.69/4.90 proper @ in_range ).
% 4.69/4.90
% 4.69/4.90 % bool_assn_proper(1)
% 4.69/4.90 thf(fact_500_refl__on__domain,axiom,
% 4.69/4.90 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o] :
% 4.69/4.90 ( ( refl_o1075864025857821388_nat_o @ A @ R2 )
% 4.69/4.90 => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( ( member6576561426505652726_nat_o @ A2 @ A )
% 4.69/4.90 & ( member6576561426505652726_nat_o @ B @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % refl_on_domain
% 4.69/4.90 thf(fact_501_refl__on__domain,axiom,
% 4.69/4.90 ! [A: set_o,R2: set_Product_prod_o_o,A2: $o,B: $o] :
% 4.69/4.90 ( ( refl_on_o @ A @ R2 )
% 4.69/4.90 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( ( member_o @ A2 @ A )
% 4.69/4.90 & ( member_o @ B @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % refl_on_domain
% 4.69/4.90 thf(fact_502_refl__on__domain,axiom,
% 4.69/4.90 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit,A2: product_unit,B: product_unit] :
% 4.69/4.90 ( ( refl_on_Product_unit @ A @ R2 )
% 4.69/4.90 => ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( ( member_Product_unit @ A2 @ A )
% 4.69/4.90 & ( member_Product_unit @ B @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % refl_on_domain
% 4.69/4.90 thf(fact_503_refl__on__domain,axiom,
% 4.69/4.90 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,A2: nat,B: nat] :
% 4.69/4.90 ( ( refl_on_nat @ A @ R2 )
% 4.69/4.90 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( ( member_nat @ A2 @ A )
% 4.69/4.90 & ( member_nat @ B @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % refl_on_domain
% 4.69/4.90 thf(fact_504_refl__on__domain,axiom,
% 4.69/4.90 ! [A: set_int,R2: set_Pr958786334691620121nt_int,A2: int,B: int] :
% 4.69/4.90 ( ( refl_on_int @ A @ R2 )
% 4.69/4.90 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( ( member_int @ A2 @ A )
% 4.69/4.90 & ( member_int @ B @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % refl_on_domain
% 4.69/4.90 thf(fact_505_rev__ImageI,axiom,
% 4.69/4.90 ! [A2: nat,A: set_nat,B: int,R2: set_Pr7995236796853374141at_int] :
% 4.69/4.90 ( ( member_nat @ A2 @ A )
% 4.69/4.90 => ( ( member4262671552274231302at_int @ ( product_Pair_nat_int @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( member_int @ B @ ( image_nat_int @ R2 @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % rev_ImageI
% 4.69/4.90 thf(fact_506_rev__ImageI,axiom,
% 4.69/4.90 ! [A2: nat,A: set_nat,B: $o,R2: set_Pr3149072824959771635_nat_o] :
% 4.69/4.90 ( ( member_nat @ A2 @ A )
% 4.69/4.90 => ( ( member6310962623043647828_nat_o @ ( product_Pair_nat_o @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( member_o @ B @ ( image_nat_o @ R2 @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % rev_ImageI
% 4.69/4.90 thf(fact_507_rev__ImageI,axiom,
% 4.69/4.90 ! [A2: nat,A: set_nat,B: product_unit,R2: set_Pr4334478416066269672t_unit] :
% 4.69/4.90 ( ( member_nat @ A2 @ A )
% 4.69/4.90 => ( ( member348563419383025609t_unit @ ( produc3434450474625521892t_unit @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( member_Product_unit @ B @ ( image_4288904962331477416t_unit @ R2 @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % rev_ImageI
% 4.69/4.90 thf(fact_508_rev__ImageI,axiom,
% 4.69/4.90 ! [A2: int,A: set_int,B: nat,R2: set_Pr3448869479623346877nt_nat] :
% 4.69/4.90 ( ( member_int @ A2 @ A )
% 4.69/4.90 => ( ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( member_nat @ B @ ( image_int_nat @ R2 @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % rev_ImageI
% 4.69/4.90 thf(fact_509_rev__ImageI,axiom,
% 4.69/4.90 ! [A2: int,A: set_int,B: $o,R2: set_Pr903927857289325719_int_o] :
% 4.69/4.90 ( ( member_int @ A2 @ A )
% 4.69/4.90 => ( ( member4489920277610959864_int_o @ ( product_Pair_int_o @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( member_o @ B @ ( image_int_o @ R2 @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % rev_ImageI
% 4.69/4.90 thf(fact_510_rev__ImageI,axiom,
% 4.69/4.90 ! [A2: int,A: set_int,B: product_unit,R2: set_Pr5889264611543340172t_unit] :
% 4.69/4.90 ( ( member_int @ A2 @ A )
% 4.69/4.90 => ( ( member6688357403439981677t_unit @ ( produc550872421827702152t_unit @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( member_Product_unit @ B @ ( image_1405326909533657676t_unit @ R2 @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % rev_ImageI
% 4.69/4.90 thf(fact_511_rev__ImageI,axiom,
% 4.69/4.90 ! [A2: $o,A: set_o,B: nat,R2: set_Pr2101469702781467981_o_nat] :
% 4.69/4.90 ( ( member_o @ A2 @ A )
% 4.69/4.90 => ( ( member2802428098988154798_o_nat @ ( product_Pair_o_nat @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( member_nat @ B @ ( image_o_nat @ R2 @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % rev_ImageI
% 4.69/4.90 thf(fact_512_rev__ImageI,axiom,
% 4.69/4.90 ! [A2: $o,A: set_o,B: int,R2: set_Pr8834758594704517033_o_int] :
% 4.69/4.90 ( ( member_o @ A2 @ A )
% 4.69/4.90 => ( ( member7847949116333733898_o_int @ ( product_Pair_o_int @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( member_int @ B @ ( image_o_int @ R2 @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % rev_ImageI
% 4.69/4.90 thf(fact_513_rev__ImageI,axiom,
% 4.69/4.90 ! [A2: $o,A: set_o,B: $o,R2: set_Product_prod_o_o] :
% 4.69/4.90 ( ( member_o @ A2 @ A )
% 4.69/4.90 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( member_o @ B @ ( image_o_o @ R2 @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % rev_ImageI
% 4.69/4.90 thf(fact_514_rev__ImageI,axiom,
% 4.69/4.90 ! [A2: $o,A: set_o,B: product_unit,R2: set_Pr6671815714118170108t_unit] :
% 4.69/4.90 ( ( member_o @ A2 @ A )
% 4.69/4.90 => ( ( member9215336023991391429t_unit @ ( produc3901946521647900940t_unit @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( member_Product_unit @ B @ ( image_o_Product_unit @ R2 @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % rev_ImageI
% 4.69/4.90 thf(fact_515_Image__iff,axiom,
% 4.69/4.90 ! [B: set_nat,R2: set_Pr3948176798113811640et_nat,A: set_he8644174446132254637t_unit] :
% 4.69/4.90 ( ( member_set_nat @ B @ ( image_3942343239045813184et_nat @ R2 @ A ) )
% 4.69/4.90 = ( ? [X2: heap_e7401611519738050253t_unit] :
% 4.69/4.90 ( ( member242389114213480694t_unit @ X2 @ A )
% 4.69/4.90 & ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Image_iff
% 4.69/4.90 thf(fact_516_Image__iff,axiom,
% 4.69/4.90 ! [B: nat,R2: set_Pr1261947904930325089at_nat,A: set_nat] :
% 4.69/4.90 ( ( member_nat @ B @ ( image_nat_nat @ R2 @ A ) )
% 4.69/4.90 = ( ? [X2: nat] :
% 4.69/4.90 ( ( member_nat @ X2 @ A )
% 4.69/4.90 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Image_iff
% 4.69/4.90 thf(fact_517_Image__iff,axiom,
% 4.69/4.90 ! [B: int,R2: set_Pr958786334691620121nt_int,A: set_int] :
% 4.69/4.90 ( ( member_int @ B @ ( image_int_int @ R2 @ A ) )
% 4.69/4.90 = ( ? [X2: int] :
% 4.69/4.90 ( ( member_int @ X2 @ A )
% 4.69/4.90 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Image_iff
% 4.69/4.90 thf(fact_518_Image__iff,axiom,
% 4.69/4.90 ! [B: produc3658429121746597890et_nat,R2: set_Pr3286484037609594932et_nat,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.90 ( ( member6260224972018164377et_nat @ B @ ( image_1814916760386648892et_nat @ R2 @ A ) )
% 4.69/4.90 = ( ? [X2: produc3658429121746597890et_nat > $o] :
% 4.69/4.90 ( ( member6576561426505652726_nat_o @ X2 @ A )
% 4.69/4.90 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Image_iff
% 4.69/4.90 thf(fact_519_Image__iff,axiom,
% 4.69/4.90 ! [B: produc3925858234332021118et_nat,R2: set_Pr8536935166611901872et_nat,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.90 ( ( member1996754912294343701et_nat @ B @ ( image_7240710759097644216et_nat @ R2 @ A ) )
% 4.69/4.90 = ( ? [X2: produc3658429121746597890et_nat > $o] :
% 4.69/4.90 ( ( member6576561426505652726_nat_o @ X2 @ A )
% 4.69/4.90 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Image_iff
% 4.69/4.90 thf(fact_520_ImageE,axiom,
% 4.69/4.90 ! [B: nat,R2: set_Pr3448869479623346877nt_nat,A: set_int] :
% 4.69/4.90 ( ( member_nat @ B @ ( image_int_nat @ R2 @ A ) )
% 4.69/4.90 => ~ ! [X3: int] :
% 4.69/4.90 ( ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ X3 @ B ) @ R2 )
% 4.69/4.90 => ~ ( member_int @ X3 @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % ImageE
% 4.69/4.90 thf(fact_521_ImageE,axiom,
% 4.69/4.90 ! [B: nat,R2: set_Pr2101469702781467981_o_nat,A: set_o] :
% 4.69/4.90 ( ( member_nat @ B @ ( image_o_nat @ R2 @ A ) )
% 4.69/4.90 => ~ ! [X3: $o] :
% 4.69/4.90 ( ( member2802428098988154798_o_nat @ ( product_Pair_o_nat @ X3 @ B ) @ R2 )
% 4.69/4.90 => ~ ( member_o @ X3 @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % ImageE
% 4.69/4.90 thf(fact_522_ImageE,axiom,
% 4.69/4.90 ! [B: nat,R2: set_Pr1763845938948868674it_nat,A: set_Product_unit] :
% 4.69/4.90 ( ( member_nat @ B @ ( image_5657742817519485770it_nat @ R2 @ A ) )
% 4.69/4.90 => ~ ! [X3: product_unit] :
% 4.69/4.90 ( ( member423003724879500579it_nat @ ( produc4803288329813530246it_nat @ X3 @ B ) @ R2 )
% 4.69/4.90 => ~ ( member_Product_unit @ X3 @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % ImageE
% 4.69/4.90 thf(fact_523_ImageE,axiom,
% 4.69/4.90 ! [B: int,R2: set_Pr7995236796853374141at_int,A: set_nat] :
% 4.69/4.90 ( ( member_int @ B @ ( image_nat_int @ R2 @ A ) )
% 4.69/4.90 => ~ ! [X3: nat] :
% 4.69/4.90 ( ( member4262671552274231302at_int @ ( product_Pair_nat_int @ X3 @ B ) @ R2 )
% 4.69/4.90 => ~ ( member_nat @ X3 @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % ImageE
% 4.69/4.90 thf(fact_524_ImageE,axiom,
% 4.69/4.90 ! [B: int,R2: set_Pr8834758594704517033_o_int,A: set_o] :
% 4.69/4.90 ( ( member_int @ B @ ( image_o_int @ R2 @ A ) )
% 4.69/4.90 => ~ ! [X3: $o] :
% 4.69/4.90 ( ( member7847949116333733898_o_int @ ( product_Pair_o_int @ X3 @ B ) @ R2 )
% 4.69/4.90 => ~ ( member_o @ X3 @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % ImageE
% 4.69/4.90 thf(fact_525_ImageE,axiom,
% 4.69/4.90 ! [B: int,R2: set_Pr8497134830871917726it_int,A: set_Product_unit] :
% 4.69/4.90 ( ( member_int @ B @ ( image_5655252347010435494it_int @ R2 @ A ) )
% 4.69/4.90 => ~ ! [X3: product_unit] :
% 4.69/4.90 ( ( member5468524742225079679it_int @ ( produc4800797859304479970it_int @ X3 @ B ) @ R2 )
% 4.69/4.90 => ~ ( member_Product_unit @ X3 @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % ImageE
% 4.69/4.90 thf(fact_526_ImageE,axiom,
% 4.69/4.90 ! [B: $o,R2: set_Pr3149072824959771635_nat_o,A: set_nat] :
% 4.69/4.90 ( ( member_o @ B @ ( image_nat_o @ R2 @ A ) )
% 4.69/4.90 => ~ ! [X3: nat] :
% 4.69/4.90 ( ( member6310962623043647828_nat_o @ ( product_Pair_nat_o @ X3 @ B ) @ R2 )
% 4.69/4.90 => ~ ( member_nat @ X3 @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % ImageE
% 4.69/4.90 thf(fact_527_ImageE,axiom,
% 4.69/4.90 ! [B: $o,R2: set_Pr903927857289325719_int_o,A: set_int] :
% 4.69/4.90 ( ( member_o @ B @ ( image_int_o @ R2 @ A ) )
% 4.69/4.90 => ~ ! [X3: int] :
% 4.69/4.90 ( ( member4489920277610959864_int_o @ ( product_Pair_int_o @ X3 @ B ) @ R2 )
% 4.69/4.90 => ~ ( member_int @ X3 @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % ImageE
% 4.69/4.90 thf(fact_528_ImageE,axiom,
% 4.69/4.90 ! [B: $o,R2: set_Product_prod_o_o,A: set_o] :
% 4.69/4.90 ( ( member_o @ B @ ( image_o_o @ R2 @ A ) )
% 4.69/4.90 => ~ ! [X3: $o] :
% 4.69/4.90 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X3 @ B ) @ R2 )
% 4.69/4.90 => ~ ( member_o @ X3 @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % ImageE
% 4.69/4.90 thf(fact_529_ImageE,axiom,
% 4.69/4.90 ! [B: $o,R2: set_Pr5464989305201766866unit_o,A: set_Product_unit] :
% 4.69/4.90 ( ( member_o @ B @ ( image_Product_unit_o @ R2 @ A ) )
% 4.69/4.90 => ~ ! [X3: product_unit] :
% 4.69/4.90 ( ( member3689400097658526619unit_o @ ( produc8487917018914037602unit_o @ X3 @ B ) @ R2 )
% 4.69/4.90 => ~ ( member_Product_unit @ X3 @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % ImageE
% 4.69/4.90 thf(fact_530_refl__onD2,axiom,
% 4.69/4.90 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o] :
% 4.69/4.90 ( ( refl_o1075864025857821388_nat_o @ A @ R2 )
% 4.69/4.90 => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ R2 )
% 4.69/4.90 => ( member6576561426505652726_nat_o @ Y @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % refl_onD2
% 4.69/4.90 thf(fact_531_refl__onD2,axiom,
% 4.69/4.90 ! [A: set_o,R2: set_Product_prod_o_o,X: $o,Y: $o] :
% 4.69/4.90 ( ( refl_on_o @ A @ R2 )
% 4.69/4.90 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ R2 )
% 4.69/4.90 => ( member_o @ Y @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % refl_onD2
% 4.69/4.90 thf(fact_532_refl__onD2,axiom,
% 4.69/4.90 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit,X: product_unit,Y: product_unit] :
% 4.69/4.90 ( ( refl_on_Product_unit @ A @ R2 )
% 4.69/4.90 => ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X @ Y ) @ R2 )
% 4.69/4.90 => ( member_Product_unit @ Y @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % refl_onD2
% 4.69/4.90 thf(fact_533_refl__onD2,axiom,
% 4.69/4.90 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,X: nat,Y: nat] :
% 4.69/4.90 ( ( refl_on_nat @ A @ R2 )
% 4.69/4.90 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R2 )
% 4.69/4.90 => ( member_nat @ Y @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % refl_onD2
% 4.69/4.90 thf(fact_534_refl__onD2,axiom,
% 4.69/4.90 ! [A: set_int,R2: set_Pr958786334691620121nt_int,X: int,Y: int] :
% 4.69/4.90 ( ( refl_on_int @ A @ R2 )
% 4.69/4.90 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R2 )
% 4.69/4.90 => ( member_int @ Y @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % refl_onD2
% 4.69/4.90 thf(fact_535_refl__onD1,axiom,
% 4.69/4.90 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o] :
% 4.69/4.90 ( ( refl_o1075864025857821388_nat_o @ A @ R2 )
% 4.69/4.90 => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ R2 )
% 4.69/4.90 => ( member6576561426505652726_nat_o @ X @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % refl_onD1
% 4.69/4.90 thf(fact_536_refl__onD1,axiom,
% 4.69/4.90 ! [A: set_o,R2: set_Product_prod_o_o,X: $o,Y: $o] :
% 4.69/4.90 ( ( refl_on_o @ A @ R2 )
% 4.69/4.90 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ R2 )
% 4.69/4.90 => ( member_o @ X @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % refl_onD1
% 4.69/4.90 thf(fact_537_refl__onD1,axiom,
% 4.69/4.90 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit,X: product_unit,Y: product_unit] :
% 4.69/4.90 ( ( refl_on_Product_unit @ A @ R2 )
% 4.69/4.90 => ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X @ Y ) @ R2 )
% 4.69/4.90 => ( member_Product_unit @ X @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % refl_onD1
% 4.69/4.90 thf(fact_538_refl__onD1,axiom,
% 4.69/4.90 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,X: nat,Y: nat] :
% 4.69/4.90 ( ( refl_on_nat @ A @ R2 )
% 4.69/4.90 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R2 )
% 4.69/4.90 => ( member_nat @ X @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % refl_onD1
% 4.69/4.90 thf(fact_539_refl__onD1,axiom,
% 4.69/4.90 ! [A: set_int,R2: set_Pr958786334691620121nt_int,X: int,Y: int] :
% 4.69/4.90 ( ( refl_on_int @ A @ R2 )
% 4.69/4.90 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R2 )
% 4.69/4.90 => ( member_int @ X @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % refl_onD1
% 4.69/4.90 thf(fact_540_refl__onD,axiom,
% 4.69/4.90 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/4.90 ( ( refl_o1075864025857821388_nat_o @ A @ R2 )
% 4.69/4.90 => ( ( member6576561426505652726_nat_o @ A2 @ A )
% 4.69/4.90 => ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ A2 ) @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % refl_onD
% 4.69/4.90 thf(fact_541_refl__onD,axiom,
% 4.69/4.90 ! [A: set_o,R2: set_Product_prod_o_o,A2: $o] :
% 4.69/4.90 ( ( refl_on_o @ A @ R2 )
% 4.69/4.90 => ( ( member_o @ A2 @ A )
% 4.69/4.90 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ A2 ) @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % refl_onD
% 4.69/4.90 thf(fact_542_refl__onD,axiom,
% 4.69/4.90 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit,A2: product_unit] :
% 4.69/4.90 ( ( refl_on_Product_unit @ A @ R2 )
% 4.69/4.90 => ( ( member_Product_unit @ A2 @ A )
% 4.69/4.90 => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A2 @ A2 ) @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % refl_onD
% 4.69/4.90 thf(fact_543_refl__onD,axiom,
% 4.69/4.90 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,A2: nat] :
% 4.69/4.90 ( ( refl_on_nat @ A @ R2 )
% 4.69/4.90 => ( ( member_nat @ A2 @ A )
% 4.69/4.90 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ A2 ) @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % refl_onD
% 4.69/4.90 thf(fact_544_refl__onD,axiom,
% 4.69/4.90 ! [A: set_int,R2: set_Pr958786334691620121nt_int,A2: int] :
% 4.69/4.90 ( ( refl_on_int @ A @ R2 )
% 4.69/4.90 => ( ( member_int @ A2 @ A )
% 4.69/4.90 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ A2 ) @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % refl_onD
% 4.69/4.90 thf(fact_545_total__on__def,axiom,
% 4.69/4.90 ( total_on_nat
% 4.69/4.90 = ( ^ [A3: set_nat,R4: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ! [X2: nat] :
% 4.69/4.90 ( ( member_nat @ X2 @ A3 )
% 4.69/4.90 => ! [Y3: nat] :
% 4.69/4.90 ( ( member_nat @ Y3 @ A3 )
% 4.69/4.90 => ( ( X2 != Y3 )
% 4.69/4.90 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ R4 )
% 4.69/4.90 | ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ X2 ) @ R4 ) ) ) ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % total_on_def
% 4.69/4.90 thf(fact_546_total__on__def,axiom,
% 4.69/4.90 ( total_on_int
% 4.69/4.90 = ( ^ [A3: set_int,R4: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ! [X2: int] :
% 4.69/4.90 ( ( member_int @ X2 @ A3 )
% 4.69/4.90 => ! [Y3: int] :
% 4.69/4.90 ( ( member_int @ Y3 @ A3 )
% 4.69/4.90 => ( ( X2 != Y3 )
% 4.69/4.90 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ R4 )
% 4.69/4.90 | ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ X2 ) @ R4 ) ) ) ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % total_on_def
% 4.69/4.90 thf(fact_547_total__onI,axiom,
% 4.69/4.90 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o] :
% 4.69/4.90 ( ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat > $o] :
% 4.69/4.90 ( ( member6576561426505652726_nat_o @ X3 @ A )
% 4.69/4.90 => ( ( member6576561426505652726_nat_o @ Y2 @ A )
% 4.69/4.90 => ( ( X3 != Y2 )
% 4.69/4.90 => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X3 @ Y2 ) @ R2 )
% 4.69/4.90 | ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ Y2 @ X3 ) @ R2 ) ) ) ) )
% 4.69/4.90 => ( total_7429123086324524369_nat_o @ A @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % total_onI
% 4.69/4.90 thf(fact_548_total__onI,axiom,
% 4.69/4.90 ! [A: set_o,R2: set_Product_prod_o_o] :
% 4.69/4.90 ( ! [X3: $o,Y2: $o] :
% 4.69/4.90 ( ( member_o @ X3 @ A )
% 4.69/4.90 => ( ( member_o @ Y2 @ A )
% 4.69/4.90 => ( ( X3 != Y2 )
% 4.69/4.90 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X3 @ Y2 ) @ R2 )
% 4.69/4.90 | ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ Y2 @ X3 ) @ R2 ) ) ) ) )
% 4.69/4.90 => ( total_on_o @ A @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % total_onI
% 4.69/4.90 thf(fact_549_total__onI,axiom,
% 4.69/4.90 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit] :
% 4.69/4.90 ( ! [X3: product_unit,Y2: product_unit] :
% 4.69/4.90 ( ( member_Product_unit @ X3 @ A )
% 4.69/4.90 => ( ( member_Product_unit @ Y2 @ A )
% 4.69/4.90 => ( ( X3 != Y2 )
% 4.69/4.90 => ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X3 @ Y2 ) @ R2 )
% 4.69/4.90 | ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ Y2 @ X3 ) @ R2 ) ) ) ) )
% 4.69/4.90 => ( total_5665700600833547665t_unit @ A @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % total_onI
% 4.69/4.90 thf(fact_550_total__onI,axiom,
% 4.69/4.90 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ! [X3: nat,Y2: nat] :
% 4.69/4.90 ( ( member_nat @ X3 @ A )
% 4.69/4.90 => ( ( member_nat @ Y2 @ A )
% 4.69/4.90 => ( ( X3 != Y2 )
% 4.69/4.90 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ R2 )
% 4.69/4.90 | ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ X3 ) @ R2 ) ) ) ) )
% 4.69/4.90 => ( total_on_nat @ A @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % total_onI
% 4.69/4.90 thf(fact_551_total__onI,axiom,
% 4.69/4.90 ! [A: set_int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ! [X3: int,Y2: int] :
% 4.69/4.90 ( ( member_int @ X3 @ A )
% 4.69/4.90 => ( ( member_int @ Y2 @ A )
% 4.69/4.90 => ( ( X3 != Y2 )
% 4.69/4.90 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y2 ) @ R2 )
% 4.69/4.90 | ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y2 @ X3 ) @ R2 ) ) ) ) )
% 4.69/4.90 => ( total_on_int @ A @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % total_onI
% 4.69/4.90 thf(fact_552_total__on__empty,axiom,
% 4.69/4.90 ! [R2: set_Pr5094982260447487303t_unit] : ( total_5665700600833547665t_unit @ bot_bo3957492148770167129t_unit @ R2 ) ).
% 4.69/4.90
% 4.69/4.90 % total_on_empty
% 4.69/4.90 thf(fact_553_total__on__empty,axiom,
% 4.69/4.90 ! [R2: set_Product_prod_o_o] : ( total_on_o @ bot_bot_set_o @ R2 ) ).
% 4.69/4.90
% 4.69/4.90 % total_on_empty
% 4.69/4.90 thf(fact_554_total__on__empty,axiom,
% 4.69/4.90 ! [R2: set_Pr1261947904930325089at_nat] : ( total_on_nat @ bot_bot_set_nat @ R2 ) ).
% 4.69/4.90
% 4.69/4.90 % total_on_empty
% 4.69/4.90 thf(fact_555_total__on__empty,axiom,
% 4.69/4.90 ! [R2: set_Pr958786334691620121nt_int] : ( total_on_int @ bot_bot_set_int @ R2 ) ).
% 4.69/4.90
% 4.69/4.90 % total_on_empty
% 4.69/4.90 thf(fact_556_total__on__empty,axiom,
% 4.69/4.90 ! [R2: set_Pr2161125870931222855_nat_o] : ( total_7429123086324524369_nat_o @ bot_bo7824918357723582233_nat_o @ R2 ) ).
% 4.69/4.90
% 4.69/4.90 % total_on_empty
% 4.69/4.90 thf(fact_557_models__in__range,axiom,
% 4.69/4.90 ! [P: assn,H2: produc3658429121746597890et_nat] :
% 4.69/4.90 ( ( rep_assn @ P @ H2 )
% 4.69/4.90 => ( in_range @ H2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % models_in_range
% 4.69/4.90 thf(fact_558_Id__on__iff,axiom,
% 4.69/4.90 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.90 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ ( id_on_7438695062414216554_nat_o @ A ) )
% 4.69/4.90 = ( ( X = Y )
% 4.69/4.90 & ( member6576561426505652726_nat_o @ X @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Id_on_iff
% 4.69/4.90 thf(fact_559_Id__on__iff,axiom,
% 4.69/4.90 ! [X: $o,Y: $o,A: set_o] :
% 4.69/4.90 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ ( id_on_o @ A ) )
% 4.69/4.90 = ( ( X = Y )
% 4.69/4.90 & ( member_o @ X @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Id_on_iff
% 4.69/4.90 thf(fact_560_Id__on__iff,axiom,
% 4.69/4.90 ! [X: product_unit,Y: product_unit,A: set_Product_unit] :
% 4.69/4.90 ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X @ Y ) @ ( id_on_Product_unit @ A ) )
% 4.69/4.90 = ( ( X = Y )
% 4.69/4.90 & ( member_Product_unit @ X @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Id_on_iff
% 4.69/4.90 thf(fact_561_Id__on__iff,axiom,
% 4.69/4.90 ! [X: nat,Y: nat,A: set_nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( id_on_nat @ A ) )
% 4.69/4.90 = ( ( X = Y )
% 4.69/4.90 & ( member_nat @ X @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Id_on_iff
% 4.69/4.90 thf(fact_562_Id__on__iff,axiom,
% 4.69/4.90 ! [X: int,Y: int,A: set_int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( id_on_int @ A ) )
% 4.69/4.90 = ( ( X = Y )
% 4.69/4.90 & ( member_int @ X @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Id_on_iff
% 4.69/4.90 thf(fact_563_Id__on__eqI,axiom,
% 4.69/4.90 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.90 ( ( A2 = B )
% 4.69/4.90 => ( ( member6576561426505652726_nat_o @ A2 @ A )
% 4.69/4.90 => ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ B ) @ ( id_on_7438695062414216554_nat_o @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Id_on_eqI
% 4.69/4.90 thf(fact_564_Id__on__eqI,axiom,
% 4.69/4.90 ! [A2: $o,B: $o,A: set_o] :
% 4.69/4.90 ( ( A2 = B )
% 4.69/4.90 => ( ( member_o @ A2 @ A )
% 4.69/4.90 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ B ) @ ( id_on_o @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Id_on_eqI
% 4.69/4.90 thf(fact_565_Id__on__eqI,axiom,
% 4.69/4.90 ! [A2: product_unit,B: product_unit,A: set_Product_unit] :
% 4.69/4.90 ( ( A2 = B )
% 4.69/4.90 => ( ( member_Product_unit @ A2 @ A )
% 4.69/4.90 => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A2 @ B ) @ ( id_on_Product_unit @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Id_on_eqI
% 4.69/4.90 thf(fact_566_Id__on__eqI,axiom,
% 4.69/4.90 ! [A2: nat,B: nat,A: set_nat] :
% 4.69/4.90 ( ( A2 = B )
% 4.69/4.90 => ( ( member_nat @ A2 @ A )
% 4.69/4.90 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( id_on_nat @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Id_on_eqI
% 4.69/4.90 thf(fact_567_Id__on__eqI,axiom,
% 4.69/4.90 ! [A2: int,B: int,A: set_int] :
% 4.69/4.90 ( ( A2 = B )
% 4.69/4.90 => ( ( member_int @ A2 @ A )
% 4.69/4.90 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( id_on_int @ A ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Id_on_eqI
% 4.69/4.90 thf(fact_568_Id__onE,axiom,
% 4.69/4.90 ! [C: produc4928098042776334183_nat_o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.90 ( ( member8781333585448626064_nat_o @ C @ ( id_on_7438695062414216554_nat_o @ A ) )
% 4.69/4.90 => ~ ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.90 ( ( member6576561426505652726_nat_o @ X3 @ A )
% 4.69/4.90 => ( C
% 4.69/4.90 != ( produc7368190662567826135_nat_o @ X3 @ X3 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Id_onE
% 4.69/4.90 thf(fact_569_Id__onE,axiom,
% 4.69/4.90 ! [C: product_prod_o_o,A: set_o] :
% 4.69/4.90 ( ( member7466972457876170832od_o_o @ C @ ( id_on_o @ A ) )
% 4.69/4.90 => ~ ! [X3: $o] :
% 4.69/4.90 ( ( member_o @ X3 @ A )
% 4.69/4.90 => ( C
% 4.69/4.90 != ( product_Pair_o_o @ X3 @ X3 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Id_onE
% 4.69/4.90 thf(fact_570_Id__onE,axiom,
% 4.69/4.90 ! [C: produc8459935480633519975t_unit,A: set_Product_unit] :
% 4.69/4.90 ( ( member7821138191923116944t_unit @ C @ ( id_on_Product_unit @ A ) )
% 4.69/4.90 => ~ ! [X3: product_unit] :
% 4.69/4.90 ( ( member_Product_unit @ X3 @ A )
% 4.69/4.90 => ( C
% 4.69/4.90 != ( produc5692694829384537815t_unit @ X3 @ X3 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Id_onE
% 4.69/4.90 thf(fact_571_Id__onE,axiom,
% 4.69/4.90 ! [C: product_prod_nat_nat,A: set_nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ C @ ( id_on_nat @ A ) )
% 4.69/4.90 => ~ ! [X3: nat] :
% 4.69/4.90 ( ( member_nat @ X3 @ A )
% 4.69/4.90 => ( C
% 4.69/4.90 != ( product_Pair_nat_nat @ X3 @ X3 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Id_onE
% 4.69/4.90 thf(fact_572_Id__onE,axiom,
% 4.69/4.90 ! [C: product_prod_int_int,A: set_int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ C @ ( id_on_int @ A ) )
% 4.69/4.90 => ~ ! [X3: int] :
% 4.69/4.90 ( ( member_int @ X3 @ A )
% 4.69/4.90 => ( C
% 4.69/4.90 != ( product_Pair_int_int @ X3 @ X3 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Id_onE
% 4.69/4.90 thf(fact_573_lnear__order__on__empty,axiom,
% 4.69/4.90 order_888282469287196226t_unit @ bot_bo3957492148770167129t_unit @ bot_bo1654022762305692595t_unit ).
% 4.69/4.90
% 4.69/4.90 % lnear_order_on_empty
% 4.69/4.90 thf(fact_574_lnear__order__on__empty,axiom,
% 4.69/4.90 order_6238756238976269133r_on_o @ bot_bot_set_o @ bot_bo7073875226086086771od_o_o ).
% 4.69/4.90
% 4.69/4.90 % lnear_order_on_empty
% 4.69/4.90 thf(fact_575_lnear__order__on__empty,axiom,
% 4.69/4.90 order_4473980167227706203on_nat @ bot_bot_set_nat @ bot_bo2099793752762293965at_nat ).
% 4.69/4.90
% 4.69/4.90 % lnear_order_on_empty
% 4.69/4.90 thf(fact_576_lnear__order__on__empty,axiom,
% 4.69/4.90 order_4471489696718655927on_int @ bot_bot_set_int @ bot_bo1796632182523588997nt_int ).
% 4.69/4.90
% 4.69/4.90 % lnear_order_on_empty
% 4.69/4.90 thf(fact_577_lnear__order__on__empty,axiom,
% 4.69/4.90 order_1145710701291701250_nat_o @ bot_bo7824918357723582233_nat_o @ bot_bo3657187498359500723_nat_o ).
% 4.69/4.90
% 4.69/4.90 % lnear_order_on_empty
% 4.69/4.90 thf(fact_578_refl__on__empty,axiom,
% 4.69/4.90 refl_on_Product_unit @ bot_bo3957492148770167129t_unit @ bot_bo1654022762305692595t_unit ).
% 4.69/4.90
% 4.69/4.90 % refl_on_empty
% 4.69/4.90 thf(fact_579_refl__on__empty,axiom,
% 4.69/4.90 refl_on_o @ bot_bot_set_o @ bot_bo7073875226086086771od_o_o ).
% 4.69/4.90
% 4.69/4.90 % refl_on_empty
% 4.69/4.90 thf(fact_580_refl__on__empty,axiom,
% 4.69/4.90 refl_on_nat @ bot_bot_set_nat @ bot_bo2099793752762293965at_nat ).
% 4.69/4.90
% 4.69/4.90 % refl_on_empty
% 4.69/4.90 thf(fact_581_refl__on__empty,axiom,
% 4.69/4.90 refl_on_int @ bot_bot_set_int @ bot_bo1796632182523588997nt_int ).
% 4.69/4.90
% 4.69/4.90 % refl_on_empty
% 4.69/4.90 thf(fact_582_refl__on__empty,axiom,
% 4.69/4.90 refl_o1075864025857821388_nat_o @ bot_bo7824918357723582233_nat_o @ bot_bo3657187498359500723_nat_o ).
% 4.69/4.90
% 4.69/4.90 % refl_on_empty
% 4.69/4.90 thf(fact_583_properD1,axiom,
% 4.69/4.90 ! [P: produc3658429121746597890et_nat > $o,H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 4.69/4.90 ( ( proper @ P )
% 4.69/4.90 => ( ( P @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 4.69/4.90 => ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % properD1
% 4.69/4.90 thf(fact_584_proper__iff,axiom,
% 4.69/4.90 ! [P: produc3658429121746597890et_nat > $o,As: set_nat,H2: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit] :
% 4.69/4.90 ( ( proper @ P )
% 4.69/4.90 => ( ( relH @ As @ H2 @ H3 )
% 4.69/4.90 => ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 4.69/4.90 => ( ( P @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 4.69/4.90 = ( P @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % proper_iff
% 4.69/4.90 thf(fact_585_proper__def,axiom,
% 4.69/4.90 ( proper
% 4.69/4.90 = ( ^ [P2: produc3658429121746597890et_nat > $o] :
% 4.69/4.90 ! [H4: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit,As3: set_nat] :
% 4.69/4.90 ( ( ( P2 @ ( produc7507926704131184380et_nat @ H4 @ As3 ) )
% 4.69/4.90 => ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As3 ) ) )
% 4.69/4.90 & ( ( ( P2 @ ( produc7507926704131184380et_nat @ H4 @ As3 ) )
% 4.69/4.90 & ( relH @ As3 @ H4 @ H5 )
% 4.69/4.90 & ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As3 ) ) )
% 4.69/4.90 => ( P2 @ ( produc7507926704131184380et_nat @ H5 @ As3 ) ) ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % proper_def
% 4.69/4.90 thf(fact_586_properD2,axiom,
% 4.69/4.90 ! [P: produc3658429121746597890et_nat > $o,H2: heap_e7401611519738050253t_unit,As: set_nat,H3: heap_e7401611519738050253t_unit] :
% 4.69/4.90 ( ( proper @ P )
% 4.69/4.90 => ( ( P @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 4.69/4.90 => ( ( relH @ As @ H2 @ H3 )
% 4.69/4.90 => ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 4.69/4.90 => ( P @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % properD2
% 4.69/4.90 thf(fact_587_properI,axiom,
% 4.69/4.90 ! [P: produc3658429121746597890et_nat > $o] :
% 4.69/4.90 ( ! [As2: set_nat,H: heap_e7401611519738050253t_unit] :
% 4.69/4.90 ( ( P @ ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.90 => ( in_range @ ( produc7507926704131184380et_nat @ H @ As2 ) ) )
% 4.69/4.90 => ( ! [As2: set_nat,H: heap_e7401611519738050253t_unit,H6: heap_e7401611519738050253t_unit] :
% 4.69/4.90 ( ( P @ ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.90 => ( ( relH @ As2 @ H @ H6 )
% 4.69/4.90 => ( ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As2 ) )
% 4.69/4.90 => ( P @ ( produc7507926704131184380et_nat @ H6 @ As2 ) ) ) ) )
% 4.69/4.90 => ( proper @ P ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % properI
% 4.69/4.90 thf(fact_588_pair__vimage__is__Image,axiom,
% 4.69/4.90 ! [U: heap_e7401611519738050253t_unit,E: set_Pr3948176798113811640et_nat] :
% 4.69/4.90 ( ( vimage5412618565253405765et_nat @ ( produc7507926704131184380et_nat @ U ) @ E )
% 4.69/4.90 = ( image_3942343239045813184et_nat @ E @ ( insert8563697753282147485t_unit @ U @ bot_bo3686245532977126937t_unit ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % pair_vimage_is_Image
% 4.69/4.90 thf(fact_589_pair__vimage__is__Image,axiom,
% 4.69/4.90 ! [U: nat,E: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ( vimage8013328719654469172at_nat @ ( product_Pair_nat_nat @ U ) @ E )
% 4.69/4.90 = ( image_nat_nat @ E @ ( insert_nat @ U @ bot_bot_set_nat ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % pair_vimage_is_Image
% 4.69/4.90 thf(fact_590_pair__vimage__is__Image,axiom,
% 4.69/4.90 ! [U: int,E: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ( vimage7872673496510460816nt_int @ ( product_Pair_int_int @ U ) @ E )
% 4.69/4.90 = ( image_int_int @ E @ ( insert_int @ U @ bot_bot_set_int ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % pair_vimage_is_Image
% 4.69/4.90 thf(fact_591_pair__vimage__is__Image,axiom,
% 4.69/4.90 ! [U: produc3658429121746597890et_nat > $o,E: set_Pr3286484037609594932et_nat] :
% 4.69/4.90 ( ( vimage1990136491886319165et_nat @ ( produc5001842942810119800et_nat @ U ) @ E )
% 4.69/4.90 = ( image_1814916760386648892et_nat @ E @ ( insert5175938949040314269_nat_o @ U @ bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % pair_vimage_is_Image
% 4.69/4.90 thf(fact_592_pair__vimage__is__Image,axiom,
% 4.69/4.90 ! [U: produc3658429121746597890et_nat > $o,E: set_Pr8536935166611901872et_nat] :
% 4.69/4.90 ( ( vimage7160910655466636085et_nat @ ( produc2245416461498447860et_nat @ U ) @ E )
% 4.69/4.90 = ( image_7240710759097644216et_nat @ E @ ( insert5175938949040314269_nat_o @ U @ bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % pair_vimage_is_Image
% 4.69/4.90 thf(fact_593_Range__insert,axiom,
% 4.69/4.90 ! [A2: heap_e7401611519738050253t_unit,B: set_nat,R2: set_Pr3948176798113811640et_nat] :
% 4.69/4.90 ( ( range_9132311542094983838et_nat @ ( insert1271470778893645362et_nat @ ( produc7507926704131184380et_nat @ A2 @ B ) @ R2 ) )
% 4.69/4.90 = ( insert_set_nat @ B @ ( range_9132311542094983838et_nat @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range_insert
% 4.69/4.90 thf(fact_594_Range__insert,axiom,
% 4.69/4.90 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ( range_nat_nat @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 ) )
% 4.69/4.90 = ( insert_nat @ B @ ( range_nat_nat @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range_insert
% 4.69/4.90 thf(fact_595_Range__insert,axiom,
% 4.69/4.90 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ( range_int_int @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 ) )
% 4.69/4.90 = ( insert_int @ B @ ( range_int_int @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range_insert
% 4.69/4.90 thf(fact_596_Range__insert,axiom,
% 4.69/4.90 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,R2: set_Pr3286484037609594932et_nat] :
% 4.69/4.90 ( ( range_3398330936903821850et_nat @ ( insert3111075074545270702et_nat @ ( produc5001842942810119800et_nat @ A2 @ B ) @ R2 ) )
% 4.69/4.90 = ( insert1271470778893645362et_nat @ B @ ( range_3398330936903821850et_nat @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range_insert
% 4.69/4.90 thf(fact_597_Range__insert,axiom,
% 4.69/4.90 ! [A2: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,R2: set_Pr8536935166611901872et_nat] :
% 4.69/4.90 ( ( range_7260058354244137878et_nat @ ( insert8297122186708525866et_nat @ ( produc2245416461498447860et_nat @ A2 @ B ) @ R2 ) )
% 4.69/4.90 = ( insert3111075074545270702et_nat @ B @ ( range_7260058354244137878et_nat @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range_insert
% 4.69/4.90 thf(fact_598_Domain__insert,axiom,
% 4.69/4.90 ! [A2: heap_e7401611519738050253t_unit,B: set_nat,R2: set_Pr3948176798113811640et_nat] :
% 4.69/4.90 ( ( domain2007548326387822151et_nat @ ( insert1271470778893645362et_nat @ ( produc7507926704131184380et_nat @ A2 @ B ) @ R2 ) )
% 4.69/4.90 = ( insert8563697753282147485t_unit @ A2 @ ( domain2007548326387822151et_nat @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain_insert
% 4.69/4.90 thf(fact_599_Domain__insert,axiom,
% 4.69/4.90 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ( domain_nat_nat @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 ) )
% 4.69/4.90 = ( insert_nat @ A2 @ ( domain_nat_nat @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain_insert
% 4.69/4.90 thf(fact_600_Domain__insert,axiom,
% 4.69/4.90 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ( domain_int_int @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 ) )
% 4.69/4.90 = ( insert_int @ A2 @ ( domain_int_int @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain_insert
% 4.69/4.90 thf(fact_601_Domain__insert,axiom,
% 4.69/4.90 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,R2: set_Pr3286484037609594932et_nat] :
% 4.69/4.90 ( ( domain2358961613337345475et_nat @ ( insert3111075074545270702et_nat @ ( produc5001842942810119800et_nat @ A2 @ B ) @ R2 ) )
% 4.69/4.90 = ( insert5175938949040314269_nat_o @ A2 @ ( domain2358961613337345475et_nat @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain_insert
% 4.69/4.90 thf(fact_602_Domain__insert,axiom,
% 4.69/4.90 ! [A2: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,R2: set_Pr8536935166611901872et_nat] :
% 4.69/4.90 ( ( domain3618434998481624895et_nat @ ( insert8297122186708525866et_nat @ ( produc2245416461498447860et_nat @ A2 @ B ) @ R2 ) )
% 4.69/4.90 = ( insert5175938949040314269_nat_o @ A2 @ ( domain3618434998481624895et_nat @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain_insert
% 4.69/4.90 thf(fact_603_preorder__on__empty,axiom,
% 4.69/4.90 order_7534304569044981540t_unit @ bot_bo3957492148770167129t_unit @ bot_bo1654022762305692595t_unit ).
% 4.69/4.90
% 4.69/4.90 % preorder_on_empty
% 4.69/4.90 thf(fact_604_preorder__on__empty,axiom,
% 4.69/4.90 order_preorder_on_o @ bot_bot_set_o @ bot_bo7073875226086086771od_o_o ).
% 4.69/4.90
% 4.69/4.90 % preorder_on_empty
% 4.69/4.90 thf(fact_605_preorder__on__empty,axiom,
% 4.69/4.90 order_4861654808422542329on_nat @ bot_bot_set_nat @ bot_bo2099793752762293965at_nat ).
% 4.69/4.90
% 4.69/4.90 % preorder_on_empty
% 4.69/4.90 thf(fact_606_preorder__on__empty,axiom,
% 4.69/4.90 order_4859164337913492053on_int @ bot_bot_set_int @ bot_bo1796632182523588997nt_int ).
% 4.69/4.90
% 4.69/4.90 % preorder_on_empty
% 4.69/4.90 thf(fact_607_preorder__on__empty,axiom,
% 4.69/4.90 order_174704566861754596_nat_o @ bot_bo7824918357723582233_nat_o @ bot_bo3657187498359500723_nat_o ).
% 4.69/4.90
% 4.69/4.90 % preorder_on_empty
% 4.69/4.90 thf(fact_608_trancl__single,axiom,
% 4.69/4.90 ! [A2: nat,B: nat] :
% 4.69/4.90 ( ( transi6264000038957366511cl_nat @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ bot_bo2099793752762293965at_nat ) )
% 4.69/4.90 = ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ bot_bo2099793752762293965at_nat ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_single
% 4.69/4.90 thf(fact_609_trancl__single,axiom,
% 4.69/4.90 ! [A2: int,B: int] :
% 4.69/4.90 ( ( transi6261509568448316235cl_int @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A2 @ B ) @ bot_bo1796632182523588997nt_int ) )
% 4.69/4.90 = ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A2 @ B ) @ bot_bo1796632182523588997nt_int ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_single
% 4.69/4.90 thf(fact_610_trans__singleton,axiom,
% 4.69/4.90 ! [A2: nat] : ( trans_nat @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A2 @ A2 ) @ bot_bo2099793752762293965at_nat ) ) ).
% 4.69/4.90
% 4.69/4.90 % trans_singleton
% 4.69/4.90 thf(fact_611_trans__singleton,axiom,
% 4.69/4.90 ! [A2: int] : ( trans_int @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A2 @ A2 ) @ bot_bo1796632182523588997nt_int ) ) ).
% 4.69/4.90
% 4.69/4.90 % trans_singleton
% 4.69/4.90 thf(fact_612_mult_Osafe__commute,axiom,
% 4.69/4.90 ! [X: assn,Y: assn,A2: assn,B: assn] :
% 4.69/4.90 ( ( syntax7398250324933576852n_assn @ ( times_times_assn @ X @ Y ) @ A2 )
% 4.69/4.90 => ( ( times_times_assn @ A2 @ B )
% 4.69/4.90 = ( times_times_assn @ B @ A2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % mult.safe_commute
% 4.69/4.90 thf(fact_613_mult_Osafe__commute,axiom,
% 4.69/4.90 ! [X: rat,Y: rat,A2: rat,B: rat] :
% 4.69/4.90 ( ( syntax3730441303064801268at_rat @ ( times_times_rat @ X @ Y ) @ A2 )
% 4.69/4.90 => ( ( times_times_rat @ A2 @ B )
% 4.69/4.90 = ( times_times_rat @ B @ A2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % mult.safe_commute
% 4.69/4.90 thf(fact_614_mult_Osafe__commute,axiom,
% 4.69/4.90 ! [X: nat,Y: nat,A2: nat,B: nat] :
% 4.69/4.90 ( ( syntax4682126007086162916at_nat @ ( times_times_nat @ X @ Y ) @ A2 )
% 4.69/4.90 => ( ( times_times_nat @ A2 @ B )
% 4.69/4.90 = ( times_times_nat @ B @ A2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % mult.safe_commute
% 4.69/4.90 thf(fact_615_mult_Osafe__commute,axiom,
% 4.69/4.90 ! [X: int,Y: int,A2: int,B: int] :
% 4.69/4.90 ( ( syntax5678989248478167196nt_int @ ( times_times_int @ X @ Y ) @ A2 )
% 4.69/4.90 => ( ( times_times_int @ A2 @ B )
% 4.69/4.90 = ( times_times_int @ B @ A2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % mult.safe_commute
% 4.69/4.90 thf(fact_616_vimage__eq,axiom,
% 4.69/4.90 ! [A2: nat,F: nat > nat,B4: set_nat] :
% 4.69/4.90 ( ( member_nat @ A2 @ ( vimage_nat_nat @ F @ B4 ) )
% 4.69/4.90 = ( member_nat @ ( F @ A2 ) @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_eq
% 4.69/4.90 thf(fact_617_vimage__eq,axiom,
% 4.69/4.90 ! [A2: nat,F: nat > int,B4: set_int] :
% 4.69/4.90 ( ( member_nat @ A2 @ ( vimage_nat_int @ F @ B4 ) )
% 4.69/4.90 = ( member_int @ ( F @ A2 ) @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_eq
% 4.69/4.90 thf(fact_618_vimage__eq,axiom,
% 4.69/4.90 ! [A2: nat,F: nat > $o,B4: set_o] :
% 4.69/4.90 ( ( member_nat @ A2 @ ( vimage_nat_o @ F @ B4 ) )
% 4.69/4.90 = ( member_o @ ( F @ A2 ) @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_eq
% 4.69/4.90 thf(fact_619_vimage__eq,axiom,
% 4.69/4.90 ! [A2: nat,F: nat > product_unit,B4: set_Product_unit] :
% 4.69/4.90 ( ( member_nat @ A2 @ ( vimage4884490618288580032t_unit @ F @ B4 ) )
% 4.69/4.90 = ( member_Product_unit @ ( F @ A2 ) @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_eq
% 4.69/4.90 thf(fact_620_vimage__eq,axiom,
% 4.69/4.90 ! [A2: int,F: int > nat,B4: set_nat] :
% 4.69/4.90 ( ( member_int @ A2 @ ( vimage_int_nat @ F @ B4 ) )
% 4.69/4.90 = ( member_nat @ ( F @ A2 ) @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_eq
% 4.69/4.90 thf(fact_621_vimage__eq,axiom,
% 4.69/4.90 ! [A2: int,F: int > int,B4: set_int] :
% 4.69/4.90 ( ( member_int @ A2 @ ( vimage_int_int @ F @ B4 ) )
% 4.69/4.90 = ( member_int @ ( F @ A2 ) @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_eq
% 4.69/4.90 thf(fact_622_vimage__eq,axiom,
% 4.69/4.90 ! [A2: int,F: int > $o,B4: set_o] :
% 4.69/4.90 ( ( member_int @ A2 @ ( vimage_int_o @ F @ B4 ) )
% 4.69/4.90 = ( member_o @ ( F @ A2 ) @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_eq
% 4.69/4.90 thf(fact_623_vimage__eq,axiom,
% 4.69/4.90 ! [A2: int,F: int > product_unit,B4: set_Product_unit] :
% 4.69/4.90 ( ( member_int @ A2 @ ( vimage2000912565490760292t_unit @ F @ B4 ) )
% 4.69/4.90 = ( member_Product_unit @ ( F @ A2 ) @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_eq
% 4.69/4.90 thf(fact_624_vimage__eq,axiom,
% 4.69/4.90 ! [A2: $o,F: $o > nat,B4: set_nat] :
% 4.69/4.90 ( ( member_o @ A2 @ ( vimage_o_nat @ F @ B4 ) )
% 4.69/4.90 = ( member_nat @ ( F @ A2 ) @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_eq
% 4.69/4.90 thf(fact_625_vimage__eq,axiom,
% 4.69/4.90 ! [A2: $o,F: $o > int,B4: set_int] :
% 4.69/4.90 ( ( member_o @ A2 @ ( vimage_o_int @ F @ B4 ) )
% 4.69/4.90 = ( member_int @ ( F @ A2 ) @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_eq
% 4.69/4.90 thf(fact_626_vimageI,axiom,
% 4.69/4.90 ! [F: nat > nat,A2: nat,B: nat,B4: set_nat] :
% 4.69/4.90 ( ( ( F @ A2 )
% 4.69/4.90 = B )
% 4.69/4.90 => ( ( member_nat @ B @ B4 )
% 4.69/4.90 => ( member_nat @ A2 @ ( vimage_nat_nat @ F @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageI
% 4.69/4.90 thf(fact_627_vimageI,axiom,
% 4.69/4.90 ! [F: int > nat,A2: int,B: nat,B4: set_nat] :
% 4.69/4.90 ( ( ( F @ A2 )
% 4.69/4.90 = B )
% 4.69/4.90 => ( ( member_nat @ B @ B4 )
% 4.69/4.90 => ( member_int @ A2 @ ( vimage_int_nat @ F @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageI
% 4.69/4.90 thf(fact_628_vimageI,axiom,
% 4.69/4.90 ! [F: $o > nat,A2: $o,B: nat,B4: set_nat] :
% 4.69/4.90 ( ( ( F @ A2 )
% 4.69/4.90 = B )
% 4.69/4.90 => ( ( member_nat @ B @ B4 )
% 4.69/4.90 => ( member_o @ A2 @ ( vimage_o_nat @ F @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageI
% 4.69/4.90 thf(fact_629_vimageI,axiom,
% 4.69/4.90 ! [F: product_unit > nat,A2: product_unit,B: nat,B4: set_nat] :
% 4.69/4.90 ( ( ( F @ A2 )
% 4.69/4.90 = B )
% 4.69/4.90 => ( ( member_nat @ B @ B4 )
% 4.69/4.90 => ( member_Product_unit @ A2 @ ( vimage6253328473476588386it_nat @ F @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageI
% 4.69/4.90 thf(fact_630_vimageI,axiom,
% 4.69/4.90 ! [F: nat > int,A2: nat,B: int,B4: set_int] :
% 4.69/4.90 ( ( ( F @ A2 )
% 4.69/4.90 = B )
% 4.69/4.90 => ( ( member_int @ B @ B4 )
% 4.69/4.90 => ( member_nat @ A2 @ ( vimage_nat_int @ F @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageI
% 4.69/4.90 thf(fact_631_vimageI,axiom,
% 4.69/4.90 ! [F: int > int,A2: int,B: int,B4: set_int] :
% 4.69/4.90 ( ( ( F @ A2 )
% 4.69/4.90 = B )
% 4.69/4.90 => ( ( member_int @ B @ B4 )
% 4.69/4.90 => ( member_int @ A2 @ ( vimage_int_int @ F @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageI
% 4.69/4.90 thf(fact_632_vimageI,axiom,
% 4.69/4.90 ! [F: $o > int,A2: $o,B: int,B4: set_int] :
% 4.69/4.90 ( ( ( F @ A2 )
% 4.69/4.90 = B )
% 4.69/4.90 => ( ( member_int @ B @ B4 )
% 4.69/4.90 => ( member_o @ A2 @ ( vimage_o_int @ F @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageI
% 4.69/4.90 thf(fact_633_vimageI,axiom,
% 4.69/4.90 ! [F: product_unit > int,A2: product_unit,B: int,B4: set_int] :
% 4.69/4.90 ( ( ( F @ A2 )
% 4.69/4.90 = B )
% 4.69/4.90 => ( ( member_int @ B @ B4 )
% 4.69/4.90 => ( member_Product_unit @ A2 @ ( vimage6250838002967538110it_int @ F @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageI
% 4.69/4.90 thf(fact_634_vimageI,axiom,
% 4.69/4.90 ! [F: nat > $o,A2: nat,B: $o,B4: set_o] :
% 4.69/4.90 ( ( ( F @ A2 )
% 4.69/4.90 = B )
% 4.69/4.90 => ( ( member_o @ B @ B4 )
% 4.69/4.90 => ( member_nat @ A2 @ ( vimage_nat_o @ F @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageI
% 4.69/4.90 thf(fact_635_vimageI,axiom,
% 4.69/4.90 ! [F: int > $o,A2: int,B: $o,B4: set_o] :
% 4.69/4.90 ( ( ( F @ A2 )
% 4.69/4.90 = B )
% 4.69/4.90 => ( ( member_o @ B @ B4 )
% 4.69/4.90 => ( member_int @ A2 @ ( vimage_int_o @ F @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageI
% 4.69/4.90 thf(fact_636_vimage__empty,axiom,
% 4.69/4.90 ! [F: product_unit > product_unit] :
% 4.69/4.90 ( ( vimage7995052115951654139t_unit @ F @ bot_bo3957492148770167129t_unit )
% 4.69/4.90 = bot_bo3957492148770167129t_unit ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_empty
% 4.69/4.90 thf(fact_637_vimage__empty,axiom,
% 4.69/4.90 ! [F: $o > product_unit] :
% 4.69/4.90 ( ( vimage4222377557387472176t_unit @ F @ bot_bo3957492148770167129t_unit )
% 4.69/4.90 = bot_bot_set_o ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_empty
% 4.69/4.90 thf(fact_638_vimage__empty,axiom,
% 4.69/4.90 ! [F: nat > product_unit] :
% 4.69/4.90 ( ( vimage4884490618288580032t_unit @ F @ bot_bo3957492148770167129t_unit )
% 4.69/4.90 = bot_bot_set_nat ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_empty
% 4.69/4.90 thf(fact_639_vimage__empty,axiom,
% 4.69/4.90 ! [F: int > product_unit] :
% 4.69/4.90 ( ( vimage2000912565490760292t_unit @ F @ bot_bo3957492148770167129t_unit )
% 4.69/4.90 = bot_bot_set_int ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_empty
% 4.69/4.90 thf(fact_640_vimage__empty,axiom,
% 4.69/4.90 ! [F: product_unit > $o] :
% 4.69/4.90 ( ( vimage8808348054653608838unit_o @ F @ bot_bot_set_o )
% 4.69/4.90 = bot_bo3957492148770167129t_unit ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_empty
% 4.69/4.90 thf(fact_641_vimage__empty,axiom,
% 4.69/4.90 ! [F: $o > $o] :
% 4.69/4.90 ( ( vimage_o_o @ F @ bot_bot_set_o )
% 4.69/4.90 = bot_bot_set_o ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_empty
% 4.69/4.90 thf(fact_642_vimage__empty,axiom,
% 4.69/4.90 ! [F: nat > $o] :
% 4.69/4.90 ( ( vimage_nat_o @ F @ bot_bot_set_o )
% 4.69/4.90 = bot_bot_set_nat ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_empty
% 4.69/4.90 thf(fact_643_vimage__empty,axiom,
% 4.69/4.90 ! [F: int > $o] :
% 4.69/4.90 ( ( vimage_int_o @ F @ bot_bot_set_o )
% 4.69/4.90 = bot_bot_set_int ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_empty
% 4.69/4.90 thf(fact_644_vimage__empty,axiom,
% 4.69/4.90 ! [F: product_unit > nat] :
% 4.69/4.90 ( ( vimage6253328473476588386it_nat @ F @ bot_bot_set_nat )
% 4.69/4.90 = bot_bo3957492148770167129t_unit ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_empty
% 4.69/4.90 thf(fact_645_vimage__empty,axiom,
% 4.69/4.90 ! [F: $o > nat] :
% 4.69/4.90 ( ( vimage_o_nat @ F @ bot_bot_set_nat )
% 4.69/4.90 = bot_bot_set_o ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_empty
% 4.69/4.90 thf(fact_646_relH__sym,axiom,
% 4.69/4.90 ! [As: set_nat,H2: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit] :
% 4.69/4.90 ( ( relH @ As @ H2 @ H3 )
% 4.69/4.90 => ( relH @ As @ H3 @ H2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % relH_sym
% 4.69/4.90 thf(fact_647_relH__trans,axiom,
% 4.69/4.90 ! [As: set_nat,H12: heap_e7401611519738050253t_unit,H23: heap_e7401611519738050253t_unit,H32: heap_e7401611519738050253t_unit] :
% 4.69/4.90 ( ( relH @ As @ H12 @ H23 )
% 4.69/4.90 => ( ( relH @ As @ H23 @ H32 )
% 4.69/4.90 => ( relH @ As @ H12 @ H32 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % relH_trans
% 4.69/4.90 thf(fact_648_vimage__Collect,axiom,
% 4.69/4.90 ! [P: nat > $o,F: nat > nat,Q2: nat > $o] :
% 4.69/4.90 ( ! [X3: nat] :
% 4.69/4.90 ( ( P @ ( F @ X3 ) )
% 4.69/4.90 = ( Q2 @ X3 ) )
% 4.69/4.90 => ( ( vimage_nat_nat @ F @ ( collect_nat @ P ) )
% 4.69/4.90 = ( collect_nat @ Q2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_Collect
% 4.69/4.90 thf(fact_649_vimage__Collect,axiom,
% 4.69/4.90 ! [P: nat > $o,F: int > nat,Q2: int > $o] :
% 4.69/4.90 ( ! [X3: int] :
% 4.69/4.90 ( ( P @ ( F @ X3 ) )
% 4.69/4.90 = ( Q2 @ X3 ) )
% 4.69/4.90 => ( ( vimage_int_nat @ F @ ( collect_nat @ P ) )
% 4.69/4.90 = ( collect_int @ Q2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_Collect
% 4.69/4.90 thf(fact_650_vimage__Collect,axiom,
% 4.69/4.90 ! [P: nat > $o,F: $o > nat,Q2: $o > $o] :
% 4.69/4.90 ( ! [X3: $o] :
% 4.69/4.90 ( ( P @ ( F @ X3 ) )
% 4.69/4.90 = ( Q2 @ X3 ) )
% 4.69/4.90 => ( ( vimage_o_nat @ F @ ( collect_nat @ P ) )
% 4.69/4.90 = ( collect_o @ Q2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_Collect
% 4.69/4.90 thf(fact_651_vimage__Collect,axiom,
% 4.69/4.90 ! [P: nat > $o,F: product_unit > nat,Q2: product_unit > $o] :
% 4.69/4.90 ( ! [X3: product_unit] :
% 4.69/4.90 ( ( P @ ( F @ X3 ) )
% 4.69/4.90 = ( Q2 @ X3 ) )
% 4.69/4.90 => ( ( vimage6253328473476588386it_nat @ F @ ( collect_nat @ P ) )
% 4.69/4.90 = ( collect_Product_unit @ Q2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_Collect
% 4.69/4.90 thf(fact_652_vimage__Collect,axiom,
% 4.69/4.90 ! [P: int > $o,F: nat > int,Q2: nat > $o] :
% 4.69/4.90 ( ! [X3: nat] :
% 4.69/4.90 ( ( P @ ( F @ X3 ) )
% 4.69/4.90 = ( Q2 @ X3 ) )
% 4.69/4.90 => ( ( vimage_nat_int @ F @ ( collect_int @ P ) )
% 4.69/4.90 = ( collect_nat @ Q2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_Collect
% 4.69/4.90 thf(fact_653_vimage__Collect,axiom,
% 4.69/4.90 ! [P: int > $o,F: int > int,Q2: int > $o] :
% 4.69/4.90 ( ! [X3: int] :
% 4.69/4.90 ( ( P @ ( F @ X3 ) )
% 4.69/4.90 = ( Q2 @ X3 ) )
% 4.69/4.90 => ( ( vimage_int_int @ F @ ( collect_int @ P ) )
% 4.69/4.90 = ( collect_int @ Q2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_Collect
% 4.69/4.90 thf(fact_654_vimage__Collect,axiom,
% 4.69/4.90 ! [P: int > $o,F: $o > int,Q2: $o > $o] :
% 4.69/4.90 ( ! [X3: $o] :
% 4.69/4.90 ( ( P @ ( F @ X3 ) )
% 4.69/4.90 = ( Q2 @ X3 ) )
% 4.69/4.90 => ( ( vimage_o_int @ F @ ( collect_int @ P ) )
% 4.69/4.90 = ( collect_o @ Q2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_Collect
% 4.69/4.90 thf(fact_655_vimage__Collect,axiom,
% 4.69/4.90 ! [P: int > $o,F: product_unit > int,Q2: product_unit > $o] :
% 4.69/4.90 ( ! [X3: product_unit] :
% 4.69/4.90 ( ( P @ ( F @ X3 ) )
% 4.69/4.90 = ( Q2 @ X3 ) )
% 4.69/4.90 => ( ( vimage6250838002967538110it_int @ F @ ( collect_int @ P ) )
% 4.69/4.90 = ( collect_Product_unit @ Q2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_Collect
% 4.69/4.90 thf(fact_656_vimage__Collect,axiom,
% 4.69/4.90 ! [P: $o > $o,F: nat > $o,Q2: nat > $o] :
% 4.69/4.90 ( ! [X3: nat] :
% 4.69/4.90 ( ( P @ ( F @ X3 ) )
% 4.69/4.90 = ( Q2 @ X3 ) )
% 4.69/4.90 => ( ( vimage_nat_o @ F @ ( collect_o @ P ) )
% 4.69/4.90 = ( collect_nat @ Q2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_Collect
% 4.69/4.90 thf(fact_657_vimage__Collect,axiom,
% 4.69/4.90 ! [P: $o > $o,F: int > $o,Q2: int > $o] :
% 4.69/4.90 ( ! [X3: int] :
% 4.69/4.90 ( ( P @ ( F @ X3 ) )
% 4.69/4.90 = ( Q2 @ X3 ) )
% 4.69/4.90 => ( ( vimage_int_o @ F @ ( collect_o @ P ) )
% 4.69/4.90 = ( collect_int @ Q2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_Collect
% 4.69/4.90 thf(fact_658_vimageI2,axiom,
% 4.69/4.90 ! [F: nat > nat,A2: nat,A: set_nat] :
% 4.69/4.90 ( ( member_nat @ ( F @ A2 ) @ A )
% 4.69/4.90 => ( member_nat @ A2 @ ( vimage_nat_nat @ F @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageI2
% 4.69/4.90 thf(fact_659_vimageI2,axiom,
% 4.69/4.90 ! [F: int > nat,A2: int,A: set_nat] :
% 4.69/4.90 ( ( member_nat @ ( F @ A2 ) @ A )
% 4.69/4.90 => ( member_int @ A2 @ ( vimage_int_nat @ F @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageI2
% 4.69/4.90 thf(fact_660_vimageI2,axiom,
% 4.69/4.90 ! [F: $o > nat,A2: $o,A: set_nat] :
% 4.69/4.90 ( ( member_nat @ ( F @ A2 ) @ A )
% 4.69/4.90 => ( member_o @ A2 @ ( vimage_o_nat @ F @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageI2
% 4.69/4.90 thf(fact_661_vimageI2,axiom,
% 4.69/4.90 ! [F: product_unit > nat,A2: product_unit,A: set_nat] :
% 4.69/4.90 ( ( member_nat @ ( F @ A2 ) @ A )
% 4.69/4.90 => ( member_Product_unit @ A2 @ ( vimage6253328473476588386it_nat @ F @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageI2
% 4.69/4.90 thf(fact_662_vimageI2,axiom,
% 4.69/4.90 ! [F: nat > int,A2: nat,A: set_int] :
% 4.69/4.90 ( ( member_int @ ( F @ A2 ) @ A )
% 4.69/4.90 => ( member_nat @ A2 @ ( vimage_nat_int @ F @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageI2
% 4.69/4.90 thf(fact_663_vimageI2,axiom,
% 4.69/4.90 ! [F: int > int,A2: int,A: set_int] :
% 4.69/4.90 ( ( member_int @ ( F @ A2 ) @ A )
% 4.69/4.90 => ( member_int @ A2 @ ( vimage_int_int @ F @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageI2
% 4.69/4.90 thf(fact_664_vimageI2,axiom,
% 4.69/4.90 ! [F: $o > int,A2: $o,A: set_int] :
% 4.69/4.90 ( ( member_int @ ( F @ A2 ) @ A )
% 4.69/4.90 => ( member_o @ A2 @ ( vimage_o_int @ F @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageI2
% 4.69/4.90 thf(fact_665_vimageI2,axiom,
% 4.69/4.90 ! [F: product_unit > int,A2: product_unit,A: set_int] :
% 4.69/4.90 ( ( member_int @ ( F @ A2 ) @ A )
% 4.69/4.90 => ( member_Product_unit @ A2 @ ( vimage6250838002967538110it_int @ F @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageI2
% 4.69/4.90 thf(fact_666_vimageI2,axiom,
% 4.69/4.90 ! [F: nat > $o,A2: nat,A: set_o] :
% 4.69/4.90 ( ( member_o @ ( F @ A2 ) @ A )
% 4.69/4.90 => ( member_nat @ A2 @ ( vimage_nat_o @ F @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageI2
% 4.69/4.90 thf(fact_667_vimageI2,axiom,
% 4.69/4.90 ! [F: int > $o,A2: int,A: set_o] :
% 4.69/4.90 ( ( member_o @ ( F @ A2 ) @ A )
% 4.69/4.90 => ( member_int @ A2 @ ( vimage_int_o @ F @ A ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageI2
% 4.69/4.90 thf(fact_668_vimageE,axiom,
% 4.69/4.90 ! [A2: nat,F: nat > nat,B4: set_nat] :
% 4.69/4.90 ( ( member_nat @ A2 @ ( vimage_nat_nat @ F @ B4 ) )
% 4.69/4.90 => ( member_nat @ ( F @ A2 ) @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageE
% 4.69/4.90 thf(fact_669_vimageE,axiom,
% 4.69/4.90 ! [A2: nat,F: nat > int,B4: set_int] :
% 4.69/4.90 ( ( member_nat @ A2 @ ( vimage_nat_int @ F @ B4 ) )
% 4.69/4.90 => ( member_int @ ( F @ A2 ) @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageE
% 4.69/4.90 thf(fact_670_vimageE,axiom,
% 4.69/4.90 ! [A2: nat,F: nat > $o,B4: set_o] :
% 4.69/4.90 ( ( member_nat @ A2 @ ( vimage_nat_o @ F @ B4 ) )
% 4.69/4.90 => ( member_o @ ( F @ A2 ) @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageE
% 4.69/4.90 thf(fact_671_vimageE,axiom,
% 4.69/4.90 ! [A2: nat,F: nat > product_unit,B4: set_Product_unit] :
% 4.69/4.90 ( ( member_nat @ A2 @ ( vimage4884490618288580032t_unit @ F @ B4 ) )
% 4.69/4.90 => ( member_Product_unit @ ( F @ A2 ) @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageE
% 4.69/4.90 thf(fact_672_vimageE,axiom,
% 4.69/4.90 ! [A2: int,F: int > nat,B4: set_nat] :
% 4.69/4.90 ( ( member_int @ A2 @ ( vimage_int_nat @ F @ B4 ) )
% 4.69/4.90 => ( member_nat @ ( F @ A2 ) @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageE
% 4.69/4.90 thf(fact_673_vimageE,axiom,
% 4.69/4.90 ! [A2: int,F: int > int,B4: set_int] :
% 4.69/4.90 ( ( member_int @ A2 @ ( vimage_int_int @ F @ B4 ) )
% 4.69/4.90 => ( member_int @ ( F @ A2 ) @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageE
% 4.69/4.90 thf(fact_674_vimageE,axiom,
% 4.69/4.90 ! [A2: int,F: int > $o,B4: set_o] :
% 4.69/4.90 ( ( member_int @ A2 @ ( vimage_int_o @ F @ B4 ) )
% 4.69/4.90 => ( member_o @ ( F @ A2 ) @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageE
% 4.69/4.90 thf(fact_675_vimageE,axiom,
% 4.69/4.90 ! [A2: int,F: int > product_unit,B4: set_Product_unit] :
% 4.69/4.90 ( ( member_int @ A2 @ ( vimage2000912565490760292t_unit @ F @ B4 ) )
% 4.69/4.90 => ( member_Product_unit @ ( F @ A2 ) @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageE
% 4.69/4.90 thf(fact_676_vimageE,axiom,
% 4.69/4.90 ! [A2: $o,F: $o > nat,B4: set_nat] :
% 4.69/4.90 ( ( member_o @ A2 @ ( vimage_o_nat @ F @ B4 ) )
% 4.69/4.90 => ( member_nat @ ( F @ A2 ) @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageE
% 4.69/4.90 thf(fact_677_vimageE,axiom,
% 4.69/4.90 ! [A2: $o,F: $o > int,B4: set_int] :
% 4.69/4.90 ( ( member_o @ A2 @ ( vimage_o_int @ F @ B4 ) )
% 4.69/4.90 => ( member_int @ ( F @ A2 ) @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageE
% 4.69/4.90 thf(fact_678_vimageD,axiom,
% 4.69/4.90 ! [A2: nat,F: nat > nat,A: set_nat] :
% 4.69/4.90 ( ( member_nat @ A2 @ ( vimage_nat_nat @ F @ A ) )
% 4.69/4.90 => ( member_nat @ ( F @ A2 ) @ A ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageD
% 4.69/4.90 thf(fact_679_vimageD,axiom,
% 4.69/4.90 ! [A2: nat,F: nat > int,A: set_int] :
% 4.69/4.90 ( ( member_nat @ A2 @ ( vimage_nat_int @ F @ A ) )
% 4.69/4.90 => ( member_int @ ( F @ A2 ) @ A ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageD
% 4.69/4.90 thf(fact_680_vimageD,axiom,
% 4.69/4.90 ! [A2: nat,F: nat > $o,A: set_o] :
% 4.69/4.90 ( ( member_nat @ A2 @ ( vimage_nat_o @ F @ A ) )
% 4.69/4.90 => ( member_o @ ( F @ A2 ) @ A ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageD
% 4.69/4.90 thf(fact_681_vimageD,axiom,
% 4.69/4.90 ! [A2: nat,F: nat > product_unit,A: set_Product_unit] :
% 4.69/4.90 ( ( member_nat @ A2 @ ( vimage4884490618288580032t_unit @ F @ A ) )
% 4.69/4.90 => ( member_Product_unit @ ( F @ A2 ) @ A ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageD
% 4.69/4.90 thf(fact_682_vimageD,axiom,
% 4.69/4.90 ! [A2: int,F: int > nat,A: set_nat] :
% 4.69/4.90 ( ( member_int @ A2 @ ( vimage_int_nat @ F @ A ) )
% 4.69/4.90 => ( member_nat @ ( F @ A2 ) @ A ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageD
% 4.69/4.90 thf(fact_683_vimageD,axiom,
% 4.69/4.90 ! [A2: int,F: int > int,A: set_int] :
% 4.69/4.90 ( ( member_int @ A2 @ ( vimage_int_int @ F @ A ) )
% 4.69/4.90 => ( member_int @ ( F @ A2 ) @ A ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageD
% 4.69/4.90 thf(fact_684_vimageD,axiom,
% 4.69/4.90 ! [A2: int,F: int > $o,A: set_o] :
% 4.69/4.90 ( ( member_int @ A2 @ ( vimage_int_o @ F @ A ) )
% 4.69/4.90 => ( member_o @ ( F @ A2 ) @ A ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageD
% 4.69/4.90 thf(fact_685_vimageD,axiom,
% 4.69/4.90 ! [A2: int,F: int > product_unit,A: set_Product_unit] :
% 4.69/4.90 ( ( member_int @ A2 @ ( vimage2000912565490760292t_unit @ F @ A ) )
% 4.69/4.90 => ( member_Product_unit @ ( F @ A2 ) @ A ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageD
% 4.69/4.90 thf(fact_686_vimageD,axiom,
% 4.69/4.90 ! [A2: $o,F: $o > nat,A: set_nat] :
% 4.69/4.90 ( ( member_o @ A2 @ ( vimage_o_nat @ F @ A ) )
% 4.69/4.90 => ( member_nat @ ( F @ A2 ) @ A ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageD
% 4.69/4.90 thf(fact_687_vimageD,axiom,
% 4.69/4.90 ! [A2: $o,F: $o > int,A: set_int] :
% 4.69/4.90 ( ( member_o @ A2 @ ( vimage_o_int @ F @ A ) )
% 4.69/4.90 => ( member_int @ ( F @ A2 ) @ A ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimageD
% 4.69/4.90 thf(fact_688_transD,axiom,
% 4.69/4.90 ! [R2: set_Pr1261947904930325089at_nat,X: nat,Y: nat,Z: nat] :
% 4.69/4.90 ( ( trans_nat @ R2 )
% 4.69/4.90 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R2 )
% 4.69/4.90 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ Z ) @ R2 )
% 4.69/4.90 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % transD
% 4.69/4.90 thf(fact_689_transD,axiom,
% 4.69/4.90 ! [R2: set_Pr958786334691620121nt_int,X: int,Y: int,Z: int] :
% 4.69/4.90 ( ( trans_int @ R2 )
% 4.69/4.90 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R2 )
% 4.69/4.90 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y @ Z ) @ R2 )
% 4.69/4.90 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Z ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % transD
% 4.69/4.90 thf(fact_690_transE,axiom,
% 4.69/4.90 ! [R2: set_Pr1261947904930325089at_nat,X: nat,Y: nat,Z: nat] :
% 4.69/4.90 ( ( trans_nat @ R2 )
% 4.69/4.90 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R2 )
% 4.69/4.90 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ Z ) @ R2 )
% 4.69/4.90 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % transE
% 4.69/4.90 thf(fact_691_transE,axiom,
% 4.69/4.90 ! [R2: set_Pr958786334691620121nt_int,X: int,Y: int,Z: int] :
% 4.69/4.90 ( ( trans_int @ R2 )
% 4.69/4.90 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R2 )
% 4.69/4.90 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y @ Z ) @ R2 )
% 4.69/4.90 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Z ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % transE
% 4.69/4.90 thf(fact_692_transI,axiom,
% 4.69/4.90 ! [R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ! [X3: nat,Y2: nat,Z3: nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ R2 )
% 4.69/4.90 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ Z3 ) @ R2 )
% 4.69/4.90 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Z3 ) @ R2 ) ) )
% 4.69/4.90 => ( trans_nat @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % transI
% 4.69/4.90 thf(fact_693_transI,axiom,
% 4.69/4.90 ! [R2: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ! [X3: int,Y2: int,Z3: int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y2 ) @ R2 )
% 4.69/4.90 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y2 @ Z3 ) @ R2 )
% 4.69/4.90 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Z3 ) @ R2 ) ) )
% 4.69/4.90 => ( trans_int @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % transI
% 4.69/4.90 thf(fact_694_trans__def,axiom,
% 4.69/4.90 ( trans_nat
% 4.69/4.90 = ( ^ [R4: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ! [X2: nat,Y3: nat,Z2: nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ R4 )
% 4.69/4.90 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ Z2 ) @ R4 )
% 4.69/4.90 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Z2 ) @ R4 ) ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trans_def
% 4.69/4.90 thf(fact_695_trans__def,axiom,
% 4.69/4.90 ( trans_int
% 4.69/4.90 = ( ^ [R4: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ! [X2: int,Y3: int,Z2: int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ R4 )
% 4.69/4.90 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ Z2 ) @ R4 )
% 4.69/4.90 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Z2 ) @ R4 ) ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trans_def
% 4.69/4.90 thf(fact_696_Domain_Ocases,axiom,
% 4.69/4.90 ! [A2: heap_e7401611519738050253t_unit,R2: set_Pr3948176798113811640et_nat] :
% 4.69/4.90 ( ( member242389114213480694t_unit @ A2 @ ( domain2007548326387822151et_nat @ R2 ) )
% 4.69/4.90 => ~ ! [B2: set_nat] :
% 4.69/4.90 ~ ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ B2 ) @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain.cases
% 4.69/4.90 thf(fact_697_Domain_Ocases,axiom,
% 4.69/4.90 ! [A2: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ( member_nat @ A2 @ ( domain_nat_nat @ R2 ) )
% 4.69/4.90 => ~ ! [B2: nat] :
% 4.69/4.90 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain.cases
% 4.69/4.90 thf(fact_698_Domain_Ocases,axiom,
% 4.69/4.90 ! [A2: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ( member_int @ A2 @ ( domain_int_int @ R2 ) )
% 4.69/4.90 => ~ ! [B2: int] :
% 4.69/4.90 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B2 ) @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain.cases
% 4.69/4.90 thf(fact_699_Domain_Ocases,axiom,
% 4.69/4.90 ! [A2: produc3658429121746597890et_nat > $o,R2: set_Pr3286484037609594932et_nat] :
% 4.69/4.90 ( ( member6576561426505652726_nat_o @ A2 @ ( domain2358961613337345475et_nat @ R2 ) )
% 4.69/4.90 => ~ ! [B2: produc3658429121746597890et_nat] :
% 4.69/4.90 ~ ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ B2 ) @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain.cases
% 4.69/4.90 thf(fact_700_Domain_Ocases,axiom,
% 4.69/4.90 ! [A2: produc3658429121746597890et_nat > $o,R2: set_Pr8536935166611901872et_nat] :
% 4.69/4.90 ( ( member6576561426505652726_nat_o @ A2 @ ( domain3618434998481624895et_nat @ R2 ) )
% 4.69/4.90 => ~ ! [B2: produc3925858234332021118et_nat] :
% 4.69/4.90 ~ ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ B2 ) @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain.cases
% 4.69/4.90 thf(fact_701_Domain_Osimps,axiom,
% 4.69/4.90 ! [A2: heap_e7401611519738050253t_unit,R2: set_Pr3948176798113811640et_nat] :
% 4.69/4.90 ( ( member242389114213480694t_unit @ A2 @ ( domain2007548326387822151et_nat @ R2 ) )
% 4.69/4.90 = ( ? [A6: heap_e7401611519738050253t_unit,B6: set_nat] :
% 4.69/4.90 ( ( A2 = A6 )
% 4.69/4.90 & ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A6 @ B6 ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain.simps
% 4.69/4.90 thf(fact_702_Domain_Osimps,axiom,
% 4.69/4.90 ! [A2: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ( member_nat @ A2 @ ( domain_nat_nat @ R2 ) )
% 4.69/4.90 = ( ? [A6: nat,B6: nat] :
% 4.69/4.90 ( ( A2 = A6 )
% 4.69/4.90 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A6 @ B6 ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain.simps
% 4.69/4.90 thf(fact_703_Domain_Osimps,axiom,
% 4.69/4.90 ! [A2: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ( member_int @ A2 @ ( domain_int_int @ R2 ) )
% 4.69/4.90 = ( ? [A6: int,B6: int] :
% 4.69/4.90 ( ( A2 = A6 )
% 4.69/4.90 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A6 @ B6 ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain.simps
% 4.69/4.90 thf(fact_704_Domain_Osimps,axiom,
% 4.69/4.90 ! [A2: produc3658429121746597890et_nat > $o,R2: set_Pr3286484037609594932et_nat] :
% 4.69/4.90 ( ( member6576561426505652726_nat_o @ A2 @ ( domain2358961613337345475et_nat @ R2 ) )
% 4.69/4.90 = ( ? [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat] :
% 4.69/4.90 ( ( A2 = A6 )
% 4.69/4.90 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A6 @ B6 ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain.simps
% 4.69/4.90 thf(fact_705_Domain_Osimps,axiom,
% 4.69/4.90 ! [A2: produc3658429121746597890et_nat > $o,R2: set_Pr8536935166611901872et_nat] :
% 4.69/4.90 ( ( member6576561426505652726_nat_o @ A2 @ ( domain3618434998481624895et_nat @ R2 ) )
% 4.69/4.90 = ( ? [A6: produc3658429121746597890et_nat > $o,B6: produc3925858234332021118et_nat] :
% 4.69/4.90 ( ( A2 = A6 )
% 4.69/4.90 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A6 @ B6 ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain.simps
% 4.69/4.90 thf(fact_706_Domain_ODomainI,axiom,
% 4.69/4.90 ! [A2: heap_e7401611519738050253t_unit,B: set_nat,R2: set_Pr3948176798113811640et_nat] :
% 4.69/4.90 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( member242389114213480694t_unit @ A2 @ ( domain2007548326387822151et_nat @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain.DomainI
% 4.69/4.90 thf(fact_707_Domain_ODomainI,axiom,
% 4.69/4.90 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( member_nat @ A2 @ ( domain_nat_nat @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain.DomainI
% 4.69/4.90 thf(fact_708_Domain_ODomainI,axiom,
% 4.69/4.90 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( member_int @ A2 @ ( domain_int_int @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain.DomainI
% 4.69/4.90 thf(fact_709_Domain_ODomainI,axiom,
% 4.69/4.90 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,R2: set_Pr3286484037609594932et_nat] :
% 4.69/4.90 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( member6576561426505652726_nat_o @ A2 @ ( domain2358961613337345475et_nat @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain.DomainI
% 4.69/4.90 thf(fact_710_Domain_ODomainI,axiom,
% 4.69/4.90 ! [A2: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,R2: set_Pr8536935166611901872et_nat] :
% 4.69/4.90 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( member6576561426505652726_nat_o @ A2 @ ( domain3618434998481624895et_nat @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain.DomainI
% 4.69/4.90 thf(fact_711_DomainE,axiom,
% 4.69/4.90 ! [A2: heap_e7401611519738050253t_unit,R2: set_Pr3948176798113811640et_nat] :
% 4.69/4.90 ( ( member242389114213480694t_unit @ A2 @ ( domain2007548326387822151et_nat @ R2 ) )
% 4.69/4.90 => ~ ! [B2: set_nat] :
% 4.69/4.90 ~ ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ B2 ) @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % DomainE
% 4.69/4.90 thf(fact_712_DomainE,axiom,
% 4.69/4.90 ! [A2: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ( member_nat @ A2 @ ( domain_nat_nat @ R2 ) )
% 4.69/4.90 => ~ ! [B2: nat] :
% 4.69/4.90 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % DomainE
% 4.69/4.90 thf(fact_713_DomainE,axiom,
% 4.69/4.90 ! [A2: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ( member_int @ A2 @ ( domain_int_int @ R2 ) )
% 4.69/4.90 => ~ ! [B2: int] :
% 4.69/4.90 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B2 ) @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % DomainE
% 4.69/4.90 thf(fact_714_DomainE,axiom,
% 4.69/4.90 ! [A2: produc3658429121746597890et_nat > $o,R2: set_Pr3286484037609594932et_nat] :
% 4.69/4.90 ( ( member6576561426505652726_nat_o @ A2 @ ( domain2358961613337345475et_nat @ R2 ) )
% 4.69/4.90 => ~ ! [B2: produc3658429121746597890et_nat] :
% 4.69/4.90 ~ ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ B2 ) @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % DomainE
% 4.69/4.90 thf(fact_715_DomainE,axiom,
% 4.69/4.90 ! [A2: produc3658429121746597890et_nat > $o,R2: set_Pr8536935166611901872et_nat] :
% 4.69/4.90 ( ( member6576561426505652726_nat_o @ A2 @ ( domain3618434998481624895et_nat @ R2 ) )
% 4.69/4.90 => ~ ! [B2: produc3925858234332021118et_nat] :
% 4.69/4.90 ~ ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ B2 ) @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % DomainE
% 4.69/4.90 thf(fact_716_Domain__iff,axiom,
% 4.69/4.90 ! [A2: heap_e7401611519738050253t_unit,R2: set_Pr3948176798113811640et_nat] :
% 4.69/4.90 ( ( member242389114213480694t_unit @ A2 @ ( domain2007548326387822151et_nat @ R2 ) )
% 4.69/4.90 = ( ? [Y3: set_nat] : ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ Y3 ) @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain_iff
% 4.69/4.90 thf(fact_717_Domain__iff,axiom,
% 4.69/4.90 ! [A2: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ( member_nat @ A2 @ ( domain_nat_nat @ R2 ) )
% 4.69/4.90 = ( ? [Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ Y3 ) @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain_iff
% 4.69/4.90 thf(fact_718_Domain__iff,axiom,
% 4.69/4.90 ! [A2: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ( member_int @ A2 @ ( domain_int_int @ R2 ) )
% 4.69/4.90 = ( ? [Y3: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ Y3 ) @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain_iff
% 4.69/4.90 thf(fact_719_Domain__iff,axiom,
% 4.69/4.90 ! [A2: produc3658429121746597890et_nat > $o,R2: set_Pr3286484037609594932et_nat] :
% 4.69/4.90 ( ( member6576561426505652726_nat_o @ A2 @ ( domain2358961613337345475et_nat @ R2 ) )
% 4.69/4.90 = ( ? [Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ Y3 ) @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain_iff
% 4.69/4.90 thf(fact_720_Domain__iff,axiom,
% 4.69/4.90 ! [A2: produc3658429121746597890et_nat > $o,R2: set_Pr8536935166611901872et_nat] :
% 4.69/4.90 ( ( member6576561426505652726_nat_o @ A2 @ ( domain3618434998481624895et_nat @ R2 ) )
% 4.69/4.90 = ( ? [Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ Y3 ) @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Domain_iff
% 4.69/4.90 thf(fact_721_Range_Ocases,axiom,
% 4.69/4.90 ! [A2: set_nat,R2: set_Pr3948176798113811640et_nat] :
% 4.69/4.90 ( ( member_set_nat @ A2 @ ( range_9132311542094983838et_nat @ R2 ) )
% 4.69/4.90 => ~ ! [A4: heap_e7401611519738050253t_unit] :
% 4.69/4.90 ~ ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A4 @ A2 ) @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range.cases
% 4.69/4.90 thf(fact_722_Range_Ocases,axiom,
% 4.69/4.90 ! [A2: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ( member_nat @ A2 @ ( range_nat_nat @ R2 ) )
% 4.69/4.90 => ~ ! [A4: nat] :
% 4.69/4.90 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A4 @ A2 ) @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range.cases
% 4.69/4.90 thf(fact_723_Range_Ocases,axiom,
% 4.69/4.90 ! [A2: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ( member_int @ A2 @ ( range_int_int @ R2 ) )
% 4.69/4.90 => ~ ! [A4: int] :
% 4.69/4.90 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A4 @ A2 ) @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range.cases
% 4.69/4.90 thf(fact_724_Range_Ocases,axiom,
% 4.69/4.90 ! [A2: produc3658429121746597890et_nat,R2: set_Pr3286484037609594932et_nat] :
% 4.69/4.90 ( ( member6260224972018164377et_nat @ A2 @ ( range_3398330936903821850et_nat @ R2 ) )
% 4.69/4.90 => ~ ! [A4: produc3658429121746597890et_nat > $o] :
% 4.69/4.90 ~ ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A4 @ A2 ) @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range.cases
% 4.69/4.90 thf(fact_725_Range_Ocases,axiom,
% 4.69/4.90 ! [A2: produc3925858234332021118et_nat,R2: set_Pr8536935166611901872et_nat] :
% 4.69/4.90 ( ( member1996754912294343701et_nat @ A2 @ ( range_7260058354244137878et_nat @ R2 ) )
% 4.69/4.90 => ~ ! [A4: produc3658429121746597890et_nat > $o] :
% 4.69/4.90 ~ ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A4 @ A2 ) @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range.cases
% 4.69/4.90 thf(fact_726_Range_Osimps,axiom,
% 4.69/4.90 ! [A2: set_nat,R2: set_Pr3948176798113811640et_nat] :
% 4.69/4.90 ( ( member_set_nat @ A2 @ ( range_9132311542094983838et_nat @ R2 ) )
% 4.69/4.90 = ( ? [A6: heap_e7401611519738050253t_unit,B6: set_nat] :
% 4.69/4.90 ( ( A2 = B6 )
% 4.69/4.90 & ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A6 @ B6 ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range.simps
% 4.69/4.90 thf(fact_727_Range_Osimps,axiom,
% 4.69/4.90 ! [A2: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ( member_nat @ A2 @ ( range_nat_nat @ R2 ) )
% 4.69/4.90 = ( ? [A6: nat,B6: nat] :
% 4.69/4.90 ( ( A2 = B6 )
% 4.69/4.90 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A6 @ B6 ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range.simps
% 4.69/4.90 thf(fact_728_Range_Osimps,axiom,
% 4.69/4.90 ! [A2: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ( member_int @ A2 @ ( range_int_int @ R2 ) )
% 4.69/4.90 = ( ? [A6: int,B6: int] :
% 4.69/4.90 ( ( A2 = B6 )
% 4.69/4.90 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A6 @ B6 ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range.simps
% 4.69/4.90 thf(fact_729_Range_Osimps,axiom,
% 4.69/4.90 ! [A2: produc3658429121746597890et_nat,R2: set_Pr3286484037609594932et_nat] :
% 4.69/4.90 ( ( member6260224972018164377et_nat @ A2 @ ( range_3398330936903821850et_nat @ R2 ) )
% 4.69/4.90 = ( ? [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat] :
% 4.69/4.90 ( ( A2 = B6 )
% 4.69/4.90 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A6 @ B6 ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range.simps
% 4.69/4.90 thf(fact_730_Range_Osimps,axiom,
% 4.69/4.90 ! [A2: produc3925858234332021118et_nat,R2: set_Pr8536935166611901872et_nat] :
% 4.69/4.90 ( ( member1996754912294343701et_nat @ A2 @ ( range_7260058354244137878et_nat @ R2 ) )
% 4.69/4.90 = ( ? [A6: produc3658429121746597890et_nat > $o,B6: produc3925858234332021118et_nat] :
% 4.69/4.90 ( ( A2 = B6 )
% 4.69/4.90 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A6 @ B6 ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range.simps
% 4.69/4.90 thf(fact_731_Range_Ointros,axiom,
% 4.69/4.90 ! [A2: heap_e7401611519738050253t_unit,B: set_nat,R2: set_Pr3948176798113811640et_nat] :
% 4.69/4.90 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( member_set_nat @ B @ ( range_9132311542094983838et_nat @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range.intros
% 4.69/4.90 thf(fact_732_Range_Ointros,axiom,
% 4.69/4.90 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( member_nat @ B @ ( range_nat_nat @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range.intros
% 4.69/4.90 thf(fact_733_Range_Ointros,axiom,
% 4.69/4.90 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( member_int @ B @ ( range_int_int @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range.intros
% 4.69/4.90 thf(fact_734_Range_Ointros,axiom,
% 4.69/4.90 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,R2: set_Pr3286484037609594932et_nat] :
% 4.69/4.90 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( member6260224972018164377et_nat @ B @ ( range_3398330936903821850et_nat @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range.intros
% 4.69/4.90 thf(fact_735_Range_Ointros,axiom,
% 4.69/4.90 ! [A2: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,R2: set_Pr8536935166611901872et_nat] :
% 4.69/4.90 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( member1996754912294343701et_nat @ B @ ( range_7260058354244137878et_nat @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range.intros
% 4.69/4.90 thf(fact_736_RangeE,axiom,
% 4.69/4.90 ! [B: set_nat,R2: set_Pr3948176798113811640et_nat] :
% 4.69/4.90 ( ( member_set_nat @ B @ ( range_9132311542094983838et_nat @ R2 ) )
% 4.69/4.90 => ~ ! [A4: heap_e7401611519738050253t_unit] :
% 4.69/4.90 ~ ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A4 @ B ) @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % RangeE
% 4.69/4.90 thf(fact_737_RangeE,axiom,
% 4.69/4.90 ! [B: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ( member_nat @ B @ ( range_nat_nat @ R2 ) )
% 4.69/4.90 => ~ ! [A4: nat] :
% 4.69/4.90 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A4 @ B ) @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % RangeE
% 4.69/4.90 thf(fact_738_RangeE,axiom,
% 4.69/4.90 ! [B: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ( member_int @ B @ ( range_int_int @ R2 ) )
% 4.69/4.90 => ~ ! [A4: int] :
% 4.69/4.90 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A4 @ B ) @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % RangeE
% 4.69/4.90 thf(fact_739_RangeE,axiom,
% 4.69/4.90 ! [B: produc3658429121746597890et_nat,R2: set_Pr3286484037609594932et_nat] :
% 4.69/4.90 ( ( member6260224972018164377et_nat @ B @ ( range_3398330936903821850et_nat @ R2 ) )
% 4.69/4.90 => ~ ! [A4: produc3658429121746597890et_nat > $o] :
% 4.69/4.90 ~ ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A4 @ B ) @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % RangeE
% 4.69/4.90 thf(fact_740_RangeE,axiom,
% 4.69/4.90 ! [B: produc3925858234332021118et_nat,R2: set_Pr8536935166611901872et_nat] :
% 4.69/4.90 ( ( member1996754912294343701et_nat @ B @ ( range_7260058354244137878et_nat @ R2 ) )
% 4.69/4.90 => ~ ! [A4: produc3658429121746597890et_nat > $o] :
% 4.69/4.90 ~ ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A4 @ B ) @ R2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % RangeE
% 4.69/4.90 thf(fact_741_Range__iff,axiom,
% 4.69/4.90 ! [A2: set_nat,R2: set_Pr3948176798113811640et_nat] :
% 4.69/4.90 ( ( member_set_nat @ A2 @ ( range_9132311542094983838et_nat @ R2 ) )
% 4.69/4.90 = ( ? [Y3: heap_e7401611519738050253t_unit] : ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ Y3 @ A2 ) @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range_iff
% 4.69/4.90 thf(fact_742_Range__iff,axiom,
% 4.69/4.90 ! [A2: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ( member_nat @ A2 @ ( range_nat_nat @ R2 ) )
% 4.69/4.90 = ( ? [Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ A2 ) @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range_iff
% 4.69/4.90 thf(fact_743_Range__iff,axiom,
% 4.69/4.90 ! [A2: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ( member_int @ A2 @ ( range_int_int @ R2 ) )
% 4.69/4.90 = ( ? [Y3: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ A2 ) @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range_iff
% 4.69/4.90 thf(fact_744_Range__iff,axiom,
% 4.69/4.90 ! [A2: produc3658429121746597890et_nat,R2: set_Pr3286484037609594932et_nat] :
% 4.69/4.90 ( ( member6260224972018164377et_nat @ A2 @ ( range_3398330936903821850et_nat @ R2 ) )
% 4.69/4.90 = ( ? [Y3: produc3658429121746597890et_nat > $o] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ Y3 @ A2 ) @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range_iff
% 4.69/4.90 thf(fact_745_Range__iff,axiom,
% 4.69/4.90 ! [A2: produc3925858234332021118et_nat,R2: set_Pr8536935166611901872et_nat] :
% 4.69/4.90 ( ( member1996754912294343701et_nat @ A2 @ ( range_7260058354244137878et_nat @ R2 ) )
% 4.69/4.90 = ( ? [Y3: produc3658429121746597890et_nat > $o] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ Y3 @ A2 ) @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Range_iff
% 4.69/4.90 thf(fact_746_vimage__singleton__eq,axiom,
% 4.69/4.90 ! [A2: nat,F: nat > product_unit,B: product_unit] :
% 4.69/4.90 ( ( member_nat @ A2 @ ( vimage4884490618288580032t_unit @ F @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.90 = ( ( F @ A2 )
% 4.69/4.90 = B ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_singleton_eq
% 4.69/4.90 thf(fact_747_vimage__singleton__eq,axiom,
% 4.69/4.90 ! [A2: int,F: int > product_unit,B: product_unit] :
% 4.69/4.90 ( ( member_int @ A2 @ ( vimage2000912565490760292t_unit @ F @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.90 = ( ( F @ A2 )
% 4.69/4.90 = B ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_singleton_eq
% 4.69/4.90 thf(fact_748_vimage__singleton__eq,axiom,
% 4.69/4.90 ! [A2: $o,F: $o > product_unit,B: product_unit] :
% 4.69/4.90 ( ( member_o @ A2 @ ( vimage4222377557387472176t_unit @ F @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.90 = ( ( F @ A2 )
% 4.69/4.90 = B ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_singleton_eq
% 4.69/4.90 thf(fact_749_vimage__singleton__eq,axiom,
% 4.69/4.90 ! [A2: product_unit,F: product_unit > product_unit,B: product_unit] :
% 4.69/4.90 ( ( member_Product_unit @ A2 @ ( vimage7995052115951654139t_unit @ F @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.90 = ( ( F @ A2 )
% 4.69/4.90 = B ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_singleton_eq
% 4.69/4.90 thf(fact_750_vimage__singleton__eq,axiom,
% 4.69/4.90 ! [A2: nat,F: nat > $o,B: $o] :
% 4.69/4.90 ( ( member_nat @ A2 @ ( vimage_nat_o @ F @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 4.69/4.90 = ( ( F @ A2 )
% 4.69/4.90 = B ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_singleton_eq
% 4.69/4.90 thf(fact_751_vimage__singleton__eq,axiom,
% 4.69/4.90 ! [A2: int,F: int > $o,B: $o] :
% 4.69/4.90 ( ( member_int @ A2 @ ( vimage_int_o @ F @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 4.69/4.90 = ( ( F @ A2 )
% 4.69/4.90 = B ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_singleton_eq
% 4.69/4.90 thf(fact_752_vimage__singleton__eq,axiom,
% 4.69/4.90 ! [A2: $o,F: $o > $o,B: $o] :
% 4.69/4.90 ( ( member_o @ A2 @ ( vimage_o_o @ F @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 4.69/4.90 = ( ( F @ A2 )
% 4.69/4.90 = B ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_singleton_eq
% 4.69/4.90 thf(fact_753_vimage__singleton__eq,axiom,
% 4.69/4.90 ! [A2: product_unit,F: product_unit > $o,B: $o] :
% 4.69/4.90 ( ( member_Product_unit @ A2 @ ( vimage8808348054653608838unit_o @ F @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 4.69/4.90 = ( ( F @ A2 )
% 4.69/4.90 = B ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_singleton_eq
% 4.69/4.90 thf(fact_754_vimage__singleton__eq,axiom,
% 4.69/4.90 ! [A2: nat,F: nat > nat,B: nat] :
% 4.69/4.90 ( ( member_nat @ A2 @ ( vimage_nat_nat @ F @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 4.69/4.90 = ( ( F @ A2 )
% 4.69/4.90 = B ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_singleton_eq
% 4.69/4.90 thf(fact_755_vimage__singleton__eq,axiom,
% 4.69/4.90 ! [A2: int,F: int > nat,B: nat] :
% 4.69/4.90 ( ( member_int @ A2 @ ( vimage_int_nat @ F @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 4.69/4.90 = ( ( F @ A2 )
% 4.69/4.90 = B ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_singleton_eq
% 4.69/4.90 thf(fact_756_relH__in__rangeI_I2_J,axiom,
% 4.69/4.90 ! [As: set_nat,H2: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit] :
% 4.69/4.90 ( ( relH @ As @ H2 @ H3 )
% 4.69/4.90 => ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % relH_in_rangeI(2)
% 4.69/4.90 thf(fact_757_relH__in__rangeI_I1_J,axiom,
% 4.69/4.90 ! [As: set_nat,H2: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit] :
% 4.69/4.90 ( ( relH @ As @ H2 @ H3 )
% 4.69/4.90 => ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % relH_in_rangeI(1)
% 4.69/4.90 thf(fact_758_relH__refl,axiom,
% 4.69/4.90 ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 4.69/4.90 ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 4.69/4.90 => ( relH @ As @ H2 @ H2 ) ) ).
% 4.69/4.90
% 4.69/4.90 % relH_refl
% 4.69/4.90 thf(fact_759_Image__empty__trancl__Image__empty,axiom,
% 4.69/4.90 ! [R3: set_Pr5094982260447487303t_unit,V: product_unit] :
% 4.69/4.90 ( ( ( image_8431784415008483091t_unit @ R3 @ ( insert_Product_unit @ V @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.90 = bot_bo3957492148770167129t_unit )
% 4.69/4.90 => ( ( image_8431784415008483091t_unit @ ( transi430408012122777006t_unit @ R3 ) @ ( insert_Product_unit @ V @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.90 = bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.90
% 4.69/4.90 % Image_empty_trancl_Image_empty
% 4.69/4.90 thf(fact_760_Image__empty__trancl__Image__empty,axiom,
% 4.69/4.90 ! [R3: set_Product_prod_o_o,V: $o] :
% 4.69/4.90 ( ( ( image_o_o @ R3 @ ( insert_o @ V @ bot_bot_set_o ) )
% 4.69/4.90 = bot_bot_set_o )
% 4.69/4.90 => ( ( image_o_o @ ( transitive_trancl_o @ R3 ) @ ( insert_o @ V @ bot_bot_set_o ) )
% 4.69/4.90 = bot_bot_set_o ) ) ).
% 4.69/4.90
% 4.69/4.90 % Image_empty_trancl_Image_empty
% 4.69/4.90 thf(fact_761_Image__empty__trancl__Image__empty,axiom,
% 4.69/4.90 ! [R3: set_Pr1261947904930325089at_nat,V: nat] :
% 4.69/4.90 ( ( ( image_nat_nat @ R3 @ ( insert_nat @ V @ bot_bot_set_nat ) )
% 4.69/4.90 = bot_bot_set_nat )
% 4.69/4.90 => ( ( image_nat_nat @ ( transi6264000038957366511cl_nat @ R3 ) @ ( insert_nat @ V @ bot_bot_set_nat ) )
% 4.69/4.90 = bot_bot_set_nat ) ) ).
% 4.69/4.90
% 4.69/4.90 % Image_empty_trancl_Image_empty
% 4.69/4.90 thf(fact_762_Image__empty__trancl__Image__empty,axiom,
% 4.69/4.90 ! [R3: set_Pr958786334691620121nt_int,V: int] :
% 4.69/4.90 ( ( ( image_int_int @ R3 @ ( insert_int @ V @ bot_bot_set_int ) )
% 4.69/4.90 = bot_bot_set_int )
% 4.69/4.90 => ( ( image_int_int @ ( transi6261509568448316235cl_int @ R3 ) @ ( insert_int @ V @ bot_bot_set_int ) )
% 4.69/4.90 = bot_bot_set_int ) ) ).
% 4.69/4.90
% 4.69/4.90 % Image_empty_trancl_Image_empty
% 4.69/4.90 thf(fact_763_Image__empty__trancl__Image__empty,axiom,
% 4.69/4.90 ! [R3: set_Pr2161125870931222855_nat_o,V: produc3658429121746597890et_nat > $o] :
% 4.69/4.90 ( ( ( image_2232984160439939859_nat_o @ R3 @ ( insert5175938949040314269_nat_o @ V @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.90 = bot_bo7824918357723582233_nat_o )
% 4.69/4.90 => ( ( image_2232984160439939859_nat_o @ ( transi4009562729418357614_nat_o @ R3 ) @ ( insert5175938949040314269_nat_o @ V @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.90 = bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.90
% 4.69/4.90 % Image_empty_trancl_Image_empty
% 4.69/4.90 thf(fact_764_mod__relH,axiom,
% 4.69/4.90 ! [As: set_nat,H2: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,P: assn] :
% 4.69/4.90 ( ( relH @ As @ H2 @ H3 )
% 4.69/4.90 => ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 4.69/4.90 = ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % mod_relH
% 4.69/4.90 thf(fact_765_for__in__RI,axiom,
% 4.69/4.90 ! [X: heap_e7401611519738050253t_unit,R3: set_Pr3948176798113811640et_nat] :
% 4.69/4.90 ( ( member242389114213480694t_unit @ X @ ( domain2007548326387822151et_nat @ R3 ) )
% 4.69/4.90 => ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X @ ( fun_of5878246503291251064et_nat @ R3 @ X ) ) @ R3 ) ) ).
% 4.69/4.90
% 4.69/4.90 % for_in_RI
% 4.69/4.90 thf(fact_766_for__in__RI,axiom,
% 4.69/4.90 ! [X: nat,R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ( member_nat @ X @ ( domain_nat_nat @ R3 ) )
% 4.69/4.90 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ ( fun_of_rel_nat_nat @ R3 @ X ) ) @ R3 ) ) ).
% 4.69/4.90
% 4.69/4.90 % for_in_RI
% 4.69/4.90 thf(fact_767_for__in__RI,axiom,
% 4.69/4.90 ! [X: int,R3: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ( member_int @ X @ ( domain_int_int @ R3 ) )
% 4.69/4.90 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ ( fun_of_rel_int_int @ R3 @ X ) ) @ R3 ) ) ).
% 4.69/4.90
% 4.69/4.90 % for_in_RI
% 4.69/4.90 thf(fact_768_for__in__RI,axiom,
% 4.69/4.90 ! [X: produc3658429121746597890et_nat > $o,R3: set_Pr3286484037609594932et_nat] :
% 4.69/4.90 ( ( member6576561426505652726_nat_o @ X @ ( domain2358961613337345475et_nat @ R3 ) )
% 4.69/4.90 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X @ ( fun_of3673525222065131764et_nat @ R3 @ X ) ) @ R3 ) ) ).
% 4.69/4.90
% 4.69/4.90 % for_in_RI
% 4.69/4.90 thf(fact_769_for__in__RI,axiom,
% 4.69/4.90 ! [X: produc3658429121746597890et_nat > $o,R3: set_Pr8536935166611901872et_nat] :
% 4.69/4.90 ( ( member6576561426505652726_nat_o @ X @ ( domain3618434998481624895et_nat @ R3 ) )
% 4.69/4.90 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X @ ( fun_of384177504262425200et_nat @ R3 @ X ) ) @ R3 ) ) ).
% 4.69/4.90
% 4.69/4.90 % for_in_RI
% 4.69/4.90 thf(fact_770_trancl_Ocases,axiom,
% 4.69/4.90 ! [A1: nat,A22: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A1 @ A22 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.90 => ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A1 @ A22 ) @ R2 )
% 4.69/4.90 => ~ ! [B2: nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A1 @ B2 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.90 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B2 @ A22 ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl.cases
% 4.69/4.90 thf(fact_771_trancl_Ocases,axiom,
% 4.69/4.90 ! [A1: int,A22: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A1 @ A22 ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.90 => ( ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A1 @ A22 ) @ R2 )
% 4.69/4.90 => ~ ! [B2: int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A1 @ B2 ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.90 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B2 @ A22 ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl.cases
% 4.69/4.90 thf(fact_772_trancl_Osimps,axiom,
% 4.69/4.90 ! [A1: nat,A22: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A1 @ A22 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.90 = ( ? [A6: nat,B6: nat] :
% 4.69/4.90 ( ( A1 = A6 )
% 4.69/4.90 & ( A22 = B6 )
% 4.69/4.90 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A6 @ B6 ) @ R2 ) )
% 4.69/4.90 | ? [A6: nat,B6: nat,C4: nat] :
% 4.69/4.90 ( ( A1 = A6 )
% 4.69/4.90 & ( A22 = C4 )
% 4.69/4.90 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A6 @ B6 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.90 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B6 @ C4 ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl.simps
% 4.69/4.90 thf(fact_773_trancl_Osimps,axiom,
% 4.69/4.90 ! [A1: int,A22: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A1 @ A22 ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.90 = ( ? [A6: int,B6: int] :
% 4.69/4.90 ( ( A1 = A6 )
% 4.69/4.90 & ( A22 = B6 )
% 4.69/4.90 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A6 @ B6 ) @ R2 ) )
% 4.69/4.90 | ? [A6: int,B6: int,C4: int] :
% 4.69/4.90 ( ( A1 = A6 )
% 4.69/4.90 & ( A22 = C4 )
% 4.69/4.90 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A6 @ B6 ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.90 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B6 @ C4 ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl.simps
% 4.69/4.90 thf(fact_774_trancl_Or__into__trancl,axiom,
% 4.69/4.90 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl.r_into_trancl
% 4.69/4.90 thf(fact_775_trancl_Or__into__trancl,axiom,
% 4.69/4.90 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( transi6261509568448316235cl_int @ R2 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl.r_into_trancl
% 4.69/4.90 thf(fact_776_tranclE,axiom,
% 4.69/4.90 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.90 => ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 )
% 4.69/4.90 => ~ ! [C2: nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ C2 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.90 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ C2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % tranclE
% 4.69/4.90 thf(fact_777_tranclE,axiom,
% 4.69/4.90 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.90 => ( ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 )
% 4.69/4.90 => ~ ! [C2: int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ C2 ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.90 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ C2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % tranclE
% 4.69/4.90 thf(fact_778_trancl__trans,axiom,
% 4.69/4.90 ! [X: nat,Y: nat,R2: set_Pr1261947904930325089at_nat,Z: nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.90 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ Z ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.90 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_trans
% 4.69/4.90 thf(fact_779_trancl__trans,axiom,
% 4.69/4.90 ! [X: int,Y: int,R2: set_Pr958786334691620121nt_int,Z: int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.90 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y @ Z ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.90 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Z ) @ ( transi6261509568448316235cl_int @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_trans
% 4.69/4.90 thf(fact_780_trancl__induct,axiom,
% 4.69/4.90 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat,P: nat > $o] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.90 => ( ! [Y2: nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ Y2 ) @ R2 )
% 4.69/4.90 => ( P @ Y2 ) )
% 4.69/4.90 => ( ! [Y2: nat,Z3: nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ Y2 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.90 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ Z3 ) @ R2 )
% 4.69/4.90 => ( ( P @ Y2 )
% 4.69/4.90 => ( P @ Z3 ) ) ) )
% 4.69/4.90 => ( P @ B ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_induct
% 4.69/4.90 thf(fact_781_trancl__induct,axiom,
% 4.69/4.90 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int,P: int > $o] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.90 => ( ! [Y2: int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ Y2 ) @ R2 )
% 4.69/4.90 => ( P @ Y2 ) )
% 4.69/4.90 => ( ! [Y2: int,Z3: int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ Y2 ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.90 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y2 @ Z3 ) @ R2 )
% 4.69/4.90 => ( ( P @ Y2 )
% 4.69/4.90 => ( P @ Z3 ) ) ) )
% 4.69/4.90 => ( P @ B ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_induct
% 4.69/4.90 thf(fact_782_r__r__into__trancl,axiom,
% 4.69/4.90 ! [A2: nat,B: nat,R3: set_Pr1261947904930325089at_nat,C: nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R3 )
% 4.69/4.90 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C ) @ R3 )
% 4.69/4.90 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ C ) @ ( transi6264000038957366511cl_nat @ R3 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % r_r_into_trancl
% 4.69/4.90 thf(fact_783_r__r__into__trancl,axiom,
% 4.69/4.90 ! [A2: int,B: int,R3: set_Pr958786334691620121nt_int,C: int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R3 )
% 4.69/4.90 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C ) @ R3 )
% 4.69/4.90 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ C ) @ ( transi6261509568448316235cl_int @ R3 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % r_r_into_trancl
% 4.69/4.90 thf(fact_784_converse__tranclE,axiom,
% 4.69/4.90 ! [X: nat,Z: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.90 => ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ R2 )
% 4.69/4.90 => ~ ! [Y2: nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y2 ) @ R2 )
% 4.69/4.90 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ Z ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % converse_tranclE
% 4.69/4.90 thf(fact_785_converse__tranclE,axiom,
% 4.69/4.90 ! [X: int,Z: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Z ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.90 => ( ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Z ) @ R2 )
% 4.69/4.90 => ~ ! [Y2: int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y2 ) @ R2 )
% 4.69/4.90 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y2 @ Z ) @ ( transi6261509568448316235cl_int @ R2 ) ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % converse_tranclE
% 4.69/4.90 thf(fact_786_trancl__induct2,axiom,
% 4.69/4.90 ! [Ax: heap_e7401611519738050253t_unit,Ay: set_nat,Bx: heap_e7401611519738050253t_unit,By: set_nat,R2: set_Pr719794911490849221et_nat,P: heap_e7401611519738050253t_unit > set_nat > $o] :
% 4.69/4.90 ( ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ ( produc7507926704131184380et_nat @ Ax @ Ay ) @ ( produc7507926704131184380et_nat @ Bx @ By ) ) @ ( transi4137310414928362273et_nat @ R2 ) )
% 4.69/4.90 => ( ! [A4: heap_e7401611519738050253t_unit,B2: set_nat] :
% 4.69/4.90 ( ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ ( produc7507926704131184380et_nat @ Ax @ Ay ) @ ( produc7507926704131184380et_nat @ A4 @ B2 ) ) @ R2 )
% 4.69/4.90 => ( P @ A4 @ B2 ) )
% 4.69/4.90 => ( ! [A4: heap_e7401611519738050253t_unit,B2: set_nat,Aa: heap_e7401611519738050253t_unit,Ba: set_nat] :
% 4.69/4.90 ( ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ ( produc7507926704131184380et_nat @ Ax @ Ay ) @ ( produc7507926704131184380et_nat @ A4 @ B2 ) ) @ ( transi4137310414928362273et_nat @ R2 ) )
% 4.69/4.90 => ( ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ ( produc7507926704131184380et_nat @ A4 @ B2 ) @ ( produc7507926704131184380et_nat @ Aa @ Ba ) ) @ R2 )
% 4.69/4.90 => ( ( P @ A4 @ B2 )
% 4.69/4.90 => ( P @ Aa @ Ba ) ) ) )
% 4.69/4.90 => ( P @ Bx @ By ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_induct2
% 4.69/4.90 thf(fact_787_trancl__induct2,axiom,
% 4.69/4.90 ! [Ax: nat,Ay: nat,Bx: nat,By: nat,R2: set_Pr8693737435421807431at_nat,P: nat > nat > $o] :
% 4.69/4.90 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ Ax @ Ay ) @ ( product_Pair_nat_nat @ Bx @ By ) ) @ ( transi243908449541399842at_nat @ R2 ) )
% 4.69/4.90 => ( ! [A4: nat,B2: nat] :
% 4.69/4.90 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ Ax @ Ay ) @ ( product_Pair_nat_nat @ A4 @ B2 ) ) @ R2 )
% 4.69/4.90 => ( P @ A4 @ B2 ) )
% 4.69/4.90 => ( ! [A4: nat,B2: nat,Aa: nat,Ba: nat] :
% 4.69/4.90 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ Ax @ Ay ) @ ( product_Pair_nat_nat @ A4 @ B2 ) ) @ ( transi243908449541399842at_nat @ R2 ) )
% 4.69/4.90 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A4 @ B2 ) @ ( product_Pair_nat_nat @ Aa @ Ba ) ) @ R2 )
% 4.69/4.90 => ( ( P @ A4 @ B2 )
% 4.69/4.90 => ( P @ Aa @ Ba ) ) ) )
% 4.69/4.90 => ( P @ Bx @ By ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_induct2
% 4.69/4.90 thf(fact_788_trancl__induct2,axiom,
% 4.69/4.90 ! [Ax: int,Ay: int,Bx: int,By: int,R2: set_Pr2560585780119916871nt_int,P: int > int > $o] :
% 4.69/4.90 ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ Ax @ Ay ) @ ( product_Pair_int_int @ Bx @ By ) ) @ ( transi6288783178788033498nt_int @ R2 ) )
% 4.69/4.90 => ( ! [A4: int,B2: int] :
% 4.69/4.90 ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ Ax @ Ay ) @ ( product_Pair_int_int @ A4 @ B2 ) ) @ R2 )
% 4.69/4.90 => ( P @ A4 @ B2 ) )
% 4.69/4.90 => ( ! [A4: int,B2: int,Aa: int,Ba: int] :
% 4.69/4.90 ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ Ax @ Ay ) @ ( product_Pair_int_int @ A4 @ B2 ) ) @ ( transi6288783178788033498nt_int @ R2 ) )
% 4.69/4.90 => ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ A4 @ B2 ) @ ( product_Pair_int_int @ Aa @ Ba ) ) @ R2 )
% 4.69/4.90 => ( ( P @ A4 @ B2 )
% 4.69/4.90 => ( P @ Aa @ Ba ) ) ) )
% 4.69/4.90 => ( P @ Bx @ By ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_induct2
% 4.69/4.90 thf(fact_789_trancl__induct2,axiom,
% 4.69/4.90 ! [Ax: produc3658429121746597890et_nat > $o,Ay: produc3658429121746597890et_nat,Bx: produc3658429121746597890et_nat > $o,By: produc3658429121746597890et_nat,R2: set_Pr7928877670098842301et_nat,P: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 4.69/4.90 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ Ax @ Ay ) @ ( produc5001842942810119800et_nat @ Bx @ By ) ) @ ( transi3145040225084697757et_nat @ R2 ) )
% 4.69/4.90 => ( ! [A4: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 4.69/4.90 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ Ax @ Ay ) @ ( produc5001842942810119800et_nat @ A4 @ B2 ) ) @ R2 )
% 4.69/4.90 => ( P @ A4 @ B2 ) )
% 4.69/4.90 => ( ! [A4: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat,Aa: produc3658429121746597890et_nat > $o,Ba: produc3658429121746597890et_nat] :
% 4.69/4.90 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ Ax @ Ay ) @ ( produc5001842942810119800et_nat @ A4 @ B2 ) ) @ ( transi3145040225084697757et_nat @ R2 ) )
% 4.69/4.90 => ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ A4 @ B2 ) @ ( produc5001842942810119800et_nat @ Aa @ Ba ) ) @ R2 )
% 4.69/4.90 => ( ( P @ A4 @ B2 )
% 4.69/4.90 => ( P @ Aa @ Ba ) ) ) )
% 4.69/4.90 => ( P @ Bx @ By ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_induct2
% 4.69/4.90 thf(fact_790_trancl__induct2,axiom,
% 4.69/4.90 ! [Ax: produc3658429121746597890et_nat > $o,Ay: produc3925858234332021118et_nat,Bx: produc3658429121746597890et_nat > $o,By: produc3925858234332021118et_nat,R2: set_Pr3444600963470892981et_nat,P: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 4.69/4.90 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ Ax @ Ay ) @ ( produc2245416461498447860et_nat @ Bx @ By ) ) @ ( transi5221092739591632921et_nat @ R2 ) )
% 4.69/4.90 => ( ! [A4: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 4.69/4.90 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ Ax @ Ay ) @ ( produc2245416461498447860et_nat @ A4 @ B2 ) ) @ R2 )
% 4.69/4.90 => ( P @ A4 @ B2 ) )
% 4.69/4.90 => ( ! [A4: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat,Aa: produc3658429121746597890et_nat > $o,Ba: produc3925858234332021118et_nat] :
% 4.69/4.90 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ Ax @ Ay ) @ ( produc2245416461498447860et_nat @ A4 @ B2 ) ) @ ( transi5221092739591632921et_nat @ R2 ) )
% 4.69/4.90 => ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ A4 @ B2 ) @ ( produc2245416461498447860et_nat @ Aa @ Ba ) ) @ R2 )
% 4.69/4.90 => ( ( P @ A4 @ B2 )
% 4.69/4.90 => ( P @ Aa @ Ba ) ) ) )
% 4.69/4.90 => ( P @ Bx @ By ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_induct2
% 4.69/4.90 thf(fact_791_converse__trancl__induct,axiom,
% 4.69/4.90 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat,P: nat > $o] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.90 => ( ! [Y2: nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ B ) @ R2 )
% 4.69/4.90 => ( P @ Y2 ) )
% 4.69/4.90 => ( ! [Y2: nat,Z3: nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ Z3 ) @ R2 )
% 4.69/4.90 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Z3 @ B ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.90 => ( ( P @ Z3 )
% 4.69/4.90 => ( P @ Y2 ) ) ) )
% 4.69/4.90 => ( P @ A2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % converse_trancl_induct
% 4.69/4.90 thf(fact_792_converse__trancl__induct,axiom,
% 4.69/4.90 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int,P: int > $o] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.90 => ( ! [Y2: int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y2 @ B ) @ R2 )
% 4.69/4.90 => ( P @ Y2 ) )
% 4.69/4.90 => ( ! [Y2: int,Z3: int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y2 @ Z3 ) @ R2 )
% 4.69/4.90 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Z3 @ B ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.90 => ( ( P @ Z3 )
% 4.69/4.90 => ( P @ Y2 ) ) ) )
% 4.69/4.90 => ( P @ A2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % converse_trancl_induct
% 4.69/4.90 thf(fact_793_trancl__trans__induct,axiom,
% 4.69/4.90 ! [X: nat,Y: nat,R2: set_Pr1261947904930325089at_nat,P: nat > nat > $o] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.90 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ R2 )
% 4.69/4.90 => ( P @ X3 @ Y2 ) )
% 4.69/4.90 => ( ! [X3: nat,Y2: nat,Z3: nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.90 => ( ( P @ X3 @ Y2 )
% 4.69/4.90 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ Z3 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.90 => ( ( P @ Y2 @ Z3 )
% 4.69/4.90 => ( P @ X3 @ Z3 ) ) ) ) )
% 4.69/4.90 => ( P @ X @ Y ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_trans_induct
% 4.69/4.90 thf(fact_794_trancl__trans__induct,axiom,
% 4.69/4.90 ! [X: int,Y: int,R2: set_Pr958786334691620121nt_int,P: int > int > $o] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.90 => ( ! [X3: int,Y2: int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y2 ) @ R2 )
% 4.69/4.90 => ( P @ X3 @ Y2 ) )
% 4.69/4.90 => ( ! [X3: int,Y2: int,Z3: int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y2 ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.90 => ( ( P @ X3 @ Y2 )
% 4.69/4.90 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y2 @ Z3 ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.90 => ( ( P @ Y2 @ Z3 )
% 4.69/4.90 => ( P @ X3 @ Z3 ) ) ) ) )
% 4.69/4.90 => ( P @ X @ Y ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_trans_induct
% 4.69/4.90 thf(fact_795_trancl__into__trancl2,axiom,
% 4.69/4.90 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat,C: nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.90 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ C ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_into_trancl2
% 4.69/4.90 thf(fact_796_trancl__into__trancl2,axiom,
% 4.69/4.90 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int,C: int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 )
% 4.69/4.90 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.90 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ C ) @ ( transi6261509568448316235cl_int @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_into_trancl2
% 4.69/4.90 thf(fact_797_Transitive__Closure_Otrancl__into__trancl,axiom,
% 4.69/4.90 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat,C: nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.90 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C ) @ R2 )
% 4.69/4.90 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ C ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Transitive_Closure.trancl_into_trancl
% 4.69/4.90 thf(fact_798_Transitive__Closure_Otrancl__into__trancl,axiom,
% 4.69/4.90 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int,C: int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.90 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C ) @ R2 )
% 4.69/4.90 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ C ) @ ( transi6261509568448316235cl_int @ R2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Transitive_Closure.trancl_into_trancl
% 4.69/4.90 thf(fact_799_irrefl__trancl__rD,axiom,
% 4.69/4.90 ! [R2: set_Pr1261947904930325089at_nat,X: nat,Y: nat] :
% 4.69/4.90 ( ! [X3: nat] :
% 4.69/4.90 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ X3 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.90 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R2 )
% 4.69/4.90 => ( X != Y ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % irrefl_trancl_rD
% 4.69/4.90 thf(fact_800_irrefl__trancl__rD,axiom,
% 4.69/4.90 ! [R2: set_Pr958786334691620121nt_int,X: int,Y: int] :
% 4.69/4.90 ( ! [X3: int] :
% 4.69/4.90 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ X3 ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.90 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R2 )
% 4.69/4.90 => ( X != Y ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % irrefl_trancl_rD
% 4.69/4.90 thf(fact_801_trancl__Image__advance__ss,axiom,
% 4.69/4.90 ! [U: product_unit,V: product_unit,E: set_Pr5094982260447487303t_unit] :
% 4.69/4.90 ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ U @ V ) @ E )
% 4.69/4.90 => ( ord_le3507040750410214029t_unit @ ( image_8431784415008483091t_unit @ ( transi430408012122777006t_unit @ E ) @ ( insert_Product_unit @ V @ bot_bo3957492148770167129t_unit ) ) @ ( image_8431784415008483091t_unit @ ( transi430408012122777006t_unit @ E ) @ ( insert_Product_unit @ U @ bot_bo3957492148770167129t_unit ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_Image_advance_ss
% 4.69/4.90 thf(fact_802_trancl__Image__advance__ss,axiom,
% 4.69/4.90 ! [U: $o,V: $o,E: set_Product_prod_o_o] :
% 4.69/4.90 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ U @ V ) @ E )
% 4.69/4.90 => ( ord_less_eq_set_o @ ( image_o_o @ ( transitive_trancl_o @ E ) @ ( insert_o @ V @ bot_bot_set_o ) ) @ ( image_o_o @ ( transitive_trancl_o @ E ) @ ( insert_o @ U @ bot_bot_set_o ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_Image_advance_ss
% 4.69/4.90 thf(fact_803_trancl__Image__advance__ss,axiom,
% 4.69/4.90 ! [U: int,V: int,E: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ U @ V ) @ E )
% 4.69/4.90 => ( ord_less_eq_set_int @ ( image_int_int @ ( transi6261509568448316235cl_int @ E ) @ ( insert_int @ V @ bot_bot_set_int ) ) @ ( image_int_int @ ( transi6261509568448316235cl_int @ E ) @ ( insert_int @ U @ bot_bot_set_int ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_Image_advance_ss
% 4.69/4.90 thf(fact_804_trancl__Image__advance__ss,axiom,
% 4.69/4.90 ! [U: produc3658429121746597890et_nat > $o,V: produc3658429121746597890et_nat > $o,E: set_Pr2161125870931222855_nat_o] :
% 4.69/4.90 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ U @ V ) @ E )
% 4.69/4.90 => ( ord_le2965882846123202637_nat_o @ ( image_2232984160439939859_nat_o @ ( transi4009562729418357614_nat_o @ E ) @ ( insert5175938949040314269_nat_o @ V @ bot_bo7824918357723582233_nat_o ) ) @ ( image_2232984160439939859_nat_o @ ( transi4009562729418357614_nat_o @ E ) @ ( insert5175938949040314269_nat_o @ U @ bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_Image_advance_ss
% 4.69/4.90 thf(fact_805_trancl__Image__advance__ss,axiom,
% 4.69/4.90 ! [U: nat,V: nat,E: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ U @ V ) @ E )
% 4.69/4.90 => ( ord_less_eq_set_nat @ ( image_nat_nat @ ( transi6264000038957366511cl_nat @ E ) @ ( insert_nat @ V @ bot_bot_set_nat ) ) @ ( image_nat_nat @ ( transi6264000038957366511cl_nat @ E ) @ ( insert_nat @ U @ bot_bot_set_nat ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_Image_advance_ss
% 4.69/4.90 thf(fact_806_wand__assnI,axiom,
% 4.69/4.90 ! [H2: heap_e7401611519738050253t_unit,As: set_nat,Q2: assn,R3: assn] :
% 4.69/4.90 ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 4.69/4.90 => ( ! [H6: heap_e7401611519738050253t_unit,As4: set_nat] :
% 4.69/4.90 ( ( ( inf_inf_set_nat @ As @ As4 )
% 4.69/4.90 = bot_bot_set_nat )
% 4.69/4.90 => ( ( relH @ As @ H2 @ H6 )
% 4.69/4.90 => ( ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As ) )
% 4.69/4.90 => ( ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H6 @ As4 ) )
% 4.69/4.90 => ( rep_assn @ R3 @ ( produc7507926704131184380et_nat @ H6 @ ( sup_sup_set_nat @ As @ As4 ) ) ) ) ) ) )
% 4.69/4.90 => ( rep_assn @ ( wand_assn @ Q2 @ R3 ) @ ( produc7507926704131184380et_nat @ H2 @ As ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % wand_assnI
% 4.69/4.90 thf(fact_807_trancl__Image__in__Range,axiom,
% 4.69/4.90 ! [R3: set_Pr1261947904930325089at_nat,V2: set_nat] : ( ord_less_eq_set_nat @ ( image_nat_nat @ ( transi6264000038957366511cl_nat @ R3 ) @ V2 ) @ ( range_nat_nat @ R3 ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_Image_in_Range
% 4.69/4.90 thf(fact_808_Pair__vimage__Sigma,axiom,
% 4.69/4.90 ! [X: nat,A: set_nat,F: nat > set_Product_unit] :
% 4.69/4.90 ( ( ( member_nat @ X @ A )
% 4.69/4.90 => ( ( vimage7305857734363866308t_unit @ ( produc3434450474625521892t_unit @ X ) @ ( produc5506539147108004339t_unit @ A @ F ) )
% 4.69/4.90 = ( F @ X ) ) )
% 4.69/4.90 & ( ~ ( member_nat @ X @ A )
% 4.69/4.90 => ( ( vimage7305857734363866308t_unit @ ( produc3434450474625521892t_unit @ X ) @ ( produc5506539147108004339t_unit @ A @ F ) )
% 4.69/4.90 = bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Pair_vimage_Sigma
% 4.69/4.90 thf(fact_809_Pair__vimage__Sigma,axiom,
% 4.69/4.90 ! [X: int,A: set_int,F: int > set_Product_unit] :
% 4.69/4.90 ( ( ( member_int @ X @ A )
% 4.69/4.90 => ( ( vimage4422279681566046568t_unit @ ( produc550872421827702152t_unit @ X ) @ ( produc2622961094310184599t_unit @ A @ F ) )
% 4.69/4.90 = ( F @ X ) ) )
% 4.69/4.90 & ( ~ ( member_int @ X @ A )
% 4.69/4.90 => ( ( vimage4422279681566046568t_unit @ ( produc550872421827702152t_unit @ X ) @ ( produc2622961094310184599t_unit @ A @ F ) )
% 4.69/4.90 = bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Pair_vimage_Sigma
% 4.69/4.90 thf(fact_810_Pair__vimage__Sigma,axiom,
% 4.69/4.90 ! [X: $o,A: set_o,F: $o > set_Product_unit] :
% 4.69/4.90 ( ( ( member_o @ X @ A )
% 4.69/4.90 => ( ( vimage508909887551888138t_unit @ ( produc3901946521647900940t_unit @ X ) @ ( produc411009820408249917t_unit @ A @ F ) )
% 4.69/4.90 = ( F @ X ) ) )
% 4.69/4.90 & ( ~ ( member_o @ X @ A )
% 4.69/4.90 => ( ( vimage508909887551888138t_unit @ ( produc3901946521647900940t_unit @ X ) @ ( produc411009820408249917t_unit @ A @ F ) )
% 4.69/4.90 = bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Pair_vimage_Sigma
% 4.69/4.90 thf(fact_811_Pair__vimage__Sigma,axiom,
% 4.69/4.90 ! [X: product_unit,A: set_Product_unit,F: product_unit > set_Product_unit] :
% 4.69/4.90 ( ( ( member_Product_unit @ X @ A )
% 4.69/4.90 => ( ( vimage8114940889160087125t_unit @ ( produc5692694829384537815t_unit @ X ) @ ( produc6121607364029222536t_unit @ A @ F ) )
% 4.69/4.90 = ( F @ X ) ) )
% 4.69/4.90 & ( ~ ( member_Product_unit @ X @ A )
% 4.69/4.90 => ( ( vimage8114940889160087125t_unit @ ( produc5692694829384537815t_unit @ X ) @ ( produc6121607364029222536t_unit @ A @ F ) )
% 4.69/4.90 = bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Pair_vimage_Sigma
% 4.69/4.90 thf(fact_812_Pair__vimage__Sigma,axiom,
% 4.69/4.90 ! [X: nat,A: set_nat,F: nat > set_o] :
% 4.69/4.90 ( ( ( member_nat @ X @ A )
% 4.69/4.90 => ( ( vimage6125388955539849434_nat_o @ ( product_Pair_nat_o @ X ) @ ( product_Sigma_nat_o @ A @ F ) )
% 4.69/4.90 = ( F @ X ) ) )
% 4.69/4.90 & ( ~ ( member_nat @ X @ A )
% 4.69/4.90 => ( ( vimage6125388955539849434_nat_o @ ( product_Pair_nat_o @ X ) @ ( product_Sigma_nat_o @ A @ F ) )
% 4.69/4.90 = bot_bot_set_o ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Pair_vimage_Sigma
% 4.69/4.90 thf(fact_813_Pair__vimage__Sigma,axiom,
% 4.69/4.90 ! [X: int,A: set_int,F: int > set_o] :
% 4.69/4.90 ( ( ( member_int @ X @ A )
% 4.69/4.90 => ( ( vimage4304346610107161470_int_o @ ( product_Pair_int_o @ X ) @ ( product_Sigma_int_o @ A @ F ) )
% 4.69/4.90 = ( F @ X ) ) )
% 4.69/4.90 & ( ~ ( member_int @ X @ A )
% 4.69/4.90 => ( ( vimage4304346610107161470_int_o @ ( product_Pair_int_o @ X ) @ ( product_Sigma_int_o @ A @ F ) )
% 4.69/4.90 = bot_bot_set_o ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Pair_vimage_Sigma
% 4.69/4.90 thf(fact_814_Pair__vimage__Sigma,axiom,
% 4.69/4.90 ! [X: $o,A: set_o,F: $o > set_o] :
% 4.69/4.90 ( ( ( member_o @ X @ A )
% 4.69/4.90 => ( ( vimage8945963521958007626od_o_o @ ( product_Pair_o_o @ X ) @ ( product_Sigma_o_o @ A @ F ) )
% 4.69/4.90 = ( F @ X ) ) )
% 4.69/4.90 & ( ~ ( member_o @ X @ A )
% 4.69/4.90 => ( ( vimage8945963521958007626od_o_o @ ( product_Pair_o_o @ X ) @ ( product_Sigma_o_o @ A @ F ) )
% 4.69/4.90 = bot_bot_set_o ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Pair_vimage_Sigma
% 4.69/4.90 thf(fact_815_Pair__vimage__Sigma,axiom,
% 4.69/4.90 ! [X: product_unit,A: set_Product_unit,F: product_unit > set_o] :
% 4.69/4.90 ( ( ( member_Product_unit @ X @ A )
% 4.69/4.90 => ( ( vimage9156843197228287893unit_o @ ( produc8487917018914037602unit_o @ X ) @ ( produc4996980317674386579unit_o @ A @ F ) )
% 4.69/4.90 = ( F @ X ) ) )
% 4.69/4.90 & ( ~ ( member_Product_unit @ X @ A )
% 4.69/4.90 => ( ( vimage9156843197228287893unit_o @ ( produc8487917018914037602unit_o @ X ) @ ( produc4996980317674386579unit_o @ A @ F ) )
% 4.69/4.90 = bot_bot_set_o ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Pair_vimage_Sigma
% 4.69/4.90 thf(fact_816_Pair__vimage__Sigma,axiom,
% 4.69/4.90 ! [X: int,A: set_int,F: int > set_nat] :
% 4.69/4.90 ( ( ( member_int @ X @ A )
% 4.69/4.90 => ( ( vimage9012682431555523728nt_nat @ ( product_Pair_int_nat @ X ) @ ( produc1456381018704787142nt_nat @ A @ F ) )
% 4.69/4.90 = ( F @ X ) ) )
% 4.69/4.90 & ( ~ ( member_int @ X @ A )
% 4.69/4.90 => ( ( vimage9012682431555523728nt_nat @ ( product_Pair_int_nat @ X ) @ ( produc1456381018704787142nt_nat @ A @ F ) )
% 4.69/4.90 = bot_bot_set_nat ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Pair_vimage_Sigma
% 4.69/4.90 thf(fact_817_Pair__vimage__Sigma,axiom,
% 4.69/4.90 ! [X: $o,A: set_o,F: $o > set_nat] :
% 4.69/4.90 ( ( ( member_o @ X @ A )
% 4.69/4.90 => ( ( vimage5656379182745576100_o_nat @ ( product_Pair_o_nat @ X ) @ ( product_Sigma_o_nat @ A @ F ) )
% 4.69/4.90 = ( F @ X ) ) )
% 4.69/4.90 & ( ~ ( member_o @ X @ A )
% 4.69/4.90 => ( ( vimage5656379182745576100_o_nat @ ( product_Pair_o_nat @ X ) @ ( product_Sigma_o_nat @ A @ F ) )
% 4.69/4.90 = bot_bot_set_nat ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Pair_vimage_Sigma
% 4.69/4.90 thf(fact_818_relH__def,axiom,
% 4.69/4.90 ( relH
% 4.69/4.90 = ( ^ [As3: set_nat,H4: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 4.69/4.90 ( ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As3 ) )
% 4.69/4.90 & ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As3 ) )
% 4.69/4.90 & ! [T: typerep,X2: nat] :
% 4.69/4.90 ( ( member_nat @ X2 @ As3 )
% 4.69/4.90 => ( ( ( refs_Product_unit @ H4 @ T @ X2 )
% 4.69/4.90 = ( refs_Product_unit @ H5 @ T @ X2 ) )
% 4.69/4.90 & ( ( arrays_Product_unit @ H4 @ T @ X2 )
% 4.69/4.90 = ( arrays_Product_unit @ H5 @ T @ X2 ) ) ) ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % relH_def
% 4.69/4.90 thf(fact_819_vimage__insert,axiom,
% 4.69/4.90 ! [F: nat > product_unit,A2: product_unit,B4: set_Product_unit] :
% 4.69/4.90 ( ( vimage4884490618288580032t_unit @ F @ ( insert_Product_unit @ A2 @ B4 ) )
% 4.69/4.90 = ( sup_sup_set_nat @ ( vimage4884490618288580032t_unit @ F @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) @ ( vimage4884490618288580032t_unit @ F @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_insert
% 4.69/4.90 thf(fact_820_vimage__insert,axiom,
% 4.69/4.90 ! [F: nat > $o,A2: $o,B4: set_o] :
% 4.69/4.90 ( ( vimage_nat_o @ F @ ( insert_o @ A2 @ B4 ) )
% 4.69/4.90 = ( sup_sup_set_nat @ ( vimage_nat_o @ F @ ( insert_o @ A2 @ bot_bot_set_o ) ) @ ( vimage_nat_o @ F @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_insert
% 4.69/4.90 thf(fact_821_vimage__insert,axiom,
% 4.69/4.90 ! [F: nat > nat,A2: nat,B4: set_nat] :
% 4.69/4.90 ( ( vimage_nat_nat @ F @ ( insert_nat @ A2 @ B4 ) )
% 4.69/4.90 = ( sup_sup_set_nat @ ( vimage_nat_nat @ F @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) @ ( vimage_nat_nat @ F @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_insert
% 4.69/4.90 thf(fact_822_vimage__insert,axiom,
% 4.69/4.90 ! [F: nat > int,A2: int,B4: set_int] :
% 4.69/4.90 ( ( vimage_nat_int @ F @ ( insert_int @ A2 @ B4 ) )
% 4.69/4.90 = ( sup_sup_set_nat @ ( vimage_nat_int @ F @ ( insert_int @ A2 @ bot_bot_set_int ) ) @ ( vimage_nat_int @ F @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_insert
% 4.69/4.90 thf(fact_823_vimage__insert,axiom,
% 4.69/4.90 ! [F: nat > produc3658429121746597890et_nat > $o,A2: produc3658429121746597890et_nat > $o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.90 ( ( vimage8201027140005291904_nat_o @ F @ ( insert5175938949040314269_nat_o @ A2 @ B4 ) )
% 4.69/4.90 = ( sup_sup_set_nat @ ( vimage8201027140005291904_nat_o @ F @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) @ ( vimage8201027140005291904_nat_o @ F @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % vimage_insert
% 4.69/4.90 thf(fact_824_trancl__over__edgeE,axiom,
% 4.69/4.90 ! [U: nat,W: nat,V1: nat,V22: nat,E: set_Pr1261947904930325089at_nat] :
% 4.69/4.90 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ U @ W ) @ ( transi6264000038957366511cl_nat @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ V1 @ V22 ) @ E ) ) )
% 4.69/4.90 => ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ U @ W ) @ ( transi6264000038957366511cl_nat @ E ) )
% 4.69/4.90 => ~ ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ U @ V1 ) @ ( transi2905341329935302413cl_nat @ E ) )
% 4.69/4.90 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ V22 @ W ) @ ( transi2905341329935302413cl_nat @ E ) ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_over_edgeE
% 4.69/4.90 thf(fact_825_trancl__over__edgeE,axiom,
% 4.69/4.90 ! [U: int,W: int,V1: int,V22: int,E: set_Pr958786334691620121nt_int] :
% 4.69/4.90 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ U @ W ) @ ( transi6261509568448316235cl_int @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ V1 @ V22 ) @ E ) ) )
% 4.69/4.90 => ( ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ U @ W ) @ ( transi6261509568448316235cl_int @ E ) )
% 4.69/4.90 => ~ ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ U @ V1 ) @ ( transi2902850859426252137cl_int @ E ) )
% 4.69/4.90 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ V22 @ W ) @ ( transi2902850859426252137cl_int @ E ) ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % trancl_over_edgeE
% 4.69/4.90 thf(fact_826_partial__order__on__empty,axiom,
% 4.69/4.90 order_2505591618835473410t_unit @ bot_bo3957492148770167129t_unit @ bot_bo1654022762305692595t_unit ).
% 4.69/4.90
% 4.69/4.90 % partial_order_on_empty
% 4.69/4.90 thf(fact_827_partial__order__on__empty,axiom,
% 4.69/4.90 order_8538205470752950541r_on_o @ bot_bot_set_o @ bot_bo7073875226086086771od_o_o ).
% 4.69/4.90
% 4.69/4.90 % partial_order_on_empty
% 4.69/4.90 thf(fact_828_partial__order__on__empty,axiom,
% 4.69/4.90 order_5251275573222108571on_nat @ bot_bot_set_nat @ bot_bo2099793752762293965at_nat ).
% 4.69/4.90
% 4.69/4.90 % partial_order_on_empty
% 4.69/4.90 thf(fact_829_partial__order__on__empty,axiom,
% 4.69/4.90 order_5248785102713058295on_int @ bot_bot_set_int @ bot_bo1796632182523588997nt_int ).
% 4.69/4.90
% 4.69/4.90 % partial_order_on_empty
% 4.69/4.90 thf(fact_830_partial__order__on__empty,axiom,
% 4.69/4.90 order_3690095022144090562_nat_o @ bot_bo7824918357723582233_nat_o @ bot_bo3657187498359500723_nat_o ).
% 4.69/4.90
% 4.69/4.90 % partial_order_on_empty
% 4.69/4.90 thf(fact_831_prod__set__simps_I2_J,axiom,
% 4.69/4.90 ! [X: heap_e7401611519738050253t_unit,Y: set_nat] :
% 4.69/4.90 ( ( basic_2698842327037663054et_nat @ ( produc7507926704131184380et_nat @ X @ Y ) )
% 4.69/4.90 = ( insert_set_nat @ Y @ bot_bot_set_set_nat ) ) ).
% 4.69/4.90
% 4.69/4.90 % prod_set_simps(2)
% 4.69/4.90 thf(fact_832_prod__set__simps_I2_J,axiom,
% 4.69/4.90 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 4.69/4.90 ( ( basic_8479756702517612234et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 4.69/4.90 = ( insert1271470778893645362et_nat @ Y @ bot_bo3771712512152092492et_nat ) ) ).
% 4.69/4.90
% 4.69/4.90 % prod_set_simps(2)
% 4.69/4.90 thf(fact_833_prod__set__simps_I2_J,axiom,
% 4.69/4.90 ! [X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 4.69/4.90 ( ( basic_2768200282441914438et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 4.69/4.90 = ( insert3111075074545270702et_nat @ Y @ bot_bo1481135142794719944et_nat ) ) ).
% 4.69/4.90
% 4.69/4.90 % prod_set_simps(2)
% 4.69/4.90 thf(fact_834_prod__set__simps_I2_J,axiom,
% 4.69/4.90 ! [X: nat,Y: nat] :
% 4.69/4.90 ( ( basic_snds_nat_nat @ ( product_Pair_nat_nat @ X @ Y ) )
% 4.69/4.90 = ( insert_nat @ Y @ bot_bot_set_nat ) ) ).
% 4.69/4.90
% 4.69/4.90 % prod_set_simps(2)
% 4.69/4.90 thf(fact_835_prod__set__simps_I2_J,axiom,
% 4.69/4.90 ! [X: int,Y: int] :
% 4.69/4.90 ( ( basic_snds_int_int @ ( product_Pair_int_int @ X @ Y ) )
% 4.69/4.90 = ( insert_int @ Y @ bot_bot_set_int ) ) ).
% 4.69/4.90
% 4.69/4.90 % prod_set_simps(2)
% 4.69/4.90 thf(fact_836_dual__order_Orefl,axiom,
% 4.69/4.90 ! [A2: filter_nat] : ( ord_le2510731241096832064er_nat @ A2 @ A2 ) ).
% 4.69/4.90
% 4.69/4.90 % dual_order.refl
% 4.69/4.90 thf(fact_837_dual__order_Orefl,axiom,
% 4.69/4.90 ! [A2: set_nat] : ( ord_less_eq_set_nat @ A2 @ A2 ) ).
% 4.69/4.90
% 4.69/4.90 % dual_order.refl
% 4.69/4.90 thf(fact_838_dual__order_Orefl,axiom,
% 4.69/4.90 ! [A2: rat] : ( ord_less_eq_rat @ A2 @ A2 ) ).
% 4.69/4.90
% 4.69/4.90 % dual_order.refl
% 4.69/4.90 thf(fact_839_dual__order_Orefl,axiom,
% 4.69/4.90 ! [A2: nat] : ( ord_less_eq_nat @ A2 @ A2 ) ).
% 4.69/4.90
% 4.69/4.90 % dual_order.refl
% 4.69/4.90 thf(fact_840_dual__order_Orefl,axiom,
% 4.69/4.90 ! [A2: int] : ( ord_less_eq_int @ A2 @ A2 ) ).
% 4.69/4.90
% 4.69/4.90 % dual_order.refl
% 4.69/4.90 thf(fact_841_order__refl,axiom,
% 4.69/4.90 ! [X: filter_nat] : ( ord_le2510731241096832064er_nat @ X @ X ) ).
% 4.69/4.90
% 4.69/4.90 % order_refl
% 4.69/4.90 thf(fact_842_order__refl,axiom,
% 4.69/4.90 ! [X: set_nat] : ( ord_less_eq_set_nat @ X @ X ) ).
% 4.69/4.90
% 4.69/4.90 % order_refl
% 4.69/4.90 thf(fact_843_order__refl,axiom,
% 4.69/4.90 ! [X: rat] : ( ord_less_eq_rat @ X @ X ) ).
% 4.69/4.90
% 4.69/4.90 % order_refl
% 4.69/4.90 thf(fact_844_order__refl,axiom,
% 4.69/4.90 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 4.69/4.90
% 4.69/4.90 % order_refl
% 4.69/4.90 thf(fact_845_order__refl,axiom,
% 4.69/4.90 ! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% 4.69/4.90
% 4.69/4.90 % order_refl
% 4.69/4.90 thf(fact_846_subset__antisym,axiom,
% 4.69/4.90 ! [A: set_nat,B4: set_nat] :
% 4.69/4.90 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.90 => ( ( ord_less_eq_set_nat @ B4 @ A )
% 4.69/4.90 => ( A = B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % subset_antisym
% 4.69/4.90 thf(fact_847_subsetI,axiom,
% 4.69/4.90 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.90 ( ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.90 ( ( member6576561426505652726_nat_o @ X3 @ A )
% 4.69/4.90 => ( member6576561426505652726_nat_o @ X3 @ B4 ) )
% 4.69/4.90 => ( ord_le2965882846123202637_nat_o @ A @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % subsetI
% 4.69/4.90 thf(fact_848_subsetI,axiom,
% 4.69/4.90 ! [A: set_int,B4: set_int] :
% 4.69/4.90 ( ! [X3: int] :
% 4.69/4.90 ( ( member_int @ X3 @ A )
% 4.69/4.90 => ( member_int @ X3 @ B4 ) )
% 4.69/4.90 => ( ord_less_eq_set_int @ A @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % subsetI
% 4.69/4.90 thf(fact_849_subsetI,axiom,
% 4.69/4.90 ! [A: set_o,B4: set_o] :
% 4.69/4.90 ( ! [X3: $o] :
% 4.69/4.90 ( ( member_o @ X3 @ A )
% 4.69/4.90 => ( member_o @ X3 @ B4 ) )
% 4.69/4.90 => ( ord_less_eq_set_o @ A @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % subsetI
% 4.69/4.90 thf(fact_850_subsetI,axiom,
% 4.69/4.90 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.90 ( ! [X3: product_unit] :
% 4.69/4.90 ( ( member_Product_unit @ X3 @ A )
% 4.69/4.90 => ( member_Product_unit @ X3 @ B4 ) )
% 4.69/4.90 => ( ord_le3507040750410214029t_unit @ A @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % subsetI
% 4.69/4.90 thf(fact_851_subsetI,axiom,
% 4.69/4.90 ! [A: set_nat,B4: set_nat] :
% 4.69/4.90 ( ! [X3: nat] :
% 4.69/4.90 ( ( member_nat @ X3 @ A )
% 4.69/4.90 => ( member_nat @ X3 @ B4 ) )
% 4.69/4.90 => ( ord_less_eq_set_nat @ A @ B4 ) ) ).
% 4.69/4.90
% 4.69/4.90 % subsetI
% 4.69/4.90 thf(fact_852_Int__iff,axiom,
% 4.69/4.90 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.90 ( ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A @ B4 ) )
% 4.69/4.90 = ( ( member6576561426505652726_nat_o @ C @ A )
% 4.69/4.90 & ( member6576561426505652726_nat_o @ C @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Int_iff
% 4.69/4.90 thf(fact_853_Int__iff,axiom,
% 4.69/4.90 ! [C: int,A: set_int,B4: set_int] :
% 4.69/4.90 ( ( member_int @ C @ ( inf_inf_set_int @ A @ B4 ) )
% 4.69/4.90 = ( ( member_int @ C @ A )
% 4.69/4.90 & ( member_int @ C @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Int_iff
% 4.69/4.90 thf(fact_854_Int__iff,axiom,
% 4.69/4.90 ! [C: $o,A: set_o,B4: set_o] :
% 4.69/4.90 ( ( member_o @ C @ ( inf_inf_set_o @ A @ B4 ) )
% 4.69/4.90 = ( ( member_o @ C @ A )
% 4.69/4.90 & ( member_o @ C @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Int_iff
% 4.69/4.90 thf(fact_855_Int__iff,axiom,
% 4.69/4.90 ! [C: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.90 ( ( member_Product_unit @ C @ ( inf_in4660618365625256667t_unit @ A @ B4 ) )
% 4.69/4.90 = ( ( member_Product_unit @ C @ A )
% 4.69/4.90 & ( member_Product_unit @ C @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Int_iff
% 4.69/4.90 thf(fact_856_Int__iff,axiom,
% 4.69/4.90 ! [C: nat,A: set_nat,B4: set_nat] :
% 4.69/4.90 ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B4 ) )
% 4.69/4.90 = ( ( member_nat @ C @ A )
% 4.69/4.90 & ( member_nat @ C @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Int_iff
% 4.69/4.90 thf(fact_857_IntI,axiom,
% 4.69/4.90 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.90 ( ( member6576561426505652726_nat_o @ C @ A )
% 4.69/4.90 => ( ( member6576561426505652726_nat_o @ C @ B4 )
% 4.69/4.90 => ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % IntI
% 4.69/4.90 thf(fact_858_IntI,axiom,
% 4.69/4.90 ! [C: int,A: set_int,B4: set_int] :
% 4.69/4.90 ( ( member_int @ C @ A )
% 4.69/4.90 => ( ( member_int @ C @ B4 )
% 4.69/4.90 => ( member_int @ C @ ( inf_inf_set_int @ A @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % IntI
% 4.69/4.90 thf(fact_859_IntI,axiom,
% 4.69/4.90 ! [C: $o,A: set_o,B4: set_o] :
% 4.69/4.90 ( ( member_o @ C @ A )
% 4.69/4.90 => ( ( member_o @ C @ B4 )
% 4.69/4.90 => ( member_o @ C @ ( inf_inf_set_o @ A @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % IntI
% 4.69/4.90 thf(fact_860_IntI,axiom,
% 4.69/4.90 ! [C: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.90 ( ( member_Product_unit @ C @ A )
% 4.69/4.90 => ( ( member_Product_unit @ C @ B4 )
% 4.69/4.90 => ( member_Product_unit @ C @ ( inf_in4660618365625256667t_unit @ A @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % IntI
% 4.69/4.90 thf(fact_861_IntI,axiom,
% 4.69/4.90 ! [C: nat,A: set_nat,B4: set_nat] :
% 4.69/4.90 ( ( member_nat @ C @ A )
% 4.69/4.90 => ( ( member_nat @ C @ B4 )
% 4.69/4.90 => ( member_nat @ C @ ( inf_inf_set_nat @ A @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % IntI
% 4.69/4.90 thf(fact_862_Un__iff,axiom,
% 4.69/4.90 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.90 ( ( member6576561426505652726_nat_o @ C @ ( sup_su5209123915105501825_nat_o @ A @ B4 ) )
% 4.69/4.90 = ( ( member6576561426505652726_nat_o @ C @ A )
% 4.69/4.90 | ( member6576561426505652726_nat_o @ C @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Un_iff
% 4.69/4.90 thf(fact_863_Un__iff,axiom,
% 4.69/4.90 ! [C: int,A: set_int,B4: set_int] :
% 4.69/4.90 ( ( member_int @ C @ ( sup_sup_set_int @ A @ B4 ) )
% 4.69/4.90 = ( ( member_int @ C @ A )
% 4.69/4.90 | ( member_int @ C @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Un_iff
% 4.69/4.90 thf(fact_864_Un__iff,axiom,
% 4.69/4.90 ! [C: $o,A: set_o,B4: set_o] :
% 4.69/4.90 ( ( member_o @ C @ ( sup_sup_set_o @ A @ B4 ) )
% 4.69/4.90 = ( ( member_o @ C @ A )
% 4.69/4.90 | ( member_o @ C @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Un_iff
% 4.69/4.90 thf(fact_865_Un__iff,axiom,
% 4.69/4.90 ! [C: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.90 ( ( member_Product_unit @ C @ ( sup_su793286257634532545t_unit @ A @ B4 ) )
% 4.69/4.90 = ( ( member_Product_unit @ C @ A )
% 4.69/4.90 | ( member_Product_unit @ C @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Un_iff
% 4.69/4.90 thf(fact_866_Un__iff,axiom,
% 4.69/4.90 ! [C: nat,A: set_nat,B4: set_nat] :
% 4.69/4.90 ( ( member_nat @ C @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.90 = ( ( member_nat @ C @ A )
% 4.69/4.90 | ( member_nat @ C @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Un_iff
% 4.69/4.90 thf(fact_867_UnCI,axiom,
% 4.69/4.90 ! [C: produc3658429121746597890et_nat > $o,B4: set_Pr4532377907799695533_nat_o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.90 ( ( ~ ( member6576561426505652726_nat_o @ C @ B4 )
% 4.69/4.90 => ( member6576561426505652726_nat_o @ C @ A ) )
% 4.69/4.90 => ( member6576561426505652726_nat_o @ C @ ( sup_su5209123915105501825_nat_o @ A @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % UnCI
% 4.69/4.90 thf(fact_868_UnCI,axiom,
% 4.69/4.90 ! [C: int,B4: set_int,A: set_int] :
% 4.69/4.90 ( ( ~ ( member_int @ C @ B4 )
% 4.69/4.90 => ( member_int @ C @ A ) )
% 4.69/4.90 => ( member_int @ C @ ( sup_sup_set_int @ A @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % UnCI
% 4.69/4.90 thf(fact_869_UnCI,axiom,
% 4.69/4.90 ! [C: $o,B4: set_o,A: set_o] :
% 4.69/4.90 ( ( ~ ( member_o @ C @ B4 )
% 4.69/4.90 => ( member_o @ C @ A ) )
% 4.69/4.90 => ( member_o @ C @ ( sup_sup_set_o @ A @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % UnCI
% 4.69/4.90 thf(fact_870_UnCI,axiom,
% 4.69/4.90 ! [C: product_unit,B4: set_Product_unit,A: set_Product_unit] :
% 4.69/4.90 ( ( ~ ( member_Product_unit @ C @ B4 )
% 4.69/4.90 => ( member_Product_unit @ C @ A ) )
% 4.69/4.90 => ( member_Product_unit @ C @ ( sup_su793286257634532545t_unit @ A @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % UnCI
% 4.69/4.90 thf(fact_871_UnCI,axiom,
% 4.69/4.90 ! [C: nat,B4: set_nat,A: set_nat] :
% 4.69/4.90 ( ( ~ ( member_nat @ C @ B4 )
% 4.69/4.90 => ( member_nat @ C @ A ) )
% 4.69/4.90 => ( member_nat @ C @ ( sup_sup_set_nat @ A @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % UnCI
% 4.69/4.90 thf(fact_872_empty__subsetI,axiom,
% 4.69/4.90 ! [A: set_Product_unit] : ( ord_le3507040750410214029t_unit @ bot_bo3957492148770167129t_unit @ A ) ).
% 4.69/4.90
% 4.69/4.90 % empty_subsetI
% 4.69/4.90 thf(fact_873_empty__subsetI,axiom,
% 4.69/4.90 ! [A: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A ) ).
% 4.69/4.90
% 4.69/4.90 % empty_subsetI
% 4.69/4.90 thf(fact_874_empty__subsetI,axiom,
% 4.69/4.90 ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 4.69/4.90
% 4.69/4.90 % empty_subsetI
% 4.69/4.90 thf(fact_875_empty__subsetI,axiom,
% 4.69/4.90 ! [A: set_Pr4532377907799695533_nat_o] : ( ord_le2965882846123202637_nat_o @ bot_bo7824918357723582233_nat_o @ A ) ).
% 4.69/4.90
% 4.69/4.90 % empty_subsetI
% 4.69/4.90 thf(fact_876_empty__subsetI,axiom,
% 4.69/4.90 ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 4.69/4.90
% 4.69/4.90 % empty_subsetI
% 4.69/4.90 thf(fact_877_subset__empty,axiom,
% 4.69/4.90 ! [A: set_Product_unit] :
% 4.69/4.90 ( ( ord_le3507040750410214029t_unit @ A @ bot_bo3957492148770167129t_unit )
% 4.69/4.90 = ( A = bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.90
% 4.69/4.90 % subset_empty
% 4.69/4.90 thf(fact_878_subset__empty,axiom,
% 4.69/4.90 ! [A: set_o] :
% 4.69/4.90 ( ( ord_less_eq_set_o @ A @ bot_bot_set_o )
% 4.69/4.90 = ( A = bot_bot_set_o ) ) ).
% 4.69/4.90
% 4.69/4.90 % subset_empty
% 4.69/4.90 thf(fact_879_subset__empty,axiom,
% 4.69/4.90 ! [A: set_int] :
% 4.69/4.90 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 4.69/4.90 = ( A = bot_bot_set_int ) ) ).
% 4.69/4.90
% 4.69/4.90 % subset_empty
% 4.69/4.90 thf(fact_880_subset__empty,axiom,
% 4.69/4.90 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.90 ( ( ord_le2965882846123202637_nat_o @ A @ bot_bo7824918357723582233_nat_o )
% 4.69/4.90 = ( A = bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.90
% 4.69/4.90 % subset_empty
% 4.69/4.90 thf(fact_881_subset__empty,axiom,
% 4.69/4.90 ! [A: set_nat] :
% 4.69/4.90 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 4.69/4.90 = ( A = bot_bot_set_nat ) ) ).
% 4.69/4.90
% 4.69/4.90 % subset_empty
% 4.69/4.90 thf(fact_882_insert__subset,axiom,
% 4.69/4.90 ! [X: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.90 ( ( ord_le2965882846123202637_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) @ B4 )
% 4.69/4.90 = ( ( member6576561426505652726_nat_o @ X @ B4 )
% 4.69/4.90 & ( ord_le2965882846123202637_nat_o @ A @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % insert_subset
% 4.69/4.90 thf(fact_883_insert__subset,axiom,
% 4.69/4.90 ! [X: int,A: set_int,B4: set_int] :
% 4.69/4.90 ( ( ord_less_eq_set_int @ ( insert_int @ X @ A ) @ B4 )
% 4.69/4.90 = ( ( member_int @ X @ B4 )
% 4.69/4.90 & ( ord_less_eq_set_int @ A @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % insert_subset
% 4.69/4.90 thf(fact_884_insert__subset,axiom,
% 4.69/4.90 ! [X: $o,A: set_o,B4: set_o] :
% 4.69/4.90 ( ( ord_less_eq_set_o @ ( insert_o @ X @ A ) @ B4 )
% 4.69/4.90 = ( ( member_o @ X @ B4 )
% 4.69/4.90 & ( ord_less_eq_set_o @ A @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % insert_subset
% 4.69/4.90 thf(fact_885_insert__subset,axiom,
% 4.69/4.90 ! [X: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.90 ( ( ord_le3507040750410214029t_unit @ ( insert_Product_unit @ X @ A ) @ B4 )
% 4.69/4.90 = ( ( member_Product_unit @ X @ B4 )
% 4.69/4.90 & ( ord_le3507040750410214029t_unit @ A @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % insert_subset
% 4.69/4.90 thf(fact_886_insert__subset,axiom,
% 4.69/4.90 ! [X: nat,A: set_nat,B4: set_nat] :
% 4.69/4.90 ( ( ord_less_eq_set_nat @ ( insert_nat @ X @ A ) @ B4 )
% 4.69/4.90 = ( ( member_nat @ X @ B4 )
% 4.69/4.90 & ( ord_less_eq_set_nat @ A @ B4 ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % insert_subset
% 4.69/4.90 thf(fact_887_SigmaI,axiom,
% 4.69/4.90 ! [A2: nat,A: set_nat,B: int,B4: nat > set_int] :
% 4.69/4.90 ( ( member_nat @ A2 @ A )
% 4.69/4.90 => ( ( member_int @ B @ ( B4 @ A2 ) )
% 4.69/4.90 => ( member4262671552274231302at_int @ ( product_Pair_nat_int @ A2 @ B ) @ ( produc454536836294682310at_int @ A @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % SigmaI
% 4.69/4.90 thf(fact_888_SigmaI,axiom,
% 4.69/4.90 ! [A2: nat,A: set_nat,B: $o,B4: nat > set_o] :
% 4.69/4.90 ( ( member_nat @ A2 @ A )
% 4.69/4.90 => ( ( member_o @ B @ ( B4 @ A2 ) )
% 4.69/4.90 => ( member6310962623043647828_nat_o @ ( product_Pair_nat_o @ A2 @ B ) @ ( product_Sigma_nat_o @ A @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % SigmaI
% 4.69/4.90 thf(fact_889_SigmaI,axiom,
% 4.69/4.90 ! [A2: nat,A: set_nat,B: product_unit,B4: nat > set_Product_unit] :
% 4.69/4.90 ( ( member_nat @ A2 @ A )
% 4.69/4.90 => ( ( member_Product_unit @ B @ ( B4 @ A2 ) )
% 4.69/4.90 => ( member348563419383025609t_unit @ ( produc3434450474625521892t_unit @ A2 @ B ) @ ( produc5506539147108004339t_unit @ A @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % SigmaI
% 4.69/4.90 thf(fact_890_SigmaI,axiom,
% 4.69/4.90 ! [A2: int,A: set_int,B: nat,B4: int > set_nat] :
% 4.69/4.90 ( ( member_int @ A2 @ A )
% 4.69/4.90 => ( ( member_nat @ B @ ( B4 @ A2 ) )
% 4.69/4.90 => ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ A2 @ B ) @ ( produc1456381018704787142nt_nat @ A @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % SigmaI
% 4.69/4.90 thf(fact_891_SigmaI,axiom,
% 4.69/4.90 ! [A2: int,A: set_int,B: $o,B4: int > set_o] :
% 4.69/4.90 ( ( member_int @ A2 @ A )
% 4.69/4.90 => ( ( member_o @ B @ ( B4 @ A2 ) )
% 4.69/4.90 => ( member4489920277610959864_int_o @ ( product_Pair_int_o @ A2 @ B ) @ ( product_Sigma_int_o @ A @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % SigmaI
% 4.69/4.90 thf(fact_892_SigmaI,axiom,
% 4.69/4.90 ! [A2: int,A: set_int,B: product_unit,B4: int > set_Product_unit] :
% 4.69/4.90 ( ( member_int @ A2 @ A )
% 4.69/4.90 => ( ( member_Product_unit @ B @ ( B4 @ A2 ) )
% 4.69/4.90 => ( member6688357403439981677t_unit @ ( produc550872421827702152t_unit @ A2 @ B ) @ ( produc2622961094310184599t_unit @ A @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % SigmaI
% 4.69/4.90 thf(fact_893_SigmaI,axiom,
% 4.69/4.90 ! [A2: $o,A: set_o,B: nat,B4: $o > set_nat] :
% 4.69/4.90 ( ( member_o @ A2 @ A )
% 4.69/4.90 => ( ( member_nat @ B @ ( B4 @ A2 ) )
% 4.69/4.90 => ( member2802428098988154798_o_nat @ ( product_Pair_o_nat @ A2 @ B ) @ ( product_Sigma_o_nat @ A @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % SigmaI
% 4.69/4.90 thf(fact_894_SigmaI,axiom,
% 4.69/4.90 ! [A2: $o,A: set_o,B: int,B4: $o > set_int] :
% 4.69/4.90 ( ( member_o @ A2 @ A )
% 4.69/4.90 => ( ( member_int @ B @ ( B4 @ A2 ) )
% 4.69/4.90 => ( member7847949116333733898_o_int @ ( product_Pair_o_int @ A2 @ B ) @ ( product_Sigma_o_int @ A @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % SigmaI
% 4.69/4.90 thf(fact_895_SigmaI,axiom,
% 4.69/4.90 ! [A2: $o,A: set_o,B: $o,B4: $o > set_o] :
% 4.69/4.90 ( ( member_o @ A2 @ A )
% 4.69/4.90 => ( ( member_o @ B @ ( B4 @ A2 ) )
% 4.69/4.90 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ B ) @ ( product_Sigma_o_o @ A @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % SigmaI
% 4.69/4.90 thf(fact_896_SigmaI,axiom,
% 4.69/4.90 ! [A2: $o,A: set_o,B: product_unit,B4: $o > set_Product_unit] :
% 4.69/4.90 ( ( member_o @ A2 @ A )
% 4.69/4.90 => ( ( member_Product_unit @ B @ ( B4 @ A2 ) )
% 4.69/4.90 => ( member9215336023991391429t_unit @ ( produc3901946521647900940t_unit @ A2 @ B ) @ ( produc411009820408249917t_unit @ A @ B4 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % SigmaI
% 4.69/4.90 thf(fact_897_mem__Sigma__iff,axiom,
% 4.69/4.90 ! [A2: nat,B: int,A: set_nat,B4: nat > set_int] :
% 4.69/4.90 ( ( member4262671552274231302at_int @ ( product_Pair_nat_int @ A2 @ B ) @ ( produc454536836294682310at_int @ A @ B4 ) )
% 4.69/4.90 = ( ( member_nat @ A2 @ A )
% 4.69/4.90 & ( member_int @ B @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % mem_Sigma_iff
% 4.69/4.90 thf(fact_898_mem__Sigma__iff,axiom,
% 4.69/4.90 ! [A2: nat,B: $o,A: set_nat,B4: nat > set_o] :
% 4.69/4.90 ( ( member6310962623043647828_nat_o @ ( product_Pair_nat_o @ A2 @ B ) @ ( product_Sigma_nat_o @ A @ B4 ) )
% 4.69/4.90 = ( ( member_nat @ A2 @ A )
% 4.69/4.90 & ( member_o @ B @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % mem_Sigma_iff
% 4.69/4.90 thf(fact_899_mem__Sigma__iff,axiom,
% 4.69/4.90 ! [A2: nat,B: product_unit,A: set_nat,B4: nat > set_Product_unit] :
% 4.69/4.90 ( ( member348563419383025609t_unit @ ( produc3434450474625521892t_unit @ A2 @ B ) @ ( produc5506539147108004339t_unit @ A @ B4 ) )
% 4.69/4.90 = ( ( member_nat @ A2 @ A )
% 4.69/4.90 & ( member_Product_unit @ B @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % mem_Sigma_iff
% 4.69/4.90 thf(fact_900_mem__Sigma__iff,axiom,
% 4.69/4.90 ! [A2: int,B: nat,A: set_int,B4: int > set_nat] :
% 4.69/4.90 ( ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ A2 @ B ) @ ( produc1456381018704787142nt_nat @ A @ B4 ) )
% 4.69/4.90 = ( ( member_int @ A2 @ A )
% 4.69/4.90 & ( member_nat @ B @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % mem_Sigma_iff
% 4.69/4.90 thf(fact_901_mem__Sigma__iff,axiom,
% 4.69/4.90 ! [A2: int,B: $o,A: set_int,B4: int > set_o] :
% 4.69/4.90 ( ( member4489920277610959864_int_o @ ( product_Pair_int_o @ A2 @ B ) @ ( product_Sigma_int_o @ A @ B4 ) )
% 4.69/4.90 = ( ( member_int @ A2 @ A )
% 4.69/4.90 & ( member_o @ B @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % mem_Sigma_iff
% 4.69/4.90 thf(fact_902_mem__Sigma__iff,axiom,
% 4.69/4.90 ! [A2: int,B: product_unit,A: set_int,B4: int > set_Product_unit] :
% 4.69/4.90 ( ( member6688357403439981677t_unit @ ( produc550872421827702152t_unit @ A2 @ B ) @ ( produc2622961094310184599t_unit @ A @ B4 ) )
% 4.69/4.90 = ( ( member_int @ A2 @ A )
% 4.69/4.90 & ( member_Product_unit @ B @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % mem_Sigma_iff
% 4.69/4.90 thf(fact_903_mem__Sigma__iff,axiom,
% 4.69/4.90 ! [A2: $o,B: nat,A: set_o,B4: $o > set_nat] :
% 4.69/4.90 ( ( member2802428098988154798_o_nat @ ( product_Pair_o_nat @ A2 @ B ) @ ( product_Sigma_o_nat @ A @ B4 ) )
% 4.69/4.90 = ( ( member_o @ A2 @ A )
% 4.69/4.90 & ( member_nat @ B @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % mem_Sigma_iff
% 4.69/4.90 thf(fact_904_mem__Sigma__iff,axiom,
% 4.69/4.90 ! [A2: $o,B: int,A: set_o,B4: $o > set_int] :
% 4.69/4.90 ( ( member7847949116333733898_o_int @ ( product_Pair_o_int @ A2 @ B ) @ ( product_Sigma_o_int @ A @ B4 ) )
% 4.69/4.90 = ( ( member_o @ A2 @ A )
% 4.69/4.90 & ( member_int @ B @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % mem_Sigma_iff
% 4.69/4.90 thf(fact_905_mem__Sigma__iff,axiom,
% 4.69/4.90 ! [A2: $o,B: $o,A: set_o,B4: $o > set_o] :
% 4.69/4.90 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ B ) @ ( product_Sigma_o_o @ A @ B4 ) )
% 4.69/4.90 = ( ( member_o @ A2 @ A )
% 4.69/4.90 & ( member_o @ B @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % mem_Sigma_iff
% 4.69/4.90 thf(fact_906_mem__Sigma__iff,axiom,
% 4.69/4.90 ! [A2: $o,B: product_unit,A: set_o,B4: $o > set_Product_unit] :
% 4.69/4.90 ( ( member9215336023991391429t_unit @ ( produc3901946521647900940t_unit @ A2 @ B ) @ ( produc411009820408249917t_unit @ A @ B4 ) )
% 4.69/4.90 = ( ( member_o @ A2 @ A )
% 4.69/4.90 & ( member_Product_unit @ B @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % mem_Sigma_iff
% 4.69/4.90 thf(fact_907_Un__empty,axiom,
% 4.69/4.90 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.90 ( ( ( sup_su793286257634532545t_unit @ A @ B4 )
% 4.69/4.90 = bot_bo3957492148770167129t_unit )
% 4.69/4.90 = ( ( A = bot_bo3957492148770167129t_unit )
% 4.69/4.90 & ( B4 = bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Un_empty
% 4.69/4.90 thf(fact_908_Un__empty,axiom,
% 4.69/4.90 ! [A: set_o,B4: set_o] :
% 4.69/4.90 ( ( ( sup_sup_set_o @ A @ B4 )
% 4.69/4.90 = bot_bot_set_o )
% 4.69/4.90 = ( ( A = bot_bot_set_o )
% 4.69/4.90 & ( B4 = bot_bot_set_o ) ) ) ).
% 4.69/4.90
% 4.69/4.90 % Un_empty
% 4.69/4.90 thf(fact_909_Un__empty,axiom,
% 4.69/4.90 ! [A: set_nat,B4: set_nat] :
% 4.69/4.90 ( ( ( sup_sup_set_nat @ A @ B4 )
% 4.69/4.90 = bot_bot_set_nat )
% 4.69/4.90 = ( ( A = bot_bot_set_nat )
% 4.69/4.90 & ( B4 = bot_bot_set_nat ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_empty
% 4.69/4.91 thf(fact_910_Un__empty,axiom,
% 4.69/4.91 ! [A: set_int,B4: set_int] :
% 4.69/4.91 ( ( ( sup_sup_set_int @ A @ B4 )
% 4.69/4.91 = bot_bot_set_int )
% 4.69/4.91 = ( ( A = bot_bot_set_int )
% 4.69/4.91 & ( B4 = bot_bot_set_int ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_empty
% 4.69/4.91 thf(fact_911_Un__empty,axiom,
% 4.69/4.91 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.91 ( ( ( sup_su5209123915105501825_nat_o @ A @ B4 )
% 4.69/4.91 = bot_bo7824918357723582233_nat_o )
% 4.69/4.91 = ( ( A = bot_bo7824918357723582233_nat_o )
% 4.69/4.91 & ( B4 = bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_empty
% 4.69/4.91 thf(fact_912_Int__subset__iff,axiom,
% 4.69/4.91 ! [C5: set_nat,A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ C5 @ ( inf_inf_set_nat @ A @ B4 ) )
% 4.69/4.91 = ( ( ord_less_eq_set_nat @ C5 @ A )
% 4.69/4.91 & ( ord_less_eq_set_nat @ C5 @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_subset_iff
% 4.69/4.91 thf(fact_913_Int__insert__right__if1,axiom,
% 4.69/4.91 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.91 ( ( member6576561426505652726_nat_o @ A2 @ A )
% 4.69/4.91 => ( ( inf_in1906310914598751387_nat_o @ A @ ( insert5175938949040314269_nat_o @ A2 @ B4 ) )
% 4.69/4.91 = ( insert5175938949040314269_nat_o @ A2 @ ( inf_in1906310914598751387_nat_o @ A @ B4 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_insert_right_if1
% 4.69/4.91 thf(fact_914_Int__insert__right__if1,axiom,
% 4.69/4.91 ! [A2: int,A: set_int,B4: set_int] :
% 4.69/4.91 ( ( member_int @ A2 @ A )
% 4.69/4.91 => ( ( inf_inf_set_int @ A @ ( insert_int @ A2 @ B4 ) )
% 4.69/4.91 = ( insert_int @ A2 @ ( inf_inf_set_int @ A @ B4 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_insert_right_if1
% 4.69/4.91 thf(fact_915_Int__insert__right__if1,axiom,
% 4.69/4.91 ! [A2: $o,A: set_o,B4: set_o] :
% 4.69/4.91 ( ( member_o @ A2 @ A )
% 4.69/4.91 => ( ( inf_inf_set_o @ A @ ( insert_o @ A2 @ B4 ) )
% 4.69/4.91 = ( insert_o @ A2 @ ( inf_inf_set_o @ A @ B4 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_insert_right_if1
% 4.69/4.91 thf(fact_916_Int__insert__right__if1,axiom,
% 4.69/4.91 ! [A2: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.91 ( ( member_Product_unit @ A2 @ A )
% 4.69/4.91 => ( ( inf_in4660618365625256667t_unit @ A @ ( insert_Product_unit @ A2 @ B4 ) )
% 4.69/4.91 = ( insert_Product_unit @ A2 @ ( inf_in4660618365625256667t_unit @ A @ B4 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_insert_right_if1
% 4.69/4.91 thf(fact_917_Int__insert__right__if1,axiom,
% 4.69/4.91 ! [A2: nat,A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( member_nat @ A2 @ A )
% 4.69/4.91 => ( ( inf_inf_set_nat @ A @ ( insert_nat @ A2 @ B4 ) )
% 4.69/4.91 = ( insert_nat @ A2 @ ( inf_inf_set_nat @ A @ B4 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_insert_right_if1
% 4.69/4.91 thf(fact_918_Int__insert__right__if0,axiom,
% 4.69/4.91 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.91 ( ~ ( member6576561426505652726_nat_o @ A2 @ A )
% 4.69/4.91 => ( ( inf_in1906310914598751387_nat_o @ A @ ( insert5175938949040314269_nat_o @ A2 @ B4 ) )
% 4.69/4.91 = ( inf_in1906310914598751387_nat_o @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_insert_right_if0
% 4.69/4.91 thf(fact_919_Int__insert__right__if0,axiom,
% 4.69/4.91 ! [A2: int,A: set_int,B4: set_int] :
% 4.69/4.91 ( ~ ( member_int @ A2 @ A )
% 4.69/4.91 => ( ( inf_inf_set_int @ A @ ( insert_int @ A2 @ B4 ) )
% 4.69/4.91 = ( inf_inf_set_int @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_insert_right_if0
% 4.69/4.91 thf(fact_920_Int__insert__right__if0,axiom,
% 4.69/4.91 ! [A2: $o,A: set_o,B4: set_o] :
% 4.69/4.91 ( ~ ( member_o @ A2 @ A )
% 4.69/4.91 => ( ( inf_inf_set_o @ A @ ( insert_o @ A2 @ B4 ) )
% 4.69/4.91 = ( inf_inf_set_o @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_insert_right_if0
% 4.69/4.91 thf(fact_921_Int__insert__right__if0,axiom,
% 4.69/4.91 ! [A2: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.91 ( ~ ( member_Product_unit @ A2 @ A )
% 4.69/4.91 => ( ( inf_in4660618365625256667t_unit @ A @ ( insert_Product_unit @ A2 @ B4 ) )
% 4.69/4.91 = ( inf_in4660618365625256667t_unit @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_insert_right_if0
% 4.69/4.91 thf(fact_922_Int__insert__right__if0,axiom,
% 4.69/4.91 ! [A2: nat,A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ~ ( member_nat @ A2 @ A )
% 4.69/4.91 => ( ( inf_inf_set_nat @ A @ ( insert_nat @ A2 @ B4 ) )
% 4.69/4.91 = ( inf_inf_set_nat @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_insert_right_if0
% 4.69/4.91 thf(fact_923_insert__inter__insert,axiom,
% 4.69/4.91 ! [A2: int,A: set_int,B4: set_int] :
% 4.69/4.91 ( ( inf_inf_set_int @ ( insert_int @ A2 @ A ) @ ( insert_int @ A2 @ B4 ) )
% 4.69/4.91 = ( insert_int @ A2 @ ( inf_inf_set_int @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % insert_inter_insert
% 4.69/4.91 thf(fact_924_insert__inter__insert,axiom,
% 4.69/4.91 ! [A2: $o,A: set_o,B4: set_o] :
% 4.69/4.91 ( ( inf_inf_set_o @ ( insert_o @ A2 @ A ) @ ( insert_o @ A2 @ B4 ) )
% 4.69/4.91 = ( insert_o @ A2 @ ( inf_inf_set_o @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % insert_inter_insert
% 4.69/4.91 thf(fact_925_insert__inter__insert,axiom,
% 4.69/4.91 ! [A2: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.91 ( ( inf_in4660618365625256667t_unit @ ( insert_Product_unit @ A2 @ A ) @ ( insert_Product_unit @ A2 @ B4 ) )
% 4.69/4.91 = ( insert_Product_unit @ A2 @ ( inf_in4660618365625256667t_unit @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % insert_inter_insert
% 4.69/4.91 thf(fact_926_insert__inter__insert,axiom,
% 4.69/4.91 ! [A2: nat,A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( inf_inf_set_nat @ ( insert_nat @ A2 @ A ) @ ( insert_nat @ A2 @ B4 ) )
% 4.69/4.91 = ( insert_nat @ A2 @ ( inf_inf_set_nat @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % insert_inter_insert
% 4.69/4.91 thf(fact_927_Int__insert__left__if1,axiom,
% 4.69/4.91 ! [A2: produc3658429121746597890et_nat > $o,C5: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.91 ( ( member6576561426505652726_nat_o @ A2 @ C5 )
% 4.69/4.91 => ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A2 @ B4 ) @ C5 )
% 4.69/4.91 = ( insert5175938949040314269_nat_o @ A2 @ ( inf_in1906310914598751387_nat_o @ B4 @ C5 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_insert_left_if1
% 4.69/4.91 thf(fact_928_Int__insert__left__if1,axiom,
% 4.69/4.91 ! [A2: int,C5: set_int,B4: set_int] :
% 4.69/4.91 ( ( member_int @ A2 @ C5 )
% 4.69/4.91 => ( ( inf_inf_set_int @ ( insert_int @ A2 @ B4 ) @ C5 )
% 4.69/4.91 = ( insert_int @ A2 @ ( inf_inf_set_int @ B4 @ C5 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_insert_left_if1
% 4.69/4.91 thf(fact_929_Int__insert__left__if1,axiom,
% 4.69/4.91 ! [A2: $o,C5: set_o,B4: set_o] :
% 4.69/4.91 ( ( member_o @ A2 @ C5 )
% 4.69/4.91 => ( ( inf_inf_set_o @ ( insert_o @ A2 @ B4 ) @ C5 )
% 4.69/4.91 = ( insert_o @ A2 @ ( inf_inf_set_o @ B4 @ C5 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_insert_left_if1
% 4.69/4.91 thf(fact_930_Int__insert__left__if1,axiom,
% 4.69/4.91 ! [A2: product_unit,C5: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.91 ( ( member_Product_unit @ A2 @ C5 )
% 4.69/4.91 => ( ( inf_in4660618365625256667t_unit @ ( insert_Product_unit @ A2 @ B4 ) @ C5 )
% 4.69/4.91 = ( insert_Product_unit @ A2 @ ( inf_in4660618365625256667t_unit @ B4 @ C5 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_insert_left_if1
% 4.69/4.91 thf(fact_931_Int__insert__left__if1,axiom,
% 4.69/4.91 ! [A2: nat,C5: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( member_nat @ A2 @ C5 )
% 4.69/4.91 => ( ( inf_inf_set_nat @ ( insert_nat @ A2 @ B4 ) @ C5 )
% 4.69/4.91 = ( insert_nat @ A2 @ ( inf_inf_set_nat @ B4 @ C5 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_insert_left_if1
% 4.69/4.91 thf(fact_932_Int__insert__left__if0,axiom,
% 4.69/4.91 ! [A2: produc3658429121746597890et_nat > $o,C5: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.91 ( ~ ( member6576561426505652726_nat_o @ A2 @ C5 )
% 4.69/4.91 => ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A2 @ B4 ) @ C5 )
% 4.69/4.91 = ( inf_in1906310914598751387_nat_o @ B4 @ C5 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_insert_left_if0
% 4.69/4.91 thf(fact_933_Int__insert__left__if0,axiom,
% 4.69/4.91 ! [A2: int,C5: set_int,B4: set_int] :
% 4.69/4.91 ( ~ ( member_int @ A2 @ C5 )
% 4.69/4.91 => ( ( inf_inf_set_int @ ( insert_int @ A2 @ B4 ) @ C5 )
% 4.69/4.91 = ( inf_inf_set_int @ B4 @ C5 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_insert_left_if0
% 4.69/4.91 thf(fact_934_Int__insert__left__if0,axiom,
% 4.69/4.91 ! [A2: $o,C5: set_o,B4: set_o] :
% 4.69/4.91 ( ~ ( member_o @ A2 @ C5 )
% 4.69/4.91 => ( ( inf_inf_set_o @ ( insert_o @ A2 @ B4 ) @ C5 )
% 4.69/4.91 = ( inf_inf_set_o @ B4 @ C5 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_insert_left_if0
% 4.69/4.91 thf(fact_935_Int__insert__left__if0,axiom,
% 4.69/4.91 ! [A2: product_unit,C5: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.91 ( ~ ( member_Product_unit @ A2 @ C5 )
% 4.69/4.91 => ( ( inf_in4660618365625256667t_unit @ ( insert_Product_unit @ A2 @ B4 ) @ C5 )
% 4.69/4.91 = ( inf_in4660618365625256667t_unit @ B4 @ C5 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_insert_left_if0
% 4.69/4.91 thf(fact_936_Int__insert__left__if0,axiom,
% 4.69/4.91 ! [A2: nat,C5: set_nat,B4: set_nat] :
% 4.69/4.91 ( ~ ( member_nat @ A2 @ C5 )
% 4.69/4.91 => ( ( inf_inf_set_nat @ ( insert_nat @ A2 @ B4 ) @ C5 )
% 4.69/4.91 = ( inf_inf_set_nat @ B4 @ C5 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_insert_left_if0
% 4.69/4.91 thf(fact_937_Un__subset__iff,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat,C5: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B4 ) @ C5 )
% 4.69/4.91 = ( ( ord_less_eq_set_nat @ A @ C5 )
% 4.69/4.91 & ( ord_less_eq_set_nat @ B4 @ C5 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_subset_iff
% 4.69/4.91 thf(fact_938_Un__insert__right,axiom,
% 4.69/4.91 ! [A: set_int,A2: int,B4: set_int] :
% 4.69/4.91 ( ( sup_sup_set_int @ A @ ( insert_int @ A2 @ B4 ) )
% 4.69/4.91 = ( insert_int @ A2 @ ( sup_sup_set_int @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_insert_right
% 4.69/4.91 thf(fact_939_Un__insert__right,axiom,
% 4.69/4.91 ! [A: set_o,A2: $o,B4: set_o] :
% 4.69/4.91 ( ( sup_sup_set_o @ A @ ( insert_o @ A2 @ B4 ) )
% 4.69/4.91 = ( insert_o @ A2 @ ( sup_sup_set_o @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_insert_right
% 4.69/4.91 thf(fact_940_Un__insert__right,axiom,
% 4.69/4.91 ! [A: set_Product_unit,A2: product_unit,B4: set_Product_unit] :
% 4.69/4.91 ( ( sup_su793286257634532545t_unit @ A @ ( insert_Product_unit @ A2 @ B4 ) )
% 4.69/4.91 = ( insert_Product_unit @ A2 @ ( sup_su793286257634532545t_unit @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_insert_right
% 4.69/4.91 thf(fact_941_Un__insert__right,axiom,
% 4.69/4.91 ! [A: set_nat,A2: nat,B4: set_nat] :
% 4.69/4.91 ( ( sup_sup_set_nat @ A @ ( insert_nat @ A2 @ B4 ) )
% 4.69/4.91 = ( insert_nat @ A2 @ ( sup_sup_set_nat @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_insert_right
% 4.69/4.91 thf(fact_942_Un__insert__left,axiom,
% 4.69/4.91 ! [A2: int,B4: set_int,C5: set_int] :
% 4.69/4.91 ( ( sup_sup_set_int @ ( insert_int @ A2 @ B4 ) @ C5 )
% 4.69/4.91 = ( insert_int @ A2 @ ( sup_sup_set_int @ B4 @ C5 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_insert_left
% 4.69/4.91 thf(fact_943_Un__insert__left,axiom,
% 4.69/4.91 ! [A2: $o,B4: set_o,C5: set_o] :
% 4.69/4.91 ( ( sup_sup_set_o @ ( insert_o @ A2 @ B4 ) @ C5 )
% 4.69/4.91 = ( insert_o @ A2 @ ( sup_sup_set_o @ B4 @ C5 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_insert_left
% 4.69/4.91 thf(fact_944_Un__insert__left,axiom,
% 4.69/4.91 ! [A2: product_unit,B4: set_Product_unit,C5: set_Product_unit] :
% 4.69/4.91 ( ( sup_su793286257634532545t_unit @ ( insert_Product_unit @ A2 @ B4 ) @ C5 )
% 4.69/4.91 = ( insert_Product_unit @ A2 @ ( sup_su793286257634532545t_unit @ B4 @ C5 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_insert_left
% 4.69/4.91 thf(fact_945_Un__insert__left,axiom,
% 4.69/4.91 ! [A2: nat,B4: set_nat,C5: set_nat] :
% 4.69/4.91 ( ( sup_sup_set_nat @ ( insert_nat @ A2 @ B4 ) @ C5 )
% 4.69/4.91 = ( insert_nat @ A2 @ ( sup_sup_set_nat @ B4 @ C5 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_insert_left
% 4.69/4.91 thf(fact_946_Un__Int__eq_I1_J,axiom,
% 4.69/4.91 ! [S: set_nat,T2: set_nat] :
% 4.69/4.91 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ S @ T2 ) @ S )
% 4.69/4.91 = S ) ).
% 4.69/4.91
% 4.69/4.91 % Un_Int_eq(1)
% 4.69/4.91 thf(fact_947_Un__Int__eq_I2_J,axiom,
% 4.69/4.91 ! [S: set_nat,T2: set_nat] :
% 4.69/4.91 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ S @ T2 ) @ T2 )
% 4.69/4.91 = T2 ) ).
% 4.69/4.91
% 4.69/4.91 % Un_Int_eq(2)
% 4.69/4.91 thf(fact_948_Un__Int__eq_I3_J,axiom,
% 4.69/4.91 ! [S: set_nat,T2: set_nat] :
% 4.69/4.91 ( ( inf_inf_set_nat @ S @ ( sup_sup_set_nat @ S @ T2 ) )
% 4.69/4.91 = S ) ).
% 4.69/4.91
% 4.69/4.91 % Un_Int_eq(3)
% 4.69/4.91 thf(fact_949_Un__Int__eq_I4_J,axiom,
% 4.69/4.91 ! [T2: set_nat,S: set_nat] :
% 4.69/4.91 ( ( inf_inf_set_nat @ T2 @ ( sup_sup_set_nat @ S @ T2 ) )
% 4.69/4.91 = T2 ) ).
% 4.69/4.91
% 4.69/4.91 % Un_Int_eq(4)
% 4.69/4.91 thf(fact_950_Int__Un__eq_I1_J,axiom,
% 4.69/4.91 ! [S: set_nat,T2: set_nat] :
% 4.69/4.91 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ S @ T2 ) @ S )
% 4.69/4.91 = S ) ).
% 4.69/4.91
% 4.69/4.91 % Int_Un_eq(1)
% 4.69/4.91 thf(fact_951_Int__Un__eq_I2_J,axiom,
% 4.69/4.91 ! [S: set_nat,T2: set_nat] :
% 4.69/4.91 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ S @ T2 ) @ T2 )
% 4.69/4.91 = T2 ) ).
% 4.69/4.91
% 4.69/4.91 % Int_Un_eq(2)
% 4.69/4.91 thf(fact_952_Int__Un__eq_I3_J,axiom,
% 4.69/4.91 ! [S: set_nat,T2: set_nat] :
% 4.69/4.91 ( ( sup_sup_set_nat @ S @ ( inf_inf_set_nat @ S @ T2 ) )
% 4.69/4.91 = S ) ).
% 4.69/4.91
% 4.69/4.91 % Int_Un_eq(3)
% 4.69/4.91 thf(fact_953_Int__Un__eq_I4_J,axiom,
% 4.69/4.91 ! [T2: set_nat,S: set_nat] :
% 4.69/4.91 ( ( sup_sup_set_nat @ T2 @ ( inf_inf_set_nat @ S @ T2 ) )
% 4.69/4.91 = T2 ) ).
% 4.69/4.91
% 4.69/4.91 % Int_Un_eq(4)
% 4.69/4.91 thf(fact_954_vimage__Int,axiom,
% 4.69/4.91 ! [F: nat > nat,A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( vimage_nat_nat @ F @ ( inf_inf_set_nat @ A @ B4 ) )
% 4.69/4.91 = ( inf_inf_set_nat @ ( vimage_nat_nat @ F @ A ) @ ( vimage_nat_nat @ F @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % vimage_Int
% 4.69/4.91 thf(fact_955_vimage__Un,axiom,
% 4.69/4.91 ! [F: nat > nat,A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( vimage_nat_nat @ F @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.91 = ( sup_sup_set_nat @ ( vimage_nat_nat @ F @ A ) @ ( vimage_nat_nat @ F @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % vimage_Un
% 4.69/4.91 thf(fact_956_relH__dist__union,axiom,
% 4.69/4.91 ! [As: set_nat,As5: set_nat,H2: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit] :
% 4.69/4.91 ( ( relH @ ( sup_sup_set_nat @ As @ As5 ) @ H2 @ H3 )
% 4.69/4.91 = ( ( relH @ As @ H2 @ H3 )
% 4.69/4.91 & ( relH @ As5 @ H2 @ H3 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % relH_dist_union
% 4.69/4.91 thf(fact_957_singleton__insert__inj__eq,axiom,
% 4.69/4.91 ! [B: product_unit,A2: product_unit,A: set_Product_unit] :
% 4.69/4.91 ( ( ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit )
% 4.69/4.91 = ( insert_Product_unit @ A2 @ A ) )
% 4.69/4.91 = ( ( A2 = B )
% 4.69/4.91 & ( ord_le3507040750410214029t_unit @ A @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % singleton_insert_inj_eq
% 4.69/4.91 thf(fact_958_singleton__insert__inj__eq,axiom,
% 4.69/4.91 ! [B: $o,A2: $o,A: set_o] :
% 4.69/4.91 ( ( ( insert_o @ B @ bot_bot_set_o )
% 4.69/4.91 = ( insert_o @ A2 @ A ) )
% 4.69/4.91 = ( ( A2 = B )
% 4.69/4.91 & ( ord_less_eq_set_o @ A @ ( insert_o @ B @ bot_bot_set_o ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % singleton_insert_inj_eq
% 4.69/4.91 thf(fact_959_singleton__insert__inj__eq,axiom,
% 4.69/4.91 ! [B: int,A2: int,A: set_int] :
% 4.69/4.91 ( ( ( insert_int @ B @ bot_bot_set_int )
% 4.69/4.91 = ( insert_int @ A2 @ A ) )
% 4.69/4.91 = ( ( A2 = B )
% 4.69/4.91 & ( ord_less_eq_set_int @ A @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % singleton_insert_inj_eq
% 4.69/4.91 thf(fact_960_singleton__insert__inj__eq,axiom,
% 4.69/4.91 ! [B: produc3658429121746597890et_nat > $o,A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.91 ( ( ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o )
% 4.69/4.91 = ( insert5175938949040314269_nat_o @ A2 @ A ) )
% 4.69/4.91 = ( ( A2 = B )
% 4.69/4.91 & ( ord_le2965882846123202637_nat_o @ A @ ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % singleton_insert_inj_eq
% 4.69/4.91 thf(fact_961_singleton__insert__inj__eq,axiom,
% 4.69/4.91 ! [B: nat,A2: nat,A: set_nat] :
% 4.69/4.91 ( ( ( insert_nat @ B @ bot_bot_set_nat )
% 4.69/4.91 = ( insert_nat @ A2 @ A ) )
% 4.69/4.91 = ( ( A2 = B )
% 4.69/4.91 & ( ord_less_eq_set_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % singleton_insert_inj_eq
% 4.69/4.91 thf(fact_962_singleton__insert__inj__eq_H,axiom,
% 4.69/4.91 ! [A2: product_unit,A: set_Product_unit,B: product_unit] :
% 4.69/4.91 ( ( ( insert_Product_unit @ A2 @ A )
% 4.69/4.91 = ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.91 = ( ( A2 = B )
% 4.69/4.91 & ( ord_le3507040750410214029t_unit @ A @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % singleton_insert_inj_eq'
% 4.69/4.91 thf(fact_963_singleton__insert__inj__eq_H,axiom,
% 4.69/4.91 ! [A2: $o,A: set_o,B: $o] :
% 4.69/4.91 ( ( ( insert_o @ A2 @ A )
% 4.69/4.91 = ( insert_o @ B @ bot_bot_set_o ) )
% 4.69/4.91 = ( ( A2 = B )
% 4.69/4.91 & ( ord_less_eq_set_o @ A @ ( insert_o @ B @ bot_bot_set_o ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % singleton_insert_inj_eq'
% 4.69/4.91 thf(fact_964_singleton__insert__inj__eq_H,axiom,
% 4.69/4.91 ! [A2: int,A: set_int,B: int] :
% 4.69/4.91 ( ( ( insert_int @ A2 @ A )
% 4.69/4.91 = ( insert_int @ B @ bot_bot_set_int ) )
% 4.69/4.91 = ( ( A2 = B )
% 4.69/4.91 & ( ord_less_eq_set_int @ A @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % singleton_insert_inj_eq'
% 4.69/4.91 thf(fact_965_singleton__insert__inj__eq_H,axiom,
% 4.69/4.91 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B: produc3658429121746597890et_nat > $o] :
% 4.69/4.91 ( ( ( insert5175938949040314269_nat_o @ A2 @ A )
% 4.69/4.91 = ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.91 = ( ( A2 = B )
% 4.69/4.91 & ( ord_le2965882846123202637_nat_o @ A @ ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % singleton_insert_inj_eq'
% 4.69/4.91 thf(fact_966_singleton__insert__inj__eq_H,axiom,
% 4.69/4.91 ! [A2: nat,A: set_nat,B: nat] :
% 4.69/4.91 ( ( ( insert_nat @ A2 @ A )
% 4.69/4.91 = ( insert_nat @ B @ bot_bot_set_nat ) )
% 4.69/4.91 = ( ( A2 = B )
% 4.69/4.91 & ( ord_less_eq_set_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % singleton_insert_inj_eq'
% 4.69/4.91 thf(fact_967_disjoint__insert_I2_J,axiom,
% 4.69/4.91 ! [A: set_Product_unit,B: product_unit,B4: set_Product_unit] :
% 4.69/4.91 ( ( bot_bo3957492148770167129t_unit
% 4.69/4.91 = ( inf_in4660618365625256667t_unit @ A @ ( insert_Product_unit @ B @ B4 ) ) )
% 4.69/4.91 = ( ~ ( member_Product_unit @ B @ A )
% 4.69/4.91 & ( bot_bo3957492148770167129t_unit
% 4.69/4.91 = ( inf_in4660618365625256667t_unit @ A @ B4 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % disjoint_insert(2)
% 4.69/4.91 thf(fact_968_disjoint__insert_I2_J,axiom,
% 4.69/4.91 ! [A: set_o,B: $o,B4: set_o] :
% 4.69/4.91 ( ( bot_bot_set_o
% 4.69/4.91 = ( inf_inf_set_o @ A @ ( insert_o @ B @ B4 ) ) )
% 4.69/4.91 = ( ~ ( member_o @ B @ A )
% 4.69/4.91 & ( bot_bot_set_o
% 4.69/4.91 = ( inf_inf_set_o @ A @ B4 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % disjoint_insert(2)
% 4.69/4.91 thf(fact_969_disjoint__insert_I2_J,axiom,
% 4.69/4.91 ! [A: set_nat,B: nat,B4: set_nat] :
% 4.69/4.91 ( ( bot_bot_set_nat
% 4.69/4.91 = ( inf_inf_set_nat @ A @ ( insert_nat @ B @ B4 ) ) )
% 4.69/4.91 = ( ~ ( member_nat @ B @ A )
% 4.69/4.91 & ( bot_bot_set_nat
% 4.69/4.91 = ( inf_inf_set_nat @ A @ B4 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % disjoint_insert(2)
% 4.69/4.91 thf(fact_970_disjoint__insert_I2_J,axiom,
% 4.69/4.91 ! [A: set_int,B: int,B4: set_int] :
% 4.69/4.91 ( ( bot_bot_set_int
% 4.69/4.91 = ( inf_inf_set_int @ A @ ( insert_int @ B @ B4 ) ) )
% 4.69/4.91 = ( ~ ( member_int @ B @ A )
% 4.69/4.91 & ( bot_bot_set_int
% 4.69/4.91 = ( inf_inf_set_int @ A @ B4 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % disjoint_insert(2)
% 4.69/4.91 thf(fact_971_disjoint__insert_I2_J,axiom,
% 4.69/4.91 ! [A: set_Pr4532377907799695533_nat_o,B: produc3658429121746597890et_nat > $o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.91 ( ( bot_bo7824918357723582233_nat_o
% 4.69/4.91 = ( inf_in1906310914598751387_nat_o @ A @ ( insert5175938949040314269_nat_o @ B @ B4 ) ) )
% 4.69/4.91 = ( ~ ( member6576561426505652726_nat_o @ B @ A )
% 4.69/4.91 & ( bot_bo7824918357723582233_nat_o
% 4.69/4.91 = ( inf_in1906310914598751387_nat_o @ A @ B4 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % disjoint_insert(2)
% 4.69/4.91 thf(fact_972_disjoint__insert_I1_J,axiom,
% 4.69/4.91 ! [B4: set_Product_unit,A2: product_unit,A: set_Product_unit] :
% 4.69/4.91 ( ( ( inf_in4660618365625256667t_unit @ B4 @ ( insert_Product_unit @ A2 @ A ) )
% 4.69/4.91 = bot_bo3957492148770167129t_unit )
% 4.69/4.91 = ( ~ ( member_Product_unit @ A2 @ B4 )
% 4.69/4.91 & ( ( inf_in4660618365625256667t_unit @ B4 @ A )
% 4.69/4.91 = bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % disjoint_insert(1)
% 4.69/4.91 thf(fact_973_disjoint__insert_I1_J,axiom,
% 4.69/4.91 ! [B4: set_o,A2: $o,A: set_o] :
% 4.69/4.91 ( ( ( inf_inf_set_o @ B4 @ ( insert_o @ A2 @ A ) )
% 4.69/4.91 = bot_bot_set_o )
% 4.69/4.91 = ( ~ ( member_o @ A2 @ B4 )
% 4.69/4.91 & ( ( inf_inf_set_o @ B4 @ A )
% 4.69/4.91 = bot_bot_set_o ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % disjoint_insert(1)
% 4.69/4.91 thf(fact_974_disjoint__insert_I1_J,axiom,
% 4.69/4.91 ! [B4: set_nat,A2: nat,A: set_nat] :
% 4.69/4.91 ( ( ( inf_inf_set_nat @ B4 @ ( insert_nat @ A2 @ A ) )
% 4.69/4.91 = bot_bot_set_nat )
% 4.69/4.91 = ( ~ ( member_nat @ A2 @ B4 )
% 4.69/4.91 & ( ( inf_inf_set_nat @ B4 @ A )
% 4.69/4.91 = bot_bot_set_nat ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % disjoint_insert(1)
% 4.69/4.91 thf(fact_975_disjoint__insert_I1_J,axiom,
% 4.69/4.91 ! [B4: set_int,A2: int,A: set_int] :
% 4.69/4.91 ( ( ( inf_inf_set_int @ B4 @ ( insert_int @ A2 @ A ) )
% 4.69/4.91 = bot_bot_set_int )
% 4.69/4.91 = ( ~ ( member_int @ A2 @ B4 )
% 4.69/4.91 & ( ( inf_inf_set_int @ B4 @ A )
% 4.69/4.91 = bot_bot_set_int ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % disjoint_insert(1)
% 4.69/4.91 thf(fact_976_disjoint__insert_I1_J,axiom,
% 4.69/4.91 ! [B4: set_Pr4532377907799695533_nat_o,A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.91 ( ( ( inf_in1906310914598751387_nat_o @ B4 @ ( insert5175938949040314269_nat_o @ A2 @ A ) )
% 4.69/4.91 = bot_bo7824918357723582233_nat_o )
% 4.69/4.91 = ( ~ ( member6576561426505652726_nat_o @ A2 @ B4 )
% 4.69/4.91 & ( ( inf_in1906310914598751387_nat_o @ B4 @ A )
% 4.69/4.91 = bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % disjoint_insert(1)
% 4.69/4.91 thf(fact_977_insert__disjoint_I2_J,axiom,
% 4.69/4.91 ! [A2: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.91 ( ( bot_bo3957492148770167129t_unit
% 4.69/4.91 = ( inf_in4660618365625256667t_unit @ ( insert_Product_unit @ A2 @ A ) @ B4 ) )
% 4.69/4.91 = ( ~ ( member_Product_unit @ A2 @ B4 )
% 4.69/4.91 & ( bot_bo3957492148770167129t_unit
% 4.69/4.91 = ( inf_in4660618365625256667t_unit @ A @ B4 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % insert_disjoint(2)
% 4.69/4.91 thf(fact_978_insert__disjoint_I2_J,axiom,
% 4.69/4.91 ! [A2: $o,A: set_o,B4: set_o] :
% 4.69/4.91 ( ( bot_bot_set_o
% 4.69/4.91 = ( inf_inf_set_o @ ( insert_o @ A2 @ A ) @ B4 ) )
% 4.69/4.91 = ( ~ ( member_o @ A2 @ B4 )
% 4.69/4.91 & ( bot_bot_set_o
% 4.69/4.91 = ( inf_inf_set_o @ A @ B4 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % insert_disjoint(2)
% 4.69/4.91 thf(fact_979_insert__disjoint_I2_J,axiom,
% 4.69/4.91 ! [A2: nat,A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( bot_bot_set_nat
% 4.69/4.91 = ( inf_inf_set_nat @ ( insert_nat @ A2 @ A ) @ B4 ) )
% 4.69/4.91 = ( ~ ( member_nat @ A2 @ B4 )
% 4.69/4.91 & ( bot_bot_set_nat
% 4.69/4.91 = ( inf_inf_set_nat @ A @ B4 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % insert_disjoint(2)
% 4.69/4.91 thf(fact_980_insert__disjoint_I2_J,axiom,
% 4.69/4.91 ! [A2: int,A: set_int,B4: set_int] :
% 4.69/4.91 ( ( bot_bot_set_int
% 4.69/4.91 = ( inf_inf_set_int @ ( insert_int @ A2 @ A ) @ B4 ) )
% 4.69/4.91 = ( ~ ( member_int @ A2 @ B4 )
% 4.69/4.91 & ( bot_bot_set_int
% 4.69/4.91 = ( inf_inf_set_int @ A @ B4 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % insert_disjoint(2)
% 4.69/4.91 thf(fact_981_insert__disjoint_I2_J,axiom,
% 4.69/4.91 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.91 ( ( bot_bo7824918357723582233_nat_o
% 4.69/4.91 = ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A2 @ A ) @ B4 ) )
% 4.69/4.91 = ( ~ ( member6576561426505652726_nat_o @ A2 @ B4 )
% 4.69/4.91 & ( bot_bo7824918357723582233_nat_o
% 4.69/4.91 = ( inf_in1906310914598751387_nat_o @ A @ B4 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % insert_disjoint(2)
% 4.69/4.91 thf(fact_982_insert__disjoint_I1_J,axiom,
% 4.69/4.91 ! [A2: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.91 ( ( ( inf_in4660618365625256667t_unit @ ( insert_Product_unit @ A2 @ A ) @ B4 )
% 4.69/4.91 = bot_bo3957492148770167129t_unit )
% 4.69/4.91 = ( ~ ( member_Product_unit @ A2 @ B4 )
% 4.69/4.91 & ( ( inf_in4660618365625256667t_unit @ A @ B4 )
% 4.69/4.91 = bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % insert_disjoint(1)
% 4.69/4.91 thf(fact_983_insert__disjoint_I1_J,axiom,
% 4.69/4.91 ! [A2: $o,A: set_o,B4: set_o] :
% 4.69/4.91 ( ( ( inf_inf_set_o @ ( insert_o @ A2 @ A ) @ B4 )
% 4.69/4.91 = bot_bot_set_o )
% 4.69/4.91 = ( ~ ( member_o @ A2 @ B4 )
% 4.69/4.91 & ( ( inf_inf_set_o @ A @ B4 )
% 4.69/4.91 = bot_bot_set_o ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % insert_disjoint(1)
% 4.69/4.91 thf(fact_984_insert__disjoint_I1_J,axiom,
% 4.69/4.91 ! [A2: nat,A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( ( inf_inf_set_nat @ ( insert_nat @ A2 @ A ) @ B4 )
% 4.69/4.91 = bot_bot_set_nat )
% 4.69/4.91 = ( ~ ( member_nat @ A2 @ B4 )
% 4.69/4.91 & ( ( inf_inf_set_nat @ A @ B4 )
% 4.69/4.91 = bot_bot_set_nat ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % insert_disjoint(1)
% 4.69/4.91 thf(fact_985_insert__disjoint_I1_J,axiom,
% 4.69/4.91 ! [A2: int,A: set_int,B4: set_int] :
% 4.69/4.91 ( ( ( inf_inf_set_int @ ( insert_int @ A2 @ A ) @ B4 )
% 4.69/4.91 = bot_bot_set_int )
% 4.69/4.91 = ( ~ ( member_int @ A2 @ B4 )
% 4.69/4.91 & ( ( inf_inf_set_int @ A @ B4 )
% 4.69/4.91 = bot_bot_set_int ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % insert_disjoint(1)
% 4.69/4.91 thf(fact_986_insert__disjoint_I1_J,axiom,
% 4.69/4.91 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.91 ( ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A2 @ A ) @ B4 )
% 4.69/4.91 = bot_bo7824918357723582233_nat_o )
% 4.69/4.91 = ( ~ ( member6576561426505652726_nat_o @ A2 @ B4 )
% 4.69/4.91 & ( ( inf_in1906310914598751387_nat_o @ A @ B4 )
% 4.69/4.91 = bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % insert_disjoint(1)
% 4.69/4.91 thf(fact_987_Image__Id__on,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( image_nat_nat @ ( id_on_nat @ A ) @ B4 )
% 4.69/4.91 = ( inf_inf_set_nat @ A @ B4 ) ) ).
% 4.69/4.91
% 4.69/4.91 % Image_Id_on
% 4.69/4.91 thf(fact_988_in__range__dist__union,axiom,
% 4.69/4.91 ! [H2: heap_e7401611519738050253t_unit,As: set_nat,As5: set_nat] :
% 4.69/4.91 ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ ( sup_sup_set_nat @ As @ As5 ) ) )
% 4.69/4.91 = ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 4.69/4.91 & ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As5 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % in_range_dist_union
% 4.69/4.91 thf(fact_989_reachable__mono,axiom,
% 4.69/4.91 ! [R3: set_Pr1261947904930325089at_nat,R5: set_Pr1261947904930325089at_nat,X4: set_nat,X5: set_nat] :
% 4.69/4.91 ( ( ord_le3146513528884898305at_nat @ R3 @ R5 )
% 4.69/4.91 => ( ( ord_less_eq_set_nat @ X4 @ X5 )
% 4.69/4.91 => ( ord_less_eq_set_nat @ ( image_nat_nat @ ( transi2905341329935302413cl_nat @ R3 ) @ X4 ) @ ( image_nat_nat @ ( transi2905341329935302413cl_nat @ R5 ) @ X5 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % reachable_mono
% 4.69/4.91 thf(fact_990_order__antisym__conv,axiom,
% 4.69/4.91 ! [Y: filter_nat,X: filter_nat] :
% 4.69/4.91 ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 4.69/4.91 => ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 4.69/4.91 = ( X = Y ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_antisym_conv
% 4.69/4.91 thf(fact_991_order__antisym__conv,axiom,
% 4.69/4.91 ! [Y: set_nat,X: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ Y @ X )
% 4.69/4.91 => ( ( ord_less_eq_set_nat @ X @ Y )
% 4.69/4.91 = ( X = Y ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_antisym_conv
% 4.69/4.91 thf(fact_992_order__antisym__conv,axiom,
% 4.69/4.91 ! [Y: rat,X: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ Y @ X )
% 4.69/4.91 => ( ( ord_less_eq_rat @ X @ Y )
% 4.69/4.91 = ( X = Y ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_antisym_conv
% 4.69/4.91 thf(fact_993_order__antisym__conv,axiom,
% 4.69/4.91 ! [Y: nat,X: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ Y @ X )
% 4.69/4.91 => ( ( ord_less_eq_nat @ X @ Y )
% 4.69/4.91 = ( X = Y ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_antisym_conv
% 4.69/4.91 thf(fact_994_order__antisym__conv,axiom,
% 4.69/4.91 ! [Y: int,X: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ Y @ X )
% 4.69/4.91 => ( ( ord_less_eq_int @ X @ Y )
% 4.69/4.91 = ( X = Y ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_antisym_conv
% 4.69/4.91 thf(fact_995_linorder__le__cases,axiom,
% 4.69/4.91 ! [X: rat,Y: rat] :
% 4.69/4.91 ( ~ ( ord_less_eq_rat @ X @ Y )
% 4.69/4.91 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 4.69/4.91
% 4.69/4.91 % linorder_le_cases
% 4.69/4.91 thf(fact_996_linorder__le__cases,axiom,
% 4.69/4.91 ! [X: nat,Y: nat] :
% 4.69/4.91 ( ~ ( ord_less_eq_nat @ X @ Y )
% 4.69/4.91 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 4.69/4.91
% 4.69/4.91 % linorder_le_cases
% 4.69/4.91 thf(fact_997_linorder__le__cases,axiom,
% 4.69/4.91 ! [X: int,Y: int] :
% 4.69/4.91 ( ~ ( ord_less_eq_int @ X @ Y )
% 4.69/4.91 => ( ord_less_eq_int @ Y @ X ) ) ).
% 4.69/4.91
% 4.69/4.91 % linorder_le_cases
% 4.69/4.91 thf(fact_998_ord__le__eq__subst,axiom,
% 4.69/4.91 ! [A2: rat,B: rat,F: rat > rat,C: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/4.91 => ( ( ( F @ B )
% 4.69/4.91 = C )
% 4.69/4.91 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_le_eq_subst
% 4.69/4.91 thf(fact_999_ord__le__eq__subst,axiom,
% 4.69/4.91 ! [A2: rat,B: rat,F: rat > nat,C: nat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/4.91 => ( ( ( F @ B )
% 4.69/4.91 = C )
% 4.69/4.91 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_le_eq_subst
% 4.69/4.91 thf(fact_1000_ord__le__eq__subst,axiom,
% 4.69/4.91 ! [A2: rat,B: rat,F: rat > int,C: int] :
% 4.69/4.91 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/4.91 => ( ( ( F @ B )
% 4.69/4.91 = C )
% 4.69/4.91 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_le_eq_subst
% 4.69/4.91 thf(fact_1001_ord__le__eq__subst,axiom,
% 4.69/4.91 ! [A2: nat,B: nat,F: nat > rat,C: rat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/4.91 => ( ( ( F @ B )
% 4.69/4.91 = C )
% 4.69/4.91 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_le_eq_subst
% 4.69/4.91 thf(fact_1002_ord__le__eq__subst,axiom,
% 4.69/4.91 ! [A2: nat,B: nat,F: nat > nat,C: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/4.91 => ( ( ( F @ B )
% 4.69/4.91 = C )
% 4.69/4.91 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_le_eq_subst
% 4.69/4.91 thf(fact_1003_ord__le__eq__subst,axiom,
% 4.69/4.91 ! [A2: nat,B: nat,F: nat > int,C: int] :
% 4.69/4.91 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/4.91 => ( ( ( F @ B )
% 4.69/4.91 = C )
% 4.69/4.91 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_le_eq_subst
% 4.69/4.91 thf(fact_1004_ord__le__eq__subst,axiom,
% 4.69/4.91 ! [A2: int,B: int,F: int > rat,C: rat] :
% 4.69/4.91 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/4.91 => ( ( ( F @ B )
% 4.69/4.91 = C )
% 4.69/4.91 => ( ! [X3: int,Y2: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_le_eq_subst
% 4.69/4.91 thf(fact_1005_ord__le__eq__subst,axiom,
% 4.69/4.91 ! [A2: int,B: int,F: int > nat,C: nat] :
% 4.69/4.91 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/4.91 => ( ( ( F @ B )
% 4.69/4.91 = C )
% 4.69/4.91 => ( ! [X3: int,Y2: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_le_eq_subst
% 4.69/4.91 thf(fact_1006_ord__le__eq__subst,axiom,
% 4.69/4.91 ! [A2: int,B: int,F: int > int,C: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/4.91 => ( ( ( F @ B )
% 4.69/4.91 = C )
% 4.69/4.91 => ( ! [X3: int,Y2: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_le_eq_subst
% 4.69/4.91 thf(fact_1007_ord__le__eq__subst,axiom,
% 4.69/4.91 ! [A2: filter_nat,B: filter_nat,F: filter_nat > rat,C: rat] :
% 4.69/4.91 ( ( ord_le2510731241096832064er_nat @ A2 @ B )
% 4.69/4.91 => ( ( ( F @ B )
% 4.69/4.91 = C )
% 4.69/4.91 => ( ! [X3: filter_nat,Y2: filter_nat] :
% 4.69/4.91 ( ( ord_le2510731241096832064er_nat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_le_eq_subst
% 4.69/4.91 thf(fact_1008_ord__eq__le__subst,axiom,
% 4.69/4.91 ! [A2: rat,F: rat > rat,B: rat,C: rat] :
% 4.69/4.91 ( ( A2
% 4.69/4.91 = ( F @ B ) )
% 4.69/4.91 => ( ( ord_less_eq_rat @ B @ C )
% 4.69/4.91 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_eq_le_subst
% 4.69/4.91 thf(fact_1009_ord__eq__le__subst,axiom,
% 4.69/4.91 ! [A2: nat,F: rat > nat,B: rat,C: rat] :
% 4.69/4.91 ( ( A2
% 4.69/4.91 = ( F @ B ) )
% 4.69/4.91 => ( ( ord_less_eq_rat @ B @ C )
% 4.69/4.91 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_eq_le_subst
% 4.69/4.91 thf(fact_1010_ord__eq__le__subst,axiom,
% 4.69/4.91 ! [A2: int,F: rat > int,B: rat,C: rat] :
% 4.69/4.91 ( ( A2
% 4.69/4.91 = ( F @ B ) )
% 4.69/4.91 => ( ( ord_less_eq_rat @ B @ C )
% 4.69/4.91 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_eq_le_subst
% 4.69/4.91 thf(fact_1011_ord__eq__le__subst,axiom,
% 4.69/4.91 ! [A2: rat,F: nat > rat,B: nat,C: nat] :
% 4.69/4.91 ( ( A2
% 4.69/4.91 = ( F @ B ) )
% 4.69/4.91 => ( ( ord_less_eq_nat @ B @ C )
% 4.69/4.91 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_eq_le_subst
% 4.69/4.91 thf(fact_1012_ord__eq__le__subst,axiom,
% 4.69/4.91 ! [A2: nat,F: nat > nat,B: nat,C: nat] :
% 4.69/4.91 ( ( A2
% 4.69/4.91 = ( F @ B ) )
% 4.69/4.91 => ( ( ord_less_eq_nat @ B @ C )
% 4.69/4.91 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_eq_le_subst
% 4.69/4.91 thf(fact_1013_ord__eq__le__subst,axiom,
% 4.69/4.91 ! [A2: int,F: nat > int,B: nat,C: nat] :
% 4.69/4.91 ( ( A2
% 4.69/4.91 = ( F @ B ) )
% 4.69/4.91 => ( ( ord_less_eq_nat @ B @ C )
% 4.69/4.91 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_eq_le_subst
% 4.69/4.91 thf(fact_1014_ord__eq__le__subst,axiom,
% 4.69/4.91 ! [A2: rat,F: int > rat,B: int,C: int] :
% 4.69/4.91 ( ( A2
% 4.69/4.91 = ( F @ B ) )
% 4.69/4.91 => ( ( ord_less_eq_int @ B @ C )
% 4.69/4.91 => ( ! [X3: int,Y2: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_eq_le_subst
% 4.69/4.91 thf(fact_1015_ord__eq__le__subst,axiom,
% 4.69/4.91 ! [A2: nat,F: int > nat,B: int,C: int] :
% 4.69/4.91 ( ( A2
% 4.69/4.91 = ( F @ B ) )
% 4.69/4.91 => ( ( ord_less_eq_int @ B @ C )
% 4.69/4.91 => ( ! [X3: int,Y2: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_eq_le_subst
% 4.69/4.91 thf(fact_1016_ord__eq__le__subst,axiom,
% 4.69/4.91 ! [A2: int,F: int > int,B: int,C: int] :
% 4.69/4.91 ( ( A2
% 4.69/4.91 = ( F @ B ) )
% 4.69/4.91 => ( ( ord_less_eq_int @ B @ C )
% 4.69/4.91 => ( ! [X3: int,Y2: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_eq_le_subst
% 4.69/4.91 thf(fact_1017_ord__eq__le__subst,axiom,
% 4.69/4.91 ! [A2: rat,F: filter_nat > rat,B: filter_nat,C: filter_nat] :
% 4.69/4.91 ( ( A2
% 4.69/4.91 = ( F @ B ) )
% 4.69/4.91 => ( ( ord_le2510731241096832064er_nat @ B @ C )
% 4.69/4.91 => ( ! [X3: filter_nat,Y2: filter_nat] :
% 4.69/4.91 ( ( ord_le2510731241096832064er_nat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_eq_le_subst
% 4.69/4.91 thf(fact_1018_linorder__linear,axiom,
% 4.69/4.91 ! [X: rat,Y: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ X @ Y )
% 4.69/4.91 | ( ord_less_eq_rat @ Y @ X ) ) ).
% 4.69/4.91
% 4.69/4.91 % linorder_linear
% 4.69/4.91 thf(fact_1019_linorder__linear,axiom,
% 4.69/4.91 ! [X: nat,Y: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ X @ Y )
% 4.69/4.91 | ( ord_less_eq_nat @ Y @ X ) ) ).
% 4.69/4.91
% 4.69/4.91 % linorder_linear
% 4.69/4.91 thf(fact_1020_linorder__linear,axiom,
% 4.69/4.91 ! [X: int,Y: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ X @ Y )
% 4.69/4.91 | ( ord_less_eq_int @ Y @ X ) ) ).
% 4.69/4.91
% 4.69/4.91 % linorder_linear
% 4.69/4.91 thf(fact_1021_subset__Collect__conv,axiom,
% 4.69/4.91 ! [S: set_Pr4532377907799695533_nat_o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 4.69/4.91 ( ( ord_le2965882846123202637_nat_o @ S @ ( collec939566748876313656_nat_o @ P ) )
% 4.69/4.91 = ( ! [X2: produc3658429121746597890et_nat > $o] :
% 4.69/4.91 ( ( member6576561426505652726_nat_o @ X2 @ S )
% 4.69/4.91 => ( P @ X2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subset_Collect_conv
% 4.69/4.91 thf(fact_1022_subset__Collect__conv,axiom,
% 4.69/4.91 ! [S: set_int,P: int > $o] :
% 4.69/4.91 ( ( ord_less_eq_set_int @ S @ ( collect_int @ P ) )
% 4.69/4.91 = ( ! [X2: int] :
% 4.69/4.91 ( ( member_int @ X2 @ S )
% 4.69/4.91 => ( P @ X2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subset_Collect_conv
% 4.69/4.91 thf(fact_1023_subset__Collect__conv,axiom,
% 4.69/4.91 ! [S: set_o,P: $o > $o] :
% 4.69/4.91 ( ( ord_less_eq_set_o @ S @ ( collect_o @ P ) )
% 4.69/4.91 = ( ! [X2: $o] :
% 4.69/4.91 ( ( member_o @ X2 @ S )
% 4.69/4.91 => ( P @ X2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subset_Collect_conv
% 4.69/4.91 thf(fact_1024_subset__Collect__conv,axiom,
% 4.69/4.91 ! [S: set_Product_unit,P: product_unit > $o] :
% 4.69/4.91 ( ( ord_le3507040750410214029t_unit @ S @ ( collect_Product_unit @ P ) )
% 4.69/4.91 = ( ! [X2: product_unit] :
% 4.69/4.91 ( ( member_Product_unit @ X2 @ S )
% 4.69/4.91 => ( P @ X2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subset_Collect_conv
% 4.69/4.91 thf(fact_1025_subset__Collect__conv,axiom,
% 4.69/4.91 ! [S: set_nat,P: nat > $o] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ S @ ( collect_nat @ P ) )
% 4.69/4.91 = ( ! [X2: nat] :
% 4.69/4.91 ( ( member_nat @ X2 @ S )
% 4.69/4.91 => ( P @ X2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subset_Collect_conv
% 4.69/4.91 thf(fact_1026_order__eq__refl,axiom,
% 4.69/4.91 ! [X: filter_nat,Y: filter_nat] :
% 4.69/4.91 ( ( X = Y )
% 4.69/4.91 => ( ord_le2510731241096832064er_nat @ X @ Y ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_eq_refl
% 4.69/4.91 thf(fact_1027_order__eq__refl,axiom,
% 4.69/4.91 ! [X: set_nat,Y: set_nat] :
% 4.69/4.91 ( ( X = Y )
% 4.69/4.91 => ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_eq_refl
% 4.69/4.91 thf(fact_1028_order__eq__refl,axiom,
% 4.69/4.91 ! [X: rat,Y: rat] :
% 4.69/4.91 ( ( X = Y )
% 4.69/4.91 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_eq_refl
% 4.69/4.91 thf(fact_1029_order__eq__refl,axiom,
% 4.69/4.91 ! [X: nat,Y: nat] :
% 4.69/4.91 ( ( X = Y )
% 4.69/4.91 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_eq_refl
% 4.69/4.91 thf(fact_1030_order__eq__refl,axiom,
% 4.69/4.91 ! [X: int,Y: int] :
% 4.69/4.91 ( ( X = Y )
% 4.69/4.91 => ( ord_less_eq_int @ X @ Y ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_eq_refl
% 4.69/4.91 thf(fact_1031_ord__eq__le__eq__trans,axiom,
% 4.69/4.91 ! [A2: filter_nat,B: filter_nat,C: filter_nat,D2: filter_nat] :
% 4.69/4.91 ( ( A2 = B )
% 4.69/4.91 => ( ( ord_le2510731241096832064er_nat @ B @ C )
% 4.69/4.91 => ( ( C = D2 )
% 4.69/4.91 => ( ord_le2510731241096832064er_nat @ A2 @ D2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_eq_le_eq_trans
% 4.69/4.91 thf(fact_1032_ord__eq__le__eq__trans,axiom,
% 4.69/4.91 ! [A2: set_nat,B: set_nat,C: set_nat,D2: set_nat] :
% 4.69/4.91 ( ( A2 = B )
% 4.69/4.91 => ( ( ord_less_eq_set_nat @ B @ C )
% 4.69/4.91 => ( ( C = D2 )
% 4.69/4.91 => ( ord_less_eq_set_nat @ A2 @ D2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_eq_le_eq_trans
% 4.69/4.91 thf(fact_1033_ord__eq__le__eq__trans,axiom,
% 4.69/4.91 ! [A2: rat,B: rat,C: rat,D2: rat] :
% 4.69/4.91 ( ( A2 = B )
% 4.69/4.91 => ( ( ord_less_eq_rat @ B @ C )
% 4.69/4.91 => ( ( C = D2 )
% 4.69/4.91 => ( ord_less_eq_rat @ A2 @ D2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_eq_le_eq_trans
% 4.69/4.91 thf(fact_1034_ord__eq__le__eq__trans,axiom,
% 4.69/4.91 ! [A2: nat,B: nat,C: nat,D2: nat] :
% 4.69/4.91 ( ( A2 = B )
% 4.69/4.91 => ( ( ord_less_eq_nat @ B @ C )
% 4.69/4.91 => ( ( C = D2 )
% 4.69/4.91 => ( ord_less_eq_nat @ A2 @ D2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_eq_le_eq_trans
% 4.69/4.91 thf(fact_1035_ord__eq__le__eq__trans,axiom,
% 4.69/4.91 ! [A2: int,B: int,C: int,D2: int] :
% 4.69/4.91 ( ( A2 = B )
% 4.69/4.91 => ( ( ord_less_eq_int @ B @ C )
% 4.69/4.91 => ( ( C = D2 )
% 4.69/4.91 => ( ord_less_eq_int @ A2 @ D2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_eq_le_eq_trans
% 4.69/4.91 thf(fact_1036_order__subst2,axiom,
% 4.69/4.91 ! [A2: rat,B: rat,F: rat > rat,C: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/4.91 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 4.69/4.91 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_subst2
% 4.69/4.91 thf(fact_1037_order__subst2,axiom,
% 4.69/4.91 ! [A2: rat,B: rat,F: rat > nat,C: nat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/4.91 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 4.69/4.91 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_subst2
% 4.69/4.91 thf(fact_1038_order__subst2,axiom,
% 4.69/4.91 ! [A2: rat,B: rat,F: rat > int,C: int] :
% 4.69/4.91 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/4.91 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 4.69/4.91 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_subst2
% 4.69/4.91 thf(fact_1039_order__subst2,axiom,
% 4.69/4.91 ! [A2: nat,B: nat,F: nat > rat,C: rat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/4.91 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 4.69/4.91 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_subst2
% 4.69/4.91 thf(fact_1040_order__subst2,axiom,
% 4.69/4.91 ! [A2: nat,B: nat,F: nat > nat,C: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/4.91 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 4.69/4.91 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_subst2
% 4.69/4.91 thf(fact_1041_order__subst2,axiom,
% 4.69/4.91 ! [A2: nat,B: nat,F: nat > int,C: int] :
% 4.69/4.91 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/4.91 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 4.69/4.91 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_subst2
% 4.69/4.91 thf(fact_1042_order__subst2,axiom,
% 4.69/4.91 ! [A2: int,B: int,F: int > rat,C: rat] :
% 4.69/4.91 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/4.91 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 4.69/4.91 => ( ! [X3: int,Y2: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_subst2
% 4.69/4.91 thf(fact_1043_order__subst2,axiom,
% 4.69/4.91 ! [A2: int,B: int,F: int > nat,C: nat] :
% 4.69/4.91 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/4.91 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 4.69/4.91 => ( ! [X3: int,Y2: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_subst2
% 4.69/4.91 thf(fact_1044_order__subst2,axiom,
% 4.69/4.91 ! [A2: int,B: int,F: int > int,C: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/4.91 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 4.69/4.91 => ( ! [X3: int,Y2: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_subst2
% 4.69/4.91 thf(fact_1045_order__subst2,axiom,
% 4.69/4.91 ! [A2: filter_nat,B: filter_nat,F: filter_nat > rat,C: rat] :
% 4.69/4.91 ( ( ord_le2510731241096832064er_nat @ A2 @ B )
% 4.69/4.91 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 4.69/4.91 => ( ! [X3: filter_nat,Y2: filter_nat] :
% 4.69/4.91 ( ( ord_le2510731241096832064er_nat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_subst2
% 4.69/4.91 thf(fact_1046_order__subst1,axiom,
% 4.69/4.91 ! [A2: rat,F: rat > rat,B: rat,C: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ A2 @ ( F @ B ) )
% 4.69/4.91 => ( ( ord_less_eq_rat @ B @ C )
% 4.69/4.91 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_subst1
% 4.69/4.91 thf(fact_1047_order__subst1,axiom,
% 4.69/4.91 ! [A2: rat,F: nat > rat,B: nat,C: nat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ A2 @ ( F @ B ) )
% 4.69/4.91 => ( ( ord_less_eq_nat @ B @ C )
% 4.69/4.91 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_subst1
% 4.69/4.91 thf(fact_1048_order__subst1,axiom,
% 4.69/4.91 ! [A2: rat,F: int > rat,B: int,C: int] :
% 4.69/4.91 ( ( ord_less_eq_rat @ A2 @ ( F @ B ) )
% 4.69/4.91 => ( ( ord_less_eq_int @ B @ C )
% 4.69/4.91 => ( ! [X3: int,Y2: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_subst1
% 4.69/4.91 thf(fact_1049_order__subst1,axiom,
% 4.69/4.91 ! [A2: nat,F: rat > nat,B: rat,C: rat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ A2 @ ( F @ B ) )
% 4.69/4.91 => ( ( ord_less_eq_rat @ B @ C )
% 4.69/4.91 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_subst1
% 4.69/4.91 thf(fact_1050_order__subst1,axiom,
% 4.69/4.91 ! [A2: nat,F: nat > nat,B: nat,C: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ A2 @ ( F @ B ) )
% 4.69/4.91 => ( ( ord_less_eq_nat @ B @ C )
% 4.69/4.91 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_subst1
% 4.69/4.91 thf(fact_1051_order__subst1,axiom,
% 4.69/4.91 ! [A2: nat,F: int > nat,B: int,C: int] :
% 4.69/4.91 ( ( ord_less_eq_nat @ A2 @ ( F @ B ) )
% 4.69/4.91 => ( ( ord_less_eq_int @ B @ C )
% 4.69/4.91 => ( ! [X3: int,Y2: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_subst1
% 4.69/4.91 thf(fact_1052_order__subst1,axiom,
% 4.69/4.91 ! [A2: int,F: rat > int,B: rat,C: rat] :
% 4.69/4.91 ( ( ord_less_eq_int @ A2 @ ( F @ B ) )
% 4.69/4.91 => ( ( ord_less_eq_rat @ B @ C )
% 4.69/4.91 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_subst1
% 4.69/4.91 thf(fact_1053_order__subst1,axiom,
% 4.69/4.91 ! [A2: int,F: nat > int,B: nat,C: nat] :
% 4.69/4.91 ( ( ord_less_eq_int @ A2 @ ( F @ B ) )
% 4.69/4.91 => ( ( ord_less_eq_nat @ B @ C )
% 4.69/4.91 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_subst1
% 4.69/4.91 thf(fact_1054_order__subst1,axiom,
% 4.69/4.91 ! [A2: int,F: int > int,B: int,C: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ A2 @ ( F @ B ) )
% 4.69/4.91 => ( ( ord_less_eq_int @ B @ C )
% 4.69/4.91 => ( ! [X3: int,Y2: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ X3 @ Y2 )
% 4.69/4.91 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_less_eq_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_subst1
% 4.69/4.91 thf(fact_1055_order__subst1,axiom,
% 4.69/4.91 ! [A2: filter_nat,F: rat > filter_nat,B: rat,C: rat] :
% 4.69/4.91 ( ( ord_le2510731241096832064er_nat @ A2 @ ( F @ B ) )
% 4.69/4.91 => ( ( ord_less_eq_rat @ B @ C )
% 4.69/4.91 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.91 => ( ord_le2510731241096832064er_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.91 => ( ord_le2510731241096832064er_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_subst1
% 4.69/4.91 thf(fact_1056_Orderings_Oorder__eq__iff,axiom,
% 4.69/4.91 ( ( ^ [Y4: filter_nat,Z4: filter_nat] : ( Y4 = Z4 ) )
% 4.69/4.91 = ( ^ [A6: filter_nat,B6: filter_nat] :
% 4.69/4.91 ( ( ord_le2510731241096832064er_nat @ A6 @ B6 )
% 4.69/4.91 & ( ord_le2510731241096832064er_nat @ B6 @ A6 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Orderings.order_eq_iff
% 4.69/4.91 thf(fact_1057_Orderings_Oorder__eq__iff,axiom,
% 4.69/4.91 ( ( ^ [Y4: set_nat,Z4: set_nat] : ( Y4 = Z4 ) )
% 4.69/4.91 = ( ^ [A6: set_nat,B6: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ A6 @ B6 )
% 4.69/4.91 & ( ord_less_eq_set_nat @ B6 @ A6 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Orderings.order_eq_iff
% 4.69/4.91 thf(fact_1058_Orderings_Oorder__eq__iff,axiom,
% 4.69/4.91 ( ( ^ [Y4: rat,Z4: rat] : ( Y4 = Z4 ) )
% 4.69/4.91 = ( ^ [A6: rat,B6: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ A6 @ B6 )
% 4.69/4.91 & ( ord_less_eq_rat @ B6 @ A6 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Orderings.order_eq_iff
% 4.69/4.91 thf(fact_1059_Orderings_Oorder__eq__iff,axiom,
% 4.69/4.91 ( ( ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 ) )
% 4.69/4.91 = ( ^ [A6: nat,B6: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ A6 @ B6 )
% 4.69/4.91 & ( ord_less_eq_nat @ B6 @ A6 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Orderings.order_eq_iff
% 4.69/4.91 thf(fact_1060_Orderings_Oorder__eq__iff,axiom,
% 4.69/4.91 ( ( ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 4.69/4.91 = ( ^ [A6: int,B6: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ A6 @ B6 )
% 4.69/4.91 & ( ord_less_eq_int @ B6 @ A6 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Orderings.order_eq_iff
% 4.69/4.91 thf(fact_1061_inter__eq__subsetI,axiom,
% 4.69/4.91 ! [S: set_nat,S4: set_nat,A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ S @ S4 )
% 4.69/4.91 => ( ( ( inf_inf_set_nat @ A @ S4 )
% 4.69/4.91 = ( inf_inf_set_nat @ B4 @ S4 ) )
% 4.69/4.91 => ( ( inf_inf_set_nat @ A @ S )
% 4.69/4.91 = ( inf_inf_set_nat @ B4 @ S ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % inter_eq_subsetI
% 4.69/4.91 thf(fact_1062_Int__left__commute,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat,C5: set_nat] :
% 4.69/4.91 ( ( inf_inf_set_nat @ A @ ( inf_inf_set_nat @ B4 @ C5 ) )
% 4.69/4.91 = ( inf_inf_set_nat @ B4 @ ( inf_inf_set_nat @ A @ C5 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_left_commute
% 4.69/4.91 thf(fact_1063_Int__Collect__mono,axiom,
% 4.69/4.91 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o,P: ( produc3658429121746597890et_nat > $o ) > $o,Q2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 4.69/4.91 ( ( ord_le2965882846123202637_nat_o @ A @ B4 )
% 4.69/4.91 => ( ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.91 ( ( member6576561426505652726_nat_o @ X3 @ A )
% 4.69/4.91 => ( ( P @ X3 )
% 4.69/4.91 => ( Q2 @ X3 ) ) )
% 4.69/4.91 => ( ord_le2965882846123202637_nat_o @ ( inf_in1906310914598751387_nat_o @ A @ ( collec939566748876313656_nat_o @ P ) ) @ ( inf_in1906310914598751387_nat_o @ B4 @ ( collec939566748876313656_nat_o @ Q2 ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_Collect_mono
% 4.69/4.91 thf(fact_1064_Int__Collect__mono,axiom,
% 4.69/4.91 ! [A: set_int,B4: set_int,P: int > $o,Q2: int > $o] :
% 4.69/4.91 ( ( ord_less_eq_set_int @ A @ B4 )
% 4.69/4.91 => ( ! [X3: int] :
% 4.69/4.91 ( ( member_int @ X3 @ A )
% 4.69/4.91 => ( ( P @ X3 )
% 4.69/4.91 => ( Q2 @ X3 ) ) )
% 4.69/4.91 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A @ ( collect_int @ P ) ) @ ( inf_inf_set_int @ B4 @ ( collect_int @ Q2 ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_Collect_mono
% 4.69/4.91 thf(fact_1065_Int__Collect__mono,axiom,
% 4.69/4.91 ! [A: set_o,B4: set_o,P: $o > $o,Q2: $o > $o] :
% 4.69/4.91 ( ( ord_less_eq_set_o @ A @ B4 )
% 4.69/4.91 => ( ! [X3: $o] :
% 4.69/4.91 ( ( member_o @ X3 @ A )
% 4.69/4.91 => ( ( P @ X3 )
% 4.69/4.91 => ( Q2 @ X3 ) ) )
% 4.69/4.91 => ( ord_less_eq_set_o @ ( inf_inf_set_o @ A @ ( collect_o @ P ) ) @ ( inf_inf_set_o @ B4 @ ( collect_o @ Q2 ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_Collect_mono
% 4.69/4.91 thf(fact_1066_Int__Collect__mono,axiom,
% 4.69/4.91 ! [A: set_Product_unit,B4: set_Product_unit,P: product_unit > $o,Q2: product_unit > $o] :
% 4.69/4.91 ( ( ord_le3507040750410214029t_unit @ A @ B4 )
% 4.69/4.91 => ( ! [X3: product_unit] :
% 4.69/4.91 ( ( member_Product_unit @ X3 @ A )
% 4.69/4.91 => ( ( P @ X3 )
% 4.69/4.91 => ( Q2 @ X3 ) ) )
% 4.69/4.91 => ( ord_le3507040750410214029t_unit @ ( inf_in4660618365625256667t_unit @ A @ ( collect_Product_unit @ P ) ) @ ( inf_in4660618365625256667t_unit @ B4 @ ( collect_Product_unit @ Q2 ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_Collect_mono
% 4.69/4.91 thf(fact_1067_Int__Collect__mono,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat,P: nat > $o,Q2: nat > $o] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.91 => ( ! [X3: nat] :
% 4.69/4.91 ( ( member_nat @ X3 @ A )
% 4.69/4.91 => ( ( P @ X3 )
% 4.69/4.91 => ( Q2 @ X3 ) ) )
% 4.69/4.91 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ ( collect_nat @ P ) ) @ ( inf_inf_set_nat @ B4 @ ( collect_nat @ Q2 ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_Collect_mono
% 4.69/4.91 thf(fact_1068_Collect__mono__iff,axiom,
% 4.69/4.91 ! [P: ( produc3658429121746597890et_nat > $o ) > $o,Q2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 4.69/4.91 ( ( ord_le2965882846123202637_nat_o @ ( collec939566748876313656_nat_o @ P ) @ ( collec939566748876313656_nat_o @ Q2 ) )
% 4.69/4.91 = ( ! [X2: produc3658429121746597890et_nat > $o] :
% 4.69/4.91 ( ( P @ X2 )
% 4.69/4.91 => ( Q2 @ X2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Collect_mono_iff
% 4.69/4.91 thf(fact_1069_Collect__mono__iff,axiom,
% 4.69/4.91 ! [P: int > $o,Q2: int > $o] :
% 4.69/4.91 ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q2 ) )
% 4.69/4.91 = ( ! [X2: int] :
% 4.69/4.91 ( ( P @ X2 )
% 4.69/4.91 => ( Q2 @ X2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Collect_mono_iff
% 4.69/4.91 thf(fact_1070_Collect__mono__iff,axiom,
% 4.69/4.91 ! [P: $o > $o,Q2: $o > $o] :
% 4.69/4.91 ( ( ord_less_eq_set_o @ ( collect_o @ P ) @ ( collect_o @ Q2 ) )
% 4.69/4.91 = ( ! [X2: $o] :
% 4.69/4.91 ( ( P @ X2 )
% 4.69/4.91 => ( Q2 @ X2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Collect_mono_iff
% 4.69/4.91 thf(fact_1071_Collect__mono__iff,axiom,
% 4.69/4.91 ! [P: product_unit > $o,Q2: product_unit > $o] :
% 4.69/4.91 ( ( ord_le3507040750410214029t_unit @ ( collect_Product_unit @ P ) @ ( collect_Product_unit @ Q2 ) )
% 4.69/4.91 = ( ! [X2: product_unit] :
% 4.69/4.91 ( ( P @ X2 )
% 4.69/4.91 => ( Q2 @ X2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Collect_mono_iff
% 4.69/4.91 thf(fact_1072_Collect__mono__iff,axiom,
% 4.69/4.91 ! [P: nat > $o,Q2: nat > $o] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q2 ) )
% 4.69/4.91 = ( ! [X2: nat] :
% 4.69/4.91 ( ( P @ X2 )
% 4.69/4.91 => ( Q2 @ X2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Collect_mono_iff
% 4.69/4.91 thf(fact_1073_Un__left__commute,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat,C5: set_nat] :
% 4.69/4.91 ( ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ B4 @ C5 ) )
% 4.69/4.91 = ( sup_sup_set_nat @ B4 @ ( sup_sup_set_nat @ A @ C5 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_left_commute
% 4.69/4.91 thf(fact_1074_Un__Int__distrib2,axiom,
% 4.69/4.91 ! [B4: set_nat,C5: set_nat,A: set_nat] :
% 4.69/4.91 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ B4 @ C5 ) @ A )
% 4.69/4.91 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ B4 @ A ) @ ( sup_sup_set_nat @ C5 @ A ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_Int_distrib2
% 4.69/4.91 thf(fact_1075_Un__Int__assoc__eq,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat,C5: set_nat] :
% 4.69/4.91 ( ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ A @ B4 ) @ C5 )
% 4.69/4.91 = ( inf_inf_set_nat @ A @ ( sup_sup_set_nat @ B4 @ C5 ) ) )
% 4.69/4.91 = ( ord_less_eq_set_nat @ C5 @ A ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_Int_assoc_eq
% 4.69/4.91 thf(fact_1076_Int__left__absorb,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( inf_inf_set_nat @ A @ ( inf_inf_set_nat @ A @ B4 ) )
% 4.69/4.91 = ( inf_inf_set_nat @ A @ B4 ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_left_absorb
% 4.69/4.91 thf(fact_1077_Int__Un__distrib2,axiom,
% 4.69/4.91 ! [B4: set_nat,C5: set_nat,A: set_nat] :
% 4.69/4.91 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ B4 @ C5 ) @ A )
% 4.69/4.91 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ B4 @ A ) @ ( inf_inf_set_nat @ C5 @ A ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_Un_distrib2
% 4.69/4.91 thf(fact_1078_Un__left__absorb,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.91 = ( sup_sup_set_nat @ A @ B4 ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_left_absorb
% 4.69/4.91 thf(fact_1079_Un__Int__distrib,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat,C5: set_nat] :
% 4.69/4.91 ( ( sup_sup_set_nat @ A @ ( inf_inf_set_nat @ B4 @ C5 ) )
% 4.69/4.91 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ A @ B4 ) @ ( sup_sup_set_nat @ A @ C5 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_Int_distrib
% 4.69/4.91 thf(fact_1080_Int__Un__distrib,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat,C5: set_nat] :
% 4.69/4.91 ( ( inf_inf_set_nat @ A @ ( sup_sup_set_nat @ B4 @ C5 ) )
% 4.69/4.91 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ A @ B4 ) @ ( inf_inf_set_nat @ A @ C5 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_Un_distrib
% 4.69/4.91 thf(fact_1081_set__eq__subset,axiom,
% 4.69/4.91 ( ( ^ [Y4: set_nat,Z4: set_nat] : ( Y4 = Z4 ) )
% 4.69/4.91 = ( ^ [A3: set_nat,B7: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ A3 @ B7 )
% 4.69/4.91 & ( ord_less_eq_set_nat @ B7 @ A3 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % set_eq_subset
% 4.69/4.91 thf(fact_1082_antisym,axiom,
% 4.69/4.91 ! [A2: filter_nat,B: filter_nat] :
% 4.69/4.91 ( ( ord_le2510731241096832064er_nat @ A2 @ B )
% 4.69/4.91 => ( ( ord_le2510731241096832064er_nat @ B @ A2 )
% 4.69/4.91 => ( A2 = B ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % antisym
% 4.69/4.91 thf(fact_1083_antisym,axiom,
% 4.69/4.91 ! [A2: set_nat,B: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ A2 @ B )
% 4.69/4.91 => ( ( ord_less_eq_set_nat @ B @ A2 )
% 4.69/4.91 => ( A2 = B ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % antisym
% 4.69/4.91 thf(fact_1084_antisym,axiom,
% 4.69/4.91 ! [A2: rat,B: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/4.91 => ( ( ord_less_eq_rat @ B @ A2 )
% 4.69/4.91 => ( A2 = B ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % antisym
% 4.69/4.91 thf(fact_1085_antisym,axiom,
% 4.69/4.91 ! [A2: nat,B: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/4.91 => ( ( ord_less_eq_nat @ B @ A2 )
% 4.69/4.91 => ( A2 = B ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % antisym
% 4.69/4.91 thf(fact_1086_antisym,axiom,
% 4.69/4.91 ! [A2: int,B: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/4.91 => ( ( ord_less_eq_int @ B @ A2 )
% 4.69/4.91 => ( A2 = B ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % antisym
% 4.69/4.91 thf(fact_1087_subset__trans,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat,C5: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.91 => ( ( ord_less_eq_set_nat @ B4 @ C5 )
% 4.69/4.91 => ( ord_less_eq_set_nat @ A @ C5 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subset_trans
% 4.69/4.91 thf(fact_1088_subset__Un__eq,axiom,
% 4.69/4.91 ( ord_less_eq_set_nat
% 4.69/4.91 = ( ^ [A3: set_nat,B7: set_nat] :
% 4.69/4.91 ( ( sup_sup_set_nat @ A3 @ B7 )
% 4.69/4.91 = B7 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subset_Un_eq
% 4.69/4.91 thf(fact_1089_Un__Int__crazy,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat,C5: set_nat] :
% 4.69/4.91 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ ( inf_inf_set_nat @ A @ B4 ) @ ( inf_inf_set_nat @ B4 @ C5 ) ) @ ( inf_inf_set_nat @ C5 @ A ) )
% 4.69/4.91 = ( inf_inf_set_nat @ ( inf_inf_set_nat @ ( sup_sup_set_nat @ A @ B4 ) @ ( sup_sup_set_nat @ B4 @ C5 ) ) @ ( sup_sup_set_nat @ C5 @ A ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_Int_crazy
% 4.69/4.91 thf(fact_1090_Int__greatest,axiom,
% 4.69/4.91 ! [C5: set_nat,A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ C5 @ A )
% 4.69/4.91 => ( ( ord_less_eq_set_nat @ C5 @ B4 )
% 4.69/4.91 => ( ord_less_eq_set_nat @ C5 @ ( inf_inf_set_nat @ A @ B4 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_greatest
% 4.69/4.91 thf(fact_1091_Collect__mono,axiom,
% 4.69/4.91 ! [P: ( produc3658429121746597890et_nat > $o ) > $o,Q2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 4.69/4.91 ( ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.91 ( ( P @ X3 )
% 4.69/4.91 => ( Q2 @ X3 ) )
% 4.69/4.91 => ( ord_le2965882846123202637_nat_o @ ( collec939566748876313656_nat_o @ P ) @ ( collec939566748876313656_nat_o @ Q2 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Collect_mono
% 4.69/4.91 thf(fact_1092_Collect__mono,axiom,
% 4.69/4.91 ! [P: int > $o,Q2: int > $o] :
% 4.69/4.91 ( ! [X3: int] :
% 4.69/4.91 ( ( P @ X3 )
% 4.69/4.91 => ( Q2 @ X3 ) )
% 4.69/4.91 => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q2 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Collect_mono
% 4.69/4.91 thf(fact_1093_Collect__mono,axiom,
% 4.69/4.91 ! [P: $o > $o,Q2: $o > $o] :
% 4.69/4.91 ( ! [X3: $o] :
% 4.69/4.91 ( ( P @ X3 )
% 4.69/4.91 => ( Q2 @ X3 ) )
% 4.69/4.91 => ( ord_less_eq_set_o @ ( collect_o @ P ) @ ( collect_o @ Q2 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Collect_mono
% 4.69/4.91 thf(fact_1094_Collect__mono,axiom,
% 4.69/4.91 ! [P: product_unit > $o,Q2: product_unit > $o] :
% 4.69/4.91 ( ! [X3: product_unit] :
% 4.69/4.91 ( ( P @ X3 )
% 4.69/4.91 => ( Q2 @ X3 ) )
% 4.69/4.91 => ( ord_le3507040750410214029t_unit @ ( collect_Product_unit @ P ) @ ( collect_Product_unit @ Q2 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Collect_mono
% 4.69/4.91 thf(fact_1095_Collect__mono,axiom,
% 4.69/4.91 ! [P: nat > $o,Q2: nat > $o] :
% 4.69/4.91 ( ! [X3: nat] :
% 4.69/4.91 ( ( P @ X3 )
% 4.69/4.91 => ( Q2 @ X3 ) )
% 4.69/4.91 => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q2 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Collect_mono
% 4.69/4.91 thf(fact_1096_subset__refl,axiom,
% 4.69/4.91 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 4.69/4.91
% 4.69/4.91 % subset_refl
% 4.69/4.91 thf(fact_1097_Int__commute,axiom,
% 4.69/4.91 ( inf_inf_set_nat
% 4.69/4.91 = ( ^ [A3: set_nat,B7: set_nat] : ( inf_inf_set_nat @ B7 @ A3 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_commute
% 4.69/4.91 thf(fact_1098_Int__absorb2,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.91 => ( ( inf_inf_set_nat @ A @ B4 )
% 4.69/4.91 = A ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_absorb2
% 4.69/4.91 thf(fact_1099_Int__absorb1,axiom,
% 4.69/4.91 ! [B4: set_nat,A: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ B4 @ A )
% 4.69/4.91 => ( ( inf_inf_set_nat @ A @ B4 )
% 4.69/4.91 = B4 ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_absorb1
% 4.69/4.91 thf(fact_1100_subset__iff,axiom,
% 4.69/4.91 ( ord_le2965882846123202637_nat_o
% 4.69/4.91 = ( ^ [A3: set_Pr4532377907799695533_nat_o,B7: set_Pr4532377907799695533_nat_o] :
% 4.69/4.91 ! [T: produc3658429121746597890et_nat > $o] :
% 4.69/4.91 ( ( member6576561426505652726_nat_o @ T @ A3 )
% 4.69/4.91 => ( member6576561426505652726_nat_o @ T @ B7 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subset_iff
% 4.69/4.91 thf(fact_1101_subset__iff,axiom,
% 4.69/4.91 ( ord_less_eq_set_int
% 4.69/4.91 = ( ^ [A3: set_int,B7: set_int] :
% 4.69/4.91 ! [T: int] :
% 4.69/4.91 ( ( member_int @ T @ A3 )
% 4.69/4.91 => ( member_int @ T @ B7 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subset_iff
% 4.69/4.91 thf(fact_1102_subset__iff,axiom,
% 4.69/4.91 ( ord_less_eq_set_o
% 4.69/4.91 = ( ^ [A3: set_o,B7: set_o] :
% 4.69/4.91 ! [T: $o] :
% 4.69/4.91 ( ( member_o @ T @ A3 )
% 4.69/4.91 => ( member_o @ T @ B7 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subset_iff
% 4.69/4.91 thf(fact_1103_subset__iff,axiom,
% 4.69/4.91 ( ord_le3507040750410214029t_unit
% 4.69/4.91 = ( ^ [A3: set_Product_unit,B7: set_Product_unit] :
% 4.69/4.91 ! [T: product_unit] :
% 4.69/4.91 ( ( member_Product_unit @ T @ A3 )
% 4.69/4.91 => ( member_Product_unit @ T @ B7 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subset_iff
% 4.69/4.91 thf(fact_1104_subset__iff,axiom,
% 4.69/4.91 ( ord_less_eq_set_nat
% 4.69/4.91 = ( ^ [A3: set_nat,B7: set_nat] :
% 4.69/4.91 ! [T: nat] :
% 4.69/4.91 ( ( member_nat @ T @ A3 )
% 4.69/4.91 => ( member_nat @ T @ B7 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subset_iff
% 4.69/4.91 thf(fact_1105_subset__UnE,axiom,
% 4.69/4.91 ! [C5: set_nat,A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ C5 @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.91 => ~ ! [A7: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ A7 @ A )
% 4.69/4.91 => ! [B8: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ B8 @ B4 )
% 4.69/4.91 => ( C5
% 4.69/4.91 != ( sup_sup_set_nat @ A7 @ B8 ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subset_UnE
% 4.69/4.91 thf(fact_1106_equalityD2,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( A = B4 )
% 4.69/4.91 => ( ord_less_eq_set_nat @ B4 @ A ) ) ).
% 4.69/4.91
% 4.69/4.91 % equalityD2
% 4.69/4.91 thf(fact_1107_equalityD1,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( A = B4 )
% 4.69/4.91 => ( ord_less_eq_set_nat @ A @ B4 ) ) ).
% 4.69/4.91
% 4.69/4.91 % equalityD1
% 4.69/4.91 thf(fact_1108_Un__commute,axiom,
% 4.69/4.91 ( sup_sup_set_nat
% 4.69/4.91 = ( ^ [A3: set_nat,B7: set_nat] : ( sup_sup_set_nat @ B7 @ A3 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_commute
% 4.69/4.91 thf(fact_1109_Un__absorb2,axiom,
% 4.69/4.91 ! [B4: set_nat,A: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ B4 @ A )
% 4.69/4.91 => ( ( sup_sup_set_nat @ A @ B4 )
% 4.69/4.91 = A ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_absorb2
% 4.69/4.91 thf(fact_1110_Un__absorb1,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.91 => ( ( sup_sup_set_nat @ A @ B4 )
% 4.69/4.91 = B4 ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_absorb1
% 4.69/4.91 thf(fact_1111_Int__lower2,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B4 ) @ B4 ) ).
% 4.69/4.91
% 4.69/4.91 % Int_lower2
% 4.69/4.91 thf(fact_1112_Int__lower1,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B4 ) @ A ) ).
% 4.69/4.91
% 4.69/4.91 % Int_lower1
% 4.69/4.91 thf(fact_1113_Int__absorb,axiom,
% 4.69/4.91 ! [A: set_nat] :
% 4.69/4.91 ( ( inf_inf_set_nat @ A @ A )
% 4.69/4.91 = A ) ).
% 4.69/4.91
% 4.69/4.91 % Int_absorb
% 4.69/4.91 thf(fact_1114_subset__eq,axiom,
% 4.69/4.91 ( ord_le2965882846123202637_nat_o
% 4.69/4.91 = ( ^ [A3: set_Pr4532377907799695533_nat_o,B7: set_Pr4532377907799695533_nat_o] :
% 4.69/4.91 ! [X2: produc3658429121746597890et_nat > $o] :
% 4.69/4.91 ( ( member6576561426505652726_nat_o @ X2 @ A3 )
% 4.69/4.91 => ( member6576561426505652726_nat_o @ X2 @ B7 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subset_eq
% 4.69/4.91 thf(fact_1115_subset__eq,axiom,
% 4.69/4.91 ( ord_less_eq_set_int
% 4.69/4.91 = ( ^ [A3: set_int,B7: set_int] :
% 4.69/4.91 ! [X2: int] :
% 4.69/4.91 ( ( member_int @ X2 @ A3 )
% 4.69/4.91 => ( member_int @ X2 @ B7 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subset_eq
% 4.69/4.91 thf(fact_1116_subset__eq,axiom,
% 4.69/4.91 ( ord_less_eq_set_o
% 4.69/4.91 = ( ^ [A3: set_o,B7: set_o] :
% 4.69/4.91 ! [X2: $o] :
% 4.69/4.91 ( ( member_o @ X2 @ A3 )
% 4.69/4.91 => ( member_o @ X2 @ B7 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subset_eq
% 4.69/4.91 thf(fact_1117_subset__eq,axiom,
% 4.69/4.91 ( ord_le3507040750410214029t_unit
% 4.69/4.91 = ( ^ [A3: set_Product_unit,B7: set_Product_unit] :
% 4.69/4.91 ! [X2: product_unit] :
% 4.69/4.91 ( ( member_Product_unit @ X2 @ A3 )
% 4.69/4.91 => ( member_Product_unit @ X2 @ B7 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subset_eq
% 4.69/4.91 thf(fact_1118_subset__eq,axiom,
% 4.69/4.91 ( ord_less_eq_set_nat
% 4.69/4.91 = ( ^ [A3: set_nat,B7: set_nat] :
% 4.69/4.91 ! [X2: nat] :
% 4.69/4.91 ( ( member_nat @ X2 @ A3 )
% 4.69/4.91 => ( member_nat @ X2 @ B7 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subset_eq
% 4.69/4.91 thf(fact_1119_equalityE,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( A = B4 )
% 4.69/4.91 => ~ ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.91 => ~ ( ord_less_eq_set_nat @ B4 @ A ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % equalityE
% 4.69/4.91 thf(fact_1120_Un__upper2,axiom,
% 4.69/4.91 ! [B4: set_nat,A: set_nat] : ( ord_less_eq_set_nat @ B4 @ ( sup_sup_set_nat @ A @ B4 ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_upper2
% 4.69/4.91 thf(fact_1121_Un__upper1,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat] : ( ord_less_eq_set_nat @ A @ ( sup_sup_set_nat @ A @ B4 ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_upper1
% 4.69/4.91 thf(fact_1122_Un__absorb,axiom,
% 4.69/4.91 ! [A: set_nat] :
% 4.69/4.91 ( ( sup_sup_set_nat @ A @ A )
% 4.69/4.91 = A ) ).
% 4.69/4.91
% 4.69/4.91 % Un_absorb
% 4.69/4.91 thf(fact_1123_Int__assoc,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat,C5: set_nat] :
% 4.69/4.91 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A @ B4 ) @ C5 )
% 4.69/4.91 = ( inf_inf_set_nat @ A @ ( inf_inf_set_nat @ B4 @ C5 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_assoc
% 4.69/4.91 thf(fact_1124_Un__least,axiom,
% 4.69/4.91 ! [A: set_nat,C5: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ A @ C5 )
% 4.69/4.91 => ( ( ord_less_eq_set_nat @ B4 @ C5 )
% 4.69/4.91 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B4 ) @ C5 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_least
% 4.69/4.91 thf(fact_1125_Un__assoc,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat,C5: set_nat] :
% 4.69/4.91 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A @ B4 ) @ C5 )
% 4.69/4.91 = ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ B4 @ C5 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_assoc
% 4.69/4.91 thf(fact_1126_Int__mono,axiom,
% 4.69/4.91 ! [A: set_nat,C5: set_nat,B4: set_nat,D3: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ A @ C5 )
% 4.69/4.91 => ( ( ord_less_eq_set_nat @ B4 @ D3 )
% 4.69/4.91 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B4 ) @ ( inf_inf_set_nat @ C5 @ D3 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Int_mono
% 4.69/4.91 thf(fact_1127_subsetD,axiom,
% 4.69/4.91 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o,C: produc3658429121746597890et_nat > $o] :
% 4.69/4.91 ( ( ord_le2965882846123202637_nat_o @ A @ B4 )
% 4.69/4.91 => ( ( member6576561426505652726_nat_o @ C @ A )
% 4.69/4.91 => ( member6576561426505652726_nat_o @ C @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subsetD
% 4.69/4.91 thf(fact_1128_subsetD,axiom,
% 4.69/4.91 ! [A: set_int,B4: set_int,C: int] :
% 4.69/4.91 ( ( ord_less_eq_set_int @ A @ B4 )
% 4.69/4.91 => ( ( member_int @ C @ A )
% 4.69/4.91 => ( member_int @ C @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subsetD
% 4.69/4.91 thf(fact_1129_subsetD,axiom,
% 4.69/4.91 ! [A: set_o,B4: set_o,C: $o] :
% 4.69/4.91 ( ( ord_less_eq_set_o @ A @ B4 )
% 4.69/4.91 => ( ( member_o @ C @ A )
% 4.69/4.91 => ( member_o @ C @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subsetD
% 4.69/4.91 thf(fact_1130_subsetD,axiom,
% 4.69/4.91 ! [A: set_Product_unit,B4: set_Product_unit,C: product_unit] :
% 4.69/4.91 ( ( ord_le3507040750410214029t_unit @ A @ B4 )
% 4.69/4.91 => ( ( member_Product_unit @ C @ A )
% 4.69/4.91 => ( member_Product_unit @ C @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subsetD
% 4.69/4.91 thf(fact_1131_subsetD,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat,C: nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.91 => ( ( member_nat @ C @ A )
% 4.69/4.91 => ( member_nat @ C @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % subsetD
% 4.69/4.91 thf(fact_1132_in__mono,axiom,
% 4.69/4.91 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/4.91 ( ( ord_le2965882846123202637_nat_o @ A @ B4 )
% 4.69/4.91 => ( ( member6576561426505652726_nat_o @ X @ A )
% 4.69/4.91 => ( member6576561426505652726_nat_o @ X @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % in_mono
% 4.69/4.91 thf(fact_1133_in__mono,axiom,
% 4.69/4.91 ! [A: set_int,B4: set_int,X: int] :
% 4.69/4.91 ( ( ord_less_eq_set_int @ A @ B4 )
% 4.69/4.91 => ( ( member_int @ X @ A )
% 4.69/4.91 => ( member_int @ X @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % in_mono
% 4.69/4.91 thf(fact_1134_in__mono,axiom,
% 4.69/4.91 ! [A: set_o,B4: set_o,X: $o] :
% 4.69/4.91 ( ( ord_less_eq_set_o @ A @ B4 )
% 4.69/4.91 => ( ( member_o @ X @ A )
% 4.69/4.91 => ( member_o @ X @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % in_mono
% 4.69/4.91 thf(fact_1135_in__mono,axiom,
% 4.69/4.91 ! [A: set_Product_unit,B4: set_Product_unit,X: product_unit] :
% 4.69/4.91 ( ( ord_le3507040750410214029t_unit @ A @ B4 )
% 4.69/4.91 => ( ( member_Product_unit @ X @ A )
% 4.69/4.91 => ( member_Product_unit @ X @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % in_mono
% 4.69/4.91 thf(fact_1136_in__mono,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat,X: nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.91 => ( ( member_nat @ X @ A )
% 4.69/4.91 => ( member_nat @ X @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % in_mono
% 4.69/4.91 thf(fact_1137_ball__Un,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat,P: nat > $o] :
% 4.69/4.91 ( ( ! [X2: nat] :
% 4.69/4.91 ( ( member_nat @ X2 @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.91 => ( P @ X2 ) ) )
% 4.69/4.91 = ( ! [X2: nat] :
% 4.69/4.91 ( ( member_nat @ X2 @ A )
% 4.69/4.91 => ( P @ X2 ) )
% 4.69/4.91 & ! [X2: nat] :
% 4.69/4.91 ( ( member_nat @ X2 @ B4 )
% 4.69/4.91 => ( P @ X2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ball_Un
% 4.69/4.91 thf(fact_1138_Un__mono,axiom,
% 4.69/4.91 ! [A: set_nat,C5: set_nat,B4: set_nat,D3: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ A @ C5 )
% 4.69/4.91 => ( ( ord_less_eq_set_nat @ B4 @ D3 )
% 4.69/4.91 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B4 ) @ ( sup_sup_set_nat @ C5 @ D3 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Un_mono
% 4.69/4.91 thf(fact_1139_bex__Un,axiom,
% 4.69/4.91 ! [A: set_nat,B4: set_nat,P: nat > $o] :
% 4.69/4.91 ( ( ? [X2: nat] :
% 4.69/4.91 ( ( member_nat @ X2 @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.91 & ( P @ X2 ) ) )
% 4.69/4.91 = ( ? [X2: nat] :
% 4.69/4.91 ( ( member_nat @ X2 @ A )
% 4.69/4.91 & ( P @ X2 ) )
% 4.69/4.91 | ? [X2: nat] :
% 4.69/4.91 ( ( member_nat @ X2 @ B4 )
% 4.69/4.91 & ( P @ X2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % bex_Un
% 4.69/4.91 thf(fact_1140_IntD2,axiom,
% 4.69/4.91 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.91 ( ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A @ B4 ) )
% 4.69/4.91 => ( member6576561426505652726_nat_o @ C @ B4 ) ) ).
% 4.69/4.91
% 4.69/4.91 % IntD2
% 4.69/4.91 thf(fact_1141_IntD2,axiom,
% 4.69/4.91 ! [C: int,A: set_int,B4: set_int] :
% 4.69/4.91 ( ( member_int @ C @ ( inf_inf_set_int @ A @ B4 ) )
% 4.69/4.91 => ( member_int @ C @ B4 ) ) ).
% 4.69/4.91
% 4.69/4.91 % IntD2
% 4.69/4.91 thf(fact_1142_IntD2,axiom,
% 4.69/4.91 ! [C: $o,A: set_o,B4: set_o] :
% 4.69/4.91 ( ( member_o @ C @ ( inf_inf_set_o @ A @ B4 ) )
% 4.69/4.91 => ( member_o @ C @ B4 ) ) ).
% 4.69/4.91
% 4.69/4.91 % IntD2
% 4.69/4.91 thf(fact_1143_IntD2,axiom,
% 4.69/4.91 ! [C: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.91 ( ( member_Product_unit @ C @ ( inf_in4660618365625256667t_unit @ A @ B4 ) )
% 4.69/4.91 => ( member_Product_unit @ C @ B4 ) ) ).
% 4.69/4.91
% 4.69/4.91 % IntD2
% 4.69/4.91 thf(fact_1144_IntD2,axiom,
% 4.69/4.91 ! [C: nat,A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B4 ) )
% 4.69/4.91 => ( member_nat @ C @ B4 ) ) ).
% 4.69/4.91
% 4.69/4.91 % IntD2
% 4.69/4.91 thf(fact_1145_IntD1,axiom,
% 4.69/4.91 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.91 ( ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A @ B4 ) )
% 4.69/4.91 => ( member6576561426505652726_nat_o @ C @ A ) ) ).
% 4.69/4.91
% 4.69/4.91 % IntD1
% 4.69/4.91 thf(fact_1146_IntD1,axiom,
% 4.69/4.91 ! [C: int,A: set_int,B4: set_int] :
% 4.69/4.91 ( ( member_int @ C @ ( inf_inf_set_int @ A @ B4 ) )
% 4.69/4.91 => ( member_int @ C @ A ) ) ).
% 4.69/4.91
% 4.69/4.91 % IntD1
% 4.69/4.91 thf(fact_1147_IntD1,axiom,
% 4.69/4.91 ! [C: $o,A: set_o,B4: set_o] :
% 4.69/4.91 ( ( member_o @ C @ ( inf_inf_set_o @ A @ B4 ) )
% 4.69/4.91 => ( member_o @ C @ A ) ) ).
% 4.69/4.91
% 4.69/4.91 % IntD1
% 4.69/4.91 thf(fact_1148_IntD1,axiom,
% 4.69/4.91 ! [C: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.91 ( ( member_Product_unit @ C @ ( inf_in4660618365625256667t_unit @ A @ B4 ) )
% 4.69/4.91 => ( member_Product_unit @ C @ A ) ) ).
% 4.69/4.91
% 4.69/4.91 % IntD1
% 4.69/4.91 thf(fact_1149_IntD1,axiom,
% 4.69/4.91 ! [C: nat,A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B4 ) )
% 4.69/4.91 => ( member_nat @ C @ A ) ) ).
% 4.69/4.91
% 4.69/4.91 % IntD1
% 4.69/4.91 thf(fact_1150_UnI2,axiom,
% 4.69/4.91 ! [C: produc3658429121746597890et_nat > $o,B4: set_Pr4532377907799695533_nat_o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.91 ( ( member6576561426505652726_nat_o @ C @ B4 )
% 4.69/4.91 => ( member6576561426505652726_nat_o @ C @ ( sup_su5209123915105501825_nat_o @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % UnI2
% 4.69/4.91 thf(fact_1151_UnI2,axiom,
% 4.69/4.91 ! [C: int,B4: set_int,A: set_int] :
% 4.69/4.91 ( ( member_int @ C @ B4 )
% 4.69/4.91 => ( member_int @ C @ ( sup_sup_set_int @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % UnI2
% 4.69/4.91 thf(fact_1152_UnI2,axiom,
% 4.69/4.91 ! [C: $o,B4: set_o,A: set_o] :
% 4.69/4.91 ( ( member_o @ C @ B4 )
% 4.69/4.91 => ( member_o @ C @ ( sup_sup_set_o @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % UnI2
% 4.69/4.91 thf(fact_1153_UnI2,axiom,
% 4.69/4.91 ! [C: product_unit,B4: set_Product_unit,A: set_Product_unit] :
% 4.69/4.91 ( ( member_Product_unit @ C @ B4 )
% 4.69/4.91 => ( member_Product_unit @ C @ ( sup_su793286257634532545t_unit @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % UnI2
% 4.69/4.91 thf(fact_1154_UnI2,axiom,
% 4.69/4.91 ! [C: nat,B4: set_nat,A: set_nat] :
% 4.69/4.91 ( ( member_nat @ C @ B4 )
% 4.69/4.91 => ( member_nat @ C @ ( sup_sup_set_nat @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % UnI2
% 4.69/4.91 thf(fact_1155_UnI1,axiom,
% 4.69/4.91 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.91 ( ( member6576561426505652726_nat_o @ C @ A )
% 4.69/4.91 => ( member6576561426505652726_nat_o @ C @ ( sup_su5209123915105501825_nat_o @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % UnI1
% 4.69/4.91 thf(fact_1156_UnI1,axiom,
% 4.69/4.91 ! [C: int,A: set_int,B4: set_int] :
% 4.69/4.91 ( ( member_int @ C @ A )
% 4.69/4.91 => ( member_int @ C @ ( sup_sup_set_int @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % UnI1
% 4.69/4.91 thf(fact_1157_UnI1,axiom,
% 4.69/4.91 ! [C: $o,A: set_o,B4: set_o] :
% 4.69/4.91 ( ( member_o @ C @ A )
% 4.69/4.91 => ( member_o @ C @ ( sup_sup_set_o @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % UnI1
% 4.69/4.91 thf(fact_1158_UnI1,axiom,
% 4.69/4.91 ! [C: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.91 ( ( member_Product_unit @ C @ A )
% 4.69/4.91 => ( member_Product_unit @ C @ ( sup_su793286257634532545t_unit @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % UnI1
% 4.69/4.91 thf(fact_1159_UnI1,axiom,
% 4.69/4.91 ! [C: nat,A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( member_nat @ C @ A )
% 4.69/4.91 => ( member_nat @ C @ ( sup_sup_set_nat @ A @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % UnI1
% 4.69/4.91 thf(fact_1160_IntE,axiom,
% 4.69/4.91 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.91 ( ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A @ B4 ) )
% 4.69/4.91 => ~ ( ( member6576561426505652726_nat_o @ C @ A )
% 4.69/4.91 => ~ ( member6576561426505652726_nat_o @ C @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % IntE
% 4.69/4.91 thf(fact_1161_IntE,axiom,
% 4.69/4.91 ! [C: int,A: set_int,B4: set_int] :
% 4.69/4.91 ( ( member_int @ C @ ( inf_inf_set_int @ A @ B4 ) )
% 4.69/4.91 => ~ ( ( member_int @ C @ A )
% 4.69/4.91 => ~ ( member_int @ C @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % IntE
% 4.69/4.91 thf(fact_1162_IntE,axiom,
% 4.69/4.91 ! [C: $o,A: set_o,B4: set_o] :
% 4.69/4.91 ( ( member_o @ C @ ( inf_inf_set_o @ A @ B4 ) )
% 4.69/4.91 => ~ ( ( member_o @ C @ A )
% 4.69/4.91 => ~ ( member_o @ C @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % IntE
% 4.69/4.91 thf(fact_1163_IntE,axiom,
% 4.69/4.91 ! [C: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.91 ( ( member_Product_unit @ C @ ( inf_in4660618365625256667t_unit @ A @ B4 ) )
% 4.69/4.91 => ~ ( ( member_Product_unit @ C @ A )
% 4.69/4.91 => ~ ( member_Product_unit @ C @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % IntE
% 4.69/4.91 thf(fact_1164_IntE,axiom,
% 4.69/4.91 ! [C: nat,A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( member_nat @ C @ ( inf_inf_set_nat @ A @ B4 ) )
% 4.69/4.91 => ~ ( ( member_nat @ C @ A )
% 4.69/4.91 => ~ ( member_nat @ C @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % IntE
% 4.69/4.91 thf(fact_1165_UnE,axiom,
% 4.69/4.91 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.91 ( ( member6576561426505652726_nat_o @ C @ ( sup_su5209123915105501825_nat_o @ A @ B4 ) )
% 4.69/4.91 => ( ~ ( member6576561426505652726_nat_o @ C @ A )
% 4.69/4.91 => ( member6576561426505652726_nat_o @ C @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % UnE
% 4.69/4.91 thf(fact_1166_UnE,axiom,
% 4.69/4.91 ! [C: int,A: set_int,B4: set_int] :
% 4.69/4.91 ( ( member_int @ C @ ( sup_sup_set_int @ A @ B4 ) )
% 4.69/4.91 => ( ~ ( member_int @ C @ A )
% 4.69/4.91 => ( member_int @ C @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % UnE
% 4.69/4.91 thf(fact_1167_UnE,axiom,
% 4.69/4.91 ! [C: $o,A: set_o,B4: set_o] :
% 4.69/4.91 ( ( member_o @ C @ ( sup_sup_set_o @ A @ B4 ) )
% 4.69/4.91 => ( ~ ( member_o @ C @ A )
% 4.69/4.91 => ( member_o @ C @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % UnE
% 4.69/4.91 thf(fact_1168_UnE,axiom,
% 4.69/4.91 ! [C: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.91 ( ( member_Product_unit @ C @ ( sup_su793286257634532545t_unit @ A @ B4 ) )
% 4.69/4.91 => ( ~ ( member_Product_unit @ C @ A )
% 4.69/4.91 => ( member_Product_unit @ C @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % UnE
% 4.69/4.91 thf(fact_1169_UnE,axiom,
% 4.69/4.91 ! [C: nat,A: set_nat,B4: set_nat] :
% 4.69/4.91 ( ( member_nat @ C @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.91 => ( ~ ( member_nat @ C @ A )
% 4.69/4.91 => ( member_nat @ C @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % UnE
% 4.69/4.91 thf(fact_1170_dual__order_Otrans,axiom,
% 4.69/4.91 ! [B: filter_nat,A2: filter_nat,C: filter_nat] :
% 4.69/4.91 ( ( ord_le2510731241096832064er_nat @ B @ A2 )
% 4.69/4.91 => ( ( ord_le2510731241096832064er_nat @ C @ B )
% 4.69/4.91 => ( ord_le2510731241096832064er_nat @ C @ A2 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % dual_order.trans
% 4.69/4.91 thf(fact_1171_dual__order_Otrans,axiom,
% 4.69/4.91 ! [B: set_nat,A2: set_nat,C: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ B @ A2 )
% 4.69/4.91 => ( ( ord_less_eq_set_nat @ C @ B )
% 4.69/4.91 => ( ord_less_eq_set_nat @ C @ A2 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % dual_order.trans
% 4.69/4.91 thf(fact_1172_dual__order_Otrans,axiom,
% 4.69/4.91 ! [B: rat,A2: rat,C: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ B @ A2 )
% 4.69/4.91 => ( ( ord_less_eq_rat @ C @ B )
% 4.69/4.91 => ( ord_less_eq_rat @ C @ A2 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % dual_order.trans
% 4.69/4.91 thf(fact_1173_dual__order_Otrans,axiom,
% 4.69/4.91 ! [B: nat,A2: nat,C: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ B @ A2 )
% 4.69/4.91 => ( ( ord_less_eq_nat @ C @ B )
% 4.69/4.91 => ( ord_less_eq_nat @ C @ A2 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % dual_order.trans
% 4.69/4.91 thf(fact_1174_dual__order_Otrans,axiom,
% 4.69/4.91 ! [B: int,A2: int,C: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ B @ A2 )
% 4.69/4.91 => ( ( ord_less_eq_int @ C @ B )
% 4.69/4.91 => ( ord_less_eq_int @ C @ A2 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % dual_order.trans
% 4.69/4.91 thf(fact_1175_dual__order_Oantisym,axiom,
% 4.69/4.91 ! [B: filter_nat,A2: filter_nat] :
% 4.69/4.91 ( ( ord_le2510731241096832064er_nat @ B @ A2 )
% 4.69/4.91 => ( ( ord_le2510731241096832064er_nat @ A2 @ B )
% 4.69/4.91 => ( A2 = B ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % dual_order.antisym
% 4.69/4.91 thf(fact_1176_dual__order_Oantisym,axiom,
% 4.69/4.91 ! [B: set_nat,A2: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ B @ A2 )
% 4.69/4.91 => ( ( ord_less_eq_set_nat @ A2 @ B )
% 4.69/4.91 => ( A2 = B ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % dual_order.antisym
% 4.69/4.91 thf(fact_1177_dual__order_Oantisym,axiom,
% 4.69/4.91 ! [B: rat,A2: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ B @ A2 )
% 4.69/4.91 => ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/4.91 => ( A2 = B ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % dual_order.antisym
% 4.69/4.91 thf(fact_1178_dual__order_Oantisym,axiom,
% 4.69/4.91 ! [B: nat,A2: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ B @ A2 )
% 4.69/4.91 => ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/4.91 => ( A2 = B ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % dual_order.antisym
% 4.69/4.91 thf(fact_1179_dual__order_Oantisym,axiom,
% 4.69/4.91 ! [B: int,A2: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ B @ A2 )
% 4.69/4.91 => ( ( ord_less_eq_int @ A2 @ B )
% 4.69/4.91 => ( A2 = B ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % dual_order.antisym
% 4.69/4.91 thf(fact_1180_dual__order_Oeq__iff,axiom,
% 4.69/4.91 ( ( ^ [Y4: filter_nat,Z4: filter_nat] : ( Y4 = Z4 ) )
% 4.69/4.91 = ( ^ [A6: filter_nat,B6: filter_nat] :
% 4.69/4.91 ( ( ord_le2510731241096832064er_nat @ B6 @ A6 )
% 4.69/4.91 & ( ord_le2510731241096832064er_nat @ A6 @ B6 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % dual_order.eq_iff
% 4.69/4.91 thf(fact_1181_dual__order_Oeq__iff,axiom,
% 4.69/4.91 ( ( ^ [Y4: set_nat,Z4: set_nat] : ( Y4 = Z4 ) )
% 4.69/4.91 = ( ^ [A6: set_nat,B6: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ B6 @ A6 )
% 4.69/4.91 & ( ord_less_eq_set_nat @ A6 @ B6 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % dual_order.eq_iff
% 4.69/4.91 thf(fact_1182_dual__order_Oeq__iff,axiom,
% 4.69/4.91 ( ( ^ [Y4: rat,Z4: rat] : ( Y4 = Z4 ) )
% 4.69/4.91 = ( ^ [A6: rat,B6: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ B6 @ A6 )
% 4.69/4.91 & ( ord_less_eq_rat @ A6 @ B6 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % dual_order.eq_iff
% 4.69/4.91 thf(fact_1183_dual__order_Oeq__iff,axiom,
% 4.69/4.91 ( ( ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 ) )
% 4.69/4.91 = ( ^ [A6: nat,B6: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ B6 @ A6 )
% 4.69/4.91 & ( ord_less_eq_nat @ A6 @ B6 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % dual_order.eq_iff
% 4.69/4.91 thf(fact_1184_dual__order_Oeq__iff,axiom,
% 4.69/4.91 ( ( ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 4.69/4.91 = ( ^ [A6: int,B6: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ B6 @ A6 )
% 4.69/4.91 & ( ord_less_eq_int @ A6 @ B6 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % dual_order.eq_iff
% 4.69/4.91 thf(fact_1185_linorder__wlog,axiom,
% 4.69/4.91 ! [P: rat > rat > $o,A2: rat,B: rat] :
% 4.69/4.91 ( ! [A4: rat,B2: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ A4 @ B2 )
% 4.69/4.91 => ( P @ A4 @ B2 ) )
% 4.69/4.91 => ( ! [A4: rat,B2: rat] :
% 4.69/4.91 ( ( P @ B2 @ A4 )
% 4.69/4.91 => ( P @ A4 @ B2 ) )
% 4.69/4.91 => ( P @ A2 @ B ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % linorder_wlog
% 4.69/4.91 thf(fact_1186_linorder__wlog,axiom,
% 4.69/4.91 ! [P: nat > nat > $o,A2: nat,B: nat] :
% 4.69/4.91 ( ! [A4: nat,B2: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ A4 @ B2 )
% 4.69/4.91 => ( P @ A4 @ B2 ) )
% 4.69/4.91 => ( ! [A4: nat,B2: nat] :
% 4.69/4.91 ( ( P @ B2 @ A4 )
% 4.69/4.91 => ( P @ A4 @ B2 ) )
% 4.69/4.91 => ( P @ A2 @ B ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % linorder_wlog
% 4.69/4.91 thf(fact_1187_linorder__wlog,axiom,
% 4.69/4.91 ! [P: int > int > $o,A2: int,B: int] :
% 4.69/4.91 ( ! [A4: int,B2: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ A4 @ B2 )
% 4.69/4.91 => ( P @ A4 @ B2 ) )
% 4.69/4.91 => ( ! [A4: int,B2: int] :
% 4.69/4.91 ( ( P @ B2 @ A4 )
% 4.69/4.91 => ( P @ A4 @ B2 ) )
% 4.69/4.91 => ( P @ A2 @ B ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % linorder_wlog
% 4.69/4.91 thf(fact_1188_order__trans,axiom,
% 4.69/4.91 ! [X: filter_nat,Y: filter_nat,Z: filter_nat] :
% 4.69/4.91 ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 4.69/4.91 => ( ( ord_le2510731241096832064er_nat @ Y @ Z )
% 4.69/4.91 => ( ord_le2510731241096832064er_nat @ X @ Z ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_trans
% 4.69/4.91 thf(fact_1189_order__trans,axiom,
% 4.69/4.91 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ X @ Y )
% 4.69/4.91 => ( ( ord_less_eq_set_nat @ Y @ Z )
% 4.69/4.91 => ( ord_less_eq_set_nat @ X @ Z ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_trans
% 4.69/4.91 thf(fact_1190_order__trans,axiom,
% 4.69/4.91 ! [X: rat,Y: rat,Z: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ X @ Y )
% 4.69/4.91 => ( ( ord_less_eq_rat @ Y @ Z )
% 4.69/4.91 => ( ord_less_eq_rat @ X @ Z ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_trans
% 4.69/4.91 thf(fact_1191_order__trans,axiom,
% 4.69/4.91 ! [X: nat,Y: nat,Z: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ X @ Y )
% 4.69/4.91 => ( ( ord_less_eq_nat @ Y @ Z )
% 4.69/4.91 => ( ord_less_eq_nat @ X @ Z ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_trans
% 4.69/4.91 thf(fact_1192_order__trans,axiom,
% 4.69/4.91 ! [X: int,Y: int,Z: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ X @ Y )
% 4.69/4.91 => ( ( ord_less_eq_int @ Y @ Z )
% 4.69/4.91 => ( ord_less_eq_int @ X @ Z ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_trans
% 4.69/4.91 thf(fact_1193_order_Otrans,axiom,
% 4.69/4.91 ! [A2: filter_nat,B: filter_nat,C: filter_nat] :
% 4.69/4.91 ( ( ord_le2510731241096832064er_nat @ A2 @ B )
% 4.69/4.91 => ( ( ord_le2510731241096832064er_nat @ B @ C )
% 4.69/4.91 => ( ord_le2510731241096832064er_nat @ A2 @ C ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order.trans
% 4.69/4.91 thf(fact_1194_order_Otrans,axiom,
% 4.69/4.91 ! [A2: set_nat,B: set_nat,C: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ A2 @ B )
% 4.69/4.91 => ( ( ord_less_eq_set_nat @ B @ C )
% 4.69/4.91 => ( ord_less_eq_set_nat @ A2 @ C ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order.trans
% 4.69/4.91 thf(fact_1195_order_Otrans,axiom,
% 4.69/4.91 ! [A2: rat,B: rat,C: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/4.91 => ( ( ord_less_eq_rat @ B @ C )
% 4.69/4.91 => ( ord_less_eq_rat @ A2 @ C ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order.trans
% 4.69/4.91 thf(fact_1196_order_Otrans,axiom,
% 4.69/4.91 ! [A2: nat,B: nat,C: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/4.91 => ( ( ord_less_eq_nat @ B @ C )
% 4.69/4.91 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order.trans
% 4.69/4.91 thf(fact_1197_order_Otrans,axiom,
% 4.69/4.91 ! [A2: int,B: int,C: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/4.91 => ( ( ord_less_eq_int @ B @ C )
% 4.69/4.91 => ( ord_less_eq_int @ A2 @ C ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order.trans
% 4.69/4.91 thf(fact_1198_order__antisym,axiom,
% 4.69/4.91 ! [X: filter_nat,Y: filter_nat] :
% 4.69/4.91 ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 4.69/4.91 => ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 4.69/4.91 => ( X = Y ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_antisym
% 4.69/4.91 thf(fact_1199_order__antisym,axiom,
% 4.69/4.91 ! [X: set_nat,Y: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ X @ Y )
% 4.69/4.91 => ( ( ord_less_eq_set_nat @ Y @ X )
% 4.69/4.91 => ( X = Y ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_antisym
% 4.69/4.91 thf(fact_1200_order__antisym,axiom,
% 4.69/4.91 ! [X: rat,Y: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ X @ Y )
% 4.69/4.91 => ( ( ord_less_eq_rat @ Y @ X )
% 4.69/4.91 => ( X = Y ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_antisym
% 4.69/4.91 thf(fact_1201_order__antisym,axiom,
% 4.69/4.91 ! [X: nat,Y: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ X @ Y )
% 4.69/4.91 => ( ( ord_less_eq_nat @ Y @ X )
% 4.69/4.91 => ( X = Y ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_antisym
% 4.69/4.91 thf(fact_1202_order__antisym,axiom,
% 4.69/4.91 ! [X: int,Y: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ X @ Y )
% 4.69/4.91 => ( ( ord_less_eq_int @ Y @ X )
% 4.69/4.91 => ( X = Y ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_antisym
% 4.69/4.91 thf(fact_1203_ord__le__eq__trans,axiom,
% 4.69/4.91 ! [A2: filter_nat,B: filter_nat,C: filter_nat] :
% 4.69/4.91 ( ( ord_le2510731241096832064er_nat @ A2 @ B )
% 4.69/4.91 => ( ( B = C )
% 4.69/4.91 => ( ord_le2510731241096832064er_nat @ A2 @ C ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_le_eq_trans
% 4.69/4.91 thf(fact_1204_ord__le__eq__trans,axiom,
% 4.69/4.91 ! [A2: set_nat,B: set_nat,C: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ A2 @ B )
% 4.69/4.91 => ( ( B = C )
% 4.69/4.91 => ( ord_less_eq_set_nat @ A2 @ C ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_le_eq_trans
% 4.69/4.91 thf(fact_1205_ord__le__eq__trans,axiom,
% 4.69/4.91 ! [A2: rat,B: rat,C: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/4.91 => ( ( B = C )
% 4.69/4.91 => ( ord_less_eq_rat @ A2 @ C ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_le_eq_trans
% 4.69/4.91 thf(fact_1206_ord__le__eq__trans,axiom,
% 4.69/4.91 ! [A2: nat,B: nat,C: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/4.91 => ( ( B = C )
% 4.69/4.91 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_le_eq_trans
% 4.69/4.91 thf(fact_1207_ord__le__eq__trans,axiom,
% 4.69/4.91 ! [A2: int,B: int,C: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/4.91 => ( ( B = C )
% 4.69/4.91 => ( ord_less_eq_int @ A2 @ C ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_le_eq_trans
% 4.69/4.91 thf(fact_1208_ord__eq__le__trans,axiom,
% 4.69/4.91 ! [A2: filter_nat,B: filter_nat,C: filter_nat] :
% 4.69/4.91 ( ( A2 = B )
% 4.69/4.91 => ( ( ord_le2510731241096832064er_nat @ B @ C )
% 4.69/4.91 => ( ord_le2510731241096832064er_nat @ A2 @ C ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_eq_le_trans
% 4.69/4.91 thf(fact_1209_ord__eq__le__trans,axiom,
% 4.69/4.91 ! [A2: set_nat,B: set_nat,C: set_nat] :
% 4.69/4.91 ( ( A2 = B )
% 4.69/4.91 => ( ( ord_less_eq_set_nat @ B @ C )
% 4.69/4.91 => ( ord_less_eq_set_nat @ A2 @ C ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_eq_le_trans
% 4.69/4.91 thf(fact_1210_ord__eq__le__trans,axiom,
% 4.69/4.91 ! [A2: rat,B: rat,C: rat] :
% 4.69/4.91 ( ( A2 = B )
% 4.69/4.91 => ( ( ord_less_eq_rat @ B @ C )
% 4.69/4.91 => ( ord_less_eq_rat @ A2 @ C ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_eq_le_trans
% 4.69/4.91 thf(fact_1211_ord__eq__le__trans,axiom,
% 4.69/4.91 ! [A2: nat,B: nat,C: nat] :
% 4.69/4.91 ( ( A2 = B )
% 4.69/4.91 => ( ( ord_less_eq_nat @ B @ C )
% 4.69/4.91 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_eq_le_trans
% 4.69/4.91 thf(fact_1212_ord__eq__le__trans,axiom,
% 4.69/4.91 ! [A2: int,B: int,C: int] :
% 4.69/4.91 ( ( A2 = B )
% 4.69/4.91 => ( ( ord_less_eq_int @ B @ C )
% 4.69/4.91 => ( ord_less_eq_int @ A2 @ C ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % ord_eq_le_trans
% 4.69/4.91 thf(fact_1213_order__class_Oorder__eq__iff,axiom,
% 4.69/4.91 ( ( ^ [Y4: filter_nat,Z4: filter_nat] : ( Y4 = Z4 ) )
% 4.69/4.91 = ( ^ [X2: filter_nat,Y3: filter_nat] :
% 4.69/4.91 ( ( ord_le2510731241096832064er_nat @ X2 @ Y3 )
% 4.69/4.91 & ( ord_le2510731241096832064er_nat @ Y3 @ X2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_class.order_eq_iff
% 4.69/4.91 thf(fact_1214_order__class_Oorder__eq__iff,axiom,
% 4.69/4.91 ( ( ^ [Y4: set_nat,Z4: set_nat] : ( Y4 = Z4 ) )
% 4.69/4.91 = ( ^ [X2: set_nat,Y3: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ X2 @ Y3 )
% 4.69/4.91 & ( ord_less_eq_set_nat @ Y3 @ X2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_class.order_eq_iff
% 4.69/4.91 thf(fact_1215_order__class_Oorder__eq__iff,axiom,
% 4.69/4.91 ( ( ^ [Y4: rat,Z4: rat] : ( Y4 = Z4 ) )
% 4.69/4.91 = ( ^ [X2: rat,Y3: rat] :
% 4.69/4.91 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 4.69/4.91 & ( ord_less_eq_rat @ Y3 @ X2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_class.order_eq_iff
% 4.69/4.91 thf(fact_1216_order__class_Oorder__eq__iff,axiom,
% 4.69/4.91 ( ( ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 ) )
% 4.69/4.91 = ( ^ [X2: nat,Y3: nat] :
% 4.69/4.91 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 4.69/4.91 & ( ord_less_eq_nat @ Y3 @ X2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_class.order_eq_iff
% 4.69/4.91 thf(fact_1217_order__class_Oorder__eq__iff,axiom,
% 4.69/4.91 ( ( ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 4.69/4.91 = ( ^ [X2: int,Y3: int] :
% 4.69/4.91 ( ( ord_less_eq_int @ X2 @ Y3 )
% 4.69/4.91 & ( ord_less_eq_int @ Y3 @ X2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % order_class.order_eq_iff
% 4.69/4.91 thf(fact_1218_le__cases3,axiom,
% 4.69/4.91 ! [X: rat,Y: rat,Z: rat] :
% 4.69/4.91 ( ( ( ord_less_eq_rat @ X @ Y )
% 4.69/4.91 => ~ ( ord_less_eq_rat @ Y @ Z ) )
% 4.69/4.91 => ( ( ( ord_less_eq_rat @ Y @ X )
% 4.69/4.91 => ~ ( ord_less_eq_rat @ X @ Z ) )
% 4.69/4.91 => ( ( ( ord_less_eq_rat @ X @ Z )
% 4.69/4.91 => ~ ( ord_less_eq_rat @ Z @ Y ) )
% 4.69/4.91 => ( ( ( ord_less_eq_rat @ Z @ Y )
% 4.69/4.91 => ~ ( ord_less_eq_rat @ Y @ X ) )
% 4.69/4.91 => ( ( ( ord_less_eq_rat @ Y @ Z )
% 4.69/4.91 => ~ ( ord_less_eq_rat @ Z @ X ) )
% 4.69/4.91 => ~ ( ( ord_less_eq_rat @ Z @ X )
% 4.69/4.91 => ~ ( ord_less_eq_rat @ X @ Y ) ) ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % le_cases3
% 4.69/4.91 thf(fact_1219_le__cases3,axiom,
% 4.69/4.91 ! [X: nat,Y: nat,Z: nat] :
% 4.69/4.91 ( ( ( ord_less_eq_nat @ X @ Y )
% 4.69/4.91 => ~ ( ord_less_eq_nat @ Y @ Z ) )
% 4.69/4.91 => ( ( ( ord_less_eq_nat @ Y @ X )
% 4.69/4.91 => ~ ( ord_less_eq_nat @ X @ Z ) )
% 4.69/4.91 => ( ( ( ord_less_eq_nat @ X @ Z )
% 4.69/4.91 => ~ ( ord_less_eq_nat @ Z @ Y ) )
% 4.69/4.91 => ( ( ( ord_less_eq_nat @ Z @ Y )
% 4.69/4.91 => ~ ( ord_less_eq_nat @ Y @ X ) )
% 4.69/4.91 => ( ( ( ord_less_eq_nat @ Y @ Z )
% 4.69/4.91 => ~ ( ord_less_eq_nat @ Z @ X ) )
% 4.69/4.91 => ~ ( ( ord_less_eq_nat @ Z @ X )
% 4.69/4.91 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % le_cases3
% 4.69/4.91 thf(fact_1220_le__cases3,axiom,
% 4.69/4.91 ! [X: int,Y: int,Z: int] :
% 4.69/4.91 ( ( ( ord_less_eq_int @ X @ Y )
% 4.69/4.91 => ~ ( ord_less_eq_int @ Y @ Z ) )
% 4.69/4.91 => ( ( ( ord_less_eq_int @ Y @ X )
% 4.69/4.91 => ~ ( ord_less_eq_int @ X @ Z ) )
% 4.69/4.91 => ( ( ( ord_less_eq_int @ X @ Z )
% 4.69/4.91 => ~ ( ord_less_eq_int @ Z @ Y ) )
% 4.69/4.91 => ( ( ( ord_less_eq_int @ Z @ Y )
% 4.69/4.91 => ~ ( ord_less_eq_int @ Y @ X ) )
% 4.69/4.91 => ( ( ( ord_less_eq_int @ Y @ Z )
% 4.69/4.91 => ~ ( ord_less_eq_int @ Z @ X ) )
% 4.69/4.91 => ~ ( ( ord_less_eq_int @ Z @ X )
% 4.69/4.91 => ~ ( ord_less_eq_int @ X @ Y ) ) ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % le_cases3
% 4.69/4.91 thf(fact_1221_nle__le,axiom,
% 4.69/4.91 ! [A2: rat,B: rat] :
% 4.69/4.91 ( ( ~ ( ord_less_eq_rat @ A2 @ B ) )
% 4.69/4.91 = ( ( ord_less_eq_rat @ B @ A2 )
% 4.69/4.91 & ( B != A2 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % nle_le
% 4.69/4.91 thf(fact_1222_nle__le,axiom,
% 4.69/4.91 ! [A2: nat,B: nat] :
% 4.69/4.91 ( ( ~ ( ord_less_eq_nat @ A2 @ B ) )
% 4.69/4.91 = ( ( ord_less_eq_nat @ B @ A2 )
% 4.69/4.91 & ( B != A2 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % nle_le
% 4.69/4.91 thf(fact_1223_nle__le,axiom,
% 4.69/4.91 ! [A2: int,B: int] :
% 4.69/4.91 ( ( ~ ( ord_less_eq_int @ A2 @ B ) )
% 4.69/4.91 = ( ( ord_less_eq_int @ B @ A2 )
% 4.69/4.91 & ( B != A2 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % nle_le
% 4.69/4.91 thf(fact_1224_Sigma__mono,axiom,
% 4.69/4.91 ! [A: set_Pr4532377907799695533_nat_o,C5: set_Pr4532377907799695533_nat_o,B4: ( produc3658429121746597890et_nat > $o ) > set_nat,D3: ( produc3658429121746597890et_nat > $o ) > set_nat] :
% 4.69/4.91 ( ( ord_le2965882846123202637_nat_o @ A @ C5 )
% 4.69/4.91 => ( ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.91 ( ( member6576561426505652726_nat_o @ X3 @ A )
% 4.69/4.91 => ( ord_less_eq_set_nat @ ( B4 @ X3 ) @ ( D3 @ X3 ) ) )
% 4.69/4.91 => ( ord_le4460016228128491106_o_nat @ ( produc3142209312014666069_o_nat @ A @ B4 ) @ ( produc3142209312014666069_o_nat @ C5 @ D3 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Sigma_mono
% 4.69/4.91 thf(fact_1225_Sigma__mono,axiom,
% 4.69/4.91 ! [A: set_int,C5: set_int,B4: int > set_nat,D3: int > set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_int @ A @ C5 )
% 4.69/4.91 => ( ! [X3: int] :
% 4.69/4.91 ( ( member_int @ X3 @ A )
% 4.69/4.91 => ( ord_less_eq_set_nat @ ( B4 @ X3 ) @ ( D3 @ X3 ) ) )
% 4.69/4.91 => ( ord_le5333435103577920093nt_nat @ ( produc1456381018704787142nt_nat @ A @ B4 ) @ ( produc1456381018704787142nt_nat @ C5 @ D3 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Sigma_mono
% 4.69/4.91 thf(fact_1226_Sigma__mono,axiom,
% 4.69/4.91 ! [A: set_o,C5: set_o,B4: $o > set_nat,D3: $o > set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_o @ A @ C5 )
% 4.69/4.91 => ( ! [X3: $o] :
% 4.69/4.91 ( ( member_o @ X3 @ A )
% 4.69/4.91 => ( ord_less_eq_set_nat @ ( B4 @ X3 ) @ ( D3 @ X3 ) ) )
% 4.69/4.91 => ( ord_le6472378536984071597_o_nat @ ( product_Sigma_o_nat @ A @ B4 ) @ ( product_Sigma_o_nat @ C5 @ D3 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Sigma_mono
% 4.69/4.91 thf(fact_1227_Sigma__mono,axiom,
% 4.69/4.91 ! [A: set_Product_unit,C5: set_Product_unit,B4: product_unit > set_nat,D3: product_unit > set_nat] :
% 4.69/4.91 ( ( ord_le3507040750410214029t_unit @ A @ C5 )
% 4.69/4.91 => ( ! [X3: product_unit] :
% 4.69/4.91 ( ( member_Product_unit @ X3 @ A )
% 4.69/4.91 => ( ord_less_eq_set_nat @ ( B4 @ X3 ) @ ( D3 @ X3 ) ) )
% 4.69/4.91 => ( ord_le8121013740822022818it_nat @ ( produc6875377002296012693it_nat @ A @ B4 ) @ ( produc6875377002296012693it_nat @ C5 @ D3 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Sigma_mono
% 4.69/4.91 thf(fact_1228_Sigma__mono,axiom,
% 4.69/4.91 ! [A: set_nat,C5: set_nat,B4: nat > set_nat,D3: nat > set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ A @ C5 )
% 4.69/4.91 => ( ! [X3: nat] :
% 4.69/4.91 ( ( member_nat @ X3 @ A )
% 4.69/4.91 => ( ord_less_eq_set_nat @ ( B4 @ X3 ) @ ( D3 @ X3 ) ) )
% 4.69/4.91 => ( ord_le3146513528884898305at_nat @ ( produc457027306803732586at_nat @ A @ B4 ) @ ( produc457027306803732586at_nat @ C5 @ D3 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Sigma_mono
% 4.69/4.91 thf(fact_1229_rtrancl__Un__separator__converseE,axiom,
% 4.69/4.91 ! [A2: nat,B: nat,P: set_Pr1261947904930325089at_nat,Q2: set_Pr1261947904930325089at_nat] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( transi2905341329935302413cl_nat @ ( sup_su6327502436637775413at_nat @ P @ Q2 ) ) )
% 4.69/4.91 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ B ) @ ( transi2905341329935302413cl_nat @ P ) )
% 4.69/4.91 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ X3 ) @ Q2 )
% 4.69/4.91 => ( Y2 = X3 ) ) )
% 4.69/4.91 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( transi2905341329935302413cl_nat @ P ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % rtrancl_Un_separator_converseE
% 4.69/4.91 thf(fact_1230_rtrancl__Un__separator__converseE,axiom,
% 4.69/4.91 ! [A2: int,B: int,P: set_Pr958786334691620121nt_int,Q2: set_Pr958786334691620121nt_int] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( transi2902850859426252137cl_int @ ( sup_su6024340866399070445nt_int @ P @ Q2 ) ) )
% 4.69/4.91 => ( ! [X3: int,Y2: int] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ B ) @ ( transi2902850859426252137cl_int @ P ) )
% 4.69/4.91 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y2 @ X3 ) @ Q2 )
% 4.69/4.91 => ( Y2 = X3 ) ) )
% 4.69/4.91 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( transi2902850859426252137cl_int @ P ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % rtrancl_Un_separator_converseE
% 4.69/4.91 thf(fact_1231_rtrancl__Un__separatorE,axiom,
% 4.69/4.91 ! [A2: nat,B: nat,P: set_Pr1261947904930325089at_nat,Q2: set_Pr1261947904930325089at_nat] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( transi2905341329935302413cl_nat @ ( sup_su6327502436637775413at_nat @ P @ Q2 ) ) )
% 4.69/4.91 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ X3 ) @ ( transi2905341329935302413cl_nat @ P ) )
% 4.69/4.91 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ Q2 )
% 4.69/4.91 => ( X3 = Y2 ) ) )
% 4.69/4.91 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( transi2905341329935302413cl_nat @ P ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % rtrancl_Un_separatorE
% 4.69/4.91 thf(fact_1232_rtrancl__Un__separatorE,axiom,
% 4.69/4.91 ! [A2: int,B: int,P: set_Pr958786334691620121nt_int,Q2: set_Pr958786334691620121nt_int] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( transi2902850859426252137cl_int @ ( sup_su6024340866399070445nt_int @ P @ Q2 ) ) )
% 4.69/4.91 => ( ! [X3: int,Y2: int] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ X3 ) @ ( transi2902850859426252137cl_int @ P ) )
% 4.69/4.91 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y2 ) @ Q2 )
% 4.69/4.91 => ( X3 = Y2 ) ) )
% 4.69/4.91 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( transi2902850859426252137cl_int @ P ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % rtrancl_Un_separatorE
% 4.69/4.91 thf(fact_1233_disjoint__mono,axiom,
% 4.69/4.91 ! [A2: set_Product_unit,A5: set_Product_unit,B: set_Product_unit,B3: set_Product_unit] :
% 4.69/4.91 ( ( ord_le3507040750410214029t_unit @ A2 @ A5 )
% 4.69/4.91 => ( ( ord_le3507040750410214029t_unit @ B @ B3 )
% 4.69/4.91 => ( ( ( inf_in4660618365625256667t_unit @ A5 @ B3 )
% 4.69/4.91 = bot_bo3957492148770167129t_unit )
% 4.69/4.91 => ( ( inf_in4660618365625256667t_unit @ A2 @ B )
% 4.69/4.91 = bot_bo3957492148770167129t_unit ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % disjoint_mono
% 4.69/4.91 thf(fact_1234_disjoint__mono,axiom,
% 4.69/4.91 ! [A2: set_o,A5: set_o,B: set_o,B3: set_o] :
% 4.69/4.91 ( ( ord_less_eq_set_o @ A2 @ A5 )
% 4.69/4.91 => ( ( ord_less_eq_set_o @ B @ B3 )
% 4.69/4.91 => ( ( ( inf_inf_set_o @ A5 @ B3 )
% 4.69/4.91 = bot_bot_set_o )
% 4.69/4.91 => ( ( inf_inf_set_o @ A2 @ B )
% 4.69/4.91 = bot_bot_set_o ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % disjoint_mono
% 4.69/4.91 thf(fact_1235_disjoint__mono,axiom,
% 4.69/4.91 ! [A2: set_int,A5: set_int,B: set_int,B3: set_int] :
% 4.69/4.91 ( ( ord_less_eq_set_int @ A2 @ A5 )
% 4.69/4.91 => ( ( ord_less_eq_set_int @ B @ B3 )
% 4.69/4.91 => ( ( ( inf_inf_set_int @ A5 @ B3 )
% 4.69/4.91 = bot_bot_set_int )
% 4.69/4.91 => ( ( inf_inf_set_int @ A2 @ B )
% 4.69/4.91 = bot_bot_set_int ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % disjoint_mono
% 4.69/4.91 thf(fact_1236_disjoint__mono,axiom,
% 4.69/4.91 ! [A2: set_Pr4532377907799695533_nat_o,A5: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o,B3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.91 ( ( ord_le2965882846123202637_nat_o @ A2 @ A5 )
% 4.69/4.91 => ( ( ord_le2965882846123202637_nat_o @ B @ B3 )
% 4.69/4.91 => ( ( ( inf_in1906310914598751387_nat_o @ A5 @ B3 )
% 4.69/4.91 = bot_bo7824918357723582233_nat_o )
% 4.69/4.91 => ( ( inf_in1906310914598751387_nat_o @ A2 @ B )
% 4.69/4.91 = bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % disjoint_mono
% 4.69/4.91 thf(fact_1237_disjoint__mono,axiom,
% 4.69/4.91 ! [A2: set_nat,A5: set_nat,B: set_nat,B3: set_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ A2 @ A5 )
% 4.69/4.91 => ( ( ord_less_eq_set_nat @ B @ B3 )
% 4.69/4.91 => ( ( ( inf_inf_set_nat @ A5 @ B3 )
% 4.69/4.91 = bot_bot_set_nat )
% 4.69/4.91 => ( ( inf_inf_set_nat @ A2 @ B )
% 4.69/4.91 = bot_bot_set_nat ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % disjoint_mono
% 4.69/4.91 thf(fact_1238_rtrancl__image__unfold__right,axiom,
% 4.69/4.91 ! [E: set_Pr1261947904930325089at_nat,V2: set_nat] : ( ord_less_eq_set_nat @ ( image_nat_nat @ E @ ( image_nat_nat @ ( transi2905341329935302413cl_nat @ E ) @ V2 ) ) @ ( image_nat_nat @ ( transi2905341329935302413cl_nat @ E ) @ V2 ) ) ).
% 4.69/4.91
% 4.69/4.91 % rtrancl_image_unfold_right
% 4.69/4.91 thf(fact_1239_rtrancl__reachable__induct,axiom,
% 4.69/4.91 ! [I: set_nat,INV: set_nat,E: set_Pr1261947904930325089at_nat] :
% 4.69/4.91 ( ( ord_less_eq_set_nat @ I @ INV )
% 4.69/4.91 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ E @ INV ) @ INV )
% 4.69/4.91 => ( ord_less_eq_set_nat @ ( image_nat_nat @ ( transi2905341329935302413cl_nat @ E ) @ I ) @ INV ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % rtrancl_reachable_induct
% 4.69/4.91 thf(fact_1240_Image__Int__subset,axiom,
% 4.69/4.91 ! [R3: set_Pr1261947904930325089at_nat,A: set_nat,B4: set_nat] : ( ord_less_eq_set_nat @ ( image_nat_nat @ R3 @ ( inf_inf_set_nat @ A @ B4 ) ) @ ( inf_inf_set_nat @ ( image_nat_nat @ R3 @ A ) @ ( image_nat_nat @ R3 @ B4 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Image_Int_subset
% 4.69/4.91 thf(fact_1241_Image__mono,axiom,
% 4.69/4.91 ! [R6: set_Pr1261947904930325089at_nat,R2: set_Pr1261947904930325089at_nat,A8: set_nat,A: set_nat] :
% 4.69/4.91 ( ( ord_le3146513528884898305at_nat @ R6 @ R2 )
% 4.69/4.91 => ( ( ord_less_eq_set_nat @ A8 @ A )
% 4.69/4.91 => ( ord_less_eq_set_nat @ ( image_nat_nat @ R6 @ A8 ) @ ( image_nat_nat @ R2 @ A ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % Image_mono
% 4.69/4.91 thf(fact_1242_refl__on__Un,axiom,
% 4.69/4.91 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,B4: set_nat,S2: set_Pr1261947904930325089at_nat] :
% 4.69/4.91 ( ( refl_on_nat @ A @ R2 )
% 4.69/4.91 => ( ( refl_on_nat @ B4 @ S2 )
% 4.69/4.91 => ( refl_on_nat @ ( sup_sup_set_nat @ A @ B4 ) @ ( sup_su6327502436637775413at_nat @ R2 @ S2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % refl_on_Un
% 4.69/4.91 thf(fact_1243_refl__on__Int,axiom,
% 4.69/4.91 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,B4: set_nat,S2: set_Pr1261947904930325089at_nat] :
% 4.69/4.91 ( ( refl_on_nat @ A @ R2 )
% 4.69/4.91 => ( ( refl_on_nat @ B4 @ S2 )
% 4.69/4.91 => ( refl_on_nat @ ( inf_inf_set_nat @ A @ B4 ) @ ( inf_in2572325071724192079at_nat @ R2 @ S2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % refl_on_Int
% 4.69/4.91 thf(fact_1244_trancl__union__outside,axiom,
% 4.69/4.91 ! [V: nat,W: nat,E: set_Pr1261947904930325089at_nat,U2: set_Pr1261947904930325089at_nat] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ V @ W ) @ ( transi6264000038957366511cl_nat @ ( sup_su6327502436637775413at_nat @ E @ U2 ) ) )
% 4.69/4.91 => ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ V @ W ) @ ( transi6264000038957366511cl_nat @ E ) )
% 4.69/4.91 => ? [X3: nat,Y2: nat] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ V @ X3 ) @ ( transi2905341329935302413cl_nat @ ( sup_su6327502436637775413at_nat @ E @ U2 ) ) )
% 4.69/4.91 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ U2 )
% 4.69/4.91 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ W ) @ ( transi2905341329935302413cl_nat @ ( sup_su6327502436637775413at_nat @ E @ U2 ) ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % trancl_union_outside
% 4.69/4.91 thf(fact_1245_trancl__union__outside,axiom,
% 4.69/4.91 ! [V: int,W: int,E: set_Pr958786334691620121nt_int,U2: set_Pr958786334691620121nt_int] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ V @ W ) @ ( transi6261509568448316235cl_int @ ( sup_su6024340866399070445nt_int @ E @ U2 ) ) )
% 4.69/4.91 => ( ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ V @ W ) @ ( transi6261509568448316235cl_int @ E ) )
% 4.69/4.91 => ? [X3: int,Y2: int] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ V @ X3 ) @ ( transi2902850859426252137cl_int @ ( sup_su6024340866399070445nt_int @ E @ U2 ) ) )
% 4.69/4.91 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y2 ) @ U2 )
% 4.69/4.91 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y2 @ W ) @ ( transi2902850859426252137cl_int @ ( sup_su6024340866399070445nt_int @ E @ U2 ) ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % trancl_union_outside
% 4.69/4.91 thf(fact_1246_SigmaE,axiom,
% 4.69/4.91 ! [C: product_prod_nat_int,A: set_nat,B4: nat > set_int] :
% 4.69/4.91 ( ( member4262671552274231302at_int @ C @ ( produc454536836294682310at_int @ A @ B4 ) )
% 4.69/4.91 => ~ ! [X3: nat] :
% 4.69/4.91 ( ( member_nat @ X3 @ A )
% 4.69/4.91 => ! [Y2: int] :
% 4.69/4.91 ( ( member_int @ Y2 @ ( B4 @ X3 ) )
% 4.69/4.91 => ( C
% 4.69/4.91 != ( product_Pair_nat_int @ X3 @ Y2 ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaE
% 4.69/4.91 thf(fact_1247_SigmaE,axiom,
% 4.69/4.91 ! [C: product_prod_nat_o,A: set_nat,B4: nat > set_o] :
% 4.69/4.91 ( ( member6310962623043647828_nat_o @ C @ ( product_Sigma_nat_o @ A @ B4 ) )
% 4.69/4.91 => ~ ! [X3: nat] :
% 4.69/4.91 ( ( member_nat @ X3 @ A )
% 4.69/4.91 => ! [Y2: $o] :
% 4.69/4.91 ( ( member_o @ Y2 @ ( B4 @ X3 ) )
% 4.69/4.91 => ( C
% 4.69/4.91 != ( product_Pair_nat_o @ X3 @ Y2 ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaE
% 4.69/4.91 thf(fact_1248_SigmaE,axiom,
% 4.69/4.91 ! [C: produc526117512892780850t_unit,A: set_nat,B4: nat > set_Product_unit] :
% 4.69/4.91 ( ( member348563419383025609t_unit @ C @ ( produc5506539147108004339t_unit @ A @ B4 ) )
% 4.69/4.91 => ~ ! [X3: nat] :
% 4.69/4.91 ( ( member_nat @ X3 @ A )
% 4.69/4.91 => ! [Y2: product_unit] :
% 4.69/4.91 ( ( member_Product_unit @ Y2 @ ( B4 @ X3 ) )
% 4.69/4.91 => ( C
% 4.69/4.91 != ( produc3434450474625521892t_unit @ X3 @ Y2 ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaE
% 4.69/4.91 thf(fact_1249_SigmaE,axiom,
% 4.69/4.91 ! [C: product_prod_int_nat,A: set_int,B4: int > set_nat] :
% 4.69/4.91 ( ( member216504246829706758nt_nat @ C @ ( produc1456381018704787142nt_nat @ A @ B4 ) )
% 4.69/4.91 => ~ ! [X3: int] :
% 4.69/4.91 ( ( member_int @ X3 @ A )
% 4.69/4.91 => ! [Y2: nat] :
% 4.69/4.91 ( ( member_nat @ Y2 @ ( B4 @ X3 ) )
% 4.69/4.91 => ( C
% 4.69/4.91 != ( product_Pair_int_nat @ X3 @ Y2 ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaE
% 4.69/4.91 thf(fact_1250_SigmaE,axiom,
% 4.69/4.91 ! [C: product_prod_int_o,A: set_int,B4: int > set_o] :
% 4.69/4.91 ( ( member4489920277610959864_int_o @ C @ ( product_Sigma_int_o @ A @ B4 ) )
% 4.69/4.91 => ~ ! [X3: int] :
% 4.69/4.91 ( ( member_int @ X3 @ A )
% 4.69/4.91 => ! [Y2: $o] :
% 4.69/4.91 ( ( member_o @ Y2 @ ( B4 @ X3 ) )
% 4.69/4.91 => ( C
% 4.69/4.91 != ( product_Pair_int_o @ X3 @ Y2 ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaE
% 4.69/4.91 thf(fact_1251_SigmaE,axiom,
% 4.69/4.91 ! [C: produc6865911496949736918t_unit,A: set_int,B4: int > set_Product_unit] :
% 4.69/4.91 ( ( member6688357403439981677t_unit @ C @ ( produc2622961094310184599t_unit @ A @ B4 ) )
% 4.69/4.91 => ~ ! [X3: int] :
% 4.69/4.91 ( ( member_int @ X3 @ A )
% 4.69/4.91 => ! [Y2: product_unit] :
% 4.69/4.91 ( ( member_Product_unit @ Y2 @ ( B4 @ X3 ) )
% 4.69/4.91 => ( C
% 4.69/4.91 != ( produc550872421827702152t_unit @ X3 @ Y2 ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaE
% 4.69/4.91 thf(fact_1252_SigmaE,axiom,
% 4.69/4.91 ! [C: product_prod_o_nat,A: set_o,B4: $o > set_nat] :
% 4.69/4.91 ( ( member2802428098988154798_o_nat @ C @ ( product_Sigma_o_nat @ A @ B4 ) )
% 4.69/4.91 => ~ ! [X3: $o] :
% 4.69/4.91 ( ( member_o @ X3 @ A )
% 4.69/4.91 => ! [Y2: nat] :
% 4.69/4.91 ( ( member_nat @ Y2 @ ( B4 @ X3 ) )
% 4.69/4.91 => ( C
% 4.69/4.91 != ( product_Pair_o_nat @ X3 @ Y2 ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaE
% 4.69/4.91 thf(fact_1253_SigmaE,axiom,
% 4.69/4.91 ! [C: product_prod_o_int,A: set_o,B4: $o > set_int] :
% 4.69/4.91 ( ( member7847949116333733898_o_int @ C @ ( product_Sigma_o_int @ A @ B4 ) )
% 4.69/4.91 => ~ ! [X3: $o] :
% 4.69/4.91 ( ( member_o @ X3 @ A )
% 4.69/4.91 => ! [Y2: int] :
% 4.69/4.91 ( ( member_int @ Y2 @ ( B4 @ X3 ) )
% 4.69/4.91 => ( C
% 4.69/4.91 != ( product_Pair_o_int @ X3 @ Y2 ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaE
% 4.69/4.91 thf(fact_1254_SigmaE,axiom,
% 4.69/4.91 ! [C: product_prod_o_o,A: set_o,B4: $o > set_o] :
% 4.69/4.91 ( ( member7466972457876170832od_o_o @ C @ ( product_Sigma_o_o @ A @ B4 ) )
% 4.69/4.91 => ~ ! [X3: $o] :
% 4.69/4.91 ( ( member_o @ X3 @ A )
% 4.69/4.91 => ! [Y2: $o] :
% 4.69/4.91 ( ( member_o @ Y2 @ ( B4 @ X3 ) )
% 4.69/4.91 => ( C
% 4.69/4.91 != ( product_Pair_o_o @ X3 @ Y2 ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaE
% 4.69/4.91 thf(fact_1255_SigmaE,axiom,
% 4.69/4.91 ! [C: produc3788275437394581276t_unit,A: set_o,B4: $o > set_Product_unit] :
% 4.69/4.91 ( ( member9215336023991391429t_unit @ C @ ( produc411009820408249917t_unit @ A @ B4 ) )
% 4.69/4.91 => ~ ! [X3: $o] :
% 4.69/4.91 ( ( member_o @ X3 @ A )
% 4.69/4.91 => ! [Y2: product_unit] :
% 4.69/4.91 ( ( member_Product_unit @ Y2 @ ( B4 @ X3 ) )
% 4.69/4.91 => ( C
% 4.69/4.91 != ( produc3901946521647900940t_unit @ X3 @ Y2 ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaE
% 4.69/4.91 thf(fact_1256_SigmaD1,axiom,
% 4.69/4.91 ! [A2: heap_e7401611519738050253t_unit,B: set_nat,A: set_he8644174446132254637t_unit,B4: heap_e7401611519738050253t_unit > set_set_nat] :
% 4.69/4.91 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ B ) @ ( produc5260988393495149579et_nat @ A @ B4 ) )
% 4.69/4.91 => ( member242389114213480694t_unit @ A2 @ A ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaD1
% 4.69/4.91 thf(fact_1257_SigmaD1,axiom,
% 4.69/4.91 ! [A2: nat,B: nat,A: set_nat,B4: nat > set_nat] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( produc457027306803732586at_nat @ A @ B4 ) )
% 4.69/4.91 => ( member_nat @ A2 @ A ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaD1
% 4.69/4.91 thf(fact_1258_SigmaD1,axiom,
% 4.69/4.91 ! [A2: int,B: int,A: set_int,B4: int > set_int] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( produc1453890548195736866nt_int @ A @ B4 ) )
% 4.69/4.91 => ( member_int @ A2 @ A ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaD1
% 4.69/4.91 thf(fact_1259_SigmaD1,axiom,
% 4.69/4.91 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A: set_Pr4532377907799695533_nat_o,B4: ( produc3658429121746597890et_nat > $o ) > set_Pr3948176798113811640et_nat] :
% 4.69/4.91 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ B ) @ ( produc8052021730408606599et_nat @ A @ B4 ) )
% 4.69/4.91 => ( member6576561426505652726_nat_o @ A2 @ A ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaD1
% 4.69/4.91 thf(fact_1260_SigmaD1,axiom,
% 4.69/4.91 ! [A2: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A: set_Pr4532377907799695533_nat_o,B4: ( produc3658429121746597890et_nat > $o ) > set_Pr3286484037609594932et_nat] :
% 4.69/4.91 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ B ) @ ( produc7016705354093686019et_nat @ A @ B4 ) )
% 4.69/4.91 => ( member6576561426505652726_nat_o @ A2 @ A ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaD1
% 4.69/4.91 thf(fact_1261_SigmaD2,axiom,
% 4.69/4.91 ! [A2: heap_e7401611519738050253t_unit,B: set_nat,A: set_he8644174446132254637t_unit,B4: heap_e7401611519738050253t_unit > set_set_nat] :
% 4.69/4.91 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ B ) @ ( produc5260988393495149579et_nat @ A @ B4 ) )
% 4.69/4.91 => ( member_set_nat @ B @ ( B4 @ A2 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaD2
% 4.69/4.91 thf(fact_1262_SigmaD2,axiom,
% 4.69/4.91 ! [A2: nat,B: nat,A: set_nat,B4: nat > set_nat] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( produc457027306803732586at_nat @ A @ B4 ) )
% 4.69/4.91 => ( member_nat @ B @ ( B4 @ A2 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaD2
% 4.69/4.91 thf(fact_1263_SigmaD2,axiom,
% 4.69/4.91 ! [A2: int,B: int,A: set_int,B4: int > set_int] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( produc1453890548195736866nt_int @ A @ B4 ) )
% 4.69/4.91 => ( member_int @ B @ ( B4 @ A2 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaD2
% 4.69/4.91 thf(fact_1264_SigmaD2,axiom,
% 4.69/4.91 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A: set_Pr4532377907799695533_nat_o,B4: ( produc3658429121746597890et_nat > $o ) > set_Pr3948176798113811640et_nat] :
% 4.69/4.91 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ B ) @ ( produc8052021730408606599et_nat @ A @ B4 ) )
% 4.69/4.91 => ( member6260224972018164377et_nat @ B @ ( B4 @ A2 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaD2
% 4.69/4.91 thf(fact_1265_SigmaD2,axiom,
% 4.69/4.91 ! [A2: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A: set_Pr4532377907799695533_nat_o,B4: ( produc3658429121746597890et_nat > $o ) > set_Pr3286484037609594932et_nat] :
% 4.69/4.91 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ B ) @ ( produc7016705354093686019et_nat @ A @ B4 ) )
% 4.69/4.91 => ( member1996754912294343701et_nat @ B @ ( B4 @ A2 ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaD2
% 4.69/4.91 thf(fact_1266_SigmaE2,axiom,
% 4.69/4.91 ! [A2: nat,B: int,A: set_nat,B4: nat > set_int] :
% 4.69/4.91 ( ( member4262671552274231302at_int @ ( product_Pair_nat_int @ A2 @ B ) @ ( produc454536836294682310at_int @ A @ B4 ) )
% 4.69/4.91 => ~ ( ( member_nat @ A2 @ A )
% 4.69/4.91 => ~ ( member_int @ B @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaE2
% 4.69/4.91 thf(fact_1267_SigmaE2,axiom,
% 4.69/4.91 ! [A2: nat,B: $o,A: set_nat,B4: nat > set_o] :
% 4.69/4.91 ( ( member6310962623043647828_nat_o @ ( product_Pair_nat_o @ A2 @ B ) @ ( product_Sigma_nat_o @ A @ B4 ) )
% 4.69/4.91 => ~ ( ( member_nat @ A2 @ A )
% 4.69/4.91 => ~ ( member_o @ B @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaE2
% 4.69/4.91 thf(fact_1268_SigmaE2,axiom,
% 4.69/4.91 ! [A2: nat,B: product_unit,A: set_nat,B4: nat > set_Product_unit] :
% 4.69/4.91 ( ( member348563419383025609t_unit @ ( produc3434450474625521892t_unit @ A2 @ B ) @ ( produc5506539147108004339t_unit @ A @ B4 ) )
% 4.69/4.91 => ~ ( ( member_nat @ A2 @ A )
% 4.69/4.91 => ~ ( member_Product_unit @ B @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaE2
% 4.69/4.91 thf(fact_1269_SigmaE2,axiom,
% 4.69/4.91 ! [A2: int,B: nat,A: set_int,B4: int > set_nat] :
% 4.69/4.91 ( ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ A2 @ B ) @ ( produc1456381018704787142nt_nat @ A @ B4 ) )
% 4.69/4.91 => ~ ( ( member_int @ A2 @ A )
% 4.69/4.91 => ~ ( member_nat @ B @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaE2
% 4.69/4.91 thf(fact_1270_SigmaE2,axiom,
% 4.69/4.91 ! [A2: int,B: $o,A: set_int,B4: int > set_o] :
% 4.69/4.91 ( ( member4489920277610959864_int_o @ ( product_Pair_int_o @ A2 @ B ) @ ( product_Sigma_int_o @ A @ B4 ) )
% 4.69/4.91 => ~ ( ( member_int @ A2 @ A )
% 4.69/4.91 => ~ ( member_o @ B @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaE2
% 4.69/4.91 thf(fact_1271_SigmaE2,axiom,
% 4.69/4.91 ! [A2: int,B: product_unit,A: set_int,B4: int > set_Product_unit] :
% 4.69/4.91 ( ( member6688357403439981677t_unit @ ( produc550872421827702152t_unit @ A2 @ B ) @ ( produc2622961094310184599t_unit @ A @ B4 ) )
% 4.69/4.91 => ~ ( ( member_int @ A2 @ A )
% 4.69/4.91 => ~ ( member_Product_unit @ B @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaE2
% 4.69/4.91 thf(fact_1272_SigmaE2,axiom,
% 4.69/4.91 ! [A2: $o,B: nat,A: set_o,B4: $o > set_nat] :
% 4.69/4.91 ( ( member2802428098988154798_o_nat @ ( product_Pair_o_nat @ A2 @ B ) @ ( product_Sigma_o_nat @ A @ B4 ) )
% 4.69/4.91 => ~ ( ( member_o @ A2 @ A )
% 4.69/4.91 => ~ ( member_nat @ B @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaE2
% 4.69/4.91 thf(fact_1273_SigmaE2,axiom,
% 4.69/4.91 ! [A2: $o,B: int,A: set_o,B4: $o > set_int] :
% 4.69/4.91 ( ( member7847949116333733898_o_int @ ( product_Pair_o_int @ A2 @ B ) @ ( product_Sigma_o_int @ A @ B4 ) )
% 4.69/4.91 => ~ ( ( member_o @ A2 @ A )
% 4.69/4.91 => ~ ( member_int @ B @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaE2
% 4.69/4.91 thf(fact_1274_SigmaE2,axiom,
% 4.69/4.91 ! [A2: $o,B: $o,A: set_o,B4: $o > set_o] :
% 4.69/4.91 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ B ) @ ( product_Sigma_o_o @ A @ B4 ) )
% 4.69/4.91 => ~ ( ( member_o @ A2 @ A )
% 4.69/4.91 => ~ ( member_o @ B @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaE2
% 4.69/4.91 thf(fact_1275_SigmaE2,axiom,
% 4.69/4.91 ! [A2: $o,B: product_unit,A: set_o,B4: $o > set_Product_unit] :
% 4.69/4.91 ( ( member9215336023991391429t_unit @ ( produc3901946521647900940t_unit @ A2 @ B ) @ ( produc411009820408249917t_unit @ A @ B4 ) )
% 4.69/4.91 => ~ ( ( member_o @ A2 @ A )
% 4.69/4.91 => ~ ( member_Product_unit @ B @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % SigmaE2
% 4.69/4.91 thf(fact_1276_trancl__image__by__rtrancl,axiom,
% 4.69/4.91 ! [E: set_Pr1261947904930325089at_nat,Vi: set_nat] :
% 4.69/4.91 ( ( sup_sup_set_nat @ ( image_nat_nat @ ( transi6264000038957366511cl_nat @ E ) @ Vi ) @ Vi )
% 4.69/4.91 = ( image_nat_nat @ ( transi2905341329935302413cl_nat @ E ) @ Vi ) ) ).
% 4.69/4.91
% 4.69/4.91 % trancl_image_by_rtrancl
% 4.69/4.91 thf(fact_1277_converse__rtranclE_H,axiom,
% 4.69/4.91 ! [U: nat,V: nat,R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ U @ V ) @ ( transi2905341329935302413cl_nat @ R3 ) )
% 4.69/4.91 => ( ( U != V )
% 4.69/4.91 => ~ ! [Vh: nat] :
% 4.69/4.91 ( ( U != Vh )
% 4.69/4.91 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ U @ Vh ) @ R3 )
% 4.69/4.91 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Vh @ V ) @ ( transi2905341329935302413cl_nat @ R3 ) ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % converse_rtranclE'
% 4.69/4.91 thf(fact_1278_converse__rtranclE_H,axiom,
% 4.69/4.91 ! [U: int,V: int,R3: set_Pr958786334691620121nt_int] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ U @ V ) @ ( transi2902850859426252137cl_int @ R3 ) )
% 4.69/4.91 => ( ( U != V )
% 4.69/4.91 => ~ ! [Vh: int] :
% 4.69/4.91 ( ( U != Vh )
% 4.69/4.91 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ U @ Vh ) @ R3 )
% 4.69/4.91 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Vh @ V ) @ ( transi2902850859426252137cl_int @ R3 ) ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % converse_rtranclE'
% 4.69/4.91 thf(fact_1279_rtrancl_Ocases,axiom,
% 4.69/4.91 ! [A1: nat,A22: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A1 @ A22 ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.91 => ( ( A22 != A1 )
% 4.69/4.91 => ~ ! [B2: nat] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A1 @ B2 ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.91 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B2 @ A22 ) @ R2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % rtrancl.cases
% 4.69/4.91 thf(fact_1280_rtrancl_Ocases,axiom,
% 4.69/4.91 ! [A1: int,A22: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A1 @ A22 ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.91 => ( ( A22 != A1 )
% 4.69/4.91 => ~ ! [B2: int] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A1 @ B2 ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.91 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B2 @ A22 ) @ R2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % rtrancl.cases
% 4.69/4.91 thf(fact_1281_rtrancl_Osimps,axiom,
% 4.69/4.91 ! [A1: nat,A22: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A1 @ A22 ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.91 = ( ? [A6: nat] :
% 4.69/4.91 ( ( A1 = A6 )
% 4.69/4.91 & ( A22 = A6 ) )
% 4.69/4.91 | ? [A6: nat,B6: nat,C4: nat] :
% 4.69/4.91 ( ( A1 = A6 )
% 4.69/4.91 & ( A22 = C4 )
% 4.69/4.91 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A6 @ B6 ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.91 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B6 @ C4 ) @ R2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % rtrancl.simps
% 4.69/4.91 thf(fact_1282_rtrancl_Osimps,axiom,
% 4.69/4.91 ! [A1: int,A22: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A1 @ A22 ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.91 = ( ? [A6: int] :
% 4.69/4.91 ( ( A1 = A6 )
% 4.69/4.91 & ( A22 = A6 ) )
% 4.69/4.91 | ? [A6: int,B6: int,C4: int] :
% 4.69/4.91 ( ( A1 = A6 )
% 4.69/4.91 & ( A22 = C4 )
% 4.69/4.91 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A6 @ B6 ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.91 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B6 @ C4 ) @ R2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % rtrancl.simps
% 4.69/4.91 thf(fact_1283_rtrancl_Ortrancl__refl,axiom,
% 4.69/4.91 ! [A2: nat,R2: set_Pr1261947904930325089at_nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ A2 ) @ ( transi2905341329935302413cl_nat @ R2 ) ) ).
% 4.69/4.91
% 4.69/4.91 % rtrancl.rtrancl_refl
% 4.69/4.91 thf(fact_1284_rtrancl_Ortrancl__refl,axiom,
% 4.69/4.91 ! [A2: int,R2: set_Pr958786334691620121nt_int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ A2 ) @ ( transi2902850859426252137cl_int @ R2 ) ) ).
% 4.69/4.91
% 4.69/4.91 % rtrancl.rtrancl_refl
% 4.69/4.91 thf(fact_1285_rtrancl_Ortrancl__into__rtrancl,axiom,
% 4.69/4.91 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat,C: nat] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.91 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C ) @ R2 )
% 4.69/4.91 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ C ) @ ( transi2905341329935302413cl_nat @ R2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % rtrancl.rtrancl_into_rtrancl
% 4.69/4.91 thf(fact_1286_rtrancl_Ortrancl__into__rtrancl,axiom,
% 4.69/4.91 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int,C: int] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.91 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C ) @ R2 )
% 4.69/4.91 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ C ) @ ( transi2902850859426252137cl_int @ R2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % rtrancl.rtrancl_into_rtrancl
% 4.69/4.91 thf(fact_1287_rtranclE,axiom,
% 4.69/4.91 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.91 => ( ( A2 != B )
% 4.69/4.91 => ~ ! [Y2: nat] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ Y2 ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.91 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % rtranclE
% 4.69/4.91 thf(fact_1288_rtranclE,axiom,
% 4.69/4.91 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.91 => ( ( A2 != B )
% 4.69/4.91 => ~ ! [Y2: int] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ Y2 ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.91 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % rtranclE
% 4.69/4.91 thf(fact_1289_rtrancl__trans,axiom,
% 4.69/4.91 ! [X: nat,Y: nat,R2: set_Pr1261947904930325089at_nat,Z: nat] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.91 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ Z ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.91 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ ( transi2905341329935302413cl_nat @ R2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % rtrancl_trans
% 4.69/4.91 thf(fact_1290_rtrancl__trans,axiom,
% 4.69/4.91 ! [X: int,Y: int,R2: set_Pr958786334691620121nt_int,Z: int] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.91 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y @ Z ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.91 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Z ) @ ( transi2902850859426252137cl_int @ R2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % rtrancl_trans
% 4.69/4.91 thf(fact_1291_rtrancl__induct,axiom,
% 4.69/4.91 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat,P: nat > $o] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.91 => ( ( P @ A2 )
% 4.69/4.91 => ( ! [Y2: nat,Z3: nat] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ Y2 ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.91 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ Z3 ) @ R2 )
% 4.69/4.91 => ( ( P @ Y2 )
% 4.69/4.91 => ( P @ Z3 ) ) ) )
% 4.69/4.91 => ( P @ B ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % rtrancl_induct
% 4.69/4.91 thf(fact_1292_rtrancl__induct,axiom,
% 4.69/4.91 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int,P: int > $o] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.91 => ( ( P @ A2 )
% 4.69/4.91 => ( ! [Y2: int,Z3: int] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ Y2 ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.91 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y2 @ Z3 ) @ R2 )
% 4.69/4.91 => ( ( P @ Y2 )
% 4.69/4.91 => ( P @ Z3 ) ) ) )
% 4.69/4.91 => ( P @ B ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % rtrancl_induct
% 4.69/4.91 thf(fact_1293_converse__rtranclE,axiom,
% 4.69/4.91 ! [X: nat,Z: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.91 => ( ( X != Z )
% 4.69/4.91 => ~ ! [Y2: nat] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y2 ) @ R2 )
% 4.69/4.91 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ Z ) @ ( transi2905341329935302413cl_nat @ R2 ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % converse_rtranclE
% 4.69/4.91 thf(fact_1294_converse__rtranclE,axiom,
% 4.69/4.91 ! [X: int,Z: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Z ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.91 => ( ( X != Z )
% 4.69/4.91 => ~ ! [Y2: int] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y2 ) @ R2 )
% 4.69/4.91 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y2 @ Z ) @ ( transi2902850859426252137cl_int @ R2 ) ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % converse_rtranclE
% 4.69/4.91 thf(fact_1295_converse__rtrancl__induct,axiom,
% 4.69/4.91 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat,P: nat > $o] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.91 => ( ( P @ B )
% 4.69/4.91 => ( ! [Y2: nat,Z3: nat] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ Z3 ) @ R2 )
% 4.69/4.91 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Z3 @ B ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.91 => ( ( P @ Z3 )
% 4.69/4.91 => ( P @ Y2 ) ) ) )
% 4.69/4.91 => ( P @ A2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % converse_rtrancl_induct
% 4.69/4.91 thf(fact_1296_converse__rtrancl__induct,axiom,
% 4.69/4.91 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int,P: int > $o] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.91 => ( ( P @ B )
% 4.69/4.91 => ( ! [Y2: int,Z3: int] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y2 @ Z3 ) @ R2 )
% 4.69/4.91 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Z3 @ B ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.91 => ( ( P @ Z3 )
% 4.69/4.91 => ( P @ Y2 ) ) ) )
% 4.69/4.91 => ( P @ A2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % converse_rtrancl_induct
% 4.69/4.91 thf(fact_1297_converse__rtrancl__into__rtrancl,axiom,
% 4.69/4.91 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat,C: nat] :
% 4.69/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 )
% 4.69/4.91 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.91 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ C ) @ ( transi2905341329935302413cl_nat @ R2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % converse_rtrancl_into_rtrancl
% 4.69/4.91 thf(fact_1298_converse__rtrancl__into__rtrancl,axiom,
% 4.69/4.91 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int,C: int] :
% 4.69/4.91 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 )
% 4.69/4.91 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.91 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ C ) @ ( transi2902850859426252137cl_int @ R2 ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % converse_rtrancl_into_rtrancl
% 4.69/4.91 thf(fact_1299_rtrancl__induct2,axiom,
% 4.69/4.91 ! [Ax: heap_e7401611519738050253t_unit,Ay: set_nat,Bx: heap_e7401611519738050253t_unit,By: set_nat,R2: set_Pr719794911490849221et_nat,P: heap_e7401611519738050253t_unit > set_nat > $o] :
% 4.69/4.91 ( ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ ( produc7507926704131184380et_nat @ Ax @ Ay ) @ ( produc7507926704131184380et_nat @ Bx @ By ) ) @ ( transi6919426408697524543et_nat @ R2 ) )
% 4.69/4.91 => ( ( P @ Ax @ Ay )
% 4.69/4.91 => ( ! [A4: heap_e7401611519738050253t_unit,B2: set_nat,Aa: heap_e7401611519738050253t_unit,Ba: set_nat] :
% 4.69/4.91 ( ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ ( produc7507926704131184380et_nat @ Ax @ Ay ) @ ( produc7507926704131184380et_nat @ A4 @ B2 ) ) @ ( transi6919426408697524543et_nat @ R2 ) )
% 4.69/4.91 => ( ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ ( produc7507926704131184380et_nat @ A4 @ B2 ) @ ( produc7507926704131184380et_nat @ Aa @ Ba ) ) @ R2 )
% 4.69/4.91 => ( ( P @ A4 @ B2 )
% 4.69/4.91 => ( P @ Aa @ Ba ) ) ) )
% 4.69/4.91 => ( P @ Bx @ By ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % rtrancl_induct2
% 4.69/4.91 thf(fact_1300_rtrancl__induct2,axiom,
% 4.69/4.91 ! [Ax: nat,Ay: nat,Bx: nat,By: nat,R2: set_Pr8693737435421807431at_nat,P: nat > nat > $o] :
% 4.69/4.91 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ Ax @ Ay ) @ ( product_Pair_nat_nat @ Bx @ By ) ) @ ( transi8609417484261754244at_nat @ R2 ) )
% 4.69/4.91 => ( ( P @ Ax @ Ay )
% 4.69/4.91 => ( ! [A4: nat,B2: nat,Aa: nat,Ba: nat] :
% 4.69/4.91 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ Ax @ Ay ) @ ( product_Pair_nat_nat @ A4 @ B2 ) ) @ ( transi8609417484261754244at_nat @ R2 ) )
% 4.69/4.91 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A4 @ B2 ) @ ( product_Pair_nat_nat @ Aa @ Ba ) ) @ R2 )
% 4.69/4.91 => ( ( P @ A4 @ B2 )
% 4.69/4.91 => ( P @ Aa @ Ba ) ) ) )
% 4.69/4.91 => ( P @ Bx @ By ) ) ) ) ).
% 4.69/4.91
% 4.69/4.91 % rtrancl_induct2
% 4.69/4.91 thf(fact_1301_rtrancl__induct2,axiom,
% 4.69/4.91 ! [Ax: int,Ay: int,Bx: int,By: int,R2: set_Pr2560585780119916871nt_int,P: int > int > $o] :
% 4.69/4.91 ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ Ax @ Ay ) @ ( product_Pair_int_int @ Bx @ By ) ) @ ( transi5430920176653612092nt_int @ R2 ) )
% 4.69/4.91 => ( ( P @ Ax @ Ay )
% 4.69/4.91 => ( ! [A4: int,B2: int,Aa: int,Ba: int] :
% 4.69/4.91 ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ Ax @ Ay ) @ ( product_Pair_int_int @ A4 @ B2 ) ) @ ( transi5430920176653612092nt_int @ R2 ) )
% 4.69/4.92 => ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ A4 @ B2 ) @ ( product_Pair_int_int @ Aa @ Ba ) ) @ R2 )
% 4.69/4.92 => ( ( P @ A4 @ B2 )
% 4.69/4.92 => ( P @ Aa @ Ba ) ) ) )
% 4.69/4.92 => ( P @ Bx @ By ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_induct2
% 4.69/4.92 thf(fact_1302_rtrancl__induct2,axiom,
% 4.69/4.92 ! [Ax: produc3658429121746597890et_nat > $o,Ay: produc3658429121746597890et_nat,Bx: produc3658429121746597890et_nat > $o,By: produc3658429121746597890et_nat,R2: set_Pr7928877670098842301et_nat,P: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 4.69/4.92 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ Ax @ Ay ) @ ( produc5001842942810119800et_nat @ Bx @ By ) ) @ ( transi2414916928880341691et_nat @ R2 ) )
% 4.69/4.92 => ( ( P @ Ax @ Ay )
% 4.69/4.92 => ( ! [A4: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat,Aa: produc3658429121746597890et_nat > $o,Ba: produc3658429121746597890et_nat] :
% 4.69/4.92 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ Ax @ Ay ) @ ( produc5001842942810119800et_nat @ A4 @ B2 ) ) @ ( transi2414916928880341691et_nat @ R2 ) )
% 4.69/4.92 => ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ A4 @ B2 ) @ ( produc5001842942810119800et_nat @ Aa @ Ba ) ) @ R2 )
% 4.69/4.92 => ( ( P @ A4 @ B2 )
% 4.69/4.92 => ( P @ Aa @ Ba ) ) ) )
% 4.69/4.92 => ( P @ Bx @ By ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_induct2
% 4.69/4.92 thf(fact_1303_rtrancl__induct2,axiom,
% 4.69/4.92 ! [Ax: produc3658429121746597890et_nat > $o,Ay: produc3925858234332021118et_nat,Bx: produc3658429121746597890et_nat > $o,By: produc3925858234332021118et_nat,R2: set_Pr3444600963470892981et_nat,P: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 4.69/4.92 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ Ax @ Ay ) @ ( produc2245416461498447860et_nat @ Bx @ By ) ) @ ( transi344104063936286263et_nat @ R2 ) )
% 4.69/4.92 => ( ( P @ Ax @ Ay )
% 4.69/4.92 => ( ! [A4: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat,Aa: produc3658429121746597890et_nat > $o,Ba: produc3925858234332021118et_nat] :
% 4.69/4.92 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ Ax @ Ay ) @ ( produc2245416461498447860et_nat @ A4 @ B2 ) ) @ ( transi344104063936286263et_nat @ R2 ) )
% 4.69/4.92 => ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ A4 @ B2 ) @ ( produc2245416461498447860et_nat @ Aa @ Ba ) ) @ R2 )
% 4.69/4.92 => ( ( P @ A4 @ B2 )
% 4.69/4.92 => ( P @ Aa @ Ba ) ) ) )
% 4.69/4.92 => ( P @ Bx @ By ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_induct2
% 4.69/4.92 thf(fact_1304_converse__rtranclE2,axiom,
% 4.69/4.92 ! [Xa: heap_e7401611519738050253t_unit,Xb: set_nat,Za: heap_e7401611519738050253t_unit,Zb: set_nat,R2: set_Pr719794911490849221et_nat] :
% 4.69/4.92 ( ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ ( produc7507926704131184380et_nat @ Xa @ Xb ) @ ( produc7507926704131184380et_nat @ Za @ Zb ) ) @ ( transi6919426408697524543et_nat @ R2 ) )
% 4.69/4.92 => ( ( ( produc7507926704131184380et_nat @ Xa @ Xb )
% 4.69/4.92 != ( produc7507926704131184380et_nat @ Za @ Zb ) )
% 4.69/4.92 => ~ ! [A4: heap_e7401611519738050253t_unit,B2: set_nat] :
% 4.69/4.92 ( ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ ( produc7507926704131184380et_nat @ Xa @ Xb ) @ ( produc7507926704131184380et_nat @ A4 @ B2 ) ) @ R2 )
% 4.69/4.92 => ~ ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ ( produc7507926704131184380et_nat @ A4 @ B2 ) @ ( produc7507926704131184380et_nat @ Za @ Zb ) ) @ ( transi6919426408697524543et_nat @ R2 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % converse_rtranclE2
% 4.69/4.92 thf(fact_1305_converse__rtranclE2,axiom,
% 4.69/4.92 ! [Xa: nat,Xb: nat,Za: nat,Zb: nat,R2: set_Pr8693737435421807431at_nat] :
% 4.69/4.92 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ Xa @ Xb ) @ ( product_Pair_nat_nat @ Za @ Zb ) ) @ ( transi8609417484261754244at_nat @ R2 ) )
% 4.69/4.92 => ( ( ( product_Pair_nat_nat @ Xa @ Xb )
% 4.69/4.92 != ( product_Pair_nat_nat @ Za @ Zb ) )
% 4.69/4.92 => ~ ! [A4: nat,B2: nat] :
% 4.69/4.92 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ Xa @ Xb ) @ ( product_Pair_nat_nat @ A4 @ B2 ) ) @ R2 )
% 4.69/4.92 => ~ ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A4 @ B2 ) @ ( product_Pair_nat_nat @ Za @ Zb ) ) @ ( transi8609417484261754244at_nat @ R2 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % converse_rtranclE2
% 4.69/4.92 thf(fact_1306_converse__rtranclE2,axiom,
% 4.69/4.92 ! [Xa: int,Xb: int,Za: int,Zb: int,R2: set_Pr2560585780119916871nt_int] :
% 4.69/4.92 ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ Xa @ Xb ) @ ( product_Pair_int_int @ Za @ Zb ) ) @ ( transi5430920176653612092nt_int @ R2 ) )
% 4.69/4.92 => ( ( ( product_Pair_int_int @ Xa @ Xb )
% 4.69/4.92 != ( product_Pair_int_int @ Za @ Zb ) )
% 4.69/4.92 => ~ ! [A4: int,B2: int] :
% 4.69/4.92 ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ Xa @ Xb ) @ ( product_Pair_int_int @ A4 @ B2 ) ) @ R2 )
% 4.69/4.92 => ~ ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ A4 @ B2 ) @ ( product_Pair_int_int @ Za @ Zb ) ) @ ( transi5430920176653612092nt_int @ R2 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % converse_rtranclE2
% 4.69/4.92 thf(fact_1307_converse__rtranclE2,axiom,
% 4.69/4.92 ! [Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Za: produc3658429121746597890et_nat > $o,Zb: produc3658429121746597890et_nat,R2: set_Pr7928877670098842301et_nat] :
% 4.69/4.92 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ Xa @ Xb ) @ ( produc5001842942810119800et_nat @ Za @ Zb ) ) @ ( transi2414916928880341691et_nat @ R2 ) )
% 4.69/4.92 => ( ( ( produc5001842942810119800et_nat @ Xa @ Xb )
% 4.69/4.92 != ( produc5001842942810119800et_nat @ Za @ Zb ) )
% 4.69/4.92 => ~ ! [A4: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 4.69/4.92 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ Xa @ Xb ) @ ( produc5001842942810119800et_nat @ A4 @ B2 ) ) @ R2 )
% 4.69/4.92 => ~ ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ A4 @ B2 ) @ ( produc5001842942810119800et_nat @ Za @ Zb ) ) @ ( transi2414916928880341691et_nat @ R2 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % converse_rtranclE2
% 4.69/4.92 thf(fact_1308_converse__rtranclE2,axiom,
% 4.69/4.92 ! [Xa: produc3658429121746597890et_nat > $o,Xb: produc3925858234332021118et_nat,Za: produc3658429121746597890et_nat > $o,Zb: produc3925858234332021118et_nat,R2: set_Pr3444600963470892981et_nat] :
% 4.69/4.92 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ Xa @ Xb ) @ ( produc2245416461498447860et_nat @ Za @ Zb ) ) @ ( transi344104063936286263et_nat @ R2 ) )
% 4.69/4.92 => ( ( ( produc2245416461498447860et_nat @ Xa @ Xb )
% 4.69/4.92 != ( produc2245416461498447860et_nat @ Za @ Zb ) )
% 4.69/4.92 => ~ ! [A4: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 4.69/4.92 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ Xa @ Xb ) @ ( produc2245416461498447860et_nat @ A4 @ B2 ) ) @ R2 )
% 4.69/4.92 => ~ ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ A4 @ B2 ) @ ( produc2245416461498447860et_nat @ Za @ Zb ) ) @ ( transi344104063936286263et_nat @ R2 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % converse_rtranclE2
% 4.69/4.92 thf(fact_1309_converse__rtrancl__induct2,axiom,
% 4.69/4.92 ! [Ax: heap_e7401611519738050253t_unit,Ay: set_nat,Bx: heap_e7401611519738050253t_unit,By: set_nat,R2: set_Pr719794911490849221et_nat,P: heap_e7401611519738050253t_unit > set_nat > $o] :
% 4.69/4.92 ( ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ ( produc7507926704131184380et_nat @ Ax @ Ay ) @ ( produc7507926704131184380et_nat @ Bx @ By ) ) @ ( transi6919426408697524543et_nat @ R2 ) )
% 4.69/4.92 => ( ( P @ Bx @ By )
% 4.69/4.92 => ( ! [A4: heap_e7401611519738050253t_unit,B2: set_nat,Aa: heap_e7401611519738050253t_unit,Ba: set_nat] :
% 4.69/4.92 ( ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ ( produc7507926704131184380et_nat @ A4 @ B2 ) @ ( produc7507926704131184380et_nat @ Aa @ Ba ) ) @ R2 )
% 4.69/4.92 => ( ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ ( produc7507926704131184380et_nat @ Aa @ Ba ) @ ( produc7507926704131184380et_nat @ Bx @ By ) ) @ ( transi6919426408697524543et_nat @ R2 ) )
% 4.69/4.92 => ( ( P @ Aa @ Ba )
% 4.69/4.92 => ( P @ A4 @ B2 ) ) ) )
% 4.69/4.92 => ( P @ Ax @ Ay ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % converse_rtrancl_induct2
% 4.69/4.92 thf(fact_1310_converse__rtrancl__induct2,axiom,
% 4.69/4.92 ! [Ax: nat,Ay: nat,Bx: nat,By: nat,R2: set_Pr8693737435421807431at_nat,P: nat > nat > $o] :
% 4.69/4.92 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ Ax @ Ay ) @ ( product_Pair_nat_nat @ Bx @ By ) ) @ ( transi8609417484261754244at_nat @ R2 ) )
% 4.69/4.92 => ( ( P @ Bx @ By )
% 4.69/4.92 => ( ! [A4: nat,B2: nat,Aa: nat,Ba: nat] :
% 4.69/4.92 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A4 @ B2 ) @ ( product_Pair_nat_nat @ Aa @ Ba ) ) @ R2 )
% 4.69/4.92 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ Aa @ Ba ) @ ( product_Pair_nat_nat @ Bx @ By ) ) @ ( transi8609417484261754244at_nat @ R2 ) )
% 4.69/4.92 => ( ( P @ Aa @ Ba )
% 4.69/4.92 => ( P @ A4 @ B2 ) ) ) )
% 4.69/4.92 => ( P @ Ax @ Ay ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % converse_rtrancl_induct2
% 4.69/4.92 thf(fact_1311_converse__rtrancl__induct2,axiom,
% 4.69/4.92 ! [Ax: int,Ay: int,Bx: int,By: int,R2: set_Pr2560585780119916871nt_int,P: int > int > $o] :
% 4.69/4.92 ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ Ax @ Ay ) @ ( product_Pair_int_int @ Bx @ By ) ) @ ( transi5430920176653612092nt_int @ R2 ) )
% 4.69/4.92 => ( ( P @ Bx @ By )
% 4.69/4.92 => ( ! [A4: int,B2: int,Aa: int,Ba: int] :
% 4.69/4.92 ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ A4 @ B2 ) @ ( product_Pair_int_int @ Aa @ Ba ) ) @ R2 )
% 4.69/4.92 => ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ Aa @ Ba ) @ ( product_Pair_int_int @ Bx @ By ) ) @ ( transi5430920176653612092nt_int @ R2 ) )
% 4.69/4.92 => ( ( P @ Aa @ Ba )
% 4.69/4.92 => ( P @ A4 @ B2 ) ) ) )
% 4.69/4.92 => ( P @ Ax @ Ay ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % converse_rtrancl_induct2
% 4.69/4.92 thf(fact_1312_converse__rtrancl__induct2,axiom,
% 4.69/4.92 ! [Ax: produc3658429121746597890et_nat > $o,Ay: produc3658429121746597890et_nat,Bx: produc3658429121746597890et_nat > $o,By: produc3658429121746597890et_nat,R2: set_Pr7928877670098842301et_nat,P: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 4.69/4.92 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ Ax @ Ay ) @ ( produc5001842942810119800et_nat @ Bx @ By ) ) @ ( transi2414916928880341691et_nat @ R2 ) )
% 4.69/4.92 => ( ( P @ Bx @ By )
% 4.69/4.92 => ( ! [A4: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat,Aa: produc3658429121746597890et_nat > $o,Ba: produc3658429121746597890et_nat] :
% 4.69/4.92 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ A4 @ B2 ) @ ( produc5001842942810119800et_nat @ Aa @ Ba ) ) @ R2 )
% 4.69/4.92 => ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ Aa @ Ba ) @ ( produc5001842942810119800et_nat @ Bx @ By ) ) @ ( transi2414916928880341691et_nat @ R2 ) )
% 4.69/4.92 => ( ( P @ Aa @ Ba )
% 4.69/4.92 => ( P @ A4 @ B2 ) ) ) )
% 4.69/4.92 => ( P @ Ax @ Ay ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % converse_rtrancl_induct2
% 4.69/4.92 thf(fact_1313_converse__rtrancl__induct2,axiom,
% 4.69/4.92 ! [Ax: produc3658429121746597890et_nat > $o,Ay: produc3925858234332021118et_nat,Bx: produc3658429121746597890et_nat > $o,By: produc3925858234332021118et_nat,R2: set_Pr3444600963470892981et_nat,P: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 4.69/4.92 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ Ax @ Ay ) @ ( produc2245416461498447860et_nat @ Bx @ By ) ) @ ( transi344104063936286263et_nat @ R2 ) )
% 4.69/4.92 => ( ( P @ Bx @ By )
% 4.69/4.92 => ( ! [A4: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat,Aa: produc3658429121746597890et_nat > $o,Ba: produc3925858234332021118et_nat] :
% 4.69/4.92 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ A4 @ B2 ) @ ( produc2245416461498447860et_nat @ Aa @ Ba ) ) @ R2 )
% 4.69/4.92 => ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ Aa @ Ba ) @ ( produc2245416461498447860et_nat @ Bx @ By ) ) @ ( transi344104063936286263et_nat @ R2 ) )
% 4.69/4.92 => ( ( P @ Aa @ Ba )
% 4.69/4.92 => ( P @ A4 @ B2 ) ) ) )
% 4.69/4.92 => ( P @ Ax @ Ay ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % converse_rtrancl_induct2
% 4.69/4.92 thf(fact_1314_Un__empty__right,axiom,
% 4.69/4.92 ! [A: set_Product_unit] :
% 4.69/4.92 ( ( sup_su793286257634532545t_unit @ A @ bot_bo3957492148770167129t_unit )
% 4.69/4.92 = A ) ).
% 4.69/4.92
% 4.69/4.92 % Un_empty_right
% 4.69/4.92 thf(fact_1315_Un__empty__right,axiom,
% 4.69/4.92 ! [A: set_o] :
% 4.69/4.92 ( ( sup_sup_set_o @ A @ bot_bot_set_o )
% 4.69/4.92 = A ) ).
% 4.69/4.92
% 4.69/4.92 % Un_empty_right
% 4.69/4.92 thf(fact_1316_Un__empty__right,axiom,
% 4.69/4.92 ! [A: set_nat] :
% 4.69/4.92 ( ( sup_sup_set_nat @ A @ bot_bot_set_nat )
% 4.69/4.92 = A ) ).
% 4.69/4.92
% 4.69/4.92 % Un_empty_right
% 4.69/4.92 thf(fact_1317_Un__empty__right,axiom,
% 4.69/4.92 ! [A: set_int] :
% 4.69/4.92 ( ( sup_sup_set_int @ A @ bot_bot_set_int )
% 4.69/4.92 = A ) ).
% 4.69/4.92
% 4.69/4.92 % Un_empty_right
% 4.69/4.92 thf(fact_1318_Un__empty__right,axiom,
% 4.69/4.92 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( sup_su5209123915105501825_nat_o @ A @ bot_bo7824918357723582233_nat_o )
% 4.69/4.92 = A ) ).
% 4.69/4.92
% 4.69/4.92 % Un_empty_right
% 4.69/4.92 thf(fact_1319_Un__empty__left,axiom,
% 4.69/4.92 ! [B4: set_Product_unit] :
% 4.69/4.92 ( ( sup_su793286257634532545t_unit @ bot_bo3957492148770167129t_unit @ B4 )
% 4.69/4.92 = B4 ) ).
% 4.69/4.92
% 4.69/4.92 % Un_empty_left
% 4.69/4.92 thf(fact_1320_Un__empty__left,axiom,
% 4.69/4.92 ! [B4: set_o] :
% 4.69/4.92 ( ( sup_sup_set_o @ bot_bot_set_o @ B4 )
% 4.69/4.92 = B4 ) ).
% 4.69/4.92
% 4.69/4.92 % Un_empty_left
% 4.69/4.92 thf(fact_1321_Un__empty__left,axiom,
% 4.69/4.92 ! [B4: set_nat] :
% 4.69/4.92 ( ( sup_sup_set_nat @ bot_bot_set_nat @ B4 )
% 4.69/4.92 = B4 ) ).
% 4.69/4.92
% 4.69/4.92 % Un_empty_left
% 4.69/4.92 thf(fact_1322_Un__empty__left,axiom,
% 4.69/4.92 ! [B4: set_int] :
% 4.69/4.92 ( ( sup_sup_set_int @ bot_bot_set_int @ B4 )
% 4.69/4.92 = B4 ) ).
% 4.69/4.92
% 4.69/4.92 % Un_empty_left
% 4.69/4.92 thf(fact_1323_Un__empty__left,axiom,
% 4.69/4.92 ! [B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( sup_su5209123915105501825_nat_o @ bot_bo7824918357723582233_nat_o @ B4 )
% 4.69/4.92 = B4 ) ).
% 4.69/4.92
% 4.69/4.92 % Un_empty_left
% 4.69/4.92 thf(fact_1324_disjoint__iff__not__equal,axiom,
% 4.69/4.92 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.92 ( ( ( inf_in4660618365625256667t_unit @ A @ B4 )
% 4.69/4.92 = bot_bo3957492148770167129t_unit )
% 4.69/4.92 = ( ! [X2: product_unit] :
% 4.69/4.92 ( ( member_Product_unit @ X2 @ A )
% 4.69/4.92 => ! [Y3: product_unit] :
% 4.69/4.92 ( ( member_Product_unit @ Y3 @ B4 )
% 4.69/4.92 => ( X2 != Y3 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % disjoint_iff_not_equal
% 4.69/4.92 thf(fact_1325_disjoint__iff__not__equal,axiom,
% 4.69/4.92 ! [A: set_o,B4: set_o] :
% 4.69/4.92 ( ( ( inf_inf_set_o @ A @ B4 )
% 4.69/4.92 = bot_bot_set_o )
% 4.69/4.92 = ( ! [X2: $o] :
% 4.69/4.92 ( ( member_o @ X2 @ A )
% 4.69/4.92 => ! [Y3: $o] :
% 4.69/4.92 ( ( member_o @ Y3 @ B4 )
% 4.69/4.92 => ( X2 = ~ Y3 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % disjoint_iff_not_equal
% 4.69/4.92 thf(fact_1326_disjoint__iff__not__equal,axiom,
% 4.69/4.92 ! [A: set_nat,B4: set_nat] :
% 4.69/4.92 ( ( ( inf_inf_set_nat @ A @ B4 )
% 4.69/4.92 = bot_bot_set_nat )
% 4.69/4.92 = ( ! [X2: nat] :
% 4.69/4.92 ( ( member_nat @ X2 @ A )
% 4.69/4.92 => ! [Y3: nat] :
% 4.69/4.92 ( ( member_nat @ Y3 @ B4 )
% 4.69/4.92 => ( X2 != Y3 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % disjoint_iff_not_equal
% 4.69/4.92 thf(fact_1327_disjoint__iff__not__equal,axiom,
% 4.69/4.92 ! [A: set_int,B4: set_int] :
% 4.69/4.92 ( ( ( inf_inf_set_int @ A @ B4 )
% 4.69/4.92 = bot_bot_set_int )
% 4.69/4.92 = ( ! [X2: int] :
% 4.69/4.92 ( ( member_int @ X2 @ A )
% 4.69/4.92 => ! [Y3: int] :
% 4.69/4.92 ( ( member_int @ Y3 @ B4 )
% 4.69/4.92 => ( X2 != Y3 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % disjoint_iff_not_equal
% 4.69/4.92 thf(fact_1328_disjoint__iff__not__equal,axiom,
% 4.69/4.92 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( ( inf_in1906310914598751387_nat_o @ A @ B4 )
% 4.69/4.92 = bot_bo7824918357723582233_nat_o )
% 4.69/4.92 = ( ! [X2: produc3658429121746597890et_nat > $o] :
% 4.69/4.92 ( ( member6576561426505652726_nat_o @ X2 @ A )
% 4.69/4.92 => ! [Y3: produc3658429121746597890et_nat > $o] :
% 4.69/4.92 ( ( member6576561426505652726_nat_o @ Y3 @ B4 )
% 4.69/4.92 => ( X2 != Y3 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % disjoint_iff_not_equal
% 4.69/4.92 thf(fact_1329_Int__empty__right,axiom,
% 4.69/4.92 ! [A: set_Product_unit] :
% 4.69/4.92 ( ( inf_in4660618365625256667t_unit @ A @ bot_bo3957492148770167129t_unit )
% 4.69/4.92 = bot_bo3957492148770167129t_unit ) ).
% 4.69/4.92
% 4.69/4.92 % Int_empty_right
% 4.69/4.92 thf(fact_1330_Int__empty__right,axiom,
% 4.69/4.92 ! [A: set_o] :
% 4.69/4.92 ( ( inf_inf_set_o @ A @ bot_bot_set_o )
% 4.69/4.92 = bot_bot_set_o ) ).
% 4.69/4.92
% 4.69/4.92 % Int_empty_right
% 4.69/4.92 thf(fact_1331_Int__empty__right,axiom,
% 4.69/4.92 ! [A: set_nat] :
% 4.69/4.92 ( ( inf_inf_set_nat @ A @ bot_bot_set_nat )
% 4.69/4.92 = bot_bot_set_nat ) ).
% 4.69/4.92
% 4.69/4.92 % Int_empty_right
% 4.69/4.92 thf(fact_1332_Int__empty__right,axiom,
% 4.69/4.92 ! [A: set_int] :
% 4.69/4.92 ( ( inf_inf_set_int @ A @ bot_bot_set_int )
% 4.69/4.92 = bot_bot_set_int ) ).
% 4.69/4.92
% 4.69/4.92 % Int_empty_right
% 4.69/4.92 thf(fact_1333_Int__empty__right,axiom,
% 4.69/4.92 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( inf_in1906310914598751387_nat_o @ A @ bot_bo7824918357723582233_nat_o )
% 4.69/4.92 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/4.92
% 4.69/4.92 % Int_empty_right
% 4.69/4.92 thf(fact_1334_Int__empty__left,axiom,
% 4.69/4.92 ! [B4: set_Product_unit] :
% 4.69/4.92 ( ( inf_in4660618365625256667t_unit @ bot_bo3957492148770167129t_unit @ B4 )
% 4.69/4.92 = bot_bo3957492148770167129t_unit ) ).
% 4.69/4.92
% 4.69/4.92 % Int_empty_left
% 4.69/4.92 thf(fact_1335_Int__empty__left,axiom,
% 4.69/4.92 ! [B4: set_o] :
% 4.69/4.92 ( ( inf_inf_set_o @ bot_bot_set_o @ B4 )
% 4.69/4.92 = bot_bot_set_o ) ).
% 4.69/4.92
% 4.69/4.92 % Int_empty_left
% 4.69/4.92 thf(fact_1336_Int__empty__left,axiom,
% 4.69/4.92 ! [B4: set_nat] :
% 4.69/4.92 ( ( inf_inf_set_nat @ bot_bot_set_nat @ B4 )
% 4.69/4.92 = bot_bot_set_nat ) ).
% 4.69/4.92
% 4.69/4.92 % Int_empty_left
% 4.69/4.92 thf(fact_1337_Int__empty__left,axiom,
% 4.69/4.92 ! [B4: set_int] :
% 4.69/4.92 ( ( inf_inf_set_int @ bot_bot_set_int @ B4 )
% 4.69/4.92 = bot_bot_set_int ) ).
% 4.69/4.92
% 4.69/4.92 % Int_empty_left
% 4.69/4.92 thf(fact_1338_Int__empty__left,axiom,
% 4.69/4.92 ! [B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( inf_in1906310914598751387_nat_o @ bot_bo7824918357723582233_nat_o @ B4 )
% 4.69/4.92 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/4.92
% 4.69/4.92 % Int_empty_left
% 4.69/4.92 thf(fact_1339_disjoint__iff,axiom,
% 4.69/4.92 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.92 ( ( ( inf_in4660618365625256667t_unit @ A @ B4 )
% 4.69/4.92 = bot_bo3957492148770167129t_unit )
% 4.69/4.92 = ( ! [X2: product_unit] :
% 4.69/4.92 ( ( member_Product_unit @ X2 @ A )
% 4.69/4.92 => ~ ( member_Product_unit @ X2 @ B4 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % disjoint_iff
% 4.69/4.92 thf(fact_1340_disjoint__iff,axiom,
% 4.69/4.92 ! [A: set_o,B4: set_o] :
% 4.69/4.92 ( ( ( inf_inf_set_o @ A @ B4 )
% 4.69/4.92 = bot_bot_set_o )
% 4.69/4.92 = ( ! [X2: $o] :
% 4.69/4.92 ( ( member_o @ X2 @ A )
% 4.69/4.92 => ~ ( member_o @ X2 @ B4 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % disjoint_iff
% 4.69/4.92 thf(fact_1341_disjoint__iff,axiom,
% 4.69/4.92 ! [A: set_nat,B4: set_nat] :
% 4.69/4.92 ( ( ( inf_inf_set_nat @ A @ B4 )
% 4.69/4.92 = bot_bot_set_nat )
% 4.69/4.92 = ( ! [X2: nat] :
% 4.69/4.92 ( ( member_nat @ X2 @ A )
% 4.69/4.92 => ~ ( member_nat @ X2 @ B4 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % disjoint_iff
% 4.69/4.92 thf(fact_1342_disjoint__iff,axiom,
% 4.69/4.92 ! [A: set_int,B4: set_int] :
% 4.69/4.92 ( ( ( inf_inf_set_int @ A @ B4 )
% 4.69/4.92 = bot_bot_set_int )
% 4.69/4.92 = ( ! [X2: int] :
% 4.69/4.92 ( ( member_int @ X2 @ A )
% 4.69/4.92 => ~ ( member_int @ X2 @ B4 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % disjoint_iff
% 4.69/4.92 thf(fact_1343_disjoint__iff,axiom,
% 4.69/4.92 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( ( inf_in1906310914598751387_nat_o @ A @ B4 )
% 4.69/4.92 = bot_bo7824918357723582233_nat_o )
% 4.69/4.92 = ( ! [X2: produc3658429121746597890et_nat > $o] :
% 4.69/4.92 ( ( member6576561426505652726_nat_o @ X2 @ A )
% 4.69/4.92 => ~ ( member6576561426505652726_nat_o @ X2 @ B4 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % disjoint_iff
% 4.69/4.92 thf(fact_1344_Int__emptyI,axiom,
% 4.69/4.92 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.92 ( ! [X3: product_unit] :
% 4.69/4.92 ( ( member_Product_unit @ X3 @ A )
% 4.69/4.92 => ~ ( member_Product_unit @ X3 @ B4 ) )
% 4.69/4.92 => ( ( inf_in4660618365625256667t_unit @ A @ B4 )
% 4.69/4.92 = bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.92
% 4.69/4.92 % Int_emptyI
% 4.69/4.92 thf(fact_1345_Int__emptyI,axiom,
% 4.69/4.92 ! [A: set_o,B4: set_o] :
% 4.69/4.92 ( ! [X3: $o] :
% 4.69/4.92 ( ( member_o @ X3 @ A )
% 4.69/4.92 => ~ ( member_o @ X3 @ B4 ) )
% 4.69/4.92 => ( ( inf_inf_set_o @ A @ B4 )
% 4.69/4.92 = bot_bot_set_o ) ) ).
% 4.69/4.92
% 4.69/4.92 % Int_emptyI
% 4.69/4.92 thf(fact_1346_Int__emptyI,axiom,
% 4.69/4.92 ! [A: set_nat,B4: set_nat] :
% 4.69/4.92 ( ! [X3: nat] :
% 4.69/4.92 ( ( member_nat @ X3 @ A )
% 4.69/4.92 => ~ ( member_nat @ X3 @ B4 ) )
% 4.69/4.92 => ( ( inf_inf_set_nat @ A @ B4 )
% 4.69/4.92 = bot_bot_set_nat ) ) ).
% 4.69/4.92
% 4.69/4.92 % Int_emptyI
% 4.69/4.92 thf(fact_1347_Int__emptyI,axiom,
% 4.69/4.92 ! [A: set_int,B4: set_int] :
% 4.69/4.92 ( ! [X3: int] :
% 4.69/4.92 ( ( member_int @ X3 @ A )
% 4.69/4.92 => ~ ( member_int @ X3 @ B4 ) )
% 4.69/4.92 => ( ( inf_inf_set_int @ A @ B4 )
% 4.69/4.92 = bot_bot_set_int ) ) ).
% 4.69/4.92
% 4.69/4.92 % Int_emptyI
% 4.69/4.92 thf(fact_1348_Int__emptyI,axiom,
% 4.69/4.92 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.92 ( ( member6576561426505652726_nat_o @ X3 @ A )
% 4.69/4.92 => ~ ( member6576561426505652726_nat_o @ X3 @ B4 ) )
% 4.69/4.92 => ( ( inf_in1906310914598751387_nat_o @ A @ B4 )
% 4.69/4.92 = bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.92
% 4.69/4.92 % Int_emptyI
% 4.69/4.92 thf(fact_1349_disjointI,axiom,
% 4.69/4.92 ! [A2: set_Product_unit,B: set_Product_unit] :
% 4.69/4.92 ( ! [X3: product_unit] :
% 4.69/4.92 ( ( member_Product_unit @ X3 @ A2 )
% 4.69/4.92 => ~ ( member_Product_unit @ X3 @ B ) )
% 4.69/4.92 => ( ( inf_in4660618365625256667t_unit @ A2 @ B )
% 4.69/4.92 = bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.92
% 4.69/4.92 % disjointI
% 4.69/4.92 thf(fact_1350_disjointI,axiom,
% 4.69/4.92 ! [A2: set_o,B: set_o] :
% 4.69/4.92 ( ! [X3: $o] :
% 4.69/4.92 ( ( member_o @ X3 @ A2 )
% 4.69/4.92 => ~ ( member_o @ X3 @ B ) )
% 4.69/4.92 => ( ( inf_inf_set_o @ A2 @ B )
% 4.69/4.92 = bot_bot_set_o ) ) ).
% 4.69/4.92
% 4.69/4.92 % disjointI
% 4.69/4.92 thf(fact_1351_disjointI,axiom,
% 4.69/4.92 ! [A2: set_nat,B: set_nat] :
% 4.69/4.92 ( ! [X3: nat] :
% 4.69/4.92 ( ( member_nat @ X3 @ A2 )
% 4.69/4.92 => ~ ( member_nat @ X3 @ B ) )
% 4.69/4.92 => ( ( inf_inf_set_nat @ A2 @ B )
% 4.69/4.92 = bot_bot_set_nat ) ) ).
% 4.69/4.92
% 4.69/4.92 % disjointI
% 4.69/4.92 thf(fact_1352_disjointI,axiom,
% 4.69/4.92 ! [A2: set_int,B: set_int] :
% 4.69/4.92 ( ! [X3: int] :
% 4.69/4.92 ( ( member_int @ X3 @ A2 )
% 4.69/4.92 => ~ ( member_int @ X3 @ B ) )
% 4.69/4.92 => ( ( inf_inf_set_int @ A2 @ B )
% 4.69/4.92 = bot_bot_set_int ) ) ).
% 4.69/4.92
% 4.69/4.92 % disjointI
% 4.69/4.92 thf(fact_1353_disjointI,axiom,
% 4.69/4.92 ! [A2: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.92 ( ( member6576561426505652726_nat_o @ X3 @ A2 )
% 4.69/4.92 => ~ ( member6576561426505652726_nat_o @ X3 @ B ) )
% 4.69/4.92 => ( ( inf_in1906310914598751387_nat_o @ A2 @ B )
% 4.69/4.92 = bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.92
% 4.69/4.92 % disjointI
% 4.69/4.92 thf(fact_1354_Int__insert__right,axiom,
% 4.69/4.92 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( ( member6576561426505652726_nat_o @ A2 @ A )
% 4.69/4.92 => ( ( inf_in1906310914598751387_nat_o @ A @ ( insert5175938949040314269_nat_o @ A2 @ B4 ) )
% 4.69/4.92 = ( insert5175938949040314269_nat_o @ A2 @ ( inf_in1906310914598751387_nat_o @ A @ B4 ) ) ) )
% 4.69/4.92 & ( ~ ( member6576561426505652726_nat_o @ A2 @ A )
% 4.69/4.92 => ( ( inf_in1906310914598751387_nat_o @ A @ ( insert5175938949040314269_nat_o @ A2 @ B4 ) )
% 4.69/4.92 = ( inf_in1906310914598751387_nat_o @ A @ B4 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Int_insert_right
% 4.69/4.92 thf(fact_1355_Int__insert__right,axiom,
% 4.69/4.92 ! [A2: int,A: set_int,B4: set_int] :
% 4.69/4.92 ( ( ( member_int @ A2 @ A )
% 4.69/4.92 => ( ( inf_inf_set_int @ A @ ( insert_int @ A2 @ B4 ) )
% 4.69/4.92 = ( insert_int @ A2 @ ( inf_inf_set_int @ A @ B4 ) ) ) )
% 4.69/4.92 & ( ~ ( member_int @ A2 @ A )
% 4.69/4.92 => ( ( inf_inf_set_int @ A @ ( insert_int @ A2 @ B4 ) )
% 4.69/4.92 = ( inf_inf_set_int @ A @ B4 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Int_insert_right
% 4.69/4.92 thf(fact_1356_Int__insert__right,axiom,
% 4.69/4.92 ! [A2: $o,A: set_o,B4: set_o] :
% 4.69/4.92 ( ( ( member_o @ A2 @ A )
% 4.69/4.92 => ( ( inf_inf_set_o @ A @ ( insert_o @ A2 @ B4 ) )
% 4.69/4.92 = ( insert_o @ A2 @ ( inf_inf_set_o @ A @ B4 ) ) ) )
% 4.69/4.92 & ( ~ ( member_o @ A2 @ A )
% 4.69/4.92 => ( ( inf_inf_set_o @ A @ ( insert_o @ A2 @ B4 ) )
% 4.69/4.92 = ( inf_inf_set_o @ A @ B4 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Int_insert_right
% 4.69/4.92 thf(fact_1357_Int__insert__right,axiom,
% 4.69/4.92 ! [A2: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.92 ( ( ( member_Product_unit @ A2 @ A )
% 4.69/4.92 => ( ( inf_in4660618365625256667t_unit @ A @ ( insert_Product_unit @ A2 @ B4 ) )
% 4.69/4.92 = ( insert_Product_unit @ A2 @ ( inf_in4660618365625256667t_unit @ A @ B4 ) ) ) )
% 4.69/4.92 & ( ~ ( member_Product_unit @ A2 @ A )
% 4.69/4.92 => ( ( inf_in4660618365625256667t_unit @ A @ ( insert_Product_unit @ A2 @ B4 ) )
% 4.69/4.92 = ( inf_in4660618365625256667t_unit @ A @ B4 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Int_insert_right
% 4.69/4.92 thf(fact_1358_Int__insert__right,axiom,
% 4.69/4.92 ! [A2: nat,A: set_nat,B4: set_nat] :
% 4.69/4.92 ( ( ( member_nat @ A2 @ A )
% 4.69/4.92 => ( ( inf_inf_set_nat @ A @ ( insert_nat @ A2 @ B4 ) )
% 4.69/4.92 = ( insert_nat @ A2 @ ( inf_inf_set_nat @ A @ B4 ) ) ) )
% 4.69/4.92 & ( ~ ( member_nat @ A2 @ A )
% 4.69/4.92 => ( ( inf_inf_set_nat @ A @ ( insert_nat @ A2 @ B4 ) )
% 4.69/4.92 = ( inf_inf_set_nat @ A @ B4 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Int_insert_right
% 4.69/4.92 thf(fact_1359_Int__insert__left,axiom,
% 4.69/4.92 ! [A2: produc3658429121746597890et_nat > $o,C5: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( ( member6576561426505652726_nat_o @ A2 @ C5 )
% 4.69/4.92 => ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A2 @ B4 ) @ C5 )
% 4.69/4.92 = ( insert5175938949040314269_nat_o @ A2 @ ( inf_in1906310914598751387_nat_o @ B4 @ C5 ) ) ) )
% 4.69/4.92 & ( ~ ( member6576561426505652726_nat_o @ A2 @ C5 )
% 4.69/4.92 => ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A2 @ B4 ) @ C5 )
% 4.69/4.92 = ( inf_in1906310914598751387_nat_o @ B4 @ C5 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Int_insert_left
% 4.69/4.92 thf(fact_1360_Int__insert__left,axiom,
% 4.69/4.92 ! [A2: int,C5: set_int,B4: set_int] :
% 4.69/4.92 ( ( ( member_int @ A2 @ C5 )
% 4.69/4.92 => ( ( inf_inf_set_int @ ( insert_int @ A2 @ B4 ) @ C5 )
% 4.69/4.92 = ( insert_int @ A2 @ ( inf_inf_set_int @ B4 @ C5 ) ) ) )
% 4.69/4.92 & ( ~ ( member_int @ A2 @ C5 )
% 4.69/4.92 => ( ( inf_inf_set_int @ ( insert_int @ A2 @ B4 ) @ C5 )
% 4.69/4.92 = ( inf_inf_set_int @ B4 @ C5 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Int_insert_left
% 4.69/4.92 thf(fact_1361_Int__insert__left,axiom,
% 4.69/4.92 ! [A2: $o,C5: set_o,B4: set_o] :
% 4.69/4.92 ( ( ( member_o @ A2 @ C5 )
% 4.69/4.92 => ( ( inf_inf_set_o @ ( insert_o @ A2 @ B4 ) @ C5 )
% 4.69/4.92 = ( insert_o @ A2 @ ( inf_inf_set_o @ B4 @ C5 ) ) ) )
% 4.69/4.92 & ( ~ ( member_o @ A2 @ C5 )
% 4.69/4.92 => ( ( inf_inf_set_o @ ( insert_o @ A2 @ B4 ) @ C5 )
% 4.69/4.92 = ( inf_inf_set_o @ B4 @ C5 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Int_insert_left
% 4.69/4.92 thf(fact_1362_Int__insert__left,axiom,
% 4.69/4.92 ! [A2: product_unit,C5: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.92 ( ( ( member_Product_unit @ A2 @ C5 )
% 4.69/4.92 => ( ( inf_in4660618365625256667t_unit @ ( insert_Product_unit @ A2 @ B4 ) @ C5 )
% 4.69/4.92 = ( insert_Product_unit @ A2 @ ( inf_in4660618365625256667t_unit @ B4 @ C5 ) ) ) )
% 4.69/4.92 & ( ~ ( member_Product_unit @ A2 @ C5 )
% 4.69/4.92 => ( ( inf_in4660618365625256667t_unit @ ( insert_Product_unit @ A2 @ B4 ) @ C5 )
% 4.69/4.92 = ( inf_in4660618365625256667t_unit @ B4 @ C5 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Int_insert_left
% 4.69/4.92 thf(fact_1363_Int__insert__left,axiom,
% 4.69/4.92 ! [A2: nat,C5: set_nat,B4: set_nat] :
% 4.69/4.92 ( ( ( member_nat @ A2 @ C5 )
% 4.69/4.92 => ( ( inf_inf_set_nat @ ( insert_nat @ A2 @ B4 ) @ C5 )
% 4.69/4.92 = ( insert_nat @ A2 @ ( inf_inf_set_nat @ B4 @ C5 ) ) ) )
% 4.69/4.92 & ( ~ ( member_nat @ A2 @ C5 )
% 4.69/4.92 => ( ( inf_inf_set_nat @ ( insert_nat @ A2 @ B4 ) @ C5 )
% 4.69/4.92 = ( inf_inf_set_nat @ B4 @ C5 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Int_insert_left
% 4.69/4.92 thf(fact_1364_subrelI,axiom,
% 4.69/4.92 ! [R2: set_Pr3948176798113811640et_nat,S2: set_Pr3948176798113811640et_nat] :
% 4.69/4.92 ( ! [X3: heap_e7401611519738050253t_unit,Y2: set_nat] :
% 4.69/4.92 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X3 @ Y2 ) @ R2 )
% 4.69/4.92 => ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X3 @ Y2 ) @ S2 ) )
% 4.69/4.92 => ( ord_le8090042543978450200et_nat @ R2 @ S2 ) ) ).
% 4.69/4.92
% 4.69/4.92 % subrelI
% 4.69/4.92 thf(fact_1365_subrelI,axiom,
% 4.69/4.92 ! [R2: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 4.69/4.92 ( ! [X3: nat,Y2: nat] :
% 4.69/4.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ R2 )
% 4.69/4.92 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ S2 ) )
% 4.69/4.92 => ( ord_le3146513528884898305at_nat @ R2 @ S2 ) ) ).
% 4.69/4.92
% 4.69/4.92 % subrelI
% 4.69/4.92 thf(fact_1366_subrelI,axiom,
% 4.69/4.92 ! [R2: set_Pr958786334691620121nt_int,S2: set_Pr958786334691620121nt_int] :
% 4.69/4.92 ( ! [X3: int,Y2: int] :
% 4.69/4.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y2 ) @ R2 )
% 4.69/4.92 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y2 ) @ S2 ) )
% 4.69/4.92 => ( ord_le2843351958646193337nt_int @ R2 @ S2 ) ) ).
% 4.69/4.92
% 4.69/4.92 % subrelI
% 4.69/4.92 thf(fact_1367_subrelI,axiom,
% 4.69/4.92 ! [R2: set_Pr3286484037609594932et_nat,S2: set_Pr3286484037609594932et_nat] :
% 4.69/4.92 ( ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 4.69/4.92 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y2 ) @ R2 )
% 4.69/4.92 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y2 ) @ S2 ) )
% 4.69/4.92 => ( ord_le5966269811547037844et_nat @ R2 @ S2 ) ) ).
% 4.69/4.92
% 4.69/4.92 % subrelI
% 4.69/4.92 thf(fact_1368_subrelI,axiom,
% 4.69/4.92 ! [R2: set_Pr8536935166611901872et_nat,S2: set_Pr8536935166611901872et_nat] :
% 4.69/4.92 ( ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3925858234332021118et_nat] :
% 4.69/4.92 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y2 ) @ R2 )
% 4.69/4.92 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y2 ) @ S2 ) )
% 4.69/4.92 => ( ord_le4763372923235995152et_nat @ R2 @ S2 ) ) ).
% 4.69/4.92
% 4.69/4.92 % subrelI
% 4.69/4.92 thf(fact_1369_bot_Oextremum__uniqueI,axiom,
% 4.69/4.92 ! [A2: set_Product_unit] :
% 4.69/4.92 ( ( ord_le3507040750410214029t_unit @ A2 @ bot_bo3957492148770167129t_unit )
% 4.69/4.92 => ( A2 = bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.92
% 4.69/4.92 % bot.extremum_uniqueI
% 4.69/4.92 thf(fact_1370_bot_Oextremum__uniqueI,axiom,
% 4.69/4.92 ! [A2: set_o] :
% 4.69/4.92 ( ( ord_less_eq_set_o @ A2 @ bot_bot_set_o )
% 4.69/4.92 => ( A2 = bot_bot_set_o ) ) ).
% 4.69/4.92
% 4.69/4.92 % bot.extremum_uniqueI
% 4.69/4.92 thf(fact_1371_bot_Oextremum__uniqueI,axiom,
% 4.69/4.92 ! [A2: set_int] :
% 4.69/4.92 ( ( ord_less_eq_set_int @ A2 @ bot_bot_set_int )
% 4.69/4.92 => ( A2 = bot_bot_set_int ) ) ).
% 4.69/4.92
% 4.69/4.92 % bot.extremum_uniqueI
% 4.69/4.92 thf(fact_1372_bot_Oextremum__uniqueI,axiom,
% 4.69/4.92 ! [A2: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( ord_le2965882846123202637_nat_o @ A2 @ bot_bo7824918357723582233_nat_o )
% 4.69/4.92 => ( A2 = bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.92
% 4.69/4.92 % bot.extremum_uniqueI
% 4.69/4.92 thf(fact_1373_bot_Oextremum__uniqueI,axiom,
% 4.69/4.92 ! [A2: filter_nat] :
% 4.69/4.92 ( ( ord_le2510731241096832064er_nat @ A2 @ bot_bot_filter_nat )
% 4.69/4.92 => ( A2 = bot_bot_filter_nat ) ) ).
% 4.69/4.92
% 4.69/4.92 % bot.extremum_uniqueI
% 4.69/4.92 thf(fact_1374_bot_Oextremum__uniqueI,axiom,
% 4.69/4.92 ! [A2: set_nat] :
% 4.69/4.92 ( ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat )
% 4.69/4.92 => ( A2 = bot_bot_set_nat ) ) ).
% 4.69/4.92
% 4.69/4.92 % bot.extremum_uniqueI
% 4.69/4.92 thf(fact_1375_bot_Oextremum__uniqueI,axiom,
% 4.69/4.92 ! [A2: nat] :
% 4.69/4.92 ( ( ord_less_eq_nat @ A2 @ bot_bot_nat )
% 4.69/4.92 => ( A2 = bot_bot_nat ) ) ).
% 4.69/4.92
% 4.69/4.92 % bot.extremum_uniqueI
% 4.69/4.92 thf(fact_1376_bot_Oextremum__unique,axiom,
% 4.69/4.92 ! [A2: set_Product_unit] :
% 4.69/4.92 ( ( ord_le3507040750410214029t_unit @ A2 @ bot_bo3957492148770167129t_unit )
% 4.69/4.92 = ( A2 = bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.92
% 4.69/4.92 % bot.extremum_unique
% 4.69/4.92 thf(fact_1377_bot_Oextremum__unique,axiom,
% 4.69/4.92 ! [A2: set_o] :
% 4.69/4.92 ( ( ord_less_eq_set_o @ A2 @ bot_bot_set_o )
% 4.69/4.92 = ( A2 = bot_bot_set_o ) ) ).
% 4.69/4.92
% 4.69/4.92 % bot.extremum_unique
% 4.69/4.92 thf(fact_1378_bot_Oextremum__unique,axiom,
% 4.69/4.92 ! [A2: set_int] :
% 4.69/4.92 ( ( ord_less_eq_set_int @ A2 @ bot_bot_set_int )
% 4.69/4.92 = ( A2 = bot_bot_set_int ) ) ).
% 4.69/4.92
% 4.69/4.92 % bot.extremum_unique
% 4.69/4.92 thf(fact_1379_bot_Oextremum__unique,axiom,
% 4.69/4.92 ! [A2: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( ord_le2965882846123202637_nat_o @ A2 @ bot_bo7824918357723582233_nat_o )
% 4.69/4.92 = ( A2 = bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.92
% 4.69/4.92 % bot.extremum_unique
% 4.69/4.92 thf(fact_1380_bot_Oextremum__unique,axiom,
% 4.69/4.92 ! [A2: filter_nat] :
% 4.69/4.92 ( ( ord_le2510731241096832064er_nat @ A2 @ bot_bot_filter_nat )
% 4.69/4.92 = ( A2 = bot_bot_filter_nat ) ) ).
% 4.69/4.92
% 4.69/4.92 % bot.extremum_unique
% 4.69/4.92 thf(fact_1381_bot_Oextremum__unique,axiom,
% 4.69/4.92 ! [A2: set_nat] :
% 4.69/4.92 ( ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat )
% 4.69/4.92 = ( A2 = bot_bot_set_nat ) ) ).
% 4.69/4.92
% 4.69/4.92 % bot.extremum_unique
% 4.69/4.92 thf(fact_1382_bot_Oextremum__unique,axiom,
% 4.69/4.92 ! [A2: nat] :
% 4.69/4.92 ( ( ord_less_eq_nat @ A2 @ bot_bot_nat )
% 4.69/4.92 = ( A2 = bot_bot_nat ) ) ).
% 4.69/4.92
% 4.69/4.92 % bot.extremum_unique
% 4.69/4.92 thf(fact_1383_bot_Oextremum,axiom,
% 4.69/4.92 ! [A2: set_Product_unit] : ( ord_le3507040750410214029t_unit @ bot_bo3957492148770167129t_unit @ A2 ) ).
% 4.69/4.92
% 4.69/4.92 % bot.extremum
% 4.69/4.92 thf(fact_1384_bot_Oextremum,axiom,
% 4.69/4.92 ! [A2: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A2 ) ).
% 4.69/4.92
% 4.69/4.92 % bot.extremum
% 4.69/4.92 thf(fact_1385_bot_Oextremum,axiom,
% 4.69/4.92 ! [A2: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A2 ) ).
% 4.69/4.92
% 4.69/4.92 % bot.extremum
% 4.69/4.92 thf(fact_1386_bot_Oextremum,axiom,
% 4.69/4.92 ! [A2: set_Pr4532377907799695533_nat_o] : ( ord_le2965882846123202637_nat_o @ bot_bo7824918357723582233_nat_o @ A2 ) ).
% 4.69/4.92
% 4.69/4.92 % bot.extremum
% 4.69/4.92 thf(fact_1387_bot_Oextremum,axiom,
% 4.69/4.92 ! [A2: filter_nat] : ( ord_le2510731241096832064er_nat @ bot_bot_filter_nat @ A2 ) ).
% 4.69/4.92
% 4.69/4.92 % bot.extremum
% 4.69/4.92 thf(fact_1388_bot_Oextremum,axiom,
% 4.69/4.92 ! [A2: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A2 ) ).
% 4.69/4.92
% 4.69/4.92 % bot.extremum
% 4.69/4.92 thf(fact_1389_bot_Oextremum,axiom,
% 4.69/4.92 ! [A2: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A2 ) ).
% 4.69/4.92
% 4.69/4.92 % bot.extremum
% 4.69/4.92 thf(fact_1390_subset__emptyI,axiom,
% 4.69/4.92 ! [A: set_Product_unit] :
% 4.69/4.92 ( ! [X3: product_unit] :
% 4.69/4.92 ~ ( member_Product_unit @ X3 @ A )
% 4.69/4.92 => ( ord_le3507040750410214029t_unit @ A @ bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_emptyI
% 4.69/4.92 thf(fact_1391_subset__emptyI,axiom,
% 4.69/4.92 ! [A: set_o] :
% 4.69/4.92 ( ! [X3: $o] :
% 4.69/4.92 ~ ( member_o @ X3 @ A )
% 4.69/4.92 => ( ord_less_eq_set_o @ A @ bot_bot_set_o ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_emptyI
% 4.69/4.92 thf(fact_1392_subset__emptyI,axiom,
% 4.69/4.92 ! [A: set_int] :
% 4.69/4.92 ( ! [X3: int] :
% 4.69/4.92 ~ ( member_int @ X3 @ A )
% 4.69/4.92 => ( ord_less_eq_set_int @ A @ bot_bot_set_int ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_emptyI
% 4.69/4.92 thf(fact_1393_subset__emptyI,axiom,
% 4.69/4.92 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.92 ~ ( member6576561426505652726_nat_o @ X3 @ A )
% 4.69/4.92 => ( ord_le2965882846123202637_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_emptyI
% 4.69/4.92 thf(fact_1394_subset__emptyI,axiom,
% 4.69/4.92 ! [A: set_nat] :
% 4.69/4.92 ( ! [X3: nat] :
% 4.69/4.92 ~ ( member_nat @ X3 @ A )
% 4.69/4.92 => ( ord_less_eq_set_nat @ A @ bot_bot_set_nat ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_emptyI
% 4.69/4.92 thf(fact_1395_insert__subsetI,axiom,
% 4.69/4.92 ! [X: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,X4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( member6576561426505652726_nat_o @ X @ A )
% 4.69/4.92 => ( ( ord_le2965882846123202637_nat_o @ X4 @ A )
% 4.69/4.92 => ( ord_le2965882846123202637_nat_o @ ( insert5175938949040314269_nat_o @ X @ X4 ) @ A ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % insert_subsetI
% 4.69/4.92 thf(fact_1396_insert__subsetI,axiom,
% 4.69/4.92 ! [X: int,A: set_int,X4: set_int] :
% 4.69/4.92 ( ( member_int @ X @ A )
% 4.69/4.92 => ( ( ord_less_eq_set_int @ X4 @ A )
% 4.69/4.92 => ( ord_less_eq_set_int @ ( insert_int @ X @ X4 ) @ A ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % insert_subsetI
% 4.69/4.92 thf(fact_1397_insert__subsetI,axiom,
% 4.69/4.92 ! [X: $o,A: set_o,X4: set_o] :
% 4.69/4.92 ( ( member_o @ X @ A )
% 4.69/4.92 => ( ( ord_less_eq_set_o @ X4 @ A )
% 4.69/4.92 => ( ord_less_eq_set_o @ ( insert_o @ X @ X4 ) @ A ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % insert_subsetI
% 4.69/4.92 thf(fact_1398_insert__subsetI,axiom,
% 4.69/4.92 ! [X: product_unit,A: set_Product_unit,X4: set_Product_unit] :
% 4.69/4.92 ( ( member_Product_unit @ X @ A )
% 4.69/4.92 => ( ( ord_le3507040750410214029t_unit @ X4 @ A )
% 4.69/4.92 => ( ord_le3507040750410214029t_unit @ ( insert_Product_unit @ X @ X4 ) @ A ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % insert_subsetI
% 4.69/4.92 thf(fact_1399_insert__subsetI,axiom,
% 4.69/4.92 ! [X: nat,A: set_nat,X4: set_nat] :
% 4.69/4.92 ( ( member_nat @ X @ A )
% 4.69/4.92 => ( ( ord_less_eq_set_nat @ X4 @ A )
% 4.69/4.92 => ( ord_less_eq_set_nat @ ( insert_nat @ X @ X4 ) @ A ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % insert_subsetI
% 4.69/4.92 thf(fact_1400_subset__insertI2,axiom,
% 4.69/4.92 ! [A: set_int,B4: set_int,B: int] :
% 4.69/4.92 ( ( ord_less_eq_set_int @ A @ B4 )
% 4.69/4.92 => ( ord_less_eq_set_int @ A @ ( insert_int @ B @ B4 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_insertI2
% 4.69/4.92 thf(fact_1401_subset__insertI2,axiom,
% 4.69/4.92 ! [A: set_o,B4: set_o,B: $o] :
% 4.69/4.92 ( ( ord_less_eq_set_o @ A @ B4 )
% 4.69/4.92 => ( ord_less_eq_set_o @ A @ ( insert_o @ B @ B4 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_insertI2
% 4.69/4.92 thf(fact_1402_subset__insertI2,axiom,
% 4.69/4.92 ! [A: set_Product_unit,B4: set_Product_unit,B: product_unit] :
% 4.69/4.92 ( ( ord_le3507040750410214029t_unit @ A @ B4 )
% 4.69/4.92 => ( ord_le3507040750410214029t_unit @ A @ ( insert_Product_unit @ B @ B4 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_insertI2
% 4.69/4.92 thf(fact_1403_subset__insertI2,axiom,
% 4.69/4.92 ! [A: set_nat,B4: set_nat,B: nat] :
% 4.69/4.92 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.92 => ( ord_less_eq_set_nat @ A @ ( insert_nat @ B @ B4 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_insertI2
% 4.69/4.92 thf(fact_1404_subset__insertI,axiom,
% 4.69/4.92 ! [B4: set_int,A2: int] : ( ord_less_eq_set_int @ B4 @ ( insert_int @ A2 @ B4 ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_insertI
% 4.69/4.92 thf(fact_1405_subset__insertI,axiom,
% 4.69/4.92 ! [B4: set_o,A2: $o] : ( ord_less_eq_set_o @ B4 @ ( insert_o @ A2 @ B4 ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_insertI
% 4.69/4.92 thf(fact_1406_subset__insertI,axiom,
% 4.69/4.92 ! [B4: set_Product_unit,A2: product_unit] : ( ord_le3507040750410214029t_unit @ B4 @ ( insert_Product_unit @ A2 @ B4 ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_insertI
% 4.69/4.92 thf(fact_1407_subset__insertI,axiom,
% 4.69/4.92 ! [B4: set_nat,A2: nat] : ( ord_less_eq_set_nat @ B4 @ ( insert_nat @ A2 @ B4 ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_insertI
% 4.69/4.92 thf(fact_1408_subset__insert,axiom,
% 4.69/4.92 ! [X: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ~ ( member6576561426505652726_nat_o @ X @ A )
% 4.69/4.92 => ( ( ord_le2965882846123202637_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ B4 ) )
% 4.69/4.92 = ( ord_le2965882846123202637_nat_o @ A @ B4 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_insert
% 4.69/4.92 thf(fact_1409_subset__insert,axiom,
% 4.69/4.92 ! [X: int,A: set_int,B4: set_int] :
% 4.69/4.92 ( ~ ( member_int @ X @ A )
% 4.69/4.92 => ( ( ord_less_eq_set_int @ A @ ( insert_int @ X @ B4 ) )
% 4.69/4.92 = ( ord_less_eq_set_int @ A @ B4 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_insert
% 4.69/4.92 thf(fact_1410_subset__insert,axiom,
% 4.69/4.92 ! [X: $o,A: set_o,B4: set_o] :
% 4.69/4.92 ( ~ ( member_o @ X @ A )
% 4.69/4.92 => ( ( ord_less_eq_set_o @ A @ ( insert_o @ X @ B4 ) )
% 4.69/4.92 = ( ord_less_eq_set_o @ A @ B4 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_insert
% 4.69/4.92 thf(fact_1411_subset__insert,axiom,
% 4.69/4.92 ! [X: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.92 ( ~ ( member_Product_unit @ X @ A )
% 4.69/4.92 => ( ( ord_le3507040750410214029t_unit @ A @ ( insert_Product_unit @ X @ B4 ) )
% 4.69/4.92 = ( ord_le3507040750410214029t_unit @ A @ B4 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_insert
% 4.69/4.92 thf(fact_1412_subset__insert,axiom,
% 4.69/4.92 ! [X: nat,A: set_nat,B4: set_nat] :
% 4.69/4.92 ( ~ ( member_nat @ X @ A )
% 4.69/4.92 => ( ( ord_less_eq_set_nat @ A @ ( insert_nat @ X @ B4 ) )
% 4.69/4.92 = ( ord_less_eq_set_nat @ A @ B4 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_insert
% 4.69/4.92 thf(fact_1413_insert__mono,axiom,
% 4.69/4.92 ! [C5: set_int,D3: set_int,A2: int] :
% 4.69/4.92 ( ( ord_less_eq_set_int @ C5 @ D3 )
% 4.69/4.92 => ( ord_less_eq_set_int @ ( insert_int @ A2 @ C5 ) @ ( insert_int @ A2 @ D3 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % insert_mono
% 4.69/4.92 thf(fact_1414_insert__mono,axiom,
% 4.69/4.92 ! [C5: set_o,D3: set_o,A2: $o] :
% 4.69/4.92 ( ( ord_less_eq_set_o @ C5 @ D3 )
% 4.69/4.92 => ( ord_less_eq_set_o @ ( insert_o @ A2 @ C5 ) @ ( insert_o @ A2 @ D3 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % insert_mono
% 4.69/4.92 thf(fact_1415_insert__mono,axiom,
% 4.69/4.92 ! [C5: set_Product_unit,D3: set_Product_unit,A2: product_unit] :
% 4.69/4.92 ( ( ord_le3507040750410214029t_unit @ C5 @ D3 )
% 4.69/4.92 => ( ord_le3507040750410214029t_unit @ ( insert_Product_unit @ A2 @ C5 ) @ ( insert_Product_unit @ A2 @ D3 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % insert_mono
% 4.69/4.92 thf(fact_1416_insert__mono,axiom,
% 4.69/4.92 ! [C5: set_nat,D3: set_nat,A2: nat] :
% 4.69/4.92 ( ( ord_less_eq_set_nat @ C5 @ D3 )
% 4.69/4.92 => ( ord_less_eq_set_nat @ ( insert_nat @ A2 @ C5 ) @ ( insert_nat @ A2 @ D3 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % insert_mono
% 4.69/4.92 thf(fact_1417_Image__Un,axiom,
% 4.69/4.92 ! [R3: set_Pr1261947904930325089at_nat,A: set_nat,B4: set_nat] :
% 4.69/4.92 ( ( image_nat_nat @ R3 @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.92 = ( sup_sup_set_nat @ ( image_nat_nat @ R3 @ A ) @ ( image_nat_nat @ R3 @ B4 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Image_Un
% 4.69/4.92 thf(fact_1418_subset__vimage__iff,axiom,
% 4.69/4.92 ! [A: set_nat,F: nat > produc3658429121746597890et_nat > $o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( ord_less_eq_set_nat @ A @ ( vimage8201027140005291904_nat_o @ F @ B4 ) )
% 4.69/4.92 = ( ! [X2: nat] :
% 4.69/4.92 ( ( member_nat @ X2 @ A )
% 4.69/4.92 => ( member6576561426505652726_nat_o @ ( F @ X2 ) @ B4 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_vimage_iff
% 4.69/4.92 thf(fact_1419_subset__vimage__iff,axiom,
% 4.69/4.92 ! [A: set_nat,F: nat > nat,B4: set_nat] :
% 4.69/4.92 ( ( ord_less_eq_set_nat @ A @ ( vimage_nat_nat @ F @ B4 ) )
% 4.69/4.92 = ( ! [X2: nat] :
% 4.69/4.92 ( ( member_nat @ X2 @ A )
% 4.69/4.92 => ( member_nat @ ( F @ X2 ) @ B4 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_vimage_iff
% 4.69/4.92 thf(fact_1420_subset__vimage__iff,axiom,
% 4.69/4.92 ! [A: set_nat,F: nat > int,B4: set_int] :
% 4.69/4.92 ( ( ord_less_eq_set_nat @ A @ ( vimage_nat_int @ F @ B4 ) )
% 4.69/4.92 = ( ! [X2: nat] :
% 4.69/4.92 ( ( member_nat @ X2 @ A )
% 4.69/4.92 => ( member_int @ ( F @ X2 ) @ B4 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_vimage_iff
% 4.69/4.92 thf(fact_1421_subset__vimage__iff,axiom,
% 4.69/4.92 ! [A: set_nat,F: nat > $o,B4: set_o] :
% 4.69/4.92 ( ( ord_less_eq_set_nat @ A @ ( vimage_nat_o @ F @ B4 ) )
% 4.69/4.92 = ( ! [X2: nat] :
% 4.69/4.92 ( ( member_nat @ X2 @ A )
% 4.69/4.92 => ( member_o @ ( F @ X2 ) @ B4 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_vimage_iff
% 4.69/4.92 thf(fact_1422_subset__vimage__iff,axiom,
% 4.69/4.92 ! [A: set_nat,F: nat > product_unit,B4: set_Product_unit] :
% 4.69/4.92 ( ( ord_less_eq_set_nat @ A @ ( vimage4884490618288580032t_unit @ F @ B4 ) )
% 4.69/4.92 = ( ! [X2: nat] :
% 4.69/4.92 ( ( member_nat @ X2 @ A )
% 4.69/4.92 => ( member_Product_unit @ ( F @ X2 ) @ B4 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_vimage_iff
% 4.69/4.92 thf(fact_1423_vimage__mono,axiom,
% 4.69/4.92 ! [A: set_nat,B4: set_nat,F: nat > nat] :
% 4.69/4.92 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.92 => ( ord_less_eq_set_nat @ ( vimage_nat_nat @ F @ A ) @ ( vimage_nat_nat @ F @ B4 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % vimage_mono
% 4.69/4.92 thf(fact_1424_relH__subset,axiom,
% 4.69/4.92 ! [Bs: set_nat,H2: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 4.69/4.92 ( ( relH @ Bs @ H2 @ H3 )
% 4.69/4.92 => ( ( ord_less_eq_set_nat @ As @ Bs )
% 4.69/4.92 => ( relH @ As @ H2 @ H3 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % relH_subset
% 4.69/4.92 thf(fact_1425_rtrancl__apply__insert,axiom,
% 4.69/4.92 ! [R3: set_Pr5094982260447487303t_unit,X: product_unit,S: set_Product_unit] :
% 4.69/4.92 ( ( image_8431784415008483091t_unit @ ( transi6481887417741755664t_unit @ R3 ) @ ( insert_Product_unit @ X @ S ) )
% 4.69/4.92 = ( insert_Product_unit @ X @ ( image_8431784415008483091t_unit @ ( transi6481887417741755664t_unit @ R3 ) @ ( sup_su793286257634532545t_unit @ S @ ( image_8431784415008483091t_unit @ R3 @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_apply_insert
% 4.69/4.92 thf(fact_1426_rtrancl__apply__insert,axiom,
% 4.69/4.92 ! [R3: set_Product_prod_o_o,X: $o,S: set_o] :
% 4.69/4.92 ( ( image_o_o @ ( transitive_rtrancl_o @ R3 ) @ ( insert_o @ X @ S ) )
% 4.69/4.92 = ( insert_o @ X @ ( image_o_o @ ( transitive_rtrancl_o @ R3 ) @ ( sup_sup_set_o @ S @ ( image_o_o @ R3 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_apply_insert
% 4.69/4.92 thf(fact_1427_rtrancl__apply__insert,axiom,
% 4.69/4.92 ! [R3: set_Pr1261947904930325089at_nat,X: nat,S: set_nat] :
% 4.69/4.92 ( ( image_nat_nat @ ( transi2905341329935302413cl_nat @ R3 ) @ ( insert_nat @ X @ S ) )
% 4.69/4.92 = ( insert_nat @ X @ ( image_nat_nat @ ( transi2905341329935302413cl_nat @ R3 ) @ ( sup_sup_set_nat @ S @ ( image_nat_nat @ R3 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_apply_insert
% 4.69/4.92 thf(fact_1428_rtrancl__apply__insert,axiom,
% 4.69/4.92 ! [R3: set_Pr958786334691620121nt_int,X: int,S: set_int] :
% 4.69/4.92 ( ( image_int_int @ ( transi2902850859426252137cl_int @ R3 ) @ ( insert_int @ X @ S ) )
% 4.69/4.92 = ( insert_int @ X @ ( image_int_int @ ( transi2902850859426252137cl_int @ R3 ) @ ( sup_sup_set_int @ S @ ( image_int_int @ R3 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_apply_insert
% 4.69/4.92 thf(fact_1429_rtrancl__apply__insert,axiom,
% 4.69/4.92 ! [R3: set_Pr2161125870931222855_nat_o,X: produc3658429121746597890et_nat > $o,S: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( image_2232984160439939859_nat_o @ ( transi712980445759334096_nat_o @ R3 ) @ ( insert5175938949040314269_nat_o @ X @ S ) )
% 4.69/4.92 = ( insert5175938949040314269_nat_o @ X @ ( image_2232984160439939859_nat_o @ ( transi712980445759334096_nat_o @ R3 ) @ ( sup_su5209123915105501825_nat_o @ S @ ( image_2232984160439939859_nat_o @ R3 @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_apply_insert
% 4.69/4.92 thf(fact_1430_antisymD,axiom,
% 4.69/4.92 ! [R2: set_Pr1261947904930325089at_nat,A2: nat,B: nat] :
% 4.69/4.92 ( ( antisym_nat @ R2 )
% 4.69/4.92 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 )
% 4.69/4.92 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ A2 ) @ R2 )
% 4.69/4.92 => ( A2 = B ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % antisymD
% 4.69/4.92 thf(fact_1431_antisymD,axiom,
% 4.69/4.92 ! [R2: set_Pr958786334691620121nt_int,A2: int,B: int] :
% 4.69/4.92 ( ( antisym_int @ R2 )
% 4.69/4.92 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 )
% 4.69/4.92 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ A2 ) @ R2 )
% 4.69/4.92 => ( A2 = B ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % antisymD
% 4.69/4.92 thf(fact_1432_antisymI,axiom,
% 4.69/4.92 ! [R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.92 ( ! [X3: nat,Y2: nat] :
% 4.69/4.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ R2 )
% 4.69/4.92 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ X3 ) @ R2 )
% 4.69/4.92 => ( X3 = Y2 ) ) )
% 4.69/4.92 => ( antisym_nat @ R2 ) ) ).
% 4.69/4.92
% 4.69/4.92 % antisymI
% 4.69/4.92 thf(fact_1433_antisymI,axiom,
% 4.69/4.92 ! [R2: set_Pr958786334691620121nt_int] :
% 4.69/4.92 ( ! [X3: int,Y2: int] :
% 4.69/4.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y2 ) @ R2 )
% 4.69/4.92 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y2 @ X3 ) @ R2 )
% 4.69/4.92 => ( X3 = Y2 ) ) )
% 4.69/4.92 => ( antisym_int @ R2 ) ) ).
% 4.69/4.92
% 4.69/4.92 % antisymI
% 4.69/4.92 thf(fact_1434_antisym__def,axiom,
% 4.69/4.92 ( antisym_nat
% 4.69/4.92 = ( ^ [R4: set_Pr1261947904930325089at_nat] :
% 4.69/4.92 ! [X2: nat,Y3: nat] :
% 4.69/4.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ R4 )
% 4.69/4.92 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ X2 ) @ R4 )
% 4.69/4.92 => ( X2 = Y3 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % antisym_def
% 4.69/4.92 thf(fact_1435_antisym__def,axiom,
% 4.69/4.92 ( antisym_int
% 4.69/4.92 = ( ^ [R4: set_Pr958786334691620121nt_int] :
% 4.69/4.92 ! [X2: int,Y3: int] :
% 4.69/4.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ R4 )
% 4.69/4.92 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ X2 ) @ R4 )
% 4.69/4.92 => ( X2 = Y3 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % antisym_def
% 4.69/4.92 thf(fact_1436_Image__absorb__rtrancl,axiom,
% 4.69/4.92 ! [A: set_Pr1261947904930325089at_nat,B4: set_nat,C5: set_nat] :
% 4.69/4.92 ( ( trans_nat @ A )
% 4.69/4.92 => ( ( refl_on_nat @ B4 @ A )
% 4.69/4.92 => ( ( ord_less_eq_set_nat @ C5 @ B4 )
% 4.69/4.92 => ( ( image_nat_nat @ ( transi2905341329935302413cl_nat @ A ) @ C5 )
% 4.69/4.92 = ( image_nat_nat @ A @ C5 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Image_absorb_rtrancl
% 4.69/4.92 thf(fact_1437_times__assn__raw_Osimps,axiom,
% 4.69/4.92 ! [P: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o,H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 4.69/4.92 ( ( times_assn_raw @ P @ Q2 @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 4.69/4.92 = ( ? [As1: set_nat,As22: set_nat] :
% 4.69/4.92 ( ( As
% 4.69/4.92 = ( sup_sup_set_nat @ As1 @ As22 ) )
% 4.69/4.92 & ( ( inf_inf_set_nat @ As1 @ As22 )
% 4.69/4.92 = bot_bot_set_nat )
% 4.69/4.92 & ( P @ ( produc7507926704131184380et_nat @ H2 @ As1 ) )
% 4.69/4.92 & ( Q2 @ ( produc7507926704131184380et_nat @ H2 @ As22 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % times_assn_raw.simps
% 4.69/4.92 thf(fact_1438_times__assn__raw_Oelims_I1_J,axiom,
% 4.69/4.92 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 4.69/4.92 ( ( ( times_assn_raw @ X @ Xa @ Xb )
% 4.69/4.92 = Y )
% 4.69/4.92 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.92 ( ( Xb
% 4.69/4.92 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.92 => ( Y
% 4.69/4.92 = ( ~ ? [As1: set_nat,As22: set_nat] :
% 4.69/4.92 ( ( As2
% 4.69/4.92 = ( sup_sup_set_nat @ As1 @ As22 ) )
% 4.69/4.92 & ( ( inf_inf_set_nat @ As1 @ As22 )
% 4.69/4.92 = bot_bot_set_nat )
% 4.69/4.92 & ( X @ ( produc7507926704131184380et_nat @ H @ As1 ) )
% 4.69/4.92 & ( Xa @ ( produc7507926704131184380et_nat @ H @ As22 ) ) ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % times_assn_raw.elims(1)
% 4.69/4.92 thf(fact_1439_times__assn__raw_Oelims_I2_J,axiom,
% 4.69/4.92 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 4.69/4.92 ( ( times_assn_raw @ X @ Xa @ Xb )
% 4.69/4.92 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.92 ( ( Xb
% 4.69/4.92 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.92 => ~ ? [As12: set_nat,As23: set_nat] :
% 4.69/4.92 ( ( As2
% 4.69/4.92 = ( sup_sup_set_nat @ As12 @ As23 ) )
% 4.69/4.92 & ( ( inf_inf_set_nat @ As12 @ As23 )
% 4.69/4.92 = bot_bot_set_nat )
% 4.69/4.92 & ( X @ ( produc7507926704131184380et_nat @ H @ As12 ) )
% 4.69/4.92 & ( Xa @ ( produc7507926704131184380et_nat @ H @ As23 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % times_assn_raw.elims(2)
% 4.69/4.92 thf(fact_1440_times__assn__raw_Oelims_I3_J,axiom,
% 4.69/4.92 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 4.69/4.92 ( ~ ( times_assn_raw @ X @ Xa @ Xb )
% 4.69/4.92 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.92 ( ( Xb
% 4.69/4.92 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.92 => ? [As13: set_nat,As24: set_nat] :
% 4.69/4.92 ( ( As2
% 4.69/4.92 = ( sup_sup_set_nat @ As13 @ As24 ) )
% 4.69/4.92 & ( ( inf_inf_set_nat @ As13 @ As24 )
% 4.69/4.92 = bot_bot_set_nat )
% 4.69/4.92 & ( X @ ( produc7507926704131184380et_nat @ H @ As13 ) )
% 4.69/4.92 & ( Xa @ ( produc7507926704131184380et_nat @ H @ As24 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % times_assn_raw.elims(3)
% 4.69/4.92 thf(fact_1441_rtrancl__Image__advance__ss,axiom,
% 4.69/4.92 ! [U: product_unit,V: product_unit,E: set_Pr5094982260447487303t_unit] :
% 4.69/4.92 ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ U @ V ) @ E )
% 4.69/4.92 => ( ord_le3507040750410214029t_unit @ ( image_8431784415008483091t_unit @ ( transi6481887417741755664t_unit @ E ) @ ( insert_Product_unit @ V @ bot_bo3957492148770167129t_unit ) ) @ ( image_8431784415008483091t_unit @ ( transi6481887417741755664t_unit @ E ) @ ( insert_Product_unit @ U @ bot_bo3957492148770167129t_unit ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_Image_advance_ss
% 4.69/4.92 thf(fact_1442_rtrancl__Image__advance__ss,axiom,
% 4.69/4.92 ! [U: $o,V: $o,E: set_Product_prod_o_o] :
% 4.69/4.92 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ U @ V ) @ E )
% 4.69/4.92 => ( ord_less_eq_set_o @ ( image_o_o @ ( transitive_rtrancl_o @ E ) @ ( insert_o @ V @ bot_bot_set_o ) ) @ ( image_o_o @ ( transitive_rtrancl_o @ E ) @ ( insert_o @ U @ bot_bot_set_o ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_Image_advance_ss
% 4.69/4.92 thf(fact_1443_rtrancl__Image__advance__ss,axiom,
% 4.69/4.92 ! [U: int,V: int,E: set_Pr958786334691620121nt_int] :
% 4.69/4.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ U @ V ) @ E )
% 4.69/4.92 => ( ord_less_eq_set_int @ ( image_int_int @ ( transi2902850859426252137cl_int @ E ) @ ( insert_int @ V @ bot_bot_set_int ) ) @ ( image_int_int @ ( transi2902850859426252137cl_int @ E ) @ ( insert_int @ U @ bot_bot_set_int ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_Image_advance_ss
% 4.69/4.92 thf(fact_1444_rtrancl__Image__advance__ss,axiom,
% 4.69/4.92 ! [U: produc3658429121746597890et_nat > $o,V: produc3658429121746597890et_nat > $o,E: set_Pr2161125870931222855_nat_o] :
% 4.69/4.92 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ U @ V ) @ E )
% 4.69/4.92 => ( ord_le2965882846123202637_nat_o @ ( image_2232984160439939859_nat_o @ ( transi712980445759334096_nat_o @ E ) @ ( insert5175938949040314269_nat_o @ V @ bot_bo7824918357723582233_nat_o ) ) @ ( image_2232984160439939859_nat_o @ ( transi712980445759334096_nat_o @ E ) @ ( insert5175938949040314269_nat_o @ U @ bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_Image_advance_ss
% 4.69/4.92 thf(fact_1445_rtrancl__Image__advance__ss,axiom,
% 4.69/4.92 ! [U: nat,V: nat,E: set_Pr1261947904930325089at_nat] :
% 4.69/4.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ U @ V ) @ E )
% 4.69/4.92 => ( ord_less_eq_set_nat @ ( image_nat_nat @ ( transi2905341329935302413cl_nat @ E ) @ ( insert_nat @ V @ bot_bot_set_nat ) ) @ ( image_nat_nat @ ( transi2905341329935302413cl_nat @ E ) @ ( insert_nat @ U @ bot_bot_set_nat ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_Image_advance_ss
% 4.69/4.92 thf(fact_1446_rtrancl__image__advance__rtrancl,axiom,
% 4.69/4.92 ! [Q4: produc3658429121746597890et_nat > $o,R3: set_Pr2161125870931222855_nat_o,Q0: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/4.92 ( ( member6576561426505652726_nat_o @ Q4 @ ( image_2232984160439939859_nat_o @ ( transi712980445759334096_nat_o @ R3 ) @ Q0 ) )
% 4.69/4.92 => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ Q4 @ X ) @ ( transi712980445759334096_nat_o @ R3 ) )
% 4.69/4.92 => ( member6576561426505652726_nat_o @ X @ ( image_2232984160439939859_nat_o @ ( transi712980445759334096_nat_o @ R3 ) @ Q0 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_image_advance_rtrancl
% 4.69/4.92 thf(fact_1447_rtrancl__image__advance__rtrancl,axiom,
% 4.69/4.92 ! [Q4: $o,R3: set_Product_prod_o_o,Q0: set_o,X: $o] :
% 4.69/4.92 ( ( member_o @ Q4 @ ( image_o_o @ ( transitive_rtrancl_o @ R3 ) @ Q0 ) )
% 4.69/4.92 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ Q4 @ X ) @ ( transitive_rtrancl_o @ R3 ) )
% 4.69/4.92 => ( member_o @ X @ ( image_o_o @ ( transitive_rtrancl_o @ R3 ) @ Q0 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_image_advance_rtrancl
% 4.69/4.92 thf(fact_1448_rtrancl__image__advance__rtrancl,axiom,
% 4.69/4.92 ! [Q4: product_unit,R3: set_Pr5094982260447487303t_unit,Q0: set_Product_unit,X: product_unit] :
% 4.69/4.92 ( ( member_Product_unit @ Q4 @ ( image_8431784415008483091t_unit @ ( transi6481887417741755664t_unit @ R3 ) @ Q0 ) )
% 4.69/4.92 => ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ Q4 @ X ) @ ( transi6481887417741755664t_unit @ R3 ) )
% 4.69/4.92 => ( member_Product_unit @ X @ ( image_8431784415008483091t_unit @ ( transi6481887417741755664t_unit @ R3 ) @ Q0 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_image_advance_rtrancl
% 4.69/4.92 thf(fact_1449_rtrancl__image__advance__rtrancl,axiom,
% 4.69/4.92 ! [Q4: nat,R3: set_Pr1261947904930325089at_nat,Q0: set_nat,X: nat] :
% 4.69/4.92 ( ( member_nat @ Q4 @ ( image_nat_nat @ ( transi2905341329935302413cl_nat @ R3 ) @ Q0 ) )
% 4.69/4.92 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Q4 @ X ) @ ( transi2905341329935302413cl_nat @ R3 ) )
% 4.69/4.92 => ( member_nat @ X @ ( image_nat_nat @ ( transi2905341329935302413cl_nat @ R3 ) @ Q0 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_image_advance_rtrancl
% 4.69/4.92 thf(fact_1450_rtrancl__image__advance__rtrancl,axiom,
% 4.69/4.92 ! [Q4: int,R3: set_Pr958786334691620121nt_int,Q0: set_int,X: int] :
% 4.69/4.92 ( ( member_int @ Q4 @ ( image_int_int @ ( transi2902850859426252137cl_int @ R3 ) @ Q0 ) )
% 4.69/4.92 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Q4 @ X ) @ ( transi2902850859426252137cl_int @ R3 ) )
% 4.69/4.92 => ( member_int @ X @ ( image_int_int @ ( transi2902850859426252137cl_int @ R3 ) @ Q0 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_image_advance_rtrancl
% 4.69/4.92 thf(fact_1451_rtrancl__image__advance,axiom,
% 4.69/4.92 ! [Q4: produc3658429121746597890et_nat > $o,R3: set_Pr2161125870931222855_nat_o,Q0: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/4.92 ( ( member6576561426505652726_nat_o @ Q4 @ ( image_2232984160439939859_nat_o @ ( transi712980445759334096_nat_o @ R3 ) @ Q0 ) )
% 4.69/4.92 => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ Q4 @ X ) @ R3 )
% 4.69/4.92 => ( member6576561426505652726_nat_o @ X @ ( image_2232984160439939859_nat_o @ ( transi712980445759334096_nat_o @ R3 ) @ Q0 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_image_advance
% 4.69/4.92 thf(fact_1452_rtrancl__image__advance,axiom,
% 4.69/4.92 ! [Q4: $o,R3: set_Product_prod_o_o,Q0: set_o,X: $o] :
% 4.69/4.92 ( ( member_o @ Q4 @ ( image_o_o @ ( transitive_rtrancl_o @ R3 ) @ Q0 ) )
% 4.69/4.92 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ Q4 @ X ) @ R3 )
% 4.69/4.92 => ( member_o @ X @ ( image_o_o @ ( transitive_rtrancl_o @ R3 ) @ Q0 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_image_advance
% 4.69/4.92 thf(fact_1453_rtrancl__image__advance,axiom,
% 4.69/4.92 ! [Q4: product_unit,R3: set_Pr5094982260447487303t_unit,Q0: set_Product_unit,X: product_unit] :
% 4.69/4.92 ( ( member_Product_unit @ Q4 @ ( image_8431784415008483091t_unit @ ( transi6481887417741755664t_unit @ R3 ) @ Q0 ) )
% 4.69/4.92 => ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ Q4 @ X ) @ R3 )
% 4.69/4.92 => ( member_Product_unit @ X @ ( image_8431784415008483091t_unit @ ( transi6481887417741755664t_unit @ R3 ) @ Q0 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_image_advance
% 4.69/4.92 thf(fact_1454_rtrancl__image__advance,axiom,
% 4.69/4.92 ! [Q4: nat,R3: set_Pr1261947904930325089at_nat,Q0: set_nat,X: nat] :
% 4.69/4.92 ( ( member_nat @ Q4 @ ( image_nat_nat @ ( transi2905341329935302413cl_nat @ R3 ) @ Q0 ) )
% 4.69/4.92 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Q4 @ X ) @ R3 )
% 4.69/4.92 => ( member_nat @ X @ ( image_nat_nat @ ( transi2905341329935302413cl_nat @ R3 ) @ Q0 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_image_advance
% 4.69/4.92 thf(fact_1455_rtrancl__image__advance,axiom,
% 4.69/4.92 ! [Q4: int,R3: set_Pr958786334691620121nt_int,Q0: set_int,X: int] :
% 4.69/4.92 ( ( member_int @ Q4 @ ( image_int_int @ ( transi2902850859426252137cl_int @ R3 ) @ Q0 ) )
% 4.69/4.92 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Q4 @ X ) @ R3 )
% 4.69/4.92 => ( member_int @ X @ ( image_int_int @ ( transi2902850859426252137cl_int @ R3 ) @ Q0 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_image_advance
% 4.69/4.92 thf(fact_1456_trancl__rtrancl__trancl,axiom,
% 4.69/4.92 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat,C: nat] :
% 4.69/4.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.92 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.92 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ C ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % trancl_rtrancl_trancl
% 4.69/4.92 thf(fact_1457_trancl__rtrancl__trancl,axiom,
% 4.69/4.92 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int,C: int] :
% 4.69/4.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.92 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.92 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ C ) @ ( transi6261509568448316235cl_int @ R2 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % trancl_rtrancl_trancl
% 4.69/4.92 thf(fact_1458_rtrancl__trancl__trancl,axiom,
% 4.69/4.92 ! [X: nat,Y: nat,R2: set_Pr1261947904930325089at_nat,Z: nat] :
% 4.69/4.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.92 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ Z ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.92 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_trancl_trancl
% 4.69/4.92 thf(fact_1459_rtrancl__trancl__trancl,axiom,
% 4.69/4.92 ! [X: int,Y: int,R2: set_Pr958786334691620121nt_int,Z: int] :
% 4.69/4.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.92 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y @ Z ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.92 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Z ) @ ( transi6261509568448316235cl_int @ R2 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_trancl_trancl
% 4.69/4.92 thf(fact_1460_rtrancl__into__trancl2,axiom,
% 4.69/4.92 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat,C: nat] :
% 4.69/4.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 )
% 4.69/4.92 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.92 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ C ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_into_trancl2
% 4.69/4.92 thf(fact_1461_rtrancl__into__trancl2,axiom,
% 4.69/4.92 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int,C: int] :
% 4.69/4.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 )
% 4.69/4.92 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.92 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ C ) @ ( transi6261509568448316235cl_int @ R2 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_into_trancl2
% 4.69/4.92 thf(fact_1462_rtrancl__into__trancl1,axiom,
% 4.69/4.92 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat,C: nat] :
% 4.69/4.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.92 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C ) @ R2 )
% 4.69/4.92 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ C ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_into_trancl1
% 4.69/4.92 thf(fact_1463_rtrancl__into__trancl1,axiom,
% 4.69/4.92 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int,C: int] :
% 4.69/4.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.92 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C ) @ R2 )
% 4.69/4.92 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ C ) @ ( transi6261509568448316235cl_int @ R2 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_into_trancl1
% 4.69/4.92 thf(fact_1464_rtrancl__eq__or__trancl,axiom,
% 4.69/4.92 ! [X: nat,Y: nat,R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi2905341329935302413cl_nat @ R3 ) )
% 4.69/4.92 = ( ( X = Y )
% 4.69/4.92 | ( ( X != Y )
% 4.69/4.92 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi6264000038957366511cl_nat @ R3 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_eq_or_trancl
% 4.69/4.92 thf(fact_1465_rtrancl__eq__or__trancl,axiom,
% 4.69/4.92 ! [X: int,Y: int,R3: set_Pr958786334691620121nt_int] :
% 4.69/4.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi2902850859426252137cl_int @ R3 ) )
% 4.69/4.92 = ( ( X = Y )
% 4.69/4.92 | ( ( X != Y )
% 4.69/4.92 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi6261509568448316235cl_int @ R3 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtrancl_eq_or_trancl
% 4.69/4.92 thf(fact_1466_trancl__into__rtrancl,axiom,
% 4.69/4.92 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.92 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( transi2905341329935302413cl_nat @ R2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % trancl_into_rtrancl
% 4.69/4.92 thf(fact_1467_trancl__into__rtrancl,axiom,
% 4.69/4.92 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.92 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( transi2902850859426252137cl_int @ R2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % trancl_into_rtrancl
% 4.69/4.92 thf(fact_1468_tranclD2,axiom,
% 4.69/4.92 ! [X: nat,Y: nat,R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi6264000038957366511cl_nat @ R3 ) )
% 4.69/4.92 => ? [Z3: nat] :
% 4.69/4.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z3 ) @ ( transi2905341329935302413cl_nat @ R3 ) )
% 4.69/4.92 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Z3 @ Y ) @ R3 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % tranclD2
% 4.69/4.92 thf(fact_1469_tranclD2,axiom,
% 4.69/4.92 ! [X: int,Y: int,R3: set_Pr958786334691620121nt_int] :
% 4.69/4.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi6261509568448316235cl_int @ R3 ) )
% 4.69/4.92 => ? [Z3: int] :
% 4.69/4.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Z3 ) @ ( transi2902850859426252137cl_int @ R3 ) )
% 4.69/4.92 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Z3 @ Y ) @ R3 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % tranclD2
% 4.69/4.92 thf(fact_1470_rtranclD,axiom,
% 4.69/4.92 ! [A2: nat,B: nat,R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( transi2905341329935302413cl_nat @ R3 ) )
% 4.69/4.92 => ( ( A2 = B )
% 4.69/4.92 | ( ( A2 != B )
% 4.69/4.92 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( transi6264000038957366511cl_nat @ R3 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtranclD
% 4.69/4.92 thf(fact_1471_rtranclD,axiom,
% 4.69/4.92 ! [A2: int,B: int,R3: set_Pr958786334691620121nt_int] :
% 4.69/4.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( transi2902850859426252137cl_int @ R3 ) )
% 4.69/4.92 => ( ( A2 = B )
% 4.69/4.92 | ( ( A2 != B )
% 4.69/4.92 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( transi6261509568448316235cl_int @ R3 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % rtranclD
% 4.69/4.92 thf(fact_1472_tranclD,axiom,
% 4.69/4.92 ! [X: nat,Y: nat,R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi6264000038957366511cl_nat @ R3 ) )
% 4.69/4.92 => ? [Z3: nat] :
% 4.69/4.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z3 ) @ R3 )
% 4.69/4.92 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Z3 @ Y ) @ ( transi2905341329935302413cl_nat @ R3 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % tranclD
% 4.69/4.92 thf(fact_1473_tranclD,axiom,
% 4.69/4.92 ! [X: int,Y: int,R3: set_Pr958786334691620121nt_int] :
% 4.69/4.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi6261509568448316235cl_int @ R3 ) )
% 4.69/4.92 => ? [Z3: int] :
% 4.69/4.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Z3 ) @ R3 )
% 4.69/4.92 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Z3 @ Y ) @ ( transi2902850859426252137cl_int @ R3 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % tranclD
% 4.69/4.92 thf(fact_1474_insert__is__Un,axiom,
% 4.69/4.92 ( insert_Product_unit
% 4.69/4.92 = ( ^ [A6: product_unit] : ( sup_su793286257634532545t_unit @ ( insert_Product_unit @ A6 @ bot_bo3957492148770167129t_unit ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % insert_is_Un
% 4.69/4.92 thf(fact_1475_insert__is__Un,axiom,
% 4.69/4.92 ( insert_o
% 4.69/4.92 = ( ^ [A6: $o] : ( sup_sup_set_o @ ( insert_o @ A6 @ bot_bot_set_o ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % insert_is_Un
% 4.69/4.92 thf(fact_1476_insert__is__Un,axiom,
% 4.69/4.92 ( insert_nat
% 4.69/4.92 = ( ^ [A6: nat] : ( sup_sup_set_nat @ ( insert_nat @ A6 @ bot_bot_set_nat ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % insert_is_Un
% 4.69/4.92 thf(fact_1477_insert__is__Un,axiom,
% 4.69/4.92 ( insert_int
% 4.69/4.92 = ( ^ [A6: int] : ( sup_sup_set_int @ ( insert_int @ A6 @ bot_bot_set_int ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % insert_is_Un
% 4.69/4.92 thf(fact_1478_insert__is__Un,axiom,
% 4.69/4.92 ( insert5175938949040314269_nat_o
% 4.69/4.92 = ( ^ [A6: produc3658429121746597890et_nat > $o] : ( sup_su5209123915105501825_nat_o @ ( insert5175938949040314269_nat_o @ A6 @ bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % insert_is_Un
% 4.69/4.92 thf(fact_1479_Un__singleton__iff,axiom,
% 4.69/4.92 ! [A: set_Product_unit,B4: set_Product_unit,X: product_unit] :
% 4.69/4.92 ( ( ( sup_su793286257634532545t_unit @ A @ B4 )
% 4.69/4.92 = ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.92 = ( ( ( A = bot_bo3957492148770167129t_unit )
% 4.69/4.92 & ( B4
% 4.69/4.92 = ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.92 | ( ( A
% 4.69/4.92 = ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.92 & ( B4 = bot_bo3957492148770167129t_unit ) )
% 4.69/4.92 | ( ( A
% 4.69/4.92 = ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.92 & ( B4
% 4.69/4.92 = ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Un_singleton_iff
% 4.69/4.92 thf(fact_1480_Un__singleton__iff,axiom,
% 4.69/4.92 ! [A: set_o,B4: set_o,X: $o] :
% 4.69/4.92 ( ( ( sup_sup_set_o @ A @ B4 )
% 4.69/4.92 = ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.92 = ( ( ( A = bot_bot_set_o )
% 4.69/4.92 & ( B4
% 4.69/4.92 = ( insert_o @ X @ bot_bot_set_o ) ) )
% 4.69/4.92 | ( ( A
% 4.69/4.92 = ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.92 & ( B4 = bot_bot_set_o ) )
% 4.69/4.92 | ( ( A
% 4.69/4.92 = ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.92 & ( B4
% 4.69/4.92 = ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Un_singleton_iff
% 4.69/4.92 thf(fact_1481_Un__singleton__iff,axiom,
% 4.69/4.92 ! [A: set_nat,B4: set_nat,X: nat] :
% 4.69/4.92 ( ( ( sup_sup_set_nat @ A @ B4 )
% 4.69/4.92 = ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.92 = ( ( ( A = bot_bot_set_nat )
% 4.69/4.92 & ( B4
% 4.69/4.92 = ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 4.69/4.92 | ( ( A
% 4.69/4.92 = ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.92 & ( B4 = bot_bot_set_nat ) )
% 4.69/4.92 | ( ( A
% 4.69/4.92 = ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.92 & ( B4
% 4.69/4.92 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Un_singleton_iff
% 4.69/4.92 thf(fact_1482_Un__singleton__iff,axiom,
% 4.69/4.92 ! [A: set_int,B4: set_int,X: int] :
% 4.69/4.92 ( ( ( sup_sup_set_int @ A @ B4 )
% 4.69/4.92 = ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.92 = ( ( ( A = bot_bot_set_int )
% 4.69/4.92 & ( B4
% 4.69/4.92 = ( insert_int @ X @ bot_bot_set_int ) ) )
% 4.69/4.92 | ( ( A
% 4.69/4.92 = ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.92 & ( B4 = bot_bot_set_int ) )
% 4.69/4.92 | ( ( A
% 4.69/4.92 = ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.92 & ( B4
% 4.69/4.92 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Un_singleton_iff
% 4.69/4.92 thf(fact_1483_Un__singleton__iff,axiom,
% 4.69/4.92 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/4.92 ( ( ( sup_su5209123915105501825_nat_o @ A @ B4 )
% 4.69/4.92 = ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.92 = ( ( ( A = bot_bo7824918357723582233_nat_o )
% 4.69/4.92 & ( B4
% 4.69/4.92 = ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/4.92 | ( ( A
% 4.69/4.92 = ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.92 & ( B4 = bot_bo7824918357723582233_nat_o ) )
% 4.69/4.92 | ( ( A
% 4.69/4.92 = ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.92 & ( B4
% 4.69/4.92 = ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Un_singleton_iff
% 4.69/4.92 thf(fact_1484_singleton__Un__iff,axiom,
% 4.69/4.92 ! [X: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.92 ( ( ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit )
% 4.69/4.92 = ( sup_su793286257634532545t_unit @ A @ B4 ) )
% 4.69/4.92 = ( ( ( A = bot_bo3957492148770167129t_unit )
% 4.69/4.92 & ( B4
% 4.69/4.92 = ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.92 | ( ( A
% 4.69/4.92 = ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.92 & ( B4 = bot_bo3957492148770167129t_unit ) )
% 4.69/4.92 | ( ( A
% 4.69/4.92 = ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.92 & ( B4
% 4.69/4.92 = ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % singleton_Un_iff
% 4.69/4.92 thf(fact_1485_singleton__Un__iff,axiom,
% 4.69/4.92 ! [X: $o,A: set_o,B4: set_o] :
% 4.69/4.92 ( ( ( insert_o @ X @ bot_bot_set_o )
% 4.69/4.92 = ( sup_sup_set_o @ A @ B4 ) )
% 4.69/4.92 = ( ( ( A = bot_bot_set_o )
% 4.69/4.92 & ( B4
% 4.69/4.92 = ( insert_o @ X @ bot_bot_set_o ) ) )
% 4.69/4.92 | ( ( A
% 4.69/4.92 = ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.92 & ( B4 = bot_bot_set_o ) )
% 4.69/4.92 | ( ( A
% 4.69/4.92 = ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.92 & ( B4
% 4.69/4.92 = ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % singleton_Un_iff
% 4.69/4.92 thf(fact_1486_singleton__Un__iff,axiom,
% 4.69/4.92 ! [X: nat,A: set_nat,B4: set_nat] :
% 4.69/4.92 ( ( ( insert_nat @ X @ bot_bot_set_nat )
% 4.69/4.92 = ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.92 = ( ( ( A = bot_bot_set_nat )
% 4.69/4.92 & ( B4
% 4.69/4.92 = ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 4.69/4.92 | ( ( A
% 4.69/4.92 = ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.92 & ( B4 = bot_bot_set_nat ) )
% 4.69/4.92 | ( ( A
% 4.69/4.92 = ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.92 & ( B4
% 4.69/4.92 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % singleton_Un_iff
% 4.69/4.92 thf(fact_1487_singleton__Un__iff,axiom,
% 4.69/4.92 ! [X: int,A: set_int,B4: set_int] :
% 4.69/4.92 ( ( ( insert_int @ X @ bot_bot_set_int )
% 4.69/4.92 = ( sup_sup_set_int @ A @ B4 ) )
% 4.69/4.92 = ( ( ( A = bot_bot_set_int )
% 4.69/4.92 & ( B4
% 4.69/4.92 = ( insert_int @ X @ bot_bot_set_int ) ) )
% 4.69/4.92 | ( ( A
% 4.69/4.92 = ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.92 & ( B4 = bot_bot_set_int ) )
% 4.69/4.92 | ( ( A
% 4.69/4.92 = ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.92 & ( B4
% 4.69/4.92 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % singleton_Un_iff
% 4.69/4.92 thf(fact_1488_singleton__Un__iff,axiom,
% 4.69/4.92 ! [X: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o )
% 4.69/4.92 = ( sup_su5209123915105501825_nat_o @ A @ B4 ) )
% 4.69/4.92 = ( ( ( A = bot_bo7824918357723582233_nat_o )
% 4.69/4.92 & ( B4
% 4.69/4.92 = ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/4.92 | ( ( A
% 4.69/4.92 = ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.92 & ( B4 = bot_bo7824918357723582233_nat_o ) )
% 4.69/4.92 | ( ( A
% 4.69/4.92 = ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.92 & ( B4
% 4.69/4.92 = ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % singleton_Un_iff
% 4.69/4.92 thf(fact_1489_Not__Domain__rtrancl,axiom,
% 4.69/4.92 ! [X: produc3658429121746597890et_nat > $o,R3: set_Pr2161125870931222855_nat_o,Y: produc3658429121746597890et_nat > $o] :
% 4.69/4.92 ( ~ ( member6576561426505652726_nat_o @ X @ ( domain4881241903163524940_nat_o @ R3 ) )
% 4.69/4.92 => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ ( transi712980445759334096_nat_o @ R3 ) )
% 4.69/4.92 = ( X = Y ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Not_Domain_rtrancl
% 4.69/4.92 thf(fact_1490_Not__Domain__rtrancl,axiom,
% 4.69/4.92 ! [X: $o,R3: set_Product_prod_o_o,Y: $o] :
% 4.69/4.92 ( ~ ( member_o @ X @ ( domain_o_o @ R3 ) )
% 4.69/4.92 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ ( transitive_rtrancl_o @ R3 ) )
% 4.69/4.92 = ( X = Y ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Not_Domain_rtrancl
% 4.69/4.92 thf(fact_1491_Not__Domain__rtrancl,axiom,
% 4.69/4.92 ! [X: product_unit,R3: set_Pr5094982260447487303t_unit,Y: product_unit] :
% 4.69/4.92 ( ~ ( member_Product_unit @ X @ ( domain4292024440186670924t_unit @ R3 ) )
% 4.69/4.92 => ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X @ Y ) @ ( transi6481887417741755664t_unit @ R3 ) )
% 4.69/4.92 = ( X = Y ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Not_Domain_rtrancl
% 4.69/4.92 thf(fact_1492_Not__Domain__rtrancl,axiom,
% 4.69/4.92 ! [X: nat,R3: set_Pr1261947904930325089at_nat,Y: nat] :
% 4.69/4.92 ( ~ ( member_nat @ X @ ( domain_nat_nat @ R3 ) )
% 4.69/4.92 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi2905341329935302413cl_nat @ R3 ) )
% 4.69/4.92 = ( X = Y ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Not_Domain_rtrancl
% 4.69/4.92 thf(fact_1493_Not__Domain__rtrancl,axiom,
% 4.69/4.92 ! [X: int,R3: set_Pr958786334691620121nt_int,Y: int] :
% 4.69/4.92 ( ~ ( member_int @ X @ ( domain_int_int @ R3 ) )
% 4.69/4.92 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi2902850859426252137cl_int @ R3 ) )
% 4.69/4.92 = ( X = Y ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Not_Domain_rtrancl
% 4.69/4.92 thf(fact_1494_subset__singletonD,axiom,
% 4.69/4.92 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.92 ( ( ord_le3507040750410214029t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.92 => ( ( A = bot_bo3957492148770167129t_unit )
% 4.69/4.92 | ( A
% 4.69/4.92 = ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_singletonD
% 4.69/4.92 thf(fact_1495_subset__singletonD,axiom,
% 4.69/4.92 ! [A: set_o,X: $o] :
% 4.69/4.92 ( ( ord_less_eq_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.92 => ( ( A = bot_bot_set_o )
% 4.69/4.92 | ( A
% 4.69/4.92 = ( insert_o @ X @ bot_bot_set_o ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_singletonD
% 4.69/4.92 thf(fact_1496_subset__singletonD,axiom,
% 4.69/4.92 ! [A: set_int,X: int] :
% 4.69/4.92 ( ( ord_less_eq_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.92 => ( ( A = bot_bot_set_int )
% 4.69/4.92 | ( A
% 4.69/4.92 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_singletonD
% 4.69/4.92 thf(fact_1497_subset__singletonD,axiom,
% 4.69/4.92 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/4.92 ( ( ord_le2965882846123202637_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.92 => ( ( A = bot_bo7824918357723582233_nat_o )
% 4.69/4.92 | ( A
% 4.69/4.92 = ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_singletonD
% 4.69/4.92 thf(fact_1498_subset__singletonD,axiom,
% 4.69/4.92 ! [A: set_nat,X: nat] :
% 4.69/4.92 ( ( ord_less_eq_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.92 => ( ( A = bot_bot_set_nat )
% 4.69/4.92 | ( A
% 4.69/4.92 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_singletonD
% 4.69/4.92 thf(fact_1499_subset__singleton__iff,axiom,
% 4.69/4.92 ! [X4: set_Product_unit,A2: product_unit] :
% 4.69/4.92 ( ( ord_le3507040750410214029t_unit @ X4 @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.92 = ( ( X4 = bot_bo3957492148770167129t_unit )
% 4.69/4.92 | ( X4
% 4.69/4.92 = ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_singleton_iff
% 4.69/4.92 thf(fact_1500_subset__singleton__iff,axiom,
% 4.69/4.92 ! [X4: set_o,A2: $o] :
% 4.69/4.92 ( ( ord_less_eq_set_o @ X4 @ ( insert_o @ A2 @ bot_bot_set_o ) )
% 4.69/4.92 = ( ( X4 = bot_bot_set_o )
% 4.69/4.92 | ( X4
% 4.69/4.92 = ( insert_o @ A2 @ bot_bot_set_o ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_singleton_iff
% 4.69/4.92 thf(fact_1501_subset__singleton__iff,axiom,
% 4.69/4.92 ! [X4: set_int,A2: int] :
% 4.69/4.92 ( ( ord_less_eq_set_int @ X4 @ ( insert_int @ A2 @ bot_bot_set_int ) )
% 4.69/4.92 = ( ( X4 = bot_bot_set_int )
% 4.69/4.92 | ( X4
% 4.69/4.92 = ( insert_int @ A2 @ bot_bot_set_int ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_singleton_iff
% 4.69/4.92 thf(fact_1502_subset__singleton__iff,axiom,
% 4.69/4.92 ! [X4: set_Pr4532377907799695533_nat_o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/4.92 ( ( ord_le2965882846123202637_nat_o @ X4 @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.92 = ( ( X4 = bot_bo7824918357723582233_nat_o )
% 4.69/4.92 | ( X4
% 4.69/4.92 = ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_singleton_iff
% 4.69/4.92 thf(fact_1503_subset__singleton__iff,axiom,
% 4.69/4.92 ! [X4: set_nat,A2: nat] :
% 4.69/4.92 ( ( ord_less_eq_set_nat @ X4 @ ( insert_nat @ A2 @ bot_bot_set_nat ) )
% 4.69/4.92 = ( ( X4 = bot_bot_set_nat )
% 4.69/4.92 | ( X4
% 4.69/4.92 = ( insert_nat @ A2 @ bot_bot_set_nat ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_singleton_iff
% 4.69/4.92 thf(fact_1504_mod__star__conv,axiom,
% 4.69/4.92 ! [A: assn,B4: assn,H2: produc3658429121746597890et_nat] :
% 4.69/4.92 ( ( rep_assn @ ( times_times_assn @ A @ B4 ) @ H2 )
% 4.69/4.92 = ( ? [Hr: heap_e7401611519738050253t_unit,As1: set_nat,As22: set_nat] :
% 4.69/4.92 ( ( H2
% 4.69/4.92 = ( produc7507926704131184380et_nat @ Hr @ ( sup_sup_set_nat @ As1 @ As22 ) ) )
% 4.69/4.92 & ( ( inf_inf_set_nat @ As1 @ As22 )
% 4.69/4.92 = bot_bot_set_nat )
% 4.69/4.92 & ( rep_assn @ A @ ( produc7507926704131184380et_nat @ Hr @ As1 ) )
% 4.69/4.92 & ( rep_assn @ B4 @ ( produc7507926704131184380et_nat @ Hr @ As22 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % mod_star_conv
% 4.69/4.92 thf(fact_1505_star__assnI,axiom,
% 4.69/4.92 ! [P: assn,H2: heap_e7401611519738050253t_unit,As: set_nat,Q2: assn,As5: set_nat] :
% 4.69/4.92 ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 4.69/4.92 => ( ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H2 @ As5 ) )
% 4.69/4.92 => ( ( ( inf_inf_set_nat @ As @ As5 )
% 4.69/4.92 = bot_bot_set_nat )
% 4.69/4.92 => ( rep_assn @ ( times_times_assn @ P @ Q2 ) @ ( produc7507926704131184380et_nat @ H2 @ ( sup_sup_set_nat @ As @ As5 ) ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % star_assnI
% 4.69/4.92 thf(fact_1506_in__range__subset,axiom,
% 4.69/4.92 ! [As: set_nat,As5: set_nat,H2: heap_e7401611519738050253t_unit] :
% 4.69/4.92 ( ( ord_less_eq_set_nat @ As @ As5 )
% 4.69/4.92 => ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As5 ) )
% 4.69/4.92 => ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % in_range_subset
% 4.69/4.92 thf(fact_1507_wand__raw_Osimps,axiom,
% 4.69/4.92 ! [P: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o,H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 4.69/4.92 ( ( wand_raw @ P @ Q2 @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 4.69/4.92 = ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 4.69/4.92 & ! [H5: heap_e7401611519738050253t_unit,As6: set_nat] :
% 4.69/4.92 ( ( ( ( inf_inf_set_nat @ As @ As6 )
% 4.69/4.92 = bot_bot_set_nat )
% 4.69/4.92 & ( relH @ As @ H2 @ H5 )
% 4.69/4.92 & ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As ) )
% 4.69/4.92 & ( P @ ( produc7507926704131184380et_nat @ H5 @ As6 ) ) )
% 4.69/4.92 => ( Q2 @ ( produc7507926704131184380et_nat @ H5 @ ( sup_sup_set_nat @ As @ As6 ) ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % wand_raw.simps
% 4.69/4.92 thf(fact_1508_wand__raw_Oelims_I1_J,axiom,
% 4.69/4.92 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 4.69/4.92 ( ( ( wand_raw @ X @ Xa @ Xb )
% 4.69/4.92 = Y )
% 4.69/4.92 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.92 ( ( Xb
% 4.69/4.92 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.92 => ( Y
% 4.69/4.92 = ( ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.92 & ! [H5: heap_e7401611519738050253t_unit,As6: set_nat] :
% 4.69/4.92 ( ( ( ( inf_inf_set_nat @ As2 @ As6 )
% 4.69/4.92 = bot_bot_set_nat )
% 4.69/4.92 & ( relH @ As2 @ H @ H5 )
% 4.69/4.92 & ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As2 ) )
% 4.69/4.92 & ( X @ ( produc7507926704131184380et_nat @ H5 @ As6 ) ) )
% 4.69/4.92 => ( Xa @ ( produc7507926704131184380et_nat @ H5 @ ( sup_sup_set_nat @ As2 @ As6 ) ) ) ) ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % wand_raw.elims(1)
% 4.69/4.92 thf(fact_1509_wand__raw_Oelims_I2_J,axiom,
% 4.69/4.92 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 4.69/4.92 ( ( wand_raw @ X @ Xa @ Xb )
% 4.69/4.92 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.92 ( ( Xb
% 4.69/4.92 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.92 => ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.92 & ! [H7: heap_e7401611519738050253t_unit,As7: set_nat] :
% 4.69/4.92 ( ( ( ( inf_inf_set_nat @ As2 @ As7 )
% 4.69/4.92 = bot_bot_set_nat )
% 4.69/4.92 & ( relH @ As2 @ H @ H7 )
% 4.69/4.92 & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As2 ) )
% 4.69/4.92 & ( X @ ( produc7507926704131184380et_nat @ H7 @ As7 ) ) )
% 4.69/4.92 => ( Xa @ ( produc7507926704131184380et_nat @ H7 @ ( sup_sup_set_nat @ As2 @ As7 ) ) ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % wand_raw.elims(2)
% 4.69/4.92 thf(fact_1510_wand__raw_Oelims_I3_J,axiom,
% 4.69/4.92 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 4.69/4.92 ( ~ ( wand_raw @ X @ Xa @ Xb )
% 4.69/4.92 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.92 ( ( Xb
% 4.69/4.92 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.92 => ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.92 & ! [H6: heap_e7401611519738050253t_unit,As4: set_nat] :
% 4.69/4.92 ( ( ( ( inf_inf_set_nat @ As2 @ As4 )
% 4.69/4.92 = bot_bot_set_nat )
% 4.69/4.92 & ( relH @ As2 @ H @ H6 )
% 4.69/4.92 & ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As2 ) )
% 4.69/4.92 & ( X @ ( produc7507926704131184380et_nat @ H6 @ As4 ) ) )
% 4.69/4.92 => ( Xa @ ( produc7507926704131184380et_nat @ H6 @ ( sup_sup_set_nat @ As2 @ As4 ) ) ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % wand_raw.elims(3)
% 4.69/4.92 thf(fact_1511_Image__empty__rtrancl__Image__id,axiom,
% 4.69/4.92 ! [R3: set_Pr5094982260447487303t_unit,V: product_unit] :
% 4.69/4.92 ( ( ( image_8431784415008483091t_unit @ R3 @ ( insert_Product_unit @ V @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.92 = bot_bo3957492148770167129t_unit )
% 4.69/4.92 => ( ( image_8431784415008483091t_unit @ ( transi6481887417741755664t_unit @ R3 ) @ ( insert_Product_unit @ V @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.92 = ( insert_Product_unit @ V @ bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Image_empty_rtrancl_Image_id
% 4.69/4.92 thf(fact_1512_Image__empty__rtrancl__Image__id,axiom,
% 4.69/4.92 ! [R3: set_Product_prod_o_o,V: $o] :
% 4.69/4.92 ( ( ( image_o_o @ R3 @ ( insert_o @ V @ bot_bot_set_o ) )
% 4.69/4.92 = bot_bot_set_o )
% 4.69/4.92 => ( ( image_o_o @ ( transitive_rtrancl_o @ R3 ) @ ( insert_o @ V @ bot_bot_set_o ) )
% 4.69/4.92 = ( insert_o @ V @ bot_bot_set_o ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Image_empty_rtrancl_Image_id
% 4.69/4.92 thf(fact_1513_Image__empty__rtrancl__Image__id,axiom,
% 4.69/4.92 ! [R3: set_Pr1261947904930325089at_nat,V: nat] :
% 4.69/4.92 ( ( ( image_nat_nat @ R3 @ ( insert_nat @ V @ bot_bot_set_nat ) )
% 4.69/4.92 = bot_bot_set_nat )
% 4.69/4.92 => ( ( image_nat_nat @ ( transi2905341329935302413cl_nat @ R3 ) @ ( insert_nat @ V @ bot_bot_set_nat ) )
% 4.69/4.92 = ( insert_nat @ V @ bot_bot_set_nat ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Image_empty_rtrancl_Image_id
% 4.69/4.92 thf(fact_1514_Image__empty__rtrancl__Image__id,axiom,
% 4.69/4.92 ! [R3: set_Pr958786334691620121nt_int,V: int] :
% 4.69/4.92 ( ( ( image_int_int @ R3 @ ( insert_int @ V @ bot_bot_set_int ) )
% 4.69/4.92 = bot_bot_set_int )
% 4.69/4.92 => ( ( image_int_int @ ( transi2902850859426252137cl_int @ R3 ) @ ( insert_int @ V @ bot_bot_set_int ) )
% 4.69/4.92 = ( insert_int @ V @ bot_bot_set_int ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Image_empty_rtrancl_Image_id
% 4.69/4.92 thf(fact_1515_Image__empty__rtrancl__Image__id,axiom,
% 4.69/4.92 ! [R3: set_Pr2161125870931222855_nat_o,V: produc3658429121746597890et_nat > $o] :
% 4.69/4.92 ( ( ( image_2232984160439939859_nat_o @ R3 @ ( insert5175938949040314269_nat_o @ V @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.92 = bot_bo7824918357723582233_nat_o )
% 4.69/4.92 => ( ( image_2232984160439939859_nat_o @ ( transi712980445759334096_nat_o @ R3 ) @ ( insert5175938949040314269_nat_o @ V @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.92 = ( insert5175938949040314269_nat_o @ V @ bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Image_empty_rtrancl_Image_id
% 4.69/4.92 thf(fact_1516_sup__bot_Oright__neutral,axiom,
% 4.69/4.92 ! [A2: assn] :
% 4.69/4.92 ( ( sup_sup_assn @ A2 @ bot_bot_assn )
% 4.69/4.92 = A2 ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.right_neutral
% 4.69/4.92 thf(fact_1517_sup__bot_Oright__neutral,axiom,
% 4.69/4.92 ! [A2: product_unit] :
% 4.69/4.92 ( ( sup_sup_Product_unit @ A2 @ bot_bot_Product_unit )
% 4.69/4.92 = A2 ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.right_neutral
% 4.69/4.92 thf(fact_1518_sup__bot_Oright__neutral,axiom,
% 4.69/4.92 ! [A2: set_Product_unit] :
% 4.69/4.92 ( ( sup_su793286257634532545t_unit @ A2 @ bot_bo3957492148770167129t_unit )
% 4.69/4.92 = A2 ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.right_neutral
% 4.69/4.92 thf(fact_1519_sup__bot_Oright__neutral,axiom,
% 4.69/4.92 ! [A2: set_o] :
% 4.69/4.92 ( ( sup_sup_set_o @ A2 @ bot_bot_set_o )
% 4.69/4.92 = A2 ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.right_neutral
% 4.69/4.92 thf(fact_1520_sup__bot_Oright__neutral,axiom,
% 4.69/4.92 ! [A2: set_nat] :
% 4.69/4.92 ( ( sup_sup_set_nat @ A2 @ bot_bot_set_nat )
% 4.69/4.92 = A2 ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.right_neutral
% 4.69/4.92 thf(fact_1521_sup__bot_Oright__neutral,axiom,
% 4.69/4.92 ! [A2: set_int] :
% 4.69/4.92 ( ( sup_sup_set_int @ A2 @ bot_bot_set_int )
% 4.69/4.92 = A2 ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.right_neutral
% 4.69/4.92 thf(fact_1522_sup__bot_Oright__neutral,axiom,
% 4.69/4.92 ! [A2: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( sup_su5209123915105501825_nat_o @ A2 @ bot_bo7824918357723582233_nat_o )
% 4.69/4.92 = A2 ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.right_neutral
% 4.69/4.92 thf(fact_1523_sup__bot_Oneutr__eq__iff,axiom,
% 4.69/4.92 ! [A2: assn,B: assn] :
% 4.69/4.92 ( ( bot_bot_assn
% 4.69/4.92 = ( sup_sup_assn @ A2 @ B ) )
% 4.69/4.92 = ( ( A2 = bot_bot_assn )
% 4.69/4.92 & ( B = bot_bot_assn ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.neutr_eq_iff
% 4.69/4.92 thf(fact_1524_sup__bot_Oneutr__eq__iff,axiom,
% 4.69/4.92 ! [A2: product_unit,B: product_unit] :
% 4.69/4.92 ( ( bot_bot_Product_unit
% 4.69/4.92 = ( sup_sup_Product_unit @ A2 @ B ) )
% 4.69/4.92 = ( ( A2 = bot_bot_Product_unit )
% 4.69/4.92 & ( B = bot_bot_Product_unit ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.neutr_eq_iff
% 4.69/4.92 thf(fact_1525_sup__bot_Oneutr__eq__iff,axiom,
% 4.69/4.92 ! [A2: set_Product_unit,B: set_Product_unit] :
% 4.69/4.92 ( ( bot_bo3957492148770167129t_unit
% 4.69/4.92 = ( sup_su793286257634532545t_unit @ A2 @ B ) )
% 4.69/4.92 = ( ( A2 = bot_bo3957492148770167129t_unit )
% 4.69/4.92 & ( B = bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.neutr_eq_iff
% 4.69/4.92 thf(fact_1526_sup__bot_Oneutr__eq__iff,axiom,
% 4.69/4.92 ! [A2: set_o,B: set_o] :
% 4.69/4.92 ( ( bot_bot_set_o
% 4.69/4.92 = ( sup_sup_set_o @ A2 @ B ) )
% 4.69/4.92 = ( ( A2 = bot_bot_set_o )
% 4.69/4.92 & ( B = bot_bot_set_o ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.neutr_eq_iff
% 4.69/4.92 thf(fact_1527_sup__bot_Oneutr__eq__iff,axiom,
% 4.69/4.92 ! [A2: set_nat,B: set_nat] :
% 4.69/4.92 ( ( bot_bot_set_nat
% 4.69/4.92 = ( sup_sup_set_nat @ A2 @ B ) )
% 4.69/4.92 = ( ( A2 = bot_bot_set_nat )
% 4.69/4.92 & ( B = bot_bot_set_nat ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.neutr_eq_iff
% 4.69/4.92 thf(fact_1528_sup__bot_Oneutr__eq__iff,axiom,
% 4.69/4.92 ! [A2: set_int,B: set_int] :
% 4.69/4.92 ( ( bot_bot_set_int
% 4.69/4.92 = ( sup_sup_set_int @ A2 @ B ) )
% 4.69/4.92 = ( ( A2 = bot_bot_set_int )
% 4.69/4.92 & ( B = bot_bot_set_int ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.neutr_eq_iff
% 4.69/4.92 thf(fact_1529_sup__bot_Oneutr__eq__iff,axiom,
% 4.69/4.92 ! [A2: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( bot_bo7824918357723582233_nat_o
% 4.69/4.92 = ( sup_su5209123915105501825_nat_o @ A2 @ B ) )
% 4.69/4.92 = ( ( A2 = bot_bo7824918357723582233_nat_o )
% 4.69/4.92 & ( B = bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.neutr_eq_iff
% 4.69/4.92 thf(fact_1530_sup__bot_Oleft__neutral,axiom,
% 4.69/4.92 ! [A2: assn] :
% 4.69/4.92 ( ( sup_sup_assn @ bot_bot_assn @ A2 )
% 4.69/4.92 = A2 ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.left_neutral
% 4.69/4.92 thf(fact_1531_sup__bot_Oleft__neutral,axiom,
% 4.69/4.92 ! [A2: product_unit] :
% 4.69/4.92 ( ( sup_sup_Product_unit @ bot_bot_Product_unit @ A2 )
% 4.69/4.92 = A2 ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.left_neutral
% 4.69/4.92 thf(fact_1532_sup__bot_Oleft__neutral,axiom,
% 4.69/4.92 ! [A2: set_Product_unit] :
% 4.69/4.92 ( ( sup_su793286257634532545t_unit @ bot_bo3957492148770167129t_unit @ A2 )
% 4.69/4.92 = A2 ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.left_neutral
% 4.69/4.92 thf(fact_1533_sup__bot_Oleft__neutral,axiom,
% 4.69/4.92 ! [A2: set_o] :
% 4.69/4.92 ( ( sup_sup_set_o @ bot_bot_set_o @ A2 )
% 4.69/4.92 = A2 ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.left_neutral
% 4.69/4.92 thf(fact_1534_sup__bot_Oleft__neutral,axiom,
% 4.69/4.92 ! [A2: set_nat] :
% 4.69/4.92 ( ( sup_sup_set_nat @ bot_bot_set_nat @ A2 )
% 4.69/4.92 = A2 ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.left_neutral
% 4.69/4.92 thf(fact_1535_sup__bot_Oleft__neutral,axiom,
% 4.69/4.92 ! [A2: set_int] :
% 4.69/4.92 ( ( sup_sup_set_int @ bot_bot_set_int @ A2 )
% 4.69/4.92 = A2 ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.left_neutral
% 4.69/4.92 thf(fact_1536_sup__bot_Oleft__neutral,axiom,
% 4.69/4.92 ! [A2: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( sup_su5209123915105501825_nat_o @ bot_bo7824918357723582233_nat_o @ A2 )
% 4.69/4.92 = A2 ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.left_neutral
% 4.69/4.92 thf(fact_1537_sup__bot_Oeq__neutr__iff,axiom,
% 4.69/4.92 ! [A2: assn,B: assn] :
% 4.69/4.92 ( ( ( sup_sup_assn @ A2 @ B )
% 4.69/4.92 = bot_bot_assn )
% 4.69/4.92 = ( ( A2 = bot_bot_assn )
% 4.69/4.92 & ( B = bot_bot_assn ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.eq_neutr_iff
% 4.69/4.92 thf(fact_1538_sup__bot_Oeq__neutr__iff,axiom,
% 4.69/4.92 ! [A2: product_unit,B: product_unit] :
% 4.69/4.92 ( ( ( sup_sup_Product_unit @ A2 @ B )
% 4.69/4.92 = bot_bot_Product_unit )
% 4.69/4.92 = ( ( A2 = bot_bot_Product_unit )
% 4.69/4.92 & ( B = bot_bot_Product_unit ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.eq_neutr_iff
% 4.69/4.92 thf(fact_1539_sup__bot_Oeq__neutr__iff,axiom,
% 4.69/4.92 ! [A2: set_Product_unit,B: set_Product_unit] :
% 4.69/4.92 ( ( ( sup_su793286257634532545t_unit @ A2 @ B )
% 4.69/4.92 = bot_bo3957492148770167129t_unit )
% 4.69/4.92 = ( ( A2 = bot_bo3957492148770167129t_unit )
% 4.69/4.92 & ( B = bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.eq_neutr_iff
% 4.69/4.92 thf(fact_1540_sup__bot_Oeq__neutr__iff,axiom,
% 4.69/4.92 ! [A2: set_o,B: set_o] :
% 4.69/4.92 ( ( ( sup_sup_set_o @ A2 @ B )
% 4.69/4.92 = bot_bot_set_o )
% 4.69/4.92 = ( ( A2 = bot_bot_set_o )
% 4.69/4.92 & ( B = bot_bot_set_o ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.eq_neutr_iff
% 4.69/4.92 thf(fact_1541_sup__bot_Oeq__neutr__iff,axiom,
% 4.69/4.92 ! [A2: set_nat,B: set_nat] :
% 4.69/4.92 ( ( ( sup_sup_set_nat @ A2 @ B )
% 4.69/4.92 = bot_bot_set_nat )
% 4.69/4.92 = ( ( A2 = bot_bot_set_nat )
% 4.69/4.92 & ( B = bot_bot_set_nat ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.eq_neutr_iff
% 4.69/4.92 thf(fact_1542_sup__bot_Oeq__neutr__iff,axiom,
% 4.69/4.92 ! [A2: set_int,B: set_int] :
% 4.69/4.92 ( ( ( sup_sup_set_int @ A2 @ B )
% 4.69/4.92 = bot_bot_set_int )
% 4.69/4.92 = ( ( A2 = bot_bot_set_int )
% 4.69/4.92 & ( B = bot_bot_set_int ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.eq_neutr_iff
% 4.69/4.92 thf(fact_1543_sup__bot_Oeq__neutr__iff,axiom,
% 4.69/4.92 ! [A2: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( ( sup_su5209123915105501825_nat_o @ A2 @ B )
% 4.69/4.92 = bot_bo7824918357723582233_nat_o )
% 4.69/4.92 = ( ( A2 = bot_bo7824918357723582233_nat_o )
% 4.69/4.92 & ( B = bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot.eq_neutr_iff
% 4.69/4.92 thf(fact_1544_sup__eq__bot__iff,axiom,
% 4.69/4.92 ! [X: assn,Y: assn] :
% 4.69/4.92 ( ( ( sup_sup_assn @ X @ Y )
% 4.69/4.92 = bot_bot_assn )
% 4.69/4.92 = ( ( X = bot_bot_assn )
% 4.69/4.92 & ( Y = bot_bot_assn ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % sup_eq_bot_iff
% 4.69/4.92 thf(fact_1545_sup__eq__bot__iff,axiom,
% 4.69/4.92 ! [X: product_unit,Y: product_unit] :
% 4.69/4.92 ( ( ( sup_sup_Product_unit @ X @ Y )
% 4.69/4.92 = bot_bot_Product_unit )
% 4.69/4.92 = ( ( X = bot_bot_Product_unit )
% 4.69/4.92 & ( Y = bot_bot_Product_unit ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % sup_eq_bot_iff
% 4.69/4.92 thf(fact_1546_sup__eq__bot__iff,axiom,
% 4.69/4.92 ! [X: set_Product_unit,Y: set_Product_unit] :
% 4.69/4.92 ( ( ( sup_su793286257634532545t_unit @ X @ Y )
% 4.69/4.92 = bot_bo3957492148770167129t_unit )
% 4.69/4.92 = ( ( X = bot_bo3957492148770167129t_unit )
% 4.69/4.92 & ( Y = bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % sup_eq_bot_iff
% 4.69/4.92 thf(fact_1547_sup__eq__bot__iff,axiom,
% 4.69/4.92 ! [X: set_o,Y: set_o] :
% 4.69/4.92 ( ( ( sup_sup_set_o @ X @ Y )
% 4.69/4.92 = bot_bot_set_o )
% 4.69/4.92 = ( ( X = bot_bot_set_o )
% 4.69/4.92 & ( Y = bot_bot_set_o ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % sup_eq_bot_iff
% 4.69/4.92 thf(fact_1548_sup__eq__bot__iff,axiom,
% 4.69/4.92 ! [X: set_nat,Y: set_nat] :
% 4.69/4.92 ( ( ( sup_sup_set_nat @ X @ Y )
% 4.69/4.92 = bot_bot_set_nat )
% 4.69/4.92 = ( ( X = bot_bot_set_nat )
% 4.69/4.92 & ( Y = bot_bot_set_nat ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % sup_eq_bot_iff
% 4.69/4.92 thf(fact_1549_sup__eq__bot__iff,axiom,
% 4.69/4.92 ! [X: set_int,Y: set_int] :
% 4.69/4.92 ( ( ( sup_sup_set_int @ X @ Y )
% 4.69/4.92 = bot_bot_set_int )
% 4.69/4.92 = ( ( X = bot_bot_set_int )
% 4.69/4.92 & ( Y = bot_bot_set_int ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % sup_eq_bot_iff
% 4.69/4.92 thf(fact_1550_sup__eq__bot__iff,axiom,
% 4.69/4.92 ! [X: set_Pr4532377907799695533_nat_o,Y: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( ( sup_su5209123915105501825_nat_o @ X @ Y )
% 4.69/4.92 = bot_bo7824918357723582233_nat_o )
% 4.69/4.92 = ( ( X = bot_bo7824918357723582233_nat_o )
% 4.69/4.92 & ( Y = bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % sup_eq_bot_iff
% 4.69/4.92 thf(fact_1551_bot__eq__sup__iff,axiom,
% 4.69/4.92 ! [X: assn,Y: assn] :
% 4.69/4.92 ( ( bot_bot_assn
% 4.69/4.92 = ( sup_sup_assn @ X @ Y ) )
% 4.69/4.92 = ( ( X = bot_bot_assn )
% 4.69/4.92 & ( Y = bot_bot_assn ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % bot_eq_sup_iff
% 4.69/4.92 thf(fact_1552_bot__eq__sup__iff,axiom,
% 4.69/4.92 ! [X: product_unit,Y: product_unit] :
% 4.69/4.92 ( ( bot_bot_Product_unit
% 4.69/4.92 = ( sup_sup_Product_unit @ X @ Y ) )
% 4.69/4.92 = ( ( X = bot_bot_Product_unit )
% 4.69/4.92 & ( Y = bot_bot_Product_unit ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % bot_eq_sup_iff
% 4.69/4.92 thf(fact_1553_bot__eq__sup__iff,axiom,
% 4.69/4.92 ! [X: set_Product_unit,Y: set_Product_unit] :
% 4.69/4.92 ( ( bot_bo3957492148770167129t_unit
% 4.69/4.92 = ( sup_su793286257634532545t_unit @ X @ Y ) )
% 4.69/4.92 = ( ( X = bot_bo3957492148770167129t_unit )
% 4.69/4.92 & ( Y = bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % bot_eq_sup_iff
% 4.69/4.92 thf(fact_1554_bot__eq__sup__iff,axiom,
% 4.69/4.92 ! [X: set_o,Y: set_o] :
% 4.69/4.92 ( ( bot_bot_set_o
% 4.69/4.92 = ( sup_sup_set_o @ X @ Y ) )
% 4.69/4.92 = ( ( X = bot_bot_set_o )
% 4.69/4.92 & ( Y = bot_bot_set_o ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % bot_eq_sup_iff
% 4.69/4.92 thf(fact_1555_bot__eq__sup__iff,axiom,
% 4.69/4.92 ! [X: set_nat,Y: set_nat] :
% 4.69/4.92 ( ( bot_bot_set_nat
% 4.69/4.92 = ( sup_sup_set_nat @ X @ Y ) )
% 4.69/4.92 = ( ( X = bot_bot_set_nat )
% 4.69/4.92 & ( Y = bot_bot_set_nat ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % bot_eq_sup_iff
% 4.69/4.92 thf(fact_1556_bot__eq__sup__iff,axiom,
% 4.69/4.92 ! [X: set_int,Y: set_int] :
% 4.69/4.92 ( ( bot_bot_set_int
% 4.69/4.92 = ( sup_sup_set_int @ X @ Y ) )
% 4.69/4.92 = ( ( X = bot_bot_set_int )
% 4.69/4.92 & ( Y = bot_bot_set_int ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % bot_eq_sup_iff
% 4.69/4.92 thf(fact_1557_bot__eq__sup__iff,axiom,
% 4.69/4.92 ! [X: set_Pr4532377907799695533_nat_o,Y: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( bot_bo7824918357723582233_nat_o
% 4.69/4.92 = ( sup_su5209123915105501825_nat_o @ X @ Y ) )
% 4.69/4.92 = ( ( X = bot_bo7824918357723582233_nat_o )
% 4.69/4.92 & ( Y = bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % bot_eq_sup_iff
% 4.69/4.92 thf(fact_1558_sup__bot__right,axiom,
% 4.69/4.92 ! [X: assn] :
% 4.69/4.92 ( ( sup_sup_assn @ X @ bot_bot_assn )
% 4.69/4.92 = X ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot_right
% 4.69/4.92 thf(fact_1559_sup__bot__right,axiom,
% 4.69/4.92 ! [X: product_unit] :
% 4.69/4.92 ( ( sup_sup_Product_unit @ X @ bot_bot_Product_unit )
% 4.69/4.92 = X ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot_right
% 4.69/4.92 thf(fact_1560_sup__bot__right,axiom,
% 4.69/4.92 ! [X: set_Product_unit] :
% 4.69/4.92 ( ( sup_su793286257634532545t_unit @ X @ bot_bo3957492148770167129t_unit )
% 4.69/4.92 = X ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot_right
% 4.69/4.92 thf(fact_1561_sup__bot__right,axiom,
% 4.69/4.92 ! [X: set_o] :
% 4.69/4.92 ( ( sup_sup_set_o @ X @ bot_bot_set_o )
% 4.69/4.92 = X ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot_right
% 4.69/4.92 thf(fact_1562_sup__bot__right,axiom,
% 4.69/4.92 ! [X: set_nat] :
% 4.69/4.92 ( ( sup_sup_set_nat @ X @ bot_bot_set_nat )
% 4.69/4.92 = X ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot_right
% 4.69/4.92 thf(fact_1563_sup__bot__right,axiom,
% 4.69/4.92 ! [X: set_int] :
% 4.69/4.92 ( ( sup_sup_set_int @ X @ bot_bot_set_int )
% 4.69/4.92 = X ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot_right
% 4.69/4.92 thf(fact_1564_sup__bot__right,axiom,
% 4.69/4.92 ! [X: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( sup_su5209123915105501825_nat_o @ X @ bot_bo7824918357723582233_nat_o )
% 4.69/4.92 = X ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot_right
% 4.69/4.92 thf(fact_1565_sup__bot__left,axiom,
% 4.69/4.92 ! [X: assn] :
% 4.69/4.92 ( ( sup_sup_assn @ bot_bot_assn @ X )
% 4.69/4.92 = X ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot_left
% 4.69/4.92 thf(fact_1566_sup__bot__left,axiom,
% 4.69/4.92 ! [X: product_unit] :
% 4.69/4.92 ( ( sup_sup_Product_unit @ bot_bot_Product_unit @ X )
% 4.69/4.92 = X ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot_left
% 4.69/4.92 thf(fact_1567_sup__bot__left,axiom,
% 4.69/4.92 ! [X: set_Product_unit] :
% 4.69/4.92 ( ( sup_su793286257634532545t_unit @ bot_bo3957492148770167129t_unit @ X )
% 4.69/4.92 = X ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot_left
% 4.69/4.92 thf(fact_1568_sup__bot__left,axiom,
% 4.69/4.92 ! [X: set_o] :
% 4.69/4.92 ( ( sup_sup_set_o @ bot_bot_set_o @ X )
% 4.69/4.92 = X ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot_left
% 4.69/4.92 thf(fact_1569_sup__bot__left,axiom,
% 4.69/4.92 ! [X: set_nat] :
% 4.69/4.92 ( ( sup_sup_set_nat @ bot_bot_set_nat @ X )
% 4.69/4.92 = X ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot_left
% 4.69/4.92 thf(fact_1570_sup__bot__left,axiom,
% 4.69/4.92 ! [X: set_int] :
% 4.69/4.92 ( ( sup_sup_set_int @ bot_bot_set_int @ X )
% 4.69/4.92 = X ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot_left
% 4.69/4.92 thf(fact_1571_sup__bot__left,axiom,
% 4.69/4.92 ! [X: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( sup_su5209123915105501825_nat_o @ bot_bo7824918357723582233_nat_o @ X )
% 4.69/4.92 = X ) ).
% 4.69/4.92
% 4.69/4.92 % sup_bot_left
% 4.69/4.92 thf(fact_1572_boolean__algebra_Oconj__zero__right,axiom,
% 4.69/4.92 ! [X: assn] :
% 4.69/4.92 ( ( inf_inf_assn @ X @ bot_bot_assn )
% 4.69/4.92 = bot_bot_assn ) ).
% 4.69/4.92
% 4.69/4.92 % boolean_algebra.conj_zero_right
% 4.69/4.92 thf(fact_1573_boolean__algebra_Oconj__zero__right,axiom,
% 4.69/4.92 ! [X: product_unit] :
% 4.69/4.92 ( ( inf_inf_Product_unit @ X @ bot_bot_Product_unit )
% 4.69/4.92 = bot_bot_Product_unit ) ).
% 4.69/4.92
% 4.69/4.92 % boolean_algebra.conj_zero_right
% 4.69/4.92 thf(fact_1574_boolean__algebra_Oconj__zero__right,axiom,
% 4.69/4.92 ! [X: set_Product_unit] :
% 4.69/4.92 ( ( inf_in4660618365625256667t_unit @ X @ bot_bo3957492148770167129t_unit )
% 4.69/4.92 = bot_bo3957492148770167129t_unit ) ).
% 4.69/4.92
% 4.69/4.92 % boolean_algebra.conj_zero_right
% 4.69/4.92 thf(fact_1575_boolean__algebra_Oconj__zero__right,axiom,
% 4.69/4.92 ! [X: set_o] :
% 4.69/4.92 ( ( inf_inf_set_o @ X @ bot_bot_set_o )
% 4.69/4.92 = bot_bot_set_o ) ).
% 4.69/4.92
% 4.69/4.92 % boolean_algebra.conj_zero_right
% 4.69/4.92 thf(fact_1576_boolean__algebra_Oconj__zero__right,axiom,
% 4.69/4.92 ! [X: set_nat] :
% 4.69/4.92 ( ( inf_inf_set_nat @ X @ bot_bot_set_nat )
% 4.69/4.92 = bot_bot_set_nat ) ).
% 4.69/4.92
% 4.69/4.92 % boolean_algebra.conj_zero_right
% 4.69/4.92 thf(fact_1577_boolean__algebra_Oconj__zero__right,axiom,
% 4.69/4.92 ! [X: set_int] :
% 4.69/4.92 ( ( inf_inf_set_int @ X @ bot_bot_set_int )
% 4.69/4.92 = bot_bot_set_int ) ).
% 4.69/4.92
% 4.69/4.92 % boolean_algebra.conj_zero_right
% 4.69/4.92 thf(fact_1578_boolean__algebra_Oconj__zero__right,axiom,
% 4.69/4.92 ! [X: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( inf_in1906310914598751387_nat_o @ X @ bot_bo7824918357723582233_nat_o )
% 4.69/4.92 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/4.92
% 4.69/4.92 % boolean_algebra.conj_zero_right
% 4.69/4.92 thf(fact_1579_boolean__algebra_Oconj__zero__left,axiom,
% 4.69/4.92 ! [X: assn] :
% 4.69/4.92 ( ( inf_inf_assn @ bot_bot_assn @ X )
% 4.69/4.92 = bot_bot_assn ) ).
% 4.69/4.92
% 4.69/4.92 % boolean_algebra.conj_zero_left
% 4.69/4.92 thf(fact_1580_boolean__algebra_Oconj__zero__left,axiom,
% 4.69/4.92 ! [X: product_unit] :
% 4.69/4.92 ( ( inf_inf_Product_unit @ bot_bot_Product_unit @ X )
% 4.69/4.92 = bot_bot_Product_unit ) ).
% 4.69/4.92
% 4.69/4.92 % boolean_algebra.conj_zero_left
% 4.69/4.92 thf(fact_1581_boolean__algebra_Oconj__zero__left,axiom,
% 4.69/4.92 ! [X: set_Product_unit] :
% 4.69/4.92 ( ( inf_in4660618365625256667t_unit @ bot_bo3957492148770167129t_unit @ X )
% 4.69/4.92 = bot_bo3957492148770167129t_unit ) ).
% 4.69/4.92
% 4.69/4.92 % boolean_algebra.conj_zero_left
% 4.69/4.92 thf(fact_1582_boolean__algebra_Oconj__zero__left,axiom,
% 4.69/4.92 ! [X: set_o] :
% 4.69/4.92 ( ( inf_inf_set_o @ bot_bot_set_o @ X )
% 4.69/4.92 = bot_bot_set_o ) ).
% 4.69/4.92
% 4.69/4.92 % boolean_algebra.conj_zero_left
% 4.69/4.92 thf(fact_1583_boolean__algebra_Oconj__zero__left,axiom,
% 4.69/4.92 ! [X: set_nat] :
% 4.69/4.92 ( ( inf_inf_set_nat @ bot_bot_set_nat @ X )
% 4.69/4.92 = bot_bot_set_nat ) ).
% 4.69/4.92
% 4.69/4.92 % boolean_algebra.conj_zero_left
% 4.69/4.92 thf(fact_1584_boolean__algebra_Oconj__zero__left,axiom,
% 4.69/4.92 ! [X: set_int] :
% 4.69/4.92 ( ( inf_inf_set_int @ bot_bot_set_int @ X )
% 4.69/4.92 = bot_bot_set_int ) ).
% 4.69/4.92
% 4.69/4.92 % boolean_algebra.conj_zero_left
% 4.69/4.92 thf(fact_1585_boolean__algebra_Oconj__zero__left,axiom,
% 4.69/4.92 ! [X: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( inf_in1906310914598751387_nat_o @ bot_bo7824918357723582233_nat_o @ X )
% 4.69/4.92 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/4.92
% 4.69/4.92 % boolean_algebra.conj_zero_left
% 4.69/4.92 thf(fact_1586_inf__bot__right,axiom,
% 4.69/4.92 ! [X: assn] :
% 4.69/4.92 ( ( inf_inf_assn @ X @ bot_bot_assn )
% 4.69/4.92 = bot_bot_assn ) ).
% 4.69/4.92
% 4.69/4.92 % inf_bot_right
% 4.69/4.92 thf(fact_1587_inf__bot__right,axiom,
% 4.69/4.92 ! [X: product_unit] :
% 4.69/4.92 ( ( inf_inf_Product_unit @ X @ bot_bot_Product_unit )
% 4.69/4.92 = bot_bot_Product_unit ) ).
% 4.69/4.92
% 4.69/4.92 % inf_bot_right
% 4.69/4.92 thf(fact_1588_inf__bot__right,axiom,
% 4.69/4.92 ! [X: set_Product_unit] :
% 4.69/4.92 ( ( inf_in4660618365625256667t_unit @ X @ bot_bo3957492148770167129t_unit )
% 4.69/4.92 = bot_bo3957492148770167129t_unit ) ).
% 4.69/4.92
% 4.69/4.92 % inf_bot_right
% 4.69/4.92 thf(fact_1589_inf__bot__right,axiom,
% 4.69/4.92 ! [X: set_o] :
% 4.69/4.92 ( ( inf_inf_set_o @ X @ bot_bot_set_o )
% 4.69/4.92 = bot_bot_set_o ) ).
% 4.69/4.92
% 4.69/4.92 % inf_bot_right
% 4.69/4.92 thf(fact_1590_inf__bot__right,axiom,
% 4.69/4.92 ! [X: set_nat] :
% 4.69/4.92 ( ( inf_inf_set_nat @ X @ bot_bot_set_nat )
% 4.69/4.92 = bot_bot_set_nat ) ).
% 4.69/4.92
% 4.69/4.92 % inf_bot_right
% 4.69/4.92 thf(fact_1591_inf__bot__right,axiom,
% 4.69/4.92 ! [X: set_int] :
% 4.69/4.92 ( ( inf_inf_set_int @ X @ bot_bot_set_int )
% 4.69/4.92 = bot_bot_set_int ) ).
% 4.69/4.92
% 4.69/4.92 % inf_bot_right
% 4.69/4.92 thf(fact_1592_inf__bot__right,axiom,
% 4.69/4.92 ! [X: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( inf_in1906310914598751387_nat_o @ X @ bot_bo7824918357723582233_nat_o )
% 4.69/4.92 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/4.92
% 4.69/4.92 % inf_bot_right
% 4.69/4.92 thf(fact_1593_merge__pure__or,axiom,
% 4.69/4.92 ! [A2: $o,B: $o] :
% 4.69/4.92 ( ( sup_sup_assn @ ( pure_assn @ A2 ) @ ( pure_assn @ B ) )
% 4.69/4.92 = ( pure_assn
% 4.69/4.92 @ ( A2
% 4.69/4.92 | B ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % merge_pure_or
% 4.69/4.92 thf(fact_1594_merge__pure__and,axiom,
% 4.69/4.92 ! [A2: $o,B: $o] :
% 4.69/4.92 ( ( inf_inf_assn @ ( pure_assn @ A2 ) @ ( pure_assn @ B ) )
% 4.69/4.92 = ( pure_assn
% 4.69/4.92 @ ( A2
% 4.69/4.92 & B ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % merge_pure_and
% 4.69/4.92 thf(fact_1595_inf__bot__left,axiom,
% 4.69/4.92 ! [X: assn] :
% 4.69/4.92 ( ( inf_inf_assn @ bot_bot_assn @ X )
% 4.69/4.92 = bot_bot_assn ) ).
% 4.69/4.92
% 4.69/4.92 % inf_bot_left
% 4.69/4.92 thf(fact_1596_inf__bot__left,axiom,
% 4.69/4.92 ! [X: product_unit] :
% 4.69/4.92 ( ( inf_inf_Product_unit @ bot_bot_Product_unit @ X )
% 4.69/4.92 = bot_bot_Product_unit ) ).
% 4.69/4.92
% 4.69/4.92 % inf_bot_left
% 4.69/4.92 thf(fact_1597_inf__bot__left,axiom,
% 4.69/4.92 ! [X: set_Product_unit] :
% 4.69/4.92 ( ( inf_in4660618365625256667t_unit @ bot_bo3957492148770167129t_unit @ X )
% 4.69/4.92 = bot_bo3957492148770167129t_unit ) ).
% 4.69/4.92
% 4.69/4.92 % inf_bot_left
% 4.69/4.92 thf(fact_1598_inf__bot__left,axiom,
% 4.69/4.92 ! [X: set_o] :
% 4.69/4.92 ( ( inf_inf_set_o @ bot_bot_set_o @ X )
% 4.69/4.92 = bot_bot_set_o ) ).
% 4.69/4.92
% 4.69/4.92 % inf_bot_left
% 4.69/4.92 thf(fact_1599_inf__bot__left,axiom,
% 4.69/4.92 ! [X: set_nat] :
% 4.69/4.92 ( ( inf_inf_set_nat @ bot_bot_set_nat @ X )
% 4.69/4.92 = bot_bot_set_nat ) ).
% 4.69/4.92
% 4.69/4.92 % inf_bot_left
% 4.69/4.92 thf(fact_1600_inf__bot__left,axiom,
% 4.69/4.92 ! [X: set_int] :
% 4.69/4.92 ( ( inf_inf_set_int @ bot_bot_set_int @ X )
% 4.69/4.92 = bot_bot_set_int ) ).
% 4.69/4.92
% 4.69/4.92 % inf_bot_left
% 4.69/4.92 thf(fact_1601_inf__bot__left,axiom,
% 4.69/4.92 ! [X: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( inf_in1906310914598751387_nat_o @ bot_bo7824918357723582233_nat_o @ X )
% 4.69/4.92 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/4.92
% 4.69/4.92 % inf_bot_left
% 4.69/4.92 thf(fact_1602_boolean__algebra_Odisj__zero__right,axiom,
% 4.69/4.92 ! [X: assn] :
% 4.69/4.92 ( ( sup_sup_assn @ X @ bot_bot_assn )
% 4.69/4.92 = X ) ).
% 4.69/4.92
% 4.69/4.92 % boolean_algebra.disj_zero_right
% 4.69/4.92 thf(fact_1603_boolean__algebra_Odisj__zero__right,axiom,
% 4.69/4.92 ! [X: product_unit] :
% 4.69/4.92 ( ( sup_sup_Product_unit @ X @ bot_bot_Product_unit )
% 4.69/4.92 = X ) ).
% 4.69/4.92
% 4.69/4.92 % boolean_algebra.disj_zero_right
% 4.69/4.92 thf(fact_1604_boolean__algebra_Odisj__zero__right,axiom,
% 4.69/4.92 ! [X: set_Product_unit] :
% 4.69/4.92 ( ( sup_su793286257634532545t_unit @ X @ bot_bo3957492148770167129t_unit )
% 4.69/4.92 = X ) ).
% 4.69/4.92
% 4.69/4.92 % boolean_algebra.disj_zero_right
% 4.69/4.92 thf(fact_1605_boolean__algebra_Odisj__zero__right,axiom,
% 4.69/4.92 ! [X: set_o] :
% 4.69/4.92 ( ( sup_sup_set_o @ X @ bot_bot_set_o )
% 4.69/4.92 = X ) ).
% 4.69/4.92
% 4.69/4.92 % boolean_algebra.disj_zero_right
% 4.69/4.92 thf(fact_1606_boolean__algebra_Odisj__zero__right,axiom,
% 4.69/4.92 ! [X: set_nat] :
% 4.69/4.92 ( ( sup_sup_set_nat @ X @ bot_bot_set_nat )
% 4.69/4.92 = X ) ).
% 4.69/4.92
% 4.69/4.92 % boolean_algebra.disj_zero_right
% 4.69/4.92 thf(fact_1607_boolean__algebra_Odisj__zero__right,axiom,
% 4.69/4.92 ! [X: set_int] :
% 4.69/4.92 ( ( sup_sup_set_int @ X @ bot_bot_set_int )
% 4.69/4.92 = X ) ).
% 4.69/4.92
% 4.69/4.92 % boolean_algebra.disj_zero_right
% 4.69/4.92 thf(fact_1608_boolean__algebra_Odisj__zero__right,axiom,
% 4.69/4.92 ! [X: set_Pr4532377907799695533_nat_o] :
% 4.69/4.92 ( ( sup_su5209123915105501825_nat_o @ X @ bot_bo7824918357723582233_nat_o )
% 4.69/4.92 = X ) ).
% 4.69/4.92
% 4.69/4.92 % boolean_algebra.disj_zero_right
% 4.69/4.92 thf(fact_1609_prod__set__defs_I2_J,axiom,
% 4.69/4.92 ( basic_2698842327037663054et_nat
% 4.69/4.92 = ( ^ [P5: produc3658429121746597890et_nat] : ( insert_set_nat @ ( produc8586169260539613262et_nat @ P5 ) @ bot_bot_set_set_nat ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % prod_set_defs(2)
% 4.69/4.92 thf(fact_1610_prod__set__defs_I2_J,axiom,
% 4.69/4.92 ( basic_snds_int_int
% 4.69/4.92 = ( ^ [P5: product_prod_int_int] : ( insert_int @ ( product_snd_int_int @ P5 ) @ bot_bot_set_int ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % prod_set_defs(2)
% 4.69/4.92 thf(fact_1611_snds_Ocases,axiom,
% 4.69/4.92 ! [A2: set_nat,P3: produc3658429121746597890et_nat] :
% 4.69/4.92 ( ( member_set_nat @ A2 @ ( basic_2698842327037663054et_nat @ P3 ) )
% 4.69/4.92 => ( A2
% 4.69/4.92 = ( produc8586169260539613262et_nat @ P3 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % snds.cases
% 4.69/4.92 thf(fact_1612_snds_Ocases,axiom,
% 4.69/4.92 ! [A2: int,P3: product_prod_int_int] :
% 4.69/4.92 ( ( member_int @ A2 @ ( basic_snds_int_int @ P3 ) )
% 4.69/4.92 => ( A2
% 4.69/4.92 = ( product_snd_int_int @ P3 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % snds.cases
% 4.69/4.92 thf(fact_1613_snds_Osimps,axiom,
% 4.69/4.92 ! [A2: set_nat,P3: produc3658429121746597890et_nat] :
% 4.69/4.92 ( ( member_set_nat @ A2 @ ( basic_2698842327037663054et_nat @ P3 ) )
% 4.69/4.92 = ( A2
% 4.69/4.92 = ( produc8586169260539613262et_nat @ P3 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % snds.simps
% 4.69/4.92 thf(fact_1614_snds_Osimps,axiom,
% 4.69/4.92 ! [A2: int,P3: product_prod_int_int] :
% 4.69/4.92 ( ( member_int @ A2 @ ( basic_snds_int_int @ P3 ) )
% 4.69/4.92 = ( A2
% 4.69/4.92 = ( product_snd_int_int @ P3 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % snds.simps
% 4.69/4.92 thf(fact_1615_snds_Ointros,axiom,
% 4.69/4.92 ! [P3: produc3658429121746597890et_nat] : ( member_set_nat @ ( produc8586169260539613262et_nat @ P3 ) @ ( basic_2698842327037663054et_nat @ P3 ) ) ).
% 4.69/4.92
% 4.69/4.92 % snds.intros
% 4.69/4.92 thf(fact_1616_snds_Ointros,axiom,
% 4.69/4.92 ! [P3: product_prod_int_int] : ( member_int @ ( product_snd_int_int @ P3 ) @ ( basic_snds_int_int @ P3 ) ) ).
% 4.69/4.92
% 4.69/4.92 % snds.intros
% 4.69/4.92 thf(fact_1617_wand__raw_Opelims_I1_J,axiom,
% 4.69/4.92 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 4.69/4.92 ( ( ( wand_raw @ X @ Xa @ Xb )
% 4.69/4.92 = Y )
% 4.69/4.92 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 4.69/4.92 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.92 ( ( Xb
% 4.69/4.92 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.92 => ( ( Y
% 4.69/4.92 = ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.92 & ! [H5: heap_e7401611519738050253t_unit,As6: set_nat] :
% 4.69/4.92 ( ( ( ( inf_inf_set_nat @ As2 @ As6 )
% 4.69/4.92 = bot_bot_set_nat )
% 4.69/4.92 & ( relH @ As2 @ H @ H5 )
% 4.69/4.92 & ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As2 ) )
% 4.69/4.92 & ( X @ ( produc7507926704131184380et_nat @ H5 @ As6 ) ) )
% 4.69/4.92 => ( Xa @ ( produc7507926704131184380et_nat @ H5 @ ( sup_sup_set_nat @ As2 @ As6 ) ) ) ) ) )
% 4.69/4.92 => ~ ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As2 ) ) ) ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % wand_raw.pelims(1)
% 4.69/4.92 thf(fact_1618_wand__raw_Opelims_I2_J,axiom,
% 4.69/4.92 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 4.69/4.92 ( ( wand_raw @ X @ Xa @ Xb )
% 4.69/4.92 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 4.69/4.92 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.92 ( ( Xb
% 4.69/4.92 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.92 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As2 ) ) ) )
% 4.69/4.92 => ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.92 & ! [H7: heap_e7401611519738050253t_unit,As7: set_nat] :
% 4.69/4.92 ( ( ( ( inf_inf_set_nat @ As2 @ As7 )
% 4.69/4.92 = bot_bot_set_nat )
% 4.69/4.92 & ( relH @ As2 @ H @ H7 )
% 4.69/4.92 & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As2 ) )
% 4.69/4.92 & ( X @ ( produc7507926704131184380et_nat @ H7 @ As7 ) ) )
% 4.69/4.92 => ( Xa @ ( produc7507926704131184380et_nat @ H7 @ ( sup_sup_set_nat @ As2 @ As7 ) ) ) ) ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % wand_raw.pelims(2)
% 4.69/4.92 thf(fact_1619_wand__raw_Opelims_I3_J,axiom,
% 4.69/4.92 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 4.69/4.92 ( ~ ( wand_raw @ X @ Xa @ Xb )
% 4.69/4.92 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 4.69/4.92 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.92 ( ( Xb
% 4.69/4.92 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.92 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As2 ) ) ) )
% 4.69/4.92 => ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.92 & ! [H6: heap_e7401611519738050253t_unit,As4: set_nat] :
% 4.69/4.92 ( ( ( ( inf_inf_set_nat @ As2 @ As4 )
% 4.69/4.92 = bot_bot_set_nat )
% 4.69/4.92 & ( relH @ As2 @ H @ H6 )
% 4.69/4.92 & ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As2 ) )
% 4.69/4.92 & ( X @ ( produc7507926704131184380et_nat @ H6 @ As4 ) ) )
% 4.69/4.92 => ( Xa @ ( produc7507926704131184380et_nat @ H6 @ ( sup_sup_set_nat @ As2 @ As4 ) ) ) ) ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % wand_raw.pelims(3)
% 4.69/4.92 thf(fact_1620_le__numeral__extra_I4_J,axiom,
% 4.69/4.92 ord_le3102999989581377725nteger @ one_one_Code_integer @ one_one_Code_integer ).
% 4.69/4.92
% 4.69/4.92 % le_numeral_extra(4)
% 4.69/4.92 thf(fact_1621_le__numeral__extra_I4_J,axiom,
% 4.69/4.92 ord_le1926595141338095240atural @ one_one_Code_natural @ one_one_Code_natural ).
% 4.69/4.92
% 4.69/4.92 % le_numeral_extra(4)
% 4.69/4.92 thf(fact_1622_le__numeral__extra_I4_J,axiom,
% 4.69/4.92 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 4.69/4.92
% 4.69/4.92 % le_numeral_extra(4)
% 4.69/4.92 thf(fact_1623_le__numeral__extra_I4_J,axiom,
% 4.69/4.92 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 4.69/4.92
% 4.69/4.92 % le_numeral_extra(4)
% 4.69/4.92 thf(fact_1624_le__numeral__extra_I4_J,axiom,
% 4.69/4.92 ord_less_eq_int @ one_one_int @ one_one_int ).
% 4.69/4.92
% 4.69/4.92 % le_numeral_extra(4)
% 4.69/4.92 thf(fact_1625_less__eq__assn__def,axiom,
% 4.69/4.92 ( ord_less_eq_assn
% 4.69/4.92 = ( ^ [A6: assn,B6: assn] :
% 4.69/4.92 ( A6
% 4.69/4.92 = ( inf_inf_assn @ A6 @ B6 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % less_eq_assn_def
% 4.69/4.92 thf(fact_1626_times__assn__raw_Opelims_I3_J,axiom,
% 4.69/4.92 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 4.69/4.92 ( ~ ( times_assn_raw @ X @ Xa @ Xb )
% 4.69/4.92 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 4.69/4.92 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.92 ( ( Xb
% 4.69/4.92 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.92 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As2 ) ) ) )
% 4.69/4.92 => ? [As13: set_nat,As24: set_nat] :
% 4.69/4.92 ( ( As2
% 4.69/4.92 = ( sup_sup_set_nat @ As13 @ As24 ) )
% 4.69/4.92 & ( ( inf_inf_set_nat @ As13 @ As24 )
% 4.69/4.92 = bot_bot_set_nat )
% 4.69/4.92 & ( X @ ( produc7507926704131184380et_nat @ H @ As13 ) )
% 4.69/4.92 & ( Xa @ ( produc7507926704131184380et_nat @ H @ As24 ) ) ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % times_assn_raw.pelims(3)
% 4.69/4.92 thf(fact_1627_times__assn__raw_Opelims_I2_J,axiom,
% 4.69/4.92 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 4.69/4.92 ( ( times_assn_raw @ X @ Xa @ Xb )
% 4.69/4.92 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 4.69/4.92 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.92 ( ( Xb
% 4.69/4.92 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.92 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As2 ) ) ) )
% 4.69/4.92 => ~ ? [As12: set_nat,As23: set_nat] :
% 4.69/4.92 ( ( As2
% 4.69/4.92 = ( sup_sup_set_nat @ As12 @ As23 ) )
% 4.69/4.92 & ( ( inf_inf_set_nat @ As12 @ As23 )
% 4.69/4.92 = bot_bot_set_nat )
% 4.69/4.92 & ( X @ ( produc7507926704131184380et_nat @ H @ As12 ) )
% 4.69/4.92 & ( Xa @ ( produc7507926704131184380et_nat @ H @ As23 ) ) ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % times_assn_raw.pelims(2)
% 4.69/4.92 thf(fact_1628_times__assn__raw_Opelims_I1_J,axiom,
% 4.69/4.92 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 4.69/4.92 ( ( ( times_assn_raw @ X @ Xa @ Xb )
% 4.69/4.92 = Y )
% 4.69/4.92 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 4.69/4.92 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/4.92 ( ( Xb
% 4.69/4.92 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/4.92 => ( ( Y
% 4.69/4.92 = ( ? [As1: set_nat,As22: set_nat] :
% 4.69/4.92 ( ( As2
% 4.69/4.92 = ( sup_sup_set_nat @ As1 @ As22 ) )
% 4.69/4.92 & ( ( inf_inf_set_nat @ As1 @ As22 )
% 4.69/4.92 = bot_bot_set_nat )
% 4.69/4.92 & ( X @ ( produc7507926704131184380et_nat @ H @ As1 ) )
% 4.69/4.92 & ( Xa @ ( produc7507926704131184380et_nat @ H @ As22 ) ) ) ) )
% 4.69/4.92 => ~ ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As2 ) ) ) ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % times_assn_raw.pelims(1)
% 4.69/4.92 thf(fact_1629_subset__Image1__Image1__iff,axiom,
% 4.69/4.92 ! [R2: set_Pr5094982260447487303t_unit,A2: product_unit,B: product_unit] :
% 4.69/4.92 ( ( order_7534304569044981540t_unit @ ( field_Product_unit @ R2 ) @ R2 )
% 4.69/4.92 => ( ( member_Product_unit @ A2 @ ( field_Product_unit @ R2 ) )
% 4.69/4.92 => ( ( member_Product_unit @ B @ ( field_Product_unit @ R2 ) )
% 4.69/4.92 => ( ( ord_le3507040750410214029t_unit @ ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) @ ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.92 = ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ B @ A2 ) @ R2 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_Image1_Image1_iff
% 4.69/4.92 thf(fact_1630_subset__Image1__Image1__iff,axiom,
% 4.69/4.92 ! [R2: set_Product_prod_o_o,A2: $o,B: $o] :
% 4.69/4.92 ( ( order_preorder_on_o @ ( field_o @ R2 ) @ R2 )
% 4.69/4.92 => ( ( member_o @ A2 @ ( field_o @ R2 ) )
% 4.69/4.92 => ( ( member_o @ B @ ( field_o @ R2 ) )
% 4.69/4.92 => ( ( ord_less_eq_set_o @ ( image_o_o @ R2 @ ( insert_o @ A2 @ bot_bot_set_o ) ) @ ( image_o_o @ R2 @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 4.69/4.92 = ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ B @ A2 ) @ R2 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_Image1_Image1_iff
% 4.69/4.92 thf(fact_1631_subset__Image1__Image1__iff,axiom,
% 4.69/4.92 ! [R2: set_Pr958786334691620121nt_int,A2: int,B: int] :
% 4.69/4.92 ( ( order_4859164337913492053on_int @ ( field_int @ R2 ) @ R2 )
% 4.69/4.92 => ( ( member_int @ A2 @ ( field_int @ R2 ) )
% 4.69/4.92 => ( ( member_int @ B @ ( field_int @ R2 ) )
% 4.69/4.92 => ( ( ord_less_eq_set_int @ ( image_int_int @ R2 @ ( insert_int @ A2 @ bot_bot_set_int ) ) @ ( image_int_int @ R2 @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 4.69/4.92 = ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ A2 ) @ R2 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_Image1_Image1_iff
% 4.69/4.92 thf(fact_1632_subset__Image1__Image1__iff,axiom,
% 4.69/4.92 ! [R2: set_Pr2161125870931222855_nat_o,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o] :
% 4.69/4.92 ( ( order_174704566861754596_nat_o @ ( field_81821745747897882_nat_o @ R2 ) @ R2 )
% 4.69/4.92 => ( ( member6576561426505652726_nat_o @ A2 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.92 => ( ( member6576561426505652726_nat_o @ B @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.92 => ( ( ord_le2965882846123202637_nat_o @ ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) @ ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/4.92 = ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ B @ A2 ) @ R2 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_Image1_Image1_iff
% 4.69/4.92 thf(fact_1633_subset__Image1__Image1__iff,axiom,
% 4.69/4.92 ! [R2: set_Pr1261947904930325089at_nat,A2: nat,B: nat] :
% 4.69/4.92 ( ( order_4861654808422542329on_nat @ ( field_nat @ R2 ) @ R2 )
% 4.69/4.92 => ( ( member_nat @ A2 @ ( field_nat @ R2 ) )
% 4.69/4.92 => ( ( member_nat @ B @ ( field_nat @ R2 ) )
% 4.69/4.92 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ R2 @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) @ ( image_nat_nat @ R2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 4.69/4.92 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ A2 ) @ R2 ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % subset_Image1_Image1_iff
% 4.69/4.92 thf(fact_1634_Field__insert,axiom,
% 4.69/4.92 ! [A2: product_unit,B: product_unit,R2: set_Pr5094982260447487303t_unit] :
% 4.69/4.92 ( ( field_Product_unit @ ( insert4616891024742550839t_unit @ ( produc5692694829384537815t_unit @ A2 @ B ) @ R2 ) )
% 4.69/4.92 = ( sup_su793286257634532545t_unit @ ( insert_Product_unit @ A2 @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) @ ( field_Product_unit @ R2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Field_insert
% 4.69/4.92 thf(fact_1635_Field__insert,axiom,
% 4.69/4.92 ! [A2: $o,B: $o,R2: set_Product_prod_o_o] :
% 4.69/4.92 ( ( field_o @ ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ A2 @ B ) @ R2 ) )
% 4.69/4.92 = ( sup_sup_set_o @ ( insert_o @ A2 @ ( insert_o @ B @ bot_bot_set_o ) ) @ ( field_o @ R2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Field_insert
% 4.69/4.92 thf(fact_1636_Field__insert,axiom,
% 4.69/4.92 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.92 ( ( field_nat @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 ) )
% 4.69/4.92 = ( sup_sup_set_nat @ ( insert_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) @ ( field_nat @ R2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Field_insert
% 4.69/4.92 thf(fact_1637_Field__insert,axiom,
% 4.69/4.92 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.92 ( ( field_int @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 ) )
% 4.69/4.92 = ( sup_sup_set_int @ ( insert_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) @ ( field_int @ R2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Field_insert
% 4.69/4.92 thf(fact_1638_Field__insert,axiom,
% 4.69/4.92 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o,R2: set_Pr2161125870931222855_nat_o] :
% 4.69/4.92 ( ( field_81821745747897882_nat_o @ ( insert5309882203591314743_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ B ) @ R2 ) )
% 4.69/4.92 = ( sup_su5209123915105501825_nat_o @ ( insert5175938949040314269_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o ) ) @ ( field_81821745747897882_nat_o @ R2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Field_insert
% 4.69/4.92 thf(fact_1639_dom__ran__disj__comp,axiom,
% 4.69/4.92 ! [R3: set_Pr5094982260447487303t_unit] :
% 4.69/4.92 ( ( ( inf_in4660618365625256667t_unit @ ( domain4292024440186670924t_unit @ R3 ) @ ( range_6617724647562260917t_unit @ R3 ) )
% 4.69/4.92 = bot_bo3957492148770167129t_unit )
% 4.69/4.92 => ( ( relcom848357998638694028t_unit @ R3 @ R3 )
% 4.69/4.92 = bot_bo1654022762305692595t_unit ) ) ).
% 4.69/4.92
% 4.69/4.92 % dom_ran_disj_comp
% 4.69/4.92 thf(fact_1640_dom__ran__disj__comp,axiom,
% 4.69/4.92 ! [R3: set_Product_prod_o_o] :
% 4.69/4.92 ( ( ( inf_inf_set_o @ ( domain_o_o @ R3 ) @ ( range_o_o @ R3 ) )
% 4.69/4.92 = bot_bot_set_o )
% 4.69/4.92 => ( ( relcomp_o_o_o @ R3 @ R3 )
% 4.69/4.92 = bot_bo7073875226086086771od_o_o ) ) ).
% 4.69/4.92
% 4.69/4.92 % dom_ran_disj_comp
% 4.69/4.92 thf(fact_1641_dom__ran__disj__comp,axiom,
% 4.69/4.92 ! [R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.92 ( ( ( inf_inf_set_nat @ ( domain_nat_nat @ R3 ) @ ( range_nat_nat @ R3 ) )
% 4.69/4.92 = bot_bot_set_nat )
% 4.69/4.92 => ( ( relcomp_nat_nat_nat @ R3 @ R3 )
% 4.69/4.92 = bot_bo2099793752762293965at_nat ) ) ).
% 4.69/4.92
% 4.69/4.92 % dom_ran_disj_comp
% 4.69/4.92 thf(fact_1642_dom__ran__disj__comp,axiom,
% 4.69/4.92 ! [R3: set_Pr958786334691620121nt_int] :
% 4.69/4.92 ( ( ( inf_inf_set_int @ ( domain_int_int @ R3 ) @ ( range_int_int @ R3 ) )
% 4.69/4.92 = bot_bot_set_int )
% 4.69/4.92 => ( ( relcomp_int_int_int @ R3 @ R3 )
% 4.69/4.92 = bot_bo1796632182523588997nt_int ) ) ).
% 4.69/4.92
% 4.69/4.92 % dom_ran_disj_comp
% 4.69/4.92 thf(fact_1643_dom__ran__disj__comp,axiom,
% 4.69/4.92 ! [R3: set_Pr2161125870931222855_nat_o] :
% 4.69/4.92 ( ( ( inf_in1906310914598751387_nat_o @ ( domain4881241903163524940_nat_o @ R3 ) @ ( range_5289318983786108341_nat_o @ R3 ) )
% 4.69/4.92 = bot_bo7824918357723582233_nat_o )
% 4.69/4.92 => ( ( relcom6251035627269349452_nat_o @ R3 @ R3 )
% 4.69/4.92 = bot_bo3657187498359500723_nat_o ) ) ).
% 4.69/4.92
% 4.69/4.92 % dom_ran_disj_comp
% 4.69/4.92 thf(fact_1644_proj__iff,axiom,
% 4.69/4.92 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit,X: product_unit,Y: product_unit] :
% 4.69/4.92 ( ( equiv_4189356295871601603t_unit @ A @ R2 )
% 4.69/4.92 => ( ( ord_le3507040750410214029t_unit @ ( insert_Product_unit @ X @ ( insert_Product_unit @ Y @ bot_bo3957492148770167129t_unit ) ) @ A )
% 4.69/4.92 => ( ( ( equiv_5763582929720877514t_unit @ R2 @ X )
% 4.69/4.92 = ( equiv_5763582929720877514t_unit @ R2 @ Y ) )
% 4.69/4.92 = ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X @ Y ) @ R2 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % proj_iff
% 4.69/4.92 thf(fact_1645_proj__iff,axiom,
% 4.69/4.92 ! [A: set_o,R2: set_Product_prod_o_o,X: $o,Y: $o] :
% 4.69/4.92 ( ( equiv_equiv_o @ A @ R2 )
% 4.69/4.92 => ( ( ord_less_eq_set_o @ ( insert_o @ X @ ( insert_o @ Y @ bot_bot_set_o ) ) @ A )
% 4.69/4.92 => ( ( ( equiv_proj_o_o @ R2 @ X )
% 4.69/4.92 = ( equiv_proj_o_o @ R2 @ Y ) )
% 4.69/4.92 = ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ R2 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % proj_iff
% 4.69/4.92 thf(fact_1646_proj__iff,axiom,
% 4.69/4.92 ! [A: set_int,R2: set_Pr958786334691620121nt_int,X: int,Y: int] :
% 4.69/4.92 ( ( equiv_equiv_int @ A @ R2 )
% 4.69/4.92 => ( ( ord_less_eq_set_int @ ( insert_int @ X @ ( insert_int @ Y @ bot_bot_set_int ) ) @ A )
% 4.69/4.92 => ( ( ( equiv_proj_int_int @ R2 @ X )
% 4.69/4.92 = ( equiv_proj_int_int @ R2 @ Y ) )
% 4.69/4.92 = ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R2 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % proj_iff
% 4.69/4.92 thf(fact_1647_proj__iff,axiom,
% 4.69/4.92 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o] :
% 4.69/4.92 ( ( equiv_6726761681920839555_nat_o @ A @ R2 )
% 4.69/4.92 => ( ( ord_le2965882846123202637_nat_o @ ( insert5175938949040314269_nat_o @ X @ ( insert5175938949040314269_nat_o @ Y @ bot_bo7824918357723582233_nat_o ) ) @ A )
% 4.69/4.92 => ( ( ( equiv_3235788788526563786_nat_o @ R2 @ X )
% 4.69/4.92 = ( equiv_3235788788526563786_nat_o @ R2 @ Y ) )
% 4.69/4.92 = ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ R2 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % proj_iff
% 4.69/4.92 thf(fact_1648_proj__iff,axiom,
% 4.69/4.92 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,X: nat,Y: nat] :
% 4.69/4.92 ( ( equiv_equiv_nat @ A @ R2 )
% 4.69/4.92 => ( ( ord_less_eq_set_nat @ ( insert_nat @ X @ ( insert_nat @ Y @ bot_bot_set_nat ) ) @ A )
% 4.69/4.92 => ( ( ( equiv_proj_nat_nat @ R2 @ X )
% 4.69/4.92 = ( equiv_proj_nat_nat @ R2 @ Y ) )
% 4.69/4.92 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R2 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % proj_iff
% 4.69/4.92 thf(fact_1649_Refl__antisym__eq__Image1__Image1__iff,axiom,
% 4.69/4.92 ! [R2: set_Pr5094982260447487303t_unit,A2: product_unit,B: product_unit] :
% 4.69/4.92 ( ( refl_on_Product_unit @ ( field_Product_unit @ R2 ) @ R2 )
% 4.69/4.92 => ( ( antisym_Product_unit @ R2 )
% 4.69/4.92 => ( ( member_Product_unit @ A2 @ ( field_Product_unit @ R2 ) )
% 4.69/4.92 => ( ( member_Product_unit @ B @ ( field_Product_unit @ R2 ) )
% 4.69/4.92 => ( ( ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.92 = ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.92 = ( A2 = B ) ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Refl_antisym_eq_Image1_Image1_iff
% 4.69/4.92 thf(fact_1650_Refl__antisym__eq__Image1__Image1__iff,axiom,
% 4.69/4.92 ! [R2: set_Product_prod_o_o,A2: $o,B: $o] :
% 4.69/4.92 ( ( refl_on_o @ ( field_o @ R2 ) @ R2 )
% 4.69/4.92 => ( ( antisym_o @ R2 )
% 4.69/4.92 => ( ( member_o @ A2 @ ( field_o @ R2 ) )
% 4.69/4.92 => ( ( member_o @ B @ ( field_o @ R2 ) )
% 4.69/4.92 => ( ( ( image_o_o @ R2 @ ( insert_o @ A2 @ bot_bot_set_o ) )
% 4.69/4.92 = ( image_o_o @ R2 @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 4.69/4.92 = ( A2 = B ) ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Refl_antisym_eq_Image1_Image1_iff
% 4.69/4.92 thf(fact_1651_Refl__antisym__eq__Image1__Image1__iff,axiom,
% 4.69/4.92 ! [R2: set_Pr1261947904930325089at_nat,A2: nat,B: nat] :
% 4.69/4.92 ( ( refl_on_nat @ ( field_nat @ R2 ) @ R2 )
% 4.69/4.92 => ( ( antisym_nat @ R2 )
% 4.69/4.92 => ( ( member_nat @ A2 @ ( field_nat @ R2 ) )
% 4.69/4.92 => ( ( member_nat @ B @ ( field_nat @ R2 ) )
% 4.69/4.92 => ( ( ( image_nat_nat @ R2 @ ( insert_nat @ A2 @ bot_bot_set_nat ) )
% 4.69/4.92 = ( image_nat_nat @ R2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 4.69/4.92 = ( A2 = B ) ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Refl_antisym_eq_Image1_Image1_iff
% 4.69/4.92 thf(fact_1652_Refl__antisym__eq__Image1__Image1__iff,axiom,
% 4.69/4.92 ! [R2: set_Pr958786334691620121nt_int,A2: int,B: int] :
% 4.69/4.92 ( ( refl_on_int @ ( field_int @ R2 ) @ R2 )
% 4.69/4.92 => ( ( antisym_int @ R2 )
% 4.69/4.92 => ( ( member_int @ A2 @ ( field_int @ R2 ) )
% 4.69/4.92 => ( ( member_int @ B @ ( field_int @ R2 ) )
% 4.69/4.92 => ( ( ( image_int_int @ R2 @ ( insert_int @ A2 @ bot_bot_set_int ) )
% 4.69/4.92 = ( image_int_int @ R2 @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 4.69/4.92 = ( A2 = B ) ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Refl_antisym_eq_Image1_Image1_iff
% 4.69/4.92 thf(fact_1653_Refl__antisym__eq__Image1__Image1__iff,axiom,
% 4.69/4.92 ! [R2: set_Pr2161125870931222855_nat_o,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o] :
% 4.69/4.92 ( ( refl_o1075864025857821388_nat_o @ ( field_81821745747897882_nat_o @ R2 ) @ R2 )
% 4.69/4.92 => ( ( antisy9190549550370998639_nat_o @ R2 )
% 4.69/4.92 => ( ( member6576561426505652726_nat_o @ A2 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.92 => ( ( member6576561426505652726_nat_o @ B @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.92 => ( ( ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.92 = ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/4.92 = ( A2 = B ) ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Refl_antisym_eq_Image1_Image1_iff
% 4.69/4.92 thf(fact_1654_equiv__class__nondisjoint,axiom,
% 4.69/4.92 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit,X: product_unit,A2: product_unit,B: product_unit] :
% 4.69/4.92 ( ( equiv_4189356295871601603t_unit @ A @ R2 )
% 4.69/4.92 => ( ( member_Product_unit @ X @ ( inf_in4660618365625256667t_unit @ ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) @ ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) ) )
% 4.69/4.92 => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A2 @ B ) @ R2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % equiv_class_nondisjoint
% 4.69/4.92 thf(fact_1655_equiv__class__nondisjoint,axiom,
% 4.69/4.92 ! [A: set_o,R2: set_Product_prod_o_o,X: $o,A2: $o,B: $o] :
% 4.69/4.92 ( ( equiv_equiv_o @ A @ R2 )
% 4.69/4.92 => ( ( member_o @ X @ ( inf_inf_set_o @ ( image_o_o @ R2 @ ( insert_o @ A2 @ bot_bot_set_o ) ) @ ( image_o_o @ R2 @ ( insert_o @ B @ bot_bot_set_o ) ) ) )
% 4.69/4.92 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ B ) @ R2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % equiv_class_nondisjoint
% 4.69/4.92 thf(fact_1656_equiv__class__nondisjoint,axiom,
% 4.69/4.92 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,X: nat,A2: nat,B: nat] :
% 4.69/4.92 ( ( equiv_equiv_nat @ A @ R2 )
% 4.69/4.92 => ( ( member_nat @ X @ ( inf_inf_set_nat @ ( image_nat_nat @ R2 @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) @ ( image_nat_nat @ R2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) )
% 4.69/4.92 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % equiv_class_nondisjoint
% 4.69/4.92 thf(fact_1657_equiv__class__nondisjoint,axiom,
% 4.69/4.92 ! [A: set_int,R2: set_Pr958786334691620121nt_int,X: int,A2: int,B: int] :
% 4.69/4.92 ( ( equiv_equiv_int @ A @ R2 )
% 4.69/4.92 => ( ( member_int @ X @ ( inf_inf_set_int @ ( image_int_int @ R2 @ ( insert_int @ A2 @ bot_bot_set_int ) ) @ ( image_int_int @ R2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) )
% 4.69/4.92 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % equiv_class_nondisjoint
% 4.69/4.92 thf(fact_1658_equiv__class__nondisjoint,axiom,
% 4.69/4.92 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o,X: produc3658429121746597890et_nat > $o,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o] :
% 4.69/4.92 ( ( equiv_6726761681920839555_nat_o @ A @ R2 )
% 4.69/4.92 => ( ( member6576561426505652726_nat_o @ X @ ( inf_in1906310914598751387_nat_o @ ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) @ ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o ) ) ) )
% 4.69/4.92 => ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ B ) @ R2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % equiv_class_nondisjoint
% 4.69/4.92 thf(fact_1659_finite__reachable__advance,axiom,
% 4.69/4.92 ! [E: set_Pr4811707699266497531nteger,V0: code_integer,V: code_integer] :
% 4.69/4.92 ( ( finite6017078050557962740nteger @ ( image_4147621952751189391nteger @ ( transi3984306202085910426nteger @ E ) @ ( insert_Code_integer @ V0 @ bot_bo3990330152332043303nteger ) ) )
% 4.69/4.92 => ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ V0 @ V ) @ ( transi3984306202085910426nteger @ E ) )
% 4.69/4.92 => ( finite6017078050557962740nteger @ ( image_4147621952751189391nteger @ ( transi3984306202085910426nteger @ E ) @ ( insert_Code_integer @ V @ bot_bo3990330152332043303nteger ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % finite_reachable_advance
% 4.69/4.92 thf(fact_1660_finite__reachable__advance,axiom,
% 4.69/4.92 ! [E: set_Pr5094982260447487303t_unit,V0: product_unit,V: product_unit] :
% 4.69/4.92 ( ( finite4290736615968046902t_unit @ ( image_8431784415008483091t_unit @ ( transi6481887417741755664t_unit @ E ) @ ( insert_Product_unit @ V0 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.92 => ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ V0 @ V ) @ ( transi6481887417741755664t_unit @ E ) )
% 4.69/4.92 => ( finite4290736615968046902t_unit @ ( image_8431784415008483091t_unit @ ( transi6481887417741755664t_unit @ E ) @ ( insert_Product_unit @ V @ bot_bo3957492148770167129t_unit ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % finite_reachable_advance
% 4.69/4.92 thf(fact_1661_finite__reachable__advance,axiom,
% 4.69/4.92 ! [E: set_Product_prod_o_o,V0: $o,V: $o] :
% 4.69/4.92 ( ( finite_finite_o @ ( image_o_o @ ( transitive_rtrancl_o @ E ) @ ( insert_o @ V0 @ bot_bot_set_o ) ) )
% 4.69/4.92 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ V0 @ V ) @ ( transitive_rtrancl_o @ E ) )
% 4.69/4.92 => ( finite_finite_o @ ( image_o_o @ ( transitive_rtrancl_o @ E ) @ ( insert_o @ V @ bot_bot_set_o ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % finite_reachable_advance
% 4.69/4.92 thf(fact_1662_finite__reachable__advance,axiom,
% 4.69/4.92 ! [E: set_Pr1261947904930325089at_nat,V0: nat,V: nat] :
% 4.69/4.92 ( ( finite_finite_nat @ ( image_nat_nat @ ( transi2905341329935302413cl_nat @ E ) @ ( insert_nat @ V0 @ bot_bot_set_nat ) ) )
% 4.69/4.92 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ V0 @ V ) @ ( transi2905341329935302413cl_nat @ E ) )
% 4.69/4.92 => ( finite_finite_nat @ ( image_nat_nat @ ( transi2905341329935302413cl_nat @ E ) @ ( insert_nat @ V @ bot_bot_set_nat ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % finite_reachable_advance
% 4.69/4.92 thf(fact_1663_finite__reachable__advance,axiom,
% 4.69/4.92 ! [E: set_Pr958786334691620121nt_int,V0: int,V: int] :
% 4.69/4.92 ( ( finite_finite_int @ ( image_int_int @ ( transi2902850859426252137cl_int @ E ) @ ( insert_int @ V0 @ bot_bot_set_int ) ) )
% 4.69/4.92 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ V0 @ V ) @ ( transi2902850859426252137cl_int @ E ) )
% 4.69/4.92 => ( finite_finite_int @ ( image_int_int @ ( transi2902850859426252137cl_int @ E ) @ ( insert_int @ V @ bot_bot_set_int ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % finite_reachable_advance
% 4.69/4.92 thf(fact_1664_finite__reachable__advance,axiom,
% 4.69/4.92 ! [E: set_Pr2161125870931222855_nat_o,V0: produc3658429121746597890et_nat > $o,V: produc3658429121746597890et_nat > $o] :
% 4.69/4.92 ( ( finite3252695134891459830_nat_o @ ( image_2232984160439939859_nat_o @ ( transi712980445759334096_nat_o @ E ) @ ( insert5175938949040314269_nat_o @ V0 @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/4.92 => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ V0 @ V ) @ ( transi712980445759334096_nat_o @ E ) )
% 4.69/4.92 => ( finite3252695134891459830_nat_o @ ( image_2232984160439939859_nat_o @ ( transi712980445759334096_nat_o @ E ) @ ( insert5175938949040314269_nat_o @ V @ bot_bo7824918357723582233_nat_o ) ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % finite_reachable_advance
% 4.69/4.92 thf(fact_1665_finite__Field__eq__finite,axiom,
% 4.69/4.92 ! [R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.92 ( ( finite_finite_nat @ ( field_nat @ R3 ) )
% 4.69/4.92 = ( finite6177210948735845034at_nat @ R3 ) ) ).
% 4.69/4.92
% 4.69/4.92 % finite_Field_eq_finite
% 4.69/4.92 thf(fact_1666_finite__Field__eq__finite,axiom,
% 4.69/4.92 ! [R3: set_Pr4811707699266497531nteger] :
% 4.69/4.92 ( ( finite6017078050557962740nteger @ ( field_Code_integer @ R3 ) )
% 4.69/4.92 = ( finite2154694888287295812nteger @ R3 ) ) ).
% 4.69/4.92
% 4.69/4.92 % finite_Field_eq_finite
% 4.69/4.92 thf(fact_1667_Field__empty,axiom,
% 4.69/4.92 ( ( field_Product_unit @ bot_bo1654022762305692595t_unit )
% 4.69/4.92 = bot_bo3957492148770167129t_unit ) ).
% 4.69/4.92
% 4.69/4.92 % Field_empty
% 4.69/4.92 thf(fact_1668_Field__empty,axiom,
% 4.69/4.92 ( ( field_o @ bot_bo7073875226086086771od_o_o )
% 4.69/4.92 = bot_bot_set_o ) ).
% 4.69/4.92
% 4.69/4.92 % Field_empty
% 4.69/4.92 thf(fact_1669_Field__empty,axiom,
% 4.69/4.92 ( ( field_nat @ bot_bo2099793752762293965at_nat )
% 4.69/4.92 = bot_bot_set_nat ) ).
% 4.69/4.92
% 4.69/4.92 % Field_empty
% 4.69/4.92 thf(fact_1670_Field__empty,axiom,
% 4.69/4.92 ( ( field_int @ bot_bo1796632182523588997nt_int )
% 4.69/4.92 = bot_bot_set_int ) ).
% 4.69/4.92
% 4.69/4.92 % Field_empty
% 4.69/4.92 thf(fact_1671_Field__empty,axiom,
% 4.69/4.92 ( ( field_81821745747897882_nat_o @ bot_bo3657187498359500723_nat_o )
% 4.69/4.92 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/4.92
% 4.69/4.92 % Field_empty
% 4.69/4.92 thf(fact_1672_Field__Un,axiom,
% 4.69/4.92 ! [R2: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 4.69/4.92 ( ( field_nat @ ( sup_su6327502436637775413at_nat @ R2 @ S2 ) )
% 4.69/4.92 = ( sup_sup_set_nat @ ( field_nat @ R2 ) @ ( field_nat @ S2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % Field_Un
% 4.69/4.92 thf(fact_1673_finite__Field,axiom,
% 4.69/4.92 ! [R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.92 ( ( finite6177210948735845034at_nat @ R2 )
% 4.69/4.92 => ( finite_finite_nat @ ( field_nat @ R2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % finite_Field
% 4.69/4.92 thf(fact_1674_finite__Field,axiom,
% 4.69/4.92 ! [R2: set_Pr4811707699266497531nteger] :
% 4.69/4.92 ( ( finite2154694888287295812nteger @ R2 )
% 4.69/4.92 => ( finite6017078050557962740nteger @ ( field_Code_integer @ R2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % finite_Field
% 4.69/4.92 thf(fact_1675_relcompEpair,axiom,
% 4.69/4.92 ! [A2: heap_e7401611519738050253t_unit,C: set_nat,R2: set_Pr1776176089890104647t_unit,S2: set_Pr3948176798113811640et_nat] :
% 4.69/4.92 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ C ) @ ( relcom4930750947919833671et_nat @ R2 @ S2 ) )
% 4.69/4.92 => ~ ! [B2: heap_e7401611519738050253t_unit] :
% 4.69/4.92 ( ( member5046970461208427408t_unit @ ( produc8256076736985659095t_unit @ A2 @ B2 ) @ R2 )
% 4.69/4.92 => ~ ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ B2 @ C ) @ S2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % relcompEpair
% 4.69/4.92 thf(fact_1676_relcompEpair,axiom,
% 4.69/4.92 ! [A2: heap_e7401611519738050253t_unit,C: set_nat,R2: set_Pr3948176798113811640et_nat,S2: set_Pr5488025237498180813et_nat] :
% 4.69/4.92 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ C ) @ ( relcom8881708762719574682et_nat @ R2 @ S2 ) )
% 4.69/4.92 => ~ ! [B2: set_nat] :
% 4.69/4.92 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ B2 ) @ R2 )
% 4.69/4.92 => ~ ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ B2 @ C ) @ S2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % relcompEpair
% 4.69/4.92 thf(fact_1677_relcompEpair,axiom,
% 4.69/4.92 ! [A2: nat,C: nat,R2: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 4.69/4.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ C ) @ ( relcomp_nat_nat_nat @ R2 @ S2 ) )
% 4.69/4.92 => ~ ! [B2: nat] :
% 4.69/4.92 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ R2 )
% 4.69/4.92 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B2 @ C ) @ S2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % relcompEpair
% 4.69/4.92 thf(fact_1678_relcompEpair,axiom,
% 4.69/4.92 ! [A2: int,C: int,R2: set_Pr958786334691620121nt_int,S2: set_Pr958786334691620121nt_int] :
% 4.69/4.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ C ) @ ( relcomp_int_int_int @ R2 @ S2 ) )
% 4.69/4.92 => ~ ! [B2: int] :
% 4.69/4.92 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B2 ) @ R2 )
% 4.69/4.92 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B2 @ C ) @ S2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % relcompEpair
% 4.69/4.92 thf(fact_1679_relcompEpair,axiom,
% 4.69/4.92 ! [A2: produc3658429121746597890et_nat > $o,C: produc3658429121746597890et_nat,R2: set_Pr2161125870931222855_nat_o,S2: set_Pr3286484037609594932et_nat] :
% 4.69/4.92 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ C ) @ ( relcom6619595054755144899et_nat @ R2 @ S2 ) )
% 4.69/4.92 => ~ ! [B2: produc3658429121746597890et_nat > $o] :
% 4.69/4.92 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ B2 ) @ R2 )
% 4.69/4.92 => ~ ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ B2 @ C ) @ S2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % relcompEpair
% 4.69/4.92 thf(fact_1680_relcompEpair,axiom,
% 4.69/4.92 ! [A2: produc3658429121746597890et_nat > $o,C: produc3658429121746597890et_nat,R2: set_Pr3286484037609594932et_nat,S2: set_Pr719794911490849221et_nat] :
% 4.69/4.92 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ C ) @ ( relcom5975814107203797650et_nat @ R2 @ S2 ) )
% 4.69/4.92 => ~ ! [B2: produc3658429121746597890et_nat] :
% 4.69/4.92 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ B2 ) @ R2 )
% 4.69/4.92 => ~ ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ B2 @ C ) @ S2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % relcompEpair
% 4.69/4.92 thf(fact_1681_relcompEpair,axiom,
% 4.69/4.92 ! [A2: produc3658429121746597890et_nat > $o,C: produc3658429121746597890et_nat,R2: set_Pr8536935166611901872et_nat,S2: set_Pr3721596426557623617et_nat] :
% 4.69/4.92 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ C ) @ ( relcom430014394250001422et_nat @ R2 @ S2 ) )
% 4.69/4.92 => ~ ! [B2: produc3925858234332021118et_nat] :
% 4.69/4.92 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ B2 ) @ R2 )
% 4.69/4.92 => ~ ( member6613709072892554et_nat @ ( produc5530789758353788441et_nat @ B2 @ C ) @ S2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % relcompEpair
% 4.69/4.92 thf(fact_1682_relcompEpair,axiom,
% 4.69/4.92 ! [A2: produc3658429121746597890et_nat > $o,C: produc3925858234332021118et_nat,R2: set_Pr2161125870931222855_nat_o,S2: set_Pr8536935166611901872et_nat] :
% 4.69/4.92 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ C ) @ ( relcom2608444778321954367et_nat @ R2 @ S2 ) )
% 4.69/4.92 => ~ ! [B2: produc3658429121746597890et_nat > $o] :
% 4.69/4.92 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ B2 ) @ R2 )
% 4.69/4.92 => ~ ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ B2 @ C ) @ S2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % relcompEpair
% 4.69/4.92 thf(fact_1683_relcompEpair,axiom,
% 4.69/4.92 ! [A2: produc3658429121746597890et_nat > $o,C: produc3925858234332021118et_nat,R2: set_Pr3286484037609594932et_nat,S2: set_Pr8807100098903490369et_nat] :
% 4.69/4.92 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ C ) @ ( relcom8031709186682293262et_nat @ R2 @ S2 ) )
% 4.69/4.92 => ~ ! [B2: produc3658429121746597890et_nat] :
% 4.69/4.92 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ B2 ) @ R2 )
% 4.69/4.92 => ~ ( member2737525317995836554et_nat @ ( produc3909112513931304473et_nat @ B2 @ C ) @ S2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % relcompEpair
% 4.69/4.92 thf(fact_1684_relcompEpair,axiom,
% 4.69/4.92 ! [A2: produc3658429121746597890et_nat > $o,C: produc3925858234332021118et_nat,R2: set_Pr8536935166611901872et_nat,S2: set_Pr7928877670098842301et_nat] :
% 4.69/4.92 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ C ) @ ( relcom8303140135939483018et_nat @ R2 @ S2 ) )
% 4.69/4.92 => ~ ! [B2: produc3925858234332021118et_nat] :
% 4.69/4.92 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ B2 ) @ R2 )
% 4.69/4.92 => ~ ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ B2 @ C ) @ S2 ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % relcompEpair
% 4.69/4.92 thf(fact_1685_relcompE,axiom,
% 4.69/4.92 ! [Xz: produc3658429121746597890et_nat,R2: set_Pr1776176089890104647t_unit,S2: set_Pr3948176798113811640et_nat] :
% 4.69/4.92 ( ( member6260224972018164377et_nat @ Xz @ ( relcom4930750947919833671et_nat @ R2 @ S2 ) )
% 4.69/4.92 => ~ ! [X3: heap_e7401611519738050253t_unit,Y2: heap_e7401611519738050253t_unit,Z3: set_nat] :
% 4.69/4.92 ( ( Xz
% 4.69/4.92 = ( produc7507926704131184380et_nat @ X3 @ Z3 ) )
% 4.69/4.92 => ( ( member5046970461208427408t_unit @ ( produc8256076736985659095t_unit @ X3 @ Y2 ) @ R2 )
% 4.69/4.92 => ~ ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ Y2 @ Z3 ) @ S2 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % relcompE
% 4.69/4.92 thf(fact_1686_relcompE,axiom,
% 4.69/4.92 ! [Xz: produc3658429121746597890et_nat,R2: set_Pr3948176798113811640et_nat,S2: set_Pr5488025237498180813et_nat] :
% 4.69/4.92 ( ( member6260224972018164377et_nat @ Xz @ ( relcom8881708762719574682et_nat @ R2 @ S2 ) )
% 4.69/4.92 => ~ ! [X3: heap_e7401611519738050253t_unit,Y2: set_nat,Z3: set_nat] :
% 4.69/4.92 ( ( Xz
% 4.69/4.92 = ( produc7507926704131184380et_nat @ X3 @ Z3 ) )
% 4.69/4.92 => ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X3 @ Y2 ) @ R2 )
% 4.69/4.92 => ~ ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ Y2 @ Z3 ) @ S2 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % relcompE
% 4.69/4.92 thf(fact_1687_relcompE,axiom,
% 4.69/4.92 ! [Xz: product_prod_nat_nat,R2: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 4.69/4.92 ( ( member8440522571783428010at_nat @ Xz @ ( relcomp_nat_nat_nat @ R2 @ S2 ) )
% 4.69/4.92 => ~ ! [X3: nat,Y2: nat,Z3: nat] :
% 4.69/4.92 ( ( Xz
% 4.69/4.92 = ( product_Pair_nat_nat @ X3 @ Z3 ) )
% 4.69/4.92 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ R2 )
% 4.69/4.92 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ Z3 ) @ S2 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % relcompE
% 4.69/4.92 thf(fact_1688_relcompE,axiom,
% 4.69/4.92 ! [Xz: product_prod_int_int,R2: set_Pr958786334691620121nt_int,S2: set_Pr958786334691620121nt_int] :
% 4.69/4.92 ( ( member5262025264175285858nt_int @ Xz @ ( relcomp_int_int_int @ R2 @ S2 ) )
% 4.69/4.92 => ~ ! [X3: int,Y2: int,Z3: int] :
% 4.69/4.92 ( ( Xz
% 4.69/4.92 = ( product_Pair_int_int @ X3 @ Z3 ) )
% 4.69/4.92 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y2 ) @ R2 )
% 4.69/4.92 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y2 @ Z3 ) @ S2 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % relcompE
% 4.69/4.92 thf(fact_1689_relcompE,axiom,
% 4.69/4.92 ! [Xz: produc3925858234332021118et_nat,R2: set_Pr2161125870931222855_nat_o,S2: set_Pr3286484037609594932et_nat] :
% 4.69/4.92 ( ( member1996754912294343701et_nat @ Xz @ ( relcom6619595054755144899et_nat @ R2 @ S2 ) )
% 4.69/4.92 => ~ ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat > $o,Z3: produc3658429121746597890et_nat] :
% 4.69/4.92 ( ( Xz
% 4.69/4.92 = ( produc5001842942810119800et_nat @ X3 @ Z3 ) )
% 4.69/4.92 => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X3 @ Y2 ) @ R2 )
% 4.69/4.92 => ~ ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ Y2 @ Z3 ) @ S2 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % relcompE
% 4.69/4.92 thf(fact_1690_relcompE,axiom,
% 4.69/4.92 ! [Xz: produc3925858234332021118et_nat,R2: set_Pr3286484037609594932et_nat,S2: set_Pr719794911490849221et_nat] :
% 4.69/4.92 ( ( member1996754912294343701et_nat @ Xz @ ( relcom5975814107203797650et_nat @ R2 @ S2 ) )
% 4.69/4.92 => ~ ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat,Z3: produc3658429121746597890et_nat] :
% 4.69/4.92 ( ( Xz
% 4.69/4.92 = ( produc5001842942810119800et_nat @ X3 @ Z3 ) )
% 4.69/4.92 => ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y2 ) @ R2 )
% 4.69/4.92 => ~ ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ Y2 @ Z3 ) @ S2 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % relcompE
% 4.69/4.92 thf(fact_1691_relcompE,axiom,
% 4.69/4.92 ! [Xz: produc3925858234332021118et_nat,R2: set_Pr8536935166611901872et_nat,S2: set_Pr3721596426557623617et_nat] :
% 4.69/4.92 ( ( member1996754912294343701et_nat @ Xz @ ( relcom430014394250001422et_nat @ R2 @ S2 ) )
% 4.69/4.92 => ~ ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3925858234332021118et_nat,Z3: produc3658429121746597890et_nat] :
% 4.69/4.92 ( ( Xz
% 4.69/4.92 = ( produc5001842942810119800et_nat @ X3 @ Z3 ) )
% 4.69/4.92 => ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y2 ) @ R2 )
% 4.69/4.92 => ~ ( member6613709072892554et_nat @ ( produc5530789758353788441et_nat @ Y2 @ Z3 ) @ S2 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % relcompE
% 4.69/4.92 thf(fact_1692_relcompE,axiom,
% 4.69/4.92 ! [Xz: produc2732055786443039994et_nat,R2: set_Pr2161125870931222855_nat_o,S2: set_Pr8536935166611901872et_nat] :
% 4.69/4.92 ( ( member6124377750444531601et_nat @ Xz @ ( relcom2608444778321954367et_nat @ R2 @ S2 ) )
% 4.69/4.92 => ~ ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat > $o,Z3: produc3925858234332021118et_nat] :
% 4.69/4.92 ( ( Xz
% 4.69/4.92 = ( produc2245416461498447860et_nat @ X3 @ Z3 ) )
% 4.69/4.92 => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X3 @ Y2 ) @ R2 )
% 4.69/4.92 => ~ ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ Y2 @ Z3 ) @ S2 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % relcompE
% 4.69/4.92 thf(fact_1693_relcompE,axiom,
% 4.69/4.92 ! [Xz: produc2732055786443039994et_nat,R2: set_Pr3286484037609594932et_nat,S2: set_Pr8807100098903490369et_nat] :
% 4.69/4.92 ( ( member6124377750444531601et_nat @ Xz @ ( relcom8031709186682293262et_nat @ R2 @ S2 ) )
% 4.69/4.92 => ~ ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat,Z3: produc3925858234332021118et_nat] :
% 4.69/4.92 ( ( Xz
% 4.69/4.92 = ( produc2245416461498447860et_nat @ X3 @ Z3 ) )
% 4.69/4.92 => ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y2 ) @ R2 )
% 4.69/4.92 => ~ ( member2737525317995836554et_nat @ ( produc3909112513931304473et_nat @ Y2 @ Z3 ) @ S2 ) ) ) ) ).
% 4.69/4.92
% 4.69/4.92 % relcompE
% 4.69/4.93 thf(fact_1694_relcompE,axiom,
% 4.69/4.93 ! [Xz: produc2732055786443039994et_nat,R2: set_Pr8536935166611901872et_nat,S2: set_Pr7928877670098842301et_nat] :
% 4.69/4.93 ( ( member6124377750444531601et_nat @ Xz @ ( relcom8303140135939483018et_nat @ R2 @ S2 ) )
% 4.69/4.93 => ~ ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3925858234332021118et_nat,Z3: produc3925858234332021118et_nat] :
% 4.69/4.93 ( ( Xz
% 4.69/4.93 = ( produc2245416461498447860et_nat @ X3 @ Z3 ) )
% 4.69/4.93 => ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y2 ) @ R2 )
% 4.69/4.93 => ~ ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ Y2 @ Z3 ) @ S2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcompE
% 4.69/4.93 thf(fact_1695_relcomp_OrelcompI,axiom,
% 4.69/4.93 ! [A2: heap_e7401611519738050253t_unit,B: heap_e7401611519738050253t_unit,R2: set_Pr1776176089890104647t_unit,C: set_nat,S2: set_Pr3948176798113811640et_nat] :
% 4.69/4.93 ( ( member5046970461208427408t_unit @ ( produc8256076736985659095t_unit @ A2 @ B ) @ R2 )
% 4.69/4.93 => ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ B @ C ) @ S2 )
% 4.69/4.93 => ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ C ) @ ( relcom4930750947919833671et_nat @ R2 @ S2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.relcompI
% 4.69/4.93 thf(fact_1696_relcomp_OrelcompI,axiom,
% 4.69/4.93 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o,R2: set_Pr2161125870931222855_nat_o,C: produc3658429121746597890et_nat,S2: set_Pr3286484037609594932et_nat] :
% 4.69/4.93 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ B ) @ R2 )
% 4.69/4.93 => ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ B @ C ) @ S2 )
% 4.69/4.93 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ C ) @ ( relcom6619595054755144899et_nat @ R2 @ S2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.relcompI
% 4.69/4.93 thf(fact_1697_relcomp_OrelcompI,axiom,
% 4.69/4.93 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o,R2: set_Pr2161125870931222855_nat_o,C: produc3925858234332021118et_nat,S2: set_Pr8536935166611901872et_nat] :
% 4.69/4.93 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ B ) @ R2 )
% 4.69/4.93 => ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ B @ C ) @ S2 )
% 4.69/4.93 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ C ) @ ( relcom2608444778321954367et_nat @ R2 @ S2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.relcompI
% 4.69/4.93 thf(fact_1698_relcomp_OrelcompI,axiom,
% 4.69/4.93 ! [A2: heap_e7401611519738050253t_unit,B: set_nat,R2: set_Pr3948176798113811640et_nat,C: set_nat,S2: set_Pr5488025237498180813et_nat] :
% 4.69/4.93 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ B ) @ R2 )
% 4.69/4.93 => ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ B @ C ) @ S2 )
% 4.69/4.93 => ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ C ) @ ( relcom8881708762719574682et_nat @ R2 @ S2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.relcompI
% 4.69/4.93 thf(fact_1699_relcomp_OrelcompI,axiom,
% 4.69/4.93 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat,C: nat,S2: set_Pr1261947904930325089at_nat] :
% 4.69/4.93 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 )
% 4.69/4.93 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C ) @ S2 )
% 4.69/4.93 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ C ) @ ( relcomp_nat_nat_nat @ R2 @ S2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.relcompI
% 4.69/4.93 thf(fact_1700_relcomp_OrelcompI,axiom,
% 4.69/4.93 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int,C: int,S2: set_Pr958786334691620121nt_int] :
% 4.69/4.93 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 )
% 4.69/4.93 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C ) @ S2 )
% 4.69/4.93 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ C ) @ ( relcomp_int_int_int @ R2 @ S2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.relcompI
% 4.69/4.93 thf(fact_1701_relcomp_OrelcompI,axiom,
% 4.69/4.93 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,R2: set_Pr3286484037609594932et_nat,C: produc3658429121746597890et_nat,S2: set_Pr719794911490849221et_nat] :
% 4.69/4.93 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ B ) @ R2 )
% 4.69/4.93 => ( ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ B @ C ) @ S2 )
% 4.69/4.93 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ C ) @ ( relcom5975814107203797650et_nat @ R2 @ S2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.relcompI
% 4.69/4.93 thf(fact_1702_relcomp_OrelcompI,axiom,
% 4.69/4.93 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,R2: set_Pr3286484037609594932et_nat,C: produc3925858234332021118et_nat,S2: set_Pr8807100098903490369et_nat] :
% 4.69/4.93 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ B ) @ R2 )
% 4.69/4.93 => ( ( member2737525317995836554et_nat @ ( produc3909112513931304473et_nat @ B @ C ) @ S2 )
% 4.69/4.93 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ C ) @ ( relcom8031709186682293262et_nat @ R2 @ S2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.relcompI
% 4.69/4.93 thf(fact_1703_relcomp_OrelcompI,axiom,
% 4.69/4.93 ! [A2: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,R2: set_Pr8536935166611901872et_nat,C: produc3658429121746597890et_nat,S2: set_Pr3721596426557623617et_nat] :
% 4.69/4.93 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ B ) @ R2 )
% 4.69/4.93 => ( ( member6613709072892554et_nat @ ( produc5530789758353788441et_nat @ B @ C ) @ S2 )
% 4.69/4.93 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ C ) @ ( relcom430014394250001422et_nat @ R2 @ S2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.relcompI
% 4.69/4.93 thf(fact_1704_relcomp_OrelcompI,axiom,
% 4.69/4.93 ! [A2: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,R2: set_Pr8536935166611901872et_nat,C: produc3925858234332021118et_nat,S2: set_Pr7928877670098842301et_nat] :
% 4.69/4.93 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ B ) @ R2 )
% 4.69/4.93 => ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ B @ C ) @ S2 )
% 4.69/4.93 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ C ) @ ( relcom8303140135939483018et_nat @ R2 @ S2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.relcompI
% 4.69/4.93 thf(fact_1705_relcomp_Osimps,axiom,
% 4.69/4.93 ! [A1: heap_e7401611519738050253t_unit,A22: set_nat,R2: set_Pr1776176089890104647t_unit,S2: set_Pr3948176798113811640et_nat] :
% 4.69/4.93 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A1 @ A22 ) @ ( relcom4930750947919833671et_nat @ R2 @ S2 ) )
% 4.69/4.93 = ( ? [A6: heap_e7401611519738050253t_unit,B6: heap_e7401611519738050253t_unit,C4: set_nat] :
% 4.69/4.93 ( ( A1 = A6 )
% 4.69/4.93 & ( A22 = C4 )
% 4.69/4.93 & ( member5046970461208427408t_unit @ ( produc8256076736985659095t_unit @ A6 @ B6 ) @ R2 )
% 4.69/4.93 & ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ B6 @ C4 ) @ S2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.simps
% 4.69/4.93 thf(fact_1706_relcomp_Osimps,axiom,
% 4.69/4.93 ! [A1: heap_e7401611519738050253t_unit,A22: set_nat,R2: set_Pr3948176798113811640et_nat,S2: set_Pr5488025237498180813et_nat] :
% 4.69/4.93 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A1 @ A22 ) @ ( relcom8881708762719574682et_nat @ R2 @ S2 ) )
% 4.69/4.93 = ( ? [A6: heap_e7401611519738050253t_unit,B6: set_nat,C4: set_nat] :
% 4.69/4.93 ( ( A1 = A6 )
% 4.69/4.93 & ( A22 = C4 )
% 4.69/4.93 & ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A6 @ B6 ) @ R2 )
% 4.69/4.93 & ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ B6 @ C4 ) @ S2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.simps
% 4.69/4.93 thf(fact_1707_relcomp_Osimps,axiom,
% 4.69/4.93 ! [A1: nat,A22: nat,R2: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 4.69/4.93 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A1 @ A22 ) @ ( relcomp_nat_nat_nat @ R2 @ S2 ) )
% 4.69/4.93 = ( ? [A6: nat,B6: nat,C4: nat] :
% 4.69/4.93 ( ( A1 = A6 )
% 4.69/4.93 & ( A22 = C4 )
% 4.69/4.93 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A6 @ B6 ) @ R2 )
% 4.69/4.93 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B6 @ C4 ) @ S2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.simps
% 4.69/4.93 thf(fact_1708_relcomp_Osimps,axiom,
% 4.69/4.93 ! [A1: int,A22: int,R2: set_Pr958786334691620121nt_int,S2: set_Pr958786334691620121nt_int] :
% 4.69/4.93 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A1 @ A22 ) @ ( relcomp_int_int_int @ R2 @ S2 ) )
% 4.69/4.93 = ( ? [A6: int,B6: int,C4: int] :
% 4.69/4.93 ( ( A1 = A6 )
% 4.69/4.93 & ( A22 = C4 )
% 4.69/4.93 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A6 @ B6 ) @ R2 )
% 4.69/4.93 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B6 @ C4 ) @ S2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.simps
% 4.69/4.93 thf(fact_1709_relcomp_Osimps,axiom,
% 4.69/4.93 ! [A1: produc3658429121746597890et_nat > $o,A22: produc3658429121746597890et_nat,R2: set_Pr2161125870931222855_nat_o,S2: set_Pr3286484037609594932et_nat] :
% 4.69/4.93 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A1 @ A22 ) @ ( relcom6619595054755144899et_nat @ R2 @ S2 ) )
% 4.69/4.93 = ( ? [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat > $o,C4: produc3658429121746597890et_nat] :
% 4.69/4.93 ( ( A1 = A6 )
% 4.69/4.93 & ( A22 = C4 )
% 4.69/4.93 & ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A6 @ B6 ) @ R2 )
% 4.69/4.93 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ B6 @ C4 ) @ S2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.simps
% 4.69/4.93 thf(fact_1710_relcomp_Osimps,axiom,
% 4.69/4.93 ! [A1: produc3658429121746597890et_nat > $o,A22: produc3658429121746597890et_nat,R2: set_Pr3286484037609594932et_nat,S2: set_Pr719794911490849221et_nat] :
% 4.69/4.93 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A1 @ A22 ) @ ( relcom5975814107203797650et_nat @ R2 @ S2 ) )
% 4.69/4.93 = ( ? [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat,C4: produc3658429121746597890et_nat] :
% 4.69/4.93 ( ( A1 = A6 )
% 4.69/4.93 & ( A22 = C4 )
% 4.69/4.93 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A6 @ B6 ) @ R2 )
% 4.69/4.93 & ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ B6 @ C4 ) @ S2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.simps
% 4.69/4.93 thf(fact_1711_relcomp_Osimps,axiom,
% 4.69/4.93 ! [A1: produc3658429121746597890et_nat > $o,A22: produc3658429121746597890et_nat,R2: set_Pr8536935166611901872et_nat,S2: set_Pr3721596426557623617et_nat] :
% 4.69/4.93 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A1 @ A22 ) @ ( relcom430014394250001422et_nat @ R2 @ S2 ) )
% 4.69/4.93 = ( ? [A6: produc3658429121746597890et_nat > $o,B6: produc3925858234332021118et_nat,C4: produc3658429121746597890et_nat] :
% 4.69/4.93 ( ( A1 = A6 )
% 4.69/4.93 & ( A22 = C4 )
% 4.69/4.93 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A6 @ B6 ) @ R2 )
% 4.69/4.93 & ( member6613709072892554et_nat @ ( produc5530789758353788441et_nat @ B6 @ C4 ) @ S2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.simps
% 4.69/4.93 thf(fact_1712_relcomp_Osimps,axiom,
% 4.69/4.93 ! [A1: produc3658429121746597890et_nat > $o,A22: produc3925858234332021118et_nat,R2: set_Pr2161125870931222855_nat_o,S2: set_Pr8536935166611901872et_nat] :
% 4.69/4.93 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A1 @ A22 ) @ ( relcom2608444778321954367et_nat @ R2 @ S2 ) )
% 4.69/4.93 = ( ? [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat > $o,C4: produc3925858234332021118et_nat] :
% 4.69/4.93 ( ( A1 = A6 )
% 4.69/4.93 & ( A22 = C4 )
% 4.69/4.93 & ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A6 @ B6 ) @ R2 )
% 4.69/4.93 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ B6 @ C4 ) @ S2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.simps
% 4.69/4.93 thf(fact_1713_relcomp_Osimps,axiom,
% 4.69/4.93 ! [A1: produc3658429121746597890et_nat > $o,A22: produc3925858234332021118et_nat,R2: set_Pr3286484037609594932et_nat,S2: set_Pr8807100098903490369et_nat] :
% 4.69/4.93 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A1 @ A22 ) @ ( relcom8031709186682293262et_nat @ R2 @ S2 ) )
% 4.69/4.93 = ( ? [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat,C4: produc3925858234332021118et_nat] :
% 4.69/4.93 ( ( A1 = A6 )
% 4.69/4.93 & ( A22 = C4 )
% 4.69/4.93 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A6 @ B6 ) @ R2 )
% 4.69/4.93 & ( member2737525317995836554et_nat @ ( produc3909112513931304473et_nat @ B6 @ C4 ) @ S2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.simps
% 4.69/4.93 thf(fact_1714_relcomp_Osimps,axiom,
% 4.69/4.93 ! [A1: produc3658429121746597890et_nat > $o,A22: produc3925858234332021118et_nat,R2: set_Pr8536935166611901872et_nat,S2: set_Pr7928877670098842301et_nat] :
% 4.69/4.93 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A1 @ A22 ) @ ( relcom8303140135939483018et_nat @ R2 @ S2 ) )
% 4.69/4.93 = ( ? [A6: produc3658429121746597890et_nat > $o,B6: produc3925858234332021118et_nat,C4: produc3925858234332021118et_nat] :
% 4.69/4.93 ( ( A1 = A6 )
% 4.69/4.93 & ( A22 = C4 )
% 4.69/4.93 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A6 @ B6 ) @ R2 )
% 4.69/4.93 & ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ B6 @ C4 ) @ S2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.simps
% 4.69/4.93 thf(fact_1715_relcomp_Ocases,axiom,
% 4.69/4.93 ! [A1: heap_e7401611519738050253t_unit,A22: set_nat,R2: set_Pr1776176089890104647t_unit,S2: set_Pr3948176798113811640et_nat] :
% 4.69/4.93 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A1 @ A22 ) @ ( relcom4930750947919833671et_nat @ R2 @ S2 ) )
% 4.69/4.93 => ~ ! [B2: heap_e7401611519738050253t_unit] :
% 4.69/4.93 ( ( member5046970461208427408t_unit @ ( produc8256076736985659095t_unit @ A1 @ B2 ) @ R2 )
% 4.69/4.93 => ~ ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ B2 @ A22 ) @ S2 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.cases
% 4.69/4.93 thf(fact_1716_relcomp_Ocases,axiom,
% 4.69/4.93 ! [A1: heap_e7401611519738050253t_unit,A22: set_nat,R2: set_Pr3948176798113811640et_nat,S2: set_Pr5488025237498180813et_nat] :
% 4.69/4.93 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A1 @ A22 ) @ ( relcom8881708762719574682et_nat @ R2 @ S2 ) )
% 4.69/4.93 => ~ ! [B2: set_nat] :
% 4.69/4.93 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A1 @ B2 ) @ R2 )
% 4.69/4.93 => ~ ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ B2 @ A22 ) @ S2 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.cases
% 4.69/4.93 thf(fact_1717_relcomp_Ocases,axiom,
% 4.69/4.93 ! [A1: nat,A22: nat,R2: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 4.69/4.93 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A1 @ A22 ) @ ( relcomp_nat_nat_nat @ R2 @ S2 ) )
% 4.69/4.93 => ~ ! [B2: nat] :
% 4.69/4.93 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A1 @ B2 ) @ R2 )
% 4.69/4.93 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B2 @ A22 ) @ S2 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.cases
% 4.69/4.93 thf(fact_1718_relcomp_Ocases,axiom,
% 4.69/4.93 ! [A1: int,A22: int,R2: set_Pr958786334691620121nt_int,S2: set_Pr958786334691620121nt_int] :
% 4.69/4.93 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A1 @ A22 ) @ ( relcomp_int_int_int @ R2 @ S2 ) )
% 4.69/4.93 => ~ ! [B2: int] :
% 4.69/4.93 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A1 @ B2 ) @ R2 )
% 4.69/4.93 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B2 @ A22 ) @ S2 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.cases
% 4.69/4.93 thf(fact_1719_relcomp_Ocases,axiom,
% 4.69/4.93 ! [A1: produc3658429121746597890et_nat > $o,A22: produc3658429121746597890et_nat,R2: set_Pr2161125870931222855_nat_o,S2: set_Pr3286484037609594932et_nat] :
% 4.69/4.93 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A1 @ A22 ) @ ( relcom6619595054755144899et_nat @ R2 @ S2 ) )
% 4.69/4.93 => ~ ! [B2: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A1 @ B2 ) @ R2 )
% 4.69/4.93 => ~ ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ B2 @ A22 ) @ S2 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.cases
% 4.69/4.93 thf(fact_1720_relcomp_Ocases,axiom,
% 4.69/4.93 ! [A1: produc3658429121746597890et_nat > $o,A22: produc3658429121746597890et_nat,R2: set_Pr3286484037609594932et_nat,S2: set_Pr719794911490849221et_nat] :
% 4.69/4.93 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A1 @ A22 ) @ ( relcom5975814107203797650et_nat @ R2 @ S2 ) )
% 4.69/4.93 => ~ ! [B2: produc3658429121746597890et_nat] :
% 4.69/4.93 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A1 @ B2 ) @ R2 )
% 4.69/4.93 => ~ ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ B2 @ A22 ) @ S2 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.cases
% 4.69/4.93 thf(fact_1721_relcomp_Ocases,axiom,
% 4.69/4.93 ! [A1: produc3658429121746597890et_nat > $o,A22: produc3658429121746597890et_nat,R2: set_Pr8536935166611901872et_nat,S2: set_Pr3721596426557623617et_nat] :
% 4.69/4.93 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A1 @ A22 ) @ ( relcom430014394250001422et_nat @ R2 @ S2 ) )
% 4.69/4.93 => ~ ! [B2: produc3925858234332021118et_nat] :
% 4.69/4.93 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A1 @ B2 ) @ R2 )
% 4.69/4.93 => ~ ( member6613709072892554et_nat @ ( produc5530789758353788441et_nat @ B2 @ A22 ) @ S2 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.cases
% 4.69/4.93 thf(fact_1722_relcomp_Ocases,axiom,
% 4.69/4.93 ! [A1: produc3658429121746597890et_nat > $o,A22: produc3925858234332021118et_nat,R2: set_Pr2161125870931222855_nat_o,S2: set_Pr8536935166611901872et_nat] :
% 4.69/4.93 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A1 @ A22 ) @ ( relcom2608444778321954367et_nat @ R2 @ S2 ) )
% 4.69/4.93 => ~ ! [B2: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A1 @ B2 ) @ R2 )
% 4.69/4.93 => ~ ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ B2 @ A22 ) @ S2 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.cases
% 4.69/4.93 thf(fact_1723_relcomp_Ocases,axiom,
% 4.69/4.93 ! [A1: produc3658429121746597890et_nat > $o,A22: produc3925858234332021118et_nat,R2: set_Pr3286484037609594932et_nat,S2: set_Pr8807100098903490369et_nat] :
% 4.69/4.93 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A1 @ A22 ) @ ( relcom8031709186682293262et_nat @ R2 @ S2 ) )
% 4.69/4.93 => ~ ! [B2: produc3658429121746597890et_nat] :
% 4.69/4.93 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A1 @ B2 ) @ R2 )
% 4.69/4.93 => ~ ( member2737525317995836554et_nat @ ( produc3909112513931304473et_nat @ B2 @ A22 ) @ S2 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.cases
% 4.69/4.93 thf(fact_1724_relcomp_Ocases,axiom,
% 4.69/4.93 ! [A1: produc3658429121746597890et_nat > $o,A22: produc3925858234332021118et_nat,R2: set_Pr8536935166611901872et_nat,S2: set_Pr7928877670098842301et_nat] :
% 4.69/4.93 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A1 @ A22 ) @ ( relcom8303140135939483018et_nat @ R2 @ S2 ) )
% 4.69/4.93 => ~ ! [B2: produc3925858234332021118et_nat] :
% 4.69/4.93 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A1 @ B2 ) @ R2 )
% 4.69/4.93 => ~ ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ B2 @ A22 ) @ S2 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % relcomp.cases
% 4.69/4.93 thf(fact_1725_FieldI2,axiom,
% 4.69/4.93 ! [I2: produc3658429121746597890et_nat > $o,J: produc3658429121746597890et_nat > $o,R3: set_Pr2161125870931222855_nat_o] :
% 4.69/4.93 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ I2 @ J ) @ R3 )
% 4.69/4.93 => ( member6576561426505652726_nat_o @ J @ ( field_81821745747897882_nat_o @ R3 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % FieldI2
% 4.69/4.93 thf(fact_1726_FieldI2,axiom,
% 4.69/4.93 ! [I2: $o,J: $o,R3: set_Product_prod_o_o] :
% 4.69/4.93 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ I2 @ J ) @ R3 )
% 4.69/4.93 => ( member_o @ J @ ( field_o @ R3 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % FieldI2
% 4.69/4.93 thf(fact_1727_FieldI2,axiom,
% 4.69/4.93 ! [I2: product_unit,J: product_unit,R3: set_Pr5094982260447487303t_unit] :
% 4.69/4.93 ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ I2 @ J ) @ R3 )
% 4.69/4.93 => ( member_Product_unit @ J @ ( field_Product_unit @ R3 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % FieldI2
% 4.69/4.93 thf(fact_1728_FieldI2,axiom,
% 4.69/4.93 ! [I2: nat,J: nat,R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.93 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I2 @ J ) @ R3 )
% 4.69/4.93 => ( member_nat @ J @ ( field_nat @ R3 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % FieldI2
% 4.69/4.93 thf(fact_1729_FieldI2,axiom,
% 4.69/4.93 ! [I2: int,J: int,R3: set_Pr958786334691620121nt_int] :
% 4.69/4.93 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I2 @ J ) @ R3 )
% 4.69/4.93 => ( member_int @ J @ ( field_int @ R3 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % FieldI2
% 4.69/4.93 thf(fact_1730_FieldI1,axiom,
% 4.69/4.93 ! [I2: produc3658429121746597890et_nat > $o,J: produc3658429121746597890et_nat > $o,R3: set_Pr2161125870931222855_nat_o] :
% 4.69/4.93 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ I2 @ J ) @ R3 )
% 4.69/4.93 => ( member6576561426505652726_nat_o @ I2 @ ( field_81821745747897882_nat_o @ R3 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % FieldI1
% 4.69/4.93 thf(fact_1731_FieldI1,axiom,
% 4.69/4.93 ! [I2: $o,J: $o,R3: set_Product_prod_o_o] :
% 4.69/4.93 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ I2 @ J ) @ R3 )
% 4.69/4.93 => ( member_o @ I2 @ ( field_o @ R3 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % FieldI1
% 4.69/4.93 thf(fact_1732_FieldI1,axiom,
% 4.69/4.93 ! [I2: product_unit,J: product_unit,R3: set_Pr5094982260447487303t_unit] :
% 4.69/4.93 ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ I2 @ J ) @ R3 )
% 4.69/4.93 => ( member_Product_unit @ I2 @ ( field_Product_unit @ R3 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % FieldI1
% 4.69/4.93 thf(fact_1733_FieldI1,axiom,
% 4.69/4.93 ! [I2: nat,J: nat,R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.93 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I2 @ J ) @ R3 )
% 4.69/4.93 => ( member_nat @ I2 @ ( field_nat @ R3 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % FieldI1
% 4.69/4.93 thf(fact_1734_FieldI1,axiom,
% 4.69/4.93 ! [I2: int,J: int,R3: set_Pr958786334691620121nt_int] :
% 4.69/4.93 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I2 @ J ) @ R3 )
% 4.69/4.93 => ( member_int @ I2 @ ( field_int @ R3 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % FieldI1
% 4.69/4.93 thf(fact_1735_mono__Field,axiom,
% 4.69/4.93 ! [R2: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 4.69/4.93 ( ( ord_le3146513528884898305at_nat @ R2 @ S2 )
% 4.69/4.93 => ( ord_less_eq_set_nat @ ( field_nat @ R2 ) @ ( field_nat @ S2 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % mono_Field
% 4.69/4.93 thf(fact_1736_equiv__class__self,axiom,
% 4.69/4.93 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit,A2: product_unit] :
% 4.69/4.93 ( ( equiv_4189356295871601603t_unit @ A @ R2 )
% 4.69/4.93 => ( ( member_Product_unit @ A2 @ A )
% 4.69/4.93 => ( member_Product_unit @ A2 @ ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % equiv_class_self
% 4.69/4.93 thf(fact_1737_equiv__class__self,axiom,
% 4.69/4.93 ! [A: set_o,R2: set_Product_prod_o_o,A2: $o] :
% 4.69/4.93 ( ( equiv_equiv_o @ A @ R2 )
% 4.69/4.93 => ( ( member_o @ A2 @ A )
% 4.69/4.93 => ( member_o @ A2 @ ( image_o_o @ R2 @ ( insert_o @ A2 @ bot_bot_set_o ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % equiv_class_self
% 4.69/4.93 thf(fact_1738_equiv__class__self,axiom,
% 4.69/4.93 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,A2: nat] :
% 4.69/4.93 ( ( equiv_equiv_nat @ A @ R2 )
% 4.69/4.93 => ( ( member_nat @ A2 @ A )
% 4.69/4.93 => ( member_nat @ A2 @ ( image_nat_nat @ R2 @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % equiv_class_self
% 4.69/4.93 thf(fact_1739_equiv__class__self,axiom,
% 4.69/4.93 ! [A: set_int,R2: set_Pr958786334691620121nt_int,A2: int] :
% 4.69/4.93 ( ( equiv_equiv_int @ A @ R2 )
% 4.69/4.93 => ( ( member_int @ A2 @ A )
% 4.69/4.93 => ( member_int @ A2 @ ( image_int_int @ R2 @ ( insert_int @ A2 @ bot_bot_set_int ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % equiv_class_self
% 4.69/4.93 thf(fact_1740_equiv__class__self,axiom,
% 4.69/4.93 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( equiv_6726761681920839555_nat_o @ A @ R2 )
% 4.69/4.93 => ( ( member6576561426505652726_nat_o @ A2 @ A )
% 4.69/4.93 => ( member6576561426505652726_nat_o @ A2 @ ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % equiv_class_self
% 4.69/4.93 thf(fact_1741_Field__def,axiom,
% 4.69/4.93 ( field_nat
% 4.69/4.93 = ( ^ [R4: set_Pr1261947904930325089at_nat] : ( sup_sup_set_nat @ ( domain_nat_nat @ R4 ) @ ( range_nat_nat @ R4 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Field_def
% 4.69/4.93 thf(fact_1742_equiv__class__eq__iff,axiom,
% 4.69/4.93 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit,X: product_unit,Y: product_unit] :
% 4.69/4.93 ( ( equiv_4189356295871601603t_unit @ A @ R2 )
% 4.69/4.93 => ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X @ Y ) @ R2 )
% 4.69/4.93 = ( ( ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.93 = ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ Y @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.93 & ( member_Product_unit @ X @ A )
% 4.69/4.93 & ( member_Product_unit @ Y @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % equiv_class_eq_iff
% 4.69/4.93 thf(fact_1743_equiv__class__eq__iff,axiom,
% 4.69/4.93 ! [A: set_o,R2: set_Product_prod_o_o,X: $o,Y: $o] :
% 4.69/4.93 ( ( equiv_equiv_o @ A @ R2 )
% 4.69/4.93 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ R2 )
% 4.69/4.93 = ( ( ( image_o_o @ R2 @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.93 = ( image_o_o @ R2 @ ( insert_o @ Y @ bot_bot_set_o ) ) )
% 4.69/4.93 & ( member_o @ X @ A )
% 4.69/4.93 & ( member_o @ Y @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % equiv_class_eq_iff
% 4.69/4.93 thf(fact_1744_equiv__class__eq__iff,axiom,
% 4.69/4.93 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,X: nat,Y: nat] :
% 4.69/4.93 ( ( equiv_equiv_nat @ A @ R2 )
% 4.69/4.93 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R2 )
% 4.69/4.93 = ( ( ( image_nat_nat @ R2 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.93 = ( image_nat_nat @ R2 @ ( insert_nat @ Y @ bot_bot_set_nat ) ) )
% 4.69/4.93 & ( member_nat @ X @ A )
% 4.69/4.93 & ( member_nat @ Y @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % equiv_class_eq_iff
% 4.69/4.93 thf(fact_1745_equiv__class__eq__iff,axiom,
% 4.69/4.93 ! [A: set_int,R2: set_Pr958786334691620121nt_int,X: int,Y: int] :
% 4.69/4.93 ( ( equiv_equiv_int @ A @ R2 )
% 4.69/4.93 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R2 )
% 4.69/4.93 = ( ( ( image_int_int @ R2 @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.93 = ( image_int_int @ R2 @ ( insert_int @ Y @ bot_bot_set_int ) ) )
% 4.69/4.93 & ( member_int @ X @ A )
% 4.69/4.93 & ( member_int @ Y @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % equiv_class_eq_iff
% 4.69/4.93 thf(fact_1746_equiv__class__eq__iff,axiom,
% 4.69/4.93 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( equiv_6726761681920839555_nat_o @ A @ R2 )
% 4.69/4.93 => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ R2 )
% 4.69/4.93 = ( ( ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.93 = ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ Y @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/4.93 & ( member6576561426505652726_nat_o @ X @ A )
% 4.69/4.93 & ( member6576561426505652726_nat_o @ Y @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % equiv_class_eq_iff
% 4.69/4.93 thf(fact_1747_eq__equiv__class__iff,axiom,
% 4.69/4.93 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit,X: product_unit,Y: product_unit] :
% 4.69/4.93 ( ( equiv_4189356295871601603t_unit @ A @ R2 )
% 4.69/4.93 => ( ( member_Product_unit @ X @ A )
% 4.69/4.93 => ( ( member_Product_unit @ Y @ A )
% 4.69/4.93 => ( ( ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.93 = ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ Y @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.93 = ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X @ Y ) @ R2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % eq_equiv_class_iff
% 4.69/4.93 thf(fact_1748_eq__equiv__class__iff,axiom,
% 4.69/4.93 ! [A: set_o,R2: set_Product_prod_o_o,X: $o,Y: $o] :
% 4.69/4.93 ( ( equiv_equiv_o @ A @ R2 )
% 4.69/4.93 => ( ( member_o @ X @ A )
% 4.69/4.93 => ( ( member_o @ Y @ A )
% 4.69/4.93 => ( ( ( image_o_o @ R2 @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.93 = ( image_o_o @ R2 @ ( insert_o @ Y @ bot_bot_set_o ) ) )
% 4.69/4.93 = ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ R2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % eq_equiv_class_iff
% 4.69/4.93 thf(fact_1749_eq__equiv__class__iff,axiom,
% 4.69/4.93 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,X: nat,Y: nat] :
% 4.69/4.93 ( ( equiv_equiv_nat @ A @ R2 )
% 4.69/4.93 => ( ( member_nat @ X @ A )
% 4.69/4.93 => ( ( member_nat @ Y @ A )
% 4.69/4.93 => ( ( ( image_nat_nat @ R2 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.93 = ( image_nat_nat @ R2 @ ( insert_nat @ Y @ bot_bot_set_nat ) ) )
% 4.69/4.93 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % eq_equiv_class_iff
% 4.69/4.93 thf(fact_1750_eq__equiv__class__iff,axiom,
% 4.69/4.93 ! [A: set_int,R2: set_Pr958786334691620121nt_int,X: int,Y: int] :
% 4.69/4.93 ( ( equiv_equiv_int @ A @ R2 )
% 4.69/4.93 => ( ( member_int @ X @ A )
% 4.69/4.93 => ( ( member_int @ Y @ A )
% 4.69/4.93 => ( ( ( image_int_int @ R2 @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.93 = ( image_int_int @ R2 @ ( insert_int @ Y @ bot_bot_set_int ) ) )
% 4.69/4.93 = ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % eq_equiv_class_iff
% 4.69/4.93 thf(fact_1751_eq__equiv__class__iff,axiom,
% 4.69/4.93 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( equiv_6726761681920839555_nat_o @ A @ R2 )
% 4.69/4.93 => ( ( member6576561426505652726_nat_o @ X @ A )
% 4.69/4.93 => ( ( member6576561426505652726_nat_o @ Y @ A )
% 4.69/4.93 => ( ( ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.93 = ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ Y @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/4.93 = ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ R2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % eq_equiv_class_iff
% 4.69/4.93 thf(fact_1752_equiv__class__eq,axiom,
% 4.69/4.93 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit,A2: product_unit,B: product_unit] :
% 4.69/4.93 ( ( equiv_4189356295871601603t_unit @ A @ R2 )
% 4.69/4.93 => ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A2 @ B ) @ R2 )
% 4.69/4.93 => ( ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.93 = ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % equiv_class_eq
% 4.69/4.93 thf(fact_1753_equiv__class__eq,axiom,
% 4.69/4.93 ! [A: set_o,R2: set_Product_prod_o_o,A2: $o,B: $o] :
% 4.69/4.93 ( ( equiv_equiv_o @ A @ R2 )
% 4.69/4.93 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ B ) @ R2 )
% 4.69/4.93 => ( ( image_o_o @ R2 @ ( insert_o @ A2 @ bot_bot_set_o ) )
% 4.69/4.93 = ( image_o_o @ R2 @ ( insert_o @ B @ bot_bot_set_o ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % equiv_class_eq
% 4.69/4.93 thf(fact_1754_equiv__class__eq,axiom,
% 4.69/4.93 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,A2: nat,B: nat] :
% 4.69/4.93 ( ( equiv_equiv_nat @ A @ R2 )
% 4.69/4.93 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 )
% 4.69/4.93 => ( ( image_nat_nat @ R2 @ ( insert_nat @ A2 @ bot_bot_set_nat ) )
% 4.69/4.93 = ( image_nat_nat @ R2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % equiv_class_eq
% 4.69/4.93 thf(fact_1755_equiv__class__eq,axiom,
% 4.69/4.93 ! [A: set_int,R2: set_Pr958786334691620121nt_int,A2: int,B: int] :
% 4.69/4.93 ( ( equiv_equiv_int @ A @ R2 )
% 4.69/4.93 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 )
% 4.69/4.93 => ( ( image_int_int @ R2 @ ( insert_int @ A2 @ bot_bot_set_int ) )
% 4.69/4.93 = ( image_int_int @ R2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % equiv_class_eq
% 4.69/4.93 thf(fact_1756_equiv__class__eq,axiom,
% 4.69/4.93 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( equiv_6726761681920839555_nat_o @ A @ R2 )
% 4.69/4.93 => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ B ) @ R2 )
% 4.69/4.93 => ( ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.93 = ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % equiv_class_eq
% 4.69/4.93 thf(fact_1757_eq__equiv__class,axiom,
% 4.69/4.93 ! [R2: set_Pr5094982260447487303t_unit,A2: product_unit,B: product_unit,A: set_Product_unit] :
% 4.69/4.93 ( ( ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.93 = ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.93 => ( ( equiv_4189356295871601603t_unit @ A @ R2 )
% 4.69/4.93 => ( ( member_Product_unit @ B @ A )
% 4.69/4.93 => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % eq_equiv_class
% 4.69/4.93 thf(fact_1758_eq__equiv__class,axiom,
% 4.69/4.93 ! [R2: set_Product_prod_o_o,A2: $o,B: $o,A: set_o] :
% 4.69/4.93 ( ( ( image_o_o @ R2 @ ( insert_o @ A2 @ bot_bot_set_o ) )
% 4.69/4.93 = ( image_o_o @ R2 @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 4.69/4.93 => ( ( equiv_equiv_o @ A @ R2 )
% 4.69/4.93 => ( ( member_o @ B @ A )
% 4.69/4.93 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % eq_equiv_class
% 4.69/4.93 thf(fact_1759_eq__equiv__class,axiom,
% 4.69/4.93 ! [R2: set_Pr1261947904930325089at_nat,A2: nat,B: nat,A: set_nat] :
% 4.69/4.93 ( ( ( image_nat_nat @ R2 @ ( insert_nat @ A2 @ bot_bot_set_nat ) )
% 4.69/4.93 = ( image_nat_nat @ R2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 4.69/4.93 => ( ( equiv_equiv_nat @ A @ R2 )
% 4.69/4.93 => ( ( member_nat @ B @ A )
% 4.69/4.93 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % eq_equiv_class
% 4.69/4.93 thf(fact_1760_eq__equiv__class,axiom,
% 4.69/4.93 ! [R2: set_Pr958786334691620121nt_int,A2: int,B: int,A: set_int] :
% 4.69/4.93 ( ( ( image_int_int @ R2 @ ( insert_int @ A2 @ bot_bot_set_int ) )
% 4.69/4.93 = ( image_int_int @ R2 @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 4.69/4.93 => ( ( equiv_equiv_int @ A @ R2 )
% 4.69/4.93 => ( ( member_int @ B @ A )
% 4.69/4.93 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % eq_equiv_class
% 4.69/4.93 thf(fact_1761_eq__equiv__class,axiom,
% 4.69/4.93 ! [R2: set_Pr2161125870931222855_nat_o,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ( ( ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.93 = ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/4.93 => ( ( equiv_6726761681920839555_nat_o @ A @ R2 )
% 4.69/4.93 => ( ( member6576561426505652726_nat_o @ B @ A )
% 4.69/4.93 => ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % eq_equiv_class
% 4.69/4.93 thf(fact_1762_rtrancl__Image__in__Field,axiom,
% 4.69/4.93 ! [R3: set_Pr1261947904930325089at_nat,V2: set_nat] : ( ord_less_eq_set_nat @ ( image_nat_nat @ ( transi2905341329935302413cl_nat @ R3 ) @ V2 ) @ ( sup_sup_set_nat @ ( field_nat @ R3 ) @ V2 ) ) ).
% 4.69/4.93
% 4.69/4.93 % rtrancl_Image_in_Field
% 4.69/4.93 thf(fact_1763_refines__equiv__class__eq2,axiom,
% 4.69/4.93 ! [R3: set_Pr5094982260447487303t_unit,S: set_Pr5094982260447487303t_unit,A: set_Product_unit,A2: product_unit] :
% 4.69/4.93 ( ( ord_le930853871177014503t_unit @ R3 @ S )
% 4.69/4.93 => ( ( equiv_4189356295871601603t_unit @ A @ R3 )
% 4.69/4.93 => ( ( equiv_4189356295871601603t_unit @ A @ S )
% 4.69/4.93 => ( ( image_8431784415008483091t_unit @ S @ ( image_8431784415008483091t_unit @ R3 @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.93 = ( image_8431784415008483091t_unit @ S @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % refines_equiv_class_eq2
% 4.69/4.93 thf(fact_1764_refines__equiv__class__eq2,axiom,
% 4.69/4.93 ! [R3: set_Product_prod_o_o,S: set_Product_prod_o_o,A: set_o,A2: $o] :
% 4.69/4.93 ( ( ord_le192195778054999463od_o_o @ R3 @ S )
% 4.69/4.93 => ( ( equiv_equiv_o @ A @ R3 )
% 4.69/4.93 => ( ( equiv_equiv_o @ A @ S )
% 4.69/4.93 => ( ( image_o_o @ S @ ( image_o_o @ R3 @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 4.69/4.93 = ( image_o_o @ S @ ( insert_o @ A2 @ bot_bot_set_o ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % refines_equiv_class_eq2
% 4.69/4.93 thf(fact_1765_refines__equiv__class__eq2,axiom,
% 4.69/4.93 ! [R3: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat,A: set_nat,A2: nat] :
% 4.69/4.93 ( ( ord_le3146513528884898305at_nat @ R3 @ S )
% 4.69/4.93 => ( ( equiv_equiv_nat @ A @ R3 )
% 4.69/4.93 => ( ( equiv_equiv_nat @ A @ S )
% 4.69/4.93 => ( ( image_nat_nat @ S @ ( image_nat_nat @ R3 @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 4.69/4.93 = ( image_nat_nat @ S @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % refines_equiv_class_eq2
% 4.69/4.93 thf(fact_1766_refines__equiv__class__eq2,axiom,
% 4.69/4.93 ! [R3: set_Pr958786334691620121nt_int,S: set_Pr958786334691620121nt_int,A: set_int,A2: int] :
% 4.69/4.93 ( ( ord_le2843351958646193337nt_int @ R3 @ S )
% 4.69/4.93 => ( ( equiv_equiv_int @ A @ R3 )
% 4.69/4.93 => ( ( equiv_equiv_int @ A @ S )
% 4.69/4.93 => ( ( image_int_int @ S @ ( image_int_int @ R3 @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 4.69/4.93 = ( image_int_int @ S @ ( insert_int @ A2 @ bot_bot_set_int ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % refines_equiv_class_eq2
% 4.69/4.93 thf(fact_1767_refines__equiv__class__eq2,axiom,
% 4.69/4.93 ! [R3: set_Pr2161125870931222855_nat_o,S: set_Pr2161125870931222855_nat_o,A: set_Pr4532377907799695533_nat_o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( ord_le6659818918159358183_nat_o @ R3 @ S )
% 4.69/4.93 => ( ( equiv_6726761681920839555_nat_o @ A @ R3 )
% 4.69/4.93 => ( ( equiv_6726761681920839555_nat_o @ A @ S )
% 4.69/4.93 => ( ( image_2232984160439939859_nat_o @ S @ ( image_2232984160439939859_nat_o @ R3 @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/4.93 = ( image_2232984160439939859_nat_o @ S @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % refines_equiv_class_eq2
% 4.69/4.93 thf(fact_1768_refines__equiv__class__eq,axiom,
% 4.69/4.93 ! [R3: set_Pr5094982260447487303t_unit,S: set_Pr5094982260447487303t_unit,A: set_Product_unit,A2: product_unit] :
% 4.69/4.93 ( ( ord_le930853871177014503t_unit @ R3 @ S )
% 4.69/4.93 => ( ( equiv_4189356295871601603t_unit @ A @ R3 )
% 4.69/4.93 => ( ( equiv_4189356295871601603t_unit @ A @ S )
% 4.69/4.93 => ( ( image_8431784415008483091t_unit @ R3 @ ( image_8431784415008483091t_unit @ S @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.93 = ( image_8431784415008483091t_unit @ S @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % refines_equiv_class_eq
% 4.69/4.93 thf(fact_1769_refines__equiv__class__eq,axiom,
% 4.69/4.93 ! [R3: set_Product_prod_o_o,S: set_Product_prod_o_o,A: set_o,A2: $o] :
% 4.69/4.93 ( ( ord_le192195778054999463od_o_o @ R3 @ S )
% 4.69/4.93 => ( ( equiv_equiv_o @ A @ R3 )
% 4.69/4.93 => ( ( equiv_equiv_o @ A @ S )
% 4.69/4.93 => ( ( image_o_o @ R3 @ ( image_o_o @ S @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 4.69/4.93 = ( image_o_o @ S @ ( insert_o @ A2 @ bot_bot_set_o ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % refines_equiv_class_eq
% 4.69/4.93 thf(fact_1770_refines__equiv__class__eq,axiom,
% 4.69/4.93 ! [R3: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat,A: set_nat,A2: nat] :
% 4.69/4.93 ( ( ord_le3146513528884898305at_nat @ R3 @ S )
% 4.69/4.93 => ( ( equiv_equiv_nat @ A @ R3 )
% 4.69/4.93 => ( ( equiv_equiv_nat @ A @ S )
% 4.69/4.93 => ( ( image_nat_nat @ R3 @ ( image_nat_nat @ S @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 4.69/4.93 = ( image_nat_nat @ S @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % refines_equiv_class_eq
% 4.69/4.93 thf(fact_1771_refines__equiv__class__eq,axiom,
% 4.69/4.93 ! [R3: set_Pr958786334691620121nt_int,S: set_Pr958786334691620121nt_int,A: set_int,A2: int] :
% 4.69/4.93 ( ( ord_le2843351958646193337nt_int @ R3 @ S )
% 4.69/4.93 => ( ( equiv_equiv_int @ A @ R3 )
% 4.69/4.93 => ( ( equiv_equiv_int @ A @ S )
% 4.69/4.93 => ( ( image_int_int @ R3 @ ( image_int_int @ S @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 4.69/4.93 = ( image_int_int @ S @ ( insert_int @ A2 @ bot_bot_set_int ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % refines_equiv_class_eq
% 4.69/4.93 thf(fact_1772_refines__equiv__class__eq,axiom,
% 4.69/4.93 ! [R3: set_Pr2161125870931222855_nat_o,S: set_Pr2161125870931222855_nat_o,A: set_Pr4532377907799695533_nat_o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( ord_le6659818918159358183_nat_o @ R3 @ S )
% 4.69/4.93 => ( ( equiv_6726761681920839555_nat_o @ A @ R3 )
% 4.69/4.93 => ( ( equiv_6726761681920839555_nat_o @ A @ S )
% 4.69/4.93 => ( ( image_2232984160439939859_nat_o @ R3 @ ( image_2232984160439939859_nat_o @ S @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/4.93 = ( image_2232984160439939859_nat_o @ S @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % refines_equiv_class_eq
% 4.69/4.93 thf(fact_1773_Partial__order__eq__Image1__Image1__iff,axiom,
% 4.69/4.93 ! [R2: set_Pr5094982260447487303t_unit,A2: product_unit,B: product_unit] :
% 4.69/4.93 ( ( order_2505591618835473410t_unit @ ( field_Product_unit @ R2 ) @ R2 )
% 4.69/4.93 => ( ( member_Product_unit @ A2 @ ( field_Product_unit @ R2 ) )
% 4.69/4.93 => ( ( member_Product_unit @ B @ ( field_Product_unit @ R2 ) )
% 4.69/4.93 => ( ( ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.93 = ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.93 = ( A2 = B ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Partial_order_eq_Image1_Image1_iff
% 4.69/4.93 thf(fact_1774_Partial__order__eq__Image1__Image1__iff,axiom,
% 4.69/4.93 ! [R2: set_Product_prod_o_o,A2: $o,B: $o] :
% 4.69/4.93 ( ( order_8538205470752950541r_on_o @ ( field_o @ R2 ) @ R2 )
% 4.69/4.93 => ( ( member_o @ A2 @ ( field_o @ R2 ) )
% 4.69/4.93 => ( ( member_o @ B @ ( field_o @ R2 ) )
% 4.69/4.93 => ( ( ( image_o_o @ R2 @ ( insert_o @ A2 @ bot_bot_set_o ) )
% 4.69/4.93 = ( image_o_o @ R2 @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 4.69/4.93 = ( A2 = B ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Partial_order_eq_Image1_Image1_iff
% 4.69/4.93 thf(fact_1775_Partial__order__eq__Image1__Image1__iff,axiom,
% 4.69/4.93 ! [R2: set_Pr1261947904930325089at_nat,A2: nat,B: nat] :
% 4.69/4.93 ( ( order_5251275573222108571on_nat @ ( field_nat @ R2 ) @ R2 )
% 4.69/4.93 => ( ( member_nat @ A2 @ ( field_nat @ R2 ) )
% 4.69/4.93 => ( ( member_nat @ B @ ( field_nat @ R2 ) )
% 4.69/4.93 => ( ( ( image_nat_nat @ R2 @ ( insert_nat @ A2 @ bot_bot_set_nat ) )
% 4.69/4.93 = ( image_nat_nat @ R2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 4.69/4.93 = ( A2 = B ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Partial_order_eq_Image1_Image1_iff
% 4.69/4.93 thf(fact_1776_Partial__order__eq__Image1__Image1__iff,axiom,
% 4.69/4.93 ! [R2: set_Pr958786334691620121nt_int,A2: int,B: int] :
% 4.69/4.93 ( ( order_5248785102713058295on_int @ ( field_int @ R2 ) @ R2 )
% 4.69/4.93 => ( ( member_int @ A2 @ ( field_int @ R2 ) )
% 4.69/4.93 => ( ( member_int @ B @ ( field_int @ R2 ) )
% 4.69/4.93 => ( ( ( image_int_int @ R2 @ ( insert_int @ A2 @ bot_bot_set_int ) )
% 4.69/4.93 = ( image_int_int @ R2 @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 4.69/4.93 = ( A2 = B ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Partial_order_eq_Image1_Image1_iff
% 4.69/4.93 thf(fact_1777_Partial__order__eq__Image1__Image1__iff,axiom,
% 4.69/4.93 ! [R2: set_Pr2161125870931222855_nat_o,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( order_3690095022144090562_nat_o @ ( field_81821745747897882_nat_o @ R2 ) @ R2 )
% 4.69/4.93 => ( ( member6576561426505652726_nat_o @ A2 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.93 => ( ( member6576561426505652726_nat_o @ B @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.93 => ( ( ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.93 = ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/4.93 = ( A2 = B ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Partial_order_eq_Image1_Image1_iff
% 4.69/4.93 thf(fact_1778_finite__reachable__restrictedI,axiom,
% 4.69/4.93 ! [Q2: set_Code_integer,I: set_Code_integer,E: set_Pr4811707699266497531nteger] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ Q2 )
% 4.69/4.93 => ( ( ord_le7084787975880047091nteger @ I @ Q2 )
% 4.69/4.93 => ( ( ord_le7084787975880047091nteger @ ( range_1907724884897625393nteger @ E ) @ Q2 )
% 4.69/4.93 => ( finite6017078050557962740nteger @ ( image_4147621952751189391nteger @ ( transi3984306202085910426nteger @ E ) @ I ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_reachable_restrictedI
% 4.69/4.93 thf(fact_1779_finite__reachable__restrictedI,axiom,
% 4.69/4.93 ! [Q2: set_nat,I: set_nat,E: set_Pr1261947904930325089at_nat] :
% 4.69/4.93 ( ( finite_finite_nat @ Q2 )
% 4.69/4.93 => ( ( ord_less_eq_set_nat @ I @ Q2 )
% 4.69/4.93 => ( ( ord_less_eq_set_nat @ ( range_nat_nat @ E ) @ Q2 )
% 4.69/4.93 => ( finite_finite_nat @ ( image_nat_nat @ ( transi2905341329935302413cl_nat @ E ) @ I ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_reachable_restrictedI
% 4.69/4.93 thf(fact_1780_subset__Image__Image__iff,axiom,
% 4.69/4.93 ! [R2: set_Pr958786334691620121nt_int,A: set_int,B4: set_int] :
% 4.69/4.93 ( ( order_4859164337913492053on_int @ ( field_int @ R2 ) @ R2 )
% 4.69/4.93 => ( ( ord_less_eq_set_int @ A @ ( field_int @ R2 ) )
% 4.69/4.93 => ( ( ord_less_eq_set_int @ B4 @ ( field_int @ R2 ) )
% 4.69/4.93 => ( ( ord_less_eq_set_int @ ( image_int_int @ R2 @ A ) @ ( image_int_int @ R2 @ B4 ) )
% 4.69/4.93 = ( ! [X2: int] :
% 4.69/4.93 ( ( member_int @ X2 @ A )
% 4.69/4.93 => ? [Y3: int] :
% 4.69/4.93 ( ( member_int @ Y3 @ B4 )
% 4.69/4.93 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ X2 ) @ R2 ) ) ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % subset_Image_Image_iff
% 4.69/4.93 thf(fact_1781_subset__Image__Image__iff,axiom,
% 4.69/4.93 ! [R2: set_Pr1261947904930325089at_nat,A: set_nat,B4: set_nat] :
% 4.69/4.93 ( ( order_4861654808422542329on_nat @ ( field_nat @ R2 ) @ R2 )
% 4.69/4.93 => ( ( ord_less_eq_set_nat @ A @ ( field_nat @ R2 ) )
% 4.69/4.93 => ( ( ord_less_eq_set_nat @ B4 @ ( field_nat @ R2 ) )
% 4.69/4.93 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ R2 @ A ) @ ( image_nat_nat @ R2 @ B4 ) )
% 4.69/4.93 = ( ! [X2: nat] :
% 4.69/4.93 ( ( member_nat @ X2 @ A )
% 4.69/4.93 => ? [Y3: nat] :
% 4.69/4.93 ( ( member_nat @ Y3 @ B4 )
% 4.69/4.93 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ X2 ) @ R2 ) ) ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % subset_Image_Image_iff
% 4.69/4.93 thf(fact_1782_equiv__class__subset,axiom,
% 4.69/4.93 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit,A2: product_unit,B: product_unit] :
% 4.69/4.93 ( ( equiv_4189356295871601603t_unit @ A @ R2 )
% 4.69/4.93 => ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A2 @ B ) @ R2 )
% 4.69/4.93 => ( ord_le3507040750410214029t_unit @ ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) @ ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % equiv_class_subset
% 4.69/4.93 thf(fact_1783_equiv__class__subset,axiom,
% 4.69/4.93 ! [A: set_o,R2: set_Product_prod_o_o,A2: $o,B: $o] :
% 4.69/4.93 ( ( equiv_equiv_o @ A @ R2 )
% 4.69/4.93 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ B ) @ R2 )
% 4.69/4.93 => ( ord_less_eq_set_o @ ( image_o_o @ R2 @ ( insert_o @ A2 @ bot_bot_set_o ) ) @ ( image_o_o @ R2 @ ( insert_o @ B @ bot_bot_set_o ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % equiv_class_subset
% 4.69/4.93 thf(fact_1784_equiv__class__subset,axiom,
% 4.69/4.93 ! [A: set_int,R2: set_Pr958786334691620121nt_int,A2: int,B: int] :
% 4.69/4.93 ( ( equiv_equiv_int @ A @ R2 )
% 4.69/4.93 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 )
% 4.69/4.93 => ( ord_less_eq_set_int @ ( image_int_int @ R2 @ ( insert_int @ A2 @ bot_bot_set_int ) ) @ ( image_int_int @ R2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % equiv_class_subset
% 4.69/4.93 thf(fact_1785_equiv__class__subset,axiom,
% 4.69/4.93 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( equiv_6726761681920839555_nat_o @ A @ R2 )
% 4.69/4.93 => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ B ) @ R2 )
% 4.69/4.93 => ( ord_le2965882846123202637_nat_o @ ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) @ ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % equiv_class_subset
% 4.69/4.93 thf(fact_1786_equiv__class__subset,axiom,
% 4.69/4.93 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,A2: nat,B: nat] :
% 4.69/4.93 ( ( equiv_equiv_nat @ A @ R2 )
% 4.69/4.93 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 )
% 4.69/4.93 => ( ord_less_eq_set_nat @ ( image_nat_nat @ R2 @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) @ ( image_nat_nat @ R2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % equiv_class_subset
% 4.69/4.93 thf(fact_1787_subset__equiv__class,axiom,
% 4.69/4.93 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit,B: product_unit,A2: product_unit] :
% 4.69/4.93 ( ( equiv_4189356295871601603t_unit @ A @ R2 )
% 4.69/4.93 => ( ( ord_le3507040750410214029t_unit @ ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) @ ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.93 => ( ( member_Product_unit @ B @ A )
% 4.69/4.93 => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % subset_equiv_class
% 4.69/4.93 thf(fact_1788_subset__equiv__class,axiom,
% 4.69/4.93 ! [A: set_o,R2: set_Product_prod_o_o,B: $o,A2: $o] :
% 4.69/4.93 ( ( equiv_equiv_o @ A @ R2 )
% 4.69/4.93 => ( ( ord_less_eq_set_o @ ( image_o_o @ R2 @ ( insert_o @ B @ bot_bot_set_o ) ) @ ( image_o_o @ R2 @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 4.69/4.93 => ( ( member_o @ B @ A )
% 4.69/4.93 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % subset_equiv_class
% 4.69/4.93 thf(fact_1789_subset__equiv__class,axiom,
% 4.69/4.93 ! [A: set_int,R2: set_Pr958786334691620121nt_int,B: int,A2: int] :
% 4.69/4.93 ( ( equiv_equiv_int @ A @ R2 )
% 4.69/4.93 => ( ( ord_less_eq_set_int @ ( image_int_int @ R2 @ ( insert_int @ B @ bot_bot_set_int ) ) @ ( image_int_int @ R2 @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 4.69/4.93 => ( ( member_int @ B @ A )
% 4.69/4.93 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % subset_equiv_class
% 4.69/4.93 thf(fact_1790_subset__equiv__class,axiom,
% 4.69/4.93 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o,B: produc3658429121746597890et_nat > $o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( equiv_6726761681920839555_nat_o @ A @ R2 )
% 4.69/4.93 => ( ( ord_le2965882846123202637_nat_o @ ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o ) ) @ ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/4.93 => ( ( member6576561426505652726_nat_o @ B @ A )
% 4.69/4.93 => ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % subset_equiv_class
% 4.69/4.93 thf(fact_1791_subset__equiv__class,axiom,
% 4.69/4.93 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,B: nat,A2: nat] :
% 4.69/4.93 ( ( equiv_equiv_nat @ A @ R2 )
% 4.69/4.93 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ R2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) @ ( image_nat_nat @ R2 @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 4.69/4.93 => ( ( member_nat @ B @ A )
% 4.69/4.93 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % subset_equiv_class
% 4.69/4.93 thf(fact_1792_finite__finite__vimage__IntI,axiom,
% 4.69/4.93 ! [F2: set_Code_integer,H2: code_integer > code_integer,A: set_Code_integer] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ F2 )
% 4.69/4.93 => ( ! [Y2: code_integer] :
% 4.69/4.93 ( ( member_Code_integer @ Y2 @ F2 )
% 4.69/4.93 => ( finite6017078050557962740nteger @ ( inf_in1364745209274528805nteger @ ( vimage1318793397690208119nteger @ H2 @ ( insert_Code_integer @ Y2 @ bot_bo3990330152332043303nteger ) ) @ A ) ) )
% 4.69/4.93 => ( finite6017078050557962740nteger @ ( inf_in1364745209274528805nteger @ ( vimage1318793397690208119nteger @ H2 @ F2 ) @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_finite_vimage_IntI
% 4.69/4.93 thf(fact_1793_finite__finite__vimage__IntI,axiom,
% 4.69/4.93 ! [F2: set_Code_integer,H2: nat > code_integer,A: set_nat] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ F2 )
% 4.69/4.93 => ( ! [Y2: code_integer] :
% 4.69/4.93 ( ( member_Code_integer @ Y2 @ F2 )
% 4.69/4.93 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage6104394758324456170nteger @ H2 @ ( insert_Code_integer @ Y2 @ bot_bo3990330152332043303nteger ) ) @ A ) ) )
% 4.69/4.93 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage6104394758324456170nteger @ H2 @ F2 ) @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_finite_vimage_IntI
% 4.69/4.93 thf(fact_1794_finite__finite__vimage__IntI,axiom,
% 4.69/4.93 ! [F2: set_Product_unit,H2: code_integer > product_unit,A: set_Code_integer] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ F2 )
% 4.69/4.93 => ( ! [Y2: product_unit] :
% 4.69/4.93 ( ( member_Product_unit @ Y2 @ F2 )
% 4.69/4.93 => ( finite6017078050557962740nteger @ ( inf_in1364745209274528805nteger @ ( vimage5651688891684837235t_unit @ H2 @ ( insert_Product_unit @ Y2 @ bot_bo3957492148770167129t_unit ) ) @ A ) ) )
% 4.69/4.93 => ( finite6017078050557962740nteger @ ( inf_in1364745209274528805nteger @ ( vimage5651688891684837235t_unit @ H2 @ F2 ) @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_finite_vimage_IntI
% 4.69/4.93 thf(fact_1795_finite__finite__vimage__IntI,axiom,
% 4.69/4.93 ! [F2: set_Product_unit,H2: nat > product_unit,A: set_nat] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ F2 )
% 4.69/4.93 => ( ! [Y2: product_unit] :
% 4.69/4.93 ( ( member_Product_unit @ Y2 @ F2 )
% 4.69/4.93 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage4884490618288580032t_unit @ H2 @ ( insert_Product_unit @ Y2 @ bot_bo3957492148770167129t_unit ) ) @ A ) ) )
% 4.69/4.93 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage4884490618288580032t_unit @ H2 @ F2 ) @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_finite_vimage_IntI
% 4.69/4.93 thf(fact_1796_finite__finite__vimage__IntI,axiom,
% 4.69/4.93 ! [F2: set_o,H2: code_integer > $o,A: set_Code_integer] :
% 4.69/4.93 ( ( finite_finite_o @ F2 )
% 4.69/4.93 => ( ! [Y2: $o] :
% 4.69/4.93 ( ( member_o @ Y2 @ F2 )
% 4.69/4.93 => ( finite6017078050557962740nteger @ ( inf_in1364745209274528805nteger @ ( vimage3005800680117336574eger_o @ H2 @ ( insert_o @ Y2 @ bot_bot_set_o ) ) @ A ) ) )
% 4.69/4.93 => ( finite6017078050557962740nteger @ ( inf_in1364745209274528805nteger @ ( vimage3005800680117336574eger_o @ H2 @ F2 ) @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_finite_vimage_IntI
% 4.69/4.93 thf(fact_1797_finite__finite__vimage__IntI,axiom,
% 4.69/4.93 ! [F2: set_o,H2: nat > $o,A: set_nat] :
% 4.69/4.93 ( ( finite_finite_o @ F2 )
% 4.69/4.93 => ( ! [Y2: $o] :
% 4.69/4.93 ( ( member_o @ Y2 @ F2 )
% 4.69/4.93 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_o @ H2 @ ( insert_o @ Y2 @ bot_bot_set_o ) ) @ A ) ) )
% 4.69/4.93 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_o @ H2 @ F2 ) @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_finite_vimage_IntI
% 4.69/4.93 thf(fact_1798_finite__finite__vimage__IntI,axiom,
% 4.69/4.93 ! [F2: set_nat,H2: code_integer > nat,A: set_Code_integer] :
% 4.69/4.93 ( ( finite_finite_nat @ F2 )
% 4.69/4.93 => ( ! [Y2: nat] :
% 4.69/4.93 ( ( member_nat @ Y2 @ F2 )
% 4.69/4.93 => ( finite6017078050557962740nteger @ ( inf_in1364745209274528805nteger @ ( vimage5839839309545413354er_nat @ H2 @ ( insert_nat @ Y2 @ bot_bot_set_nat ) ) @ A ) ) )
% 4.69/4.93 => ( finite6017078050557962740nteger @ ( inf_in1364745209274528805nteger @ ( vimage5839839309545413354er_nat @ H2 @ F2 ) @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_finite_vimage_IntI
% 4.69/4.93 thf(fact_1799_finite__finite__vimage__IntI,axiom,
% 4.69/4.93 ! [F2: set_nat,H2: nat > nat,A: set_nat] :
% 4.69/4.93 ( ( finite_finite_nat @ F2 )
% 4.69/4.93 => ( ! [Y2: nat] :
% 4.69/4.93 ( ( member_nat @ Y2 @ F2 )
% 4.69/4.93 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_nat @ H2 @ ( insert_nat @ Y2 @ bot_bot_set_nat ) ) @ A ) ) )
% 4.69/4.93 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_nat @ H2 @ F2 ) @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_finite_vimage_IntI
% 4.69/4.93 thf(fact_1800_finite__finite__vimage__IntI,axiom,
% 4.69/4.93 ! [F2: set_int,H2: code_integer > int,A: set_Code_integer] :
% 4.69/4.93 ( ( finite_finite_int @ F2 )
% 4.69/4.93 => ( ! [Y2: int] :
% 4.69/4.93 ( ( member_int @ Y2 @ F2 )
% 4.69/4.93 => ( finite6017078050557962740nteger @ ( inf_in1364745209274528805nteger @ ( vimage5837348839036363078er_int @ H2 @ ( insert_int @ Y2 @ bot_bot_set_int ) ) @ A ) ) )
% 4.69/4.93 => ( finite6017078050557962740nteger @ ( inf_in1364745209274528805nteger @ ( vimage5837348839036363078er_int @ H2 @ F2 ) @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_finite_vimage_IntI
% 4.69/4.93 thf(fact_1801_finite__finite__vimage__IntI,axiom,
% 4.69/4.93 ! [F2: set_int,H2: nat > int,A: set_nat] :
% 4.69/4.93 ( ( finite_finite_int @ F2 )
% 4.69/4.93 => ( ! [Y2: int] :
% 4.69/4.93 ( ( member_int @ Y2 @ F2 )
% 4.69/4.93 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_int @ H2 @ ( insert_int @ Y2 @ bot_bot_set_int ) ) @ A ) ) )
% 4.69/4.93 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_int @ H2 @ F2 ) @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_finite_vimage_IntI
% 4.69/4.93 thf(fact_1802_finite__insert,axiom,
% 4.69/4.93 ! [A2: int,A: set_int] :
% 4.69/4.93 ( ( finite_finite_int @ ( insert_int @ A2 @ A ) )
% 4.69/4.93 = ( finite_finite_int @ A ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_insert
% 4.69/4.93 thf(fact_1803_finite__insert,axiom,
% 4.69/4.93 ! [A2: $o,A: set_o] :
% 4.69/4.93 ( ( finite_finite_o @ ( insert_o @ A2 @ A ) )
% 4.69/4.93 = ( finite_finite_o @ A ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_insert
% 4.69/4.93 thf(fact_1804_finite__insert,axiom,
% 4.69/4.93 ! [A2: product_unit,A: set_Product_unit] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ ( insert_Product_unit @ A2 @ A ) )
% 4.69/4.93 = ( finite4290736615968046902t_unit @ A ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_insert
% 4.69/4.93 thf(fact_1805_finite__insert,axiom,
% 4.69/4.93 ! [A2: nat,A: set_nat] :
% 4.69/4.93 ( ( finite_finite_nat @ ( insert_nat @ A2 @ A ) )
% 4.69/4.93 = ( finite_finite_nat @ A ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_insert
% 4.69/4.93 thf(fact_1806_finite__insert,axiom,
% 4.69/4.93 ! [A2: code_integer,A: set_Code_integer] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ ( insert_Code_integer @ A2 @ A ) )
% 4.69/4.93 = ( finite6017078050557962740nteger @ A ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_insert
% 4.69/4.93 thf(fact_1807_finite__subset__induct_H,axiom,
% 4.69/4.93 ! [F2: set_Code_integer,A: set_Code_integer,P: set_Code_integer > $o] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ F2 )
% 4.69/4.93 => ( ( ord_le7084787975880047091nteger @ F2 @ A )
% 4.69/4.93 => ( ( P @ bot_bo3990330152332043303nteger )
% 4.69/4.93 => ( ! [A4: code_integer,F3: set_Code_integer] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ F3 )
% 4.69/4.93 => ( ( member_Code_integer @ A4 @ A )
% 4.69/4.93 => ( ( ord_le7084787975880047091nteger @ F3 @ A )
% 4.69/4.93 => ( ~ ( member_Code_integer @ A4 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_Code_integer @ A4 @ F3 ) ) ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_subset_induct'
% 4.69/4.93 thf(fact_1808_finite__subset__induct_H,axiom,
% 4.69/4.93 ! [F2: set_Product_unit,A: set_Product_unit,P: set_Product_unit > $o] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ F2 )
% 4.69/4.93 => ( ( ord_le3507040750410214029t_unit @ F2 @ A )
% 4.69/4.93 => ( ( P @ bot_bo3957492148770167129t_unit )
% 4.69/4.93 => ( ! [A4: product_unit,F3: set_Product_unit] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ F3 )
% 4.69/4.93 => ( ( member_Product_unit @ A4 @ A )
% 4.69/4.93 => ( ( ord_le3507040750410214029t_unit @ F3 @ A )
% 4.69/4.93 => ( ~ ( member_Product_unit @ A4 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_Product_unit @ A4 @ F3 ) ) ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_subset_induct'
% 4.69/4.93 thf(fact_1809_finite__subset__induct_H,axiom,
% 4.69/4.93 ! [F2: set_o,A: set_o,P: set_o > $o] :
% 4.69/4.93 ( ( finite_finite_o @ F2 )
% 4.69/4.93 => ( ( ord_less_eq_set_o @ F2 @ A )
% 4.69/4.93 => ( ( P @ bot_bot_set_o )
% 4.69/4.93 => ( ! [A4: $o,F3: set_o] :
% 4.69/4.93 ( ( finite_finite_o @ F3 )
% 4.69/4.93 => ( ( member_o @ A4 @ A )
% 4.69/4.93 => ( ( ord_less_eq_set_o @ F3 @ A )
% 4.69/4.93 => ( ~ ( member_o @ A4 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_o @ A4 @ F3 ) ) ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_subset_induct'
% 4.69/4.93 thf(fact_1810_finite__subset__induct_H,axiom,
% 4.69/4.93 ! [F2: set_int,A: set_int,P: set_int > $o] :
% 4.69/4.93 ( ( finite_finite_int @ F2 )
% 4.69/4.93 => ( ( ord_less_eq_set_int @ F2 @ A )
% 4.69/4.93 => ( ( P @ bot_bot_set_int )
% 4.69/4.93 => ( ! [A4: int,F3: set_int] :
% 4.69/4.93 ( ( finite_finite_int @ F3 )
% 4.69/4.93 => ( ( member_int @ A4 @ A )
% 4.69/4.93 => ( ( ord_less_eq_set_int @ F3 @ A )
% 4.69/4.93 => ( ~ ( member_int @ A4 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_int @ A4 @ F3 ) ) ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_subset_induct'
% 4.69/4.93 thf(fact_1811_finite__subset__induct_H,axiom,
% 4.69/4.93 ! [F2: set_Pr4532377907799695533_nat_o,A: set_Pr4532377907799695533_nat_o,P: set_Pr4532377907799695533_nat_o > $o] :
% 4.69/4.93 ( ( finite3252695134891459830_nat_o @ F2 )
% 4.69/4.93 => ( ( ord_le2965882846123202637_nat_o @ F2 @ A )
% 4.69/4.93 => ( ( P @ bot_bo7824918357723582233_nat_o )
% 4.69/4.93 => ( ! [A4: produc3658429121746597890et_nat > $o,F3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ( ( finite3252695134891459830_nat_o @ F3 )
% 4.69/4.93 => ( ( member6576561426505652726_nat_o @ A4 @ A )
% 4.69/4.93 => ( ( ord_le2965882846123202637_nat_o @ F3 @ A )
% 4.69/4.93 => ( ~ ( member6576561426505652726_nat_o @ A4 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert5175938949040314269_nat_o @ A4 @ F3 ) ) ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_subset_induct'
% 4.69/4.93 thf(fact_1812_finite__subset__induct_H,axiom,
% 4.69/4.93 ! [F2: set_nat,A: set_nat,P: set_nat > $o] :
% 4.69/4.93 ( ( finite_finite_nat @ F2 )
% 4.69/4.93 => ( ( ord_less_eq_set_nat @ F2 @ A )
% 4.69/4.93 => ( ( P @ bot_bot_set_nat )
% 4.69/4.93 => ( ! [A4: nat,F3: set_nat] :
% 4.69/4.93 ( ( finite_finite_nat @ F3 )
% 4.69/4.93 => ( ( member_nat @ A4 @ A )
% 4.69/4.93 => ( ( ord_less_eq_set_nat @ F3 @ A )
% 4.69/4.93 => ( ~ ( member_nat @ A4 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_nat @ A4 @ F3 ) ) ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_subset_induct'
% 4.69/4.93 thf(fact_1813_finite__subset__induct,axiom,
% 4.69/4.93 ! [F2: set_Code_integer,A: set_Code_integer,P: set_Code_integer > $o] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ F2 )
% 4.69/4.93 => ( ( ord_le7084787975880047091nteger @ F2 @ A )
% 4.69/4.93 => ( ( P @ bot_bo3990330152332043303nteger )
% 4.69/4.93 => ( ! [A4: code_integer,F3: set_Code_integer] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ F3 )
% 4.69/4.93 => ( ( member_Code_integer @ A4 @ A )
% 4.69/4.93 => ( ~ ( member_Code_integer @ A4 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_Code_integer @ A4 @ F3 ) ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_subset_induct
% 4.69/4.93 thf(fact_1814_finite__subset__induct,axiom,
% 4.69/4.93 ! [F2: set_Product_unit,A: set_Product_unit,P: set_Product_unit > $o] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ F2 )
% 4.69/4.93 => ( ( ord_le3507040750410214029t_unit @ F2 @ A )
% 4.69/4.93 => ( ( P @ bot_bo3957492148770167129t_unit )
% 4.69/4.93 => ( ! [A4: product_unit,F3: set_Product_unit] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ F3 )
% 4.69/4.93 => ( ( member_Product_unit @ A4 @ A )
% 4.69/4.93 => ( ~ ( member_Product_unit @ A4 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_Product_unit @ A4 @ F3 ) ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_subset_induct
% 4.69/4.93 thf(fact_1815_finite__subset__induct,axiom,
% 4.69/4.93 ! [F2: set_o,A: set_o,P: set_o > $o] :
% 4.69/4.93 ( ( finite_finite_o @ F2 )
% 4.69/4.93 => ( ( ord_less_eq_set_o @ F2 @ A )
% 4.69/4.93 => ( ( P @ bot_bot_set_o )
% 4.69/4.93 => ( ! [A4: $o,F3: set_o] :
% 4.69/4.93 ( ( finite_finite_o @ F3 )
% 4.69/4.93 => ( ( member_o @ A4 @ A )
% 4.69/4.93 => ( ~ ( member_o @ A4 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_o @ A4 @ F3 ) ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_subset_induct
% 4.69/4.93 thf(fact_1816_finite__subset__induct,axiom,
% 4.69/4.93 ! [F2: set_int,A: set_int,P: set_int > $o] :
% 4.69/4.93 ( ( finite_finite_int @ F2 )
% 4.69/4.93 => ( ( ord_less_eq_set_int @ F2 @ A )
% 4.69/4.93 => ( ( P @ bot_bot_set_int )
% 4.69/4.93 => ( ! [A4: int,F3: set_int] :
% 4.69/4.93 ( ( finite_finite_int @ F3 )
% 4.69/4.93 => ( ( member_int @ A4 @ A )
% 4.69/4.93 => ( ~ ( member_int @ A4 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_int @ A4 @ F3 ) ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_subset_induct
% 4.69/4.93 thf(fact_1817_finite__subset__induct,axiom,
% 4.69/4.93 ! [F2: set_Pr4532377907799695533_nat_o,A: set_Pr4532377907799695533_nat_o,P: set_Pr4532377907799695533_nat_o > $o] :
% 4.69/4.93 ( ( finite3252695134891459830_nat_o @ F2 )
% 4.69/4.93 => ( ( ord_le2965882846123202637_nat_o @ F2 @ A )
% 4.69/4.93 => ( ( P @ bot_bo7824918357723582233_nat_o )
% 4.69/4.93 => ( ! [A4: produc3658429121746597890et_nat > $o,F3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ( ( finite3252695134891459830_nat_o @ F3 )
% 4.69/4.93 => ( ( member6576561426505652726_nat_o @ A4 @ A )
% 4.69/4.93 => ( ~ ( member6576561426505652726_nat_o @ A4 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert5175938949040314269_nat_o @ A4 @ F3 ) ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_subset_induct
% 4.69/4.93 thf(fact_1818_finite__subset__induct,axiom,
% 4.69/4.93 ! [F2: set_nat,A: set_nat,P: set_nat > $o] :
% 4.69/4.93 ( ( finite_finite_nat @ F2 )
% 4.69/4.93 => ( ( ord_less_eq_set_nat @ F2 @ A )
% 4.69/4.93 => ( ( P @ bot_bot_set_nat )
% 4.69/4.93 => ( ! [A4: nat,F3: set_nat] :
% 4.69/4.93 ( ( finite_finite_nat @ F3 )
% 4.69/4.93 => ( ( member_nat @ A4 @ A )
% 4.69/4.93 => ( ~ ( member_nat @ A4 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_nat @ A4 @ F3 ) ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_subset_induct
% 4.69/4.93 thf(fact_1819_finite__ranking__induct,axiom,
% 4.69/4.93 ! [S: set_Code_integer,P: set_Code_integer > $o,F: code_integer > rat] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ S )
% 4.69/4.93 => ( ( P @ bot_bo3990330152332043303nteger )
% 4.69/4.93 => ( ! [X3: code_integer,S5: set_Code_integer] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ S5 )
% 4.69/4.93 => ( ! [Y5: code_integer] :
% 4.69/4.93 ( ( member_Code_integer @ Y5 @ S5 )
% 4.69/4.93 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 4.69/4.93 => ( ( P @ S5 )
% 4.69/4.93 => ( P @ ( insert_Code_integer @ X3 @ S5 ) ) ) ) )
% 4.69/4.93 => ( P @ S ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_ranking_induct
% 4.69/4.93 thf(fact_1820_finite__ranking__induct,axiom,
% 4.69/4.93 ! [S: set_Product_unit,P: set_Product_unit > $o,F: product_unit > rat] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ S )
% 4.69/4.93 => ( ( P @ bot_bo3957492148770167129t_unit )
% 4.69/4.93 => ( ! [X3: product_unit,S5: set_Product_unit] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ S5 )
% 4.69/4.93 => ( ! [Y5: product_unit] :
% 4.69/4.93 ( ( member_Product_unit @ Y5 @ S5 )
% 4.69/4.93 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 4.69/4.93 => ( ( P @ S5 )
% 4.69/4.93 => ( P @ ( insert_Product_unit @ X3 @ S5 ) ) ) ) )
% 4.69/4.93 => ( P @ S ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_ranking_induct
% 4.69/4.93 thf(fact_1821_finite__ranking__induct,axiom,
% 4.69/4.93 ! [S: set_o,P: set_o > $o,F: $o > rat] :
% 4.69/4.93 ( ( finite_finite_o @ S )
% 4.69/4.93 => ( ( P @ bot_bot_set_o )
% 4.69/4.93 => ( ! [X3: $o,S5: set_o] :
% 4.69/4.93 ( ( finite_finite_o @ S5 )
% 4.69/4.93 => ( ! [Y5: $o] :
% 4.69/4.93 ( ( member_o @ Y5 @ S5 )
% 4.69/4.93 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 4.69/4.93 => ( ( P @ S5 )
% 4.69/4.93 => ( P @ ( insert_o @ X3 @ S5 ) ) ) ) )
% 4.69/4.93 => ( P @ S ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_ranking_induct
% 4.69/4.93 thf(fact_1822_finite__ranking__induct,axiom,
% 4.69/4.93 ! [S: set_nat,P: set_nat > $o,F: nat > rat] :
% 4.69/4.93 ( ( finite_finite_nat @ S )
% 4.69/4.93 => ( ( P @ bot_bot_set_nat )
% 4.69/4.93 => ( ! [X3: nat,S5: set_nat] :
% 4.69/4.93 ( ( finite_finite_nat @ S5 )
% 4.69/4.93 => ( ! [Y5: nat] :
% 4.69/4.93 ( ( member_nat @ Y5 @ S5 )
% 4.69/4.93 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 4.69/4.93 => ( ( P @ S5 )
% 4.69/4.93 => ( P @ ( insert_nat @ X3 @ S5 ) ) ) ) )
% 4.69/4.93 => ( P @ S ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_ranking_induct
% 4.69/4.93 thf(fact_1823_finite__ranking__induct,axiom,
% 4.69/4.93 ! [S: set_int,P: set_int > $o,F: int > rat] :
% 4.69/4.93 ( ( finite_finite_int @ S )
% 4.69/4.93 => ( ( P @ bot_bot_set_int )
% 4.69/4.93 => ( ! [X3: int,S5: set_int] :
% 4.69/4.93 ( ( finite_finite_int @ S5 )
% 4.69/4.93 => ( ! [Y5: int] :
% 4.69/4.93 ( ( member_int @ Y5 @ S5 )
% 4.69/4.93 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 4.69/4.93 => ( ( P @ S5 )
% 4.69/4.93 => ( P @ ( insert_int @ X3 @ S5 ) ) ) ) )
% 4.69/4.93 => ( P @ S ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_ranking_induct
% 4.69/4.93 thf(fact_1824_finite__ranking__induct,axiom,
% 4.69/4.93 ! [S: set_Code_integer,P: set_Code_integer > $o,F: code_integer > nat] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ S )
% 4.69/4.93 => ( ( P @ bot_bo3990330152332043303nteger )
% 4.69/4.93 => ( ! [X3: code_integer,S5: set_Code_integer] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ S5 )
% 4.69/4.93 => ( ! [Y5: code_integer] :
% 4.69/4.93 ( ( member_Code_integer @ Y5 @ S5 )
% 4.69/4.93 => ( ord_less_eq_nat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 4.69/4.93 => ( ( P @ S5 )
% 4.69/4.93 => ( P @ ( insert_Code_integer @ X3 @ S5 ) ) ) ) )
% 4.69/4.93 => ( P @ S ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_ranking_induct
% 4.69/4.93 thf(fact_1825_finite__ranking__induct,axiom,
% 4.69/4.93 ! [S: set_Product_unit,P: set_Product_unit > $o,F: product_unit > nat] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ S )
% 4.69/4.93 => ( ( P @ bot_bo3957492148770167129t_unit )
% 4.69/4.93 => ( ! [X3: product_unit,S5: set_Product_unit] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ S5 )
% 4.69/4.93 => ( ! [Y5: product_unit] :
% 4.69/4.93 ( ( member_Product_unit @ Y5 @ S5 )
% 4.69/4.93 => ( ord_less_eq_nat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 4.69/4.93 => ( ( P @ S5 )
% 4.69/4.93 => ( P @ ( insert_Product_unit @ X3 @ S5 ) ) ) ) )
% 4.69/4.93 => ( P @ S ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_ranking_induct
% 4.69/4.93 thf(fact_1826_finite__ranking__induct,axiom,
% 4.69/4.93 ! [S: set_o,P: set_o > $o,F: $o > nat] :
% 4.69/4.93 ( ( finite_finite_o @ S )
% 4.69/4.93 => ( ( P @ bot_bot_set_o )
% 4.69/4.93 => ( ! [X3: $o,S5: set_o] :
% 4.69/4.93 ( ( finite_finite_o @ S5 )
% 4.69/4.93 => ( ! [Y5: $o] :
% 4.69/4.93 ( ( member_o @ Y5 @ S5 )
% 4.69/4.93 => ( ord_less_eq_nat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 4.69/4.93 => ( ( P @ S5 )
% 4.69/4.93 => ( P @ ( insert_o @ X3 @ S5 ) ) ) ) )
% 4.69/4.93 => ( P @ S ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_ranking_induct
% 4.69/4.93 thf(fact_1827_finite__ranking__induct,axiom,
% 4.69/4.93 ! [S: set_nat,P: set_nat > $o,F: nat > nat] :
% 4.69/4.93 ( ( finite_finite_nat @ S )
% 4.69/4.93 => ( ( P @ bot_bot_set_nat )
% 4.69/4.93 => ( ! [X3: nat,S5: set_nat] :
% 4.69/4.93 ( ( finite_finite_nat @ S5 )
% 4.69/4.93 => ( ! [Y5: nat] :
% 4.69/4.93 ( ( member_nat @ Y5 @ S5 )
% 4.69/4.93 => ( ord_less_eq_nat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 4.69/4.93 => ( ( P @ S5 )
% 4.69/4.93 => ( P @ ( insert_nat @ X3 @ S5 ) ) ) ) )
% 4.69/4.93 => ( P @ S ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_ranking_induct
% 4.69/4.93 thf(fact_1828_finite__ranking__induct,axiom,
% 4.69/4.93 ! [S: set_int,P: set_int > $o,F: int > nat] :
% 4.69/4.93 ( ( finite_finite_int @ S )
% 4.69/4.93 => ( ( P @ bot_bot_set_int )
% 4.69/4.93 => ( ! [X3: int,S5: set_int] :
% 4.69/4.93 ( ( finite_finite_int @ S5 )
% 4.69/4.93 => ( ! [Y5: int] :
% 4.69/4.93 ( ( member_int @ Y5 @ S5 )
% 4.69/4.93 => ( ord_less_eq_nat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 4.69/4.93 => ( ( P @ S5 )
% 4.69/4.93 => ( P @ ( insert_int @ X3 @ S5 ) ) ) ) )
% 4.69/4.93 => ( P @ S ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_ranking_induct
% 4.69/4.93 thf(fact_1829_infinite__finite__induct,axiom,
% 4.69/4.93 ! [P: set_Code_integer > $o,A: set_Code_integer] :
% 4.69/4.93 ( ! [A9: set_Code_integer] :
% 4.69/4.93 ( ~ ( finite6017078050557962740nteger @ A9 )
% 4.69/4.93 => ( P @ A9 ) )
% 4.69/4.93 => ( ( P @ bot_bo3990330152332043303nteger )
% 4.69/4.93 => ( ! [X3: code_integer,F3: set_Code_integer] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ F3 )
% 4.69/4.93 => ( ~ ( member_Code_integer @ X3 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_Code_integer @ X3 @ F3 ) ) ) ) )
% 4.69/4.93 => ( P @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % infinite_finite_induct
% 4.69/4.93 thf(fact_1830_infinite__finite__induct,axiom,
% 4.69/4.93 ! [P: set_Product_unit > $o,A: set_Product_unit] :
% 4.69/4.93 ( ! [A9: set_Product_unit] :
% 4.69/4.93 ( ~ ( finite4290736615968046902t_unit @ A9 )
% 4.69/4.93 => ( P @ A9 ) )
% 4.69/4.93 => ( ( P @ bot_bo3957492148770167129t_unit )
% 4.69/4.93 => ( ! [X3: product_unit,F3: set_Product_unit] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ F3 )
% 4.69/4.93 => ( ~ ( member_Product_unit @ X3 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_Product_unit @ X3 @ F3 ) ) ) ) )
% 4.69/4.93 => ( P @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % infinite_finite_induct
% 4.69/4.93 thf(fact_1831_infinite__finite__induct,axiom,
% 4.69/4.93 ! [P: set_o > $o,A: set_o] :
% 4.69/4.93 ( ! [A9: set_o] :
% 4.69/4.93 ( ~ ( finite_finite_o @ A9 )
% 4.69/4.93 => ( P @ A9 ) )
% 4.69/4.93 => ( ( P @ bot_bot_set_o )
% 4.69/4.93 => ( ! [X3: $o,F3: set_o] :
% 4.69/4.93 ( ( finite_finite_o @ F3 )
% 4.69/4.93 => ( ~ ( member_o @ X3 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_o @ X3 @ F3 ) ) ) ) )
% 4.69/4.93 => ( P @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % infinite_finite_induct
% 4.69/4.93 thf(fact_1832_infinite__finite__induct,axiom,
% 4.69/4.93 ! [P: set_nat > $o,A: set_nat] :
% 4.69/4.93 ( ! [A9: set_nat] :
% 4.69/4.93 ( ~ ( finite_finite_nat @ A9 )
% 4.69/4.93 => ( P @ A9 ) )
% 4.69/4.93 => ( ( P @ bot_bot_set_nat )
% 4.69/4.93 => ( ! [X3: nat,F3: set_nat] :
% 4.69/4.93 ( ( finite_finite_nat @ F3 )
% 4.69/4.93 => ( ~ ( member_nat @ X3 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_nat @ X3 @ F3 ) ) ) ) )
% 4.69/4.93 => ( P @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % infinite_finite_induct
% 4.69/4.93 thf(fact_1833_infinite__finite__induct,axiom,
% 4.69/4.93 ! [P: set_int > $o,A: set_int] :
% 4.69/4.93 ( ! [A9: set_int] :
% 4.69/4.93 ( ~ ( finite_finite_int @ A9 )
% 4.69/4.93 => ( P @ A9 ) )
% 4.69/4.93 => ( ( P @ bot_bot_set_int )
% 4.69/4.93 => ( ! [X3: int,F3: set_int] :
% 4.69/4.93 ( ( finite_finite_int @ F3 )
% 4.69/4.93 => ( ~ ( member_int @ X3 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_int @ X3 @ F3 ) ) ) ) )
% 4.69/4.93 => ( P @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % infinite_finite_induct
% 4.69/4.93 thf(fact_1834_infinite__finite__induct,axiom,
% 4.69/4.93 ! [P: set_Pr4532377907799695533_nat_o > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ( ! [A9: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ( ~ ( finite3252695134891459830_nat_o @ A9 )
% 4.69/4.93 => ( P @ A9 ) )
% 4.69/4.93 => ( ( P @ bot_bo7824918357723582233_nat_o )
% 4.69/4.93 => ( ! [X3: produc3658429121746597890et_nat > $o,F3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ( ( finite3252695134891459830_nat_o @ F3 )
% 4.69/4.93 => ( ~ ( member6576561426505652726_nat_o @ X3 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert5175938949040314269_nat_o @ X3 @ F3 ) ) ) ) )
% 4.69/4.93 => ( P @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % infinite_finite_induct
% 4.69/4.93 thf(fact_1835_finite__ne__induct,axiom,
% 4.69/4.93 ! [F2: set_Code_integer,P: set_Code_integer > $o] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ F2 )
% 4.69/4.93 => ( ( F2 != bot_bo3990330152332043303nteger )
% 4.69/4.93 => ( ! [X3: code_integer] : ( P @ ( insert_Code_integer @ X3 @ bot_bo3990330152332043303nteger ) )
% 4.69/4.93 => ( ! [X3: code_integer,F3: set_Code_integer] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ F3 )
% 4.69/4.93 => ( ( F3 != bot_bo3990330152332043303nteger )
% 4.69/4.93 => ( ~ ( member_Code_integer @ X3 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_Code_integer @ X3 @ F3 ) ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_ne_induct
% 4.69/4.93 thf(fact_1836_finite__ne__induct,axiom,
% 4.69/4.93 ! [F2: set_Product_unit,P: set_Product_unit > $o] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ F2 )
% 4.69/4.93 => ( ( F2 != bot_bo3957492148770167129t_unit )
% 4.69/4.93 => ( ! [X3: product_unit] : ( P @ ( insert_Product_unit @ X3 @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.93 => ( ! [X3: product_unit,F3: set_Product_unit] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ F3 )
% 4.69/4.93 => ( ( F3 != bot_bo3957492148770167129t_unit )
% 4.69/4.93 => ( ~ ( member_Product_unit @ X3 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_Product_unit @ X3 @ F3 ) ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_ne_induct
% 4.69/4.93 thf(fact_1837_finite__ne__induct,axiom,
% 4.69/4.93 ! [F2: set_o,P: set_o > $o] :
% 4.69/4.93 ( ( finite_finite_o @ F2 )
% 4.69/4.93 => ( ( F2 != bot_bot_set_o )
% 4.69/4.93 => ( ! [X3: $o] : ( P @ ( insert_o @ X3 @ bot_bot_set_o ) )
% 4.69/4.93 => ( ! [X3: $o,F3: set_o] :
% 4.69/4.93 ( ( finite_finite_o @ F3 )
% 4.69/4.93 => ( ( F3 != bot_bot_set_o )
% 4.69/4.93 => ( ~ ( member_o @ X3 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_o @ X3 @ F3 ) ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_ne_induct
% 4.69/4.93 thf(fact_1838_finite__ne__induct,axiom,
% 4.69/4.93 ! [F2: set_nat,P: set_nat > $o] :
% 4.69/4.93 ( ( finite_finite_nat @ F2 )
% 4.69/4.93 => ( ( F2 != bot_bot_set_nat )
% 4.69/4.93 => ( ! [X3: nat] : ( P @ ( insert_nat @ X3 @ bot_bot_set_nat ) )
% 4.69/4.93 => ( ! [X3: nat,F3: set_nat] :
% 4.69/4.93 ( ( finite_finite_nat @ F3 )
% 4.69/4.93 => ( ( F3 != bot_bot_set_nat )
% 4.69/4.93 => ( ~ ( member_nat @ X3 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_nat @ X3 @ F3 ) ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_ne_induct
% 4.69/4.93 thf(fact_1839_finite__ne__induct,axiom,
% 4.69/4.93 ! [F2: set_int,P: set_int > $o] :
% 4.69/4.93 ( ( finite_finite_int @ F2 )
% 4.69/4.93 => ( ( F2 != bot_bot_set_int )
% 4.69/4.93 => ( ! [X3: int] : ( P @ ( insert_int @ X3 @ bot_bot_set_int ) )
% 4.69/4.93 => ( ! [X3: int,F3: set_int] :
% 4.69/4.93 ( ( finite_finite_int @ F3 )
% 4.69/4.93 => ( ( F3 != bot_bot_set_int )
% 4.69/4.93 => ( ~ ( member_int @ X3 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_int @ X3 @ F3 ) ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_ne_induct
% 4.69/4.93 thf(fact_1840_finite__ne__induct,axiom,
% 4.69/4.93 ! [F2: set_Pr4532377907799695533_nat_o,P: set_Pr4532377907799695533_nat_o > $o] :
% 4.69/4.93 ( ( finite3252695134891459830_nat_o @ F2 )
% 4.69/4.93 => ( ( F2 != bot_bo7824918357723582233_nat_o )
% 4.69/4.93 => ( ! [X3: produc3658429121746597890et_nat > $o] : ( P @ ( insert5175938949040314269_nat_o @ X3 @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.93 => ( ! [X3: produc3658429121746597890et_nat > $o,F3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ( ( finite3252695134891459830_nat_o @ F3 )
% 4.69/4.93 => ( ( F3 != bot_bo7824918357723582233_nat_o )
% 4.69/4.93 => ( ~ ( member6576561426505652726_nat_o @ X3 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert5175938949040314269_nat_o @ X3 @ F3 ) ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_ne_induct
% 4.69/4.93 thf(fact_1841_finite__induct,axiom,
% 4.69/4.93 ! [F2: set_Code_integer,P: set_Code_integer > $o] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ F2 )
% 4.69/4.93 => ( ( P @ bot_bo3990330152332043303nteger )
% 4.69/4.93 => ( ! [X3: code_integer,F3: set_Code_integer] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ F3 )
% 4.69/4.93 => ( ~ ( member_Code_integer @ X3 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_Code_integer @ X3 @ F3 ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_induct
% 4.69/4.93 thf(fact_1842_finite__induct,axiom,
% 4.69/4.93 ! [F2: set_Product_unit,P: set_Product_unit > $o] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ F2 )
% 4.69/4.93 => ( ( P @ bot_bo3957492148770167129t_unit )
% 4.69/4.93 => ( ! [X3: product_unit,F3: set_Product_unit] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ F3 )
% 4.69/4.93 => ( ~ ( member_Product_unit @ X3 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_Product_unit @ X3 @ F3 ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_induct
% 4.69/4.93 thf(fact_1843_finite__induct,axiom,
% 4.69/4.93 ! [F2: set_o,P: set_o > $o] :
% 4.69/4.93 ( ( finite_finite_o @ F2 )
% 4.69/4.93 => ( ( P @ bot_bot_set_o )
% 4.69/4.93 => ( ! [X3: $o,F3: set_o] :
% 4.69/4.93 ( ( finite_finite_o @ F3 )
% 4.69/4.93 => ( ~ ( member_o @ X3 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_o @ X3 @ F3 ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_induct
% 4.69/4.93 thf(fact_1844_finite__induct,axiom,
% 4.69/4.93 ! [F2: set_nat,P: set_nat > $o] :
% 4.69/4.93 ( ( finite_finite_nat @ F2 )
% 4.69/4.93 => ( ( P @ bot_bot_set_nat )
% 4.69/4.93 => ( ! [X3: nat,F3: set_nat] :
% 4.69/4.93 ( ( finite_finite_nat @ F3 )
% 4.69/4.93 => ( ~ ( member_nat @ X3 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_nat @ X3 @ F3 ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_induct
% 4.69/4.93 thf(fact_1845_finite__induct,axiom,
% 4.69/4.93 ! [F2: set_int,P: set_int > $o] :
% 4.69/4.93 ( ( finite_finite_int @ F2 )
% 4.69/4.93 => ( ( P @ bot_bot_set_int )
% 4.69/4.93 => ( ! [X3: int,F3: set_int] :
% 4.69/4.93 ( ( finite_finite_int @ F3 )
% 4.69/4.93 => ( ~ ( member_int @ X3 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert_int @ X3 @ F3 ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_induct
% 4.69/4.93 thf(fact_1846_finite__induct,axiom,
% 4.69/4.93 ! [F2: set_Pr4532377907799695533_nat_o,P: set_Pr4532377907799695533_nat_o > $o] :
% 4.69/4.93 ( ( finite3252695134891459830_nat_o @ F2 )
% 4.69/4.93 => ( ( P @ bot_bo7824918357723582233_nat_o )
% 4.69/4.93 => ( ! [X3: produc3658429121746597890et_nat > $o,F3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ( ( finite3252695134891459830_nat_o @ F3 )
% 4.69/4.93 => ( ~ ( member6576561426505652726_nat_o @ X3 @ F3 )
% 4.69/4.93 => ( ( P @ F3 )
% 4.69/4.93 => ( P @ ( insert5175938949040314269_nat_o @ X3 @ F3 ) ) ) ) )
% 4.69/4.93 => ( P @ F2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_induct
% 4.69/4.93 thf(fact_1847_finite_Osimps,axiom,
% 4.69/4.93 ( finite6017078050557962740nteger
% 4.69/4.93 = ( ^ [A6: set_Code_integer] :
% 4.69/4.93 ( ( A6 = bot_bo3990330152332043303nteger )
% 4.69/4.93 | ? [A3: set_Code_integer,B6: code_integer] :
% 4.69/4.93 ( ( A6
% 4.69/4.93 = ( insert_Code_integer @ B6 @ A3 ) )
% 4.69/4.93 & ( finite6017078050557962740nteger @ A3 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite.simps
% 4.69/4.93 thf(fact_1848_finite_Osimps,axiom,
% 4.69/4.93 ( finite4290736615968046902t_unit
% 4.69/4.93 = ( ^ [A6: set_Product_unit] :
% 4.69/4.93 ( ( A6 = bot_bo3957492148770167129t_unit )
% 4.69/4.93 | ? [A3: set_Product_unit,B6: product_unit] :
% 4.69/4.93 ( ( A6
% 4.69/4.93 = ( insert_Product_unit @ B6 @ A3 ) )
% 4.69/4.93 & ( finite4290736615968046902t_unit @ A3 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite.simps
% 4.69/4.93 thf(fact_1849_finite_Osimps,axiom,
% 4.69/4.93 ( finite_finite_o
% 4.69/4.93 = ( ^ [A6: set_o] :
% 4.69/4.93 ( ( A6 = bot_bot_set_o )
% 4.69/4.93 | ? [A3: set_o,B6: $o] :
% 4.69/4.93 ( ( A6
% 4.69/4.93 = ( insert_o @ B6 @ A3 ) )
% 4.69/4.93 & ( finite_finite_o @ A3 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite.simps
% 4.69/4.93 thf(fact_1850_finite_Osimps,axiom,
% 4.69/4.93 ( finite_finite_nat
% 4.69/4.93 = ( ^ [A6: set_nat] :
% 4.69/4.93 ( ( A6 = bot_bot_set_nat )
% 4.69/4.93 | ? [A3: set_nat,B6: nat] :
% 4.69/4.93 ( ( A6
% 4.69/4.93 = ( insert_nat @ B6 @ A3 ) )
% 4.69/4.93 & ( finite_finite_nat @ A3 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite.simps
% 4.69/4.93 thf(fact_1851_finite_Osimps,axiom,
% 4.69/4.93 ( finite_finite_int
% 4.69/4.93 = ( ^ [A6: set_int] :
% 4.69/4.93 ( ( A6 = bot_bot_set_int )
% 4.69/4.93 | ? [A3: set_int,B6: int] :
% 4.69/4.93 ( ( A6
% 4.69/4.93 = ( insert_int @ B6 @ A3 ) )
% 4.69/4.93 & ( finite_finite_int @ A3 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite.simps
% 4.69/4.93 thf(fact_1852_finite_Osimps,axiom,
% 4.69/4.93 ( finite3252695134891459830_nat_o
% 4.69/4.93 = ( ^ [A6: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ( ( A6 = bot_bo7824918357723582233_nat_o )
% 4.69/4.93 | ? [A3: set_Pr4532377907799695533_nat_o,B6: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( A6
% 4.69/4.93 = ( insert5175938949040314269_nat_o @ B6 @ A3 ) )
% 4.69/4.93 & ( finite3252695134891459830_nat_o @ A3 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite.simps
% 4.69/4.93 thf(fact_1853_infinite__imp__nonempty,axiom,
% 4.69/4.93 ! [S: set_Code_integer] :
% 4.69/4.93 ( ~ ( finite6017078050557962740nteger @ S )
% 4.69/4.93 => ( S != bot_bo3990330152332043303nteger ) ) ).
% 4.69/4.93
% 4.69/4.93 % infinite_imp_nonempty
% 4.69/4.93 thf(fact_1854_infinite__imp__nonempty,axiom,
% 4.69/4.93 ! [S: set_Product_unit] :
% 4.69/4.93 ( ~ ( finite4290736615968046902t_unit @ S )
% 4.69/4.93 => ( S != bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.93
% 4.69/4.93 % infinite_imp_nonempty
% 4.69/4.93 thf(fact_1855_infinite__imp__nonempty,axiom,
% 4.69/4.93 ! [S: set_o] :
% 4.69/4.93 ( ~ ( finite_finite_o @ S )
% 4.69/4.93 => ( S != bot_bot_set_o ) ) ).
% 4.69/4.93
% 4.69/4.93 % infinite_imp_nonempty
% 4.69/4.93 thf(fact_1856_infinite__imp__nonempty,axiom,
% 4.69/4.93 ! [S: set_nat] :
% 4.69/4.93 ( ~ ( finite_finite_nat @ S )
% 4.69/4.93 => ( S != bot_bot_set_nat ) ) ).
% 4.69/4.93
% 4.69/4.93 % infinite_imp_nonempty
% 4.69/4.93 thf(fact_1857_infinite__imp__nonempty,axiom,
% 4.69/4.93 ! [S: set_int] :
% 4.69/4.93 ( ~ ( finite_finite_int @ S )
% 4.69/4.93 => ( S != bot_bot_set_int ) ) ).
% 4.69/4.93
% 4.69/4.93 % infinite_imp_nonempty
% 4.69/4.93 thf(fact_1858_infinite__imp__nonempty,axiom,
% 4.69/4.93 ! [S: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ( ~ ( finite3252695134891459830_nat_o @ S )
% 4.69/4.93 => ( S != bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.93
% 4.69/4.93 % infinite_imp_nonempty
% 4.69/4.93 thf(fact_1859_finite_OemptyI,axiom,
% 4.69/4.93 finite6017078050557962740nteger @ bot_bo3990330152332043303nteger ).
% 4.69/4.93
% 4.69/4.93 % finite.emptyI
% 4.69/4.93 thf(fact_1860_finite_OemptyI,axiom,
% 4.69/4.93 finite4290736615968046902t_unit @ bot_bo3957492148770167129t_unit ).
% 4.69/4.93
% 4.69/4.93 % finite.emptyI
% 4.69/4.93 thf(fact_1861_finite_OemptyI,axiom,
% 4.69/4.93 finite_finite_o @ bot_bot_set_o ).
% 4.69/4.93
% 4.69/4.93 % finite.emptyI
% 4.69/4.93 thf(fact_1862_finite_OemptyI,axiom,
% 4.69/4.93 finite_finite_nat @ bot_bot_set_nat ).
% 4.69/4.93
% 4.69/4.93 % finite.emptyI
% 4.69/4.93 thf(fact_1863_finite_OemptyI,axiom,
% 4.69/4.93 finite_finite_int @ bot_bot_set_int ).
% 4.69/4.93
% 4.69/4.93 % finite.emptyI
% 4.69/4.93 thf(fact_1864_finite_OemptyI,axiom,
% 4.69/4.93 finite3252695134891459830_nat_o @ bot_bo7824918357723582233_nat_o ).
% 4.69/4.93
% 4.69/4.93 % finite.emptyI
% 4.69/4.93 thf(fact_1865_finite_OinsertI,axiom,
% 4.69/4.93 ! [A: set_int,A2: int] :
% 4.69/4.93 ( ( finite_finite_int @ A )
% 4.69/4.93 => ( finite_finite_int @ ( insert_int @ A2 @ A ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite.insertI
% 4.69/4.93 thf(fact_1866_finite_OinsertI,axiom,
% 4.69/4.93 ! [A: set_o,A2: $o] :
% 4.69/4.93 ( ( finite_finite_o @ A )
% 4.69/4.93 => ( finite_finite_o @ ( insert_o @ A2 @ A ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite.insertI
% 4.69/4.93 thf(fact_1867_finite_OinsertI,axiom,
% 4.69/4.93 ! [A: set_Product_unit,A2: product_unit] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.93 => ( finite4290736615968046902t_unit @ ( insert_Product_unit @ A2 @ A ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite.insertI
% 4.69/4.93 thf(fact_1868_finite_OinsertI,axiom,
% 4.69/4.93 ! [A: set_nat,A2: nat] :
% 4.69/4.93 ( ( finite_finite_nat @ A )
% 4.69/4.93 => ( finite_finite_nat @ ( insert_nat @ A2 @ A ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite.insertI
% 4.69/4.93 thf(fact_1869_finite_OinsertI,axiom,
% 4.69/4.93 ! [A: set_Code_integer,A2: code_integer] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.93 => ( finite6017078050557962740nteger @ ( insert_Code_integer @ A2 @ A ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite.insertI
% 4.69/4.93 thf(fact_1870_finite__has__minimal,axiom,
% 4.69/4.93 ! [A: set_Code_integer] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.93 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/4.93 => ? [X3: code_integer] :
% 4.69/4.93 ( ( member_Code_integer @ X3 @ A )
% 4.69/4.93 & ! [Xa2: code_integer] :
% 4.69/4.93 ( ( member_Code_integer @ Xa2 @ A )
% 4.69/4.93 => ( ( ord_le3102999989581377725nteger @ Xa2 @ X3 )
% 4.69/4.93 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_has_minimal
% 4.69/4.93 thf(fact_1871_finite__has__minimal,axiom,
% 4.69/4.93 ! [A: set_Product_unit] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.93 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.93 => ? [X3: product_unit] :
% 4.69/4.93 ( ( member_Product_unit @ X3 @ A )
% 4.69/4.93 & ! [Xa2: product_unit] :
% 4.69/4.93 ( ( member_Product_unit @ Xa2 @ A )
% 4.69/4.93 => ( ( ord_le3221252021190050221t_unit @ Xa2 @ X3 )
% 4.69/4.93 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_has_minimal
% 4.69/4.93 thf(fact_1872_finite__has__minimal,axiom,
% 4.69/4.93 ! [A: set_o] :
% 4.69/4.93 ( ( finite_finite_o @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_o )
% 4.69/4.93 => ? [X3: $o] :
% 4.69/4.93 ( ( member_o @ X3 @ A )
% 4.69/4.93 & ! [Xa2: $o] :
% 4.69/4.93 ( ( member_o @ Xa2 @ A )
% 4.69/4.93 => ( ( ord_less_eq_o @ Xa2 @ X3 )
% 4.69/4.93 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_has_minimal
% 4.69/4.93 thf(fact_1873_finite__has__minimal,axiom,
% 4.69/4.93 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.93 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.93 => ? [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( member6576561426505652726_nat_o @ X3 @ A )
% 4.69/4.93 & ! [Xa2: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( member6576561426505652726_nat_o @ Xa2 @ A )
% 4.69/4.93 => ( ( ord_le729326519192465773_nat_o @ Xa2 @ X3 )
% 4.69/4.93 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_has_minimal
% 4.69/4.93 thf(fact_1874_finite__has__minimal,axiom,
% 4.69/4.93 ! [A: set_filter_nat] :
% 4.69/4.93 ( ( finite2119507909894593271er_nat @ A )
% 4.69/4.93 => ( ( A != bot_bo498966703094740906er_nat )
% 4.69/4.93 => ? [X3: filter_nat] :
% 4.69/4.93 ( ( member_filter_nat @ X3 @ A )
% 4.69/4.93 & ! [Xa2: filter_nat] :
% 4.69/4.93 ( ( member_filter_nat @ Xa2 @ A )
% 4.69/4.93 => ( ( ord_le2510731241096832064er_nat @ Xa2 @ X3 )
% 4.69/4.93 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_has_minimal
% 4.69/4.93 thf(fact_1875_finite__has__minimal,axiom,
% 4.69/4.93 ! [A: set_set_nat] :
% 4.69/4.93 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_set_nat )
% 4.69/4.93 => ? [X3: set_nat] :
% 4.69/4.93 ( ( member_set_nat @ X3 @ A )
% 4.69/4.93 & ! [Xa2: set_nat] :
% 4.69/4.93 ( ( member_set_nat @ Xa2 @ A )
% 4.69/4.93 => ( ( ord_less_eq_set_nat @ Xa2 @ X3 )
% 4.69/4.93 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_has_minimal
% 4.69/4.93 thf(fact_1876_finite__has__minimal,axiom,
% 4.69/4.93 ! [A: set_rat] :
% 4.69/4.93 ( ( finite_finite_rat @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_rat )
% 4.69/4.93 => ? [X3: rat] :
% 4.69/4.93 ( ( member_rat @ X3 @ A )
% 4.69/4.93 & ! [Xa2: rat] :
% 4.69/4.93 ( ( member_rat @ Xa2 @ A )
% 4.69/4.93 => ( ( ord_less_eq_rat @ Xa2 @ X3 )
% 4.69/4.93 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_has_minimal
% 4.69/4.93 thf(fact_1877_finite__has__minimal,axiom,
% 4.69/4.93 ! [A: set_nat] :
% 4.69/4.93 ( ( finite_finite_nat @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_nat )
% 4.69/4.93 => ? [X3: nat] :
% 4.69/4.93 ( ( member_nat @ X3 @ A )
% 4.69/4.93 & ! [Xa2: nat] :
% 4.69/4.93 ( ( member_nat @ Xa2 @ A )
% 4.69/4.93 => ( ( ord_less_eq_nat @ Xa2 @ X3 )
% 4.69/4.93 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_has_minimal
% 4.69/4.93 thf(fact_1878_finite__has__minimal,axiom,
% 4.69/4.93 ! [A: set_int] :
% 4.69/4.93 ( ( finite_finite_int @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_int )
% 4.69/4.93 => ? [X3: int] :
% 4.69/4.93 ( ( member_int @ X3 @ A )
% 4.69/4.93 & ! [Xa2: int] :
% 4.69/4.93 ( ( member_int @ Xa2 @ A )
% 4.69/4.93 => ( ( ord_less_eq_int @ Xa2 @ X3 )
% 4.69/4.93 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_has_minimal
% 4.69/4.93 thf(fact_1879_finite__has__maximal,axiom,
% 4.69/4.93 ! [A: set_Code_integer] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.93 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/4.93 => ? [X3: code_integer] :
% 4.69/4.93 ( ( member_Code_integer @ X3 @ A )
% 4.69/4.93 & ! [Xa2: code_integer] :
% 4.69/4.93 ( ( member_Code_integer @ Xa2 @ A )
% 4.69/4.93 => ( ( ord_le3102999989581377725nteger @ X3 @ Xa2 )
% 4.69/4.93 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_has_maximal
% 4.69/4.93 thf(fact_1880_finite__has__maximal,axiom,
% 4.69/4.93 ! [A: set_Product_unit] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.93 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.93 => ? [X3: product_unit] :
% 4.69/4.93 ( ( member_Product_unit @ X3 @ A )
% 4.69/4.93 & ! [Xa2: product_unit] :
% 4.69/4.93 ( ( member_Product_unit @ Xa2 @ A )
% 4.69/4.93 => ( ( ord_le3221252021190050221t_unit @ X3 @ Xa2 )
% 4.69/4.93 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_has_maximal
% 4.69/4.93 thf(fact_1881_finite__has__maximal,axiom,
% 4.69/4.93 ! [A: set_o] :
% 4.69/4.93 ( ( finite_finite_o @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_o )
% 4.69/4.93 => ? [X3: $o] :
% 4.69/4.93 ( ( member_o @ X3 @ A )
% 4.69/4.93 & ! [Xa2: $o] :
% 4.69/4.93 ( ( member_o @ Xa2 @ A )
% 4.69/4.93 => ( ( ord_less_eq_o @ X3 @ Xa2 )
% 4.69/4.93 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_has_maximal
% 4.69/4.93 thf(fact_1882_finite__has__maximal,axiom,
% 4.69/4.93 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.93 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.93 => ? [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( member6576561426505652726_nat_o @ X3 @ A )
% 4.69/4.93 & ! [Xa2: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( member6576561426505652726_nat_o @ Xa2 @ A )
% 4.69/4.93 => ( ( ord_le729326519192465773_nat_o @ X3 @ Xa2 )
% 4.69/4.93 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_has_maximal
% 4.69/4.93 thf(fact_1883_finite__has__maximal,axiom,
% 4.69/4.93 ! [A: set_filter_nat] :
% 4.69/4.93 ( ( finite2119507909894593271er_nat @ A )
% 4.69/4.93 => ( ( A != bot_bo498966703094740906er_nat )
% 4.69/4.93 => ? [X3: filter_nat] :
% 4.69/4.93 ( ( member_filter_nat @ X3 @ A )
% 4.69/4.93 & ! [Xa2: filter_nat] :
% 4.69/4.93 ( ( member_filter_nat @ Xa2 @ A )
% 4.69/4.93 => ( ( ord_le2510731241096832064er_nat @ X3 @ Xa2 )
% 4.69/4.93 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_has_maximal
% 4.69/4.93 thf(fact_1884_finite__has__maximal,axiom,
% 4.69/4.93 ! [A: set_set_nat] :
% 4.69/4.93 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_set_nat )
% 4.69/4.93 => ? [X3: set_nat] :
% 4.69/4.93 ( ( member_set_nat @ X3 @ A )
% 4.69/4.93 & ! [Xa2: set_nat] :
% 4.69/4.93 ( ( member_set_nat @ Xa2 @ A )
% 4.69/4.93 => ( ( ord_less_eq_set_nat @ X3 @ Xa2 )
% 4.69/4.93 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_has_maximal
% 4.69/4.93 thf(fact_1885_finite__has__maximal,axiom,
% 4.69/4.93 ! [A: set_rat] :
% 4.69/4.93 ( ( finite_finite_rat @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_rat )
% 4.69/4.93 => ? [X3: rat] :
% 4.69/4.93 ( ( member_rat @ X3 @ A )
% 4.69/4.93 & ! [Xa2: rat] :
% 4.69/4.93 ( ( member_rat @ Xa2 @ A )
% 4.69/4.93 => ( ( ord_less_eq_rat @ X3 @ Xa2 )
% 4.69/4.93 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_has_maximal
% 4.69/4.93 thf(fact_1886_finite__has__maximal,axiom,
% 4.69/4.93 ! [A: set_nat] :
% 4.69/4.93 ( ( finite_finite_nat @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_nat )
% 4.69/4.93 => ? [X3: nat] :
% 4.69/4.93 ( ( member_nat @ X3 @ A )
% 4.69/4.93 & ! [Xa2: nat] :
% 4.69/4.93 ( ( member_nat @ Xa2 @ A )
% 4.69/4.93 => ( ( ord_less_eq_nat @ X3 @ Xa2 )
% 4.69/4.93 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_has_maximal
% 4.69/4.93 thf(fact_1887_finite__has__maximal,axiom,
% 4.69/4.93 ! [A: set_int] :
% 4.69/4.93 ( ( finite_finite_int @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_int )
% 4.69/4.93 => ? [X3: int] :
% 4.69/4.93 ( ( member_int @ X3 @ A )
% 4.69/4.93 & ! [Xa2: int] :
% 4.69/4.93 ( ( member_int @ Xa2 @ A )
% 4.69/4.93 => ( ( ord_less_eq_int @ X3 @ Xa2 )
% 4.69/4.93 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_has_maximal
% 4.69/4.93 thf(fact_1888_finite_Ocases,axiom,
% 4.69/4.93 ! [A2: set_Code_integer] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ A2 )
% 4.69/4.93 => ( ( A2 != bot_bo3990330152332043303nteger )
% 4.69/4.93 => ~ ! [A9: set_Code_integer] :
% 4.69/4.93 ( ? [A4: code_integer] :
% 4.69/4.93 ( A2
% 4.69/4.93 = ( insert_Code_integer @ A4 @ A9 ) )
% 4.69/4.93 => ~ ( finite6017078050557962740nteger @ A9 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite.cases
% 4.69/4.93 thf(fact_1889_finite_Ocases,axiom,
% 4.69/4.93 ! [A2: set_Product_unit] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ A2 )
% 4.69/4.93 => ( ( A2 != bot_bo3957492148770167129t_unit )
% 4.69/4.93 => ~ ! [A9: set_Product_unit] :
% 4.69/4.93 ( ? [A4: product_unit] :
% 4.69/4.93 ( A2
% 4.69/4.93 = ( insert_Product_unit @ A4 @ A9 ) )
% 4.69/4.93 => ~ ( finite4290736615968046902t_unit @ A9 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite.cases
% 4.69/4.93 thf(fact_1890_finite_Ocases,axiom,
% 4.69/4.93 ! [A2: set_o] :
% 4.69/4.93 ( ( finite_finite_o @ A2 )
% 4.69/4.93 => ( ( A2 != bot_bot_set_o )
% 4.69/4.93 => ~ ! [A9: set_o] :
% 4.69/4.93 ( ? [A4: $o] :
% 4.69/4.93 ( A2
% 4.69/4.93 = ( insert_o @ A4 @ A9 ) )
% 4.69/4.93 => ~ ( finite_finite_o @ A9 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite.cases
% 4.69/4.93 thf(fact_1891_finite_Ocases,axiom,
% 4.69/4.93 ! [A2: set_nat] :
% 4.69/4.93 ( ( finite_finite_nat @ A2 )
% 4.69/4.93 => ( ( A2 != bot_bot_set_nat )
% 4.69/4.93 => ~ ! [A9: set_nat] :
% 4.69/4.93 ( ? [A4: nat] :
% 4.69/4.93 ( A2
% 4.69/4.93 = ( insert_nat @ A4 @ A9 ) )
% 4.69/4.93 => ~ ( finite_finite_nat @ A9 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite.cases
% 4.69/4.93 thf(fact_1892_finite_Ocases,axiom,
% 4.69/4.93 ! [A2: set_int] :
% 4.69/4.93 ( ( finite_finite_int @ A2 )
% 4.69/4.93 => ( ( A2 != bot_bot_set_int )
% 4.69/4.93 => ~ ! [A9: set_int] :
% 4.69/4.93 ( ? [A4: int] :
% 4.69/4.93 ( A2
% 4.69/4.93 = ( insert_int @ A4 @ A9 ) )
% 4.69/4.93 => ~ ( finite_finite_int @ A9 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite.cases
% 4.69/4.93 thf(fact_1893_finite_Ocases,axiom,
% 4.69/4.93 ! [A2: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ( ( finite3252695134891459830_nat_o @ A2 )
% 4.69/4.93 => ( ( A2 != bot_bo7824918357723582233_nat_o )
% 4.69/4.93 => ~ ! [A9: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ( ? [A4: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( A2
% 4.69/4.93 = ( insert5175938949040314269_nat_o @ A4 @ A9 ) )
% 4.69/4.93 => ~ ( finite3252695134891459830_nat_o @ A9 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite.cases
% 4.69/4.93 thf(fact_1894_min__ext__compat,axiom,
% 4.69/4.93 ! [R3: set_Pr5094982260447487303t_unit,S: set_Pr5094982260447487303t_unit] :
% 4.69/4.93 ( ( ord_le930853871177014503t_unit @ ( relcom848357998638694028t_unit @ R3 @ S ) @ R3 )
% 4.69/4.93 => ( ord_le8072594200992201959t_unit @ ( relcom7108816970757792620t_unit @ ( min_ext_Product_unit @ R3 ) @ ( sup_su3573767163274163995t_unit @ ( min_ext_Product_unit @ S ) @ ( insert6793119152790066487t_unit @ ( produc7269801343787132631t_unit @ bot_bo3957492148770167129t_unit @ bot_bo3957492148770167129t_unit ) @ bot_bo5113747506523071411t_unit ) ) ) @ ( min_ext_Product_unit @ R3 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % min_ext_compat
% 4.69/4.93 thf(fact_1895_min__ext__compat,axiom,
% 4.69/4.93 ! [R3: set_Product_prod_o_o,S: set_Product_prod_o_o] :
% 4.69/4.93 ( ( ord_le192195778054999463od_o_o @ ( relcomp_o_o_o @ R3 @ S ) @ R3 )
% 4.69/4.93 => ( ord_le2885120122233735591_set_o @ ( relcom7534720040753365047_set_o @ ( min_ext_o @ R3 ) @ ( sup_su7766833992073560027_set_o @ ( min_ext_o @ S ) @ ( insert1494450971503307511_set_o @ ( produc5838405689764958487_set_o @ bot_bot_set_o @ bot_bot_set_o ) @ bot_bo8143257439550059635_set_o ) ) ) @ ( min_ext_o @ R3 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % min_ext_compat
% 4.69/4.93 thf(fact_1896_min__ext__compat,axiom,
% 4.69/4.93 ! [R3: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 4.69/4.93 ( ( ord_le3146513528884898305at_nat @ ( relcomp_nat_nat_nat @ R3 @ S ) @ R3 )
% 4.69/4.93 => ( ord_le4402255868550298733et_nat @ ( relcom236561585145426837et_nat @ ( min_ext_nat @ R3 ) @ ( sup_su4251893418135750817et_nat @ ( min_ext_nat @ S ) @ ( insert3810226134351308605et_nat @ ( produc4532415448927165861et_nat @ bot_bot_set_nat @ bot_bot_set_nat ) @ bot_bo4952753636535259449et_nat ) ) ) @ ( min_ext_nat @ R3 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % min_ext_compat
% 4.69/4.93 thf(fact_1897_min__ext__compat,axiom,
% 4.69/4.93 ! [R3: set_Pr958786334691620121nt_int,S: set_Pr958786334691620121nt_int] :
% 4.69/4.93 ( ( ord_le2843351958646193337nt_int @ ( relcomp_int_int_int @ R3 @ S ) @ R3 )
% 4.69/4.93 => ( ord_le1436784781161120549et_int @ ( relcom4034950705519254697et_int @ ( min_ext_int @ R3 ) @ ( sup_su1286422330746572633et_int @ ( min_ext_int @ S ) @ ( insert7328952640415156725et_int @ ( produc6363374080413544029et_int @ bot_bot_set_int @ bot_bot_set_int ) @ bot_bo1987282549146081265et_int ) ) ) @ ( min_ext_int @ R3 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % min_ext_compat
% 4.69/4.93 thf(fact_1898_min__ext__compat,axiom,
% 4.69/4.93 ! [R3: set_Pr2161125870931222855_nat_o,S: set_Pr2161125870931222855_nat_o] :
% 4.69/4.93 ( ( ord_le6659818918159358183_nat_o @ ( relcom6251035627269349452_nat_o @ R3 @ S ) @ R3 )
% 4.69/4.93 => ( ord_le8001614231985977575_nat_o @ ( relcom7236094467932586796_nat_o @ ( min_ex3730736537596016502_nat_o @ R3 ) @ ( sup_su4863159966000489243_nat_o @ ( min_ex3730736537596016502_nat_o @ S ) @ ( insert3244108804717745463_nat_o @ ( produc5149316574908490455_nat_o @ bot_bo7824918357723582233_nat_o @ bot_bo7824918357723582233_nat_o ) @ bot_bo7535334947429593011_nat_o ) ) ) @ ( min_ex3730736537596016502_nat_o @ R3 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % min_ext_compat
% 4.69/4.93 thf(fact_1899_arg__min__least,axiom,
% 4.69/4.93 ! [S: set_Code_integer,Y: code_integer,F: code_integer > rat] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ S )
% 4.69/4.93 => ( ( S != bot_bo3990330152332043303nteger )
% 4.69/4.93 => ( ( member_Code_integer @ Y @ S )
% 4.69/4.93 => ( ord_less_eq_rat @ ( F @ ( lattic5439806495466278992er_rat @ F @ S ) ) @ ( F @ Y ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % arg_min_least
% 4.69/4.93 thf(fact_1900_arg__min__least,axiom,
% 4.69/4.93 ! [S: set_Product_unit,Y: product_unit,F: product_unit > rat] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ S )
% 4.69/4.93 => ( ( S != bot_bo3957492148770167129t_unit )
% 4.69/4.93 => ( ( member_Product_unit @ Y @ S )
% 4.69/4.93 => ( ord_less_eq_rat @ ( F @ ( lattic725702332050428812it_rat @ F @ S ) ) @ ( F @ Y ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % arg_min_least
% 4.69/4.93 thf(fact_1901_arg__min__least,axiom,
% 4.69/4.93 ! [S: set_o,Y: $o,F: $o > rat] :
% 4.69/4.93 ( ( finite_finite_o @ S )
% 4.69/4.93 => ( ( S != bot_bot_set_o )
% 4.69/4.93 => ( ( member_o @ Y @ S )
% 4.69/4.93 => ( ord_less_eq_rat @ ( F @ ( lattic2140725968369957399_o_rat @ F @ S ) ) @ ( F @ Y ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % arg_min_least
% 4.69/4.93 thf(fact_1902_arg__min__least,axiom,
% 4.69/4.93 ! [S: set_nat,Y: nat,F: nat > rat] :
% 4.69/4.93 ( ( finite_finite_nat @ S )
% 4.69/4.93 => ( ( S != bot_bot_set_nat )
% 4.69/4.93 => ( ( member_nat @ Y @ S )
% 4.69/4.93 => ( ord_less_eq_rat @ ( F @ ( lattic6811802900495863747at_rat @ F @ S ) ) @ ( F @ Y ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % arg_min_least
% 4.69/4.93 thf(fact_1903_arg__min__least,axiom,
% 4.69/4.93 ! [S: set_int,Y: int,F: int > rat] :
% 4.69/4.93 ( ( finite_finite_int @ S )
% 4.69/4.93 => ( ( S != bot_bot_set_int )
% 4.69/4.93 => ( ( member_int @ Y @ S )
% 4.69/4.93 => ( ord_less_eq_rat @ ( F @ ( lattic7811156612396918303nt_rat @ F @ S ) ) @ ( F @ Y ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % arg_min_least
% 4.69/4.93 thf(fact_1904_arg__min__least,axiom,
% 4.69/4.93 ! [S: set_Code_integer,Y: code_integer,F: code_integer > nat] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ S )
% 4.69/4.93 => ( ( S != bot_bo3990330152332043303nteger )
% 4.69/4.93 => ( ( member_Code_integer @ Y @ S )
% 4.69/4.93 => ( ord_less_eq_nat @ ( F @ ( lattic6074936555552774728er_nat @ F @ S ) ) @ ( F @ Y ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % arg_min_least
% 4.69/4.93 thf(fact_1905_arg__min__least,axiom,
% 4.69/4.93 ! [S: set_Product_unit,Y: product_unit,F: product_unit > nat] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ S )
% 4.69/4.93 => ( ( S != bot_bo3957492148770167129t_unit )
% 4.69/4.93 => ( ( member_Product_unit @ Y @ S )
% 4.69/4.93 => ( ord_less_eq_nat @ ( F @ ( lattic1360832392136924548it_nat @ F @ S ) ) @ ( F @ Y ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % arg_min_least
% 4.69/4.93 thf(fact_1906_arg__min__least,axiom,
% 4.69/4.93 ! [S: set_o,Y: $o,F: $o > nat] :
% 4.69/4.93 ( ( finite_finite_o @ S )
% 4.69/4.93 => ( ( S != bot_bot_set_o )
% 4.69/4.93 => ( ( member_o @ Y @ S )
% 4.69/4.93 => ( ord_less_eq_nat @ ( F @ ( lattic2775856028456453135_o_nat @ F @ S ) ) @ ( F @ Y ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % arg_min_least
% 4.69/4.93 thf(fact_1907_arg__min__least,axiom,
% 4.69/4.93 ! [S: set_nat,Y: nat,F: nat > nat] :
% 4.69/4.93 ( ( finite_finite_nat @ S )
% 4.69/4.93 => ( ( S != bot_bot_set_nat )
% 4.69/4.93 => ( ( member_nat @ Y @ S )
% 4.69/4.93 => ( ord_less_eq_nat @ ( F @ ( lattic7446932960582359483at_nat @ F @ S ) ) @ ( F @ Y ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % arg_min_least
% 4.69/4.93 thf(fact_1908_arg__min__least,axiom,
% 4.69/4.93 ! [S: set_int,Y: int,F: int > nat] :
% 4.69/4.93 ( ( finite_finite_int @ S )
% 4.69/4.93 => ( ( S != bot_bot_set_int )
% 4.69/4.93 => ( ( member_int @ Y @ S )
% 4.69/4.93 => ( ord_less_eq_nat @ ( F @ ( lattic8446286672483414039nt_nat @ F @ S ) ) @ ( F @ Y ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % arg_min_least
% 4.69/4.93 thf(fact_1909_Total__subset__Id,axiom,
% 4.69/4.93 ! [R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.93 ( ( total_on_nat @ ( field_nat @ R2 ) @ R2 )
% 4.69/4.93 => ( ( ord_le3146513528884898305at_nat @ R2 @ id_nat )
% 4.69/4.93 => ( ( R2 = bot_bo2099793752762293965at_nat )
% 4.69/4.93 | ? [A4: nat] :
% 4.69/4.93 ( R2
% 4.69/4.93 = ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A4 @ A4 ) @ bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Total_subset_Id
% 4.69/4.93 thf(fact_1910_Total__subset__Id,axiom,
% 4.69/4.93 ! [R2: set_Pr958786334691620121nt_int] :
% 4.69/4.93 ( ( total_on_int @ ( field_int @ R2 ) @ R2 )
% 4.69/4.93 => ( ( ord_le2843351958646193337nt_int @ R2 @ id_int )
% 4.69/4.93 => ( ( R2 = bot_bo1796632182523588997nt_int )
% 4.69/4.93 | ? [A4: int] :
% 4.69/4.93 ( R2
% 4.69/4.93 = ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A4 @ A4 ) @ bot_bo1796632182523588997nt_int ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Total_subset_Id
% 4.69/4.93 thf(fact_1911_finite__transitivity__chain,axiom,
% 4.69/4.93 ! [A: set_Code_integer,R3: code_integer > code_integer > $o] :
% 4.69/4.93 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.93 => ( ! [X3: code_integer] :
% 4.69/4.93 ~ ( R3 @ X3 @ X3 )
% 4.69/4.93 => ( ! [X3: code_integer,Y2: code_integer,Z3: code_integer] :
% 4.69/4.93 ( ( R3 @ X3 @ Y2 )
% 4.69/4.93 => ( ( R3 @ Y2 @ Z3 )
% 4.69/4.93 => ( R3 @ X3 @ Z3 ) ) )
% 4.69/4.93 => ( ! [X3: code_integer] :
% 4.69/4.93 ( ( member_Code_integer @ X3 @ A )
% 4.69/4.93 => ? [Y5: code_integer] :
% 4.69/4.93 ( ( member_Code_integer @ Y5 @ A )
% 4.69/4.93 & ( R3 @ X3 @ Y5 ) ) )
% 4.69/4.93 => ( A = bot_bo3990330152332043303nteger ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_transitivity_chain
% 4.69/4.93 thf(fact_1912_finite__transitivity__chain,axiom,
% 4.69/4.93 ! [A: set_Product_unit,R3: product_unit > product_unit > $o] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.93 => ( ! [X3: product_unit] :
% 4.69/4.93 ~ ( R3 @ X3 @ X3 )
% 4.69/4.93 => ( ! [X3: product_unit,Y2: product_unit,Z3: product_unit] :
% 4.69/4.93 ( ( R3 @ X3 @ Y2 )
% 4.69/4.93 => ( ( R3 @ Y2 @ Z3 )
% 4.69/4.93 => ( R3 @ X3 @ Z3 ) ) )
% 4.69/4.93 => ( ! [X3: product_unit] :
% 4.69/4.93 ( ( member_Product_unit @ X3 @ A )
% 4.69/4.93 => ? [Y5: product_unit] :
% 4.69/4.93 ( ( member_Product_unit @ Y5 @ A )
% 4.69/4.93 & ( R3 @ X3 @ Y5 ) ) )
% 4.69/4.93 => ( A = bot_bo3957492148770167129t_unit ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_transitivity_chain
% 4.69/4.93 thf(fact_1913_finite__transitivity__chain,axiom,
% 4.69/4.93 ! [A: set_o,R3: $o > $o > $o] :
% 4.69/4.93 ( ( finite_finite_o @ A )
% 4.69/4.93 => ( ! [X3: $o] :
% 4.69/4.93 ~ ( R3 @ X3 @ X3 )
% 4.69/4.93 => ( ! [X3: $o,Y2: $o,Z3: $o] :
% 4.69/4.93 ( ( R3 @ X3 @ Y2 )
% 4.69/4.93 => ( ( R3 @ Y2 @ Z3 )
% 4.69/4.93 => ( R3 @ X3 @ Z3 ) ) )
% 4.69/4.93 => ( ! [X3: $o] :
% 4.69/4.93 ( ( member_o @ X3 @ A )
% 4.69/4.93 => ? [Y5: $o] :
% 4.69/4.93 ( ( member_o @ Y5 @ A )
% 4.69/4.93 & ( R3 @ X3 @ Y5 ) ) )
% 4.69/4.93 => ( A = bot_bot_set_o ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_transitivity_chain
% 4.69/4.93 thf(fact_1914_finite__transitivity__chain,axiom,
% 4.69/4.93 ! [A: set_nat,R3: nat > nat > $o] :
% 4.69/4.93 ( ( finite_finite_nat @ A )
% 4.69/4.93 => ( ! [X3: nat] :
% 4.69/4.93 ~ ( R3 @ X3 @ X3 )
% 4.69/4.93 => ( ! [X3: nat,Y2: nat,Z3: nat] :
% 4.69/4.93 ( ( R3 @ X3 @ Y2 )
% 4.69/4.93 => ( ( R3 @ Y2 @ Z3 )
% 4.69/4.93 => ( R3 @ X3 @ Z3 ) ) )
% 4.69/4.93 => ( ! [X3: nat] :
% 4.69/4.93 ( ( member_nat @ X3 @ A )
% 4.69/4.93 => ? [Y5: nat] :
% 4.69/4.93 ( ( member_nat @ Y5 @ A )
% 4.69/4.93 & ( R3 @ X3 @ Y5 ) ) )
% 4.69/4.93 => ( A = bot_bot_set_nat ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_transitivity_chain
% 4.69/4.93 thf(fact_1915_finite__transitivity__chain,axiom,
% 4.69/4.93 ! [A: set_int,R3: int > int > $o] :
% 4.69/4.93 ( ( finite_finite_int @ A )
% 4.69/4.93 => ( ! [X3: int] :
% 4.69/4.93 ~ ( R3 @ X3 @ X3 )
% 4.69/4.93 => ( ! [X3: int,Y2: int,Z3: int] :
% 4.69/4.93 ( ( R3 @ X3 @ Y2 )
% 4.69/4.93 => ( ( R3 @ Y2 @ Z3 )
% 4.69/4.93 => ( R3 @ X3 @ Z3 ) ) )
% 4.69/4.93 => ( ! [X3: int] :
% 4.69/4.93 ( ( member_int @ X3 @ A )
% 4.69/4.93 => ? [Y5: int] :
% 4.69/4.93 ( ( member_int @ Y5 @ A )
% 4.69/4.93 & ( R3 @ X3 @ Y5 ) ) )
% 4.69/4.93 => ( A = bot_bot_set_int ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_transitivity_chain
% 4.69/4.93 thf(fact_1916_finite__transitivity__chain,axiom,
% 4.69/4.93 ! [A: set_Pr4532377907799695533_nat_o,R3: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o] :
% 4.69/4.93 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.93 => ( ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ~ ( R3 @ X3 @ X3 )
% 4.69/4.93 => ( ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat > $o,Z3: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( R3 @ X3 @ Y2 )
% 4.69/4.93 => ( ( R3 @ Y2 @ Z3 )
% 4.69/4.93 => ( R3 @ X3 @ Z3 ) ) )
% 4.69/4.93 => ( ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( member6576561426505652726_nat_o @ X3 @ A )
% 4.69/4.93 => ? [Y5: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( member6576561426505652726_nat_o @ Y5 @ A )
% 4.69/4.93 & ( R3 @ X3 @ Y5 ) ) )
% 4.69/4.93 => ( A = bot_bo7824918357723582233_nat_o ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % finite_transitivity_chain
% 4.69/4.93 thf(fact_1917_disjnt__equiv__class,axiom,
% 4.69/4.93 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit,A2: product_unit,B: product_unit] :
% 4.69/4.93 ( ( equiv_4189356295871601603t_unit @ A @ R2 )
% 4.69/4.93 => ( ( disjnt_Product_unit @ ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) @ ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.93 = ( ~ ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_equiv_class
% 4.69/4.93 thf(fact_1918_disjnt__equiv__class,axiom,
% 4.69/4.93 ! [A: set_o,R2: set_Product_prod_o_o,A2: $o,B: $o] :
% 4.69/4.93 ( ( equiv_equiv_o @ A @ R2 )
% 4.69/4.93 => ( ( disjnt_o @ ( image_o_o @ R2 @ ( insert_o @ A2 @ bot_bot_set_o ) ) @ ( image_o_o @ R2 @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 4.69/4.93 = ( ~ ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_equiv_class
% 4.69/4.93 thf(fact_1919_disjnt__equiv__class,axiom,
% 4.69/4.93 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,A2: nat,B: nat] :
% 4.69/4.93 ( ( equiv_equiv_nat @ A @ R2 )
% 4.69/4.93 => ( ( disjnt_nat @ ( image_nat_nat @ R2 @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) @ ( image_nat_nat @ R2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 4.69/4.93 = ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_equiv_class
% 4.69/4.93 thf(fact_1920_disjnt__equiv__class,axiom,
% 4.69/4.93 ! [A: set_int,R2: set_Pr958786334691620121nt_int,A2: int,B: int] :
% 4.69/4.93 ( ( equiv_equiv_int @ A @ R2 )
% 4.69/4.93 => ( ( disjnt_int @ ( image_int_int @ R2 @ ( insert_int @ A2 @ bot_bot_set_int ) ) @ ( image_int_int @ R2 @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 4.69/4.93 = ( ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_equiv_class
% 4.69/4.93 thf(fact_1921_disjnt__equiv__class,axiom,
% 4.69/4.93 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( equiv_6726761681920839555_nat_o @ A @ R2 )
% 4.69/4.93 => ( ( disjnt7869448817988085652_nat_o @ ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) @ ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/4.93 = ( ~ ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ B ) @ R2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_equiv_class
% 4.69/4.93 thf(fact_1922_Sup__fin_Oinsert,axiom,
% 4.69/4.93 ! [A: set_set_nat,X: set_nat] :
% 4.69/4.93 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_set_nat )
% 4.69/4.93 => ( ( lattic3835124923745554447et_nat @ ( insert_set_nat @ X @ A ) )
% 4.69/4.93 = ( sup_sup_set_nat @ X @ ( lattic3835124923745554447et_nat @ A ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Sup_fin.insert
% 4.69/4.93 thf(fact_1923_Sup__fin_Oinsert,axiom,
% 4.69/4.93 ! [A: set_assn,X: assn] :
% 4.69/4.93 ( ( finite_finite_assn @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_assn )
% 4.69/4.93 => ( ( lattic2150320897289308081n_assn @ ( insert_assn @ X @ A ) )
% 4.69/4.93 = ( sup_sup_assn @ X @ ( lattic2150320897289308081n_assn @ A ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Sup_fin.insert
% 4.69/4.93 thf(fact_1924_Sup__fin_Oinsert,axiom,
% 4.69/4.93 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.93 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.93 => ( ( lattic5294303975357428420t_unit @ ( insert_Product_unit @ X @ A ) )
% 4.69/4.93 = ( sup_sup_Product_unit @ X @ ( lattic5294303975357428420t_unit @ A ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Sup_fin.insert
% 4.69/4.93 thf(fact_1925_Sup__fin_Oinsert,axiom,
% 4.69/4.93 ! [A: set_o,X: $o] :
% 4.69/4.93 ( ( finite_finite_o @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_o )
% 4.69/4.93 => ( ( lattic1508158080041050831_fin_o @ ( insert_o @ X @ A ) )
% 4.69/4.93 = ( sup_sup_o @ X @ ( lattic1508158080041050831_fin_o @ A ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Sup_fin.insert
% 4.69/4.93 thf(fact_1926_Sup__fin_Oinsert,axiom,
% 4.69/4.93 ! [A: set_nat,X: nat] :
% 4.69/4.93 ( ( finite_finite_nat @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_nat )
% 4.69/4.93 => ( ( lattic1093996805478795353in_nat @ ( insert_nat @ X @ A ) )
% 4.69/4.93 = ( sup_sup_nat @ X @ ( lattic1093996805478795353in_nat @ A ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Sup_fin.insert
% 4.69/4.93 thf(fact_1927_Sup__fin_Oinsert,axiom,
% 4.69/4.93 ! [A: set_int,X: int] :
% 4.69/4.93 ( ( finite_finite_int @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_int )
% 4.69/4.93 => ( ( lattic1091506334969745077in_int @ ( insert_int @ X @ A ) )
% 4.69/4.93 = ( sup_sup_int @ X @ ( lattic1091506334969745077in_int @ A ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Sup_fin.insert
% 4.69/4.93 thf(fact_1928_Sup__fin_Oinsert,axiom,
% 4.69/4.93 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.93 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.93 => ( ( lattic7320199455484906628_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) )
% 4.69/4.93 = ( sup_su5453871518329203617_nat_o @ X @ ( lattic7320199455484906628_nat_o @ A ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Sup_fin.insert
% 4.69/4.93 thf(fact_1929_Inf__fin_Oinsert,axiom,
% 4.69/4.93 ! [A: set_set_nat,X: set_nat] :
% 4.69/4.93 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_set_nat )
% 4.69/4.93 => ( ( lattic3014633134055518761et_nat @ ( insert_set_nat @ X @ A ) )
% 4.69/4.93 = ( inf_inf_set_nat @ X @ ( lattic3014633134055518761et_nat @ A ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Inf_fin.insert
% 4.69/4.93 thf(fact_1930_Inf__fin_Oinsert,axiom,
% 4.69/4.93 ! [A: set_assn,X: assn] :
% 4.69/4.93 ( ( finite_finite_assn @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_assn )
% 4.69/4.93 => ( ( lattic47131356835913163n_assn @ ( insert_assn @ X @ A ) )
% 4.69/4.93 = ( inf_inf_assn @ X @ ( lattic47131356835913163n_assn @ A ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Inf_fin.insert
% 4.69/4.93 thf(fact_1931_Inf__fin_Oinsert,axiom,
% 4.69/4.93 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.93 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.93 => ( ( lattic1263872656861969706t_unit @ ( insert_Product_unit @ X @ A ) )
% 4.69/4.93 = ( inf_inf_Product_unit @ X @ ( lattic1263872656861969706t_unit @ A ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Inf_fin.insert
% 4.69/4.93 thf(fact_1932_Inf__fin_Oinsert,axiom,
% 4.69/4.93 ! [A: set_o,X: $o] :
% 4.69/4.93 ( ( finite_finite_o @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_o )
% 4.69/4.93 => ( ( lattic4107685809792843317_fin_o @ ( insert_o @ X @ A ) )
% 4.69/4.93 = ( inf_inf_o @ X @ ( lattic4107685809792843317_fin_o @ A ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Inf_fin.insert
% 4.69/4.93 thf(fact_1933_Inf__fin_Oinsert,axiom,
% 4.69/4.93 ! [A: set_nat,X: nat] :
% 4.69/4.93 ( ( finite_finite_nat @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_nat )
% 4.69/4.93 => ( ( lattic5238388535129920115in_nat @ ( insert_nat @ X @ A ) )
% 4.69/4.93 = ( inf_inf_nat @ X @ ( lattic5238388535129920115in_nat @ A ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Inf_fin.insert
% 4.69/4.93 thf(fact_1934_Inf__fin_Oinsert,axiom,
% 4.69/4.93 ! [A: set_int,X: int] :
% 4.69/4.93 ( ( finite_finite_int @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_int )
% 4.69/4.93 => ( ( lattic5235898064620869839in_int @ ( insert_int @ X @ A ) )
% 4.69/4.93 = ( inf_inf_int @ X @ ( lattic5235898064620869839in_int @ A ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Inf_fin.insert
% 4.69/4.93 thf(fact_1935_Inf__fin_Oinsert,axiom,
% 4.69/4.93 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.93 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.93 => ( ( lattic956194824204696298_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) )
% 4.69/4.93 = ( inf_in1318976480646536635_nat_o @ X @ ( lattic956194824204696298_nat_o @ A ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Inf_fin.insert
% 4.69/4.93 thf(fact_1936_in__quotient__imp__in__rel,axiom,
% 4.69/4.93 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit,X4: set_Product_unit,X: product_unit,Y: product_unit] :
% 4.69/4.93 ( ( equiv_4189356295871601603t_unit @ A @ R2 )
% 4.69/4.93 => ( ( member5877623283571906838t_unit @ X4 @ ( equiv_5172566880711946708t_unit @ A @ R2 ) )
% 4.69/4.93 => ( ( ord_le3507040750410214029t_unit @ ( insert_Product_unit @ X @ ( insert_Product_unit @ Y @ bot_bo3957492148770167129t_unit ) ) @ X4 )
% 4.69/4.93 => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X @ Y ) @ R2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % in_quotient_imp_in_rel
% 4.69/4.93 thf(fact_1937_in__quotient__imp__in__rel,axiom,
% 4.69/4.93 ! [A: set_o,R2: set_Product_prod_o_o,X4: set_o,X: $o,Y: $o] :
% 4.69/4.93 ( ( equiv_equiv_o @ A @ R2 )
% 4.69/4.93 => ( ( member_set_o @ X4 @ ( equiv_quotient_o @ A @ R2 ) )
% 4.69/4.93 => ( ( ord_less_eq_set_o @ ( insert_o @ X @ ( insert_o @ Y @ bot_bot_set_o ) ) @ X4 )
% 4.69/4.93 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ R2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % in_quotient_imp_in_rel
% 4.69/4.93 thf(fact_1938_in__quotient__imp__in__rel,axiom,
% 4.69/4.93 ! [A: set_int,R2: set_Pr958786334691620121nt_int,X4: set_int,X: int,Y: int] :
% 4.69/4.93 ( ( equiv_equiv_int @ A @ R2 )
% 4.69/4.93 => ( ( member_set_int @ X4 @ ( equiv_quotient_int @ A @ R2 ) )
% 4.69/4.93 => ( ( ord_less_eq_set_int @ ( insert_int @ X @ ( insert_int @ Y @ bot_bot_set_int ) ) @ X4 )
% 4.69/4.93 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % in_quotient_imp_in_rel
% 4.69/4.93 thf(fact_1939_in__quotient__imp__in__rel,axiom,
% 4.69/4.93 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o,X4: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( equiv_6726761681920839555_nat_o @ A @ R2 )
% 4.69/4.93 => ( ( member1452989533377600726_nat_o @ X4 @ ( equiv_7899955228204526484_nat_o @ A @ R2 ) )
% 4.69/4.93 => ( ( ord_le2965882846123202637_nat_o @ ( insert5175938949040314269_nat_o @ X @ ( insert5175938949040314269_nat_o @ Y @ bot_bo7824918357723582233_nat_o ) ) @ X4 )
% 4.69/4.93 => ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ R2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % in_quotient_imp_in_rel
% 4.69/4.93 thf(fact_1940_in__quotient__imp__in__rel,axiom,
% 4.69/4.93 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,X4: set_nat,X: nat,Y: nat] :
% 4.69/4.93 ( ( equiv_equiv_nat @ A @ R2 )
% 4.69/4.93 => ( ( member_set_nat @ X4 @ ( equiv_quotient_nat @ A @ R2 ) )
% 4.69/4.93 => ( ( ord_less_eq_set_nat @ ( insert_nat @ X @ ( insert_nat @ Y @ bot_bot_set_nat ) ) @ X4 )
% 4.69/4.93 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R2 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % in_quotient_imp_in_rel
% 4.69/4.93 thf(fact_1941_prod__set__simps_I1_J,axiom,
% 4.69/4.93 ! [X: heap_e7401611519738050253t_unit,Y: set_nat] :
% 4.69/4.93 ( ( basic_7833836874476830220et_nat @ ( produc7507926704131184380et_nat @ X @ Y ) )
% 4.69/4.93 = ( insert8563697753282147485t_unit @ X @ bot_bo3686245532977126937t_unit ) ) ).
% 4.69/4.93
% 4.69/4.93 % prod_set_simps(1)
% 4.69/4.93 thf(fact_1942_prod__set__simps_I1_J,axiom,
% 4.69/4.93 ! [X: nat,Y: nat] :
% 4.69/4.93 ( ( basic_fsts_nat_nat @ ( product_Pair_nat_nat @ X @ Y ) )
% 4.69/4.93 = ( insert_nat @ X @ bot_bot_set_nat ) ) ).
% 4.69/4.93
% 4.69/4.93 % prod_set_simps(1)
% 4.69/4.93 thf(fact_1943_prod__set__simps_I1_J,axiom,
% 4.69/4.93 ! [X: int,Y: int] :
% 4.69/4.93 ( ( basic_fsts_int_int @ ( product_Pair_int_int @ X @ Y ) )
% 4.69/4.93 = ( insert_int @ X @ bot_bot_set_int ) ) ).
% 4.69/4.93
% 4.69/4.93 % prod_set_simps(1)
% 4.69/4.93 thf(fact_1944_prod__set__simps_I1_J,axiom,
% 4.69/4.93 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 4.69/4.93 ( ( basic_8654530971723826568et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 4.69/4.93 = ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.93
% 4.69/4.93 % prod_set_simps(1)
% 4.69/4.93 thf(fact_1945_prod__set__simps_I1_J,axiom,
% 4.69/4.93 ! [X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 4.69/4.93 ( ( basic_3966130907827183364et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 4.69/4.93 = ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.93
% 4.69/4.93 % prod_set_simps(1)
% 4.69/4.93 thf(fact_1946_rel__restrict__tranclI,axiom,
% 4.69/4.93 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o,E: set_Pr2161125870931222855_nat_o,R3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ ( transi4009562729418357614_nat_o @ E ) )
% 4.69/4.93 => ( ~ ( member6576561426505652726_nat_o @ X @ R3 )
% 4.69/4.93 => ( ~ ( member6576561426505652726_nat_o @ Y @ R3 )
% 4.69/4.93 => ( ( ord_le2965882846123202637_nat_o @ ( image_2232984160439939859_nat_o @ E @ R3 ) @ R3 )
% 4.69/4.93 => ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ ( transi4009562729418357614_nat_o @ ( rel_re3331361160397388719_nat_o @ E @ R3 ) ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_tranclI
% 4.69/4.93 thf(fact_1947_rel__restrict__tranclI,axiom,
% 4.69/4.93 ! [X: $o,Y: $o,E: set_Product_prod_o_o,R3: set_o] :
% 4.69/4.93 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ ( transitive_trancl_o @ E ) )
% 4.69/4.93 => ( ~ ( member_o @ X @ R3 )
% 4.69/4.93 => ( ~ ( member_o @ Y @ R3 )
% 4.69/4.93 => ( ( ord_less_eq_set_o @ ( image_o_o @ E @ R3 ) @ R3 )
% 4.69/4.93 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ ( transitive_trancl_o @ ( rel_restrict_o @ E @ R3 ) ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_tranclI
% 4.69/4.93 thf(fact_1948_rel__restrict__tranclI,axiom,
% 4.69/4.93 ! [X: product_unit,Y: product_unit,E: set_Pr5094982260447487303t_unit,R3: set_Product_unit] :
% 4.69/4.93 ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X @ Y ) @ ( transi430408012122777006t_unit @ E ) )
% 4.69/4.93 => ( ~ ( member_Product_unit @ X @ R3 )
% 4.69/4.93 => ( ~ ( member_Product_unit @ Y @ R3 )
% 4.69/4.93 => ( ( ord_le3507040750410214029t_unit @ ( image_8431784415008483091t_unit @ E @ R3 ) @ R3 )
% 4.69/4.93 => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X @ Y ) @ ( transi430408012122777006t_unit @ ( rel_re9207996470947987439t_unit @ E @ R3 ) ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_tranclI
% 4.69/4.93 thf(fact_1949_rel__restrict__tranclI,axiom,
% 4.69/4.93 ! [X: int,Y: int,E: set_Pr958786334691620121nt_int,R3: set_int] :
% 4.69/4.93 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi6261509568448316235cl_int @ E ) )
% 4.69/4.93 => ( ~ ( member_int @ X @ R3 )
% 4.69/4.93 => ( ~ ( member_int @ Y @ R3 )
% 4.69/4.93 => ( ( ord_less_eq_set_int @ ( image_int_int @ E @ R3 ) @ R3 )
% 4.69/4.93 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi6261509568448316235cl_int @ ( rel_restrict_int @ E @ R3 ) ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_tranclI
% 4.69/4.93 thf(fact_1950_rel__restrict__tranclI,axiom,
% 4.69/4.93 ! [X: nat,Y: nat,E: set_Pr1261947904930325089at_nat,R3: set_nat] :
% 4.69/4.93 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi6264000038957366511cl_nat @ E ) )
% 4.69/4.93 => ( ~ ( member_nat @ X @ R3 )
% 4.69/4.93 => ( ~ ( member_nat @ Y @ R3 )
% 4.69/4.93 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ E @ R3 ) @ R3 )
% 4.69/4.93 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi6264000038957366511cl_nat @ ( rel_restrict_nat @ E @ R3 ) ) ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_tranclI
% 4.69/4.93 thf(fact_1951_pair__in__Id__conv,axiom,
% 4.69/4.93 ! [A2: nat,B: nat] :
% 4.69/4.93 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ id_nat )
% 4.69/4.93 = ( A2 = B ) ) ).
% 4.69/4.93
% 4.69/4.93 % pair_in_Id_conv
% 4.69/4.93 thf(fact_1952_pair__in__Id__conv,axiom,
% 4.69/4.93 ! [A2: int,B: int] :
% 4.69/4.93 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ id_int )
% 4.69/4.93 = ( A2 = B ) ) ).
% 4.69/4.93
% 4.69/4.93 % pair_in_Id_conv
% 4.69/4.93 thf(fact_1953_IdI,axiom,
% 4.69/4.93 ! [A2: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ A2 ) @ id_nat ) ).
% 4.69/4.93
% 4.69/4.93 % IdI
% 4.69/4.93 thf(fact_1954_IdI,axiom,
% 4.69/4.93 ! [A2: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ A2 ) @ id_int ) ).
% 4.69/4.93
% 4.69/4.93 % IdI
% 4.69/4.93 thf(fact_1955_quotient__empty,axiom,
% 4.69/4.93 ! [R2: set_Pr5094982260447487303t_unit] :
% 4.69/4.93 ( ( equiv_5172566880711946708t_unit @ bot_bo3957492148770167129t_unit @ R2 )
% 4.69/4.93 = bot_bo6284674557190688313t_unit ) ).
% 4.69/4.93
% 4.69/4.93 % quotient_empty
% 4.69/4.93 thf(fact_1956_quotient__empty,axiom,
% 4.69/4.93 ! [R2: set_Product_prod_o_o] :
% 4.69/4.93 ( ( equiv_quotient_o @ bot_bot_set_o @ R2 )
% 4.69/4.93 = bot_bot_set_set_o ) ).
% 4.69/4.93
% 4.69/4.93 % quotient_empty
% 4.69/4.93 thf(fact_1957_quotient__empty,axiom,
% 4.69/4.93 ! [R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.93 ( ( equiv_quotient_nat @ bot_bot_set_nat @ R2 )
% 4.69/4.93 = bot_bot_set_set_nat ) ).
% 4.69/4.93
% 4.69/4.93 % quotient_empty
% 4.69/4.93 thf(fact_1958_quotient__empty,axiom,
% 4.69/4.93 ! [R2: set_Pr958786334691620121nt_int] :
% 4.69/4.93 ( ( equiv_quotient_int @ bot_bot_set_int @ R2 )
% 4.69/4.93 = bot_bot_set_set_int ) ).
% 4.69/4.93
% 4.69/4.93 % quotient_empty
% 4.69/4.93 thf(fact_1959_quotient__empty,axiom,
% 4.69/4.93 ! [R2: set_Pr2161125870931222855_nat_o] :
% 4.69/4.93 ( ( equiv_7899955228204526484_nat_o @ bot_bo7824918357723582233_nat_o @ R2 )
% 4.69/4.93 = bot_bo3736544561982865913_nat_o ) ).
% 4.69/4.93
% 4.69/4.93 % quotient_empty
% 4.69/4.93 thf(fact_1960_quotient__is__empty,axiom,
% 4.69/4.93 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit] :
% 4.69/4.93 ( ( ( equiv_5172566880711946708t_unit @ A @ R2 )
% 4.69/4.93 = bot_bo6284674557190688313t_unit )
% 4.69/4.93 = ( A = bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.93
% 4.69/4.93 % quotient_is_empty
% 4.69/4.93 thf(fact_1961_quotient__is__empty,axiom,
% 4.69/4.93 ! [A: set_o,R2: set_Product_prod_o_o] :
% 4.69/4.93 ( ( ( equiv_quotient_o @ A @ R2 )
% 4.69/4.93 = bot_bot_set_set_o )
% 4.69/4.93 = ( A = bot_bot_set_o ) ) ).
% 4.69/4.93
% 4.69/4.93 % quotient_is_empty
% 4.69/4.93 thf(fact_1962_quotient__is__empty,axiom,
% 4.69/4.93 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.93 ( ( ( equiv_quotient_nat @ A @ R2 )
% 4.69/4.93 = bot_bot_set_set_nat )
% 4.69/4.93 = ( A = bot_bot_set_nat ) ) ).
% 4.69/4.93
% 4.69/4.93 % quotient_is_empty
% 4.69/4.93 thf(fact_1963_quotient__is__empty,axiom,
% 4.69/4.93 ! [A: set_int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.93 ( ( ( equiv_quotient_int @ A @ R2 )
% 4.69/4.93 = bot_bot_set_set_int )
% 4.69/4.93 = ( A = bot_bot_set_int ) ) ).
% 4.69/4.93
% 4.69/4.93 % quotient_is_empty
% 4.69/4.93 thf(fact_1964_quotient__is__empty,axiom,
% 4.69/4.93 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o] :
% 4.69/4.93 ( ( ( equiv_7899955228204526484_nat_o @ A @ R2 )
% 4.69/4.93 = bot_bo3736544561982865913_nat_o )
% 4.69/4.93 = ( A = bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.93
% 4.69/4.93 % quotient_is_empty
% 4.69/4.93 thf(fact_1965_quotient__is__empty2,axiom,
% 4.69/4.93 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit] :
% 4.69/4.93 ( ( bot_bo6284674557190688313t_unit
% 4.69/4.93 = ( equiv_5172566880711946708t_unit @ A @ R2 ) )
% 4.69/4.93 = ( A = bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.93
% 4.69/4.93 % quotient_is_empty2
% 4.69/4.93 thf(fact_1966_quotient__is__empty2,axiom,
% 4.69/4.93 ! [A: set_o,R2: set_Product_prod_o_o] :
% 4.69/4.93 ( ( bot_bot_set_set_o
% 4.69/4.93 = ( equiv_quotient_o @ A @ R2 ) )
% 4.69/4.93 = ( A = bot_bot_set_o ) ) ).
% 4.69/4.93
% 4.69/4.93 % quotient_is_empty2
% 4.69/4.93 thf(fact_1967_quotient__is__empty2,axiom,
% 4.69/4.93 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.93 ( ( bot_bot_set_set_nat
% 4.69/4.93 = ( equiv_quotient_nat @ A @ R2 ) )
% 4.69/4.93 = ( A = bot_bot_set_nat ) ) ).
% 4.69/4.93
% 4.69/4.93 % quotient_is_empty2
% 4.69/4.93 thf(fact_1968_quotient__is__empty2,axiom,
% 4.69/4.93 ! [A: set_int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.93 ( ( bot_bot_set_set_int
% 4.69/4.93 = ( equiv_quotient_int @ A @ R2 ) )
% 4.69/4.93 = ( A = bot_bot_set_int ) ) ).
% 4.69/4.93
% 4.69/4.93 % quotient_is_empty2
% 4.69/4.93 thf(fact_1969_quotient__is__empty2,axiom,
% 4.69/4.93 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o] :
% 4.69/4.93 ( ( bot_bo3736544561982865913_nat_o
% 4.69/4.93 = ( equiv_7899955228204526484_nat_o @ A @ R2 ) )
% 4.69/4.93 = ( A = bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.93
% 4.69/4.93 % quotient_is_empty2
% 4.69/4.93 thf(fact_1970_disjnt__self__iff__empty,axiom,
% 4.69/4.93 ! [S: set_Product_unit] :
% 4.69/4.93 ( ( disjnt_Product_unit @ S @ S )
% 4.69/4.93 = ( S = bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_self_iff_empty
% 4.69/4.93 thf(fact_1971_disjnt__self__iff__empty,axiom,
% 4.69/4.93 ! [S: set_o] :
% 4.69/4.93 ( ( disjnt_o @ S @ S )
% 4.69/4.93 = ( S = bot_bot_set_o ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_self_iff_empty
% 4.69/4.93 thf(fact_1972_disjnt__self__iff__empty,axiom,
% 4.69/4.93 ! [S: set_nat] :
% 4.69/4.93 ( ( disjnt_nat @ S @ S )
% 4.69/4.93 = ( S = bot_bot_set_nat ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_self_iff_empty
% 4.69/4.93 thf(fact_1973_disjnt__self__iff__empty,axiom,
% 4.69/4.93 ! [S: set_int] :
% 4.69/4.93 ( ( disjnt_int @ S @ S )
% 4.69/4.93 = ( S = bot_bot_set_int ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_self_iff_empty
% 4.69/4.93 thf(fact_1974_disjnt__self__iff__empty,axiom,
% 4.69/4.93 ! [S: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ( ( disjnt7869448817988085652_nat_o @ S @ S )
% 4.69/4.93 = ( S = bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_self_iff_empty
% 4.69/4.93 thf(fact_1975_disjnt__insert1,axiom,
% 4.69/4.93 ! [A2: produc3658429121746597890et_nat > $o,X4: set_Pr4532377907799695533_nat_o,Y6: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ( ( disjnt7869448817988085652_nat_o @ ( insert5175938949040314269_nat_o @ A2 @ X4 ) @ Y6 )
% 4.69/4.93 = ( ~ ( member6576561426505652726_nat_o @ A2 @ Y6 )
% 4.69/4.93 & ( disjnt7869448817988085652_nat_o @ X4 @ Y6 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_insert1
% 4.69/4.93 thf(fact_1976_disjnt__insert1,axiom,
% 4.69/4.93 ! [A2: nat,X4: set_nat,Y6: set_nat] :
% 4.69/4.93 ( ( disjnt_nat @ ( insert_nat @ A2 @ X4 ) @ Y6 )
% 4.69/4.93 = ( ~ ( member_nat @ A2 @ Y6 )
% 4.69/4.93 & ( disjnt_nat @ X4 @ Y6 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_insert1
% 4.69/4.93 thf(fact_1977_disjnt__insert1,axiom,
% 4.69/4.93 ! [A2: int,X4: set_int,Y6: set_int] :
% 4.69/4.93 ( ( disjnt_int @ ( insert_int @ A2 @ X4 ) @ Y6 )
% 4.69/4.93 = ( ~ ( member_int @ A2 @ Y6 )
% 4.69/4.93 & ( disjnt_int @ X4 @ Y6 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_insert1
% 4.69/4.93 thf(fact_1978_disjnt__insert1,axiom,
% 4.69/4.93 ! [A2: $o,X4: set_o,Y6: set_o] :
% 4.69/4.93 ( ( disjnt_o @ ( insert_o @ A2 @ X4 ) @ Y6 )
% 4.69/4.93 = ( ~ ( member_o @ A2 @ Y6 )
% 4.69/4.93 & ( disjnt_o @ X4 @ Y6 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_insert1
% 4.69/4.93 thf(fact_1979_disjnt__insert1,axiom,
% 4.69/4.93 ! [A2: product_unit,X4: set_Product_unit,Y6: set_Product_unit] :
% 4.69/4.93 ( ( disjnt_Product_unit @ ( insert_Product_unit @ A2 @ X4 ) @ Y6 )
% 4.69/4.93 = ( ~ ( member_Product_unit @ A2 @ Y6 )
% 4.69/4.93 & ( disjnt_Product_unit @ X4 @ Y6 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_insert1
% 4.69/4.93 thf(fact_1980_disjnt__insert2,axiom,
% 4.69/4.93 ! [Y6: set_Pr4532377907799695533_nat_o,A2: produc3658429121746597890et_nat > $o,X4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ( ( disjnt7869448817988085652_nat_o @ Y6 @ ( insert5175938949040314269_nat_o @ A2 @ X4 ) )
% 4.69/4.93 = ( ~ ( member6576561426505652726_nat_o @ A2 @ Y6 )
% 4.69/4.93 & ( disjnt7869448817988085652_nat_o @ Y6 @ X4 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_insert2
% 4.69/4.93 thf(fact_1981_disjnt__insert2,axiom,
% 4.69/4.93 ! [Y6: set_nat,A2: nat,X4: set_nat] :
% 4.69/4.93 ( ( disjnt_nat @ Y6 @ ( insert_nat @ A2 @ X4 ) )
% 4.69/4.93 = ( ~ ( member_nat @ A2 @ Y6 )
% 4.69/4.93 & ( disjnt_nat @ Y6 @ X4 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_insert2
% 4.69/4.93 thf(fact_1982_disjnt__insert2,axiom,
% 4.69/4.93 ! [Y6: set_int,A2: int,X4: set_int] :
% 4.69/4.93 ( ( disjnt_int @ Y6 @ ( insert_int @ A2 @ X4 ) )
% 4.69/4.93 = ( ~ ( member_int @ A2 @ Y6 )
% 4.69/4.93 & ( disjnt_int @ Y6 @ X4 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_insert2
% 4.69/4.93 thf(fact_1983_disjnt__insert2,axiom,
% 4.69/4.93 ! [Y6: set_o,A2: $o,X4: set_o] :
% 4.69/4.93 ( ( disjnt_o @ Y6 @ ( insert_o @ A2 @ X4 ) )
% 4.69/4.93 = ( ~ ( member_o @ A2 @ Y6 )
% 4.69/4.93 & ( disjnt_o @ Y6 @ X4 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_insert2
% 4.69/4.93 thf(fact_1984_disjnt__insert2,axiom,
% 4.69/4.93 ! [Y6: set_Product_unit,A2: product_unit,X4: set_Product_unit] :
% 4.69/4.93 ( ( disjnt_Product_unit @ Y6 @ ( insert_Product_unit @ A2 @ X4 ) )
% 4.69/4.93 = ( ~ ( member_Product_unit @ A2 @ Y6 )
% 4.69/4.93 & ( disjnt_Product_unit @ Y6 @ X4 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_insert2
% 4.69/4.93 thf(fact_1985_rel__restrict__empty,axiom,
% 4.69/4.93 ! [R3: set_Pr5094982260447487303t_unit] :
% 4.69/4.93 ( ( rel_re9207996470947987439t_unit @ R3 @ bot_bo3957492148770167129t_unit )
% 4.69/4.93 = R3 ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_empty
% 4.69/4.93 thf(fact_1986_rel__restrict__empty,axiom,
% 4.69/4.93 ! [R3: set_Product_prod_o_o] :
% 4.69/4.93 ( ( rel_restrict_o @ R3 @ bot_bot_set_o )
% 4.69/4.93 = R3 ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_empty
% 4.69/4.93 thf(fact_1987_rel__restrict__empty,axiom,
% 4.69/4.93 ! [R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.93 ( ( rel_restrict_nat @ R3 @ bot_bot_set_nat )
% 4.69/4.93 = R3 ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_empty
% 4.69/4.93 thf(fact_1988_rel__restrict__empty,axiom,
% 4.69/4.93 ! [R3: set_Pr958786334691620121nt_int] :
% 4.69/4.93 ( ( rel_restrict_int @ R3 @ bot_bot_set_int )
% 4.69/4.93 = R3 ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_empty
% 4.69/4.93 thf(fact_1989_rel__restrict__empty,axiom,
% 4.69/4.93 ! [R3: set_Pr2161125870931222855_nat_o] :
% 4.69/4.93 ( ( rel_re3331361160397388719_nat_o @ R3 @ bot_bo7824918357723582233_nat_o )
% 4.69/4.93 = R3 ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_empty
% 4.69/4.93 thf(fact_1990_disjnt__Un1,axiom,
% 4.69/4.93 ! [A: set_nat,B4: set_nat,C5: set_nat] :
% 4.69/4.93 ( ( disjnt_nat @ ( sup_sup_set_nat @ A @ B4 ) @ C5 )
% 4.69/4.93 = ( ( disjnt_nat @ A @ C5 )
% 4.69/4.93 & ( disjnt_nat @ B4 @ C5 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_Un1
% 4.69/4.93 thf(fact_1991_disjnt__Un2,axiom,
% 4.69/4.93 ! [C5: set_nat,A: set_nat,B4: set_nat] :
% 4.69/4.93 ( ( disjnt_nat @ C5 @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.93 = ( ( disjnt_nat @ C5 @ A )
% 4.69/4.93 & ( disjnt_nat @ C5 @ B4 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_Un2
% 4.69/4.93 thf(fact_1992_Sup__fin_Osingleton,axiom,
% 4.69/4.93 ! [X: product_unit] :
% 4.69/4.93 ( ( lattic5294303975357428420t_unit @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.93 = X ) ).
% 4.69/4.93
% 4.69/4.93 % Sup_fin.singleton
% 4.69/4.93 thf(fact_1993_Sup__fin_Osingleton,axiom,
% 4.69/4.93 ! [X: $o] :
% 4.69/4.93 ( ( lattic1508158080041050831_fin_o @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.93 = X ) ).
% 4.69/4.93
% 4.69/4.93 % Sup_fin.singleton
% 4.69/4.93 thf(fact_1994_Sup__fin_Osingleton,axiom,
% 4.69/4.93 ! [X: nat] :
% 4.69/4.93 ( ( lattic1093996805478795353in_nat @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.93 = X ) ).
% 4.69/4.93
% 4.69/4.93 % Sup_fin.singleton
% 4.69/4.93 thf(fact_1995_Sup__fin_Osingleton,axiom,
% 4.69/4.93 ! [X: int] :
% 4.69/4.93 ( ( lattic1091506334969745077in_int @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.93 = X ) ).
% 4.69/4.93
% 4.69/4.93 % Sup_fin.singleton
% 4.69/4.93 thf(fact_1996_Sup__fin_Osingleton,axiom,
% 4.69/4.93 ! [X: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( lattic7320199455484906628_nat_o @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.93 = X ) ).
% 4.69/4.93
% 4.69/4.93 % Sup_fin.singleton
% 4.69/4.93 thf(fact_1997_Inf__fin_Osingleton,axiom,
% 4.69/4.93 ! [X: product_unit] :
% 4.69/4.93 ( ( lattic1263872656861969706t_unit @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.93 = X ) ).
% 4.69/4.93
% 4.69/4.93 % Inf_fin.singleton
% 4.69/4.93 thf(fact_1998_Inf__fin_Osingleton,axiom,
% 4.69/4.93 ! [X: $o] :
% 4.69/4.93 ( ( lattic4107685809792843317_fin_o @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.93 = X ) ).
% 4.69/4.93
% 4.69/4.93 % Inf_fin.singleton
% 4.69/4.93 thf(fact_1999_Inf__fin_Osingleton,axiom,
% 4.69/4.93 ! [X: nat] :
% 4.69/4.93 ( ( lattic5238388535129920115in_nat @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.93 = X ) ).
% 4.69/4.93
% 4.69/4.93 % Inf_fin.singleton
% 4.69/4.93 thf(fact_2000_Inf__fin_Osingleton,axiom,
% 4.69/4.93 ! [X: int] :
% 4.69/4.93 ( ( lattic5235898064620869839in_int @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.93 = X ) ).
% 4.69/4.93
% 4.69/4.93 % Inf_fin.singleton
% 4.69/4.93 thf(fact_2001_Inf__fin_Osingleton,axiom,
% 4.69/4.93 ! [X: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ( ( lattic956194824204696298_nat_o @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.93 = X ) ).
% 4.69/4.93
% 4.69/4.93 % Inf_fin.singleton
% 4.69/4.93 thf(fact_2002_disjnt__iff,axiom,
% 4.69/4.93 ( disjnt7869448817988085652_nat_o
% 4.69/4.93 = ( ^ [A3: set_Pr4532377907799695533_nat_o,B7: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ! [X2: produc3658429121746597890et_nat > $o] :
% 4.69/4.93 ~ ( ( member6576561426505652726_nat_o @ X2 @ A3 )
% 4.69/4.93 & ( member6576561426505652726_nat_o @ X2 @ B7 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_iff
% 4.69/4.93 thf(fact_2003_disjnt__iff,axiom,
% 4.69/4.93 ( disjnt_nat
% 4.69/4.93 = ( ^ [A3: set_nat,B7: set_nat] :
% 4.69/4.93 ! [X2: nat] :
% 4.69/4.93 ~ ( ( member_nat @ X2 @ A3 )
% 4.69/4.93 & ( member_nat @ X2 @ B7 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_iff
% 4.69/4.93 thf(fact_2004_disjnt__iff,axiom,
% 4.69/4.93 ( disjnt_int
% 4.69/4.93 = ( ^ [A3: set_int,B7: set_int] :
% 4.69/4.93 ! [X2: int] :
% 4.69/4.93 ~ ( ( member_int @ X2 @ A3 )
% 4.69/4.93 & ( member_int @ X2 @ B7 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_iff
% 4.69/4.93 thf(fact_2005_disjnt__iff,axiom,
% 4.69/4.93 ( disjnt_o
% 4.69/4.93 = ( ^ [A3: set_o,B7: set_o] :
% 4.69/4.93 ! [X2: $o] :
% 4.69/4.93 ~ ( ( member_o @ X2 @ A3 )
% 4.69/4.93 & ( member_o @ X2 @ B7 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_iff
% 4.69/4.93 thf(fact_2006_disjnt__iff,axiom,
% 4.69/4.93 ( disjnt_Product_unit
% 4.69/4.93 = ( ^ [A3: set_Product_unit,B7: set_Product_unit] :
% 4.69/4.93 ! [X2: product_unit] :
% 4.69/4.93 ~ ( ( member_Product_unit @ X2 @ A3 )
% 4.69/4.93 & ( member_Product_unit @ X2 @ B7 ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_iff
% 4.69/4.93 thf(fact_2007_IdE,axiom,
% 4.69/4.93 ! [P3: product_prod_nat_nat] :
% 4.69/4.93 ( ( member8440522571783428010at_nat @ P3 @ id_nat )
% 4.69/4.93 => ~ ! [X3: nat] :
% 4.69/4.93 ( P3
% 4.69/4.93 != ( product_Pair_nat_nat @ X3 @ X3 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % IdE
% 4.69/4.93 thf(fact_2008_IdE,axiom,
% 4.69/4.93 ! [P3: product_prod_int_int] :
% 4.69/4.93 ( ( member5262025264175285858nt_int @ P3 @ id_int )
% 4.69/4.93 => ~ ! [X3: int] :
% 4.69/4.93 ( P3
% 4.69/4.93 != ( product_Pair_int_int @ X3 @ X3 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % IdE
% 4.69/4.93 thf(fact_2009_disjnt__empty1,axiom,
% 4.69/4.93 ! [A: set_Product_unit] : ( disjnt_Product_unit @ bot_bo3957492148770167129t_unit @ A ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_empty1
% 4.69/4.93 thf(fact_2010_disjnt__empty1,axiom,
% 4.69/4.93 ! [A: set_o] : ( disjnt_o @ bot_bot_set_o @ A ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_empty1
% 4.69/4.93 thf(fact_2011_disjnt__empty1,axiom,
% 4.69/4.93 ! [A: set_nat] : ( disjnt_nat @ bot_bot_set_nat @ A ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_empty1
% 4.69/4.93 thf(fact_2012_disjnt__empty1,axiom,
% 4.69/4.93 ! [A: set_int] : ( disjnt_int @ bot_bot_set_int @ A ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_empty1
% 4.69/4.93 thf(fact_2013_disjnt__empty1,axiom,
% 4.69/4.93 ! [A: set_Pr4532377907799695533_nat_o] : ( disjnt7869448817988085652_nat_o @ bot_bo7824918357723582233_nat_o @ A ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_empty1
% 4.69/4.93 thf(fact_2014_disjnt__empty2,axiom,
% 4.69/4.93 ! [A: set_Product_unit] : ( disjnt_Product_unit @ A @ bot_bo3957492148770167129t_unit ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_empty2
% 4.69/4.93 thf(fact_2015_disjnt__empty2,axiom,
% 4.69/4.93 ! [A: set_o] : ( disjnt_o @ A @ bot_bot_set_o ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_empty2
% 4.69/4.93 thf(fact_2016_disjnt__empty2,axiom,
% 4.69/4.93 ! [A: set_nat] : ( disjnt_nat @ A @ bot_bot_set_nat ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_empty2
% 4.69/4.93 thf(fact_2017_disjnt__empty2,axiom,
% 4.69/4.93 ! [A: set_int] : ( disjnt_int @ A @ bot_bot_set_int ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_empty2
% 4.69/4.93 thf(fact_2018_disjnt__empty2,axiom,
% 4.69/4.93 ! [A: set_Pr4532377907799695533_nat_o] : ( disjnt7869448817988085652_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_empty2
% 4.69/4.93 thf(fact_2019_disjnt__subset1,axiom,
% 4.69/4.93 ! [X4: set_nat,Y6: set_nat,Z5: set_nat] :
% 4.69/4.93 ( ( disjnt_nat @ X4 @ Y6 )
% 4.69/4.93 => ( ( ord_less_eq_set_nat @ Z5 @ X4 )
% 4.69/4.93 => ( disjnt_nat @ Z5 @ Y6 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_subset1
% 4.69/4.93 thf(fact_2020_disjnt__subset2,axiom,
% 4.69/4.93 ! [X4: set_nat,Y6: set_nat,Z5: set_nat] :
% 4.69/4.93 ( ( disjnt_nat @ X4 @ Y6 )
% 4.69/4.93 => ( ( ord_less_eq_set_nat @ Z5 @ Y6 )
% 4.69/4.93 => ( disjnt_nat @ X4 @ Z5 ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_subset2
% 4.69/4.93 thf(fact_2021_disjnt__insert,axiom,
% 4.69/4.93 ! [X: produc3658429121746597890et_nat > $o,N: set_Pr4532377907799695533_nat_o,M: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ( ~ ( member6576561426505652726_nat_o @ X @ N )
% 4.69/4.93 => ( ( disjnt7869448817988085652_nat_o @ M @ N )
% 4.69/4.93 => ( disjnt7869448817988085652_nat_o @ ( insert5175938949040314269_nat_o @ X @ M ) @ N ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_insert
% 4.69/4.93 thf(fact_2022_disjnt__insert,axiom,
% 4.69/4.93 ! [X: nat,N: set_nat,M: set_nat] :
% 4.69/4.93 ( ~ ( member_nat @ X @ N )
% 4.69/4.93 => ( ( disjnt_nat @ M @ N )
% 4.69/4.93 => ( disjnt_nat @ ( insert_nat @ X @ M ) @ N ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_insert
% 4.69/4.93 thf(fact_2023_disjnt__insert,axiom,
% 4.69/4.93 ! [X: int,N: set_int,M: set_int] :
% 4.69/4.93 ( ~ ( member_int @ X @ N )
% 4.69/4.93 => ( ( disjnt_int @ M @ N )
% 4.69/4.93 => ( disjnt_int @ ( insert_int @ X @ M ) @ N ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_insert
% 4.69/4.93 thf(fact_2024_disjnt__insert,axiom,
% 4.69/4.93 ! [X: $o,N: set_o,M: set_o] :
% 4.69/4.93 ( ~ ( member_o @ X @ N )
% 4.69/4.93 => ( ( disjnt_o @ M @ N )
% 4.69/4.93 => ( disjnt_o @ ( insert_o @ X @ M ) @ N ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_insert
% 4.69/4.93 thf(fact_2025_disjnt__insert,axiom,
% 4.69/4.93 ! [X: product_unit,N: set_Product_unit,M: set_Product_unit] :
% 4.69/4.93 ( ~ ( member_Product_unit @ X @ N )
% 4.69/4.93 => ( ( disjnt_Product_unit @ M @ N )
% 4.69/4.93 => ( disjnt_Product_unit @ ( insert_Product_unit @ X @ M ) @ N ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % disjnt_insert
% 4.69/4.93 thf(fact_2026_rel__restrict__notR_I2_J,axiom,
% 4.69/4.93 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o,A: set_Pr2161125870931222855_nat_o,R3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ ( rel_re3331361160397388719_nat_o @ A @ R3 ) )
% 4.69/4.93 => ~ ( member6576561426505652726_nat_o @ Y @ R3 ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_notR(2)
% 4.69/4.93 thf(fact_2027_rel__restrict__notR_I2_J,axiom,
% 4.69/4.93 ! [X: $o,Y: $o,A: set_Product_prod_o_o,R3: set_o] :
% 4.69/4.93 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ ( rel_restrict_o @ A @ R3 ) )
% 4.69/4.93 => ~ ( member_o @ Y @ R3 ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_notR(2)
% 4.69/4.93 thf(fact_2028_rel__restrict__notR_I2_J,axiom,
% 4.69/4.93 ! [X: product_unit,Y: product_unit,A: set_Pr5094982260447487303t_unit,R3: set_Product_unit] :
% 4.69/4.93 ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X @ Y ) @ ( rel_re9207996470947987439t_unit @ A @ R3 ) )
% 4.69/4.93 => ~ ( member_Product_unit @ Y @ R3 ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_notR(2)
% 4.69/4.93 thf(fact_2029_rel__restrict__notR_I2_J,axiom,
% 4.69/4.93 ! [X: nat,Y: nat,A: set_Pr1261947904930325089at_nat,R3: set_nat] :
% 4.69/4.93 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( rel_restrict_nat @ A @ R3 ) )
% 4.69/4.93 => ~ ( member_nat @ Y @ R3 ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_notR(2)
% 4.69/4.93 thf(fact_2030_rel__restrict__notR_I2_J,axiom,
% 4.69/4.93 ! [X: int,Y: int,A: set_Pr958786334691620121nt_int,R3: set_int] :
% 4.69/4.93 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( rel_restrict_int @ A @ R3 ) )
% 4.69/4.93 => ~ ( member_int @ Y @ R3 ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_notR(2)
% 4.69/4.93 thf(fact_2031_rel__restrict__notR_I1_J,axiom,
% 4.69/4.93 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o,A: set_Pr2161125870931222855_nat_o,R3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ ( rel_re3331361160397388719_nat_o @ A @ R3 ) )
% 4.69/4.93 => ~ ( member6576561426505652726_nat_o @ X @ R3 ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_notR(1)
% 4.69/4.93 thf(fact_2032_rel__restrict__notR_I1_J,axiom,
% 4.69/4.93 ! [X: $o,Y: $o,A: set_Product_prod_o_o,R3: set_o] :
% 4.69/4.93 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ ( rel_restrict_o @ A @ R3 ) )
% 4.69/4.93 => ~ ( member_o @ X @ R3 ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_notR(1)
% 4.69/4.93 thf(fact_2033_rel__restrict__notR_I1_J,axiom,
% 4.69/4.93 ! [X: product_unit,Y: product_unit,A: set_Pr5094982260447487303t_unit,R3: set_Product_unit] :
% 4.69/4.93 ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X @ Y ) @ ( rel_re9207996470947987439t_unit @ A @ R3 ) )
% 4.69/4.93 => ~ ( member_Product_unit @ X @ R3 ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_notR(1)
% 4.69/4.93 thf(fact_2034_rel__restrict__notR_I1_J,axiom,
% 4.69/4.93 ! [X: nat,Y: nat,A: set_Pr1261947904930325089at_nat,R3: set_nat] :
% 4.69/4.93 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( rel_restrict_nat @ A @ R3 ) )
% 4.69/4.93 => ~ ( member_nat @ X @ R3 ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_notR(1)
% 4.69/4.93 thf(fact_2035_rel__restrict__notR_I1_J,axiom,
% 4.69/4.93 ! [X: int,Y: int,A: set_Pr958786334691620121nt_int,R3: set_int] :
% 4.69/4.93 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( rel_restrict_int @ A @ R3 ) )
% 4.69/4.93 => ~ ( member_int @ X @ R3 ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_notR(1)
% 4.69/4.93 thf(fact_2036_rel__restrictI,axiom,
% 4.69/4.93 ! [X: produc3658429121746597890et_nat > $o,R3: set_Pr4532377907799695533_nat_o,Y: produc3658429121746597890et_nat > $o,E: set_Pr2161125870931222855_nat_o] :
% 4.69/4.93 ( ~ ( member6576561426505652726_nat_o @ X @ R3 )
% 4.69/4.93 => ( ~ ( member6576561426505652726_nat_o @ Y @ R3 )
% 4.69/4.93 => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ E )
% 4.69/4.93 => ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ ( rel_re3331361160397388719_nat_o @ E @ R3 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrictI
% 4.69/4.93 thf(fact_2037_rel__restrictI,axiom,
% 4.69/4.93 ! [X: $o,R3: set_o,Y: $o,E: set_Product_prod_o_o] :
% 4.69/4.93 ( ~ ( member_o @ X @ R3 )
% 4.69/4.93 => ( ~ ( member_o @ Y @ R3 )
% 4.69/4.93 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ E )
% 4.69/4.93 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ ( rel_restrict_o @ E @ R3 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrictI
% 4.69/4.93 thf(fact_2038_rel__restrictI,axiom,
% 4.69/4.93 ! [X: product_unit,R3: set_Product_unit,Y: product_unit,E: set_Pr5094982260447487303t_unit] :
% 4.69/4.93 ( ~ ( member_Product_unit @ X @ R3 )
% 4.69/4.93 => ( ~ ( member_Product_unit @ Y @ R3 )
% 4.69/4.93 => ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X @ Y ) @ E )
% 4.69/4.93 => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X @ Y ) @ ( rel_re9207996470947987439t_unit @ E @ R3 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrictI
% 4.69/4.93 thf(fact_2039_rel__restrictI,axiom,
% 4.69/4.93 ! [X: nat,R3: set_nat,Y: nat,E: set_Pr1261947904930325089at_nat] :
% 4.69/4.93 ( ~ ( member_nat @ X @ R3 )
% 4.69/4.93 => ( ~ ( member_nat @ Y @ R3 )
% 4.69/4.93 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ E )
% 4.69/4.93 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( rel_restrict_nat @ E @ R3 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrictI
% 4.69/4.93 thf(fact_2040_rel__restrictI,axiom,
% 4.69/4.93 ! [X: int,R3: set_int,Y: int,E: set_Pr958786334691620121nt_int] :
% 4.69/4.93 ( ~ ( member_int @ X @ R3 )
% 4.69/4.93 => ( ~ ( member_int @ Y @ R3 )
% 4.69/4.93 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ E )
% 4.69/4.93 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( rel_restrict_int @ E @ R3 ) ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrictI
% 4.69/4.93 thf(fact_2041_rel__restrict__lift,axiom,
% 4.69/4.93 ! [X: nat,Y: nat,E: set_Pr1261947904930325089at_nat,R3: set_nat] :
% 4.69/4.93 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( rel_restrict_nat @ E @ R3 ) )
% 4.69/4.93 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ E ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_lift
% 4.69/4.93 thf(fact_2042_rel__restrict__lift,axiom,
% 4.69/4.93 ! [X: int,Y: int,E: set_Pr958786334691620121nt_int,R3: set_int] :
% 4.69/4.93 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( rel_restrict_int @ E @ R3 ) )
% 4.69/4.93 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ E ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_lift
% 4.69/4.93 thf(fact_2043_rel__restrict__union,axiom,
% 4.69/4.93 ! [R3: set_Pr1261947904930325089at_nat,A: set_nat,B4: set_nat] :
% 4.69/4.93 ( ( rel_restrict_nat @ R3 @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.93 = ( rel_restrict_nat @ ( rel_restrict_nat @ R3 @ A ) @ B4 ) ) ).
% 4.69/4.93
% 4.69/4.93 % rel_restrict_union
% 4.69/4.93 thf(fact_2044_Inf__fin__le__Sup__fin,axiom,
% 4.69/4.93 ! [A: set_Product_unit] :
% 4.69/4.93 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.93 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.93 => ( ord_le3221252021190050221t_unit @ ( lattic1263872656861969706t_unit @ A ) @ ( lattic5294303975357428420t_unit @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Inf_fin_le_Sup_fin
% 4.69/4.93 thf(fact_2045_Inf__fin__le__Sup__fin,axiom,
% 4.69/4.93 ! [A: set_o] :
% 4.69/4.93 ( ( finite_finite_o @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_o )
% 4.69/4.93 => ( ord_less_eq_o @ ( lattic4107685809792843317_fin_o @ A ) @ ( lattic1508158080041050831_fin_o @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Inf_fin_le_Sup_fin
% 4.69/4.93 thf(fact_2046_Inf__fin__le__Sup__fin,axiom,
% 4.69/4.93 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.93 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.93 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.93 => ( ord_le729326519192465773_nat_o @ ( lattic956194824204696298_nat_o @ A ) @ ( lattic7320199455484906628_nat_o @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Inf_fin_le_Sup_fin
% 4.69/4.93 thf(fact_2047_Inf__fin__le__Sup__fin,axiom,
% 4.69/4.93 ! [A: set_filter_nat] :
% 4.69/4.93 ( ( finite2119507909894593271er_nat @ A )
% 4.69/4.93 => ( ( A != bot_bo498966703094740906er_nat )
% 4.69/4.93 => ( ord_le2510731241096832064er_nat @ ( lattic9128708996678779395er_nat @ A ) @ ( lattic5930898082463196905er_nat @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Inf_fin_le_Sup_fin
% 4.69/4.93 thf(fact_2048_Inf__fin__le__Sup__fin,axiom,
% 4.69/4.93 ! [A: set_set_nat] :
% 4.69/4.93 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_set_nat )
% 4.69/4.93 => ( ord_less_eq_set_nat @ ( lattic3014633134055518761et_nat @ A ) @ ( lattic3835124923745554447et_nat @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Inf_fin_le_Sup_fin
% 4.69/4.93 thf(fact_2049_Inf__fin__le__Sup__fin,axiom,
% 4.69/4.93 ! [A: set_rat] :
% 4.69/4.93 ( ( finite_finite_rat @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_rat )
% 4.69/4.93 => ( ord_less_eq_rat @ ( lattic4603258475043424379in_rat @ A ) @ ( lattic458866745392299617in_rat @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Inf_fin_le_Sup_fin
% 4.69/4.93 thf(fact_2050_Inf__fin__le__Sup__fin,axiom,
% 4.69/4.93 ! [A: set_nat] :
% 4.69/4.93 ( ( finite_finite_nat @ A )
% 4.69/4.93 => ( ( A != bot_bot_set_nat )
% 4.69/4.93 => ( ord_less_eq_nat @ ( lattic5238388535129920115in_nat @ A ) @ ( lattic1093996805478795353in_nat @ A ) ) ) ) ).
% 4.69/4.93
% 4.69/4.93 % Inf_fin_le_Sup_fin
% 4.69/4.93 thf(fact_2051_Inf__fin__le__Sup__fin,axiom,
% 4.69/4.93 ! [A: set_int] :
% 4.69/4.94 ( ( finite_finite_int @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_int )
% 4.69/4.94 => ( ord_less_eq_int @ ( lattic5235898064620869839in_int @ A ) @ ( lattic1091506334969745077in_int @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin_le_Sup_fin
% 4.69/4.94 thf(fact_2052_disjnt__Sigma__iff,axiom,
% 4.69/4.94 ! [A: set_nat,C5: nat > set_Product_unit,B4: set_nat] :
% 4.69/4.94 ( ( disjnt595863415355979947t_unit @ ( produc5506539147108004339t_unit @ A @ C5 ) @ ( produc5506539147108004339t_unit @ B4 @ C5 ) )
% 4.69/4.94 = ( ! [X2: nat] :
% 4.69/4.94 ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A @ B4 ) )
% 4.69/4.94 => ( ( C5 @ X2 )
% 4.69/4.94 = bot_bo3957492148770167129t_unit ) )
% 4.69/4.94 | ( disjnt_nat @ A @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % disjnt_Sigma_iff
% 4.69/4.94 thf(fact_2053_disjnt__Sigma__iff,axiom,
% 4.69/4.94 ! [A: set_nat,C5: nat > set_o,B4: set_nat] :
% 4.69/4.94 ( ( disjnt5652777605541633334_nat_o @ ( product_Sigma_nat_o @ A @ C5 ) @ ( product_Sigma_nat_o @ B4 @ C5 ) )
% 4.69/4.94 = ( ! [X2: nat] :
% 4.69/4.94 ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A @ B4 ) )
% 4.69/4.94 => ( ( C5 @ X2 )
% 4.69/4.94 = bot_bot_set_o ) )
% 4.69/4.94 | ( disjnt_nat @ A @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % disjnt_Sigma_iff
% 4.69/4.94 thf(fact_2054_disjnt__Sigma__iff,axiom,
% 4.69/4.94 ! [A: set_nat,C5: nat > set_nat,B4: set_nat] :
% 4.69/4.94 ( ( disjnt2713546992526078024at_nat @ ( produc457027306803732586at_nat @ A @ C5 ) @ ( produc457027306803732586at_nat @ B4 @ C5 ) )
% 4.69/4.94 = ( ! [X2: nat] :
% 4.69/4.94 ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A @ B4 ) )
% 4.69/4.94 => ( ( C5 @ X2 )
% 4.69/4.94 = bot_bot_set_nat ) )
% 4.69/4.94 | ( disjnt_nat @ A @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % disjnt_Sigma_iff
% 4.69/4.94 thf(fact_2055_disjnt__Sigma__iff,axiom,
% 4.69/4.94 ! [A: set_nat,C5: nat > set_int,B4: set_nat] :
% 4.69/4.94 ( ( disjnt7759068009871657124at_int @ ( produc454536836294682310at_int @ A @ C5 ) @ ( produc454536836294682310at_int @ B4 @ C5 ) )
% 4.69/4.94 = ( ! [X2: nat] :
% 4.69/4.94 ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A @ B4 ) )
% 4.69/4.94 => ( ( C5 @ X2 )
% 4.69/4.94 = bot_bot_set_int ) )
% 4.69/4.94 | ( disjnt_nat @ A @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % disjnt_Sigma_iff
% 4.69/4.94 thf(fact_2056_disjnt__Sigma__iff,axiom,
% 4.69/4.94 ! [A: set_nat,C5: nat > set_Pr4532377907799695533_nat_o,B4: set_nat] :
% 4.69/4.94 ( ( disjnt4476176636800211563_nat_o @ ( produc5650067098820117939_nat_o @ A @ C5 ) @ ( produc5650067098820117939_nat_o @ B4 @ C5 ) )
% 4.69/4.94 = ( ! [X2: nat] :
% 4.69/4.94 ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A @ B4 ) )
% 4.69/4.94 => ( ( C5 @ X2 )
% 4.69/4.94 = bot_bo7824918357723582233_nat_o ) )
% 4.69/4.94 | ( disjnt_nat @ A @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % disjnt_Sigma_iff
% 4.69/4.94 thf(fact_2057_disjnt__def,axiom,
% 4.69/4.94 ( disjnt_Product_unit
% 4.69/4.94 = ( ^ [A3: set_Product_unit,B7: set_Product_unit] :
% 4.69/4.94 ( ( inf_in4660618365625256667t_unit @ A3 @ B7 )
% 4.69/4.94 = bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % disjnt_def
% 4.69/4.94 thf(fact_2058_disjnt__def,axiom,
% 4.69/4.94 ( disjnt_o
% 4.69/4.94 = ( ^ [A3: set_o,B7: set_o] :
% 4.69/4.94 ( ( inf_inf_set_o @ A3 @ B7 )
% 4.69/4.94 = bot_bot_set_o ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % disjnt_def
% 4.69/4.94 thf(fact_2059_disjnt__def,axiom,
% 4.69/4.94 ( disjnt_nat
% 4.69/4.94 = ( ^ [A3: set_nat,B7: set_nat] :
% 4.69/4.94 ( ( inf_inf_set_nat @ A3 @ B7 )
% 4.69/4.94 = bot_bot_set_nat ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % disjnt_def
% 4.69/4.94 thf(fact_2060_disjnt__def,axiom,
% 4.69/4.94 ( disjnt_int
% 4.69/4.94 = ( ^ [A3: set_int,B7: set_int] :
% 4.69/4.94 ( ( inf_inf_set_int @ A3 @ B7 )
% 4.69/4.94 = bot_bot_set_int ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % disjnt_def
% 4.69/4.94 thf(fact_2061_disjnt__def,axiom,
% 4.69/4.94 ( disjnt7869448817988085652_nat_o
% 4.69/4.94 = ( ^ [A3: set_Pr4532377907799695533_nat_o,B7: set_Pr4532377907799695533_nat_o] :
% 4.69/4.94 ( ( inf_in1906310914598751387_nat_o @ A3 @ B7 )
% 4.69/4.94 = bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % disjnt_def
% 4.69/4.94 thf(fact_2062_quotient__eqI,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o,X4: set_Pr4532377907799695533_nat_o,Y6: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( equiv_6726761681920839555_nat_o @ A @ R2 )
% 4.69/4.94 => ( ( member1452989533377600726_nat_o @ X4 @ ( equiv_7899955228204526484_nat_o @ A @ R2 ) )
% 4.69/4.94 => ( ( member1452989533377600726_nat_o @ Y6 @ ( equiv_7899955228204526484_nat_o @ A @ R2 ) )
% 4.69/4.94 => ( ( member6576561426505652726_nat_o @ X @ X4 )
% 4.69/4.94 => ( ( member6576561426505652726_nat_o @ Y @ Y6 )
% 4.69/4.94 => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ R2 )
% 4.69/4.94 => ( X4 = Y6 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotient_eqI
% 4.69/4.94 thf(fact_2063_quotient__eqI,axiom,
% 4.69/4.94 ! [A: set_o,R2: set_Product_prod_o_o,X4: set_o,Y6: set_o,X: $o,Y: $o] :
% 4.69/4.94 ( ( equiv_equiv_o @ A @ R2 )
% 4.69/4.94 => ( ( member_set_o @ X4 @ ( equiv_quotient_o @ A @ R2 ) )
% 4.69/4.94 => ( ( member_set_o @ Y6 @ ( equiv_quotient_o @ A @ R2 ) )
% 4.69/4.94 => ( ( member_o @ X @ X4 )
% 4.69/4.94 => ( ( member_o @ Y @ Y6 )
% 4.69/4.94 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ R2 )
% 4.69/4.94 => ( X4 = Y6 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotient_eqI
% 4.69/4.94 thf(fact_2064_quotient__eqI,axiom,
% 4.69/4.94 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit,X4: set_Product_unit,Y6: set_Product_unit,X: product_unit,Y: product_unit] :
% 4.69/4.94 ( ( equiv_4189356295871601603t_unit @ A @ R2 )
% 4.69/4.94 => ( ( member5877623283571906838t_unit @ X4 @ ( equiv_5172566880711946708t_unit @ A @ R2 ) )
% 4.69/4.94 => ( ( member5877623283571906838t_unit @ Y6 @ ( equiv_5172566880711946708t_unit @ A @ R2 ) )
% 4.69/4.94 => ( ( member_Product_unit @ X @ X4 )
% 4.69/4.94 => ( ( member_Product_unit @ Y @ Y6 )
% 4.69/4.94 => ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X @ Y ) @ R2 )
% 4.69/4.94 => ( X4 = Y6 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotient_eqI
% 4.69/4.94 thf(fact_2065_quotient__eqI,axiom,
% 4.69/4.94 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,X4: set_nat,Y6: set_nat,X: nat,Y: nat] :
% 4.69/4.94 ( ( equiv_equiv_nat @ A @ R2 )
% 4.69/4.94 => ( ( member_set_nat @ X4 @ ( equiv_quotient_nat @ A @ R2 ) )
% 4.69/4.94 => ( ( member_set_nat @ Y6 @ ( equiv_quotient_nat @ A @ R2 ) )
% 4.69/4.94 => ( ( member_nat @ X @ X4 )
% 4.69/4.94 => ( ( member_nat @ Y @ Y6 )
% 4.69/4.94 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R2 )
% 4.69/4.94 => ( X4 = Y6 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotient_eqI
% 4.69/4.94 thf(fact_2066_quotient__eqI,axiom,
% 4.69/4.94 ! [A: set_int,R2: set_Pr958786334691620121nt_int,X4: set_int,Y6: set_int,X: int,Y: int] :
% 4.69/4.94 ( ( equiv_equiv_int @ A @ R2 )
% 4.69/4.94 => ( ( member_set_int @ X4 @ ( equiv_quotient_int @ A @ R2 ) )
% 4.69/4.94 => ( ( member_set_int @ Y6 @ ( equiv_quotient_int @ A @ R2 ) )
% 4.69/4.94 => ( ( member_int @ X @ X4 )
% 4.69/4.94 => ( ( member_int @ Y @ Y6 )
% 4.69/4.94 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R2 )
% 4.69/4.94 => ( X4 = Y6 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotient_eqI
% 4.69/4.94 thf(fact_2067_quotient__eq__iff,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o,X4: set_Pr4532377907799695533_nat_o,Y6: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( equiv_6726761681920839555_nat_o @ A @ R2 )
% 4.69/4.94 => ( ( member1452989533377600726_nat_o @ X4 @ ( equiv_7899955228204526484_nat_o @ A @ R2 ) )
% 4.69/4.94 => ( ( member1452989533377600726_nat_o @ Y6 @ ( equiv_7899955228204526484_nat_o @ A @ R2 ) )
% 4.69/4.94 => ( ( member6576561426505652726_nat_o @ X @ X4 )
% 4.69/4.94 => ( ( member6576561426505652726_nat_o @ Y @ Y6 )
% 4.69/4.94 => ( ( X4 = Y6 )
% 4.69/4.94 = ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ R2 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotient_eq_iff
% 4.69/4.94 thf(fact_2068_quotient__eq__iff,axiom,
% 4.69/4.94 ! [A: set_o,R2: set_Product_prod_o_o,X4: set_o,Y6: set_o,X: $o,Y: $o] :
% 4.69/4.94 ( ( equiv_equiv_o @ A @ R2 )
% 4.69/4.94 => ( ( member_set_o @ X4 @ ( equiv_quotient_o @ A @ R2 ) )
% 4.69/4.94 => ( ( member_set_o @ Y6 @ ( equiv_quotient_o @ A @ R2 ) )
% 4.69/4.94 => ( ( member_o @ X @ X4 )
% 4.69/4.94 => ( ( member_o @ Y @ Y6 )
% 4.69/4.94 => ( ( X4 = Y6 )
% 4.69/4.94 = ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ R2 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotient_eq_iff
% 4.69/4.94 thf(fact_2069_quotient__eq__iff,axiom,
% 4.69/4.94 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit,X4: set_Product_unit,Y6: set_Product_unit,X: product_unit,Y: product_unit] :
% 4.69/4.94 ( ( equiv_4189356295871601603t_unit @ A @ R2 )
% 4.69/4.94 => ( ( member5877623283571906838t_unit @ X4 @ ( equiv_5172566880711946708t_unit @ A @ R2 ) )
% 4.69/4.94 => ( ( member5877623283571906838t_unit @ Y6 @ ( equiv_5172566880711946708t_unit @ A @ R2 ) )
% 4.69/4.94 => ( ( member_Product_unit @ X @ X4 )
% 4.69/4.94 => ( ( member_Product_unit @ Y @ Y6 )
% 4.69/4.94 => ( ( X4 = Y6 )
% 4.69/4.94 = ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X @ Y ) @ R2 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotient_eq_iff
% 4.69/4.94 thf(fact_2070_quotient__eq__iff,axiom,
% 4.69/4.94 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,X4: set_nat,Y6: set_nat,X: nat,Y: nat] :
% 4.69/4.94 ( ( equiv_equiv_nat @ A @ R2 )
% 4.69/4.94 => ( ( member_set_nat @ X4 @ ( equiv_quotient_nat @ A @ R2 ) )
% 4.69/4.94 => ( ( member_set_nat @ Y6 @ ( equiv_quotient_nat @ A @ R2 ) )
% 4.69/4.94 => ( ( member_nat @ X @ X4 )
% 4.69/4.94 => ( ( member_nat @ Y @ Y6 )
% 4.69/4.94 => ( ( X4 = Y6 )
% 4.69/4.94 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R2 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotient_eq_iff
% 4.69/4.94 thf(fact_2071_quotient__eq__iff,axiom,
% 4.69/4.94 ! [A: set_int,R2: set_Pr958786334691620121nt_int,X4: set_int,Y6: set_int,X: int,Y: int] :
% 4.69/4.94 ( ( equiv_equiv_int @ A @ R2 )
% 4.69/4.94 => ( ( member_set_int @ X4 @ ( equiv_quotient_int @ A @ R2 ) )
% 4.69/4.94 => ( ( member_set_int @ Y6 @ ( equiv_quotient_int @ A @ R2 ) )
% 4.69/4.94 => ( ( member_int @ X @ X4 )
% 4.69/4.94 => ( ( member_int @ Y @ Y6 )
% 4.69/4.94 => ( ( X4 = Y6 )
% 4.69/4.94 = ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R2 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotient_eq_iff
% 4.69/4.94 thf(fact_2072_in__quotient__imp__closed,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o,X4: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( equiv_6726761681920839555_nat_o @ A @ R2 )
% 4.69/4.94 => ( ( member1452989533377600726_nat_o @ X4 @ ( equiv_7899955228204526484_nat_o @ A @ R2 ) )
% 4.69/4.94 => ( ( member6576561426505652726_nat_o @ X @ X4 )
% 4.69/4.94 => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ R2 )
% 4.69/4.94 => ( member6576561426505652726_nat_o @ Y @ X4 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % in_quotient_imp_closed
% 4.69/4.94 thf(fact_2073_in__quotient__imp__closed,axiom,
% 4.69/4.94 ! [A: set_o,R2: set_Product_prod_o_o,X4: set_o,X: $o,Y: $o] :
% 4.69/4.94 ( ( equiv_equiv_o @ A @ R2 )
% 4.69/4.94 => ( ( member_set_o @ X4 @ ( equiv_quotient_o @ A @ R2 ) )
% 4.69/4.94 => ( ( member_o @ X @ X4 )
% 4.69/4.94 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ R2 )
% 4.69/4.94 => ( member_o @ Y @ X4 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % in_quotient_imp_closed
% 4.69/4.94 thf(fact_2074_in__quotient__imp__closed,axiom,
% 4.69/4.94 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit,X4: set_Product_unit,X: product_unit,Y: product_unit] :
% 4.69/4.94 ( ( equiv_4189356295871601603t_unit @ A @ R2 )
% 4.69/4.94 => ( ( member5877623283571906838t_unit @ X4 @ ( equiv_5172566880711946708t_unit @ A @ R2 ) )
% 4.69/4.94 => ( ( member_Product_unit @ X @ X4 )
% 4.69/4.94 => ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X @ Y ) @ R2 )
% 4.69/4.94 => ( member_Product_unit @ Y @ X4 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % in_quotient_imp_closed
% 4.69/4.94 thf(fact_2075_in__quotient__imp__closed,axiom,
% 4.69/4.94 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,X4: set_nat,X: nat,Y: nat] :
% 4.69/4.94 ( ( equiv_equiv_nat @ A @ R2 )
% 4.69/4.94 => ( ( member_set_nat @ X4 @ ( equiv_quotient_nat @ A @ R2 ) )
% 4.69/4.94 => ( ( member_nat @ X @ X4 )
% 4.69/4.94 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R2 )
% 4.69/4.94 => ( member_nat @ Y @ X4 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % in_quotient_imp_closed
% 4.69/4.94 thf(fact_2076_in__quotient__imp__closed,axiom,
% 4.69/4.94 ! [A: set_int,R2: set_Pr958786334691620121nt_int,X4: set_int,X: int,Y: int] :
% 4.69/4.94 ( ( equiv_equiv_int @ A @ R2 )
% 4.69/4.94 => ( ( member_set_int @ X4 @ ( equiv_quotient_int @ A @ R2 ) )
% 4.69/4.94 => ( ( member_int @ X @ X4 )
% 4.69/4.94 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R2 )
% 4.69/4.94 => ( member_int @ Y @ X4 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % in_quotient_imp_closed
% 4.69/4.94 thf(fact_2077_in__quotient__imp__non__empty,axiom,
% 4.69/4.94 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit,X4: set_Product_unit] :
% 4.69/4.94 ( ( equiv_4189356295871601603t_unit @ A @ R2 )
% 4.69/4.94 => ( ( member5877623283571906838t_unit @ X4 @ ( equiv_5172566880711946708t_unit @ A @ R2 ) )
% 4.69/4.94 => ( X4 != bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % in_quotient_imp_non_empty
% 4.69/4.94 thf(fact_2078_in__quotient__imp__non__empty,axiom,
% 4.69/4.94 ! [A: set_o,R2: set_Product_prod_o_o,X4: set_o] :
% 4.69/4.94 ( ( equiv_equiv_o @ A @ R2 )
% 4.69/4.94 => ( ( member_set_o @ X4 @ ( equiv_quotient_o @ A @ R2 ) )
% 4.69/4.94 => ( X4 != bot_bot_set_o ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % in_quotient_imp_non_empty
% 4.69/4.94 thf(fact_2079_in__quotient__imp__non__empty,axiom,
% 4.69/4.94 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,X4: set_nat] :
% 4.69/4.94 ( ( equiv_equiv_nat @ A @ R2 )
% 4.69/4.94 => ( ( member_set_nat @ X4 @ ( equiv_quotient_nat @ A @ R2 ) )
% 4.69/4.94 => ( X4 != bot_bot_set_nat ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % in_quotient_imp_non_empty
% 4.69/4.94 thf(fact_2080_in__quotient__imp__non__empty,axiom,
% 4.69/4.94 ! [A: set_int,R2: set_Pr958786334691620121nt_int,X4: set_int] :
% 4.69/4.94 ( ( equiv_equiv_int @ A @ R2 )
% 4.69/4.94 => ( ( member_set_int @ X4 @ ( equiv_quotient_int @ A @ R2 ) )
% 4.69/4.94 => ( X4 != bot_bot_set_int ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % in_quotient_imp_non_empty
% 4.69/4.94 thf(fact_2081_in__quotient__imp__non__empty,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o,X4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.94 ( ( equiv_6726761681920839555_nat_o @ A @ R2 )
% 4.69/4.94 => ( ( member1452989533377600726_nat_o @ X4 @ ( equiv_7899955228204526484_nat_o @ A @ R2 ) )
% 4.69/4.94 => ( X4 != bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % in_quotient_imp_non_empty
% 4.69/4.94 thf(fact_2082_rel__restrict__trancl__notR_I2_J,axiom,
% 4.69/4.94 ! [V: produc3658429121746597890et_nat > $o,W: produc3658429121746597890et_nat > $o,E: set_Pr2161125870931222855_nat_o,R3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.94 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ V @ W ) @ ( transi4009562729418357614_nat_o @ ( rel_re3331361160397388719_nat_o @ E @ R3 ) ) )
% 4.69/4.94 => ~ ( member6576561426505652726_nat_o @ W @ R3 ) ) ).
% 4.69/4.94
% 4.69/4.94 % rel_restrict_trancl_notR(2)
% 4.69/4.94 thf(fact_2083_rel__restrict__trancl__notR_I2_J,axiom,
% 4.69/4.94 ! [V: $o,W: $o,E: set_Product_prod_o_o,R3: set_o] :
% 4.69/4.94 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ V @ W ) @ ( transitive_trancl_o @ ( rel_restrict_o @ E @ R3 ) ) )
% 4.69/4.94 => ~ ( member_o @ W @ R3 ) ) ).
% 4.69/4.94
% 4.69/4.94 % rel_restrict_trancl_notR(2)
% 4.69/4.94 thf(fact_2084_rel__restrict__trancl__notR_I2_J,axiom,
% 4.69/4.94 ! [V: product_unit,W: product_unit,E: set_Pr5094982260447487303t_unit,R3: set_Product_unit] :
% 4.69/4.94 ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ V @ W ) @ ( transi430408012122777006t_unit @ ( rel_re9207996470947987439t_unit @ E @ R3 ) ) )
% 4.69/4.94 => ~ ( member_Product_unit @ W @ R3 ) ) ).
% 4.69/4.94
% 4.69/4.94 % rel_restrict_trancl_notR(2)
% 4.69/4.94 thf(fact_2085_rel__restrict__trancl__notR_I2_J,axiom,
% 4.69/4.94 ! [V: nat,W: nat,E: set_Pr1261947904930325089at_nat,R3: set_nat] :
% 4.69/4.94 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ V @ W ) @ ( transi6264000038957366511cl_nat @ ( rel_restrict_nat @ E @ R3 ) ) )
% 4.69/4.94 => ~ ( member_nat @ W @ R3 ) ) ).
% 4.69/4.94
% 4.69/4.94 % rel_restrict_trancl_notR(2)
% 4.69/4.94 thf(fact_2086_rel__restrict__trancl__notR_I2_J,axiom,
% 4.69/4.94 ! [V: int,W: int,E: set_Pr958786334691620121nt_int,R3: set_int] :
% 4.69/4.94 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ V @ W ) @ ( transi6261509568448316235cl_int @ ( rel_restrict_int @ E @ R3 ) ) )
% 4.69/4.94 => ~ ( member_int @ W @ R3 ) ) ).
% 4.69/4.94
% 4.69/4.94 % rel_restrict_trancl_notR(2)
% 4.69/4.94 thf(fact_2087_rel__restrict__trancl__notR_I1_J,axiom,
% 4.69/4.94 ! [V: produc3658429121746597890et_nat > $o,W: produc3658429121746597890et_nat > $o,E: set_Pr2161125870931222855_nat_o,R3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.94 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ V @ W ) @ ( transi4009562729418357614_nat_o @ ( rel_re3331361160397388719_nat_o @ E @ R3 ) ) )
% 4.69/4.94 => ~ ( member6576561426505652726_nat_o @ V @ R3 ) ) ).
% 4.69/4.94
% 4.69/4.94 % rel_restrict_trancl_notR(1)
% 4.69/4.94 thf(fact_2088_rel__restrict__trancl__notR_I1_J,axiom,
% 4.69/4.94 ! [V: $o,W: $o,E: set_Product_prod_o_o,R3: set_o] :
% 4.69/4.94 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ V @ W ) @ ( transitive_trancl_o @ ( rel_restrict_o @ E @ R3 ) ) )
% 4.69/4.94 => ~ ( member_o @ V @ R3 ) ) ).
% 4.69/4.94
% 4.69/4.94 % rel_restrict_trancl_notR(1)
% 4.69/4.94 thf(fact_2089_rel__restrict__trancl__notR_I1_J,axiom,
% 4.69/4.94 ! [V: product_unit,W: product_unit,E: set_Pr5094982260447487303t_unit,R3: set_Product_unit] :
% 4.69/4.94 ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ V @ W ) @ ( transi430408012122777006t_unit @ ( rel_re9207996470947987439t_unit @ E @ R3 ) ) )
% 4.69/4.94 => ~ ( member_Product_unit @ V @ R3 ) ) ).
% 4.69/4.94
% 4.69/4.94 % rel_restrict_trancl_notR(1)
% 4.69/4.94 thf(fact_2090_rel__restrict__trancl__notR_I1_J,axiom,
% 4.69/4.94 ! [V: nat,W: nat,E: set_Pr1261947904930325089at_nat,R3: set_nat] :
% 4.69/4.94 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ V @ W ) @ ( transi6264000038957366511cl_nat @ ( rel_restrict_nat @ E @ R3 ) ) )
% 4.69/4.94 => ~ ( member_nat @ V @ R3 ) ) ).
% 4.69/4.94
% 4.69/4.94 % rel_restrict_trancl_notR(1)
% 4.69/4.94 thf(fact_2091_rel__restrict__trancl__notR_I1_J,axiom,
% 4.69/4.94 ! [V: int,W: int,E: set_Pr958786334691620121nt_int,R3: set_int] :
% 4.69/4.94 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ V @ W ) @ ( transi6261509568448316235cl_int @ ( rel_restrict_int @ E @ R3 ) ) )
% 4.69/4.94 => ~ ( member_int @ V @ R3 ) ) ).
% 4.69/4.94
% 4.69/4.94 % rel_restrict_trancl_notR(1)
% 4.69/4.94 thf(fact_2092_rel__restrict__trancl__mem,axiom,
% 4.69/4.94 ! [A2: nat,B: nat,A: set_Pr1261947904930325089at_nat,R3: set_nat] :
% 4.69/4.94 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( transi6264000038957366511cl_nat @ ( rel_restrict_nat @ A @ R3 ) ) )
% 4.69/4.94 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( rel_restrict_nat @ ( transi6264000038957366511cl_nat @ A ) @ R3 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % rel_restrict_trancl_mem
% 4.69/4.94 thf(fact_2093_rel__restrict__trancl__mem,axiom,
% 4.69/4.94 ! [A2: int,B: int,A: set_Pr958786334691620121nt_int,R3: set_int] :
% 4.69/4.94 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( transi6261509568448316235cl_int @ ( rel_restrict_int @ A @ R3 ) ) )
% 4.69/4.94 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( rel_restrict_int @ ( transi6261509568448316235cl_int @ A ) @ R3 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % rel_restrict_trancl_mem
% 4.69/4.94 thf(fact_2094_rel__restrict__mono2,axiom,
% 4.69/4.94 ! [R3: set_nat,S: set_nat,A: set_Pr1261947904930325089at_nat] :
% 4.69/4.94 ( ( ord_less_eq_set_nat @ R3 @ S )
% 4.69/4.94 => ( ord_le3146513528884898305at_nat @ ( rel_restrict_nat @ A @ S ) @ ( rel_restrict_nat @ A @ R3 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % rel_restrict_mono2
% 4.69/4.94 thf(fact_2095_singleton__quotient,axiom,
% 4.69/4.94 ! [X: product_unit,R2: set_Pr5094982260447487303t_unit] :
% 4.69/4.94 ( ( equiv_5172566880711946708t_unit @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) @ R2 )
% 4.69/4.94 = ( insert8986028188087627965t_unit @ ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) @ bot_bo6284674557190688313t_unit ) ) ).
% 4.69/4.94
% 4.69/4.94 % singleton_quotient
% 4.69/4.94 thf(fact_2096_singleton__quotient,axiom,
% 4.69/4.94 ! [X: $o,R2: set_Product_prod_o_o] :
% 4.69/4.94 ( ( equiv_quotient_o @ ( insert_o @ X @ bot_bot_set_o ) @ R2 )
% 4.69/4.94 = ( insert_set_o @ ( image_o_o @ R2 @ ( insert_o @ X @ bot_bot_set_o ) ) @ bot_bot_set_set_o ) ) ).
% 4.69/4.94
% 4.69/4.94 % singleton_quotient
% 4.69/4.94 thf(fact_2097_singleton__quotient,axiom,
% 4.69/4.94 ! [X: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.94 ( ( equiv_quotient_nat @ ( insert_nat @ X @ bot_bot_set_nat ) @ R2 )
% 4.69/4.94 = ( insert_set_nat @ ( image_nat_nat @ R2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ bot_bot_set_set_nat ) ) ).
% 4.69/4.94
% 4.69/4.94 % singleton_quotient
% 4.69/4.94 thf(fact_2098_singleton__quotient,axiom,
% 4.69/4.94 ! [X: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.94 ( ( equiv_quotient_int @ ( insert_int @ X @ bot_bot_set_int ) @ R2 )
% 4.69/4.94 = ( insert_set_int @ ( image_int_int @ R2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ bot_bot_set_set_int ) ) ).
% 4.69/4.94
% 4.69/4.94 % singleton_quotient
% 4.69/4.94 thf(fact_2099_singleton__quotient,axiom,
% 4.69/4.94 ! [X: produc3658429121746597890et_nat > $o,R2: set_Pr2161125870931222855_nat_o] :
% 4.69/4.94 ( ( equiv_7899955228204526484_nat_o @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) @ R2 )
% 4.69/4.94 = ( insert2507855216428400253_nat_o @ ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) @ bot_bo3736544561982865913_nat_o ) ) ).
% 4.69/4.94
% 4.69/4.94 % singleton_quotient
% 4.69/4.94 thf(fact_2100_quotientI,axiom,
% 4.69/4.94 ! [X: product_unit,A: set_Product_unit,R2: set_Pr5094982260447487303t_unit] :
% 4.69/4.94 ( ( member_Product_unit @ X @ A )
% 4.69/4.94 => ( member5877623283571906838t_unit @ ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) @ ( equiv_5172566880711946708t_unit @ A @ R2 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotientI
% 4.69/4.94 thf(fact_2101_quotientI,axiom,
% 4.69/4.94 ! [X: $o,A: set_o,R2: set_Product_prod_o_o] :
% 4.69/4.94 ( ( member_o @ X @ A )
% 4.69/4.94 => ( member_set_o @ ( image_o_o @ R2 @ ( insert_o @ X @ bot_bot_set_o ) ) @ ( equiv_quotient_o @ A @ R2 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotientI
% 4.69/4.94 thf(fact_2102_quotientI,axiom,
% 4.69/4.94 ! [X: nat,A: set_nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.94 ( ( member_nat @ X @ A )
% 4.69/4.94 => ( member_set_nat @ ( image_nat_nat @ R2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ ( equiv_quotient_nat @ A @ R2 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotientI
% 4.69/4.94 thf(fact_2103_quotientI,axiom,
% 4.69/4.94 ! [X: int,A: set_int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.94 ( ( member_int @ X @ A )
% 4.69/4.94 => ( member_set_int @ ( image_int_int @ R2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ ( equiv_quotient_int @ A @ R2 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotientI
% 4.69/4.94 thf(fact_2104_quotientI,axiom,
% 4.69/4.94 ! [X: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o] :
% 4.69/4.94 ( ( member6576561426505652726_nat_o @ X @ A )
% 4.69/4.94 => ( member1452989533377600726_nat_o @ ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) @ ( equiv_7899955228204526484_nat_o @ A @ R2 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotientI
% 4.69/4.94 thf(fact_2105_quotientE,axiom,
% 4.69/4.94 ! [X4: set_Product_unit,A: set_Product_unit,R2: set_Pr5094982260447487303t_unit] :
% 4.69/4.94 ( ( member5877623283571906838t_unit @ X4 @ ( equiv_5172566880711946708t_unit @ A @ R2 ) )
% 4.69/4.94 => ~ ! [X3: product_unit] :
% 4.69/4.94 ( ( X4
% 4.69/4.94 = ( image_8431784415008483091t_unit @ R2 @ ( insert_Product_unit @ X3 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.94 => ~ ( member_Product_unit @ X3 @ A ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotientE
% 4.69/4.94 thf(fact_2106_quotientE,axiom,
% 4.69/4.94 ! [X4: set_o,A: set_o,R2: set_Product_prod_o_o] :
% 4.69/4.94 ( ( member_set_o @ X4 @ ( equiv_quotient_o @ A @ R2 ) )
% 4.69/4.94 => ~ ! [X3: $o] :
% 4.69/4.94 ( ( X4
% 4.69/4.94 = ( image_o_o @ R2 @ ( insert_o @ X3 @ bot_bot_set_o ) ) )
% 4.69/4.94 => ~ ( member_o @ X3 @ A ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotientE
% 4.69/4.94 thf(fact_2107_quotientE,axiom,
% 4.69/4.94 ! [X4: set_nat,A: set_nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.94 ( ( member_set_nat @ X4 @ ( equiv_quotient_nat @ A @ R2 ) )
% 4.69/4.94 => ~ ! [X3: nat] :
% 4.69/4.94 ( ( X4
% 4.69/4.94 = ( image_nat_nat @ R2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) )
% 4.69/4.94 => ~ ( member_nat @ X3 @ A ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotientE
% 4.69/4.94 thf(fact_2108_quotientE,axiom,
% 4.69/4.94 ! [X4: set_int,A: set_int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.94 ( ( member_set_int @ X4 @ ( equiv_quotient_int @ A @ R2 ) )
% 4.69/4.94 => ~ ! [X3: int] :
% 4.69/4.94 ( ( X4
% 4.69/4.94 = ( image_int_int @ R2 @ ( insert_int @ X3 @ bot_bot_set_int ) ) )
% 4.69/4.94 => ~ ( member_int @ X3 @ A ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotientE
% 4.69/4.94 thf(fact_2109_quotientE,axiom,
% 4.69/4.94 ! [X4: set_Pr4532377907799695533_nat_o,A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o] :
% 4.69/4.94 ( ( member1452989533377600726_nat_o @ X4 @ ( equiv_7899955228204526484_nat_o @ A @ R2 ) )
% 4.69/4.94 => ~ ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( X4
% 4.69/4.94 = ( image_2232984160439939859_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ X3 @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/4.94 => ~ ( member6576561426505652726_nat_o @ X3 @ A ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotientE
% 4.69/4.94 thf(fact_2110_Inf__fin_OboundedE,axiom,
% 4.69/4.94 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.94 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.94 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( ord_le3221252021190050221t_unit @ X @ ( lattic1263872656861969706t_unit @ A ) )
% 4.69/4.94 => ! [A10: product_unit] :
% 4.69/4.94 ( ( member_Product_unit @ A10 @ A )
% 4.69/4.94 => ( ord_le3221252021190050221t_unit @ X @ A10 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.boundedE
% 4.69/4.94 thf(fact_2111_Inf__fin_OboundedE,axiom,
% 4.69/4.94 ! [A: set_o,X: $o] :
% 4.69/4.94 ( ( finite_finite_o @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_o )
% 4.69/4.94 => ( ( ord_less_eq_o @ X @ ( lattic4107685809792843317_fin_o @ A ) )
% 4.69/4.94 => ! [A10: $o] :
% 4.69/4.94 ( ( member_o @ A10 @ A )
% 4.69/4.94 => ( ord_less_eq_o @ X @ A10 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.boundedE
% 4.69/4.94 thf(fact_2112_Inf__fin_OboundedE,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.94 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( ord_le729326519192465773_nat_o @ X @ ( lattic956194824204696298_nat_o @ A ) )
% 4.69/4.94 => ! [A10: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( member6576561426505652726_nat_o @ A10 @ A )
% 4.69/4.94 => ( ord_le729326519192465773_nat_o @ X @ A10 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.boundedE
% 4.69/4.94 thf(fact_2113_Inf__fin_OboundedE,axiom,
% 4.69/4.94 ! [A: set_filter_nat,X: filter_nat] :
% 4.69/4.94 ( ( finite2119507909894593271er_nat @ A )
% 4.69/4.94 => ( ( A != bot_bo498966703094740906er_nat )
% 4.69/4.94 => ( ( ord_le2510731241096832064er_nat @ X @ ( lattic9128708996678779395er_nat @ A ) )
% 4.69/4.94 => ! [A10: filter_nat] :
% 4.69/4.94 ( ( member_filter_nat @ A10 @ A )
% 4.69/4.94 => ( ord_le2510731241096832064er_nat @ X @ A10 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.boundedE
% 4.69/4.94 thf(fact_2114_Inf__fin_OboundedE,axiom,
% 4.69/4.94 ! [A: set_set_nat,X: set_nat] :
% 4.69/4.94 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_set_nat )
% 4.69/4.94 => ( ( ord_less_eq_set_nat @ X @ ( lattic3014633134055518761et_nat @ A ) )
% 4.69/4.94 => ! [A10: set_nat] :
% 4.69/4.94 ( ( member_set_nat @ A10 @ A )
% 4.69/4.94 => ( ord_less_eq_set_nat @ X @ A10 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.boundedE
% 4.69/4.94 thf(fact_2115_Inf__fin_OboundedE,axiom,
% 4.69/4.94 ! [A: set_rat,X: rat] :
% 4.69/4.94 ( ( finite_finite_rat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_rat )
% 4.69/4.94 => ( ( ord_less_eq_rat @ X @ ( lattic4603258475043424379in_rat @ A ) )
% 4.69/4.94 => ! [A10: rat] :
% 4.69/4.94 ( ( member_rat @ A10 @ A )
% 4.69/4.94 => ( ord_less_eq_rat @ X @ A10 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.boundedE
% 4.69/4.94 thf(fact_2116_Inf__fin_OboundedE,axiom,
% 4.69/4.94 ! [A: set_nat,X: nat] :
% 4.69/4.94 ( ( finite_finite_nat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_nat )
% 4.69/4.94 => ( ( ord_less_eq_nat @ X @ ( lattic5238388535129920115in_nat @ A ) )
% 4.69/4.94 => ! [A10: nat] :
% 4.69/4.94 ( ( member_nat @ A10 @ A )
% 4.69/4.94 => ( ord_less_eq_nat @ X @ A10 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.boundedE
% 4.69/4.94 thf(fact_2117_Inf__fin_OboundedE,axiom,
% 4.69/4.94 ! [A: set_int,X: int] :
% 4.69/4.94 ( ( finite_finite_int @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_int )
% 4.69/4.94 => ( ( ord_less_eq_int @ X @ ( lattic5235898064620869839in_int @ A ) )
% 4.69/4.94 => ! [A10: int] :
% 4.69/4.94 ( ( member_int @ A10 @ A )
% 4.69/4.94 => ( ord_less_eq_int @ X @ A10 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.boundedE
% 4.69/4.94 thf(fact_2118_Inf__fin_OboundedI,axiom,
% 4.69/4.94 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.94 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.94 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ! [A4: product_unit] :
% 4.69/4.94 ( ( member_Product_unit @ A4 @ A )
% 4.69/4.94 => ( ord_le3221252021190050221t_unit @ X @ A4 ) )
% 4.69/4.94 => ( ord_le3221252021190050221t_unit @ X @ ( lattic1263872656861969706t_unit @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.boundedI
% 4.69/4.94 thf(fact_2119_Inf__fin_OboundedI,axiom,
% 4.69/4.94 ! [A: set_o,X: $o] :
% 4.69/4.94 ( ( finite_finite_o @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_o )
% 4.69/4.94 => ( ! [A4: $o] :
% 4.69/4.94 ( ( member_o @ A4 @ A )
% 4.69/4.94 => ( ord_less_eq_o @ X @ A4 ) )
% 4.69/4.94 => ( ord_less_eq_o @ X @ ( lattic4107685809792843317_fin_o @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.boundedI
% 4.69/4.94 thf(fact_2120_Inf__fin_OboundedI,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.94 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ! [A4: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( member6576561426505652726_nat_o @ A4 @ A )
% 4.69/4.94 => ( ord_le729326519192465773_nat_o @ X @ A4 ) )
% 4.69/4.94 => ( ord_le729326519192465773_nat_o @ X @ ( lattic956194824204696298_nat_o @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.boundedI
% 4.69/4.94 thf(fact_2121_Inf__fin_OboundedI,axiom,
% 4.69/4.94 ! [A: set_filter_nat,X: filter_nat] :
% 4.69/4.94 ( ( finite2119507909894593271er_nat @ A )
% 4.69/4.94 => ( ( A != bot_bo498966703094740906er_nat )
% 4.69/4.94 => ( ! [A4: filter_nat] :
% 4.69/4.94 ( ( member_filter_nat @ A4 @ A )
% 4.69/4.94 => ( ord_le2510731241096832064er_nat @ X @ A4 ) )
% 4.69/4.94 => ( ord_le2510731241096832064er_nat @ X @ ( lattic9128708996678779395er_nat @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.boundedI
% 4.69/4.94 thf(fact_2122_Inf__fin_OboundedI,axiom,
% 4.69/4.94 ! [A: set_set_nat,X: set_nat] :
% 4.69/4.94 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_set_nat )
% 4.69/4.94 => ( ! [A4: set_nat] :
% 4.69/4.94 ( ( member_set_nat @ A4 @ A )
% 4.69/4.94 => ( ord_less_eq_set_nat @ X @ A4 ) )
% 4.69/4.94 => ( ord_less_eq_set_nat @ X @ ( lattic3014633134055518761et_nat @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.boundedI
% 4.69/4.94 thf(fact_2123_Inf__fin_OboundedI,axiom,
% 4.69/4.94 ! [A: set_rat,X: rat] :
% 4.69/4.94 ( ( finite_finite_rat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_rat )
% 4.69/4.94 => ( ! [A4: rat] :
% 4.69/4.94 ( ( member_rat @ A4 @ A )
% 4.69/4.94 => ( ord_less_eq_rat @ X @ A4 ) )
% 4.69/4.94 => ( ord_less_eq_rat @ X @ ( lattic4603258475043424379in_rat @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.boundedI
% 4.69/4.94 thf(fact_2124_Inf__fin_OboundedI,axiom,
% 4.69/4.94 ! [A: set_nat,X: nat] :
% 4.69/4.94 ( ( finite_finite_nat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_nat )
% 4.69/4.94 => ( ! [A4: nat] :
% 4.69/4.94 ( ( member_nat @ A4 @ A )
% 4.69/4.94 => ( ord_less_eq_nat @ X @ A4 ) )
% 4.69/4.94 => ( ord_less_eq_nat @ X @ ( lattic5238388535129920115in_nat @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.boundedI
% 4.69/4.94 thf(fact_2125_Inf__fin_OboundedI,axiom,
% 4.69/4.94 ! [A: set_int,X: int] :
% 4.69/4.94 ( ( finite_finite_int @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_int )
% 4.69/4.94 => ( ! [A4: int] :
% 4.69/4.94 ( ( member_int @ A4 @ A )
% 4.69/4.94 => ( ord_less_eq_int @ X @ A4 ) )
% 4.69/4.94 => ( ord_less_eq_int @ X @ ( lattic5235898064620869839in_int @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.boundedI
% 4.69/4.94 thf(fact_2126_Sup__fin_OboundedE,axiom,
% 4.69/4.94 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.94 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.94 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( ord_le3221252021190050221t_unit @ ( lattic5294303975357428420t_unit @ A ) @ X )
% 4.69/4.94 => ! [A10: product_unit] :
% 4.69/4.94 ( ( member_Product_unit @ A10 @ A )
% 4.69/4.94 => ( ord_le3221252021190050221t_unit @ A10 @ X ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.boundedE
% 4.69/4.94 thf(fact_2127_Sup__fin_OboundedE,axiom,
% 4.69/4.94 ! [A: set_o,X: $o] :
% 4.69/4.94 ( ( finite_finite_o @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_o )
% 4.69/4.94 => ( ( ord_less_eq_o @ ( lattic1508158080041050831_fin_o @ A ) @ X )
% 4.69/4.94 => ! [A10: $o] :
% 4.69/4.94 ( ( member_o @ A10 @ A )
% 4.69/4.94 => ( ord_less_eq_o @ A10 @ X ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.boundedE
% 4.69/4.94 thf(fact_2128_Sup__fin_OboundedE,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.94 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( ord_le729326519192465773_nat_o @ ( lattic7320199455484906628_nat_o @ A ) @ X )
% 4.69/4.94 => ! [A10: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( member6576561426505652726_nat_o @ A10 @ A )
% 4.69/4.94 => ( ord_le729326519192465773_nat_o @ A10 @ X ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.boundedE
% 4.69/4.94 thf(fact_2129_Sup__fin_OboundedE,axiom,
% 4.69/4.94 ! [A: set_filter_nat,X: filter_nat] :
% 4.69/4.94 ( ( finite2119507909894593271er_nat @ A )
% 4.69/4.94 => ( ( A != bot_bo498966703094740906er_nat )
% 4.69/4.94 => ( ( ord_le2510731241096832064er_nat @ ( lattic5930898082463196905er_nat @ A ) @ X )
% 4.69/4.94 => ! [A10: filter_nat] :
% 4.69/4.94 ( ( member_filter_nat @ A10 @ A )
% 4.69/4.94 => ( ord_le2510731241096832064er_nat @ A10 @ X ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.boundedE
% 4.69/4.94 thf(fact_2130_Sup__fin_OboundedE,axiom,
% 4.69/4.94 ! [A: set_set_nat,X: set_nat] :
% 4.69/4.94 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_set_nat )
% 4.69/4.94 => ( ( ord_less_eq_set_nat @ ( lattic3835124923745554447et_nat @ A ) @ X )
% 4.69/4.94 => ! [A10: set_nat] :
% 4.69/4.94 ( ( member_set_nat @ A10 @ A )
% 4.69/4.94 => ( ord_less_eq_set_nat @ A10 @ X ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.boundedE
% 4.69/4.94 thf(fact_2131_Sup__fin_OboundedE,axiom,
% 4.69/4.94 ! [A: set_rat,X: rat] :
% 4.69/4.94 ( ( finite_finite_rat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_rat )
% 4.69/4.94 => ( ( ord_less_eq_rat @ ( lattic458866745392299617in_rat @ A ) @ X )
% 4.69/4.94 => ! [A10: rat] :
% 4.69/4.94 ( ( member_rat @ A10 @ A )
% 4.69/4.94 => ( ord_less_eq_rat @ A10 @ X ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.boundedE
% 4.69/4.94 thf(fact_2132_Sup__fin_OboundedE,axiom,
% 4.69/4.94 ! [A: set_nat,X: nat] :
% 4.69/4.94 ( ( finite_finite_nat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_nat )
% 4.69/4.94 => ( ( ord_less_eq_nat @ ( lattic1093996805478795353in_nat @ A ) @ X )
% 4.69/4.94 => ! [A10: nat] :
% 4.69/4.94 ( ( member_nat @ A10 @ A )
% 4.69/4.94 => ( ord_less_eq_nat @ A10 @ X ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.boundedE
% 4.69/4.94 thf(fact_2133_Sup__fin_OboundedE,axiom,
% 4.69/4.94 ! [A: set_int,X: int] :
% 4.69/4.94 ( ( finite_finite_int @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_int )
% 4.69/4.94 => ( ( ord_less_eq_int @ ( lattic1091506334969745077in_int @ A ) @ X )
% 4.69/4.94 => ! [A10: int] :
% 4.69/4.94 ( ( member_int @ A10 @ A )
% 4.69/4.94 => ( ord_less_eq_int @ A10 @ X ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.boundedE
% 4.69/4.94 thf(fact_2134_Sup__fin_OboundedI,axiom,
% 4.69/4.94 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.94 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.94 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ! [A4: product_unit] :
% 4.69/4.94 ( ( member_Product_unit @ A4 @ A )
% 4.69/4.94 => ( ord_le3221252021190050221t_unit @ A4 @ X ) )
% 4.69/4.94 => ( ord_le3221252021190050221t_unit @ ( lattic5294303975357428420t_unit @ A ) @ X ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.boundedI
% 4.69/4.94 thf(fact_2135_Sup__fin_OboundedI,axiom,
% 4.69/4.94 ! [A: set_o,X: $o] :
% 4.69/4.94 ( ( finite_finite_o @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_o )
% 4.69/4.94 => ( ! [A4: $o] :
% 4.69/4.94 ( ( member_o @ A4 @ A )
% 4.69/4.94 => ( ord_less_eq_o @ A4 @ X ) )
% 4.69/4.94 => ( ord_less_eq_o @ ( lattic1508158080041050831_fin_o @ A ) @ X ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.boundedI
% 4.69/4.94 thf(fact_2136_Sup__fin_OboundedI,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.94 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ! [A4: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( member6576561426505652726_nat_o @ A4 @ A )
% 4.69/4.94 => ( ord_le729326519192465773_nat_o @ A4 @ X ) )
% 4.69/4.94 => ( ord_le729326519192465773_nat_o @ ( lattic7320199455484906628_nat_o @ A ) @ X ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.boundedI
% 4.69/4.94 thf(fact_2137_Sup__fin_OboundedI,axiom,
% 4.69/4.94 ! [A: set_filter_nat,X: filter_nat] :
% 4.69/4.94 ( ( finite2119507909894593271er_nat @ A )
% 4.69/4.94 => ( ( A != bot_bo498966703094740906er_nat )
% 4.69/4.94 => ( ! [A4: filter_nat] :
% 4.69/4.94 ( ( member_filter_nat @ A4 @ A )
% 4.69/4.94 => ( ord_le2510731241096832064er_nat @ A4 @ X ) )
% 4.69/4.94 => ( ord_le2510731241096832064er_nat @ ( lattic5930898082463196905er_nat @ A ) @ X ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.boundedI
% 4.69/4.94 thf(fact_2138_Sup__fin_OboundedI,axiom,
% 4.69/4.94 ! [A: set_set_nat,X: set_nat] :
% 4.69/4.94 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_set_nat )
% 4.69/4.94 => ( ! [A4: set_nat] :
% 4.69/4.94 ( ( member_set_nat @ A4 @ A )
% 4.69/4.94 => ( ord_less_eq_set_nat @ A4 @ X ) )
% 4.69/4.94 => ( ord_less_eq_set_nat @ ( lattic3835124923745554447et_nat @ A ) @ X ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.boundedI
% 4.69/4.94 thf(fact_2139_Sup__fin_OboundedI,axiom,
% 4.69/4.94 ! [A: set_rat,X: rat] :
% 4.69/4.94 ( ( finite_finite_rat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_rat )
% 4.69/4.94 => ( ! [A4: rat] :
% 4.69/4.94 ( ( member_rat @ A4 @ A )
% 4.69/4.94 => ( ord_less_eq_rat @ A4 @ X ) )
% 4.69/4.94 => ( ord_less_eq_rat @ ( lattic458866745392299617in_rat @ A ) @ X ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.boundedI
% 4.69/4.94 thf(fact_2140_Sup__fin_OboundedI,axiom,
% 4.69/4.94 ! [A: set_nat,X: nat] :
% 4.69/4.94 ( ( finite_finite_nat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_nat )
% 4.69/4.94 => ( ! [A4: nat] :
% 4.69/4.94 ( ( member_nat @ A4 @ A )
% 4.69/4.94 => ( ord_less_eq_nat @ A4 @ X ) )
% 4.69/4.94 => ( ord_less_eq_nat @ ( lattic1093996805478795353in_nat @ A ) @ X ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.boundedI
% 4.69/4.94 thf(fact_2141_Sup__fin_OboundedI,axiom,
% 4.69/4.94 ! [A: set_int,X: int] :
% 4.69/4.94 ( ( finite_finite_int @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_int )
% 4.69/4.94 => ( ! [A4: int] :
% 4.69/4.94 ( ( member_int @ A4 @ A )
% 4.69/4.94 => ( ord_less_eq_int @ A4 @ X ) )
% 4.69/4.94 => ( ord_less_eq_int @ ( lattic1091506334969745077in_int @ A ) @ X ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.boundedI
% 4.69/4.94 thf(fact_2142_Inf__fin_Obounded__iff,axiom,
% 4.69/4.94 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.94 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.94 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( ord_le3221252021190050221t_unit @ X @ ( lattic1263872656861969706t_unit @ A ) )
% 4.69/4.94 = ( ! [X2: product_unit] :
% 4.69/4.94 ( ( member_Product_unit @ X2 @ A )
% 4.69/4.94 => ( ord_le3221252021190050221t_unit @ X @ X2 ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.bounded_iff
% 4.69/4.94 thf(fact_2143_Inf__fin_Obounded__iff,axiom,
% 4.69/4.94 ! [A: set_o,X: $o] :
% 4.69/4.94 ( ( finite_finite_o @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_o )
% 4.69/4.94 => ( ( ord_less_eq_o @ X @ ( lattic4107685809792843317_fin_o @ A ) )
% 4.69/4.94 = ( ! [X2: $o] :
% 4.69/4.94 ( ( member_o @ X2 @ A )
% 4.69/4.94 => ( ord_less_eq_o @ X @ X2 ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.bounded_iff
% 4.69/4.94 thf(fact_2144_Inf__fin_Obounded__iff,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.94 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( ord_le729326519192465773_nat_o @ X @ ( lattic956194824204696298_nat_o @ A ) )
% 4.69/4.94 = ( ! [X2: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( member6576561426505652726_nat_o @ X2 @ A )
% 4.69/4.94 => ( ord_le729326519192465773_nat_o @ X @ X2 ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.bounded_iff
% 4.69/4.94 thf(fact_2145_Inf__fin_Obounded__iff,axiom,
% 4.69/4.94 ! [A: set_filter_nat,X: filter_nat] :
% 4.69/4.94 ( ( finite2119507909894593271er_nat @ A )
% 4.69/4.94 => ( ( A != bot_bo498966703094740906er_nat )
% 4.69/4.94 => ( ( ord_le2510731241096832064er_nat @ X @ ( lattic9128708996678779395er_nat @ A ) )
% 4.69/4.94 = ( ! [X2: filter_nat] :
% 4.69/4.94 ( ( member_filter_nat @ X2 @ A )
% 4.69/4.94 => ( ord_le2510731241096832064er_nat @ X @ X2 ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.bounded_iff
% 4.69/4.94 thf(fact_2146_Inf__fin_Obounded__iff,axiom,
% 4.69/4.94 ! [A: set_set_nat,X: set_nat] :
% 4.69/4.94 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_set_nat )
% 4.69/4.94 => ( ( ord_less_eq_set_nat @ X @ ( lattic3014633134055518761et_nat @ A ) )
% 4.69/4.94 = ( ! [X2: set_nat] :
% 4.69/4.94 ( ( member_set_nat @ X2 @ A )
% 4.69/4.94 => ( ord_less_eq_set_nat @ X @ X2 ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.bounded_iff
% 4.69/4.94 thf(fact_2147_Inf__fin_Obounded__iff,axiom,
% 4.69/4.94 ! [A: set_rat,X: rat] :
% 4.69/4.94 ( ( finite_finite_rat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_rat )
% 4.69/4.94 => ( ( ord_less_eq_rat @ X @ ( lattic4603258475043424379in_rat @ A ) )
% 4.69/4.94 = ( ! [X2: rat] :
% 4.69/4.94 ( ( member_rat @ X2 @ A )
% 4.69/4.94 => ( ord_less_eq_rat @ X @ X2 ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.bounded_iff
% 4.69/4.94 thf(fact_2148_Inf__fin_Obounded__iff,axiom,
% 4.69/4.94 ! [A: set_nat,X: nat] :
% 4.69/4.94 ( ( finite_finite_nat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_nat )
% 4.69/4.94 => ( ( ord_less_eq_nat @ X @ ( lattic5238388535129920115in_nat @ A ) )
% 4.69/4.94 = ( ! [X2: nat] :
% 4.69/4.94 ( ( member_nat @ X2 @ A )
% 4.69/4.94 => ( ord_less_eq_nat @ X @ X2 ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.bounded_iff
% 4.69/4.94 thf(fact_2149_Inf__fin_Obounded__iff,axiom,
% 4.69/4.94 ! [A: set_int,X: int] :
% 4.69/4.94 ( ( finite_finite_int @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_int )
% 4.69/4.94 => ( ( ord_less_eq_int @ X @ ( lattic5235898064620869839in_int @ A ) )
% 4.69/4.94 = ( ! [X2: int] :
% 4.69/4.94 ( ( member_int @ X2 @ A )
% 4.69/4.94 => ( ord_less_eq_int @ X @ X2 ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.bounded_iff
% 4.69/4.94 thf(fact_2150_Sup__fin_Obounded__iff,axiom,
% 4.69/4.94 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.94 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.94 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( ord_le3221252021190050221t_unit @ ( lattic5294303975357428420t_unit @ A ) @ X )
% 4.69/4.94 = ( ! [X2: product_unit] :
% 4.69/4.94 ( ( member_Product_unit @ X2 @ A )
% 4.69/4.94 => ( ord_le3221252021190050221t_unit @ X2 @ X ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.bounded_iff
% 4.69/4.94 thf(fact_2151_Sup__fin_Obounded__iff,axiom,
% 4.69/4.94 ! [A: set_o,X: $o] :
% 4.69/4.94 ( ( finite_finite_o @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_o )
% 4.69/4.94 => ( ( ord_less_eq_o @ ( lattic1508158080041050831_fin_o @ A ) @ X )
% 4.69/4.94 = ( ! [X2: $o] :
% 4.69/4.94 ( ( member_o @ X2 @ A )
% 4.69/4.94 => ( ord_less_eq_o @ X2 @ X ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.bounded_iff
% 4.69/4.94 thf(fact_2152_Sup__fin_Obounded__iff,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.94 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( ord_le729326519192465773_nat_o @ ( lattic7320199455484906628_nat_o @ A ) @ X )
% 4.69/4.94 = ( ! [X2: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( member6576561426505652726_nat_o @ X2 @ A )
% 4.69/4.94 => ( ord_le729326519192465773_nat_o @ X2 @ X ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.bounded_iff
% 4.69/4.94 thf(fact_2153_Sup__fin_Obounded__iff,axiom,
% 4.69/4.94 ! [A: set_filter_nat,X: filter_nat] :
% 4.69/4.94 ( ( finite2119507909894593271er_nat @ A )
% 4.69/4.94 => ( ( A != bot_bo498966703094740906er_nat )
% 4.69/4.94 => ( ( ord_le2510731241096832064er_nat @ ( lattic5930898082463196905er_nat @ A ) @ X )
% 4.69/4.94 = ( ! [X2: filter_nat] :
% 4.69/4.94 ( ( member_filter_nat @ X2 @ A )
% 4.69/4.94 => ( ord_le2510731241096832064er_nat @ X2 @ X ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.bounded_iff
% 4.69/4.94 thf(fact_2154_Sup__fin_Obounded__iff,axiom,
% 4.69/4.94 ! [A: set_set_nat,X: set_nat] :
% 4.69/4.94 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_set_nat )
% 4.69/4.94 => ( ( ord_less_eq_set_nat @ ( lattic3835124923745554447et_nat @ A ) @ X )
% 4.69/4.94 = ( ! [X2: set_nat] :
% 4.69/4.94 ( ( member_set_nat @ X2 @ A )
% 4.69/4.94 => ( ord_less_eq_set_nat @ X2 @ X ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.bounded_iff
% 4.69/4.94 thf(fact_2155_Sup__fin_Obounded__iff,axiom,
% 4.69/4.94 ! [A: set_rat,X: rat] :
% 4.69/4.94 ( ( finite_finite_rat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_rat )
% 4.69/4.94 => ( ( ord_less_eq_rat @ ( lattic458866745392299617in_rat @ A ) @ X )
% 4.69/4.94 = ( ! [X2: rat] :
% 4.69/4.94 ( ( member_rat @ X2 @ A )
% 4.69/4.94 => ( ord_less_eq_rat @ X2 @ X ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.bounded_iff
% 4.69/4.94 thf(fact_2156_Sup__fin_Obounded__iff,axiom,
% 4.69/4.94 ! [A: set_nat,X: nat] :
% 4.69/4.94 ( ( finite_finite_nat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_nat )
% 4.69/4.94 => ( ( ord_less_eq_nat @ ( lattic1093996805478795353in_nat @ A ) @ X )
% 4.69/4.94 = ( ! [X2: nat] :
% 4.69/4.94 ( ( member_nat @ X2 @ A )
% 4.69/4.94 => ( ord_less_eq_nat @ X2 @ X ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.bounded_iff
% 4.69/4.94 thf(fact_2157_Sup__fin_Obounded__iff,axiom,
% 4.69/4.94 ! [A: set_int,X: int] :
% 4.69/4.94 ( ( finite_finite_int @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_int )
% 4.69/4.94 => ( ( ord_less_eq_int @ ( lattic1091506334969745077in_int @ A ) @ X )
% 4.69/4.94 = ( ! [X2: int] :
% 4.69/4.94 ( ( member_int @ X2 @ A )
% 4.69/4.94 => ( ord_less_eq_int @ X2 @ X ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.bounded_iff
% 4.69/4.94 thf(fact_2158_quotient__disj,axiom,
% 4.69/4.94 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit,X4: set_Product_unit,Y6: set_Product_unit] :
% 4.69/4.94 ( ( equiv_4189356295871601603t_unit @ A @ R2 )
% 4.69/4.94 => ( ( member5877623283571906838t_unit @ X4 @ ( equiv_5172566880711946708t_unit @ A @ R2 ) )
% 4.69/4.94 => ( ( member5877623283571906838t_unit @ Y6 @ ( equiv_5172566880711946708t_unit @ A @ R2 ) )
% 4.69/4.94 => ( ( X4 = Y6 )
% 4.69/4.94 | ( ( inf_in4660618365625256667t_unit @ X4 @ Y6 )
% 4.69/4.94 = bot_bo3957492148770167129t_unit ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotient_disj
% 4.69/4.94 thf(fact_2159_quotient__disj,axiom,
% 4.69/4.94 ! [A: set_o,R2: set_Product_prod_o_o,X4: set_o,Y6: set_o] :
% 4.69/4.94 ( ( equiv_equiv_o @ A @ R2 )
% 4.69/4.94 => ( ( member_set_o @ X4 @ ( equiv_quotient_o @ A @ R2 ) )
% 4.69/4.94 => ( ( member_set_o @ Y6 @ ( equiv_quotient_o @ A @ R2 ) )
% 4.69/4.94 => ( ( X4 = Y6 )
% 4.69/4.94 | ( ( inf_inf_set_o @ X4 @ Y6 )
% 4.69/4.94 = bot_bot_set_o ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotient_disj
% 4.69/4.94 thf(fact_2160_quotient__disj,axiom,
% 4.69/4.94 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,X4: set_nat,Y6: set_nat] :
% 4.69/4.94 ( ( equiv_equiv_nat @ A @ R2 )
% 4.69/4.94 => ( ( member_set_nat @ X4 @ ( equiv_quotient_nat @ A @ R2 ) )
% 4.69/4.94 => ( ( member_set_nat @ Y6 @ ( equiv_quotient_nat @ A @ R2 ) )
% 4.69/4.94 => ( ( X4 = Y6 )
% 4.69/4.94 | ( ( inf_inf_set_nat @ X4 @ Y6 )
% 4.69/4.94 = bot_bot_set_nat ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotient_disj
% 4.69/4.94 thf(fact_2161_quotient__disj,axiom,
% 4.69/4.94 ! [A: set_int,R2: set_Pr958786334691620121nt_int,X4: set_int,Y6: set_int] :
% 4.69/4.94 ( ( equiv_equiv_int @ A @ R2 )
% 4.69/4.94 => ( ( member_set_int @ X4 @ ( equiv_quotient_int @ A @ R2 ) )
% 4.69/4.94 => ( ( member_set_int @ Y6 @ ( equiv_quotient_int @ A @ R2 ) )
% 4.69/4.94 => ( ( X4 = Y6 )
% 4.69/4.94 | ( ( inf_inf_set_int @ X4 @ Y6 )
% 4.69/4.94 = bot_bot_set_int ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotient_disj
% 4.69/4.94 thf(fact_2162_quotient__disj,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o,X4: set_Pr4532377907799695533_nat_o,Y6: set_Pr4532377907799695533_nat_o] :
% 4.69/4.94 ( ( equiv_6726761681920839555_nat_o @ A @ R2 )
% 4.69/4.94 => ( ( member1452989533377600726_nat_o @ X4 @ ( equiv_7899955228204526484_nat_o @ A @ R2 ) )
% 4.69/4.94 => ( ( member1452989533377600726_nat_o @ Y6 @ ( equiv_7899955228204526484_nat_o @ A @ R2 ) )
% 4.69/4.94 => ( ( X4 = Y6 )
% 4.69/4.94 | ( ( inf_in1906310914598751387_nat_o @ X4 @ Y6 )
% 4.69/4.94 = bot_bo7824918357723582233_nat_o ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % quotient_disj
% 4.69/4.94 thf(fact_2163_rel__restrict__Int__empty,axiom,
% 4.69/4.94 ! [A: set_Product_unit,R3: set_Pr5094982260447487303t_unit] :
% 4.69/4.94 ( ( ( inf_in4660618365625256667t_unit @ A @ ( field_Product_unit @ R3 ) )
% 4.69/4.94 = bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( rel_re9207996470947987439t_unit @ R3 @ A )
% 4.69/4.94 = R3 ) ) ).
% 4.69/4.94
% 4.69/4.94 % rel_restrict_Int_empty
% 4.69/4.94 thf(fact_2164_rel__restrict__Int__empty,axiom,
% 4.69/4.94 ! [A: set_o,R3: set_Product_prod_o_o] :
% 4.69/4.94 ( ( ( inf_inf_set_o @ A @ ( field_o @ R3 ) )
% 4.69/4.94 = bot_bot_set_o )
% 4.69/4.94 => ( ( rel_restrict_o @ R3 @ A )
% 4.69/4.94 = R3 ) ) ).
% 4.69/4.94
% 4.69/4.94 % rel_restrict_Int_empty
% 4.69/4.94 thf(fact_2165_rel__restrict__Int__empty,axiom,
% 4.69/4.94 ! [A: set_nat,R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.94 ( ( ( inf_inf_set_nat @ A @ ( field_nat @ R3 ) )
% 4.69/4.94 = bot_bot_set_nat )
% 4.69/4.94 => ( ( rel_restrict_nat @ R3 @ A )
% 4.69/4.94 = R3 ) ) ).
% 4.69/4.94
% 4.69/4.94 % rel_restrict_Int_empty
% 4.69/4.94 thf(fact_2166_rel__restrict__Int__empty,axiom,
% 4.69/4.94 ! [A: set_int,R3: set_Pr958786334691620121nt_int] :
% 4.69/4.94 ( ( ( inf_inf_set_int @ A @ ( field_int @ R3 ) )
% 4.69/4.94 = bot_bot_set_int )
% 4.69/4.94 => ( ( rel_restrict_int @ R3 @ A )
% 4.69/4.94 = R3 ) ) ).
% 4.69/4.94
% 4.69/4.94 % rel_restrict_Int_empty
% 4.69/4.94 thf(fact_2167_rel__restrict__Int__empty,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,R3: set_Pr2161125870931222855_nat_o] :
% 4.69/4.94 ( ( ( inf_in1906310914598751387_nat_o @ A @ ( field_81821745747897882_nat_o @ R3 ) )
% 4.69/4.94 = bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( rel_re3331361160397388719_nat_o @ R3 @ A )
% 4.69/4.94 = R3 ) ) ).
% 4.69/4.94
% 4.69/4.94 % rel_restrict_Int_empty
% 4.69/4.94 thf(fact_2168_eq__equiv__class__iff2,axiom,
% 4.69/4.94 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit,X: product_unit,Y: product_unit] :
% 4.69/4.94 ( ( equiv_4189356295871601603t_unit @ A @ R2 )
% 4.69/4.94 => ( ( member_Product_unit @ X @ A )
% 4.69/4.94 => ( ( member_Product_unit @ Y @ A )
% 4.69/4.94 => ( ( ( equiv_5172566880711946708t_unit @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) @ R2 )
% 4.69/4.94 = ( equiv_5172566880711946708t_unit @ ( insert_Product_unit @ Y @ bot_bo3957492148770167129t_unit ) @ R2 ) )
% 4.69/4.94 = ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X @ Y ) @ R2 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % eq_equiv_class_iff2
% 4.69/4.94 thf(fact_2169_eq__equiv__class__iff2,axiom,
% 4.69/4.94 ! [A: set_o,R2: set_Product_prod_o_o,X: $o,Y: $o] :
% 4.69/4.94 ( ( equiv_equiv_o @ A @ R2 )
% 4.69/4.94 => ( ( member_o @ X @ A )
% 4.69/4.94 => ( ( member_o @ Y @ A )
% 4.69/4.94 => ( ( ( equiv_quotient_o @ ( insert_o @ X @ bot_bot_set_o ) @ R2 )
% 4.69/4.94 = ( equiv_quotient_o @ ( insert_o @ Y @ bot_bot_set_o ) @ R2 ) )
% 4.69/4.94 = ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ R2 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % eq_equiv_class_iff2
% 4.69/4.94 thf(fact_2170_eq__equiv__class__iff2,axiom,
% 4.69/4.94 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,X: nat,Y: nat] :
% 4.69/4.94 ( ( equiv_equiv_nat @ A @ R2 )
% 4.69/4.94 => ( ( member_nat @ X @ A )
% 4.69/4.94 => ( ( member_nat @ Y @ A )
% 4.69/4.94 => ( ( ( equiv_quotient_nat @ ( insert_nat @ X @ bot_bot_set_nat ) @ R2 )
% 4.69/4.94 = ( equiv_quotient_nat @ ( insert_nat @ Y @ bot_bot_set_nat ) @ R2 ) )
% 4.69/4.94 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R2 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % eq_equiv_class_iff2
% 4.69/4.94 thf(fact_2171_eq__equiv__class__iff2,axiom,
% 4.69/4.94 ! [A: set_int,R2: set_Pr958786334691620121nt_int,X: int,Y: int] :
% 4.69/4.94 ( ( equiv_equiv_int @ A @ R2 )
% 4.69/4.94 => ( ( member_int @ X @ A )
% 4.69/4.94 => ( ( member_int @ Y @ A )
% 4.69/4.94 => ( ( ( equiv_quotient_int @ ( insert_int @ X @ bot_bot_set_int ) @ R2 )
% 4.69/4.94 = ( equiv_quotient_int @ ( insert_int @ Y @ bot_bot_set_int ) @ R2 ) )
% 4.69/4.94 = ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R2 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % eq_equiv_class_iff2
% 4.69/4.94 thf(fact_2172_eq__equiv__class__iff2,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( equiv_6726761681920839555_nat_o @ A @ R2 )
% 4.69/4.94 => ( ( member6576561426505652726_nat_o @ X @ A )
% 4.69/4.94 => ( ( member6576561426505652726_nat_o @ Y @ A )
% 4.69/4.94 => ( ( ( equiv_7899955228204526484_nat_o @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) @ R2 )
% 4.69/4.94 = ( equiv_7899955228204526484_nat_o @ ( insert5175938949040314269_nat_o @ Y @ bot_bo7824918357723582233_nat_o ) @ R2 ) )
% 4.69/4.94 = ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ R2 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % eq_equiv_class_iff2
% 4.69/4.94 thf(fact_2173_Inf__fin_Osubset__imp,axiom,
% 4.69/4.94 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.94 ( ( ord_le3507040750410214029t_unit @ A @ B4 )
% 4.69/4.94 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( finite4290736615968046902t_unit @ B4 )
% 4.69/4.94 => ( ord_le3221252021190050221t_unit @ ( lattic1263872656861969706t_unit @ B4 ) @ ( lattic1263872656861969706t_unit @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.subset_imp
% 4.69/4.94 thf(fact_2174_Inf__fin_Osubset__imp,axiom,
% 4.69/4.94 ! [A: set_o,B4: set_o] :
% 4.69/4.94 ( ( ord_less_eq_set_o @ A @ B4 )
% 4.69/4.94 => ( ( A != bot_bot_set_o )
% 4.69/4.94 => ( ( finite_finite_o @ B4 )
% 4.69/4.94 => ( ord_less_eq_o @ ( lattic4107685809792843317_fin_o @ B4 ) @ ( lattic4107685809792843317_fin_o @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.subset_imp
% 4.69/4.94 thf(fact_2175_Inf__fin_Osubset__imp,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.94 ( ( ord_le2965882846123202637_nat_o @ A @ B4 )
% 4.69/4.94 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( finite3252695134891459830_nat_o @ B4 )
% 4.69/4.94 => ( ord_le729326519192465773_nat_o @ ( lattic956194824204696298_nat_o @ B4 ) @ ( lattic956194824204696298_nat_o @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.subset_imp
% 4.69/4.94 thf(fact_2176_Inf__fin_Osubset__imp,axiom,
% 4.69/4.94 ! [A: set_filter_nat,B4: set_filter_nat] :
% 4.69/4.94 ( ( ord_le2426478655948331894er_nat @ A @ B4 )
% 4.69/4.94 => ( ( A != bot_bo498966703094740906er_nat )
% 4.69/4.94 => ( ( finite2119507909894593271er_nat @ B4 )
% 4.69/4.94 => ( ord_le2510731241096832064er_nat @ ( lattic9128708996678779395er_nat @ B4 ) @ ( lattic9128708996678779395er_nat @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.subset_imp
% 4.69/4.94 thf(fact_2177_Inf__fin_Osubset__imp,axiom,
% 4.69/4.94 ! [A: set_set_nat,B4: set_set_nat] :
% 4.69/4.94 ( ( ord_le6893508408891458716et_nat @ A @ B4 )
% 4.69/4.94 => ( ( A != bot_bot_set_set_nat )
% 4.69/4.94 => ( ( finite1152437895449049373et_nat @ B4 )
% 4.69/4.94 => ( ord_less_eq_set_nat @ ( lattic3014633134055518761et_nat @ B4 ) @ ( lattic3014633134055518761et_nat @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.subset_imp
% 4.69/4.94 thf(fact_2178_Inf__fin_Osubset__imp,axiom,
% 4.69/4.94 ! [A: set_rat,B4: set_rat] :
% 4.69/4.94 ( ( ord_less_eq_set_rat @ A @ B4 )
% 4.69/4.94 => ( ( A != bot_bot_set_rat )
% 4.69/4.94 => ( ( finite_finite_rat @ B4 )
% 4.69/4.94 => ( ord_less_eq_rat @ ( lattic4603258475043424379in_rat @ B4 ) @ ( lattic4603258475043424379in_rat @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.subset_imp
% 4.69/4.94 thf(fact_2179_Inf__fin_Osubset__imp,axiom,
% 4.69/4.94 ! [A: set_int,B4: set_int] :
% 4.69/4.94 ( ( ord_less_eq_set_int @ A @ B4 )
% 4.69/4.94 => ( ( A != bot_bot_set_int )
% 4.69/4.94 => ( ( finite_finite_int @ B4 )
% 4.69/4.94 => ( ord_less_eq_int @ ( lattic5235898064620869839in_int @ B4 ) @ ( lattic5235898064620869839in_int @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.subset_imp
% 4.69/4.94 thf(fact_2180_Inf__fin_Osubset__imp,axiom,
% 4.69/4.94 ! [A: set_nat,B4: set_nat] :
% 4.69/4.94 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.94 => ( ( A != bot_bot_set_nat )
% 4.69/4.94 => ( ( finite_finite_nat @ B4 )
% 4.69/4.94 => ( ord_less_eq_nat @ ( lattic5238388535129920115in_nat @ B4 ) @ ( lattic5238388535129920115in_nat @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.subset_imp
% 4.69/4.94 thf(fact_2181_Sup__fin_Osubset__imp,axiom,
% 4.69/4.94 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.94 ( ( ord_le3507040750410214029t_unit @ A @ B4 )
% 4.69/4.94 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( finite4290736615968046902t_unit @ B4 )
% 4.69/4.94 => ( ord_le3221252021190050221t_unit @ ( lattic5294303975357428420t_unit @ A ) @ ( lattic5294303975357428420t_unit @ B4 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.subset_imp
% 4.69/4.94 thf(fact_2182_Sup__fin_Osubset__imp,axiom,
% 4.69/4.94 ! [A: set_o,B4: set_o] :
% 4.69/4.94 ( ( ord_less_eq_set_o @ A @ B4 )
% 4.69/4.94 => ( ( A != bot_bot_set_o )
% 4.69/4.94 => ( ( finite_finite_o @ B4 )
% 4.69/4.94 => ( ord_less_eq_o @ ( lattic1508158080041050831_fin_o @ A ) @ ( lattic1508158080041050831_fin_o @ B4 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.subset_imp
% 4.69/4.94 thf(fact_2183_Sup__fin_Osubset__imp,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.94 ( ( ord_le2965882846123202637_nat_o @ A @ B4 )
% 4.69/4.94 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( finite3252695134891459830_nat_o @ B4 )
% 4.69/4.94 => ( ord_le729326519192465773_nat_o @ ( lattic7320199455484906628_nat_o @ A ) @ ( lattic7320199455484906628_nat_o @ B4 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.subset_imp
% 4.69/4.94 thf(fact_2184_Sup__fin_Osubset__imp,axiom,
% 4.69/4.94 ! [A: set_filter_nat,B4: set_filter_nat] :
% 4.69/4.94 ( ( ord_le2426478655948331894er_nat @ A @ B4 )
% 4.69/4.94 => ( ( A != bot_bo498966703094740906er_nat )
% 4.69/4.94 => ( ( finite2119507909894593271er_nat @ B4 )
% 4.69/4.94 => ( ord_le2510731241096832064er_nat @ ( lattic5930898082463196905er_nat @ A ) @ ( lattic5930898082463196905er_nat @ B4 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.subset_imp
% 4.69/4.94 thf(fact_2185_Sup__fin_Osubset__imp,axiom,
% 4.69/4.94 ! [A: set_set_nat,B4: set_set_nat] :
% 4.69/4.94 ( ( ord_le6893508408891458716et_nat @ A @ B4 )
% 4.69/4.94 => ( ( A != bot_bot_set_set_nat )
% 4.69/4.94 => ( ( finite1152437895449049373et_nat @ B4 )
% 4.69/4.94 => ( ord_less_eq_set_nat @ ( lattic3835124923745554447et_nat @ A ) @ ( lattic3835124923745554447et_nat @ B4 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.subset_imp
% 4.69/4.94 thf(fact_2186_Sup__fin_Osubset__imp,axiom,
% 4.69/4.94 ! [A: set_rat,B4: set_rat] :
% 4.69/4.94 ( ( ord_less_eq_set_rat @ A @ B4 )
% 4.69/4.94 => ( ( A != bot_bot_set_rat )
% 4.69/4.94 => ( ( finite_finite_rat @ B4 )
% 4.69/4.94 => ( ord_less_eq_rat @ ( lattic458866745392299617in_rat @ A ) @ ( lattic458866745392299617in_rat @ B4 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.subset_imp
% 4.69/4.94 thf(fact_2187_Sup__fin_Osubset__imp,axiom,
% 4.69/4.94 ! [A: set_int,B4: set_int] :
% 4.69/4.94 ( ( ord_less_eq_set_int @ A @ B4 )
% 4.69/4.94 => ( ( A != bot_bot_set_int )
% 4.69/4.94 => ( ( finite_finite_int @ B4 )
% 4.69/4.94 => ( ord_less_eq_int @ ( lattic1091506334969745077in_int @ A ) @ ( lattic1091506334969745077in_int @ B4 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.subset_imp
% 4.69/4.94 thf(fact_2188_Sup__fin_Osubset__imp,axiom,
% 4.69/4.94 ! [A: set_nat,B4: set_nat] :
% 4.69/4.94 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.94 => ( ( A != bot_bot_set_nat )
% 4.69/4.94 => ( ( finite_finite_nat @ B4 )
% 4.69/4.94 => ( ord_less_eq_nat @ ( lattic1093996805478795353in_nat @ A ) @ ( lattic1093996805478795353in_nat @ B4 ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.subset_imp
% 4.69/4.94 thf(fact_2189_Inf__fin_Osubset,axiom,
% 4.69/4.94 ! [A: set_set_nat,B4: set_set_nat] :
% 4.69/4.94 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.94 => ( ( B4 != bot_bot_set_set_nat )
% 4.69/4.94 => ( ( ord_le6893508408891458716et_nat @ B4 @ A )
% 4.69/4.94 => ( ( inf_inf_set_nat @ ( lattic3014633134055518761et_nat @ B4 ) @ ( lattic3014633134055518761et_nat @ A ) )
% 4.69/4.94 = ( lattic3014633134055518761et_nat @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.subset
% 4.69/4.94 thf(fact_2190_Inf__fin_Osubset,axiom,
% 4.69/4.94 ! [A: set_assn,B4: set_assn] :
% 4.69/4.94 ( ( finite_finite_assn @ A )
% 4.69/4.94 => ( ( B4 != bot_bot_set_assn )
% 4.69/4.94 => ( ( ord_less_eq_set_assn @ B4 @ A )
% 4.69/4.94 => ( ( inf_inf_assn @ ( lattic47131356835913163n_assn @ B4 ) @ ( lattic47131356835913163n_assn @ A ) )
% 4.69/4.94 = ( lattic47131356835913163n_assn @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.subset
% 4.69/4.94 thf(fact_2191_Inf__fin_Osubset,axiom,
% 4.69/4.94 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.94 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.94 => ( ( B4 != bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( ord_le3507040750410214029t_unit @ B4 @ A )
% 4.69/4.94 => ( ( inf_inf_Product_unit @ ( lattic1263872656861969706t_unit @ B4 ) @ ( lattic1263872656861969706t_unit @ A ) )
% 4.69/4.94 = ( lattic1263872656861969706t_unit @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.subset
% 4.69/4.94 thf(fact_2192_Inf__fin_Osubset,axiom,
% 4.69/4.94 ! [A: set_o,B4: set_o] :
% 4.69/4.94 ( ( finite_finite_o @ A )
% 4.69/4.94 => ( ( B4 != bot_bot_set_o )
% 4.69/4.94 => ( ( ord_less_eq_set_o @ B4 @ A )
% 4.69/4.94 => ( ( inf_inf_o @ ( lattic4107685809792843317_fin_o @ B4 ) @ ( lattic4107685809792843317_fin_o @ A ) )
% 4.69/4.94 = ( lattic4107685809792843317_fin_o @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.subset
% 4.69/4.94 thf(fact_2193_Inf__fin_Osubset,axiom,
% 4.69/4.94 ! [A: set_int,B4: set_int] :
% 4.69/4.94 ( ( finite_finite_int @ A )
% 4.69/4.94 => ( ( B4 != bot_bot_set_int )
% 4.69/4.94 => ( ( ord_less_eq_set_int @ B4 @ A )
% 4.69/4.94 => ( ( inf_inf_int @ ( lattic5235898064620869839in_int @ B4 ) @ ( lattic5235898064620869839in_int @ A ) )
% 4.69/4.94 = ( lattic5235898064620869839in_int @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.subset
% 4.69/4.94 thf(fact_2194_Inf__fin_Osubset,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.94 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.94 => ( ( B4 != bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( ord_le2965882846123202637_nat_o @ B4 @ A )
% 4.69/4.94 => ( ( inf_in1318976480646536635_nat_o @ ( lattic956194824204696298_nat_o @ B4 ) @ ( lattic956194824204696298_nat_o @ A ) )
% 4.69/4.94 = ( lattic956194824204696298_nat_o @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.subset
% 4.69/4.94 thf(fact_2195_Inf__fin_Osubset,axiom,
% 4.69/4.94 ! [A: set_nat,B4: set_nat] :
% 4.69/4.94 ( ( finite_finite_nat @ A )
% 4.69/4.94 => ( ( B4 != bot_bot_set_nat )
% 4.69/4.94 => ( ( ord_less_eq_set_nat @ B4 @ A )
% 4.69/4.94 => ( ( inf_inf_nat @ ( lattic5238388535129920115in_nat @ B4 ) @ ( lattic5238388535129920115in_nat @ A ) )
% 4.69/4.94 = ( lattic5238388535129920115in_nat @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.subset
% 4.69/4.94 thf(fact_2196_Sup__fin_Osubset,axiom,
% 4.69/4.94 ! [A: set_set_nat,B4: set_set_nat] :
% 4.69/4.94 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.94 => ( ( B4 != bot_bot_set_set_nat )
% 4.69/4.94 => ( ( ord_le6893508408891458716et_nat @ B4 @ A )
% 4.69/4.94 => ( ( sup_sup_set_nat @ ( lattic3835124923745554447et_nat @ B4 ) @ ( lattic3835124923745554447et_nat @ A ) )
% 4.69/4.94 = ( lattic3835124923745554447et_nat @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.subset
% 4.69/4.94 thf(fact_2197_Sup__fin_Osubset,axiom,
% 4.69/4.94 ! [A: set_assn,B4: set_assn] :
% 4.69/4.94 ( ( finite_finite_assn @ A )
% 4.69/4.94 => ( ( B4 != bot_bot_set_assn )
% 4.69/4.94 => ( ( ord_less_eq_set_assn @ B4 @ A )
% 4.69/4.94 => ( ( sup_sup_assn @ ( lattic2150320897289308081n_assn @ B4 ) @ ( lattic2150320897289308081n_assn @ A ) )
% 4.69/4.94 = ( lattic2150320897289308081n_assn @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.subset
% 4.69/4.94 thf(fact_2198_Sup__fin_Osubset,axiom,
% 4.69/4.94 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.94 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.94 => ( ( B4 != bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( ord_le3507040750410214029t_unit @ B4 @ A )
% 4.69/4.94 => ( ( sup_sup_Product_unit @ ( lattic5294303975357428420t_unit @ B4 ) @ ( lattic5294303975357428420t_unit @ A ) )
% 4.69/4.94 = ( lattic5294303975357428420t_unit @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.subset
% 4.69/4.94 thf(fact_2199_Sup__fin_Osubset,axiom,
% 4.69/4.94 ! [A: set_o,B4: set_o] :
% 4.69/4.94 ( ( finite_finite_o @ A )
% 4.69/4.94 => ( ( B4 != bot_bot_set_o )
% 4.69/4.94 => ( ( ord_less_eq_set_o @ B4 @ A )
% 4.69/4.94 => ( ( sup_sup_o @ ( lattic1508158080041050831_fin_o @ B4 ) @ ( lattic1508158080041050831_fin_o @ A ) )
% 4.69/4.94 = ( lattic1508158080041050831_fin_o @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.subset
% 4.69/4.94 thf(fact_2200_Sup__fin_Osubset,axiom,
% 4.69/4.94 ! [A: set_int,B4: set_int] :
% 4.69/4.94 ( ( finite_finite_int @ A )
% 4.69/4.94 => ( ( B4 != bot_bot_set_int )
% 4.69/4.94 => ( ( ord_less_eq_set_int @ B4 @ A )
% 4.69/4.94 => ( ( sup_sup_int @ ( lattic1091506334969745077in_int @ B4 ) @ ( lattic1091506334969745077in_int @ A ) )
% 4.69/4.94 = ( lattic1091506334969745077in_int @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.subset
% 4.69/4.94 thf(fact_2201_Sup__fin_Osubset,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.94 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.94 => ( ( B4 != bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( ord_le2965882846123202637_nat_o @ B4 @ A )
% 4.69/4.94 => ( ( sup_su5453871518329203617_nat_o @ ( lattic7320199455484906628_nat_o @ B4 ) @ ( lattic7320199455484906628_nat_o @ A ) )
% 4.69/4.94 = ( lattic7320199455484906628_nat_o @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.subset
% 4.69/4.94 thf(fact_2202_Sup__fin_Osubset,axiom,
% 4.69/4.94 ! [A: set_nat,B4: set_nat] :
% 4.69/4.94 ( ( finite_finite_nat @ A )
% 4.69/4.94 => ( ( B4 != bot_bot_set_nat )
% 4.69/4.94 => ( ( ord_less_eq_set_nat @ B4 @ A )
% 4.69/4.94 => ( ( sup_sup_nat @ ( lattic1093996805478795353in_nat @ B4 ) @ ( lattic1093996805478795353in_nat @ A ) )
% 4.69/4.94 = ( lattic1093996805478795353in_nat @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.subset
% 4.69/4.94 thf(fact_2203_Inf__fin_Oclosed,axiom,
% 4.69/4.94 ! [A: set_set_nat] :
% 4.69/4.94 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_set_nat )
% 4.69/4.94 => ( ! [X3: set_nat,Y2: set_nat] : ( member_set_nat @ ( inf_inf_set_nat @ X3 @ Y2 ) @ ( insert_set_nat @ X3 @ ( insert_set_nat @ Y2 @ bot_bot_set_set_nat ) ) )
% 4.69/4.94 => ( member_set_nat @ ( lattic3014633134055518761et_nat @ A ) @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.closed
% 4.69/4.94 thf(fact_2204_Inf__fin_Oclosed,axiom,
% 4.69/4.94 ! [A: set_assn] :
% 4.69/4.94 ( ( finite_finite_assn @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_assn )
% 4.69/4.94 => ( ! [X3: assn,Y2: assn] : ( member_assn @ ( inf_inf_assn @ X3 @ Y2 ) @ ( insert_assn @ X3 @ ( insert_assn @ Y2 @ bot_bot_set_assn ) ) )
% 4.69/4.94 => ( member_assn @ ( lattic47131356835913163n_assn @ A ) @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.closed
% 4.69/4.94 thf(fact_2205_Inf__fin_Oclosed,axiom,
% 4.69/4.94 ! [A: set_Product_unit] :
% 4.69/4.94 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.94 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ! [X3: product_unit,Y2: product_unit] : ( member_Product_unit @ ( inf_inf_Product_unit @ X3 @ Y2 ) @ ( insert_Product_unit @ X3 @ ( insert_Product_unit @ Y2 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.94 => ( member_Product_unit @ ( lattic1263872656861969706t_unit @ A ) @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.closed
% 4.69/4.94 thf(fact_2206_Inf__fin_Oclosed,axiom,
% 4.69/4.94 ! [A: set_o] :
% 4.69/4.94 ( ( finite_finite_o @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_o )
% 4.69/4.94 => ( ! [X3: $o,Y2: $o] : ( member_o @ ( inf_inf_o @ X3 @ Y2 ) @ ( insert_o @ X3 @ ( insert_o @ Y2 @ bot_bot_set_o ) ) )
% 4.69/4.94 => ( member_o @ ( lattic4107685809792843317_fin_o @ A ) @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.closed
% 4.69/4.94 thf(fact_2207_Inf__fin_Oclosed,axiom,
% 4.69/4.94 ! [A: set_nat] :
% 4.69/4.94 ( ( finite_finite_nat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_nat )
% 4.69/4.94 => ( ! [X3: nat,Y2: nat] : ( member_nat @ ( inf_inf_nat @ X3 @ Y2 ) @ ( insert_nat @ X3 @ ( insert_nat @ Y2 @ bot_bot_set_nat ) ) )
% 4.69/4.94 => ( member_nat @ ( lattic5238388535129920115in_nat @ A ) @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.closed
% 4.69/4.94 thf(fact_2208_Inf__fin_Oclosed,axiom,
% 4.69/4.94 ! [A: set_int] :
% 4.69/4.94 ( ( finite_finite_int @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_int )
% 4.69/4.94 => ( ! [X3: int,Y2: int] : ( member_int @ ( inf_inf_int @ X3 @ Y2 ) @ ( insert_int @ X3 @ ( insert_int @ Y2 @ bot_bot_set_int ) ) )
% 4.69/4.94 => ( member_int @ ( lattic5235898064620869839in_int @ A ) @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.closed
% 4.69/4.94 thf(fact_2209_Inf__fin_Oclosed,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.94 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.94 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ ( inf_in1318976480646536635_nat_o @ X3 @ Y2 ) @ ( insert5175938949040314269_nat_o @ X3 @ ( insert5175938949040314269_nat_o @ Y2 @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/4.94 => ( member6576561426505652726_nat_o @ ( lattic956194824204696298_nat_o @ A ) @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.closed
% 4.69/4.94 thf(fact_2210_Inf__fin_Oinsert__not__elem,axiom,
% 4.69/4.94 ! [A: set_set_nat,X: set_nat] :
% 4.69/4.94 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.94 => ( ~ ( member_set_nat @ X @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_set_nat )
% 4.69/4.94 => ( ( lattic3014633134055518761et_nat @ ( insert_set_nat @ X @ A ) )
% 4.69/4.94 = ( inf_inf_set_nat @ X @ ( lattic3014633134055518761et_nat @ A ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.insert_not_elem
% 4.69/4.94 thf(fact_2211_Inf__fin_Oinsert__not__elem,axiom,
% 4.69/4.94 ! [A: set_assn,X: assn] :
% 4.69/4.94 ( ( finite_finite_assn @ A )
% 4.69/4.94 => ( ~ ( member_assn @ X @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_assn )
% 4.69/4.94 => ( ( lattic47131356835913163n_assn @ ( insert_assn @ X @ A ) )
% 4.69/4.94 = ( inf_inf_assn @ X @ ( lattic47131356835913163n_assn @ A ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.insert_not_elem
% 4.69/4.94 thf(fact_2212_Inf__fin_Oinsert__not__elem,axiom,
% 4.69/4.94 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.94 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.94 => ( ~ ( member_Product_unit @ X @ A )
% 4.69/4.94 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( lattic1263872656861969706t_unit @ ( insert_Product_unit @ X @ A ) )
% 4.69/4.94 = ( inf_inf_Product_unit @ X @ ( lattic1263872656861969706t_unit @ A ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.insert_not_elem
% 4.69/4.94 thf(fact_2213_Inf__fin_Oinsert__not__elem,axiom,
% 4.69/4.94 ! [A: set_o,X: $o] :
% 4.69/4.94 ( ( finite_finite_o @ A )
% 4.69/4.94 => ( ~ ( member_o @ X @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_o )
% 4.69/4.94 => ( ( lattic4107685809792843317_fin_o @ ( insert_o @ X @ A ) )
% 4.69/4.94 = ( inf_inf_o @ X @ ( lattic4107685809792843317_fin_o @ A ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.insert_not_elem
% 4.69/4.94 thf(fact_2214_Inf__fin_Oinsert__not__elem,axiom,
% 4.69/4.94 ! [A: set_nat,X: nat] :
% 4.69/4.94 ( ( finite_finite_nat @ A )
% 4.69/4.94 => ( ~ ( member_nat @ X @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_nat )
% 4.69/4.94 => ( ( lattic5238388535129920115in_nat @ ( insert_nat @ X @ A ) )
% 4.69/4.94 = ( inf_inf_nat @ X @ ( lattic5238388535129920115in_nat @ A ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.insert_not_elem
% 4.69/4.94 thf(fact_2215_Inf__fin_Oinsert__not__elem,axiom,
% 4.69/4.94 ! [A: set_int,X: int] :
% 4.69/4.94 ( ( finite_finite_int @ A )
% 4.69/4.94 => ( ~ ( member_int @ X @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_int )
% 4.69/4.94 => ( ( lattic5235898064620869839in_int @ ( insert_int @ X @ A ) )
% 4.69/4.94 = ( inf_inf_int @ X @ ( lattic5235898064620869839in_int @ A ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.insert_not_elem
% 4.69/4.94 thf(fact_2216_Inf__fin_Oinsert__not__elem,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.94 => ( ~ ( member6576561426505652726_nat_o @ X @ A )
% 4.69/4.94 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( lattic956194824204696298_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) )
% 4.69/4.94 = ( inf_in1318976480646536635_nat_o @ X @ ( lattic956194824204696298_nat_o @ A ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.insert_not_elem
% 4.69/4.94 thf(fact_2217_Sup__fin_Oclosed,axiom,
% 4.69/4.94 ! [A: set_set_nat] :
% 4.69/4.94 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_set_nat )
% 4.69/4.94 => ( ! [X3: set_nat,Y2: set_nat] : ( member_set_nat @ ( sup_sup_set_nat @ X3 @ Y2 ) @ ( insert_set_nat @ X3 @ ( insert_set_nat @ Y2 @ bot_bot_set_set_nat ) ) )
% 4.69/4.94 => ( member_set_nat @ ( lattic3835124923745554447et_nat @ A ) @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.closed
% 4.69/4.94 thf(fact_2218_Sup__fin_Oclosed,axiom,
% 4.69/4.94 ! [A: set_assn] :
% 4.69/4.94 ( ( finite_finite_assn @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_assn )
% 4.69/4.94 => ( ! [X3: assn,Y2: assn] : ( member_assn @ ( sup_sup_assn @ X3 @ Y2 ) @ ( insert_assn @ X3 @ ( insert_assn @ Y2 @ bot_bot_set_assn ) ) )
% 4.69/4.94 => ( member_assn @ ( lattic2150320897289308081n_assn @ A ) @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.closed
% 4.69/4.94 thf(fact_2219_Sup__fin_Oclosed,axiom,
% 4.69/4.94 ! [A: set_Product_unit] :
% 4.69/4.94 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.94 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ! [X3: product_unit,Y2: product_unit] : ( member_Product_unit @ ( sup_sup_Product_unit @ X3 @ Y2 ) @ ( insert_Product_unit @ X3 @ ( insert_Product_unit @ Y2 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.94 => ( member_Product_unit @ ( lattic5294303975357428420t_unit @ A ) @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.closed
% 4.69/4.94 thf(fact_2220_Sup__fin_Oclosed,axiom,
% 4.69/4.94 ! [A: set_o] :
% 4.69/4.94 ( ( finite_finite_o @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_o )
% 4.69/4.94 => ( ! [X3: $o,Y2: $o] : ( member_o @ ( sup_sup_o @ X3 @ Y2 ) @ ( insert_o @ X3 @ ( insert_o @ Y2 @ bot_bot_set_o ) ) )
% 4.69/4.94 => ( member_o @ ( lattic1508158080041050831_fin_o @ A ) @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.closed
% 4.69/4.94 thf(fact_2221_Sup__fin_Oclosed,axiom,
% 4.69/4.94 ! [A: set_nat] :
% 4.69/4.94 ( ( finite_finite_nat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_nat )
% 4.69/4.94 => ( ! [X3: nat,Y2: nat] : ( member_nat @ ( sup_sup_nat @ X3 @ Y2 ) @ ( insert_nat @ X3 @ ( insert_nat @ Y2 @ bot_bot_set_nat ) ) )
% 4.69/4.94 => ( member_nat @ ( lattic1093996805478795353in_nat @ A ) @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.closed
% 4.69/4.94 thf(fact_2222_Sup__fin_Oclosed,axiom,
% 4.69/4.94 ! [A: set_int] :
% 4.69/4.94 ( ( finite_finite_int @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_int )
% 4.69/4.94 => ( ! [X3: int,Y2: int] : ( member_int @ ( sup_sup_int @ X3 @ Y2 ) @ ( insert_int @ X3 @ ( insert_int @ Y2 @ bot_bot_set_int ) ) )
% 4.69/4.94 => ( member_int @ ( lattic1091506334969745077in_int @ A ) @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.closed
% 4.69/4.94 thf(fact_2223_Sup__fin_Oclosed,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.94 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.94 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ ( sup_su5453871518329203617_nat_o @ X3 @ Y2 ) @ ( insert5175938949040314269_nat_o @ X3 @ ( insert5175938949040314269_nat_o @ Y2 @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/4.94 => ( member6576561426505652726_nat_o @ ( lattic7320199455484906628_nat_o @ A ) @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.closed
% 4.69/4.94 thf(fact_2224_Sup__fin_Oinsert__not__elem,axiom,
% 4.69/4.94 ! [A: set_set_nat,X: set_nat] :
% 4.69/4.94 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.94 => ( ~ ( member_set_nat @ X @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_set_nat )
% 4.69/4.94 => ( ( lattic3835124923745554447et_nat @ ( insert_set_nat @ X @ A ) )
% 4.69/4.94 = ( sup_sup_set_nat @ X @ ( lattic3835124923745554447et_nat @ A ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.insert_not_elem
% 4.69/4.94 thf(fact_2225_Sup__fin_Oinsert__not__elem,axiom,
% 4.69/4.94 ! [A: set_assn,X: assn] :
% 4.69/4.94 ( ( finite_finite_assn @ A )
% 4.69/4.94 => ( ~ ( member_assn @ X @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_assn )
% 4.69/4.94 => ( ( lattic2150320897289308081n_assn @ ( insert_assn @ X @ A ) )
% 4.69/4.94 = ( sup_sup_assn @ X @ ( lattic2150320897289308081n_assn @ A ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.insert_not_elem
% 4.69/4.94 thf(fact_2226_Sup__fin_Oinsert__not__elem,axiom,
% 4.69/4.94 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.94 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.94 => ( ~ ( member_Product_unit @ X @ A )
% 4.69/4.94 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( lattic5294303975357428420t_unit @ ( insert_Product_unit @ X @ A ) )
% 4.69/4.94 = ( sup_sup_Product_unit @ X @ ( lattic5294303975357428420t_unit @ A ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.insert_not_elem
% 4.69/4.94 thf(fact_2227_Sup__fin_Oinsert__not__elem,axiom,
% 4.69/4.94 ! [A: set_o,X: $o] :
% 4.69/4.94 ( ( finite_finite_o @ A )
% 4.69/4.94 => ( ~ ( member_o @ X @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_o )
% 4.69/4.94 => ( ( lattic1508158080041050831_fin_o @ ( insert_o @ X @ A ) )
% 4.69/4.94 = ( sup_sup_o @ X @ ( lattic1508158080041050831_fin_o @ A ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.insert_not_elem
% 4.69/4.94 thf(fact_2228_Sup__fin_Oinsert__not__elem,axiom,
% 4.69/4.94 ! [A: set_nat,X: nat] :
% 4.69/4.94 ( ( finite_finite_nat @ A )
% 4.69/4.94 => ( ~ ( member_nat @ X @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_nat )
% 4.69/4.94 => ( ( lattic1093996805478795353in_nat @ ( insert_nat @ X @ A ) )
% 4.69/4.94 = ( sup_sup_nat @ X @ ( lattic1093996805478795353in_nat @ A ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.insert_not_elem
% 4.69/4.94 thf(fact_2229_Sup__fin_Oinsert__not__elem,axiom,
% 4.69/4.94 ! [A: set_int,X: int] :
% 4.69/4.94 ( ( finite_finite_int @ A )
% 4.69/4.94 => ( ~ ( member_int @ X @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_int )
% 4.69/4.94 => ( ( lattic1091506334969745077in_int @ ( insert_int @ X @ A ) )
% 4.69/4.94 = ( sup_sup_int @ X @ ( lattic1091506334969745077in_int @ A ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.insert_not_elem
% 4.69/4.94 thf(fact_2230_Sup__fin_Oinsert__not__elem,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.94 => ( ~ ( member6576561426505652726_nat_o @ X @ A )
% 4.69/4.94 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( lattic7320199455484906628_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) )
% 4.69/4.94 = ( sup_su5453871518329203617_nat_o @ X @ ( lattic7320199455484906628_nat_o @ A ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.insert_not_elem
% 4.69/4.94 thf(fact_2231_Inf__fin_Ounion,axiom,
% 4.69/4.94 ! [A: set_set_nat,B4: set_set_nat] :
% 4.69/4.94 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_set_nat )
% 4.69/4.94 => ( ( finite1152437895449049373et_nat @ B4 )
% 4.69/4.94 => ( ( B4 != bot_bot_set_set_nat )
% 4.69/4.94 => ( ( lattic3014633134055518761et_nat @ ( sup_sup_set_set_nat @ A @ B4 ) )
% 4.69/4.94 = ( inf_inf_set_nat @ ( lattic3014633134055518761et_nat @ A ) @ ( lattic3014633134055518761et_nat @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.union
% 4.69/4.94 thf(fact_2232_Inf__fin_Ounion,axiom,
% 4.69/4.94 ! [A: set_assn,B4: set_assn] :
% 4.69/4.94 ( ( finite_finite_assn @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_assn )
% 4.69/4.94 => ( ( finite_finite_assn @ B4 )
% 4.69/4.94 => ( ( B4 != bot_bot_set_assn )
% 4.69/4.94 => ( ( lattic47131356835913163n_assn @ ( sup_sup_set_assn @ A @ B4 ) )
% 4.69/4.94 = ( inf_inf_assn @ ( lattic47131356835913163n_assn @ A ) @ ( lattic47131356835913163n_assn @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.union
% 4.69/4.94 thf(fact_2233_Inf__fin_Ounion,axiom,
% 4.69/4.94 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.94 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.94 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( finite4290736615968046902t_unit @ B4 )
% 4.69/4.94 => ( ( B4 != bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( lattic1263872656861969706t_unit @ ( sup_su793286257634532545t_unit @ A @ B4 ) )
% 4.69/4.94 = ( inf_inf_Product_unit @ ( lattic1263872656861969706t_unit @ A ) @ ( lattic1263872656861969706t_unit @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.union
% 4.69/4.94 thf(fact_2234_Inf__fin_Ounion,axiom,
% 4.69/4.94 ! [A: set_o,B4: set_o] :
% 4.69/4.94 ( ( finite_finite_o @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_o )
% 4.69/4.94 => ( ( finite_finite_o @ B4 )
% 4.69/4.94 => ( ( B4 != bot_bot_set_o )
% 4.69/4.94 => ( ( lattic4107685809792843317_fin_o @ ( sup_sup_set_o @ A @ B4 ) )
% 4.69/4.94 = ( inf_inf_o @ ( lattic4107685809792843317_fin_o @ A ) @ ( lattic4107685809792843317_fin_o @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.union
% 4.69/4.94 thf(fact_2235_Inf__fin_Ounion,axiom,
% 4.69/4.94 ! [A: set_nat,B4: set_nat] :
% 4.69/4.94 ( ( finite_finite_nat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_nat )
% 4.69/4.94 => ( ( finite_finite_nat @ B4 )
% 4.69/4.94 => ( ( B4 != bot_bot_set_nat )
% 4.69/4.94 => ( ( lattic5238388535129920115in_nat @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.94 = ( inf_inf_nat @ ( lattic5238388535129920115in_nat @ A ) @ ( lattic5238388535129920115in_nat @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.union
% 4.69/4.94 thf(fact_2236_Inf__fin_Ounion,axiom,
% 4.69/4.94 ! [A: set_int,B4: set_int] :
% 4.69/4.94 ( ( finite_finite_int @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_int )
% 4.69/4.94 => ( ( finite_finite_int @ B4 )
% 4.69/4.94 => ( ( B4 != bot_bot_set_int )
% 4.69/4.94 => ( ( lattic5235898064620869839in_int @ ( sup_sup_set_int @ A @ B4 ) )
% 4.69/4.94 = ( inf_inf_int @ ( lattic5235898064620869839in_int @ A ) @ ( lattic5235898064620869839in_int @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.union
% 4.69/4.94 thf(fact_2237_Inf__fin_Ounion,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.94 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.94 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( finite3252695134891459830_nat_o @ B4 )
% 4.69/4.94 => ( ( B4 != bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( lattic956194824204696298_nat_o @ ( sup_su5209123915105501825_nat_o @ A @ B4 ) )
% 4.69/4.94 = ( inf_in1318976480646536635_nat_o @ ( lattic956194824204696298_nat_o @ A ) @ ( lattic956194824204696298_nat_o @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.union
% 4.69/4.94 thf(fact_2238_Sup__fin_Ounion,axiom,
% 4.69/4.94 ! [A: set_set_nat,B4: set_set_nat] :
% 4.69/4.94 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_set_nat )
% 4.69/4.94 => ( ( finite1152437895449049373et_nat @ B4 )
% 4.69/4.94 => ( ( B4 != bot_bot_set_set_nat )
% 4.69/4.94 => ( ( lattic3835124923745554447et_nat @ ( sup_sup_set_set_nat @ A @ B4 ) )
% 4.69/4.94 = ( sup_sup_set_nat @ ( lattic3835124923745554447et_nat @ A ) @ ( lattic3835124923745554447et_nat @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.union
% 4.69/4.94 thf(fact_2239_Sup__fin_Ounion,axiom,
% 4.69/4.94 ! [A: set_assn,B4: set_assn] :
% 4.69/4.94 ( ( finite_finite_assn @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_assn )
% 4.69/4.94 => ( ( finite_finite_assn @ B4 )
% 4.69/4.94 => ( ( B4 != bot_bot_set_assn )
% 4.69/4.94 => ( ( lattic2150320897289308081n_assn @ ( sup_sup_set_assn @ A @ B4 ) )
% 4.69/4.94 = ( sup_sup_assn @ ( lattic2150320897289308081n_assn @ A ) @ ( lattic2150320897289308081n_assn @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.union
% 4.69/4.94 thf(fact_2240_Sup__fin_Ounion,axiom,
% 4.69/4.94 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.94 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.94 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( finite4290736615968046902t_unit @ B4 )
% 4.69/4.94 => ( ( B4 != bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( lattic5294303975357428420t_unit @ ( sup_su793286257634532545t_unit @ A @ B4 ) )
% 4.69/4.94 = ( sup_sup_Product_unit @ ( lattic5294303975357428420t_unit @ A ) @ ( lattic5294303975357428420t_unit @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.union
% 4.69/4.94 thf(fact_2241_Sup__fin_Ounion,axiom,
% 4.69/4.94 ! [A: set_o,B4: set_o] :
% 4.69/4.94 ( ( finite_finite_o @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_o )
% 4.69/4.94 => ( ( finite_finite_o @ B4 )
% 4.69/4.94 => ( ( B4 != bot_bot_set_o )
% 4.69/4.94 => ( ( lattic1508158080041050831_fin_o @ ( sup_sup_set_o @ A @ B4 ) )
% 4.69/4.94 = ( sup_sup_o @ ( lattic1508158080041050831_fin_o @ A ) @ ( lattic1508158080041050831_fin_o @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.union
% 4.69/4.94 thf(fact_2242_Sup__fin_Ounion,axiom,
% 4.69/4.94 ! [A: set_nat,B4: set_nat] :
% 4.69/4.94 ( ( finite_finite_nat @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_nat )
% 4.69/4.94 => ( ( finite_finite_nat @ B4 )
% 4.69/4.94 => ( ( B4 != bot_bot_set_nat )
% 4.69/4.94 => ( ( lattic1093996805478795353in_nat @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.94 = ( sup_sup_nat @ ( lattic1093996805478795353in_nat @ A ) @ ( lattic1093996805478795353in_nat @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.union
% 4.69/4.94 thf(fact_2243_Sup__fin_Ounion,axiom,
% 4.69/4.94 ! [A: set_int,B4: set_int] :
% 4.69/4.94 ( ( finite_finite_int @ A )
% 4.69/4.94 => ( ( A != bot_bot_set_int )
% 4.69/4.94 => ( ( finite_finite_int @ B4 )
% 4.69/4.94 => ( ( B4 != bot_bot_set_int )
% 4.69/4.94 => ( ( lattic1091506334969745077in_int @ ( sup_sup_set_int @ A @ B4 ) )
% 4.69/4.94 = ( sup_sup_int @ ( lattic1091506334969745077in_int @ A ) @ ( lattic1091506334969745077in_int @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.union
% 4.69/4.94 thf(fact_2244_Sup__fin_Ounion,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.94 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.94 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( finite3252695134891459830_nat_o @ B4 )
% 4.69/4.94 => ( ( B4 != bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( lattic7320199455484906628_nat_o @ ( sup_su5209123915105501825_nat_o @ A @ B4 ) )
% 4.69/4.94 = ( sup_su5453871518329203617_nat_o @ ( lattic7320199455484906628_nat_o @ A ) @ ( lattic7320199455484906628_nat_o @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.union
% 4.69/4.94 thf(fact_2245_refl__on__reflcl__Image,axiom,
% 4.69/4.94 ! [B4: set_nat,A: set_Pr1261947904930325089at_nat,C5: set_nat] :
% 4.69/4.94 ( ( refl_on_nat @ B4 @ A )
% 4.69/4.94 => ( ( ord_less_eq_set_nat @ C5 @ B4 )
% 4.69/4.94 => ( ( image_nat_nat @ ( sup_su6327502436637775413at_nat @ A @ id_nat ) @ C5 )
% 4.69/4.94 = ( image_nat_nat @ A @ C5 ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % refl_on_reflcl_Image
% 4.69/4.94 thf(fact_2246_E__closed__restr__reach__cases,axiom,
% 4.69/4.94 ! [U: produc3658429121746597890et_nat > $o,V: produc3658429121746597890et_nat > $o,E: set_Pr2161125870931222855_nat_o,R3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.94 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ U @ V ) @ ( transi712980445759334096_nat_o @ E ) )
% 4.69/4.94 => ( ( ord_le2965882846123202637_nat_o @ ( image_2232984160439939859_nat_o @ E @ R3 ) @ R3 )
% 4.69/4.94 => ( ~ ( member6576561426505652726_nat_o @ V @ R3 )
% 4.69/4.94 => ~ ( ~ ( member6576561426505652726_nat_o @ U @ R3 )
% 4.69/4.94 => ~ ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ U @ V ) @ ( transi712980445759334096_nat_o @ ( rel_re3331361160397388719_nat_o @ E @ R3 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % E_closed_restr_reach_cases
% 4.69/4.94 thf(fact_2247_E__closed__restr__reach__cases,axiom,
% 4.69/4.94 ! [U: $o,V: $o,E: set_Product_prod_o_o,R3: set_o] :
% 4.69/4.94 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ U @ V ) @ ( transitive_rtrancl_o @ E ) )
% 4.69/4.94 => ( ( ord_less_eq_set_o @ ( image_o_o @ E @ R3 ) @ R3 )
% 4.69/4.94 => ( ~ ( member_o @ V @ R3 )
% 4.69/4.94 => ~ ( ~ ( member_o @ U @ R3 )
% 4.69/4.94 => ~ ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ U @ V ) @ ( transitive_rtrancl_o @ ( rel_restrict_o @ E @ R3 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % E_closed_restr_reach_cases
% 4.69/4.94 thf(fact_2248_E__closed__restr__reach__cases,axiom,
% 4.69/4.94 ! [U: product_unit,V: product_unit,E: set_Pr5094982260447487303t_unit,R3: set_Product_unit] :
% 4.69/4.94 ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ U @ V ) @ ( transi6481887417741755664t_unit @ E ) )
% 4.69/4.94 => ( ( ord_le3507040750410214029t_unit @ ( image_8431784415008483091t_unit @ E @ R3 ) @ R3 )
% 4.69/4.94 => ( ~ ( member_Product_unit @ V @ R3 )
% 4.69/4.94 => ~ ( ~ ( member_Product_unit @ U @ R3 )
% 4.69/4.94 => ~ ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ U @ V ) @ ( transi6481887417741755664t_unit @ ( rel_re9207996470947987439t_unit @ E @ R3 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % E_closed_restr_reach_cases
% 4.69/4.94 thf(fact_2249_E__closed__restr__reach__cases,axiom,
% 4.69/4.94 ! [U: int,V: int,E: set_Pr958786334691620121nt_int,R3: set_int] :
% 4.69/4.94 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ U @ V ) @ ( transi2902850859426252137cl_int @ E ) )
% 4.69/4.94 => ( ( ord_less_eq_set_int @ ( image_int_int @ E @ R3 ) @ R3 )
% 4.69/4.94 => ( ~ ( member_int @ V @ R3 )
% 4.69/4.94 => ~ ( ~ ( member_int @ U @ R3 )
% 4.69/4.94 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ U @ V ) @ ( transi2902850859426252137cl_int @ ( rel_restrict_int @ E @ R3 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % E_closed_restr_reach_cases
% 4.69/4.94 thf(fact_2250_E__closed__restr__reach__cases,axiom,
% 4.69/4.94 ! [U: nat,V: nat,E: set_Pr1261947904930325089at_nat,R3: set_nat] :
% 4.69/4.94 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ U @ V ) @ ( transi2905341329935302413cl_nat @ E ) )
% 4.69/4.94 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ E @ R3 ) @ R3 )
% 4.69/4.94 => ( ~ ( member_nat @ V @ R3 )
% 4.69/4.94 => ~ ( ~ ( member_nat @ U @ R3 )
% 4.69/4.94 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ U @ V ) @ ( transi2905341329935302413cl_nat @ ( rel_restrict_nat @ E @ R3 ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % E_closed_restr_reach_cases
% 4.69/4.94 thf(fact_2251_max__ext__compat,axiom,
% 4.69/4.94 ! [R3: set_Pr5094982260447487303t_unit,S: set_Pr5094982260447487303t_unit] :
% 4.69/4.94 ( ( ord_le930853871177014503t_unit @ ( relcom848357998638694028t_unit @ R3 @ S ) @ R3 )
% 4.69/4.94 => ( ord_le8072594200992201959t_unit @ ( relcom7108816970757792620t_unit @ ( max_ext_Product_unit @ R3 ) @ ( sup_su3573767163274163995t_unit @ ( max_ext_Product_unit @ S ) @ ( insert6793119152790066487t_unit @ ( produc7269801343787132631t_unit @ bot_bo3957492148770167129t_unit @ bot_bo3957492148770167129t_unit ) @ bot_bo5113747506523071411t_unit ) ) ) @ ( max_ext_Product_unit @ R3 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % max_ext_compat
% 4.69/4.94 thf(fact_2252_max__ext__compat,axiom,
% 4.69/4.94 ! [R3: set_Product_prod_o_o,S: set_Product_prod_o_o] :
% 4.69/4.94 ( ( ord_le192195778054999463od_o_o @ ( relcomp_o_o_o @ R3 @ S ) @ R3 )
% 4.69/4.94 => ( ord_le2885120122233735591_set_o @ ( relcom7534720040753365047_set_o @ ( max_ext_o @ R3 ) @ ( sup_su7766833992073560027_set_o @ ( max_ext_o @ S ) @ ( insert1494450971503307511_set_o @ ( produc5838405689764958487_set_o @ bot_bot_set_o @ bot_bot_set_o ) @ bot_bo8143257439550059635_set_o ) ) ) @ ( max_ext_o @ R3 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % max_ext_compat
% 4.69/4.94 thf(fact_2253_max__ext__compat,axiom,
% 4.69/4.94 ! [R3: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 4.69/4.94 ( ( ord_le3146513528884898305at_nat @ ( relcomp_nat_nat_nat @ R3 @ S ) @ R3 )
% 4.69/4.94 => ( ord_le4402255868550298733et_nat @ ( relcom236561585145426837et_nat @ ( max_ext_nat @ R3 ) @ ( sup_su4251893418135750817et_nat @ ( max_ext_nat @ S ) @ ( insert3810226134351308605et_nat @ ( produc4532415448927165861et_nat @ bot_bot_set_nat @ bot_bot_set_nat ) @ bot_bo4952753636535259449et_nat ) ) ) @ ( max_ext_nat @ R3 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % max_ext_compat
% 4.69/4.94 thf(fact_2254_max__ext__compat,axiom,
% 4.69/4.94 ! [R3: set_Pr958786334691620121nt_int,S: set_Pr958786334691620121nt_int] :
% 4.69/4.94 ( ( ord_le2843351958646193337nt_int @ ( relcomp_int_int_int @ R3 @ S ) @ R3 )
% 4.69/4.94 => ( ord_le1436784781161120549et_int @ ( relcom4034950705519254697et_int @ ( max_ext_int @ R3 ) @ ( sup_su1286422330746572633et_int @ ( max_ext_int @ S ) @ ( insert7328952640415156725et_int @ ( produc6363374080413544029et_int @ bot_bot_set_int @ bot_bot_set_int ) @ bot_bo1987282549146081265et_int ) ) ) @ ( max_ext_int @ R3 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % max_ext_compat
% 4.69/4.94 thf(fact_2255_max__ext__compat,axiom,
% 4.69/4.94 ! [R3: set_Pr2161125870931222855_nat_o,S: set_Pr2161125870931222855_nat_o] :
% 4.69/4.94 ( ( ord_le6659818918159358183_nat_o @ ( relcom6251035627269349452_nat_o @ R3 @ S ) @ R3 )
% 4.69/4.94 => ( ord_le8001614231985977575_nat_o @ ( relcom7236094467932586796_nat_o @ ( max_ex5265246208886859912_nat_o @ R3 ) @ ( sup_su4863159966000489243_nat_o @ ( max_ex5265246208886859912_nat_o @ S ) @ ( insert3244108804717745463_nat_o @ ( produc5149316574908490455_nat_o @ bot_bo7824918357723582233_nat_o @ bot_bo7824918357723582233_nat_o ) @ bot_bo7535334947429593011_nat_o ) ) ) @ ( max_ex5265246208886859912_nat_o @ R3 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % max_ext_compat
% 4.69/4.94 thf(fact_2256_BNF__Greatest__Fixpoint_OIdD,axiom,
% 4.69/4.94 ! [A2: nat,B: nat] :
% 4.69/4.94 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ id_nat )
% 4.69/4.94 => ( A2 = B ) ) ).
% 4.69/4.94
% 4.69/4.94 % BNF_Greatest_Fixpoint.IdD
% 4.69/4.94 thf(fact_2257_BNF__Greatest__Fixpoint_OIdD,axiom,
% 4.69/4.94 ! [A2: int,B: int] :
% 4.69/4.94 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ id_int )
% 4.69/4.94 => ( A2 = B ) ) ).
% 4.69/4.94
% 4.69/4.94 % BNF_Greatest_Fixpoint.IdD
% 4.69/4.94 thf(fact_2258_Sup__fin_Oremove,axiom,
% 4.69/4.94 ! [A: set_set_nat,X: set_nat] :
% 4.69/4.94 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.94 => ( ( member_set_nat @ X @ A )
% 4.69/4.94 => ( ( ( ( minus_2163939370556025621et_nat @ A @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 4.69/4.94 = bot_bot_set_set_nat )
% 4.69/4.94 => ( ( lattic3835124923745554447et_nat @ A )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_2163939370556025621et_nat @ A @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 4.69/4.94 != bot_bot_set_set_nat )
% 4.69/4.94 => ( ( lattic3835124923745554447et_nat @ A )
% 4.69/4.94 = ( sup_sup_set_nat @ X @ ( lattic3835124923745554447et_nat @ ( minus_2163939370556025621et_nat @ A @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.remove
% 4.69/4.94 thf(fact_2259_Sup__fin_Oremove,axiom,
% 4.69/4.94 ! [A: set_assn,X: assn] :
% 4.69/4.94 ( ( finite_finite_assn @ A )
% 4.69/4.94 => ( ( member_assn @ X @ A )
% 4.69/4.94 => ( ( ( ( minus_minus_set_assn @ A @ ( insert_assn @ X @ bot_bot_set_assn ) )
% 4.69/4.94 = bot_bot_set_assn )
% 4.69/4.94 => ( ( lattic2150320897289308081n_assn @ A )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_minus_set_assn @ A @ ( insert_assn @ X @ bot_bot_set_assn ) )
% 4.69/4.94 != bot_bot_set_assn )
% 4.69/4.94 => ( ( lattic2150320897289308081n_assn @ A )
% 4.69/4.94 = ( sup_sup_assn @ X @ ( lattic2150320897289308081n_assn @ ( minus_minus_set_assn @ A @ ( insert_assn @ X @ bot_bot_set_assn ) ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.remove
% 4.69/4.94 thf(fact_2260_Sup__fin_Oremove,axiom,
% 4.69/4.94 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.94 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.94 => ( ( member_Product_unit @ X @ A )
% 4.69/4.94 => ( ( ( ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.94 = bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( lattic5294303975357428420t_unit @ A )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.94 != bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( lattic5294303975357428420t_unit @ A )
% 4.69/4.94 = ( sup_sup_Product_unit @ X @ ( lattic5294303975357428420t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.remove
% 4.69/4.94 thf(fact_2261_Sup__fin_Oremove,axiom,
% 4.69/4.94 ! [A: set_o,X: $o] :
% 4.69/4.94 ( ( finite_finite_o @ A )
% 4.69/4.94 => ( ( member_o @ X @ A )
% 4.69/4.94 => ( ( lattic1508158080041050831_fin_o @ A )
% 4.69/4.94 = ( ( ( ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.94 = bot_bot_set_o )
% 4.69/4.94 => X )
% 4.69/4.94 & ( ( ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.94 != bot_bot_set_o )
% 4.69/4.94 => ( sup_sup_o @ X @ ( lattic1508158080041050831_fin_o @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.remove
% 4.69/4.94 thf(fact_2262_Sup__fin_Oremove,axiom,
% 4.69/4.94 ! [A: set_int,X: int] :
% 4.69/4.94 ( ( finite_finite_int @ A )
% 4.69/4.94 => ( ( member_int @ X @ A )
% 4.69/4.94 => ( ( ( ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.94 = bot_bot_set_int )
% 4.69/4.94 => ( ( lattic1091506334969745077in_int @ A )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.94 != bot_bot_set_int )
% 4.69/4.94 => ( ( lattic1091506334969745077in_int @ A )
% 4.69/4.94 = ( sup_sup_int @ X @ ( lattic1091506334969745077in_int @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.remove
% 4.69/4.94 thf(fact_2263_Sup__fin_Oremove,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.94 => ( ( member6576561426505652726_nat_o @ X @ A )
% 4.69/4.94 => ( ( ( ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.94 = bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( lattic7320199455484906628_nat_o @ A )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.94 != bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( lattic7320199455484906628_nat_o @ A )
% 4.69/4.94 = ( sup_su5453871518329203617_nat_o @ X @ ( lattic7320199455484906628_nat_o @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.remove
% 4.69/4.94 thf(fact_2264_Sup__fin_Oremove,axiom,
% 4.69/4.94 ! [A: set_nat,X: nat] :
% 4.69/4.94 ( ( finite_finite_nat @ A )
% 4.69/4.94 => ( ( member_nat @ X @ A )
% 4.69/4.94 => ( ( ( ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.94 = bot_bot_set_nat )
% 4.69/4.94 => ( ( lattic1093996805478795353in_nat @ A )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.94 != bot_bot_set_nat )
% 4.69/4.94 => ( ( lattic1093996805478795353in_nat @ A )
% 4.69/4.94 = ( sup_sup_nat @ X @ ( lattic1093996805478795353in_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.remove
% 4.69/4.94 thf(fact_2265_Sup__fin_Oinsert__remove,axiom,
% 4.69/4.94 ! [A: set_set_nat,X: set_nat] :
% 4.69/4.94 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.94 => ( ( ( ( minus_2163939370556025621et_nat @ A @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 4.69/4.94 = bot_bot_set_set_nat )
% 4.69/4.94 => ( ( lattic3835124923745554447et_nat @ ( insert_set_nat @ X @ A ) )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_2163939370556025621et_nat @ A @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 4.69/4.94 != bot_bot_set_set_nat )
% 4.69/4.94 => ( ( lattic3835124923745554447et_nat @ ( insert_set_nat @ X @ A ) )
% 4.69/4.94 = ( sup_sup_set_nat @ X @ ( lattic3835124923745554447et_nat @ ( minus_2163939370556025621et_nat @ A @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.insert_remove
% 4.69/4.94 thf(fact_2266_Sup__fin_Oinsert__remove,axiom,
% 4.69/4.94 ! [A: set_assn,X: assn] :
% 4.69/4.94 ( ( finite_finite_assn @ A )
% 4.69/4.94 => ( ( ( ( minus_minus_set_assn @ A @ ( insert_assn @ X @ bot_bot_set_assn ) )
% 4.69/4.94 = bot_bot_set_assn )
% 4.69/4.94 => ( ( lattic2150320897289308081n_assn @ ( insert_assn @ X @ A ) )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_minus_set_assn @ A @ ( insert_assn @ X @ bot_bot_set_assn ) )
% 4.69/4.94 != bot_bot_set_assn )
% 4.69/4.94 => ( ( lattic2150320897289308081n_assn @ ( insert_assn @ X @ A ) )
% 4.69/4.94 = ( sup_sup_assn @ X @ ( lattic2150320897289308081n_assn @ ( minus_minus_set_assn @ A @ ( insert_assn @ X @ bot_bot_set_assn ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.insert_remove
% 4.69/4.94 thf(fact_2267_Sup__fin_Oinsert__remove,axiom,
% 4.69/4.94 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.94 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.94 => ( ( ( ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.94 = bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( lattic5294303975357428420t_unit @ ( insert_Product_unit @ X @ A ) )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.94 != bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( lattic5294303975357428420t_unit @ ( insert_Product_unit @ X @ A ) )
% 4.69/4.94 = ( sup_sup_Product_unit @ X @ ( lattic5294303975357428420t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.insert_remove
% 4.69/4.94 thf(fact_2268_Sup__fin_Oinsert__remove,axiom,
% 4.69/4.94 ! [A: set_o,X: $o] :
% 4.69/4.94 ( ( finite_finite_o @ A )
% 4.69/4.94 => ( ( lattic1508158080041050831_fin_o @ ( insert_o @ X @ A ) )
% 4.69/4.94 = ( ( ( ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.94 = bot_bot_set_o )
% 4.69/4.94 => X )
% 4.69/4.94 & ( ( ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.94 != bot_bot_set_o )
% 4.69/4.94 => ( sup_sup_o @ X @ ( lattic1508158080041050831_fin_o @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.insert_remove
% 4.69/4.94 thf(fact_2269_Sup__fin_Oinsert__remove,axiom,
% 4.69/4.94 ! [A: set_int,X: int] :
% 4.69/4.94 ( ( finite_finite_int @ A )
% 4.69/4.94 => ( ( ( ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.94 = bot_bot_set_int )
% 4.69/4.94 => ( ( lattic1091506334969745077in_int @ ( insert_int @ X @ A ) )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.94 != bot_bot_set_int )
% 4.69/4.94 => ( ( lattic1091506334969745077in_int @ ( insert_int @ X @ A ) )
% 4.69/4.94 = ( sup_sup_int @ X @ ( lattic1091506334969745077in_int @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.insert_remove
% 4.69/4.94 thf(fact_2270_Sup__fin_Oinsert__remove,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.94 => ( ( ( ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.94 = bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( lattic7320199455484906628_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.94 != bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( lattic7320199455484906628_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) )
% 4.69/4.94 = ( sup_su5453871518329203617_nat_o @ X @ ( lattic7320199455484906628_nat_o @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.insert_remove
% 4.69/4.94 thf(fact_2271_Sup__fin_Oinsert__remove,axiom,
% 4.69/4.94 ! [A: set_nat,X: nat] :
% 4.69/4.94 ( ( finite_finite_nat @ A )
% 4.69/4.94 => ( ( ( ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.94 = bot_bot_set_nat )
% 4.69/4.94 => ( ( lattic1093996805478795353in_nat @ ( insert_nat @ X @ A ) )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.94 != bot_bot_set_nat )
% 4.69/4.94 => ( ( lattic1093996805478795353in_nat @ ( insert_nat @ X @ A ) )
% 4.69/4.94 = ( sup_sup_nat @ X @ ( lattic1093996805478795353in_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Sup_fin.insert_remove
% 4.69/4.94 thf(fact_2272_Inf__fin_Oremove,axiom,
% 4.69/4.94 ! [A: set_set_nat,X: set_nat] :
% 4.69/4.94 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.94 => ( ( member_set_nat @ X @ A )
% 4.69/4.94 => ( ( ( ( minus_2163939370556025621et_nat @ A @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 4.69/4.94 = bot_bot_set_set_nat )
% 4.69/4.94 => ( ( lattic3014633134055518761et_nat @ A )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_2163939370556025621et_nat @ A @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 4.69/4.94 != bot_bot_set_set_nat )
% 4.69/4.94 => ( ( lattic3014633134055518761et_nat @ A )
% 4.69/4.94 = ( inf_inf_set_nat @ X @ ( lattic3014633134055518761et_nat @ ( minus_2163939370556025621et_nat @ A @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.remove
% 4.69/4.94 thf(fact_2273_Inf__fin_Oremove,axiom,
% 4.69/4.94 ! [A: set_assn,X: assn] :
% 4.69/4.94 ( ( finite_finite_assn @ A )
% 4.69/4.94 => ( ( member_assn @ X @ A )
% 4.69/4.94 => ( ( ( ( minus_minus_set_assn @ A @ ( insert_assn @ X @ bot_bot_set_assn ) )
% 4.69/4.94 = bot_bot_set_assn )
% 4.69/4.94 => ( ( lattic47131356835913163n_assn @ A )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_minus_set_assn @ A @ ( insert_assn @ X @ bot_bot_set_assn ) )
% 4.69/4.94 != bot_bot_set_assn )
% 4.69/4.94 => ( ( lattic47131356835913163n_assn @ A )
% 4.69/4.94 = ( inf_inf_assn @ X @ ( lattic47131356835913163n_assn @ ( minus_minus_set_assn @ A @ ( insert_assn @ X @ bot_bot_set_assn ) ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.remove
% 4.69/4.94 thf(fact_2274_Inf__fin_Oremove,axiom,
% 4.69/4.94 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.94 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.94 => ( ( member_Product_unit @ X @ A )
% 4.69/4.94 => ( ( ( ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.94 = bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( lattic1263872656861969706t_unit @ A )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.94 != bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( lattic1263872656861969706t_unit @ A )
% 4.69/4.94 = ( inf_inf_Product_unit @ X @ ( lattic1263872656861969706t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.remove
% 4.69/4.94 thf(fact_2275_Inf__fin_Oremove,axiom,
% 4.69/4.94 ! [A: set_o,X: $o] :
% 4.69/4.94 ( ( finite_finite_o @ A )
% 4.69/4.94 => ( ( member_o @ X @ A )
% 4.69/4.94 => ( ( lattic4107685809792843317_fin_o @ A )
% 4.69/4.94 = ( ( ( ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.94 = bot_bot_set_o )
% 4.69/4.94 => X )
% 4.69/4.94 & ( ( ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.94 != bot_bot_set_o )
% 4.69/4.94 => ( inf_inf_o @ X @ ( lattic4107685809792843317_fin_o @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.remove
% 4.69/4.94 thf(fact_2276_Inf__fin_Oremove,axiom,
% 4.69/4.94 ! [A: set_int,X: int] :
% 4.69/4.94 ( ( finite_finite_int @ A )
% 4.69/4.94 => ( ( member_int @ X @ A )
% 4.69/4.94 => ( ( ( ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.94 = bot_bot_set_int )
% 4.69/4.94 => ( ( lattic5235898064620869839in_int @ A )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.94 != bot_bot_set_int )
% 4.69/4.94 => ( ( lattic5235898064620869839in_int @ A )
% 4.69/4.94 = ( inf_inf_int @ X @ ( lattic5235898064620869839in_int @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.remove
% 4.69/4.94 thf(fact_2277_Inf__fin_Oremove,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.94 => ( ( member6576561426505652726_nat_o @ X @ A )
% 4.69/4.94 => ( ( ( ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.94 = bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( lattic956194824204696298_nat_o @ A )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.94 != bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( lattic956194824204696298_nat_o @ A )
% 4.69/4.94 = ( inf_in1318976480646536635_nat_o @ X @ ( lattic956194824204696298_nat_o @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.remove
% 4.69/4.94 thf(fact_2278_Inf__fin_Oremove,axiom,
% 4.69/4.94 ! [A: set_nat,X: nat] :
% 4.69/4.94 ( ( finite_finite_nat @ A )
% 4.69/4.94 => ( ( member_nat @ X @ A )
% 4.69/4.94 => ( ( ( ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.94 = bot_bot_set_nat )
% 4.69/4.94 => ( ( lattic5238388535129920115in_nat @ A )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.94 != bot_bot_set_nat )
% 4.69/4.94 => ( ( lattic5238388535129920115in_nat @ A )
% 4.69/4.94 = ( inf_inf_nat @ X @ ( lattic5238388535129920115in_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.remove
% 4.69/4.94 thf(fact_2279_Inf__fin_Oinsert__remove,axiom,
% 4.69/4.94 ! [A: set_set_nat,X: set_nat] :
% 4.69/4.94 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.94 => ( ( ( ( minus_2163939370556025621et_nat @ A @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 4.69/4.94 = bot_bot_set_set_nat )
% 4.69/4.94 => ( ( lattic3014633134055518761et_nat @ ( insert_set_nat @ X @ A ) )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_2163939370556025621et_nat @ A @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 4.69/4.94 != bot_bot_set_set_nat )
% 4.69/4.94 => ( ( lattic3014633134055518761et_nat @ ( insert_set_nat @ X @ A ) )
% 4.69/4.94 = ( inf_inf_set_nat @ X @ ( lattic3014633134055518761et_nat @ ( minus_2163939370556025621et_nat @ A @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.insert_remove
% 4.69/4.94 thf(fact_2280_Inf__fin_Oinsert__remove,axiom,
% 4.69/4.94 ! [A: set_assn,X: assn] :
% 4.69/4.94 ( ( finite_finite_assn @ A )
% 4.69/4.94 => ( ( ( ( minus_minus_set_assn @ A @ ( insert_assn @ X @ bot_bot_set_assn ) )
% 4.69/4.94 = bot_bot_set_assn )
% 4.69/4.94 => ( ( lattic47131356835913163n_assn @ ( insert_assn @ X @ A ) )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_minus_set_assn @ A @ ( insert_assn @ X @ bot_bot_set_assn ) )
% 4.69/4.94 != bot_bot_set_assn )
% 4.69/4.94 => ( ( lattic47131356835913163n_assn @ ( insert_assn @ X @ A ) )
% 4.69/4.94 = ( inf_inf_assn @ X @ ( lattic47131356835913163n_assn @ ( minus_minus_set_assn @ A @ ( insert_assn @ X @ bot_bot_set_assn ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.insert_remove
% 4.69/4.94 thf(fact_2281_Inf__fin_Oinsert__remove,axiom,
% 4.69/4.94 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.94 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.94 => ( ( ( ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.94 = bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( lattic1263872656861969706t_unit @ ( insert_Product_unit @ X @ A ) )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.94 != bot_bo3957492148770167129t_unit )
% 4.69/4.94 => ( ( lattic1263872656861969706t_unit @ ( insert_Product_unit @ X @ A ) )
% 4.69/4.94 = ( inf_inf_Product_unit @ X @ ( lattic1263872656861969706t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.insert_remove
% 4.69/4.94 thf(fact_2282_Inf__fin_Oinsert__remove,axiom,
% 4.69/4.94 ! [A: set_o,X: $o] :
% 4.69/4.94 ( ( finite_finite_o @ A )
% 4.69/4.94 => ( ( lattic4107685809792843317_fin_o @ ( insert_o @ X @ A ) )
% 4.69/4.94 = ( ( ( ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.94 = bot_bot_set_o )
% 4.69/4.94 => X )
% 4.69/4.94 & ( ( ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.94 != bot_bot_set_o )
% 4.69/4.94 => ( inf_inf_o @ X @ ( lattic4107685809792843317_fin_o @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.insert_remove
% 4.69/4.94 thf(fact_2283_Inf__fin_Oinsert__remove,axiom,
% 4.69/4.94 ! [A: set_int,X: int] :
% 4.69/4.94 ( ( finite_finite_int @ A )
% 4.69/4.94 => ( ( ( ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.94 = bot_bot_set_int )
% 4.69/4.94 => ( ( lattic5235898064620869839in_int @ ( insert_int @ X @ A ) )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.94 != bot_bot_set_int )
% 4.69/4.94 => ( ( lattic5235898064620869839in_int @ ( insert_int @ X @ A ) )
% 4.69/4.94 = ( inf_inf_int @ X @ ( lattic5235898064620869839in_int @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.insert_remove
% 4.69/4.94 thf(fact_2284_Inf__fin_Oinsert__remove,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/4.94 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.94 => ( ( ( ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.94 = bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( lattic956194824204696298_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.94 != bot_bo7824918357723582233_nat_o )
% 4.69/4.94 => ( ( lattic956194824204696298_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) )
% 4.69/4.94 = ( inf_in1318976480646536635_nat_o @ X @ ( lattic956194824204696298_nat_o @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.insert_remove
% 4.69/4.94 thf(fact_2285_Inf__fin_Oinsert__remove,axiom,
% 4.69/4.94 ! [A: set_nat,X: nat] :
% 4.69/4.94 ( ( finite_finite_nat @ A )
% 4.69/4.94 => ( ( ( ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.94 = bot_bot_set_nat )
% 4.69/4.94 => ( ( lattic5238388535129920115in_nat @ ( insert_nat @ X @ A ) )
% 4.69/4.94 = X ) )
% 4.69/4.94 & ( ( ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.94 != bot_bot_set_nat )
% 4.69/4.94 => ( ( lattic5238388535129920115in_nat @ ( insert_nat @ X @ A ) )
% 4.69/4.94 = ( inf_inf_nat @ X @ ( lattic5238388535129920115in_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Inf_fin.insert_remove
% 4.69/4.94 thf(fact_2286_acyclic__insert,axiom,
% 4.69/4.94 ! [Y: nat,X: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.94 ( ( transi3139058337892597825ic_nat @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ Y @ X ) @ R2 ) )
% 4.69/4.94 = ( ( transi3139058337892597825ic_nat @ R2 )
% 4.69/4.94 & ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi2905341329935302413cl_nat @ R2 ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % acyclic_insert
% 4.69/4.94 thf(fact_2287_acyclic__insert,axiom,
% 4.69/4.94 ! [Y: int,X: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.94 ( ( transi3136567867383547549ic_int @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ Y @ X ) @ R2 ) )
% 4.69/4.94 = ( ( transi3136567867383547549ic_int @ R2 )
% 4.69/4.94 & ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi2902850859426252137cl_int @ R2 ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % acyclic_insert
% 4.69/4.94 thf(fact_2288_irrefl__tranclI,axiom,
% 4.69/4.94 ! [R2: set_Pr1261947904930325089at_nat,X: nat] :
% 4.69/4.94 ( ( ( inf_in2572325071724192079at_nat @ ( converse_nat_nat @ R2 ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.94 = bot_bo2099793752762293965at_nat )
% 4.69/4.94 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ X ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % irrefl_tranclI
% 4.69/4.94 thf(fact_2289_irrefl__tranclI,axiom,
% 4.69/4.94 ! [R2: set_Pr958786334691620121nt_int,X: int] :
% 4.69/4.94 ( ( ( inf_in2269163501485487111nt_int @ ( converse_int_int @ R2 ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.94 = bot_bo1796632182523588997nt_int )
% 4.69/4.94 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ X ) @ ( transi6261509568448316235cl_int @ R2 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % irrefl_tranclI
% 4.69/4.94 thf(fact_2290_inf__img__fin__dom_H,axiom,
% 4.69/4.94 ! [F: code_integer > code_integer,A: set_Code_integer] :
% 4.69/4.94 ( ( finite6017078050557962740nteger @ ( image_4470545334726330049nteger @ F @ A ) )
% 4.69/4.94 => ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/4.94 => ? [X3: code_integer] :
% 4.69/4.94 ( ( member_Code_integer @ X3 @ ( image_4470545334726330049nteger @ F @ A ) )
% 4.69/4.94 & ~ ( finite6017078050557962740nteger @ ( inf_in1364745209274528805nteger @ ( vimage1318793397690208119nteger @ F @ ( insert_Code_integer @ X3 @ bot_bo3990330152332043303nteger ) ) @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % inf_img_fin_dom'
% 4.69/4.94 thf(fact_2291_inf__img__fin__dom_H,axiom,
% 4.69/4.94 ! [F: nat > code_integer,A: set_nat] :
% 4.69/4.94 ( ( finite6017078050557962740nteger @ ( image_1215581382706833972nteger @ F @ A ) )
% 4.69/4.94 => ( ~ ( finite_finite_nat @ A )
% 4.69/4.94 => ? [X3: code_integer] :
% 4.69/4.94 ( ( member_Code_integer @ X3 @ ( image_1215581382706833972nteger @ F @ A ) )
% 4.69/4.94 & ~ ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage6104394758324456170nteger @ F @ ( insert_Code_integer @ X3 @ bot_bo3990330152332043303nteger ) ) @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % inf_img_fin_dom'
% 4.69/4.94 thf(fact_2292_inf__img__fin__dom_H,axiom,
% 4.69/4.94 ! [F: code_integer > product_unit,A: set_Code_integer] :
% 4.69/4.94 ( ( finite4290736615968046902t_unit @ ( image_7182656606676592809t_unit @ F @ A ) )
% 4.69/4.94 => ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/4.94 => ? [X3: product_unit] :
% 4.69/4.94 ( ( member_Product_unit @ X3 @ ( image_7182656606676592809t_unit @ F @ A ) )
% 4.69/4.94 & ~ ( finite6017078050557962740nteger @ ( inf_in1364745209274528805nteger @ ( vimage5651688891684837235t_unit @ F @ ( insert_Product_unit @ X3 @ bot_bo3957492148770167129t_unit ) ) @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % inf_img_fin_dom'
% 4.69/4.94 thf(fact_2293_inf__img__fin__dom_H,axiom,
% 4.69/4.94 ! [F: nat > product_unit,A: set_nat] :
% 4.69/4.94 ( ( finite4290736615968046902t_unit @ ( image_8730104196221521654t_unit @ F @ A ) )
% 4.69/4.94 => ( ~ ( finite_finite_nat @ A )
% 4.69/4.94 => ? [X3: product_unit] :
% 4.69/4.94 ( ( member_Product_unit @ X3 @ ( image_8730104196221521654t_unit @ F @ A ) )
% 4.69/4.94 & ~ ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage4884490618288580032t_unit @ F @ ( insert_Product_unit @ X3 @ bot_bo3957492148770167129t_unit ) ) @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % inf_img_fin_dom'
% 4.69/4.94 thf(fact_2294_inf__img__fin__dom_H,axiom,
% 4.69/4.94 ! [F: code_integer > $o,A: set_Code_integer] :
% 4.69/4.94 ( ( finite_finite_o @ ( image_Code_integer_o @ F @ A ) )
% 4.69/4.94 => ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/4.94 => ? [X3: $o] :
% 4.69/4.94 ( ( member_o @ X3 @ ( image_Code_integer_o @ F @ A ) )
% 4.69/4.94 & ~ ( finite6017078050557962740nteger @ ( inf_in1364745209274528805nteger @ ( vimage3005800680117336574eger_o @ F @ ( insert_o @ X3 @ bot_bot_set_o ) ) @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % inf_img_fin_dom'
% 4.69/4.94 thf(fact_2295_inf__img__fin__dom_H,axiom,
% 4.69/4.94 ! [F: nat > $o,A: set_nat] :
% 4.69/4.94 ( ( finite_finite_o @ ( image_nat_o2 @ F @ A ) )
% 4.69/4.94 => ( ~ ( finite_finite_nat @ A )
% 4.69/4.94 => ? [X3: $o] :
% 4.69/4.94 ( ( member_o @ X3 @ ( image_nat_o2 @ F @ A ) )
% 4.69/4.94 & ~ ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_o @ F @ ( insert_o @ X3 @ bot_bot_set_o ) ) @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % inf_img_fin_dom'
% 4.69/4.94 thf(fact_2296_inf__img__fin__dom_H,axiom,
% 4.69/4.94 ! [F: code_integer > nat,A: set_Code_integer] :
% 4.69/4.94 ( ( finite_finite_nat @ ( image_951025933927791156er_nat @ F @ A ) )
% 4.69/4.94 => ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/4.94 => ? [X3: nat] :
% 4.69/4.94 ( ( member_nat @ X3 @ ( image_951025933927791156er_nat @ F @ A ) )
% 4.69/4.94 & ~ ( finite6017078050557962740nteger @ ( inf_in1364745209274528805nteger @ ( vimage5839839309545413354er_nat @ F @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % inf_img_fin_dom'
% 4.69/4.94 thf(fact_2297_inf__img__fin__dom_H,axiom,
% 4.69/4.94 ! [F: nat > nat,A: set_nat] :
% 4.69/4.94 ( ( finite_finite_nat @ ( image_nat_nat2 @ F @ A ) )
% 4.69/4.94 => ( ~ ( finite_finite_nat @ A )
% 4.69/4.94 => ? [X3: nat] :
% 4.69/4.94 ( ( member_nat @ X3 @ ( image_nat_nat2 @ F @ A ) )
% 4.69/4.94 & ~ ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_nat @ F @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % inf_img_fin_dom'
% 4.69/4.94 thf(fact_2298_inf__img__fin__dom_H,axiom,
% 4.69/4.94 ! [F: code_integer > int,A: set_Code_integer] :
% 4.69/4.94 ( ( finite_finite_int @ ( image_948535463418740880er_int @ F @ A ) )
% 4.69/4.94 => ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/4.94 => ? [X3: int] :
% 4.69/4.94 ( ( member_int @ X3 @ ( image_948535463418740880er_int @ F @ A ) )
% 4.69/4.94 & ~ ( finite6017078050557962740nteger @ ( inf_in1364745209274528805nteger @ ( vimage5837348839036363078er_int @ F @ ( insert_int @ X3 @ bot_bot_set_int ) ) @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % inf_img_fin_dom'
% 4.69/4.94 thf(fact_2299_inf__img__fin__dom_H,axiom,
% 4.69/4.94 ! [F: nat > int,A: set_nat] :
% 4.69/4.94 ( ( finite_finite_int @ ( image_nat_int2 @ F @ A ) )
% 4.69/4.94 => ( ~ ( finite_finite_nat @ A )
% 4.69/4.94 => ? [X3: int] :
% 4.69/4.94 ( ( member_int @ X3 @ ( image_nat_int2 @ F @ A ) )
% 4.69/4.94 & ~ ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_int @ F @ ( insert_int @ X3 @ bot_bot_set_int ) ) @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % inf_img_fin_dom'
% 4.69/4.94 thf(fact_2300_inf__img__fin__domE_H,axiom,
% 4.69/4.94 ! [F: code_integer > code_integer,A: set_Code_integer] :
% 4.69/4.94 ( ( finite6017078050557962740nteger @ ( image_4470545334726330049nteger @ F @ A ) )
% 4.69/4.94 => ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/4.94 => ~ ! [Y2: code_integer] :
% 4.69/4.94 ( ( member_Code_integer @ Y2 @ ( image_4470545334726330049nteger @ F @ A ) )
% 4.69/4.94 => ( finite6017078050557962740nteger @ ( inf_in1364745209274528805nteger @ ( vimage1318793397690208119nteger @ F @ ( insert_Code_integer @ Y2 @ bot_bo3990330152332043303nteger ) ) @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % inf_img_fin_domE'
% 4.69/4.94 thf(fact_2301_inf__img__fin__domE_H,axiom,
% 4.69/4.94 ! [F: nat > code_integer,A: set_nat] :
% 4.69/4.94 ( ( finite6017078050557962740nteger @ ( image_1215581382706833972nteger @ F @ A ) )
% 4.69/4.94 => ( ~ ( finite_finite_nat @ A )
% 4.69/4.94 => ~ ! [Y2: code_integer] :
% 4.69/4.94 ( ( member_Code_integer @ Y2 @ ( image_1215581382706833972nteger @ F @ A ) )
% 4.69/4.94 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage6104394758324456170nteger @ F @ ( insert_Code_integer @ Y2 @ bot_bo3990330152332043303nteger ) ) @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % inf_img_fin_domE'
% 4.69/4.94 thf(fact_2302_inf__img__fin__domE_H,axiom,
% 4.69/4.94 ! [F: code_integer > product_unit,A: set_Code_integer] :
% 4.69/4.94 ( ( finite4290736615968046902t_unit @ ( image_7182656606676592809t_unit @ F @ A ) )
% 4.69/4.94 => ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/4.94 => ~ ! [Y2: product_unit] :
% 4.69/4.94 ( ( member_Product_unit @ Y2 @ ( image_7182656606676592809t_unit @ F @ A ) )
% 4.69/4.94 => ( finite6017078050557962740nteger @ ( inf_in1364745209274528805nteger @ ( vimage5651688891684837235t_unit @ F @ ( insert_Product_unit @ Y2 @ bot_bo3957492148770167129t_unit ) ) @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % inf_img_fin_domE'
% 4.69/4.94 thf(fact_2303_inf__img__fin__domE_H,axiom,
% 4.69/4.94 ! [F: nat > product_unit,A: set_nat] :
% 4.69/4.94 ( ( finite4290736615968046902t_unit @ ( image_8730104196221521654t_unit @ F @ A ) )
% 4.69/4.94 => ( ~ ( finite_finite_nat @ A )
% 4.69/4.94 => ~ ! [Y2: product_unit] :
% 4.69/4.94 ( ( member_Product_unit @ Y2 @ ( image_8730104196221521654t_unit @ F @ A ) )
% 4.69/4.94 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage4884490618288580032t_unit @ F @ ( insert_Product_unit @ Y2 @ bot_bo3957492148770167129t_unit ) ) @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % inf_img_fin_domE'
% 4.69/4.94 thf(fact_2304_inf__img__fin__domE_H,axiom,
% 4.69/4.94 ! [F: code_integer > $o,A: set_Code_integer] :
% 4.69/4.94 ( ( finite_finite_o @ ( image_Code_integer_o @ F @ A ) )
% 4.69/4.94 => ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/4.94 => ~ ! [Y2: $o] :
% 4.69/4.94 ( ( member_o @ Y2 @ ( image_Code_integer_o @ F @ A ) )
% 4.69/4.94 => ( finite6017078050557962740nteger @ ( inf_in1364745209274528805nteger @ ( vimage3005800680117336574eger_o @ F @ ( insert_o @ Y2 @ bot_bot_set_o ) ) @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % inf_img_fin_domE'
% 4.69/4.94 thf(fact_2305_inf__img__fin__domE_H,axiom,
% 4.69/4.94 ! [F: nat > $o,A: set_nat] :
% 4.69/4.94 ( ( finite_finite_o @ ( image_nat_o2 @ F @ A ) )
% 4.69/4.94 => ( ~ ( finite_finite_nat @ A )
% 4.69/4.94 => ~ ! [Y2: $o] :
% 4.69/4.94 ( ( member_o @ Y2 @ ( image_nat_o2 @ F @ A ) )
% 4.69/4.94 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_o @ F @ ( insert_o @ Y2 @ bot_bot_set_o ) ) @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % inf_img_fin_domE'
% 4.69/4.94 thf(fact_2306_inf__img__fin__domE_H,axiom,
% 4.69/4.94 ! [F: code_integer > nat,A: set_Code_integer] :
% 4.69/4.94 ( ( finite_finite_nat @ ( image_951025933927791156er_nat @ F @ A ) )
% 4.69/4.94 => ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/4.94 => ~ ! [Y2: nat] :
% 4.69/4.94 ( ( member_nat @ Y2 @ ( image_951025933927791156er_nat @ F @ A ) )
% 4.69/4.94 => ( finite6017078050557962740nteger @ ( inf_in1364745209274528805nteger @ ( vimage5839839309545413354er_nat @ F @ ( insert_nat @ Y2 @ bot_bot_set_nat ) ) @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % inf_img_fin_domE'
% 4.69/4.94 thf(fact_2307_inf__img__fin__domE_H,axiom,
% 4.69/4.94 ! [F: nat > nat,A: set_nat] :
% 4.69/4.94 ( ( finite_finite_nat @ ( image_nat_nat2 @ F @ A ) )
% 4.69/4.94 => ( ~ ( finite_finite_nat @ A )
% 4.69/4.94 => ~ ! [Y2: nat] :
% 4.69/4.94 ( ( member_nat @ Y2 @ ( image_nat_nat2 @ F @ A ) )
% 4.69/4.94 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_nat @ F @ ( insert_nat @ Y2 @ bot_bot_set_nat ) ) @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % inf_img_fin_domE'
% 4.69/4.94 thf(fact_2308_inf__img__fin__domE_H,axiom,
% 4.69/4.94 ! [F: code_integer > int,A: set_Code_integer] :
% 4.69/4.94 ( ( finite_finite_int @ ( image_948535463418740880er_int @ F @ A ) )
% 4.69/4.94 => ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/4.94 => ~ ! [Y2: int] :
% 4.69/4.94 ( ( member_int @ Y2 @ ( image_948535463418740880er_int @ F @ A ) )
% 4.69/4.94 => ( finite6017078050557962740nteger @ ( inf_in1364745209274528805nteger @ ( vimage5837348839036363078er_int @ F @ ( insert_int @ Y2 @ bot_bot_set_int ) ) @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % inf_img_fin_domE'
% 4.69/4.94 thf(fact_2309_inf__img__fin__domE_H,axiom,
% 4.69/4.94 ! [F: nat > int,A: set_nat] :
% 4.69/4.94 ( ( finite_finite_int @ ( image_nat_int2 @ F @ A ) )
% 4.69/4.94 => ( ~ ( finite_finite_nat @ A )
% 4.69/4.94 => ~ ! [Y2: int] :
% 4.69/4.94 ( ( member_int @ Y2 @ ( image_nat_int2 @ F @ A ) )
% 4.69/4.94 => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_int @ F @ ( insert_int @ Y2 @ bot_bot_set_int ) ) @ A ) ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % inf_img_fin_domE'
% 4.69/4.94 thf(fact_2310_image__eqI,axiom,
% 4.69/4.94 ! [B: code_integer,F: code_integer > code_integer,X: code_integer,A: set_Code_integer] :
% 4.69/4.94 ( ( B
% 4.69/4.94 = ( F @ X ) )
% 4.69/4.94 => ( ( member_Code_integer @ X @ A )
% 4.69/4.94 => ( member_Code_integer @ B @ ( image_4470545334726330049nteger @ F @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_eqI
% 4.69/4.94 thf(fact_2311_image__eqI,axiom,
% 4.69/4.94 ! [B: code_integer,F: nat > code_integer,X: nat,A: set_nat] :
% 4.69/4.94 ( ( B
% 4.69/4.94 = ( F @ X ) )
% 4.69/4.94 => ( ( member_nat @ X @ A )
% 4.69/4.94 => ( member_Code_integer @ B @ ( image_1215581382706833972nteger @ F @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_eqI
% 4.69/4.94 thf(fact_2312_image__eqI,axiom,
% 4.69/4.94 ! [B: nat,F: nat > nat,X: nat,A: set_nat] :
% 4.69/4.94 ( ( B
% 4.69/4.94 = ( F @ X ) )
% 4.69/4.94 => ( ( member_nat @ X @ A )
% 4.69/4.94 => ( member_nat @ B @ ( image_nat_nat2 @ F @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_eqI
% 4.69/4.94 thf(fact_2313_image__eqI,axiom,
% 4.69/4.94 ! [B: int,F: nat > int,X: nat,A: set_nat] :
% 4.69/4.94 ( ( B
% 4.69/4.94 = ( F @ X ) )
% 4.69/4.94 => ( ( member_nat @ X @ A )
% 4.69/4.94 => ( member_int @ B @ ( image_nat_int2 @ F @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_eqI
% 4.69/4.94 thf(fact_2314_image__eqI,axiom,
% 4.69/4.94 ! [B: $o,F: nat > $o,X: nat,A: set_nat] :
% 4.69/4.94 ( ( B
% 4.69/4.94 = ( F @ X ) )
% 4.69/4.94 => ( ( member_nat @ X @ A )
% 4.69/4.94 => ( member_o @ B @ ( image_nat_o2 @ F @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_eqI
% 4.69/4.94 thf(fact_2315_image__eqI,axiom,
% 4.69/4.94 ! [B: product_unit,F: nat > product_unit,X: nat,A: set_nat] :
% 4.69/4.94 ( ( B
% 4.69/4.94 = ( F @ X ) )
% 4.69/4.94 => ( ( member_nat @ X @ A )
% 4.69/4.94 => ( member_Product_unit @ B @ ( image_8730104196221521654t_unit @ F @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_eqI
% 4.69/4.94 thf(fact_2316_image__eqI,axiom,
% 4.69/4.94 ! [B: nat,F: int > nat,X: int,A: set_int] :
% 4.69/4.94 ( ( B
% 4.69/4.94 = ( F @ X ) )
% 4.69/4.94 => ( ( member_int @ X @ A )
% 4.69/4.94 => ( member_nat @ B @ ( image_int_nat2 @ F @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_eqI
% 4.69/4.94 thf(fact_2317_image__eqI,axiom,
% 4.69/4.94 ! [B: int,F: int > int,X: int,A: set_int] :
% 4.69/4.94 ( ( B
% 4.69/4.94 = ( F @ X ) )
% 4.69/4.94 => ( ( member_int @ X @ A )
% 4.69/4.94 => ( member_int @ B @ ( image_int_int2 @ F @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_eqI
% 4.69/4.94 thf(fact_2318_image__eqI,axiom,
% 4.69/4.94 ! [B: $o,F: int > $o,X: int,A: set_int] :
% 4.69/4.94 ( ( B
% 4.69/4.94 = ( F @ X ) )
% 4.69/4.94 => ( ( member_int @ X @ A )
% 4.69/4.94 => ( member_o @ B @ ( image_int_o2 @ F @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_eqI
% 4.69/4.94 thf(fact_2319_image__eqI,axiom,
% 4.69/4.94 ! [B: product_unit,F: int > product_unit,X: int,A: set_int] :
% 4.69/4.94 ( ( B
% 4.69/4.94 = ( F @ X ) )
% 4.69/4.94 => ( ( member_int @ X @ A )
% 4.69/4.94 => ( member_Product_unit @ B @ ( image_5846526143423701914t_unit @ F @ A ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_eqI
% 4.69/4.94 thf(fact_2320_Diff__idemp,axiom,
% 4.69/4.94 ! [A: set_nat,B4: set_nat] :
% 4.69/4.94 ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A @ B4 ) @ B4 )
% 4.69/4.94 = ( minus_minus_set_nat @ A @ B4 ) ) ).
% 4.69/4.94
% 4.69/4.94 % Diff_idemp
% 4.69/4.94 thf(fact_2321_Diff__iff,axiom,
% 4.69/4.94 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.94 ( ( member6576561426505652726_nat_o @ C @ ( minus_1801376950450012436_nat_o @ A @ B4 ) )
% 4.69/4.94 = ( ( member6576561426505652726_nat_o @ C @ A )
% 4.69/4.94 & ~ ( member6576561426505652726_nat_o @ C @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Diff_iff
% 4.69/4.94 thf(fact_2322_Diff__iff,axiom,
% 4.69/4.94 ! [C: int,A: set_int,B4: set_int] :
% 4.69/4.94 ( ( member_int @ C @ ( minus_minus_set_int @ A @ B4 ) )
% 4.69/4.94 = ( ( member_int @ C @ A )
% 4.69/4.94 & ~ ( member_int @ C @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Diff_iff
% 4.69/4.94 thf(fact_2323_Diff__iff,axiom,
% 4.69/4.94 ! [C: $o,A: set_o,B4: set_o] :
% 4.69/4.94 ( ( member_o @ C @ ( minus_minus_set_o @ A @ B4 ) )
% 4.69/4.94 = ( ( member_o @ C @ A )
% 4.69/4.94 & ~ ( member_o @ C @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Diff_iff
% 4.69/4.94 thf(fact_2324_Diff__iff,axiom,
% 4.69/4.94 ! [C: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.94 ( ( member_Product_unit @ C @ ( minus_6452836326544984404t_unit @ A @ B4 ) )
% 4.69/4.94 = ( ( member_Product_unit @ C @ A )
% 4.69/4.94 & ~ ( member_Product_unit @ C @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Diff_iff
% 4.69/4.94 thf(fact_2325_Diff__iff,axiom,
% 4.69/4.94 ! [C: nat,A: set_nat,B4: set_nat] :
% 4.69/4.94 ( ( member_nat @ C @ ( minus_minus_set_nat @ A @ B4 ) )
% 4.69/4.94 = ( ( member_nat @ C @ A )
% 4.69/4.94 & ~ ( member_nat @ C @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Diff_iff
% 4.69/4.94 thf(fact_2326_DiffI,axiom,
% 4.69/4.94 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.94 ( ( member6576561426505652726_nat_o @ C @ A )
% 4.69/4.94 => ( ~ ( member6576561426505652726_nat_o @ C @ B4 )
% 4.69/4.94 => ( member6576561426505652726_nat_o @ C @ ( minus_1801376950450012436_nat_o @ A @ B4 ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % DiffI
% 4.69/4.94 thf(fact_2327_DiffI,axiom,
% 4.69/4.94 ! [C: int,A: set_int,B4: set_int] :
% 4.69/4.94 ( ( member_int @ C @ A )
% 4.69/4.94 => ( ~ ( member_int @ C @ B4 )
% 4.69/4.94 => ( member_int @ C @ ( minus_minus_set_int @ A @ B4 ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % DiffI
% 4.69/4.94 thf(fact_2328_DiffI,axiom,
% 4.69/4.94 ! [C: $o,A: set_o,B4: set_o] :
% 4.69/4.94 ( ( member_o @ C @ A )
% 4.69/4.94 => ( ~ ( member_o @ C @ B4 )
% 4.69/4.94 => ( member_o @ C @ ( minus_minus_set_o @ A @ B4 ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % DiffI
% 4.69/4.94 thf(fact_2329_DiffI,axiom,
% 4.69/4.94 ! [C: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.94 ( ( member_Product_unit @ C @ A )
% 4.69/4.94 => ( ~ ( member_Product_unit @ C @ B4 )
% 4.69/4.94 => ( member_Product_unit @ C @ ( minus_6452836326544984404t_unit @ A @ B4 ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % DiffI
% 4.69/4.94 thf(fact_2330_DiffI,axiom,
% 4.69/4.94 ! [C: nat,A: set_nat,B4: set_nat] :
% 4.69/4.94 ( ( member_nat @ C @ A )
% 4.69/4.94 => ( ~ ( member_nat @ C @ B4 )
% 4.69/4.94 => ( member_nat @ C @ ( minus_minus_set_nat @ A @ B4 ) ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % DiffI
% 4.69/4.94 thf(fact_2331_image__is__empty,axiom,
% 4.69/4.94 ! [F: code_integer > code_integer,A: set_Code_integer] :
% 4.69/4.94 ( ( ( image_4470545334726330049nteger @ F @ A )
% 4.69/4.94 = bot_bo3990330152332043303nteger )
% 4.69/4.94 = ( A = bot_bo3990330152332043303nteger ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_is_empty
% 4.69/4.94 thf(fact_2332_image__is__empty,axiom,
% 4.69/4.94 ! [F: nat > code_integer,A: set_nat] :
% 4.69/4.94 ( ( ( image_1215581382706833972nteger @ F @ A )
% 4.69/4.94 = bot_bo3990330152332043303nteger )
% 4.69/4.94 = ( A = bot_bot_set_nat ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_is_empty
% 4.69/4.94 thf(fact_2333_image__is__empty,axiom,
% 4.69/4.94 ! [F: product_unit > product_unit,A: set_Product_unit] :
% 4.69/4.94 ( ( ( image_405062704495631173t_unit @ F @ A )
% 4.69/4.94 = bot_bo3957492148770167129t_unit )
% 4.69/4.94 = ( A = bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_is_empty
% 4.69/4.94 thf(fact_2334_image__is__empty,axiom,
% 4.69/4.94 ! [F: $o > product_unit,A: set_o] :
% 4.69/4.94 ( ( ( image_o_Product_unit2 @ F @ A )
% 4.69/4.94 = bot_bo3957492148770167129t_unit )
% 4.69/4.94 = ( A = bot_bot_set_o ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_is_empty
% 4.69/4.94 thf(fact_2335_image__is__empty,axiom,
% 4.69/4.94 ! [F: nat > product_unit,A: set_nat] :
% 4.69/4.94 ( ( ( image_8730104196221521654t_unit @ F @ A )
% 4.69/4.94 = bot_bo3957492148770167129t_unit )
% 4.69/4.94 = ( A = bot_bot_set_nat ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_is_empty
% 4.69/4.94 thf(fact_2336_image__is__empty,axiom,
% 4.69/4.94 ! [F: int > product_unit,A: set_int] :
% 4.69/4.94 ( ( ( image_5846526143423701914t_unit @ F @ A )
% 4.69/4.94 = bot_bo3957492148770167129t_unit )
% 4.69/4.94 = ( A = bot_bot_set_int ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_is_empty
% 4.69/4.94 thf(fact_2337_image__is__empty,axiom,
% 4.69/4.94 ! [F: product_unit > $o,A: set_Product_unit] :
% 4.69/4.94 ( ( ( image_Product_unit_o2 @ F @ A )
% 4.69/4.94 = bot_bot_set_o )
% 4.69/4.94 = ( A = bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_is_empty
% 4.69/4.94 thf(fact_2338_image__is__empty,axiom,
% 4.69/4.94 ! [F: $o > $o,A: set_o] :
% 4.69/4.94 ( ( ( image_o_o2 @ F @ A )
% 4.69/4.94 = bot_bot_set_o )
% 4.69/4.94 = ( A = bot_bot_set_o ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_is_empty
% 4.69/4.94 thf(fact_2339_image__is__empty,axiom,
% 4.69/4.94 ! [F: nat > $o,A: set_nat] :
% 4.69/4.94 ( ( ( image_nat_o2 @ F @ A )
% 4.69/4.94 = bot_bot_set_o )
% 4.69/4.94 = ( A = bot_bot_set_nat ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_is_empty
% 4.69/4.94 thf(fact_2340_image__is__empty,axiom,
% 4.69/4.94 ! [F: int > $o,A: set_int] :
% 4.69/4.94 ( ( ( image_int_o2 @ F @ A )
% 4.69/4.94 = bot_bot_set_o )
% 4.69/4.94 = ( A = bot_bot_set_int ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_is_empty
% 4.69/4.94 thf(fact_2341_empty__is__image,axiom,
% 4.69/4.94 ! [F: code_integer > code_integer,A: set_Code_integer] :
% 4.69/4.94 ( ( bot_bo3990330152332043303nteger
% 4.69/4.94 = ( image_4470545334726330049nteger @ F @ A ) )
% 4.69/4.94 = ( A = bot_bo3990330152332043303nteger ) ) ).
% 4.69/4.94
% 4.69/4.94 % empty_is_image
% 4.69/4.94 thf(fact_2342_empty__is__image,axiom,
% 4.69/4.94 ! [F: nat > code_integer,A: set_nat] :
% 4.69/4.94 ( ( bot_bo3990330152332043303nteger
% 4.69/4.94 = ( image_1215581382706833972nteger @ F @ A ) )
% 4.69/4.94 = ( A = bot_bot_set_nat ) ) ).
% 4.69/4.94
% 4.69/4.94 % empty_is_image
% 4.69/4.94 thf(fact_2343_empty__is__image,axiom,
% 4.69/4.94 ! [F: product_unit > product_unit,A: set_Product_unit] :
% 4.69/4.94 ( ( bot_bo3957492148770167129t_unit
% 4.69/4.94 = ( image_405062704495631173t_unit @ F @ A ) )
% 4.69/4.94 = ( A = bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.94
% 4.69/4.94 % empty_is_image
% 4.69/4.94 thf(fact_2344_empty__is__image,axiom,
% 4.69/4.94 ! [F: $o > product_unit,A: set_o] :
% 4.69/4.94 ( ( bot_bo3957492148770167129t_unit
% 4.69/4.94 = ( image_o_Product_unit2 @ F @ A ) )
% 4.69/4.94 = ( A = bot_bot_set_o ) ) ).
% 4.69/4.94
% 4.69/4.94 % empty_is_image
% 4.69/4.94 thf(fact_2345_empty__is__image,axiom,
% 4.69/4.94 ! [F: nat > product_unit,A: set_nat] :
% 4.69/4.94 ( ( bot_bo3957492148770167129t_unit
% 4.69/4.94 = ( image_8730104196221521654t_unit @ F @ A ) )
% 4.69/4.94 = ( A = bot_bot_set_nat ) ) ).
% 4.69/4.94
% 4.69/4.94 % empty_is_image
% 4.69/4.94 thf(fact_2346_empty__is__image,axiom,
% 4.69/4.94 ! [F: int > product_unit,A: set_int] :
% 4.69/4.94 ( ( bot_bo3957492148770167129t_unit
% 4.69/4.94 = ( image_5846526143423701914t_unit @ F @ A ) )
% 4.69/4.94 = ( A = bot_bot_set_int ) ) ).
% 4.69/4.94
% 4.69/4.94 % empty_is_image
% 4.69/4.94 thf(fact_2347_empty__is__image,axiom,
% 4.69/4.94 ! [F: product_unit > $o,A: set_Product_unit] :
% 4.69/4.94 ( ( bot_bot_set_o
% 4.69/4.94 = ( image_Product_unit_o2 @ F @ A ) )
% 4.69/4.94 = ( A = bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.94
% 4.69/4.94 % empty_is_image
% 4.69/4.94 thf(fact_2348_empty__is__image,axiom,
% 4.69/4.94 ! [F: $o > $o,A: set_o] :
% 4.69/4.94 ( ( bot_bot_set_o
% 4.69/4.94 = ( image_o_o2 @ F @ A ) )
% 4.69/4.94 = ( A = bot_bot_set_o ) ) ).
% 4.69/4.94
% 4.69/4.94 % empty_is_image
% 4.69/4.94 thf(fact_2349_empty__is__image,axiom,
% 4.69/4.94 ! [F: nat > $o,A: set_nat] :
% 4.69/4.94 ( ( bot_bot_set_o
% 4.69/4.94 = ( image_nat_o2 @ F @ A ) )
% 4.69/4.94 = ( A = bot_bot_set_nat ) ) ).
% 4.69/4.94
% 4.69/4.94 % empty_is_image
% 4.69/4.94 thf(fact_2350_empty__is__image,axiom,
% 4.69/4.94 ! [F: int > $o,A: set_int] :
% 4.69/4.94 ( ( bot_bot_set_o
% 4.69/4.94 = ( image_int_o2 @ F @ A ) )
% 4.69/4.94 = ( A = bot_bot_set_int ) ) ).
% 4.69/4.94
% 4.69/4.94 % empty_is_image
% 4.69/4.94 thf(fact_2351_image__empty,axiom,
% 4.69/4.94 ! [F: code_integer > code_integer] :
% 4.69/4.94 ( ( image_4470545334726330049nteger @ F @ bot_bo3990330152332043303nteger )
% 4.69/4.94 = bot_bo3990330152332043303nteger ) ).
% 4.69/4.94
% 4.69/4.94 % image_empty
% 4.69/4.94 thf(fact_2352_image__empty,axiom,
% 4.69/4.94 ! [F: product_unit > product_unit] :
% 4.69/4.94 ( ( image_405062704495631173t_unit @ F @ bot_bo3957492148770167129t_unit )
% 4.69/4.94 = bot_bo3957492148770167129t_unit ) ).
% 4.69/4.94
% 4.69/4.94 % image_empty
% 4.69/4.94 thf(fact_2353_image__empty,axiom,
% 4.69/4.94 ! [F: product_unit > $o] :
% 4.69/4.94 ( ( image_Product_unit_o2 @ F @ bot_bo3957492148770167129t_unit )
% 4.69/4.94 = bot_bot_set_o ) ).
% 4.69/4.94
% 4.69/4.94 % image_empty
% 4.69/4.94 thf(fact_2354_image__empty,axiom,
% 4.69/4.94 ! [F: product_unit > nat] :
% 4.69/4.94 ( ( image_875570014554754200it_nat @ F @ bot_bo3957492148770167129t_unit )
% 4.69/4.94 = bot_bot_set_nat ) ).
% 4.69/4.94
% 4.69/4.94 % image_empty
% 4.69/4.94 thf(fact_2355_image__empty,axiom,
% 4.69/4.94 ! [F: product_unit > int] :
% 4.69/4.94 ( ( image_873079544045703924it_int @ F @ bot_bo3957492148770167129t_unit )
% 4.69/4.94 = bot_bot_set_int ) ).
% 4.69/4.94
% 4.69/4.94 % image_empty
% 4.69/4.94 thf(fact_2356_image__empty,axiom,
% 4.69/4.94 ! [F: $o > product_unit] :
% 4.69/4.94 ( ( image_o_Product_unit2 @ F @ bot_bot_set_o )
% 4.69/4.94 = bot_bo3957492148770167129t_unit ) ).
% 4.69/4.94
% 4.69/4.94 % image_empty
% 4.69/4.94 thf(fact_2357_image__empty,axiom,
% 4.69/4.94 ! [F: $o > $o] :
% 4.69/4.94 ( ( image_o_o2 @ F @ bot_bot_set_o )
% 4.69/4.94 = bot_bot_set_o ) ).
% 4.69/4.94
% 4.69/4.94 % image_empty
% 4.69/4.94 thf(fact_2358_image__empty,axiom,
% 4.69/4.94 ! [F: $o > nat] :
% 4.69/4.94 ( ( image_o_nat2 @ F @ bot_bot_set_o )
% 4.69/4.94 = bot_bot_set_nat ) ).
% 4.69/4.94
% 4.69/4.94 % image_empty
% 4.69/4.94 thf(fact_2359_image__empty,axiom,
% 4.69/4.94 ! [F: $o > int] :
% 4.69/4.94 ( ( image_o_int2 @ F @ bot_bot_set_o )
% 4.69/4.94 = bot_bot_set_int ) ).
% 4.69/4.94
% 4.69/4.94 % image_empty
% 4.69/4.94 thf(fact_2360_image__empty,axiom,
% 4.69/4.94 ! [F: nat > code_integer] :
% 4.69/4.94 ( ( image_1215581382706833972nteger @ F @ bot_bot_set_nat )
% 4.69/4.94 = bot_bo3990330152332043303nteger ) ).
% 4.69/4.94
% 4.69/4.94 % image_empty
% 4.69/4.94 thf(fact_2361_insert__image,axiom,
% 4.69/4.94 ! [X: code_integer,A: set_Code_integer,F: code_integer > code_integer] :
% 4.69/4.94 ( ( member_Code_integer @ X @ A )
% 4.69/4.94 => ( ( insert_Code_integer @ ( F @ X ) @ ( image_4470545334726330049nteger @ F @ A ) )
% 4.69/4.94 = ( image_4470545334726330049nteger @ F @ A ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % insert_image
% 4.69/4.94 thf(fact_2362_insert__image,axiom,
% 4.69/4.94 ! [X: nat,A: set_nat,F: nat > code_integer] :
% 4.69/4.94 ( ( member_nat @ X @ A )
% 4.69/4.94 => ( ( insert_Code_integer @ ( F @ X ) @ ( image_1215581382706833972nteger @ F @ A ) )
% 4.69/4.94 = ( image_1215581382706833972nteger @ F @ A ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % insert_image
% 4.69/4.94 thf(fact_2363_insert__image,axiom,
% 4.69/4.94 ! [X: nat,A: set_nat,F: nat > nat] :
% 4.69/4.94 ( ( member_nat @ X @ A )
% 4.69/4.94 => ( ( insert_nat @ ( F @ X ) @ ( image_nat_nat2 @ F @ A ) )
% 4.69/4.94 = ( image_nat_nat2 @ F @ A ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % insert_image
% 4.69/4.94 thf(fact_2364_insert__image,axiom,
% 4.69/4.94 ! [X: nat,A: set_nat,F: nat > int] :
% 4.69/4.94 ( ( member_nat @ X @ A )
% 4.69/4.94 => ( ( insert_int @ ( F @ X ) @ ( image_nat_int2 @ F @ A ) )
% 4.69/4.94 = ( image_nat_int2 @ F @ A ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % insert_image
% 4.69/4.94 thf(fact_2365_insert__image,axiom,
% 4.69/4.94 ! [X: nat,A: set_nat,F: nat > $o] :
% 4.69/4.94 ( ( member_nat @ X @ A )
% 4.69/4.94 => ( ( insert_o @ ( F @ X ) @ ( image_nat_o2 @ F @ A ) )
% 4.69/4.94 = ( image_nat_o2 @ F @ A ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % insert_image
% 4.69/4.94 thf(fact_2366_insert__image,axiom,
% 4.69/4.94 ! [X: nat,A: set_nat,F: nat > product_unit] :
% 4.69/4.94 ( ( member_nat @ X @ A )
% 4.69/4.94 => ( ( insert_Product_unit @ ( F @ X ) @ ( image_8730104196221521654t_unit @ F @ A ) )
% 4.69/4.94 = ( image_8730104196221521654t_unit @ F @ A ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % insert_image
% 4.69/4.94 thf(fact_2367_insert__image,axiom,
% 4.69/4.94 ! [X: int,A: set_int,F: int > nat] :
% 4.69/4.94 ( ( member_int @ X @ A )
% 4.69/4.94 => ( ( insert_nat @ ( F @ X ) @ ( image_int_nat2 @ F @ A ) )
% 4.69/4.94 = ( image_int_nat2 @ F @ A ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % insert_image
% 4.69/4.94 thf(fact_2368_insert__image,axiom,
% 4.69/4.94 ! [X: int,A: set_int,F: int > int] :
% 4.69/4.94 ( ( member_int @ X @ A )
% 4.69/4.94 => ( ( insert_int @ ( F @ X ) @ ( image_int_int2 @ F @ A ) )
% 4.69/4.94 = ( image_int_int2 @ F @ A ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % insert_image
% 4.69/4.94 thf(fact_2369_insert__image,axiom,
% 4.69/4.94 ! [X: int,A: set_int,F: int > $o] :
% 4.69/4.94 ( ( member_int @ X @ A )
% 4.69/4.94 => ( ( insert_o @ ( F @ X ) @ ( image_int_o2 @ F @ A ) )
% 4.69/4.94 = ( image_int_o2 @ F @ A ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % insert_image
% 4.69/4.94 thf(fact_2370_insert__image,axiom,
% 4.69/4.94 ! [X: int,A: set_int,F: int > product_unit] :
% 4.69/4.94 ( ( member_int @ X @ A )
% 4.69/4.94 => ( ( insert_Product_unit @ ( F @ X ) @ ( image_5846526143423701914t_unit @ F @ A ) )
% 4.69/4.94 = ( image_5846526143423701914t_unit @ F @ A ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % insert_image
% 4.69/4.94 thf(fact_2371_image__insert,axiom,
% 4.69/4.94 ! [F: code_integer > code_integer,A2: code_integer,B4: set_Code_integer] :
% 4.69/4.94 ( ( image_4470545334726330049nteger @ F @ ( insert_Code_integer @ A2 @ B4 ) )
% 4.69/4.94 = ( insert_Code_integer @ ( F @ A2 ) @ ( image_4470545334726330049nteger @ F @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_insert
% 4.69/4.94 thf(fact_2372_image__insert,axiom,
% 4.69/4.94 ! [F: nat > code_integer,A2: nat,B4: set_nat] :
% 4.69/4.94 ( ( image_1215581382706833972nteger @ F @ ( insert_nat @ A2 @ B4 ) )
% 4.69/4.94 = ( insert_Code_integer @ ( F @ A2 ) @ ( image_1215581382706833972nteger @ F @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_insert
% 4.69/4.94 thf(fact_2373_image__insert,axiom,
% 4.69/4.94 ! [F: nat > nat,A2: nat,B4: set_nat] :
% 4.69/4.94 ( ( image_nat_nat2 @ F @ ( insert_nat @ A2 @ B4 ) )
% 4.69/4.94 = ( insert_nat @ ( F @ A2 ) @ ( image_nat_nat2 @ F @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_insert
% 4.69/4.94 thf(fact_2374_image__insert,axiom,
% 4.69/4.94 ! [F: nat > int,A2: nat,B4: set_nat] :
% 4.69/4.94 ( ( image_nat_int2 @ F @ ( insert_nat @ A2 @ B4 ) )
% 4.69/4.94 = ( insert_int @ ( F @ A2 ) @ ( image_nat_int2 @ F @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_insert
% 4.69/4.94 thf(fact_2375_image__insert,axiom,
% 4.69/4.94 ! [F: nat > $o,A2: nat,B4: set_nat] :
% 4.69/4.94 ( ( image_nat_o2 @ F @ ( insert_nat @ A2 @ B4 ) )
% 4.69/4.94 = ( insert_o @ ( F @ A2 ) @ ( image_nat_o2 @ F @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_insert
% 4.69/4.94 thf(fact_2376_image__insert,axiom,
% 4.69/4.94 ! [F: nat > product_unit,A2: nat,B4: set_nat] :
% 4.69/4.94 ( ( image_8730104196221521654t_unit @ F @ ( insert_nat @ A2 @ B4 ) )
% 4.69/4.94 = ( insert_Product_unit @ ( F @ A2 ) @ ( image_8730104196221521654t_unit @ F @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_insert
% 4.69/4.94 thf(fact_2377_image__insert,axiom,
% 4.69/4.94 ! [F: int > nat,A2: int,B4: set_int] :
% 4.69/4.94 ( ( image_int_nat2 @ F @ ( insert_int @ A2 @ B4 ) )
% 4.69/4.94 = ( insert_nat @ ( F @ A2 ) @ ( image_int_nat2 @ F @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_insert
% 4.69/4.94 thf(fact_2378_image__insert,axiom,
% 4.69/4.94 ! [F: int > int,A2: int,B4: set_int] :
% 4.69/4.94 ( ( image_int_int2 @ F @ ( insert_int @ A2 @ B4 ) )
% 4.69/4.94 = ( insert_int @ ( F @ A2 ) @ ( image_int_int2 @ F @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_insert
% 4.69/4.94 thf(fact_2379_image__insert,axiom,
% 4.69/4.94 ! [F: int > $o,A2: int,B4: set_int] :
% 4.69/4.94 ( ( image_int_o2 @ F @ ( insert_int @ A2 @ B4 ) )
% 4.69/4.94 = ( insert_o @ ( F @ A2 ) @ ( image_int_o2 @ F @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_insert
% 4.69/4.94 thf(fact_2380_image__insert,axiom,
% 4.69/4.94 ! [F: int > product_unit,A2: int,B4: set_int] :
% 4.69/4.94 ( ( image_5846526143423701914t_unit @ F @ ( insert_int @ A2 @ B4 ) )
% 4.69/4.94 = ( insert_Product_unit @ ( F @ A2 ) @ ( image_5846526143423701914t_unit @ F @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % image_insert
% 4.69/4.94 thf(fact_2381_img__snd,axiom,
% 4.69/4.94 ! [A2: nat,B: nat,S: set_Pr1261947904930325089at_nat] :
% 4.69/4.94 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ S )
% 4.69/4.94 => ( member_nat @ B @ ( image_2486076414777270412at_nat @ product_snd_nat_nat @ S ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % img_snd
% 4.69/4.94 thf(fact_2382_img__snd,axiom,
% 4.69/4.94 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,S: set_Pr3286484037609594932et_nat] :
% 4.69/4.94 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ B ) @ S )
% 4.69/4.94 => ( member6260224972018164377et_nat @ B @ ( image_4390311411407041927et_nat @ produc4011572625026189258et_nat @ S ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % img_snd
% 4.69/4.94 thf(fact_2383_img__snd,axiom,
% 4.69/4.94 ! [A2: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,S: set_Pr8536935166611901872et_nat] :
% 4.69/4.94 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ B ) @ S )
% 4.69/4.94 => ( member1996754912294343701et_nat @ B @ ( image_4557310310409863807et_nat @ produc5374455773327741254et_nat @ S ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % img_snd
% 4.69/4.94 thf(fact_2384_img__snd,axiom,
% 4.69/4.94 ! [A2: heap_e7401611519738050253t_unit,B: set_nat,S: set_Pr3948176798113811640et_nat] :
% 4.69/4.94 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ B ) @ S )
% 4.69/4.94 => ( member_set_nat @ B @ ( image_6088997261112373647et_nat @ produc8586169260539613262et_nat @ S ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % img_snd
% 4.69/4.94 thf(fact_2385_img__snd,axiom,
% 4.69/4.94 ! [A2: int,B: int,S: set_Pr958786334691620121nt_int] :
% 4.69/4.94 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ S )
% 4.69/4.94 => ( member_int @ B @ ( image_5042161079198086560nt_int @ product_snd_int_int @ S ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % img_snd
% 4.69/4.94 thf(fact_2386_Diff__cancel,axiom,
% 4.69/4.94 ! [A: set_Product_unit] :
% 4.69/4.94 ( ( minus_6452836326544984404t_unit @ A @ A )
% 4.69/4.94 = bot_bo3957492148770167129t_unit ) ).
% 4.69/4.94
% 4.69/4.94 % Diff_cancel
% 4.69/4.94 thf(fact_2387_Diff__cancel,axiom,
% 4.69/4.94 ! [A: set_o] :
% 4.69/4.94 ( ( minus_minus_set_o @ A @ A )
% 4.69/4.94 = bot_bot_set_o ) ).
% 4.69/4.94
% 4.69/4.94 % Diff_cancel
% 4.69/4.94 thf(fact_2388_Diff__cancel,axiom,
% 4.69/4.94 ! [A: set_int] :
% 4.69/4.94 ( ( minus_minus_set_int @ A @ A )
% 4.69/4.94 = bot_bot_set_int ) ).
% 4.69/4.94
% 4.69/4.94 % Diff_cancel
% 4.69/4.94 thf(fact_2389_Diff__cancel,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.94 ( ( minus_1801376950450012436_nat_o @ A @ A )
% 4.69/4.94 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/4.94
% 4.69/4.94 % Diff_cancel
% 4.69/4.94 thf(fact_2390_Diff__cancel,axiom,
% 4.69/4.94 ! [A: set_nat] :
% 4.69/4.94 ( ( minus_minus_set_nat @ A @ A )
% 4.69/4.94 = bot_bot_set_nat ) ).
% 4.69/4.94
% 4.69/4.94 % Diff_cancel
% 4.69/4.94 thf(fact_2391_empty__Diff,axiom,
% 4.69/4.94 ! [A: set_Product_unit] :
% 4.69/4.94 ( ( minus_6452836326544984404t_unit @ bot_bo3957492148770167129t_unit @ A )
% 4.69/4.94 = bot_bo3957492148770167129t_unit ) ).
% 4.69/4.94
% 4.69/4.94 % empty_Diff
% 4.69/4.94 thf(fact_2392_empty__Diff,axiom,
% 4.69/4.94 ! [A: set_o] :
% 4.69/4.94 ( ( minus_minus_set_o @ bot_bot_set_o @ A )
% 4.69/4.94 = bot_bot_set_o ) ).
% 4.69/4.94
% 4.69/4.94 % empty_Diff
% 4.69/4.94 thf(fact_2393_empty__Diff,axiom,
% 4.69/4.94 ! [A: set_int] :
% 4.69/4.94 ( ( minus_minus_set_int @ bot_bot_set_int @ A )
% 4.69/4.94 = bot_bot_set_int ) ).
% 4.69/4.94
% 4.69/4.94 % empty_Diff
% 4.69/4.94 thf(fact_2394_empty__Diff,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.94 ( ( minus_1801376950450012436_nat_o @ bot_bo7824918357723582233_nat_o @ A )
% 4.69/4.94 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/4.94
% 4.69/4.94 % empty_Diff
% 4.69/4.94 thf(fact_2395_empty__Diff,axiom,
% 4.69/4.94 ! [A: set_nat] :
% 4.69/4.94 ( ( minus_minus_set_nat @ bot_bot_set_nat @ A )
% 4.69/4.94 = bot_bot_set_nat ) ).
% 4.69/4.94
% 4.69/4.94 % empty_Diff
% 4.69/4.94 thf(fact_2396_Diff__empty,axiom,
% 4.69/4.94 ! [A: set_Product_unit] :
% 4.69/4.94 ( ( minus_6452836326544984404t_unit @ A @ bot_bo3957492148770167129t_unit )
% 4.69/4.94 = A ) ).
% 4.69/4.94
% 4.69/4.94 % Diff_empty
% 4.69/4.94 thf(fact_2397_Diff__empty,axiom,
% 4.69/4.94 ! [A: set_o] :
% 4.69/4.94 ( ( minus_minus_set_o @ A @ bot_bot_set_o )
% 4.69/4.94 = A ) ).
% 4.69/4.94
% 4.69/4.94 % Diff_empty
% 4.69/4.94 thf(fact_2398_Diff__empty,axiom,
% 4.69/4.94 ! [A: set_int] :
% 4.69/4.94 ( ( minus_minus_set_int @ A @ bot_bot_set_int )
% 4.69/4.94 = A ) ).
% 4.69/4.94
% 4.69/4.94 % Diff_empty
% 4.69/4.94 thf(fact_2399_Diff__empty,axiom,
% 4.69/4.94 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.94 ( ( minus_1801376950450012436_nat_o @ A @ bot_bo7824918357723582233_nat_o )
% 4.69/4.94 = A ) ).
% 4.69/4.94
% 4.69/4.94 % Diff_empty
% 4.69/4.94 thf(fact_2400_Diff__empty,axiom,
% 4.69/4.94 ! [A: set_nat] :
% 4.69/4.94 ( ( minus_minus_set_nat @ A @ bot_bot_set_nat )
% 4.69/4.94 = A ) ).
% 4.69/4.94
% 4.69/4.94 % Diff_empty
% 4.69/4.94 thf(fact_2401_insert__Diff1,axiom,
% 4.69/4.94 ! [X: produc3658429121746597890et_nat > $o,B4: set_Pr4532377907799695533_nat_o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.94 ( ( member6576561426505652726_nat_o @ X @ B4 )
% 4.69/4.94 => ( ( minus_1801376950450012436_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) @ B4 )
% 4.69/4.94 = ( minus_1801376950450012436_nat_o @ A @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % insert_Diff1
% 4.69/4.94 thf(fact_2402_insert__Diff1,axiom,
% 4.69/4.94 ! [X: int,B4: set_int,A: set_int] :
% 4.69/4.94 ( ( member_int @ X @ B4 )
% 4.69/4.94 => ( ( minus_minus_set_int @ ( insert_int @ X @ A ) @ B4 )
% 4.69/4.94 = ( minus_minus_set_int @ A @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % insert_Diff1
% 4.69/4.94 thf(fact_2403_insert__Diff1,axiom,
% 4.69/4.94 ! [X: $o,B4: set_o,A: set_o] :
% 4.69/4.94 ( ( member_o @ X @ B4 )
% 4.69/4.94 => ( ( minus_minus_set_o @ ( insert_o @ X @ A ) @ B4 )
% 4.69/4.94 = ( minus_minus_set_o @ A @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % insert_Diff1
% 4.69/4.94 thf(fact_2404_insert__Diff1,axiom,
% 4.69/4.94 ! [X: product_unit,B4: set_Product_unit,A: set_Product_unit] :
% 4.69/4.94 ( ( member_Product_unit @ X @ B4 )
% 4.69/4.94 => ( ( minus_6452836326544984404t_unit @ ( insert_Product_unit @ X @ A ) @ B4 )
% 4.69/4.94 = ( minus_6452836326544984404t_unit @ A @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % insert_Diff1
% 4.69/4.94 thf(fact_2405_insert__Diff1,axiom,
% 4.69/4.94 ! [X: nat,B4: set_nat,A: set_nat] :
% 4.69/4.94 ( ( member_nat @ X @ B4 )
% 4.69/4.94 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A ) @ B4 )
% 4.69/4.94 = ( minus_minus_set_nat @ A @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % insert_Diff1
% 4.69/4.94 thf(fact_2406_Diff__insert0,axiom,
% 4.69/4.94 ! [X: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.94 ( ~ ( member6576561426505652726_nat_o @ X @ A )
% 4.69/4.94 => ( ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ B4 ) )
% 4.69/4.94 = ( minus_1801376950450012436_nat_o @ A @ B4 ) ) ) ).
% 4.69/4.94
% 4.69/4.94 % Diff_insert0
% 4.69/4.94 thf(fact_2407_Diff__insert0,axiom,
% 4.69/4.94 ! [X: int,A: set_int,B4: set_int] :
% 4.69/4.94 ( ~ ( member_int @ X @ A )
% 4.69/4.94 => ( ( minus_minus_set_int @ A @ ( insert_int @ X @ B4 ) )
% 4.69/4.95 = ( minus_minus_set_int @ A @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_insert0
% 4.69/4.95 thf(fact_2408_Diff__insert0,axiom,
% 4.69/4.95 ! [X: $o,A: set_o,B4: set_o] :
% 4.69/4.95 ( ~ ( member_o @ X @ A )
% 4.69/4.95 => ( ( minus_minus_set_o @ A @ ( insert_o @ X @ B4 ) )
% 4.69/4.95 = ( minus_minus_set_o @ A @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_insert0
% 4.69/4.95 thf(fact_2409_Diff__insert0,axiom,
% 4.69/4.95 ! [X: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.95 ( ~ ( member_Product_unit @ X @ A )
% 4.69/4.95 => ( ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ B4 ) )
% 4.69/4.95 = ( minus_6452836326544984404t_unit @ A @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_insert0
% 4.69/4.95 thf(fact_2410_Diff__insert0,axiom,
% 4.69/4.95 ! [X: nat,A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ~ ( member_nat @ X @ A )
% 4.69/4.95 => ( ( minus_minus_set_nat @ A @ ( insert_nat @ X @ B4 ) )
% 4.69/4.95 = ( minus_minus_set_nat @ A @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_insert0
% 4.69/4.95 thf(fact_2411_Un__Diff__cancel2,axiom,
% 4.69/4.95 ! [B4: set_nat,A: set_nat] :
% 4.69/4.95 ( ( sup_sup_set_nat @ ( minus_minus_set_nat @ B4 @ A ) @ A )
% 4.69/4.95 = ( sup_sup_set_nat @ B4 @ A ) ) ).
% 4.69/4.95
% 4.69/4.95 % Un_Diff_cancel2
% 4.69/4.95 thf(fact_2412_Un__Diff__cancel,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( sup_sup_set_nat @ A @ ( minus_minus_set_nat @ B4 @ A ) )
% 4.69/4.95 = ( sup_sup_set_nat @ A @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % Un_Diff_cancel
% 4.69/4.95 thf(fact_2413_converse__iff,axiom,
% 4.69/4.95 ! [A2: set_nat,B: heap_e7401611519738050253t_unit,R2: set_Pr3948176798113811640et_nat] :
% 4.69/4.95 ( ( member727419437372278867t_unit @ ( produc2471974422597015918t_unit @ A2 @ B ) @ ( conver7272282955447398104et_nat @ R2 ) )
% 4.69/4.95 = ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ B @ A2 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse_iff
% 4.69/4.95 thf(fact_2414_converse__iff,axiom,
% 4.69/4.95 ! [A2: produc3658429121746597890et_nat,B: produc3658429121746597890et_nat > $o,R2: set_Pr3286484037609594932et_nat] :
% 4.69/4.95 ( ( member4978015717948814295_nat_o @ ( produc2829238748666232050_nat_o @ A2 @ B ) @ ( conver4003969491454187092et_nat @ R2 ) )
% 4.69/4.95 = ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ B @ A2 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse_iff
% 4.69/4.95 thf(fact_2415_converse__iff,axiom,
% 4.69/4.95 ! [A2: produc3925858234332021118et_nat,B: produc3658429121746597890et_nat > $o,R2: set_Pr8536935166611901872et_nat] :
% 4.69/4.95 ( ( member8354763867512313179_nat_o @ ( produc3674526432113299062_nat_o @ A2 @ B ) @ ( conver3577387295554834384et_nat @ R2 ) )
% 4.69/4.95 = ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ B @ A2 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse_iff
% 4.69/4.95 thf(fact_2416_converse__iff,axiom,
% 4.69/4.95 ! [A2: heap_e7401611519738050253t_unit,B: set_nat,R2: set_Pr4071100604818519410t_unit] :
% 4.69/4.95 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ B ) @ ( conver2236330673913229642t_unit @ R2 ) )
% 4.69/4.95 = ( member727419437372278867t_unit @ ( produc2471974422597015918t_unit @ B @ A2 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse_iff
% 4.69/4.95 thf(fact_2417_converse__iff,axiom,
% 4.69/4.95 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.95 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( converse_nat_nat @ R2 ) )
% 4.69/4.95 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ A2 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse_iff
% 4.69/4.95 thf(fact_2418_converse__iff,axiom,
% 4.69/4.95 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.95 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( converse_int_int @ R2 ) )
% 4.69/4.95 = ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ A2 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse_iff
% 4.69/4.95 thf(fact_2419_converse__iff,axiom,
% 4.69/4.95 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,R2: set_Pr4208978187861016310_nat_o] :
% 4.69/4.95 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ B ) @ ( conver1831365297310299342_nat_o @ R2 ) )
% 4.69/4.95 = ( member4978015717948814295_nat_o @ ( produc2829238748666232050_nat_o @ B @ A2 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse_iff
% 4.69/4.95 thf(fact_2420_converse__iff,axiom,
% 4.69/4.95 ! [A2: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,R2: set_Pr7705059561495379578_nat_o] :
% 4.69/4.95 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ B ) @ ( conver5006497266169685586_nat_o @ R2 ) )
% 4.69/4.95 = ( member8354763867512313179_nat_o @ ( produc3674526432113299062_nat_o @ B @ A2 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse_iff
% 4.69/4.95 thf(fact_2421_Diff__eq__empty__iff,axiom,
% 4.69/4.95 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.95 ( ( ( minus_6452836326544984404t_unit @ A @ B4 )
% 4.69/4.95 = bot_bo3957492148770167129t_unit )
% 4.69/4.95 = ( ord_le3507040750410214029t_unit @ A @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_eq_empty_iff
% 4.69/4.95 thf(fact_2422_Diff__eq__empty__iff,axiom,
% 4.69/4.95 ! [A: set_o,B4: set_o] :
% 4.69/4.95 ( ( ( minus_minus_set_o @ A @ B4 )
% 4.69/4.95 = bot_bot_set_o )
% 4.69/4.95 = ( ord_less_eq_set_o @ A @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_eq_empty_iff
% 4.69/4.95 thf(fact_2423_Diff__eq__empty__iff,axiom,
% 4.69/4.95 ! [A: set_int,B4: set_int] :
% 4.69/4.95 ( ( ( minus_minus_set_int @ A @ B4 )
% 4.69/4.95 = bot_bot_set_int )
% 4.69/4.95 = ( ord_less_eq_set_int @ A @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_eq_empty_iff
% 4.69/4.95 thf(fact_2424_Diff__eq__empty__iff,axiom,
% 4.69/4.95 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( ( minus_1801376950450012436_nat_o @ A @ B4 )
% 4.69/4.95 = bot_bo7824918357723582233_nat_o )
% 4.69/4.95 = ( ord_le2965882846123202637_nat_o @ A @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_eq_empty_iff
% 4.69/4.95 thf(fact_2425_Diff__eq__empty__iff,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( ( minus_minus_set_nat @ A @ B4 )
% 4.69/4.95 = bot_bot_set_nat )
% 4.69/4.95 = ( ord_less_eq_set_nat @ A @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_eq_empty_iff
% 4.69/4.95 thf(fact_2426_insert__Diff__single,axiom,
% 4.69/4.95 ! [A2: product_unit,A: set_Product_unit] :
% 4.69/4.95 ( ( insert_Product_unit @ A2 @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.95 = ( insert_Product_unit @ A2 @ A ) ) ).
% 4.69/4.95
% 4.69/4.95 % insert_Diff_single
% 4.69/4.95 thf(fact_2427_insert__Diff__single,axiom,
% 4.69/4.95 ! [A2: $o,A: set_o] :
% 4.69/4.95 ( ( insert_o @ A2 @ ( minus_minus_set_o @ A @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 4.69/4.95 = ( insert_o @ A2 @ A ) ) ).
% 4.69/4.95
% 4.69/4.95 % insert_Diff_single
% 4.69/4.95 thf(fact_2428_insert__Diff__single,axiom,
% 4.69/4.95 ! [A2: int,A: set_int] :
% 4.69/4.95 ( ( insert_int @ A2 @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 4.69/4.95 = ( insert_int @ A2 @ A ) ) ).
% 4.69/4.95
% 4.69/4.95 % insert_Diff_single
% 4.69/4.95 thf(fact_2429_insert__Diff__single,axiom,
% 4.69/4.95 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( insert5175938949040314269_nat_o @ A2 @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/4.95 = ( insert5175938949040314269_nat_o @ A2 @ A ) ) ).
% 4.69/4.95
% 4.69/4.95 % insert_Diff_single
% 4.69/4.95 thf(fact_2430_insert__Diff__single,axiom,
% 4.69/4.95 ! [A2: nat,A: set_nat] :
% 4.69/4.95 ( ( insert_nat @ A2 @ ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 4.69/4.95 = ( insert_nat @ A2 @ A ) ) ).
% 4.69/4.95
% 4.69/4.95 % insert_Diff_single
% 4.69/4.95 thf(fact_2431_finite__Diff__insert,axiom,
% 4.69/4.95 ! [A: set_int,A2: int,B4: set_int] :
% 4.69/4.95 ( ( finite_finite_int @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ B4 ) ) )
% 4.69/4.95 = ( finite_finite_int @ ( minus_minus_set_int @ A @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % finite_Diff_insert
% 4.69/4.95 thf(fact_2432_finite__Diff__insert,axiom,
% 4.69/4.95 ! [A: set_o,A2: $o,B4: set_o] :
% 4.69/4.95 ( ( finite_finite_o @ ( minus_minus_set_o @ A @ ( insert_o @ A2 @ B4 ) ) )
% 4.69/4.95 = ( finite_finite_o @ ( minus_minus_set_o @ A @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % finite_Diff_insert
% 4.69/4.95 thf(fact_2433_finite__Diff__insert,axiom,
% 4.69/4.95 ! [A: set_Product_unit,A2: product_unit,B4: set_Product_unit] :
% 4.69/4.95 ( ( finite4290736615968046902t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ A2 @ B4 ) ) )
% 4.69/4.95 = ( finite4290736615968046902t_unit @ ( minus_6452836326544984404t_unit @ A @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % finite_Diff_insert
% 4.69/4.95 thf(fact_2434_finite__Diff__insert,axiom,
% 4.69/4.95 ! [A: set_Code_integer,A2: code_integer,B4: set_Code_integer] :
% 4.69/4.95 ( ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ A2 @ B4 ) ) )
% 4.69/4.95 = ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ A @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % finite_Diff_insert
% 4.69/4.95 thf(fact_2435_finite__Diff__insert,axiom,
% 4.69/4.95 ! [A: set_nat,A2: nat,B4: set_nat] :
% 4.69/4.95 ( ( finite_finite_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ B4 ) ) )
% 4.69/4.95 = ( finite_finite_nat @ ( minus_minus_set_nat @ A @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % finite_Diff_insert
% 4.69/4.95 thf(fact_2436_Diff__disjoint,axiom,
% 4.69/4.95 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.95 ( ( inf_in4660618365625256667t_unit @ A @ ( minus_6452836326544984404t_unit @ B4 @ A ) )
% 4.69/4.95 = bot_bo3957492148770167129t_unit ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_disjoint
% 4.69/4.95 thf(fact_2437_Diff__disjoint,axiom,
% 4.69/4.95 ! [A: set_o,B4: set_o] :
% 4.69/4.95 ( ( inf_inf_set_o @ A @ ( minus_minus_set_o @ B4 @ A ) )
% 4.69/4.95 = bot_bot_set_o ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_disjoint
% 4.69/4.95 thf(fact_2438_Diff__disjoint,axiom,
% 4.69/4.95 ! [A: set_int,B4: set_int] :
% 4.69/4.95 ( ( inf_inf_set_int @ A @ ( minus_minus_set_int @ B4 @ A ) )
% 4.69/4.95 = bot_bot_set_int ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_disjoint
% 4.69/4.95 thf(fact_2439_Diff__disjoint,axiom,
% 4.69/4.95 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( inf_in1906310914598751387_nat_o @ A @ ( minus_1801376950450012436_nat_o @ B4 @ A ) )
% 4.69/4.95 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_disjoint
% 4.69/4.95 thf(fact_2440_Diff__disjoint,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( inf_inf_set_nat @ A @ ( minus_minus_set_nat @ B4 @ A ) )
% 4.69/4.95 = bot_bot_set_nat ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_disjoint
% 4.69/4.95 thf(fact_2441_image__diff__subset,axiom,
% 4.69/4.95 ! [F: code_integer > code_integer,A: set_Code_integer,B4: set_Code_integer] : ( ord_le7084787975880047091nteger @ ( minus_2355218937544613996nteger @ ( image_4470545334726330049nteger @ F @ A ) @ ( image_4470545334726330049nteger @ F @ B4 ) ) @ ( image_4470545334726330049nteger @ F @ ( minus_2355218937544613996nteger @ A @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_diff_subset
% 4.69/4.95 thf(fact_2442_image__diff__subset,axiom,
% 4.69/4.95 ! [F: nat > set_nat,A: set_nat,B4: set_nat] : ( ord_le6893508408891458716et_nat @ ( minus_2163939370556025621et_nat @ ( image_nat_set_nat @ F @ A ) @ ( image_nat_set_nat @ F @ B4 ) ) @ ( image_nat_set_nat @ F @ ( minus_minus_set_nat @ A @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_diff_subset
% 4.69/4.95 thf(fact_2443_image__diff__subset,axiom,
% 4.69/4.95 ! [F: nat > code_integer,A: set_nat,B4: set_nat] : ( ord_le7084787975880047091nteger @ ( minus_2355218937544613996nteger @ ( image_1215581382706833972nteger @ F @ A ) @ ( image_1215581382706833972nteger @ F @ B4 ) ) @ ( image_1215581382706833972nteger @ F @ ( minus_minus_set_nat @ A @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_diff_subset
% 4.69/4.95 thf(fact_2444_image__diff__subset,axiom,
% 4.69/4.95 ! [F: nat > nat,A: set_nat,B4: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ ( image_nat_nat2 @ F @ A ) @ ( image_nat_nat2 @ F @ B4 ) ) @ ( image_nat_nat2 @ F @ ( minus_minus_set_nat @ A @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_diff_subset
% 4.69/4.95 thf(fact_2445_rev__image__eqI,axiom,
% 4.69/4.95 ! [X: code_integer,A: set_Code_integer,B: code_integer,F: code_integer > code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ X @ A )
% 4.69/4.95 => ( ( B
% 4.69/4.95 = ( F @ X ) )
% 4.69/4.95 => ( member_Code_integer @ B @ ( image_4470545334726330049nteger @ F @ A ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % rev_image_eqI
% 4.69/4.95 thf(fact_2446_rev__image__eqI,axiom,
% 4.69/4.95 ! [X: nat,A: set_nat,B: code_integer,F: nat > code_integer] :
% 4.69/4.95 ( ( member_nat @ X @ A )
% 4.69/4.95 => ( ( B
% 4.69/4.95 = ( F @ X ) )
% 4.69/4.95 => ( member_Code_integer @ B @ ( image_1215581382706833972nteger @ F @ A ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % rev_image_eqI
% 4.69/4.95 thf(fact_2447_rev__image__eqI,axiom,
% 4.69/4.95 ! [X: nat,A: set_nat,B: nat,F: nat > nat] :
% 4.69/4.95 ( ( member_nat @ X @ A )
% 4.69/4.95 => ( ( B
% 4.69/4.95 = ( F @ X ) )
% 4.69/4.95 => ( member_nat @ B @ ( image_nat_nat2 @ F @ A ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % rev_image_eqI
% 4.69/4.95 thf(fact_2448_rev__image__eqI,axiom,
% 4.69/4.95 ! [X: nat,A: set_nat,B: int,F: nat > int] :
% 4.69/4.95 ( ( member_nat @ X @ A )
% 4.69/4.95 => ( ( B
% 4.69/4.95 = ( F @ X ) )
% 4.69/4.95 => ( member_int @ B @ ( image_nat_int2 @ F @ A ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % rev_image_eqI
% 4.69/4.95 thf(fact_2449_rev__image__eqI,axiom,
% 4.69/4.95 ! [X: nat,A: set_nat,B: $o,F: nat > $o] :
% 4.69/4.95 ( ( member_nat @ X @ A )
% 4.69/4.95 => ( ( B
% 4.69/4.95 = ( F @ X ) )
% 4.69/4.95 => ( member_o @ B @ ( image_nat_o2 @ F @ A ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % rev_image_eqI
% 4.69/4.95 thf(fact_2450_rev__image__eqI,axiom,
% 4.69/4.95 ! [X: nat,A: set_nat,B: product_unit,F: nat > product_unit] :
% 4.69/4.95 ( ( member_nat @ X @ A )
% 4.69/4.95 => ( ( B
% 4.69/4.95 = ( F @ X ) )
% 4.69/4.95 => ( member_Product_unit @ B @ ( image_8730104196221521654t_unit @ F @ A ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % rev_image_eqI
% 4.69/4.95 thf(fact_2451_rev__image__eqI,axiom,
% 4.69/4.95 ! [X: int,A: set_int,B: nat,F: int > nat] :
% 4.69/4.95 ( ( member_int @ X @ A )
% 4.69/4.95 => ( ( B
% 4.69/4.95 = ( F @ X ) )
% 4.69/4.95 => ( member_nat @ B @ ( image_int_nat2 @ F @ A ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % rev_image_eqI
% 4.69/4.95 thf(fact_2452_rev__image__eqI,axiom,
% 4.69/4.95 ! [X: int,A: set_int,B: int,F: int > int] :
% 4.69/4.95 ( ( member_int @ X @ A )
% 4.69/4.95 => ( ( B
% 4.69/4.95 = ( F @ X ) )
% 4.69/4.95 => ( member_int @ B @ ( image_int_int2 @ F @ A ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % rev_image_eqI
% 4.69/4.95 thf(fact_2453_rev__image__eqI,axiom,
% 4.69/4.95 ! [X: int,A: set_int,B: $o,F: int > $o] :
% 4.69/4.95 ( ( member_int @ X @ A )
% 4.69/4.95 => ( ( B
% 4.69/4.95 = ( F @ X ) )
% 4.69/4.95 => ( member_o @ B @ ( image_int_o2 @ F @ A ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % rev_image_eqI
% 4.69/4.95 thf(fact_2454_rev__image__eqI,axiom,
% 4.69/4.95 ! [X: int,A: set_int,B: product_unit,F: int > product_unit] :
% 4.69/4.95 ( ( member_int @ X @ A )
% 4.69/4.95 => ( ( B
% 4.69/4.95 = ( F @ X ) )
% 4.69/4.95 => ( member_Product_unit @ B @ ( image_5846526143423701914t_unit @ F @ A ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % rev_image_eqI
% 4.69/4.95 thf(fact_2455_ball__imageD,axiom,
% 4.69/4.95 ! [F: nat > set_nat,A: set_nat,P: set_nat > $o] :
% 4.69/4.95 ( ! [X3: set_nat] :
% 4.69/4.95 ( ( member_set_nat @ X3 @ ( image_nat_set_nat @ F @ A ) )
% 4.69/4.95 => ( P @ X3 ) )
% 4.69/4.95 => ! [X6: nat] :
% 4.69/4.95 ( ( member_nat @ X6 @ A )
% 4.69/4.95 => ( P @ ( F @ X6 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % ball_imageD
% 4.69/4.95 thf(fact_2456_ball__imageD,axiom,
% 4.69/4.95 ! [F: nat > nat,A: set_nat,P: nat > $o] :
% 4.69/4.95 ( ! [X3: nat] :
% 4.69/4.95 ( ( member_nat @ X3 @ ( image_nat_nat2 @ F @ A ) )
% 4.69/4.95 => ( P @ X3 ) )
% 4.69/4.95 => ! [X6: nat] :
% 4.69/4.95 ( ( member_nat @ X6 @ A )
% 4.69/4.95 => ( P @ ( F @ X6 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % ball_imageD
% 4.69/4.95 thf(fact_2457_ball__imageD,axiom,
% 4.69/4.95 ! [F: code_integer > code_integer,A: set_Code_integer,P: code_integer > $o] :
% 4.69/4.95 ( ! [X3: code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ X3 @ ( image_4470545334726330049nteger @ F @ A ) )
% 4.69/4.95 => ( P @ X3 ) )
% 4.69/4.95 => ! [X6: code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ X6 @ A )
% 4.69/4.95 => ( P @ ( F @ X6 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % ball_imageD
% 4.69/4.95 thf(fact_2458_ball__imageD,axiom,
% 4.69/4.95 ! [F: nat > code_integer,A: set_nat,P: code_integer > $o] :
% 4.69/4.95 ( ! [X3: code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ X3 @ ( image_1215581382706833972nteger @ F @ A ) )
% 4.69/4.95 => ( P @ X3 ) )
% 4.69/4.95 => ! [X6: nat] :
% 4.69/4.95 ( ( member_nat @ X6 @ A )
% 4.69/4.95 => ( P @ ( F @ X6 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % ball_imageD
% 4.69/4.95 thf(fact_2459_image__cong,axiom,
% 4.69/4.95 ! [M: set_Code_integer,N: set_Code_integer,F: code_integer > code_integer,G: code_integer > code_integer] :
% 4.69/4.95 ( ( M = N )
% 4.69/4.95 => ( ! [X3: code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ X3 @ N )
% 4.69/4.95 => ( ( F @ X3 )
% 4.69/4.95 = ( G @ X3 ) ) )
% 4.69/4.95 => ( ( image_4470545334726330049nteger @ F @ M )
% 4.69/4.95 = ( image_4470545334726330049nteger @ G @ N ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_cong
% 4.69/4.95 thf(fact_2460_image__cong,axiom,
% 4.69/4.95 ! [M: set_nat,N: set_nat,F: nat > set_nat,G: nat > set_nat] :
% 4.69/4.95 ( ( M = N )
% 4.69/4.95 => ( ! [X3: nat] :
% 4.69/4.95 ( ( member_nat @ X3 @ N )
% 4.69/4.95 => ( ( F @ X3 )
% 4.69/4.95 = ( G @ X3 ) ) )
% 4.69/4.95 => ( ( image_nat_set_nat @ F @ M )
% 4.69/4.95 = ( image_nat_set_nat @ G @ N ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_cong
% 4.69/4.95 thf(fact_2461_image__cong,axiom,
% 4.69/4.95 ! [M: set_nat,N: set_nat,F: nat > nat,G: nat > nat] :
% 4.69/4.95 ( ( M = N )
% 4.69/4.95 => ( ! [X3: nat] :
% 4.69/4.95 ( ( member_nat @ X3 @ N )
% 4.69/4.95 => ( ( F @ X3 )
% 4.69/4.95 = ( G @ X3 ) ) )
% 4.69/4.95 => ( ( image_nat_nat2 @ F @ M )
% 4.69/4.95 = ( image_nat_nat2 @ G @ N ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_cong
% 4.69/4.95 thf(fact_2462_image__cong,axiom,
% 4.69/4.95 ! [M: set_nat,N: set_nat,F: nat > code_integer,G: nat > code_integer] :
% 4.69/4.95 ( ( M = N )
% 4.69/4.95 => ( ! [X3: nat] :
% 4.69/4.95 ( ( member_nat @ X3 @ N )
% 4.69/4.95 => ( ( F @ X3 )
% 4.69/4.95 = ( G @ X3 ) ) )
% 4.69/4.95 => ( ( image_1215581382706833972nteger @ F @ M )
% 4.69/4.95 = ( image_1215581382706833972nteger @ G @ N ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_cong
% 4.69/4.95 thf(fact_2463_bex__imageD,axiom,
% 4.69/4.95 ! [F: nat > set_nat,A: set_nat,P: set_nat > $o] :
% 4.69/4.95 ( ? [X6: set_nat] :
% 4.69/4.95 ( ( member_set_nat @ X6 @ ( image_nat_set_nat @ F @ A ) )
% 4.69/4.95 & ( P @ X6 ) )
% 4.69/4.95 => ? [X3: nat] :
% 4.69/4.95 ( ( member_nat @ X3 @ A )
% 4.69/4.95 & ( P @ ( F @ X3 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % bex_imageD
% 4.69/4.95 thf(fact_2464_bex__imageD,axiom,
% 4.69/4.95 ! [F: nat > nat,A: set_nat,P: nat > $o] :
% 4.69/4.95 ( ? [X6: nat] :
% 4.69/4.95 ( ( member_nat @ X6 @ ( image_nat_nat2 @ F @ A ) )
% 4.69/4.95 & ( P @ X6 ) )
% 4.69/4.95 => ? [X3: nat] :
% 4.69/4.95 ( ( member_nat @ X3 @ A )
% 4.69/4.95 & ( P @ ( F @ X3 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % bex_imageD
% 4.69/4.95 thf(fact_2465_bex__imageD,axiom,
% 4.69/4.95 ! [F: code_integer > code_integer,A: set_Code_integer,P: code_integer > $o] :
% 4.69/4.95 ( ? [X6: code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ X6 @ ( image_4470545334726330049nteger @ F @ A ) )
% 4.69/4.95 & ( P @ X6 ) )
% 4.69/4.95 => ? [X3: code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ X3 @ A )
% 4.69/4.95 & ( P @ ( F @ X3 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % bex_imageD
% 4.69/4.95 thf(fact_2466_bex__imageD,axiom,
% 4.69/4.95 ! [F: nat > code_integer,A: set_nat,P: code_integer > $o] :
% 4.69/4.95 ( ? [X6: code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ X6 @ ( image_1215581382706833972nteger @ F @ A ) )
% 4.69/4.95 & ( P @ X6 ) )
% 4.69/4.95 => ? [X3: nat] :
% 4.69/4.95 ( ( member_nat @ X3 @ A )
% 4.69/4.95 & ( P @ ( F @ X3 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % bex_imageD
% 4.69/4.95 thf(fact_2467_image__iff,axiom,
% 4.69/4.95 ! [Z: set_nat,F: nat > set_nat,A: set_nat] :
% 4.69/4.95 ( ( member_set_nat @ Z @ ( image_nat_set_nat @ F @ A ) )
% 4.69/4.95 = ( ? [X2: nat] :
% 4.69/4.95 ( ( member_nat @ X2 @ A )
% 4.69/4.95 & ( Z
% 4.69/4.95 = ( F @ X2 ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_iff
% 4.69/4.95 thf(fact_2468_image__iff,axiom,
% 4.69/4.95 ! [Z: code_integer,F: code_integer > code_integer,A: set_Code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ Z @ ( image_4470545334726330049nteger @ F @ A ) )
% 4.69/4.95 = ( ? [X2: code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ X2 @ A )
% 4.69/4.95 & ( Z
% 4.69/4.95 = ( F @ X2 ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_iff
% 4.69/4.95 thf(fact_2469_image__iff,axiom,
% 4.69/4.95 ! [Z: code_integer,F: nat > code_integer,A: set_nat] :
% 4.69/4.95 ( ( member_Code_integer @ Z @ ( image_1215581382706833972nteger @ F @ A ) )
% 4.69/4.95 = ( ? [X2: nat] :
% 4.69/4.95 ( ( member_nat @ X2 @ A )
% 4.69/4.95 & ( Z
% 4.69/4.95 = ( F @ X2 ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_iff
% 4.69/4.95 thf(fact_2470_image__iff,axiom,
% 4.69/4.95 ! [Z: nat,F: nat > nat,A: set_nat] :
% 4.69/4.95 ( ( member_nat @ Z @ ( image_nat_nat2 @ F @ A ) )
% 4.69/4.95 = ( ? [X2: nat] :
% 4.69/4.95 ( ( member_nat @ X2 @ A )
% 4.69/4.95 & ( Z
% 4.69/4.95 = ( F @ X2 ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_iff
% 4.69/4.95 thf(fact_2471_imageI,axiom,
% 4.69/4.95 ! [X: code_integer,A: set_Code_integer,F: code_integer > code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ X @ A )
% 4.69/4.95 => ( member_Code_integer @ ( F @ X ) @ ( image_4470545334726330049nteger @ F @ A ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % imageI
% 4.69/4.95 thf(fact_2472_imageI,axiom,
% 4.69/4.95 ! [X: nat,A: set_nat,F: nat > code_integer] :
% 4.69/4.95 ( ( member_nat @ X @ A )
% 4.69/4.95 => ( member_Code_integer @ ( F @ X ) @ ( image_1215581382706833972nteger @ F @ A ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % imageI
% 4.69/4.95 thf(fact_2473_imageI,axiom,
% 4.69/4.95 ! [X: nat,A: set_nat,F: nat > nat] :
% 4.69/4.95 ( ( member_nat @ X @ A )
% 4.69/4.95 => ( member_nat @ ( F @ X ) @ ( image_nat_nat2 @ F @ A ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % imageI
% 4.69/4.95 thf(fact_2474_imageI,axiom,
% 4.69/4.95 ! [X: nat,A: set_nat,F: nat > int] :
% 4.69/4.95 ( ( member_nat @ X @ A )
% 4.69/4.95 => ( member_int @ ( F @ X ) @ ( image_nat_int2 @ F @ A ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % imageI
% 4.69/4.95 thf(fact_2475_imageI,axiom,
% 4.69/4.95 ! [X: nat,A: set_nat,F: nat > $o] :
% 4.69/4.95 ( ( member_nat @ X @ A )
% 4.69/4.95 => ( member_o @ ( F @ X ) @ ( image_nat_o2 @ F @ A ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % imageI
% 4.69/4.95 thf(fact_2476_imageI,axiom,
% 4.69/4.95 ! [X: nat,A: set_nat,F: nat > product_unit] :
% 4.69/4.95 ( ( member_nat @ X @ A )
% 4.69/4.95 => ( member_Product_unit @ ( F @ X ) @ ( image_8730104196221521654t_unit @ F @ A ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % imageI
% 4.69/4.95 thf(fact_2477_imageI,axiom,
% 4.69/4.95 ! [X: int,A: set_int,F: int > nat] :
% 4.69/4.95 ( ( member_int @ X @ A )
% 4.69/4.95 => ( member_nat @ ( F @ X ) @ ( image_int_nat2 @ F @ A ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % imageI
% 4.69/4.95 thf(fact_2478_imageI,axiom,
% 4.69/4.95 ! [X: int,A: set_int,F: int > int] :
% 4.69/4.95 ( ( member_int @ X @ A )
% 4.69/4.95 => ( member_int @ ( F @ X ) @ ( image_int_int2 @ F @ A ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % imageI
% 4.69/4.95 thf(fact_2479_imageI,axiom,
% 4.69/4.95 ! [X: int,A: set_int,F: int > $o] :
% 4.69/4.95 ( ( member_int @ X @ A )
% 4.69/4.95 => ( member_o @ ( F @ X ) @ ( image_int_o2 @ F @ A ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % imageI
% 4.69/4.95 thf(fact_2480_imageI,axiom,
% 4.69/4.95 ! [X: int,A: set_int,F: int > product_unit] :
% 4.69/4.95 ( ( member_int @ X @ A )
% 4.69/4.95 => ( member_Product_unit @ ( F @ X ) @ ( image_5846526143423701914t_unit @ F @ A ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % imageI
% 4.69/4.95 thf(fact_2481_DiffD2,axiom,
% 4.69/4.95 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( member6576561426505652726_nat_o @ C @ ( minus_1801376950450012436_nat_o @ A @ B4 ) )
% 4.69/4.95 => ~ ( member6576561426505652726_nat_o @ C @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % DiffD2
% 4.69/4.95 thf(fact_2482_DiffD2,axiom,
% 4.69/4.95 ! [C: int,A: set_int,B4: set_int] :
% 4.69/4.95 ( ( member_int @ C @ ( minus_minus_set_int @ A @ B4 ) )
% 4.69/4.95 => ~ ( member_int @ C @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % DiffD2
% 4.69/4.95 thf(fact_2483_DiffD2,axiom,
% 4.69/4.95 ! [C: $o,A: set_o,B4: set_o] :
% 4.69/4.95 ( ( member_o @ C @ ( minus_minus_set_o @ A @ B4 ) )
% 4.69/4.95 => ~ ( member_o @ C @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % DiffD2
% 4.69/4.95 thf(fact_2484_DiffD2,axiom,
% 4.69/4.95 ! [C: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.95 ( ( member_Product_unit @ C @ ( minus_6452836326544984404t_unit @ A @ B4 ) )
% 4.69/4.95 => ~ ( member_Product_unit @ C @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % DiffD2
% 4.69/4.95 thf(fact_2485_DiffD2,axiom,
% 4.69/4.95 ! [C: nat,A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( member_nat @ C @ ( minus_minus_set_nat @ A @ B4 ) )
% 4.69/4.95 => ~ ( member_nat @ C @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % DiffD2
% 4.69/4.95 thf(fact_2486_DiffD1,axiom,
% 4.69/4.95 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( member6576561426505652726_nat_o @ C @ ( minus_1801376950450012436_nat_o @ A @ B4 ) )
% 4.69/4.95 => ( member6576561426505652726_nat_o @ C @ A ) ) ).
% 4.69/4.95
% 4.69/4.95 % DiffD1
% 4.69/4.95 thf(fact_2487_DiffD1,axiom,
% 4.69/4.95 ! [C: int,A: set_int,B4: set_int] :
% 4.69/4.95 ( ( member_int @ C @ ( minus_minus_set_int @ A @ B4 ) )
% 4.69/4.95 => ( member_int @ C @ A ) ) ).
% 4.69/4.95
% 4.69/4.95 % DiffD1
% 4.69/4.95 thf(fact_2488_DiffD1,axiom,
% 4.69/4.95 ! [C: $o,A: set_o,B4: set_o] :
% 4.69/4.95 ( ( member_o @ C @ ( minus_minus_set_o @ A @ B4 ) )
% 4.69/4.95 => ( member_o @ C @ A ) ) ).
% 4.69/4.95
% 4.69/4.95 % DiffD1
% 4.69/4.95 thf(fact_2489_DiffD1,axiom,
% 4.69/4.95 ! [C: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.95 ( ( member_Product_unit @ C @ ( minus_6452836326544984404t_unit @ A @ B4 ) )
% 4.69/4.95 => ( member_Product_unit @ C @ A ) ) ).
% 4.69/4.95
% 4.69/4.95 % DiffD1
% 4.69/4.95 thf(fact_2490_DiffD1,axiom,
% 4.69/4.95 ! [C: nat,A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( member_nat @ C @ ( minus_minus_set_nat @ A @ B4 ) )
% 4.69/4.95 => ( member_nat @ C @ A ) ) ).
% 4.69/4.95
% 4.69/4.95 % DiffD1
% 4.69/4.95 thf(fact_2491_DiffE,axiom,
% 4.69/4.95 ! [C: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( member6576561426505652726_nat_o @ C @ ( minus_1801376950450012436_nat_o @ A @ B4 ) )
% 4.69/4.95 => ~ ( ( member6576561426505652726_nat_o @ C @ A )
% 4.69/4.95 => ( member6576561426505652726_nat_o @ C @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % DiffE
% 4.69/4.95 thf(fact_2492_DiffE,axiom,
% 4.69/4.95 ! [C: int,A: set_int,B4: set_int] :
% 4.69/4.95 ( ( member_int @ C @ ( minus_minus_set_int @ A @ B4 ) )
% 4.69/4.95 => ~ ( ( member_int @ C @ A )
% 4.69/4.95 => ( member_int @ C @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % DiffE
% 4.69/4.95 thf(fact_2493_DiffE,axiom,
% 4.69/4.95 ! [C: $o,A: set_o,B4: set_o] :
% 4.69/4.95 ( ( member_o @ C @ ( minus_minus_set_o @ A @ B4 ) )
% 4.69/4.95 => ~ ( ( member_o @ C @ A )
% 4.69/4.95 => ( member_o @ C @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % DiffE
% 4.69/4.95 thf(fact_2494_DiffE,axiom,
% 4.69/4.95 ! [C: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.95 ( ( member_Product_unit @ C @ ( minus_6452836326544984404t_unit @ A @ B4 ) )
% 4.69/4.95 => ~ ( ( member_Product_unit @ C @ A )
% 4.69/4.95 => ( member_Product_unit @ C @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % DiffE
% 4.69/4.95 thf(fact_2495_DiffE,axiom,
% 4.69/4.95 ! [C: nat,A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( member_nat @ C @ ( minus_minus_set_nat @ A @ B4 ) )
% 4.69/4.95 => ~ ( ( member_nat @ C @ A )
% 4.69/4.95 => ( member_nat @ C @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % DiffE
% 4.69/4.95 thf(fact_2496_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 4.69/4.95 ! [A2: rat,C: rat,B: rat] :
% 4.69/4.95 ( ( minus_minus_rat @ ( minus_minus_rat @ A2 @ C ) @ B )
% 4.69/4.95 = ( minus_minus_rat @ ( minus_minus_rat @ A2 @ B ) @ C ) ) ).
% 4.69/4.95
% 4.69/4.95 % cancel_ab_semigroup_add_class.diff_right_commute
% 4.69/4.95 thf(fact_2497_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 4.69/4.95 ! [A2: nat,C: nat,B: nat] :
% 4.69/4.95 ( ( minus_minus_nat @ ( minus_minus_nat @ A2 @ C ) @ B )
% 4.69/4.95 = ( minus_minus_nat @ ( minus_minus_nat @ A2 @ B ) @ C ) ) ).
% 4.69/4.95
% 4.69/4.95 % cancel_ab_semigroup_add_class.diff_right_commute
% 4.69/4.95 thf(fact_2498_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 4.69/4.95 ! [A2: int,C: int,B: int] :
% 4.69/4.95 ( ( minus_minus_int @ ( minus_minus_int @ A2 @ C ) @ B )
% 4.69/4.95 = ( minus_minus_int @ ( minus_minus_int @ A2 @ B ) @ C ) ) ).
% 4.69/4.95
% 4.69/4.95 % cancel_ab_semigroup_add_class.diff_right_commute
% 4.69/4.95 thf(fact_2499_diff__eq__diff__eq,axiom,
% 4.69/4.95 ! [A2: rat,B: rat,C: rat,D2: rat] :
% 4.69/4.95 ( ( ( minus_minus_rat @ A2 @ B )
% 4.69/4.95 = ( minus_minus_rat @ C @ D2 ) )
% 4.69/4.95 => ( ( A2 = B )
% 4.69/4.95 = ( C = D2 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % diff_eq_diff_eq
% 4.69/4.95 thf(fact_2500_diff__eq__diff__eq,axiom,
% 4.69/4.95 ! [A2: int,B: int,C: int,D2: int] :
% 4.69/4.95 ( ( ( minus_minus_int @ A2 @ B )
% 4.69/4.95 = ( minus_minus_int @ C @ D2 ) )
% 4.69/4.95 => ( ( A2 = B )
% 4.69/4.95 = ( C = D2 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % diff_eq_diff_eq
% 4.69/4.95 thf(fact_2501_in__image__insert__iff,axiom,
% 4.69/4.95 ! [B4: set_set_Product_unit,X: product_unit,A: set_Product_unit] :
% 4.69/4.95 ( ! [C6: set_Product_unit] :
% 4.69/4.95 ( ( member5877623283571906838t_unit @ C6 @ B4 )
% 4.69/4.95 => ~ ( member_Product_unit @ X @ C6 ) )
% 4.69/4.95 => ( ( member5877623283571906838t_unit @ A @ ( image_4019945301284682565t_unit @ ( insert_Product_unit @ X ) @ B4 ) )
% 4.69/4.95 = ( ( member_Product_unit @ X @ A )
% 4.69/4.95 & ( member5877623283571906838t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % in_image_insert_iff
% 4.69/4.95 thf(fact_2502_in__image__insert__iff,axiom,
% 4.69/4.95 ! [B4: set_set_o,X: $o,A: set_o] :
% 4.69/4.95 ( ! [C6: set_o] :
% 4.69/4.95 ( ( member_set_o @ C6 @ B4 )
% 4.69/4.95 => ~ ( member_o @ X @ C6 ) )
% 4.69/4.95 => ( ( member_set_o @ A @ ( image_set_o_set_o @ ( insert_o @ X ) @ B4 ) )
% 4.69/4.95 = ( ( member_o @ X @ A )
% 4.69/4.95 & ( member_set_o @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % in_image_insert_iff
% 4.69/4.95 thf(fact_2503_in__image__insert__iff,axiom,
% 4.69/4.95 ! [B4: set_set_int,X: int,A: set_int] :
% 4.69/4.95 ( ! [C6: set_int] :
% 4.69/4.95 ( ( member_set_int @ C6 @ B4 )
% 4.69/4.95 => ~ ( member_int @ X @ C6 ) )
% 4.69/4.95 => ( ( member_set_int @ A @ ( image_524474410958335435et_int @ ( insert_int @ X ) @ B4 ) )
% 4.69/4.95 = ( ( member_int @ X @ A )
% 4.69/4.95 & ( member_set_int @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % in_image_insert_iff
% 4.69/4.95 thf(fact_2504_in__image__insert__iff,axiom,
% 4.69/4.95 ! [B4: set_se1353816476878259085_nat_o,X: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ! [C6: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( member1452989533377600726_nat_o @ C6 @ B4 )
% 4.69/4.95 => ~ ( member6576561426505652726_nat_o @ X @ C6 ) )
% 4.69/4.95 => ( ( member1452989533377600726_nat_o @ A @ ( image_8925030434418351941_nat_o @ ( insert5175938949040314269_nat_o @ X ) @ B4 ) )
% 4.69/4.95 = ( ( member6576561426505652726_nat_o @ X @ A )
% 4.69/4.95 & ( member1452989533377600726_nat_o @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % in_image_insert_iff
% 4.69/4.95 thf(fact_2505_in__image__insert__iff,axiom,
% 4.69/4.95 ! [B4: set_set_nat,X: nat,A: set_nat] :
% 4.69/4.95 ( ! [C6: set_nat] :
% 4.69/4.95 ( ( member_set_nat @ C6 @ B4 )
% 4.69/4.95 => ~ ( member_nat @ X @ C6 ) )
% 4.69/4.95 => ( ( member_set_nat @ A @ ( image_7916887816326733075et_nat @ ( insert_nat @ X ) @ B4 ) )
% 4.69/4.95 = ( ( member_nat @ X @ A )
% 4.69/4.95 & ( member_set_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % in_image_insert_iff
% 4.69/4.95 thf(fact_2506_converse_Ocases,axiom,
% 4.69/4.95 ! [A1: set_nat,A22: heap_e7401611519738050253t_unit,R2: set_Pr3948176798113811640et_nat] :
% 4.69/4.95 ( ( member727419437372278867t_unit @ ( produc2471974422597015918t_unit @ A1 @ A22 ) @ ( conver7272282955447398104et_nat @ R2 ) )
% 4.69/4.95 => ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A22 @ A1 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse.cases
% 4.69/4.95 thf(fact_2507_converse_Ocases,axiom,
% 4.69/4.95 ! [A1: produc3658429121746597890et_nat,A22: produc3658429121746597890et_nat > $o,R2: set_Pr3286484037609594932et_nat] :
% 4.69/4.95 ( ( member4978015717948814295_nat_o @ ( produc2829238748666232050_nat_o @ A1 @ A22 ) @ ( conver4003969491454187092et_nat @ R2 ) )
% 4.69/4.95 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A22 @ A1 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse.cases
% 4.69/4.95 thf(fact_2508_converse_Ocases,axiom,
% 4.69/4.95 ! [A1: produc3925858234332021118et_nat,A22: produc3658429121746597890et_nat > $o,R2: set_Pr8536935166611901872et_nat] :
% 4.69/4.95 ( ( member8354763867512313179_nat_o @ ( produc3674526432113299062_nat_o @ A1 @ A22 ) @ ( conver3577387295554834384et_nat @ R2 ) )
% 4.69/4.95 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A22 @ A1 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse.cases
% 4.69/4.95 thf(fact_2509_converse_Ocases,axiom,
% 4.69/4.95 ! [A1: heap_e7401611519738050253t_unit,A22: set_nat,R2: set_Pr4071100604818519410t_unit] :
% 4.69/4.95 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A1 @ A22 ) @ ( conver2236330673913229642t_unit @ R2 ) )
% 4.69/4.95 => ( member727419437372278867t_unit @ ( produc2471974422597015918t_unit @ A22 @ A1 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse.cases
% 4.69/4.95 thf(fact_2510_converse_Ocases,axiom,
% 4.69/4.95 ! [A1: nat,A22: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.95 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A1 @ A22 ) @ ( converse_nat_nat @ R2 ) )
% 4.69/4.95 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A22 @ A1 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse.cases
% 4.69/4.95 thf(fact_2511_converse_Ocases,axiom,
% 4.69/4.95 ! [A1: int,A22: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.95 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A1 @ A22 ) @ ( converse_int_int @ R2 ) )
% 4.69/4.95 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A22 @ A1 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse.cases
% 4.69/4.95 thf(fact_2512_converse_Ocases,axiom,
% 4.69/4.95 ! [A1: produc3658429121746597890et_nat > $o,A22: produc3658429121746597890et_nat,R2: set_Pr4208978187861016310_nat_o] :
% 4.69/4.95 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A1 @ A22 ) @ ( conver1831365297310299342_nat_o @ R2 ) )
% 4.69/4.95 => ( member4978015717948814295_nat_o @ ( produc2829238748666232050_nat_o @ A22 @ A1 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse.cases
% 4.69/4.95 thf(fact_2513_converse_Ocases,axiom,
% 4.69/4.95 ! [A1: produc3658429121746597890et_nat > $o,A22: produc3925858234332021118et_nat,R2: set_Pr7705059561495379578_nat_o] :
% 4.69/4.95 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A1 @ A22 ) @ ( conver5006497266169685586_nat_o @ R2 ) )
% 4.69/4.95 => ( member8354763867512313179_nat_o @ ( produc3674526432113299062_nat_o @ A22 @ A1 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse.cases
% 4.69/4.95 thf(fact_2514_converse_Osimps,axiom,
% 4.69/4.95 ! [A1: set_nat,A22: heap_e7401611519738050253t_unit,R2: set_Pr3948176798113811640et_nat] :
% 4.69/4.95 ( ( member727419437372278867t_unit @ ( produc2471974422597015918t_unit @ A1 @ A22 ) @ ( conver7272282955447398104et_nat @ R2 ) )
% 4.69/4.95 = ( ? [A6: heap_e7401611519738050253t_unit,B6: set_nat] :
% 4.69/4.95 ( ( A1 = B6 )
% 4.69/4.95 & ( A22 = A6 )
% 4.69/4.95 & ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A6 @ B6 ) @ R2 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse.simps
% 4.69/4.95 thf(fact_2515_converse_Osimps,axiom,
% 4.69/4.95 ! [A1: produc3658429121746597890et_nat,A22: produc3658429121746597890et_nat > $o,R2: set_Pr3286484037609594932et_nat] :
% 4.69/4.95 ( ( member4978015717948814295_nat_o @ ( produc2829238748666232050_nat_o @ A1 @ A22 ) @ ( conver4003969491454187092et_nat @ R2 ) )
% 4.69/4.95 = ( ? [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat] :
% 4.69/4.95 ( ( A1 = B6 )
% 4.69/4.95 & ( A22 = A6 )
% 4.69/4.95 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A6 @ B6 ) @ R2 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse.simps
% 4.69/4.95 thf(fact_2516_converse_Osimps,axiom,
% 4.69/4.95 ! [A1: produc3925858234332021118et_nat,A22: produc3658429121746597890et_nat > $o,R2: set_Pr8536935166611901872et_nat] :
% 4.69/4.95 ( ( member8354763867512313179_nat_o @ ( produc3674526432113299062_nat_o @ A1 @ A22 ) @ ( conver3577387295554834384et_nat @ R2 ) )
% 4.69/4.95 = ( ? [A6: produc3658429121746597890et_nat > $o,B6: produc3925858234332021118et_nat] :
% 4.69/4.95 ( ( A1 = B6 )
% 4.69/4.95 & ( A22 = A6 )
% 4.69/4.95 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A6 @ B6 ) @ R2 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse.simps
% 4.69/4.95 thf(fact_2517_converse_Osimps,axiom,
% 4.69/4.95 ! [A1: heap_e7401611519738050253t_unit,A22: set_nat,R2: set_Pr4071100604818519410t_unit] :
% 4.69/4.95 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A1 @ A22 ) @ ( conver2236330673913229642t_unit @ R2 ) )
% 4.69/4.95 = ( ? [A6: set_nat,B6: heap_e7401611519738050253t_unit] :
% 4.69/4.95 ( ( A1 = B6 )
% 4.69/4.95 & ( A22 = A6 )
% 4.69/4.95 & ( member727419437372278867t_unit @ ( produc2471974422597015918t_unit @ A6 @ B6 ) @ R2 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse.simps
% 4.69/4.95 thf(fact_2518_converse_Osimps,axiom,
% 4.69/4.95 ! [A1: nat,A22: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.95 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A1 @ A22 ) @ ( converse_nat_nat @ R2 ) )
% 4.69/4.95 = ( ? [A6: nat,B6: nat] :
% 4.69/4.95 ( ( A1 = B6 )
% 4.69/4.95 & ( A22 = A6 )
% 4.69/4.95 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A6 @ B6 ) @ R2 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse.simps
% 4.69/4.95 thf(fact_2519_converse_Osimps,axiom,
% 4.69/4.95 ! [A1: int,A22: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.95 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A1 @ A22 ) @ ( converse_int_int @ R2 ) )
% 4.69/4.95 = ( ? [A6: int,B6: int] :
% 4.69/4.95 ( ( A1 = B6 )
% 4.69/4.95 & ( A22 = A6 )
% 4.69/4.95 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A6 @ B6 ) @ R2 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse.simps
% 4.69/4.95 thf(fact_2520_converse_Osimps,axiom,
% 4.69/4.95 ! [A1: produc3658429121746597890et_nat > $o,A22: produc3658429121746597890et_nat,R2: set_Pr4208978187861016310_nat_o] :
% 4.69/4.95 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A1 @ A22 ) @ ( conver1831365297310299342_nat_o @ R2 ) )
% 4.69/4.95 = ( ? [A6: produc3658429121746597890et_nat,B6: produc3658429121746597890et_nat > $o] :
% 4.69/4.95 ( ( A1 = B6 )
% 4.69/4.95 & ( A22 = A6 )
% 4.69/4.95 & ( member4978015717948814295_nat_o @ ( produc2829238748666232050_nat_o @ A6 @ B6 ) @ R2 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse.simps
% 4.69/4.95 thf(fact_2521_converse_Osimps,axiom,
% 4.69/4.95 ! [A1: produc3658429121746597890et_nat > $o,A22: produc3925858234332021118et_nat,R2: set_Pr7705059561495379578_nat_o] :
% 4.69/4.95 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A1 @ A22 ) @ ( conver5006497266169685586_nat_o @ R2 ) )
% 4.69/4.95 = ( ? [A6: produc3925858234332021118et_nat,B6: produc3658429121746597890et_nat > $o] :
% 4.69/4.95 ( ( A1 = B6 )
% 4.69/4.95 & ( A22 = A6 )
% 4.69/4.95 & ( member8354763867512313179_nat_o @ ( produc3674526432113299062_nat_o @ A6 @ B6 ) @ R2 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converse.simps
% 4.69/4.95 thf(fact_2522_converseD,axiom,
% 4.69/4.95 ! [A2: set_nat,B: heap_e7401611519738050253t_unit,R2: set_Pr3948176798113811640et_nat] :
% 4.69/4.95 ( ( member727419437372278867t_unit @ ( produc2471974422597015918t_unit @ A2 @ B ) @ ( conver7272282955447398104et_nat @ R2 ) )
% 4.69/4.95 => ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ B @ A2 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseD
% 4.69/4.95 thf(fact_2523_converseD,axiom,
% 4.69/4.95 ! [A2: produc3658429121746597890et_nat,B: produc3658429121746597890et_nat > $o,R2: set_Pr3286484037609594932et_nat] :
% 4.69/4.95 ( ( member4978015717948814295_nat_o @ ( produc2829238748666232050_nat_o @ A2 @ B ) @ ( conver4003969491454187092et_nat @ R2 ) )
% 4.69/4.95 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ B @ A2 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseD
% 4.69/4.95 thf(fact_2524_converseD,axiom,
% 4.69/4.95 ! [A2: produc3925858234332021118et_nat,B: produc3658429121746597890et_nat > $o,R2: set_Pr8536935166611901872et_nat] :
% 4.69/4.95 ( ( member8354763867512313179_nat_o @ ( produc3674526432113299062_nat_o @ A2 @ B ) @ ( conver3577387295554834384et_nat @ R2 ) )
% 4.69/4.95 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ B @ A2 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseD
% 4.69/4.95 thf(fact_2525_converseD,axiom,
% 4.69/4.95 ! [A2: heap_e7401611519738050253t_unit,B: set_nat,R2: set_Pr4071100604818519410t_unit] :
% 4.69/4.95 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ B ) @ ( conver2236330673913229642t_unit @ R2 ) )
% 4.69/4.95 => ( member727419437372278867t_unit @ ( produc2471974422597015918t_unit @ B @ A2 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseD
% 4.69/4.95 thf(fact_2526_converseD,axiom,
% 4.69/4.95 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.95 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( converse_nat_nat @ R2 ) )
% 4.69/4.95 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ A2 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseD
% 4.69/4.95 thf(fact_2527_converseD,axiom,
% 4.69/4.95 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.95 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( converse_int_int @ R2 ) )
% 4.69/4.95 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ A2 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseD
% 4.69/4.95 thf(fact_2528_converseD,axiom,
% 4.69/4.95 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,R2: set_Pr4208978187861016310_nat_o] :
% 4.69/4.95 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ B ) @ ( conver1831365297310299342_nat_o @ R2 ) )
% 4.69/4.95 => ( member4978015717948814295_nat_o @ ( produc2829238748666232050_nat_o @ B @ A2 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseD
% 4.69/4.95 thf(fact_2529_converseD,axiom,
% 4.69/4.95 ! [A2: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,R2: set_Pr7705059561495379578_nat_o] :
% 4.69/4.95 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ B ) @ ( conver5006497266169685586_nat_o @ R2 ) )
% 4.69/4.95 => ( member8354763867512313179_nat_o @ ( produc3674526432113299062_nat_o @ B @ A2 ) @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseD
% 4.69/4.95 thf(fact_2530_converseE,axiom,
% 4.69/4.95 ! [Yx: produc7348995623955488188t_unit,R2: set_Pr3948176798113811640et_nat] :
% 4.69/4.95 ( ( member727419437372278867t_unit @ Yx @ ( conver7272282955447398104et_nat @ R2 ) )
% 4.69/4.95 => ~ ! [X3: heap_e7401611519738050253t_unit,Y2: set_nat] :
% 4.69/4.95 ( ( Yx
% 4.69/4.95 = ( produc2471974422597015918t_unit @ Y2 @ X3 ) )
% 4.69/4.95 => ~ ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X3 @ Y2 ) @ R2 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseE
% 4.69/4.95 thf(fact_2531_converseE,axiom,
% 4.69/4.95 ! [Yx: produc6907119039986491712_nat_o,R2: set_Pr3286484037609594932et_nat] :
% 4.69/4.95 ( ( member4978015717948814295_nat_o @ Yx @ ( conver4003969491454187092et_nat @ R2 ) )
% 4.69/4.95 => ~ ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 4.69/4.95 ( ( Yx
% 4.69/4.95 = ( produc2829238748666232050_nat_o @ Y2 @ X3 ) )
% 4.69/4.95 => ~ ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y2 ) @ R2 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseE
% 4.69/4.95 thf(fact_2532_converseE,axiom,
% 4.69/4.95 ! [Yx: produc4962441903510821572_nat_o,R2: set_Pr8536935166611901872et_nat] :
% 4.69/4.95 ( ( member8354763867512313179_nat_o @ Yx @ ( conver3577387295554834384et_nat @ R2 ) )
% 4.69/4.95 => ~ ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3925858234332021118et_nat] :
% 4.69/4.95 ( ( Yx
% 4.69/4.95 = ( produc3674526432113299062_nat_o @ Y2 @ X3 ) )
% 4.69/4.95 => ~ ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y2 ) @ R2 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseE
% 4.69/4.95 thf(fact_2533_converseE,axiom,
% 4.69/4.95 ! [Yx: produc3658429121746597890et_nat,R2: set_Pr4071100604818519410t_unit] :
% 4.69/4.95 ( ( member6260224972018164377et_nat @ Yx @ ( conver2236330673913229642t_unit @ R2 ) )
% 4.69/4.95 => ~ ! [X3: set_nat,Y2: heap_e7401611519738050253t_unit] :
% 4.69/4.95 ( ( Yx
% 4.69/4.95 = ( produc7507926704131184380et_nat @ Y2 @ X3 ) )
% 4.69/4.95 => ~ ( member727419437372278867t_unit @ ( produc2471974422597015918t_unit @ X3 @ Y2 ) @ R2 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseE
% 4.69/4.95 thf(fact_2534_converseE,axiom,
% 4.69/4.95 ! [Yx: product_prod_nat_nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.95 ( ( member8440522571783428010at_nat @ Yx @ ( converse_nat_nat @ R2 ) )
% 4.69/4.95 => ~ ! [X3: nat,Y2: nat] :
% 4.69/4.95 ( ( Yx
% 4.69/4.95 = ( product_Pair_nat_nat @ Y2 @ X3 ) )
% 4.69/4.95 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ R2 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseE
% 4.69/4.95 thf(fact_2535_converseE,axiom,
% 4.69/4.95 ! [Yx: product_prod_int_int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.95 ( ( member5262025264175285858nt_int @ Yx @ ( converse_int_int @ R2 ) )
% 4.69/4.95 => ~ ! [X3: int,Y2: int] :
% 4.69/4.95 ( ( Yx
% 4.69/4.95 = ( product_Pair_int_int @ Y2 @ X3 ) )
% 4.69/4.95 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y2 ) @ R2 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseE
% 4.69/4.95 thf(fact_2536_converseE,axiom,
% 4.69/4.95 ! [Yx: produc3925858234332021118et_nat,R2: set_Pr4208978187861016310_nat_o] :
% 4.69/4.95 ( ( member1996754912294343701et_nat @ Yx @ ( conver1831365297310299342_nat_o @ R2 ) )
% 4.69/4.95 => ~ ! [X3: produc3658429121746597890et_nat,Y2: produc3658429121746597890et_nat > $o] :
% 4.69/4.95 ( ( Yx
% 4.69/4.95 = ( produc5001842942810119800et_nat @ Y2 @ X3 ) )
% 4.69/4.95 => ~ ( member4978015717948814295_nat_o @ ( produc2829238748666232050_nat_o @ X3 @ Y2 ) @ R2 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseE
% 4.69/4.95 thf(fact_2537_converseE,axiom,
% 4.69/4.95 ! [Yx: produc2732055786443039994et_nat,R2: set_Pr7705059561495379578_nat_o] :
% 4.69/4.95 ( ( member6124377750444531601et_nat @ Yx @ ( conver5006497266169685586_nat_o @ R2 ) )
% 4.69/4.95 => ~ ! [X3: produc3925858234332021118et_nat,Y2: produc3658429121746597890et_nat > $o] :
% 4.69/4.95 ( ( Yx
% 4.69/4.95 = ( produc2245416461498447860et_nat @ Y2 @ X3 ) )
% 4.69/4.95 => ~ ( member8354763867512313179_nat_o @ ( produc3674526432113299062_nat_o @ X3 @ Y2 ) @ R2 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseE
% 4.69/4.95 thf(fact_2538_converseI,axiom,
% 4.69/4.95 ! [A2: set_nat,B: heap_e7401611519738050253t_unit,R2: set_Pr4071100604818519410t_unit] :
% 4.69/4.95 ( ( member727419437372278867t_unit @ ( produc2471974422597015918t_unit @ A2 @ B ) @ R2 )
% 4.69/4.95 => ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ B @ A2 ) @ ( conver2236330673913229642t_unit @ R2 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseI
% 4.69/4.95 thf(fact_2539_converseI,axiom,
% 4.69/4.95 ! [A2: produc3658429121746597890et_nat,B: produc3658429121746597890et_nat > $o,R2: set_Pr4208978187861016310_nat_o] :
% 4.69/4.95 ( ( member4978015717948814295_nat_o @ ( produc2829238748666232050_nat_o @ A2 @ B ) @ R2 )
% 4.69/4.95 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ B @ A2 ) @ ( conver1831365297310299342_nat_o @ R2 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseI
% 4.69/4.95 thf(fact_2540_converseI,axiom,
% 4.69/4.95 ! [A2: produc3925858234332021118et_nat,B: produc3658429121746597890et_nat > $o,R2: set_Pr7705059561495379578_nat_o] :
% 4.69/4.95 ( ( member8354763867512313179_nat_o @ ( produc3674526432113299062_nat_o @ A2 @ B ) @ R2 )
% 4.69/4.95 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ B @ A2 ) @ ( conver5006497266169685586_nat_o @ R2 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseI
% 4.69/4.95 thf(fact_2541_converseI,axiom,
% 4.69/4.95 ! [A2: heap_e7401611519738050253t_unit,B: set_nat,R2: set_Pr3948176798113811640et_nat] :
% 4.69/4.95 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ B ) @ R2 )
% 4.69/4.95 => ( member727419437372278867t_unit @ ( produc2471974422597015918t_unit @ B @ A2 ) @ ( conver7272282955447398104et_nat @ R2 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseI
% 4.69/4.95 thf(fact_2542_converseI,axiom,
% 4.69/4.95 ! [A2: nat,B: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.95 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 )
% 4.69/4.95 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ A2 ) @ ( converse_nat_nat @ R2 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseI
% 4.69/4.95 thf(fact_2543_converseI,axiom,
% 4.69/4.95 ! [A2: int,B: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.95 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 )
% 4.69/4.95 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ A2 ) @ ( converse_int_int @ R2 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseI
% 4.69/4.95 thf(fact_2544_converseI,axiom,
% 4.69/4.95 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,R2: set_Pr3286484037609594932et_nat] :
% 4.69/4.95 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ B ) @ R2 )
% 4.69/4.95 => ( member4978015717948814295_nat_o @ ( produc2829238748666232050_nat_o @ B @ A2 ) @ ( conver4003969491454187092et_nat @ R2 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseI
% 4.69/4.95 thf(fact_2545_converseI,axiom,
% 4.69/4.95 ! [A2: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,R2: set_Pr8536935166611901872et_nat] :
% 4.69/4.95 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ B ) @ R2 )
% 4.69/4.95 => ( member8354763867512313179_nat_o @ ( produc3674526432113299062_nat_o @ B @ A2 ) @ ( conver3577387295554834384et_nat @ R2 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % converseI
% 4.69/4.95 thf(fact_2546_diff__eq__diff__less__eq,axiom,
% 4.69/4.95 ! [A2: rat,B: rat,C: rat,D2: rat] :
% 4.69/4.95 ( ( ( minus_minus_rat @ A2 @ B )
% 4.69/4.95 = ( minus_minus_rat @ C @ D2 ) )
% 4.69/4.95 => ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/4.95 = ( ord_less_eq_rat @ C @ D2 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % diff_eq_diff_less_eq
% 4.69/4.95 thf(fact_2547_diff__eq__diff__less__eq,axiom,
% 4.69/4.95 ! [A2: int,B: int,C: int,D2: int] :
% 4.69/4.95 ( ( ( minus_minus_int @ A2 @ B )
% 4.69/4.95 = ( minus_minus_int @ C @ D2 ) )
% 4.69/4.95 => ( ( ord_less_eq_int @ A2 @ B )
% 4.69/4.95 = ( ord_less_eq_int @ C @ D2 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % diff_eq_diff_less_eq
% 4.69/4.95 thf(fact_2548_diff__right__mono,axiom,
% 4.69/4.95 ! [A2: rat,B: rat,C: rat] :
% 4.69/4.95 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/4.95 => ( ord_less_eq_rat @ ( minus_minus_rat @ A2 @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % diff_right_mono
% 4.69/4.95 thf(fact_2549_diff__right__mono,axiom,
% 4.69/4.95 ! [A2: int,B: int,C: int] :
% 4.69/4.95 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/4.95 => ( ord_less_eq_int @ ( minus_minus_int @ A2 @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % diff_right_mono
% 4.69/4.95 thf(fact_2550_diff__left__mono,axiom,
% 4.69/4.95 ! [B: rat,A2: rat,C: rat] :
% 4.69/4.95 ( ( ord_less_eq_rat @ B @ A2 )
% 4.69/4.95 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A2 ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % diff_left_mono
% 4.69/4.95 thf(fact_2551_diff__left__mono,axiom,
% 4.69/4.95 ! [B: int,A2: int,C: int] :
% 4.69/4.95 ( ( ord_less_eq_int @ B @ A2 )
% 4.69/4.95 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A2 ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % diff_left_mono
% 4.69/4.95 thf(fact_2552_diff__mono,axiom,
% 4.69/4.95 ! [A2: rat,B: rat,D2: rat,C: rat] :
% 4.69/4.95 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/4.95 => ( ( ord_less_eq_rat @ D2 @ C )
% 4.69/4.95 => ( ord_less_eq_rat @ ( minus_minus_rat @ A2 @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % diff_mono
% 4.69/4.95 thf(fact_2553_diff__mono,axiom,
% 4.69/4.95 ! [A2: int,B: int,D2: int,C: int] :
% 4.69/4.95 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/4.95 => ( ( ord_less_eq_int @ D2 @ C )
% 4.69/4.95 => ( ord_less_eq_int @ ( minus_minus_int @ A2 @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % diff_mono
% 4.69/4.95 thf(fact_2554_subset__image__iff,axiom,
% 4.69/4.95 ! [B4: set_Code_integer,F: code_integer > code_integer,A: set_Code_integer] :
% 4.69/4.95 ( ( ord_le7084787975880047091nteger @ B4 @ ( image_4470545334726330049nteger @ F @ A ) )
% 4.69/4.95 = ( ? [AA: set_Code_integer] :
% 4.69/4.95 ( ( ord_le7084787975880047091nteger @ AA @ A )
% 4.69/4.95 & ( B4
% 4.69/4.95 = ( image_4470545334726330049nteger @ F @ AA ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_image_iff
% 4.69/4.95 thf(fact_2555_subset__image__iff,axiom,
% 4.69/4.95 ! [B4: set_set_nat,F: nat > set_nat,A: set_nat] :
% 4.69/4.95 ( ( ord_le6893508408891458716et_nat @ B4 @ ( image_nat_set_nat @ F @ A ) )
% 4.69/4.95 = ( ? [AA: set_nat] :
% 4.69/4.95 ( ( ord_less_eq_set_nat @ AA @ A )
% 4.69/4.95 & ( B4
% 4.69/4.95 = ( image_nat_set_nat @ F @ AA ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_image_iff
% 4.69/4.95 thf(fact_2556_subset__image__iff,axiom,
% 4.69/4.95 ! [B4: set_Code_integer,F: nat > code_integer,A: set_nat] :
% 4.69/4.95 ( ( ord_le7084787975880047091nteger @ B4 @ ( image_1215581382706833972nteger @ F @ A ) )
% 4.69/4.95 = ( ? [AA: set_nat] :
% 4.69/4.95 ( ( ord_less_eq_set_nat @ AA @ A )
% 4.69/4.95 & ( B4
% 4.69/4.95 = ( image_1215581382706833972nteger @ F @ AA ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_image_iff
% 4.69/4.95 thf(fact_2557_subset__image__iff,axiom,
% 4.69/4.95 ! [B4: set_nat,F: nat > nat,A: set_nat] :
% 4.69/4.95 ( ( ord_less_eq_set_nat @ B4 @ ( image_nat_nat2 @ F @ A ) )
% 4.69/4.95 = ( ? [AA: set_nat] :
% 4.69/4.95 ( ( ord_less_eq_set_nat @ AA @ A )
% 4.69/4.95 & ( B4
% 4.69/4.95 = ( image_nat_nat2 @ F @ AA ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_image_iff
% 4.69/4.95 thf(fact_2558_image__subset__iff,axiom,
% 4.69/4.95 ! [F: nat > set_nat,A: set_nat,B4: set_set_nat] :
% 4.69/4.95 ( ( ord_le6893508408891458716et_nat @ ( image_nat_set_nat @ F @ A ) @ B4 )
% 4.69/4.95 = ( ! [X2: nat] :
% 4.69/4.95 ( ( member_nat @ X2 @ A )
% 4.69/4.95 => ( member_set_nat @ ( F @ X2 ) @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_subset_iff
% 4.69/4.95 thf(fact_2559_image__subset__iff,axiom,
% 4.69/4.95 ! [F: code_integer > code_integer,A: set_Code_integer,B4: set_Code_integer] :
% 4.69/4.95 ( ( ord_le7084787975880047091nteger @ ( image_4470545334726330049nteger @ F @ A ) @ B4 )
% 4.69/4.95 = ( ! [X2: code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ X2 @ A )
% 4.69/4.95 => ( member_Code_integer @ ( F @ X2 ) @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_subset_iff
% 4.69/4.95 thf(fact_2560_image__subset__iff,axiom,
% 4.69/4.95 ! [F: nat > code_integer,A: set_nat,B4: set_Code_integer] :
% 4.69/4.95 ( ( ord_le7084787975880047091nteger @ ( image_1215581382706833972nteger @ F @ A ) @ B4 )
% 4.69/4.95 = ( ! [X2: nat] :
% 4.69/4.95 ( ( member_nat @ X2 @ A )
% 4.69/4.95 => ( member_Code_integer @ ( F @ X2 ) @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_subset_iff
% 4.69/4.95 thf(fact_2561_image__subset__iff,axiom,
% 4.69/4.95 ! [F: nat > nat,A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( ord_less_eq_set_nat @ ( image_nat_nat2 @ F @ A ) @ B4 )
% 4.69/4.95 = ( ! [X2: nat] :
% 4.69/4.95 ( ( member_nat @ X2 @ A )
% 4.69/4.95 => ( member_nat @ ( F @ X2 ) @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_subset_iff
% 4.69/4.95 thf(fact_2562_subset__imageE,axiom,
% 4.69/4.95 ! [B4: set_Code_integer,F: code_integer > code_integer,A: set_Code_integer] :
% 4.69/4.95 ( ( ord_le7084787975880047091nteger @ B4 @ ( image_4470545334726330049nteger @ F @ A ) )
% 4.69/4.95 => ~ ! [C6: set_Code_integer] :
% 4.69/4.95 ( ( ord_le7084787975880047091nteger @ C6 @ A )
% 4.69/4.95 => ( B4
% 4.69/4.95 != ( image_4470545334726330049nteger @ F @ C6 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_imageE
% 4.69/4.95 thf(fact_2563_subset__imageE,axiom,
% 4.69/4.95 ! [B4: set_set_nat,F: nat > set_nat,A: set_nat] :
% 4.69/4.95 ( ( ord_le6893508408891458716et_nat @ B4 @ ( image_nat_set_nat @ F @ A ) )
% 4.69/4.95 => ~ ! [C6: set_nat] :
% 4.69/4.95 ( ( ord_less_eq_set_nat @ C6 @ A )
% 4.69/4.95 => ( B4
% 4.69/4.95 != ( image_nat_set_nat @ F @ C6 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_imageE
% 4.69/4.95 thf(fact_2564_subset__imageE,axiom,
% 4.69/4.95 ! [B4: set_Code_integer,F: nat > code_integer,A: set_nat] :
% 4.69/4.95 ( ( ord_le7084787975880047091nteger @ B4 @ ( image_1215581382706833972nteger @ F @ A ) )
% 4.69/4.95 => ~ ! [C6: set_nat] :
% 4.69/4.95 ( ( ord_less_eq_set_nat @ C6 @ A )
% 4.69/4.95 => ( B4
% 4.69/4.95 != ( image_1215581382706833972nteger @ F @ C6 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_imageE
% 4.69/4.95 thf(fact_2565_subset__imageE,axiom,
% 4.69/4.95 ! [B4: set_nat,F: nat > nat,A: set_nat] :
% 4.69/4.95 ( ( ord_less_eq_set_nat @ B4 @ ( image_nat_nat2 @ F @ A ) )
% 4.69/4.95 => ~ ! [C6: set_nat] :
% 4.69/4.95 ( ( ord_less_eq_set_nat @ C6 @ A )
% 4.69/4.95 => ( B4
% 4.69/4.95 != ( image_nat_nat2 @ F @ C6 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_imageE
% 4.69/4.95 thf(fact_2566_image__subsetI,axiom,
% 4.69/4.95 ! [A: set_Code_integer,F: code_integer > code_integer,B4: set_Code_integer] :
% 4.69/4.95 ( ! [X3: code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ X3 @ A )
% 4.69/4.95 => ( member_Code_integer @ ( F @ X3 ) @ B4 ) )
% 4.69/4.95 => ( ord_le7084787975880047091nteger @ ( image_4470545334726330049nteger @ F @ A ) @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_subsetI
% 4.69/4.95 thf(fact_2567_image__subsetI,axiom,
% 4.69/4.95 ! [A: set_nat,F: nat > code_integer,B4: set_Code_integer] :
% 4.69/4.95 ( ! [X3: nat] :
% 4.69/4.95 ( ( member_nat @ X3 @ A )
% 4.69/4.95 => ( member_Code_integer @ ( F @ X3 ) @ B4 ) )
% 4.69/4.95 => ( ord_le7084787975880047091nteger @ ( image_1215581382706833972nteger @ F @ A ) @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_subsetI
% 4.69/4.95 thf(fact_2568_image__subsetI,axiom,
% 4.69/4.95 ! [A: set_nat,F: nat > int,B4: set_int] :
% 4.69/4.95 ( ! [X3: nat] :
% 4.69/4.95 ( ( member_nat @ X3 @ A )
% 4.69/4.95 => ( member_int @ ( F @ X3 ) @ B4 ) )
% 4.69/4.95 => ( ord_less_eq_set_int @ ( image_nat_int2 @ F @ A ) @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_subsetI
% 4.69/4.95 thf(fact_2569_image__subsetI,axiom,
% 4.69/4.95 ! [A: set_nat,F: nat > $o,B4: set_o] :
% 4.69/4.95 ( ! [X3: nat] :
% 4.69/4.95 ( ( member_nat @ X3 @ A )
% 4.69/4.95 => ( member_o @ ( F @ X3 ) @ B4 ) )
% 4.69/4.95 => ( ord_less_eq_set_o @ ( image_nat_o2 @ F @ A ) @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_subsetI
% 4.69/4.95 thf(fact_2570_image__subsetI,axiom,
% 4.69/4.95 ! [A: set_nat,F: nat > product_unit,B4: set_Product_unit] :
% 4.69/4.95 ( ! [X3: nat] :
% 4.69/4.95 ( ( member_nat @ X3 @ A )
% 4.69/4.95 => ( member_Product_unit @ ( F @ X3 ) @ B4 ) )
% 4.69/4.95 => ( ord_le3507040750410214029t_unit @ ( image_8730104196221521654t_unit @ F @ A ) @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_subsetI
% 4.69/4.95 thf(fact_2571_image__subsetI,axiom,
% 4.69/4.95 ! [A: set_int,F: int > int,B4: set_int] :
% 4.69/4.95 ( ! [X3: int] :
% 4.69/4.95 ( ( member_int @ X3 @ A )
% 4.69/4.95 => ( member_int @ ( F @ X3 ) @ B4 ) )
% 4.69/4.95 => ( ord_less_eq_set_int @ ( image_int_int2 @ F @ A ) @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_subsetI
% 4.69/4.95 thf(fact_2572_image__subsetI,axiom,
% 4.69/4.95 ! [A: set_int,F: int > $o,B4: set_o] :
% 4.69/4.95 ( ! [X3: int] :
% 4.69/4.95 ( ( member_int @ X3 @ A )
% 4.69/4.95 => ( member_o @ ( F @ X3 ) @ B4 ) )
% 4.69/4.95 => ( ord_less_eq_set_o @ ( image_int_o2 @ F @ A ) @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_subsetI
% 4.69/4.95 thf(fact_2573_image__subsetI,axiom,
% 4.69/4.95 ! [A: set_int,F: int > product_unit,B4: set_Product_unit] :
% 4.69/4.95 ( ! [X3: int] :
% 4.69/4.95 ( ( member_int @ X3 @ A )
% 4.69/4.95 => ( member_Product_unit @ ( F @ X3 ) @ B4 ) )
% 4.69/4.95 => ( ord_le3507040750410214029t_unit @ ( image_5846526143423701914t_unit @ F @ A ) @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_subsetI
% 4.69/4.95 thf(fact_2574_image__subsetI,axiom,
% 4.69/4.95 ! [A: set_o,F: $o > int,B4: set_int] :
% 4.69/4.95 ( ! [X3: $o] :
% 4.69/4.95 ( ( member_o @ X3 @ A )
% 4.69/4.95 => ( member_int @ ( F @ X3 ) @ B4 ) )
% 4.69/4.95 => ( ord_less_eq_set_int @ ( image_o_int2 @ F @ A ) @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_subsetI
% 4.69/4.95 thf(fact_2575_image__subsetI,axiom,
% 4.69/4.95 ! [A: set_o,F: $o > $o,B4: set_o] :
% 4.69/4.95 ( ! [X3: $o] :
% 4.69/4.95 ( ( member_o @ X3 @ A )
% 4.69/4.95 => ( member_o @ ( F @ X3 ) @ B4 ) )
% 4.69/4.95 => ( ord_less_eq_set_o @ ( image_o_o2 @ F @ A ) @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_subsetI
% 4.69/4.95 thf(fact_2576_image__mono,axiom,
% 4.69/4.95 ! [A: set_Code_integer,B4: set_Code_integer,F: code_integer > code_integer] :
% 4.69/4.95 ( ( ord_le7084787975880047091nteger @ A @ B4 )
% 4.69/4.95 => ( ord_le7084787975880047091nteger @ ( image_4470545334726330049nteger @ F @ A ) @ ( image_4470545334726330049nteger @ F @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_mono
% 4.69/4.95 thf(fact_2577_image__mono,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat,F: nat > set_nat] :
% 4.69/4.95 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.95 => ( ord_le6893508408891458716et_nat @ ( image_nat_set_nat @ F @ A ) @ ( image_nat_set_nat @ F @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_mono
% 4.69/4.95 thf(fact_2578_image__mono,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat,F: nat > code_integer] :
% 4.69/4.95 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.95 => ( ord_le7084787975880047091nteger @ ( image_1215581382706833972nteger @ F @ A ) @ ( image_1215581382706833972nteger @ F @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_mono
% 4.69/4.95 thf(fact_2579_image__mono,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat,F: nat > nat] :
% 4.69/4.95 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.95 => ( ord_less_eq_set_nat @ ( image_nat_nat2 @ F @ A ) @ ( image_nat_nat2 @ F @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_mono
% 4.69/4.95 thf(fact_2580_image__Un,axiom,
% 4.69/4.95 ! [F: code_integer > code_integer,A: set_Code_integer,B4: set_Code_integer] :
% 4.69/4.95 ( ( image_4470545334726330049nteger @ F @ ( sup_su848401254843788991nteger @ A @ B4 ) )
% 4.69/4.95 = ( sup_su848401254843788991nteger @ ( image_4470545334726330049nteger @ F @ A ) @ ( image_4470545334726330049nteger @ F @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_Un
% 4.69/4.95 thf(fact_2581_image__Un,axiom,
% 4.69/4.95 ! [F: nat > set_nat,A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( image_nat_set_nat @ F @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.95 = ( sup_sup_set_set_nat @ ( image_nat_set_nat @ F @ A ) @ ( image_nat_set_nat @ F @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_Un
% 4.69/4.95 thf(fact_2582_image__Un,axiom,
% 4.69/4.95 ! [F: nat > code_integer,A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( image_1215581382706833972nteger @ F @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.95 = ( sup_su848401254843788991nteger @ ( image_1215581382706833972nteger @ F @ A ) @ ( image_1215581382706833972nteger @ F @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_Un
% 4.69/4.95 thf(fact_2583_image__Un,axiom,
% 4.69/4.95 ! [F: nat > nat,A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( image_nat_nat2 @ F @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.95 = ( sup_sup_set_nat @ ( image_nat_nat2 @ F @ A ) @ ( image_nat_nat2 @ F @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_Un
% 4.69/4.95 thf(fact_2584_double__diff,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat,C5: set_nat] :
% 4.69/4.95 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.95 => ( ( ord_less_eq_set_nat @ B4 @ C5 )
% 4.69/4.95 => ( ( minus_minus_set_nat @ B4 @ ( minus_minus_set_nat @ C5 @ A ) )
% 4.69/4.95 = A ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % double_diff
% 4.69/4.95 thf(fact_2585_Diff__subset,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A @ B4 ) @ A ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_subset
% 4.69/4.95 thf(fact_2586_Diff__mono,axiom,
% 4.69/4.95 ! [A: set_nat,C5: set_nat,D3: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( ord_less_eq_set_nat @ A @ C5 )
% 4.69/4.95 => ( ( ord_less_eq_set_nat @ D3 @ B4 )
% 4.69/4.95 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A @ B4 ) @ ( minus_minus_set_nat @ C5 @ D3 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_mono
% 4.69/4.95 thf(fact_2587_insert__Diff__if,axiom,
% 4.69/4.95 ! [X: produc3658429121746597890et_nat > $o,B4: set_Pr4532377907799695533_nat_o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( ( member6576561426505652726_nat_o @ X @ B4 )
% 4.69/4.95 => ( ( minus_1801376950450012436_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) @ B4 )
% 4.69/4.95 = ( minus_1801376950450012436_nat_o @ A @ B4 ) ) )
% 4.69/4.95 & ( ~ ( member6576561426505652726_nat_o @ X @ B4 )
% 4.69/4.95 => ( ( minus_1801376950450012436_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) @ B4 )
% 4.69/4.95 = ( insert5175938949040314269_nat_o @ X @ ( minus_1801376950450012436_nat_o @ A @ B4 ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % insert_Diff_if
% 4.69/4.95 thf(fact_2588_insert__Diff__if,axiom,
% 4.69/4.95 ! [X: int,B4: set_int,A: set_int] :
% 4.69/4.95 ( ( ( member_int @ X @ B4 )
% 4.69/4.95 => ( ( minus_minus_set_int @ ( insert_int @ X @ A ) @ B4 )
% 4.69/4.95 = ( minus_minus_set_int @ A @ B4 ) ) )
% 4.69/4.95 & ( ~ ( member_int @ X @ B4 )
% 4.69/4.95 => ( ( minus_minus_set_int @ ( insert_int @ X @ A ) @ B4 )
% 4.69/4.95 = ( insert_int @ X @ ( minus_minus_set_int @ A @ B4 ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % insert_Diff_if
% 4.69/4.95 thf(fact_2589_insert__Diff__if,axiom,
% 4.69/4.95 ! [X: $o,B4: set_o,A: set_o] :
% 4.69/4.95 ( ( ( member_o @ X @ B4 )
% 4.69/4.95 => ( ( minus_minus_set_o @ ( insert_o @ X @ A ) @ B4 )
% 4.69/4.95 = ( minus_minus_set_o @ A @ B4 ) ) )
% 4.69/4.95 & ( ~ ( member_o @ X @ B4 )
% 4.69/4.95 => ( ( minus_minus_set_o @ ( insert_o @ X @ A ) @ B4 )
% 4.69/4.95 = ( insert_o @ X @ ( minus_minus_set_o @ A @ B4 ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % insert_Diff_if
% 4.69/4.95 thf(fact_2590_insert__Diff__if,axiom,
% 4.69/4.95 ! [X: product_unit,B4: set_Product_unit,A: set_Product_unit] :
% 4.69/4.95 ( ( ( member_Product_unit @ X @ B4 )
% 4.69/4.95 => ( ( minus_6452836326544984404t_unit @ ( insert_Product_unit @ X @ A ) @ B4 )
% 4.69/4.95 = ( minus_6452836326544984404t_unit @ A @ B4 ) ) )
% 4.69/4.95 & ( ~ ( member_Product_unit @ X @ B4 )
% 4.69/4.95 => ( ( minus_6452836326544984404t_unit @ ( insert_Product_unit @ X @ A ) @ B4 )
% 4.69/4.95 = ( insert_Product_unit @ X @ ( minus_6452836326544984404t_unit @ A @ B4 ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % insert_Diff_if
% 4.69/4.95 thf(fact_2591_insert__Diff__if,axiom,
% 4.69/4.95 ! [X: nat,B4: set_nat,A: set_nat] :
% 4.69/4.95 ( ( ( member_nat @ X @ B4 )
% 4.69/4.95 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A ) @ B4 )
% 4.69/4.95 = ( minus_minus_set_nat @ A @ B4 ) ) )
% 4.69/4.95 & ( ~ ( member_nat @ X @ B4 )
% 4.69/4.95 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A ) @ B4 )
% 4.69/4.95 = ( insert_nat @ X @ ( minus_minus_set_nat @ A @ B4 ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % insert_Diff_if
% 4.69/4.95 thf(fact_2592_Diff__Int__distrib2,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat,C5: set_nat] :
% 4.69/4.95 ( ( inf_inf_set_nat @ ( minus_minus_set_nat @ A @ B4 ) @ C5 )
% 4.69/4.95 = ( minus_minus_set_nat @ ( inf_inf_set_nat @ A @ C5 ) @ ( inf_inf_set_nat @ B4 @ C5 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_Int_distrib2
% 4.69/4.95 thf(fact_2593_Diff__Int__distrib,axiom,
% 4.69/4.95 ! [C5: set_nat,A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( inf_inf_set_nat @ C5 @ ( minus_minus_set_nat @ A @ B4 ) )
% 4.69/4.95 = ( minus_minus_set_nat @ ( inf_inf_set_nat @ C5 @ A ) @ ( inf_inf_set_nat @ C5 @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_Int_distrib
% 4.69/4.95 thf(fact_2594_Diff__Diff__Int,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( minus_minus_set_nat @ A @ ( minus_minus_set_nat @ A @ B4 ) )
% 4.69/4.95 = ( inf_inf_set_nat @ A @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_Diff_Int
% 4.69/4.95 thf(fact_2595_Diff__Int2,axiom,
% 4.69/4.95 ! [A: set_nat,C5: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( minus_minus_set_nat @ ( inf_inf_set_nat @ A @ C5 ) @ ( inf_inf_set_nat @ B4 @ C5 ) )
% 4.69/4.95 = ( minus_minus_set_nat @ ( inf_inf_set_nat @ A @ C5 ) @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_Int2
% 4.69/4.95 thf(fact_2596_Int__Diff,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat,C5: set_nat] :
% 4.69/4.95 ( ( minus_minus_set_nat @ ( inf_inf_set_nat @ A @ B4 ) @ C5 )
% 4.69/4.95 = ( inf_inf_set_nat @ A @ ( minus_minus_set_nat @ B4 @ C5 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Int_Diff
% 4.69/4.95 thf(fact_2597_set__diff__diff__left,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat,C5: set_nat] :
% 4.69/4.95 ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A @ B4 ) @ C5 )
% 4.69/4.95 = ( minus_minus_set_nat @ A @ ( sup_sup_set_nat @ B4 @ C5 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % set_diff_diff_left
% 4.69/4.95 thf(fact_2598_Un__Diff,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat,C5: set_nat] :
% 4.69/4.95 ( ( minus_minus_set_nat @ ( sup_sup_set_nat @ A @ B4 ) @ C5 )
% 4.69/4.95 = ( sup_sup_set_nat @ ( minus_minus_set_nat @ A @ C5 ) @ ( minus_minus_set_nat @ B4 @ C5 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Un_Diff
% 4.69/4.95 thf(fact_2599_vimage__Diff,axiom,
% 4.69/4.95 ! [F: nat > nat,A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( vimage_nat_nat @ F @ ( minus_minus_set_nat @ A @ B4 ) )
% 4.69/4.95 = ( minus_minus_set_nat @ ( vimage_nat_nat @ F @ A ) @ ( vimage_nat_nat @ F @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % vimage_Diff
% 4.69/4.95 thf(fact_2600_rtrancl__converseI,axiom,
% 4.69/4.95 ! [Y: nat,X: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.95 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ X ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.95 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi2905341329935302413cl_nat @ ( converse_nat_nat @ R2 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % rtrancl_converseI
% 4.69/4.95 thf(fact_2601_rtrancl__converseI,axiom,
% 4.69/4.95 ! [Y: int,X: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.95 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y @ X ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.95 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi2902850859426252137cl_int @ ( converse_int_int @ R2 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % rtrancl_converseI
% 4.69/4.95 thf(fact_2602_rtrancl__converseD,axiom,
% 4.69/4.95 ! [X: nat,Y: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.95 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi2905341329935302413cl_nat @ ( converse_nat_nat @ R2 ) ) )
% 4.69/4.95 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ X ) @ ( transi2905341329935302413cl_nat @ R2 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % rtrancl_converseD
% 4.69/4.95 thf(fact_2603_rtrancl__converseD,axiom,
% 4.69/4.95 ! [X: int,Y: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.95 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi2902850859426252137cl_int @ ( converse_int_int @ R2 ) ) )
% 4.69/4.95 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y @ X ) @ ( transi2902850859426252137cl_int @ R2 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % rtrancl_converseD
% 4.69/4.95 thf(fact_2604_trancl__converseI,axiom,
% 4.69/4.95 ! [X: nat,Y: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.95 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( converse_nat_nat @ ( transi6264000038957366511cl_nat @ R2 ) ) )
% 4.69/4.95 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi6264000038957366511cl_nat @ ( converse_nat_nat @ R2 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % trancl_converseI
% 4.69/4.95 thf(fact_2605_trancl__converseI,axiom,
% 4.69/4.95 ! [X: int,Y: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.95 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( converse_int_int @ ( transi6261509568448316235cl_int @ R2 ) ) )
% 4.69/4.95 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi6261509568448316235cl_int @ ( converse_int_int @ R2 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % trancl_converseI
% 4.69/4.95 thf(fact_2606_trancl__converseD,axiom,
% 4.69/4.95 ! [X: nat,Y: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.95 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi6264000038957366511cl_nat @ ( converse_nat_nat @ R2 ) ) )
% 4.69/4.95 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( converse_nat_nat @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % trancl_converseD
% 4.69/4.95 thf(fact_2607_trancl__converseD,axiom,
% 4.69/4.95 ! [X: int,Y: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.95 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi6261509568448316235cl_int @ ( converse_int_int @ R2 ) ) )
% 4.69/4.95 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( converse_int_int @ ( transi6261509568448316235cl_int @ R2 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % trancl_converseD
% 4.69/4.95 thf(fact_2608_diff__shunt__var,axiom,
% 4.69/4.95 ! [X: set_Product_unit,Y: set_Product_unit] :
% 4.69/4.95 ( ( ( minus_6452836326544984404t_unit @ X @ Y )
% 4.69/4.95 = bot_bo3957492148770167129t_unit )
% 4.69/4.95 = ( ord_le3507040750410214029t_unit @ X @ Y ) ) ).
% 4.69/4.95
% 4.69/4.95 % diff_shunt_var
% 4.69/4.95 thf(fact_2609_diff__shunt__var,axiom,
% 4.69/4.95 ! [X: set_o,Y: set_o] :
% 4.69/4.95 ( ( ( minus_minus_set_o @ X @ Y )
% 4.69/4.95 = bot_bot_set_o )
% 4.69/4.95 = ( ord_less_eq_set_o @ X @ Y ) ) ).
% 4.69/4.95
% 4.69/4.95 % diff_shunt_var
% 4.69/4.95 thf(fact_2610_diff__shunt__var,axiom,
% 4.69/4.95 ! [X: set_int,Y: set_int] :
% 4.69/4.95 ( ( ( minus_minus_set_int @ X @ Y )
% 4.69/4.95 = bot_bot_set_int )
% 4.69/4.95 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 4.69/4.95
% 4.69/4.95 % diff_shunt_var
% 4.69/4.95 thf(fact_2611_diff__shunt__var,axiom,
% 4.69/4.95 ! [X: set_Pr4532377907799695533_nat_o,Y: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( ( minus_1801376950450012436_nat_o @ X @ Y )
% 4.69/4.95 = bot_bo7824918357723582233_nat_o )
% 4.69/4.95 = ( ord_le2965882846123202637_nat_o @ X @ Y ) ) ).
% 4.69/4.95
% 4.69/4.95 % diff_shunt_var
% 4.69/4.95 thf(fact_2612_diff__shunt__var,axiom,
% 4.69/4.95 ! [X: assn,Y: assn] :
% 4.69/4.95 ( ( ( minus_minus_assn @ X @ Y )
% 4.69/4.95 = bot_bot_assn )
% 4.69/4.95 = ( ord_less_eq_assn @ X @ Y ) ) ).
% 4.69/4.95
% 4.69/4.95 % diff_shunt_var
% 4.69/4.95 thf(fact_2613_diff__shunt__var,axiom,
% 4.69/4.95 ! [X: set_nat,Y: set_nat] :
% 4.69/4.95 ( ( ( minus_minus_set_nat @ X @ Y )
% 4.69/4.95 = bot_bot_set_nat )
% 4.69/4.95 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 4.69/4.95
% 4.69/4.95 % diff_shunt_var
% 4.69/4.95 thf(fact_2614_in__snd__imageE,axiom,
% 4.69/4.95 ! [Y: nat,S: set_Pr1261947904930325089at_nat] :
% 4.69/4.95 ( ( member_nat @ Y @ ( image_2486076414777270412at_nat @ product_snd_nat_nat @ S ) )
% 4.69/4.95 => ~ ! [X3: nat] :
% 4.69/4.95 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y ) @ S ) ) ).
% 4.69/4.95
% 4.69/4.95 % in_snd_imageE
% 4.69/4.95 thf(fact_2615_in__snd__imageE,axiom,
% 4.69/4.95 ! [Y: produc3658429121746597890et_nat,S: set_Pr3286484037609594932et_nat] :
% 4.69/4.95 ( ( member6260224972018164377et_nat @ Y @ ( image_4390311411407041927et_nat @ produc4011572625026189258et_nat @ S ) )
% 4.69/4.95 => ~ ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.95 ~ ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y ) @ S ) ) ).
% 4.69/4.95
% 4.69/4.95 % in_snd_imageE
% 4.69/4.95 thf(fact_2616_in__snd__imageE,axiom,
% 4.69/4.95 ! [Y: produc3925858234332021118et_nat,S: set_Pr8536935166611901872et_nat] :
% 4.69/4.95 ( ( member1996754912294343701et_nat @ Y @ ( image_4557310310409863807et_nat @ produc5374455773327741254et_nat @ S ) )
% 4.69/4.95 => ~ ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.95 ~ ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y ) @ S ) ) ).
% 4.69/4.95
% 4.69/4.95 % in_snd_imageE
% 4.69/4.95 thf(fact_2617_in__snd__imageE,axiom,
% 4.69/4.95 ! [Y: set_nat,S: set_Pr3948176798113811640et_nat] :
% 4.69/4.95 ( ( member_set_nat @ Y @ ( image_6088997261112373647et_nat @ produc8586169260539613262et_nat @ S ) )
% 4.69/4.95 => ~ ! [X3: heap_e7401611519738050253t_unit] :
% 4.69/4.95 ~ ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X3 @ Y ) @ S ) ) ).
% 4.69/4.95
% 4.69/4.95 % in_snd_imageE
% 4.69/4.95 thf(fact_2618_in__snd__imageE,axiom,
% 4.69/4.95 ! [Y: int,S: set_Pr958786334691620121nt_int] :
% 4.69/4.95 ( ( member_int @ Y @ ( image_5042161079198086560nt_int @ product_snd_int_int @ S ) )
% 4.69/4.95 => ~ ! [X3: int] :
% 4.69/4.95 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y ) @ S ) ) ).
% 4.69/4.95
% 4.69/4.95 % in_snd_imageE
% 4.69/4.95 thf(fact_2619_image__Int__subset,axiom,
% 4.69/4.95 ! [F: code_integer > code_integer,A: set_Code_integer,B4: set_Code_integer] : ( ord_le7084787975880047091nteger @ ( image_4470545334726330049nteger @ F @ ( inf_in1364745209274528805nteger @ A @ B4 ) ) @ ( inf_in1364745209274528805nteger @ ( image_4470545334726330049nteger @ F @ A ) @ ( image_4470545334726330049nteger @ F @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_Int_subset
% 4.69/4.95 thf(fact_2620_image__Int__subset,axiom,
% 4.69/4.95 ! [F: nat > set_nat,A: set_nat,B4: set_nat] : ( ord_le6893508408891458716et_nat @ ( image_nat_set_nat @ F @ ( inf_inf_set_nat @ A @ B4 ) ) @ ( inf_inf_set_set_nat @ ( image_nat_set_nat @ F @ A ) @ ( image_nat_set_nat @ F @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_Int_subset
% 4.69/4.95 thf(fact_2621_image__Int__subset,axiom,
% 4.69/4.95 ! [F: nat > code_integer,A: set_nat,B4: set_nat] : ( ord_le7084787975880047091nteger @ ( image_1215581382706833972nteger @ F @ ( inf_inf_set_nat @ A @ B4 ) ) @ ( inf_in1364745209274528805nteger @ ( image_1215581382706833972nteger @ F @ A ) @ ( image_1215581382706833972nteger @ F @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_Int_subset
% 4.69/4.95 thf(fact_2622_image__Int__subset,axiom,
% 4.69/4.95 ! [F: nat > nat,A: set_nat,B4: set_nat] : ( ord_less_eq_set_nat @ ( image_nat_nat2 @ F @ ( inf_inf_set_nat @ A @ B4 ) ) @ ( inf_inf_set_nat @ ( image_nat_nat2 @ F @ A ) @ ( image_nat_nat2 @ F @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_Int_subset
% 4.69/4.95 thf(fact_2623_subset__minus__empty,axiom,
% 4.69/4.95 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.95 ( ( ord_le3507040750410214029t_unit @ A @ B4 )
% 4.69/4.95 => ( ( minus_6452836326544984404t_unit @ A @ B4 )
% 4.69/4.95 = bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_minus_empty
% 4.69/4.95 thf(fact_2624_subset__minus__empty,axiom,
% 4.69/4.95 ! [A: set_o,B4: set_o] :
% 4.69/4.95 ( ( ord_less_eq_set_o @ A @ B4 )
% 4.69/4.95 => ( ( minus_minus_set_o @ A @ B4 )
% 4.69/4.95 = bot_bot_set_o ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_minus_empty
% 4.69/4.95 thf(fact_2625_subset__minus__empty,axiom,
% 4.69/4.95 ! [A: set_int,B4: set_int] :
% 4.69/4.95 ( ( ord_less_eq_set_int @ A @ B4 )
% 4.69/4.95 => ( ( minus_minus_set_int @ A @ B4 )
% 4.69/4.95 = bot_bot_set_int ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_minus_empty
% 4.69/4.95 thf(fact_2626_subset__minus__empty,axiom,
% 4.69/4.95 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( ord_le2965882846123202637_nat_o @ A @ B4 )
% 4.69/4.95 => ( ( minus_1801376950450012436_nat_o @ A @ B4 )
% 4.69/4.95 = bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_minus_empty
% 4.69/4.95 thf(fact_2627_subset__minus__empty,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.95 => ( ( minus_minus_set_nat @ A @ B4 )
% 4.69/4.95 = bot_bot_set_nat ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_minus_empty
% 4.69/4.95 thf(fact_2628_image__subset__iff__subset__vimage,axiom,
% 4.69/4.95 ! [F: code_integer > code_integer,A: set_Code_integer,B4: set_Code_integer] :
% 4.69/4.95 ( ( ord_le7084787975880047091nteger @ ( image_4470545334726330049nteger @ F @ A ) @ B4 )
% 4.69/4.95 = ( ord_le7084787975880047091nteger @ A @ ( vimage1318793397690208119nteger @ F @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_subset_iff_subset_vimage
% 4.69/4.95 thf(fact_2629_image__subset__iff__subset__vimage,axiom,
% 4.69/4.95 ! [F: nat > set_nat,A: set_nat,B4: set_set_nat] :
% 4.69/4.95 ( ( ord_le6893508408891458716et_nat @ ( image_nat_set_nat @ F @ A ) @ B4 )
% 4.69/4.95 = ( ord_less_eq_set_nat @ A @ ( vimage_nat_set_nat @ F @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_subset_iff_subset_vimage
% 4.69/4.95 thf(fact_2630_image__subset__iff__subset__vimage,axiom,
% 4.69/4.95 ! [F: nat > code_integer,A: set_nat,B4: set_Code_integer] :
% 4.69/4.95 ( ( ord_le7084787975880047091nteger @ ( image_1215581382706833972nteger @ F @ A ) @ B4 )
% 4.69/4.95 = ( ord_less_eq_set_nat @ A @ ( vimage6104394758324456170nteger @ F @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_subset_iff_subset_vimage
% 4.69/4.95 thf(fact_2631_image__subset__iff__subset__vimage,axiom,
% 4.69/4.95 ! [F: nat > nat,A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( ord_less_eq_set_nat @ ( image_nat_nat2 @ F @ A ) @ B4 )
% 4.69/4.95 = ( ord_less_eq_set_nat @ A @ ( vimage_nat_nat @ F @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % image_subset_iff_subset_vimage
% 4.69/4.95 thf(fact_2632_image__vimage__subset,axiom,
% 4.69/4.95 ! [F: nat > set_nat,A: set_set_nat] : ( ord_le6893508408891458716et_nat @ ( image_nat_set_nat @ F @ ( vimage_nat_set_nat @ F @ A ) ) @ A ) ).
% 4.69/4.95
% 4.69/4.95 % image_vimage_subset
% 4.69/4.95 thf(fact_2633_image__vimage__subset,axiom,
% 4.69/4.95 ! [F: code_integer > code_integer,A: set_Code_integer] : ( ord_le7084787975880047091nteger @ ( image_4470545334726330049nteger @ F @ ( vimage1318793397690208119nteger @ F @ A ) ) @ A ) ).
% 4.69/4.95
% 4.69/4.95 % image_vimage_subset
% 4.69/4.95 thf(fact_2634_image__vimage__subset,axiom,
% 4.69/4.95 ! [F: nat > code_integer,A: set_Code_integer] : ( ord_le7084787975880047091nteger @ ( image_1215581382706833972nteger @ F @ ( vimage6104394758324456170nteger @ F @ A ) ) @ A ) ).
% 4.69/4.95
% 4.69/4.95 % image_vimage_subset
% 4.69/4.95 thf(fact_2635_image__vimage__subset,axiom,
% 4.69/4.95 ! [F: nat > nat,A: set_nat] : ( ord_less_eq_set_nat @ ( image_nat_nat2 @ F @ ( vimage_nat_nat @ F @ A ) ) @ A ) ).
% 4.69/4.95
% 4.69/4.95 % image_vimage_subset
% 4.69/4.95 thf(fact_2636_Diff__insert,axiom,
% 4.69/4.95 ! [A: set_Product_unit,A2: product_unit,B4: set_Product_unit] :
% 4.69/4.95 ( ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ A2 @ B4 ) )
% 4.69/4.95 = ( minus_6452836326544984404t_unit @ ( minus_6452836326544984404t_unit @ A @ B4 ) @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_insert
% 4.69/4.95 thf(fact_2637_Diff__insert,axiom,
% 4.69/4.95 ! [A: set_o,A2: $o,B4: set_o] :
% 4.69/4.95 ( ( minus_minus_set_o @ A @ ( insert_o @ A2 @ B4 ) )
% 4.69/4.95 = ( minus_minus_set_o @ ( minus_minus_set_o @ A @ B4 ) @ ( insert_o @ A2 @ bot_bot_set_o ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_insert
% 4.69/4.95 thf(fact_2638_Diff__insert,axiom,
% 4.69/4.95 ! [A: set_int,A2: int,B4: set_int] :
% 4.69/4.95 ( ( minus_minus_set_int @ A @ ( insert_int @ A2 @ B4 ) )
% 4.69/4.95 = ( minus_minus_set_int @ ( minus_minus_set_int @ A @ B4 ) @ ( insert_int @ A2 @ bot_bot_set_int ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_insert
% 4.69/4.95 thf(fact_2639_Diff__insert,axiom,
% 4.69/4.95 ! [A: set_Pr4532377907799695533_nat_o,A2: produc3658429121746597890et_nat > $o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ A2 @ B4 ) )
% 4.69/4.95 = ( minus_1801376950450012436_nat_o @ ( minus_1801376950450012436_nat_o @ A @ B4 ) @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_insert
% 4.69/4.95 thf(fact_2640_Diff__insert,axiom,
% 4.69/4.95 ! [A: set_nat,A2: nat,B4: set_nat] :
% 4.69/4.95 ( ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ B4 ) )
% 4.69/4.95 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A @ B4 ) @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_insert
% 4.69/4.95 thf(fact_2641_insert__Diff,axiom,
% 4.69/4.95 ! [A2: product_unit,A: set_Product_unit] :
% 4.69/4.95 ( ( member_Product_unit @ A2 @ A )
% 4.69/4.95 => ( ( insert_Product_unit @ A2 @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.95 = A ) ) ).
% 4.69/4.95
% 4.69/4.95 % insert_Diff
% 4.69/4.95 thf(fact_2642_insert__Diff,axiom,
% 4.69/4.95 ! [A2: $o,A: set_o] :
% 4.69/4.95 ( ( member_o @ A2 @ A )
% 4.69/4.95 => ( ( insert_o @ A2 @ ( minus_minus_set_o @ A @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 4.69/4.95 = A ) ) ).
% 4.69/4.95
% 4.69/4.95 % insert_Diff
% 4.69/4.95 thf(fact_2643_insert__Diff,axiom,
% 4.69/4.95 ! [A2: int,A: set_int] :
% 4.69/4.95 ( ( member_int @ A2 @ A )
% 4.69/4.95 => ( ( insert_int @ A2 @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 4.69/4.95 = A ) ) ).
% 4.69/4.95
% 4.69/4.95 % insert_Diff
% 4.69/4.95 thf(fact_2644_insert__Diff,axiom,
% 4.69/4.95 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( member6576561426505652726_nat_o @ A2 @ A )
% 4.69/4.95 => ( ( insert5175938949040314269_nat_o @ A2 @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/4.95 = A ) ) ).
% 4.69/4.95
% 4.69/4.95 % insert_Diff
% 4.69/4.95 thf(fact_2645_insert__Diff,axiom,
% 4.69/4.95 ! [A2: nat,A: set_nat] :
% 4.69/4.95 ( ( member_nat @ A2 @ A )
% 4.69/4.95 => ( ( insert_nat @ A2 @ ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 4.69/4.95 = A ) ) ).
% 4.69/4.95
% 4.69/4.95 % insert_Diff
% 4.69/4.95 thf(fact_2646_Diff__insert2,axiom,
% 4.69/4.95 ! [A: set_Product_unit,A2: product_unit,B4: set_Product_unit] :
% 4.69/4.95 ( ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ A2 @ B4 ) )
% 4.69/4.95 = ( minus_6452836326544984404t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_insert2
% 4.69/4.95 thf(fact_2647_Diff__insert2,axiom,
% 4.69/4.95 ! [A: set_o,A2: $o,B4: set_o] :
% 4.69/4.95 ( ( minus_minus_set_o @ A @ ( insert_o @ A2 @ B4 ) )
% 4.69/4.95 = ( minus_minus_set_o @ ( minus_minus_set_o @ A @ ( insert_o @ A2 @ bot_bot_set_o ) ) @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_insert2
% 4.69/4.95 thf(fact_2648_Diff__insert2,axiom,
% 4.69/4.95 ! [A: set_int,A2: int,B4: set_int] :
% 4.69/4.95 ( ( minus_minus_set_int @ A @ ( insert_int @ A2 @ B4 ) )
% 4.69/4.95 = ( minus_minus_set_int @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ bot_bot_set_int ) ) @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_insert2
% 4.69/4.95 thf(fact_2649_Diff__insert2,axiom,
% 4.69/4.95 ! [A: set_Pr4532377907799695533_nat_o,A2: produc3658429121746597890et_nat > $o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ A2 @ B4 ) )
% 4.69/4.95 = ( minus_1801376950450012436_nat_o @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_insert2
% 4.69/4.95 thf(fact_2650_Diff__insert2,axiom,
% 4.69/4.95 ! [A: set_nat,A2: nat,B4: set_nat] :
% 4.69/4.95 ( ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ B4 ) )
% 4.69/4.95 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) @ B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_insert2
% 4.69/4.95 thf(fact_2651_insert__minus__eq,axiom,
% 4.69/4.95 ! [X: product_unit,Y: product_unit,A: set_Product_unit] :
% 4.69/4.95 ( ( X != Y )
% 4.69/4.95 => ( ( minus_6452836326544984404t_unit @ ( insert_Product_unit @ X @ A ) @ ( insert_Product_unit @ Y @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.95 = ( insert_Product_unit @ X @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ Y @ bot_bo3957492148770167129t_unit ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % insert_minus_eq
% 4.69/4.95 thf(fact_2652_insert__minus__eq,axiom,
% 4.69/4.95 ! [X: $o,Y: $o,A: set_o] :
% 4.69/4.95 ( ( X != Y )
% 4.69/4.95 => ( ( minus_minus_set_o @ ( insert_o @ X @ A ) @ ( insert_o @ Y @ bot_bot_set_o ) )
% 4.69/4.95 = ( insert_o @ X @ ( minus_minus_set_o @ A @ ( insert_o @ Y @ bot_bot_set_o ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % insert_minus_eq
% 4.69/4.95 thf(fact_2653_insert__minus__eq,axiom,
% 4.69/4.95 ! [X: int,Y: int,A: set_int] :
% 4.69/4.95 ( ( X != Y )
% 4.69/4.95 => ( ( minus_minus_set_int @ ( insert_int @ X @ A ) @ ( insert_int @ Y @ bot_bot_set_int ) )
% 4.69/4.95 = ( insert_int @ X @ ( minus_minus_set_int @ A @ ( insert_int @ Y @ bot_bot_set_int ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % insert_minus_eq
% 4.69/4.95 thf(fact_2654_insert__minus__eq,axiom,
% 4.69/4.95 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( X != Y )
% 4.69/4.95 => ( ( minus_1801376950450012436_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) @ ( insert5175938949040314269_nat_o @ Y @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.95 = ( insert5175938949040314269_nat_o @ X @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ Y @ bot_bo7824918357723582233_nat_o ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % insert_minus_eq
% 4.69/4.95 thf(fact_2655_insert__minus__eq,axiom,
% 4.69/4.95 ! [X: nat,Y: nat,A: set_nat] :
% 4.69/4.95 ( ( X != Y )
% 4.69/4.95 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A ) @ ( insert_nat @ Y @ bot_bot_set_nat ) )
% 4.69/4.95 = ( insert_nat @ X @ ( minus_minus_set_nat @ A @ ( insert_nat @ Y @ bot_bot_set_nat ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % insert_minus_eq
% 4.69/4.95 thf(fact_2656_Diff__insert__absorb,axiom,
% 4.69/4.95 ! [X: product_unit,A: set_Product_unit] :
% 4.69/4.95 ( ~ ( member_Product_unit @ X @ A )
% 4.69/4.95 => ( ( minus_6452836326544984404t_unit @ ( insert_Product_unit @ X @ A ) @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.95 = A ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_insert_absorb
% 4.69/4.95 thf(fact_2657_Diff__insert__absorb,axiom,
% 4.69/4.95 ! [X: $o,A: set_o] :
% 4.69/4.95 ( ~ ( member_o @ X @ A )
% 4.69/4.95 => ( ( minus_minus_set_o @ ( insert_o @ X @ A ) @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.95 = A ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_insert_absorb
% 4.69/4.95 thf(fact_2658_Diff__insert__absorb,axiom,
% 4.69/4.95 ! [X: int,A: set_int] :
% 4.69/4.95 ( ~ ( member_int @ X @ A )
% 4.69/4.95 => ( ( minus_minus_set_int @ ( insert_int @ X @ A ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.95 = A ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_insert_absorb
% 4.69/4.95 thf(fact_2659_Diff__insert__absorb,axiom,
% 4.69/4.95 ! [X: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ~ ( member6576561426505652726_nat_o @ X @ A )
% 4.69/4.95 => ( ( minus_1801376950450012436_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.95 = A ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_insert_absorb
% 4.69/4.95 thf(fact_2660_Diff__insert__absorb,axiom,
% 4.69/4.95 ! [X: nat,A: set_nat] :
% 4.69/4.95 ( ~ ( member_nat @ X @ A )
% 4.69/4.95 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.95 = A ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_insert_absorb
% 4.69/4.95 thf(fact_2661_set__minus__singleton__eq,axiom,
% 4.69/4.95 ! [X: product_unit,X4: set_Product_unit] :
% 4.69/4.95 ( ~ ( member_Product_unit @ X @ X4 )
% 4.69/4.95 => ( ( minus_6452836326544984404t_unit @ X4 @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.95 = X4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % set_minus_singleton_eq
% 4.69/4.95 thf(fact_2662_set__minus__singleton__eq,axiom,
% 4.69/4.95 ! [X: $o,X4: set_o] :
% 4.69/4.95 ( ~ ( member_o @ X @ X4 )
% 4.69/4.95 => ( ( minus_minus_set_o @ X4 @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.95 = X4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % set_minus_singleton_eq
% 4.69/4.95 thf(fact_2663_set__minus__singleton__eq,axiom,
% 4.69/4.95 ! [X: int,X4: set_int] :
% 4.69/4.95 ( ~ ( member_int @ X @ X4 )
% 4.69/4.95 => ( ( minus_minus_set_int @ X4 @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.95 = X4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % set_minus_singleton_eq
% 4.69/4.95 thf(fact_2664_set__minus__singleton__eq,axiom,
% 4.69/4.95 ! [X: produc3658429121746597890et_nat > $o,X4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ~ ( member6576561426505652726_nat_o @ X @ X4 )
% 4.69/4.95 => ( ( minus_1801376950450012436_nat_o @ X4 @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.95 = X4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % set_minus_singleton_eq
% 4.69/4.95 thf(fact_2665_set__minus__singleton__eq,axiom,
% 4.69/4.95 ! [X: nat,X4: set_nat] :
% 4.69/4.95 ( ~ ( member_nat @ X @ X4 )
% 4.69/4.95 => ( ( minus_minus_set_nat @ X4 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.95 = X4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % set_minus_singleton_eq
% 4.69/4.95 thf(fact_2666_subset__Diff__insert,axiom,
% 4.69/4.95 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,C5: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( ord_le2965882846123202637_nat_o @ A @ ( minus_1801376950450012436_nat_o @ B4 @ ( insert5175938949040314269_nat_o @ X @ C5 ) ) )
% 4.69/4.95 = ( ( ord_le2965882846123202637_nat_o @ A @ ( minus_1801376950450012436_nat_o @ B4 @ C5 ) )
% 4.69/4.95 & ~ ( member6576561426505652726_nat_o @ X @ A ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_Diff_insert
% 4.69/4.95 thf(fact_2667_subset__Diff__insert,axiom,
% 4.69/4.95 ! [A: set_int,B4: set_int,X: int,C5: set_int] :
% 4.69/4.95 ( ( ord_less_eq_set_int @ A @ ( minus_minus_set_int @ B4 @ ( insert_int @ X @ C5 ) ) )
% 4.69/4.95 = ( ( ord_less_eq_set_int @ A @ ( minus_minus_set_int @ B4 @ C5 ) )
% 4.69/4.95 & ~ ( member_int @ X @ A ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_Diff_insert
% 4.69/4.95 thf(fact_2668_subset__Diff__insert,axiom,
% 4.69/4.95 ! [A: set_o,B4: set_o,X: $o,C5: set_o] :
% 4.69/4.95 ( ( ord_less_eq_set_o @ A @ ( minus_minus_set_o @ B4 @ ( insert_o @ X @ C5 ) ) )
% 4.69/4.95 = ( ( ord_less_eq_set_o @ A @ ( minus_minus_set_o @ B4 @ C5 ) )
% 4.69/4.95 & ~ ( member_o @ X @ A ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_Diff_insert
% 4.69/4.95 thf(fact_2669_subset__Diff__insert,axiom,
% 4.69/4.95 ! [A: set_Product_unit,B4: set_Product_unit,X: product_unit,C5: set_Product_unit] :
% 4.69/4.95 ( ( ord_le3507040750410214029t_unit @ A @ ( minus_6452836326544984404t_unit @ B4 @ ( insert_Product_unit @ X @ C5 ) ) )
% 4.69/4.95 = ( ( ord_le3507040750410214029t_unit @ A @ ( minus_6452836326544984404t_unit @ B4 @ C5 ) )
% 4.69/4.95 & ~ ( member_Product_unit @ X @ A ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_Diff_insert
% 4.69/4.95 thf(fact_2670_subset__Diff__insert,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat,X: nat,C5: set_nat] :
% 4.69/4.95 ( ( ord_less_eq_set_nat @ A @ ( minus_minus_set_nat @ B4 @ ( insert_nat @ X @ C5 ) ) )
% 4.69/4.95 = ( ( ord_less_eq_set_nat @ A @ ( minus_minus_set_nat @ B4 @ C5 ) )
% 4.69/4.95 & ~ ( member_nat @ X @ A ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_Diff_insert
% 4.69/4.95 thf(fact_2671_Diff__triv,axiom,
% 4.69/4.95 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.95 ( ( ( inf_in4660618365625256667t_unit @ A @ B4 )
% 4.69/4.95 = bot_bo3957492148770167129t_unit )
% 4.69/4.95 => ( ( minus_6452836326544984404t_unit @ A @ B4 )
% 4.69/4.95 = A ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_triv
% 4.69/4.95 thf(fact_2672_Diff__triv,axiom,
% 4.69/4.95 ! [A: set_o,B4: set_o] :
% 4.69/4.95 ( ( ( inf_inf_set_o @ A @ B4 )
% 4.69/4.95 = bot_bot_set_o )
% 4.69/4.95 => ( ( minus_minus_set_o @ A @ B4 )
% 4.69/4.95 = A ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_triv
% 4.69/4.95 thf(fact_2673_Diff__triv,axiom,
% 4.69/4.95 ! [A: set_int,B4: set_int] :
% 4.69/4.95 ( ( ( inf_inf_set_int @ A @ B4 )
% 4.69/4.95 = bot_bot_set_int )
% 4.69/4.95 => ( ( minus_minus_set_int @ A @ B4 )
% 4.69/4.95 = A ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_triv
% 4.69/4.95 thf(fact_2674_Diff__triv,axiom,
% 4.69/4.95 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( ( inf_in1906310914598751387_nat_o @ A @ B4 )
% 4.69/4.95 = bot_bo7824918357723582233_nat_o )
% 4.69/4.95 => ( ( minus_1801376950450012436_nat_o @ A @ B4 )
% 4.69/4.95 = A ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_triv
% 4.69/4.95 thf(fact_2675_Diff__triv,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( ( inf_inf_set_nat @ A @ B4 )
% 4.69/4.95 = bot_bot_set_nat )
% 4.69/4.95 => ( ( minus_minus_set_nat @ A @ B4 )
% 4.69/4.95 = A ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_triv
% 4.69/4.95 thf(fact_2676_Int__Diff__disjoint,axiom,
% 4.69/4.95 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.95 ( ( inf_in4660618365625256667t_unit @ ( inf_in4660618365625256667t_unit @ A @ B4 ) @ ( minus_6452836326544984404t_unit @ A @ B4 ) )
% 4.69/4.95 = bot_bo3957492148770167129t_unit ) ).
% 4.69/4.95
% 4.69/4.95 % Int_Diff_disjoint
% 4.69/4.95 thf(fact_2677_Int__Diff__disjoint,axiom,
% 4.69/4.95 ! [A: set_o,B4: set_o] :
% 4.69/4.95 ( ( inf_inf_set_o @ ( inf_inf_set_o @ A @ B4 ) @ ( minus_minus_set_o @ A @ B4 ) )
% 4.69/4.95 = bot_bot_set_o ) ).
% 4.69/4.95
% 4.69/4.95 % Int_Diff_disjoint
% 4.69/4.95 thf(fact_2678_Int__Diff__disjoint,axiom,
% 4.69/4.95 ! [A: set_int,B4: set_int] :
% 4.69/4.95 ( ( inf_inf_set_int @ ( inf_inf_set_int @ A @ B4 ) @ ( minus_minus_set_int @ A @ B4 ) )
% 4.69/4.95 = bot_bot_set_int ) ).
% 4.69/4.95
% 4.69/4.95 % Int_Diff_disjoint
% 4.69/4.95 thf(fact_2679_Int__Diff__disjoint,axiom,
% 4.69/4.95 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( inf_in1906310914598751387_nat_o @ ( inf_in1906310914598751387_nat_o @ A @ B4 ) @ ( minus_1801376950450012436_nat_o @ A @ B4 ) )
% 4.69/4.95 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/4.95
% 4.69/4.95 % Int_Diff_disjoint
% 4.69/4.95 thf(fact_2680_Int__Diff__disjoint,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A @ B4 ) @ ( minus_minus_set_nat @ A @ B4 ) )
% 4.69/4.95 = bot_bot_set_nat ) ).
% 4.69/4.95
% 4.69/4.95 % Int_Diff_disjoint
% 4.69/4.95 thf(fact_2681_disjoint__alt__simp1,axiom,
% 4.69/4.95 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.95 ( ( ( minus_6452836326544984404t_unit @ A @ B4 )
% 4.69/4.95 = A )
% 4.69/4.95 = ( ( inf_in4660618365625256667t_unit @ A @ B4 )
% 4.69/4.95 = bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.95
% 4.69/4.95 % disjoint_alt_simp1
% 4.69/4.95 thf(fact_2682_disjoint__alt__simp1,axiom,
% 4.69/4.95 ! [A: set_o,B4: set_o] :
% 4.69/4.95 ( ( ( minus_minus_set_o @ A @ B4 )
% 4.69/4.95 = A )
% 4.69/4.95 = ( ( inf_inf_set_o @ A @ B4 )
% 4.69/4.95 = bot_bot_set_o ) ) ).
% 4.69/4.95
% 4.69/4.95 % disjoint_alt_simp1
% 4.69/4.95 thf(fact_2683_disjoint__alt__simp1,axiom,
% 4.69/4.95 ! [A: set_int,B4: set_int] :
% 4.69/4.95 ( ( ( minus_minus_set_int @ A @ B4 )
% 4.69/4.95 = A )
% 4.69/4.95 = ( ( inf_inf_set_int @ A @ B4 )
% 4.69/4.95 = bot_bot_set_int ) ) ).
% 4.69/4.95
% 4.69/4.95 % disjoint_alt_simp1
% 4.69/4.95 thf(fact_2684_disjoint__alt__simp1,axiom,
% 4.69/4.95 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( ( minus_1801376950450012436_nat_o @ A @ B4 )
% 4.69/4.95 = A )
% 4.69/4.95 = ( ( inf_in1906310914598751387_nat_o @ A @ B4 )
% 4.69/4.95 = bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.95
% 4.69/4.95 % disjoint_alt_simp1
% 4.69/4.95 thf(fact_2685_disjoint__alt__simp1,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( ( minus_minus_set_nat @ A @ B4 )
% 4.69/4.95 = A )
% 4.69/4.95 = ( ( inf_inf_set_nat @ A @ B4 )
% 4.69/4.95 = bot_bot_set_nat ) ) ).
% 4.69/4.95
% 4.69/4.95 % disjoint_alt_simp1
% 4.69/4.95 thf(fact_2686_disjoint__alt__simp2,axiom,
% 4.69/4.95 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.95 ( ( ( minus_6452836326544984404t_unit @ A @ B4 )
% 4.69/4.95 != A )
% 4.69/4.95 = ( ( inf_in4660618365625256667t_unit @ A @ B4 )
% 4.69/4.95 != bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.95
% 4.69/4.95 % disjoint_alt_simp2
% 4.69/4.95 thf(fact_2687_disjoint__alt__simp2,axiom,
% 4.69/4.95 ! [A: set_o,B4: set_o] :
% 4.69/4.95 ( ( ( minus_minus_set_o @ A @ B4 )
% 4.69/4.95 != A )
% 4.69/4.95 = ( ( inf_inf_set_o @ A @ B4 )
% 4.69/4.95 != bot_bot_set_o ) ) ).
% 4.69/4.95
% 4.69/4.95 % disjoint_alt_simp2
% 4.69/4.95 thf(fact_2688_disjoint__alt__simp2,axiom,
% 4.69/4.95 ! [A: set_int,B4: set_int] :
% 4.69/4.95 ( ( ( minus_minus_set_int @ A @ B4 )
% 4.69/4.95 != A )
% 4.69/4.95 = ( ( inf_inf_set_int @ A @ B4 )
% 4.69/4.95 != bot_bot_set_int ) ) ).
% 4.69/4.95
% 4.69/4.95 % disjoint_alt_simp2
% 4.69/4.95 thf(fact_2689_disjoint__alt__simp2,axiom,
% 4.69/4.95 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( ( minus_1801376950450012436_nat_o @ A @ B4 )
% 4.69/4.95 != A )
% 4.69/4.95 = ( ( inf_in1906310914598751387_nat_o @ A @ B4 )
% 4.69/4.95 != bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.95
% 4.69/4.95 % disjoint_alt_simp2
% 4.69/4.95 thf(fact_2690_disjoint__alt__simp2,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( ( minus_minus_set_nat @ A @ B4 )
% 4.69/4.95 != A )
% 4.69/4.95 = ( ( inf_inf_set_nat @ A @ B4 )
% 4.69/4.95 != bot_bot_set_nat ) ) ).
% 4.69/4.95
% 4.69/4.95 % disjoint_alt_simp2
% 4.69/4.95 thf(fact_2691_Diff__subset__conv,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat,C5: set_nat] :
% 4.69/4.95 ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A @ B4 ) @ C5 )
% 4.69/4.95 = ( ord_less_eq_set_nat @ A @ ( sup_sup_set_nat @ B4 @ C5 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_subset_conv
% 4.69/4.95 thf(fact_2692_Diff__partition,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.95 => ( ( sup_sup_set_nat @ A @ ( minus_minus_set_nat @ B4 @ A ) )
% 4.69/4.95 = B4 ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_partition
% 4.69/4.95 thf(fact_2693_Un__Diff__Int,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( sup_sup_set_nat @ ( minus_minus_set_nat @ A @ B4 ) @ ( inf_inf_set_nat @ A @ B4 ) )
% 4.69/4.95 = A ) ).
% 4.69/4.95
% 4.69/4.95 % Un_Diff_Int
% 4.69/4.95 thf(fact_2694_Int__Diff__Un,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat] :
% 4.69/4.95 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ A @ B4 ) @ ( minus_minus_set_nat @ A @ B4 ) )
% 4.69/4.95 = A ) ).
% 4.69/4.95
% 4.69/4.95 % Int_Diff_Un
% 4.69/4.95 thf(fact_2695_Diff__Int,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat,C5: set_nat] :
% 4.69/4.95 ( ( minus_minus_set_nat @ A @ ( inf_inf_set_nat @ B4 @ C5 ) )
% 4.69/4.95 = ( sup_sup_set_nat @ ( minus_minus_set_nat @ A @ B4 ) @ ( minus_minus_set_nat @ A @ C5 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_Int
% 4.69/4.95 thf(fact_2696_Diff__Un,axiom,
% 4.69/4.95 ! [A: set_nat,B4: set_nat,C5: set_nat] :
% 4.69/4.95 ( ( minus_minus_set_nat @ A @ ( sup_sup_set_nat @ B4 @ C5 ) )
% 4.69/4.95 = ( inf_inf_set_nat @ ( minus_minus_set_nat @ A @ B4 ) @ ( minus_minus_set_nat @ A @ C5 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_Un
% 4.69/4.95 thf(fact_2697_Range__snd,axiom,
% 4.69/4.95 ( range_9132311542094983838et_nat
% 4.69/4.95 = ( image_6088997261112373647et_nat @ produc8586169260539613262et_nat ) ) ).
% 4.69/4.95
% 4.69/4.95 % Range_snd
% 4.69/4.95 thf(fact_2698_Range__snd,axiom,
% 4.69/4.95 ( range_int_int
% 4.69/4.95 = ( image_5042161079198086560nt_int @ product_snd_int_int ) ) ).
% 4.69/4.95
% 4.69/4.95 % Range_snd
% 4.69/4.95 thf(fact_2699_snd__eq__Range,axiom,
% 4.69/4.95 ! [R3: set_Pr3948176798113811640et_nat] :
% 4.69/4.95 ( ( image_6088997261112373647et_nat @ produc8586169260539613262et_nat @ R3 )
% 4.69/4.95 = ( range_9132311542094983838et_nat @ R3 ) ) ).
% 4.69/4.95
% 4.69/4.95 % snd_eq_Range
% 4.69/4.95 thf(fact_2700_snd__eq__Range,axiom,
% 4.69/4.95 ! [R3: set_Pr958786334691620121nt_int] :
% 4.69/4.95 ( ( image_5042161079198086560nt_int @ product_snd_int_int @ R3 )
% 4.69/4.95 = ( range_int_int @ R3 ) ) ).
% 4.69/4.95
% 4.69/4.95 % snd_eq_Range
% 4.69/4.95 thf(fact_2701_the__elem__image__unique,axiom,
% 4.69/4.95 ! [A: set_Code_integer,F: code_integer > code_integer,X: code_integer] :
% 4.69/4.95 ( ( A != bot_bo3990330152332043303nteger )
% 4.69/4.95 => ( ! [Y2: code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ Y2 @ A )
% 4.69/4.95 => ( ( F @ Y2 )
% 4.69/4.95 = ( F @ X ) ) )
% 4.69/4.95 => ( ( the_el4656377885804969768nteger @ ( image_4470545334726330049nteger @ F @ A ) )
% 4.69/4.95 = ( F @ X ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % the_elem_image_unique
% 4.69/4.95 thf(fact_2702_the__elem__image__unique,axiom,
% 4.69/4.95 ! [A: set_nat,F: nat > set_nat,X: nat] :
% 4.69/4.95 ( ( A != bot_bot_set_nat )
% 4.69/4.95 => ( ! [Y2: nat] :
% 4.69/4.95 ( ( member_nat @ Y2 @ A )
% 4.69/4.95 => ( ( F @ Y2 )
% 4.69/4.95 = ( F @ X ) ) )
% 4.69/4.95 => ( ( the_elem_set_nat @ ( image_nat_set_nat @ F @ A ) )
% 4.69/4.95 = ( F @ X ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % the_elem_image_unique
% 4.69/4.95 thf(fact_2703_the__elem__image__unique,axiom,
% 4.69/4.95 ! [A: set_nat,F: nat > nat,X: nat] :
% 4.69/4.95 ( ( A != bot_bot_set_nat )
% 4.69/4.95 => ( ! [Y2: nat] :
% 4.69/4.95 ( ( member_nat @ Y2 @ A )
% 4.69/4.95 => ( ( F @ Y2 )
% 4.69/4.95 = ( F @ X ) ) )
% 4.69/4.95 => ( ( the_elem_nat @ ( image_nat_nat2 @ F @ A ) )
% 4.69/4.95 = ( F @ X ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % the_elem_image_unique
% 4.69/4.95 thf(fact_2704_the__elem__image__unique,axiom,
% 4.69/4.95 ! [A: set_nat,F: nat > code_integer,X: nat] :
% 4.69/4.95 ( ( A != bot_bot_set_nat )
% 4.69/4.95 => ( ! [Y2: nat] :
% 4.69/4.95 ( ( member_nat @ Y2 @ A )
% 4.69/4.95 => ( ( F @ Y2 )
% 4.69/4.95 = ( F @ X ) ) )
% 4.69/4.95 => ( ( the_el4656377885804969768nteger @ ( image_1215581382706833972nteger @ F @ A ) )
% 4.69/4.95 = ( F @ X ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % the_elem_image_unique
% 4.69/4.95 thf(fact_2705_cyclicE,axiom,
% 4.69/4.95 ! [G: set_Pr1261947904930325089at_nat] :
% 4.69/4.95 ( ~ ( transi3139058337892597825ic_nat @ G )
% 4.69/4.95 => ~ ! [X3: nat] :
% 4.69/4.95 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ X3 ) @ ( transi6264000038957366511cl_nat @ G ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % cyclicE
% 4.69/4.95 thf(fact_2706_cyclicE,axiom,
% 4.69/4.95 ! [G: set_Pr958786334691620121nt_int] :
% 4.69/4.95 ( ~ ( transi3136567867383547549ic_int @ G )
% 4.69/4.95 => ~ ! [X3: int] :
% 4.69/4.95 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ X3 ) @ ( transi6261509568448316235cl_int @ G ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % cyclicE
% 4.69/4.95 thf(fact_2707_acyclic__def,axiom,
% 4.69/4.95 ( transi3139058337892597825ic_nat
% 4.69/4.95 = ( ^ [R4: set_Pr1261947904930325089at_nat] :
% 4.69/4.95 ! [X2: nat] :
% 4.69/4.95 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ X2 ) @ ( transi6264000038957366511cl_nat @ R4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % acyclic_def
% 4.69/4.95 thf(fact_2708_acyclic__def,axiom,
% 4.69/4.95 ( transi3136567867383547549ic_int
% 4.69/4.95 = ( ^ [R4: set_Pr958786334691620121nt_int] :
% 4.69/4.95 ! [X2: int] :
% 4.69/4.95 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ X2 ) @ ( transi6261509568448316235cl_int @ R4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % acyclic_def
% 4.69/4.95 thf(fact_2709_acyclicI,axiom,
% 4.69/4.95 ! [R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.95 ( ! [X3: nat] :
% 4.69/4.95 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ X3 ) @ ( transi6264000038957366511cl_nat @ R2 ) )
% 4.69/4.95 => ( transi3139058337892597825ic_nat @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % acyclicI
% 4.69/4.95 thf(fact_2710_acyclicI,axiom,
% 4.69/4.95 ! [R2: set_Pr958786334691620121nt_int] :
% 4.69/4.95 ( ! [X3: int] :
% 4.69/4.95 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ X3 ) @ ( transi6261509568448316235cl_int @ R2 ) )
% 4.69/4.95 => ( transi3136567867383547549ic_int @ R2 ) ) ).
% 4.69/4.95
% 4.69/4.95 % acyclicI
% 4.69/4.95 thf(fact_2711_snd__image__mp,axiom,
% 4.69/4.95 ! [A: set_Pr3286484037609594932et_nat,B4: set_Pr3948176798113811640et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 4.69/4.95 ( ( ord_le8090042543978450200et_nat @ ( image_4390311411407041927et_nat @ produc4011572625026189258et_nat @ A ) @ B4 )
% 4.69/4.95 => ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) @ A )
% 4.69/4.95 => ( member6260224972018164377et_nat @ Y @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % snd_image_mp
% 4.69/4.95 thf(fact_2712_snd__image__mp,axiom,
% 4.69/4.95 ! [A: set_Pr8536935166611901872et_nat,B4: set_Pr3286484037609594932et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 4.69/4.95 ( ( ord_le5966269811547037844et_nat @ ( image_4557310310409863807et_nat @ produc5374455773327741254et_nat @ A ) @ B4 )
% 4.69/4.95 => ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) @ A )
% 4.69/4.95 => ( member1996754912294343701et_nat @ Y @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % snd_image_mp
% 4.69/4.95 thf(fact_2713_snd__image__mp,axiom,
% 4.69/4.95 ! [A: set_Pr3948176798113811640et_nat,B4: set_set_nat,X: heap_e7401611519738050253t_unit,Y: set_nat] :
% 4.69/4.95 ( ( ord_le6893508408891458716et_nat @ ( image_6088997261112373647et_nat @ produc8586169260539613262et_nat @ A ) @ B4 )
% 4.69/4.95 => ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X @ Y ) @ A )
% 4.69/4.95 => ( member_set_nat @ Y @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % snd_image_mp
% 4.69/4.95 thf(fact_2714_snd__image__mp,axiom,
% 4.69/4.95 ! [A: set_Pr958786334691620121nt_int,B4: set_int,X: int,Y: int] :
% 4.69/4.95 ( ( ord_less_eq_set_int @ ( image_5042161079198086560nt_int @ product_snd_int_int @ A ) @ B4 )
% 4.69/4.95 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ A )
% 4.69/4.95 => ( member_int @ Y @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % snd_image_mp
% 4.69/4.95 thf(fact_2715_snd__image__mp,axiom,
% 4.69/4.95 ! [A: set_Pr1261947904930325089at_nat,B4: set_nat,X: nat,Y: nat] :
% 4.69/4.95 ( ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ product_snd_nat_nat @ A ) @ B4 )
% 4.69/4.95 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ A )
% 4.69/4.95 => ( member_nat @ Y @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % snd_image_mp
% 4.69/4.95 thf(fact_2716_snd__in__Field,axiom,
% 4.69/4.95 ! [R3: set_Pr958786334691620121nt_int] : ( ord_less_eq_set_int @ ( image_5042161079198086560nt_int @ product_snd_int_int @ R3 ) @ ( field_int @ R3 ) ) ).
% 4.69/4.95
% 4.69/4.95 % snd_in_Field
% 4.69/4.95 thf(fact_2717_snd__in__Field,axiom,
% 4.69/4.95 ! [R3: set_Pr1261947904930325089at_nat] : ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ product_snd_nat_nat @ R3 ) @ ( field_nat @ R3 ) ) ).
% 4.69/4.95
% 4.69/4.95 % snd_in_Field
% 4.69/4.95 thf(fact_2718_Image__subset__snd__image,axiom,
% 4.69/4.95 ! [A: set_Pr3948176798113811640et_nat,B4: set_he8644174446132254637t_unit] : ( ord_le6893508408891458716et_nat @ ( image_3942343239045813184et_nat @ A @ B4 ) @ ( image_6088997261112373647et_nat @ produc8586169260539613262et_nat @ A ) ) ).
% 4.69/4.95
% 4.69/4.95 % Image_subset_snd_image
% 4.69/4.95 thf(fact_2719_Image__subset__snd__image,axiom,
% 4.69/4.95 ! [A: set_Pr958786334691620121nt_int,B4: set_int] : ( ord_less_eq_set_int @ ( image_int_int @ A @ B4 ) @ ( image_5042161079198086560nt_int @ product_snd_int_int @ A ) ) ).
% 4.69/4.95
% 4.69/4.95 % Image_subset_snd_image
% 4.69/4.95 thf(fact_2720_infinite__remove,axiom,
% 4.69/4.95 ! [S: set_Code_integer,A2: code_integer] :
% 4.69/4.95 ( ~ ( finite6017078050557962740nteger @ S )
% 4.69/4.95 => ~ ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ S @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % infinite_remove
% 4.69/4.95 thf(fact_2721_infinite__remove,axiom,
% 4.69/4.95 ! [S: set_Product_unit,A2: product_unit] :
% 4.69/4.95 ( ~ ( finite4290736615968046902t_unit @ S )
% 4.69/4.95 => ~ ( finite4290736615968046902t_unit @ ( minus_6452836326544984404t_unit @ S @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % infinite_remove
% 4.69/4.95 thf(fact_2722_infinite__remove,axiom,
% 4.69/4.95 ! [S: set_o,A2: $o] :
% 4.69/4.95 ( ~ ( finite_finite_o @ S )
% 4.69/4.95 => ~ ( finite_finite_o @ ( minus_minus_set_o @ S @ ( insert_o @ A2 @ bot_bot_set_o ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % infinite_remove
% 4.69/4.95 thf(fact_2723_infinite__remove,axiom,
% 4.69/4.95 ! [S: set_int,A2: int] :
% 4.69/4.95 ( ~ ( finite_finite_int @ S )
% 4.69/4.95 => ~ ( finite_finite_int @ ( minus_minus_set_int @ S @ ( insert_int @ A2 @ bot_bot_set_int ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % infinite_remove
% 4.69/4.95 thf(fact_2724_infinite__remove,axiom,
% 4.69/4.95 ! [S: set_Pr4532377907799695533_nat_o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/4.95 ( ~ ( finite3252695134891459830_nat_o @ S )
% 4.69/4.95 => ~ ( finite3252695134891459830_nat_o @ ( minus_1801376950450012436_nat_o @ S @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % infinite_remove
% 4.69/4.95 thf(fact_2725_infinite__remove,axiom,
% 4.69/4.95 ! [S: set_nat,A2: nat] :
% 4.69/4.95 ( ~ ( finite_finite_nat @ S )
% 4.69/4.95 => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % infinite_remove
% 4.69/4.95 thf(fact_2726_infinite__coinduct,axiom,
% 4.69/4.95 ! [X4: set_Code_integer > $o,A: set_Code_integer] :
% 4.69/4.95 ( ( X4 @ A )
% 4.69/4.95 => ( ! [A9: set_Code_integer] :
% 4.69/4.95 ( ( X4 @ A9 )
% 4.69/4.95 => ? [X6: code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ X6 @ A9 )
% 4.69/4.95 & ( ( X4 @ ( minus_2355218937544613996nteger @ A9 @ ( insert_Code_integer @ X6 @ bot_bo3990330152332043303nteger ) ) )
% 4.69/4.95 | ~ ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ A9 @ ( insert_Code_integer @ X6 @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 4.69/4.95 => ~ ( finite6017078050557962740nteger @ A ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % infinite_coinduct
% 4.69/4.95 thf(fact_2727_infinite__coinduct,axiom,
% 4.69/4.95 ! [X4: set_Product_unit > $o,A: set_Product_unit] :
% 4.69/4.95 ( ( X4 @ A )
% 4.69/4.95 => ( ! [A9: set_Product_unit] :
% 4.69/4.95 ( ( X4 @ A9 )
% 4.69/4.95 => ? [X6: product_unit] :
% 4.69/4.95 ( ( member_Product_unit @ X6 @ A9 )
% 4.69/4.95 & ( ( X4 @ ( minus_6452836326544984404t_unit @ A9 @ ( insert_Product_unit @ X6 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.95 | ~ ( finite4290736615968046902t_unit @ ( minus_6452836326544984404t_unit @ A9 @ ( insert_Product_unit @ X6 @ bot_bo3957492148770167129t_unit ) ) ) ) ) )
% 4.69/4.95 => ~ ( finite4290736615968046902t_unit @ A ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % infinite_coinduct
% 4.69/4.95 thf(fact_2728_infinite__coinduct,axiom,
% 4.69/4.95 ! [X4: set_o > $o,A: set_o] :
% 4.69/4.95 ( ( X4 @ A )
% 4.69/4.95 => ( ! [A9: set_o] :
% 4.69/4.95 ( ( X4 @ A9 )
% 4.69/4.95 => ? [X6: $o] :
% 4.69/4.95 ( ( member_o @ X6 @ A9 )
% 4.69/4.95 & ( ( X4 @ ( minus_minus_set_o @ A9 @ ( insert_o @ X6 @ bot_bot_set_o ) ) )
% 4.69/4.95 | ~ ( finite_finite_o @ ( minus_minus_set_o @ A9 @ ( insert_o @ X6 @ bot_bot_set_o ) ) ) ) ) )
% 4.69/4.95 => ~ ( finite_finite_o @ A ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % infinite_coinduct
% 4.69/4.95 thf(fact_2729_infinite__coinduct,axiom,
% 4.69/4.95 ! [X4: set_int > $o,A: set_int] :
% 4.69/4.95 ( ( X4 @ A )
% 4.69/4.95 => ( ! [A9: set_int] :
% 4.69/4.95 ( ( X4 @ A9 )
% 4.69/4.95 => ? [X6: int] :
% 4.69/4.95 ( ( member_int @ X6 @ A9 )
% 4.69/4.95 & ( ( X4 @ ( minus_minus_set_int @ A9 @ ( insert_int @ X6 @ bot_bot_set_int ) ) )
% 4.69/4.95 | ~ ( finite_finite_int @ ( minus_minus_set_int @ A9 @ ( insert_int @ X6 @ bot_bot_set_int ) ) ) ) ) )
% 4.69/4.95 => ~ ( finite_finite_int @ A ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % infinite_coinduct
% 4.69/4.95 thf(fact_2730_infinite__coinduct,axiom,
% 4.69/4.95 ! [X4: set_Pr4532377907799695533_nat_o > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( X4 @ A )
% 4.69/4.95 => ( ! [A9: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( X4 @ A9 )
% 4.69/4.95 => ? [X6: produc3658429121746597890et_nat > $o] :
% 4.69/4.95 ( ( member6576561426505652726_nat_o @ X6 @ A9 )
% 4.69/4.95 & ( ( X4 @ ( minus_1801376950450012436_nat_o @ A9 @ ( insert5175938949040314269_nat_o @ X6 @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/4.95 | ~ ( finite3252695134891459830_nat_o @ ( minus_1801376950450012436_nat_o @ A9 @ ( insert5175938949040314269_nat_o @ X6 @ bot_bo7824918357723582233_nat_o ) ) ) ) ) )
% 4.69/4.95 => ~ ( finite3252695134891459830_nat_o @ A ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % infinite_coinduct
% 4.69/4.95 thf(fact_2731_infinite__coinduct,axiom,
% 4.69/4.95 ! [X4: set_nat > $o,A: set_nat] :
% 4.69/4.95 ( ( X4 @ A )
% 4.69/4.95 => ( ! [A9: set_nat] :
% 4.69/4.95 ( ( X4 @ A9 )
% 4.69/4.95 => ? [X6: nat] :
% 4.69/4.95 ( ( member_nat @ X6 @ A9 )
% 4.69/4.95 & ( ( X4 @ ( minus_minus_set_nat @ A9 @ ( insert_nat @ X6 @ bot_bot_set_nat ) ) )
% 4.69/4.95 | ~ ( finite_finite_nat @ ( minus_minus_set_nat @ A9 @ ( insert_nat @ X6 @ bot_bot_set_nat ) ) ) ) ) )
% 4.69/4.95 => ~ ( finite_finite_nat @ A ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % infinite_coinduct
% 4.69/4.95 thf(fact_2732_finite__empty__induct,axiom,
% 4.69/4.95 ! [A: set_Code_integer,P: set_Code_integer > $o] :
% 4.69/4.95 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.95 => ( ( P @ A )
% 4.69/4.95 => ( ! [A4: code_integer,A9: set_Code_integer] :
% 4.69/4.95 ( ( finite6017078050557962740nteger @ A9 )
% 4.69/4.95 => ( ( member_Code_integer @ A4 @ A9 )
% 4.69/4.95 => ( ( P @ A9 )
% 4.69/4.95 => ( P @ ( minus_2355218937544613996nteger @ A9 @ ( insert_Code_integer @ A4 @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 4.69/4.95 => ( P @ bot_bo3990330152332043303nteger ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % finite_empty_induct
% 4.69/4.95 thf(fact_2733_finite__empty__induct,axiom,
% 4.69/4.95 ! [A: set_Product_unit,P: set_Product_unit > $o] :
% 4.69/4.95 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.95 => ( ( P @ A )
% 4.69/4.95 => ( ! [A4: product_unit,A9: set_Product_unit] :
% 4.69/4.95 ( ( finite4290736615968046902t_unit @ A9 )
% 4.69/4.95 => ( ( member_Product_unit @ A4 @ A9 )
% 4.69/4.95 => ( ( P @ A9 )
% 4.69/4.95 => ( P @ ( minus_6452836326544984404t_unit @ A9 @ ( insert_Product_unit @ A4 @ bot_bo3957492148770167129t_unit ) ) ) ) ) )
% 4.69/4.95 => ( P @ bot_bo3957492148770167129t_unit ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % finite_empty_induct
% 4.69/4.95 thf(fact_2734_finite__empty__induct,axiom,
% 4.69/4.95 ! [A: set_o,P: set_o > $o] :
% 4.69/4.95 ( ( finite_finite_o @ A )
% 4.69/4.95 => ( ( P @ A )
% 4.69/4.95 => ( ! [A4: $o,A9: set_o] :
% 4.69/4.95 ( ( finite_finite_o @ A9 )
% 4.69/4.95 => ( ( member_o @ A4 @ A9 )
% 4.69/4.95 => ( ( P @ A9 )
% 4.69/4.95 => ( P @ ( minus_minus_set_o @ A9 @ ( insert_o @ A4 @ bot_bot_set_o ) ) ) ) ) )
% 4.69/4.95 => ( P @ bot_bot_set_o ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % finite_empty_induct
% 4.69/4.95 thf(fact_2735_finite__empty__induct,axiom,
% 4.69/4.95 ! [A: set_int,P: set_int > $o] :
% 4.69/4.95 ( ( finite_finite_int @ A )
% 4.69/4.95 => ( ( P @ A )
% 4.69/4.95 => ( ! [A4: int,A9: set_int] :
% 4.69/4.95 ( ( finite_finite_int @ A9 )
% 4.69/4.95 => ( ( member_int @ A4 @ A9 )
% 4.69/4.95 => ( ( P @ A9 )
% 4.69/4.95 => ( P @ ( minus_minus_set_int @ A9 @ ( insert_int @ A4 @ bot_bot_set_int ) ) ) ) ) )
% 4.69/4.95 => ( P @ bot_bot_set_int ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % finite_empty_induct
% 4.69/4.95 thf(fact_2736_finite__empty__induct,axiom,
% 4.69/4.95 ! [A: set_Pr4532377907799695533_nat_o,P: set_Pr4532377907799695533_nat_o > $o] :
% 4.69/4.95 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.95 => ( ( P @ A )
% 4.69/4.95 => ( ! [A4: produc3658429121746597890et_nat > $o,A9: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( finite3252695134891459830_nat_o @ A9 )
% 4.69/4.95 => ( ( member6576561426505652726_nat_o @ A4 @ A9 )
% 4.69/4.95 => ( ( P @ A9 )
% 4.69/4.95 => ( P @ ( minus_1801376950450012436_nat_o @ A9 @ ( insert5175938949040314269_nat_o @ A4 @ bot_bo7824918357723582233_nat_o ) ) ) ) ) )
% 4.69/4.95 => ( P @ bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % finite_empty_induct
% 4.69/4.95 thf(fact_2737_finite__empty__induct,axiom,
% 4.69/4.95 ! [A: set_nat,P: set_nat > $o] :
% 4.69/4.95 ( ( finite_finite_nat @ A )
% 4.69/4.95 => ( ( P @ A )
% 4.69/4.95 => ( ! [A4: nat,A9: set_nat] :
% 4.69/4.95 ( ( finite_finite_nat @ A9 )
% 4.69/4.95 => ( ( member_nat @ A4 @ A9 )
% 4.69/4.95 => ( ( P @ A9 )
% 4.69/4.95 => ( P @ ( minus_minus_set_nat @ A9 @ ( insert_nat @ A4 @ bot_bot_set_nat ) ) ) ) ) )
% 4.69/4.95 => ( P @ bot_bot_set_nat ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % finite_empty_induct
% 4.69/4.95 thf(fact_2738_subset__insert__iff,axiom,
% 4.69/4.95 ! [A: set_Product_unit,X: product_unit,B4: set_Product_unit] :
% 4.69/4.95 ( ( ord_le3507040750410214029t_unit @ A @ ( insert_Product_unit @ X @ B4 ) )
% 4.69/4.95 = ( ( ( member_Product_unit @ X @ A )
% 4.69/4.95 => ( ord_le3507040750410214029t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) @ B4 ) )
% 4.69/4.95 & ( ~ ( member_Product_unit @ X @ A )
% 4.69/4.95 => ( ord_le3507040750410214029t_unit @ A @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_insert_iff
% 4.69/4.95 thf(fact_2739_subset__insert__iff,axiom,
% 4.69/4.95 ! [A: set_o,X: $o,B4: set_o] :
% 4.69/4.95 ( ( ord_less_eq_set_o @ A @ ( insert_o @ X @ B4 ) )
% 4.69/4.95 = ( ( ( member_o @ X @ A )
% 4.69/4.95 => ( ord_less_eq_set_o @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) @ B4 ) )
% 4.69/4.95 & ( ~ ( member_o @ X @ A )
% 4.69/4.95 => ( ord_less_eq_set_o @ A @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_insert_iff
% 4.69/4.95 thf(fact_2740_subset__insert__iff,axiom,
% 4.69/4.95 ! [A: set_int,X: int,B4: set_int] :
% 4.69/4.95 ( ( ord_less_eq_set_int @ A @ ( insert_int @ X @ B4 ) )
% 4.69/4.95 = ( ( ( member_int @ X @ A )
% 4.69/4.95 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) @ B4 ) )
% 4.69/4.95 & ( ~ ( member_int @ X @ A )
% 4.69/4.95 => ( ord_less_eq_set_int @ A @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_insert_iff
% 4.69/4.95 thf(fact_2741_subset__insert__iff,axiom,
% 4.69/4.95 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( ord_le2965882846123202637_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ B4 ) )
% 4.69/4.95 = ( ( ( member6576561426505652726_nat_o @ X @ A )
% 4.69/4.95 => ( ord_le2965882846123202637_nat_o @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) @ B4 ) )
% 4.69/4.95 & ( ~ ( member6576561426505652726_nat_o @ X @ A )
% 4.69/4.95 => ( ord_le2965882846123202637_nat_o @ A @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_insert_iff
% 4.69/4.95 thf(fact_2742_subset__insert__iff,axiom,
% 4.69/4.95 ! [A: set_nat,X: nat,B4: set_nat] :
% 4.69/4.95 ( ( ord_less_eq_set_nat @ A @ ( insert_nat @ X @ B4 ) )
% 4.69/4.95 = ( ( ( member_nat @ X @ A )
% 4.69/4.95 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B4 ) )
% 4.69/4.95 & ( ~ ( member_nat @ X @ A )
% 4.69/4.95 => ( ord_less_eq_set_nat @ A @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % subset_insert_iff
% 4.69/4.95 thf(fact_2743_Diff__single__insert,axiom,
% 4.69/4.95 ! [A: set_Product_unit,X: product_unit,B4: set_Product_unit] :
% 4.69/4.95 ( ( ord_le3507040750410214029t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) @ B4 )
% 4.69/4.95 => ( ord_le3507040750410214029t_unit @ A @ ( insert_Product_unit @ X @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_single_insert
% 4.69/4.95 thf(fact_2744_Diff__single__insert,axiom,
% 4.69/4.95 ! [A: set_o,X: $o,B4: set_o] :
% 4.69/4.95 ( ( ord_less_eq_set_o @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) @ B4 )
% 4.69/4.95 => ( ord_less_eq_set_o @ A @ ( insert_o @ X @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_single_insert
% 4.69/4.95 thf(fact_2745_Diff__single__insert,axiom,
% 4.69/4.95 ! [A: set_int,X: int,B4: set_int] :
% 4.69/4.95 ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) @ B4 )
% 4.69/4.95 => ( ord_less_eq_set_int @ A @ ( insert_int @ X @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_single_insert
% 4.69/4.95 thf(fact_2746_Diff__single__insert,axiom,
% 4.69/4.95 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( ord_le2965882846123202637_nat_o @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) @ B4 )
% 4.69/4.95 => ( ord_le2965882846123202637_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_single_insert
% 4.69/4.95 thf(fact_2747_Diff__single__insert,axiom,
% 4.69/4.95 ! [A: set_nat,X: nat,B4: set_nat] :
% 4.69/4.95 ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B4 )
% 4.69/4.95 => ( ord_less_eq_set_nat @ A @ ( insert_nat @ X @ B4 ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Diff_single_insert
% 4.69/4.95 thf(fact_2748_Field__rel__restrict,axiom,
% 4.69/4.95 ! [R3: set_Pr1261947904930325089at_nat,A: set_nat] : ( ord_less_eq_set_nat @ ( field_nat @ ( rel_restrict_nat @ R3 @ A ) ) @ ( minus_minus_set_nat @ ( field_nat @ R3 ) @ A ) ) ).
% 4.69/4.95
% 4.69/4.95 % Field_rel_restrict
% 4.69/4.95 thf(fact_2749_Domain__rel__restrict,axiom,
% 4.69/4.95 ! [R3: set_Pr1261947904930325089at_nat,A: set_nat] : ( ord_less_eq_set_nat @ ( domain_nat_nat @ ( rel_restrict_nat @ R3 @ A ) ) @ ( minus_minus_set_nat @ ( domain_nat_nat @ R3 ) @ A ) ) ).
% 4.69/4.95
% 4.69/4.95 % Domain_rel_restrict
% 4.69/4.95 thf(fact_2750_Range__rel__restrict,axiom,
% 4.69/4.95 ! [R3: set_Pr1261947904930325089at_nat,A: set_nat] : ( ord_less_eq_set_nat @ ( range_nat_nat @ ( rel_restrict_nat @ R3 @ A ) ) @ ( minus_minus_set_nat @ ( range_nat_nat @ R3 ) @ A ) ) ).
% 4.69/4.95
% 4.69/4.95 % Range_rel_restrict
% 4.69/4.95 thf(fact_2751_inf__img__fin__domE,axiom,
% 4.69/4.95 ! [F: nat > code_integer,A: set_nat] :
% 4.69/4.95 ( ( finite6017078050557962740nteger @ ( image_1215581382706833972nteger @ F @ A ) )
% 4.69/4.95 => ( ~ ( finite_finite_nat @ A )
% 4.69/4.95 => ~ ! [Y2: code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ Y2 @ ( image_1215581382706833972nteger @ F @ A ) )
% 4.69/4.95 => ( finite_finite_nat @ ( vimage6104394758324456170nteger @ F @ ( insert_Code_integer @ Y2 @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % inf_img_fin_domE
% 4.69/4.95 thf(fact_2752_inf__img__fin__domE,axiom,
% 4.69/4.95 ! [F: code_integer > code_integer,A: set_Code_integer] :
% 4.69/4.95 ( ( finite6017078050557962740nteger @ ( image_4470545334726330049nteger @ F @ A ) )
% 4.69/4.95 => ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/4.95 => ~ ! [Y2: code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ Y2 @ ( image_4470545334726330049nteger @ F @ A ) )
% 4.69/4.95 => ( finite6017078050557962740nteger @ ( vimage1318793397690208119nteger @ F @ ( insert_Code_integer @ Y2 @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % inf_img_fin_domE
% 4.69/4.95 thf(fact_2753_inf__img__fin__domE,axiom,
% 4.69/4.95 ! [F: nat > product_unit,A: set_nat] :
% 4.69/4.95 ( ( finite4290736615968046902t_unit @ ( image_8730104196221521654t_unit @ F @ A ) )
% 4.69/4.95 => ( ~ ( finite_finite_nat @ A )
% 4.69/4.95 => ~ ! [Y2: product_unit] :
% 4.69/4.95 ( ( member_Product_unit @ Y2 @ ( image_8730104196221521654t_unit @ F @ A ) )
% 4.69/4.95 => ( finite_finite_nat @ ( vimage4884490618288580032t_unit @ F @ ( insert_Product_unit @ Y2 @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % inf_img_fin_domE
% 4.69/4.95 thf(fact_2754_inf__img__fin__domE,axiom,
% 4.69/4.95 ! [F: code_integer > product_unit,A: set_Code_integer] :
% 4.69/4.95 ( ( finite4290736615968046902t_unit @ ( image_7182656606676592809t_unit @ F @ A ) )
% 4.69/4.95 => ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/4.95 => ~ ! [Y2: product_unit] :
% 4.69/4.95 ( ( member_Product_unit @ Y2 @ ( image_7182656606676592809t_unit @ F @ A ) )
% 4.69/4.95 => ( finite6017078050557962740nteger @ ( vimage5651688891684837235t_unit @ F @ ( insert_Product_unit @ Y2 @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % inf_img_fin_domE
% 4.69/4.95 thf(fact_2755_inf__img__fin__domE,axiom,
% 4.69/4.95 ! [F: nat > $o,A: set_nat] :
% 4.69/4.95 ( ( finite_finite_o @ ( image_nat_o2 @ F @ A ) )
% 4.69/4.95 => ( ~ ( finite_finite_nat @ A )
% 4.69/4.95 => ~ ! [Y2: $o] :
% 4.69/4.95 ( ( member_o @ Y2 @ ( image_nat_o2 @ F @ A ) )
% 4.69/4.95 => ( finite_finite_nat @ ( vimage_nat_o @ F @ ( insert_o @ Y2 @ bot_bot_set_o ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % inf_img_fin_domE
% 4.69/4.95 thf(fact_2756_inf__img__fin__domE,axiom,
% 4.69/4.95 ! [F: code_integer > $o,A: set_Code_integer] :
% 4.69/4.95 ( ( finite_finite_o @ ( image_Code_integer_o @ F @ A ) )
% 4.69/4.95 => ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/4.95 => ~ ! [Y2: $o] :
% 4.69/4.95 ( ( member_o @ Y2 @ ( image_Code_integer_o @ F @ A ) )
% 4.69/4.95 => ( finite6017078050557962740nteger @ ( vimage3005800680117336574eger_o @ F @ ( insert_o @ Y2 @ bot_bot_set_o ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % inf_img_fin_domE
% 4.69/4.95 thf(fact_2757_inf__img__fin__domE,axiom,
% 4.69/4.95 ! [F: nat > nat,A: set_nat] :
% 4.69/4.95 ( ( finite_finite_nat @ ( image_nat_nat2 @ F @ A ) )
% 4.69/4.95 => ( ~ ( finite_finite_nat @ A )
% 4.69/4.95 => ~ ! [Y2: nat] :
% 4.69/4.95 ( ( member_nat @ Y2 @ ( image_nat_nat2 @ F @ A ) )
% 4.69/4.95 => ( finite_finite_nat @ ( vimage_nat_nat @ F @ ( insert_nat @ Y2 @ bot_bot_set_nat ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % inf_img_fin_domE
% 4.69/4.95 thf(fact_2758_inf__img__fin__domE,axiom,
% 4.69/4.95 ! [F: code_integer > nat,A: set_Code_integer] :
% 4.69/4.95 ( ( finite_finite_nat @ ( image_951025933927791156er_nat @ F @ A ) )
% 4.69/4.95 => ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/4.95 => ~ ! [Y2: nat] :
% 4.69/4.95 ( ( member_nat @ Y2 @ ( image_951025933927791156er_nat @ F @ A ) )
% 4.69/4.95 => ( finite6017078050557962740nteger @ ( vimage5839839309545413354er_nat @ F @ ( insert_nat @ Y2 @ bot_bot_set_nat ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % inf_img_fin_domE
% 4.69/4.95 thf(fact_2759_inf__img__fin__domE,axiom,
% 4.69/4.95 ! [F: nat > int,A: set_nat] :
% 4.69/4.95 ( ( finite_finite_int @ ( image_nat_int2 @ F @ A ) )
% 4.69/4.95 => ( ~ ( finite_finite_nat @ A )
% 4.69/4.95 => ~ ! [Y2: int] :
% 4.69/4.95 ( ( member_int @ Y2 @ ( image_nat_int2 @ F @ A ) )
% 4.69/4.95 => ( finite_finite_nat @ ( vimage_nat_int @ F @ ( insert_int @ Y2 @ bot_bot_set_int ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % inf_img_fin_domE
% 4.69/4.95 thf(fact_2760_inf__img__fin__domE,axiom,
% 4.69/4.95 ! [F: code_integer > int,A: set_Code_integer] :
% 4.69/4.95 ( ( finite_finite_int @ ( image_948535463418740880er_int @ F @ A ) )
% 4.69/4.95 => ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/4.95 => ~ ! [Y2: int] :
% 4.69/4.95 ( ( member_int @ Y2 @ ( image_948535463418740880er_int @ F @ A ) )
% 4.69/4.95 => ( finite6017078050557962740nteger @ ( vimage5837348839036363078er_int @ F @ ( insert_int @ Y2 @ bot_bot_set_int ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % inf_img_fin_domE
% 4.69/4.95 thf(fact_2761_inf__img__fin__dom,axiom,
% 4.69/4.95 ! [F: nat > code_integer,A: set_nat] :
% 4.69/4.95 ( ( finite6017078050557962740nteger @ ( image_1215581382706833972nteger @ F @ A ) )
% 4.69/4.95 => ( ~ ( finite_finite_nat @ A )
% 4.69/4.95 => ? [X3: code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ X3 @ ( image_1215581382706833972nteger @ F @ A ) )
% 4.69/4.95 & ~ ( finite_finite_nat @ ( vimage6104394758324456170nteger @ F @ ( insert_Code_integer @ X3 @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % inf_img_fin_dom
% 4.69/4.95 thf(fact_2762_inf__img__fin__dom,axiom,
% 4.69/4.95 ! [F: code_integer > code_integer,A: set_Code_integer] :
% 4.69/4.95 ( ( finite6017078050557962740nteger @ ( image_4470545334726330049nteger @ F @ A ) )
% 4.69/4.95 => ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/4.95 => ? [X3: code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ X3 @ ( image_4470545334726330049nteger @ F @ A ) )
% 4.69/4.95 & ~ ( finite6017078050557962740nteger @ ( vimage1318793397690208119nteger @ F @ ( insert_Code_integer @ X3 @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % inf_img_fin_dom
% 4.69/4.95 thf(fact_2763_inf__img__fin__dom,axiom,
% 4.69/4.95 ! [F: nat > product_unit,A: set_nat] :
% 4.69/4.95 ( ( finite4290736615968046902t_unit @ ( image_8730104196221521654t_unit @ F @ A ) )
% 4.69/4.95 => ( ~ ( finite_finite_nat @ A )
% 4.69/4.95 => ? [X3: product_unit] :
% 4.69/4.95 ( ( member_Product_unit @ X3 @ ( image_8730104196221521654t_unit @ F @ A ) )
% 4.69/4.95 & ~ ( finite_finite_nat @ ( vimage4884490618288580032t_unit @ F @ ( insert_Product_unit @ X3 @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % inf_img_fin_dom
% 4.69/4.95 thf(fact_2764_inf__img__fin__dom,axiom,
% 4.69/4.95 ! [F: code_integer > product_unit,A: set_Code_integer] :
% 4.69/4.95 ( ( finite4290736615968046902t_unit @ ( image_7182656606676592809t_unit @ F @ A ) )
% 4.69/4.95 => ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/4.95 => ? [X3: product_unit] :
% 4.69/4.95 ( ( member_Product_unit @ X3 @ ( image_7182656606676592809t_unit @ F @ A ) )
% 4.69/4.95 & ~ ( finite6017078050557962740nteger @ ( vimage5651688891684837235t_unit @ F @ ( insert_Product_unit @ X3 @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % inf_img_fin_dom
% 4.69/4.95 thf(fact_2765_inf__img__fin__dom,axiom,
% 4.69/4.95 ! [F: nat > $o,A: set_nat] :
% 4.69/4.95 ( ( finite_finite_o @ ( image_nat_o2 @ F @ A ) )
% 4.69/4.95 => ( ~ ( finite_finite_nat @ A )
% 4.69/4.95 => ? [X3: $o] :
% 4.69/4.95 ( ( member_o @ X3 @ ( image_nat_o2 @ F @ A ) )
% 4.69/4.95 & ~ ( finite_finite_nat @ ( vimage_nat_o @ F @ ( insert_o @ X3 @ bot_bot_set_o ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % inf_img_fin_dom
% 4.69/4.95 thf(fact_2766_inf__img__fin__dom,axiom,
% 4.69/4.95 ! [F: code_integer > $o,A: set_Code_integer] :
% 4.69/4.95 ( ( finite_finite_o @ ( image_Code_integer_o @ F @ A ) )
% 4.69/4.95 => ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/4.95 => ? [X3: $o] :
% 4.69/4.95 ( ( member_o @ X3 @ ( image_Code_integer_o @ F @ A ) )
% 4.69/4.95 & ~ ( finite6017078050557962740nteger @ ( vimage3005800680117336574eger_o @ F @ ( insert_o @ X3 @ bot_bot_set_o ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % inf_img_fin_dom
% 4.69/4.95 thf(fact_2767_inf__img__fin__dom,axiom,
% 4.69/4.95 ! [F: nat > nat,A: set_nat] :
% 4.69/4.95 ( ( finite_finite_nat @ ( image_nat_nat2 @ F @ A ) )
% 4.69/4.95 => ( ~ ( finite_finite_nat @ A )
% 4.69/4.95 => ? [X3: nat] :
% 4.69/4.95 ( ( member_nat @ X3 @ ( image_nat_nat2 @ F @ A ) )
% 4.69/4.95 & ~ ( finite_finite_nat @ ( vimage_nat_nat @ F @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % inf_img_fin_dom
% 4.69/4.95 thf(fact_2768_inf__img__fin__dom,axiom,
% 4.69/4.95 ! [F: code_integer > nat,A: set_Code_integer] :
% 4.69/4.95 ( ( finite_finite_nat @ ( image_951025933927791156er_nat @ F @ A ) )
% 4.69/4.95 => ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/4.95 => ? [X3: nat] :
% 4.69/4.95 ( ( member_nat @ X3 @ ( image_951025933927791156er_nat @ F @ A ) )
% 4.69/4.95 & ~ ( finite6017078050557962740nteger @ ( vimage5839839309545413354er_nat @ F @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % inf_img_fin_dom
% 4.69/4.95 thf(fact_2769_inf__img__fin__dom,axiom,
% 4.69/4.95 ! [F: nat > int,A: set_nat] :
% 4.69/4.95 ( ( finite_finite_int @ ( image_nat_int2 @ F @ A ) )
% 4.69/4.95 => ( ~ ( finite_finite_nat @ A )
% 4.69/4.95 => ? [X3: int] :
% 4.69/4.95 ( ( member_int @ X3 @ ( image_nat_int2 @ F @ A ) )
% 4.69/4.95 & ~ ( finite_finite_nat @ ( vimage_nat_int @ F @ ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % inf_img_fin_dom
% 4.69/4.95 thf(fact_2770_inf__img__fin__dom,axiom,
% 4.69/4.95 ! [F: code_integer > int,A: set_Code_integer] :
% 4.69/4.95 ( ( finite_finite_int @ ( image_948535463418740880er_int @ F @ A ) )
% 4.69/4.95 => ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/4.95 => ? [X3: int] :
% 4.69/4.95 ( ( member_int @ X3 @ ( image_948535463418740880er_int @ F @ A ) )
% 4.69/4.95 & ~ ( finite6017078050557962740nteger @ ( vimage5837348839036363078er_int @ F @ ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % inf_img_fin_dom
% 4.69/4.95 thf(fact_2771_acyclic__insert__cyclic,axiom,
% 4.69/4.95 ! [G: set_Pr1261947904930325089at_nat,X: nat,Y: nat] :
% 4.69/4.95 ( ( transi3139058337892597825ic_nat @ G )
% 4.69/4.95 => ( ~ ( transi3139058337892597825ic_nat @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ G ) )
% 4.69/4.95 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ X ) @ ( transi2905341329935302413cl_nat @ G ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % acyclic_insert_cyclic
% 4.69/4.95 thf(fact_2772_acyclic__insert__cyclic,axiom,
% 4.69/4.95 ! [G: set_Pr958786334691620121nt_int,X: int,Y: int] :
% 4.69/4.95 ( ( transi3136567867383547549ic_int @ G )
% 4.69/4.95 => ( ~ ( transi3136567867383547549ic_int @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ X @ Y ) @ G ) )
% 4.69/4.95 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y @ X ) @ ( transi2902850859426252137cl_int @ G ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % acyclic_insert_cyclic
% 4.69/4.95 thf(fact_2773_Inf__fin_Ohom__commute,axiom,
% 4.69/4.95 ! [H2: set_nat > set_nat,N: set_set_nat] :
% 4.69/4.95 ( ! [X3: set_nat,Y2: set_nat] :
% 4.69/4.95 ( ( H2 @ ( inf_inf_set_nat @ X3 @ Y2 ) )
% 4.69/4.95 = ( inf_inf_set_nat @ ( H2 @ X3 ) @ ( H2 @ Y2 ) ) )
% 4.69/4.95 => ( ( finite1152437895449049373et_nat @ N )
% 4.69/4.95 => ( ( N != bot_bot_set_set_nat )
% 4.69/4.95 => ( ( H2 @ ( lattic3014633134055518761et_nat @ N ) )
% 4.69/4.95 = ( lattic3014633134055518761et_nat @ ( image_7916887816326733075et_nat @ H2 @ N ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Inf_fin.hom_commute
% 4.69/4.95 thf(fact_2774_Inf__fin_Ohom__commute,axiom,
% 4.69/4.95 ! [H2: assn > assn,N: set_assn] :
% 4.69/4.95 ( ! [X3: assn,Y2: assn] :
% 4.69/4.95 ( ( H2 @ ( inf_inf_assn @ X3 @ Y2 ) )
% 4.69/4.95 = ( inf_inf_assn @ ( H2 @ X3 ) @ ( H2 @ Y2 ) ) )
% 4.69/4.95 => ( ( finite_finite_assn @ N )
% 4.69/4.95 => ( ( N != bot_bot_set_assn )
% 4.69/4.95 => ( ( H2 @ ( lattic47131356835913163n_assn @ N ) )
% 4.69/4.95 = ( lattic47131356835913163n_assn @ ( image_assn_assn @ H2 @ N ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Inf_fin.hom_commute
% 4.69/4.95 thf(fact_2775_Inf__fin_Ohom__commute,axiom,
% 4.69/4.95 ! [H2: product_unit > product_unit,N: set_Product_unit] :
% 4.69/4.95 ( ! [X3: product_unit,Y2: product_unit] :
% 4.69/4.95 ( ( H2 @ ( inf_inf_Product_unit @ X3 @ Y2 ) )
% 4.69/4.95 = ( inf_inf_Product_unit @ ( H2 @ X3 ) @ ( H2 @ Y2 ) ) )
% 4.69/4.95 => ( ( finite4290736615968046902t_unit @ N )
% 4.69/4.95 => ( ( N != bot_bo3957492148770167129t_unit )
% 4.69/4.95 => ( ( H2 @ ( lattic1263872656861969706t_unit @ N ) )
% 4.69/4.95 = ( lattic1263872656861969706t_unit @ ( image_405062704495631173t_unit @ H2 @ N ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Inf_fin.hom_commute
% 4.69/4.95 thf(fact_2776_Inf__fin_Ohom__commute,axiom,
% 4.69/4.95 ! [H2: $o > $o,N: set_o] :
% 4.69/4.95 ( ! [X3: $o,Y2: $o] :
% 4.69/4.95 ( ( H2 @ ( inf_inf_o @ X3 @ Y2 ) )
% 4.69/4.95 = ( inf_inf_o @ ( H2 @ X3 ) @ ( H2 @ Y2 ) ) )
% 4.69/4.95 => ( ( finite_finite_o @ N )
% 4.69/4.95 => ( ( N != bot_bot_set_o )
% 4.69/4.95 => ( ( H2 @ ( lattic4107685809792843317_fin_o @ N ) )
% 4.69/4.95 = ( lattic4107685809792843317_fin_o @ ( image_o_o2 @ H2 @ N ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Inf_fin.hom_commute
% 4.69/4.95 thf(fact_2777_Inf__fin_Ohom__commute,axiom,
% 4.69/4.95 ! [H2: nat > nat,N: set_nat] :
% 4.69/4.95 ( ! [X3: nat,Y2: nat] :
% 4.69/4.95 ( ( H2 @ ( inf_inf_nat @ X3 @ Y2 ) )
% 4.69/4.95 = ( inf_inf_nat @ ( H2 @ X3 ) @ ( H2 @ Y2 ) ) )
% 4.69/4.95 => ( ( finite_finite_nat @ N )
% 4.69/4.95 => ( ( N != bot_bot_set_nat )
% 4.69/4.95 => ( ( H2 @ ( lattic5238388535129920115in_nat @ N ) )
% 4.69/4.95 = ( lattic5238388535129920115in_nat @ ( image_nat_nat2 @ H2 @ N ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Inf_fin.hom_commute
% 4.69/4.95 thf(fact_2778_Inf__fin_Ohom__commute,axiom,
% 4.69/4.95 ! [H2: int > int,N: set_int] :
% 4.69/4.95 ( ! [X3: int,Y2: int] :
% 4.69/4.95 ( ( H2 @ ( inf_inf_int @ X3 @ Y2 ) )
% 4.69/4.95 = ( inf_inf_int @ ( H2 @ X3 ) @ ( H2 @ Y2 ) ) )
% 4.69/4.95 => ( ( finite_finite_int @ N )
% 4.69/4.95 => ( ( N != bot_bot_set_int )
% 4.69/4.95 => ( ( H2 @ ( lattic5235898064620869839in_int @ N ) )
% 4.69/4.95 = ( lattic5235898064620869839in_int @ ( image_int_int2 @ H2 @ N ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Inf_fin.hom_commute
% 4.69/4.95 thf(fact_2779_Inf__fin_Ohom__commute,axiom,
% 4.69/4.95 ! [H2: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,N: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat > $o] :
% 4.69/4.95 ( ( H2 @ ( inf_in1318976480646536635_nat_o @ X3 @ Y2 ) )
% 4.69/4.95 = ( inf_in1318976480646536635_nat_o @ ( H2 @ X3 ) @ ( H2 @ Y2 ) ) )
% 4.69/4.95 => ( ( finite3252695134891459830_nat_o @ N )
% 4.69/4.95 => ( ( N != bot_bo7824918357723582233_nat_o )
% 4.69/4.95 => ( ( H2 @ ( lattic956194824204696298_nat_o @ N ) )
% 4.69/4.95 = ( lattic956194824204696298_nat_o @ ( image_3399141053782081349_nat_o @ H2 @ N ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Inf_fin.hom_commute
% 4.69/4.95 thf(fact_2780_Sup__fin_Ohom__commute,axiom,
% 4.69/4.95 ! [H2: set_nat > set_nat,N: set_set_nat] :
% 4.69/4.95 ( ! [X3: set_nat,Y2: set_nat] :
% 4.69/4.95 ( ( H2 @ ( sup_sup_set_nat @ X3 @ Y2 ) )
% 4.69/4.95 = ( sup_sup_set_nat @ ( H2 @ X3 ) @ ( H2 @ Y2 ) ) )
% 4.69/4.95 => ( ( finite1152437895449049373et_nat @ N )
% 4.69/4.95 => ( ( N != bot_bot_set_set_nat )
% 4.69/4.95 => ( ( H2 @ ( lattic3835124923745554447et_nat @ N ) )
% 4.69/4.95 = ( lattic3835124923745554447et_nat @ ( image_7916887816326733075et_nat @ H2 @ N ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Sup_fin.hom_commute
% 4.69/4.95 thf(fact_2781_Sup__fin_Ohom__commute,axiom,
% 4.69/4.95 ! [H2: assn > assn,N: set_assn] :
% 4.69/4.95 ( ! [X3: assn,Y2: assn] :
% 4.69/4.95 ( ( H2 @ ( sup_sup_assn @ X3 @ Y2 ) )
% 4.69/4.95 = ( sup_sup_assn @ ( H2 @ X3 ) @ ( H2 @ Y2 ) ) )
% 4.69/4.95 => ( ( finite_finite_assn @ N )
% 4.69/4.95 => ( ( N != bot_bot_set_assn )
% 4.69/4.95 => ( ( H2 @ ( lattic2150320897289308081n_assn @ N ) )
% 4.69/4.95 = ( lattic2150320897289308081n_assn @ ( image_assn_assn @ H2 @ N ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Sup_fin.hom_commute
% 4.69/4.95 thf(fact_2782_Sup__fin_Ohom__commute,axiom,
% 4.69/4.95 ! [H2: product_unit > product_unit,N: set_Product_unit] :
% 4.69/4.95 ( ! [X3: product_unit,Y2: product_unit] :
% 4.69/4.95 ( ( H2 @ ( sup_sup_Product_unit @ X3 @ Y2 ) )
% 4.69/4.95 = ( sup_sup_Product_unit @ ( H2 @ X3 ) @ ( H2 @ Y2 ) ) )
% 4.69/4.95 => ( ( finite4290736615968046902t_unit @ N )
% 4.69/4.95 => ( ( N != bot_bo3957492148770167129t_unit )
% 4.69/4.95 => ( ( H2 @ ( lattic5294303975357428420t_unit @ N ) )
% 4.69/4.95 = ( lattic5294303975357428420t_unit @ ( image_405062704495631173t_unit @ H2 @ N ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Sup_fin.hom_commute
% 4.69/4.95 thf(fact_2783_Sup__fin_Ohom__commute,axiom,
% 4.69/4.95 ! [H2: $o > $o,N: set_o] :
% 4.69/4.95 ( ! [X3: $o,Y2: $o] :
% 4.69/4.95 ( ( H2 @ ( sup_sup_o @ X3 @ Y2 ) )
% 4.69/4.95 = ( sup_sup_o @ ( H2 @ X3 ) @ ( H2 @ Y2 ) ) )
% 4.69/4.95 => ( ( finite_finite_o @ N )
% 4.69/4.95 => ( ( N != bot_bot_set_o )
% 4.69/4.95 => ( ( H2 @ ( lattic1508158080041050831_fin_o @ N ) )
% 4.69/4.95 = ( lattic1508158080041050831_fin_o @ ( image_o_o2 @ H2 @ N ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Sup_fin.hom_commute
% 4.69/4.95 thf(fact_2784_Sup__fin_Ohom__commute,axiom,
% 4.69/4.95 ! [H2: nat > nat,N: set_nat] :
% 4.69/4.95 ( ! [X3: nat,Y2: nat] :
% 4.69/4.95 ( ( H2 @ ( sup_sup_nat @ X3 @ Y2 ) )
% 4.69/4.95 = ( sup_sup_nat @ ( H2 @ X3 ) @ ( H2 @ Y2 ) ) )
% 4.69/4.95 => ( ( finite_finite_nat @ N )
% 4.69/4.95 => ( ( N != bot_bot_set_nat )
% 4.69/4.95 => ( ( H2 @ ( lattic1093996805478795353in_nat @ N ) )
% 4.69/4.95 = ( lattic1093996805478795353in_nat @ ( image_nat_nat2 @ H2 @ N ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Sup_fin.hom_commute
% 4.69/4.95 thf(fact_2785_Sup__fin_Ohom__commute,axiom,
% 4.69/4.95 ! [H2: int > int,N: set_int] :
% 4.69/4.95 ( ! [X3: int,Y2: int] :
% 4.69/4.95 ( ( H2 @ ( sup_sup_int @ X3 @ Y2 ) )
% 4.69/4.95 = ( sup_sup_int @ ( H2 @ X3 ) @ ( H2 @ Y2 ) ) )
% 4.69/4.95 => ( ( finite_finite_int @ N )
% 4.69/4.95 => ( ( N != bot_bot_set_int )
% 4.69/4.95 => ( ( H2 @ ( lattic1091506334969745077in_int @ N ) )
% 4.69/4.95 = ( lattic1091506334969745077in_int @ ( image_int_int2 @ H2 @ N ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Sup_fin.hom_commute
% 4.69/4.95 thf(fact_2786_Sup__fin_Ohom__commute,axiom,
% 4.69/4.95 ! [H2: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,N: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat > $o] :
% 4.69/4.95 ( ( H2 @ ( sup_su5453871518329203617_nat_o @ X3 @ Y2 ) )
% 4.69/4.95 = ( sup_su5453871518329203617_nat_o @ ( H2 @ X3 ) @ ( H2 @ Y2 ) ) )
% 4.69/4.95 => ( ( finite3252695134891459830_nat_o @ N )
% 4.69/4.95 => ( ( N != bot_bo7824918357723582233_nat_o )
% 4.69/4.95 => ( ( H2 @ ( lattic7320199455484906628_nat_o @ N ) )
% 4.69/4.95 = ( lattic7320199455484906628_nat_o @ ( image_3399141053782081349_nat_o @ H2 @ N ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Sup_fin.hom_commute
% 4.69/4.95 thf(fact_2787_finite__remove__induct,axiom,
% 4.69/4.95 ! [B4: set_Code_integer,P: set_Code_integer > $o] :
% 4.69/4.95 ( ( finite6017078050557962740nteger @ B4 )
% 4.69/4.95 => ( ( P @ bot_bo3990330152332043303nteger )
% 4.69/4.95 => ( ! [A9: set_Code_integer] :
% 4.69/4.95 ( ( finite6017078050557962740nteger @ A9 )
% 4.69/4.95 => ( ( A9 != bot_bo3990330152332043303nteger )
% 4.69/4.95 => ( ( ord_le7084787975880047091nteger @ A9 @ B4 )
% 4.69/4.95 => ( ! [X6: code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ X6 @ A9 )
% 4.69/4.95 => ( P @ ( minus_2355218937544613996nteger @ A9 @ ( insert_Code_integer @ X6 @ bot_bo3990330152332043303nteger ) ) ) )
% 4.69/4.95 => ( P @ A9 ) ) ) ) )
% 4.69/4.95 => ( P @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % finite_remove_induct
% 4.69/4.95 thf(fact_2788_finite__remove__induct,axiom,
% 4.69/4.95 ! [B4: set_Product_unit,P: set_Product_unit > $o] :
% 4.69/4.95 ( ( finite4290736615968046902t_unit @ B4 )
% 4.69/4.95 => ( ( P @ bot_bo3957492148770167129t_unit )
% 4.69/4.95 => ( ! [A9: set_Product_unit] :
% 4.69/4.95 ( ( finite4290736615968046902t_unit @ A9 )
% 4.69/4.95 => ( ( A9 != bot_bo3957492148770167129t_unit )
% 4.69/4.95 => ( ( ord_le3507040750410214029t_unit @ A9 @ B4 )
% 4.69/4.95 => ( ! [X6: product_unit] :
% 4.69/4.95 ( ( member_Product_unit @ X6 @ A9 )
% 4.69/4.95 => ( P @ ( minus_6452836326544984404t_unit @ A9 @ ( insert_Product_unit @ X6 @ bot_bo3957492148770167129t_unit ) ) ) )
% 4.69/4.95 => ( P @ A9 ) ) ) ) )
% 4.69/4.95 => ( P @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % finite_remove_induct
% 4.69/4.95 thf(fact_2789_finite__remove__induct,axiom,
% 4.69/4.95 ! [B4: set_o,P: set_o > $o] :
% 4.69/4.95 ( ( finite_finite_o @ B4 )
% 4.69/4.95 => ( ( P @ bot_bot_set_o )
% 4.69/4.95 => ( ! [A9: set_o] :
% 4.69/4.95 ( ( finite_finite_o @ A9 )
% 4.69/4.95 => ( ( A9 != bot_bot_set_o )
% 4.69/4.95 => ( ( ord_less_eq_set_o @ A9 @ B4 )
% 4.69/4.95 => ( ! [X6: $o] :
% 4.69/4.95 ( ( member_o @ X6 @ A9 )
% 4.69/4.95 => ( P @ ( minus_minus_set_o @ A9 @ ( insert_o @ X6 @ bot_bot_set_o ) ) ) )
% 4.69/4.95 => ( P @ A9 ) ) ) ) )
% 4.69/4.95 => ( P @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % finite_remove_induct
% 4.69/4.95 thf(fact_2790_finite__remove__induct,axiom,
% 4.69/4.95 ! [B4: set_int,P: set_int > $o] :
% 4.69/4.95 ( ( finite_finite_int @ B4 )
% 4.69/4.95 => ( ( P @ bot_bot_set_int )
% 4.69/4.95 => ( ! [A9: set_int] :
% 4.69/4.95 ( ( finite_finite_int @ A9 )
% 4.69/4.95 => ( ( A9 != bot_bot_set_int )
% 4.69/4.95 => ( ( ord_less_eq_set_int @ A9 @ B4 )
% 4.69/4.95 => ( ! [X6: int] :
% 4.69/4.95 ( ( member_int @ X6 @ A9 )
% 4.69/4.95 => ( P @ ( minus_minus_set_int @ A9 @ ( insert_int @ X6 @ bot_bot_set_int ) ) ) )
% 4.69/4.95 => ( P @ A9 ) ) ) ) )
% 4.69/4.95 => ( P @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % finite_remove_induct
% 4.69/4.95 thf(fact_2791_finite__remove__induct,axiom,
% 4.69/4.95 ! [B4: set_Pr4532377907799695533_nat_o,P: set_Pr4532377907799695533_nat_o > $o] :
% 4.69/4.95 ( ( finite3252695134891459830_nat_o @ B4 )
% 4.69/4.95 => ( ( P @ bot_bo7824918357723582233_nat_o )
% 4.69/4.95 => ( ! [A9: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( finite3252695134891459830_nat_o @ A9 )
% 4.69/4.95 => ( ( A9 != bot_bo7824918357723582233_nat_o )
% 4.69/4.95 => ( ( ord_le2965882846123202637_nat_o @ A9 @ B4 )
% 4.69/4.95 => ( ! [X6: produc3658429121746597890et_nat > $o] :
% 4.69/4.95 ( ( member6576561426505652726_nat_o @ X6 @ A9 )
% 4.69/4.95 => ( P @ ( minus_1801376950450012436_nat_o @ A9 @ ( insert5175938949040314269_nat_o @ X6 @ bot_bo7824918357723582233_nat_o ) ) ) )
% 4.69/4.95 => ( P @ A9 ) ) ) ) )
% 4.69/4.95 => ( P @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % finite_remove_induct
% 4.69/4.95 thf(fact_2792_finite__remove__induct,axiom,
% 4.69/4.95 ! [B4: set_nat,P: set_nat > $o] :
% 4.69/4.95 ( ( finite_finite_nat @ B4 )
% 4.69/4.95 => ( ( P @ bot_bot_set_nat )
% 4.69/4.95 => ( ! [A9: set_nat] :
% 4.69/4.95 ( ( finite_finite_nat @ A9 )
% 4.69/4.95 => ( ( A9 != bot_bot_set_nat )
% 4.69/4.95 => ( ( ord_less_eq_set_nat @ A9 @ B4 )
% 4.69/4.95 => ( ! [X6: nat] :
% 4.69/4.95 ( ( member_nat @ X6 @ A9 )
% 4.69/4.95 => ( P @ ( minus_minus_set_nat @ A9 @ ( insert_nat @ X6 @ bot_bot_set_nat ) ) ) )
% 4.69/4.95 => ( P @ A9 ) ) ) ) )
% 4.69/4.95 => ( P @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % finite_remove_induct
% 4.69/4.95 thf(fact_2793_remove__induct,axiom,
% 4.69/4.95 ! [P: set_Code_integer > $o,B4: set_Code_integer] :
% 4.69/4.95 ( ( P @ bot_bo3990330152332043303nteger )
% 4.69/4.95 => ( ( ~ ( finite6017078050557962740nteger @ B4 )
% 4.69/4.95 => ( P @ B4 ) )
% 4.69/4.95 => ( ! [A9: set_Code_integer] :
% 4.69/4.95 ( ( finite6017078050557962740nteger @ A9 )
% 4.69/4.95 => ( ( A9 != bot_bo3990330152332043303nteger )
% 4.69/4.95 => ( ( ord_le7084787975880047091nteger @ A9 @ B4 )
% 4.69/4.95 => ( ! [X6: code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ X6 @ A9 )
% 4.69/4.95 => ( P @ ( minus_2355218937544613996nteger @ A9 @ ( insert_Code_integer @ X6 @ bot_bo3990330152332043303nteger ) ) ) )
% 4.69/4.95 => ( P @ A9 ) ) ) ) )
% 4.69/4.95 => ( P @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % remove_induct
% 4.69/4.95 thf(fact_2794_remove__induct,axiom,
% 4.69/4.95 ! [P: set_Product_unit > $o,B4: set_Product_unit] :
% 4.69/4.95 ( ( P @ bot_bo3957492148770167129t_unit )
% 4.69/4.95 => ( ( ~ ( finite4290736615968046902t_unit @ B4 )
% 4.69/4.95 => ( P @ B4 ) )
% 4.69/4.95 => ( ! [A9: set_Product_unit] :
% 4.69/4.95 ( ( finite4290736615968046902t_unit @ A9 )
% 4.69/4.95 => ( ( A9 != bot_bo3957492148770167129t_unit )
% 4.69/4.95 => ( ( ord_le3507040750410214029t_unit @ A9 @ B4 )
% 4.69/4.95 => ( ! [X6: product_unit] :
% 4.69/4.95 ( ( member_Product_unit @ X6 @ A9 )
% 4.69/4.95 => ( P @ ( minus_6452836326544984404t_unit @ A9 @ ( insert_Product_unit @ X6 @ bot_bo3957492148770167129t_unit ) ) ) )
% 4.69/4.95 => ( P @ A9 ) ) ) ) )
% 4.69/4.95 => ( P @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % remove_induct
% 4.69/4.95 thf(fact_2795_remove__induct,axiom,
% 4.69/4.95 ! [P: set_o > $o,B4: set_o] :
% 4.69/4.95 ( ( P @ bot_bot_set_o )
% 4.69/4.95 => ( ( ~ ( finite_finite_o @ B4 )
% 4.69/4.95 => ( P @ B4 ) )
% 4.69/4.95 => ( ! [A9: set_o] :
% 4.69/4.95 ( ( finite_finite_o @ A9 )
% 4.69/4.95 => ( ( A9 != bot_bot_set_o )
% 4.69/4.95 => ( ( ord_less_eq_set_o @ A9 @ B4 )
% 4.69/4.95 => ( ! [X6: $o] :
% 4.69/4.95 ( ( member_o @ X6 @ A9 )
% 4.69/4.95 => ( P @ ( minus_minus_set_o @ A9 @ ( insert_o @ X6 @ bot_bot_set_o ) ) ) )
% 4.69/4.95 => ( P @ A9 ) ) ) ) )
% 4.69/4.95 => ( P @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % remove_induct
% 4.69/4.95 thf(fact_2796_remove__induct,axiom,
% 4.69/4.95 ! [P: set_int > $o,B4: set_int] :
% 4.69/4.95 ( ( P @ bot_bot_set_int )
% 4.69/4.95 => ( ( ~ ( finite_finite_int @ B4 )
% 4.69/4.95 => ( P @ B4 ) )
% 4.69/4.95 => ( ! [A9: set_int] :
% 4.69/4.95 ( ( finite_finite_int @ A9 )
% 4.69/4.95 => ( ( A9 != bot_bot_set_int )
% 4.69/4.95 => ( ( ord_less_eq_set_int @ A9 @ B4 )
% 4.69/4.95 => ( ! [X6: int] :
% 4.69/4.95 ( ( member_int @ X6 @ A9 )
% 4.69/4.95 => ( P @ ( minus_minus_set_int @ A9 @ ( insert_int @ X6 @ bot_bot_set_int ) ) ) )
% 4.69/4.95 => ( P @ A9 ) ) ) ) )
% 4.69/4.95 => ( P @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % remove_induct
% 4.69/4.95 thf(fact_2797_remove__induct,axiom,
% 4.69/4.95 ! [P: set_Pr4532377907799695533_nat_o > $o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( P @ bot_bo7824918357723582233_nat_o )
% 4.69/4.95 => ( ( ~ ( finite3252695134891459830_nat_o @ B4 )
% 4.69/4.95 => ( P @ B4 ) )
% 4.69/4.95 => ( ! [A9: set_Pr4532377907799695533_nat_o] :
% 4.69/4.95 ( ( finite3252695134891459830_nat_o @ A9 )
% 4.69/4.95 => ( ( A9 != bot_bo7824918357723582233_nat_o )
% 4.69/4.95 => ( ( ord_le2965882846123202637_nat_o @ A9 @ B4 )
% 4.69/4.95 => ( ! [X6: produc3658429121746597890et_nat > $o] :
% 4.69/4.95 ( ( member6576561426505652726_nat_o @ X6 @ A9 )
% 4.69/4.95 => ( P @ ( minus_1801376950450012436_nat_o @ A9 @ ( insert5175938949040314269_nat_o @ X6 @ bot_bo7824918357723582233_nat_o ) ) ) )
% 4.69/4.95 => ( P @ A9 ) ) ) ) )
% 4.69/4.95 => ( P @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % remove_induct
% 4.69/4.95 thf(fact_2798_remove__induct,axiom,
% 4.69/4.95 ! [P: set_nat > $o,B4: set_nat] :
% 4.69/4.95 ( ( P @ bot_bot_set_nat )
% 4.69/4.95 => ( ( ~ ( finite_finite_nat @ B4 )
% 4.69/4.95 => ( P @ B4 ) )
% 4.69/4.95 => ( ! [A9: set_nat] :
% 4.69/4.95 ( ( finite_finite_nat @ A9 )
% 4.69/4.95 => ( ( A9 != bot_bot_set_nat )
% 4.69/4.95 => ( ( ord_less_eq_set_nat @ A9 @ B4 )
% 4.69/4.95 => ( ! [X6: nat] :
% 4.69/4.95 ( ( member_nat @ X6 @ A9 )
% 4.69/4.95 => ( P @ ( minus_minus_set_nat @ A9 @ ( insert_nat @ X6 @ bot_bot_set_nat ) ) ) )
% 4.69/4.95 => ( P @ A9 ) ) ) ) )
% 4.69/4.95 => ( P @ B4 ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % remove_induct
% 4.69/4.95 thf(fact_2799_Linear__order__in__diff__Id,axiom,
% 4.69/4.95 ! [R2: set_Pr2161125870931222855_nat_o,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o] :
% 4.69/4.95 ( ( order_1145710701291701250_nat_o @ ( field_81821745747897882_nat_o @ R2 ) @ R2 )
% 4.69/4.95 => ( ( member6576561426505652726_nat_o @ A2 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.95 => ( ( member6576561426505652726_nat_o @ B @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.95 => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ B ) @ R2 )
% 4.69/4.95 = ( ~ ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ B @ A2 ) @ ( minus_9189903262233110958_nat_o @ R2 @ id_Pro6775173067513470761_nat_o ) ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Linear_order_in_diff_Id
% 4.69/4.95 thf(fact_2800_Linear__order__in__diff__Id,axiom,
% 4.69/4.95 ! [R2: set_Product_prod_o_o,A2: $o,B: $o] :
% 4.69/4.95 ( ( order_6238756238976269133r_on_o @ ( field_o @ R2 ) @ R2 )
% 4.69/4.95 => ( ( member_o @ A2 @ ( field_o @ R2 ) )
% 4.69/4.95 => ( ( member_o @ B @ ( field_o @ R2 ) )
% 4.69/4.95 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ B ) @ R2 )
% 4.69/4.95 = ( ~ ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ B @ A2 ) @ ( minus_7052513330764642158od_o_o @ R2 @ id_o2 ) ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Linear_order_in_diff_Id
% 4.69/4.95 thf(fact_2801_Linear__order__in__diff__Id,axiom,
% 4.69/4.95 ! [R2: set_Pr5094982260447487303t_unit,A2: product_unit,B: product_unit] :
% 4.69/4.95 ( ( order_888282469287196226t_unit @ ( field_Product_unit @ R2 ) @ R2 )
% 4.69/4.95 => ( ( member_Product_unit @ A2 @ ( field_Product_unit @ R2 ) )
% 4.69/4.95 => ( ( member_Product_unit @ B @ ( field_Product_unit @ R2 ) )
% 4.69/4.95 => ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A2 @ B ) @ R2 )
% 4.69/4.95 = ( ~ ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ B @ A2 ) @ ( minus_6985556733573110190t_unit @ R2 @ id_Product_unit ) ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Linear_order_in_diff_Id
% 4.69/4.95 thf(fact_2802_Linear__order__in__diff__Id,axiom,
% 4.69/4.95 ! [R2: set_Pr1261947904930325089at_nat,A2: nat,B: nat] :
% 4.69/4.95 ( ( order_4473980167227706203on_nat @ ( field_nat @ R2 ) @ R2 )
% 4.69/4.95 => ( ( member_nat @ A2 @ ( field_nat @ R2 ) )
% 4.69/4.95 => ( ( member_nat @ B @ ( field_nat @ R2 ) )
% 4.69/4.95 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 )
% 4.69/4.95 = ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ A2 ) @ ( minus_1356011639430497352at_nat @ R2 @ id_nat ) ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Linear_order_in_diff_Id
% 4.69/4.95 thf(fact_2803_Linear__order__in__diff__Id,axiom,
% 4.69/4.95 ! [R2: set_Pr958786334691620121nt_int,A2: int,B: int] :
% 4.69/4.95 ( ( order_4471489696718655927on_int @ ( field_int @ R2 ) @ R2 )
% 4.69/4.95 => ( ( member_int @ A2 @ ( field_int @ R2 ) )
% 4.69/4.95 => ( ( member_int @ B @ ( field_int @ R2 ) )
% 4.69/4.95 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 )
% 4.69/4.95 = ( ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ A2 ) @ ( minus_1052850069191792384nt_int @ R2 @ id_int ) ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % Linear_order_in_diff_Id
% 4.69/4.95 thf(fact_2804_max__ext_Omax__extI,axiom,
% 4.69/4.95 ! [X4: set_Code_integer,Y6: set_Code_integer,R3: set_Pr4811707699266497531nteger] :
% 4.69/4.95 ( ( finite6017078050557962740nteger @ X4 )
% 4.69/4.95 => ( ( finite6017078050557962740nteger @ Y6 )
% 4.69/4.95 => ( ( Y6 != bot_bo3990330152332043303nteger )
% 4.69/4.95 => ( ! [X3: code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ X3 @ X4 )
% 4.69/4.95 => ? [Xa2: code_integer] :
% 4.69/4.95 ( ( member_Code_integer @ Xa2 @ Y6 )
% 4.69/4.95 & ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X3 @ Xa2 ) @ R3 ) ) )
% 4.69/4.95 => ( member4307123515891402160nteger @ ( produc7443773368509356479nteger @ X4 @ Y6 ) @ ( max_ext_Code_integer @ R3 ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % max_ext.max_extI
% 4.69/4.95 thf(fact_2805_max__ext_Omax__extI,axiom,
% 4.69/4.95 ! [X4: set_Product_unit,Y6: set_Product_unit,R3: set_Pr5094982260447487303t_unit] :
% 4.69/4.95 ( ( finite4290736615968046902t_unit @ X4 )
% 4.69/4.95 => ( ( finite4290736615968046902t_unit @ Y6 )
% 4.69/4.95 => ( ( Y6 != bot_bo3957492148770167129t_unit )
% 4.69/4.95 => ( ! [X3: product_unit] :
% 4.69/4.95 ( ( member_Product_unit @ X3 @ X4 )
% 4.69/4.95 => ? [Xa2: product_unit] :
% 4.69/4.95 ( ( member_Product_unit @ Xa2 @ Y6 )
% 4.69/4.95 & ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X3 @ Xa2 ) @ R3 ) ) )
% 4.69/4.95 => ( member4189953012975926160t_unit @ ( produc7269801343787132631t_unit @ X4 @ Y6 ) @ ( max_ext_Product_unit @ R3 ) ) ) ) ) ) ).
% 4.69/4.95
% 4.69/4.95 % max_ext.max_extI
% 4.69/4.95 thf(fact_2806_max__ext_Omax__extI,axiom,
% 4.69/4.95 ! [X4: set_o,Y6: set_o,R3: set_Product_prod_o_o] :
% 4.69/4.95 ( ( finite_finite_o @ X4 )
% 4.69/4.95 => ( ( finite_finite_o @ Y6 )
% 4.69/4.95 => ( ( Y6 != bot_bot_set_o )
% 4.69/4.96 => ( ! [X3: $o] :
% 4.69/4.96 ( ( member_o @ X3 @ X4 )
% 4.69/4.96 => ? [Xa2: $o] :
% 4.69/4.96 ( ( member_o @ Xa2 @ Y6 )
% 4.69/4.96 & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X3 @ Xa2 ) @ R3 ) ) )
% 4.69/4.96 => ( member9116954335612470352_set_o @ ( produc5838405689764958487_set_o @ X4 @ Y6 ) @ ( max_ext_o @ R3 ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % max_ext.max_extI
% 4.69/4.96 thf(fact_2807_max__ext_Omax__extI,axiom,
% 4.69/4.96 ! [X4: set_nat,Y6: set_nat,R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ( finite_finite_nat @ X4 )
% 4.69/4.96 => ( ( finite_finite_nat @ Y6 )
% 4.69/4.96 => ( ( Y6 != bot_bot_set_nat )
% 4.69/4.96 => ( ! [X3: nat] :
% 4.69/4.96 ( ( member_nat @ X3 @ X4 )
% 4.69/4.96 => ? [Xa2: nat] :
% 4.69/4.96 ( ( member_nat @ Xa2 @ Y6 )
% 4.69/4.96 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Xa2 ) @ R3 ) ) )
% 4.69/4.96 => ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ X4 @ Y6 ) @ ( max_ext_nat @ R3 ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % max_ext.max_extI
% 4.69/4.96 thf(fact_2808_max__ext_Omax__extI,axiom,
% 4.69/4.96 ! [X4: set_int,Y6: set_int,R3: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ( ( finite_finite_int @ X4 )
% 4.69/4.96 => ( ( finite_finite_int @ Y6 )
% 4.69/4.96 => ( ( Y6 != bot_bot_set_int )
% 4.69/4.96 => ( ! [X3: int] :
% 4.69/4.96 ( ( member_int @ X3 @ X4 )
% 4.69/4.96 => ? [Xa2: int] :
% 4.69/4.96 ( ( member_int @ Xa2 @ Y6 )
% 4.69/4.96 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Xa2 ) @ R3 ) ) )
% 4.69/4.96 => ( member2572552093476627150et_int @ ( produc6363374080413544029et_int @ X4 @ Y6 ) @ ( max_ext_int @ R3 ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % max_ext.max_extI
% 4.69/4.96 thf(fact_2809_max__ext_Omax__extI,axiom,
% 4.69/4.96 ! [X4: set_Pr4532377907799695533_nat_o,Y6: set_Pr4532377907799695533_nat_o,R3: set_Pr2161125870931222855_nat_o] :
% 4.69/4.96 ( ( finite3252695134891459830_nat_o @ X4 )
% 4.69/4.96 => ( ( finite3252695134891459830_nat_o @ Y6 )
% 4.69/4.96 => ( ( Y6 != bot_bo7824918357723582233_nat_o )
% 4.69/4.96 => ( ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ X3 @ X4 )
% 4.69/4.96 => ? [Xa2: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ Xa2 @ Y6 )
% 4.69/4.96 & ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X3 @ Xa2 ) @ R3 ) ) )
% 4.69/4.96 => ( member6623172407746373520_nat_o @ ( produc5149316574908490455_nat_o @ X4 @ Y6 ) @ ( max_ex5265246208886859912_nat_o @ R3 ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % max_ext.max_extI
% 4.69/4.96 thf(fact_2810_max__ext_Osimps,axiom,
% 4.69/4.96 ! [A1: set_Code_integer,A22: set_Code_integer,R3: set_Pr4811707699266497531nteger] :
% 4.69/4.96 ( ( member4307123515891402160nteger @ ( produc7443773368509356479nteger @ A1 @ A22 ) @ ( max_ext_Code_integer @ R3 ) )
% 4.69/4.96 = ( ( finite6017078050557962740nteger @ A1 )
% 4.69/4.96 & ( finite6017078050557962740nteger @ A22 )
% 4.69/4.96 & ( A22 != bot_bo3990330152332043303nteger )
% 4.69/4.96 & ! [X2: code_integer] :
% 4.69/4.96 ( ( member_Code_integer @ X2 @ A1 )
% 4.69/4.96 => ? [Y3: code_integer] :
% 4.69/4.96 ( ( member_Code_integer @ Y3 @ A22 )
% 4.69/4.96 & ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X2 @ Y3 ) @ R3 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % max_ext.simps
% 4.69/4.96 thf(fact_2811_max__ext_Osimps,axiom,
% 4.69/4.96 ! [A1: set_Product_unit,A22: set_Product_unit,R3: set_Pr5094982260447487303t_unit] :
% 4.69/4.96 ( ( member4189953012975926160t_unit @ ( produc7269801343787132631t_unit @ A1 @ A22 ) @ ( max_ext_Product_unit @ R3 ) )
% 4.69/4.96 = ( ( finite4290736615968046902t_unit @ A1 )
% 4.69/4.96 & ( finite4290736615968046902t_unit @ A22 )
% 4.69/4.96 & ( A22 != bot_bo3957492148770167129t_unit )
% 4.69/4.96 & ! [X2: product_unit] :
% 4.69/4.96 ( ( member_Product_unit @ X2 @ A1 )
% 4.69/4.96 => ? [Y3: product_unit] :
% 4.69/4.96 ( ( member_Product_unit @ Y3 @ A22 )
% 4.69/4.96 & ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X2 @ Y3 ) @ R3 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % max_ext.simps
% 4.69/4.96 thf(fact_2812_max__ext_Osimps,axiom,
% 4.69/4.96 ! [A1: set_o,A22: set_o,R3: set_Product_prod_o_o] :
% 4.69/4.96 ( ( member9116954335612470352_set_o @ ( produc5838405689764958487_set_o @ A1 @ A22 ) @ ( max_ext_o @ R3 ) )
% 4.69/4.96 = ( ( finite_finite_o @ A1 )
% 4.69/4.96 & ( finite_finite_o @ A22 )
% 4.69/4.96 & ( A22 != bot_bot_set_o )
% 4.69/4.96 & ! [X2: $o] :
% 4.69/4.96 ( ( member_o @ X2 @ A1 )
% 4.69/4.96 => ? [Y3: $o] :
% 4.69/4.96 ( ( member_o @ Y3 @ A22 )
% 4.69/4.96 & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X2 @ Y3 ) @ R3 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % max_ext.simps
% 4.69/4.96 thf(fact_2813_max__ext_Osimps,axiom,
% 4.69/4.96 ! [A1: set_nat,A22: set_nat,R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A1 @ A22 ) @ ( max_ext_nat @ R3 ) )
% 4.69/4.96 = ( ( finite_finite_nat @ A1 )
% 4.69/4.96 & ( finite_finite_nat @ A22 )
% 4.69/4.96 & ( A22 != bot_bot_set_nat )
% 4.69/4.96 & ! [X2: nat] :
% 4.69/4.96 ( ( member_nat @ X2 @ A1 )
% 4.69/4.96 => ? [Y3: nat] :
% 4.69/4.96 ( ( member_nat @ Y3 @ A22 )
% 4.69/4.96 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ R3 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % max_ext.simps
% 4.69/4.96 thf(fact_2814_max__ext_Osimps,axiom,
% 4.69/4.96 ! [A1: set_int,A22: set_int,R3: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ( ( member2572552093476627150et_int @ ( produc6363374080413544029et_int @ A1 @ A22 ) @ ( max_ext_int @ R3 ) )
% 4.69/4.96 = ( ( finite_finite_int @ A1 )
% 4.69/4.96 & ( finite_finite_int @ A22 )
% 4.69/4.96 & ( A22 != bot_bot_set_int )
% 4.69/4.96 & ! [X2: int] :
% 4.69/4.96 ( ( member_int @ X2 @ A1 )
% 4.69/4.96 => ? [Y3: int] :
% 4.69/4.96 ( ( member_int @ Y3 @ A22 )
% 4.69/4.96 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ R3 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % max_ext.simps
% 4.69/4.96 thf(fact_2815_max__ext_Osimps,axiom,
% 4.69/4.96 ! [A1: set_Pr4532377907799695533_nat_o,A22: set_Pr4532377907799695533_nat_o,R3: set_Pr2161125870931222855_nat_o] :
% 4.69/4.96 ( ( member6623172407746373520_nat_o @ ( produc5149316574908490455_nat_o @ A1 @ A22 ) @ ( max_ex5265246208886859912_nat_o @ R3 ) )
% 4.69/4.96 = ( ( finite3252695134891459830_nat_o @ A1 )
% 4.69/4.96 & ( finite3252695134891459830_nat_o @ A22 )
% 4.69/4.96 & ( A22 != bot_bo7824918357723582233_nat_o )
% 4.69/4.96 & ! [X2: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ X2 @ A1 )
% 4.69/4.96 => ? [Y3: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ Y3 @ A22 )
% 4.69/4.96 & ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X2 @ Y3 ) @ R3 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % max_ext.simps
% 4.69/4.96 thf(fact_2816_max__ext_Ocases,axiom,
% 4.69/4.96 ! [A1: set_Code_integer,A22: set_Code_integer,R3: set_Pr4811707699266497531nteger] :
% 4.69/4.96 ( ( member4307123515891402160nteger @ ( produc7443773368509356479nteger @ A1 @ A22 ) @ ( max_ext_Code_integer @ R3 ) )
% 4.69/4.96 => ~ ( ( finite6017078050557962740nteger @ A1 )
% 4.69/4.96 => ( ( finite6017078050557962740nteger @ A22 )
% 4.69/4.96 => ( ( A22 != bot_bo3990330152332043303nteger )
% 4.69/4.96 => ~ ! [X6: code_integer] :
% 4.69/4.96 ( ( member_Code_integer @ X6 @ A1 )
% 4.69/4.96 => ? [Xa3: code_integer] :
% 4.69/4.96 ( ( member_Code_integer @ Xa3 @ A22 )
% 4.69/4.96 & ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X6 @ Xa3 ) @ R3 ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % max_ext.cases
% 4.69/4.96 thf(fact_2817_max__ext_Ocases,axiom,
% 4.69/4.96 ! [A1: set_Product_unit,A22: set_Product_unit,R3: set_Pr5094982260447487303t_unit] :
% 4.69/4.96 ( ( member4189953012975926160t_unit @ ( produc7269801343787132631t_unit @ A1 @ A22 ) @ ( max_ext_Product_unit @ R3 ) )
% 4.69/4.96 => ~ ( ( finite4290736615968046902t_unit @ A1 )
% 4.69/4.96 => ( ( finite4290736615968046902t_unit @ A22 )
% 4.69/4.96 => ( ( A22 != bot_bo3957492148770167129t_unit )
% 4.69/4.96 => ~ ! [X6: product_unit] :
% 4.69/4.96 ( ( member_Product_unit @ X6 @ A1 )
% 4.69/4.96 => ? [Xa3: product_unit] :
% 4.69/4.96 ( ( member_Product_unit @ Xa3 @ A22 )
% 4.69/4.96 & ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X6 @ Xa3 ) @ R3 ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % max_ext.cases
% 4.69/4.96 thf(fact_2818_max__ext_Ocases,axiom,
% 4.69/4.96 ! [A1: set_o,A22: set_o,R3: set_Product_prod_o_o] :
% 4.69/4.96 ( ( member9116954335612470352_set_o @ ( produc5838405689764958487_set_o @ A1 @ A22 ) @ ( max_ext_o @ R3 ) )
% 4.69/4.96 => ~ ( ( finite_finite_o @ A1 )
% 4.69/4.96 => ( ( finite_finite_o @ A22 )
% 4.69/4.96 => ( ( A22 != bot_bot_set_o )
% 4.69/4.96 => ~ ! [X6: $o] :
% 4.69/4.96 ( ( member_o @ X6 @ A1 )
% 4.69/4.96 => ? [Xa3: $o] :
% 4.69/4.96 ( ( member_o @ Xa3 @ A22 )
% 4.69/4.96 & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X6 @ Xa3 ) @ R3 ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % max_ext.cases
% 4.69/4.96 thf(fact_2819_max__ext_Ocases,axiom,
% 4.69/4.96 ! [A1: set_nat,A22: set_nat,R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A1 @ A22 ) @ ( max_ext_nat @ R3 ) )
% 4.69/4.96 => ~ ( ( finite_finite_nat @ A1 )
% 4.69/4.96 => ( ( finite_finite_nat @ A22 )
% 4.69/4.96 => ( ( A22 != bot_bot_set_nat )
% 4.69/4.96 => ~ ! [X6: nat] :
% 4.69/4.96 ( ( member_nat @ X6 @ A1 )
% 4.69/4.96 => ? [Xa3: nat] :
% 4.69/4.96 ( ( member_nat @ Xa3 @ A22 )
% 4.69/4.96 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X6 @ Xa3 ) @ R3 ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % max_ext.cases
% 4.69/4.96 thf(fact_2820_max__ext_Ocases,axiom,
% 4.69/4.96 ! [A1: set_int,A22: set_int,R3: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ( ( member2572552093476627150et_int @ ( produc6363374080413544029et_int @ A1 @ A22 ) @ ( max_ext_int @ R3 ) )
% 4.69/4.96 => ~ ( ( finite_finite_int @ A1 )
% 4.69/4.96 => ( ( finite_finite_int @ A22 )
% 4.69/4.96 => ( ( A22 != bot_bot_set_int )
% 4.69/4.96 => ~ ! [X6: int] :
% 4.69/4.96 ( ( member_int @ X6 @ A1 )
% 4.69/4.96 => ? [Xa3: int] :
% 4.69/4.96 ( ( member_int @ Xa3 @ A22 )
% 4.69/4.96 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X6 @ Xa3 ) @ R3 ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % max_ext.cases
% 4.69/4.96 thf(fact_2821_max__ext_Ocases,axiom,
% 4.69/4.96 ! [A1: set_Pr4532377907799695533_nat_o,A22: set_Pr4532377907799695533_nat_o,R3: set_Pr2161125870931222855_nat_o] :
% 4.69/4.96 ( ( member6623172407746373520_nat_o @ ( produc5149316574908490455_nat_o @ A1 @ A22 ) @ ( max_ex5265246208886859912_nat_o @ R3 ) )
% 4.69/4.96 => ~ ( ( finite3252695134891459830_nat_o @ A1 )
% 4.69/4.96 => ( ( finite3252695134891459830_nat_o @ A22 )
% 4.69/4.96 => ( ( A22 != bot_bo7824918357723582233_nat_o )
% 4.69/4.96 => ~ ! [X6: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ X6 @ A1 )
% 4.69/4.96 => ? [Xa3: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ Xa3 @ A22 )
% 4.69/4.96 & ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X6 @ Xa3 ) @ R3 ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % max_ext.cases
% 4.69/4.96 thf(fact_2822_inf__period_I2_J,axiom,
% 4.69/4.96 ! [P: rat > $o,D3: rat,Q2: rat > $o] :
% 4.69/4.96 ( ! [X3: rat,K: rat] :
% 4.69/4.96 ( ( P @ X3 )
% 4.69/4.96 = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D3 ) ) ) )
% 4.69/4.96 => ( ! [X3: rat,K: rat] :
% 4.69/4.96 ( ( Q2 @ X3 )
% 4.69/4.96 = ( Q2 @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D3 ) ) ) )
% 4.69/4.96 => ! [X6: rat,K2: rat] :
% 4.69/4.96 ( ( ( P @ X6 )
% 4.69/4.96 | ( Q2 @ X6 ) )
% 4.69/4.96 = ( ( P @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K2 @ D3 ) ) )
% 4.69/4.96 | ( Q2 @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K2 @ D3 ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % inf_period(2)
% 4.69/4.96 thf(fact_2823_inf__period_I2_J,axiom,
% 4.69/4.96 ! [P: int > $o,D3: int,Q2: int > $o] :
% 4.69/4.96 ( ! [X3: int,K: int] :
% 4.69/4.96 ( ( P @ X3 )
% 4.69/4.96 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 4.69/4.96 => ( ! [X3: int,K: int] :
% 4.69/4.96 ( ( Q2 @ X3 )
% 4.69/4.96 = ( Q2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 4.69/4.96 => ! [X6: int,K2: int] :
% 4.69/4.96 ( ( ( P @ X6 )
% 4.69/4.96 | ( Q2 @ X6 ) )
% 4.69/4.96 = ( ( P @ ( minus_minus_int @ X6 @ ( times_times_int @ K2 @ D3 ) ) )
% 4.69/4.96 | ( Q2 @ ( minus_minus_int @ X6 @ ( times_times_int @ K2 @ D3 ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % inf_period(2)
% 4.69/4.96 thf(fact_2824_inf__period_I1_J,axiom,
% 4.69/4.96 ! [P: rat > $o,D3: rat,Q2: rat > $o] :
% 4.69/4.96 ( ! [X3: rat,K: rat] :
% 4.69/4.96 ( ( P @ X3 )
% 4.69/4.96 = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D3 ) ) ) )
% 4.69/4.96 => ( ! [X3: rat,K: rat] :
% 4.69/4.96 ( ( Q2 @ X3 )
% 4.69/4.96 = ( Q2 @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D3 ) ) ) )
% 4.69/4.96 => ! [X6: rat,K2: rat] :
% 4.69/4.96 ( ( ( P @ X6 )
% 4.69/4.96 & ( Q2 @ X6 ) )
% 4.69/4.96 = ( ( P @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K2 @ D3 ) ) )
% 4.69/4.96 & ( Q2 @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K2 @ D3 ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % inf_period(1)
% 4.69/4.96 thf(fact_2825_inf__period_I1_J,axiom,
% 4.69/4.96 ! [P: int > $o,D3: int,Q2: int > $o] :
% 4.69/4.96 ( ! [X3: int,K: int] :
% 4.69/4.96 ( ( P @ X3 )
% 4.69/4.96 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 4.69/4.96 => ( ! [X3: int,K: int] :
% 4.69/4.96 ( ( Q2 @ X3 )
% 4.69/4.96 = ( Q2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 4.69/4.96 => ! [X6: int,K2: int] :
% 4.69/4.96 ( ( ( P @ X6 )
% 4.69/4.96 & ( Q2 @ X6 ) )
% 4.69/4.96 = ( ( P @ ( minus_minus_int @ X6 @ ( times_times_int @ K2 @ D3 ) ) )
% 4.69/4.96 & ( Q2 @ ( minus_minus_int @ X6 @ ( times_times_int @ K2 @ D3 ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % inf_period(1)
% 4.69/4.96 thf(fact_2826_left__diff__distrib,axiom,
% 4.69/4.96 ! [A2: rat,B: rat,C: rat] :
% 4.69/4.96 ( ( times_times_rat @ ( minus_minus_rat @ A2 @ B ) @ C )
% 4.69/4.96 = ( minus_minus_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % left_diff_distrib
% 4.69/4.96 thf(fact_2827_left__diff__distrib,axiom,
% 4.69/4.96 ! [A2: int,B: int,C: int] :
% 4.69/4.96 ( ( times_times_int @ ( minus_minus_int @ A2 @ B ) @ C )
% 4.69/4.96 = ( minus_minus_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % left_diff_distrib
% 4.69/4.96 thf(fact_2828_right__diff__distrib,axiom,
% 4.69/4.96 ! [A2: rat,B: rat,C: rat] :
% 4.69/4.96 ( ( times_times_rat @ A2 @ ( minus_minus_rat @ B @ C ) )
% 4.69/4.96 = ( minus_minus_rat @ ( times_times_rat @ A2 @ B ) @ ( times_times_rat @ A2 @ C ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % right_diff_distrib
% 4.69/4.96 thf(fact_2829_right__diff__distrib,axiom,
% 4.69/4.96 ! [A2: int,B: int,C: int] :
% 4.69/4.96 ( ( times_times_int @ A2 @ ( minus_minus_int @ B @ C ) )
% 4.69/4.96 = ( minus_minus_int @ ( times_times_int @ A2 @ B ) @ ( times_times_int @ A2 @ C ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % right_diff_distrib
% 4.69/4.96 thf(fact_2830_left__diff__distrib_H,axiom,
% 4.69/4.96 ! [B: rat,C: rat,A2: rat] :
% 4.69/4.96 ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A2 )
% 4.69/4.96 = ( minus_minus_rat @ ( times_times_rat @ B @ A2 ) @ ( times_times_rat @ C @ A2 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % left_diff_distrib'
% 4.69/4.96 thf(fact_2831_left__diff__distrib_H,axiom,
% 4.69/4.96 ! [B: nat,C: nat,A2: nat] :
% 4.69/4.96 ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A2 )
% 4.69/4.96 = ( minus_minus_nat @ ( times_times_nat @ B @ A2 ) @ ( times_times_nat @ C @ A2 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % left_diff_distrib'
% 4.69/4.96 thf(fact_2832_left__diff__distrib_H,axiom,
% 4.69/4.96 ! [B: int,C: int,A2: int] :
% 4.69/4.96 ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A2 )
% 4.69/4.96 = ( minus_minus_int @ ( times_times_int @ B @ A2 ) @ ( times_times_int @ C @ A2 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % left_diff_distrib'
% 4.69/4.96 thf(fact_2833_right__diff__distrib_H,axiom,
% 4.69/4.96 ! [A2: rat,B: rat,C: rat] :
% 4.69/4.96 ( ( times_times_rat @ A2 @ ( minus_minus_rat @ B @ C ) )
% 4.69/4.96 = ( minus_minus_rat @ ( times_times_rat @ A2 @ B ) @ ( times_times_rat @ A2 @ C ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % right_diff_distrib'
% 4.69/4.96 thf(fact_2834_right__diff__distrib_H,axiom,
% 4.69/4.96 ! [A2: nat,B: nat,C: nat] :
% 4.69/4.96 ( ( times_times_nat @ A2 @ ( minus_minus_nat @ B @ C ) )
% 4.69/4.96 = ( minus_minus_nat @ ( times_times_nat @ A2 @ B ) @ ( times_times_nat @ A2 @ C ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % right_diff_distrib'
% 4.69/4.96 thf(fact_2835_right__diff__distrib_H,axiom,
% 4.69/4.96 ! [A2: int,B: int,C: int] :
% 4.69/4.96 ( ( times_times_int @ A2 @ ( minus_minus_int @ B @ C ) )
% 4.69/4.96 = ( minus_minus_int @ ( times_times_int @ A2 @ B ) @ ( times_times_int @ A2 @ C ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % right_diff_distrib'
% 4.69/4.96 thf(fact_2836_in__lex__prod,axiom,
% 4.69/4.96 ! [A2: nat,B: int,A5: nat,B3: int,R2: set_Pr1261947904930325089at_nat,S2: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ( ( member4619661753630440592at_int @ ( produc886916002739626967at_int @ ( product_Pair_nat_int @ A2 @ B ) @ ( product_Pair_nat_int @ A5 @ B3 ) ) @ ( lex_prod_nat_int @ R2 @ S2 ) )
% 4.69/4.96 = ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ A5 ) @ R2 )
% 4.69/4.96 | ( ( A2 = A5 )
% 4.69/4.96 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ B3 ) @ S2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % in_lex_prod
% 4.69/4.96 thf(fact_2837_in__lex__prod,axiom,
% 4.69/4.96 ! [A2: int,B: nat,A5: int,B3: nat,R2: set_Pr958786334691620121nt_int,S2: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ( member2930414080797523088nt_nat @ ( produc8921240378546987991nt_nat @ ( product_Pair_int_nat @ A2 @ B ) @ ( product_Pair_int_nat @ A5 @ B3 ) ) @ ( lex_prod_int_nat @ R2 @ S2 ) )
% 4.69/4.96 = ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ A5 ) @ R2 )
% 4.69/4.96 | ( ( A2 = A5 )
% 4.69/4.96 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ B3 ) @ S2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % in_lex_prod
% 4.69/4.96 thf(fact_2838_in__lex__prod,axiom,
% 4.69/4.96 ! [A2: heap_e7401611519738050253t_unit,B: set_nat,A5: heap_e7401611519738050253t_unit,B3: set_nat,R2: set_Pr1776176089890104647t_unit,S2: set_Pr5488025237498180813et_nat] :
% 4.69/4.96 ( ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ ( produc7507926704131184380et_nat @ A2 @ B ) @ ( produc7507926704131184380et_nat @ A5 @ B3 ) ) @ ( lex_pr538634069021852900et_nat @ R2 @ S2 ) )
% 4.69/4.96 = ( ( member5046970461208427408t_unit @ ( produc8256076736985659095t_unit @ A2 @ A5 ) @ R2 )
% 4.69/4.96 | ( ( A2 = A5 )
% 4.69/4.96 & ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ B @ B3 ) @ S2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % in_lex_prod
% 4.69/4.96 thf(fact_2839_in__lex__prod,axiom,
% 4.69/4.96 ! [A2: nat,B: nat,A5: nat,B3: nat,R2: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( product_Pair_nat_nat @ A5 @ B3 ) ) @ ( lex_prod_nat_nat @ R2 @ S2 ) )
% 4.69/4.96 = ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ A5 ) @ R2 )
% 4.69/4.96 | ( ( A2 = A5 )
% 4.69/4.96 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ B3 ) @ S2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % in_lex_prod
% 4.69/4.96 thf(fact_2840_in__lex__prod,axiom,
% 4.69/4.96 ! [A2: int,B: int,A5: int,B3: int,R2: set_Pr958786334691620121nt_int,S2: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( product_Pair_int_int @ A5 @ B3 ) ) @ ( lex_prod_int_int @ R2 @ S2 ) )
% 4.69/4.96 = ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ A5 ) @ R2 )
% 4.69/4.96 | ( ( A2 = A5 )
% 4.69/4.96 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ B3 ) @ S2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % in_lex_prod
% 4.69/4.96 thf(fact_2841_in__lex__prod,axiom,
% 4.69/4.96 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A5: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat,R2: set_Pr2161125870931222855_nat_o,S2: set_Pr719794911490849221et_nat] :
% 4.69/4.96 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ A2 @ B ) @ ( produc5001842942810119800et_nat @ A5 @ B3 ) ) @ ( lex_pr5340572901959109728et_nat @ R2 @ S2 ) )
% 4.69/4.96 = ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ A5 ) @ R2 )
% 4.69/4.96 | ( ( A2 = A5 )
% 4.69/4.96 & ( member6099555550032318734et_nat @ ( produc8199053930788261021et_nat @ B @ B3 ) @ S2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % in_lex_prod
% 4.69/4.96 thf(fact_2842_in__lex__prod,axiom,
% 4.69/4.96 ! [A2: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A5: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat,R2: set_Pr2161125870931222855_nat_o,S2: set_Pr7928877670098842301et_nat] :
% 4.69/4.96 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ A2 @ B ) @ ( produc2245416461498447860et_nat @ A5 @ B3 ) ) @ ( lex_pr4722427456421979612et_nat @ R2 @ S2 ) )
% 4.69/4.96 = ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ A5 ) @ R2 )
% 4.69/4.96 | ( ( A2 = A5 )
% 4.69/4.96 & ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ B @ B3 ) @ S2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % in_lex_prod
% 4.69/4.96 thf(fact_2843_Linear__order__wf__diff__Id,axiom,
% 4.69/4.96 ! [R2: set_Pr5094982260447487303t_unit] :
% 4.69/4.96 ( ( order_888282469287196226t_unit @ ( field_Product_unit @ R2 ) @ R2 )
% 4.69/4.96 => ( ( wf_Product_unit @ ( minus_6985556733573110190t_unit @ R2 @ id_Product_unit ) )
% 4.69/4.96 = ( ! [A3: set_Product_unit] :
% 4.69/4.96 ( ( ord_le3507040750410214029t_unit @ A3 @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( A3 != bot_bo3957492148770167129t_unit )
% 4.69/4.96 => ? [X2: product_unit] :
% 4.69/4.96 ( ( member_Product_unit @ X2 @ A3 )
% 4.69/4.96 & ! [Y3: product_unit] :
% 4.69/4.96 ( ( member_Product_unit @ Y3 @ A3 )
% 4.69/4.96 => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X2 @ Y3 ) @ R2 ) ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Linear_order_wf_diff_Id
% 4.69/4.96 thf(fact_2844_Linear__order__wf__diff__Id,axiom,
% 4.69/4.96 ! [R2: set_Product_prod_o_o] :
% 4.69/4.96 ( ( order_6238756238976269133r_on_o @ ( field_o @ R2 ) @ R2 )
% 4.69/4.96 => ( ( wf_o @ ( minus_7052513330764642158od_o_o @ R2 @ id_o2 ) )
% 4.69/4.96 = ( ! [A3: set_o] :
% 4.69/4.96 ( ( ord_less_eq_set_o @ A3 @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( A3 != bot_bot_set_o )
% 4.69/4.96 => ? [X2: $o] :
% 4.69/4.96 ( ( member_o @ X2 @ A3 )
% 4.69/4.96 & ! [Y3: $o] :
% 4.69/4.96 ( ( member_o @ Y3 @ A3 )
% 4.69/4.96 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X2 @ Y3 ) @ R2 ) ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Linear_order_wf_diff_Id
% 4.69/4.96 thf(fact_2845_Linear__order__wf__diff__Id,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ( ( order_4471489696718655927on_int @ ( field_int @ R2 ) @ R2 )
% 4.69/4.96 => ( ( wf_int @ ( minus_1052850069191792384nt_int @ R2 @ id_int ) )
% 4.69/4.96 = ( ! [A3: set_int] :
% 4.69/4.96 ( ( ord_less_eq_set_int @ A3 @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( A3 != bot_bot_set_int )
% 4.69/4.96 => ? [X2: int] :
% 4.69/4.96 ( ( member_int @ X2 @ A3 )
% 4.69/4.96 & ! [Y3: int] :
% 4.69/4.96 ( ( member_int @ Y3 @ A3 )
% 4.69/4.96 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ R2 ) ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Linear_order_wf_diff_Id
% 4.69/4.96 thf(fact_2846_Linear__order__wf__diff__Id,axiom,
% 4.69/4.96 ! [R2: set_Pr2161125870931222855_nat_o] :
% 4.69/4.96 ( ( order_1145710701291701250_nat_o @ ( field_81821745747897882_nat_o @ R2 ) @ R2 )
% 4.69/4.96 => ( ( wf_Pro8787509627421085110_nat_o @ ( minus_9189903262233110958_nat_o @ R2 @ id_Pro6775173067513470761_nat_o ) )
% 4.69/4.96 = ( ! [A3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.96 ( ( ord_le2965882846123202637_nat_o @ A3 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( A3 != bot_bo7824918357723582233_nat_o )
% 4.69/4.96 => ? [X2: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ X2 @ A3 )
% 4.69/4.96 & ! [Y3: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ Y3 @ A3 )
% 4.69/4.96 => ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X2 @ Y3 ) @ R2 ) ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Linear_order_wf_diff_Id
% 4.69/4.96 thf(fact_2847_Linear__order__wf__diff__Id,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ( order_4473980167227706203on_nat @ ( field_nat @ R2 ) @ R2 )
% 4.69/4.96 => ( ( wf_nat @ ( minus_1356011639430497352at_nat @ R2 @ id_nat ) )
% 4.69/4.96 = ( ! [A3: set_nat] :
% 4.69/4.96 ( ( ord_less_eq_set_nat @ A3 @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( A3 != bot_bot_set_nat )
% 4.69/4.96 => ? [X2: nat] :
% 4.69/4.96 ( ( member_nat @ X2 @ A3 )
% 4.69/4.96 & ! [Y3: nat] :
% 4.69/4.96 ( ( member_nat @ Y3 @ A3 )
% 4.69/4.96 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ R2 ) ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Linear_order_wf_diff_Id
% 4.69/4.96 thf(fact_2848_remove__def,axiom,
% 4.69/4.96 ( remove_Product_unit
% 4.69/4.96 = ( ^ [X2: product_unit,A3: set_Product_unit] : ( minus_6452836326544984404t_unit @ A3 @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % remove_def
% 4.69/4.96 thf(fact_2849_remove__def,axiom,
% 4.69/4.96 ( remove_o
% 4.69/4.96 = ( ^ [X2: $o,A3: set_o] : ( minus_minus_set_o @ A3 @ ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % remove_def
% 4.69/4.96 thf(fact_2850_remove__def,axiom,
% 4.69/4.96 ( remove_int
% 4.69/4.96 = ( ^ [X2: int,A3: set_int] : ( minus_minus_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % remove_def
% 4.69/4.96 thf(fact_2851_remove__def,axiom,
% 4.69/4.96 ( remove4651630035290841522_nat_o
% 4.69/4.96 = ( ^ [X2: produc3658429121746597890et_nat > $o,A3: set_Pr4532377907799695533_nat_o] : ( minus_1801376950450012436_nat_o @ A3 @ ( insert5175938949040314269_nat_o @ X2 @ bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % remove_def
% 4.69/4.96 thf(fact_2852_remove__def,axiom,
% 4.69/4.96 ( remove_nat
% 4.69/4.96 = ( ^ [X2: nat,A3: set_nat] : ( minus_minus_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % remove_def
% 4.69/4.96 thf(fact_2853_wo__rel_Ocases__Total3,axiom,
% 4.69/4.96 ! [R2: set_Pr5094982260447487303t_unit,A2: product_unit,B: product_unit,Phi: product_unit > product_unit > $o] :
% 4.69/4.96 ( ( bNF_We2091578341578594809t_unit @ R2 )
% 4.69/4.96 => ( ( ord_le3507040750410214029t_unit @ ( insert_Product_unit @ A2 @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A2 @ B ) @ ( minus_6985556733573110190t_unit @ R2 @ id_Product_unit ) )
% 4.69/4.96 | ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ B @ A2 ) @ ( minus_6985556733573110190t_unit @ R2 @ id_Product_unit ) ) )
% 4.69/4.96 => ( Phi @ A2 @ B ) )
% 4.69/4.96 => ( ( ( A2 = B )
% 4.69/4.96 => ( Phi @ A2 @ B ) )
% 4.69/4.96 => ( Phi @ A2 @ B ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.cases_Total3
% 4.69/4.96 thf(fact_2854_wo__rel_Ocases__Total3,axiom,
% 4.69/4.96 ! [R2: set_Product_prod_o_o,A2: $o,B: $o,Phi: $o > $o > $o] :
% 4.69/4.96 ( ( bNF_We6437023980930612612_rel_o @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_o @ ( insert_o @ A2 @ ( insert_o @ B @ bot_bot_set_o ) ) @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ B ) @ ( minus_7052513330764642158od_o_o @ R2 @ id_o2 ) )
% 4.69/4.96 | ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ B @ A2 ) @ ( minus_7052513330764642158od_o_o @ R2 @ id_o2 ) ) )
% 4.69/4.96 => ( Phi @ A2 @ B ) )
% 4.69/4.96 => ( ( ( A2 = B )
% 4.69/4.96 => ( Phi @ A2 @ B ) )
% 4.69/4.96 => ( Phi @ A2 @ B ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.cases_Total3
% 4.69/4.96 thf(fact_2855_wo__rel_Ocases__Total3,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,A2: int,B: int,Phi: int > int > $o] :
% 4.69/4.96 ( ( bNF_We3815749466139970368el_int @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_int @ ( insert_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( minus_1052850069191792384nt_int @ R2 @ id_int ) )
% 4.69/4.96 | ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ A2 ) @ ( minus_1052850069191792384nt_int @ R2 @ id_int ) ) )
% 4.69/4.96 => ( Phi @ A2 @ B ) )
% 4.69/4.96 => ( ( ( A2 = B )
% 4.69/4.96 => ( Phi @ A2 @ B ) )
% 4.69/4.96 => ( Phi @ A2 @ B ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.cases_Total3
% 4.69/4.96 thf(fact_2856_wo__rel_Ocases__Total3,axiom,
% 4.69/4.96 ! [R2: set_Pr2161125870931222855_nat_o,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o,Phi: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o] :
% 4.69/4.96 ( ( bNF_We740377018556551609_nat_o @ R2 )
% 4.69/4.96 => ( ( ord_le2965882846123202637_nat_o @ ( insert5175938949040314269_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o ) ) @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ B ) @ ( minus_9189903262233110958_nat_o @ R2 @ id_Pro6775173067513470761_nat_o ) )
% 4.69/4.96 | ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ B @ A2 ) @ ( minus_9189903262233110958_nat_o @ R2 @ id_Pro6775173067513470761_nat_o ) ) )
% 4.69/4.96 => ( Phi @ A2 @ B ) )
% 4.69/4.96 => ( ( ( A2 = B )
% 4.69/4.96 => ( Phi @ A2 @ B ) )
% 4.69/4.96 => ( Phi @ A2 @ B ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.cases_Total3
% 4.69/4.96 thf(fact_2857_wo__rel_Ocases__Total3,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,A2: nat,B: nat,Phi: nat > nat > $o] :
% 4.69/4.96 ( ( bNF_We3818239936649020644el_nat @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_nat @ ( insert_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( minus_1356011639430497352at_nat @ R2 @ id_nat ) )
% 4.69/4.96 | ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ A2 ) @ ( minus_1356011639430497352at_nat @ R2 @ id_nat ) ) )
% 4.69/4.96 => ( Phi @ A2 @ B ) )
% 4.69/4.96 => ( ( ( A2 = B )
% 4.69/4.96 => ( Phi @ A2 @ B ) )
% 4.69/4.96 => ( Phi @ A2 @ B ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.cases_Total3
% 4.69/4.96 thf(fact_2858_wf__max,axiom,
% 4.69/4.96 ! [R3: set_Pr2161125870931222855_nat_o] :
% 4.69/4.96 ( ( wf_Pro8787509627421085110_nat_o @ ( conver2764731894203590139_nat_o @ R3 ) )
% 4.69/4.96 => ( ( R3 != bot_bo3657187498359500723_nat_o )
% 4.69/4.96 => ~ ! [M2: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ~ ( member6576561426505652726_nat_o @ M2 @ ( minus_1801376950450012436_nat_o @ ( range_5289318983786108341_nat_o @ R3 ) @ ( domain4881241903163524940_nat_o @ R3 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_max
% 4.69/4.96 thf(fact_2859_wf__max,axiom,
% 4.69/4.96 ! [R3: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ( ( wf_int @ ( converse_int_int @ R3 ) )
% 4.69/4.96 => ( ( R3 != bot_bo1796632182523588997nt_int )
% 4.69/4.96 => ~ ! [M2: int] :
% 4.69/4.96 ~ ( member_int @ M2 @ ( minus_minus_set_int @ ( range_int_int @ R3 ) @ ( domain_int_int @ R3 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_max
% 4.69/4.96 thf(fact_2860_wf__max,axiom,
% 4.69/4.96 ! [R3: set_Product_prod_o_o] :
% 4.69/4.96 ( ( wf_o @ ( converse_o_o @ R3 ) )
% 4.69/4.96 => ( ( R3 != bot_bo7073875226086086771od_o_o )
% 4.69/4.96 => ~ ! [M2: $o] :
% 4.69/4.96 ~ ( member_o @ M2 @ ( minus_minus_set_o @ ( range_o_o @ R3 ) @ ( domain_o_o @ R3 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_max
% 4.69/4.96 thf(fact_2861_wf__max,axiom,
% 4.69/4.96 ! [R3: set_Pr5094982260447487303t_unit] :
% 4.69/4.96 ( ( wf_Product_unit @ ( conver2495244158383847931t_unit @ R3 ) )
% 4.69/4.96 => ( ( R3 != bot_bo1654022762305692595t_unit )
% 4.69/4.96 => ~ ! [M2: product_unit] :
% 4.69/4.96 ~ ( member_Product_unit @ M2 @ ( minus_6452836326544984404t_unit @ ( range_6617724647562260917t_unit @ R3 ) @ ( domain4292024440186670924t_unit @ R3 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_max
% 4.69/4.96 thf(fact_2862_wf__max,axiom,
% 4.69/4.96 ! [R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ( wf_nat @ ( converse_nat_nat @ R3 ) )
% 4.69/4.96 => ( ( R3 != bot_bo2099793752762293965at_nat )
% 4.69/4.96 => ~ ! [M2: nat] :
% 4.69/4.96 ~ ( member_nat @ M2 @ ( minus_minus_set_nat @ ( range_nat_nat @ R3 ) @ ( domain_nat_nat @ R3 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_max
% 4.69/4.96 thf(fact_2863_wf__Un,axiom,
% 4.69/4.96 ! [R2: set_Pr5094982260447487303t_unit,S2: set_Pr5094982260447487303t_unit] :
% 4.69/4.96 ( ( wf_Product_unit @ R2 )
% 4.69/4.96 => ( ( wf_Product_unit @ S2 )
% 4.69/4.96 => ( ( ( inf_in4660618365625256667t_unit @ ( domain4292024440186670924t_unit @ R2 ) @ ( range_6617724647562260917t_unit @ S2 ) )
% 4.69/4.96 = bot_bo3957492148770167129t_unit )
% 4.69/4.96 => ( wf_Product_unit @ ( sup_su6481247232241170203t_unit @ R2 @ S2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_Un
% 4.69/4.96 thf(fact_2864_wf__Un,axiom,
% 4.69/4.96 ! [R2: set_Product_prod_o_o,S2: set_Product_prod_o_o] :
% 4.69/4.96 ( ( wf_o @ R2 )
% 4.69/4.96 => ( ( wf_o @ S2 )
% 4.69/4.96 => ( ( ( inf_inf_set_o @ ( domain_o_o @ R2 ) @ ( range_o_o @ S2 ) )
% 4.69/4.96 = bot_bot_set_o )
% 4.69/4.96 => ( wf_o @ ( sup_su5769328420594410459od_o_o @ R2 @ S2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_Un
% 4.69/4.96 thf(fact_2865_wf__Un,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ( wf_nat @ R2 )
% 4.69/4.96 => ( ( wf_nat @ S2 )
% 4.69/4.96 => ( ( ( inf_inf_set_nat @ ( domain_nat_nat @ R2 ) @ ( range_nat_nat @ S2 ) )
% 4.69/4.96 = bot_bot_set_nat )
% 4.69/4.96 => ( wf_nat @ ( sup_su6327502436637775413at_nat @ R2 @ S2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_Un
% 4.69/4.96 thf(fact_2866_wf__Un,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,S2: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ( ( wf_int @ R2 )
% 4.69/4.96 => ( ( wf_int @ S2 )
% 4.69/4.96 => ( ( ( inf_inf_set_int @ ( domain_int_int @ R2 ) @ ( range_int_int @ S2 ) )
% 4.69/4.96 = bot_bot_set_int )
% 4.69/4.96 => ( wf_int @ ( sup_su6024340866399070445nt_int @ R2 @ S2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_Un
% 4.69/4.96 thf(fact_2867_wf__Un,axiom,
% 4.69/4.96 ! [R2: set_Pr2161125870931222855_nat_o,S2: set_Pr2161125870931222855_nat_o] :
% 4.69/4.96 ( ( wf_Pro8787509627421085110_nat_o @ R2 )
% 4.69/4.96 => ( ( wf_Pro8787509627421085110_nat_o @ S2 )
% 4.69/4.96 => ( ( ( inf_in1906310914598751387_nat_o @ ( domain4881241903163524940_nat_o @ R2 ) @ ( range_5289318983786108341_nat_o @ S2 ) )
% 4.69/4.96 = bot_bo7824918357723582233_nat_o )
% 4.69/4.96 => ( wf_Pro8787509627421085110_nat_o @ ( sup_su8328026650783933211_nat_o @ R2 @ S2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_Un
% 4.69/4.96 thf(fact_2868_Linear__order__Well__order__iff,axiom,
% 4.69/4.96 ! [R2: set_Pr5094982260447487303t_unit] :
% 4.69/4.96 ( ( order_888282469287196226t_unit @ ( field_Product_unit @ R2 ) @ R2 )
% 4.69/4.96 => ( ( order_3164716736300062379t_unit @ ( field_Product_unit @ R2 ) @ R2 )
% 4.69/4.96 = ( ! [A3: set_Product_unit] :
% 4.69/4.96 ( ( ord_le3507040750410214029t_unit @ A3 @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( A3 != bot_bo3957492148770167129t_unit )
% 4.69/4.96 => ? [X2: product_unit] :
% 4.69/4.96 ( ( member_Product_unit @ X2 @ A3 )
% 4.69/4.96 & ! [Y3: product_unit] :
% 4.69/4.96 ( ( member_Product_unit @ Y3 @ A3 )
% 4.69/4.96 => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ X2 @ Y3 ) @ R2 ) ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Linear_order_Well_order_iff
% 4.69/4.96 thf(fact_2869_Linear__order__Well__order__iff,axiom,
% 4.69/4.96 ! [R2: set_Product_prod_o_o] :
% 4.69/4.96 ( ( order_6238756238976269133r_on_o @ ( field_o @ R2 ) @ R2 )
% 4.69/4.96 => ( ( order_2615775362358406454r_on_o @ ( field_o @ R2 ) @ R2 )
% 4.69/4.96 = ( ! [A3: set_o] :
% 4.69/4.96 ( ( ord_less_eq_set_o @ A3 @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( A3 != bot_bot_set_o )
% 4.69/4.96 => ? [X2: $o] :
% 4.69/4.96 ( ( member_o @ X2 @ A3 )
% 4.69/4.96 & ! [Y3: $o] :
% 4.69/4.96 ( ( member_o @ Y3 @ A3 )
% 4.69/4.96 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X2 @ Y3 ) @ R2 ) ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Linear_order_Well_order_iff
% 4.69/4.96 thf(fact_2870_Linear__order__Well__order__iff,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ( ( order_4471489696718655927on_int @ ( field_int @ R2 ) @ R2 )
% 4.69/4.96 => ( ( order_2886507596567047182on_int @ ( field_int @ R2 ) @ R2 )
% 4.69/4.96 = ( ! [A3: set_int] :
% 4.69/4.96 ( ( ord_less_eq_set_int @ A3 @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( A3 != bot_bot_set_int )
% 4.69/4.96 => ? [X2: int] :
% 4.69/4.96 ( ( member_int @ X2 @ A3 )
% 4.69/4.96 & ! [Y3: int] :
% 4.69/4.96 ( ( member_int @ Y3 @ A3 )
% 4.69/4.96 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ R2 ) ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Linear_order_Well_order_iff
% 4.69/4.96 thf(fact_2871_Linear__order__Well__order__iff,axiom,
% 4.69/4.96 ! [R2: set_Pr2161125870931222855_nat_o] :
% 4.69/4.96 ( ( order_1145710701291701250_nat_o @ ( field_81821745747897882_nat_o @ R2 ) @ R2 )
% 4.69/4.96 => ( ( order_2118566763991480939_nat_o @ ( field_81821745747897882_nat_o @ R2 ) @ R2 )
% 4.69/4.96 = ( ! [A3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.96 ( ( ord_le2965882846123202637_nat_o @ A3 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( A3 != bot_bo7824918357723582233_nat_o )
% 4.69/4.96 => ? [X2: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ X2 @ A3 )
% 4.69/4.96 & ! [Y3: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ Y3 @ A3 )
% 4.69/4.96 => ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X2 @ Y3 ) @ R2 ) ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Linear_order_Well_order_iff
% 4.69/4.96 thf(fact_2872_Linear__order__Well__order__iff,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ( order_4473980167227706203on_nat @ ( field_nat @ R2 ) @ R2 )
% 4.69/4.96 => ( ( order_2888998067076097458on_nat @ ( field_nat @ R2 ) @ R2 )
% 4.69/4.96 = ( ! [A3: set_nat] :
% 4.69/4.96 ( ( ord_less_eq_set_nat @ A3 @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( A3 != bot_bot_set_nat )
% 4.69/4.96 => ? [X2: nat] :
% 4.69/4.96 ( ( member_nat @ X2 @ A3 )
% 4.69/4.96 & ! [Y3: nat] :
% 4.69/4.96 ( ( member_nat @ Y3 @ A3 )
% 4.69/4.96 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ R2 ) ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Linear_order_Well_order_iff
% 4.69/4.96 thf(fact_2873_underS__incr,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,A2: int,B: int] :
% 4.69/4.96 ( ( trans_int @ R2 )
% 4.69/4.96 => ( ( antisym_int @ R2 )
% 4.69/4.96 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 )
% 4.69/4.96 => ( ord_less_eq_set_int @ ( order_underS_int @ R2 @ A2 ) @ ( order_underS_int @ R2 @ B ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % underS_incr
% 4.69/4.96 thf(fact_2874_underS__incr,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,A2: nat,B: nat] :
% 4.69/4.96 ( ( trans_nat @ R2 )
% 4.69/4.96 => ( ( antisym_nat @ R2 )
% 4.69/4.96 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 )
% 4.69/4.96 => ( ord_less_eq_set_nat @ ( order_underS_nat @ R2 @ A2 ) @ ( order_underS_nat @ R2 @ B ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % underS_incr
% 4.69/4.96 thf(fact_2875_member__remove,axiom,
% 4.69/4.96 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ X @ ( remove4651630035290841522_nat_o @ Y @ A ) )
% 4.69/4.96 = ( ( member6576561426505652726_nat_o @ X @ A )
% 4.69/4.96 & ( X != Y ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % member_remove
% 4.69/4.96 thf(fact_2876_member__remove,axiom,
% 4.69/4.96 ! [X: nat,Y: nat,A: set_nat] :
% 4.69/4.96 ( ( member_nat @ X @ ( remove_nat @ Y @ A ) )
% 4.69/4.96 = ( ( member_nat @ X @ A )
% 4.69/4.96 & ( X != Y ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % member_remove
% 4.69/4.96 thf(fact_2877_member__remove,axiom,
% 4.69/4.96 ! [X: int,Y: int,A: set_int] :
% 4.69/4.96 ( ( member_int @ X @ ( remove_int @ Y @ A ) )
% 4.69/4.96 = ( ( member_int @ X @ A )
% 4.69/4.96 & ( X != Y ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % member_remove
% 4.69/4.96 thf(fact_2878_member__remove,axiom,
% 4.69/4.96 ! [X: $o,Y: $o,A: set_o] :
% 4.69/4.96 ( ( member_o @ X @ ( remove_o @ Y @ A ) )
% 4.69/4.96 = ( ( member_o @ X @ A )
% 4.69/4.96 & ( X != Y ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % member_remove
% 4.69/4.96 thf(fact_2879_member__remove,axiom,
% 4.69/4.96 ! [X: product_unit,Y: product_unit,A: set_Product_unit] :
% 4.69/4.96 ( ( member_Product_unit @ X @ ( remove_Product_unit @ Y @ A ) )
% 4.69/4.96 = ( ( member_Product_unit @ X @ A )
% 4.69/4.96 & ( X != Y ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % member_remove
% 4.69/4.96 thf(fact_2880_wf__insert,axiom,
% 4.69/4.96 ! [Y: nat,X: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ( wf_nat @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ Y @ X ) @ R2 ) )
% 4.69/4.96 = ( ( wf_nat @ R2 )
% 4.69/4.96 & ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi2905341329935302413cl_nat @ R2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_insert
% 4.69/4.96 thf(fact_2881_wf__insert,axiom,
% 4.69/4.96 ! [Y: int,X: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ( ( wf_int @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ Y @ X ) @ R2 ) )
% 4.69/4.96 = ( ( wf_int @ R2 )
% 4.69/4.96 & ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi2902850859426252137cl_int @ R2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_insert
% 4.69/4.96 thf(fact_2882_wo__rel_Owell__order__induct,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,P: nat > $o,A2: nat] :
% 4.69/4.96 ( ( bNF_We3818239936649020644el_nat @ R2 )
% 4.69/4.96 => ( ! [X3: nat] :
% 4.69/4.96 ( ! [Y5: nat] :
% 4.69/4.96 ( ( ( Y5 != X3 )
% 4.69/4.96 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y5 @ X3 ) @ R2 ) )
% 4.69/4.96 => ( P @ Y5 ) )
% 4.69/4.96 => ( P @ X3 ) )
% 4.69/4.96 => ( P @ A2 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.well_order_induct
% 4.69/4.96 thf(fact_2883_wo__rel_Owell__order__induct,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,P: int > $o,A2: int] :
% 4.69/4.96 ( ( bNF_We3815749466139970368el_int @ R2 )
% 4.69/4.96 => ( ! [X3: int] :
% 4.69/4.96 ( ! [Y5: int] :
% 4.69/4.96 ( ( ( Y5 != X3 )
% 4.69/4.96 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y5 @ X3 ) @ R2 ) )
% 4.69/4.96 => ( P @ Y5 ) )
% 4.69/4.96 => ( P @ X3 ) )
% 4.69/4.96 => ( P @ A2 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.well_order_induct
% 4.69/4.96 thf(fact_2884_wf__induct__rule,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,P: nat > $o,A2: nat] :
% 4.69/4.96 ( ( wf_nat @ R2 )
% 4.69/4.96 => ( ! [X3: nat] :
% 4.69/4.96 ( ! [Y5: nat] :
% 4.69/4.96 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y5 @ X3 ) @ R2 )
% 4.69/4.96 => ( P @ Y5 ) )
% 4.69/4.96 => ( P @ X3 ) )
% 4.69/4.96 => ( P @ A2 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_induct_rule
% 4.69/4.96 thf(fact_2885_wf__induct__rule,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,P: int > $o,A2: int] :
% 4.69/4.96 ( ( wf_int @ R2 )
% 4.69/4.96 => ( ! [X3: int] :
% 4.69/4.96 ( ! [Y5: int] :
% 4.69/4.96 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y5 @ X3 ) @ R2 )
% 4.69/4.96 => ( P @ Y5 ) )
% 4.69/4.96 => ( P @ X3 ) )
% 4.69/4.96 => ( P @ A2 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_induct_rule
% 4.69/4.96 thf(fact_2886_wf__eq__minimal,axiom,
% 4.69/4.96 ( wf_Pro8787509627421085110_nat_o
% 4.69/4.96 = ( ^ [R4: set_Pr2161125870931222855_nat_o] :
% 4.69/4.96 ! [Q: set_Pr4532377907799695533_nat_o] :
% 4.69/4.96 ( ? [X2: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X2 @ Q )
% 4.69/4.96 => ? [X2: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ X2 @ Q )
% 4.69/4.96 & ! [Y3: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ Y3 @ X2 ) @ R4 )
% 4.69/4.96 => ~ ( member6576561426505652726_nat_o @ Y3 @ Q ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_eq_minimal
% 4.69/4.96 thf(fact_2887_wf__eq__minimal,axiom,
% 4.69/4.96 ( wf_o
% 4.69/4.96 = ( ^ [R4: set_Product_prod_o_o] :
% 4.69/4.96 ! [Q: set_o] :
% 4.69/4.96 ( ? [X2: $o] : ( member_o @ X2 @ Q )
% 4.69/4.96 => ? [X2: $o] :
% 4.69/4.96 ( ( member_o @ X2 @ Q )
% 4.69/4.96 & ! [Y3: $o] :
% 4.69/4.96 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ Y3 @ X2 ) @ R4 )
% 4.69/4.96 => ~ ( member_o @ Y3 @ Q ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_eq_minimal
% 4.69/4.96 thf(fact_2888_wf__eq__minimal,axiom,
% 4.69/4.96 ( wf_Product_unit
% 4.69/4.96 = ( ^ [R4: set_Pr5094982260447487303t_unit] :
% 4.69/4.96 ! [Q: set_Product_unit] :
% 4.69/4.96 ( ? [X2: product_unit] : ( member_Product_unit @ X2 @ Q )
% 4.69/4.96 => ? [X2: product_unit] :
% 4.69/4.96 ( ( member_Product_unit @ X2 @ Q )
% 4.69/4.96 & ! [Y3: product_unit] :
% 4.69/4.96 ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ Y3 @ X2 ) @ R4 )
% 4.69/4.96 => ~ ( member_Product_unit @ Y3 @ Q ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_eq_minimal
% 4.69/4.96 thf(fact_2889_wf__eq__minimal,axiom,
% 4.69/4.96 ( wf_nat
% 4.69/4.96 = ( ^ [R4: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ! [Q: set_nat] :
% 4.69/4.96 ( ? [X2: nat] : ( member_nat @ X2 @ Q )
% 4.69/4.96 => ? [X2: nat] :
% 4.69/4.96 ( ( member_nat @ X2 @ Q )
% 4.69/4.96 & ! [Y3: nat] :
% 4.69/4.96 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ X2 ) @ R4 )
% 4.69/4.96 => ~ ( member_nat @ Y3 @ Q ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_eq_minimal
% 4.69/4.96 thf(fact_2890_wf__eq__minimal,axiom,
% 4.69/4.96 ( wf_int
% 4.69/4.96 = ( ^ [R4: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ! [Q: set_int] :
% 4.69/4.96 ( ? [X2: int] : ( member_int @ X2 @ Q )
% 4.69/4.96 => ? [X2: int] :
% 4.69/4.96 ( ( member_int @ X2 @ Q )
% 4.69/4.96 & ! [Y3: int] :
% 4.69/4.96 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ X2 ) @ R4 )
% 4.69/4.96 => ~ ( member_int @ Y3 @ Q ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_eq_minimal
% 4.69/4.96 thf(fact_2891_wf__not__refl,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,A2: nat] :
% 4.69/4.96 ( ( wf_nat @ R2 )
% 4.69/4.96 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ A2 ) @ R2 ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_not_refl
% 4.69/4.96 thf(fact_2892_wf__not__refl,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,A2: int] :
% 4.69/4.96 ( ( wf_int @ R2 )
% 4.69/4.96 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ A2 ) @ R2 ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_not_refl
% 4.69/4.96 thf(fact_2893_wf__not__sym,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,A2: nat,X: nat] :
% 4.69/4.96 ( ( wf_nat @ R2 )
% 4.69/4.96 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ X ) @ R2 )
% 4.69/4.96 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ A2 ) @ R2 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_not_sym
% 4.69/4.96 thf(fact_2894_wf__not__sym,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,A2: int,X: int] :
% 4.69/4.96 ( ( wf_int @ R2 )
% 4.69/4.96 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ X ) @ R2 )
% 4.69/4.96 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ A2 ) @ R2 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_not_sym
% 4.69/4.96 thf(fact_2895_wf__irrefl,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,A2: nat] :
% 4.69/4.96 ( ( wf_nat @ R2 )
% 4.69/4.96 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ A2 ) @ R2 ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_irrefl
% 4.69/4.96 thf(fact_2896_wf__irrefl,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,A2: int] :
% 4.69/4.96 ( ( wf_int @ R2 )
% 4.69/4.96 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ A2 ) @ R2 ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_irrefl
% 4.69/4.96 thf(fact_2897_wf__induct,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,P: nat > $o,A2: nat] :
% 4.69/4.96 ( ( wf_nat @ R2 )
% 4.69/4.96 => ( ! [X3: nat] :
% 4.69/4.96 ( ! [Y5: nat] :
% 4.69/4.96 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y5 @ X3 ) @ R2 )
% 4.69/4.96 => ( P @ Y5 ) )
% 4.69/4.96 => ( P @ X3 ) )
% 4.69/4.96 => ( P @ A2 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_induct
% 4.69/4.96 thf(fact_2898_wf__induct,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,P: int > $o,A2: int] :
% 4.69/4.96 ( ( wf_int @ R2 )
% 4.69/4.96 => ( ! [X3: int] :
% 4.69/4.96 ( ! [Y5: int] :
% 4.69/4.96 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y5 @ X3 ) @ R2 )
% 4.69/4.96 => ( P @ Y5 ) )
% 4.69/4.96 => ( P @ X3 ) )
% 4.69/4.96 => ( P @ A2 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_induct
% 4.69/4.96 thf(fact_2899_wf__asym,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,A2: nat,X: nat] :
% 4.69/4.96 ( ( wf_nat @ R2 )
% 4.69/4.96 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ X ) @ R2 )
% 4.69/4.96 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ A2 ) @ R2 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_asym
% 4.69/4.96 thf(fact_2900_wf__asym,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,A2: int,X: int] :
% 4.69/4.96 ( ( wf_int @ R2 )
% 4.69/4.96 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ X ) @ R2 )
% 4.69/4.96 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ A2 ) @ R2 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_asym
% 4.69/4.96 thf(fact_2901_wfUNIVI,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ! [P4: nat > $o,X3: nat] :
% 4.69/4.96 ( ! [Xa2: nat] :
% 4.69/4.96 ( ! [Y2: nat] :
% 4.69/4.96 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ Xa2 ) @ R2 )
% 4.69/4.96 => ( P4 @ Y2 ) )
% 4.69/4.96 => ( P4 @ Xa2 ) )
% 4.69/4.96 => ( P4 @ X3 ) )
% 4.69/4.96 => ( wf_nat @ R2 ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfUNIVI
% 4.69/4.96 thf(fact_2902_wfUNIVI,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ( ! [P4: int > $o,X3: int] :
% 4.69/4.96 ( ! [Xa2: int] :
% 4.69/4.96 ( ! [Y2: int] :
% 4.69/4.96 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y2 @ Xa2 ) @ R2 )
% 4.69/4.96 => ( P4 @ Y2 ) )
% 4.69/4.96 => ( P4 @ Xa2 ) )
% 4.69/4.96 => ( P4 @ X3 ) )
% 4.69/4.96 => ( wf_int @ R2 ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfUNIVI
% 4.69/4.96 thf(fact_2903_wfI__min,axiom,
% 4.69/4.96 ! [R3: set_Pr2161125870931222855_nat_o] :
% 4.69/4.96 ( ! [X3: produc3658429121746597890et_nat > $o,Q3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ X3 @ Q3 )
% 4.69/4.96 => ? [Xa2: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ Xa2 @ Q3 )
% 4.69/4.96 & ! [Y2: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ Y2 @ Xa2 ) @ R3 )
% 4.69/4.96 => ~ ( member6576561426505652726_nat_o @ Y2 @ Q3 ) ) ) )
% 4.69/4.96 => ( wf_Pro8787509627421085110_nat_o @ R3 ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfI_min
% 4.69/4.96 thf(fact_2904_wfI__min,axiom,
% 4.69/4.96 ! [R3: set_Product_prod_o_o] :
% 4.69/4.96 ( ! [X3: $o,Q3: set_o] :
% 4.69/4.96 ( ( member_o @ X3 @ Q3 )
% 4.69/4.96 => ? [Xa2: $o] :
% 4.69/4.96 ( ( member_o @ Xa2 @ Q3 )
% 4.69/4.96 & ! [Y2: $o] :
% 4.69/4.96 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ Y2 @ Xa2 ) @ R3 )
% 4.69/4.96 => ~ ( member_o @ Y2 @ Q3 ) ) ) )
% 4.69/4.96 => ( wf_o @ R3 ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfI_min
% 4.69/4.96 thf(fact_2905_wfI__min,axiom,
% 4.69/4.96 ! [R3: set_Pr5094982260447487303t_unit] :
% 4.69/4.96 ( ! [X3: product_unit,Q3: set_Product_unit] :
% 4.69/4.96 ( ( member_Product_unit @ X3 @ Q3 )
% 4.69/4.96 => ? [Xa2: product_unit] :
% 4.69/4.96 ( ( member_Product_unit @ Xa2 @ Q3 )
% 4.69/4.96 & ! [Y2: product_unit] :
% 4.69/4.96 ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ Y2 @ Xa2 ) @ R3 )
% 4.69/4.96 => ~ ( member_Product_unit @ Y2 @ Q3 ) ) ) )
% 4.69/4.96 => ( wf_Product_unit @ R3 ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfI_min
% 4.69/4.96 thf(fact_2906_wfI__min,axiom,
% 4.69/4.96 ! [R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ! [X3: nat,Q3: set_nat] :
% 4.69/4.96 ( ( member_nat @ X3 @ Q3 )
% 4.69/4.96 => ? [Xa2: nat] :
% 4.69/4.96 ( ( member_nat @ Xa2 @ Q3 )
% 4.69/4.96 & ! [Y2: nat] :
% 4.69/4.96 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y2 @ Xa2 ) @ R3 )
% 4.69/4.96 => ~ ( member_nat @ Y2 @ Q3 ) ) ) )
% 4.69/4.96 => ( wf_nat @ R3 ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfI_min
% 4.69/4.96 thf(fact_2907_wfI__min,axiom,
% 4.69/4.96 ! [R3: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ( ! [X3: int,Q3: set_int] :
% 4.69/4.96 ( ( member_int @ X3 @ Q3 )
% 4.69/4.96 => ? [Xa2: int] :
% 4.69/4.96 ( ( member_int @ Xa2 @ Q3 )
% 4.69/4.96 & ! [Y2: int] :
% 4.69/4.96 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y2 @ Xa2 ) @ R3 )
% 4.69/4.96 => ~ ( member_int @ Y2 @ Q3 ) ) ) )
% 4.69/4.96 => ( wf_int @ R3 ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfI_min
% 4.69/4.96 thf(fact_2908_wfE__min,axiom,
% 4.69/4.96 ! [R3: set_Pr2161125870931222855_nat_o,X: produc3658429121746597890et_nat > $o,Q2: set_Pr4532377907799695533_nat_o] :
% 4.69/4.96 ( ( wf_Pro8787509627421085110_nat_o @ R3 )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ X @ Q2 )
% 4.69/4.96 => ~ ! [Z3: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ Z3 @ Q2 )
% 4.69/4.96 => ~ ! [Y5: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ Y5 @ Z3 ) @ R3 )
% 4.69/4.96 => ~ ( member6576561426505652726_nat_o @ Y5 @ Q2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfE_min
% 4.69/4.96 thf(fact_2909_wfE__min,axiom,
% 4.69/4.96 ! [R3: set_Product_prod_o_o,X: $o,Q2: set_o] :
% 4.69/4.96 ( ( wf_o @ R3 )
% 4.69/4.96 => ( ( member_o @ X @ Q2 )
% 4.69/4.96 => ~ ! [Z3: $o] :
% 4.69/4.96 ( ( member_o @ Z3 @ Q2 )
% 4.69/4.96 => ~ ! [Y5: $o] :
% 4.69/4.96 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ Y5 @ Z3 ) @ R3 )
% 4.69/4.96 => ~ ( member_o @ Y5 @ Q2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfE_min
% 4.69/4.96 thf(fact_2910_wfE__min,axiom,
% 4.69/4.96 ! [R3: set_Pr5094982260447487303t_unit,X: product_unit,Q2: set_Product_unit] :
% 4.69/4.96 ( ( wf_Product_unit @ R3 )
% 4.69/4.96 => ( ( member_Product_unit @ X @ Q2 )
% 4.69/4.96 => ~ ! [Z3: product_unit] :
% 4.69/4.96 ( ( member_Product_unit @ Z3 @ Q2 )
% 4.69/4.96 => ~ ! [Y5: product_unit] :
% 4.69/4.96 ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ Y5 @ Z3 ) @ R3 )
% 4.69/4.96 => ~ ( member_Product_unit @ Y5 @ Q2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfE_min
% 4.69/4.96 thf(fact_2911_wfE__min,axiom,
% 4.69/4.96 ! [R3: set_Pr1261947904930325089at_nat,X: nat,Q2: set_nat] :
% 4.69/4.96 ( ( wf_nat @ R3 )
% 4.69/4.96 => ( ( member_nat @ X @ Q2 )
% 4.69/4.96 => ~ ! [Z3: nat] :
% 4.69/4.96 ( ( member_nat @ Z3 @ Q2 )
% 4.69/4.96 => ~ ! [Y5: nat] :
% 4.69/4.96 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y5 @ Z3 ) @ R3 )
% 4.69/4.96 => ~ ( member_nat @ Y5 @ Q2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfE_min
% 4.69/4.96 thf(fact_2912_wfE__min,axiom,
% 4.69/4.96 ! [R3: set_Pr958786334691620121nt_int,X: int,Q2: set_int] :
% 4.69/4.96 ( ( wf_int @ R3 )
% 4.69/4.96 => ( ( member_int @ X @ Q2 )
% 4.69/4.96 => ~ ! [Z3: int] :
% 4.69/4.96 ( ( member_int @ Z3 @ Q2 )
% 4.69/4.96 => ~ ! [Y5: int] :
% 4.69/4.96 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y5 @ Z3 ) @ R3 )
% 4.69/4.96 => ~ ( member_int @ Y5 @ Q2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfE_min
% 4.69/4.96 thf(fact_2913_wf__def,axiom,
% 4.69/4.96 ( wf_nat
% 4.69/4.96 = ( ^ [R4: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ! [P2: nat > $o] :
% 4.69/4.96 ( ! [X2: nat] :
% 4.69/4.96 ( ! [Y3: nat] :
% 4.69/4.96 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ X2 ) @ R4 )
% 4.69/4.96 => ( P2 @ Y3 ) )
% 4.69/4.96 => ( P2 @ X2 ) )
% 4.69/4.96 => ! [X7: nat] : ( P2 @ X7 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_def
% 4.69/4.96 thf(fact_2914_wf__def,axiom,
% 4.69/4.96 ( wf_int
% 4.69/4.96 = ( ^ [R4: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ! [P2: int > $o] :
% 4.69/4.96 ( ! [X2: int] :
% 4.69/4.96 ( ! [Y3: int] :
% 4.69/4.96 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ X2 ) @ R4 )
% 4.69/4.96 => ( P2 @ Y3 ) )
% 4.69/4.96 => ( P2 @ X2 ) )
% 4.69/4.96 => ! [X7: int] : ( P2 @ X7 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_def
% 4.69/4.96 thf(fact_2915_well__order__on__domain,axiom,
% 4.69/4.96 ! [A: set_Pr4532377907799695533_nat_o,R2: set_Pr2161125870931222855_nat_o,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( order_2118566763991480939_nat_o @ A @ R2 )
% 4.69/4.96 => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ B ) @ R2 )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ A2 @ A )
% 4.69/4.96 & ( member6576561426505652726_nat_o @ B @ A ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % well_order_on_domain
% 4.69/4.96 thf(fact_2916_well__order__on__domain,axiom,
% 4.69/4.96 ! [A: set_o,R2: set_Product_prod_o_o,A2: $o,B: $o] :
% 4.69/4.96 ( ( order_2615775362358406454r_on_o @ A @ R2 )
% 4.69/4.96 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ B ) @ R2 )
% 4.69/4.96 => ( ( member_o @ A2 @ A )
% 4.69/4.96 & ( member_o @ B @ A ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % well_order_on_domain
% 4.69/4.96 thf(fact_2917_well__order__on__domain,axiom,
% 4.69/4.96 ! [A: set_Product_unit,R2: set_Pr5094982260447487303t_unit,A2: product_unit,B: product_unit] :
% 4.69/4.96 ( ( order_3164716736300062379t_unit @ A @ R2 )
% 4.69/4.96 => ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A2 @ B ) @ R2 )
% 4.69/4.96 => ( ( member_Product_unit @ A2 @ A )
% 4.69/4.96 & ( member_Product_unit @ B @ A ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % well_order_on_domain
% 4.69/4.96 thf(fact_2918_well__order__on__domain,axiom,
% 4.69/4.96 ! [A: set_nat,R2: set_Pr1261947904930325089at_nat,A2: nat,B: nat] :
% 4.69/4.96 ( ( order_2888998067076097458on_nat @ A @ R2 )
% 4.69/4.96 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 )
% 4.69/4.96 => ( ( member_nat @ A2 @ A )
% 4.69/4.96 & ( member_nat @ B @ A ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % well_order_on_domain
% 4.69/4.96 thf(fact_2919_well__order__on__domain,axiom,
% 4.69/4.96 ! [A: set_int,R2: set_Pr958786334691620121nt_int,A2: int,B: int] :
% 4.69/4.96 ( ( order_2886507596567047182on_int @ A @ R2 )
% 4.69/4.96 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 )
% 4.69/4.96 => ( ( member_int @ A2 @ A )
% 4.69/4.96 & ( member_int @ B @ A ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % well_order_on_domain
% 4.69/4.96 thf(fact_2920_underS__E,axiom,
% 4.69/4.96 ! [I2: produc3658429121746597890et_nat > $o,R3: set_Pr2161125870931222855_nat_o,J: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ I2 @ ( order_7262550146012401043_nat_o @ R3 @ J ) )
% 4.69/4.96 => ( ( I2 != J )
% 4.69/4.96 & ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ I2 @ J ) @ R3 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % underS_E
% 4.69/4.96 thf(fact_2921_underS__E,axiom,
% 4.69/4.96 ! [I2: $o,R3: set_Product_prod_o_o,J: $o] :
% 4.69/4.96 ( ( member_o @ I2 @ ( order_underS_o @ R3 @ J ) )
% 4.69/4.96 => ( ( I2 != J )
% 4.69/4.96 & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ I2 @ J ) @ R3 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % underS_E
% 4.69/4.96 thf(fact_2922_underS__E,axiom,
% 4.69/4.96 ! [I2: product_unit,R3: set_Pr5094982260447487303t_unit,J: product_unit] :
% 4.69/4.96 ( ( member_Product_unit @ I2 @ ( order_5809128134054296019t_unit @ R3 @ J ) )
% 4.69/4.96 => ( ( I2 != J )
% 4.69/4.96 & ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ I2 @ J ) @ R3 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % underS_E
% 4.69/4.96 thf(fact_2923_underS__E,axiom,
% 4.69/4.96 ! [I2: nat,R3: set_Pr1261947904930325089at_nat,J: nat] :
% 4.69/4.96 ( ( member_nat @ I2 @ ( order_underS_nat @ R3 @ J ) )
% 4.69/4.96 => ( ( I2 != J )
% 4.69/4.96 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I2 @ J ) @ R3 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % underS_E
% 4.69/4.96 thf(fact_2924_underS__E,axiom,
% 4.69/4.96 ! [I2: int,R3: set_Pr958786334691620121nt_int,J: int] :
% 4.69/4.96 ( ( member_int @ I2 @ ( order_underS_int @ R3 @ J ) )
% 4.69/4.96 => ( ( I2 != J )
% 4.69/4.96 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I2 @ J ) @ R3 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % underS_E
% 4.69/4.96 thf(fact_2925_underS__I,axiom,
% 4.69/4.96 ! [I2: produc3658429121746597890et_nat > $o,J: produc3658429121746597890et_nat > $o,R3: set_Pr2161125870931222855_nat_o] :
% 4.69/4.96 ( ( I2 != J )
% 4.69/4.96 => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ I2 @ J ) @ R3 )
% 4.69/4.96 => ( member6576561426505652726_nat_o @ I2 @ ( order_7262550146012401043_nat_o @ R3 @ J ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % underS_I
% 4.69/4.96 thf(fact_2926_underS__I,axiom,
% 4.69/4.96 ! [I2: $o,J: $o,R3: set_Product_prod_o_o] :
% 4.69/4.96 ( ( I2 != J )
% 4.69/4.96 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ I2 @ J ) @ R3 )
% 4.69/4.96 => ( member_o @ I2 @ ( order_underS_o @ R3 @ J ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % underS_I
% 4.69/4.96 thf(fact_2927_underS__I,axiom,
% 4.69/4.96 ! [I2: product_unit,J: product_unit,R3: set_Pr5094982260447487303t_unit] :
% 4.69/4.96 ( ( I2 != J )
% 4.69/4.96 => ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ I2 @ J ) @ R3 )
% 4.69/4.96 => ( member_Product_unit @ I2 @ ( order_5809128134054296019t_unit @ R3 @ J ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % underS_I
% 4.69/4.96 thf(fact_2928_underS__I,axiom,
% 4.69/4.96 ! [I2: nat,J: nat,R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ( I2 != J )
% 4.69/4.96 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I2 @ J ) @ R3 )
% 4.69/4.96 => ( member_nat @ I2 @ ( order_underS_nat @ R3 @ J ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % underS_I
% 4.69/4.96 thf(fact_2929_underS__I,axiom,
% 4.69/4.96 ! [I2: int,J: int,R3: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ( ( I2 != J )
% 4.69/4.96 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I2 @ J ) @ R3 )
% 4.69/4.96 => ( member_int @ I2 @ ( order_underS_int @ R3 @ J ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % underS_I
% 4.69/4.96 thf(fact_2930_BNF__Least__Fixpoint_OunderS__Field,axiom,
% 4.69/4.96 ! [I2: produc3658429121746597890et_nat > $o,R3: set_Pr2161125870931222855_nat_o,J: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ I2 @ ( order_7262550146012401043_nat_o @ R3 @ J ) )
% 4.69/4.96 => ( member6576561426505652726_nat_o @ I2 @ ( field_81821745747897882_nat_o @ R3 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % BNF_Least_Fixpoint.underS_Field
% 4.69/4.96 thf(fact_2931_BNF__Least__Fixpoint_OunderS__Field,axiom,
% 4.69/4.96 ! [I2: nat,R3: set_Pr1261947904930325089at_nat,J: nat] :
% 4.69/4.96 ( ( member_nat @ I2 @ ( order_underS_nat @ R3 @ J ) )
% 4.69/4.96 => ( member_nat @ I2 @ ( field_nat @ R3 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % BNF_Least_Fixpoint.underS_Field
% 4.69/4.96 thf(fact_2932_BNF__Least__Fixpoint_OunderS__Field,axiom,
% 4.69/4.96 ! [I2: int,R3: set_Pr958786334691620121nt_int,J: int] :
% 4.69/4.96 ( ( member_int @ I2 @ ( order_underS_int @ R3 @ J ) )
% 4.69/4.96 => ( member_int @ I2 @ ( field_int @ R3 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % BNF_Least_Fixpoint.underS_Field
% 4.69/4.96 thf(fact_2933_BNF__Least__Fixpoint_OunderS__Field,axiom,
% 4.69/4.96 ! [I2: $o,R3: set_Product_prod_o_o,J: $o] :
% 4.69/4.96 ( ( member_o @ I2 @ ( order_underS_o @ R3 @ J ) )
% 4.69/4.96 => ( member_o @ I2 @ ( field_o @ R3 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % BNF_Least_Fixpoint.underS_Field
% 4.69/4.96 thf(fact_2934_BNF__Least__Fixpoint_OunderS__Field,axiom,
% 4.69/4.96 ! [I2: product_unit,R3: set_Pr5094982260447487303t_unit,J: product_unit] :
% 4.69/4.96 ( ( member_Product_unit @ I2 @ ( order_5809128134054296019t_unit @ R3 @ J ) )
% 4.69/4.96 => ( member_Product_unit @ I2 @ ( field_Product_unit @ R3 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % BNF_Least_Fixpoint.underS_Field
% 4.69/4.96 thf(fact_2935_wo__rel_OTOTALS,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ( bNF_We3818239936649020644el_nat @ R2 )
% 4.69/4.96 => ! [X6: nat] :
% 4.69/4.96 ( ( member_nat @ X6 @ ( field_nat @ R2 ) )
% 4.69/4.96 => ! [Xa2: nat] :
% 4.69/4.96 ( ( member_nat @ Xa2 @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X6 @ Xa2 ) @ R2 )
% 4.69/4.96 | ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Xa2 @ X6 ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.TOTALS
% 4.69/4.96 thf(fact_2936_wo__rel_OTOTALS,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ( ( bNF_We3815749466139970368el_int @ R2 )
% 4.69/4.96 => ! [X6: int] :
% 4.69/4.96 ( ( member_int @ X6 @ ( field_int @ R2 ) )
% 4.69/4.96 => ! [Xa2: int] :
% 4.69/4.96 ( ( member_int @ Xa2 @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X6 @ Xa2 ) @ R2 )
% 4.69/4.96 | ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Xa2 @ X6 ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.TOTALS
% 4.69/4.96 thf(fact_2937_wfE__min_H,axiom,
% 4.69/4.96 ! [R3: set_Pr5094982260447487303t_unit,Q2: set_Product_unit] :
% 4.69/4.96 ( ( wf_Product_unit @ R3 )
% 4.69/4.96 => ( ( Q2 != bot_bo3957492148770167129t_unit )
% 4.69/4.96 => ~ ! [Z3: product_unit] :
% 4.69/4.96 ( ( member_Product_unit @ Z3 @ Q2 )
% 4.69/4.96 => ~ ! [Y5: product_unit] :
% 4.69/4.96 ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ Y5 @ Z3 ) @ R3 )
% 4.69/4.96 => ~ ( member_Product_unit @ Y5 @ Q2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfE_min'
% 4.69/4.96 thf(fact_2938_wfE__min_H,axiom,
% 4.69/4.96 ! [R3: set_Product_prod_o_o,Q2: set_o] :
% 4.69/4.96 ( ( wf_o @ R3 )
% 4.69/4.96 => ( ( Q2 != bot_bot_set_o )
% 4.69/4.96 => ~ ! [Z3: $o] :
% 4.69/4.96 ( ( member_o @ Z3 @ Q2 )
% 4.69/4.96 => ~ ! [Y5: $o] :
% 4.69/4.96 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ Y5 @ Z3 ) @ R3 )
% 4.69/4.96 => ~ ( member_o @ Y5 @ Q2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfE_min'
% 4.69/4.96 thf(fact_2939_wfE__min_H,axiom,
% 4.69/4.96 ! [R3: set_Pr1261947904930325089at_nat,Q2: set_nat] :
% 4.69/4.96 ( ( wf_nat @ R3 )
% 4.69/4.96 => ( ( Q2 != bot_bot_set_nat )
% 4.69/4.96 => ~ ! [Z3: nat] :
% 4.69/4.96 ( ( member_nat @ Z3 @ Q2 )
% 4.69/4.96 => ~ ! [Y5: nat] :
% 4.69/4.96 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y5 @ Z3 ) @ R3 )
% 4.69/4.96 => ~ ( member_nat @ Y5 @ Q2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfE_min'
% 4.69/4.96 thf(fact_2940_wfE__min_H,axiom,
% 4.69/4.96 ! [R3: set_Pr958786334691620121nt_int,Q2: set_int] :
% 4.69/4.96 ( ( wf_int @ R3 )
% 4.69/4.96 => ( ( Q2 != bot_bot_set_int )
% 4.69/4.96 => ~ ! [Z3: int] :
% 4.69/4.96 ( ( member_int @ Z3 @ Q2 )
% 4.69/4.96 => ~ ! [Y5: int] :
% 4.69/4.96 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y5 @ Z3 ) @ R3 )
% 4.69/4.96 => ~ ( member_int @ Y5 @ Q2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfE_min'
% 4.69/4.96 thf(fact_2941_wfE__min_H,axiom,
% 4.69/4.96 ! [R3: set_Pr2161125870931222855_nat_o,Q2: set_Pr4532377907799695533_nat_o] :
% 4.69/4.96 ( ( wf_Pro8787509627421085110_nat_o @ R3 )
% 4.69/4.96 => ( ( Q2 != bot_bo7824918357723582233_nat_o )
% 4.69/4.96 => ~ ! [Z3: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ Z3 @ Q2 )
% 4.69/4.96 => ~ ! [Y5: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ Y5 @ Z3 ) @ R3 )
% 4.69/4.96 => ~ ( member6576561426505652726_nat_o @ Y5 @ Q2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfE_min'
% 4.69/4.96 thf(fact_2942_well__order__on__empty,axiom,
% 4.69/4.96 order_3164716736300062379t_unit @ bot_bo3957492148770167129t_unit @ bot_bo1654022762305692595t_unit ).
% 4.69/4.96
% 4.69/4.96 % well_order_on_empty
% 4.69/4.96 thf(fact_2943_well__order__on__empty,axiom,
% 4.69/4.96 order_2615775362358406454r_on_o @ bot_bot_set_o @ bot_bo7073875226086086771od_o_o ).
% 4.69/4.96
% 4.69/4.96 % well_order_on_empty
% 4.69/4.96 thf(fact_2944_well__order__on__empty,axiom,
% 4.69/4.96 order_2888998067076097458on_nat @ bot_bot_set_nat @ bot_bo2099793752762293965at_nat ).
% 4.69/4.96
% 4.69/4.96 % well_order_on_empty
% 4.69/4.96 thf(fact_2945_well__order__on__empty,axiom,
% 4.69/4.96 order_2886507596567047182on_int @ bot_bot_set_int @ bot_bo1796632182523588997nt_int ).
% 4.69/4.96
% 4.69/4.96 % well_order_on_empty
% 4.69/4.96 thf(fact_2946_well__order__on__empty,axiom,
% 4.69/4.96 order_2118566763991480939_nat_o @ bot_bo7824918357723582233_nat_o @ bot_bo3657187498359500723_nat_o ).
% 4.69/4.96
% 4.69/4.96 % well_order_on_empty
% 4.69/4.96 thf(fact_2947_well__order__induct__imp,axiom,
% 4.69/4.96 ! [R2: set_Pr2161125870931222855_nat_o,P: ( produc3658429121746597890et_nat > $o ) > $o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( bNF_We740377018556551609_nat_o @ R2 )
% 4.69/4.96 => ( ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ! [Y5: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( ( Y5 != X3 )
% 4.69/4.96 & ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ Y5 @ X3 ) @ R2 ) )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ Y5 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( P @ Y5 ) ) )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ X3 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( P @ X3 ) ) )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ A2 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( P @ A2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % well_order_induct_imp
% 4.69/4.96 thf(fact_2948_well__order__induct__imp,axiom,
% 4.69/4.96 ! [R2: set_Product_prod_o_o,P: $o > $o,A2: $o] :
% 4.69/4.96 ( ( bNF_We6437023980930612612_rel_o @ R2 )
% 4.69/4.96 => ( ! [X3: $o] :
% 4.69/4.96 ( ! [Y5: $o] :
% 4.69/4.96 ( ( ( Y5 != X3 )
% 4.69/4.96 & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ Y5 @ X3 ) @ R2 ) )
% 4.69/4.96 => ( ( member_o @ Y5 @ ( field_o @ R2 ) )
% 4.69/4.96 => ( P @ Y5 ) ) )
% 4.69/4.96 => ( ( member_o @ X3 @ ( field_o @ R2 ) )
% 4.69/4.96 => ( P @ X3 ) ) )
% 4.69/4.96 => ( ( member_o @ A2 @ ( field_o @ R2 ) )
% 4.69/4.96 => ( P @ A2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % well_order_induct_imp
% 4.69/4.96 thf(fact_2949_well__order__induct__imp,axiom,
% 4.69/4.96 ! [R2: set_Pr5094982260447487303t_unit,P: product_unit > $o,A2: product_unit] :
% 4.69/4.96 ( ( bNF_We2091578341578594809t_unit @ R2 )
% 4.69/4.96 => ( ! [X3: product_unit] :
% 4.69/4.96 ( ! [Y5: product_unit] :
% 4.69/4.96 ( ( ( Y5 != X3 )
% 4.69/4.96 & ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ Y5 @ X3 ) @ R2 ) )
% 4.69/4.96 => ( ( member_Product_unit @ Y5 @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( P @ Y5 ) ) )
% 4.69/4.96 => ( ( member_Product_unit @ X3 @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( P @ X3 ) ) )
% 4.69/4.96 => ( ( member_Product_unit @ A2 @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( P @ A2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % well_order_induct_imp
% 4.69/4.96 thf(fact_2950_well__order__induct__imp,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,P: nat > $o,A2: nat] :
% 4.69/4.96 ( ( bNF_We3818239936649020644el_nat @ R2 )
% 4.69/4.96 => ( ! [X3: nat] :
% 4.69/4.96 ( ! [Y5: nat] :
% 4.69/4.96 ( ( ( Y5 != X3 )
% 4.69/4.96 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y5 @ X3 ) @ R2 ) )
% 4.69/4.96 => ( ( member_nat @ Y5 @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( P @ Y5 ) ) )
% 4.69/4.96 => ( ( member_nat @ X3 @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( P @ X3 ) ) )
% 4.69/4.96 => ( ( member_nat @ A2 @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( P @ A2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % well_order_induct_imp
% 4.69/4.96 thf(fact_2951_well__order__induct__imp,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,P: int > $o,A2: int] :
% 4.69/4.96 ( ( bNF_We3815749466139970368el_int @ R2 )
% 4.69/4.96 => ( ! [X3: int] :
% 4.69/4.96 ( ! [Y5: int] :
% 4.69/4.96 ( ( ( Y5 != X3 )
% 4.69/4.96 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y5 @ X3 ) @ R2 ) )
% 4.69/4.96 => ( ( member_int @ Y5 @ ( field_int @ R2 ) )
% 4.69/4.96 => ( P @ Y5 ) ) )
% 4.69/4.96 => ( ( member_int @ X3 @ ( field_int @ R2 ) )
% 4.69/4.96 => ( P @ X3 ) ) )
% 4.69/4.96 => ( ( member_int @ A2 @ ( field_int @ R2 ) )
% 4.69/4.96 => ( P @ A2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % well_order_induct_imp
% 4.69/4.96 thf(fact_2952_underS__empty,axiom,
% 4.69/4.96 ! [A2: product_unit,R2: set_Pr5094982260447487303t_unit] :
% 4.69/4.96 ( ~ ( member_Product_unit @ A2 @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( order_5809128134054296019t_unit @ R2 @ A2 )
% 4.69/4.96 = bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.96
% 4.69/4.96 % underS_empty
% 4.69/4.96 thf(fact_2953_underS__empty,axiom,
% 4.69/4.96 ! [A2: $o,R2: set_Product_prod_o_o] :
% 4.69/4.96 ( ~ ( member_o @ A2 @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( order_underS_o @ R2 @ A2 )
% 4.69/4.96 = bot_bot_set_o ) ) ).
% 4.69/4.96
% 4.69/4.96 % underS_empty
% 4.69/4.96 thf(fact_2954_underS__empty,axiom,
% 4.69/4.96 ! [A2: nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ~ ( member_nat @ A2 @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( order_underS_nat @ R2 @ A2 )
% 4.69/4.96 = bot_bot_set_nat ) ) ).
% 4.69/4.96
% 4.69/4.96 % underS_empty
% 4.69/4.96 thf(fact_2955_underS__empty,axiom,
% 4.69/4.96 ! [A2: int,R2: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ( ~ ( member_int @ A2 @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( order_underS_int @ R2 @ A2 )
% 4.69/4.96 = bot_bot_set_int ) ) ).
% 4.69/4.96
% 4.69/4.96 % underS_empty
% 4.69/4.96 thf(fact_2956_underS__empty,axiom,
% 4.69/4.96 ! [A2: produc3658429121746597890et_nat > $o,R2: set_Pr2161125870931222855_nat_o] :
% 4.69/4.96 ( ~ ( member6576561426505652726_nat_o @ A2 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( order_7262550146012401043_nat_o @ R2 @ A2 )
% 4.69/4.96 = bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.96
% 4.69/4.96 % underS_empty
% 4.69/4.96 thf(fact_2957_wfI__pf,axiom,
% 4.69/4.96 ! [R3: set_Pr5094982260447487303t_unit] :
% 4.69/4.96 ( ! [A9: set_Product_unit] :
% 4.69/4.96 ( ( ord_le3507040750410214029t_unit @ A9 @ ( image_8431784415008483091t_unit @ R3 @ A9 ) )
% 4.69/4.96 => ( A9 = bot_bo3957492148770167129t_unit ) )
% 4.69/4.96 => ( wf_Product_unit @ R3 ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfI_pf
% 4.69/4.96 thf(fact_2958_wfI__pf,axiom,
% 4.69/4.96 ! [R3: set_Product_prod_o_o] :
% 4.69/4.96 ( ! [A9: set_o] :
% 4.69/4.96 ( ( ord_less_eq_set_o @ A9 @ ( image_o_o @ R3 @ A9 ) )
% 4.69/4.96 => ( A9 = bot_bot_set_o ) )
% 4.69/4.96 => ( wf_o @ R3 ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfI_pf
% 4.69/4.96 thf(fact_2959_wfI__pf,axiom,
% 4.69/4.96 ! [R3: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ( ! [A9: set_int] :
% 4.69/4.96 ( ( ord_less_eq_set_int @ A9 @ ( image_int_int @ R3 @ A9 ) )
% 4.69/4.96 => ( A9 = bot_bot_set_int ) )
% 4.69/4.96 => ( wf_int @ R3 ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfI_pf
% 4.69/4.96 thf(fact_2960_wfI__pf,axiom,
% 4.69/4.96 ! [R3: set_Pr2161125870931222855_nat_o] :
% 4.69/4.96 ( ! [A9: set_Pr4532377907799695533_nat_o] :
% 4.69/4.96 ( ( ord_le2965882846123202637_nat_o @ A9 @ ( image_2232984160439939859_nat_o @ R3 @ A9 ) )
% 4.69/4.96 => ( A9 = bot_bo7824918357723582233_nat_o ) )
% 4.69/4.96 => ( wf_Pro8787509627421085110_nat_o @ R3 ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfI_pf
% 4.69/4.96 thf(fact_2961_wfI__pf,axiom,
% 4.69/4.96 ! [R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ! [A9: set_nat] :
% 4.69/4.96 ( ( ord_less_eq_set_nat @ A9 @ ( image_nat_nat @ R3 @ A9 ) )
% 4.69/4.96 => ( A9 = bot_bot_set_nat ) )
% 4.69/4.96 => ( wf_nat @ R3 ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfI_pf
% 4.69/4.96 thf(fact_2962_wfE__pf,axiom,
% 4.69/4.96 ! [R3: set_Pr5094982260447487303t_unit,A: set_Product_unit] :
% 4.69/4.96 ( ( wf_Product_unit @ R3 )
% 4.69/4.96 => ( ( ord_le3507040750410214029t_unit @ A @ ( image_8431784415008483091t_unit @ R3 @ A ) )
% 4.69/4.96 => ( A = bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfE_pf
% 4.69/4.96 thf(fact_2963_wfE__pf,axiom,
% 4.69/4.96 ! [R3: set_Product_prod_o_o,A: set_o] :
% 4.69/4.96 ( ( wf_o @ R3 )
% 4.69/4.96 => ( ( ord_less_eq_set_o @ A @ ( image_o_o @ R3 @ A ) )
% 4.69/4.96 => ( A = bot_bot_set_o ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfE_pf
% 4.69/4.96 thf(fact_2964_wfE__pf,axiom,
% 4.69/4.96 ! [R3: set_Pr958786334691620121nt_int,A: set_int] :
% 4.69/4.96 ( ( wf_int @ R3 )
% 4.69/4.96 => ( ( ord_less_eq_set_int @ A @ ( image_int_int @ R3 @ A ) )
% 4.69/4.96 => ( A = bot_bot_set_int ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfE_pf
% 4.69/4.96 thf(fact_2965_wfE__pf,axiom,
% 4.69/4.96 ! [R3: set_Pr2161125870931222855_nat_o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.96 ( ( wf_Pro8787509627421085110_nat_o @ R3 )
% 4.69/4.96 => ( ( ord_le2965882846123202637_nat_o @ A @ ( image_2232984160439939859_nat_o @ R3 @ A ) )
% 4.69/4.96 => ( A = bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfE_pf
% 4.69/4.96 thf(fact_2966_wfE__pf,axiom,
% 4.69/4.96 ! [R3: set_Pr1261947904930325089at_nat,A: set_nat] :
% 4.69/4.96 ( ( wf_nat @ R3 )
% 4.69/4.96 => ( ( ord_less_eq_set_nat @ A @ ( image_nat_nat @ R3 @ A ) )
% 4.69/4.96 => ( A = bot_bot_set_nat ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wfE_pf
% 4.69/4.96 thf(fact_2967_wf__eq__minimal2,axiom,
% 4.69/4.96 ( wf_Product_unit
% 4.69/4.96 = ( ^ [R4: set_Pr5094982260447487303t_unit] :
% 4.69/4.96 ! [A3: set_Product_unit] :
% 4.69/4.96 ( ( ( ord_le3507040750410214029t_unit @ A3 @ ( field_Product_unit @ R4 ) )
% 4.69/4.96 & ( A3 != bot_bo3957492148770167129t_unit ) )
% 4.69/4.96 => ? [X2: product_unit] :
% 4.69/4.96 ( ( member_Product_unit @ X2 @ A3 )
% 4.69/4.96 & ! [Y3: product_unit] :
% 4.69/4.96 ( ( member_Product_unit @ Y3 @ A3 )
% 4.69/4.96 => ~ ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ Y3 @ X2 ) @ R4 ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_eq_minimal2
% 4.69/4.96 thf(fact_2968_wf__eq__minimal2,axiom,
% 4.69/4.96 ( wf_o
% 4.69/4.96 = ( ^ [R4: set_Product_prod_o_o] :
% 4.69/4.96 ! [A3: set_o] :
% 4.69/4.96 ( ( ( ord_less_eq_set_o @ A3 @ ( field_o @ R4 ) )
% 4.69/4.96 & ( A3 != bot_bot_set_o ) )
% 4.69/4.96 => ? [X2: $o] :
% 4.69/4.96 ( ( member_o @ X2 @ A3 )
% 4.69/4.96 & ! [Y3: $o] :
% 4.69/4.96 ( ( member_o @ Y3 @ A3 )
% 4.69/4.96 => ~ ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ Y3 @ X2 ) @ R4 ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_eq_minimal2
% 4.69/4.96 thf(fact_2969_wf__eq__minimal2,axiom,
% 4.69/4.96 ( wf_int
% 4.69/4.96 = ( ^ [R4: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ! [A3: set_int] :
% 4.69/4.96 ( ( ( ord_less_eq_set_int @ A3 @ ( field_int @ R4 ) )
% 4.69/4.96 & ( A3 != bot_bot_set_int ) )
% 4.69/4.96 => ? [X2: int] :
% 4.69/4.96 ( ( member_int @ X2 @ A3 )
% 4.69/4.96 & ! [Y3: int] :
% 4.69/4.96 ( ( member_int @ Y3 @ A3 )
% 4.69/4.96 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ X2 ) @ R4 ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_eq_minimal2
% 4.69/4.96 thf(fact_2970_wf__eq__minimal2,axiom,
% 4.69/4.96 ( wf_Pro8787509627421085110_nat_o
% 4.69/4.96 = ( ^ [R4: set_Pr2161125870931222855_nat_o] :
% 4.69/4.96 ! [A3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.96 ( ( ( ord_le2965882846123202637_nat_o @ A3 @ ( field_81821745747897882_nat_o @ R4 ) )
% 4.69/4.96 & ( A3 != bot_bo7824918357723582233_nat_o ) )
% 4.69/4.96 => ? [X2: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ X2 @ A3 )
% 4.69/4.96 & ! [Y3: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ Y3 @ A3 )
% 4.69/4.96 => ~ ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ Y3 @ X2 ) @ R4 ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_eq_minimal2
% 4.69/4.96 thf(fact_2971_wf__eq__minimal2,axiom,
% 4.69/4.96 ( wf_nat
% 4.69/4.96 = ( ^ [R4: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ! [A3: set_nat] :
% 4.69/4.96 ( ( ( ord_less_eq_set_nat @ A3 @ ( field_nat @ R4 ) )
% 4.69/4.96 & ( A3 != bot_bot_set_nat ) )
% 4.69/4.96 => ? [X2: nat] :
% 4.69/4.96 ( ( member_nat @ X2 @ A3 )
% 4.69/4.96 & ! [Y3: nat] :
% 4.69/4.96 ( ( member_nat @ Y3 @ A3 )
% 4.69/4.96 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ X2 ) @ R4 ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_eq_minimal2
% 4.69/4.96 thf(fact_2972_wo__rel_Ocases__Total,axiom,
% 4.69/4.96 ! [R2: set_Pr5094982260447487303t_unit,A2: product_unit,B: product_unit,Phi: product_unit > product_unit > $o] :
% 4.69/4.96 ( ( bNF_We2091578341578594809t_unit @ R2 )
% 4.69/4.96 => ( ( ord_le3507040750410214029t_unit @ ( insert_Product_unit @ A2 @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A2 @ B ) @ R2 )
% 4.69/4.96 => ( Phi @ A2 @ B ) )
% 4.69/4.96 => ( ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ B @ A2 ) @ R2 )
% 4.69/4.96 => ( Phi @ A2 @ B ) )
% 4.69/4.96 => ( Phi @ A2 @ B ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.cases_Total
% 4.69/4.96 thf(fact_2973_wo__rel_Ocases__Total,axiom,
% 4.69/4.96 ! [R2: set_Product_prod_o_o,A2: $o,B: $o,Phi: $o > $o > $o] :
% 4.69/4.96 ( ( bNF_We6437023980930612612_rel_o @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_o @ ( insert_o @ A2 @ ( insert_o @ B @ bot_bot_set_o ) ) @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ B ) @ R2 )
% 4.69/4.96 => ( Phi @ A2 @ B ) )
% 4.69/4.96 => ( ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ B @ A2 ) @ R2 )
% 4.69/4.96 => ( Phi @ A2 @ B ) )
% 4.69/4.96 => ( Phi @ A2 @ B ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.cases_Total
% 4.69/4.96 thf(fact_2974_wo__rel_Ocases__Total,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,A2: int,B: int,Phi: int > int > $o] :
% 4.69/4.96 ( ( bNF_We3815749466139970368el_int @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_int @ ( insert_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 )
% 4.69/4.96 => ( Phi @ A2 @ B ) )
% 4.69/4.96 => ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ A2 ) @ R2 )
% 4.69/4.96 => ( Phi @ A2 @ B ) )
% 4.69/4.96 => ( Phi @ A2 @ B ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.cases_Total
% 4.69/4.96 thf(fact_2975_wo__rel_Ocases__Total,axiom,
% 4.69/4.96 ! [R2: set_Pr2161125870931222855_nat_o,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o,Phi: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o] :
% 4.69/4.96 ( ( bNF_We740377018556551609_nat_o @ R2 )
% 4.69/4.96 => ( ( ord_le2965882846123202637_nat_o @ ( insert5175938949040314269_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o ) ) @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ B ) @ R2 )
% 4.69/4.96 => ( Phi @ A2 @ B ) )
% 4.69/4.96 => ( ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ B @ A2 ) @ R2 )
% 4.69/4.96 => ( Phi @ A2 @ B ) )
% 4.69/4.96 => ( Phi @ A2 @ B ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.cases_Total
% 4.69/4.96 thf(fact_2976_wo__rel_Ocases__Total,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,A2: nat,B: nat,Phi: nat > nat > $o] :
% 4.69/4.96 ( ( bNF_We3818239936649020644el_nat @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_nat @ ( insert_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 )
% 4.69/4.96 => ( Phi @ A2 @ B ) )
% 4.69/4.96 => ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ A2 ) @ R2 )
% 4.69/4.96 => ( Phi @ A2 @ B ) )
% 4.69/4.96 => ( Phi @ A2 @ B ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.cases_Total
% 4.69/4.96 thf(fact_2977_wf__no__path,axiom,
% 4.69/4.96 ! [R3: set_Pr5094982260447487303t_unit] :
% 4.69/4.96 ( ( ( inf_in4660618365625256667t_unit @ ( domain4292024440186670924t_unit @ R3 ) @ ( range_6617724647562260917t_unit @ R3 ) )
% 4.69/4.96 = bot_bo3957492148770167129t_unit )
% 4.69/4.96 => ( wf_Product_unit @ R3 ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_no_path
% 4.69/4.96 thf(fact_2978_wf__no__path,axiom,
% 4.69/4.96 ! [R3: set_Product_prod_o_o] :
% 4.69/4.96 ( ( ( inf_inf_set_o @ ( domain_o_o @ R3 ) @ ( range_o_o @ R3 ) )
% 4.69/4.96 = bot_bot_set_o )
% 4.69/4.96 => ( wf_o @ R3 ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_no_path
% 4.69/4.96 thf(fact_2979_wf__no__path,axiom,
% 4.69/4.96 ! [R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ( ( inf_inf_set_nat @ ( domain_nat_nat @ R3 ) @ ( range_nat_nat @ R3 ) )
% 4.69/4.96 = bot_bot_set_nat )
% 4.69/4.96 => ( wf_nat @ R3 ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_no_path
% 4.69/4.96 thf(fact_2980_wf__no__path,axiom,
% 4.69/4.96 ! [R3: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ( ( ( inf_inf_set_int @ ( domain_int_int @ R3 ) @ ( range_int_int @ R3 ) )
% 4.69/4.96 = bot_bot_set_int )
% 4.69/4.96 => ( wf_int @ R3 ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_no_path
% 4.69/4.96 thf(fact_2981_wf__no__path,axiom,
% 4.69/4.96 ! [R3: set_Pr2161125870931222855_nat_o] :
% 4.69/4.96 ( ( ( inf_in1906310914598751387_nat_o @ ( domain4881241903163524940_nat_o @ R3 ) @ ( range_5289318983786108341_nat_o @ R3 ) )
% 4.69/4.96 = bot_bo7824918357723582233_nat_o )
% 4.69/4.96 => ( wf_Pro8787509627421085110_nat_o @ R3 ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_no_path
% 4.69/4.96 thf(fact_2982_wf__min,axiom,
% 4.69/4.96 ! [R3: set_Pr2161125870931222855_nat_o] :
% 4.69/4.96 ( ( wf_Pro8787509627421085110_nat_o @ R3 )
% 4.69/4.96 => ( ( R3 != bot_bo3657187498359500723_nat_o )
% 4.69/4.96 => ~ ! [M2: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ~ ( member6576561426505652726_nat_o @ M2 @ ( minus_1801376950450012436_nat_o @ ( domain4881241903163524940_nat_o @ R3 ) @ ( range_5289318983786108341_nat_o @ R3 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_min
% 4.69/4.96 thf(fact_2983_wf__min,axiom,
% 4.69/4.96 ! [R3: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ( ( wf_int @ R3 )
% 4.69/4.96 => ( ( R3 != bot_bo1796632182523588997nt_int )
% 4.69/4.96 => ~ ! [M2: int] :
% 4.69/4.96 ~ ( member_int @ M2 @ ( minus_minus_set_int @ ( domain_int_int @ R3 ) @ ( range_int_int @ R3 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_min
% 4.69/4.96 thf(fact_2984_wf__min,axiom,
% 4.69/4.96 ! [R3: set_Product_prod_o_o] :
% 4.69/4.96 ( ( wf_o @ R3 )
% 4.69/4.96 => ( ( R3 != bot_bo7073875226086086771od_o_o )
% 4.69/4.96 => ~ ! [M2: $o] :
% 4.69/4.96 ~ ( member_o @ M2 @ ( minus_minus_set_o @ ( domain_o_o @ R3 ) @ ( range_o_o @ R3 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_min
% 4.69/4.96 thf(fact_2985_wf__min,axiom,
% 4.69/4.96 ! [R3: set_Pr5094982260447487303t_unit] :
% 4.69/4.96 ( ( wf_Product_unit @ R3 )
% 4.69/4.96 => ( ( R3 != bot_bo1654022762305692595t_unit )
% 4.69/4.96 => ~ ! [M2: product_unit] :
% 4.69/4.96 ~ ( member_Product_unit @ M2 @ ( minus_6452836326544984404t_unit @ ( domain4292024440186670924t_unit @ R3 ) @ ( range_6617724647562260917t_unit @ R3 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_min
% 4.69/4.96 thf(fact_2986_wf__min,axiom,
% 4.69/4.96 ! [R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ( wf_nat @ R3 )
% 4.69/4.96 => ( ( R3 != bot_bo2099793752762293965at_nat )
% 4.69/4.96 => ~ ! [M2: nat] :
% 4.69/4.96 ~ ( member_nat @ M2 @ ( minus_minus_set_nat @ ( domain_nat_nat @ R3 ) @ ( range_nat_nat @ R3 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_min
% 4.69/4.96 thf(fact_2987_underS__incl__iff,axiom,
% 4.69/4.96 ! [R2: set_Pr2161125870931222855_nat_o,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( order_1145710701291701250_nat_o @ ( field_81821745747897882_nat_o @ R2 ) @ R2 )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ A2 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ B @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( ord_le2965882846123202637_nat_o @ ( order_7262550146012401043_nat_o @ R2 @ A2 ) @ ( order_7262550146012401043_nat_o @ R2 @ B ) )
% 4.69/4.96 = ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ B ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % underS_incl_iff
% 4.69/4.96 thf(fact_2988_underS__incl__iff,axiom,
% 4.69/4.96 ! [R2: set_Product_prod_o_o,A2: $o,B: $o] :
% 4.69/4.96 ( ( order_6238756238976269133r_on_o @ ( field_o @ R2 ) @ R2 )
% 4.69/4.96 => ( ( member_o @ A2 @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( member_o @ B @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( ord_less_eq_set_o @ ( order_underS_o @ R2 @ A2 ) @ ( order_underS_o @ R2 @ B ) )
% 4.69/4.96 = ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ B ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % underS_incl_iff
% 4.69/4.96 thf(fact_2989_underS__incl__iff,axiom,
% 4.69/4.96 ! [R2: set_Pr5094982260447487303t_unit,A2: product_unit,B: product_unit] :
% 4.69/4.96 ( ( order_888282469287196226t_unit @ ( field_Product_unit @ R2 ) @ R2 )
% 4.69/4.96 => ( ( member_Product_unit @ A2 @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( member_Product_unit @ B @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( ord_le3507040750410214029t_unit @ ( order_5809128134054296019t_unit @ R2 @ A2 ) @ ( order_5809128134054296019t_unit @ R2 @ B ) )
% 4.69/4.96 = ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A2 @ B ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % underS_incl_iff
% 4.69/4.96 thf(fact_2990_underS__incl__iff,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,A2: int,B: int] :
% 4.69/4.96 ( ( order_4471489696718655927on_int @ ( field_int @ R2 ) @ R2 )
% 4.69/4.96 => ( ( member_int @ A2 @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( member_int @ B @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( ord_less_eq_set_int @ ( order_underS_int @ R2 @ A2 ) @ ( order_underS_int @ R2 @ B ) )
% 4.69/4.96 = ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % underS_incl_iff
% 4.69/4.96 thf(fact_2991_underS__incl__iff,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,A2: nat,B: nat] :
% 4.69/4.96 ( ( order_4473980167227706203on_nat @ ( field_nat @ R2 ) @ R2 )
% 4.69/4.96 => ( ( member_nat @ A2 @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( member_nat @ B @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( ord_less_eq_set_nat @ ( order_underS_nat @ R2 @ A2 ) @ ( order_underS_nat @ R2 @ B ) )
% 4.69/4.96 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % underS_incl_iff
% 4.69/4.96 thf(fact_2992_wo__rel_OWell__order__isMinim__exists,axiom,
% 4.69/4.96 ! [R2: set_Pr5094982260447487303t_unit,B4: set_Product_unit] :
% 4.69/4.96 ( ( bNF_We2091578341578594809t_unit @ R2 )
% 4.69/4.96 => ( ( ord_le3507040750410214029t_unit @ B4 @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( B4 != bot_bo3957492148770167129t_unit )
% 4.69/4.96 => ? [X_1: product_unit] : ( bNF_We909621271159000003t_unit @ R2 @ B4 @ X_1 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.Well_order_isMinim_exists
% 4.69/4.96 thf(fact_2993_wo__rel_OWell__order__isMinim__exists,axiom,
% 4.69/4.96 ! [R2: set_Product_prod_o_o,B4: set_o] :
% 4.69/4.96 ( ( bNF_We6437023980930612612_rel_o @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_o @ B4 @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( B4 != bot_bot_set_o )
% 4.69/4.96 => ? [X_1: $o] : ( bNF_We4647864369647134286inim_o @ R2 @ B4 @ X_1 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.Well_order_isMinim_exists
% 4.69/4.96 thf(fact_2994_wo__rel_OWell__order__isMinim__exists,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,B4: set_int] :
% 4.69/4.96 ( ( bNF_We3815749466139970368el_int @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_int @ B4 @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( B4 != bot_bot_set_int )
% 4.69/4.96 => ? [X_1: int] : ( bNF_We6511469253196982518im_int @ R2 @ B4 @ X_1 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.Well_order_isMinim_exists
% 4.69/4.96 thf(fact_2995_wo__rel_OWell__order__isMinim__exists,axiom,
% 4.69/4.96 ! [R2: set_Pr2161125870931222855_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.96 ( ( bNF_We740377018556551609_nat_o @ R2 )
% 4.69/4.96 => ( ( ord_le2965882846123202637_nat_o @ B4 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( B4 != bot_bo7824918357723582233_nat_o )
% 4.69/4.96 => ? [X_1: produc3658429121746597890et_nat > $o] : ( bNF_We5608535359669600131_nat_o @ R2 @ B4 @ X_1 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.Well_order_isMinim_exists
% 4.69/4.96 thf(fact_2996_wo__rel_OWell__order__isMinim__exists,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,B4: set_nat] :
% 4.69/4.96 ( ( bNF_We3818239936649020644el_nat @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_nat @ B4 @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( B4 != bot_bot_set_nat )
% 4.69/4.96 => ? [X_1: nat] : ( bNF_We6513959723706032794im_nat @ R2 @ B4 @ X_1 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.Well_order_isMinim_exists
% 4.69/4.96 thf(fact_2997_Refl__under__underS,axiom,
% 4.69/4.96 ! [R2: set_Pr5094982260447487303t_unit,A2: product_unit] :
% 4.69/4.96 ( ( refl_on_Product_unit @ ( field_Product_unit @ R2 ) @ R2 )
% 4.69/4.96 => ( ( member_Product_unit @ A2 @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( order_6949322460238004850t_unit @ R2 @ A2 )
% 4.69/4.96 = ( sup_su793286257634532545t_unit @ ( order_5809128134054296019t_unit @ R2 @ A2 ) @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Refl_under_underS
% 4.69/4.96 thf(fact_2998_Refl__under__underS,axiom,
% 4.69/4.96 ! [R2: set_Product_prod_o_o,A2: $o] :
% 4.69/4.96 ( ( refl_on_o @ ( field_o @ R2 ) @ R2 )
% 4.69/4.96 => ( ( member_o @ A2 @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( order_under_o @ R2 @ A2 )
% 4.69/4.96 = ( sup_sup_set_o @ ( order_underS_o @ R2 @ A2 ) @ ( insert_o @ A2 @ bot_bot_set_o ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Refl_under_underS
% 4.69/4.96 thf(fact_2999_Refl__under__underS,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,A2: nat] :
% 4.69/4.96 ( ( refl_on_nat @ ( field_nat @ R2 ) @ R2 )
% 4.69/4.96 => ( ( member_nat @ A2 @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( order_under_nat @ R2 @ A2 )
% 4.69/4.96 = ( sup_sup_set_nat @ ( order_underS_nat @ R2 @ A2 ) @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Refl_under_underS
% 4.69/4.96 thf(fact_3000_Refl__under__underS,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,A2: int] :
% 4.69/4.96 ( ( refl_on_int @ ( field_int @ R2 ) @ R2 )
% 4.69/4.96 => ( ( member_int @ A2 @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( order_under_int @ R2 @ A2 )
% 4.69/4.96 = ( sup_sup_set_int @ ( order_underS_int @ R2 @ A2 ) @ ( insert_int @ A2 @ bot_bot_set_int ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Refl_under_underS
% 4.69/4.96 thf(fact_3001_Refl__under__underS,axiom,
% 4.69/4.96 ! [R2: set_Pr2161125870931222855_nat_o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( refl_o1075864025857821388_nat_o @ ( field_81821745747897882_nat_o @ R2 ) @ R2 )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ A2 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( order_2885205318754725938_nat_o @ R2 @ A2 )
% 4.69/4.96 = ( sup_su5209123915105501825_nat_o @ ( order_7262550146012401043_nat_o @ R2 @ A2 ) @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Refl_under_underS
% 4.69/4.96 thf(fact_3002_wo__rel_Ominim__inField,axiom,
% 4.69/4.96 ! [R2: set_Pr5094982260447487303t_unit,B4: set_Product_unit] :
% 4.69/4.96 ( ( bNF_We2091578341578594809t_unit @ R2 )
% 4.69/4.96 => ( ( ord_le3507040750410214029t_unit @ B4 @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( B4 != bot_bo3957492148770167129t_unit )
% 4.69/4.96 => ( member_Product_unit @ ( bNF_We7185707985517244377t_unit @ R2 @ B4 ) @ ( field_Product_unit @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.minim_inField
% 4.69/4.96 thf(fact_3003_wo__rel_Ominim__inField,axiom,
% 4.69/4.96 ! [R2: set_Product_prod_o_o,B4: set_o] :
% 4.69/4.96 ( ( bNF_We6437023980930612612_rel_o @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_o @ B4 @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( B4 != bot_bot_set_o )
% 4.69/4.96 => ( member_o @ ( bNF_We537455116209922916inim_o @ R2 @ B4 ) @ ( field_o @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.minim_inField
% 4.69/4.96 thf(fact_3004_wo__rel_Ominim__inField,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,B4: set_int] :
% 4.69/4.96 ( ( bNF_We3815749466139970368el_int @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_int @ B4 @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( B4 != bot_bot_set_int )
% 4.69/4.96 => ( member_int @ ( bNF_We3272633801743244640im_int @ R2 @ B4 ) @ ( field_int @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.minim_inField
% 4.69/4.96 thf(fact_3005_wo__rel_Ominim__inField,axiom,
% 4.69/4.96 ! [R2: set_Pr2161125870931222855_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.96 ( ( bNF_We740377018556551609_nat_o @ R2 )
% 4.69/4.96 => ( ( ord_le2965882846123202637_nat_o @ B4 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( B4 != bot_bo7824918357723582233_nat_o )
% 4.69/4.96 => ( member6576561426505652726_nat_o @ ( bNF_We8236795211600914329_nat_o @ R2 @ B4 ) @ ( field_81821745747897882_nat_o @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.minim_inField
% 4.69/4.96 thf(fact_3006_wo__rel_Ominim__inField,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,B4: set_nat] :
% 4.69/4.96 ( ( bNF_We3818239936649020644el_nat @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_nat @ B4 @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( B4 != bot_bot_set_nat )
% 4.69/4.96 => ( member_nat @ ( bNF_We3275124272252294916im_nat @ R2 @ B4 ) @ ( field_nat @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.minim_inField
% 4.69/4.96 thf(fact_3007_wo__rel_Ominim__in,axiom,
% 4.69/4.96 ! [R2: set_Pr5094982260447487303t_unit,B4: set_Product_unit] :
% 4.69/4.96 ( ( bNF_We2091578341578594809t_unit @ R2 )
% 4.69/4.96 => ( ( ord_le3507040750410214029t_unit @ B4 @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( B4 != bot_bo3957492148770167129t_unit )
% 4.69/4.96 => ( member_Product_unit @ ( bNF_We7185707985517244377t_unit @ R2 @ B4 ) @ B4 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.minim_in
% 4.69/4.96 thf(fact_3008_wo__rel_Ominim__in,axiom,
% 4.69/4.96 ! [R2: set_Product_prod_o_o,B4: set_o] :
% 4.69/4.96 ( ( bNF_We6437023980930612612_rel_o @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_o @ B4 @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( B4 != bot_bot_set_o )
% 4.69/4.96 => ( member_o @ ( bNF_We537455116209922916inim_o @ R2 @ B4 ) @ B4 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.minim_in
% 4.69/4.96 thf(fact_3009_wo__rel_Ominim__in,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,B4: set_int] :
% 4.69/4.96 ( ( bNF_We3815749466139970368el_int @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_int @ B4 @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( B4 != bot_bot_set_int )
% 4.69/4.96 => ( member_int @ ( bNF_We3272633801743244640im_int @ R2 @ B4 ) @ B4 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.minim_in
% 4.69/4.96 thf(fact_3010_wo__rel_Ominim__in,axiom,
% 4.69/4.96 ! [R2: set_Pr2161125870931222855_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.96 ( ( bNF_We740377018556551609_nat_o @ R2 )
% 4.69/4.96 => ( ( ord_le2965882846123202637_nat_o @ B4 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( B4 != bot_bo7824918357723582233_nat_o )
% 4.69/4.96 => ( member6576561426505652726_nat_o @ ( bNF_We8236795211600914329_nat_o @ R2 @ B4 ) @ B4 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.minim_in
% 4.69/4.96 thf(fact_3011_wo__rel_Ominim__in,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,B4: set_nat] :
% 4.69/4.96 ( ( bNF_We3818239936649020644el_nat @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_nat @ B4 @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( B4 != bot_bot_set_nat )
% 4.69/4.96 => ( member_nat @ ( bNF_We3275124272252294916im_nat @ R2 @ B4 ) @ B4 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.minim_in
% 4.69/4.96 thf(fact_3012_wo__rel_Oequals__minim,axiom,
% 4.69/4.96 ! [R2: set_Pr2161125870931222855_nat_o,B4: set_Pr4532377907799695533_nat_o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( bNF_We740377018556551609_nat_o @ R2 )
% 4.69/4.96 => ( ( ord_le2965882846123202637_nat_o @ B4 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ A2 @ B4 )
% 4.69/4.96 => ( ! [B2: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ B2 @ B4 )
% 4.69/4.96 => ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ B2 ) @ R2 ) )
% 4.69/4.96 => ( A2
% 4.69/4.96 = ( bNF_We8236795211600914329_nat_o @ R2 @ B4 ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.equals_minim
% 4.69/4.96 thf(fact_3013_wo__rel_Oequals__minim,axiom,
% 4.69/4.96 ! [R2: set_Product_prod_o_o,B4: set_o,A2: $o] :
% 4.69/4.96 ( ( bNF_We6437023980930612612_rel_o @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_o @ B4 @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( member_o @ A2 @ B4 )
% 4.69/4.96 => ( ! [B2: $o] :
% 4.69/4.96 ( ( member_o @ B2 @ B4 )
% 4.69/4.96 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ B2 ) @ R2 ) )
% 4.69/4.96 => ( A2
% 4.69/4.96 = ( bNF_We537455116209922916inim_o @ R2 @ B4 ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.equals_minim
% 4.69/4.96 thf(fact_3014_wo__rel_Oequals__minim,axiom,
% 4.69/4.96 ! [R2: set_Pr5094982260447487303t_unit,B4: set_Product_unit,A2: product_unit] :
% 4.69/4.96 ( ( bNF_We2091578341578594809t_unit @ R2 )
% 4.69/4.96 => ( ( ord_le3507040750410214029t_unit @ B4 @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( member_Product_unit @ A2 @ B4 )
% 4.69/4.96 => ( ! [B2: product_unit] :
% 4.69/4.96 ( ( member_Product_unit @ B2 @ B4 )
% 4.69/4.96 => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A2 @ B2 ) @ R2 ) )
% 4.69/4.96 => ( A2
% 4.69/4.96 = ( bNF_We7185707985517244377t_unit @ R2 @ B4 ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.equals_minim
% 4.69/4.96 thf(fact_3015_wo__rel_Oequals__minim,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,B4: set_int,A2: int] :
% 4.69/4.96 ( ( bNF_We3815749466139970368el_int @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_int @ B4 @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( member_int @ A2 @ B4 )
% 4.69/4.96 => ( ! [B2: int] :
% 4.69/4.96 ( ( member_int @ B2 @ B4 )
% 4.69/4.96 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B2 ) @ R2 ) )
% 4.69/4.96 => ( A2
% 4.69/4.96 = ( bNF_We3272633801743244640im_int @ R2 @ B4 ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.equals_minim
% 4.69/4.96 thf(fact_3016_wo__rel_Oequals__minim,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,B4: set_nat,A2: nat] :
% 4.69/4.96 ( ( bNF_We3818239936649020644el_nat @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_nat @ B4 @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( member_nat @ A2 @ B4 )
% 4.69/4.96 => ( ! [B2: nat] :
% 4.69/4.96 ( ( member_nat @ B2 @ B4 )
% 4.69/4.96 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B2 ) @ R2 ) )
% 4.69/4.96 => ( A2
% 4.69/4.96 = ( bNF_We3275124272252294916im_nat @ R2 @ B4 ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.equals_minim
% 4.69/4.96 thf(fact_3017_wo__rel_Ominim__least,axiom,
% 4.69/4.96 ! [R2: set_Pr2161125870931222855_nat_o,B4: set_Pr4532377907799695533_nat_o,B: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( bNF_We740377018556551609_nat_o @ R2 )
% 4.69/4.96 => ( ( ord_le2965882846123202637_nat_o @ B4 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ B @ B4 )
% 4.69/4.96 => ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ ( bNF_We8236795211600914329_nat_o @ R2 @ B4 ) @ B ) @ R2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.minim_least
% 4.69/4.96 thf(fact_3018_wo__rel_Ominim__least,axiom,
% 4.69/4.96 ! [R2: set_Product_prod_o_o,B4: set_o,B: $o] :
% 4.69/4.96 ( ( bNF_We6437023980930612612_rel_o @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_o @ B4 @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( member_o @ B @ B4 )
% 4.69/4.96 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ ( bNF_We537455116209922916inim_o @ R2 @ B4 ) @ B ) @ R2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.minim_least
% 4.69/4.96 thf(fact_3019_wo__rel_Ominim__least,axiom,
% 4.69/4.96 ! [R2: set_Pr5094982260447487303t_unit,B4: set_Product_unit,B: product_unit] :
% 4.69/4.96 ( ( bNF_We2091578341578594809t_unit @ R2 )
% 4.69/4.96 => ( ( ord_le3507040750410214029t_unit @ B4 @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( member_Product_unit @ B @ B4 )
% 4.69/4.96 => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ ( bNF_We7185707985517244377t_unit @ R2 @ B4 ) @ B ) @ R2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.minim_least
% 4.69/4.96 thf(fact_3020_wo__rel_Ominim__least,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,B4: set_int,B: int] :
% 4.69/4.96 ( ( bNF_We3815749466139970368el_int @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_int @ B4 @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( member_int @ B @ B4 )
% 4.69/4.96 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( bNF_We3272633801743244640im_int @ R2 @ B4 ) @ B ) @ R2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.minim_least
% 4.69/4.96 thf(fact_3021_wo__rel_Ominim__least,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,B4: set_nat,B: nat] :
% 4.69/4.96 ( ( bNF_We3818239936649020644el_nat @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_nat @ B4 @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( member_nat @ B @ B4 )
% 4.69/4.96 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( bNF_We3275124272252294916im_nat @ R2 @ B4 ) @ B ) @ R2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.minim_least
% 4.69/4.96 thf(fact_3022_wo__rel_Omax2__greater__among,axiom,
% 4.69/4.96 ! [R2: set_Pr5094982260447487303t_unit,A2: product_unit,B: product_unit] :
% 4.69/4.96 ( ( bNF_We2091578341578594809t_unit @ R2 )
% 4.69/4.96 => ( ( member_Product_unit @ A2 @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( member_Product_unit @ B @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A2 @ ( bNF_We7204996500647184731t_unit @ R2 @ A2 @ B ) ) @ R2 )
% 4.69/4.96 & ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ B @ ( bNF_We7204996500647184731t_unit @ R2 @ A2 @ B ) ) @ R2 )
% 4.69/4.96 & ( member_Product_unit @ ( bNF_We7204996500647184731t_unit @ R2 @ A2 @ B ) @ ( insert_Product_unit @ A2 @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_greater_among
% 4.69/4.96 thf(fact_3023_wo__rel_Omax2__greater__among,axiom,
% 4.69/4.96 ! [R2: set_Product_prod_o_o,A2: $o,B: $o] :
% 4.69/4.96 ( ( bNF_We6437023980930612612_rel_o @ R2 )
% 4.69/4.96 => ( ( member_o @ A2 @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( member_o @ B @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ ( bNF_We3104086342435940326max2_o @ R2 @ A2 @ B ) ) @ R2 )
% 4.69/4.96 & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ B @ ( bNF_We3104086342435940326max2_o @ R2 @ A2 @ B ) ) @ R2 )
% 4.69/4.96 & ( member_o @ ( bNF_We3104086342435940326max2_o @ R2 @ A2 @ B ) @ ( insert_o @ A2 @ ( insert_o @ B @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_greater_among
% 4.69/4.96 thf(fact_3024_wo__rel_Omax2__greater__among,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,A2: nat,B: nat] :
% 4.69/4.96 ( ( bNF_We3818239936649020644el_nat @ R2 )
% 4.69/4.96 => ( ( member_nat @ A2 @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( member_nat @ B @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ ( bNF_We2380939065524664066x2_nat @ R2 @ A2 @ B ) ) @ R2 )
% 4.69/4.96 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ ( bNF_We2380939065524664066x2_nat @ R2 @ A2 @ B ) ) @ R2 )
% 4.69/4.96 & ( member_nat @ ( bNF_We2380939065524664066x2_nat @ R2 @ A2 @ B ) @ ( insert_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_greater_among
% 4.69/4.96 thf(fact_3025_wo__rel_Omax2__greater__among,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,A2: int,B: int] :
% 4.69/4.96 ( ( bNF_We3815749466139970368el_int @ R2 )
% 4.69/4.96 => ( ( member_int @ A2 @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( member_int @ B @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ ( bNF_We2378448595015613790x2_int @ R2 @ A2 @ B ) ) @ R2 )
% 4.69/4.96 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ ( bNF_We2378448595015613790x2_int @ R2 @ A2 @ B ) ) @ R2 )
% 4.69/4.96 & ( member_int @ ( bNF_We2378448595015613790x2_int @ R2 @ A2 @ B ) @ ( insert_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_greater_among
% 4.69/4.96 thf(fact_3026_wo__rel_Omax2__greater__among,axiom,
% 4.69/4.96 ! [R2: set_Pr2161125870931222855_nat_o,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( bNF_We740377018556551609_nat_o @ R2 )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ A2 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ B @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ ( bNF_We6400040844883348763_nat_o @ R2 @ A2 @ B ) ) @ R2 )
% 4.69/4.96 & ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ B @ ( bNF_We6400040844883348763_nat_o @ R2 @ A2 @ B ) ) @ R2 )
% 4.69/4.96 & ( member6576561426505652726_nat_o @ ( bNF_We6400040844883348763_nat_o @ R2 @ A2 @ B ) @ ( insert5175938949040314269_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_greater_among
% 4.69/4.96 thf(fact_3027_wo__rel_Omax2__def,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,A2: nat,B: nat] :
% 4.69/4.96 ( ( bNF_We3818239936649020644el_nat @ R2 )
% 4.69/4.96 => ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 )
% 4.69/4.96 => ( ( bNF_We2380939065524664066x2_nat @ R2 @ A2 @ B )
% 4.69/4.96 = B ) )
% 4.69/4.96 & ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 )
% 4.69/4.96 => ( ( bNF_We2380939065524664066x2_nat @ R2 @ A2 @ B )
% 4.69/4.96 = A2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_def
% 4.69/4.96 thf(fact_3028_wo__rel_Omax2__def,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,A2: int,B: int] :
% 4.69/4.96 ( ( bNF_We3815749466139970368el_int @ R2 )
% 4.69/4.96 => ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 )
% 4.69/4.96 => ( ( bNF_We2378448595015613790x2_int @ R2 @ A2 @ B )
% 4.69/4.96 = B ) )
% 4.69/4.96 & ( ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 )
% 4.69/4.96 => ( ( bNF_We2378448595015613790x2_int @ R2 @ A2 @ B )
% 4.69/4.96 = A2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_def
% 4.69/4.96 thf(fact_3029_under__incr,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,A2: int,B: int] :
% 4.69/4.96 ( ( trans_int @ R2 )
% 4.69/4.96 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 )
% 4.69/4.96 => ( ord_less_eq_set_int @ ( order_under_int @ R2 @ A2 ) @ ( order_under_int @ R2 @ B ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % under_incr
% 4.69/4.96 thf(fact_3030_under__incr,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,A2: nat,B: nat] :
% 4.69/4.96 ( ( trans_nat @ R2 )
% 4.69/4.96 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 )
% 4.69/4.96 => ( ord_less_eq_set_nat @ ( order_under_nat @ R2 @ A2 ) @ ( order_under_nat @ R2 @ B ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % under_incr
% 4.69/4.96 thf(fact_3031_wo__rel_Ominim__isMinim,axiom,
% 4.69/4.96 ! [R2: set_Pr5094982260447487303t_unit,B4: set_Product_unit] :
% 4.69/4.96 ( ( bNF_We2091578341578594809t_unit @ R2 )
% 4.69/4.96 => ( ( ord_le3507040750410214029t_unit @ B4 @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( B4 != bot_bo3957492148770167129t_unit )
% 4.69/4.96 => ( bNF_We909621271159000003t_unit @ R2 @ B4 @ ( bNF_We7185707985517244377t_unit @ R2 @ B4 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.minim_isMinim
% 4.69/4.96 thf(fact_3032_wo__rel_Ominim__isMinim,axiom,
% 4.69/4.96 ! [R2: set_Product_prod_o_o,B4: set_o] :
% 4.69/4.96 ( ( bNF_We6437023980930612612_rel_o @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_o @ B4 @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( B4 != bot_bot_set_o )
% 4.69/4.96 => ( bNF_We4647864369647134286inim_o @ R2 @ B4 @ ( bNF_We537455116209922916inim_o @ R2 @ B4 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.minim_isMinim
% 4.69/4.96 thf(fact_3033_wo__rel_Ominim__isMinim,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,B4: set_int] :
% 4.69/4.96 ( ( bNF_We3815749466139970368el_int @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_int @ B4 @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( B4 != bot_bot_set_int )
% 4.69/4.96 => ( bNF_We6511469253196982518im_int @ R2 @ B4 @ ( bNF_We3272633801743244640im_int @ R2 @ B4 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.minim_isMinim
% 4.69/4.96 thf(fact_3034_wo__rel_Ominim__isMinim,axiom,
% 4.69/4.96 ! [R2: set_Pr2161125870931222855_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.96 ( ( bNF_We740377018556551609_nat_o @ R2 )
% 4.69/4.96 => ( ( ord_le2965882846123202637_nat_o @ B4 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( B4 != bot_bo7824918357723582233_nat_o )
% 4.69/4.96 => ( bNF_We5608535359669600131_nat_o @ R2 @ B4 @ ( bNF_We8236795211600914329_nat_o @ R2 @ B4 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.minim_isMinim
% 4.69/4.96 thf(fact_3035_wo__rel_Ominim__isMinim,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,B4: set_nat] :
% 4.69/4.96 ( ( bNF_We3818239936649020644el_nat @ R2 )
% 4.69/4.96 => ( ( ord_less_eq_set_nat @ B4 @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( B4 != bot_bot_set_nat )
% 4.69/4.96 => ( bNF_We6513959723706032794im_nat @ R2 @ B4 @ ( bNF_We3275124272252294916im_nat @ R2 @ B4 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.minim_isMinim
% 4.69/4.96 thf(fact_3036_wo__rel_OisMinim__def,axiom,
% 4.69/4.96 ! [R2: set_Pr2161125870931222855_nat_o,A: set_Pr4532377907799695533_nat_o,B: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( bNF_We740377018556551609_nat_o @ R2 )
% 4.69/4.96 => ( ( bNF_We5608535359669600131_nat_o @ R2 @ A @ B )
% 4.69/4.96 = ( ( member6576561426505652726_nat_o @ B @ A )
% 4.69/4.96 & ! [X2: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ X2 @ A )
% 4.69/4.96 => ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ B @ X2 ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.isMinim_def
% 4.69/4.96 thf(fact_3037_wo__rel_OisMinim__def,axiom,
% 4.69/4.96 ! [R2: set_Product_prod_o_o,A: set_o,B: $o] :
% 4.69/4.96 ( ( bNF_We6437023980930612612_rel_o @ R2 )
% 4.69/4.96 => ( ( bNF_We4647864369647134286inim_o @ R2 @ A @ B )
% 4.69/4.96 = ( ( member_o @ B @ A )
% 4.69/4.96 & ! [X2: $o] :
% 4.69/4.96 ( ( member_o @ X2 @ A )
% 4.69/4.96 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ B @ X2 ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.isMinim_def
% 4.69/4.96 thf(fact_3038_wo__rel_OisMinim__def,axiom,
% 4.69/4.96 ! [R2: set_Pr5094982260447487303t_unit,A: set_Product_unit,B: product_unit] :
% 4.69/4.96 ( ( bNF_We2091578341578594809t_unit @ R2 )
% 4.69/4.96 => ( ( bNF_We909621271159000003t_unit @ R2 @ A @ B )
% 4.69/4.96 = ( ( member_Product_unit @ B @ A )
% 4.69/4.96 & ! [X2: product_unit] :
% 4.69/4.96 ( ( member_Product_unit @ X2 @ A )
% 4.69/4.96 => ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ B @ X2 ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.isMinim_def
% 4.69/4.96 thf(fact_3039_wo__rel_OisMinim__def,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,A: set_nat,B: nat] :
% 4.69/4.96 ( ( bNF_We3818239936649020644el_nat @ R2 )
% 4.69/4.96 => ( ( bNF_We6513959723706032794im_nat @ R2 @ A @ B )
% 4.69/4.96 = ( ( member_nat @ B @ A )
% 4.69/4.96 & ! [X2: nat] :
% 4.69/4.96 ( ( member_nat @ X2 @ A )
% 4.69/4.96 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ X2 ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.isMinim_def
% 4.69/4.96 thf(fact_3040_wo__rel_OisMinim__def,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,A: set_int,B: int] :
% 4.69/4.96 ( ( bNF_We3815749466139970368el_int @ R2 )
% 4.69/4.96 => ( ( bNF_We6511469253196982518im_int @ R2 @ A @ B )
% 4.69/4.96 = ( ( member_int @ B @ A )
% 4.69/4.96 & ! [X2: int] :
% 4.69/4.96 ( ( member_int @ X2 @ A )
% 4.69/4.96 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ X2 ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.isMinim_def
% 4.69/4.96 thf(fact_3041_wo__rel_Omax2__greater,axiom,
% 4.69/4.96 ! [R2: set_Pr2161125870931222855_nat_o,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( bNF_We740377018556551609_nat_o @ R2 )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ A2 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ B @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ ( bNF_We6400040844883348763_nat_o @ R2 @ A2 @ B ) ) @ R2 )
% 4.69/4.96 & ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ B @ ( bNF_We6400040844883348763_nat_o @ R2 @ A2 @ B ) ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_greater
% 4.69/4.96 thf(fact_3042_wo__rel_Omax2__greater,axiom,
% 4.69/4.96 ! [R2: set_Product_prod_o_o,A2: $o,B: $o] :
% 4.69/4.96 ( ( bNF_We6437023980930612612_rel_o @ R2 )
% 4.69/4.96 => ( ( member_o @ A2 @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( member_o @ B @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ ( bNF_We3104086342435940326max2_o @ R2 @ A2 @ B ) ) @ R2 )
% 4.69/4.96 & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ B @ ( bNF_We3104086342435940326max2_o @ R2 @ A2 @ B ) ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_greater
% 4.69/4.96 thf(fact_3043_wo__rel_Omax2__greater,axiom,
% 4.69/4.96 ! [R2: set_Pr5094982260447487303t_unit,A2: product_unit,B: product_unit] :
% 4.69/4.96 ( ( bNF_We2091578341578594809t_unit @ R2 )
% 4.69/4.96 => ( ( member_Product_unit @ A2 @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( member_Product_unit @ B @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A2 @ ( bNF_We7204996500647184731t_unit @ R2 @ A2 @ B ) ) @ R2 )
% 4.69/4.96 & ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ B @ ( bNF_We7204996500647184731t_unit @ R2 @ A2 @ B ) ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_greater
% 4.69/4.96 thf(fact_3044_wo__rel_Omax2__greater,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,A2: nat,B: nat] :
% 4.69/4.96 ( ( bNF_We3818239936649020644el_nat @ R2 )
% 4.69/4.96 => ( ( member_nat @ A2 @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( member_nat @ B @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ ( bNF_We2380939065524664066x2_nat @ R2 @ A2 @ B ) ) @ R2 )
% 4.69/4.96 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ ( bNF_We2380939065524664066x2_nat @ R2 @ A2 @ B ) ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_greater
% 4.69/4.96 thf(fact_3045_wo__rel_Omax2__greater,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,A2: int,B: int] :
% 4.69/4.96 ( ( bNF_We3815749466139970368el_int @ R2 )
% 4.69/4.96 => ( ( member_int @ A2 @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( member_int @ B @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ ( bNF_We2378448595015613790x2_int @ R2 @ A2 @ B ) ) @ R2 )
% 4.69/4.96 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ ( bNF_We2378448595015613790x2_int @ R2 @ A2 @ B ) ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_greater
% 4.69/4.96 thf(fact_3046_wo__rel_Omax2__equals2,axiom,
% 4.69/4.96 ! [R2: set_Pr2161125870931222855_nat_o,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( bNF_We740377018556551609_nat_o @ R2 )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ A2 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ B @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( ( bNF_We6400040844883348763_nat_o @ R2 @ A2 @ B )
% 4.69/4.96 = B )
% 4.69/4.96 = ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A2 @ B ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_equals2
% 4.69/4.96 thf(fact_3047_wo__rel_Omax2__equals2,axiom,
% 4.69/4.96 ! [R2: set_Product_prod_o_o,A2: $o,B: $o] :
% 4.69/4.96 ( ( bNF_We6437023980930612612_rel_o @ R2 )
% 4.69/4.96 => ( ( member_o @ A2 @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( member_o @ B @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( ( bNF_We3104086342435940326max2_o @ R2 @ A2 @ B )
% 4.69/4.96 = B )
% 4.69/4.96 = ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A2 @ B ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_equals2
% 4.69/4.96 thf(fact_3048_wo__rel_Omax2__equals2,axiom,
% 4.69/4.96 ! [R2: set_Pr5094982260447487303t_unit,A2: product_unit,B: product_unit] :
% 4.69/4.96 ( ( bNF_We2091578341578594809t_unit @ R2 )
% 4.69/4.96 => ( ( member_Product_unit @ A2 @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( member_Product_unit @ B @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( ( bNF_We7204996500647184731t_unit @ R2 @ A2 @ B )
% 4.69/4.96 = B )
% 4.69/4.96 = ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ A2 @ B ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_equals2
% 4.69/4.96 thf(fact_3049_wo__rel_Omax2__equals2,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,A2: nat,B: nat] :
% 4.69/4.96 ( ( bNF_We3818239936649020644el_nat @ R2 )
% 4.69/4.96 => ( ( member_nat @ A2 @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( member_nat @ B @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( ( bNF_We2380939065524664066x2_nat @ R2 @ A2 @ B )
% 4.69/4.96 = B )
% 4.69/4.96 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_equals2
% 4.69/4.96 thf(fact_3050_wo__rel_Omax2__equals2,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,A2: int,B: int] :
% 4.69/4.96 ( ( bNF_We3815749466139970368el_int @ R2 )
% 4.69/4.96 => ( ( member_int @ A2 @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( member_int @ B @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( ( bNF_We2378448595015613790x2_int @ R2 @ A2 @ B )
% 4.69/4.96 = B )
% 4.69/4.96 = ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_equals2
% 4.69/4.96 thf(fact_3051_wo__rel_Omax2__equals1,axiom,
% 4.69/4.96 ! [R2: set_Pr2161125870931222855_nat_o,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( bNF_We740377018556551609_nat_o @ R2 )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ A2 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ B @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( ( bNF_We6400040844883348763_nat_o @ R2 @ A2 @ B )
% 4.69/4.96 = A2 )
% 4.69/4.96 = ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ B @ A2 ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_equals1
% 4.69/4.96 thf(fact_3052_wo__rel_Omax2__equals1,axiom,
% 4.69/4.96 ! [R2: set_Product_prod_o_o,A2: $o,B: $o] :
% 4.69/4.96 ( ( bNF_We6437023980930612612_rel_o @ R2 )
% 4.69/4.96 => ( ( member_o @ A2 @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( member_o @ B @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( ( bNF_We3104086342435940326max2_o @ R2 @ A2 @ B )
% 4.69/4.96 = A2 )
% 4.69/4.96 = ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ B @ A2 ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_equals1
% 4.69/4.96 thf(fact_3053_wo__rel_Omax2__equals1,axiom,
% 4.69/4.96 ! [R2: set_Pr5094982260447487303t_unit,A2: product_unit,B: product_unit] :
% 4.69/4.96 ( ( bNF_We2091578341578594809t_unit @ R2 )
% 4.69/4.96 => ( ( member_Product_unit @ A2 @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( member_Product_unit @ B @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( ( bNF_We7204996500647184731t_unit @ R2 @ A2 @ B )
% 4.69/4.96 = A2 )
% 4.69/4.96 = ( member7821138191923116944t_unit @ ( produc5692694829384537815t_unit @ B @ A2 ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_equals1
% 4.69/4.96 thf(fact_3054_wo__rel_Omax2__equals1,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,A2: nat,B: nat] :
% 4.69/4.96 ( ( bNF_We3818239936649020644el_nat @ R2 )
% 4.69/4.96 => ( ( member_nat @ A2 @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( member_nat @ B @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( ( bNF_We2380939065524664066x2_nat @ R2 @ A2 @ B )
% 4.69/4.96 = A2 )
% 4.69/4.96 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ A2 ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_equals1
% 4.69/4.96 thf(fact_3055_wo__rel_Omax2__equals1,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,A2: int,B: int] :
% 4.69/4.96 ( ( bNF_We3815749466139970368el_int @ R2 )
% 4.69/4.96 => ( ( member_int @ A2 @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( member_int @ B @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( ( bNF_We2378448595015613790x2_int @ R2 @ A2 @ B )
% 4.69/4.96 = A2 )
% 4.69/4.96 = ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ A2 ) @ R2 ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_equals1
% 4.69/4.96 thf(fact_3056_wo__rel_Omax2__among,axiom,
% 4.69/4.96 ! [R2: set_Pr5094982260447487303t_unit,A2: product_unit,B: product_unit] :
% 4.69/4.96 ( ( bNF_We2091578341578594809t_unit @ R2 )
% 4.69/4.96 => ( ( member_Product_unit @ A2 @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( ( member_Product_unit @ B @ ( field_Product_unit @ R2 ) )
% 4.69/4.96 => ( member_Product_unit @ ( bNF_We7204996500647184731t_unit @ R2 @ A2 @ B ) @ ( insert_Product_unit @ A2 @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_among
% 4.69/4.96 thf(fact_3057_wo__rel_Omax2__among,axiom,
% 4.69/4.96 ! [R2: set_Product_prod_o_o,A2: $o,B: $o] :
% 4.69/4.96 ( ( bNF_We6437023980930612612_rel_o @ R2 )
% 4.69/4.96 => ( ( member_o @ A2 @ ( field_o @ R2 ) )
% 4.69/4.96 => ( ( member_o @ B @ ( field_o @ R2 ) )
% 4.69/4.96 => ( member_o @ ( bNF_We3104086342435940326max2_o @ R2 @ A2 @ B ) @ ( insert_o @ A2 @ ( insert_o @ B @ bot_bot_set_o ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_among
% 4.69/4.96 thf(fact_3058_wo__rel_Omax2__among,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,A2: nat,B: nat] :
% 4.69/4.96 ( ( bNF_We3818239936649020644el_nat @ R2 )
% 4.69/4.96 => ( ( member_nat @ A2 @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( member_nat @ B @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( member_nat @ ( bNF_We2380939065524664066x2_nat @ R2 @ A2 @ B ) @ ( insert_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_among
% 4.69/4.96 thf(fact_3059_wo__rel_Omax2__among,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,A2: int,B: int] :
% 4.69/4.96 ( ( bNF_We3815749466139970368el_int @ R2 )
% 4.69/4.96 => ( ( member_int @ A2 @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( member_int @ B @ ( field_int @ R2 ) )
% 4.69/4.96 => ( member_int @ ( bNF_We2378448595015613790x2_int @ R2 @ A2 @ B ) @ ( insert_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_among
% 4.69/4.96 thf(fact_3060_wo__rel_Omax2__among,axiom,
% 4.69/4.96 ! [R2: set_Pr2161125870931222855_nat_o,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( bNF_We740377018556551609_nat_o @ R2 )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ A2 @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ B @ ( field_81821745747897882_nat_o @ R2 ) )
% 4.69/4.96 => ( member6576561426505652726_nat_o @ ( bNF_We6400040844883348763_nat_o @ R2 @ A2 @ B ) @ ( insert5175938949040314269_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wo_rel.max2_among
% 4.69/4.96 thf(fact_3061_chains__extend,axiom,
% 4.69/4.96 ! [C: set_set_nat,S: set_set_nat,Z: set_nat] :
% 4.69/4.96 ( ( member_set_set_nat @ C @ ( chains_nat2 @ S ) )
% 4.69/4.96 => ( ( member_set_nat @ Z @ S )
% 4.69/4.96 => ( ! [X3: set_nat] :
% 4.69/4.96 ( ( member_set_nat @ X3 @ C )
% 4.69/4.96 => ( ord_less_eq_set_nat @ X3 @ Z ) )
% 4.69/4.96 => ( member_set_set_nat @ ( sup_sup_set_set_nat @ ( insert_set_nat @ Z @ bot_bot_set_set_nat ) @ C ) @ ( chains_nat2 @ S ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % chains_extend
% 4.69/4.96 thf(fact_3062_Zorns__po__lemma,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ( order_5251275573222108571on_nat @ ( field_nat @ R2 ) @ R2 )
% 4.69/4.96 => ( ! [C6: set_nat] :
% 4.69/4.96 ( ( member_set_nat @ C6 @ ( chains_nat @ R2 ) )
% 4.69/4.96 => ? [X6: nat] :
% 4.69/4.96 ( ( member_nat @ X6 @ ( field_nat @ R2 ) )
% 4.69/4.96 & ! [Xa3: nat] :
% 4.69/4.96 ( ( member_nat @ Xa3 @ C6 )
% 4.69/4.96 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Xa3 @ X6 ) @ R2 ) ) ) )
% 4.69/4.96 => ? [X3: nat] :
% 4.69/4.96 ( ( member_nat @ X3 @ ( field_nat @ R2 ) )
% 4.69/4.96 & ! [Xa2: nat] :
% 4.69/4.96 ( ( member_nat @ Xa2 @ ( field_nat @ R2 ) )
% 4.69/4.96 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Xa2 ) @ R2 )
% 4.69/4.96 => ( Xa2 = X3 ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Zorns_po_lemma
% 4.69/4.96 thf(fact_3063_Zorns__po__lemma,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ( ( order_5248785102713058295on_int @ ( field_int @ R2 ) @ R2 )
% 4.69/4.96 => ( ! [C6: set_int] :
% 4.69/4.96 ( ( member_set_int @ C6 @ ( chains_int @ R2 ) )
% 4.69/4.96 => ? [X6: int] :
% 4.69/4.96 ( ( member_int @ X6 @ ( field_int @ R2 ) )
% 4.69/4.96 & ! [Xa3: int] :
% 4.69/4.96 ( ( member_int @ Xa3 @ C6 )
% 4.69/4.96 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Xa3 @ X6 ) @ R2 ) ) ) )
% 4.69/4.96 => ? [X3: int] :
% 4.69/4.96 ( ( member_int @ X3 @ ( field_int @ R2 ) )
% 4.69/4.96 & ! [Xa2: int] :
% 4.69/4.96 ( ( member_int @ Xa2 @ ( field_int @ R2 ) )
% 4.69/4.96 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Xa2 ) @ R2 )
% 4.69/4.96 => ( Xa2 = X3 ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Zorns_po_lemma
% 4.69/4.96 thf(fact_3064_bsqr__max2,axiom,
% 4.69/4.96 ! [R2: set_Pr1261947904930325089at_nat,A1: nat,A22: nat,B1: nat,B22: nat] :
% 4.69/4.96 ( ( order_2888998067076097458on_nat @ ( field_nat @ R2 ) @ R2 )
% 4.69/4.96 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A1 @ A22 ) @ ( product_Pair_nat_nat @ B1 @ B22 ) ) @ ( bNF_We1732890022510290291qr_nat @ R2 ) )
% 4.69/4.96 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( bNF_We2380939065524664066x2_nat @ R2 @ A1 @ A22 ) @ ( bNF_We2380939065524664066x2_nat @ R2 @ B1 @ B22 ) ) @ R2 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % bsqr_max2
% 4.69/4.96 thf(fact_3065_bsqr__max2,axiom,
% 4.69/4.96 ! [R2: set_Pr958786334691620121nt_int,A1: int,A22: int,B1: int,B22: int] :
% 4.69/4.96 ( ( order_2886507596567047182on_int @ ( field_int @ R2 ) @ R2 )
% 4.69/4.96 => ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ A1 @ A22 ) @ ( product_Pair_int_int @ B1 @ B22 ) ) @ ( bNF_We1730399552001240015qr_int @ R2 ) )
% 4.69/4.96 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( bNF_We2378448595015613790x2_int @ R2 @ A1 @ A22 ) @ ( bNF_We2378448595015613790x2_int @ R2 @ B1 @ B22 ) ) @ R2 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % bsqr_max2
% 4.69/4.96 thf(fact_3066_wf__Union,axiom,
% 4.69/4.96 ! [R3: set_se8994758365886191399t_unit] :
% 4.69/4.96 ( ! [X3: set_Pr5094982260447487303t_unit] :
% 4.69/4.96 ( ( member1248447801810324848t_unit @ X3 @ R3 )
% 4.69/4.96 => ( wf_Product_unit @ X3 ) )
% 4.69/4.96 => ( ! [X3: set_Pr5094982260447487303t_unit] :
% 4.69/4.96 ( ( member1248447801810324848t_unit @ X3 @ R3 )
% 4.69/4.96 => ! [Xa3: set_Pr5094982260447487303t_unit] :
% 4.69/4.96 ( ( member1248447801810324848t_unit @ Xa3 @ R3 )
% 4.69/4.96 => ( ( X3 != Xa3 )
% 4.69/4.96 => ( ( inf_in4660618365625256667t_unit @ ( domain4292024440186670924t_unit @ X3 ) @ ( range_6617724647562260917t_unit @ Xa3 ) )
% 4.69/4.96 = bot_bo3957492148770167129t_unit ) ) ) )
% 4.69/4.96 => ( wf_Product_unit @ ( comple2798140142350441396t_unit @ R3 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_Union
% 4.69/4.96 thf(fact_3067_wf__Union,axiom,
% 4.69/4.96 ! [R3: set_se491199571785101031od_o_o] :
% 4.69/4.96 ( ! [X3: set_Product_prod_o_o] :
% 4.69/4.96 ( ( member3157015407008874800od_o_o @ X3 @ R3 )
% 4.69/4.96 => ( wf_o @ X3 ) )
% 4.69/4.96 => ( ! [X3: set_Product_prod_o_o] :
% 4.69/4.96 ( ( member3157015407008874800od_o_o @ X3 @ R3 )
% 4.69/4.96 => ! [Xa3: set_Product_prod_o_o] :
% 4.69/4.96 ( ( member3157015407008874800od_o_o @ Xa3 @ R3 )
% 4.69/4.96 => ( ( X3 != Xa3 )
% 4.69/4.96 => ( ( inf_inf_set_o @ ( domain_o_o @ X3 ) @ ( range_o_o @ Xa3 ) )
% 4.69/4.96 = bot_bot_set_o ) ) ) )
% 4.69/4.96 => ( wf_o @ ( comple2567785453016644468od_o_o @ R3 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_Union
% 4.69/4.96 thf(fact_3068_wf__Union,axiom,
% 4.69/4.96 ! [R3: set_se7855581050983116737at_nat] :
% 4.69/4.96 ( ! [X3: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ( member2643936169264416010at_nat @ X3 @ R3 )
% 4.69/4.96 => ( wf_nat @ X3 ) )
% 4.69/4.96 => ( ! [X3: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ( member2643936169264416010at_nat @ X3 @ R3 )
% 4.69/4.96 => ! [Xa3: set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ( member2643936169264416010at_nat @ Xa3 @ R3 )
% 4.69/4.96 => ( ( X3 != Xa3 )
% 4.69/4.96 => ( ( inf_inf_set_nat @ ( domain_nat_nat @ X3 ) @ ( range_nat_nat @ Xa3 ) )
% 4.69/4.96 = bot_bot_set_nat ) ) ) )
% 4.69/4.96 => ( wf_nat @ ( comple5685304695842803022at_nat @ R3 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_Union
% 4.69/4.96 thf(fact_3069_wf__Union,axiom,
% 4.69/4.96 ! [R3: set_se6260736226359567993nt_int] :
% 4.69/4.96 ( ! [X3: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ( ( member2340774599025711042nt_int @ X3 @ R3 )
% 4.69/4.96 => ( wf_int @ X3 ) )
% 4.69/4.96 => ( ! [X3: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ( ( member2340774599025711042nt_int @ X3 @ R3 )
% 4.69/4.96 => ! [Xa3: set_Pr958786334691620121nt_int] :
% 4.69/4.96 ( ( member2340774599025711042nt_int @ Xa3 @ R3 )
% 4.69/4.96 => ( ( X3 != Xa3 )
% 4.69/4.96 => ( ( inf_inf_set_int @ ( domain_int_int @ X3 ) @ ( range_int_int @ Xa3 ) )
% 4.69/4.96 = bot_bot_set_int ) ) ) )
% 4.69/4.96 => ( wf_int @ ( comple5382143125604098054nt_int @ R3 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_Union
% 4.69/4.96 thf(fact_3070_wf__Union,axiom,
% 4.69/4.96 ! [R3: set_se7663487083892625191_nat_o] :
% 4.69/4.96 ( ! [X3: set_Pr2161125870931222855_nat_o] :
% 4.69/4.96 ( ( member5475208728337331568_nat_o @ X3 @ R3 )
% 4.69/4.96 => ( wf_Pro8787509627421085110_nat_o @ X3 ) )
% 4.69/4.96 => ( ! [X3: set_Pr2161125870931222855_nat_o] :
% 4.69/4.96 ( ( member5475208728337331568_nat_o @ X3 @ R3 )
% 4.69/4.96 => ! [Xa3: set_Pr2161125870931222855_nat_o] :
% 4.69/4.96 ( ( member5475208728337331568_nat_o @ Xa3 @ R3 )
% 4.69/4.96 => ( ( X3 != Xa3 )
% 4.69/4.96 => ( ( inf_in1906310914598751387_nat_o @ ( domain4881241903163524940_nat_o @ X3 ) @ ( range_5289318983786108341_nat_o @ Xa3 ) )
% 4.69/4.96 = bot_bo7824918357723582233_nat_o ) ) ) )
% 4.69/4.96 => ( wf_Pro8787509627421085110_nat_o @ ( comple8164645552537203636_nat_o @ R3 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % wf_Union
% 4.69/4.96 thf(fact_3071_Pow__singleton__iff,axiom,
% 4.69/4.96 ! [X4: set_Product_unit,Y6: set_Product_unit] :
% 4.69/4.96 ( ( ( pow_Product_unit @ X4 )
% 4.69/4.96 = ( insert8986028188087627965t_unit @ Y6 @ bot_bo6284674557190688313t_unit ) )
% 4.69/4.96 = ( ( X4 = bot_bo3957492148770167129t_unit )
% 4.69/4.96 & ( Y6 = bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Pow_singleton_iff
% 4.69/4.96 thf(fact_3072_Pow__singleton__iff,axiom,
% 4.69/4.96 ! [X4: set_o,Y6: set_o] :
% 4.69/4.96 ( ( ( pow_o @ X4 )
% 4.69/4.96 = ( insert_set_o @ Y6 @ bot_bot_set_set_o ) )
% 4.69/4.96 = ( ( X4 = bot_bot_set_o )
% 4.69/4.96 & ( Y6 = bot_bot_set_o ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Pow_singleton_iff
% 4.69/4.96 thf(fact_3073_Pow__singleton__iff,axiom,
% 4.69/4.96 ! [X4: set_nat,Y6: set_nat] :
% 4.69/4.96 ( ( ( pow_nat @ X4 )
% 4.69/4.96 = ( insert_set_nat @ Y6 @ bot_bot_set_set_nat ) )
% 4.69/4.96 = ( ( X4 = bot_bot_set_nat )
% 4.69/4.96 & ( Y6 = bot_bot_set_nat ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Pow_singleton_iff
% 4.69/4.96 thf(fact_3074_Pow__singleton__iff,axiom,
% 4.69/4.96 ! [X4: set_int,Y6: set_int] :
% 4.69/4.96 ( ( ( pow_int @ X4 )
% 4.69/4.96 = ( insert_set_int @ Y6 @ bot_bot_set_set_int ) )
% 4.69/4.96 = ( ( X4 = bot_bot_set_int )
% 4.69/4.96 & ( Y6 = bot_bot_set_int ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Pow_singleton_iff
% 4.69/4.96 thf(fact_3075_Pow__singleton__iff,axiom,
% 4.69/4.96 ! [X4: set_Pr4532377907799695533_nat_o,Y6: set_Pr4532377907799695533_nat_o] :
% 4.69/4.96 ( ( ( pow_Pr7829143134171777386_nat_o @ X4 )
% 4.69/4.96 = ( insert2507855216428400253_nat_o @ Y6 @ bot_bo3736544561982865913_nat_o ) )
% 4.69/4.96 = ( ( X4 = bot_bo7824918357723582233_nat_o )
% 4.69/4.96 & ( Y6 = bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Pow_singleton_iff
% 4.69/4.96 thf(fact_3076_Pow__empty,axiom,
% 4.69/4.96 ( ( pow_Product_unit @ bot_bo3957492148770167129t_unit )
% 4.69/4.96 = ( insert8986028188087627965t_unit @ bot_bo3957492148770167129t_unit @ bot_bo6284674557190688313t_unit ) ) ).
% 4.69/4.96
% 4.69/4.96 % Pow_empty
% 4.69/4.96 thf(fact_3077_Pow__empty,axiom,
% 4.69/4.96 ( ( pow_o @ bot_bot_set_o )
% 4.69/4.96 = ( insert_set_o @ bot_bot_set_o @ bot_bot_set_set_o ) ) ).
% 4.69/4.96
% 4.69/4.96 % Pow_empty
% 4.69/4.96 thf(fact_3078_Pow__empty,axiom,
% 4.69/4.96 ( ( pow_nat @ bot_bot_set_nat )
% 4.69/4.96 = ( insert_set_nat @ bot_bot_set_nat @ bot_bot_set_set_nat ) ) ).
% 4.69/4.96
% 4.69/4.96 % Pow_empty
% 4.69/4.96 thf(fact_3079_Pow__empty,axiom,
% 4.69/4.96 ( ( pow_int @ bot_bot_set_int )
% 4.69/4.96 = ( insert_set_int @ bot_bot_set_int @ bot_bot_set_set_int ) ) ).
% 4.69/4.96
% 4.69/4.96 % Pow_empty
% 4.69/4.96 thf(fact_3080_Pow__empty,axiom,
% 4.69/4.96 ( ( pow_Pr7829143134171777386_nat_o @ bot_bo7824918357723582233_nat_o )
% 4.69/4.96 = ( insert2507855216428400253_nat_o @ bot_bo7824918357723582233_nat_o @ bot_bo3736544561982865913_nat_o ) ) ).
% 4.69/4.96
% 4.69/4.96 % Pow_empty
% 4.69/4.96 thf(fact_3081_rtrancl__mapI,axiom,
% 4.69/4.96 ! [A2: nat,B: nat,E: set_Pr1261947904930325089at_nat,F: nat > nat] :
% 4.69/4.96 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( transi2905341329935302413cl_nat @ E ) )
% 4.69/4.96 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ A2 ) @ ( F @ B ) ) @ ( transi2905341329935302413cl_nat @ ( image_5168914502847457605at_nat @ ( pairself_nat_nat @ F ) @ E ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % rtrancl_mapI
% 4.69/4.96 thf(fact_3082_rtrancl__mapI,axiom,
% 4.69/4.96 ! [A2: nat,B: nat,E: set_Pr1261947904930325089at_nat,F: nat > int] :
% 4.69/4.96 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ ( transi2905341329935302413cl_nat @ E ) )
% 4.69/4.96 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F @ A2 ) @ ( F @ B ) ) @ ( transi2902850859426252137cl_int @ ( image_1990417195239315453nt_int @ ( pairself_nat_int @ F ) @ E ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % rtrancl_mapI
% 4.69/4.96 thf(fact_3083_rtrancl__mapI,axiom,
% 4.69/4.96 ! [A2: int,B: int,E: set_Pr958786334691620121nt_int,F: int > nat] :
% 4.69/4.96 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( transi2902850859426252137cl_int @ E ) )
% 4.69/4.96 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ A2 ) @ ( F @ B ) ) @ ( transi2905341329935302413cl_nat @ ( image_5831868185956570253at_nat @ ( pairself_int_nat @ F ) @ E ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % rtrancl_mapI
% 4.69/4.96 thf(fact_3084_rtrancl__mapI,axiom,
% 4.69/4.96 ! [A2: int,B: int,E: set_Pr958786334691620121nt_int,F: int > int] :
% 4.69/4.96 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ ( transi2902850859426252137cl_int @ E ) )
% 4.69/4.96 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F @ A2 ) @ ( F @ B ) ) @ ( transi2902850859426252137cl_int @ ( image_2653370878348428101nt_int @ ( pairself_int_int @ F ) @ E ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % rtrancl_mapI
% 4.69/4.96 thf(fact_3085_disjoint__image__subset,axiom,
% 4.69/4.96 ! [A11: set_set_nat,F: set_nat > set_nat] :
% 4.69/4.96 ( ( pairwise_set_nat @ disjnt_nat @ A11 )
% 4.69/4.96 => ( ! [X8: set_nat] :
% 4.69/4.96 ( ( member_set_nat @ X8 @ A11 )
% 4.69/4.96 => ( ord_less_eq_set_nat @ ( F @ X8 ) @ X8 ) )
% 4.69/4.96 => ( pairwise_set_nat @ disjnt_nat @ ( image_7916887816326733075et_nat @ F @ A11 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % disjoint_image_subset
% 4.69/4.96 thf(fact_3086_pairself_Opelims,axiom,
% 4.69/4.96 ! [X: nat > nat,Xa: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 4.69/4.96 ( ( ( pairself_nat_nat @ X @ Xa )
% 4.69/4.96 = Y )
% 4.69/4.96 => ( ( accp_P4147487641329543982at_nat @ pairself_rel_nat_nat @ ( produc4237282728380940073at_nat @ X @ Xa ) )
% 4.69/4.96 => ~ ! [A4: nat,B2: nat] :
% 4.69/4.96 ( ( Xa
% 4.69/4.96 = ( product_Pair_nat_nat @ A4 @ B2 ) )
% 4.69/4.96 => ( ( Y
% 4.69/4.96 = ( product_Pair_nat_nat @ ( X @ A4 ) @ ( X @ B2 ) ) )
% 4.69/4.96 => ~ ( accp_P4147487641329543982at_nat @ pairself_rel_nat_nat @ ( produc4237282728380940073at_nat @ X @ ( product_Pair_nat_nat @ A4 @ B2 ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairself.pelims
% 4.69/4.96 thf(fact_3087_pairself_Opelims,axiom,
% 4.69/4.96 ! [X: nat > int,Xa: product_prod_nat_nat,Y: product_prod_int_int] :
% 4.69/4.96 ( ( ( pairself_nat_int @ X @ Xa )
% 4.69/4.96 = Y )
% 4.69/4.96 => ( ( accp_P3050404660685545426at_nat @ pairself_rel_nat_int @ ( produc3140199747736941517at_nat @ X @ Xa ) )
% 4.69/4.96 => ~ ! [A4: nat,B2: nat] :
% 4.69/4.96 ( ( Xa
% 4.69/4.96 = ( product_Pair_nat_nat @ A4 @ B2 ) )
% 4.69/4.96 => ( ( Y
% 4.69/4.96 = ( product_Pair_int_int @ ( X @ A4 ) @ ( X @ B2 ) ) )
% 4.69/4.96 => ~ ( accp_P3050404660685545426at_nat @ pairself_rel_nat_int @ ( produc3140199747736941517at_nat @ X @ ( product_Pair_nat_nat @ A4 @ B2 ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairself.pelims
% 4.69/4.96 thf(fact_3088_pairself_Opelims,axiom,
% 4.69/4.96 ! [X: int > nat,Xa: product_prod_int_int,Y: product_prod_nat_nat] :
% 4.69/4.96 ( ( ( pairself_int_nat @ X @ Xa )
% 4.69/4.96 = Y )
% 4.69/4.96 => ( ( accp_P5604362734843950218nt_int @ pairself_rel_int_nat @ ( produc2818822084525909125nt_int @ X @ Xa ) )
% 4.69/4.96 => ~ ! [A4: int,B2: int] :
% 4.69/4.96 ( ( Xa
% 4.69/4.96 = ( product_Pair_int_int @ A4 @ B2 ) )
% 4.69/4.96 => ( ( Y
% 4.69/4.96 = ( product_Pair_nat_nat @ ( X @ A4 ) @ ( X @ B2 ) ) )
% 4.69/4.96 => ~ ( accp_P5604362734843950218nt_int @ pairself_rel_int_nat @ ( produc2818822084525909125nt_int @ X @ ( product_Pair_int_int @ A4 @ B2 ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairself.pelims
% 4.69/4.96 thf(fact_3089_pairself_Opelims,axiom,
% 4.69/4.96 ! [X: int > int,Xa: product_prod_int_int,Y: product_prod_int_int] :
% 4.69/4.96 ( ( ( pairself_int_int @ X @ Xa )
% 4.69/4.96 = Y )
% 4.69/4.96 => ( ( accp_P4507279754199951662nt_int @ pairself_rel_int_int @ ( produc1721739103881910569nt_int @ X @ Xa ) )
% 4.69/4.96 => ~ ! [A4: int,B2: int] :
% 4.69/4.96 ( ( Xa
% 4.69/4.96 = ( product_Pair_int_int @ A4 @ B2 ) )
% 4.69/4.96 => ( ( Y
% 4.69/4.96 = ( product_Pair_int_int @ ( X @ A4 ) @ ( X @ B2 ) ) )
% 4.69/4.96 => ~ ( accp_P4507279754199951662nt_int @ pairself_rel_int_int @ ( produc1721739103881910569nt_int @ X @ ( product_Pair_int_int @ A4 @ B2 ) ) ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairself.pelims
% 4.69/4.96 thf(fact_3090_Pow__iff,axiom,
% 4.69/4.96 ! [A: set_nat,B4: set_nat] :
% 4.69/4.96 ( ( member_set_nat @ A @ ( pow_nat @ B4 ) )
% 4.69/4.96 = ( ord_less_eq_set_nat @ A @ B4 ) ) ).
% 4.69/4.96
% 4.69/4.96 % Pow_iff
% 4.69/4.96 thf(fact_3091_PowI,axiom,
% 4.69/4.96 ! [A: set_nat,B4: set_nat] :
% 4.69/4.96 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.96 => ( member_set_nat @ A @ ( pow_nat @ B4 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % PowI
% 4.69/4.96 thf(fact_3092_Pow__Int__eq,axiom,
% 4.69/4.96 ! [A: set_nat,B4: set_nat] :
% 4.69/4.96 ( ( pow_nat @ ( inf_inf_set_nat @ A @ B4 ) )
% 4.69/4.96 = ( inf_inf_set_set_nat @ ( pow_nat @ A ) @ ( pow_nat @ B4 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Pow_Int_eq
% 4.69/4.96 thf(fact_3093_pairwiseI,axiom,
% 4.69/4.96 ! [S: set_Pr4532377907799695533_nat_o,R3: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o] :
% 4.69/4.96 ( ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( member6576561426505652726_nat_o @ X3 @ S )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ Y2 @ S )
% 4.69/4.96 => ( ( X3 != Y2 )
% 4.69/4.96 => ( R3 @ X3 @ Y2 ) ) ) )
% 4.69/4.96 => ( pairwi2432143822833250616_nat_o @ R3 @ S ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairwiseI
% 4.69/4.96 thf(fact_3094_pairwiseI,axiom,
% 4.69/4.96 ! [S: set_nat,R3: nat > nat > $o] :
% 4.69/4.96 ( ! [X3: nat,Y2: nat] :
% 4.69/4.96 ( ( member_nat @ X3 @ S )
% 4.69/4.96 => ( ( member_nat @ Y2 @ S )
% 4.69/4.96 => ( ( X3 != Y2 )
% 4.69/4.96 => ( R3 @ X3 @ Y2 ) ) ) )
% 4.69/4.96 => ( pairwise_nat @ R3 @ S ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairwiseI
% 4.69/4.96 thf(fact_3095_pairwiseI,axiom,
% 4.69/4.96 ! [S: set_int,R3: int > int > $o] :
% 4.69/4.96 ( ! [X3: int,Y2: int] :
% 4.69/4.96 ( ( member_int @ X3 @ S )
% 4.69/4.96 => ( ( member_int @ Y2 @ S )
% 4.69/4.96 => ( ( X3 != Y2 )
% 4.69/4.96 => ( R3 @ X3 @ Y2 ) ) ) )
% 4.69/4.96 => ( pairwise_int @ R3 @ S ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairwiseI
% 4.69/4.96 thf(fact_3096_pairwiseI,axiom,
% 4.69/4.96 ! [S: set_o,R3: $o > $o > $o] :
% 4.69/4.96 ( ! [X3: $o,Y2: $o] :
% 4.69/4.96 ( ( member_o @ X3 @ S )
% 4.69/4.96 => ( ( member_o @ Y2 @ S )
% 4.69/4.96 => ( ( X3 != Y2 )
% 4.69/4.96 => ( R3 @ X3 @ Y2 ) ) ) )
% 4.69/4.96 => ( pairwise_o @ R3 @ S ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairwiseI
% 4.69/4.96 thf(fact_3097_pairwiseI,axiom,
% 4.69/4.96 ! [S: set_Product_unit,R3: product_unit > product_unit > $o] :
% 4.69/4.96 ( ! [X3: product_unit,Y2: product_unit] :
% 4.69/4.96 ( ( member_Product_unit @ X3 @ S )
% 4.69/4.96 => ( ( member_Product_unit @ Y2 @ S )
% 4.69/4.96 => ( ( X3 != Y2 )
% 4.69/4.96 => ( R3 @ X3 @ Y2 ) ) ) )
% 4.69/4.96 => ( pairwi7919127943033184120t_unit @ R3 @ S ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairwiseI
% 4.69/4.96 thf(fact_3098_pairwiseD,axiom,
% 4.69/4.96 ! [R3: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o,S: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( pairwi2432143822833250616_nat_o @ R3 @ S )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ X @ S )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ Y @ S )
% 4.69/4.96 => ( ( X != Y )
% 4.69/4.96 => ( R3 @ X @ Y ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairwiseD
% 4.69/4.96 thf(fact_3099_pairwiseD,axiom,
% 4.69/4.96 ! [R3: nat > nat > $o,S: set_nat,X: nat,Y: nat] :
% 4.69/4.96 ( ( pairwise_nat @ R3 @ S )
% 4.69/4.96 => ( ( member_nat @ X @ S )
% 4.69/4.96 => ( ( member_nat @ Y @ S )
% 4.69/4.96 => ( ( X != Y )
% 4.69/4.96 => ( R3 @ X @ Y ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairwiseD
% 4.69/4.96 thf(fact_3100_pairwiseD,axiom,
% 4.69/4.96 ! [R3: int > int > $o,S: set_int,X: int,Y: int] :
% 4.69/4.96 ( ( pairwise_int @ R3 @ S )
% 4.69/4.96 => ( ( member_int @ X @ S )
% 4.69/4.96 => ( ( member_int @ Y @ S )
% 4.69/4.96 => ( ( X != Y )
% 4.69/4.96 => ( R3 @ X @ Y ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairwiseD
% 4.69/4.96 thf(fact_3101_pairwiseD,axiom,
% 4.69/4.96 ! [R3: $o > $o > $o,S: set_o,X: $o,Y: $o] :
% 4.69/4.96 ( ( pairwise_o @ R3 @ S )
% 4.69/4.96 => ( ( member_o @ X @ S )
% 4.69/4.96 => ( ( member_o @ Y @ S )
% 4.69/4.96 => ( ( X != Y )
% 4.69/4.96 => ( R3 @ X @ Y ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairwiseD
% 4.69/4.96 thf(fact_3102_pairwiseD,axiom,
% 4.69/4.96 ! [R3: product_unit > product_unit > $o,S: set_Product_unit,X: product_unit,Y: product_unit] :
% 4.69/4.96 ( ( pairwi7919127943033184120t_unit @ R3 @ S )
% 4.69/4.96 => ( ( member_Product_unit @ X @ S )
% 4.69/4.96 => ( ( member_Product_unit @ Y @ S )
% 4.69/4.96 => ( ( X != Y )
% 4.69/4.96 => ( R3 @ X @ Y ) ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairwiseD
% 4.69/4.96 thf(fact_3103_refl__on__UNION,axiom,
% 4.69/4.96 ! [S: set_nat,A: nat > set_nat,R2: nat > set_Pr1261947904930325089at_nat] :
% 4.69/4.96 ( ! [X3: nat] :
% 4.69/4.96 ( ( member_nat @ X3 @ S )
% 4.69/4.96 => ( refl_on_nat @ ( A @ X3 ) @ ( R2 @ X3 ) ) )
% 4.69/4.96 => ( refl_on_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ A @ S ) ) @ ( comple5685304695842803022at_nat @ ( image_7178329752028323786at_nat @ R2 @ S ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % refl_on_UNION
% 4.69/4.96 thf(fact_3104_Pow__bottom,axiom,
% 4.69/4.96 ! [B4: set_Product_unit] : ( member5877623283571906838t_unit @ bot_bo3957492148770167129t_unit @ ( pow_Product_unit @ B4 ) ) ).
% 4.69/4.96
% 4.69/4.96 % Pow_bottom
% 4.69/4.96 thf(fact_3105_Pow__bottom,axiom,
% 4.69/4.96 ! [B4: set_o] : ( member_set_o @ bot_bot_set_o @ ( pow_o @ B4 ) ) ).
% 4.69/4.96
% 4.69/4.96 % Pow_bottom
% 4.69/4.96 thf(fact_3106_Pow__bottom,axiom,
% 4.69/4.96 ! [B4: set_nat] : ( member_set_nat @ bot_bot_set_nat @ ( pow_nat @ B4 ) ) ).
% 4.69/4.96
% 4.69/4.96 % Pow_bottom
% 4.69/4.96 thf(fact_3107_Pow__bottom,axiom,
% 4.69/4.96 ! [B4: set_int] : ( member_set_int @ bot_bot_set_int @ ( pow_int @ B4 ) ) ).
% 4.69/4.96
% 4.69/4.96 % Pow_bottom
% 4.69/4.96 thf(fact_3108_Pow__bottom,axiom,
% 4.69/4.96 ! [B4: set_Pr4532377907799695533_nat_o] : ( member1452989533377600726_nat_o @ bot_bo7824918357723582233_nat_o @ ( pow_Pr7829143134171777386_nat_o @ B4 ) ) ).
% 4.69/4.96
% 4.69/4.96 % Pow_bottom
% 4.69/4.96 thf(fact_3109_Pow__mono,axiom,
% 4.69/4.96 ! [A: set_nat,B4: set_nat] :
% 4.69/4.96 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.96 => ( ord_le6893508408891458716et_nat @ ( pow_nat @ A ) @ ( pow_nat @ B4 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Pow_mono
% 4.69/4.96 thf(fact_3110_PowD,axiom,
% 4.69/4.96 ! [A: set_nat,B4: set_nat] :
% 4.69/4.96 ( ( member_set_nat @ A @ ( pow_nat @ B4 ) )
% 4.69/4.96 => ( ord_less_eq_set_nat @ A @ B4 ) ) ).
% 4.69/4.96
% 4.69/4.96 % PowD
% 4.69/4.96 thf(fact_3111_Un__Pow__subset,axiom,
% 4.69/4.96 ! [A: set_nat,B4: set_nat] : ( ord_le6893508408891458716et_nat @ ( sup_sup_set_set_nat @ ( pow_nat @ A ) @ ( pow_nat @ B4 ) ) @ ( pow_nat @ ( sup_sup_set_nat @ A @ B4 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % Un_Pow_subset
% 4.69/4.96 thf(fact_3112_pairwise__imageI,axiom,
% 4.69/4.96 ! [A: set_Code_integer,F: code_integer > code_integer,P: code_integer > code_integer > $o] :
% 4.69/4.96 ( ! [X3: code_integer,Y2: code_integer] :
% 4.69/4.96 ( ( member_Code_integer @ X3 @ A )
% 4.69/4.96 => ( ( member_Code_integer @ Y2 @ A )
% 4.69/4.96 => ( ( X3 != Y2 )
% 4.69/4.96 => ( ( ( F @ X3 )
% 4.69/4.96 != ( F @ Y2 ) )
% 4.69/4.96 => ( P @ ( F @ X3 ) @ ( F @ Y2 ) ) ) ) ) )
% 4.69/4.96 => ( pairwi4741737654671186738nteger @ P @ ( image_4470545334726330049nteger @ F @ A ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairwise_imageI
% 4.69/4.96 thf(fact_3113_pairwise__imageI,axiom,
% 4.69/4.96 ! [A: set_nat,F: nat > set_nat,P: set_nat > set_nat > $o] :
% 4.69/4.96 ( ! [X3: nat,Y2: nat] :
% 4.69/4.96 ( ( member_nat @ X3 @ A )
% 4.69/4.96 => ( ( member_nat @ Y2 @ A )
% 4.69/4.96 => ( ( X3 != Y2 )
% 4.69/4.96 => ( ( ( F @ X3 )
% 4.69/4.96 != ( F @ Y2 ) )
% 4.69/4.96 => ( P @ ( F @ X3 ) @ ( F @ Y2 ) ) ) ) ) )
% 4.69/4.96 => ( pairwise_set_nat @ P @ ( image_nat_set_nat @ F @ A ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairwise_imageI
% 4.69/4.96 thf(fact_3114_pairwise__imageI,axiom,
% 4.69/4.96 ! [A: set_nat,F: nat > nat,P: nat > nat > $o] :
% 4.69/4.96 ( ! [X3: nat,Y2: nat] :
% 4.69/4.96 ( ( member_nat @ X3 @ A )
% 4.69/4.96 => ( ( member_nat @ Y2 @ A )
% 4.69/4.96 => ( ( X3 != Y2 )
% 4.69/4.96 => ( ( ( F @ X3 )
% 4.69/4.96 != ( F @ Y2 ) )
% 4.69/4.96 => ( P @ ( F @ X3 ) @ ( F @ Y2 ) ) ) ) ) )
% 4.69/4.96 => ( pairwise_nat @ P @ ( image_nat_nat2 @ F @ A ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairwise_imageI
% 4.69/4.96 thf(fact_3115_pairwise__imageI,axiom,
% 4.69/4.96 ! [A: set_nat,F: nat > code_integer,P: code_integer > code_integer > $o] :
% 4.69/4.96 ( ! [X3: nat,Y2: nat] :
% 4.69/4.96 ( ( member_nat @ X3 @ A )
% 4.69/4.96 => ( ( member_nat @ Y2 @ A )
% 4.69/4.96 => ( ( X3 != Y2 )
% 4.69/4.96 => ( ( ( F @ X3 )
% 4.69/4.96 != ( F @ Y2 ) )
% 4.69/4.96 => ( P @ ( F @ X3 ) @ ( F @ Y2 ) ) ) ) ) )
% 4.69/4.96 => ( pairwi4741737654671186738nteger @ P @ ( image_1215581382706833972nteger @ F @ A ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairwise_imageI
% 4.69/4.96 thf(fact_3116_pairwise__empty,axiom,
% 4.69/4.96 ! [P: product_unit > product_unit > $o] : ( pairwi7919127943033184120t_unit @ P @ bot_bo3957492148770167129t_unit ) ).
% 4.69/4.96
% 4.69/4.96 % pairwise_empty
% 4.69/4.96 thf(fact_3117_pairwise__empty,axiom,
% 4.69/4.96 ! [P: $o > $o > $o] : ( pairwise_o @ P @ bot_bot_set_o ) ).
% 4.69/4.96
% 4.69/4.96 % pairwise_empty
% 4.69/4.96 thf(fact_3118_pairwise__empty,axiom,
% 4.69/4.96 ! [P: nat > nat > $o] : ( pairwise_nat @ P @ bot_bot_set_nat ) ).
% 4.69/4.96
% 4.69/4.96 % pairwise_empty
% 4.69/4.96 thf(fact_3119_pairwise__empty,axiom,
% 4.69/4.96 ! [P: int > int > $o] : ( pairwise_int @ P @ bot_bot_set_int ) ).
% 4.69/4.96
% 4.69/4.96 % pairwise_empty
% 4.69/4.96 thf(fact_3120_pairwise__empty,axiom,
% 4.69/4.96 ! [P: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o] : ( pairwi2432143822833250616_nat_o @ P @ bot_bo7824918357723582233_nat_o ) ).
% 4.69/4.96
% 4.69/4.96 % pairwise_empty
% 4.69/4.96 thf(fact_3121_pairwise__subset,axiom,
% 4.69/4.96 ! [P: nat > nat > $o,S: set_nat,T2: set_nat] :
% 4.69/4.96 ( ( pairwise_nat @ P @ S )
% 4.69/4.96 => ( ( ord_less_eq_set_nat @ T2 @ S )
% 4.69/4.96 => ( pairwise_nat @ P @ T2 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairwise_subset
% 4.69/4.96 thf(fact_3122_pairwise__mono,axiom,
% 4.69/4.96 ! [P: nat > nat > $o,A: set_nat,Q2: nat > nat > $o,B4: set_nat] :
% 4.69/4.96 ( ( pairwise_nat @ P @ A )
% 4.69/4.96 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.96 ( ( P @ X3 @ Y2 )
% 4.69/4.96 => ( Q2 @ X3 @ Y2 ) )
% 4.69/4.96 => ( ( ord_less_eq_set_nat @ B4 @ A )
% 4.69/4.96 => ( pairwise_nat @ Q2 @ B4 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairwise_mono
% 4.69/4.96 thf(fact_3123_pairwise__insert,axiom,
% 4.69/4.96 ! [R2: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o,X: produc3658429121746597890et_nat > $o,S2: set_Pr4532377907799695533_nat_o] :
% 4.69/4.96 ( ( pairwi2432143822833250616_nat_o @ R2 @ ( insert5175938949040314269_nat_o @ X @ S2 ) )
% 4.69/4.96 = ( ! [Y3: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( ( member6576561426505652726_nat_o @ Y3 @ S2 )
% 4.69/4.96 & ( Y3 != X ) )
% 4.69/4.96 => ( ( R2 @ X @ Y3 )
% 4.69/4.96 & ( R2 @ Y3 @ X ) ) )
% 4.69/4.96 & ( pairwi2432143822833250616_nat_o @ R2 @ S2 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairwise_insert
% 4.69/4.96 thf(fact_3124_pairwise__insert,axiom,
% 4.69/4.96 ! [R2: nat > nat > $o,X: nat,S2: set_nat] :
% 4.69/4.96 ( ( pairwise_nat @ R2 @ ( insert_nat @ X @ S2 ) )
% 4.69/4.96 = ( ! [Y3: nat] :
% 4.69/4.96 ( ( ( member_nat @ Y3 @ S2 )
% 4.69/4.96 & ( Y3 != X ) )
% 4.69/4.96 => ( ( R2 @ X @ Y3 )
% 4.69/4.96 & ( R2 @ Y3 @ X ) ) )
% 4.69/4.96 & ( pairwise_nat @ R2 @ S2 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairwise_insert
% 4.69/4.96 thf(fact_3125_pairwise__insert,axiom,
% 4.69/4.96 ! [R2: int > int > $o,X: int,S2: set_int] :
% 4.69/4.96 ( ( pairwise_int @ R2 @ ( insert_int @ X @ S2 ) )
% 4.69/4.96 = ( ! [Y3: int] :
% 4.69/4.96 ( ( ( member_int @ Y3 @ S2 )
% 4.69/4.96 & ( Y3 != X ) )
% 4.69/4.96 => ( ( R2 @ X @ Y3 )
% 4.69/4.96 & ( R2 @ Y3 @ X ) ) )
% 4.69/4.96 & ( pairwise_int @ R2 @ S2 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairwise_insert
% 4.69/4.96 thf(fact_3126_pairwise__insert,axiom,
% 4.69/4.96 ! [R2: $o > $o > $o,X: $o,S2: set_o] :
% 4.69/4.96 ( ( pairwise_o @ R2 @ ( insert_o @ X @ S2 ) )
% 4.69/4.96 = ( ! [Y3: $o] :
% 4.69/4.96 ( ( ( member_o @ Y3 @ S2 )
% 4.69/4.96 & ( Y3 != X ) )
% 4.69/4.96 => ( ( R2 @ X @ Y3 )
% 4.69/4.96 & ( R2 @ Y3 @ X ) ) )
% 4.69/4.96 & ( pairwise_o @ R2 @ S2 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairwise_insert
% 4.69/4.96 thf(fact_3127_pairwise__insert,axiom,
% 4.69/4.96 ! [R2: product_unit > product_unit > $o,X: product_unit,S2: set_Product_unit] :
% 4.69/4.96 ( ( pairwi7919127943033184120t_unit @ R2 @ ( insert_Product_unit @ X @ S2 ) )
% 4.69/4.96 = ( ! [Y3: product_unit] :
% 4.69/4.96 ( ( ( member_Product_unit @ Y3 @ S2 )
% 4.69/4.96 & ( Y3 != X ) )
% 4.69/4.96 => ( ( R2 @ X @ Y3 )
% 4.69/4.96 & ( R2 @ Y3 @ X ) ) )
% 4.69/4.96 & ( pairwi7919127943033184120t_unit @ R2 @ S2 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % pairwise_insert
% 4.69/4.96 thf(fact_3128_finite__UNION__then__finite,axiom,
% 4.69/4.96 ! [B4: ( produc3658429121746597890et_nat > $o ) > set_nat,A: set_Pr4532377907799695533_nat_o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_6888641473154130958et_nat @ B4 @ A ) ) )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ A2 @ A )
% 4.69/4.96 => ( finite_finite_nat @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % finite_UNION_then_finite
% 4.69/4.96 thf(fact_3129_finite__UNION__then__finite,axiom,
% 4.69/4.96 ! [B4: nat > set_nat,A: set_nat,A2: nat] :
% 4.69/4.96 ( ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ B4 @ A ) ) )
% 4.69/4.96 => ( ( member_nat @ A2 @ A )
% 4.69/4.96 => ( finite_finite_nat @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % finite_UNION_then_finite
% 4.69/4.96 thf(fact_3130_finite__UNION__then__finite,axiom,
% 4.69/4.96 ! [B4: int > set_nat,A: set_int,A2: int] :
% 4.69/4.96 ( ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ B4 @ A ) ) )
% 4.69/4.96 => ( ( member_int @ A2 @ A )
% 4.69/4.96 => ( finite_finite_nat @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % finite_UNION_then_finite
% 4.69/4.96 thf(fact_3131_finite__UNION__then__finite,axiom,
% 4.69/4.96 ! [B4: $o > set_nat,A: set_o,A2: $o] :
% 4.69/4.96 ( ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ B4 @ A ) ) )
% 4.69/4.96 => ( ( member_o @ A2 @ A )
% 4.69/4.96 => ( finite_finite_nat @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % finite_UNION_then_finite
% 4.69/4.96 thf(fact_3132_finite__UNION__then__finite,axiom,
% 4.69/4.96 ! [B4: product_unit > set_nat,A: set_Product_unit,A2: product_unit] :
% 4.69/4.96 ( ( finite_finite_nat @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ B4 @ A ) ) )
% 4.69/4.96 => ( ( member_Product_unit @ A2 @ A )
% 4.69/4.96 => ( finite_finite_nat @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % finite_UNION_then_finite
% 4.69/4.96 thf(fact_3133_finite__UNION__then__finite,axiom,
% 4.69/4.96 ! [B4: ( produc3658429121746597890et_nat > $o ) > set_Code_integer,A: set_Pr4532377907799695533_nat_o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/4.96 ( ( finite6017078050557962740nteger @ ( comple739944243200306918nteger @ ( image_8657708916238040603nteger @ B4 @ A ) ) )
% 4.69/4.96 => ( ( member6576561426505652726_nat_o @ A2 @ A )
% 4.69/4.96 => ( finite6017078050557962740nteger @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % finite_UNION_then_finite
% 4.69/4.96 thf(fact_3134_finite__UNION__then__finite,axiom,
% 4.69/4.96 ! [B4: nat > set_Code_integer,A: set_nat,A2: nat] :
% 4.69/4.96 ( ( finite6017078050557962740nteger @ ( comple739944243200306918nteger @ ( image_2385391725447763818nteger @ B4 @ A ) ) )
% 4.69/4.96 => ( ( member_nat @ A2 @ A )
% 4.69/4.96 => ( finite6017078050557962740nteger @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % finite_UNION_then_finite
% 4.69/4.96 thf(fact_3135_finite__UNION__then__finite,axiom,
% 4.69/4.96 ! [B4: int > set_Code_integer,A: set_int,A2: int] :
% 4.69/4.96 ( ( finite6017078050557962740nteger @ ( comple739944243200306918nteger @ ( image_75573793354812870nteger @ B4 @ A ) ) )
% 4.69/4.96 => ( ( member_int @ A2 @ A )
% 4.69/4.96 => ( finite6017078050557962740nteger @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % finite_UNION_then_finite
% 4.69/4.96 thf(fact_3136_finite__UNION__then__finite,axiom,
% 4.69/4.96 ! [B4: $o > set_Code_integer,A: set_o,A2: $o] :
% 4.69/4.96 ( ( finite6017078050557962740nteger @ ( comple739944243200306918nteger @ ( image_6491638074533506790nteger @ B4 @ A ) ) )
% 4.69/4.96 => ( ( member_o @ A2 @ A )
% 4.69/4.96 => ( finite6017078050557962740nteger @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % finite_UNION_then_finite
% 4.69/4.96 thf(fact_3137_finite__UNION__then__finite,axiom,
% 4.69/4.96 ! [B4: product_unit > set_Code_integer,A: set_Product_unit,A2: product_unit] :
% 4.69/4.96 ( ( finite6017078050557962740nteger @ ( comple739944243200306918nteger @ ( image_4571654851662262875nteger @ B4 @ A ) ) )
% 4.69/4.96 => ( ( member_Product_unit @ A2 @ A )
% 4.69/4.96 => ( finite6017078050557962740nteger @ ( B4 @ A2 ) ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % finite_UNION_then_finite
% 4.69/4.96 thf(fact_3138_image__Pow__surj,axiom,
% 4.69/4.96 ! [F: nat > set_nat,A: set_nat,B4: set_set_nat] :
% 4.69/4.96 ( ( ( image_nat_set_nat @ F @ A )
% 4.69/4.96 = B4 )
% 4.69/4.96 => ( ( image_6725021117256019401et_nat @ ( image_nat_set_nat @ F ) @ ( pow_nat @ A ) )
% 4.69/4.96 = ( pow_set_nat @ B4 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % image_Pow_surj
% 4.69/4.96 thf(fact_3139_image__Pow__surj,axiom,
% 4.69/4.96 ! [F: nat > nat,A: set_nat,B4: set_nat] :
% 4.69/4.96 ( ( ( image_nat_nat2 @ F @ A )
% 4.69/4.96 = B4 )
% 4.69/4.96 => ( ( image_7916887816326733075et_nat @ ( image_nat_nat2 @ F ) @ ( pow_nat @ A ) )
% 4.69/4.96 = ( pow_nat @ B4 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % image_Pow_surj
% 4.69/4.96 thf(fact_3140_image__Pow__surj,axiom,
% 4.69/4.96 ! [F: code_integer > code_integer,A: set_Code_integer,B4: set_Code_integer] :
% 4.69/4.96 ( ( ( image_4470545334726330049nteger @ F @ A )
% 4.69/4.96 = B4 )
% 4.69/4.96 => ( ( image_6270750266955655469nteger @ ( image_4470545334726330049nteger @ F ) @ ( pow_Code_integer @ A ) )
% 4.69/4.96 = ( pow_Code_integer @ B4 ) ) ) ).
% 4.69/4.96
% 4.69/4.96 % image_Pow_surj
% 4.69/4.96 thf(fact_3141_image__Pow__surj,axiom,
% 4.69/4.96 ! [F: nat > code_integer,A: set_nat,B4: set_Code_integer] :
% 4.69/4.97 ( ( ( image_1215581382706833972nteger @ F @ A )
% 4.69/4.97 = B4 )
% 4.69/4.97 => ( ( image_6916300684244607776nteger @ ( image_1215581382706833972nteger @ F ) @ ( pow_nat @ A ) )
% 4.69/4.97 = ( pow_Code_integer @ B4 ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % image_Pow_surj
% 4.69/4.97 thf(fact_3142_Pow__insert,axiom,
% 4.69/4.97 ! [A2: nat,A: set_nat] :
% 4.69/4.97 ( ( pow_nat @ ( insert_nat @ A2 @ A ) )
% 4.69/4.97 = ( sup_sup_set_set_nat @ ( pow_nat @ A ) @ ( image_7916887816326733075et_nat @ ( insert_nat @ A2 ) @ ( pow_nat @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Pow_insert
% 4.69/4.97 thf(fact_3143_Pow__insert,axiom,
% 4.69/4.97 ! [A2: int,A: set_int] :
% 4.69/4.97 ( ( pow_int @ ( insert_int @ A2 @ A ) )
% 4.69/4.97 = ( sup_sup_set_set_int @ ( pow_int @ A ) @ ( image_524474410958335435et_int @ ( insert_int @ A2 ) @ ( pow_int @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Pow_insert
% 4.69/4.97 thf(fact_3144_Pow__insert,axiom,
% 4.69/4.97 ! [A2: $o,A: set_o] :
% 4.69/4.97 ( ( pow_o @ ( insert_o @ A2 @ A ) )
% 4.69/4.97 = ( sup_sup_set_set_o @ ( pow_o @ A ) @ ( image_set_o_set_o @ ( insert_o @ A2 ) @ ( pow_o @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Pow_insert
% 4.69/4.97 thf(fact_3145_Pow__insert,axiom,
% 4.69/4.97 ! [A2: product_unit,A: set_Product_unit] :
% 4.69/4.97 ( ( pow_Product_unit @ ( insert_Product_unit @ A2 @ A ) )
% 4.69/4.97 = ( sup_su5975557051335651745t_unit @ ( pow_Product_unit @ A ) @ ( image_4019945301284682565t_unit @ ( insert_Product_unit @ A2 ) @ ( pow_Product_unit @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Pow_insert
% 4.69/4.97 thf(fact_3146_pairself_Osimps,axiom,
% 4.69/4.97 ! [F: nat > nat,A2: nat,B: nat] :
% 4.69/4.97 ( ( pairself_nat_nat @ F @ ( product_Pair_nat_nat @ A2 @ B ) )
% 4.69/4.97 = ( product_Pair_nat_nat @ ( F @ A2 ) @ ( F @ B ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % pairself.simps
% 4.69/4.97 thf(fact_3147_pairself_Osimps,axiom,
% 4.69/4.97 ! [F: nat > int,A2: nat,B: nat] :
% 4.69/4.97 ( ( pairself_nat_int @ F @ ( product_Pair_nat_nat @ A2 @ B ) )
% 4.69/4.97 = ( product_Pair_int_int @ ( F @ A2 ) @ ( F @ B ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % pairself.simps
% 4.69/4.97 thf(fact_3148_pairself_Osimps,axiom,
% 4.69/4.97 ! [F: int > nat,A2: int,B: int] :
% 4.69/4.97 ( ( pairself_int_nat @ F @ ( product_Pair_int_int @ A2 @ B ) )
% 4.69/4.97 = ( product_Pair_nat_nat @ ( F @ A2 ) @ ( F @ B ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % pairself.simps
% 4.69/4.97 thf(fact_3149_pairself_Osimps,axiom,
% 4.69/4.97 ! [F: int > int,A2: int,B: int] :
% 4.69/4.97 ( ( pairself_int_int @ F @ ( product_Pair_int_int @ A2 @ B ) )
% 4.69/4.97 = ( product_Pair_int_int @ ( F @ A2 ) @ ( F @ B ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % pairself.simps
% 4.69/4.97 thf(fact_3150_pairself_Oelims,axiom,
% 4.69/4.97 ! [X: nat > nat,Xa: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 4.69/4.97 ( ( ( pairself_nat_nat @ X @ Xa )
% 4.69/4.97 = Y )
% 4.69/4.97 => ~ ! [A4: nat,B2: nat] :
% 4.69/4.97 ( ( Xa
% 4.69/4.97 = ( product_Pair_nat_nat @ A4 @ B2 ) )
% 4.69/4.97 => ( Y
% 4.69/4.97 != ( product_Pair_nat_nat @ ( X @ A4 ) @ ( X @ B2 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % pairself.elims
% 4.69/4.97 thf(fact_3151_pairself_Oelims,axiom,
% 4.69/4.97 ! [X: nat > int,Xa: product_prod_nat_nat,Y: product_prod_int_int] :
% 4.69/4.97 ( ( ( pairself_nat_int @ X @ Xa )
% 4.69/4.97 = Y )
% 4.69/4.97 => ~ ! [A4: nat,B2: nat] :
% 4.69/4.97 ( ( Xa
% 4.69/4.97 = ( product_Pair_nat_nat @ A4 @ B2 ) )
% 4.69/4.97 => ( Y
% 4.69/4.97 != ( product_Pair_int_int @ ( X @ A4 ) @ ( X @ B2 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % pairself.elims
% 4.69/4.97 thf(fact_3152_pairself_Oelims,axiom,
% 4.69/4.97 ! [X: int > nat,Xa: product_prod_int_int,Y: product_prod_nat_nat] :
% 4.69/4.97 ( ( ( pairself_int_nat @ X @ Xa )
% 4.69/4.97 = Y )
% 4.69/4.97 => ~ ! [A4: int,B2: int] :
% 4.69/4.97 ( ( Xa
% 4.69/4.97 = ( product_Pair_int_int @ A4 @ B2 ) )
% 4.69/4.97 => ( Y
% 4.69/4.97 != ( product_Pair_nat_nat @ ( X @ A4 ) @ ( X @ B2 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % pairself.elims
% 4.69/4.97 thf(fact_3153_pairself_Oelims,axiom,
% 4.69/4.97 ! [X: int > int,Xa: product_prod_int_int,Y: product_prod_int_int] :
% 4.69/4.97 ( ( ( pairself_int_int @ X @ Xa )
% 4.69/4.97 = Y )
% 4.69/4.97 => ~ ! [A4: int,B2: int] :
% 4.69/4.97 ( ( Xa
% 4.69/4.97 = ( product_Pair_int_int @ A4 @ B2 ) )
% 4.69/4.97 => ( Y
% 4.69/4.97 != ( product_Pair_int_int @ ( X @ A4 ) @ ( X @ B2 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % pairself.elims
% 4.69/4.97 thf(fact_3154_pairwise__singleton,axiom,
% 4.69/4.97 ! [P: product_unit > product_unit > $o,A: product_unit] : ( pairwi7919127943033184120t_unit @ P @ ( insert_Product_unit @ A @ bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.97
% 4.69/4.97 % pairwise_singleton
% 4.69/4.97 thf(fact_3155_pairwise__singleton,axiom,
% 4.69/4.97 ! [P: $o > $o > $o,A: $o] : ( pairwise_o @ P @ ( insert_o @ A @ bot_bot_set_o ) ) ).
% 4.69/4.97
% 4.69/4.97 % pairwise_singleton
% 4.69/4.97 thf(fact_3156_pairwise__singleton,axiom,
% 4.69/4.97 ! [P: nat > nat > $o,A: nat] : ( pairwise_nat @ P @ ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 4.69/4.97
% 4.69/4.97 % pairwise_singleton
% 4.69/4.97 thf(fact_3157_pairwise__singleton,axiom,
% 4.69/4.97 ! [P: int > int > $o,A: int] : ( pairwise_int @ P @ ( insert_int @ A @ bot_bot_set_int ) ) ).
% 4.69/4.97
% 4.69/4.97 % pairwise_singleton
% 4.69/4.97 thf(fact_3158_pairwise__singleton,axiom,
% 4.69/4.97 ! [P: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o,A: produc3658429121746597890et_nat > $o] : ( pairwi2432143822833250616_nat_o @ P @ ( insert5175938949040314269_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.97
% 4.69/4.97 % pairwise_singleton
% 4.69/4.97 thf(fact_3159_finite__Sup__in,axiom,
% 4.69/4.97 ! [A: set_set_nat] :
% 4.69/4.97 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.97 => ( ( A != bot_bot_set_set_nat )
% 4.69/4.97 => ( ! [X3: set_nat,Y2: set_nat] :
% 4.69/4.97 ( ( member_set_nat @ X3 @ A )
% 4.69/4.97 => ( ( member_set_nat @ Y2 @ A )
% 4.69/4.97 => ( member_set_nat @ ( sup_sup_set_nat @ X3 @ Y2 ) @ A ) ) )
% 4.69/4.97 => ( member_set_nat @ ( comple7399068483239264473et_nat @ A ) @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % finite_Sup_in
% 4.69/4.97 thf(fact_3160_finite__Sup__in,axiom,
% 4.69/4.97 ! [A: set_o] :
% 4.69/4.97 ( ( finite_finite_o @ A )
% 4.69/4.97 => ( ( A != bot_bot_set_o )
% 4.69/4.97 => ( ! [X3: $o,Y2: $o] :
% 4.69/4.97 ( ( member_o @ X3 @ A )
% 4.69/4.97 => ( ( member_o @ Y2 @ A )
% 4.69/4.97 => ( member_o @ ( sup_sup_o @ X3 @ Y2 ) @ A ) ) )
% 4.69/4.97 => ( member_o @ ( complete_Sup_Sup_o @ A ) @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % finite_Sup_in
% 4.69/4.97 thf(fact_3161_finite__Sup__in,axiom,
% 4.69/4.97 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.97 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.97 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.97 => ( ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ( member6576561426505652726_nat_o @ X3 @ A )
% 4.69/4.97 => ( ( member6576561426505652726_nat_o @ Y2 @ A )
% 4.69/4.97 => ( member6576561426505652726_nat_o @ ( sup_su5453871518329203617_nat_o @ X3 @ Y2 ) @ A ) ) )
% 4.69/4.97 => ( member6576561426505652726_nat_o @ ( comple4225350640907012154_nat_o @ A ) @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % finite_Sup_in
% 4.69/4.97 thf(fact_3162_finite__Sup__in,axiom,
% 4.69/4.97 ! [A: set_Product_unit] :
% 4.69/4.97 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.97 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ! [X3: product_unit,Y2: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X3 @ A )
% 4.69/4.97 => ( ( member_Product_unit @ Y2 @ A )
% 4.69/4.97 => ( member_Product_unit @ ( sup_sup_Product_unit @ X3 @ Y2 ) @ A ) ) )
% 4.69/4.97 => ( member_Product_unit @ ( comple4687483117567863418t_unit @ A ) @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % finite_Sup_in
% 4.69/4.97 thf(fact_3163_Sup__fin__Sup,axiom,
% 4.69/4.97 ! [A: set_o] :
% 4.69/4.97 ( ( finite_finite_o @ A )
% 4.69/4.97 => ( ( A != bot_bot_set_o )
% 4.69/4.97 => ( ( lattic1508158080041050831_fin_o @ A )
% 4.69/4.97 = ( complete_Sup_Sup_o @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_fin_Sup
% 4.69/4.97 thf(fact_3164_Sup__fin__Sup,axiom,
% 4.69/4.97 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.97 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/4.97 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.97 => ( ( lattic7320199455484906628_nat_o @ A )
% 4.69/4.97 = ( comple4225350640907012154_nat_o @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_fin_Sup
% 4.69/4.97 thf(fact_3165_Sup__fin__Sup,axiom,
% 4.69/4.97 ! [A: set_Product_unit] :
% 4.69/4.97 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.97 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( lattic5294303975357428420t_unit @ A )
% 4.69/4.97 = ( comple4687483117567863418t_unit @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_fin_Sup
% 4.69/4.97 thf(fact_3166_insert__partition,axiom,
% 4.69/4.97 ! [X: set_Product_unit,F2: set_set_Product_unit] :
% 4.69/4.97 ( ~ ( member5877623283571906838t_unit @ X @ F2 )
% 4.69/4.97 => ( ! [X3: set_Product_unit] :
% 4.69/4.97 ( ( member5877623283571906838t_unit @ X3 @ ( insert8986028188087627965t_unit @ X @ F2 ) )
% 4.69/4.97 => ! [Xa3: set_Product_unit] :
% 4.69/4.97 ( ( member5877623283571906838t_unit @ Xa3 @ ( insert8986028188087627965t_unit @ X @ F2 ) )
% 4.69/4.97 => ( ( X3 != Xa3 )
% 4.69/4.97 => ( ( inf_in4660618365625256667t_unit @ X3 @ Xa3 )
% 4.69/4.97 = bot_bo3957492148770167129t_unit ) ) ) )
% 4.69/4.97 => ( ( inf_in4660618365625256667t_unit @ X @ ( comple3349607820504768346t_unit @ F2 ) )
% 4.69/4.97 = bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % insert_partition
% 4.69/4.97 thf(fact_3167_insert__partition,axiom,
% 4.69/4.97 ! [X: set_o,F2: set_set_o] :
% 4.69/4.97 ( ~ ( member_set_o @ X @ F2 )
% 4.69/4.97 => ( ! [X3: set_o] :
% 4.69/4.97 ( ( member_set_o @ X3 @ ( insert_set_o @ X @ F2 ) )
% 4.69/4.97 => ! [Xa3: set_o] :
% 4.69/4.97 ( ( member_set_o @ Xa3 @ ( insert_set_o @ X @ F2 ) )
% 4.69/4.97 => ( ( X3 != Xa3 )
% 4.69/4.97 => ( ( inf_inf_set_o @ X3 @ Xa3 )
% 4.69/4.97 = bot_bot_set_o ) ) ) )
% 4.69/4.97 => ( ( inf_inf_set_o @ X @ ( comple90263536869209701_set_o @ F2 ) )
% 4.69/4.97 = bot_bot_set_o ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % insert_partition
% 4.69/4.97 thf(fact_3168_insert__partition,axiom,
% 4.69/4.97 ! [X: set_nat,F2: set_set_nat] :
% 4.69/4.97 ( ~ ( member_set_nat @ X @ F2 )
% 4.69/4.97 => ( ! [X3: set_nat] :
% 4.69/4.97 ( ( member_set_nat @ X3 @ ( insert_set_nat @ X @ F2 ) )
% 4.69/4.97 => ! [Xa3: set_nat] :
% 4.69/4.97 ( ( member_set_nat @ Xa3 @ ( insert_set_nat @ X @ F2 ) )
% 4.69/4.97 => ( ( X3 != Xa3 )
% 4.69/4.97 => ( ( inf_inf_set_nat @ X3 @ Xa3 )
% 4.69/4.97 = bot_bot_set_nat ) ) ) )
% 4.69/4.97 => ( ( inf_inf_set_nat @ X @ ( comple7399068483239264473et_nat @ F2 ) )
% 4.69/4.97 = bot_bot_set_nat ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % insert_partition
% 4.69/4.97 thf(fact_3169_insert__partition,axiom,
% 4.69/4.97 ! [X: set_int,F2: set_set_int] :
% 4.69/4.97 ( ~ ( member_set_int @ X @ F2 )
% 4.69/4.97 => ( ! [X3: set_int] :
% 4.69/4.97 ( ( member_set_int @ X3 @ ( insert_set_int @ X @ F2 ) )
% 4.69/4.97 => ! [Xa3: set_int] :
% 4.69/4.97 ( ( member_set_int @ Xa3 @ ( insert_set_int @ X @ F2 ) )
% 4.69/4.97 => ( ( X3 != Xa3 )
% 4.69/4.97 => ( ( inf_inf_set_int @ X3 @ Xa3 )
% 4.69/4.97 = bot_bot_set_int ) ) ) )
% 4.69/4.97 => ( ( inf_inf_set_int @ X @ ( comple3221217463730067765et_int @ F2 ) )
% 4.69/4.97 = bot_bot_set_int ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % insert_partition
% 4.69/4.97 thf(fact_3170_insert__partition,axiom,
% 4.69/4.97 ! [X: set_Pr4532377907799695533_nat_o,F2: set_se1353816476878259085_nat_o] :
% 4.69/4.97 ( ~ ( member1452989533377600726_nat_o @ X @ F2 )
% 4.69/4.97 => ( ! [X3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.97 ( ( member1452989533377600726_nat_o @ X3 @ ( insert2507855216428400253_nat_o @ X @ F2 ) )
% 4.69/4.97 => ! [Xa3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.97 ( ( member1452989533377600726_nat_o @ Xa3 @ ( insert2507855216428400253_nat_o @ X @ F2 ) )
% 4.69/4.97 => ( ( X3 != Xa3 )
% 4.69/4.97 => ( ( inf_in1906310914598751387_nat_o @ X3 @ Xa3 )
% 4.69/4.97 = bot_bo7824918357723582233_nat_o ) ) ) )
% 4.69/4.97 => ( ( inf_in1906310914598751387_nat_o @ X @ ( comple3382087578465172250_nat_o @ F2 ) )
% 4.69/4.97 = bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % insert_partition
% 4.69/4.97 thf(fact_3171_image__Pow__mono,axiom,
% 4.69/4.97 ! [F: nat > set_nat,A: set_nat,B4: set_set_nat] :
% 4.69/4.97 ( ( ord_le6893508408891458716et_nat @ ( image_nat_set_nat @ F @ A ) @ B4 )
% 4.69/4.97 => ( ord_le9131159989063066194et_nat @ ( image_6725021117256019401et_nat @ ( image_nat_set_nat @ F ) @ ( pow_nat @ A ) ) @ ( pow_set_nat @ B4 ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % image_Pow_mono
% 4.69/4.97 thf(fact_3172_image__Pow__mono,axiom,
% 4.69/4.97 ! [F: code_integer > code_integer,A: set_Code_integer,B4: set_Code_integer] :
% 4.69/4.97 ( ( ord_le7084787975880047091nteger @ ( image_4470545334726330049nteger @ F @ A ) @ B4 )
% 4.69/4.97 => ( ord_le1914454125413604393nteger @ ( image_6270750266955655469nteger @ ( image_4470545334726330049nteger @ F ) @ ( pow_Code_integer @ A ) ) @ ( pow_Code_integer @ B4 ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % image_Pow_mono
% 4.69/4.97 thf(fact_3173_image__Pow__mono,axiom,
% 4.69/4.97 ! [F: nat > code_integer,A: set_nat,B4: set_Code_integer] :
% 4.69/4.97 ( ( ord_le7084787975880047091nteger @ ( image_1215581382706833972nteger @ F @ A ) @ B4 )
% 4.69/4.97 => ( ord_le1914454125413604393nteger @ ( image_6916300684244607776nteger @ ( image_1215581382706833972nteger @ F ) @ ( pow_nat @ A ) ) @ ( pow_Code_integer @ B4 ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % image_Pow_mono
% 4.69/4.97 thf(fact_3174_image__Pow__mono,axiom,
% 4.69/4.97 ! [F: nat > nat,A: set_nat,B4: set_nat] :
% 4.69/4.97 ( ( ord_less_eq_set_nat @ ( image_nat_nat2 @ F @ A ) @ B4 )
% 4.69/4.97 => ( ord_le6893508408891458716et_nat @ ( image_7916887816326733075et_nat @ ( image_nat_nat2 @ F ) @ ( pow_nat @ A ) ) @ ( pow_nat @ B4 ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % image_Pow_mono
% 4.69/4.97 thf(fact_3175_pairwise__alt,axiom,
% 4.69/4.97 ( pairwi7919127943033184120t_unit
% 4.69/4.97 = ( ^ [R: product_unit > product_unit > $o,S6: set_Product_unit] :
% 4.69/4.97 ! [X2: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X2 @ S6 )
% 4.69/4.97 => ! [Y3: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ Y3 @ ( minus_6452836326544984404t_unit @ S6 @ ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.97 => ( R @ X2 @ Y3 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % pairwise_alt
% 4.69/4.97 thf(fact_3176_pairwise__alt,axiom,
% 4.69/4.97 ( pairwise_o
% 4.69/4.97 = ( ^ [R: $o > $o > $o,S6: set_o] :
% 4.69/4.97 ! [X2: $o] :
% 4.69/4.97 ( ( member_o @ X2 @ S6 )
% 4.69/4.97 => ! [Y3: $o] :
% 4.69/4.97 ( ( member_o @ Y3 @ ( minus_minus_set_o @ S6 @ ( insert_o @ X2 @ bot_bot_set_o ) ) )
% 4.69/4.97 => ( R @ X2 @ Y3 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % pairwise_alt
% 4.69/4.97 thf(fact_3177_pairwise__alt,axiom,
% 4.69/4.97 ( pairwise_int
% 4.69/4.97 = ( ^ [R: int > int > $o,S6: set_int] :
% 4.69/4.97 ! [X2: int] :
% 4.69/4.97 ( ( member_int @ X2 @ S6 )
% 4.69/4.97 => ! [Y3: int] :
% 4.69/4.97 ( ( member_int @ Y3 @ ( minus_minus_set_int @ S6 @ ( insert_int @ X2 @ bot_bot_set_int ) ) )
% 4.69/4.97 => ( R @ X2 @ Y3 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % pairwise_alt
% 4.69/4.97 thf(fact_3178_pairwise__alt,axiom,
% 4.69/4.97 ( pairwi2432143822833250616_nat_o
% 4.69/4.97 = ( ^ [R: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o,S6: set_Pr4532377907799695533_nat_o] :
% 4.69/4.97 ! [X2: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ( member6576561426505652726_nat_o @ X2 @ S6 )
% 4.69/4.97 => ! [Y3: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ( member6576561426505652726_nat_o @ Y3 @ ( minus_1801376950450012436_nat_o @ S6 @ ( insert5175938949040314269_nat_o @ X2 @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/4.97 => ( R @ X2 @ Y3 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % pairwise_alt
% 4.69/4.97 thf(fact_3179_pairwise__alt,axiom,
% 4.69/4.97 ( pairwise_nat
% 4.69/4.97 = ( ^ [R: nat > nat > $o,S6: set_nat] :
% 4.69/4.97 ! [X2: nat] :
% 4.69/4.97 ( ( member_nat @ X2 @ S6 )
% 4.69/4.97 => ! [Y3: nat] :
% 4.69/4.97 ( ( member_nat @ Y3 @ ( minus_minus_set_nat @ S6 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) )
% 4.69/4.97 => ( R @ X2 @ Y3 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % pairwise_alt
% 4.69/4.97 thf(fact_3180_Sup__insert,axiom,
% 4.69/4.97 ! [A2: $o,A: set_o] :
% 4.69/4.97 ( ( complete_Sup_Sup_o @ ( insert_o @ A2 @ A ) )
% 4.69/4.97 = ( sup_sup_o @ A2 @ ( complete_Sup_Sup_o @ A ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_insert
% 4.69/4.97 thf(fact_3181_Sup__insert,axiom,
% 4.69/4.97 ! [A2: set_nat,A: set_set_nat] :
% 4.69/4.97 ( ( comple7399068483239264473et_nat @ ( insert_set_nat @ A2 @ A ) )
% 4.69/4.97 = ( sup_sup_set_nat @ A2 @ ( comple7399068483239264473et_nat @ A ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_insert
% 4.69/4.97 thf(fact_3182_Sup__insert,axiom,
% 4.69/4.97 ! [A2: product_unit,A: set_Product_unit] :
% 4.69/4.97 ( ( comple4687483117567863418t_unit @ ( insert_Product_unit @ A2 @ A ) )
% 4.69/4.97 = ( sup_sup_Product_unit @ A2 @ ( comple4687483117567863418t_unit @ A ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_insert
% 4.69/4.97 thf(fact_3183_ccpo__Sup__singleton,axiom,
% 4.69/4.97 ! [X: $o] :
% 4.69/4.97 ( ( complete_Sup_Sup_o @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.97 = X ) ).
% 4.69/4.97
% 4.69/4.97 % ccpo_Sup_singleton
% 4.69/4.97 thf(fact_3184_ccpo__Sup__singleton,axiom,
% 4.69/4.97 ! [X: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ( comple4225350640907012154_nat_o @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.97 = X ) ).
% 4.69/4.97
% 4.69/4.97 % ccpo_Sup_singleton
% 4.69/4.97 thf(fact_3185_ccpo__Sup__singleton,axiom,
% 4.69/4.97 ! [X: product_unit] :
% 4.69/4.97 ( ( comple4687483117567863418t_unit @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.97 = X ) ).
% 4.69/4.97
% 4.69/4.97 % ccpo_Sup_singleton
% 4.69/4.97 thf(fact_3186_cSup__singleton,axiom,
% 4.69/4.97 ! [X: $o] :
% 4.69/4.97 ( ( complete_Sup_Sup_o @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.97 = X ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_singleton
% 4.69/4.97 thf(fact_3187_cSup__singleton,axiom,
% 4.69/4.97 ! [X: int] :
% 4.69/4.97 ( ( complete_Sup_Sup_int @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.97 = X ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_singleton
% 4.69/4.97 thf(fact_3188_cSup__singleton,axiom,
% 4.69/4.97 ! [X: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ( comple4225350640907012154_nat_o @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/4.97 = X ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_singleton
% 4.69/4.97 thf(fact_3189_cSup__singleton,axiom,
% 4.69/4.97 ! [X: nat] :
% 4.69/4.97 ( ( complete_Sup_Sup_nat @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.97 = X ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_singleton
% 4.69/4.97 thf(fact_3190_cSup__singleton,axiom,
% 4.69/4.97 ! [X: product_unit] :
% 4.69/4.97 ( ( comple4687483117567863418t_unit @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.97 = X ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_singleton
% 4.69/4.97 thf(fact_3191_Sup__empty,axiom,
% 4.69/4.97 ( ( comple3349607820504768346t_unit @ bot_bo6284674557190688313t_unit )
% 4.69/4.97 = bot_bo3957492148770167129t_unit ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_empty
% 4.69/4.97 thf(fact_3192_Sup__empty,axiom,
% 4.69/4.97 ( ( comple90263536869209701_set_o @ bot_bot_set_set_o )
% 4.69/4.97 = bot_bot_set_o ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_empty
% 4.69/4.97 thf(fact_3193_Sup__empty,axiom,
% 4.69/4.97 ( ( comple7399068483239264473et_nat @ bot_bot_set_set_nat )
% 4.69/4.97 = bot_bot_set_nat ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_empty
% 4.69/4.97 thf(fact_3194_Sup__empty,axiom,
% 4.69/4.97 ( ( comple3221217463730067765et_int @ bot_bot_set_set_int )
% 4.69/4.97 = bot_bot_set_int ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_empty
% 4.69/4.97 thf(fact_3195_Sup__empty,axiom,
% 4.69/4.97 ( ( comple3382087578465172250_nat_o @ bot_bo3736544561982865913_nat_o )
% 4.69/4.97 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_empty
% 4.69/4.97 thf(fact_3196_Sup__empty,axiom,
% 4.69/4.97 ( ( complete_Sup_Sup_o @ bot_bot_set_o )
% 4.69/4.97 = bot_bot_o ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_empty
% 4.69/4.97 thf(fact_3197_Sup__empty,axiom,
% 4.69/4.97 ( ( comple4225350640907012154_nat_o @ bot_bo7824918357723582233_nat_o )
% 4.69/4.97 = bot_bo6993851861578111033_nat_o ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_empty
% 4.69/4.97 thf(fact_3198_Sup__empty,axiom,
% 4.69/4.97 ( ( comple4687483117567863418t_unit @ bot_bo3957492148770167129t_unit )
% 4.69/4.97 = bot_bot_Product_unit ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_empty
% 4.69/4.97 thf(fact_3199_Sup__bot__conv_I1_J,axiom,
% 4.69/4.97 ! [A: set_set_Product_unit] :
% 4.69/4.97 ( ( ( comple3349607820504768346t_unit @ A )
% 4.69/4.97 = bot_bo3957492148770167129t_unit )
% 4.69/4.97 = ( ! [X2: set_Product_unit] :
% 4.69/4.97 ( ( member5877623283571906838t_unit @ X2 @ A )
% 4.69/4.97 => ( X2 = bot_bo3957492148770167129t_unit ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_bot_conv(1)
% 4.69/4.97 thf(fact_3200_Sup__bot__conv_I1_J,axiom,
% 4.69/4.97 ! [A: set_set_o] :
% 4.69/4.97 ( ( ( comple90263536869209701_set_o @ A )
% 4.69/4.97 = bot_bot_set_o )
% 4.69/4.97 = ( ! [X2: set_o] :
% 4.69/4.97 ( ( member_set_o @ X2 @ A )
% 4.69/4.97 => ( X2 = bot_bot_set_o ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_bot_conv(1)
% 4.69/4.97 thf(fact_3201_Sup__bot__conv_I1_J,axiom,
% 4.69/4.97 ! [A: set_set_nat] :
% 4.69/4.97 ( ( ( comple7399068483239264473et_nat @ A )
% 4.69/4.97 = bot_bot_set_nat )
% 4.69/4.97 = ( ! [X2: set_nat] :
% 4.69/4.97 ( ( member_set_nat @ X2 @ A )
% 4.69/4.97 => ( X2 = bot_bot_set_nat ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_bot_conv(1)
% 4.69/4.97 thf(fact_3202_Sup__bot__conv_I1_J,axiom,
% 4.69/4.97 ! [A: set_set_int] :
% 4.69/4.97 ( ( ( comple3221217463730067765et_int @ A )
% 4.69/4.97 = bot_bot_set_int )
% 4.69/4.97 = ( ! [X2: set_int] :
% 4.69/4.97 ( ( member_set_int @ X2 @ A )
% 4.69/4.97 => ( X2 = bot_bot_set_int ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_bot_conv(1)
% 4.69/4.97 thf(fact_3203_Sup__bot__conv_I1_J,axiom,
% 4.69/4.97 ! [A: set_se1353816476878259085_nat_o] :
% 4.69/4.97 ( ( ( comple3382087578465172250_nat_o @ A )
% 4.69/4.97 = bot_bo7824918357723582233_nat_o )
% 4.69/4.97 = ( ! [X2: set_Pr4532377907799695533_nat_o] :
% 4.69/4.97 ( ( member1452989533377600726_nat_o @ X2 @ A )
% 4.69/4.97 => ( X2 = bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_bot_conv(1)
% 4.69/4.97 thf(fact_3204_Sup__bot__conv_I1_J,axiom,
% 4.69/4.97 ! [A: set_Product_unit] :
% 4.69/4.97 ( ( ( comple4687483117567863418t_unit @ A )
% 4.69/4.97 = bot_bot_Product_unit )
% 4.69/4.97 = ( ! [X2: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X2 @ A )
% 4.69/4.97 => ( X2 = bot_bot_Product_unit ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_bot_conv(1)
% 4.69/4.97 thf(fact_3205_Sup__bot__conv_I2_J,axiom,
% 4.69/4.97 ! [A: set_set_Product_unit] :
% 4.69/4.97 ( ( bot_bo3957492148770167129t_unit
% 4.69/4.97 = ( comple3349607820504768346t_unit @ A ) )
% 4.69/4.97 = ( ! [X2: set_Product_unit] :
% 4.69/4.97 ( ( member5877623283571906838t_unit @ X2 @ A )
% 4.69/4.97 => ( X2 = bot_bo3957492148770167129t_unit ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_bot_conv(2)
% 4.69/4.97 thf(fact_3206_Sup__bot__conv_I2_J,axiom,
% 4.69/4.97 ! [A: set_set_o] :
% 4.69/4.97 ( ( bot_bot_set_o
% 4.69/4.97 = ( comple90263536869209701_set_o @ A ) )
% 4.69/4.97 = ( ! [X2: set_o] :
% 4.69/4.97 ( ( member_set_o @ X2 @ A )
% 4.69/4.97 => ( X2 = bot_bot_set_o ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_bot_conv(2)
% 4.69/4.97 thf(fact_3207_Sup__bot__conv_I2_J,axiom,
% 4.69/4.97 ! [A: set_set_nat] :
% 4.69/4.97 ( ( bot_bot_set_nat
% 4.69/4.97 = ( comple7399068483239264473et_nat @ A ) )
% 4.69/4.97 = ( ! [X2: set_nat] :
% 4.69/4.97 ( ( member_set_nat @ X2 @ A )
% 4.69/4.97 => ( X2 = bot_bot_set_nat ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_bot_conv(2)
% 4.69/4.97 thf(fact_3208_Sup__bot__conv_I2_J,axiom,
% 4.69/4.97 ! [A: set_set_int] :
% 4.69/4.97 ( ( bot_bot_set_int
% 4.69/4.97 = ( comple3221217463730067765et_int @ A ) )
% 4.69/4.97 = ( ! [X2: set_int] :
% 4.69/4.97 ( ( member_set_int @ X2 @ A )
% 4.69/4.97 => ( X2 = bot_bot_set_int ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_bot_conv(2)
% 4.69/4.97 thf(fact_3209_Sup__bot__conv_I2_J,axiom,
% 4.69/4.97 ! [A: set_se1353816476878259085_nat_o] :
% 4.69/4.97 ( ( bot_bo7824918357723582233_nat_o
% 4.69/4.97 = ( comple3382087578465172250_nat_o @ A ) )
% 4.69/4.97 = ( ! [X2: set_Pr4532377907799695533_nat_o] :
% 4.69/4.97 ( ( member1452989533377600726_nat_o @ X2 @ A )
% 4.69/4.97 => ( X2 = bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_bot_conv(2)
% 4.69/4.97 thf(fact_3210_Sup__bot__conv_I2_J,axiom,
% 4.69/4.97 ! [A: set_Product_unit] :
% 4.69/4.97 ( ( bot_bot_Product_unit
% 4.69/4.97 = ( comple4687483117567863418t_unit @ A ) )
% 4.69/4.97 = ( ! [X2: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X2 @ A )
% 4.69/4.97 => ( X2 = bot_bot_Product_unit ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_bot_conv(2)
% 4.69/4.97 thf(fact_3211_cSup__eq__Sup__fin,axiom,
% 4.69/4.97 ! [X4: set_o] :
% 4.69/4.97 ( ( finite_finite_o @ X4 )
% 4.69/4.97 => ( ( X4 != bot_bot_set_o )
% 4.69/4.97 => ( ( complete_Sup_Sup_o @ X4 )
% 4.69/4.97 = ( lattic1508158080041050831_fin_o @ X4 ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_eq_Sup_fin
% 4.69/4.97 thf(fact_3212_cSup__eq__Sup__fin,axiom,
% 4.69/4.97 ! [X4: set_int] :
% 4.69/4.97 ( ( finite_finite_int @ X4 )
% 4.69/4.97 => ( ( X4 != bot_bot_set_int )
% 4.69/4.97 => ( ( complete_Sup_Sup_int @ X4 )
% 4.69/4.97 = ( lattic1091506334969745077in_int @ X4 ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_eq_Sup_fin
% 4.69/4.97 thf(fact_3213_cSup__eq__Sup__fin,axiom,
% 4.69/4.97 ! [X4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.97 ( ( finite3252695134891459830_nat_o @ X4 )
% 4.69/4.97 => ( ( X4 != bot_bo7824918357723582233_nat_o )
% 4.69/4.97 => ( ( comple4225350640907012154_nat_o @ X4 )
% 4.69/4.97 = ( lattic7320199455484906628_nat_o @ X4 ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_eq_Sup_fin
% 4.69/4.97 thf(fact_3214_cSup__eq__Sup__fin,axiom,
% 4.69/4.97 ! [X4: set_nat] :
% 4.69/4.97 ( ( finite_finite_nat @ X4 )
% 4.69/4.97 => ( ( X4 != bot_bot_set_nat )
% 4.69/4.97 => ( ( complete_Sup_Sup_nat @ X4 )
% 4.69/4.97 = ( lattic1093996805478795353in_nat @ X4 ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_eq_Sup_fin
% 4.69/4.97 thf(fact_3215_cSup__eq__Sup__fin,axiom,
% 4.69/4.97 ! [X4: set_Product_unit] :
% 4.69/4.97 ( ( finite4290736615968046902t_unit @ X4 )
% 4.69/4.97 => ( ( X4 != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( comple4687483117567863418t_unit @ X4 )
% 4.69/4.97 = ( lattic5294303975357428420t_unit @ X4 ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_eq_Sup_fin
% 4.69/4.97 thf(fact_3216_Union__image__insert,axiom,
% 4.69/4.97 ! [F: nat > set_nat,A2: nat,B4: set_nat] :
% 4.69/4.97 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ ( insert_nat @ A2 @ B4 ) ) )
% 4.69/4.97 = ( sup_sup_set_nat @ ( F @ A2 ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ B4 ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Union_image_insert
% 4.69/4.97 thf(fact_3217_Union__image__insert,axiom,
% 4.69/4.97 ! [F: int > set_nat,A2: int,B4: set_int] :
% 4.69/4.97 ( ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ ( insert_int @ A2 @ B4 ) ) )
% 4.69/4.97 = ( sup_sup_set_nat @ ( F @ A2 ) @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ B4 ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Union_image_insert
% 4.69/4.97 thf(fact_3218_Union__image__insert,axiom,
% 4.69/4.97 ! [F: $o > set_nat,A2: $o,B4: set_o] :
% 4.69/4.97 ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ ( insert_o @ A2 @ B4 ) ) )
% 4.69/4.97 = ( sup_sup_set_nat @ ( F @ A2 ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ B4 ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Union_image_insert
% 4.69/4.97 thf(fact_3219_Union__image__insert,axiom,
% 4.69/4.97 ! [F: product_unit > set_nat,A2: product_unit,B4: set_Product_unit] :
% 4.69/4.97 ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ ( insert_Product_unit @ A2 @ B4 ) ) )
% 4.69/4.97 = ( sup_sup_set_nat @ ( F @ A2 ) @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ B4 ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Union_image_insert
% 4.69/4.97 thf(fact_3220_Union__image__empty,axiom,
% 4.69/4.97 ! [A: set_nat,F: product_unit > set_nat] :
% 4.69/4.97 ( ( sup_sup_set_nat @ A @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/4.97 = A ) ).
% 4.69/4.97
% 4.69/4.97 % Union_image_empty
% 4.69/4.97 thf(fact_3221_Union__image__empty,axiom,
% 4.69/4.97 ! [A: set_nat,F: $o > set_nat] :
% 4.69/4.97 ( ( sup_sup_set_nat @ A @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ bot_bot_set_o ) ) )
% 4.69/4.97 = A ) ).
% 4.69/4.97
% 4.69/4.97 % Union_image_empty
% 4.69/4.97 thf(fact_3222_Union__image__empty,axiom,
% 4.69/4.97 ! [A: set_nat,F: nat > set_nat] :
% 4.69/4.97 ( ( sup_sup_set_nat @ A @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ bot_bot_set_nat ) ) )
% 4.69/4.97 = A ) ).
% 4.69/4.97
% 4.69/4.97 % Union_image_empty
% 4.69/4.97 thf(fact_3223_Union__image__empty,axiom,
% 4.69/4.97 ! [A: set_nat,F: int > set_nat] :
% 4.69/4.97 ( ( sup_sup_set_nat @ A @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ bot_bot_set_int ) ) )
% 4.69/4.97 = A ) ).
% 4.69/4.97
% 4.69/4.97 % Union_image_empty
% 4.69/4.97 thf(fact_3224_Union__image__empty,axiom,
% 4.69/4.97 ! [A: set_nat,F: ( produc3658429121746597890et_nat > $o ) > set_nat] :
% 4.69/4.97 ( ( sup_sup_set_nat @ A @ ( comple7399068483239264473et_nat @ ( image_6888641473154130958et_nat @ F @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/4.97 = A ) ).
% 4.69/4.97
% 4.69/4.97 % Union_image_empty
% 4.69/4.97 thf(fact_3225_Sup__SUP__eq,axiom,
% 4.69/4.97 ( comple3590721164184202819at_o_o
% 4.69/4.97 = ( ^ [S6: set_Pr6409761941060870310at_o_o,X2: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X2 @ ( comple3382087578465172250_nat_o @ ( image_8639947063239330806_nat_o @ collec939566748876313656_nat_o @ S6 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_SUP_eq
% 4.69/4.97 thf(fact_3226_Sup__SUP__eq,axiom,
% 4.69/4.97 ( comple8317665133742190828_nat_o
% 4.69/4.97 = ( ^ [S6: set_nat_o,X2: nat] : ( member_nat @ X2 @ ( comple7399068483239264473et_nat @ ( image_nat_o_set_nat @ collect_nat @ S6 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_SUP_eq
% 4.69/4.97 thf(fact_3227_Sup__SUP__eq,axiom,
% 4.69/4.97 ( comple6496622788309502864_int_o
% 4.69/4.97 = ( ^ [S6: set_int_o,X2: int] : ( member_int @ X2 @ ( comple3221217463730067765et_int @ ( image_int_o_set_int @ collect_int @ S6 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_SUP_eq
% 4.69/4.97 thf(fact_3228_Sup__SUP__eq,axiom,
% 4.69/4.97 ( complete_Sup_Sup_o_o
% 4.69/4.97 = ( ^ [S6: set_o_o,X2: $o] : ( member_o @ X2 @ ( comple90263536869209701_set_o @ ( image_o_o_set_o @ collect_o @ S6 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_SUP_eq
% 4.69/4.97 thf(fact_3229_Sup__SUP__eq,axiom,
% 4.69/4.97 ( comple4773641153059738115unit_o
% 4.69/4.97 = ( ^ [S6: set_Product_unit_o,X2: product_unit] : ( member_Product_unit @ X2 @ ( comple3349607820504768346t_unit @ ( image_5138372075374782070t_unit @ collect_Product_unit @ S6 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_SUP_eq
% 4.69/4.97 thf(fact_3230_empty__Union__conv,axiom,
% 4.69/4.97 ! [A: set_set_Product_unit] :
% 4.69/4.97 ( ( bot_bo3957492148770167129t_unit
% 4.69/4.97 = ( comple3349607820504768346t_unit @ A ) )
% 4.69/4.97 = ( ! [X2: set_Product_unit] :
% 4.69/4.97 ( ( member5877623283571906838t_unit @ X2 @ A )
% 4.69/4.97 => ( X2 = bot_bo3957492148770167129t_unit ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % empty_Union_conv
% 4.69/4.97 thf(fact_3231_empty__Union__conv,axiom,
% 4.69/4.97 ! [A: set_set_o] :
% 4.69/4.97 ( ( bot_bot_set_o
% 4.69/4.97 = ( comple90263536869209701_set_o @ A ) )
% 4.69/4.97 = ( ! [X2: set_o] :
% 4.69/4.97 ( ( member_set_o @ X2 @ A )
% 4.69/4.97 => ( X2 = bot_bot_set_o ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % empty_Union_conv
% 4.69/4.97 thf(fact_3232_empty__Union__conv,axiom,
% 4.69/4.97 ! [A: set_set_nat] :
% 4.69/4.97 ( ( bot_bot_set_nat
% 4.69/4.97 = ( comple7399068483239264473et_nat @ A ) )
% 4.69/4.97 = ( ! [X2: set_nat] :
% 4.69/4.97 ( ( member_set_nat @ X2 @ A )
% 4.69/4.97 => ( X2 = bot_bot_set_nat ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % empty_Union_conv
% 4.69/4.97 thf(fact_3233_empty__Union__conv,axiom,
% 4.69/4.97 ! [A: set_set_int] :
% 4.69/4.97 ( ( bot_bot_set_int
% 4.69/4.97 = ( comple3221217463730067765et_int @ A ) )
% 4.69/4.97 = ( ! [X2: set_int] :
% 4.69/4.97 ( ( member_set_int @ X2 @ A )
% 4.69/4.97 => ( X2 = bot_bot_set_int ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % empty_Union_conv
% 4.69/4.97 thf(fact_3234_empty__Union__conv,axiom,
% 4.69/4.97 ! [A: set_se1353816476878259085_nat_o] :
% 4.69/4.97 ( ( bot_bo7824918357723582233_nat_o
% 4.69/4.97 = ( comple3382087578465172250_nat_o @ A ) )
% 4.69/4.97 = ( ! [X2: set_Pr4532377907799695533_nat_o] :
% 4.69/4.97 ( ( member1452989533377600726_nat_o @ X2 @ A )
% 4.69/4.97 => ( X2 = bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % empty_Union_conv
% 4.69/4.97 thf(fact_3235_Union__empty__conv,axiom,
% 4.69/4.97 ! [A: set_set_Product_unit] :
% 4.69/4.97 ( ( ( comple3349607820504768346t_unit @ A )
% 4.69/4.97 = bot_bo3957492148770167129t_unit )
% 4.69/4.97 = ( ! [X2: set_Product_unit] :
% 4.69/4.97 ( ( member5877623283571906838t_unit @ X2 @ A )
% 4.69/4.97 => ( X2 = bot_bo3957492148770167129t_unit ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Union_empty_conv
% 4.69/4.97 thf(fact_3236_Union__empty__conv,axiom,
% 4.69/4.97 ! [A: set_set_o] :
% 4.69/4.97 ( ( ( comple90263536869209701_set_o @ A )
% 4.69/4.97 = bot_bot_set_o )
% 4.69/4.97 = ( ! [X2: set_o] :
% 4.69/4.97 ( ( member_set_o @ X2 @ A )
% 4.69/4.97 => ( X2 = bot_bot_set_o ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Union_empty_conv
% 4.69/4.97 thf(fact_3237_Union__empty__conv,axiom,
% 4.69/4.97 ! [A: set_set_nat] :
% 4.69/4.97 ( ( ( comple7399068483239264473et_nat @ A )
% 4.69/4.97 = bot_bot_set_nat )
% 4.69/4.97 = ( ! [X2: set_nat] :
% 4.69/4.97 ( ( member_set_nat @ X2 @ A )
% 4.69/4.97 => ( X2 = bot_bot_set_nat ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Union_empty_conv
% 4.69/4.97 thf(fact_3238_Union__empty__conv,axiom,
% 4.69/4.97 ! [A: set_set_int] :
% 4.69/4.97 ( ( ( comple3221217463730067765et_int @ A )
% 4.69/4.97 = bot_bot_set_int )
% 4.69/4.97 = ( ! [X2: set_int] :
% 4.69/4.97 ( ( member_set_int @ X2 @ A )
% 4.69/4.97 => ( X2 = bot_bot_set_int ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Union_empty_conv
% 4.69/4.97 thf(fact_3239_Union__empty__conv,axiom,
% 4.69/4.97 ! [A: set_se1353816476878259085_nat_o] :
% 4.69/4.97 ( ( ( comple3382087578465172250_nat_o @ A )
% 4.69/4.97 = bot_bo7824918357723582233_nat_o )
% 4.69/4.97 = ( ! [X2: set_Pr4532377907799695533_nat_o] :
% 4.69/4.97 ( ( member1452989533377600726_nat_o @ X2 @ A )
% 4.69/4.97 => ( X2 = bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Union_empty_conv
% 4.69/4.97 thf(fact_3240_less__eq__Sup,axiom,
% 4.69/4.97 ! [A: set_o,U: $o] :
% 4.69/4.97 ( ! [V3: $o] :
% 4.69/4.97 ( ( member_o @ V3 @ A )
% 4.69/4.97 => ( ord_less_eq_o @ U @ V3 ) )
% 4.69/4.97 => ( ( A != bot_bot_set_o )
% 4.69/4.97 => ( ord_less_eq_o @ U @ ( complete_Sup_Sup_o @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % less_eq_Sup
% 4.69/4.97 thf(fact_3241_less__eq__Sup,axiom,
% 4.69/4.97 ! [A: set_Pr4532377907799695533_nat_o,U: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ! [V3: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ( member6576561426505652726_nat_o @ V3 @ A )
% 4.69/4.97 => ( ord_le729326519192465773_nat_o @ U @ V3 ) )
% 4.69/4.97 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.97 => ( ord_le729326519192465773_nat_o @ U @ ( comple4225350640907012154_nat_o @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % less_eq_Sup
% 4.69/4.97 thf(fact_3242_less__eq__Sup,axiom,
% 4.69/4.97 ! [A: set_filter_nat,U: filter_nat] :
% 4.69/4.97 ( ! [V3: filter_nat] :
% 4.69/4.97 ( ( member_filter_nat @ V3 @ A )
% 4.69/4.97 => ( ord_le2510731241096832064er_nat @ U @ V3 ) )
% 4.69/4.97 => ( ( A != bot_bo498966703094740906er_nat )
% 4.69/4.97 => ( ord_le2510731241096832064er_nat @ U @ ( comple2454491259644266675er_nat @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % less_eq_Sup
% 4.69/4.97 thf(fact_3243_less__eq__Sup,axiom,
% 4.69/4.97 ! [A: set_set_nat,U: set_nat] :
% 4.69/4.97 ( ! [V3: set_nat] :
% 4.69/4.97 ( ( member_set_nat @ V3 @ A )
% 4.69/4.97 => ( ord_less_eq_set_nat @ U @ V3 ) )
% 4.69/4.97 => ( ( A != bot_bot_set_set_nat )
% 4.69/4.97 => ( ord_less_eq_set_nat @ U @ ( comple7399068483239264473et_nat @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % less_eq_Sup
% 4.69/4.97 thf(fact_3244_less__eq__Sup,axiom,
% 4.69/4.97 ! [A: set_Product_unit,U: product_unit] :
% 4.69/4.97 ( ! [V3: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ V3 @ A )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ U @ V3 ) )
% 4.69/4.97 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ U @ ( comple4687483117567863418t_unit @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % less_eq_Sup
% 4.69/4.97 thf(fact_3245_cSup__least,axiom,
% 4.69/4.97 ! [X4: set_o,Z: $o] :
% 4.69/4.97 ( ( X4 != bot_bot_set_o )
% 4.69/4.97 => ( ! [X3: $o] :
% 4.69/4.97 ( ( member_o @ X3 @ X4 )
% 4.69/4.97 => ( ord_less_eq_o @ X3 @ Z ) )
% 4.69/4.97 => ( ord_less_eq_o @ ( complete_Sup_Sup_o @ X4 ) @ Z ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_least
% 4.69/4.97 thf(fact_3246_cSup__least,axiom,
% 4.69/4.97 ! [X4: set_Pr4532377907799695533_nat_o,Z: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ( X4 != bot_bo7824918357723582233_nat_o )
% 4.69/4.97 => ( ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ( member6576561426505652726_nat_o @ X3 @ X4 )
% 4.69/4.97 => ( ord_le729326519192465773_nat_o @ X3 @ Z ) )
% 4.69/4.97 => ( ord_le729326519192465773_nat_o @ ( comple4225350640907012154_nat_o @ X4 ) @ Z ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_least
% 4.69/4.97 thf(fact_3247_cSup__least,axiom,
% 4.69/4.97 ! [X4: set_filter_nat,Z: filter_nat] :
% 4.69/4.97 ( ( X4 != bot_bo498966703094740906er_nat )
% 4.69/4.97 => ( ! [X3: filter_nat] :
% 4.69/4.97 ( ( member_filter_nat @ X3 @ X4 )
% 4.69/4.97 => ( ord_le2510731241096832064er_nat @ X3 @ Z ) )
% 4.69/4.97 => ( ord_le2510731241096832064er_nat @ ( comple2454491259644266675er_nat @ X4 ) @ Z ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_least
% 4.69/4.97 thf(fact_3248_cSup__least,axiom,
% 4.69/4.97 ! [X4: set_set_nat,Z: set_nat] :
% 4.69/4.97 ( ( X4 != bot_bot_set_set_nat )
% 4.69/4.97 => ( ! [X3: set_nat] :
% 4.69/4.97 ( ( member_set_nat @ X3 @ X4 )
% 4.69/4.97 => ( ord_less_eq_set_nat @ X3 @ Z ) )
% 4.69/4.97 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ X4 ) @ Z ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_least
% 4.69/4.97 thf(fact_3249_cSup__least,axiom,
% 4.69/4.97 ! [X4: set_int,Z: int] :
% 4.69/4.97 ( ( X4 != bot_bot_set_int )
% 4.69/4.97 => ( ! [X3: int] :
% 4.69/4.97 ( ( member_int @ X3 @ X4 )
% 4.69/4.97 => ( ord_less_eq_int @ X3 @ Z ) )
% 4.69/4.97 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ X4 ) @ Z ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_least
% 4.69/4.97 thf(fact_3250_cSup__least,axiom,
% 4.69/4.97 ! [X4: set_nat,Z: nat] :
% 4.69/4.97 ( ( X4 != bot_bot_set_nat )
% 4.69/4.97 => ( ! [X3: nat] :
% 4.69/4.97 ( ( member_nat @ X3 @ X4 )
% 4.69/4.97 => ( ord_less_eq_nat @ X3 @ Z ) )
% 4.69/4.97 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ X4 ) @ Z ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_least
% 4.69/4.97 thf(fact_3251_cSup__least,axiom,
% 4.69/4.97 ! [X4: set_Product_unit,Z: product_unit] :
% 4.69/4.97 ( ( X4 != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ! [X3: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X3 @ X4 )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ X3 @ Z ) )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ X4 ) @ Z ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_least
% 4.69/4.97 thf(fact_3252_cSup__eq__non__empty,axiom,
% 4.69/4.97 ! [X4: set_o,A2: $o] :
% 4.69/4.97 ( ( X4 != bot_bot_set_o )
% 4.69/4.97 => ( ! [X3: $o] :
% 4.69/4.97 ( ( member_o @ X3 @ X4 )
% 4.69/4.97 => ( ord_less_eq_o @ X3 @ A2 ) )
% 4.69/4.97 => ( ! [Y2: $o] :
% 4.69/4.97 ( ! [X6: $o] :
% 4.69/4.97 ( ( member_o @ X6 @ X4 )
% 4.69/4.97 => ( ord_less_eq_o @ X6 @ Y2 ) )
% 4.69/4.97 => ( ord_less_eq_o @ A2 @ Y2 ) )
% 4.69/4.97 => ( ( complete_Sup_Sup_o @ X4 )
% 4.69/4.97 = A2 ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_eq_non_empty
% 4.69/4.97 thf(fact_3253_cSup__eq__non__empty,axiom,
% 4.69/4.97 ! [X4: set_Pr4532377907799695533_nat_o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ( X4 != bot_bo7824918357723582233_nat_o )
% 4.69/4.97 => ( ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ( member6576561426505652726_nat_o @ X3 @ X4 )
% 4.69/4.97 => ( ord_le729326519192465773_nat_o @ X3 @ A2 ) )
% 4.69/4.97 => ( ! [Y2: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ! [X6: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ( member6576561426505652726_nat_o @ X6 @ X4 )
% 4.69/4.97 => ( ord_le729326519192465773_nat_o @ X6 @ Y2 ) )
% 4.69/4.97 => ( ord_le729326519192465773_nat_o @ A2 @ Y2 ) )
% 4.69/4.97 => ( ( comple4225350640907012154_nat_o @ X4 )
% 4.69/4.97 = A2 ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_eq_non_empty
% 4.69/4.97 thf(fact_3254_cSup__eq__non__empty,axiom,
% 4.69/4.97 ! [X4: set_filter_nat,A2: filter_nat] :
% 4.69/4.97 ( ( X4 != bot_bo498966703094740906er_nat )
% 4.69/4.97 => ( ! [X3: filter_nat] :
% 4.69/4.97 ( ( member_filter_nat @ X3 @ X4 )
% 4.69/4.97 => ( ord_le2510731241096832064er_nat @ X3 @ A2 ) )
% 4.69/4.97 => ( ! [Y2: filter_nat] :
% 4.69/4.97 ( ! [X6: filter_nat] :
% 4.69/4.97 ( ( member_filter_nat @ X6 @ X4 )
% 4.69/4.97 => ( ord_le2510731241096832064er_nat @ X6 @ Y2 ) )
% 4.69/4.97 => ( ord_le2510731241096832064er_nat @ A2 @ Y2 ) )
% 4.69/4.97 => ( ( comple2454491259644266675er_nat @ X4 )
% 4.69/4.97 = A2 ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_eq_non_empty
% 4.69/4.97 thf(fact_3255_cSup__eq__non__empty,axiom,
% 4.69/4.97 ! [X4: set_set_nat,A2: set_nat] :
% 4.69/4.97 ( ( X4 != bot_bot_set_set_nat )
% 4.69/4.97 => ( ! [X3: set_nat] :
% 4.69/4.97 ( ( member_set_nat @ X3 @ X4 )
% 4.69/4.97 => ( ord_less_eq_set_nat @ X3 @ A2 ) )
% 4.69/4.97 => ( ! [Y2: set_nat] :
% 4.69/4.97 ( ! [X6: set_nat] :
% 4.69/4.97 ( ( member_set_nat @ X6 @ X4 )
% 4.69/4.97 => ( ord_less_eq_set_nat @ X6 @ Y2 ) )
% 4.69/4.97 => ( ord_less_eq_set_nat @ A2 @ Y2 ) )
% 4.69/4.97 => ( ( comple7399068483239264473et_nat @ X4 )
% 4.69/4.97 = A2 ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_eq_non_empty
% 4.69/4.97 thf(fact_3256_cSup__eq__non__empty,axiom,
% 4.69/4.97 ! [X4: set_int,A2: int] :
% 4.69/4.97 ( ( X4 != bot_bot_set_int )
% 4.69/4.97 => ( ! [X3: int] :
% 4.69/4.97 ( ( member_int @ X3 @ X4 )
% 4.69/4.97 => ( ord_less_eq_int @ X3 @ A2 ) )
% 4.69/4.97 => ( ! [Y2: int] :
% 4.69/4.97 ( ! [X6: int] :
% 4.69/4.97 ( ( member_int @ X6 @ X4 )
% 4.69/4.97 => ( ord_less_eq_int @ X6 @ Y2 ) )
% 4.69/4.97 => ( ord_less_eq_int @ A2 @ Y2 ) )
% 4.69/4.97 => ( ( complete_Sup_Sup_int @ X4 )
% 4.69/4.97 = A2 ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_eq_non_empty
% 4.69/4.97 thf(fact_3257_cSup__eq__non__empty,axiom,
% 4.69/4.97 ! [X4: set_nat,A2: nat] :
% 4.69/4.97 ( ( X4 != bot_bot_set_nat )
% 4.69/4.97 => ( ! [X3: nat] :
% 4.69/4.97 ( ( member_nat @ X3 @ X4 )
% 4.69/4.97 => ( ord_less_eq_nat @ X3 @ A2 ) )
% 4.69/4.97 => ( ! [Y2: nat] :
% 4.69/4.97 ( ! [X6: nat] :
% 4.69/4.97 ( ( member_nat @ X6 @ X4 )
% 4.69/4.97 => ( ord_less_eq_nat @ X6 @ Y2 ) )
% 4.69/4.97 => ( ord_less_eq_nat @ A2 @ Y2 ) )
% 4.69/4.97 => ( ( complete_Sup_Sup_nat @ X4 )
% 4.69/4.97 = A2 ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_eq_non_empty
% 4.69/4.97 thf(fact_3258_cSup__eq__non__empty,axiom,
% 4.69/4.97 ! [X4: set_Product_unit,A2: product_unit] :
% 4.69/4.97 ( ( X4 != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ! [X3: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X3 @ X4 )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ X3 @ A2 ) )
% 4.69/4.97 => ( ! [Y2: product_unit] :
% 4.69/4.97 ( ! [X6: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X6 @ X4 )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ X6 @ Y2 ) )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ A2 @ Y2 ) )
% 4.69/4.97 => ( ( comple4687483117567863418t_unit @ X4 )
% 4.69/4.97 = A2 ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_eq_non_empty
% 4.69/4.97 thf(fact_3259_SUP__eq__const,axiom,
% 4.69/4.97 ! [I: set_nat,F: nat > set_nat,X: set_nat] :
% 4.69/4.97 ( ( I != bot_bot_set_nat )
% 4.69/4.97 => ( ! [I3: nat] :
% 4.69/4.97 ( ( member_nat @ I3 @ I )
% 4.69/4.97 => ( ( F @ I3 )
% 4.69/4.97 = X ) )
% 4.69/4.97 => ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ I ) )
% 4.69/4.97 = X ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % SUP_eq_const
% 4.69/4.97 thf(fact_3260_SUP__eq__const,axiom,
% 4.69/4.97 ! [I: set_Product_unit,F: product_unit > product_unit,X: product_unit] :
% 4.69/4.97 ( ( I != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ! [I3: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ I3 @ I )
% 4.69/4.97 => ( ( F @ I3 )
% 4.69/4.97 = X ) )
% 4.69/4.97 => ( ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ I ) )
% 4.69/4.97 = X ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % SUP_eq_const
% 4.69/4.97 thf(fact_3261_SUP__eq__const,axiom,
% 4.69/4.97 ! [I: set_o,F: $o > product_unit,X: product_unit] :
% 4.69/4.97 ( ( I != bot_bot_set_o )
% 4.69/4.97 => ( ! [I3: $o] :
% 4.69/4.97 ( ( member_o @ I3 @ I )
% 4.69/4.97 => ( ( F @ I3 )
% 4.69/4.97 = X ) )
% 4.69/4.97 => ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit2 @ F @ I ) )
% 4.69/4.97 = X ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % SUP_eq_const
% 4.69/4.97 thf(fact_3262_SUP__eq__const,axiom,
% 4.69/4.97 ! [I: set_nat,F: nat > product_unit,X: product_unit] :
% 4.69/4.97 ( ( I != bot_bot_set_nat )
% 4.69/4.97 => ( ! [I3: nat] :
% 4.69/4.97 ( ( member_nat @ I3 @ I )
% 4.69/4.97 => ( ( F @ I3 )
% 4.69/4.97 = X ) )
% 4.69/4.97 => ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ I ) )
% 4.69/4.97 = X ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % SUP_eq_const
% 4.69/4.97 thf(fact_3263_SUP__eq__const,axiom,
% 4.69/4.97 ! [I: set_int,F: int > product_unit,X: product_unit] :
% 4.69/4.97 ( ( I != bot_bot_set_int )
% 4.69/4.97 => ( ! [I3: int] :
% 4.69/4.97 ( ( member_int @ I3 @ I )
% 4.69/4.97 => ( ( F @ I3 )
% 4.69/4.97 = X ) )
% 4.69/4.97 => ( ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ I ) )
% 4.69/4.97 = X ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % SUP_eq_const
% 4.69/4.97 thf(fact_3264_SUP__eq__const,axiom,
% 4.69/4.97 ! [I: set_Pr4532377907799695533_nat_o,F: ( produc3658429121746597890et_nat > $o ) > product_unit,X: product_unit] :
% 4.69/4.97 ( ( I != bot_bo7824918357723582233_nat_o )
% 4.69/4.97 => ( ! [I3: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ( member6576561426505652726_nat_o @ I3 @ I )
% 4.69/4.97 => ( ( F @ I3 )
% 4.69/4.97 = X ) )
% 4.69/4.97 => ( ( comple4687483117567863418t_unit @ ( image_8451000719036923781t_unit @ F @ I ) )
% 4.69/4.97 = X ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % SUP_eq_const
% 4.69/4.97 thf(fact_3265_Union__disjoint,axiom,
% 4.69/4.97 ! [C5: set_set_Product_unit,A: set_Product_unit] :
% 4.69/4.97 ( ( ( inf_in4660618365625256667t_unit @ ( comple3349607820504768346t_unit @ C5 ) @ A )
% 4.69/4.97 = bot_bo3957492148770167129t_unit )
% 4.69/4.97 = ( ! [X2: set_Product_unit] :
% 4.69/4.97 ( ( member5877623283571906838t_unit @ X2 @ C5 )
% 4.69/4.97 => ( ( inf_in4660618365625256667t_unit @ X2 @ A )
% 4.69/4.97 = bot_bo3957492148770167129t_unit ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Union_disjoint
% 4.69/4.97 thf(fact_3266_Union__disjoint,axiom,
% 4.69/4.97 ! [C5: set_set_o,A: set_o] :
% 4.69/4.97 ( ( ( inf_inf_set_o @ ( comple90263536869209701_set_o @ C5 ) @ A )
% 4.69/4.97 = bot_bot_set_o )
% 4.69/4.97 = ( ! [X2: set_o] :
% 4.69/4.97 ( ( member_set_o @ X2 @ C5 )
% 4.69/4.97 => ( ( inf_inf_set_o @ X2 @ A )
% 4.69/4.97 = bot_bot_set_o ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Union_disjoint
% 4.69/4.97 thf(fact_3267_Union__disjoint,axiom,
% 4.69/4.97 ! [C5: set_set_nat,A: set_nat] :
% 4.69/4.97 ( ( ( inf_inf_set_nat @ ( comple7399068483239264473et_nat @ C5 ) @ A )
% 4.69/4.97 = bot_bot_set_nat )
% 4.69/4.97 = ( ! [X2: set_nat] :
% 4.69/4.97 ( ( member_set_nat @ X2 @ C5 )
% 4.69/4.97 => ( ( inf_inf_set_nat @ X2 @ A )
% 4.69/4.97 = bot_bot_set_nat ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Union_disjoint
% 4.69/4.97 thf(fact_3268_Union__disjoint,axiom,
% 4.69/4.97 ! [C5: set_set_int,A: set_int] :
% 4.69/4.97 ( ( ( inf_inf_set_int @ ( comple3221217463730067765et_int @ C5 ) @ A )
% 4.69/4.97 = bot_bot_set_int )
% 4.69/4.97 = ( ! [X2: set_int] :
% 4.69/4.97 ( ( member_set_int @ X2 @ C5 )
% 4.69/4.97 => ( ( inf_inf_set_int @ X2 @ A )
% 4.69/4.97 = bot_bot_set_int ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Union_disjoint
% 4.69/4.97 thf(fact_3269_Union__disjoint,axiom,
% 4.69/4.97 ! [C5: set_se1353816476878259085_nat_o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.97 ( ( ( inf_in1906310914598751387_nat_o @ ( comple3382087578465172250_nat_o @ C5 ) @ A )
% 4.69/4.97 = bot_bo7824918357723582233_nat_o )
% 4.69/4.97 = ( ! [X2: set_Pr4532377907799695533_nat_o] :
% 4.69/4.97 ( ( member1452989533377600726_nat_o @ X2 @ C5 )
% 4.69/4.97 => ( ( inf_in1906310914598751387_nat_o @ X2 @ A )
% 4.69/4.97 = bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Union_disjoint
% 4.69/4.97 thf(fact_3270_Union__empty,axiom,
% 4.69/4.97 ( ( comple3349607820504768346t_unit @ bot_bo6284674557190688313t_unit )
% 4.69/4.97 = bot_bo3957492148770167129t_unit ) ).
% 4.69/4.97
% 4.69/4.97 % Union_empty
% 4.69/4.97 thf(fact_3271_Union__empty,axiom,
% 4.69/4.97 ( ( comple90263536869209701_set_o @ bot_bot_set_set_o )
% 4.69/4.97 = bot_bot_set_o ) ).
% 4.69/4.97
% 4.69/4.97 % Union_empty
% 4.69/4.97 thf(fact_3272_Union__empty,axiom,
% 4.69/4.97 ( ( comple7399068483239264473et_nat @ bot_bot_set_set_nat )
% 4.69/4.97 = bot_bot_set_nat ) ).
% 4.69/4.97
% 4.69/4.97 % Union_empty
% 4.69/4.97 thf(fact_3273_Union__empty,axiom,
% 4.69/4.97 ( ( comple3221217463730067765et_int @ bot_bot_set_set_int )
% 4.69/4.97 = bot_bot_set_int ) ).
% 4.69/4.97
% 4.69/4.97 % Union_empty
% 4.69/4.97 thf(fact_3274_Union__empty,axiom,
% 4.69/4.97 ( ( comple3382087578465172250_nat_o @ bot_bo3736544561982865913_nat_o )
% 4.69/4.97 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/4.97
% 4.69/4.97 % Union_empty
% 4.69/4.97 thf(fact_3275_SUP__eq__iff,axiom,
% 4.69/4.97 ! [I: set_Product_unit,C: product_unit,F: product_unit > product_unit] :
% 4.69/4.97 ( ( I != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ! [I3: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ I3 @ I )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ C @ ( F @ I3 ) ) )
% 4.69/4.97 => ( ( ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ I ) )
% 4.69/4.97 = C )
% 4.69/4.97 = ( ! [X2: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X2 @ I )
% 4.69/4.97 => ( ( F @ X2 )
% 4.69/4.97 = C ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % SUP_eq_iff
% 4.69/4.97 thf(fact_3276_SUP__eq__iff,axiom,
% 4.69/4.97 ! [I: set_o,C: product_unit,F: $o > product_unit] :
% 4.69/4.97 ( ( I != bot_bot_set_o )
% 4.69/4.97 => ( ! [I3: $o] :
% 4.69/4.97 ( ( member_o @ I3 @ I )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ C @ ( F @ I3 ) ) )
% 4.69/4.97 => ( ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit2 @ F @ I ) )
% 4.69/4.97 = C )
% 4.69/4.97 = ( ! [X2: $o] :
% 4.69/4.97 ( ( member_o @ X2 @ I )
% 4.69/4.97 => ( ( F @ X2 )
% 4.69/4.97 = C ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % SUP_eq_iff
% 4.69/4.97 thf(fact_3277_SUP__eq__iff,axiom,
% 4.69/4.97 ! [I: set_nat,C: product_unit,F: nat > product_unit] :
% 4.69/4.97 ( ( I != bot_bot_set_nat )
% 4.69/4.97 => ( ! [I3: nat] :
% 4.69/4.97 ( ( member_nat @ I3 @ I )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ C @ ( F @ I3 ) ) )
% 4.69/4.97 => ( ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ I ) )
% 4.69/4.97 = C )
% 4.69/4.97 = ( ! [X2: nat] :
% 4.69/4.97 ( ( member_nat @ X2 @ I )
% 4.69/4.97 => ( ( F @ X2 )
% 4.69/4.97 = C ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % SUP_eq_iff
% 4.69/4.97 thf(fact_3278_SUP__eq__iff,axiom,
% 4.69/4.97 ! [I: set_int,C: product_unit,F: int > product_unit] :
% 4.69/4.97 ( ( I != bot_bot_set_int )
% 4.69/4.97 => ( ! [I3: int] :
% 4.69/4.97 ( ( member_int @ I3 @ I )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ C @ ( F @ I3 ) ) )
% 4.69/4.97 => ( ( ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ I ) )
% 4.69/4.97 = C )
% 4.69/4.97 = ( ! [X2: int] :
% 4.69/4.97 ( ( member_int @ X2 @ I )
% 4.69/4.97 => ( ( F @ X2 )
% 4.69/4.97 = C ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % SUP_eq_iff
% 4.69/4.97 thf(fact_3279_SUP__eq__iff,axiom,
% 4.69/4.97 ! [I: set_Product_unit,C: filter_nat,F: product_unit > filter_nat] :
% 4.69/4.97 ( ( I != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ! [I3: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ I3 @ I )
% 4.69/4.97 => ( ord_le2510731241096832064er_nat @ C @ ( F @ I3 ) ) )
% 4.69/4.97 => ( ( ( comple2454491259644266675er_nat @ ( image_1853478764106424488er_nat @ F @ I ) )
% 4.69/4.97 = C )
% 4.69/4.97 = ( ! [X2: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X2 @ I )
% 4.69/4.97 => ( ( F @ X2 )
% 4.69/4.97 = C ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % SUP_eq_iff
% 4.69/4.97 thf(fact_3280_SUP__eq__iff,axiom,
% 4.69/4.97 ! [I: set_o,C: filter_nat,F: $o > filter_nat] :
% 4.69/4.97 ( ( I != bot_bot_set_o )
% 4.69/4.97 => ( ! [I3: $o] :
% 4.69/4.97 ( ( member_o @ I3 @ I )
% 4.69/4.97 => ( ord_le2510731241096832064er_nat @ C @ ( F @ I3 ) ) )
% 4.69/4.97 => ( ( ( comple2454491259644266675er_nat @ ( image_o_filter_nat @ F @ I ) )
% 4.69/4.97 = C )
% 4.69/4.97 = ( ! [X2: $o] :
% 4.69/4.97 ( ( member_o @ X2 @ I )
% 4.69/4.97 => ( ( F @ X2 )
% 4.69/4.97 = C ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % SUP_eq_iff
% 4.69/4.97 thf(fact_3281_SUP__eq__iff,axiom,
% 4.69/4.97 ! [I: set_nat,C: filter_nat,F: nat > filter_nat] :
% 4.69/4.97 ( ( I != bot_bot_set_nat )
% 4.69/4.97 => ( ! [I3: nat] :
% 4.69/4.97 ( ( member_nat @ I3 @ I )
% 4.69/4.97 => ( ord_le2510731241096832064er_nat @ C @ ( F @ I3 ) ) )
% 4.69/4.97 => ( ( ( comple2454491259644266675er_nat @ ( image_nat_filter_nat @ F @ I ) )
% 4.69/4.97 = C )
% 4.69/4.97 = ( ! [X2: nat] :
% 4.69/4.97 ( ( member_nat @ X2 @ I )
% 4.69/4.97 => ( ( F @ X2 )
% 4.69/4.97 = C ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % SUP_eq_iff
% 4.69/4.97 thf(fact_3282_SUP__eq__iff,axiom,
% 4.69/4.97 ! [I: set_int,C: filter_nat,F: int > filter_nat] :
% 4.69/4.97 ( ( I != bot_bot_set_int )
% 4.69/4.97 => ( ! [I3: int] :
% 4.69/4.97 ( ( member_int @ I3 @ I )
% 4.69/4.97 => ( ord_le2510731241096832064er_nat @ C @ ( F @ I3 ) ) )
% 4.69/4.97 => ( ( ( comple2454491259644266675er_nat @ ( image_int_filter_nat @ F @ I ) )
% 4.69/4.97 = C )
% 4.69/4.97 = ( ! [X2: int] :
% 4.69/4.97 ( ( member_int @ X2 @ I )
% 4.69/4.97 => ( ( F @ X2 )
% 4.69/4.97 = C ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % SUP_eq_iff
% 4.69/4.97 thf(fact_3283_SUP__eq__iff,axiom,
% 4.69/4.97 ! [I: set_Product_unit,C: set_nat,F: product_unit > set_nat] :
% 4.69/4.97 ( ( I != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ! [I3: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ I3 @ I )
% 4.69/4.97 => ( ord_less_eq_set_nat @ C @ ( F @ I3 ) ) )
% 4.69/4.97 => ( ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ I ) )
% 4.69/4.97 = C )
% 4.69/4.97 = ( ! [X2: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X2 @ I )
% 4.69/4.97 => ( ( F @ X2 )
% 4.69/4.97 = C ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % SUP_eq_iff
% 4.69/4.97 thf(fact_3284_SUP__eq__iff,axiom,
% 4.69/4.97 ! [I: set_o,C: set_nat,F: $o > set_nat] :
% 4.69/4.97 ( ( I != bot_bot_set_o )
% 4.69/4.97 => ( ! [I3: $o] :
% 4.69/4.97 ( ( member_o @ I3 @ I )
% 4.69/4.97 => ( ord_less_eq_set_nat @ C @ ( F @ I3 ) ) )
% 4.69/4.97 => ( ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ I ) )
% 4.69/4.97 = C )
% 4.69/4.97 = ( ! [X2: $o] :
% 4.69/4.97 ( ( member_o @ X2 @ I )
% 4.69/4.97 => ( ( F @ X2 )
% 4.69/4.97 = C ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % SUP_eq_iff
% 4.69/4.97 thf(fact_3285_cSUP__least,axiom,
% 4.69/4.97 ! [A: set_Product_unit,F: product_unit > int,M: int] :
% 4.69/4.97 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ! [X3: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X3 @ A )
% 4.69/4.97 => ( ord_less_eq_int @ ( F @ X3 ) @ M ) )
% 4.69/4.97 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ A ) ) @ M ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_least
% 4.69/4.97 thf(fact_3286_cSUP__least,axiom,
% 4.69/4.97 ! [A: set_o,F: $o > int,M: int] :
% 4.69/4.97 ( ( A != bot_bot_set_o )
% 4.69/4.97 => ( ! [X3: $o] :
% 4.69/4.97 ( ( member_o @ X3 @ A )
% 4.69/4.97 => ( ord_less_eq_int @ ( F @ X3 ) @ M ) )
% 4.69/4.97 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_o_int2 @ F @ A ) ) @ M ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_least
% 4.69/4.97 thf(fact_3287_cSUP__least,axiom,
% 4.69/4.97 ! [A: set_nat,F: nat > int,M: int] :
% 4.69/4.97 ( ( A != bot_bot_set_nat )
% 4.69/4.97 => ( ! [X3: nat] :
% 4.69/4.97 ( ( member_nat @ X3 @ A )
% 4.69/4.97 => ( ord_less_eq_int @ ( F @ X3 ) @ M ) )
% 4.69/4.97 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_nat_int2 @ F @ A ) ) @ M ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_least
% 4.69/4.97 thf(fact_3288_cSUP__least,axiom,
% 4.69/4.97 ! [A: set_int,F: int > int,M: int] :
% 4.69/4.97 ( ( A != bot_bot_set_int )
% 4.69/4.97 => ( ! [X3: int] :
% 4.69/4.97 ( ( member_int @ X3 @ A )
% 4.69/4.97 => ( ord_less_eq_int @ ( F @ X3 ) @ M ) )
% 4.69/4.97 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_int_int2 @ F @ A ) ) @ M ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_least
% 4.69/4.97 thf(fact_3289_cSUP__least,axiom,
% 4.69/4.97 ! [A: set_Product_unit,F: product_unit > nat,M: nat] :
% 4.69/4.97 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ! [X3: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X3 @ A )
% 4.69/4.97 => ( ord_less_eq_nat @ ( F @ X3 ) @ M ) )
% 4.69/4.97 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ F @ A ) ) @ M ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_least
% 4.69/4.97 thf(fact_3290_cSUP__least,axiom,
% 4.69/4.97 ! [A: set_o,F: $o > nat,M: nat] :
% 4.69/4.97 ( ( A != bot_bot_set_o )
% 4.69/4.97 => ( ! [X3: $o] :
% 4.69/4.97 ( ( member_o @ X3 @ A )
% 4.69/4.97 => ( ord_less_eq_nat @ ( F @ X3 ) @ M ) )
% 4.69/4.97 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_o_nat2 @ F @ A ) ) @ M ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_least
% 4.69/4.97 thf(fact_3291_cSUP__least,axiom,
% 4.69/4.97 ! [A: set_nat,F: nat > nat,M: nat] :
% 4.69/4.97 ( ( A != bot_bot_set_nat )
% 4.69/4.97 => ( ! [X3: nat] :
% 4.69/4.97 ( ( member_nat @ X3 @ A )
% 4.69/4.97 => ( ord_less_eq_nat @ ( F @ X3 ) @ M ) )
% 4.69/4.97 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_nat_nat2 @ F @ A ) ) @ M ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_least
% 4.69/4.97 thf(fact_3292_cSUP__least,axiom,
% 4.69/4.97 ! [A: set_int,F: int > nat,M: nat] :
% 4.69/4.97 ( ( A != bot_bot_set_int )
% 4.69/4.97 => ( ! [X3: int] :
% 4.69/4.97 ( ( member_int @ X3 @ A )
% 4.69/4.97 => ( ord_less_eq_nat @ ( F @ X3 ) @ M ) )
% 4.69/4.97 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_int_nat2 @ F @ A ) ) @ M ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_least
% 4.69/4.97 thf(fact_3293_cSUP__least,axiom,
% 4.69/4.97 ! [A: set_Product_unit,F: product_unit > product_unit,M: product_unit] :
% 4.69/4.97 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ! [X3: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X3 @ A )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ ( F @ X3 ) @ M ) )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A ) ) @ M ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_least
% 4.69/4.97 thf(fact_3294_cSUP__least,axiom,
% 4.69/4.97 ! [A: set_o,F: $o > product_unit,M: product_unit] :
% 4.69/4.97 ( ( A != bot_bot_set_o )
% 4.69/4.97 => ( ! [X3: $o] :
% 4.69/4.97 ( ( member_o @ X3 @ A )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ ( F @ X3 ) @ M ) )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit2 @ F @ A ) ) @ M ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_least
% 4.69/4.97 thf(fact_3295_Sup__inf__eq__bot__iff,axiom,
% 4.69/4.97 ! [B4: set_set_Product_unit,A2: set_Product_unit] :
% 4.69/4.97 ( ( ( inf_in4660618365625256667t_unit @ ( comple3349607820504768346t_unit @ B4 ) @ A2 )
% 4.69/4.97 = bot_bo3957492148770167129t_unit )
% 4.69/4.97 = ( ! [X2: set_Product_unit] :
% 4.69/4.97 ( ( member5877623283571906838t_unit @ X2 @ B4 )
% 4.69/4.97 => ( ( inf_in4660618365625256667t_unit @ X2 @ A2 )
% 4.69/4.97 = bot_bo3957492148770167129t_unit ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_inf_eq_bot_iff
% 4.69/4.97 thf(fact_3296_Sup__inf__eq__bot__iff,axiom,
% 4.69/4.97 ! [B4: set_set_o,A2: set_o] :
% 4.69/4.97 ( ( ( inf_inf_set_o @ ( comple90263536869209701_set_o @ B4 ) @ A2 )
% 4.69/4.97 = bot_bot_set_o )
% 4.69/4.97 = ( ! [X2: set_o] :
% 4.69/4.97 ( ( member_set_o @ X2 @ B4 )
% 4.69/4.97 => ( ( inf_inf_set_o @ X2 @ A2 )
% 4.69/4.97 = bot_bot_set_o ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_inf_eq_bot_iff
% 4.69/4.97 thf(fact_3297_Sup__inf__eq__bot__iff,axiom,
% 4.69/4.97 ! [B4: set_set_nat,A2: set_nat] :
% 4.69/4.97 ( ( ( inf_inf_set_nat @ ( comple7399068483239264473et_nat @ B4 ) @ A2 )
% 4.69/4.97 = bot_bot_set_nat )
% 4.69/4.97 = ( ! [X2: set_nat] :
% 4.69/4.97 ( ( member_set_nat @ X2 @ B4 )
% 4.69/4.97 => ( ( inf_inf_set_nat @ X2 @ A2 )
% 4.69/4.97 = bot_bot_set_nat ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_inf_eq_bot_iff
% 4.69/4.97 thf(fact_3298_Sup__inf__eq__bot__iff,axiom,
% 4.69/4.97 ! [B4: set_set_int,A2: set_int] :
% 4.69/4.97 ( ( ( inf_inf_set_int @ ( comple3221217463730067765et_int @ B4 ) @ A2 )
% 4.69/4.97 = bot_bot_set_int )
% 4.69/4.97 = ( ! [X2: set_int] :
% 4.69/4.97 ( ( member_set_int @ X2 @ B4 )
% 4.69/4.97 => ( ( inf_inf_set_int @ X2 @ A2 )
% 4.69/4.97 = bot_bot_set_int ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_inf_eq_bot_iff
% 4.69/4.97 thf(fact_3299_Sup__inf__eq__bot__iff,axiom,
% 4.69/4.97 ! [B4: set_se1353816476878259085_nat_o,A2: set_Pr4532377907799695533_nat_o] :
% 4.69/4.97 ( ( ( inf_in1906310914598751387_nat_o @ ( comple3382087578465172250_nat_o @ B4 ) @ A2 )
% 4.69/4.97 = bot_bo7824918357723582233_nat_o )
% 4.69/4.97 = ( ! [X2: set_Pr4532377907799695533_nat_o] :
% 4.69/4.97 ( ( member1452989533377600726_nat_o @ X2 @ B4 )
% 4.69/4.97 => ( ( inf_in1906310914598751387_nat_o @ X2 @ A2 )
% 4.69/4.97 = bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_inf_eq_bot_iff
% 4.69/4.97 thf(fact_3300_Sup__inf__eq__bot__iff,axiom,
% 4.69/4.97 ! [B4: set_Product_unit,A2: product_unit] :
% 4.69/4.97 ( ( ( inf_inf_Product_unit @ ( comple4687483117567863418t_unit @ B4 ) @ A2 )
% 4.69/4.97 = bot_bot_Product_unit )
% 4.69/4.97 = ( ! [X2: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X2 @ B4 )
% 4.69/4.97 => ( ( inf_inf_Product_unit @ X2 @ A2 )
% 4.69/4.97 = bot_bot_Product_unit ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_inf_eq_bot_iff
% 4.69/4.97 thf(fact_3301_UNION__fun__upd,axiom,
% 4.69/4.97 ! [A: product_unit > set_Product_unit,I2: product_unit,B4: set_Product_unit,J2: set_Product_unit] :
% 4.69/4.97 ( ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ ( fun_up488859312337516701t_unit @ A @ I2 @ B4 ) @ J2 ) )
% 4.69/4.97 = ( sup_su793286257634532545t_unit @ ( comple3349607820504768346t_unit @ ( image_7778121751606633509t_unit @ A @ ( minus_6452836326544984404t_unit @ J2 @ ( insert_Product_unit @ I2 @ bot_bo3957492148770167129t_unit ) ) ) ) @ ( if_set_Product_unit @ ( member_Product_unit @ I2 @ J2 ) @ B4 @ bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % UNION_fun_upd
% 4.69/4.97 thf(fact_3302_UNION__fun__upd,axiom,
% 4.69/4.97 ! [A: product_unit > set_o,I2: product_unit,B4: set_o,J2: set_Product_unit] :
% 4.69/4.97 ( ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ ( fun_up1762901246852280360_set_o @ A @ I2 @ B4 ) @ J2 ) )
% 4.69/4.97 = ( sup_sup_set_o @ ( comple90263536869209701_set_o @ ( image_6930536745178679216_set_o @ A @ ( minus_6452836326544984404t_unit @ J2 @ ( insert_Product_unit @ I2 @ bot_bo3957492148770167129t_unit ) ) ) ) @ ( if_set_o @ ( member_Product_unit @ I2 @ J2 ) @ B4 @ bot_bot_set_o ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % UNION_fun_upd
% 4.69/4.97 thf(fact_3303_UNION__fun__upd,axiom,
% 4.69/4.97 ! [A: product_unit > set_nat,I2: product_unit,B4: set_nat,J2: set_Product_unit] :
% 4.69/4.97 ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ ( fun_up4569834200710200790et_nat @ A @ I2 @ B4 ) @ J2 ) )
% 4.69/4.97 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ A @ ( minus_6452836326544984404t_unit @ J2 @ ( insert_Product_unit @ I2 @ bot_bo3957492148770167129t_unit ) ) ) ) @ ( if_set_nat @ ( member_Product_unit @ I2 @ J2 ) @ B4 @ bot_bot_set_nat ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % UNION_fun_upd
% 4.69/4.97 thf(fact_3304_UNION__fun__upd,axiom,
% 4.69/4.97 ! [A: product_unit > set_int,I2: product_unit,B4: set_int,J2: set_Product_unit] :
% 4.69/4.97 ( ( comple3221217463730067765et_int @ ( image_3995998972318789802et_int @ ( fun_up391983181201004082et_int @ A @ I2 @ B4 ) @ J2 ) )
% 4.69/4.97 = ( sup_sup_set_int @ ( comple3221217463730067765et_int @ ( image_3995998972318789802et_int @ A @ ( minus_6452836326544984404t_unit @ J2 @ ( insert_Product_unit @ I2 @ bot_bo3957492148770167129t_unit ) ) ) ) @ ( if_set_int @ ( member_Product_unit @ I2 @ J2 ) @ B4 @ bot_bot_set_int ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % UNION_fun_upd
% 4.69/4.97 thf(fact_3305_UNION__fun__upd,axiom,
% 4.69/4.97 ! [A: $o > set_Product_unit,I2: $o,B4: set_Product_unit,J2: set_o] :
% 4.69/4.97 ( ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ ( fun_up4718931970374059986t_unit @ A @ I2 @ B4 ) @ J2 ) )
% 4.69/4.97 = ( sup_su793286257634532545t_unit @ ( comple3349607820504768346t_unit @ ( image_663195431845683034t_unit @ A @ ( minus_minus_set_o @ J2 @ ( insert_o @ I2 @ bot_bot_set_o ) ) ) ) @ ( if_set_Product_unit @ ( member_o @ I2 @ J2 ) @ B4 @ bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % UNION_fun_upd
% 4.69/4.97 thf(fact_3306_UNION__fun__upd,axiom,
% 4.69/4.97 ! [A: $o > set_o,I2: $o,B4: set_o,J2: set_o] :
% 4.69/4.97 ( ( comple90263536869209701_set_o @ ( image_o_set_o @ ( fun_upd_o_set_o @ A @ I2 @ B4 ) @ J2 ) )
% 4.69/4.97 = ( sup_sup_set_o @ ( comple90263536869209701_set_o @ ( image_o_set_o @ A @ ( minus_minus_set_o @ J2 @ ( insert_o @ I2 @ bot_bot_set_o ) ) ) ) @ ( if_set_o @ ( member_o @ I2 @ J2 ) @ B4 @ bot_bot_set_o ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % UNION_fun_upd
% 4.69/4.97 thf(fact_3307_UNION__fun__upd,axiom,
% 4.69/4.97 ! [A: $o > set_nat,I2: $o,B4: set_nat,J2: set_o] :
% 4.69/4.97 ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ ( fun_upd_o_set_nat @ A @ I2 @ B4 ) @ J2 ) )
% 4.69/4.97 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ A @ ( minus_minus_set_o @ J2 @ ( insert_o @ I2 @ bot_bot_set_o ) ) ) ) @ ( if_set_nat @ ( member_o @ I2 @ J2 ) @ B4 @ bot_bot_set_nat ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % UNION_fun_upd
% 4.69/4.97 thf(fact_3308_UNION__fun__upd,axiom,
% 4.69/4.97 ! [A: $o > set_int,I2: $o,B4: set_int,J2: set_o] :
% 4.69/4.97 ( ( comple3221217463730067765et_int @ ( image_o_set_int @ ( fun_upd_o_set_int @ A @ I2 @ B4 ) @ J2 ) )
% 4.69/4.97 = ( sup_sup_set_int @ ( comple3221217463730067765et_int @ ( image_o_set_int @ A @ ( minus_minus_set_o @ J2 @ ( insert_o @ I2 @ bot_bot_set_o ) ) ) ) @ ( if_set_int @ ( member_o @ I2 @ J2 ) @ B4 @ bot_bot_set_int ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % UNION_fun_upd
% 4.69/4.97 thf(fact_3309_UNION__fun__upd,axiom,
% 4.69/4.97 ! [A: int > set_Product_unit,I2: int,B4: set_Product_unit,J2: set_int] :
% 4.69/4.97 ( ( comple3349607820504768346t_unit @ ( image_8658272795163236474t_unit @ ( fun_up5054257004045450754t_unit @ A @ I2 @ B4 ) @ J2 ) )
% 4.69/4.97 = ( sup_su793286257634532545t_unit @ ( comple3349607820504768346t_unit @ ( image_8658272795163236474t_unit @ A @ ( minus_minus_set_int @ J2 @ ( insert_int @ I2 @ bot_bot_set_int ) ) ) ) @ ( if_set_Product_unit @ ( member_int @ I2 @ J2 ) @ B4 @ bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % UNION_fun_upd
% 4.69/4.97 thf(fact_3310_UNION__fun__upd,axiom,
% 4.69/4.97 ! [A: int > set_o,I2: int,B4: set_o,J2: set_int] :
% 4.69/4.97 ( ( comple90263536869209701_set_o @ ( image_int_set_o @ ( fun_upd_int_set_o @ A @ I2 @ B4 ) @ J2 ) )
% 4.69/4.97 = ( sup_sup_set_o @ ( comple90263536869209701_set_o @ ( image_int_set_o @ A @ ( minus_minus_set_int @ J2 @ ( insert_int @ I2 @ bot_bot_set_int ) ) ) ) @ ( if_set_o @ ( member_int @ I2 @ J2 ) @ B4 @ bot_bot_set_o ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % UNION_fun_upd
% 4.69/4.97 thf(fact_3311_cSUP__union,axiom,
% 4.69/4.97 ! [A: set_Product_unit,F: product_unit > nat,B4: set_Product_unit] :
% 4.69/4.97 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_875570014554754200it_nat @ F @ A ) )
% 4.69/4.97 => ( ( B4 != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_875570014554754200it_nat @ F @ B4 ) )
% 4.69/4.97 => ( ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ F @ ( sup_su793286257634532545t_unit @ A @ B4 ) ) )
% 4.69/4.97 = ( sup_sup_nat @ ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ F @ A ) ) @ ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ F @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_union
% 4.69/4.97 thf(fact_3312_cSUP__union,axiom,
% 4.69/4.97 ! [A: set_o,F: $o > nat,B4: set_o] :
% 4.69/4.97 ( ( A != bot_bot_set_o )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_o_nat2 @ F @ A ) )
% 4.69/4.97 => ( ( B4 != bot_bot_set_o )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_o_nat2 @ F @ B4 ) )
% 4.69/4.97 => ( ( complete_Sup_Sup_nat @ ( image_o_nat2 @ F @ ( sup_sup_set_o @ A @ B4 ) ) )
% 4.69/4.97 = ( sup_sup_nat @ ( complete_Sup_Sup_nat @ ( image_o_nat2 @ F @ A ) ) @ ( complete_Sup_Sup_nat @ ( image_o_nat2 @ F @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_union
% 4.69/4.97 thf(fact_3313_cSUP__union,axiom,
% 4.69/4.97 ! [A: set_nat,F: nat > nat,B4: set_nat] :
% 4.69/4.97 ( ( A != bot_bot_set_nat )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat2 @ F @ A ) )
% 4.69/4.97 => ( ( B4 != bot_bot_set_nat )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat2 @ F @ B4 ) )
% 4.69/4.97 => ( ( complete_Sup_Sup_nat @ ( image_nat_nat2 @ F @ ( sup_sup_set_nat @ A @ B4 ) ) )
% 4.69/4.97 = ( sup_sup_nat @ ( complete_Sup_Sup_nat @ ( image_nat_nat2 @ F @ A ) ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat2 @ F @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_union
% 4.69/4.97 thf(fact_3314_cSUP__union,axiom,
% 4.69/4.97 ! [A: set_int,F: int > nat,B4: set_int] :
% 4.69/4.97 ( ( A != bot_bot_set_int )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat2 @ F @ A ) )
% 4.69/4.97 => ( ( B4 != bot_bot_set_int )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat2 @ F @ B4 ) )
% 4.69/4.97 => ( ( complete_Sup_Sup_nat @ ( image_int_nat2 @ F @ ( sup_sup_set_int @ A @ B4 ) ) )
% 4.69/4.97 = ( sup_sup_nat @ ( complete_Sup_Sup_nat @ ( image_int_nat2 @ F @ A ) ) @ ( complete_Sup_Sup_nat @ ( image_int_nat2 @ F @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_union
% 4.69/4.97 thf(fact_3315_cSUP__union,axiom,
% 4.69/4.97 ! [A: set_Product_unit,F: product_unit > product_unit,B4: set_Product_unit] :
% 4.69/4.97 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ ( image_405062704495631173t_unit @ F @ A ) )
% 4.69/4.97 => ( ( B4 != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ ( image_405062704495631173t_unit @ F @ B4 ) )
% 4.69/4.97 => ( ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ ( sup_su793286257634532545t_unit @ A @ B4 ) ) )
% 4.69/4.97 = ( sup_sup_Product_unit @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A ) ) @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_union
% 4.69/4.97 thf(fact_3316_cSUP__union,axiom,
% 4.69/4.97 ! [A: set_o,F: $o > product_unit,B4: set_o] :
% 4.69/4.97 ( ( A != bot_bot_set_o )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit2 @ F @ A ) )
% 4.69/4.97 => ( ( B4 != bot_bot_set_o )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit2 @ F @ B4 ) )
% 4.69/4.97 => ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit2 @ F @ ( sup_sup_set_o @ A @ B4 ) ) )
% 4.69/4.97 = ( sup_sup_Product_unit @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit2 @ F @ A ) ) @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit2 @ F @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_union
% 4.69/4.97 thf(fact_3317_cSUP__union,axiom,
% 4.69/4.97 ! [A: set_nat,F: nat > product_unit,B4: set_nat] :
% 4.69/4.97 ( ( A != bot_bot_set_nat )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ ( image_8730104196221521654t_unit @ F @ A ) )
% 4.69/4.97 => ( ( B4 != bot_bot_set_nat )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ ( image_8730104196221521654t_unit @ F @ B4 ) )
% 4.69/4.97 => ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ ( sup_sup_set_nat @ A @ B4 ) ) )
% 4.69/4.97 = ( sup_sup_Product_unit @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A ) ) @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_union
% 4.69/4.97 thf(fact_3318_cSUP__union,axiom,
% 4.69/4.97 ! [A: set_int,F: int > product_unit,B4: set_int] :
% 4.69/4.97 ( ( A != bot_bot_set_int )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ ( image_5846526143423701914t_unit @ F @ A ) )
% 4.69/4.97 => ( ( B4 != bot_bot_set_int )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ ( image_5846526143423701914t_unit @ F @ B4 ) )
% 4.69/4.97 => ( ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ ( sup_sup_set_int @ A @ B4 ) ) )
% 4.69/4.97 = ( sup_sup_Product_unit @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A ) ) @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_union
% 4.69/4.97 thf(fact_3319_cSUP__union,axiom,
% 4.69/4.97 ! [A: set_Product_unit,F: product_unit > set_nat,B4: set_Product_unit] :
% 4.69/4.97 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit5477540289124974626et_nat @ ( image_8173849991827986510et_nat @ F @ A ) )
% 4.69/4.97 => ( ( B4 != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit5477540289124974626et_nat @ ( image_8173849991827986510et_nat @ F @ B4 ) )
% 4.69/4.97 => ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ ( sup_su793286257634532545t_unit @ A @ B4 ) ) )
% 4.69/4.97 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ A ) ) @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_union
% 4.69/4.97 thf(fact_3320_cSUP__union,axiom,
% 4.69/4.97 ! [A: set_o,F: $o > set_nat,B4: set_o] :
% 4.69/4.97 ( ( A != bot_bot_set_o )
% 4.69/4.97 => ( ( condit5477540289124974626et_nat @ ( image_o_set_nat @ F @ A ) )
% 4.69/4.97 => ( ( B4 != bot_bot_set_o )
% 4.69/4.97 => ( ( condit5477540289124974626et_nat @ ( image_o_set_nat @ F @ B4 ) )
% 4.69/4.97 => ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ ( sup_sup_set_o @ A @ B4 ) ) )
% 4.69/4.97 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A ) ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_union
% 4.69/4.97 thf(fact_3321_pair__in__swap__image,axiom,
% 4.69/4.97 ! [Y: set_nat,X: heap_e7401611519738050253t_unit,A: set_Pr3948176798113811640et_nat] :
% 4.69/4.97 ( ( member727419437372278867t_unit @ ( produc2471974422597015918t_unit @ Y @ X ) @ ( image_1893317993577548229t_unit @ produc6300697153377358172et_nat @ A ) )
% 4.69/4.97 = ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X @ Y ) @ A ) ) ).
% 4.69/4.97
% 4.69/4.97 % pair_in_swap_image
% 4.69/4.97 thf(fact_3322_pair__in__swap__image,axiom,
% 4.69/4.97 ! [Y: produc3658429121746597890et_nat,X: produc3658429121746597890et_nat > $o,A: set_Pr3286484037609594932et_nat] :
% 4.69/4.97 ( ( member4978015717948814295_nat_o @ ( produc2829238748666232050_nat_o @ Y @ X ) @ ( image_6229134628169569989_nat_o @ produc3251101204053596376et_nat @ A ) )
% 4.69/4.97 = ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) @ A ) ) ).
% 4.69/4.97
% 4.69/4.97 % pair_in_swap_image
% 4.69/4.97 thf(fact_3323_pair__in__swap__image,axiom,
% 4.69/4.97 ! [Y: produc3925858234332021118et_nat,X: produc3658429121746597890et_nat > $o,A: set_Pr8536935166611901872et_nat] :
% 4.69/4.97 ( ( member8354763867512313179_nat_o @ ( produc3674526432113299062_nat_o @ Y @ X ) @ ( image_4071802983491761093_nat_o @ produc1151471490888544852et_nat @ A ) )
% 4.69/4.97 = ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) @ A ) ) ).
% 4.69/4.97
% 4.69/4.97 % pair_in_swap_image
% 4.69/4.97 thf(fact_3324_pair__in__swap__image,axiom,
% 4.69/4.97 ! [Y: heap_e7401611519738050253t_unit,X: set_nat,A: set_Pr4071100604818519410t_unit] :
% 4.69/4.97 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ Y @ X ) @ ( image_5838825082199883205et_nat @ produc1264744871843189710t_unit @ A ) )
% 4.69/4.97 = ( member727419437372278867t_unit @ ( produc2471974422597015918t_unit @ X @ Y ) @ A ) ) ).
% 4.69/4.97
% 4.69/4.97 % pair_in_swap_image
% 4.69/4.97 thf(fact_3325_pair__in__swap__image,axiom,
% 4.69/4.97 ! [Y: nat,X: nat,A: set_Pr1261947904930325089at_nat] :
% 4.69/4.97 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ X ) @ ( image_5168914502847457605at_nat @ product_swap_nat_nat @ A ) )
% 4.69/4.97 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ A ) ) ).
% 4.69/4.97
% 4.69/4.97 % pair_in_swap_image
% 4.69/4.97 thf(fact_3326_pair__in__swap__image,axiom,
% 4.69/4.97 ! [Y: int,X: int,A: set_Pr958786334691620121nt_int] :
% 4.69/4.97 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y @ X ) @ ( image_2653370878348428101nt_int @ product_swap_int_int @ A ) )
% 4.69/4.97 = ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ A ) ) ).
% 4.69/4.97
% 4.69/4.97 % pair_in_swap_image
% 4.69/4.97 thf(fact_3327_pair__in__swap__image,axiom,
% 4.69/4.97 ! [Y: produc3658429121746597890et_nat > $o,X: produc3658429121746597890et_nat,A: set_Pr4208978187861016310_nat_o] :
% 4.69/4.97 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ Y @ X ) @ ( image_4501728140019976901et_nat @ produc1078497009909708626_nat_o @ A ) )
% 4.69/4.97 = ( member4978015717948814295_nat_o @ ( produc2829238748666232050_nat_o @ X @ Y ) @ A ) ) ).
% 4.69/4.97
% 4.69/4.97 % pair_in_swap_image
% 4.69/4.97 thf(fact_3328_pair__in__swap__image,axiom,
% 4.69/4.97 ! [Y: produc3658429121746597890et_nat > $o,X: produc3925858234332021118et_nat,A: set_Pr7705059561495379578_nat_o] :
% 4.69/4.97 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ Y @ X ) @ ( image_7255662321850427333et_nat @ produc2580581461503396054_nat_o @ A ) )
% 4.69/4.97 = ( member8354763867512313179_nat_o @ ( produc3674526432113299062_nat_o @ X @ Y ) @ A ) ) ).
% 4.69/4.97
% 4.69/4.97 % pair_in_swap_image
% 4.69/4.97 thf(fact_3329_cSUP__insert,axiom,
% 4.69/4.97 ! [A: set_Product_unit,F: product_unit > nat,A2: product_unit] :
% 4.69/4.97 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_875570014554754200it_nat @ F @ A ) )
% 4.69/4.97 => ( ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ F @ ( insert_Product_unit @ A2 @ A ) ) )
% 4.69/4.97 = ( sup_sup_nat @ ( F @ A2 ) @ ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ F @ A ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_insert
% 4.69/4.97 thf(fact_3330_cSUP__insert,axiom,
% 4.69/4.97 ! [A: set_o,F: $o > nat,A2: $o] :
% 4.69/4.97 ( ( A != bot_bot_set_o )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_o_nat2 @ F @ A ) )
% 4.69/4.97 => ( ( complete_Sup_Sup_nat @ ( image_o_nat2 @ F @ ( insert_o @ A2 @ A ) ) )
% 4.69/4.97 = ( sup_sup_nat @ ( F @ A2 ) @ ( complete_Sup_Sup_nat @ ( image_o_nat2 @ F @ A ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_insert
% 4.69/4.97 thf(fact_3331_cSUP__insert,axiom,
% 4.69/4.97 ! [A: set_nat,F: nat > nat,A2: nat] :
% 4.69/4.97 ( ( A != bot_bot_set_nat )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat2 @ F @ A ) )
% 4.69/4.97 => ( ( complete_Sup_Sup_nat @ ( image_nat_nat2 @ F @ ( insert_nat @ A2 @ A ) ) )
% 4.69/4.97 = ( sup_sup_nat @ ( F @ A2 ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat2 @ F @ A ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_insert
% 4.69/4.97 thf(fact_3332_cSUP__insert,axiom,
% 4.69/4.97 ! [A: set_int,F: int > nat,A2: int] :
% 4.69/4.97 ( ( A != bot_bot_set_int )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat2 @ F @ A ) )
% 4.69/4.97 => ( ( complete_Sup_Sup_nat @ ( image_int_nat2 @ F @ ( insert_int @ A2 @ A ) ) )
% 4.69/4.97 = ( sup_sup_nat @ ( F @ A2 ) @ ( complete_Sup_Sup_nat @ ( image_int_nat2 @ F @ A ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_insert
% 4.69/4.97 thf(fact_3333_cSUP__insert,axiom,
% 4.69/4.97 ! [A: set_Product_unit,F: product_unit > product_unit,A2: product_unit] :
% 4.69/4.97 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ ( image_405062704495631173t_unit @ F @ A ) )
% 4.69/4.97 => ( ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ ( insert_Product_unit @ A2 @ A ) ) )
% 4.69/4.97 = ( sup_sup_Product_unit @ ( F @ A2 ) @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_insert
% 4.69/4.97 thf(fact_3334_cSUP__insert,axiom,
% 4.69/4.97 ! [A: set_o,F: $o > product_unit,A2: $o] :
% 4.69/4.97 ( ( A != bot_bot_set_o )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit2 @ F @ A ) )
% 4.69/4.97 => ( ( comple4687483117567863418t_unit @ ( image_o_Product_unit2 @ F @ ( insert_o @ A2 @ A ) ) )
% 4.69/4.97 = ( sup_sup_Product_unit @ ( F @ A2 ) @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit2 @ F @ A ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_insert
% 4.69/4.97 thf(fact_3335_cSUP__insert,axiom,
% 4.69/4.97 ! [A: set_nat,F: nat > product_unit,A2: nat] :
% 4.69/4.97 ( ( A != bot_bot_set_nat )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ ( image_8730104196221521654t_unit @ F @ A ) )
% 4.69/4.97 => ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ ( insert_nat @ A2 @ A ) ) )
% 4.69/4.97 = ( sup_sup_Product_unit @ ( F @ A2 ) @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_insert
% 4.69/4.97 thf(fact_3336_cSUP__insert,axiom,
% 4.69/4.97 ! [A: set_int,F: int > product_unit,A2: int] :
% 4.69/4.97 ( ( A != bot_bot_set_int )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ ( image_5846526143423701914t_unit @ F @ A ) )
% 4.69/4.97 => ( ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ ( insert_int @ A2 @ A ) ) )
% 4.69/4.97 = ( sup_sup_Product_unit @ ( F @ A2 ) @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_insert
% 4.69/4.97 thf(fact_3337_cSUP__insert,axiom,
% 4.69/4.97 ! [A: set_Product_unit,F: product_unit > set_nat,A2: product_unit] :
% 4.69/4.97 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit5477540289124974626et_nat @ ( image_8173849991827986510et_nat @ F @ A ) )
% 4.69/4.97 => ( ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ ( insert_Product_unit @ A2 @ A ) ) )
% 4.69/4.97 = ( sup_sup_set_nat @ ( F @ A2 ) @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ A ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_insert
% 4.69/4.97 thf(fact_3338_cSUP__insert,axiom,
% 4.69/4.97 ! [A: set_o,F: $o > set_nat,A2: $o] :
% 4.69/4.97 ( ( A != bot_bot_set_o )
% 4.69/4.97 => ( ( condit5477540289124974626et_nat @ ( image_o_set_nat @ F @ A ) )
% 4.69/4.97 => ( ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ ( insert_o @ A2 @ A ) ) )
% 4.69/4.97 = ( sup_sup_set_nat @ ( F @ A2 ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_insert
% 4.69/4.97 thf(fact_3339_cSup__inter__less__eq,axiom,
% 4.69/4.97 ! [A: set_o,B4: set_o] :
% 4.69/4.97 ( ( condit5488710616941104124bove_o @ A )
% 4.69/4.97 => ( ( condit5488710616941104124bove_o @ B4 )
% 4.69/4.97 => ( ( ( inf_inf_set_o @ A @ B4 )
% 4.69/4.97 != bot_bot_set_o )
% 4.69/4.97 => ( ord_less_eq_o @ ( complete_Sup_Sup_o @ ( inf_inf_set_o @ A @ B4 ) ) @ ( sup_sup_o @ ( complete_Sup_Sup_o @ A ) @ ( complete_Sup_Sup_o @ B4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_inter_less_eq
% 4.69/4.97 thf(fact_3340_cSup__inter__less__eq,axiom,
% 4.69/4.97 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.97 ( ( condit4352657709669162033_nat_o @ A )
% 4.69/4.97 => ( ( condit4352657709669162033_nat_o @ B4 )
% 4.69/4.97 => ( ( ( inf_in1906310914598751387_nat_o @ A @ B4 )
% 4.69/4.97 != bot_bo7824918357723582233_nat_o )
% 4.69/4.97 => ( ord_le729326519192465773_nat_o @ ( comple4225350640907012154_nat_o @ ( inf_in1906310914598751387_nat_o @ A @ B4 ) ) @ ( sup_su5453871518329203617_nat_o @ ( comple4225350640907012154_nat_o @ A ) @ ( comple4225350640907012154_nat_o @ B4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_inter_less_eq
% 4.69/4.97 thf(fact_3341_cSup__inter__less__eq,axiom,
% 4.69/4.97 ! [A: set_filter_nat,B4: set_filter_nat] :
% 4.69/4.97 ( ( condit4029664723990530684er_nat @ A )
% 4.69/4.97 => ( ( condit4029664723990530684er_nat @ B4 )
% 4.69/4.97 => ( ( ( inf_in7395780696554941096er_nat @ A @ B4 )
% 4.69/4.97 != bot_bo498966703094740906er_nat )
% 4.69/4.97 => ( ord_le2510731241096832064er_nat @ ( comple2454491259644266675er_nat @ ( inf_in7395780696554941096er_nat @ A @ B4 ) ) @ ( sup_sup_filter_nat @ ( comple2454491259644266675er_nat @ A ) @ ( comple2454491259644266675er_nat @ B4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_inter_less_eq
% 4.69/4.97 thf(fact_3342_cSup__inter__less__eq,axiom,
% 4.69/4.97 ! [A: set_set_nat,B4: set_set_nat] :
% 4.69/4.97 ( ( condit5477540289124974626et_nat @ A )
% 4.69/4.97 => ( ( condit5477540289124974626et_nat @ B4 )
% 4.69/4.97 => ( ( ( inf_inf_set_set_nat @ A @ B4 )
% 4.69/4.97 != bot_bot_set_set_nat )
% 4.69/4.97 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( inf_inf_set_set_nat @ A @ B4 ) ) @ ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ A ) @ ( comple7399068483239264473et_nat @ B4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_inter_less_eq
% 4.69/4.97 thf(fact_3343_cSup__inter__less__eq,axiom,
% 4.69/4.97 ! [A: set_int,B4: set_int] :
% 4.69/4.97 ( ( condit2212336002400062152ve_int @ A )
% 4.69/4.97 => ( ( condit2212336002400062152ve_int @ B4 )
% 4.69/4.97 => ( ( ( inf_inf_set_int @ A @ B4 )
% 4.69/4.97 != bot_bot_set_int )
% 4.69/4.97 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( inf_inf_set_int @ A @ B4 ) ) @ ( sup_sup_int @ ( complete_Sup_Sup_int @ A ) @ ( complete_Sup_Sup_int @ B4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_inter_less_eq
% 4.69/4.97 thf(fact_3344_cSup__inter__less__eq,axiom,
% 4.69/4.97 ! [A: set_nat,B4: set_nat] :
% 4.69/4.97 ( ( condit2214826472909112428ve_nat @ A )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ B4 )
% 4.69/4.97 => ( ( ( inf_inf_set_nat @ A @ B4 )
% 4.69/4.97 != bot_bot_set_nat )
% 4.69/4.97 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( inf_inf_set_nat @ A @ B4 ) ) @ ( sup_sup_nat @ ( complete_Sup_Sup_nat @ A ) @ ( complete_Sup_Sup_nat @ B4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_inter_less_eq
% 4.69/4.97 thf(fact_3345_cSup__inter__less__eq,axiom,
% 4.69/4.97 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.97 ( ( condit2080475194861589617t_unit @ A )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ B4 )
% 4.69/4.97 => ( ( ( inf_in4660618365625256667t_unit @ A @ B4 )
% 4.69/4.97 != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( inf_in4660618365625256667t_unit @ A @ B4 ) ) @ ( sup_sup_Product_unit @ ( comple4687483117567863418t_unit @ A ) @ ( comple4687483117567863418t_unit @ B4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_inter_less_eq
% 4.69/4.97 thf(fact_3346_cSUP__subset__mono,axiom,
% 4.69/4.97 ! [A: set_Product_unit,G: product_unit > int,B4: set_Product_unit,F: product_unit > int] :
% 4.69/4.97 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit2212336002400062152ve_int @ ( image_873079544045703924it_int @ G @ B4 ) )
% 4.69/4.97 => ( ( ord_le3507040750410214029t_unit @ A @ B4 )
% 4.69/4.97 => ( ! [X3: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X3 @ A )
% 4.69/4.97 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 4.69/4.97 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ A ) ) @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ G @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_subset_mono
% 4.69/4.97 thf(fact_3347_cSUP__subset__mono,axiom,
% 4.69/4.97 ! [A: set_o,G: $o > int,B4: set_o,F: $o > int] :
% 4.69/4.97 ( ( A != bot_bot_set_o )
% 4.69/4.97 => ( ( condit2212336002400062152ve_int @ ( image_o_int2 @ G @ B4 ) )
% 4.69/4.97 => ( ( ord_less_eq_set_o @ A @ B4 )
% 4.69/4.97 => ( ! [X3: $o] :
% 4.69/4.97 ( ( member_o @ X3 @ A )
% 4.69/4.97 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 4.69/4.97 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_o_int2 @ F @ A ) ) @ ( complete_Sup_Sup_int @ ( image_o_int2 @ G @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_subset_mono
% 4.69/4.97 thf(fact_3348_cSUP__subset__mono,axiom,
% 4.69/4.97 ! [A: set_int,G: int > int,B4: set_int,F: int > int] :
% 4.69/4.97 ( ( A != bot_bot_set_int )
% 4.69/4.97 => ( ( condit2212336002400062152ve_int @ ( image_int_int2 @ G @ B4 ) )
% 4.69/4.97 => ( ( ord_less_eq_set_int @ A @ B4 )
% 4.69/4.97 => ( ! [X3: int] :
% 4.69/4.97 ( ( member_int @ X3 @ A )
% 4.69/4.97 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 4.69/4.97 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_int_int2 @ F @ A ) ) @ ( complete_Sup_Sup_int @ ( image_int_int2 @ G @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_subset_mono
% 4.69/4.97 thf(fact_3349_cSUP__subset__mono,axiom,
% 4.69/4.97 ! [A: set_nat,G: nat > int,B4: set_nat,F: nat > int] :
% 4.69/4.97 ( ( A != bot_bot_set_nat )
% 4.69/4.97 => ( ( condit2212336002400062152ve_int @ ( image_nat_int2 @ G @ B4 ) )
% 4.69/4.97 => ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.97 => ( ! [X3: nat] :
% 4.69/4.97 ( ( member_nat @ X3 @ A )
% 4.69/4.97 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 4.69/4.97 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_nat_int2 @ F @ A ) ) @ ( complete_Sup_Sup_int @ ( image_nat_int2 @ G @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_subset_mono
% 4.69/4.97 thf(fact_3350_cSUP__subset__mono,axiom,
% 4.69/4.97 ! [A: set_Product_unit,G: product_unit > nat,B4: set_Product_unit,F: product_unit > nat] :
% 4.69/4.97 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_875570014554754200it_nat @ G @ B4 ) )
% 4.69/4.97 => ( ( ord_le3507040750410214029t_unit @ A @ B4 )
% 4.69/4.97 => ( ! [X3: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X3 @ A )
% 4.69/4.97 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 4.69/4.97 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ F @ A ) ) @ ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ G @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_subset_mono
% 4.69/4.97 thf(fact_3351_cSUP__subset__mono,axiom,
% 4.69/4.97 ! [A: set_o,G: $o > nat,B4: set_o,F: $o > nat] :
% 4.69/4.97 ( ( A != bot_bot_set_o )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_o_nat2 @ G @ B4 ) )
% 4.69/4.97 => ( ( ord_less_eq_set_o @ A @ B4 )
% 4.69/4.97 => ( ! [X3: $o] :
% 4.69/4.97 ( ( member_o @ X3 @ A )
% 4.69/4.97 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 4.69/4.97 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_o_nat2 @ F @ A ) ) @ ( complete_Sup_Sup_nat @ ( image_o_nat2 @ G @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_subset_mono
% 4.69/4.97 thf(fact_3352_cSUP__subset__mono,axiom,
% 4.69/4.97 ! [A: set_int,G: int > nat,B4: set_int,F: int > nat] :
% 4.69/4.97 ( ( A != bot_bot_set_int )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat2 @ G @ B4 ) )
% 4.69/4.97 => ( ( ord_less_eq_set_int @ A @ B4 )
% 4.69/4.97 => ( ! [X3: int] :
% 4.69/4.97 ( ( member_int @ X3 @ A )
% 4.69/4.97 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 4.69/4.97 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_int_nat2 @ F @ A ) ) @ ( complete_Sup_Sup_nat @ ( image_int_nat2 @ G @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_subset_mono
% 4.69/4.97 thf(fact_3353_cSUP__subset__mono,axiom,
% 4.69/4.97 ! [A: set_nat,G: nat > nat,B4: set_nat,F: nat > nat] :
% 4.69/4.97 ( ( A != bot_bot_set_nat )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat2 @ G @ B4 ) )
% 4.69/4.97 => ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.97 => ( ! [X3: nat] :
% 4.69/4.97 ( ( member_nat @ X3 @ A )
% 4.69/4.97 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 4.69/4.97 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_nat_nat2 @ F @ A ) ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat2 @ G @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_subset_mono
% 4.69/4.97 thf(fact_3354_cSUP__subset__mono,axiom,
% 4.69/4.97 ! [A: set_Product_unit,G: product_unit > product_unit,B4: set_Product_unit,F: product_unit > product_unit] :
% 4.69/4.97 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ ( image_405062704495631173t_unit @ G @ B4 ) )
% 4.69/4.97 => ( ( ord_le3507040750410214029t_unit @ A @ B4 )
% 4.69/4.97 => ( ! [X3: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X3 @ A )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A ) ) @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ G @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_subset_mono
% 4.69/4.97 thf(fact_3355_cSUP__subset__mono,axiom,
% 4.69/4.97 ! [A: set_o,G: $o > product_unit,B4: set_o,F: $o > product_unit] :
% 4.69/4.97 ( ( A != bot_bot_set_o )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit2 @ G @ B4 ) )
% 4.69/4.97 => ( ( ord_less_eq_set_o @ A @ B4 )
% 4.69/4.97 => ( ! [X3: $o] :
% 4.69/4.97 ( ( member_o @ X3 @ A )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit2 @ F @ A ) ) @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit2 @ G @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_subset_mono
% 4.69/4.97 thf(fact_3356_Image__Int__eq,axiom,
% 4.69/4.97 ! [R3: set_Pr1261947904930325089at_nat,A: set_nat,B4: set_nat] :
% 4.69/4.97 ( ( single5507084439971879973at_nat @ ( converse_nat_nat @ R3 ) )
% 4.69/4.97 => ( ( image_nat_nat @ R3 @ ( inf_inf_set_nat @ A @ B4 ) )
% 4.69/4.97 = ( inf_inf_set_nat @ ( image_nat_nat @ R3 @ A ) @ ( image_nat_nat @ R3 @ B4 ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Image_Int_eq
% 4.69/4.97 thf(fact_3357_image__update,axiom,
% 4.69/4.97 ! [X: code_integer,A: set_Code_integer,F: code_integer > code_integer,N2: code_integer] :
% 4.69/4.97 ( ~ ( member_Code_integer @ X @ A )
% 4.69/4.97 => ( ( image_4470545334726330049nteger @ ( fun_up8355007323143964473nteger @ F @ X @ N2 ) @ A )
% 4.69/4.97 = ( image_4470545334726330049nteger @ F @ A ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % image_update
% 4.69/4.97 thf(fact_3358_image__update,axiom,
% 4.69/4.97 ! [X: nat,A: set_nat,F: nat > set_nat,N2: set_nat] :
% 4.69/4.97 ( ~ ( member_nat @ X @ A )
% 4.69/4.97 => ( ( image_nat_set_nat @ ( fun_upd_nat_set_nat @ F @ X @ N2 ) @ A )
% 4.69/4.97 = ( image_nat_set_nat @ F @ A ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % image_update
% 4.69/4.97 thf(fact_3359_image__update,axiom,
% 4.69/4.97 ! [X: nat,A: set_nat,F: nat > nat,N2: nat] :
% 4.69/4.97 ( ~ ( member_nat @ X @ A )
% 4.69/4.97 => ( ( image_nat_nat2 @ ( fun_upd_nat_nat @ F @ X @ N2 ) @ A )
% 4.69/4.97 = ( image_nat_nat2 @ F @ A ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % image_update
% 4.69/4.97 thf(fact_3360_image__update,axiom,
% 4.69/4.97 ! [X: nat,A: set_nat,F: nat > code_integer,N2: code_integer] :
% 4.69/4.97 ( ~ ( member_nat @ X @ A )
% 4.69/4.97 => ( ( image_1215581382706833972nteger @ ( fun_up3904115110581602988nteger @ F @ X @ N2 ) @ A )
% 4.69/4.97 = ( image_1215581382706833972nteger @ F @ A ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % image_update
% 4.69/4.97 thf(fact_3361_bdd__above__empty,axiom,
% 4.69/4.97 condit2080475194861589617t_unit @ bot_bo3957492148770167129t_unit ).
% 4.69/4.97
% 4.69/4.97 % bdd_above_empty
% 4.69/4.97 thf(fact_3362_bdd__above__empty,axiom,
% 4.69/4.97 condit5488710616941104124bove_o @ bot_bot_set_o ).
% 4.69/4.97
% 4.69/4.97 % bdd_above_empty
% 4.69/4.97 thf(fact_3363_bdd__above__empty,axiom,
% 4.69/4.97 condit2214826472909112428ve_nat @ bot_bot_set_nat ).
% 4.69/4.97
% 4.69/4.97 % bdd_above_empty
% 4.69/4.97 thf(fact_3364_bdd__above__empty,axiom,
% 4.69/4.97 condit2212336002400062152ve_int @ bot_bot_set_int ).
% 4.69/4.97
% 4.69/4.97 % bdd_above_empty
% 4.69/4.97 thf(fact_3365_bdd__above__empty,axiom,
% 4.69/4.97 condit4352657709669162033_nat_o @ bot_bo7824918357723582233_nat_o ).
% 4.69/4.97
% 4.69/4.97 % bdd_above_empty
% 4.69/4.97 thf(fact_3366_bdd__above__insert,axiom,
% 4.69/4.97 ! [A2: nat,A: set_nat] :
% 4.69/4.97 ( ( condit2214826472909112428ve_nat @ ( insert_nat @ A2 @ A ) )
% 4.69/4.97 = ( condit2214826472909112428ve_nat @ A ) ) ).
% 4.69/4.97
% 4.69/4.97 % bdd_above_insert
% 4.69/4.97 thf(fact_3367_bdd__above__insert,axiom,
% 4.69/4.97 ! [A2: int,A: set_int] :
% 4.69/4.97 ( ( condit2212336002400062152ve_int @ ( insert_int @ A2 @ A ) )
% 4.69/4.97 = ( condit2212336002400062152ve_int @ A ) ) ).
% 4.69/4.97
% 4.69/4.97 % bdd_above_insert
% 4.69/4.97 thf(fact_3368_bdd__above__insert,axiom,
% 4.69/4.97 ! [A2: $o,A: set_o] :
% 4.69/4.97 ( ( condit5488710616941104124bove_o @ ( insert_o @ A2 @ A ) )
% 4.69/4.97 = ( condit5488710616941104124bove_o @ A ) ) ).
% 4.69/4.97
% 4.69/4.97 % bdd_above_insert
% 4.69/4.97 thf(fact_3369_bdd__above__insert,axiom,
% 4.69/4.97 ! [A2: product_unit,A: set_Product_unit] :
% 4.69/4.97 ( ( condit2080475194861589617t_unit @ ( insert_Product_unit @ A2 @ A ) )
% 4.69/4.97 = ( condit2080475194861589617t_unit @ A ) ) ).
% 4.69/4.97
% 4.69/4.97 % bdd_above_insert
% 4.69/4.97 thf(fact_3370_swap__simp,axiom,
% 4.69/4.97 ! [X: set_nat,Y: heap_e7401611519738050253t_unit] :
% 4.69/4.97 ( ( produc1264744871843189710t_unit @ ( produc2471974422597015918t_unit @ X @ Y ) )
% 4.69/4.97 = ( produc7507926704131184380et_nat @ Y @ X ) ) ).
% 4.69/4.97
% 4.69/4.97 % swap_simp
% 4.69/4.97 thf(fact_3371_swap__simp,axiom,
% 4.69/4.97 ! [X: produc3658429121746597890et_nat,Y: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ( produc1078497009909708626_nat_o @ ( produc2829238748666232050_nat_o @ X @ Y ) )
% 4.69/4.97 = ( produc5001842942810119800et_nat @ Y @ X ) ) ).
% 4.69/4.97
% 4.69/4.97 % swap_simp
% 4.69/4.97 thf(fact_3372_swap__simp,axiom,
% 4.69/4.97 ! [X: produc3925858234332021118et_nat,Y: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ( produc2580581461503396054_nat_o @ ( produc3674526432113299062_nat_o @ X @ Y ) )
% 4.69/4.97 = ( produc2245416461498447860et_nat @ Y @ X ) ) ).
% 4.69/4.97
% 4.69/4.97 % swap_simp
% 4.69/4.97 thf(fact_3373_swap__simp,axiom,
% 4.69/4.97 ! [X: heap_e7401611519738050253t_unit,Y: set_nat] :
% 4.69/4.97 ( ( produc6300697153377358172et_nat @ ( produc7507926704131184380et_nat @ X @ Y ) )
% 4.69/4.97 = ( produc2471974422597015918t_unit @ Y @ X ) ) ).
% 4.69/4.97
% 4.69/4.97 % swap_simp
% 4.69/4.97 thf(fact_3374_swap__simp,axiom,
% 4.69/4.97 ! [X: nat,Y: nat] :
% 4.69/4.97 ( ( product_swap_nat_nat @ ( product_Pair_nat_nat @ X @ Y ) )
% 4.69/4.97 = ( product_Pair_nat_nat @ Y @ X ) ) ).
% 4.69/4.97
% 4.69/4.97 % swap_simp
% 4.69/4.97 thf(fact_3375_swap__simp,axiom,
% 4.69/4.97 ! [X: int,Y: int] :
% 4.69/4.97 ( ( product_swap_int_int @ ( product_Pair_int_int @ X @ Y ) )
% 4.69/4.97 = ( product_Pair_int_int @ Y @ X ) ) ).
% 4.69/4.97
% 4.69/4.97 % swap_simp
% 4.69/4.97 thf(fact_3376_swap__simp,axiom,
% 4.69/4.97 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 4.69/4.97 ( ( produc3251101204053596376et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 4.69/4.97 = ( produc2829238748666232050_nat_o @ Y @ X ) ) ).
% 4.69/4.97
% 4.69/4.97 % swap_simp
% 4.69/4.97 thf(fact_3377_swap__simp,axiom,
% 4.69/4.97 ! [X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 4.69/4.97 ( ( produc1151471490888544852et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 4.69/4.97 = ( produc3674526432113299062_nat_o @ Y @ X ) ) ).
% 4.69/4.97
% 4.69/4.97 % swap_simp
% 4.69/4.97 thf(fact_3378_single__valuedD,axiom,
% 4.69/4.97 ! [R2: set_Pr3948176798113811640et_nat,X: heap_e7401611519738050253t_unit,Y: set_nat,Z: set_nat] :
% 4.69/4.97 ( ( single6620584844202787856et_nat @ R2 )
% 4.69/4.97 => ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X @ Y ) @ R2 )
% 4.69/4.97 => ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X @ Z ) @ R2 )
% 4.69/4.97 => ( Y = Z ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % single_valuedD
% 4.69/4.97 thf(fact_3379_single__valuedD,axiom,
% 4.69/4.97 ! [R2: set_Pr1261947904930325089at_nat,X: nat,Y: nat,Z: nat] :
% 4.69/4.97 ( ( single5507084439971879973at_nat @ R2 )
% 4.69/4.97 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R2 )
% 4.69/4.97 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ R2 )
% 4.69/4.97 => ( Y = Z ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % single_valuedD
% 4.69/4.97 thf(fact_3380_single__valuedD,axiom,
% 4.69/4.97 ! [R2: set_Pr958786334691620121nt_int,X: int,Y: int,Z: int] :
% 4.69/4.97 ( ( single6503947681363884253nt_int @ R2 )
% 4.69/4.97 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R2 )
% 4.69/4.97 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Z ) @ R2 )
% 4.69/4.97 => ( Y = Z ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % single_valuedD
% 4.69/4.97 thf(fact_3381_single__valuedD,axiom,
% 4.69/4.97 ! [R2: set_Pr3286484037609594932et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat,Z: produc3658429121746597890et_nat] :
% 4.69/4.97 ( ( single7715245794981374860et_nat @ R2 )
% 4.69/4.97 => ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) @ R2 )
% 4.69/4.97 => ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X @ Z ) @ R2 )
% 4.69/4.97 => ( Y = Z ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % single_valuedD
% 4.69/4.97 thf(fact_3382_single__valuedD,axiom,
% 4.69/4.97 ! [R2: set_Pr8536935166611901872et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat,Z: produc3925858234332021118et_nat] :
% 4.69/4.97 ( ( single261872189793494280et_nat @ R2 )
% 4.69/4.97 => ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) @ R2 )
% 4.69/4.97 => ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X @ Z ) @ R2 )
% 4.69/4.97 => ( Y = Z ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % single_valuedD
% 4.69/4.97 thf(fact_3383_single__valuedI,axiom,
% 4.69/4.97 ! [R2: set_Pr3948176798113811640et_nat] :
% 4.69/4.97 ( ! [X3: heap_e7401611519738050253t_unit,Y2: set_nat,Z3: set_nat] :
% 4.69/4.97 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X3 @ Y2 ) @ R2 )
% 4.69/4.97 => ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X3 @ Z3 ) @ R2 )
% 4.69/4.97 => ( Y2 = Z3 ) ) )
% 4.69/4.97 => ( single6620584844202787856et_nat @ R2 ) ) ).
% 4.69/4.97
% 4.69/4.97 % single_valuedI
% 4.69/4.97 thf(fact_3384_single__valuedI,axiom,
% 4.69/4.97 ! [R2: set_Pr1261947904930325089at_nat] :
% 4.69/4.97 ( ! [X3: nat,Y2: nat,Z3: nat] :
% 4.69/4.97 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ R2 )
% 4.69/4.97 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Z3 ) @ R2 )
% 4.69/4.97 => ( Y2 = Z3 ) ) )
% 4.69/4.97 => ( single5507084439971879973at_nat @ R2 ) ) ).
% 4.69/4.97
% 4.69/4.97 % single_valuedI
% 4.69/4.97 thf(fact_3385_single__valuedI,axiom,
% 4.69/4.97 ! [R2: set_Pr958786334691620121nt_int] :
% 4.69/4.97 ( ! [X3: int,Y2: int,Z3: int] :
% 4.69/4.97 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y2 ) @ R2 )
% 4.69/4.97 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Z3 ) @ R2 )
% 4.69/4.97 => ( Y2 = Z3 ) ) )
% 4.69/4.97 => ( single6503947681363884253nt_int @ R2 ) ) ).
% 4.69/4.97
% 4.69/4.97 % single_valuedI
% 4.69/4.97 thf(fact_3386_single__valuedI,axiom,
% 4.69/4.97 ! [R2: set_Pr3286484037609594932et_nat] :
% 4.69/4.97 ( ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat,Z3: produc3658429121746597890et_nat] :
% 4.69/4.97 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y2 ) @ R2 )
% 4.69/4.97 => ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Z3 ) @ R2 )
% 4.69/4.97 => ( Y2 = Z3 ) ) )
% 4.69/4.97 => ( single7715245794981374860et_nat @ R2 ) ) ).
% 4.69/4.97
% 4.69/4.97 % single_valuedI
% 4.69/4.97 thf(fact_3387_single__valuedI,axiom,
% 4.69/4.97 ! [R2: set_Pr8536935166611901872et_nat] :
% 4.69/4.97 ( ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3925858234332021118et_nat,Z3: produc3925858234332021118et_nat] :
% 4.69/4.97 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y2 ) @ R2 )
% 4.69/4.97 => ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Z3 ) @ R2 )
% 4.69/4.97 => ( Y2 = Z3 ) ) )
% 4.69/4.97 => ( single261872189793494280et_nat @ R2 ) ) ).
% 4.69/4.97
% 4.69/4.97 % single_valuedI
% 4.69/4.97 thf(fact_3388_single__valued__def,axiom,
% 4.69/4.97 ( single6620584844202787856et_nat
% 4.69/4.97 = ( ^ [R4: set_Pr3948176798113811640et_nat] :
% 4.69/4.97 ! [X2: heap_e7401611519738050253t_unit,Y3: set_nat] :
% 4.69/4.97 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X2 @ Y3 ) @ R4 )
% 4.69/4.97 => ! [Z2: set_nat] :
% 4.69/4.97 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X2 @ Z2 ) @ R4 )
% 4.69/4.97 => ( Y3 = Z2 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % single_valued_def
% 4.69/4.97 thf(fact_3389_single__valued__def,axiom,
% 4.69/4.97 ( single5507084439971879973at_nat
% 4.69/4.97 = ( ^ [R4: set_Pr1261947904930325089at_nat] :
% 4.69/4.97 ! [X2: nat,Y3: nat] :
% 4.69/4.97 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Y3 ) @ R4 )
% 4.69/4.97 => ! [Z2: nat] :
% 4.69/4.97 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X2 @ Z2 ) @ R4 )
% 4.69/4.97 => ( Y3 = Z2 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % single_valued_def
% 4.69/4.97 thf(fact_3390_single__valued__def,axiom,
% 4.69/4.97 ( single6503947681363884253nt_int
% 4.69/4.97 = ( ^ [R4: set_Pr958786334691620121nt_int] :
% 4.69/4.97 ! [X2: int,Y3: int] :
% 4.69/4.97 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Y3 ) @ R4 )
% 4.69/4.97 => ! [Z2: int] :
% 4.69/4.97 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X2 @ Z2 ) @ R4 )
% 4.69/4.97 => ( Y3 = Z2 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % single_valued_def
% 4.69/4.97 thf(fact_3391_single__valued__def,axiom,
% 4.69/4.97 ( single7715245794981374860et_nat
% 4.69/4.97 = ( ^ [R4: set_Pr3286484037609594932et_nat] :
% 4.69/4.97 ! [X2: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] :
% 4.69/4.97 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X2 @ Y3 ) @ R4 )
% 4.69/4.97 => ! [Z2: produc3658429121746597890et_nat] :
% 4.69/4.97 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X2 @ Z2 ) @ R4 )
% 4.69/4.97 => ( Y3 = Z2 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % single_valued_def
% 4.69/4.97 thf(fact_3392_single__valued__def,axiom,
% 4.69/4.97 ( single261872189793494280et_nat
% 4.69/4.97 = ( ^ [R4: set_Pr8536935166611901872et_nat] :
% 4.69/4.97 ! [X2: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] :
% 4.69/4.97 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X2 @ Y3 ) @ R4 )
% 4.69/4.97 => ! [Z2: produc3925858234332021118et_nat] :
% 4.69/4.97 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X2 @ Z2 ) @ R4 )
% 4.69/4.97 => ( Y3 = Z2 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % single_valued_def
% 4.69/4.97 thf(fact_3393_single__valued__confluent,axiom,
% 4.69/4.97 ! [R2: set_Pr1261947904930325089at_nat,X: nat,Y: nat,Z: nat] :
% 4.69/4.97 ( ( single5507084439971879973at_nat @ R2 )
% 4.69/4.97 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.97 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.97 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ Z ) @ ( transi2905341329935302413cl_nat @ R2 ) )
% 4.69/4.97 | ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Z @ Y ) @ ( transi2905341329935302413cl_nat @ R2 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % single_valued_confluent
% 4.69/4.97 thf(fact_3394_single__valued__confluent,axiom,
% 4.69/4.97 ! [R2: set_Pr958786334691620121nt_int,X: int,Y: int,Z: int] :
% 4.69/4.97 ( ( single6503947681363884253nt_int @ R2 )
% 4.69/4.97 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.97 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Z ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.97 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y @ Z ) @ ( transi2902850859426252137cl_int @ R2 ) )
% 4.69/4.97 | ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Z @ Y ) @ ( transi2902850859426252137cl_int @ R2 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % single_valued_confluent
% 4.69/4.97 thf(fact_3395_cSup__le__iff,axiom,
% 4.69/4.97 ! [S: set_o,A2: $o] :
% 4.69/4.97 ( ( S != bot_bot_set_o )
% 4.69/4.97 => ( ( condit5488710616941104124bove_o @ S )
% 4.69/4.97 => ( ( ord_less_eq_o @ ( complete_Sup_Sup_o @ S ) @ A2 )
% 4.69/4.97 = ( ! [X2: $o] :
% 4.69/4.97 ( ( member_o @ X2 @ S )
% 4.69/4.97 => ( ord_less_eq_o @ X2 @ A2 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_le_iff
% 4.69/4.97 thf(fact_3396_cSup__le__iff,axiom,
% 4.69/4.97 ! [S: set_Pr4532377907799695533_nat_o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ( S != bot_bo7824918357723582233_nat_o )
% 4.69/4.97 => ( ( condit4352657709669162033_nat_o @ S )
% 4.69/4.97 => ( ( ord_le729326519192465773_nat_o @ ( comple4225350640907012154_nat_o @ S ) @ A2 )
% 4.69/4.97 = ( ! [X2: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ( member6576561426505652726_nat_o @ X2 @ S )
% 4.69/4.97 => ( ord_le729326519192465773_nat_o @ X2 @ A2 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_le_iff
% 4.69/4.97 thf(fact_3397_cSup__le__iff,axiom,
% 4.69/4.97 ! [S: set_filter_nat,A2: filter_nat] :
% 4.69/4.97 ( ( S != bot_bo498966703094740906er_nat )
% 4.69/4.97 => ( ( condit4029664723990530684er_nat @ S )
% 4.69/4.97 => ( ( ord_le2510731241096832064er_nat @ ( comple2454491259644266675er_nat @ S ) @ A2 )
% 4.69/4.97 = ( ! [X2: filter_nat] :
% 4.69/4.97 ( ( member_filter_nat @ X2 @ S )
% 4.69/4.97 => ( ord_le2510731241096832064er_nat @ X2 @ A2 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_le_iff
% 4.69/4.97 thf(fact_3398_cSup__le__iff,axiom,
% 4.69/4.97 ! [S: set_set_nat,A2: set_nat] :
% 4.69/4.97 ( ( S != bot_bot_set_set_nat )
% 4.69/4.97 => ( ( condit5477540289124974626et_nat @ S )
% 4.69/4.97 => ( ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ S ) @ A2 )
% 4.69/4.97 = ( ! [X2: set_nat] :
% 4.69/4.97 ( ( member_set_nat @ X2 @ S )
% 4.69/4.97 => ( ord_less_eq_set_nat @ X2 @ A2 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_le_iff
% 4.69/4.97 thf(fact_3399_cSup__le__iff,axiom,
% 4.69/4.97 ! [S: set_int,A2: int] :
% 4.69/4.97 ( ( S != bot_bot_set_int )
% 4.69/4.97 => ( ( condit2212336002400062152ve_int @ S )
% 4.69/4.97 => ( ( ord_less_eq_int @ ( complete_Sup_Sup_int @ S ) @ A2 )
% 4.69/4.97 = ( ! [X2: int] :
% 4.69/4.97 ( ( member_int @ X2 @ S )
% 4.69/4.97 => ( ord_less_eq_int @ X2 @ A2 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_le_iff
% 4.69/4.97 thf(fact_3400_cSup__le__iff,axiom,
% 4.69/4.97 ! [S: set_nat,A2: nat] :
% 4.69/4.97 ( ( S != bot_bot_set_nat )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ S )
% 4.69/4.97 => ( ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ S ) @ A2 )
% 4.69/4.97 = ( ! [X2: nat] :
% 4.69/4.97 ( ( member_nat @ X2 @ S )
% 4.69/4.97 => ( ord_less_eq_nat @ X2 @ A2 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_le_iff
% 4.69/4.97 thf(fact_3401_cSup__le__iff,axiom,
% 4.69/4.97 ! [S: set_Product_unit,A2: product_unit] :
% 4.69/4.97 ( ( S != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ S )
% 4.69/4.97 => ( ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ S ) @ A2 )
% 4.69/4.97 = ( ! [X2: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X2 @ S )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ X2 @ A2 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_le_iff
% 4.69/4.97 thf(fact_3402_cSup__mono,axiom,
% 4.69/4.97 ! [B4: set_o,A: set_o] :
% 4.69/4.97 ( ( B4 != bot_bot_set_o )
% 4.69/4.97 => ( ( condit5488710616941104124bove_o @ A )
% 4.69/4.97 => ( ! [B2: $o] :
% 4.69/4.97 ( ( member_o @ B2 @ B4 )
% 4.69/4.97 => ? [X6: $o] :
% 4.69/4.97 ( ( member_o @ X6 @ A )
% 4.69/4.97 & ( ord_less_eq_o @ B2 @ X6 ) ) )
% 4.69/4.97 => ( ord_less_eq_o @ ( complete_Sup_Sup_o @ B4 ) @ ( complete_Sup_Sup_o @ A ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_mono
% 4.69/4.97 thf(fact_3403_cSup__mono,axiom,
% 4.69/4.97 ! [B4: set_Pr4532377907799695533_nat_o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.97 ( ( B4 != bot_bo7824918357723582233_nat_o )
% 4.69/4.97 => ( ( condit4352657709669162033_nat_o @ A )
% 4.69/4.97 => ( ! [B2: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ( member6576561426505652726_nat_o @ B2 @ B4 )
% 4.69/4.97 => ? [X6: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ( member6576561426505652726_nat_o @ X6 @ A )
% 4.69/4.97 & ( ord_le729326519192465773_nat_o @ B2 @ X6 ) ) )
% 4.69/4.97 => ( ord_le729326519192465773_nat_o @ ( comple4225350640907012154_nat_o @ B4 ) @ ( comple4225350640907012154_nat_o @ A ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_mono
% 4.69/4.97 thf(fact_3404_cSup__mono,axiom,
% 4.69/4.97 ! [B4: set_filter_nat,A: set_filter_nat] :
% 4.69/4.97 ( ( B4 != bot_bo498966703094740906er_nat )
% 4.69/4.97 => ( ( condit4029664723990530684er_nat @ A )
% 4.69/4.97 => ( ! [B2: filter_nat] :
% 4.69/4.97 ( ( member_filter_nat @ B2 @ B4 )
% 4.69/4.97 => ? [X6: filter_nat] :
% 4.69/4.97 ( ( member_filter_nat @ X6 @ A )
% 4.69/4.97 & ( ord_le2510731241096832064er_nat @ B2 @ X6 ) ) )
% 4.69/4.97 => ( ord_le2510731241096832064er_nat @ ( comple2454491259644266675er_nat @ B4 ) @ ( comple2454491259644266675er_nat @ A ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_mono
% 4.69/4.97 thf(fact_3405_cSup__mono,axiom,
% 4.69/4.97 ! [B4: set_set_nat,A: set_set_nat] :
% 4.69/4.97 ( ( B4 != bot_bot_set_set_nat )
% 4.69/4.97 => ( ( condit5477540289124974626et_nat @ A )
% 4.69/4.97 => ( ! [B2: set_nat] :
% 4.69/4.97 ( ( member_set_nat @ B2 @ B4 )
% 4.69/4.97 => ? [X6: set_nat] :
% 4.69/4.97 ( ( member_set_nat @ X6 @ A )
% 4.69/4.97 & ( ord_less_eq_set_nat @ B2 @ X6 ) ) )
% 4.69/4.97 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ B4 ) @ ( comple7399068483239264473et_nat @ A ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_mono
% 4.69/4.97 thf(fact_3406_cSup__mono,axiom,
% 4.69/4.97 ! [B4: set_int,A: set_int] :
% 4.69/4.97 ( ( B4 != bot_bot_set_int )
% 4.69/4.97 => ( ( condit2212336002400062152ve_int @ A )
% 4.69/4.97 => ( ! [B2: int] :
% 4.69/4.97 ( ( member_int @ B2 @ B4 )
% 4.69/4.97 => ? [X6: int] :
% 4.69/4.97 ( ( member_int @ X6 @ A )
% 4.69/4.97 & ( ord_less_eq_int @ B2 @ X6 ) ) )
% 4.69/4.97 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ B4 ) @ ( complete_Sup_Sup_int @ A ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_mono
% 4.69/4.97 thf(fact_3407_cSup__mono,axiom,
% 4.69/4.97 ! [B4: set_nat,A: set_nat] :
% 4.69/4.97 ( ( B4 != bot_bot_set_nat )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ A )
% 4.69/4.97 => ( ! [B2: nat] :
% 4.69/4.97 ( ( member_nat @ B2 @ B4 )
% 4.69/4.97 => ? [X6: nat] :
% 4.69/4.97 ( ( member_nat @ X6 @ A )
% 4.69/4.97 & ( ord_less_eq_nat @ B2 @ X6 ) ) )
% 4.69/4.97 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ B4 ) @ ( complete_Sup_Sup_nat @ A ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_mono
% 4.69/4.97 thf(fact_3408_cSup__mono,axiom,
% 4.69/4.97 ! [B4: set_Product_unit,A: set_Product_unit] :
% 4.69/4.97 ( ( B4 != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ A )
% 4.69/4.97 => ( ! [B2: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ B2 @ B4 )
% 4.69/4.97 => ? [X6: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X6 @ A )
% 4.69/4.97 & ( ord_le3221252021190050221t_unit @ B2 @ X6 ) ) )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ B4 ) @ ( comple4687483117567863418t_unit @ A ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_mono
% 4.69/4.97 thf(fact_3409_cSUP__le__iff,axiom,
% 4.69/4.97 ! [A: set_Product_unit,F: product_unit > int,U: int] :
% 4.69/4.97 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit2212336002400062152ve_int @ ( image_873079544045703924it_int @ F @ A ) )
% 4.69/4.97 => ( ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_873079544045703924it_int @ F @ A ) ) @ U )
% 4.69/4.97 = ( ! [X2: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X2 @ A )
% 4.69/4.97 => ( ord_less_eq_int @ ( F @ X2 ) @ U ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_le_iff
% 4.69/4.97 thf(fact_3410_cSUP__le__iff,axiom,
% 4.69/4.97 ! [A: set_o,F: $o > int,U: int] :
% 4.69/4.97 ( ( A != bot_bot_set_o )
% 4.69/4.97 => ( ( condit2212336002400062152ve_int @ ( image_o_int2 @ F @ A ) )
% 4.69/4.97 => ( ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_o_int2 @ F @ A ) ) @ U )
% 4.69/4.97 = ( ! [X2: $o] :
% 4.69/4.97 ( ( member_o @ X2 @ A )
% 4.69/4.97 => ( ord_less_eq_int @ ( F @ X2 ) @ U ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_le_iff
% 4.69/4.97 thf(fact_3411_cSUP__le__iff,axiom,
% 4.69/4.97 ! [A: set_nat,F: nat > int,U: int] :
% 4.69/4.97 ( ( A != bot_bot_set_nat )
% 4.69/4.97 => ( ( condit2212336002400062152ve_int @ ( image_nat_int2 @ F @ A ) )
% 4.69/4.97 => ( ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_nat_int2 @ F @ A ) ) @ U )
% 4.69/4.97 = ( ! [X2: nat] :
% 4.69/4.97 ( ( member_nat @ X2 @ A )
% 4.69/4.97 => ( ord_less_eq_int @ ( F @ X2 ) @ U ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_le_iff
% 4.69/4.97 thf(fact_3412_cSUP__le__iff,axiom,
% 4.69/4.97 ! [A: set_int,F: int > int,U: int] :
% 4.69/4.97 ( ( A != bot_bot_set_int )
% 4.69/4.97 => ( ( condit2212336002400062152ve_int @ ( image_int_int2 @ F @ A ) )
% 4.69/4.97 => ( ( ord_less_eq_int @ ( complete_Sup_Sup_int @ ( image_int_int2 @ F @ A ) ) @ U )
% 4.69/4.97 = ( ! [X2: int] :
% 4.69/4.97 ( ( member_int @ X2 @ A )
% 4.69/4.97 => ( ord_less_eq_int @ ( F @ X2 ) @ U ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_le_iff
% 4.69/4.97 thf(fact_3413_cSUP__le__iff,axiom,
% 4.69/4.97 ! [A: set_Product_unit,F: product_unit > nat,U: nat] :
% 4.69/4.97 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_875570014554754200it_nat @ F @ A ) )
% 4.69/4.97 => ( ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ F @ A ) ) @ U )
% 4.69/4.97 = ( ! [X2: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X2 @ A )
% 4.69/4.97 => ( ord_less_eq_nat @ ( F @ X2 ) @ U ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_le_iff
% 4.69/4.97 thf(fact_3414_cSUP__le__iff,axiom,
% 4.69/4.97 ! [A: set_o,F: $o > nat,U: nat] :
% 4.69/4.97 ( ( A != bot_bot_set_o )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_o_nat2 @ F @ A ) )
% 4.69/4.97 => ( ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_o_nat2 @ F @ A ) ) @ U )
% 4.69/4.97 = ( ! [X2: $o] :
% 4.69/4.97 ( ( member_o @ X2 @ A )
% 4.69/4.97 => ( ord_less_eq_nat @ ( F @ X2 ) @ U ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_le_iff
% 4.69/4.97 thf(fact_3415_cSUP__le__iff,axiom,
% 4.69/4.97 ! [A: set_nat,F: nat > nat,U: nat] :
% 4.69/4.97 ( ( A != bot_bot_set_nat )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat2 @ F @ A ) )
% 4.69/4.97 => ( ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_nat_nat2 @ F @ A ) ) @ U )
% 4.69/4.97 = ( ! [X2: nat] :
% 4.69/4.97 ( ( member_nat @ X2 @ A )
% 4.69/4.97 => ( ord_less_eq_nat @ ( F @ X2 ) @ U ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_le_iff
% 4.69/4.97 thf(fact_3416_cSUP__le__iff,axiom,
% 4.69/4.97 ! [A: set_int,F: int > nat,U: nat] :
% 4.69/4.97 ( ( A != bot_bot_set_int )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_int_nat2 @ F @ A ) )
% 4.69/4.97 => ( ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_int_nat2 @ F @ A ) ) @ U )
% 4.69/4.97 = ( ! [X2: int] :
% 4.69/4.97 ( ( member_int @ X2 @ A )
% 4.69/4.97 => ( ord_less_eq_nat @ ( F @ X2 ) @ U ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_le_iff
% 4.69/4.97 thf(fact_3417_cSUP__le__iff,axiom,
% 4.69/4.97 ! [A: set_Product_unit,F: product_unit > product_unit,U: product_unit] :
% 4.69/4.97 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ ( image_405062704495631173t_unit @ F @ A ) )
% 4.69/4.97 => ( ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A ) ) @ U )
% 4.69/4.97 = ( ! [X2: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X2 @ A )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ ( F @ X2 ) @ U ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_le_iff
% 4.69/4.97 thf(fact_3418_cSUP__le__iff,axiom,
% 4.69/4.97 ! [A: set_o,F: $o > product_unit,U: product_unit] :
% 4.69/4.97 ( ( A != bot_bot_set_o )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ ( image_o_Product_unit2 @ F @ A ) )
% 4.69/4.97 => ( ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit2 @ F @ A ) ) @ U )
% 4.69/4.97 = ( ! [X2: $o] :
% 4.69/4.97 ( ( member_o @ X2 @ A )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ ( F @ X2 ) @ U ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_le_iff
% 4.69/4.97 thf(fact_3419_cSUP__mono,axiom,
% 4.69/4.97 ! [A: set_Product_unit,G: nat > set_nat,B4: set_nat,F: product_unit > set_nat] :
% 4.69/4.97 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit5477540289124974626et_nat @ ( image_nat_set_nat @ G @ B4 ) )
% 4.69/4.97 => ( ! [N3: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ N3 @ A )
% 4.69/4.97 => ? [X6: nat] :
% 4.69/4.97 ( ( member_nat @ X6 @ B4 )
% 4.69/4.97 & ( ord_less_eq_set_nat @ ( F @ N3 ) @ ( G @ X6 ) ) ) )
% 4.69/4.97 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ A ) ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_mono
% 4.69/4.97 thf(fact_3420_cSUP__mono,axiom,
% 4.69/4.97 ! [A: set_o,G: nat > set_nat,B4: set_nat,F: $o > set_nat] :
% 4.69/4.97 ( ( A != bot_bot_set_o )
% 4.69/4.97 => ( ( condit5477540289124974626et_nat @ ( image_nat_set_nat @ G @ B4 ) )
% 4.69/4.97 => ( ! [N3: $o] :
% 4.69/4.97 ( ( member_o @ N3 @ A )
% 4.69/4.97 => ? [X6: nat] :
% 4.69/4.97 ( ( member_nat @ X6 @ B4 )
% 4.69/4.97 & ( ord_less_eq_set_nat @ ( F @ N3 ) @ ( G @ X6 ) ) ) )
% 4.69/4.97 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A ) ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_mono
% 4.69/4.97 thf(fact_3421_cSUP__mono,axiom,
% 4.69/4.97 ! [A: set_nat,G: nat > set_nat,B4: set_nat,F: nat > set_nat] :
% 4.69/4.97 ( ( A != bot_bot_set_nat )
% 4.69/4.97 => ( ( condit5477540289124974626et_nat @ ( image_nat_set_nat @ G @ B4 ) )
% 4.69/4.97 => ( ! [N3: nat] :
% 4.69/4.97 ( ( member_nat @ N3 @ A )
% 4.69/4.97 => ? [X6: nat] :
% 4.69/4.97 ( ( member_nat @ X6 @ B4 )
% 4.69/4.97 & ( ord_less_eq_set_nat @ ( F @ N3 ) @ ( G @ X6 ) ) ) )
% 4.69/4.97 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A ) ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_mono
% 4.69/4.97 thf(fact_3422_cSUP__mono,axiom,
% 4.69/4.97 ! [A: set_int,G: nat > set_nat,B4: set_nat,F: int > set_nat] :
% 4.69/4.97 ( ( A != bot_bot_set_int )
% 4.69/4.97 => ( ( condit5477540289124974626et_nat @ ( image_nat_set_nat @ G @ B4 ) )
% 4.69/4.97 => ( ! [N3: int] :
% 4.69/4.97 ( ( member_int @ N3 @ A )
% 4.69/4.97 => ? [X6: nat] :
% 4.69/4.97 ( ( member_nat @ X6 @ B4 )
% 4.69/4.97 & ( ord_less_eq_set_nat @ ( F @ N3 ) @ ( G @ X6 ) ) ) )
% 4.69/4.97 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_int_set_nat @ F @ A ) ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_mono
% 4.69/4.97 thf(fact_3423_cSUP__mono,axiom,
% 4.69/4.97 ! [A: set_Pr4532377907799695533_nat_o,G: nat > set_nat,B4: set_nat,F: ( produc3658429121746597890et_nat > $o ) > set_nat] :
% 4.69/4.97 ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.97 => ( ( condit5477540289124974626et_nat @ ( image_nat_set_nat @ G @ B4 ) )
% 4.69/4.97 => ( ! [N3: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ( member6576561426505652726_nat_o @ N3 @ A )
% 4.69/4.97 => ? [X6: nat] :
% 4.69/4.97 ( ( member_nat @ X6 @ B4 )
% 4.69/4.97 & ( ord_less_eq_set_nat @ ( F @ N3 ) @ ( G @ X6 ) ) ) )
% 4.69/4.97 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ ( image_6888641473154130958et_nat @ F @ A ) ) @ ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_mono
% 4.69/4.97 thf(fact_3424_cSUP__mono,axiom,
% 4.69/4.97 ! [A: set_Product_unit,G: nat > nat,B4: set_nat,F: product_unit > nat] :
% 4.69/4.97 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat2 @ G @ B4 ) )
% 4.69/4.97 => ( ! [N3: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ N3 @ A )
% 4.69/4.97 => ? [X6: nat] :
% 4.69/4.97 ( ( member_nat @ X6 @ B4 )
% 4.69/4.97 & ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ X6 ) ) ) )
% 4.69/4.97 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_875570014554754200it_nat @ F @ A ) ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat2 @ G @ B4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_mono
% 4.69/4.97 thf(fact_3425_cSUP__mono,axiom,
% 4.69/4.97 ! [A: set_o,G: nat > nat,B4: set_nat,F: $o > nat] :
% 4.69/4.97 ( ( A != bot_bot_set_o )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat2 @ G @ B4 ) )
% 4.69/4.97 => ( ! [N3: $o] :
% 4.69/4.97 ( ( member_o @ N3 @ A )
% 4.69/4.97 => ? [X6: nat] :
% 4.69/4.97 ( ( member_nat @ X6 @ B4 )
% 4.69/4.97 & ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ X6 ) ) ) )
% 4.69/4.97 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_o_nat2 @ F @ A ) ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat2 @ G @ B4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_mono
% 4.69/4.97 thf(fact_3426_cSUP__mono,axiom,
% 4.69/4.97 ! [A: set_nat,G: nat > nat,B4: set_nat,F: nat > nat] :
% 4.69/4.97 ( ( A != bot_bot_set_nat )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat2 @ G @ B4 ) )
% 4.69/4.97 => ( ! [N3: nat] :
% 4.69/4.97 ( ( member_nat @ N3 @ A )
% 4.69/4.97 => ? [X6: nat] :
% 4.69/4.97 ( ( member_nat @ X6 @ B4 )
% 4.69/4.97 & ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ X6 ) ) ) )
% 4.69/4.97 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_nat_nat2 @ F @ A ) ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat2 @ G @ B4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_mono
% 4.69/4.97 thf(fact_3427_cSUP__mono,axiom,
% 4.69/4.97 ! [A: set_int,G: nat > nat,B4: set_nat,F: int > nat] :
% 4.69/4.97 ( ( A != bot_bot_set_int )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat2 @ G @ B4 ) )
% 4.69/4.97 => ( ! [N3: int] :
% 4.69/4.97 ( ( member_int @ N3 @ A )
% 4.69/4.97 => ? [X6: nat] :
% 4.69/4.97 ( ( member_nat @ X6 @ B4 )
% 4.69/4.97 & ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ X6 ) ) ) )
% 4.69/4.97 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_int_nat2 @ F @ A ) ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat2 @ G @ B4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_mono
% 4.69/4.97 thf(fact_3428_cSUP__mono,axiom,
% 4.69/4.97 ! [A: set_Pr4532377907799695533_nat_o,G: nat > nat,B4: set_nat,F: ( produc3658429121746597890et_nat > $o ) > nat] :
% 4.69/4.97 ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ ( image_nat_nat2 @ G @ B4 ) )
% 4.69/4.97 => ( ! [N3: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ( member6576561426505652726_nat_o @ N3 @ A )
% 4.69/4.97 => ? [X6: nat] :
% 4.69/4.97 ( ( member_nat @ X6 @ B4 )
% 4.69/4.97 & ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ X6 ) ) ) )
% 4.69/4.97 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ ( image_2174381888560928856_o_nat @ F @ A ) ) @ ( complete_Sup_Sup_nat @ ( image_nat_nat2 @ G @ B4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSUP_mono
% 4.69/4.97 thf(fact_3429_cSup__subset__mono,axiom,
% 4.69/4.97 ! [A: set_o,B4: set_o] :
% 4.69/4.97 ( ( A != bot_bot_set_o )
% 4.69/4.97 => ( ( condit5488710616941104124bove_o @ B4 )
% 4.69/4.97 => ( ( ord_less_eq_set_o @ A @ B4 )
% 4.69/4.97 => ( ord_less_eq_o @ ( complete_Sup_Sup_o @ A ) @ ( complete_Sup_Sup_o @ B4 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_subset_mono
% 4.69/4.97 thf(fact_3430_cSup__subset__mono,axiom,
% 4.69/4.97 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.97 ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.97 => ( ( condit4352657709669162033_nat_o @ B4 )
% 4.69/4.97 => ( ( ord_le2965882846123202637_nat_o @ A @ B4 )
% 4.69/4.97 => ( ord_le729326519192465773_nat_o @ ( comple4225350640907012154_nat_o @ A ) @ ( comple4225350640907012154_nat_o @ B4 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_subset_mono
% 4.69/4.97 thf(fact_3431_cSup__subset__mono,axiom,
% 4.69/4.97 ! [A: set_filter_nat,B4: set_filter_nat] :
% 4.69/4.97 ( ( A != bot_bo498966703094740906er_nat )
% 4.69/4.97 => ( ( condit4029664723990530684er_nat @ B4 )
% 4.69/4.97 => ( ( ord_le2426478655948331894er_nat @ A @ B4 )
% 4.69/4.97 => ( ord_le2510731241096832064er_nat @ ( comple2454491259644266675er_nat @ A ) @ ( comple2454491259644266675er_nat @ B4 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_subset_mono
% 4.69/4.97 thf(fact_3432_cSup__subset__mono,axiom,
% 4.69/4.97 ! [A: set_set_nat,B4: set_set_nat] :
% 4.69/4.97 ( ( A != bot_bot_set_set_nat )
% 4.69/4.97 => ( ( condit5477540289124974626et_nat @ B4 )
% 4.69/4.97 => ( ( ord_le6893508408891458716et_nat @ A @ B4 )
% 4.69/4.97 => ( ord_less_eq_set_nat @ ( comple7399068483239264473et_nat @ A ) @ ( comple7399068483239264473et_nat @ B4 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_subset_mono
% 4.69/4.97 thf(fact_3433_cSup__subset__mono,axiom,
% 4.69/4.97 ! [A: set_int,B4: set_int] :
% 4.69/4.97 ( ( A != bot_bot_set_int )
% 4.69/4.97 => ( ( condit2212336002400062152ve_int @ B4 )
% 4.69/4.97 => ( ( ord_less_eq_set_int @ A @ B4 )
% 4.69/4.97 => ( ord_less_eq_int @ ( complete_Sup_Sup_int @ A ) @ ( complete_Sup_Sup_int @ B4 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_subset_mono
% 4.69/4.97 thf(fact_3434_cSup__subset__mono,axiom,
% 4.69/4.97 ! [A: set_nat,B4: set_nat] :
% 4.69/4.97 ( ( A != bot_bot_set_nat )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ B4 )
% 4.69/4.97 => ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.97 => ( ord_less_eq_nat @ ( complete_Sup_Sup_nat @ A ) @ ( complete_Sup_Sup_nat @ B4 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_subset_mono
% 4.69/4.97 thf(fact_3435_cSup__subset__mono,axiom,
% 4.69/4.97 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.97 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ B4 )
% 4.69/4.97 => ( ( ord_le3507040750410214029t_unit @ A @ B4 )
% 4.69/4.97 => ( ord_le3221252021190050221t_unit @ ( comple4687483117567863418t_unit @ A ) @ ( comple4687483117567863418t_unit @ B4 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_subset_mono
% 4.69/4.97 thf(fact_3436_cSup__insert__If,axiom,
% 4.69/4.97 ! [X4: set_set_nat,A2: set_nat] :
% 4.69/4.97 ( ( condit5477540289124974626et_nat @ X4 )
% 4.69/4.97 => ( ( ( X4 = bot_bot_set_set_nat )
% 4.69/4.97 => ( ( comple7399068483239264473et_nat @ ( insert_set_nat @ A2 @ X4 ) )
% 4.69/4.97 = A2 ) )
% 4.69/4.97 & ( ( X4 != bot_bot_set_set_nat )
% 4.69/4.97 => ( ( comple7399068483239264473et_nat @ ( insert_set_nat @ A2 @ X4 ) )
% 4.69/4.97 = ( sup_sup_set_nat @ A2 @ ( comple7399068483239264473et_nat @ X4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_insert_If
% 4.69/4.97 thf(fact_3437_cSup__insert__If,axiom,
% 4.69/4.97 ! [X4: set_o,A2: $o] :
% 4.69/4.97 ( ( condit5488710616941104124bove_o @ X4 )
% 4.69/4.97 => ( ( complete_Sup_Sup_o @ ( insert_o @ A2 @ X4 ) )
% 4.69/4.97 = ( ( ( X4 = bot_bot_set_o )
% 4.69/4.97 => A2 )
% 4.69/4.97 & ( ( X4 != bot_bot_set_o )
% 4.69/4.97 => ( sup_sup_o @ A2 @ ( complete_Sup_Sup_o @ X4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_insert_If
% 4.69/4.97 thf(fact_3438_cSup__insert__If,axiom,
% 4.69/4.97 ! [X4: set_int,A2: int] :
% 4.69/4.97 ( ( condit2212336002400062152ve_int @ X4 )
% 4.69/4.97 => ( ( ( X4 = bot_bot_set_int )
% 4.69/4.97 => ( ( complete_Sup_Sup_int @ ( insert_int @ A2 @ X4 ) )
% 4.69/4.97 = A2 ) )
% 4.69/4.97 & ( ( X4 != bot_bot_set_int )
% 4.69/4.97 => ( ( complete_Sup_Sup_int @ ( insert_int @ A2 @ X4 ) )
% 4.69/4.97 = ( sup_sup_int @ A2 @ ( complete_Sup_Sup_int @ X4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_insert_If
% 4.69/4.97 thf(fact_3439_cSup__insert__If,axiom,
% 4.69/4.97 ! [X4: set_Pr4532377907799695533_nat_o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ( condit4352657709669162033_nat_o @ X4 )
% 4.69/4.97 => ( ( ( X4 = bot_bo7824918357723582233_nat_o )
% 4.69/4.97 => ( ( comple4225350640907012154_nat_o @ ( insert5175938949040314269_nat_o @ A2 @ X4 ) )
% 4.69/4.97 = A2 ) )
% 4.69/4.97 & ( ( X4 != bot_bo7824918357723582233_nat_o )
% 4.69/4.97 => ( ( comple4225350640907012154_nat_o @ ( insert5175938949040314269_nat_o @ A2 @ X4 ) )
% 4.69/4.97 = ( sup_su5453871518329203617_nat_o @ A2 @ ( comple4225350640907012154_nat_o @ X4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_insert_If
% 4.69/4.97 thf(fact_3440_cSup__insert__If,axiom,
% 4.69/4.97 ! [X4: set_nat,A2: nat] :
% 4.69/4.97 ( ( condit2214826472909112428ve_nat @ X4 )
% 4.69/4.97 => ( ( ( X4 = bot_bot_set_nat )
% 4.69/4.97 => ( ( complete_Sup_Sup_nat @ ( insert_nat @ A2 @ X4 ) )
% 4.69/4.97 = A2 ) )
% 4.69/4.97 & ( ( X4 != bot_bot_set_nat )
% 4.69/4.97 => ( ( complete_Sup_Sup_nat @ ( insert_nat @ A2 @ X4 ) )
% 4.69/4.97 = ( sup_sup_nat @ A2 @ ( complete_Sup_Sup_nat @ X4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_insert_If
% 4.69/4.97 thf(fact_3441_cSup__insert__If,axiom,
% 4.69/4.97 ! [X4: set_Product_unit,A2: product_unit] :
% 4.69/4.97 ( ( condit2080475194861589617t_unit @ X4 )
% 4.69/4.97 => ( ( ( X4 = bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( comple4687483117567863418t_unit @ ( insert_Product_unit @ A2 @ X4 ) )
% 4.69/4.97 = A2 ) )
% 4.69/4.97 & ( ( X4 != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( comple4687483117567863418t_unit @ ( insert_Product_unit @ A2 @ X4 ) )
% 4.69/4.97 = ( sup_sup_Product_unit @ A2 @ ( comple4687483117567863418t_unit @ X4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_insert_If
% 4.69/4.97 thf(fact_3442_cSup__insert,axiom,
% 4.69/4.97 ! [X4: set_set_nat,A2: set_nat] :
% 4.69/4.97 ( ( X4 != bot_bot_set_set_nat )
% 4.69/4.97 => ( ( condit5477540289124974626et_nat @ X4 )
% 4.69/4.97 => ( ( comple7399068483239264473et_nat @ ( insert_set_nat @ A2 @ X4 ) )
% 4.69/4.97 = ( sup_sup_set_nat @ A2 @ ( comple7399068483239264473et_nat @ X4 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_insert
% 4.69/4.97 thf(fact_3443_cSup__insert,axiom,
% 4.69/4.97 ! [X4: set_o,A2: $o] :
% 4.69/4.97 ( ( X4 != bot_bot_set_o )
% 4.69/4.97 => ( ( condit5488710616941104124bove_o @ X4 )
% 4.69/4.97 => ( ( complete_Sup_Sup_o @ ( insert_o @ A2 @ X4 ) )
% 4.69/4.97 = ( sup_sup_o @ A2 @ ( complete_Sup_Sup_o @ X4 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_insert
% 4.69/4.97 thf(fact_3444_cSup__insert,axiom,
% 4.69/4.97 ! [X4: set_int,A2: int] :
% 4.69/4.97 ( ( X4 != bot_bot_set_int )
% 4.69/4.97 => ( ( condit2212336002400062152ve_int @ X4 )
% 4.69/4.97 => ( ( complete_Sup_Sup_int @ ( insert_int @ A2 @ X4 ) )
% 4.69/4.97 = ( sup_sup_int @ A2 @ ( complete_Sup_Sup_int @ X4 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_insert
% 4.69/4.97 thf(fact_3445_cSup__insert,axiom,
% 4.69/4.97 ! [X4: set_Pr4532377907799695533_nat_o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/4.97 ( ( X4 != bot_bo7824918357723582233_nat_o )
% 4.69/4.97 => ( ( condit4352657709669162033_nat_o @ X4 )
% 4.69/4.97 => ( ( comple4225350640907012154_nat_o @ ( insert5175938949040314269_nat_o @ A2 @ X4 ) )
% 4.69/4.97 = ( sup_su5453871518329203617_nat_o @ A2 @ ( comple4225350640907012154_nat_o @ X4 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_insert
% 4.69/4.97 thf(fact_3446_cSup__insert,axiom,
% 4.69/4.97 ! [X4: set_nat,A2: nat] :
% 4.69/4.97 ( ( X4 != bot_bot_set_nat )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ X4 )
% 4.69/4.97 => ( ( complete_Sup_Sup_nat @ ( insert_nat @ A2 @ X4 ) )
% 4.69/4.97 = ( sup_sup_nat @ A2 @ ( complete_Sup_Sup_nat @ X4 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_insert
% 4.69/4.97 thf(fact_3447_cSup__insert,axiom,
% 4.69/4.97 ! [X4: set_Product_unit,A2: product_unit] :
% 4.69/4.97 ( ( X4 != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ X4 )
% 4.69/4.97 => ( ( comple4687483117567863418t_unit @ ( insert_Product_unit @ A2 @ X4 ) )
% 4.69/4.97 = ( sup_sup_Product_unit @ A2 @ ( comple4687483117567863418t_unit @ X4 ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_insert
% 4.69/4.97 thf(fact_3448_cSup__union__distrib,axiom,
% 4.69/4.97 ! [A: set_set_nat,B4: set_set_nat] :
% 4.69/4.97 ( ( A != bot_bot_set_set_nat )
% 4.69/4.97 => ( ( condit5477540289124974626et_nat @ A )
% 4.69/4.97 => ( ( B4 != bot_bot_set_set_nat )
% 4.69/4.97 => ( ( condit5477540289124974626et_nat @ B4 )
% 4.69/4.97 => ( ( comple7399068483239264473et_nat @ ( sup_sup_set_set_nat @ A @ B4 ) )
% 4.69/4.97 = ( sup_sup_set_nat @ ( comple7399068483239264473et_nat @ A ) @ ( comple7399068483239264473et_nat @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_union_distrib
% 4.69/4.97 thf(fact_3449_cSup__union__distrib,axiom,
% 4.69/4.97 ! [A: set_o,B4: set_o] :
% 4.69/4.97 ( ( A != bot_bot_set_o )
% 4.69/4.97 => ( ( condit5488710616941104124bove_o @ A )
% 4.69/4.97 => ( ( B4 != bot_bot_set_o )
% 4.69/4.97 => ( ( condit5488710616941104124bove_o @ B4 )
% 4.69/4.97 => ( ( complete_Sup_Sup_o @ ( sup_sup_set_o @ A @ B4 ) )
% 4.69/4.97 = ( sup_sup_o @ ( complete_Sup_Sup_o @ A ) @ ( complete_Sup_Sup_o @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_union_distrib
% 4.69/4.97 thf(fact_3450_cSup__union__distrib,axiom,
% 4.69/4.97 ! [A: set_int,B4: set_int] :
% 4.69/4.97 ( ( A != bot_bot_set_int )
% 4.69/4.97 => ( ( condit2212336002400062152ve_int @ A )
% 4.69/4.97 => ( ( B4 != bot_bot_set_int )
% 4.69/4.97 => ( ( condit2212336002400062152ve_int @ B4 )
% 4.69/4.97 => ( ( complete_Sup_Sup_int @ ( sup_sup_set_int @ A @ B4 ) )
% 4.69/4.97 = ( sup_sup_int @ ( complete_Sup_Sup_int @ A ) @ ( complete_Sup_Sup_int @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_union_distrib
% 4.69/4.97 thf(fact_3451_cSup__union__distrib,axiom,
% 4.69/4.97 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.97 ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/4.97 => ( ( condit4352657709669162033_nat_o @ A )
% 4.69/4.97 => ( ( B4 != bot_bo7824918357723582233_nat_o )
% 4.69/4.97 => ( ( condit4352657709669162033_nat_o @ B4 )
% 4.69/4.97 => ( ( comple4225350640907012154_nat_o @ ( sup_su5209123915105501825_nat_o @ A @ B4 ) )
% 4.69/4.97 = ( sup_su5453871518329203617_nat_o @ ( comple4225350640907012154_nat_o @ A ) @ ( comple4225350640907012154_nat_o @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_union_distrib
% 4.69/4.97 thf(fact_3452_cSup__union__distrib,axiom,
% 4.69/4.97 ! [A: set_nat,B4: set_nat] :
% 4.69/4.97 ( ( A != bot_bot_set_nat )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ A )
% 4.69/4.97 => ( ( B4 != bot_bot_set_nat )
% 4.69/4.97 => ( ( condit2214826472909112428ve_nat @ B4 )
% 4.69/4.97 => ( ( complete_Sup_Sup_nat @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.97 = ( sup_sup_nat @ ( complete_Sup_Sup_nat @ A ) @ ( complete_Sup_Sup_nat @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_union_distrib
% 4.69/4.97 thf(fact_3453_cSup__union__distrib,axiom,
% 4.69/4.97 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.97 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ A )
% 4.69/4.97 => ( ( B4 != bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ( condit2080475194861589617t_unit @ B4 )
% 4.69/4.97 => ( ( comple4687483117567863418t_unit @ ( sup_su793286257634532545t_unit @ A @ B4 ) )
% 4.69/4.97 = ( sup_sup_Product_unit @ ( comple4687483117567863418t_unit @ A ) @ ( comple4687483117567863418t_unit @ B4 ) ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % cSup_union_distrib
% 4.69/4.97 thf(fact_3454_fun__upd__image,axiom,
% 4.69/4.97 ! [X: code_integer,A: set_Code_integer,F: code_integer > code_integer,Y: code_integer] :
% 4.69/4.97 ( ( ( member_Code_integer @ X @ A )
% 4.69/4.97 => ( ( image_4470545334726330049nteger @ ( fun_up8355007323143964473nteger @ F @ X @ Y ) @ A )
% 4.69/4.97 = ( insert_Code_integer @ Y @ ( image_4470545334726330049nteger @ F @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 4.69/4.97 & ( ~ ( member_Code_integer @ X @ A )
% 4.69/4.97 => ( ( image_4470545334726330049nteger @ ( fun_up8355007323143964473nteger @ F @ X @ Y ) @ A )
% 4.69/4.97 = ( image_4470545334726330049nteger @ F @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % fun_upd_image
% 4.69/4.97 thf(fact_3455_fun__upd__image,axiom,
% 4.69/4.97 ! [X: product_unit,A: set_Product_unit,F: product_unit > nat,Y: nat] :
% 4.69/4.97 ( ( ( member_Product_unit @ X @ A )
% 4.69/4.97 => ( ( image_875570014554754200it_nat @ ( fun_up6473050886840373792it_nat @ F @ X @ Y ) @ A )
% 4.69/4.97 = ( insert_nat @ Y @ ( image_875570014554754200it_nat @ F @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) )
% 4.69/4.97 & ( ~ ( member_Product_unit @ X @ A )
% 4.69/4.97 => ( ( image_875570014554754200it_nat @ ( fun_up6473050886840373792it_nat @ F @ X @ Y ) @ A )
% 4.69/4.97 = ( image_875570014554754200it_nat @ F @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % fun_upd_image
% 4.69/4.97 thf(fact_3456_fun__upd__image,axiom,
% 4.69/4.97 ! [X: product_unit,A: set_Product_unit,F: product_unit > int,Y: int] :
% 4.69/4.97 ( ( ( member_Product_unit @ X @ A )
% 4.69/4.97 => ( ( image_873079544045703924it_int @ ( fun_up6470560416331323516it_int @ F @ X @ Y ) @ A )
% 4.69/4.97 = ( insert_int @ Y @ ( image_873079544045703924it_int @ F @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) )
% 4.69/4.97 & ( ~ ( member_Product_unit @ X @ A )
% 4.69/4.97 => ( ( image_873079544045703924it_int @ ( fun_up6470560416331323516it_int @ F @ X @ Y ) @ A )
% 4.69/4.97 = ( image_873079544045703924it_int @ F @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % fun_upd_image
% 4.69/4.97 thf(fact_3457_fun__upd__image,axiom,
% 4.69/4.97 ! [X: product_unit,A: set_Product_unit,F: product_unit > $o,Y: $o] :
% 4.69/4.97 ( ( ( member_Product_unit @ X @ A )
% 4.69/4.97 => ( ( image_Product_unit_o2 @ ( fun_up5432024876597553480unit_o @ F @ X @ Y ) @ A )
% 4.69/4.97 = ( insert_o @ Y @ ( image_Product_unit_o2 @ F @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) )
% 4.69/4.97 & ( ~ ( member_Product_unit @ X @ A )
% 4.69/4.97 => ( ( image_Product_unit_o2 @ ( fun_up5432024876597553480unit_o @ F @ X @ Y ) @ A )
% 4.69/4.97 = ( image_Product_unit_o2 @ F @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % fun_upd_image
% 4.69/4.97 thf(fact_3458_fun__upd__image,axiom,
% 4.69/4.97 ! [X: product_unit,A: set_Product_unit,F: product_unit > product_unit,Y: product_unit] :
% 4.69/4.97 ( ( ( member_Product_unit @ X @ A )
% 4.69/4.97 => ( ( image_405062704495631173t_unit @ ( fun_up6875000483049295805t_unit @ F @ X @ Y ) @ A )
% 4.69/4.97 = ( insert_Product_unit @ Y @ ( image_405062704495631173t_unit @ F @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) )
% 4.69/4.97 & ( ~ ( member_Product_unit @ X @ A )
% 4.69/4.97 => ( ( image_405062704495631173t_unit @ ( fun_up6875000483049295805t_unit @ F @ X @ Y ) @ A )
% 4.69/4.97 = ( image_405062704495631173t_unit @ F @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % fun_upd_image
% 4.69/4.97 thf(fact_3459_fun__upd__image,axiom,
% 4.69/4.97 ! [X: $o,A: set_o,F: $o > nat,Y: nat] :
% 4.69/4.97 ( ( ( member_o @ X @ A )
% 4.69/4.97 => ( ( image_o_nat2 @ ( fun_upd_o_nat @ F @ X @ Y ) @ A )
% 4.69/4.97 = ( insert_nat @ Y @ ( image_o_nat2 @ F @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) )
% 4.69/4.97 & ( ~ ( member_o @ X @ A )
% 4.69/4.97 => ( ( image_o_nat2 @ ( fun_upd_o_nat @ F @ X @ Y ) @ A )
% 4.69/4.97 = ( image_o_nat2 @ F @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % fun_upd_image
% 4.69/4.97 thf(fact_3460_fun__upd__image,axiom,
% 4.69/4.97 ! [X: $o,A: set_o,F: $o > int,Y: int] :
% 4.69/4.97 ( ( ( member_o @ X @ A )
% 4.69/4.97 => ( ( image_o_int2 @ ( fun_upd_o_int @ F @ X @ Y ) @ A )
% 4.69/4.97 = ( insert_int @ Y @ ( image_o_int2 @ F @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) )
% 4.69/4.97 & ( ~ ( member_o @ X @ A )
% 4.69/4.97 => ( ( image_o_int2 @ ( fun_upd_o_int @ F @ X @ Y ) @ A )
% 4.69/4.97 = ( image_o_int2 @ F @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % fun_upd_image
% 4.69/4.97 thf(fact_3461_fun__upd__image,axiom,
% 4.69/4.97 ! [X: $o,A: set_o,F: $o > $o,Y: $o] :
% 4.69/4.97 ( ( ( member_o @ X @ A )
% 4.69/4.97 => ( ( image_o_o2 @ ( fun_upd_o_o @ F @ X @ Y ) @ A )
% 4.69/4.97 = ( insert_o @ Y @ ( image_o_o2 @ F @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) )
% 4.69/4.97 & ( ~ ( member_o @ X @ A )
% 4.69/4.97 => ( ( image_o_o2 @ ( fun_upd_o_o @ F @ X @ Y ) @ A )
% 4.69/4.97 = ( image_o_o2 @ F @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % fun_upd_image
% 4.69/4.97 thf(fact_3462_fun__upd__image,axiom,
% 4.69/4.97 ! [X: $o,A: set_o,F: $o > product_unit,Y: product_unit] :
% 4.69/4.97 ( ( ( member_o @ X @ A )
% 4.69/4.97 => ( ( image_o_Product_unit2 @ ( fun_up846054379331416818t_unit @ F @ X @ Y ) @ A )
% 4.69/4.97 = ( insert_Product_unit @ Y @ ( image_o_Product_unit2 @ F @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) )
% 4.69/4.97 & ( ~ ( member_o @ X @ A )
% 4.69/4.97 => ( ( image_o_Product_unit2 @ ( fun_up846054379331416818t_unit @ F @ X @ Y ) @ A )
% 4.69/4.97 = ( image_o_Product_unit2 @ F @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % fun_upd_image
% 4.69/4.97 thf(fact_3463_fun__upd__image,axiom,
% 4.69/4.97 ! [X: int,A: set_int,F: int > nat,Y: nat] :
% 4.69/4.97 ( ( ( member_int @ X @ A )
% 4.69/4.97 => ( ( image_int_nat2 @ ( fun_upd_int_nat @ F @ X @ Y ) @ A )
% 4.69/4.97 = ( insert_nat @ Y @ ( image_int_nat2 @ F @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) )
% 4.69/4.97 & ( ~ ( member_int @ X @ A )
% 4.69/4.97 => ( ( image_int_nat2 @ ( fun_upd_int_nat @ F @ X @ Y ) @ A )
% 4.69/4.97 = ( image_int_nat2 @ F @ A ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % fun_upd_image
% 4.69/4.97 thf(fact_3464_Sup__fin_Oeq__fold,axiom,
% 4.69/4.97 ! [A: set_int,X: int] :
% 4.69/4.97 ( ( finite_finite_int @ A )
% 4.69/4.97 => ( ( lattic1091506334969745077in_int @ ( insert_int @ X @ A ) )
% 4.69/4.97 = ( finite_fold_int_int @ sup_sup_int @ X @ A ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_fin.eq_fold
% 4.69/4.97 thf(fact_3465_Sup__fin_Oeq__fold,axiom,
% 4.69/4.97 ! [A: set_o,X: $o] :
% 4.69/4.97 ( ( finite_finite_o @ A )
% 4.69/4.97 => ( ( lattic1508158080041050831_fin_o @ ( insert_o @ X @ A ) )
% 4.69/4.97 = ( finite_fold_o_o @ sup_sup_o @ X @ A ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_fin.eq_fold
% 4.69/4.97 thf(fact_3466_Sup__fin_Oeq__fold,axiom,
% 4.69/4.97 ! [A: set_nat,X: nat] :
% 4.69/4.97 ( ( finite_finite_nat @ A )
% 4.69/4.97 => ( ( lattic1093996805478795353in_nat @ ( insert_nat @ X @ A ) )
% 4.69/4.97 = ( finite_fold_nat_nat @ sup_sup_nat @ X @ A ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_fin.eq_fold
% 4.69/4.97 thf(fact_3467_Sup__fin_Oeq__fold,axiom,
% 4.69/4.97 ! [A: set_set_nat,X: set_nat] :
% 4.69/4.97 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.97 => ( ( lattic3835124923745554447et_nat @ ( insert_set_nat @ X @ A ) )
% 4.69/4.97 = ( finite677925301803182934et_nat @ sup_sup_set_nat @ X @ A ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_fin.eq_fold
% 4.69/4.97 thf(fact_3468_Sup__fin_Oeq__fold,axiom,
% 4.69/4.97 ! [A: set_assn,X: assn] :
% 4.69/4.97 ( ( finite_finite_assn @ A )
% 4.69/4.97 => ( ( lattic2150320897289308081n_assn @ ( insert_assn @ X @ A ) )
% 4.69/4.97 = ( finite1440822074540989594n_assn @ sup_sup_assn @ X @ A ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_fin.eq_fold
% 4.69/4.97 thf(fact_3469_Sup__fin_Oeq__fold,axiom,
% 4.69/4.97 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.97 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.97 => ( ( lattic5294303975357428420t_unit @ ( insert_Product_unit @ X @ A ) )
% 4.69/4.97 = ( finite8834431295148555784t_unit @ sup_sup_Product_unit @ X @ A ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Sup_fin.eq_fold
% 4.69/4.97 thf(fact_3470_Inf__fin_Oeq__fold,axiom,
% 4.69/4.97 ! [A: set_int,X: int] :
% 4.69/4.97 ( ( finite_finite_int @ A )
% 4.69/4.97 => ( ( lattic5235898064620869839in_int @ ( insert_int @ X @ A ) )
% 4.69/4.97 = ( finite_fold_int_int @ inf_inf_int @ X @ A ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Inf_fin.eq_fold
% 4.69/4.97 thf(fact_3471_Inf__fin_Oeq__fold,axiom,
% 4.69/4.97 ! [A: set_o,X: $o] :
% 4.69/4.97 ( ( finite_finite_o @ A )
% 4.69/4.97 => ( ( lattic4107685809792843317_fin_o @ ( insert_o @ X @ A ) )
% 4.69/4.97 = ( finite_fold_o_o @ inf_inf_o @ X @ A ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Inf_fin.eq_fold
% 4.69/4.97 thf(fact_3472_Inf__fin_Oeq__fold,axiom,
% 4.69/4.97 ! [A: set_nat,X: nat] :
% 4.69/4.97 ( ( finite_finite_nat @ A )
% 4.69/4.97 => ( ( lattic5238388535129920115in_nat @ ( insert_nat @ X @ A ) )
% 4.69/4.97 = ( finite_fold_nat_nat @ inf_inf_nat @ X @ A ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Inf_fin.eq_fold
% 4.69/4.97 thf(fact_3473_Inf__fin_Oeq__fold,axiom,
% 4.69/4.97 ! [A: set_set_nat,X: set_nat] :
% 4.69/4.97 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.97 => ( ( lattic3014633134055518761et_nat @ ( insert_set_nat @ X @ A ) )
% 4.69/4.97 = ( finite677925301803182934et_nat @ inf_inf_set_nat @ X @ A ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Inf_fin.eq_fold
% 4.69/4.97 thf(fact_3474_Inf__fin_Oeq__fold,axiom,
% 4.69/4.97 ! [A: set_assn,X: assn] :
% 4.69/4.97 ( ( finite_finite_assn @ A )
% 4.69/4.97 => ( ( lattic47131356835913163n_assn @ ( insert_assn @ X @ A ) )
% 4.69/4.97 = ( finite1440822074540989594n_assn @ inf_inf_assn @ X @ A ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Inf_fin.eq_fold
% 4.69/4.97 thf(fact_3475_Inf__fin_Oeq__fold,axiom,
% 4.69/4.97 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.97 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.97 => ( ( lattic1263872656861969706t_unit @ ( insert_Product_unit @ X @ A ) )
% 4.69/4.97 = ( finite8834431295148555784t_unit @ inf_inf_Product_unit @ X @ A ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % Inf_fin.eq_fold
% 4.69/4.97 thf(fact_3476_wf__bounded__set,axiom,
% 4.69/4.97 ! [R2: set_Pr1261947904930325089at_nat,Ub: nat > set_Code_integer,F: nat > set_Code_integer] :
% 4.69/4.97 ( ! [A4: nat,B2: nat] :
% 4.69/4.97 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B2 @ A4 ) @ R2 )
% 4.69/4.97 => ( ( finite6017078050557962740nteger @ ( Ub @ A4 ) )
% 4.69/4.97 & ( ord_le7084787975880047091nteger @ ( Ub @ B2 ) @ ( Ub @ A4 ) )
% 4.69/4.97 & ( ord_le7084787975880047091nteger @ ( F @ B2 ) @ ( Ub @ A4 ) )
% 4.69/4.97 & ( ord_le1307284697595431911nteger @ ( F @ A4 ) @ ( F @ B2 ) ) ) )
% 4.69/4.97 => ( wf_nat @ R2 ) ) ).
% 4.69/4.97
% 4.69/4.97 % wf_bounded_set
% 4.69/4.97 thf(fact_3477_wf__bounded__set,axiom,
% 4.69/4.97 ! [R2: set_Pr958786334691620121nt_int,Ub: int > set_Code_integer,F: int > set_Code_integer] :
% 4.69/4.97 ( ! [A4: int,B2: int] :
% 4.69/4.97 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B2 @ A4 ) @ R2 )
% 4.69/4.97 => ( ( finite6017078050557962740nteger @ ( Ub @ A4 ) )
% 4.69/4.97 & ( ord_le7084787975880047091nteger @ ( Ub @ B2 ) @ ( Ub @ A4 ) )
% 4.69/4.97 & ( ord_le7084787975880047091nteger @ ( F @ B2 ) @ ( Ub @ A4 ) )
% 4.69/4.97 & ( ord_le1307284697595431911nteger @ ( F @ A4 ) @ ( F @ B2 ) ) ) )
% 4.69/4.97 => ( wf_int @ R2 ) ) ).
% 4.69/4.97
% 4.69/4.97 % wf_bounded_set
% 4.69/4.97 thf(fact_3478_wf__bounded__set,axiom,
% 4.69/4.97 ! [R2: set_Pr1261947904930325089at_nat,Ub: nat > set_nat,F: nat > set_nat] :
% 4.69/4.97 ( ! [A4: nat,B2: nat] :
% 4.69/4.97 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B2 @ A4 ) @ R2 )
% 4.69/4.97 => ( ( finite_finite_nat @ ( Ub @ A4 ) )
% 4.69/4.97 & ( ord_less_eq_set_nat @ ( Ub @ B2 ) @ ( Ub @ A4 ) )
% 4.69/4.97 & ( ord_less_eq_set_nat @ ( F @ B2 ) @ ( Ub @ A4 ) )
% 4.69/4.97 & ( ord_less_set_nat @ ( F @ A4 ) @ ( F @ B2 ) ) ) )
% 4.69/4.97 => ( wf_nat @ R2 ) ) ).
% 4.69/4.97
% 4.69/4.97 % wf_bounded_set
% 4.69/4.97 thf(fact_3479_wf__bounded__set,axiom,
% 4.69/4.97 ! [R2: set_Pr958786334691620121nt_int,Ub: int > set_nat,F: int > set_nat] :
% 4.69/4.97 ( ! [A4: int,B2: int] :
% 4.69/4.97 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B2 @ A4 ) @ R2 )
% 4.69/4.97 => ( ( finite_finite_nat @ ( Ub @ A4 ) )
% 4.69/4.97 & ( ord_less_eq_set_nat @ ( Ub @ B2 ) @ ( Ub @ A4 ) )
% 4.69/4.97 & ( ord_less_eq_set_nat @ ( F @ B2 ) @ ( Ub @ A4 ) )
% 4.69/4.97 & ( ord_less_set_nat @ ( F @ A4 ) @ ( F @ B2 ) ) ) )
% 4.69/4.97 => ( wf_int @ R2 ) ) ).
% 4.69/4.97
% 4.69/4.97 % wf_bounded_set
% 4.69/4.97 thf(fact_3480_psubset__insert__iff,axiom,
% 4.69/4.97 ! [A: set_Product_unit,X: product_unit,B4: set_Product_unit] :
% 4.69/4.97 ( ( ord_le8056459307392131481t_unit @ A @ ( insert_Product_unit @ X @ B4 ) )
% 4.69/4.97 = ( ( ( member_Product_unit @ X @ B4 )
% 4.69/4.97 => ( ord_le8056459307392131481t_unit @ A @ B4 ) )
% 4.69/4.97 & ( ~ ( member_Product_unit @ X @ B4 )
% 4.69/4.97 => ( ( ( member_Product_unit @ X @ A )
% 4.69/4.97 => ( ord_le8056459307392131481t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) @ B4 ) )
% 4.69/4.97 & ( ~ ( member_Product_unit @ X @ A )
% 4.69/4.97 => ( ord_le3507040750410214029t_unit @ A @ B4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % psubset_insert_iff
% 4.69/4.97 thf(fact_3481_psubset__insert__iff,axiom,
% 4.69/4.97 ! [A: set_o,X: $o,B4: set_o] :
% 4.69/4.97 ( ( ord_less_set_o @ A @ ( insert_o @ X @ B4 ) )
% 4.69/4.97 = ( ( ( member_o @ X @ B4 )
% 4.69/4.97 => ( ord_less_set_o @ A @ B4 ) )
% 4.69/4.97 & ( ~ ( member_o @ X @ B4 )
% 4.69/4.97 => ( ( ( member_o @ X @ A )
% 4.69/4.97 => ( ord_less_set_o @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) @ B4 ) )
% 4.69/4.97 & ( ~ ( member_o @ X @ A )
% 4.69/4.97 => ( ord_less_eq_set_o @ A @ B4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % psubset_insert_iff
% 4.69/4.97 thf(fact_3482_psubset__insert__iff,axiom,
% 4.69/4.97 ! [A: set_int,X: int,B4: set_int] :
% 4.69/4.97 ( ( ord_less_set_int @ A @ ( insert_int @ X @ B4 ) )
% 4.69/4.97 = ( ( ( member_int @ X @ B4 )
% 4.69/4.97 => ( ord_less_set_int @ A @ B4 ) )
% 4.69/4.97 & ( ~ ( member_int @ X @ B4 )
% 4.69/4.97 => ( ( ( member_int @ X @ A )
% 4.69/4.97 => ( ord_less_set_int @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) @ B4 ) )
% 4.69/4.97 & ( ~ ( member_int @ X @ A )
% 4.69/4.97 => ( ord_less_eq_set_int @ A @ B4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % psubset_insert_iff
% 4.69/4.97 thf(fact_3483_psubset__insert__iff,axiom,
% 4.69/4.97 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.97 ( ( ord_le2453136405763929_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ B4 ) )
% 4.69/4.97 = ( ( ( member6576561426505652726_nat_o @ X @ B4 )
% 4.69/4.97 => ( ord_le2453136405763929_nat_o @ A @ B4 ) )
% 4.69/4.97 & ( ~ ( member6576561426505652726_nat_o @ X @ B4 )
% 4.69/4.97 => ( ( ( member6576561426505652726_nat_o @ X @ A )
% 4.69/4.97 => ( ord_le2453136405763929_nat_o @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) @ B4 ) )
% 4.69/4.97 & ( ~ ( member6576561426505652726_nat_o @ X @ A )
% 4.69/4.97 => ( ord_le2965882846123202637_nat_o @ A @ B4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % psubset_insert_iff
% 4.69/4.97 thf(fact_3484_psubset__insert__iff,axiom,
% 4.69/4.97 ! [A: set_nat,X: nat,B4: set_nat] :
% 4.69/4.97 ( ( ord_less_set_nat @ A @ ( insert_nat @ X @ B4 ) )
% 4.69/4.97 = ( ( ( member_nat @ X @ B4 )
% 4.69/4.97 => ( ord_less_set_nat @ A @ B4 ) )
% 4.69/4.97 & ( ~ ( member_nat @ X @ B4 )
% 4.69/4.97 => ( ( ( member_nat @ X @ A )
% 4.69/4.97 => ( ord_less_set_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B4 ) )
% 4.69/4.97 & ( ~ ( member_nat @ X @ A )
% 4.69/4.97 => ( ord_less_eq_set_nat @ A @ B4 ) ) ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % psubset_insert_iff
% 4.69/4.97 thf(fact_3485_finite__induct__select,axiom,
% 4.69/4.97 ! [S: set_Code_integer,P: set_Code_integer > $o] :
% 4.69/4.97 ( ( finite6017078050557962740nteger @ S )
% 4.69/4.97 => ( ( P @ bot_bo3990330152332043303nteger )
% 4.69/4.97 => ( ! [T3: set_Code_integer] :
% 4.69/4.97 ( ( ord_le1307284697595431911nteger @ T3 @ S )
% 4.69/4.97 => ( ( P @ T3 )
% 4.69/4.97 => ? [X6: code_integer] :
% 4.69/4.97 ( ( member_Code_integer @ X6 @ ( minus_2355218937544613996nteger @ S @ T3 ) )
% 4.69/4.97 & ( P @ ( insert_Code_integer @ X6 @ T3 ) ) ) ) )
% 4.69/4.97 => ( P @ S ) ) ) ) ).
% 4.69/4.97
% 4.69/4.97 % finite_induct_select
% 4.69/4.97 thf(fact_3486_finite__induct__select,axiom,
% 4.69/4.97 ! [S: set_Product_unit,P: set_Product_unit > $o] :
% 4.69/4.97 ( ( finite4290736615968046902t_unit @ S )
% 4.69/4.97 => ( ( P @ bot_bo3957492148770167129t_unit )
% 4.69/4.97 => ( ! [T3: set_Product_unit] :
% 4.69/4.97 ( ( ord_le8056459307392131481t_unit @ T3 @ S )
% 4.69/4.97 => ( ( P @ T3 )
% 4.69/4.97 => ? [X6: product_unit] :
% 4.69/4.97 ( ( member_Product_unit @ X6 @ ( minus_6452836326544984404t_unit @ S @ T3 ) )
% 4.69/4.98 & ( P @ ( insert_Product_unit @ X6 @ T3 ) ) ) ) )
% 4.69/4.98 => ( P @ S ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % finite_induct_select
% 4.69/4.98 thf(fact_3487_finite__induct__select,axiom,
% 4.69/4.98 ! [S: set_o,P: set_o > $o] :
% 4.69/4.98 ( ( finite_finite_o @ S )
% 4.69/4.98 => ( ( P @ bot_bot_set_o )
% 4.69/4.98 => ( ! [T3: set_o] :
% 4.69/4.98 ( ( ord_less_set_o @ T3 @ S )
% 4.69/4.98 => ( ( P @ T3 )
% 4.69/4.98 => ? [X6: $o] :
% 4.69/4.98 ( ( member_o @ X6 @ ( minus_minus_set_o @ S @ T3 ) )
% 4.69/4.98 & ( P @ ( insert_o @ X6 @ T3 ) ) ) ) )
% 4.69/4.98 => ( P @ S ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % finite_induct_select
% 4.69/4.98 thf(fact_3488_finite__induct__select,axiom,
% 4.69/4.98 ! [S: set_int,P: set_int > $o] :
% 4.69/4.98 ( ( finite_finite_int @ S )
% 4.69/4.98 => ( ( P @ bot_bot_set_int )
% 4.69/4.98 => ( ! [T3: set_int] :
% 4.69/4.98 ( ( ord_less_set_int @ T3 @ S )
% 4.69/4.98 => ( ( P @ T3 )
% 4.69/4.98 => ? [X6: int] :
% 4.69/4.98 ( ( member_int @ X6 @ ( minus_minus_set_int @ S @ T3 ) )
% 4.69/4.98 & ( P @ ( insert_int @ X6 @ T3 ) ) ) ) )
% 4.69/4.98 => ( P @ S ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % finite_induct_select
% 4.69/4.98 thf(fact_3489_finite__induct__select,axiom,
% 4.69/4.98 ! [S: set_Pr4532377907799695533_nat_o,P: set_Pr4532377907799695533_nat_o > $o] :
% 4.69/4.98 ( ( finite3252695134891459830_nat_o @ S )
% 4.69/4.98 => ( ( P @ bot_bo7824918357723582233_nat_o )
% 4.69/4.98 => ( ! [T3: set_Pr4532377907799695533_nat_o] :
% 4.69/4.98 ( ( ord_le2453136405763929_nat_o @ T3 @ S )
% 4.69/4.98 => ( ( P @ T3 )
% 4.69/4.98 => ? [X6: produc3658429121746597890et_nat > $o] :
% 4.69/4.98 ( ( member6576561426505652726_nat_o @ X6 @ ( minus_1801376950450012436_nat_o @ S @ T3 ) )
% 4.69/4.98 & ( P @ ( insert5175938949040314269_nat_o @ X6 @ T3 ) ) ) ) )
% 4.69/4.98 => ( P @ S ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % finite_induct_select
% 4.69/4.98 thf(fact_3490_finite__induct__select,axiom,
% 4.69/4.98 ! [S: set_nat,P: set_nat > $o] :
% 4.69/4.98 ( ( finite_finite_nat @ S )
% 4.69/4.98 => ( ( P @ bot_bot_set_nat )
% 4.69/4.98 => ( ! [T3: set_nat] :
% 4.69/4.98 ( ( ord_less_set_nat @ T3 @ S )
% 4.69/4.98 => ( ( P @ T3 )
% 4.69/4.98 => ? [X6: nat] :
% 4.69/4.98 ( ( member_nat @ X6 @ ( minus_minus_set_nat @ S @ T3 ) )
% 4.69/4.98 & ( P @ ( insert_nat @ X6 @ T3 ) ) ) ) )
% 4.69/4.98 => ( P @ S ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % finite_induct_select
% 4.69/4.98 thf(fact_3491_Max_Osubset__imp,axiom,
% 4.69/4.98 ! [A: set_Code_integer,B4: set_Code_integer] :
% 4.69/4.98 ( ( ord_le7084787975880047091nteger @ A @ B4 )
% 4.69/4.98 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/4.98 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/4.98 => ( ord_le3102999989581377725nteger @ ( lattic4901227151466704046nteger @ A ) @ ( lattic4901227151466704046nteger @ B4 ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max.subset_imp
% 4.69/4.98 thf(fact_3492_Max_Osubset__imp,axiom,
% 4.69/4.98 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.98 ( ( ord_le3507040750410214029t_unit @ A @ B4 )
% 4.69/4.98 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.98 => ( ( finite4290736615968046902t_unit @ B4 )
% 4.69/4.98 => ( ord_le3221252021190050221t_unit @ ( lattic1210392890313158908t_unit @ A ) @ ( lattic1210392890313158908t_unit @ B4 ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max.subset_imp
% 4.69/4.98 thf(fact_3493_Max_Osubset__imp,axiom,
% 4.69/4.98 ! [A: set_o,B4: set_o] :
% 4.69/4.98 ( ( ord_less_eq_set_o @ A @ B4 )
% 4.69/4.98 => ( ( A != bot_bot_set_o )
% 4.69/4.98 => ( ( finite_finite_o @ B4 )
% 4.69/4.98 => ( ord_less_eq_o @ ( lattic1921953407002678535_Max_o @ A ) @ ( lattic1921953407002678535_Max_o @ B4 ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max.subset_imp
% 4.69/4.98 thf(fact_3494_Max_Osubset__imp,axiom,
% 4.69/4.98 ! [A: set_rat,B4: set_rat] :
% 4.69/4.98 ( ( ord_less_eq_set_rat @ A @ B4 )
% 4.69/4.98 => ( ( A != bot_bot_set_rat )
% 4.69/4.98 => ( ( finite_finite_rat @ B4 )
% 4.69/4.98 => ( ord_less_eq_rat @ ( lattic7630753665789217321ax_rat @ A ) @ ( lattic7630753665789217321ax_rat @ B4 ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max.subset_imp
% 4.69/4.98 thf(fact_3495_Max_Osubset__imp,axiom,
% 4.69/4.98 ! [A: set_int,B4: set_int] :
% 4.69/4.98 ( ( ord_less_eq_set_int @ A @ B4 )
% 4.69/4.98 => ( ( A != bot_bot_set_int )
% 4.69/4.98 => ( ( finite_finite_int @ B4 )
% 4.69/4.98 => ( ord_less_eq_int @ ( lattic8263393255366662781ax_int @ A ) @ ( lattic8263393255366662781ax_int @ B4 ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max.subset_imp
% 4.69/4.98 thf(fact_3496_Max_Osubset__imp,axiom,
% 4.69/4.98 ! [A: set_nat,B4: set_nat] :
% 4.69/4.98 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.98 => ( ( A != bot_bot_set_nat )
% 4.69/4.98 => ( ( finite_finite_nat @ B4 )
% 4.69/4.98 => ( ord_less_eq_nat @ ( lattic8265883725875713057ax_nat @ A ) @ ( lattic8265883725875713057ax_nat @ B4 ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max.subset_imp
% 4.69/4.98 thf(fact_3497_Max__mono,axiom,
% 4.69/4.98 ! [M: set_Code_integer,N: set_Code_integer] :
% 4.69/4.98 ( ( ord_le7084787975880047091nteger @ M @ N )
% 4.69/4.98 => ( ( M != bot_bo3990330152332043303nteger )
% 4.69/4.98 => ( ( finite6017078050557962740nteger @ N )
% 4.69/4.98 => ( ord_le3102999989581377725nteger @ ( lattic4901227151466704046nteger @ M ) @ ( lattic4901227151466704046nteger @ N ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max_mono
% 4.69/4.98 thf(fact_3498_Max__mono,axiom,
% 4.69/4.98 ! [M: set_Product_unit,N: set_Product_unit] :
% 4.69/4.98 ( ( ord_le3507040750410214029t_unit @ M @ N )
% 4.69/4.98 => ( ( M != bot_bo3957492148770167129t_unit )
% 4.69/4.98 => ( ( finite4290736615968046902t_unit @ N )
% 4.69/4.98 => ( ord_le3221252021190050221t_unit @ ( lattic1210392890313158908t_unit @ M ) @ ( lattic1210392890313158908t_unit @ N ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max_mono
% 4.69/4.98 thf(fact_3499_Max__mono,axiom,
% 4.69/4.98 ! [M: set_o,N: set_o] :
% 4.69/4.98 ( ( ord_less_eq_set_o @ M @ N )
% 4.69/4.98 => ( ( M != bot_bot_set_o )
% 4.69/4.98 => ( ( finite_finite_o @ N )
% 4.69/4.98 => ( ord_less_eq_o @ ( lattic1921953407002678535_Max_o @ M ) @ ( lattic1921953407002678535_Max_o @ N ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max_mono
% 4.69/4.98 thf(fact_3500_Max__mono,axiom,
% 4.69/4.98 ! [M: set_rat,N: set_rat] :
% 4.69/4.98 ( ( ord_less_eq_set_rat @ M @ N )
% 4.69/4.98 => ( ( M != bot_bot_set_rat )
% 4.69/4.98 => ( ( finite_finite_rat @ N )
% 4.69/4.98 => ( ord_less_eq_rat @ ( lattic7630753665789217321ax_rat @ M ) @ ( lattic7630753665789217321ax_rat @ N ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max_mono
% 4.69/4.98 thf(fact_3501_Max__mono,axiom,
% 4.69/4.98 ! [M: set_int,N: set_int] :
% 4.69/4.98 ( ( ord_less_eq_set_int @ M @ N )
% 4.69/4.98 => ( ( M != bot_bot_set_int )
% 4.69/4.98 => ( ( finite_finite_int @ N )
% 4.69/4.98 => ( ord_less_eq_int @ ( lattic8263393255366662781ax_int @ M ) @ ( lattic8263393255366662781ax_int @ N ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max_mono
% 4.69/4.98 thf(fact_3502_Max__mono,axiom,
% 4.69/4.98 ! [M: set_nat,N: set_nat] :
% 4.69/4.98 ( ( ord_less_eq_set_nat @ M @ N )
% 4.69/4.98 => ( ( M != bot_bot_set_nat )
% 4.69/4.98 => ( ( finite_finite_nat @ N )
% 4.69/4.98 => ( ord_less_eq_nat @ ( lattic8265883725875713057ax_nat @ M ) @ ( lattic8265883725875713057ax_nat @ N ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max_mono
% 4.69/4.98 thf(fact_3503_image__vimage__eq,axiom,
% 4.69/4.98 ! [F: code_integer > code_integer,A: set_Code_integer] :
% 4.69/4.98 ( ( image_4470545334726330049nteger @ F @ ( vimage1318793397690208119nteger @ F @ A ) )
% 4.69/4.98 = ( inf_in1364745209274528805nteger @ A @ ( image_4470545334726330049nteger @ F @ top_to4645266643341252675nteger ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % image_vimage_eq
% 4.69/4.98 thf(fact_3504_image__vimage__eq,axiom,
% 4.69/4.98 ! [F: product_unit > nat,A: set_nat] :
% 4.69/4.98 ( ( image_875570014554754200it_nat @ F @ ( vimage6253328473476588386it_nat @ F @ A ) )
% 4.69/4.98 = ( inf_inf_set_nat @ A @ ( image_875570014554754200it_nat @ F @ top_to1996260823553986621t_unit ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % image_vimage_eq
% 4.69/4.98 thf(fact_3505_image__vimage__eq,axiom,
% 4.69/4.98 ! [F: $o > nat,A: set_nat] :
% 4.69/4.98 ( ( image_o_nat2 @ F @ ( vimage_o_nat @ F @ A ) )
% 4.69/4.98 = ( inf_inf_set_nat @ A @ ( image_o_nat2 @ F @ top_top_set_o ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % image_vimage_eq
% 4.69/4.98 thf(fact_3506_image__vimage__eq,axiom,
% 4.69/4.98 ! [F: nat > set_nat,A: set_set_nat] :
% 4.69/4.98 ( ( image_nat_set_nat @ F @ ( vimage_nat_set_nat @ F @ A ) )
% 4.69/4.98 = ( inf_inf_set_set_nat @ A @ ( image_nat_set_nat @ F @ top_top_set_nat ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % image_vimage_eq
% 4.69/4.98 thf(fact_3507_image__vimage__eq,axiom,
% 4.69/4.98 ! [F: nat > code_integer,A: set_Code_integer] :
% 4.69/4.98 ( ( image_1215581382706833972nteger @ F @ ( vimage6104394758324456170nteger @ F @ A ) )
% 4.69/4.98 = ( inf_in1364745209274528805nteger @ A @ ( image_1215581382706833972nteger @ F @ top_top_set_nat ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % image_vimage_eq
% 4.69/4.98 thf(fact_3508_image__vimage__eq,axiom,
% 4.69/4.98 ! [F: nat > nat,A: set_nat] :
% 4.69/4.98 ( ( image_nat_nat2 @ F @ ( vimage_nat_nat @ F @ A ) )
% 4.69/4.98 = ( inf_inf_set_nat @ A @ ( image_nat_nat2 @ F @ top_top_set_nat ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % image_vimage_eq
% 4.69/4.98 thf(fact_3509_image__vimage__eq,axiom,
% 4.69/4.98 ! [F: int > nat,A: set_nat] :
% 4.69/4.98 ( ( image_int_nat2 @ F @ ( vimage_int_nat @ F @ A ) )
% 4.69/4.98 = ( inf_inf_set_nat @ A @ ( image_int_nat2 @ F @ top_top_set_int ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % image_vimage_eq
% 4.69/4.98 thf(fact_3510_UNIV__I,axiom,
% 4.69/4.98 ! [X: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X @ top_to4869887016220417533_nat_o ) ).
% 4.69/4.98
% 4.69/4.98 % UNIV_I
% 4.69/4.98 thf(fact_3511_UNIV__I,axiom,
% 4.69/4.98 ! [X: product_unit] : ( member_Product_unit @ X @ top_to1996260823553986621t_unit ) ).
% 4.69/4.98
% 4.69/4.98 % UNIV_I
% 4.69/4.98 thf(fact_3512_UNIV__I,axiom,
% 4.69/4.98 ! [X: $o] : ( member_o @ X @ top_top_set_o ) ).
% 4.69/4.98
% 4.69/4.98 % UNIV_I
% 4.69/4.98 thf(fact_3513_UNIV__I,axiom,
% 4.69/4.98 ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 4.69/4.98
% 4.69/4.98 % UNIV_I
% 4.69/4.98 thf(fact_3514_UNIV__I,axiom,
% 4.69/4.98 ! [X: int] : ( member_int @ X @ top_top_set_int ) ).
% 4.69/4.98
% 4.69/4.98 % UNIV_I
% 4.69/4.98 thf(fact_3515_Int__UNIV,axiom,
% 4.69/4.98 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.98 ( ( ( inf_in4660618365625256667t_unit @ A @ B4 )
% 4.69/4.98 = top_to1996260823553986621t_unit )
% 4.69/4.98 = ( ( A = top_to1996260823553986621t_unit )
% 4.69/4.98 & ( B4 = top_to1996260823553986621t_unit ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Int_UNIV
% 4.69/4.98 thf(fact_3516_Int__UNIV,axiom,
% 4.69/4.98 ! [A: set_o,B4: set_o] :
% 4.69/4.98 ( ( ( inf_inf_set_o @ A @ B4 )
% 4.69/4.98 = top_top_set_o )
% 4.69/4.98 = ( ( A = top_top_set_o )
% 4.69/4.98 & ( B4 = top_top_set_o ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Int_UNIV
% 4.69/4.98 thf(fact_3517_Int__UNIV,axiom,
% 4.69/4.98 ! [A: set_nat,B4: set_nat] :
% 4.69/4.98 ( ( ( inf_inf_set_nat @ A @ B4 )
% 4.69/4.98 = top_top_set_nat )
% 4.69/4.98 = ( ( A = top_top_set_nat )
% 4.69/4.98 & ( B4 = top_top_set_nat ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Int_UNIV
% 4.69/4.98 thf(fact_3518_Int__UNIV,axiom,
% 4.69/4.98 ! [A: set_int,B4: set_int] :
% 4.69/4.98 ( ( ( inf_inf_set_int @ A @ B4 )
% 4.69/4.98 = top_top_set_int )
% 4.69/4.98 = ( ( A = top_top_set_int )
% 4.69/4.98 & ( B4 = top_top_set_int ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Int_UNIV
% 4.69/4.98 thf(fact_3519_psubsetI,axiom,
% 4.69/4.98 ! [A: set_nat,B4: set_nat] :
% 4.69/4.98 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.98 => ( ( A != B4 )
% 4.69/4.98 => ( ord_less_set_nat @ A @ B4 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % psubsetI
% 4.69/4.98 thf(fact_3520_vimage__UNIV,axiom,
% 4.69/4.98 ! [F: product_unit > product_unit] :
% 4.69/4.98 ( ( vimage7995052115951654139t_unit @ F @ top_to1996260823553986621t_unit )
% 4.69/4.98 = top_to1996260823553986621t_unit ) ).
% 4.69/4.98
% 4.69/4.98 % vimage_UNIV
% 4.69/4.98 thf(fact_3521_vimage__UNIV,axiom,
% 4.69/4.98 ! [F: $o > product_unit] :
% 4.69/4.98 ( ( vimage4222377557387472176t_unit @ F @ top_to1996260823553986621t_unit )
% 4.69/4.98 = top_top_set_o ) ).
% 4.69/4.98
% 4.69/4.98 % vimage_UNIV
% 4.69/4.98 thf(fact_3522_vimage__UNIV,axiom,
% 4.69/4.98 ! [F: nat > product_unit] :
% 4.69/4.98 ( ( vimage4884490618288580032t_unit @ F @ top_to1996260823553986621t_unit )
% 4.69/4.98 = top_top_set_nat ) ).
% 4.69/4.98
% 4.69/4.98 % vimage_UNIV
% 4.69/4.98 thf(fact_3523_vimage__UNIV,axiom,
% 4.69/4.98 ! [F: int > product_unit] :
% 4.69/4.98 ( ( vimage2000912565490760292t_unit @ F @ top_to1996260823553986621t_unit )
% 4.69/4.98 = top_top_set_int ) ).
% 4.69/4.98
% 4.69/4.98 % vimage_UNIV
% 4.69/4.98 thf(fact_3524_vimage__UNIV,axiom,
% 4.69/4.98 ! [F: product_unit > $o] :
% 4.69/4.98 ( ( vimage8808348054653608838unit_o @ F @ top_top_set_o )
% 4.69/4.98 = top_to1996260823553986621t_unit ) ).
% 4.69/4.98
% 4.69/4.98 % vimage_UNIV
% 4.69/4.98 thf(fact_3525_vimage__UNIV,axiom,
% 4.69/4.98 ! [F: $o > $o] :
% 4.69/4.98 ( ( vimage_o_o @ F @ top_top_set_o )
% 4.69/4.98 = top_top_set_o ) ).
% 4.69/4.98
% 4.69/4.98 % vimage_UNIV
% 4.69/4.98 thf(fact_3526_vimage__UNIV,axiom,
% 4.69/4.98 ! [F: nat > $o] :
% 4.69/4.98 ( ( vimage_nat_o @ F @ top_top_set_o )
% 4.69/4.98 = top_top_set_nat ) ).
% 4.69/4.98
% 4.69/4.98 % vimage_UNIV
% 4.69/4.98 thf(fact_3527_vimage__UNIV,axiom,
% 4.69/4.98 ! [F: int > $o] :
% 4.69/4.98 ( ( vimage_int_o @ F @ top_top_set_o )
% 4.69/4.98 = top_top_set_int ) ).
% 4.69/4.98
% 4.69/4.98 % vimage_UNIV
% 4.69/4.98 thf(fact_3528_vimage__UNIV,axiom,
% 4.69/4.98 ! [F: product_unit > nat] :
% 4.69/4.98 ( ( vimage6253328473476588386it_nat @ F @ top_top_set_nat )
% 4.69/4.98 = top_to1996260823553986621t_unit ) ).
% 4.69/4.98
% 4.69/4.98 % vimage_UNIV
% 4.69/4.98 thf(fact_3529_vimage__UNIV,axiom,
% 4.69/4.98 ! [F: $o > nat] :
% 4.69/4.98 ( ( vimage_o_nat @ F @ top_top_set_nat )
% 4.69/4.98 = top_top_set_o ) ).
% 4.69/4.98
% 4.69/4.98 % vimage_UNIV
% 4.69/4.98 thf(fact_3530_Pow__UNIV,axiom,
% 4.69/4.98 ( ( pow_Product_unit @ top_to1996260823553986621t_unit )
% 4.69/4.98 = top_to1767297665138865437t_unit ) ).
% 4.69/4.98
% 4.69/4.98 % Pow_UNIV
% 4.69/4.98 thf(fact_3531_Pow__UNIV,axiom,
% 4.69/4.98 ( ( pow_o @ top_top_set_o )
% 4.69/4.98 = top_top_set_set_o ) ).
% 4.69/4.98
% 4.69/4.98 % Pow_UNIV
% 4.69/4.98 thf(fact_3532_Pow__UNIV,axiom,
% 4.69/4.98 ( ( pow_nat @ top_top_set_nat )
% 4.69/4.98 = top_top_set_set_nat ) ).
% 4.69/4.98
% 4.69/4.98 % Pow_UNIV
% 4.69/4.98 thf(fact_3533_Pow__UNIV,axiom,
% 4.69/4.98 ( ( pow_int @ top_top_set_int )
% 4.69/4.98 = top_top_set_set_int ) ).
% 4.69/4.98
% 4.69/4.98 % Pow_UNIV
% 4.69/4.98 thf(fact_3534_Diff__UNIV,axiom,
% 4.69/4.98 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.98 ( ( minus_1801376950450012436_nat_o @ A @ top_to4869887016220417533_nat_o )
% 4.69/4.98 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/4.98
% 4.69/4.98 % Diff_UNIV
% 4.69/4.98 thf(fact_3535_Diff__UNIV,axiom,
% 4.69/4.98 ! [A: set_Product_unit] :
% 4.69/4.98 ( ( minus_6452836326544984404t_unit @ A @ top_to1996260823553986621t_unit )
% 4.69/4.98 = bot_bo3957492148770167129t_unit ) ).
% 4.69/4.98
% 4.69/4.98 % Diff_UNIV
% 4.69/4.98 thf(fact_3536_Diff__UNIV,axiom,
% 4.69/4.98 ! [A: set_o] :
% 4.69/4.98 ( ( minus_minus_set_o @ A @ top_top_set_o )
% 4.69/4.98 = bot_bot_set_o ) ).
% 4.69/4.98
% 4.69/4.98 % Diff_UNIV
% 4.69/4.98 thf(fact_3537_Diff__UNIV,axiom,
% 4.69/4.98 ! [A: set_int] :
% 4.69/4.98 ( ( minus_minus_set_int @ A @ top_top_set_int )
% 4.69/4.98 = bot_bot_set_int ) ).
% 4.69/4.98
% 4.69/4.98 % Diff_UNIV
% 4.69/4.98 thf(fact_3538_Diff__UNIV,axiom,
% 4.69/4.98 ! [A: set_nat] :
% 4.69/4.98 ( ( minus_minus_set_nat @ A @ top_top_set_nat )
% 4.69/4.98 = bot_bot_set_nat ) ).
% 4.69/4.98
% 4.69/4.98 % Diff_UNIV
% 4.69/4.98 thf(fact_3539_Max__singleton,axiom,
% 4.69/4.98 ! [X: product_unit] :
% 4.69/4.98 ( ( lattic1210392890313158908t_unit @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.98 = X ) ).
% 4.69/4.98
% 4.69/4.98 % Max_singleton
% 4.69/4.98 thf(fact_3540_Max__singleton,axiom,
% 4.69/4.98 ! [X: $o] :
% 4.69/4.98 ( ( lattic1921953407002678535_Max_o @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.98 = X ) ).
% 4.69/4.98
% 4.69/4.98 % Max_singleton
% 4.69/4.98 thf(fact_3541_Max__singleton,axiom,
% 4.69/4.98 ! [X: int] :
% 4.69/4.98 ( ( lattic8263393255366662781ax_int @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.98 = X ) ).
% 4.69/4.98
% 4.69/4.98 % Max_singleton
% 4.69/4.98 thf(fact_3542_Max__singleton,axiom,
% 4.69/4.98 ! [X: nat] :
% 4.69/4.98 ( ( lattic8265883725875713057ax_nat @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.98 = X ) ).
% 4.69/4.98
% 4.69/4.98 % Max_singleton
% 4.69/4.98 thf(fact_3543_range__snd,axiom,
% 4.69/4.98 ( ( image_6088997261112373647et_nat @ produc8586169260539613262et_nat @ top_to2524957550908328808et_nat )
% 4.69/4.98 = top_top_set_set_nat ) ).
% 4.69/4.98
% 4.69/4.98 % range_snd
% 4.69/4.98 thf(fact_3544_range__snd,axiom,
% 4.69/4.98 ( ( image_5042161079198086560nt_int @ product_snd_int_int @ top_to4366644338036079209nt_int )
% 4.69/4.98 = top_top_set_int ) ).
% 4.69/4.98
% 4.69/4.98 % range_snd
% 4.69/4.98 thf(fact_3545_Domain__Id,axiom,
% 4.69/4.98 ( ( domain4292024440186670924t_unit @ id_Product_unit )
% 4.69/4.98 = top_to1996260823553986621t_unit ) ).
% 4.69/4.98
% 4.69/4.98 % Domain_Id
% 4.69/4.98 thf(fact_3546_Domain__Id,axiom,
% 4.69/4.98 ( ( domain_o_o @ id_o2 )
% 4.69/4.98 = top_top_set_o ) ).
% 4.69/4.98
% 4.69/4.98 % Domain_Id
% 4.69/4.98 thf(fact_3547_Domain__Id,axiom,
% 4.69/4.98 ( ( domain_nat_nat @ id_nat )
% 4.69/4.98 = top_top_set_nat ) ).
% 4.69/4.98
% 4.69/4.98 % Domain_Id
% 4.69/4.98 thf(fact_3548_Domain__Id,axiom,
% 4.69/4.98 ( ( domain_int_int @ id_int )
% 4.69/4.98 = top_top_set_int ) ).
% 4.69/4.98
% 4.69/4.98 % Domain_Id
% 4.69/4.98 thf(fact_3549_Range__Id,axiom,
% 4.69/4.98 ( ( range_6617724647562260917t_unit @ id_Product_unit )
% 4.69/4.98 = top_to1996260823553986621t_unit ) ).
% 4.69/4.98
% 4.69/4.98 % Range_Id
% 4.69/4.98 thf(fact_3550_Range__Id,axiom,
% 4.69/4.98 ( ( range_o_o @ id_o2 )
% 4.69/4.98 = top_top_set_o ) ).
% 4.69/4.98
% 4.69/4.98 % Range_Id
% 4.69/4.98 thf(fact_3551_Range__Id,axiom,
% 4.69/4.98 ( ( range_nat_nat @ id_nat )
% 4.69/4.98 = top_top_set_nat ) ).
% 4.69/4.98
% 4.69/4.98 % Range_Id
% 4.69/4.98 thf(fact_3552_Range__Id,axiom,
% 4.69/4.98 ( ( range_int_int @ id_int )
% 4.69/4.98 = top_top_set_int ) ).
% 4.69/4.98
% 4.69/4.98 % Range_Id
% 4.69/4.98 thf(fact_3553_Max_Obounded__iff,axiom,
% 4.69/4.98 ! [A: set_Code_integer,X: code_integer] :
% 4.69/4.98 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.98 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/4.98 => ( ( ord_le3102999989581377725nteger @ ( lattic4901227151466704046nteger @ A ) @ X )
% 4.69/4.98 = ( ! [X2: code_integer] :
% 4.69/4.98 ( ( member_Code_integer @ X2 @ A )
% 4.69/4.98 => ( ord_le3102999989581377725nteger @ X2 @ X ) ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max.bounded_iff
% 4.69/4.98 thf(fact_3554_Max_Obounded__iff,axiom,
% 4.69/4.98 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.98 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.98 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.98 => ( ( ord_le3221252021190050221t_unit @ ( lattic1210392890313158908t_unit @ A ) @ X )
% 4.69/4.98 = ( ! [X2: product_unit] :
% 4.69/4.98 ( ( member_Product_unit @ X2 @ A )
% 4.69/4.98 => ( ord_le3221252021190050221t_unit @ X2 @ X ) ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max.bounded_iff
% 4.69/4.98 thf(fact_3555_Max_Obounded__iff,axiom,
% 4.69/4.98 ! [A: set_o,X: $o] :
% 4.69/4.98 ( ( finite_finite_o @ A )
% 4.69/4.98 => ( ( A != bot_bot_set_o )
% 4.69/4.98 => ( ( ord_less_eq_o @ ( lattic1921953407002678535_Max_o @ A ) @ X )
% 4.69/4.98 = ( ! [X2: $o] :
% 4.69/4.98 ( ( member_o @ X2 @ A )
% 4.69/4.98 => ( ord_less_eq_o @ X2 @ X ) ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max.bounded_iff
% 4.69/4.98 thf(fact_3556_Max_Obounded__iff,axiom,
% 4.69/4.98 ! [A: set_rat,X: rat] :
% 4.69/4.98 ( ( finite_finite_rat @ A )
% 4.69/4.98 => ( ( A != bot_bot_set_rat )
% 4.69/4.98 => ( ( ord_less_eq_rat @ ( lattic7630753665789217321ax_rat @ A ) @ X )
% 4.69/4.98 = ( ! [X2: rat] :
% 4.69/4.98 ( ( member_rat @ X2 @ A )
% 4.69/4.98 => ( ord_less_eq_rat @ X2 @ X ) ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max.bounded_iff
% 4.69/4.98 thf(fact_3557_Max_Obounded__iff,axiom,
% 4.69/4.98 ! [A: set_int,X: int] :
% 4.69/4.98 ( ( finite_finite_int @ A )
% 4.69/4.98 => ( ( A != bot_bot_set_int )
% 4.69/4.98 => ( ( ord_less_eq_int @ ( lattic8263393255366662781ax_int @ A ) @ X )
% 4.69/4.98 = ( ! [X2: int] :
% 4.69/4.98 ( ( member_int @ X2 @ A )
% 4.69/4.98 => ( ord_less_eq_int @ X2 @ X ) ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max.bounded_iff
% 4.69/4.98 thf(fact_3558_Max_Obounded__iff,axiom,
% 4.69/4.98 ! [A: set_nat,X: nat] :
% 4.69/4.98 ( ( finite_finite_nat @ A )
% 4.69/4.98 => ( ( A != bot_bot_set_nat )
% 4.69/4.98 => ( ( ord_less_eq_nat @ ( lattic8265883725875713057ax_nat @ A ) @ X )
% 4.69/4.98 = ( ! [X2: nat] :
% 4.69/4.98 ( ( member_nat @ X2 @ A )
% 4.69/4.98 => ( ord_less_eq_nat @ X2 @ X ) ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max.bounded_iff
% 4.69/4.98 thf(fact_3559_Max__less__iff,axiom,
% 4.69/4.98 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.98 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.98 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.98 => ( ( ord_le361264281704409273t_unit @ ( lattic1210392890313158908t_unit @ A ) @ X )
% 4.69/4.98 = ( ! [X2: product_unit] :
% 4.69/4.98 ( ( member_Product_unit @ X2 @ A )
% 4.69/4.98 => ( ord_le361264281704409273t_unit @ X2 @ X ) ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max_less_iff
% 4.69/4.98 thf(fact_3560_Max__less__iff,axiom,
% 4.69/4.98 ! [A: set_o,X: $o] :
% 4.69/4.98 ( ( finite_finite_o @ A )
% 4.69/4.98 => ( ( A != bot_bot_set_o )
% 4.69/4.98 => ( ( ord_less_o @ ( lattic1921953407002678535_Max_o @ A ) @ X )
% 4.69/4.98 = ( ! [X2: $o] :
% 4.69/4.98 ( ( member_o @ X2 @ A )
% 4.69/4.98 => ( ord_less_o @ X2 @ X ) ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max_less_iff
% 4.69/4.98 thf(fact_3561_Max__less__iff,axiom,
% 4.69/4.98 ! [A: set_int,X: int] :
% 4.69/4.98 ( ( finite_finite_int @ A )
% 4.69/4.98 => ( ( A != bot_bot_set_int )
% 4.69/4.98 => ( ( ord_less_int @ ( lattic8263393255366662781ax_int @ A ) @ X )
% 4.69/4.98 = ( ! [X2: int] :
% 4.69/4.98 ( ( member_int @ X2 @ A )
% 4.69/4.98 => ( ord_less_int @ X2 @ X ) ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max_less_iff
% 4.69/4.98 thf(fact_3562_Max__less__iff,axiom,
% 4.69/4.98 ! [A: set_Code_integer,X: code_integer] :
% 4.69/4.98 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.98 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/4.98 => ( ( ord_le6747313008572928689nteger @ ( lattic4901227151466704046nteger @ A ) @ X )
% 4.69/4.98 = ( ! [X2: code_integer] :
% 4.69/4.98 ( ( member_Code_integer @ X2 @ A )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ X2 @ X ) ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max_less_iff
% 4.69/4.98 thf(fact_3563_Max__less__iff,axiom,
% 4.69/4.98 ! [A: set_rat,X: rat] :
% 4.69/4.98 ( ( finite_finite_rat @ A )
% 4.69/4.98 => ( ( A != bot_bot_set_rat )
% 4.69/4.98 => ( ( ord_less_rat @ ( lattic7630753665789217321ax_rat @ A ) @ X )
% 4.69/4.98 = ( ! [X2: rat] :
% 4.69/4.98 ( ( member_rat @ X2 @ A )
% 4.69/4.98 => ( ord_less_rat @ X2 @ X ) ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max_less_iff
% 4.69/4.98 thf(fact_3564_Max__less__iff,axiom,
% 4.69/4.98 ! [A: set_nat,X: nat] :
% 4.69/4.98 ( ( finite_finite_nat @ A )
% 4.69/4.98 => ( ( A != bot_bot_set_nat )
% 4.69/4.98 => ( ( ord_less_nat @ ( lattic8265883725875713057ax_nat @ A ) @ X )
% 4.69/4.98 = ( ! [X2: nat] :
% 4.69/4.98 ( ( member_nat @ X2 @ A )
% 4.69/4.98 => ( ord_less_nat @ X2 @ X ) ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max_less_iff
% 4.69/4.98 thf(fact_3565_lt__ex,axiom,
% 4.69/4.98 ! [X: int] :
% 4.69/4.98 ? [Y2: int] : ( ord_less_int @ Y2 @ X ) ).
% 4.69/4.98
% 4.69/4.98 % lt_ex
% 4.69/4.98 thf(fact_3566_lt__ex,axiom,
% 4.69/4.98 ! [X: rat] :
% 4.69/4.98 ? [Y2: rat] : ( ord_less_rat @ Y2 @ X ) ).
% 4.69/4.98
% 4.69/4.98 % lt_ex
% 4.69/4.98 thf(fact_3567_gt__ex,axiom,
% 4.69/4.98 ! [X: nat] :
% 4.69/4.98 ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 4.69/4.98
% 4.69/4.98 % gt_ex
% 4.69/4.98 thf(fact_3568_gt__ex,axiom,
% 4.69/4.98 ! [X: int] :
% 4.69/4.98 ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% 4.69/4.98
% 4.69/4.98 % gt_ex
% 4.69/4.98 thf(fact_3569_gt__ex,axiom,
% 4.69/4.98 ! [X: rat] :
% 4.69/4.98 ? [X_1: rat] : ( ord_less_rat @ X @ X_1 ) ).
% 4.69/4.98
% 4.69/4.98 % gt_ex
% 4.69/4.98 thf(fact_3570_dense,axiom,
% 4.69/4.98 ! [X: rat,Y: rat] :
% 4.69/4.98 ( ( ord_less_rat @ X @ Y )
% 4.69/4.98 => ? [Z3: rat] :
% 4.69/4.98 ( ( ord_less_rat @ X @ Z3 )
% 4.69/4.98 & ( ord_less_rat @ Z3 @ Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dense
% 4.69/4.98 thf(fact_3571_less__imp__neq,axiom,
% 4.69/4.98 ! [X: assn,Y: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X @ Y )
% 4.69/4.98 => ( X != Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % less_imp_neq
% 4.69/4.98 thf(fact_3572_less__imp__neq,axiom,
% 4.69/4.98 ! [X: nat,Y: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X @ Y )
% 4.69/4.98 => ( X != Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % less_imp_neq
% 4.69/4.98 thf(fact_3573_less__imp__neq,axiom,
% 4.69/4.98 ! [X: int,Y: int] :
% 4.69/4.98 ( ( ord_less_int @ X @ Y )
% 4.69/4.98 => ( X != Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % less_imp_neq
% 4.69/4.98 thf(fact_3574_less__imp__neq,axiom,
% 4.69/4.98 ! [X: code_integer,Y: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ X @ Y )
% 4.69/4.98 => ( X != Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % less_imp_neq
% 4.69/4.98 thf(fact_3575_less__imp__neq,axiom,
% 4.69/4.98 ! [X: rat,Y: rat] :
% 4.69/4.98 ( ( ord_less_rat @ X @ Y )
% 4.69/4.98 => ( X != Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % less_imp_neq
% 4.69/4.98 thf(fact_3576_order_Oasym,axiom,
% 4.69/4.98 ! [A2: assn,B: assn] :
% 4.69/4.98 ( ( ord_less_assn @ A2 @ B )
% 4.69/4.98 => ~ ( ord_less_assn @ B @ A2 ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.asym
% 4.69/4.98 thf(fact_3577_order_Oasym,axiom,
% 4.69/4.98 ! [A2: nat,B: nat] :
% 4.69/4.98 ( ( ord_less_nat @ A2 @ B )
% 4.69/4.98 => ~ ( ord_less_nat @ B @ A2 ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.asym
% 4.69/4.98 thf(fact_3578_order_Oasym,axiom,
% 4.69/4.98 ! [A2: int,B: int] :
% 4.69/4.98 ( ( ord_less_int @ A2 @ B )
% 4.69/4.98 => ~ ( ord_less_int @ B @ A2 ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.asym
% 4.69/4.98 thf(fact_3579_order_Oasym,axiom,
% 4.69/4.98 ! [A2: code_integer,B: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/4.98 => ~ ( ord_le6747313008572928689nteger @ B @ A2 ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.asym
% 4.69/4.98 thf(fact_3580_order_Oasym,axiom,
% 4.69/4.98 ! [A2: rat,B: rat] :
% 4.69/4.98 ( ( ord_less_rat @ A2 @ B )
% 4.69/4.98 => ~ ( ord_less_rat @ B @ A2 ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.asym
% 4.69/4.98 thf(fact_3581_ord__eq__less__trans,axiom,
% 4.69/4.98 ! [A2: assn,B: assn,C: assn] :
% 4.69/4.98 ( ( A2 = B )
% 4.69/4.98 => ( ( ord_less_assn @ B @ C )
% 4.69/4.98 => ( ord_less_assn @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_eq_less_trans
% 4.69/4.98 thf(fact_3582_ord__eq__less__trans,axiom,
% 4.69/4.98 ! [A2: nat,B: nat,C: nat] :
% 4.69/4.98 ( ( A2 = B )
% 4.69/4.98 => ( ( ord_less_nat @ B @ C )
% 4.69/4.98 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_eq_less_trans
% 4.69/4.98 thf(fact_3583_ord__eq__less__trans,axiom,
% 4.69/4.98 ! [A2: int,B: int,C: int] :
% 4.69/4.98 ( ( A2 = B )
% 4.69/4.98 => ( ( ord_less_int @ B @ C )
% 4.69/4.98 => ( ord_less_int @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_eq_less_trans
% 4.69/4.98 thf(fact_3584_ord__eq__less__trans,axiom,
% 4.69/4.98 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/4.98 ( ( A2 = B )
% 4.69/4.98 => ( ( ord_le6747313008572928689nteger @ B @ C )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_eq_less_trans
% 4.69/4.98 thf(fact_3585_ord__eq__less__trans,axiom,
% 4.69/4.98 ! [A2: rat,B: rat,C: rat] :
% 4.69/4.98 ( ( A2 = B )
% 4.69/4.98 => ( ( ord_less_rat @ B @ C )
% 4.69/4.98 => ( ord_less_rat @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_eq_less_trans
% 4.69/4.98 thf(fact_3586_ord__less__eq__trans,axiom,
% 4.69/4.98 ! [A2: assn,B: assn,C: assn] :
% 4.69/4.98 ( ( ord_less_assn @ A2 @ B )
% 4.69/4.98 => ( ( B = C )
% 4.69/4.98 => ( ord_less_assn @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_less_eq_trans
% 4.69/4.98 thf(fact_3587_ord__less__eq__trans,axiom,
% 4.69/4.98 ! [A2: nat,B: nat,C: nat] :
% 4.69/4.98 ( ( ord_less_nat @ A2 @ B )
% 4.69/4.98 => ( ( B = C )
% 4.69/4.98 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_less_eq_trans
% 4.69/4.98 thf(fact_3588_ord__less__eq__trans,axiom,
% 4.69/4.98 ! [A2: int,B: int,C: int] :
% 4.69/4.98 ( ( ord_less_int @ A2 @ B )
% 4.69/4.98 => ( ( B = C )
% 4.69/4.98 => ( ord_less_int @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_less_eq_trans
% 4.69/4.98 thf(fact_3589_ord__less__eq__trans,axiom,
% 4.69/4.98 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/4.98 => ( ( B = C )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_less_eq_trans
% 4.69/4.98 thf(fact_3590_ord__less__eq__trans,axiom,
% 4.69/4.98 ! [A2: rat,B: rat,C: rat] :
% 4.69/4.98 ( ( ord_less_rat @ A2 @ B )
% 4.69/4.98 => ( ( B = C )
% 4.69/4.98 => ( ord_less_rat @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_less_eq_trans
% 4.69/4.98 thf(fact_3591_less__induct,axiom,
% 4.69/4.98 ! [P: nat > $o,A2: nat] :
% 4.69/4.98 ( ! [X3: nat] :
% 4.69/4.98 ( ! [Y5: nat] :
% 4.69/4.98 ( ( ord_less_nat @ Y5 @ X3 )
% 4.69/4.98 => ( P @ Y5 ) )
% 4.69/4.98 => ( P @ X3 ) )
% 4.69/4.98 => ( P @ A2 ) ) ).
% 4.69/4.98
% 4.69/4.98 % less_induct
% 4.69/4.98 thf(fact_3592_antisym__conv3,axiom,
% 4.69/4.98 ! [Y: nat,X: nat] :
% 4.69/4.98 ( ~ ( ord_less_nat @ Y @ X )
% 4.69/4.98 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 4.69/4.98 = ( X = Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % antisym_conv3
% 4.69/4.98 thf(fact_3593_antisym__conv3,axiom,
% 4.69/4.98 ! [Y: int,X: int] :
% 4.69/4.98 ( ~ ( ord_less_int @ Y @ X )
% 4.69/4.98 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 4.69/4.98 = ( X = Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % antisym_conv3
% 4.69/4.98 thf(fact_3594_antisym__conv3,axiom,
% 4.69/4.98 ! [Y: code_integer,X: code_integer] :
% 4.69/4.98 ( ~ ( ord_le6747313008572928689nteger @ Y @ X )
% 4.69/4.98 => ( ( ~ ( ord_le6747313008572928689nteger @ X @ Y ) )
% 4.69/4.98 = ( X = Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % antisym_conv3
% 4.69/4.98 thf(fact_3595_antisym__conv3,axiom,
% 4.69/4.98 ! [Y: rat,X: rat] :
% 4.69/4.98 ( ~ ( ord_less_rat @ Y @ X )
% 4.69/4.98 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 4.69/4.98 = ( X = Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % antisym_conv3
% 4.69/4.98 thf(fact_3596_linorder__cases,axiom,
% 4.69/4.98 ! [X: nat,Y: nat] :
% 4.69/4.98 ( ~ ( ord_less_nat @ X @ Y )
% 4.69/4.98 => ( ( X != Y )
% 4.69/4.98 => ( ord_less_nat @ Y @ X ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_cases
% 4.69/4.98 thf(fact_3597_linorder__cases,axiom,
% 4.69/4.98 ! [X: int,Y: int] :
% 4.69/4.98 ( ~ ( ord_less_int @ X @ Y )
% 4.69/4.98 => ( ( X != Y )
% 4.69/4.98 => ( ord_less_int @ Y @ X ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_cases
% 4.69/4.98 thf(fact_3598_linorder__cases,axiom,
% 4.69/4.98 ! [X: code_integer,Y: code_integer] :
% 4.69/4.98 ( ~ ( ord_le6747313008572928689nteger @ X @ Y )
% 4.69/4.98 => ( ( X != Y )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ Y @ X ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_cases
% 4.69/4.98 thf(fact_3599_linorder__cases,axiom,
% 4.69/4.98 ! [X: rat,Y: rat] :
% 4.69/4.98 ( ~ ( ord_less_rat @ X @ Y )
% 4.69/4.98 => ( ( X != Y )
% 4.69/4.98 => ( ord_less_rat @ Y @ X ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_cases
% 4.69/4.98 thf(fact_3600_dual__order_Oasym,axiom,
% 4.69/4.98 ! [B: assn,A2: assn] :
% 4.69/4.98 ( ( ord_less_assn @ B @ A2 )
% 4.69/4.98 => ~ ( ord_less_assn @ A2 @ B ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.asym
% 4.69/4.98 thf(fact_3601_dual__order_Oasym,axiom,
% 4.69/4.98 ! [B: nat,A2: nat] :
% 4.69/4.98 ( ( ord_less_nat @ B @ A2 )
% 4.69/4.98 => ~ ( ord_less_nat @ A2 @ B ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.asym
% 4.69/4.98 thf(fact_3602_dual__order_Oasym,axiom,
% 4.69/4.98 ! [B: int,A2: int] :
% 4.69/4.98 ( ( ord_less_int @ B @ A2 )
% 4.69/4.98 => ~ ( ord_less_int @ A2 @ B ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.asym
% 4.69/4.98 thf(fact_3603_dual__order_Oasym,axiom,
% 4.69/4.98 ! [B: code_integer,A2: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ B @ A2 )
% 4.69/4.98 => ~ ( ord_le6747313008572928689nteger @ A2 @ B ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.asym
% 4.69/4.98 thf(fact_3604_dual__order_Oasym,axiom,
% 4.69/4.98 ! [B: rat,A2: rat] :
% 4.69/4.98 ( ( ord_less_rat @ B @ A2 )
% 4.69/4.98 => ~ ( ord_less_rat @ A2 @ B ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.asym
% 4.69/4.98 thf(fact_3605_dual__order_Oirrefl,axiom,
% 4.69/4.98 ! [A2: assn] :
% 4.69/4.98 ~ ( ord_less_assn @ A2 @ A2 ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.irrefl
% 4.69/4.98 thf(fact_3606_dual__order_Oirrefl,axiom,
% 4.69/4.98 ! [A2: nat] :
% 4.69/4.98 ~ ( ord_less_nat @ A2 @ A2 ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.irrefl
% 4.69/4.98 thf(fact_3607_dual__order_Oirrefl,axiom,
% 4.69/4.98 ! [A2: int] :
% 4.69/4.98 ~ ( ord_less_int @ A2 @ A2 ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.irrefl
% 4.69/4.98 thf(fact_3608_dual__order_Oirrefl,axiom,
% 4.69/4.98 ! [A2: code_integer] :
% 4.69/4.98 ~ ( ord_le6747313008572928689nteger @ A2 @ A2 ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.irrefl
% 4.69/4.98 thf(fact_3609_dual__order_Oirrefl,axiom,
% 4.69/4.98 ! [A2: rat] :
% 4.69/4.98 ~ ( ord_less_rat @ A2 @ A2 ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.irrefl
% 4.69/4.98 thf(fact_3610_exists__least__iff,axiom,
% 4.69/4.98 ( ( ^ [P6: nat > $o] :
% 4.69/4.98 ? [X9: nat] : ( P6 @ X9 ) )
% 4.69/4.98 = ( ^ [P2: nat > $o] :
% 4.69/4.98 ? [N4: nat] :
% 4.69/4.98 ( ( P2 @ N4 )
% 4.69/4.98 & ! [M3: nat] :
% 4.69/4.98 ( ( ord_less_nat @ M3 @ N4 )
% 4.69/4.98 => ~ ( P2 @ M3 ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % exists_least_iff
% 4.69/4.98 thf(fact_3611_linorder__less__wlog,axiom,
% 4.69/4.98 ! [P: nat > nat > $o,A2: nat,B: nat] :
% 4.69/4.98 ( ! [A4: nat,B2: nat] :
% 4.69/4.98 ( ( ord_less_nat @ A4 @ B2 )
% 4.69/4.98 => ( P @ A4 @ B2 ) )
% 4.69/4.98 => ( ! [A4: nat] : ( P @ A4 @ A4 )
% 4.69/4.98 => ( ! [A4: nat,B2: nat] :
% 4.69/4.98 ( ( P @ B2 @ A4 )
% 4.69/4.98 => ( P @ A4 @ B2 ) )
% 4.69/4.98 => ( P @ A2 @ B ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_less_wlog
% 4.69/4.98 thf(fact_3612_linorder__less__wlog,axiom,
% 4.69/4.98 ! [P: int > int > $o,A2: int,B: int] :
% 4.69/4.98 ( ! [A4: int,B2: int] :
% 4.69/4.98 ( ( ord_less_int @ A4 @ B2 )
% 4.69/4.98 => ( P @ A4 @ B2 ) )
% 4.69/4.98 => ( ! [A4: int] : ( P @ A4 @ A4 )
% 4.69/4.98 => ( ! [A4: int,B2: int] :
% 4.69/4.98 ( ( P @ B2 @ A4 )
% 4.69/4.98 => ( P @ A4 @ B2 ) )
% 4.69/4.98 => ( P @ A2 @ B ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_less_wlog
% 4.69/4.98 thf(fact_3613_linorder__less__wlog,axiom,
% 4.69/4.98 ! [P: code_integer > code_integer > $o,A2: code_integer,B: code_integer] :
% 4.69/4.98 ( ! [A4: code_integer,B2: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ A4 @ B2 )
% 4.69/4.98 => ( P @ A4 @ B2 ) )
% 4.69/4.98 => ( ! [A4: code_integer] : ( P @ A4 @ A4 )
% 4.69/4.98 => ( ! [A4: code_integer,B2: code_integer] :
% 4.69/4.98 ( ( P @ B2 @ A4 )
% 4.69/4.98 => ( P @ A4 @ B2 ) )
% 4.69/4.98 => ( P @ A2 @ B ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_less_wlog
% 4.69/4.98 thf(fact_3614_linorder__less__wlog,axiom,
% 4.69/4.98 ! [P: rat > rat > $o,A2: rat,B: rat] :
% 4.69/4.98 ( ! [A4: rat,B2: rat] :
% 4.69/4.98 ( ( ord_less_rat @ A4 @ B2 )
% 4.69/4.98 => ( P @ A4 @ B2 ) )
% 4.69/4.98 => ( ! [A4: rat] : ( P @ A4 @ A4 )
% 4.69/4.98 => ( ! [A4: rat,B2: rat] :
% 4.69/4.98 ( ( P @ B2 @ A4 )
% 4.69/4.98 => ( P @ A4 @ B2 ) )
% 4.69/4.98 => ( P @ A2 @ B ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_less_wlog
% 4.69/4.98 thf(fact_3615_order_Ostrict__trans,axiom,
% 4.69/4.98 ! [A2: assn,B: assn,C: assn] :
% 4.69/4.98 ( ( ord_less_assn @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_assn @ B @ C )
% 4.69/4.98 => ( ord_less_assn @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_trans
% 4.69/4.98 thf(fact_3616_order_Ostrict__trans,axiom,
% 4.69/4.98 ! [A2: nat,B: nat,C: nat] :
% 4.69/4.98 ( ( ord_less_nat @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_nat @ B @ C )
% 4.69/4.98 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_trans
% 4.69/4.98 thf(fact_3617_order_Ostrict__trans,axiom,
% 4.69/4.98 ! [A2: int,B: int,C: int] :
% 4.69/4.98 ( ( ord_less_int @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_int @ B @ C )
% 4.69/4.98 => ( ord_less_int @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_trans
% 4.69/4.98 thf(fact_3618_order_Ostrict__trans,axiom,
% 4.69/4.98 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/4.98 => ( ( ord_le6747313008572928689nteger @ B @ C )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_trans
% 4.69/4.98 thf(fact_3619_order_Ostrict__trans,axiom,
% 4.69/4.98 ! [A2: rat,B: rat,C: rat] :
% 4.69/4.98 ( ( ord_less_rat @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_rat @ B @ C )
% 4.69/4.98 => ( ord_less_rat @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_trans
% 4.69/4.98 thf(fact_3620_top_Oextremum__strict,axiom,
% 4.69/4.98 ! [A2: set_Product_unit] :
% 4.69/4.98 ~ ( ord_le8056459307392131481t_unit @ top_to1996260823553986621t_unit @ A2 ) ).
% 4.69/4.98
% 4.69/4.98 % top.extremum_strict
% 4.69/4.98 thf(fact_3621_top_Oextremum__strict,axiom,
% 4.69/4.98 ! [A2: set_o] :
% 4.69/4.98 ~ ( ord_less_set_o @ top_top_set_o @ A2 ) ).
% 4.69/4.98
% 4.69/4.98 % top.extremum_strict
% 4.69/4.98 thf(fact_3622_top_Oextremum__strict,axiom,
% 4.69/4.98 ! [A2: set_nat] :
% 4.69/4.98 ~ ( ord_less_set_nat @ top_top_set_nat @ A2 ) ).
% 4.69/4.98
% 4.69/4.98 % top.extremum_strict
% 4.69/4.98 thf(fact_3623_top_Oextremum__strict,axiom,
% 4.69/4.98 ! [A2: set_int] :
% 4.69/4.98 ~ ( ord_less_set_int @ top_top_set_int @ A2 ) ).
% 4.69/4.98
% 4.69/4.98 % top.extremum_strict
% 4.69/4.98 thf(fact_3624_top_Oextremum__strict,axiom,
% 4.69/4.98 ! [A2: assn] :
% 4.69/4.98 ~ ( ord_less_assn @ top_top_assn @ A2 ) ).
% 4.69/4.98
% 4.69/4.98 % top.extremum_strict
% 4.69/4.98 thf(fact_3625_top_Onot__eq__extremum,axiom,
% 4.69/4.98 ! [A2: set_Product_unit] :
% 4.69/4.98 ( ( A2 != top_to1996260823553986621t_unit )
% 4.69/4.98 = ( ord_le8056459307392131481t_unit @ A2 @ top_to1996260823553986621t_unit ) ) ).
% 4.69/4.98
% 4.69/4.98 % top.not_eq_extremum
% 4.69/4.98 thf(fact_3626_top_Onot__eq__extremum,axiom,
% 4.69/4.98 ! [A2: set_o] :
% 4.69/4.98 ( ( A2 != top_top_set_o )
% 4.69/4.98 = ( ord_less_set_o @ A2 @ top_top_set_o ) ) ).
% 4.69/4.98
% 4.69/4.98 % top.not_eq_extremum
% 4.69/4.98 thf(fact_3627_top_Onot__eq__extremum,axiom,
% 4.69/4.98 ! [A2: set_nat] :
% 4.69/4.98 ( ( A2 != top_top_set_nat )
% 4.69/4.98 = ( ord_less_set_nat @ A2 @ top_top_set_nat ) ) ).
% 4.69/4.98
% 4.69/4.98 % top.not_eq_extremum
% 4.69/4.98 thf(fact_3628_top_Onot__eq__extremum,axiom,
% 4.69/4.98 ! [A2: set_int] :
% 4.69/4.98 ( ( A2 != top_top_set_int )
% 4.69/4.98 = ( ord_less_set_int @ A2 @ top_top_set_int ) ) ).
% 4.69/4.98
% 4.69/4.98 % top.not_eq_extremum
% 4.69/4.98 thf(fact_3629_top_Onot__eq__extremum,axiom,
% 4.69/4.98 ! [A2: assn] :
% 4.69/4.98 ( ( A2 != top_top_assn )
% 4.69/4.98 = ( ord_less_assn @ A2 @ top_top_assn ) ) ).
% 4.69/4.98
% 4.69/4.98 % top.not_eq_extremum
% 4.69/4.98 thf(fact_3630_not__less__iff__gr__or__eq,axiom,
% 4.69/4.98 ! [X: nat,Y: nat] :
% 4.69/4.98 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 4.69/4.98 = ( ( ord_less_nat @ Y @ X )
% 4.69/4.98 | ( X = Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % not_less_iff_gr_or_eq
% 4.69/4.98 thf(fact_3631_not__less__iff__gr__or__eq,axiom,
% 4.69/4.98 ! [X: int,Y: int] :
% 4.69/4.98 ( ( ~ ( ord_less_int @ X @ Y ) )
% 4.69/4.98 = ( ( ord_less_int @ Y @ X )
% 4.69/4.98 | ( X = Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % not_less_iff_gr_or_eq
% 4.69/4.98 thf(fact_3632_not__less__iff__gr__or__eq,axiom,
% 4.69/4.98 ! [X: code_integer,Y: code_integer] :
% 4.69/4.98 ( ( ~ ( ord_le6747313008572928689nteger @ X @ Y ) )
% 4.69/4.98 = ( ( ord_le6747313008572928689nteger @ Y @ X )
% 4.69/4.98 | ( X = Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % not_less_iff_gr_or_eq
% 4.69/4.98 thf(fact_3633_not__less__iff__gr__or__eq,axiom,
% 4.69/4.98 ! [X: rat,Y: rat] :
% 4.69/4.98 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 4.69/4.98 = ( ( ord_less_rat @ Y @ X )
% 4.69/4.98 | ( X = Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % not_less_iff_gr_or_eq
% 4.69/4.98 thf(fact_3634_dual__order_Ostrict__trans,axiom,
% 4.69/4.98 ! [B: assn,A2: assn,C: assn] :
% 4.69/4.98 ( ( ord_less_assn @ B @ A2 )
% 4.69/4.98 => ( ( ord_less_assn @ C @ B )
% 4.69/4.98 => ( ord_less_assn @ C @ A2 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_trans
% 4.69/4.98 thf(fact_3635_dual__order_Ostrict__trans,axiom,
% 4.69/4.98 ! [B: nat,A2: nat,C: nat] :
% 4.69/4.98 ( ( ord_less_nat @ B @ A2 )
% 4.69/4.98 => ( ( ord_less_nat @ C @ B )
% 4.69/4.98 => ( ord_less_nat @ C @ A2 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_trans
% 4.69/4.98 thf(fact_3636_dual__order_Ostrict__trans,axiom,
% 4.69/4.98 ! [B: int,A2: int,C: int] :
% 4.69/4.98 ( ( ord_less_int @ B @ A2 )
% 4.69/4.98 => ( ( ord_less_int @ C @ B )
% 4.69/4.98 => ( ord_less_int @ C @ A2 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_trans
% 4.69/4.98 thf(fact_3637_dual__order_Ostrict__trans,axiom,
% 4.69/4.98 ! [B: code_integer,A2: code_integer,C: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ B @ A2 )
% 4.69/4.98 => ( ( ord_le6747313008572928689nteger @ C @ B )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ C @ A2 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_trans
% 4.69/4.98 thf(fact_3638_dual__order_Ostrict__trans,axiom,
% 4.69/4.98 ! [B: rat,A2: rat,C: rat] :
% 4.69/4.98 ( ( ord_less_rat @ B @ A2 )
% 4.69/4.98 => ( ( ord_less_rat @ C @ B )
% 4.69/4.98 => ( ord_less_rat @ C @ A2 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_trans
% 4.69/4.98 thf(fact_3639_order_Ostrict__implies__not__eq,axiom,
% 4.69/4.98 ! [A2: assn,B: assn] :
% 4.69/4.98 ( ( ord_less_assn @ A2 @ B )
% 4.69/4.98 => ( A2 != B ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_implies_not_eq
% 4.69/4.98 thf(fact_3640_order_Ostrict__implies__not__eq,axiom,
% 4.69/4.98 ! [A2: nat,B: nat] :
% 4.69/4.98 ( ( ord_less_nat @ A2 @ B )
% 4.69/4.98 => ( A2 != B ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_implies_not_eq
% 4.69/4.98 thf(fact_3641_order_Ostrict__implies__not__eq,axiom,
% 4.69/4.98 ! [A2: int,B: int] :
% 4.69/4.98 ( ( ord_less_int @ A2 @ B )
% 4.69/4.98 => ( A2 != B ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_implies_not_eq
% 4.69/4.98 thf(fact_3642_order_Ostrict__implies__not__eq,axiom,
% 4.69/4.98 ! [A2: code_integer,B: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/4.98 => ( A2 != B ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_implies_not_eq
% 4.69/4.98 thf(fact_3643_order_Ostrict__implies__not__eq,axiom,
% 4.69/4.98 ! [A2: rat,B: rat] :
% 4.69/4.98 ( ( ord_less_rat @ A2 @ B )
% 4.69/4.98 => ( A2 != B ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_implies_not_eq
% 4.69/4.98 thf(fact_3644_dual__order_Ostrict__implies__not__eq,axiom,
% 4.69/4.98 ! [B: assn,A2: assn] :
% 4.69/4.98 ( ( ord_less_assn @ B @ A2 )
% 4.69/4.98 => ( A2 != B ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_implies_not_eq
% 4.69/4.98 thf(fact_3645_dual__order_Ostrict__implies__not__eq,axiom,
% 4.69/4.98 ! [B: nat,A2: nat] :
% 4.69/4.98 ( ( ord_less_nat @ B @ A2 )
% 4.69/4.98 => ( A2 != B ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_implies_not_eq
% 4.69/4.98 thf(fact_3646_dual__order_Ostrict__implies__not__eq,axiom,
% 4.69/4.98 ! [B: int,A2: int] :
% 4.69/4.98 ( ( ord_less_int @ B @ A2 )
% 4.69/4.98 => ( A2 != B ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_implies_not_eq
% 4.69/4.98 thf(fact_3647_dual__order_Ostrict__implies__not__eq,axiom,
% 4.69/4.98 ! [B: code_integer,A2: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ B @ A2 )
% 4.69/4.98 => ( A2 != B ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_implies_not_eq
% 4.69/4.98 thf(fact_3648_dual__order_Ostrict__implies__not__eq,axiom,
% 4.69/4.98 ! [B: rat,A2: rat] :
% 4.69/4.98 ( ( ord_less_rat @ B @ A2 )
% 4.69/4.98 => ( A2 != B ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_implies_not_eq
% 4.69/4.98 thf(fact_3649_psubsetD,axiom,
% 4.69/4.98 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o,C: produc3658429121746597890et_nat > $o] :
% 4.69/4.98 ( ( ord_le2453136405763929_nat_o @ A @ B4 )
% 4.69/4.98 => ( ( member6576561426505652726_nat_o @ C @ A )
% 4.69/4.98 => ( member6576561426505652726_nat_o @ C @ B4 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % psubsetD
% 4.69/4.98 thf(fact_3650_psubsetD,axiom,
% 4.69/4.98 ! [A: set_nat,B4: set_nat,C: nat] :
% 4.69/4.98 ( ( ord_less_set_nat @ A @ B4 )
% 4.69/4.98 => ( ( member_nat @ C @ A )
% 4.69/4.98 => ( member_nat @ C @ B4 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % psubsetD
% 4.69/4.98 thf(fact_3651_psubsetD,axiom,
% 4.69/4.98 ! [A: set_int,B4: set_int,C: int] :
% 4.69/4.98 ( ( ord_less_set_int @ A @ B4 )
% 4.69/4.98 => ( ( member_int @ C @ A )
% 4.69/4.98 => ( member_int @ C @ B4 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % psubsetD
% 4.69/4.98 thf(fact_3652_psubsetD,axiom,
% 4.69/4.98 ! [A: set_o,B4: set_o,C: $o] :
% 4.69/4.98 ( ( ord_less_set_o @ A @ B4 )
% 4.69/4.98 => ( ( member_o @ C @ A )
% 4.69/4.98 => ( member_o @ C @ B4 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % psubsetD
% 4.69/4.98 thf(fact_3653_psubsetD,axiom,
% 4.69/4.98 ! [A: set_Product_unit,B4: set_Product_unit,C: product_unit] :
% 4.69/4.98 ( ( ord_le8056459307392131481t_unit @ A @ B4 )
% 4.69/4.98 => ( ( member_Product_unit @ C @ A )
% 4.69/4.98 => ( member_Product_unit @ C @ B4 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % psubsetD
% 4.69/4.98 thf(fact_3654_UNIV__eq__I,axiom,
% 4.69/4.98 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.98 ( ! [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ A )
% 4.69/4.98 => ( top_to4869887016220417533_nat_o = A ) ) ).
% 4.69/4.98
% 4.69/4.98 % UNIV_eq_I
% 4.69/4.98 thf(fact_3655_UNIV__eq__I,axiom,
% 4.69/4.98 ! [A: set_Product_unit] :
% 4.69/4.98 ( ! [X3: product_unit] : ( member_Product_unit @ X3 @ A )
% 4.69/4.98 => ( top_to1996260823553986621t_unit = A ) ) ).
% 4.69/4.98
% 4.69/4.98 % UNIV_eq_I
% 4.69/4.98 thf(fact_3656_UNIV__eq__I,axiom,
% 4.69/4.98 ! [A: set_o] :
% 4.69/4.98 ( ! [X3: $o] : ( member_o @ X3 @ A )
% 4.69/4.98 => ( top_top_set_o = A ) ) ).
% 4.69/4.98
% 4.69/4.98 % UNIV_eq_I
% 4.69/4.98 thf(fact_3657_UNIV__eq__I,axiom,
% 4.69/4.98 ! [A: set_nat] :
% 4.69/4.98 ( ! [X3: nat] : ( member_nat @ X3 @ A )
% 4.69/4.98 => ( top_top_set_nat = A ) ) ).
% 4.69/4.98
% 4.69/4.98 % UNIV_eq_I
% 4.69/4.98 thf(fact_3658_UNIV__eq__I,axiom,
% 4.69/4.98 ! [A: set_int] :
% 4.69/4.98 ( ! [X3: int] : ( member_int @ X3 @ A )
% 4.69/4.98 => ( top_top_set_int = A ) ) ).
% 4.69/4.98
% 4.69/4.98 % UNIV_eq_I
% 4.69/4.98 thf(fact_3659_UNIV__witness,axiom,
% 4.69/4.98 ? [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ top_to4869887016220417533_nat_o ) ).
% 4.69/4.98
% 4.69/4.98 % UNIV_witness
% 4.69/4.98 thf(fact_3660_UNIV__witness,axiom,
% 4.69/4.98 ? [X3: product_unit] : ( member_Product_unit @ X3 @ top_to1996260823553986621t_unit ) ).
% 4.69/4.98
% 4.69/4.98 % UNIV_witness
% 4.69/4.98 thf(fact_3661_UNIV__witness,axiom,
% 4.69/4.98 ? [X3: $o] : ( member_o @ X3 @ top_top_set_o ) ).
% 4.69/4.98
% 4.69/4.98 % UNIV_witness
% 4.69/4.98 thf(fact_3662_UNIV__witness,axiom,
% 4.69/4.98 ? [X3: nat] : ( member_nat @ X3 @ top_top_set_nat ) ).
% 4.69/4.98
% 4.69/4.98 % UNIV_witness
% 4.69/4.98 thf(fact_3663_UNIV__witness,axiom,
% 4.69/4.98 ? [X3: int] : ( member_int @ X3 @ top_top_set_int ) ).
% 4.69/4.98
% 4.69/4.98 % UNIV_witness
% 4.69/4.98 thf(fact_3664_linorder__neqE,axiom,
% 4.69/4.98 ! [X: nat,Y: nat] :
% 4.69/4.98 ( ( X != Y )
% 4.69/4.98 => ( ~ ( ord_less_nat @ X @ Y )
% 4.69/4.98 => ( ord_less_nat @ Y @ X ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_neqE
% 4.69/4.98 thf(fact_3665_linorder__neqE,axiom,
% 4.69/4.98 ! [X: int,Y: int] :
% 4.69/4.98 ( ( X != Y )
% 4.69/4.98 => ( ~ ( ord_less_int @ X @ Y )
% 4.69/4.98 => ( ord_less_int @ Y @ X ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_neqE
% 4.69/4.98 thf(fact_3666_linorder__neqE,axiom,
% 4.69/4.98 ! [X: code_integer,Y: code_integer] :
% 4.69/4.98 ( ( X != Y )
% 4.69/4.98 => ( ~ ( ord_le6747313008572928689nteger @ X @ Y )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ Y @ X ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_neqE
% 4.69/4.98 thf(fact_3667_linorder__neqE,axiom,
% 4.69/4.98 ! [X: rat,Y: rat] :
% 4.69/4.98 ( ( X != Y )
% 4.69/4.98 => ( ~ ( ord_less_rat @ X @ Y )
% 4.69/4.98 => ( ord_less_rat @ Y @ X ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_neqE
% 4.69/4.98 thf(fact_3668_order__less__asym,axiom,
% 4.69/4.98 ! [X: assn,Y: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X @ Y )
% 4.69/4.98 => ~ ( ord_less_assn @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_asym
% 4.69/4.98 thf(fact_3669_order__less__asym,axiom,
% 4.69/4.98 ! [X: nat,Y: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X @ Y )
% 4.69/4.98 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_asym
% 4.69/4.98 thf(fact_3670_order__less__asym,axiom,
% 4.69/4.98 ! [X: int,Y: int] :
% 4.69/4.98 ( ( ord_less_int @ X @ Y )
% 4.69/4.98 => ~ ( ord_less_int @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_asym
% 4.69/4.98 thf(fact_3671_order__less__asym,axiom,
% 4.69/4.98 ! [X: code_integer,Y: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ X @ Y )
% 4.69/4.98 => ~ ( ord_le6747313008572928689nteger @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_asym
% 4.69/4.98 thf(fact_3672_order__less__asym,axiom,
% 4.69/4.98 ! [X: rat,Y: rat] :
% 4.69/4.98 ( ( ord_less_rat @ X @ Y )
% 4.69/4.98 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_asym
% 4.69/4.98 thf(fact_3673_linorder__neq__iff,axiom,
% 4.69/4.98 ! [X: nat,Y: nat] :
% 4.69/4.98 ( ( X != Y )
% 4.69/4.98 = ( ( ord_less_nat @ X @ Y )
% 4.69/4.98 | ( ord_less_nat @ Y @ X ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_neq_iff
% 4.69/4.98 thf(fact_3674_linorder__neq__iff,axiom,
% 4.69/4.98 ! [X: int,Y: int] :
% 4.69/4.98 ( ( X != Y )
% 4.69/4.98 = ( ( ord_less_int @ X @ Y )
% 4.69/4.98 | ( ord_less_int @ Y @ X ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_neq_iff
% 4.69/4.98 thf(fact_3675_linorder__neq__iff,axiom,
% 4.69/4.98 ! [X: code_integer,Y: code_integer] :
% 4.69/4.98 ( ( X != Y )
% 4.69/4.98 = ( ( ord_le6747313008572928689nteger @ X @ Y )
% 4.69/4.98 | ( ord_le6747313008572928689nteger @ Y @ X ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_neq_iff
% 4.69/4.98 thf(fact_3676_linorder__neq__iff,axiom,
% 4.69/4.98 ! [X: rat,Y: rat] :
% 4.69/4.98 ( ( X != Y )
% 4.69/4.98 = ( ( ord_less_rat @ X @ Y )
% 4.69/4.98 | ( ord_less_rat @ Y @ X ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_neq_iff
% 4.69/4.98 thf(fact_3677_order__less__asym_H,axiom,
% 4.69/4.98 ! [A2: assn,B: assn] :
% 4.69/4.98 ( ( ord_less_assn @ A2 @ B )
% 4.69/4.98 => ~ ( ord_less_assn @ B @ A2 ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_asym'
% 4.69/4.98 thf(fact_3678_order__less__asym_H,axiom,
% 4.69/4.98 ! [A2: nat,B: nat] :
% 4.69/4.98 ( ( ord_less_nat @ A2 @ B )
% 4.69/4.98 => ~ ( ord_less_nat @ B @ A2 ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_asym'
% 4.69/4.98 thf(fact_3679_order__less__asym_H,axiom,
% 4.69/4.98 ! [A2: int,B: int] :
% 4.69/4.98 ( ( ord_less_int @ A2 @ B )
% 4.69/4.98 => ~ ( ord_less_int @ B @ A2 ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_asym'
% 4.69/4.98 thf(fact_3680_order__less__asym_H,axiom,
% 4.69/4.98 ! [A2: code_integer,B: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/4.98 => ~ ( ord_le6747313008572928689nteger @ B @ A2 ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_asym'
% 4.69/4.98 thf(fact_3681_order__less__asym_H,axiom,
% 4.69/4.98 ! [A2: rat,B: rat] :
% 4.69/4.98 ( ( ord_less_rat @ A2 @ B )
% 4.69/4.98 => ~ ( ord_less_rat @ B @ A2 ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_asym'
% 4.69/4.98 thf(fact_3682_order__less__trans,axiom,
% 4.69/4.98 ! [X: assn,Y: assn,Z: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X @ Y )
% 4.69/4.98 => ( ( ord_less_assn @ Y @ Z )
% 4.69/4.98 => ( ord_less_assn @ X @ Z ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_trans
% 4.69/4.98 thf(fact_3683_order__less__trans,axiom,
% 4.69/4.98 ! [X: nat,Y: nat,Z: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X @ Y )
% 4.69/4.98 => ( ( ord_less_nat @ Y @ Z )
% 4.69/4.98 => ( ord_less_nat @ X @ Z ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_trans
% 4.69/4.98 thf(fact_3684_order__less__trans,axiom,
% 4.69/4.98 ! [X: int,Y: int,Z: int] :
% 4.69/4.98 ( ( ord_less_int @ X @ Y )
% 4.69/4.98 => ( ( ord_less_int @ Y @ Z )
% 4.69/4.98 => ( ord_less_int @ X @ Z ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_trans
% 4.69/4.98 thf(fact_3685_order__less__trans,axiom,
% 4.69/4.98 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ X @ Y )
% 4.69/4.98 => ( ( ord_le6747313008572928689nteger @ Y @ Z )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ X @ Z ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_trans
% 4.69/4.98 thf(fact_3686_order__less__trans,axiom,
% 4.69/4.98 ! [X: rat,Y: rat,Z: rat] :
% 4.69/4.98 ( ( ord_less_rat @ X @ Y )
% 4.69/4.98 => ( ( ord_less_rat @ Y @ Z )
% 4.69/4.98 => ( ord_less_rat @ X @ Z ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_trans
% 4.69/4.98 thf(fact_3687_ord__eq__less__subst,axiom,
% 4.69/4.98 ! [A2: assn,F: assn > assn,B: assn,C: assn] :
% 4.69/4.98 ( ( A2
% 4.69/4.98 = ( F @ B ) )
% 4.69/4.98 => ( ( ord_less_assn @ B @ C )
% 4.69/4.98 => ( ! [X3: assn,Y2: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_assn @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_eq_less_subst
% 4.69/4.98 thf(fact_3688_ord__eq__less__subst,axiom,
% 4.69/4.98 ! [A2: nat,F: assn > nat,B: assn,C: assn] :
% 4.69/4.98 ( ( A2
% 4.69/4.98 = ( F @ B ) )
% 4.69/4.98 => ( ( ord_less_assn @ B @ C )
% 4.69/4.98 => ( ! [X3: assn,Y2: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_eq_less_subst
% 4.69/4.98 thf(fact_3689_ord__eq__less__subst,axiom,
% 4.69/4.98 ! [A2: int,F: assn > int,B: assn,C: assn] :
% 4.69/4.98 ( ( A2
% 4.69/4.98 = ( F @ B ) )
% 4.69/4.98 => ( ( ord_less_assn @ B @ C )
% 4.69/4.98 => ( ! [X3: assn,Y2: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_eq_less_subst
% 4.69/4.98 thf(fact_3690_ord__eq__less__subst,axiom,
% 4.69/4.98 ! [A2: code_integer,F: assn > code_integer,B: assn,C: assn] :
% 4.69/4.98 ( ( A2
% 4.69/4.98 = ( F @ B ) )
% 4.69/4.98 => ( ( ord_less_assn @ B @ C )
% 4.69/4.98 => ( ! [X3: assn,Y2: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X3 @ Y2 )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_eq_less_subst
% 4.69/4.98 thf(fact_3691_ord__eq__less__subst,axiom,
% 4.69/4.98 ! [A2: rat,F: assn > rat,B: assn,C: assn] :
% 4.69/4.98 ( ( A2
% 4.69/4.98 = ( F @ B ) )
% 4.69/4.98 => ( ( ord_less_assn @ B @ C )
% 4.69/4.98 => ( ! [X3: assn,Y2: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_eq_less_subst
% 4.69/4.98 thf(fact_3692_ord__eq__less__subst,axiom,
% 4.69/4.98 ! [A2: assn,F: nat > assn,B: nat,C: nat] :
% 4.69/4.98 ( ( A2
% 4.69/4.98 = ( F @ B ) )
% 4.69/4.98 => ( ( ord_less_nat @ B @ C )
% 4.69/4.98 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_assn @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_eq_less_subst
% 4.69/4.98 thf(fact_3693_ord__eq__less__subst,axiom,
% 4.69/4.98 ! [A2: nat,F: nat > nat,B: nat,C: nat] :
% 4.69/4.98 ( ( A2
% 4.69/4.98 = ( F @ B ) )
% 4.69/4.98 => ( ( ord_less_nat @ B @ C )
% 4.69/4.98 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_eq_less_subst
% 4.69/4.98 thf(fact_3694_ord__eq__less__subst,axiom,
% 4.69/4.98 ! [A2: int,F: nat > int,B: nat,C: nat] :
% 4.69/4.98 ( ( A2
% 4.69/4.98 = ( F @ B ) )
% 4.69/4.98 => ( ( ord_less_nat @ B @ C )
% 4.69/4.98 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_eq_less_subst
% 4.69/4.98 thf(fact_3695_ord__eq__less__subst,axiom,
% 4.69/4.98 ! [A2: code_integer,F: nat > code_integer,B: nat,C: nat] :
% 4.69/4.98 ( ( A2
% 4.69/4.98 = ( F @ B ) )
% 4.69/4.98 => ( ( ord_less_nat @ B @ C )
% 4.69/4.98 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X3 @ Y2 )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_eq_less_subst
% 4.69/4.98 thf(fact_3696_ord__eq__less__subst,axiom,
% 4.69/4.98 ! [A2: rat,F: nat > rat,B: nat,C: nat] :
% 4.69/4.98 ( ( A2
% 4.69/4.98 = ( F @ B ) )
% 4.69/4.98 => ( ( ord_less_nat @ B @ C )
% 4.69/4.98 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_eq_less_subst
% 4.69/4.98 thf(fact_3697_ord__less__eq__subst,axiom,
% 4.69/4.98 ! [A2: assn,B: assn,F: assn > assn,C: assn] :
% 4.69/4.98 ( ( ord_less_assn @ A2 @ B )
% 4.69/4.98 => ( ( ( F @ B )
% 4.69/4.98 = C )
% 4.69/4.98 => ( ! [X3: assn,Y2: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_assn @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_less_eq_subst
% 4.69/4.98 thf(fact_3698_ord__less__eq__subst,axiom,
% 4.69/4.98 ! [A2: assn,B: assn,F: assn > nat,C: nat] :
% 4.69/4.98 ( ( ord_less_assn @ A2 @ B )
% 4.69/4.98 => ( ( ( F @ B )
% 4.69/4.98 = C )
% 4.69/4.98 => ( ! [X3: assn,Y2: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_less_eq_subst
% 4.69/4.98 thf(fact_3699_ord__less__eq__subst,axiom,
% 4.69/4.98 ! [A2: assn,B: assn,F: assn > int,C: int] :
% 4.69/4.98 ( ( ord_less_assn @ A2 @ B )
% 4.69/4.98 => ( ( ( F @ B )
% 4.69/4.98 = C )
% 4.69/4.98 => ( ! [X3: assn,Y2: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_less_eq_subst
% 4.69/4.98 thf(fact_3700_ord__less__eq__subst,axiom,
% 4.69/4.98 ! [A2: assn,B: assn,F: assn > code_integer,C: code_integer] :
% 4.69/4.98 ( ( ord_less_assn @ A2 @ B )
% 4.69/4.98 => ( ( ( F @ B )
% 4.69/4.98 = C )
% 4.69/4.98 => ( ! [X3: assn,Y2: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X3 @ Y2 )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_less_eq_subst
% 4.69/4.98 thf(fact_3701_ord__less__eq__subst,axiom,
% 4.69/4.98 ! [A2: assn,B: assn,F: assn > rat,C: rat] :
% 4.69/4.98 ( ( ord_less_assn @ A2 @ B )
% 4.69/4.98 => ( ( ( F @ B )
% 4.69/4.98 = C )
% 4.69/4.98 => ( ! [X3: assn,Y2: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_less_eq_subst
% 4.69/4.98 thf(fact_3702_ord__less__eq__subst,axiom,
% 4.69/4.98 ! [A2: nat,B: nat,F: nat > assn,C: assn] :
% 4.69/4.98 ( ( ord_less_nat @ A2 @ B )
% 4.69/4.98 => ( ( ( F @ B )
% 4.69/4.98 = C )
% 4.69/4.98 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_assn @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_less_eq_subst
% 4.69/4.98 thf(fact_3703_ord__less__eq__subst,axiom,
% 4.69/4.98 ! [A2: nat,B: nat,F: nat > nat,C: nat] :
% 4.69/4.98 ( ( ord_less_nat @ A2 @ B )
% 4.69/4.98 => ( ( ( F @ B )
% 4.69/4.98 = C )
% 4.69/4.98 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_less_eq_subst
% 4.69/4.98 thf(fact_3704_ord__less__eq__subst,axiom,
% 4.69/4.98 ! [A2: nat,B: nat,F: nat > int,C: int] :
% 4.69/4.98 ( ( ord_less_nat @ A2 @ B )
% 4.69/4.98 => ( ( ( F @ B )
% 4.69/4.98 = C )
% 4.69/4.98 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_less_eq_subst
% 4.69/4.98 thf(fact_3705_ord__less__eq__subst,axiom,
% 4.69/4.98 ! [A2: nat,B: nat,F: nat > code_integer,C: code_integer] :
% 4.69/4.98 ( ( ord_less_nat @ A2 @ B )
% 4.69/4.98 => ( ( ( F @ B )
% 4.69/4.98 = C )
% 4.69/4.98 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X3 @ Y2 )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_less_eq_subst
% 4.69/4.98 thf(fact_3706_ord__less__eq__subst,axiom,
% 4.69/4.98 ! [A2: nat,B: nat,F: nat > rat,C: rat] :
% 4.69/4.98 ( ( ord_less_nat @ A2 @ B )
% 4.69/4.98 => ( ( ( F @ B )
% 4.69/4.98 = C )
% 4.69/4.98 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % ord_less_eq_subst
% 4.69/4.98 thf(fact_3707_order__less__irrefl,axiom,
% 4.69/4.98 ! [X: assn] :
% 4.69/4.98 ~ ( ord_less_assn @ X @ X ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_irrefl
% 4.69/4.98 thf(fact_3708_order__less__irrefl,axiom,
% 4.69/4.98 ! [X: nat] :
% 4.69/4.98 ~ ( ord_less_nat @ X @ X ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_irrefl
% 4.69/4.98 thf(fact_3709_order__less__irrefl,axiom,
% 4.69/4.98 ! [X: int] :
% 4.69/4.98 ~ ( ord_less_int @ X @ X ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_irrefl
% 4.69/4.98 thf(fact_3710_order__less__irrefl,axiom,
% 4.69/4.98 ! [X: code_integer] :
% 4.69/4.98 ~ ( ord_le6747313008572928689nteger @ X @ X ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_irrefl
% 4.69/4.98 thf(fact_3711_order__less__irrefl,axiom,
% 4.69/4.98 ! [X: rat] :
% 4.69/4.98 ~ ( ord_less_rat @ X @ X ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_irrefl
% 4.69/4.98 thf(fact_3712_order__less__subst1,axiom,
% 4.69/4.98 ! [A2: assn,F: assn > assn,B: assn,C: assn] :
% 4.69/4.98 ( ( ord_less_assn @ A2 @ ( F @ B ) )
% 4.69/4.98 => ( ( ord_less_assn @ B @ C )
% 4.69/4.98 => ( ! [X3: assn,Y2: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_assn @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_subst1
% 4.69/4.98 thf(fact_3713_order__less__subst1,axiom,
% 4.69/4.98 ! [A2: assn,F: nat > assn,B: nat,C: nat] :
% 4.69/4.98 ( ( ord_less_assn @ A2 @ ( F @ B ) )
% 4.69/4.98 => ( ( ord_less_nat @ B @ C )
% 4.69/4.98 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_assn @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_subst1
% 4.69/4.98 thf(fact_3714_order__less__subst1,axiom,
% 4.69/4.98 ! [A2: assn,F: int > assn,B: int,C: int] :
% 4.69/4.98 ( ( ord_less_assn @ A2 @ ( F @ B ) )
% 4.69/4.98 => ( ( ord_less_int @ B @ C )
% 4.69/4.98 => ( ! [X3: int,Y2: int] :
% 4.69/4.98 ( ( ord_less_int @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_assn @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_subst1
% 4.69/4.98 thf(fact_3715_order__less__subst1,axiom,
% 4.69/4.98 ! [A2: assn,F: code_integer > assn,B: code_integer,C: code_integer] :
% 4.69/4.98 ( ( ord_less_assn @ A2 @ ( F @ B ) )
% 4.69/4.98 => ( ( ord_le6747313008572928689nteger @ B @ C )
% 4.69/4.98 => ( ! [X3: code_integer,Y2: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_assn @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_subst1
% 4.69/4.98 thf(fact_3716_order__less__subst1,axiom,
% 4.69/4.98 ! [A2: assn,F: rat > assn,B: rat,C: rat] :
% 4.69/4.98 ( ( ord_less_assn @ A2 @ ( F @ B ) )
% 4.69/4.98 => ( ( ord_less_rat @ B @ C )
% 4.69/4.98 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.98 ( ( ord_less_rat @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_assn @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_subst1
% 4.69/4.98 thf(fact_3717_order__less__subst1,axiom,
% 4.69/4.98 ! [A2: nat,F: assn > nat,B: assn,C: assn] :
% 4.69/4.98 ( ( ord_less_nat @ A2 @ ( F @ B ) )
% 4.69/4.98 => ( ( ord_less_assn @ B @ C )
% 4.69/4.98 => ( ! [X3: assn,Y2: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_subst1
% 4.69/4.98 thf(fact_3718_order__less__subst1,axiom,
% 4.69/4.98 ! [A2: nat,F: nat > nat,B: nat,C: nat] :
% 4.69/4.98 ( ( ord_less_nat @ A2 @ ( F @ B ) )
% 4.69/4.98 => ( ( ord_less_nat @ B @ C )
% 4.69/4.98 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_subst1
% 4.69/4.98 thf(fact_3719_order__less__subst1,axiom,
% 4.69/4.98 ! [A2: nat,F: int > nat,B: int,C: int] :
% 4.69/4.98 ( ( ord_less_nat @ A2 @ ( F @ B ) )
% 4.69/4.98 => ( ( ord_less_int @ B @ C )
% 4.69/4.98 => ( ! [X3: int,Y2: int] :
% 4.69/4.98 ( ( ord_less_int @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_subst1
% 4.69/4.98 thf(fact_3720_order__less__subst1,axiom,
% 4.69/4.98 ! [A2: nat,F: code_integer > nat,B: code_integer,C: code_integer] :
% 4.69/4.98 ( ( ord_less_nat @ A2 @ ( F @ B ) )
% 4.69/4.98 => ( ( ord_le6747313008572928689nteger @ B @ C )
% 4.69/4.98 => ( ! [X3: code_integer,Y2: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_subst1
% 4.69/4.98 thf(fact_3721_order__less__subst1,axiom,
% 4.69/4.98 ! [A2: nat,F: rat > nat,B: rat,C: rat] :
% 4.69/4.98 ( ( ord_less_nat @ A2 @ ( F @ B ) )
% 4.69/4.98 => ( ( ord_less_rat @ B @ C )
% 4.69/4.98 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.98 ( ( ord_less_rat @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_subst1
% 4.69/4.98 thf(fact_3722_order__less__subst2,axiom,
% 4.69/4.98 ! [A2: assn,B: assn,F: assn > assn,C: assn] :
% 4.69/4.98 ( ( ord_less_assn @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_assn @ ( F @ B ) @ C )
% 4.69/4.98 => ( ! [X3: assn,Y2: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_assn @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_subst2
% 4.69/4.98 thf(fact_3723_order__less__subst2,axiom,
% 4.69/4.98 ! [A2: assn,B: assn,F: assn > nat,C: nat] :
% 4.69/4.98 ( ( ord_less_assn @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 4.69/4.98 => ( ! [X3: assn,Y2: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_subst2
% 4.69/4.98 thf(fact_3724_order__less__subst2,axiom,
% 4.69/4.98 ! [A2: assn,B: assn,F: assn > int,C: int] :
% 4.69/4.98 ( ( ord_less_assn @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_int @ ( F @ B ) @ C )
% 4.69/4.98 => ( ! [X3: assn,Y2: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_subst2
% 4.69/4.98 thf(fact_3725_order__less__subst2,axiom,
% 4.69/4.98 ! [A2: assn,B: assn,F: assn > code_integer,C: code_integer] :
% 4.69/4.98 ( ( ord_less_assn @ A2 @ B )
% 4.69/4.98 => ( ( ord_le6747313008572928689nteger @ ( F @ B ) @ C )
% 4.69/4.98 => ( ! [X3: assn,Y2: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X3 @ Y2 )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_subst2
% 4.69/4.98 thf(fact_3726_order__less__subst2,axiom,
% 4.69/4.98 ! [A2: assn,B: assn,F: assn > rat,C: rat] :
% 4.69/4.98 ( ( ord_less_assn @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 4.69/4.98 => ( ! [X3: assn,Y2: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_subst2
% 4.69/4.98 thf(fact_3727_order__less__subst2,axiom,
% 4.69/4.98 ! [A2: nat,B: nat,F: nat > assn,C: assn] :
% 4.69/4.98 ( ( ord_less_nat @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_assn @ ( F @ B ) @ C )
% 4.69/4.98 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_assn @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_subst2
% 4.69/4.98 thf(fact_3728_order__less__subst2,axiom,
% 4.69/4.98 ! [A2: nat,B: nat,F: nat > nat,C: nat] :
% 4.69/4.98 ( ( ord_less_nat @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 4.69/4.98 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_subst2
% 4.69/4.98 thf(fact_3729_order__less__subst2,axiom,
% 4.69/4.98 ! [A2: nat,B: nat,F: nat > int,C: int] :
% 4.69/4.98 ( ( ord_less_nat @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_int @ ( F @ B ) @ C )
% 4.69/4.98 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_subst2
% 4.69/4.98 thf(fact_3730_order__less__subst2,axiom,
% 4.69/4.98 ! [A2: nat,B: nat,F: nat > code_integer,C: code_integer] :
% 4.69/4.98 ( ( ord_less_nat @ A2 @ B )
% 4.69/4.98 => ( ( ord_le6747313008572928689nteger @ ( F @ B ) @ C )
% 4.69/4.98 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X3 @ Y2 )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_subst2
% 4.69/4.98 thf(fact_3731_order__less__subst2,axiom,
% 4.69/4.98 ! [A2: nat,B: nat,F: nat > rat,C: rat] :
% 4.69/4.98 ( ( ord_less_nat @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 4.69/4.98 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X3 @ Y2 )
% 4.69/4.98 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.98 => ( ord_less_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_subst2
% 4.69/4.98 thf(fact_3732_order__less__not__sym,axiom,
% 4.69/4.98 ! [X: assn,Y: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X @ Y )
% 4.69/4.98 => ~ ( ord_less_assn @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_not_sym
% 4.69/4.98 thf(fact_3733_order__less__not__sym,axiom,
% 4.69/4.98 ! [X: nat,Y: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X @ Y )
% 4.69/4.98 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_not_sym
% 4.69/4.98 thf(fact_3734_order__less__not__sym,axiom,
% 4.69/4.98 ! [X: int,Y: int] :
% 4.69/4.98 ( ( ord_less_int @ X @ Y )
% 4.69/4.98 => ~ ( ord_less_int @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_not_sym
% 4.69/4.98 thf(fact_3735_order__less__not__sym,axiom,
% 4.69/4.98 ! [X: code_integer,Y: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ X @ Y )
% 4.69/4.98 => ~ ( ord_le6747313008572928689nteger @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_not_sym
% 4.69/4.98 thf(fact_3736_order__less__not__sym,axiom,
% 4.69/4.98 ! [X: rat,Y: rat] :
% 4.69/4.98 ( ( ord_less_rat @ X @ Y )
% 4.69/4.98 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_not_sym
% 4.69/4.98 thf(fact_3737_order__less__imp__triv,axiom,
% 4.69/4.98 ! [X: assn,Y: assn,P: $o] :
% 4.69/4.98 ( ( ord_less_assn @ X @ Y )
% 4.69/4.98 => ( ( ord_less_assn @ Y @ X )
% 4.69/4.98 => P ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_triv
% 4.69/4.98 thf(fact_3738_order__less__imp__triv,axiom,
% 4.69/4.98 ! [X: nat,Y: nat,P: $o] :
% 4.69/4.98 ( ( ord_less_nat @ X @ Y )
% 4.69/4.98 => ( ( ord_less_nat @ Y @ X )
% 4.69/4.98 => P ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_triv
% 4.69/4.98 thf(fact_3739_order__less__imp__triv,axiom,
% 4.69/4.98 ! [X: int,Y: int,P: $o] :
% 4.69/4.98 ( ( ord_less_int @ X @ Y )
% 4.69/4.98 => ( ( ord_less_int @ Y @ X )
% 4.69/4.98 => P ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_triv
% 4.69/4.98 thf(fact_3740_order__less__imp__triv,axiom,
% 4.69/4.98 ! [X: code_integer,Y: code_integer,P: $o] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ X @ Y )
% 4.69/4.98 => ( ( ord_le6747313008572928689nteger @ Y @ X )
% 4.69/4.98 => P ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_triv
% 4.69/4.98 thf(fact_3741_order__less__imp__triv,axiom,
% 4.69/4.98 ! [X: rat,Y: rat,P: $o] :
% 4.69/4.98 ( ( ord_less_rat @ X @ Y )
% 4.69/4.98 => ( ( ord_less_rat @ Y @ X )
% 4.69/4.98 => P ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_triv
% 4.69/4.98 thf(fact_3742_linorder__less__linear,axiom,
% 4.69/4.98 ! [X: nat,Y: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X @ Y )
% 4.69/4.98 | ( X = Y )
% 4.69/4.98 | ( ord_less_nat @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_less_linear
% 4.69/4.98 thf(fact_3743_linorder__less__linear,axiom,
% 4.69/4.98 ! [X: int,Y: int] :
% 4.69/4.98 ( ( ord_less_int @ X @ Y )
% 4.69/4.98 | ( X = Y )
% 4.69/4.98 | ( ord_less_int @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_less_linear
% 4.69/4.98 thf(fact_3744_linorder__less__linear,axiom,
% 4.69/4.98 ! [X: code_integer,Y: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ X @ Y )
% 4.69/4.98 | ( X = Y )
% 4.69/4.98 | ( ord_le6747313008572928689nteger @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_less_linear
% 4.69/4.98 thf(fact_3745_linorder__less__linear,axiom,
% 4.69/4.98 ! [X: rat,Y: rat] :
% 4.69/4.98 ( ( ord_less_rat @ X @ Y )
% 4.69/4.98 | ( X = Y )
% 4.69/4.98 | ( ord_less_rat @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_less_linear
% 4.69/4.98 thf(fact_3746_order__less__imp__not__eq,axiom,
% 4.69/4.98 ! [X: assn,Y: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X @ Y )
% 4.69/4.98 => ( X != Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_not_eq
% 4.69/4.98 thf(fact_3747_order__less__imp__not__eq,axiom,
% 4.69/4.98 ! [X: nat,Y: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X @ Y )
% 4.69/4.98 => ( X != Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_not_eq
% 4.69/4.98 thf(fact_3748_order__less__imp__not__eq,axiom,
% 4.69/4.98 ! [X: int,Y: int] :
% 4.69/4.98 ( ( ord_less_int @ X @ Y )
% 4.69/4.98 => ( X != Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_not_eq
% 4.69/4.98 thf(fact_3749_order__less__imp__not__eq,axiom,
% 4.69/4.98 ! [X: code_integer,Y: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ X @ Y )
% 4.69/4.98 => ( X != Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_not_eq
% 4.69/4.98 thf(fact_3750_order__less__imp__not__eq,axiom,
% 4.69/4.98 ! [X: rat,Y: rat] :
% 4.69/4.98 ( ( ord_less_rat @ X @ Y )
% 4.69/4.98 => ( X != Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_not_eq
% 4.69/4.98 thf(fact_3751_order__less__imp__not__eq2,axiom,
% 4.69/4.98 ! [X: assn,Y: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X @ Y )
% 4.69/4.98 => ( Y != X ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_not_eq2
% 4.69/4.98 thf(fact_3752_order__less__imp__not__eq2,axiom,
% 4.69/4.98 ! [X: nat,Y: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X @ Y )
% 4.69/4.98 => ( Y != X ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_not_eq2
% 4.69/4.98 thf(fact_3753_order__less__imp__not__eq2,axiom,
% 4.69/4.98 ! [X: int,Y: int] :
% 4.69/4.98 ( ( ord_less_int @ X @ Y )
% 4.69/4.98 => ( Y != X ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_not_eq2
% 4.69/4.98 thf(fact_3754_order__less__imp__not__eq2,axiom,
% 4.69/4.98 ! [X: code_integer,Y: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ X @ Y )
% 4.69/4.98 => ( Y != X ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_not_eq2
% 4.69/4.98 thf(fact_3755_order__less__imp__not__eq2,axiom,
% 4.69/4.98 ! [X: rat,Y: rat] :
% 4.69/4.98 ( ( ord_less_rat @ X @ Y )
% 4.69/4.98 => ( Y != X ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_not_eq2
% 4.69/4.98 thf(fact_3756_order__less__imp__not__less,axiom,
% 4.69/4.98 ! [X: assn,Y: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X @ Y )
% 4.69/4.98 => ~ ( ord_less_assn @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_not_less
% 4.69/4.98 thf(fact_3757_order__less__imp__not__less,axiom,
% 4.69/4.98 ! [X: nat,Y: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X @ Y )
% 4.69/4.98 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_not_less
% 4.69/4.98 thf(fact_3758_order__less__imp__not__less,axiom,
% 4.69/4.98 ! [X: int,Y: int] :
% 4.69/4.98 ( ( ord_less_int @ X @ Y )
% 4.69/4.98 => ~ ( ord_less_int @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_not_less
% 4.69/4.98 thf(fact_3759_order__less__imp__not__less,axiom,
% 4.69/4.98 ! [X: code_integer,Y: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ X @ Y )
% 4.69/4.98 => ~ ( ord_le6747313008572928689nteger @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_not_less
% 4.69/4.98 thf(fact_3760_order__less__imp__not__less,axiom,
% 4.69/4.98 ! [X: rat,Y: rat] :
% 4.69/4.98 ( ( ord_less_rat @ X @ Y )
% 4.69/4.98 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_not_less
% 4.69/4.98 thf(fact_3761_Max__gr__iff,axiom,
% 4.69/4.98 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.98 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.98 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.98 => ( ( ord_le361264281704409273t_unit @ X @ ( lattic1210392890313158908t_unit @ A ) )
% 4.69/4.98 = ( ? [X2: product_unit] :
% 4.69/4.98 ( ( member_Product_unit @ X2 @ A )
% 4.69/4.98 & ( ord_le361264281704409273t_unit @ X @ X2 ) ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max_gr_iff
% 4.69/4.98 thf(fact_3762_Max__gr__iff,axiom,
% 4.69/4.98 ! [A: set_o,X: $o] :
% 4.69/4.98 ( ( finite_finite_o @ A )
% 4.69/4.98 => ( ( A != bot_bot_set_o )
% 4.69/4.98 => ( ( ord_less_o @ X @ ( lattic1921953407002678535_Max_o @ A ) )
% 4.69/4.98 = ( ? [X2: $o] :
% 4.69/4.98 ( ( member_o @ X2 @ A )
% 4.69/4.98 & ( ord_less_o @ X @ X2 ) ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max_gr_iff
% 4.69/4.98 thf(fact_3763_Max__gr__iff,axiom,
% 4.69/4.98 ! [A: set_int,X: int] :
% 4.69/4.98 ( ( finite_finite_int @ A )
% 4.69/4.98 => ( ( A != bot_bot_set_int )
% 4.69/4.98 => ( ( ord_less_int @ X @ ( lattic8263393255366662781ax_int @ A ) )
% 4.69/4.98 = ( ? [X2: int] :
% 4.69/4.98 ( ( member_int @ X2 @ A )
% 4.69/4.98 & ( ord_less_int @ X @ X2 ) ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max_gr_iff
% 4.69/4.98 thf(fact_3764_Max__gr__iff,axiom,
% 4.69/4.98 ! [A: set_Code_integer,X: code_integer] :
% 4.69/4.98 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.98 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/4.98 => ( ( ord_le6747313008572928689nteger @ X @ ( lattic4901227151466704046nteger @ A ) )
% 4.69/4.98 = ( ? [X2: code_integer] :
% 4.69/4.98 ( ( member_Code_integer @ X2 @ A )
% 4.69/4.98 & ( ord_le6747313008572928689nteger @ X @ X2 ) ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max_gr_iff
% 4.69/4.98 thf(fact_3765_Max__gr__iff,axiom,
% 4.69/4.98 ! [A: set_rat,X: rat] :
% 4.69/4.98 ( ( finite_finite_rat @ A )
% 4.69/4.98 => ( ( A != bot_bot_set_rat )
% 4.69/4.98 => ( ( ord_less_rat @ X @ ( lattic7630753665789217321ax_rat @ A ) )
% 4.69/4.98 = ( ? [X2: rat] :
% 4.69/4.98 ( ( member_rat @ X2 @ A )
% 4.69/4.98 & ( ord_less_rat @ X @ X2 ) ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max_gr_iff
% 4.69/4.98 thf(fact_3766_Max__gr__iff,axiom,
% 4.69/4.98 ! [A: set_nat,X: nat] :
% 4.69/4.98 ( ( finite_finite_nat @ A )
% 4.69/4.98 => ( ( A != bot_bot_set_nat )
% 4.69/4.98 => ( ( ord_less_nat @ X @ ( lattic8265883725875713057ax_nat @ A ) )
% 4.69/4.98 = ( ? [X2: nat] :
% 4.69/4.98 ( ( member_nat @ X2 @ A )
% 4.69/4.98 & ( ord_less_nat @ X @ X2 ) ) ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % Max_gr_iff
% 4.69/4.98 thf(fact_3767_top__greatest,axiom,
% 4.69/4.98 ! [A2: assn] : ( ord_less_eq_assn @ A2 @ top_top_assn ) ).
% 4.69/4.98
% 4.69/4.98 % top_greatest
% 4.69/4.98 thf(fact_3768_top__greatest,axiom,
% 4.69/4.98 ! [A2: set_Product_unit] : ( ord_le3507040750410214029t_unit @ A2 @ top_to1996260823553986621t_unit ) ).
% 4.69/4.98
% 4.69/4.98 % top_greatest
% 4.69/4.98 thf(fact_3769_top__greatest,axiom,
% 4.69/4.98 ! [A2: set_o] : ( ord_less_eq_set_o @ A2 @ top_top_set_o ) ).
% 4.69/4.98
% 4.69/4.98 % top_greatest
% 4.69/4.98 thf(fact_3770_top__greatest,axiom,
% 4.69/4.98 ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ top_top_set_int ) ).
% 4.69/4.98
% 4.69/4.98 % top_greatest
% 4.69/4.98 thf(fact_3771_top__greatest,axiom,
% 4.69/4.98 ! [A2: filter_nat] : ( ord_le2510731241096832064er_nat @ A2 @ top_top_filter_nat ) ).
% 4.69/4.98
% 4.69/4.98 % top_greatest
% 4.69/4.98 thf(fact_3772_top__greatest,axiom,
% 4.69/4.98 ! [A2: set_nat] : ( ord_less_eq_set_nat @ A2 @ top_top_set_nat ) ).
% 4.69/4.98
% 4.69/4.98 % top_greatest
% 4.69/4.98 thf(fact_3773_top_Oextremum__unique,axiom,
% 4.69/4.98 ! [A2: assn] :
% 4.69/4.98 ( ( ord_less_eq_assn @ top_top_assn @ A2 )
% 4.69/4.98 = ( A2 = top_top_assn ) ) ).
% 4.69/4.98
% 4.69/4.98 % top.extremum_unique
% 4.69/4.98 thf(fact_3774_top_Oextremum__unique,axiom,
% 4.69/4.98 ! [A2: set_Product_unit] :
% 4.69/4.98 ( ( ord_le3507040750410214029t_unit @ top_to1996260823553986621t_unit @ A2 )
% 4.69/4.98 = ( A2 = top_to1996260823553986621t_unit ) ) ).
% 4.69/4.98
% 4.69/4.98 % top.extremum_unique
% 4.69/4.98 thf(fact_3775_top_Oextremum__unique,axiom,
% 4.69/4.98 ! [A2: set_o] :
% 4.69/4.98 ( ( ord_less_eq_set_o @ top_top_set_o @ A2 )
% 4.69/4.98 = ( A2 = top_top_set_o ) ) ).
% 4.69/4.98
% 4.69/4.98 % top.extremum_unique
% 4.69/4.98 thf(fact_3776_top_Oextremum__unique,axiom,
% 4.69/4.98 ! [A2: set_int] :
% 4.69/4.98 ( ( ord_less_eq_set_int @ top_top_set_int @ A2 )
% 4.69/4.98 = ( A2 = top_top_set_int ) ) ).
% 4.69/4.98
% 4.69/4.98 % top.extremum_unique
% 4.69/4.98 thf(fact_3777_top_Oextremum__unique,axiom,
% 4.69/4.98 ! [A2: filter_nat] :
% 4.69/4.98 ( ( ord_le2510731241096832064er_nat @ top_top_filter_nat @ A2 )
% 4.69/4.98 = ( A2 = top_top_filter_nat ) ) ).
% 4.69/4.98
% 4.69/4.98 % top.extremum_unique
% 4.69/4.98 thf(fact_3778_top_Oextremum__unique,axiom,
% 4.69/4.98 ! [A2: set_nat] :
% 4.69/4.98 ( ( ord_less_eq_set_nat @ top_top_set_nat @ A2 )
% 4.69/4.98 = ( A2 = top_top_set_nat ) ) ).
% 4.69/4.98
% 4.69/4.98 % top.extremum_unique
% 4.69/4.98 thf(fact_3779_top_Oextremum__uniqueI,axiom,
% 4.69/4.98 ! [A2: assn] :
% 4.69/4.98 ( ( ord_less_eq_assn @ top_top_assn @ A2 )
% 4.69/4.98 => ( A2 = top_top_assn ) ) ).
% 4.69/4.98
% 4.69/4.98 % top.extremum_uniqueI
% 4.69/4.98 thf(fact_3780_top_Oextremum__uniqueI,axiom,
% 4.69/4.98 ! [A2: set_Product_unit] :
% 4.69/4.98 ( ( ord_le3507040750410214029t_unit @ top_to1996260823553986621t_unit @ A2 )
% 4.69/4.98 => ( A2 = top_to1996260823553986621t_unit ) ) ).
% 4.69/4.98
% 4.69/4.98 % top.extremum_uniqueI
% 4.69/4.98 thf(fact_3781_top_Oextremum__uniqueI,axiom,
% 4.69/4.98 ! [A2: set_o] :
% 4.69/4.98 ( ( ord_less_eq_set_o @ top_top_set_o @ A2 )
% 4.69/4.98 => ( A2 = top_top_set_o ) ) ).
% 4.69/4.98
% 4.69/4.98 % top.extremum_uniqueI
% 4.69/4.98 thf(fact_3782_top_Oextremum__uniqueI,axiom,
% 4.69/4.98 ! [A2: set_int] :
% 4.69/4.98 ( ( ord_less_eq_set_int @ top_top_set_int @ A2 )
% 4.69/4.98 => ( A2 = top_top_set_int ) ) ).
% 4.69/4.98
% 4.69/4.98 % top.extremum_uniqueI
% 4.69/4.98 thf(fact_3783_top_Oextremum__uniqueI,axiom,
% 4.69/4.98 ! [A2: filter_nat] :
% 4.69/4.98 ( ( ord_le2510731241096832064er_nat @ top_top_filter_nat @ A2 )
% 4.69/4.98 => ( A2 = top_top_filter_nat ) ) ).
% 4.69/4.98
% 4.69/4.98 % top.extremum_uniqueI
% 4.69/4.98 thf(fact_3784_top_Oextremum__uniqueI,axiom,
% 4.69/4.98 ! [A2: set_nat] :
% 4.69/4.98 ( ( ord_less_eq_set_nat @ top_top_set_nat @ A2 )
% 4.69/4.98 => ( A2 = top_top_set_nat ) ) ).
% 4.69/4.98
% 4.69/4.98 % top.extremum_uniqueI
% 4.69/4.98 thf(fact_3785_leD,axiom,
% 4.69/4.98 ! [Y: assn,X: assn] :
% 4.69/4.98 ( ( ord_less_eq_assn @ Y @ X )
% 4.69/4.98 => ~ ( ord_less_assn @ X @ Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % leD
% 4.69/4.98 thf(fact_3786_leD,axiom,
% 4.69/4.98 ! [Y: code_integer,X: code_integer] :
% 4.69/4.98 ( ( ord_le3102999989581377725nteger @ Y @ X )
% 4.69/4.98 => ~ ( ord_le6747313008572928689nteger @ X @ Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % leD
% 4.69/4.98 thf(fact_3787_leD,axiom,
% 4.69/4.98 ! [Y: filter_nat,X: filter_nat] :
% 4.69/4.98 ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 4.69/4.98 => ~ ( ord_less_filter_nat @ X @ Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % leD
% 4.69/4.98 thf(fact_3788_leD,axiom,
% 4.69/4.98 ! [Y: set_nat,X: set_nat] :
% 4.69/4.98 ( ( ord_less_eq_set_nat @ Y @ X )
% 4.69/4.98 => ~ ( ord_less_set_nat @ X @ Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % leD
% 4.69/4.98 thf(fact_3789_leD,axiom,
% 4.69/4.98 ! [Y: rat,X: rat] :
% 4.69/4.98 ( ( ord_less_eq_rat @ Y @ X )
% 4.69/4.98 => ~ ( ord_less_rat @ X @ Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % leD
% 4.69/4.98 thf(fact_3790_leD,axiom,
% 4.69/4.98 ! [Y: nat,X: nat] :
% 4.69/4.98 ( ( ord_less_eq_nat @ Y @ X )
% 4.69/4.98 => ~ ( ord_less_nat @ X @ Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % leD
% 4.69/4.98 thf(fact_3791_leD,axiom,
% 4.69/4.98 ! [Y: int,X: int] :
% 4.69/4.98 ( ( ord_less_eq_int @ Y @ X )
% 4.69/4.98 => ~ ( ord_less_int @ X @ Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % leD
% 4.69/4.98 thf(fact_3792_leI,axiom,
% 4.69/4.98 ! [X: code_integer,Y: code_integer] :
% 4.69/4.98 ( ~ ( ord_le6747313008572928689nteger @ X @ Y )
% 4.69/4.98 => ( ord_le3102999989581377725nteger @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % leI
% 4.69/4.98 thf(fact_3793_leI,axiom,
% 4.69/4.98 ! [X: rat,Y: rat] :
% 4.69/4.98 ( ~ ( ord_less_rat @ X @ Y )
% 4.69/4.98 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % leI
% 4.69/4.98 thf(fact_3794_leI,axiom,
% 4.69/4.98 ! [X: nat,Y: nat] :
% 4.69/4.98 ( ~ ( ord_less_nat @ X @ Y )
% 4.69/4.98 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % leI
% 4.69/4.98 thf(fact_3795_leI,axiom,
% 4.69/4.98 ! [X: int,Y: int] :
% 4.69/4.98 ( ~ ( ord_less_int @ X @ Y )
% 4.69/4.98 => ( ord_less_eq_int @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % leI
% 4.69/4.98 thf(fact_3796_nless__le,axiom,
% 4.69/4.98 ! [A2: assn,B: assn] :
% 4.69/4.98 ( ( ~ ( ord_less_assn @ A2 @ B ) )
% 4.69/4.98 = ( ~ ( ord_less_eq_assn @ A2 @ B )
% 4.69/4.98 | ( A2 = B ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % nless_le
% 4.69/4.98 thf(fact_3797_nless__le,axiom,
% 4.69/4.98 ! [A2: code_integer,B: code_integer] :
% 4.69/4.98 ( ( ~ ( ord_le6747313008572928689nteger @ A2 @ B ) )
% 4.69/4.98 = ( ~ ( ord_le3102999989581377725nteger @ A2 @ B )
% 4.69/4.98 | ( A2 = B ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % nless_le
% 4.69/4.98 thf(fact_3798_nless__le,axiom,
% 4.69/4.98 ! [A2: filter_nat,B: filter_nat] :
% 4.69/4.98 ( ( ~ ( ord_less_filter_nat @ A2 @ B ) )
% 4.69/4.98 = ( ~ ( ord_le2510731241096832064er_nat @ A2 @ B )
% 4.69/4.98 | ( A2 = B ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % nless_le
% 4.69/4.98 thf(fact_3799_nless__le,axiom,
% 4.69/4.98 ! [A2: set_nat,B: set_nat] :
% 4.69/4.98 ( ( ~ ( ord_less_set_nat @ A2 @ B ) )
% 4.69/4.98 = ( ~ ( ord_less_eq_set_nat @ A2 @ B )
% 4.69/4.98 | ( A2 = B ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % nless_le
% 4.69/4.98 thf(fact_3800_nless__le,axiom,
% 4.69/4.98 ! [A2: rat,B: rat] :
% 4.69/4.98 ( ( ~ ( ord_less_rat @ A2 @ B ) )
% 4.69/4.98 = ( ~ ( ord_less_eq_rat @ A2 @ B )
% 4.69/4.98 | ( A2 = B ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % nless_le
% 4.69/4.98 thf(fact_3801_nless__le,axiom,
% 4.69/4.98 ! [A2: nat,B: nat] :
% 4.69/4.98 ( ( ~ ( ord_less_nat @ A2 @ B ) )
% 4.69/4.98 = ( ~ ( ord_less_eq_nat @ A2 @ B )
% 4.69/4.98 | ( A2 = B ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % nless_le
% 4.69/4.98 thf(fact_3802_nless__le,axiom,
% 4.69/4.98 ! [A2: int,B: int] :
% 4.69/4.98 ( ( ~ ( ord_less_int @ A2 @ B ) )
% 4.69/4.98 = ( ~ ( ord_less_eq_int @ A2 @ B )
% 4.69/4.98 | ( A2 = B ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % nless_le
% 4.69/4.98 thf(fact_3803_antisym__conv1,axiom,
% 4.69/4.98 ! [X: assn,Y: assn] :
% 4.69/4.98 ( ~ ( ord_less_assn @ X @ Y )
% 4.69/4.98 => ( ( ord_less_eq_assn @ X @ Y )
% 4.69/4.98 = ( X = Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % antisym_conv1
% 4.69/4.98 thf(fact_3804_antisym__conv1,axiom,
% 4.69/4.98 ! [X: code_integer,Y: code_integer] :
% 4.69/4.98 ( ~ ( ord_le6747313008572928689nteger @ X @ Y )
% 4.69/4.98 => ( ( ord_le3102999989581377725nteger @ X @ Y )
% 4.69/4.98 = ( X = Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % antisym_conv1
% 4.69/4.98 thf(fact_3805_antisym__conv1,axiom,
% 4.69/4.98 ! [X: filter_nat,Y: filter_nat] :
% 4.69/4.98 ( ~ ( ord_less_filter_nat @ X @ Y )
% 4.69/4.98 => ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 4.69/4.98 = ( X = Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % antisym_conv1
% 4.69/4.98 thf(fact_3806_antisym__conv1,axiom,
% 4.69/4.98 ! [X: set_nat,Y: set_nat] :
% 4.69/4.98 ( ~ ( ord_less_set_nat @ X @ Y )
% 4.69/4.98 => ( ( ord_less_eq_set_nat @ X @ Y )
% 4.69/4.98 = ( X = Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % antisym_conv1
% 4.69/4.98 thf(fact_3807_antisym__conv1,axiom,
% 4.69/4.98 ! [X: rat,Y: rat] :
% 4.69/4.98 ( ~ ( ord_less_rat @ X @ Y )
% 4.69/4.98 => ( ( ord_less_eq_rat @ X @ Y )
% 4.69/4.98 = ( X = Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % antisym_conv1
% 4.69/4.98 thf(fact_3808_antisym__conv1,axiom,
% 4.69/4.98 ! [X: nat,Y: nat] :
% 4.69/4.98 ( ~ ( ord_less_nat @ X @ Y )
% 4.69/4.98 => ( ( ord_less_eq_nat @ X @ Y )
% 4.69/4.98 = ( X = Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % antisym_conv1
% 4.69/4.98 thf(fact_3809_antisym__conv1,axiom,
% 4.69/4.98 ! [X: int,Y: int] :
% 4.69/4.98 ( ~ ( ord_less_int @ X @ Y )
% 4.69/4.98 => ( ( ord_less_eq_int @ X @ Y )
% 4.69/4.98 = ( X = Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % antisym_conv1
% 4.69/4.98 thf(fact_3810_antisym__conv2,axiom,
% 4.69/4.98 ! [X: assn,Y: assn] :
% 4.69/4.98 ( ( ord_less_eq_assn @ X @ Y )
% 4.69/4.98 => ( ( ~ ( ord_less_assn @ X @ Y ) )
% 4.69/4.98 = ( X = Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % antisym_conv2
% 4.69/4.98 thf(fact_3811_antisym__conv2,axiom,
% 4.69/4.98 ! [X: code_integer,Y: code_integer] :
% 4.69/4.98 ( ( ord_le3102999989581377725nteger @ X @ Y )
% 4.69/4.98 => ( ( ~ ( ord_le6747313008572928689nteger @ X @ Y ) )
% 4.69/4.98 = ( X = Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % antisym_conv2
% 4.69/4.98 thf(fact_3812_antisym__conv2,axiom,
% 4.69/4.98 ! [X: filter_nat,Y: filter_nat] :
% 4.69/4.98 ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 4.69/4.98 => ( ( ~ ( ord_less_filter_nat @ X @ Y ) )
% 4.69/4.98 = ( X = Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % antisym_conv2
% 4.69/4.98 thf(fact_3813_antisym__conv2,axiom,
% 4.69/4.98 ! [X: set_nat,Y: set_nat] :
% 4.69/4.98 ( ( ord_less_eq_set_nat @ X @ Y )
% 4.69/4.98 => ( ( ~ ( ord_less_set_nat @ X @ Y ) )
% 4.69/4.98 = ( X = Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % antisym_conv2
% 4.69/4.98 thf(fact_3814_antisym__conv2,axiom,
% 4.69/4.98 ! [X: rat,Y: rat] :
% 4.69/4.98 ( ( ord_less_eq_rat @ X @ Y )
% 4.69/4.98 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 4.69/4.98 = ( X = Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % antisym_conv2
% 4.69/4.98 thf(fact_3815_antisym__conv2,axiom,
% 4.69/4.98 ! [X: nat,Y: nat] :
% 4.69/4.98 ( ( ord_less_eq_nat @ X @ Y )
% 4.69/4.98 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 4.69/4.98 = ( X = Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % antisym_conv2
% 4.69/4.98 thf(fact_3816_antisym__conv2,axiom,
% 4.69/4.98 ! [X: int,Y: int] :
% 4.69/4.98 ( ( ord_less_eq_int @ X @ Y )
% 4.69/4.98 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 4.69/4.98 = ( X = Y ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % antisym_conv2
% 4.69/4.98 thf(fact_3817_dense__ge,axiom,
% 4.69/4.98 ! [Z: rat,Y: rat] :
% 4.69/4.98 ( ! [X3: rat] :
% 4.69/4.98 ( ( ord_less_rat @ Z @ X3 )
% 4.69/4.98 => ( ord_less_eq_rat @ Y @ X3 ) )
% 4.69/4.98 => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 4.69/4.98
% 4.69/4.98 % dense_ge
% 4.69/4.98 thf(fact_3818_dense__le,axiom,
% 4.69/4.98 ! [Y: rat,Z: rat] :
% 4.69/4.98 ( ! [X3: rat] :
% 4.69/4.98 ( ( ord_less_rat @ X3 @ Y )
% 4.69/4.98 => ( ord_less_eq_rat @ X3 @ Z ) )
% 4.69/4.98 => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 4.69/4.98
% 4.69/4.98 % dense_le
% 4.69/4.98 thf(fact_3819_less__le__not__le,axiom,
% 4.69/4.98 ( ord_less_assn
% 4.69/4.98 = ( ^ [X2: assn,Y3: assn] :
% 4.69/4.98 ( ( ord_less_eq_assn @ X2 @ Y3 )
% 4.69/4.98 & ~ ( ord_less_eq_assn @ Y3 @ X2 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % less_le_not_le
% 4.69/4.98 thf(fact_3820_less__le__not__le,axiom,
% 4.69/4.98 ( ord_le6747313008572928689nteger
% 4.69/4.98 = ( ^ [X2: code_integer,Y3: code_integer] :
% 4.69/4.98 ( ( ord_le3102999989581377725nteger @ X2 @ Y3 )
% 4.69/4.98 & ~ ( ord_le3102999989581377725nteger @ Y3 @ X2 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % less_le_not_le
% 4.69/4.98 thf(fact_3821_less__le__not__le,axiom,
% 4.69/4.98 ( ord_less_filter_nat
% 4.69/4.98 = ( ^ [X2: filter_nat,Y3: filter_nat] :
% 4.69/4.98 ( ( ord_le2510731241096832064er_nat @ X2 @ Y3 )
% 4.69/4.98 & ~ ( ord_le2510731241096832064er_nat @ Y3 @ X2 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % less_le_not_le
% 4.69/4.98 thf(fact_3822_less__le__not__le,axiom,
% 4.69/4.98 ( ord_less_set_nat
% 4.69/4.98 = ( ^ [X2: set_nat,Y3: set_nat] :
% 4.69/4.98 ( ( ord_less_eq_set_nat @ X2 @ Y3 )
% 4.69/4.98 & ~ ( ord_less_eq_set_nat @ Y3 @ X2 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % less_le_not_le
% 4.69/4.98 thf(fact_3823_less__le__not__le,axiom,
% 4.69/4.98 ( ord_less_rat
% 4.69/4.98 = ( ^ [X2: rat,Y3: rat] :
% 4.69/4.98 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 4.69/4.98 & ~ ( ord_less_eq_rat @ Y3 @ X2 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % less_le_not_le
% 4.69/4.98 thf(fact_3824_less__le__not__le,axiom,
% 4.69/4.98 ( ord_less_nat
% 4.69/4.98 = ( ^ [X2: nat,Y3: nat] :
% 4.69/4.98 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 4.69/4.98 & ~ ( ord_less_eq_nat @ Y3 @ X2 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % less_le_not_le
% 4.69/4.98 thf(fact_3825_less__le__not__le,axiom,
% 4.69/4.98 ( ord_less_int
% 4.69/4.98 = ( ^ [X2: int,Y3: int] :
% 4.69/4.98 ( ( ord_less_eq_int @ X2 @ Y3 )
% 4.69/4.98 & ~ ( ord_less_eq_int @ Y3 @ X2 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % less_le_not_le
% 4.69/4.98 thf(fact_3826_not__le__imp__less,axiom,
% 4.69/4.98 ! [Y: code_integer,X: code_integer] :
% 4.69/4.98 ( ~ ( ord_le3102999989581377725nteger @ Y @ X )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ X @ Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % not_le_imp_less
% 4.69/4.98 thf(fact_3827_not__le__imp__less,axiom,
% 4.69/4.98 ! [Y: rat,X: rat] :
% 4.69/4.98 ( ~ ( ord_less_eq_rat @ Y @ X )
% 4.69/4.98 => ( ord_less_rat @ X @ Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % not_le_imp_less
% 4.69/4.98 thf(fact_3828_not__le__imp__less,axiom,
% 4.69/4.98 ! [Y: nat,X: nat] :
% 4.69/4.98 ( ~ ( ord_less_eq_nat @ Y @ X )
% 4.69/4.98 => ( ord_less_nat @ X @ Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % not_le_imp_less
% 4.69/4.98 thf(fact_3829_not__le__imp__less,axiom,
% 4.69/4.98 ! [Y: int,X: int] :
% 4.69/4.98 ( ~ ( ord_less_eq_int @ Y @ X )
% 4.69/4.98 => ( ord_less_int @ X @ Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % not_le_imp_less
% 4.69/4.98 thf(fact_3830_order_Oorder__iff__strict,axiom,
% 4.69/4.98 ( ord_less_eq_assn
% 4.69/4.98 = ( ^ [A6: assn,B6: assn] :
% 4.69/4.98 ( ( ord_less_assn @ A6 @ B6 )
% 4.69/4.98 | ( A6 = B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.order_iff_strict
% 4.69/4.98 thf(fact_3831_order_Oorder__iff__strict,axiom,
% 4.69/4.98 ( ord_le3102999989581377725nteger
% 4.69/4.98 = ( ^ [A6: code_integer,B6: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ A6 @ B6 )
% 4.69/4.98 | ( A6 = B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.order_iff_strict
% 4.69/4.98 thf(fact_3832_order_Oorder__iff__strict,axiom,
% 4.69/4.98 ( ord_le2510731241096832064er_nat
% 4.69/4.98 = ( ^ [A6: filter_nat,B6: filter_nat] :
% 4.69/4.98 ( ( ord_less_filter_nat @ A6 @ B6 )
% 4.69/4.98 | ( A6 = B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.order_iff_strict
% 4.69/4.98 thf(fact_3833_order_Oorder__iff__strict,axiom,
% 4.69/4.98 ( ord_less_eq_set_nat
% 4.69/4.98 = ( ^ [A6: set_nat,B6: set_nat] :
% 4.69/4.98 ( ( ord_less_set_nat @ A6 @ B6 )
% 4.69/4.98 | ( A6 = B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.order_iff_strict
% 4.69/4.98 thf(fact_3834_order_Oorder__iff__strict,axiom,
% 4.69/4.98 ( ord_less_eq_rat
% 4.69/4.98 = ( ^ [A6: rat,B6: rat] :
% 4.69/4.98 ( ( ord_less_rat @ A6 @ B6 )
% 4.69/4.98 | ( A6 = B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.order_iff_strict
% 4.69/4.98 thf(fact_3835_order_Oorder__iff__strict,axiom,
% 4.69/4.98 ( ord_less_eq_nat
% 4.69/4.98 = ( ^ [A6: nat,B6: nat] :
% 4.69/4.98 ( ( ord_less_nat @ A6 @ B6 )
% 4.69/4.98 | ( A6 = B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.order_iff_strict
% 4.69/4.98 thf(fact_3836_order_Oorder__iff__strict,axiom,
% 4.69/4.98 ( ord_less_eq_int
% 4.69/4.98 = ( ^ [A6: int,B6: int] :
% 4.69/4.98 ( ( ord_less_int @ A6 @ B6 )
% 4.69/4.98 | ( A6 = B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.order_iff_strict
% 4.69/4.98 thf(fact_3837_order_Ostrict__iff__order,axiom,
% 4.69/4.98 ( ord_less_assn
% 4.69/4.98 = ( ^ [A6: assn,B6: assn] :
% 4.69/4.98 ( ( ord_less_eq_assn @ A6 @ B6 )
% 4.69/4.98 & ( A6 != B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_iff_order
% 4.69/4.98 thf(fact_3838_order_Ostrict__iff__order,axiom,
% 4.69/4.98 ( ord_le6747313008572928689nteger
% 4.69/4.98 = ( ^ [A6: code_integer,B6: code_integer] :
% 4.69/4.98 ( ( ord_le3102999989581377725nteger @ A6 @ B6 )
% 4.69/4.98 & ( A6 != B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_iff_order
% 4.69/4.98 thf(fact_3839_order_Ostrict__iff__order,axiom,
% 4.69/4.98 ( ord_less_filter_nat
% 4.69/4.98 = ( ^ [A6: filter_nat,B6: filter_nat] :
% 4.69/4.98 ( ( ord_le2510731241096832064er_nat @ A6 @ B6 )
% 4.69/4.98 & ( A6 != B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_iff_order
% 4.69/4.98 thf(fact_3840_order_Ostrict__iff__order,axiom,
% 4.69/4.98 ( ord_less_set_nat
% 4.69/4.98 = ( ^ [A6: set_nat,B6: set_nat] :
% 4.69/4.98 ( ( ord_less_eq_set_nat @ A6 @ B6 )
% 4.69/4.98 & ( A6 != B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_iff_order
% 4.69/4.98 thf(fact_3841_order_Ostrict__iff__order,axiom,
% 4.69/4.98 ( ord_less_rat
% 4.69/4.98 = ( ^ [A6: rat,B6: rat] :
% 4.69/4.98 ( ( ord_less_eq_rat @ A6 @ B6 )
% 4.69/4.98 & ( A6 != B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_iff_order
% 4.69/4.98 thf(fact_3842_order_Ostrict__iff__order,axiom,
% 4.69/4.98 ( ord_less_nat
% 4.69/4.98 = ( ^ [A6: nat,B6: nat] :
% 4.69/4.98 ( ( ord_less_eq_nat @ A6 @ B6 )
% 4.69/4.98 & ( A6 != B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_iff_order
% 4.69/4.98 thf(fact_3843_order_Ostrict__iff__order,axiom,
% 4.69/4.98 ( ord_less_int
% 4.69/4.98 = ( ^ [A6: int,B6: int] :
% 4.69/4.98 ( ( ord_less_eq_int @ A6 @ B6 )
% 4.69/4.98 & ( A6 != B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_iff_order
% 4.69/4.98 thf(fact_3844_order_Ostrict__trans1,axiom,
% 4.69/4.98 ! [A2: assn,B: assn,C: assn] :
% 4.69/4.98 ( ( ord_less_eq_assn @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_assn @ B @ C )
% 4.69/4.98 => ( ord_less_assn @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_trans1
% 4.69/4.98 thf(fact_3845_order_Ostrict__trans1,axiom,
% 4.69/4.98 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/4.98 ( ( ord_le3102999989581377725nteger @ A2 @ B )
% 4.69/4.98 => ( ( ord_le6747313008572928689nteger @ B @ C )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_trans1
% 4.69/4.98 thf(fact_3846_order_Ostrict__trans1,axiom,
% 4.69/4.98 ! [A2: filter_nat,B: filter_nat,C: filter_nat] :
% 4.69/4.98 ( ( ord_le2510731241096832064er_nat @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_filter_nat @ B @ C )
% 4.69/4.98 => ( ord_less_filter_nat @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_trans1
% 4.69/4.98 thf(fact_3847_order_Ostrict__trans1,axiom,
% 4.69/4.98 ! [A2: set_nat,B: set_nat,C: set_nat] :
% 4.69/4.98 ( ( ord_less_eq_set_nat @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_set_nat @ B @ C )
% 4.69/4.98 => ( ord_less_set_nat @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_trans1
% 4.69/4.98 thf(fact_3848_order_Ostrict__trans1,axiom,
% 4.69/4.98 ! [A2: rat,B: rat,C: rat] :
% 4.69/4.98 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_rat @ B @ C )
% 4.69/4.98 => ( ord_less_rat @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_trans1
% 4.69/4.98 thf(fact_3849_order_Ostrict__trans1,axiom,
% 4.69/4.98 ! [A2: nat,B: nat,C: nat] :
% 4.69/4.98 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_nat @ B @ C )
% 4.69/4.98 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_trans1
% 4.69/4.98 thf(fact_3850_order_Ostrict__trans1,axiom,
% 4.69/4.98 ! [A2: int,B: int,C: int] :
% 4.69/4.98 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_int @ B @ C )
% 4.69/4.98 => ( ord_less_int @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_trans1
% 4.69/4.98 thf(fact_3851_order_Ostrict__trans2,axiom,
% 4.69/4.98 ! [A2: assn,B: assn,C: assn] :
% 4.69/4.98 ( ( ord_less_assn @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_eq_assn @ B @ C )
% 4.69/4.98 => ( ord_less_assn @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_trans2
% 4.69/4.98 thf(fact_3852_order_Ostrict__trans2,axiom,
% 4.69/4.98 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/4.98 => ( ( ord_le3102999989581377725nteger @ B @ C )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_trans2
% 4.69/4.98 thf(fact_3853_order_Ostrict__trans2,axiom,
% 4.69/4.98 ! [A2: filter_nat,B: filter_nat,C: filter_nat] :
% 4.69/4.98 ( ( ord_less_filter_nat @ A2 @ B )
% 4.69/4.98 => ( ( ord_le2510731241096832064er_nat @ B @ C )
% 4.69/4.98 => ( ord_less_filter_nat @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_trans2
% 4.69/4.98 thf(fact_3854_order_Ostrict__trans2,axiom,
% 4.69/4.98 ! [A2: set_nat,B: set_nat,C: set_nat] :
% 4.69/4.98 ( ( ord_less_set_nat @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_eq_set_nat @ B @ C )
% 4.69/4.98 => ( ord_less_set_nat @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_trans2
% 4.69/4.98 thf(fact_3855_order_Ostrict__trans2,axiom,
% 4.69/4.98 ! [A2: rat,B: rat,C: rat] :
% 4.69/4.98 ( ( ord_less_rat @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_eq_rat @ B @ C )
% 4.69/4.98 => ( ord_less_rat @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_trans2
% 4.69/4.98 thf(fact_3856_order_Ostrict__trans2,axiom,
% 4.69/4.98 ! [A2: nat,B: nat,C: nat] :
% 4.69/4.98 ( ( ord_less_nat @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_eq_nat @ B @ C )
% 4.69/4.98 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_trans2
% 4.69/4.98 thf(fact_3857_order_Ostrict__trans2,axiom,
% 4.69/4.98 ! [A2: int,B: int,C: int] :
% 4.69/4.98 ( ( ord_less_int @ A2 @ B )
% 4.69/4.98 => ( ( ord_less_eq_int @ B @ C )
% 4.69/4.98 => ( ord_less_int @ A2 @ C ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_trans2
% 4.69/4.98 thf(fact_3858_order_Ostrict__iff__not,axiom,
% 4.69/4.98 ( ord_less_assn
% 4.69/4.98 = ( ^ [A6: assn,B6: assn] :
% 4.69/4.98 ( ( ord_less_eq_assn @ A6 @ B6 )
% 4.69/4.98 & ~ ( ord_less_eq_assn @ B6 @ A6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_iff_not
% 4.69/4.98 thf(fact_3859_order_Ostrict__iff__not,axiom,
% 4.69/4.98 ( ord_le6747313008572928689nteger
% 4.69/4.98 = ( ^ [A6: code_integer,B6: code_integer] :
% 4.69/4.98 ( ( ord_le3102999989581377725nteger @ A6 @ B6 )
% 4.69/4.98 & ~ ( ord_le3102999989581377725nteger @ B6 @ A6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_iff_not
% 4.69/4.98 thf(fact_3860_order_Ostrict__iff__not,axiom,
% 4.69/4.98 ( ord_less_filter_nat
% 4.69/4.98 = ( ^ [A6: filter_nat,B6: filter_nat] :
% 4.69/4.98 ( ( ord_le2510731241096832064er_nat @ A6 @ B6 )
% 4.69/4.98 & ~ ( ord_le2510731241096832064er_nat @ B6 @ A6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_iff_not
% 4.69/4.98 thf(fact_3861_order_Ostrict__iff__not,axiom,
% 4.69/4.98 ( ord_less_set_nat
% 4.69/4.98 = ( ^ [A6: set_nat,B6: set_nat] :
% 4.69/4.98 ( ( ord_less_eq_set_nat @ A6 @ B6 )
% 4.69/4.98 & ~ ( ord_less_eq_set_nat @ B6 @ A6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_iff_not
% 4.69/4.98 thf(fact_3862_order_Ostrict__iff__not,axiom,
% 4.69/4.98 ( ord_less_rat
% 4.69/4.98 = ( ^ [A6: rat,B6: rat] :
% 4.69/4.98 ( ( ord_less_eq_rat @ A6 @ B6 )
% 4.69/4.98 & ~ ( ord_less_eq_rat @ B6 @ A6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_iff_not
% 4.69/4.98 thf(fact_3863_order_Ostrict__iff__not,axiom,
% 4.69/4.98 ( ord_less_nat
% 4.69/4.98 = ( ^ [A6: nat,B6: nat] :
% 4.69/4.98 ( ( ord_less_eq_nat @ A6 @ B6 )
% 4.69/4.98 & ~ ( ord_less_eq_nat @ B6 @ A6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_iff_not
% 4.69/4.98 thf(fact_3864_order_Ostrict__iff__not,axiom,
% 4.69/4.98 ( ord_less_int
% 4.69/4.98 = ( ^ [A6: int,B6: int] :
% 4.69/4.98 ( ( ord_less_eq_int @ A6 @ B6 )
% 4.69/4.98 & ~ ( ord_less_eq_int @ B6 @ A6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_iff_not
% 4.69/4.98 thf(fact_3865_dense__ge__bounded,axiom,
% 4.69/4.98 ! [Z: rat,X: rat,Y: rat] :
% 4.69/4.98 ( ( ord_less_rat @ Z @ X )
% 4.69/4.98 => ( ! [W2: rat] :
% 4.69/4.98 ( ( ord_less_rat @ Z @ W2 )
% 4.69/4.98 => ( ( ord_less_rat @ W2 @ X )
% 4.69/4.98 => ( ord_less_eq_rat @ Y @ W2 ) ) )
% 4.69/4.98 => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dense_ge_bounded
% 4.69/4.98 thf(fact_3866_dense__le__bounded,axiom,
% 4.69/4.98 ! [X: rat,Y: rat,Z: rat] :
% 4.69/4.98 ( ( ord_less_rat @ X @ Y )
% 4.69/4.98 => ( ! [W2: rat] :
% 4.69/4.98 ( ( ord_less_rat @ X @ W2 )
% 4.69/4.98 => ( ( ord_less_rat @ W2 @ Y )
% 4.69/4.98 => ( ord_less_eq_rat @ W2 @ Z ) ) )
% 4.69/4.98 => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dense_le_bounded
% 4.69/4.98 thf(fact_3867_dual__order_Oorder__iff__strict,axiom,
% 4.69/4.98 ( ord_less_eq_assn
% 4.69/4.98 = ( ^ [B6: assn,A6: assn] :
% 4.69/4.98 ( ( ord_less_assn @ B6 @ A6 )
% 4.69/4.98 | ( A6 = B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.order_iff_strict
% 4.69/4.98 thf(fact_3868_dual__order_Oorder__iff__strict,axiom,
% 4.69/4.98 ( ord_le3102999989581377725nteger
% 4.69/4.98 = ( ^ [B6: code_integer,A6: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ B6 @ A6 )
% 4.69/4.98 | ( A6 = B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.order_iff_strict
% 4.69/4.98 thf(fact_3869_dual__order_Oorder__iff__strict,axiom,
% 4.69/4.98 ( ord_le2510731241096832064er_nat
% 4.69/4.98 = ( ^ [B6: filter_nat,A6: filter_nat] :
% 4.69/4.98 ( ( ord_less_filter_nat @ B6 @ A6 )
% 4.69/4.98 | ( A6 = B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.order_iff_strict
% 4.69/4.98 thf(fact_3870_dual__order_Oorder__iff__strict,axiom,
% 4.69/4.98 ( ord_less_eq_set_nat
% 4.69/4.98 = ( ^ [B6: set_nat,A6: set_nat] :
% 4.69/4.98 ( ( ord_less_set_nat @ B6 @ A6 )
% 4.69/4.98 | ( A6 = B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.order_iff_strict
% 4.69/4.98 thf(fact_3871_dual__order_Oorder__iff__strict,axiom,
% 4.69/4.98 ( ord_less_eq_rat
% 4.69/4.98 = ( ^ [B6: rat,A6: rat] :
% 4.69/4.98 ( ( ord_less_rat @ B6 @ A6 )
% 4.69/4.98 | ( A6 = B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.order_iff_strict
% 4.69/4.98 thf(fact_3872_dual__order_Oorder__iff__strict,axiom,
% 4.69/4.98 ( ord_less_eq_nat
% 4.69/4.98 = ( ^ [B6: nat,A6: nat] :
% 4.69/4.98 ( ( ord_less_nat @ B6 @ A6 )
% 4.69/4.98 | ( A6 = B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.order_iff_strict
% 4.69/4.98 thf(fact_3873_dual__order_Oorder__iff__strict,axiom,
% 4.69/4.98 ( ord_less_eq_int
% 4.69/4.98 = ( ^ [B6: int,A6: int] :
% 4.69/4.98 ( ( ord_less_int @ B6 @ A6 )
% 4.69/4.98 | ( A6 = B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.order_iff_strict
% 4.69/4.98 thf(fact_3874_dual__order_Ostrict__iff__order,axiom,
% 4.69/4.98 ( ord_less_assn
% 4.69/4.98 = ( ^ [B6: assn,A6: assn] :
% 4.69/4.98 ( ( ord_less_eq_assn @ B6 @ A6 )
% 4.69/4.98 & ( A6 != B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_iff_order
% 4.69/4.98 thf(fact_3875_dual__order_Ostrict__iff__order,axiom,
% 4.69/4.98 ( ord_le6747313008572928689nteger
% 4.69/4.98 = ( ^ [B6: code_integer,A6: code_integer] :
% 4.69/4.98 ( ( ord_le3102999989581377725nteger @ B6 @ A6 )
% 4.69/4.98 & ( A6 != B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_iff_order
% 4.69/4.98 thf(fact_3876_dual__order_Ostrict__iff__order,axiom,
% 4.69/4.98 ( ord_less_filter_nat
% 4.69/4.98 = ( ^ [B6: filter_nat,A6: filter_nat] :
% 4.69/4.98 ( ( ord_le2510731241096832064er_nat @ B6 @ A6 )
% 4.69/4.98 & ( A6 != B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_iff_order
% 4.69/4.98 thf(fact_3877_dual__order_Ostrict__iff__order,axiom,
% 4.69/4.98 ( ord_less_set_nat
% 4.69/4.98 = ( ^ [B6: set_nat,A6: set_nat] :
% 4.69/4.98 ( ( ord_less_eq_set_nat @ B6 @ A6 )
% 4.69/4.98 & ( A6 != B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_iff_order
% 4.69/4.98 thf(fact_3878_dual__order_Ostrict__iff__order,axiom,
% 4.69/4.98 ( ord_less_rat
% 4.69/4.98 = ( ^ [B6: rat,A6: rat] :
% 4.69/4.98 ( ( ord_less_eq_rat @ B6 @ A6 )
% 4.69/4.98 & ( A6 != B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_iff_order
% 4.69/4.98 thf(fact_3879_dual__order_Ostrict__iff__order,axiom,
% 4.69/4.98 ( ord_less_nat
% 4.69/4.98 = ( ^ [B6: nat,A6: nat] :
% 4.69/4.98 ( ( ord_less_eq_nat @ B6 @ A6 )
% 4.69/4.98 & ( A6 != B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_iff_order
% 4.69/4.98 thf(fact_3880_dual__order_Ostrict__iff__order,axiom,
% 4.69/4.98 ( ord_less_int
% 4.69/4.98 = ( ^ [B6: int,A6: int] :
% 4.69/4.98 ( ( ord_less_eq_int @ B6 @ A6 )
% 4.69/4.98 & ( A6 != B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_iff_order
% 4.69/4.98 thf(fact_3881_dual__order_Ostrict__trans1,axiom,
% 4.69/4.98 ! [B: assn,A2: assn,C: assn] :
% 4.69/4.98 ( ( ord_less_eq_assn @ B @ A2 )
% 4.69/4.98 => ( ( ord_less_assn @ C @ B )
% 4.69/4.98 => ( ord_less_assn @ C @ A2 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_trans1
% 4.69/4.98 thf(fact_3882_dual__order_Ostrict__trans1,axiom,
% 4.69/4.98 ! [B: code_integer,A2: code_integer,C: code_integer] :
% 4.69/4.98 ( ( ord_le3102999989581377725nteger @ B @ A2 )
% 4.69/4.98 => ( ( ord_le6747313008572928689nteger @ C @ B )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ C @ A2 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_trans1
% 4.69/4.98 thf(fact_3883_dual__order_Ostrict__trans1,axiom,
% 4.69/4.98 ! [B: filter_nat,A2: filter_nat,C: filter_nat] :
% 4.69/4.98 ( ( ord_le2510731241096832064er_nat @ B @ A2 )
% 4.69/4.98 => ( ( ord_less_filter_nat @ C @ B )
% 4.69/4.98 => ( ord_less_filter_nat @ C @ A2 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_trans1
% 4.69/4.98 thf(fact_3884_dual__order_Ostrict__trans1,axiom,
% 4.69/4.98 ! [B: set_nat,A2: set_nat,C: set_nat] :
% 4.69/4.98 ( ( ord_less_eq_set_nat @ B @ A2 )
% 4.69/4.98 => ( ( ord_less_set_nat @ C @ B )
% 4.69/4.98 => ( ord_less_set_nat @ C @ A2 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_trans1
% 4.69/4.98 thf(fact_3885_dual__order_Ostrict__trans1,axiom,
% 4.69/4.98 ! [B: rat,A2: rat,C: rat] :
% 4.69/4.98 ( ( ord_less_eq_rat @ B @ A2 )
% 4.69/4.98 => ( ( ord_less_rat @ C @ B )
% 4.69/4.98 => ( ord_less_rat @ C @ A2 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_trans1
% 4.69/4.98 thf(fact_3886_dual__order_Ostrict__trans1,axiom,
% 4.69/4.98 ! [B: nat,A2: nat,C: nat] :
% 4.69/4.98 ( ( ord_less_eq_nat @ B @ A2 )
% 4.69/4.98 => ( ( ord_less_nat @ C @ B )
% 4.69/4.98 => ( ord_less_nat @ C @ A2 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_trans1
% 4.69/4.98 thf(fact_3887_dual__order_Ostrict__trans1,axiom,
% 4.69/4.98 ! [B: int,A2: int,C: int] :
% 4.69/4.98 ( ( ord_less_eq_int @ B @ A2 )
% 4.69/4.98 => ( ( ord_less_int @ C @ B )
% 4.69/4.98 => ( ord_less_int @ C @ A2 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_trans1
% 4.69/4.98 thf(fact_3888_dual__order_Ostrict__trans2,axiom,
% 4.69/4.98 ! [B: assn,A2: assn,C: assn] :
% 4.69/4.98 ( ( ord_less_assn @ B @ A2 )
% 4.69/4.98 => ( ( ord_less_eq_assn @ C @ B )
% 4.69/4.98 => ( ord_less_assn @ C @ A2 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_trans2
% 4.69/4.98 thf(fact_3889_dual__order_Ostrict__trans2,axiom,
% 4.69/4.98 ! [B: code_integer,A2: code_integer,C: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ B @ A2 )
% 4.69/4.98 => ( ( ord_le3102999989581377725nteger @ C @ B )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ C @ A2 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_trans2
% 4.69/4.98 thf(fact_3890_dual__order_Ostrict__trans2,axiom,
% 4.69/4.98 ! [B: filter_nat,A2: filter_nat,C: filter_nat] :
% 4.69/4.98 ( ( ord_less_filter_nat @ B @ A2 )
% 4.69/4.98 => ( ( ord_le2510731241096832064er_nat @ C @ B )
% 4.69/4.98 => ( ord_less_filter_nat @ C @ A2 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_trans2
% 4.69/4.98 thf(fact_3891_dual__order_Ostrict__trans2,axiom,
% 4.69/4.98 ! [B: set_nat,A2: set_nat,C: set_nat] :
% 4.69/4.98 ( ( ord_less_set_nat @ B @ A2 )
% 4.69/4.98 => ( ( ord_less_eq_set_nat @ C @ B )
% 4.69/4.98 => ( ord_less_set_nat @ C @ A2 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_trans2
% 4.69/4.98 thf(fact_3892_dual__order_Ostrict__trans2,axiom,
% 4.69/4.98 ! [B: rat,A2: rat,C: rat] :
% 4.69/4.98 ( ( ord_less_rat @ B @ A2 )
% 4.69/4.98 => ( ( ord_less_eq_rat @ C @ B )
% 4.69/4.98 => ( ord_less_rat @ C @ A2 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_trans2
% 4.69/4.98 thf(fact_3893_dual__order_Ostrict__trans2,axiom,
% 4.69/4.98 ! [B: nat,A2: nat,C: nat] :
% 4.69/4.98 ( ( ord_less_nat @ B @ A2 )
% 4.69/4.98 => ( ( ord_less_eq_nat @ C @ B )
% 4.69/4.98 => ( ord_less_nat @ C @ A2 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_trans2
% 4.69/4.98 thf(fact_3894_dual__order_Ostrict__trans2,axiom,
% 4.69/4.98 ! [B: int,A2: int,C: int] :
% 4.69/4.98 ( ( ord_less_int @ B @ A2 )
% 4.69/4.98 => ( ( ord_less_eq_int @ C @ B )
% 4.69/4.98 => ( ord_less_int @ C @ A2 ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_trans2
% 4.69/4.98 thf(fact_3895_dual__order_Ostrict__iff__not,axiom,
% 4.69/4.98 ( ord_less_assn
% 4.69/4.98 = ( ^ [B6: assn,A6: assn] :
% 4.69/4.98 ( ( ord_less_eq_assn @ B6 @ A6 )
% 4.69/4.98 & ~ ( ord_less_eq_assn @ A6 @ B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_iff_not
% 4.69/4.98 thf(fact_3896_dual__order_Ostrict__iff__not,axiom,
% 4.69/4.98 ( ord_le6747313008572928689nteger
% 4.69/4.98 = ( ^ [B6: code_integer,A6: code_integer] :
% 4.69/4.98 ( ( ord_le3102999989581377725nteger @ B6 @ A6 )
% 4.69/4.98 & ~ ( ord_le3102999989581377725nteger @ A6 @ B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_iff_not
% 4.69/4.98 thf(fact_3897_dual__order_Ostrict__iff__not,axiom,
% 4.69/4.98 ( ord_less_filter_nat
% 4.69/4.98 = ( ^ [B6: filter_nat,A6: filter_nat] :
% 4.69/4.98 ( ( ord_le2510731241096832064er_nat @ B6 @ A6 )
% 4.69/4.98 & ~ ( ord_le2510731241096832064er_nat @ A6 @ B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_iff_not
% 4.69/4.98 thf(fact_3898_dual__order_Ostrict__iff__not,axiom,
% 4.69/4.98 ( ord_less_set_nat
% 4.69/4.98 = ( ^ [B6: set_nat,A6: set_nat] :
% 4.69/4.98 ( ( ord_less_eq_set_nat @ B6 @ A6 )
% 4.69/4.98 & ~ ( ord_less_eq_set_nat @ A6 @ B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_iff_not
% 4.69/4.98 thf(fact_3899_dual__order_Ostrict__iff__not,axiom,
% 4.69/4.98 ( ord_less_rat
% 4.69/4.98 = ( ^ [B6: rat,A6: rat] :
% 4.69/4.98 ( ( ord_less_eq_rat @ B6 @ A6 )
% 4.69/4.98 & ~ ( ord_less_eq_rat @ A6 @ B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_iff_not
% 4.69/4.98 thf(fact_3900_dual__order_Ostrict__iff__not,axiom,
% 4.69/4.98 ( ord_less_nat
% 4.69/4.98 = ( ^ [B6: nat,A6: nat] :
% 4.69/4.98 ( ( ord_less_eq_nat @ B6 @ A6 )
% 4.69/4.98 & ~ ( ord_less_eq_nat @ A6 @ B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_iff_not
% 4.69/4.98 thf(fact_3901_dual__order_Ostrict__iff__not,axiom,
% 4.69/4.98 ( ord_less_int
% 4.69/4.98 = ( ^ [B6: int,A6: int] :
% 4.69/4.98 ( ( ord_less_eq_int @ B6 @ A6 )
% 4.69/4.98 & ~ ( ord_less_eq_int @ A6 @ B6 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_iff_not
% 4.69/4.98 thf(fact_3902_order_Ostrict__implies__order,axiom,
% 4.69/4.98 ! [A2: assn,B: assn] :
% 4.69/4.98 ( ( ord_less_assn @ A2 @ B )
% 4.69/4.98 => ( ord_less_eq_assn @ A2 @ B ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_implies_order
% 4.69/4.98 thf(fact_3903_order_Ostrict__implies__order,axiom,
% 4.69/4.98 ! [A2: code_integer,B: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/4.98 => ( ord_le3102999989581377725nteger @ A2 @ B ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_implies_order
% 4.69/4.98 thf(fact_3904_order_Ostrict__implies__order,axiom,
% 4.69/4.98 ! [A2: filter_nat,B: filter_nat] :
% 4.69/4.98 ( ( ord_less_filter_nat @ A2 @ B )
% 4.69/4.98 => ( ord_le2510731241096832064er_nat @ A2 @ B ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_implies_order
% 4.69/4.98 thf(fact_3905_order_Ostrict__implies__order,axiom,
% 4.69/4.98 ! [A2: set_nat,B: set_nat] :
% 4.69/4.98 ( ( ord_less_set_nat @ A2 @ B )
% 4.69/4.98 => ( ord_less_eq_set_nat @ A2 @ B ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_implies_order
% 4.69/4.98 thf(fact_3906_order_Ostrict__implies__order,axiom,
% 4.69/4.98 ! [A2: rat,B: rat] :
% 4.69/4.98 ( ( ord_less_rat @ A2 @ B )
% 4.69/4.98 => ( ord_less_eq_rat @ A2 @ B ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_implies_order
% 4.69/4.98 thf(fact_3907_order_Ostrict__implies__order,axiom,
% 4.69/4.98 ! [A2: nat,B: nat] :
% 4.69/4.98 ( ( ord_less_nat @ A2 @ B )
% 4.69/4.98 => ( ord_less_eq_nat @ A2 @ B ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_implies_order
% 4.69/4.98 thf(fact_3908_order_Ostrict__implies__order,axiom,
% 4.69/4.98 ! [A2: int,B: int] :
% 4.69/4.98 ( ( ord_less_int @ A2 @ B )
% 4.69/4.98 => ( ord_less_eq_int @ A2 @ B ) ) ).
% 4.69/4.98
% 4.69/4.98 % order.strict_implies_order
% 4.69/4.98 thf(fact_3909_dual__order_Ostrict__implies__order,axiom,
% 4.69/4.98 ! [B: assn,A2: assn] :
% 4.69/4.98 ( ( ord_less_assn @ B @ A2 )
% 4.69/4.98 => ( ord_less_eq_assn @ B @ A2 ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_implies_order
% 4.69/4.98 thf(fact_3910_dual__order_Ostrict__implies__order,axiom,
% 4.69/4.98 ! [B: code_integer,A2: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ B @ A2 )
% 4.69/4.98 => ( ord_le3102999989581377725nteger @ B @ A2 ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_implies_order
% 4.69/4.98 thf(fact_3911_dual__order_Ostrict__implies__order,axiom,
% 4.69/4.98 ! [B: filter_nat,A2: filter_nat] :
% 4.69/4.98 ( ( ord_less_filter_nat @ B @ A2 )
% 4.69/4.98 => ( ord_le2510731241096832064er_nat @ B @ A2 ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_implies_order
% 4.69/4.98 thf(fact_3912_dual__order_Ostrict__implies__order,axiom,
% 4.69/4.98 ! [B: set_nat,A2: set_nat] :
% 4.69/4.98 ( ( ord_less_set_nat @ B @ A2 )
% 4.69/4.98 => ( ord_less_eq_set_nat @ B @ A2 ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_implies_order
% 4.69/4.98 thf(fact_3913_dual__order_Ostrict__implies__order,axiom,
% 4.69/4.98 ! [B: rat,A2: rat] :
% 4.69/4.98 ( ( ord_less_rat @ B @ A2 )
% 4.69/4.98 => ( ord_less_eq_rat @ B @ A2 ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_implies_order
% 4.69/4.98 thf(fact_3914_dual__order_Ostrict__implies__order,axiom,
% 4.69/4.98 ! [B: nat,A2: nat] :
% 4.69/4.98 ( ( ord_less_nat @ B @ A2 )
% 4.69/4.98 => ( ord_less_eq_nat @ B @ A2 ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_implies_order
% 4.69/4.98 thf(fact_3915_dual__order_Ostrict__implies__order,axiom,
% 4.69/4.98 ! [B: int,A2: int] :
% 4.69/4.98 ( ( ord_less_int @ B @ A2 )
% 4.69/4.98 => ( ord_less_eq_int @ B @ A2 ) ) ).
% 4.69/4.98
% 4.69/4.98 % dual_order.strict_implies_order
% 4.69/4.98 thf(fact_3916_order__le__less,axiom,
% 4.69/4.98 ( ord_less_eq_assn
% 4.69/4.98 = ( ^ [X2: assn,Y3: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X2 @ Y3 )
% 4.69/4.98 | ( X2 = Y3 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_le_less
% 4.69/4.98 thf(fact_3917_order__le__less,axiom,
% 4.69/4.98 ( ord_le3102999989581377725nteger
% 4.69/4.98 = ( ^ [X2: code_integer,Y3: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ X2 @ Y3 )
% 4.69/4.98 | ( X2 = Y3 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_le_less
% 4.69/4.98 thf(fact_3918_order__le__less,axiom,
% 4.69/4.98 ( ord_le2510731241096832064er_nat
% 4.69/4.98 = ( ^ [X2: filter_nat,Y3: filter_nat] :
% 4.69/4.98 ( ( ord_less_filter_nat @ X2 @ Y3 )
% 4.69/4.98 | ( X2 = Y3 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_le_less
% 4.69/4.98 thf(fact_3919_order__le__less,axiom,
% 4.69/4.98 ( ord_less_eq_set_nat
% 4.69/4.98 = ( ^ [X2: set_nat,Y3: set_nat] :
% 4.69/4.98 ( ( ord_less_set_nat @ X2 @ Y3 )
% 4.69/4.98 | ( X2 = Y3 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_le_less
% 4.69/4.98 thf(fact_3920_order__le__less,axiom,
% 4.69/4.98 ( ord_less_eq_rat
% 4.69/4.98 = ( ^ [X2: rat,Y3: rat] :
% 4.69/4.98 ( ( ord_less_rat @ X2 @ Y3 )
% 4.69/4.98 | ( X2 = Y3 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_le_less
% 4.69/4.98 thf(fact_3921_order__le__less,axiom,
% 4.69/4.98 ( ord_less_eq_nat
% 4.69/4.98 = ( ^ [X2: nat,Y3: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X2 @ Y3 )
% 4.69/4.98 | ( X2 = Y3 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_le_less
% 4.69/4.98 thf(fact_3922_order__le__less,axiom,
% 4.69/4.98 ( ord_less_eq_int
% 4.69/4.98 = ( ^ [X2: int,Y3: int] :
% 4.69/4.98 ( ( ord_less_int @ X2 @ Y3 )
% 4.69/4.98 | ( X2 = Y3 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_le_less
% 4.69/4.98 thf(fact_3923_order__less__le,axiom,
% 4.69/4.98 ( ord_less_assn
% 4.69/4.98 = ( ^ [X2: assn,Y3: assn] :
% 4.69/4.98 ( ( ord_less_eq_assn @ X2 @ Y3 )
% 4.69/4.98 & ( X2 != Y3 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_le
% 4.69/4.98 thf(fact_3924_order__less__le,axiom,
% 4.69/4.98 ( ord_le6747313008572928689nteger
% 4.69/4.98 = ( ^ [X2: code_integer,Y3: code_integer] :
% 4.69/4.98 ( ( ord_le3102999989581377725nteger @ X2 @ Y3 )
% 4.69/4.98 & ( X2 != Y3 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_le
% 4.69/4.98 thf(fact_3925_order__less__le,axiom,
% 4.69/4.98 ( ord_less_filter_nat
% 4.69/4.98 = ( ^ [X2: filter_nat,Y3: filter_nat] :
% 4.69/4.98 ( ( ord_le2510731241096832064er_nat @ X2 @ Y3 )
% 4.69/4.98 & ( X2 != Y3 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_le
% 4.69/4.98 thf(fact_3926_order__less__le,axiom,
% 4.69/4.98 ( ord_less_set_nat
% 4.69/4.98 = ( ^ [X2: set_nat,Y3: set_nat] :
% 4.69/4.98 ( ( ord_less_eq_set_nat @ X2 @ Y3 )
% 4.69/4.98 & ( X2 != Y3 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_le
% 4.69/4.98 thf(fact_3927_order__less__le,axiom,
% 4.69/4.98 ( ord_less_rat
% 4.69/4.98 = ( ^ [X2: rat,Y3: rat] :
% 4.69/4.98 ( ( ord_less_eq_rat @ X2 @ Y3 )
% 4.69/4.98 & ( X2 != Y3 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_le
% 4.69/4.98 thf(fact_3928_order__less__le,axiom,
% 4.69/4.98 ( ord_less_nat
% 4.69/4.98 = ( ^ [X2: nat,Y3: nat] :
% 4.69/4.98 ( ( ord_less_eq_nat @ X2 @ Y3 )
% 4.69/4.98 & ( X2 != Y3 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_le
% 4.69/4.98 thf(fact_3929_order__less__le,axiom,
% 4.69/4.98 ( ord_less_int
% 4.69/4.98 = ( ^ [X2: int,Y3: int] :
% 4.69/4.98 ( ( ord_less_eq_int @ X2 @ Y3 )
% 4.69/4.98 & ( X2 != Y3 ) ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_le
% 4.69/4.98 thf(fact_3930_linorder__not__le,axiom,
% 4.69/4.98 ! [X: code_integer,Y: code_integer] :
% 4.69/4.98 ( ( ~ ( ord_le3102999989581377725nteger @ X @ Y ) )
% 4.69/4.98 = ( ord_le6747313008572928689nteger @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_not_le
% 4.69/4.98 thf(fact_3931_linorder__not__le,axiom,
% 4.69/4.98 ! [X: rat,Y: rat] :
% 4.69/4.98 ( ( ~ ( ord_less_eq_rat @ X @ Y ) )
% 4.69/4.98 = ( ord_less_rat @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_not_le
% 4.69/4.98 thf(fact_3932_linorder__not__le,axiom,
% 4.69/4.98 ! [X: nat,Y: nat] :
% 4.69/4.98 ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 4.69/4.98 = ( ord_less_nat @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_not_le
% 4.69/4.98 thf(fact_3933_linorder__not__le,axiom,
% 4.69/4.98 ! [X: int,Y: int] :
% 4.69/4.98 ( ( ~ ( ord_less_eq_int @ X @ Y ) )
% 4.69/4.98 = ( ord_less_int @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_not_le
% 4.69/4.98 thf(fact_3934_linorder__not__less,axiom,
% 4.69/4.98 ! [X: code_integer,Y: code_integer] :
% 4.69/4.98 ( ( ~ ( ord_le6747313008572928689nteger @ X @ Y ) )
% 4.69/4.98 = ( ord_le3102999989581377725nteger @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_not_less
% 4.69/4.98 thf(fact_3935_linorder__not__less,axiom,
% 4.69/4.98 ! [X: rat,Y: rat] :
% 4.69/4.98 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 4.69/4.98 = ( ord_less_eq_rat @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_not_less
% 4.69/4.98 thf(fact_3936_linorder__not__less,axiom,
% 4.69/4.98 ! [X: nat,Y: nat] :
% 4.69/4.98 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 4.69/4.98 = ( ord_less_eq_nat @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_not_less
% 4.69/4.98 thf(fact_3937_linorder__not__less,axiom,
% 4.69/4.98 ! [X: int,Y: int] :
% 4.69/4.98 ( ( ~ ( ord_less_int @ X @ Y ) )
% 4.69/4.98 = ( ord_less_eq_int @ Y @ X ) ) ).
% 4.69/4.98
% 4.69/4.98 % linorder_not_less
% 4.69/4.98 thf(fact_3938_order__less__imp__le,axiom,
% 4.69/4.98 ! [X: assn,Y: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X @ Y )
% 4.69/4.98 => ( ord_less_eq_assn @ X @ Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_le
% 4.69/4.98 thf(fact_3939_order__less__imp__le,axiom,
% 4.69/4.98 ! [X: code_integer,Y: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ X @ Y )
% 4.69/4.98 => ( ord_le3102999989581377725nteger @ X @ Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_le
% 4.69/4.98 thf(fact_3940_order__less__imp__le,axiom,
% 4.69/4.98 ! [X: filter_nat,Y: filter_nat] :
% 4.69/4.98 ( ( ord_less_filter_nat @ X @ Y )
% 4.69/4.98 => ( ord_le2510731241096832064er_nat @ X @ Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_le
% 4.69/4.98 thf(fact_3941_order__less__imp__le,axiom,
% 4.69/4.98 ! [X: set_nat,Y: set_nat] :
% 4.69/4.98 ( ( ord_less_set_nat @ X @ Y )
% 4.69/4.98 => ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_le
% 4.69/4.98 thf(fact_3942_order__less__imp__le,axiom,
% 4.69/4.98 ! [X: rat,Y: rat] :
% 4.69/4.98 ( ( ord_less_rat @ X @ Y )
% 4.69/4.98 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_le
% 4.69/4.98 thf(fact_3943_order__less__imp__le,axiom,
% 4.69/4.98 ! [X: nat,Y: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X @ Y )
% 4.69/4.98 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_le
% 4.69/4.98 thf(fact_3944_order__less__imp__le,axiom,
% 4.69/4.98 ! [X: int,Y: int] :
% 4.69/4.98 ( ( ord_less_int @ X @ Y )
% 4.69/4.98 => ( ord_less_eq_int @ X @ Y ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_imp_le
% 4.69/4.98 thf(fact_3945_order__le__neq__trans,axiom,
% 4.69/4.98 ! [A2: assn,B: assn] :
% 4.69/4.98 ( ( ord_less_eq_assn @ A2 @ B )
% 4.69/4.98 => ( ( A2 != B )
% 4.69/4.98 => ( ord_less_assn @ A2 @ B ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_le_neq_trans
% 4.69/4.98 thf(fact_3946_order__le__neq__trans,axiom,
% 4.69/4.98 ! [A2: code_integer,B: code_integer] :
% 4.69/4.98 ( ( ord_le3102999989581377725nteger @ A2 @ B )
% 4.69/4.98 => ( ( A2 != B )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ A2 @ B ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_le_neq_trans
% 4.69/4.98 thf(fact_3947_order__le__neq__trans,axiom,
% 4.69/4.98 ! [A2: filter_nat,B: filter_nat] :
% 4.69/4.98 ( ( ord_le2510731241096832064er_nat @ A2 @ B )
% 4.69/4.98 => ( ( A2 != B )
% 4.69/4.98 => ( ord_less_filter_nat @ A2 @ B ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_le_neq_trans
% 4.69/4.98 thf(fact_3948_order__le__neq__trans,axiom,
% 4.69/4.98 ! [A2: set_nat,B: set_nat] :
% 4.69/4.98 ( ( ord_less_eq_set_nat @ A2 @ B )
% 4.69/4.98 => ( ( A2 != B )
% 4.69/4.98 => ( ord_less_set_nat @ A2 @ B ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_le_neq_trans
% 4.69/4.98 thf(fact_3949_order__le__neq__trans,axiom,
% 4.69/4.98 ! [A2: rat,B: rat] :
% 4.69/4.98 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/4.98 => ( ( A2 != B )
% 4.69/4.98 => ( ord_less_rat @ A2 @ B ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_le_neq_trans
% 4.69/4.98 thf(fact_3950_order__le__neq__trans,axiom,
% 4.69/4.98 ! [A2: nat,B: nat] :
% 4.69/4.98 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/4.98 => ( ( A2 != B )
% 4.69/4.98 => ( ord_less_nat @ A2 @ B ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_le_neq_trans
% 4.69/4.98 thf(fact_3951_order__le__neq__trans,axiom,
% 4.69/4.98 ! [A2: int,B: int] :
% 4.69/4.98 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/4.98 => ( ( A2 != B )
% 4.69/4.98 => ( ord_less_int @ A2 @ B ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_le_neq_trans
% 4.69/4.98 thf(fact_3952_order__neq__le__trans,axiom,
% 4.69/4.98 ! [A2: assn,B: assn] :
% 4.69/4.98 ( ( A2 != B )
% 4.69/4.98 => ( ( ord_less_eq_assn @ A2 @ B )
% 4.69/4.98 => ( ord_less_assn @ A2 @ B ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_neq_le_trans
% 4.69/4.98 thf(fact_3953_order__neq__le__trans,axiom,
% 4.69/4.98 ! [A2: code_integer,B: code_integer] :
% 4.69/4.98 ( ( A2 != B )
% 4.69/4.98 => ( ( ord_le3102999989581377725nteger @ A2 @ B )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ A2 @ B ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_neq_le_trans
% 4.69/4.98 thf(fact_3954_order__neq__le__trans,axiom,
% 4.69/4.98 ! [A2: filter_nat,B: filter_nat] :
% 4.69/4.98 ( ( A2 != B )
% 4.69/4.98 => ( ( ord_le2510731241096832064er_nat @ A2 @ B )
% 4.69/4.98 => ( ord_less_filter_nat @ A2 @ B ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_neq_le_trans
% 4.69/4.98 thf(fact_3955_order__neq__le__trans,axiom,
% 4.69/4.98 ! [A2: set_nat,B: set_nat] :
% 4.69/4.98 ( ( A2 != B )
% 4.69/4.98 => ( ( ord_less_eq_set_nat @ A2 @ B )
% 4.69/4.98 => ( ord_less_set_nat @ A2 @ B ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_neq_le_trans
% 4.69/4.98 thf(fact_3956_order__neq__le__trans,axiom,
% 4.69/4.98 ! [A2: rat,B: rat] :
% 4.69/4.98 ( ( A2 != B )
% 4.69/4.98 => ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/4.98 => ( ord_less_rat @ A2 @ B ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_neq_le_trans
% 4.69/4.98 thf(fact_3957_order__neq__le__trans,axiom,
% 4.69/4.98 ! [A2: nat,B: nat] :
% 4.69/4.98 ( ( A2 != B )
% 4.69/4.98 => ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/4.98 => ( ord_less_nat @ A2 @ B ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_neq_le_trans
% 4.69/4.98 thf(fact_3958_order__neq__le__trans,axiom,
% 4.69/4.98 ! [A2: int,B: int] :
% 4.69/4.98 ( ( A2 != B )
% 4.69/4.98 => ( ( ord_less_eq_int @ A2 @ B )
% 4.69/4.98 => ( ord_less_int @ A2 @ B ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_neq_le_trans
% 4.69/4.98 thf(fact_3959_order__le__less__trans,axiom,
% 4.69/4.98 ! [X: assn,Y: assn,Z: assn] :
% 4.69/4.98 ( ( ord_less_eq_assn @ X @ Y )
% 4.69/4.98 => ( ( ord_less_assn @ Y @ Z )
% 4.69/4.98 => ( ord_less_assn @ X @ Z ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_le_less_trans
% 4.69/4.98 thf(fact_3960_order__le__less__trans,axiom,
% 4.69/4.98 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 4.69/4.98 ( ( ord_le3102999989581377725nteger @ X @ Y )
% 4.69/4.98 => ( ( ord_le6747313008572928689nteger @ Y @ Z )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ X @ Z ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_le_less_trans
% 4.69/4.98 thf(fact_3961_order__le__less__trans,axiom,
% 4.69/4.98 ! [X: filter_nat,Y: filter_nat,Z: filter_nat] :
% 4.69/4.98 ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 4.69/4.98 => ( ( ord_less_filter_nat @ Y @ Z )
% 4.69/4.98 => ( ord_less_filter_nat @ X @ Z ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_le_less_trans
% 4.69/4.98 thf(fact_3962_order__le__less__trans,axiom,
% 4.69/4.98 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 4.69/4.98 ( ( ord_less_eq_set_nat @ X @ Y )
% 4.69/4.98 => ( ( ord_less_set_nat @ Y @ Z )
% 4.69/4.98 => ( ord_less_set_nat @ X @ Z ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_le_less_trans
% 4.69/4.98 thf(fact_3963_order__le__less__trans,axiom,
% 4.69/4.98 ! [X: rat,Y: rat,Z: rat] :
% 4.69/4.98 ( ( ord_less_eq_rat @ X @ Y )
% 4.69/4.98 => ( ( ord_less_rat @ Y @ Z )
% 4.69/4.98 => ( ord_less_rat @ X @ Z ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_le_less_trans
% 4.69/4.98 thf(fact_3964_order__le__less__trans,axiom,
% 4.69/4.98 ! [X: nat,Y: nat,Z: nat] :
% 4.69/4.98 ( ( ord_less_eq_nat @ X @ Y )
% 4.69/4.98 => ( ( ord_less_nat @ Y @ Z )
% 4.69/4.98 => ( ord_less_nat @ X @ Z ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_le_less_trans
% 4.69/4.98 thf(fact_3965_order__le__less__trans,axiom,
% 4.69/4.98 ! [X: int,Y: int,Z: int] :
% 4.69/4.98 ( ( ord_less_eq_int @ X @ Y )
% 4.69/4.98 => ( ( ord_less_int @ Y @ Z )
% 4.69/4.98 => ( ord_less_int @ X @ Z ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_le_less_trans
% 4.69/4.98 thf(fact_3966_order__less__le__trans,axiom,
% 4.69/4.98 ! [X: assn,Y: assn,Z: assn] :
% 4.69/4.98 ( ( ord_less_assn @ X @ Y )
% 4.69/4.98 => ( ( ord_less_eq_assn @ Y @ Z )
% 4.69/4.98 => ( ord_less_assn @ X @ Z ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_le_trans
% 4.69/4.98 thf(fact_3967_order__less__le__trans,axiom,
% 4.69/4.98 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 4.69/4.98 ( ( ord_le6747313008572928689nteger @ X @ Y )
% 4.69/4.98 => ( ( ord_le3102999989581377725nteger @ Y @ Z )
% 4.69/4.98 => ( ord_le6747313008572928689nteger @ X @ Z ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_le_trans
% 4.69/4.98 thf(fact_3968_order__less__le__trans,axiom,
% 4.69/4.98 ! [X: filter_nat,Y: filter_nat,Z: filter_nat] :
% 4.69/4.98 ( ( ord_less_filter_nat @ X @ Y )
% 4.69/4.98 => ( ( ord_le2510731241096832064er_nat @ Y @ Z )
% 4.69/4.98 => ( ord_less_filter_nat @ X @ Z ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_le_trans
% 4.69/4.98 thf(fact_3969_order__less__le__trans,axiom,
% 4.69/4.98 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 4.69/4.98 ( ( ord_less_set_nat @ X @ Y )
% 4.69/4.98 => ( ( ord_less_eq_set_nat @ Y @ Z )
% 4.69/4.98 => ( ord_less_set_nat @ X @ Z ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_le_trans
% 4.69/4.98 thf(fact_3970_order__less__le__trans,axiom,
% 4.69/4.98 ! [X: rat,Y: rat,Z: rat] :
% 4.69/4.98 ( ( ord_less_rat @ X @ Y )
% 4.69/4.98 => ( ( ord_less_eq_rat @ Y @ Z )
% 4.69/4.98 => ( ord_less_rat @ X @ Z ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_le_trans
% 4.69/4.98 thf(fact_3971_order__less__le__trans,axiom,
% 4.69/4.98 ! [X: nat,Y: nat,Z: nat] :
% 4.69/4.98 ( ( ord_less_nat @ X @ Y )
% 4.69/4.98 => ( ( ord_less_eq_nat @ Y @ Z )
% 4.69/4.98 => ( ord_less_nat @ X @ Z ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_le_trans
% 4.69/4.98 thf(fact_3972_order__less__le__trans,axiom,
% 4.69/4.98 ! [X: int,Y: int,Z: int] :
% 4.69/4.98 ( ( ord_less_int @ X @ Y )
% 4.69/4.98 => ( ( ord_less_eq_int @ Y @ Z )
% 4.69/4.98 => ( ord_less_int @ X @ Z ) ) ) ).
% 4.69/4.98
% 4.69/4.98 % order_less_le_trans
% 4.69/4.98 thf(fact_3973_order__le__less__subst1,axiom,
% 4.69/4.98 ! [A2: assn,F: assn > assn,B: assn,C: assn] :
% 4.69/4.98 ( ( ord_less_eq_assn @ A2 @ ( F @ B ) )
% 4.69/4.98 => ( ( ord_less_assn @ B @ C )
% 4.69/4.98 => ( ! [X3: assn,Y2: assn] :
% 4.69/4.99 ( ( ord_less_assn @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_assn @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_less_subst1
% 4.69/4.99 thf(fact_3974_order__le__less__subst1,axiom,
% 4.69/4.99 ! [A2: code_integer,F: assn > code_integer,B: assn,C: assn] :
% 4.69/4.99 ( ( ord_le3102999989581377725nteger @ A2 @ ( F @ B ) )
% 4.69/4.99 => ( ( ord_less_assn @ B @ C )
% 4.69/4.99 => ( ! [X3: assn,Y2: assn] :
% 4.69/4.99 ( ( ord_less_assn @ X3 @ Y2 )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_less_subst1
% 4.69/4.99 thf(fact_3975_order__le__less__subst1,axiom,
% 4.69/4.99 ! [A2: assn,F: nat > assn,B: nat,C: nat] :
% 4.69/4.99 ( ( ord_less_eq_assn @ A2 @ ( F @ B ) )
% 4.69/4.99 => ( ( ord_less_nat @ B @ C )
% 4.69/4.99 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.99 ( ( ord_less_nat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_assn @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_less_subst1
% 4.69/4.99 thf(fact_3976_order__le__less__subst1,axiom,
% 4.69/4.99 ! [A2: code_integer,F: nat > code_integer,B: nat,C: nat] :
% 4.69/4.99 ( ( ord_le3102999989581377725nteger @ A2 @ ( F @ B ) )
% 4.69/4.99 => ( ( ord_less_nat @ B @ C )
% 4.69/4.99 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.99 ( ( ord_less_nat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_less_subst1
% 4.69/4.99 thf(fact_3977_order__le__less__subst1,axiom,
% 4.69/4.99 ! [A2: assn,F: int > assn,B: int,C: int] :
% 4.69/4.99 ( ( ord_less_eq_assn @ A2 @ ( F @ B ) )
% 4.69/4.99 => ( ( ord_less_int @ B @ C )
% 4.69/4.99 => ( ! [X3: int,Y2: int] :
% 4.69/4.99 ( ( ord_less_int @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_assn @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_less_subst1
% 4.69/4.99 thf(fact_3978_order__le__less__subst1,axiom,
% 4.69/4.99 ! [A2: code_integer,F: int > code_integer,B: int,C: int] :
% 4.69/4.99 ( ( ord_le3102999989581377725nteger @ A2 @ ( F @ B ) )
% 4.69/4.99 => ( ( ord_less_int @ B @ C )
% 4.69/4.99 => ( ! [X3: int,Y2: int] :
% 4.69/4.99 ( ( ord_less_int @ X3 @ Y2 )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_less_subst1
% 4.69/4.99 thf(fact_3979_order__le__less__subst1,axiom,
% 4.69/4.99 ! [A2: assn,F: code_integer > assn,B: code_integer,C: code_integer] :
% 4.69/4.99 ( ( ord_less_eq_assn @ A2 @ ( F @ B ) )
% 4.69/4.99 => ( ( ord_le6747313008572928689nteger @ B @ C )
% 4.69/4.99 => ( ! [X3: code_integer,Y2: code_integer] :
% 4.69/4.99 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_assn @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_less_subst1
% 4.69/4.99 thf(fact_3980_order__le__less__subst1,axiom,
% 4.69/4.99 ! [A2: code_integer,F: code_integer > code_integer,B: code_integer,C: code_integer] :
% 4.69/4.99 ( ( ord_le3102999989581377725nteger @ A2 @ ( F @ B ) )
% 4.69/4.99 => ( ( ord_le6747313008572928689nteger @ B @ C )
% 4.69/4.99 => ( ! [X3: code_integer,Y2: code_integer] :
% 4.69/4.99 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_less_subst1
% 4.69/4.99 thf(fact_3981_order__le__less__subst1,axiom,
% 4.69/4.99 ! [A2: assn,F: rat > assn,B: rat,C: rat] :
% 4.69/4.99 ( ( ord_less_eq_assn @ A2 @ ( F @ B ) )
% 4.69/4.99 => ( ( ord_less_rat @ B @ C )
% 4.69/4.99 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.99 ( ( ord_less_rat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_assn @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_less_subst1
% 4.69/4.99 thf(fact_3982_order__le__less__subst1,axiom,
% 4.69/4.99 ! [A2: code_integer,F: rat > code_integer,B: rat,C: rat] :
% 4.69/4.99 ( ( ord_le3102999989581377725nteger @ A2 @ ( F @ B ) )
% 4.69/4.99 => ( ( ord_less_rat @ B @ C )
% 4.69/4.99 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.99 ( ( ord_less_rat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_less_subst1
% 4.69/4.99 thf(fact_3983_order__le__less__subst2,axiom,
% 4.69/4.99 ! [A2: rat,B: rat,F: rat > assn,C: assn] :
% 4.69/4.99 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/4.99 => ( ( ord_less_assn @ ( F @ B ) @ C )
% 4.69/4.99 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.99 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_eq_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_assn @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_less_subst2
% 4.69/4.99 thf(fact_3984_order__le__less__subst2,axiom,
% 4.69/4.99 ! [A2: rat,B: rat,F: rat > code_integer,C: code_integer] :
% 4.69/4.99 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/4.99 => ( ( ord_le6747313008572928689nteger @ ( F @ B ) @ C )
% 4.69/4.99 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.99 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_less_subst2
% 4.69/4.99 thf(fact_3985_order__le__less__subst2,axiom,
% 4.69/4.99 ! [A2: rat,B: rat,F: rat > rat,C: rat] :
% 4.69/4.99 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/4.99 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 4.69/4.99 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.99 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_less_subst2
% 4.69/4.99 thf(fact_3986_order__le__less__subst2,axiom,
% 4.69/4.99 ! [A2: rat,B: rat,F: rat > nat,C: nat] :
% 4.69/4.99 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/4.99 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 4.69/4.99 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.99 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_less_subst2
% 4.69/4.99 thf(fact_3987_order__le__less__subst2,axiom,
% 4.69/4.99 ! [A2: rat,B: rat,F: rat > int,C: int] :
% 4.69/4.99 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/4.99 => ( ( ord_less_int @ ( F @ B ) @ C )
% 4.69/4.99 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.99 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_less_subst2
% 4.69/4.99 thf(fact_3988_order__le__less__subst2,axiom,
% 4.69/4.99 ! [A2: nat,B: nat,F: nat > assn,C: assn] :
% 4.69/4.99 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/4.99 => ( ( ord_less_assn @ ( F @ B ) @ C )
% 4.69/4.99 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.99 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_eq_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_assn @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_less_subst2
% 4.69/4.99 thf(fact_3989_order__le__less__subst2,axiom,
% 4.69/4.99 ! [A2: nat,B: nat,F: nat > code_integer,C: code_integer] :
% 4.69/4.99 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/4.99 => ( ( ord_le6747313008572928689nteger @ ( F @ B ) @ C )
% 4.69/4.99 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.99 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_less_subst2
% 4.69/4.99 thf(fact_3990_order__le__less__subst2,axiom,
% 4.69/4.99 ! [A2: nat,B: nat,F: nat > rat,C: rat] :
% 4.69/4.99 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/4.99 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 4.69/4.99 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.99 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_rat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_less_subst2
% 4.69/4.99 thf(fact_3991_order__le__less__subst2,axiom,
% 4.69/4.99 ! [A2: nat,B: nat,F: nat > nat,C: nat] :
% 4.69/4.99 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/4.99 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 4.69/4.99 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.99 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_less_subst2
% 4.69/4.99 thf(fact_3992_order__le__less__subst2,axiom,
% 4.69/4.99 ! [A2: nat,B: nat,F: nat > int,C: int] :
% 4.69/4.99 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/4.99 => ( ( ord_less_int @ ( F @ B ) @ C )
% 4.69/4.99 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.99 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_less_subst2
% 4.69/4.99 thf(fact_3993_order__less__le__subst1,axiom,
% 4.69/4.99 ! [A2: assn,F: rat > assn,B: rat,C: rat] :
% 4.69/4.99 ( ( ord_less_assn @ A2 @ ( F @ B ) )
% 4.69/4.99 => ( ( ord_less_eq_rat @ B @ C )
% 4.69/4.99 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.99 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_eq_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_assn @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_less_le_subst1
% 4.69/4.99 thf(fact_3994_order__less__le__subst1,axiom,
% 4.69/4.99 ! [A2: code_integer,F: rat > code_integer,B: rat,C: rat] :
% 4.69/4.99 ( ( ord_le6747313008572928689nteger @ A2 @ ( F @ B ) )
% 4.69/4.99 => ( ( ord_less_eq_rat @ B @ C )
% 4.69/4.99 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.99 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_less_le_subst1
% 4.69/4.99 thf(fact_3995_order__less__le__subst1,axiom,
% 4.69/4.99 ! [A2: rat,F: rat > rat,B: rat,C: rat] :
% 4.69/4.99 ( ( ord_less_rat @ A2 @ ( F @ B ) )
% 4.69/4.99 => ( ( ord_less_eq_rat @ B @ C )
% 4.69/4.99 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.99 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_less_le_subst1
% 4.69/4.99 thf(fact_3996_order__less__le__subst1,axiom,
% 4.69/4.99 ! [A2: nat,F: rat > nat,B: rat,C: rat] :
% 4.69/4.99 ( ( ord_less_nat @ A2 @ ( F @ B ) )
% 4.69/4.99 => ( ( ord_less_eq_rat @ B @ C )
% 4.69/4.99 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.99 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_less_le_subst1
% 4.69/4.99 thf(fact_3997_order__less__le__subst1,axiom,
% 4.69/4.99 ! [A2: int,F: rat > int,B: rat,C: rat] :
% 4.69/4.99 ( ( ord_less_int @ A2 @ ( F @ B ) )
% 4.69/4.99 => ( ( ord_less_eq_rat @ B @ C )
% 4.69/4.99 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.99 ( ( ord_less_eq_rat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_less_le_subst1
% 4.69/4.99 thf(fact_3998_order__less__le__subst1,axiom,
% 4.69/4.99 ! [A2: assn,F: nat > assn,B: nat,C: nat] :
% 4.69/4.99 ( ( ord_less_assn @ A2 @ ( F @ B ) )
% 4.69/4.99 => ( ( ord_less_eq_nat @ B @ C )
% 4.69/4.99 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.99 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_eq_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_assn @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_less_le_subst1
% 4.69/4.99 thf(fact_3999_order__less__le__subst1,axiom,
% 4.69/4.99 ! [A2: code_integer,F: nat > code_integer,B: nat,C: nat] :
% 4.69/4.99 ( ( ord_le6747313008572928689nteger @ A2 @ ( F @ B ) )
% 4.69/4.99 => ( ( ord_less_eq_nat @ B @ C )
% 4.69/4.99 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.99 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_less_le_subst1
% 4.69/4.99 thf(fact_4000_order__less__le__subst1,axiom,
% 4.69/4.99 ! [A2: rat,F: nat > rat,B: nat,C: nat] :
% 4.69/4.99 ( ( ord_less_rat @ A2 @ ( F @ B ) )
% 4.69/4.99 => ( ( ord_less_eq_nat @ B @ C )
% 4.69/4.99 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.99 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_rat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_less_le_subst1
% 4.69/4.99 thf(fact_4001_order__less__le__subst1,axiom,
% 4.69/4.99 ! [A2: nat,F: nat > nat,B: nat,C: nat] :
% 4.69/4.99 ( ( ord_less_nat @ A2 @ ( F @ B ) )
% 4.69/4.99 => ( ( ord_less_eq_nat @ B @ C )
% 4.69/4.99 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.99 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_less_le_subst1
% 4.69/4.99 thf(fact_4002_order__less__le__subst1,axiom,
% 4.69/4.99 ! [A2: int,F: nat > int,B: nat,C: nat] :
% 4.69/4.99 ( ( ord_less_int @ A2 @ ( F @ B ) )
% 4.69/4.99 => ( ( ord_less_eq_nat @ B @ C )
% 4.69/4.99 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.99 ( ( ord_less_eq_nat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_less_le_subst1
% 4.69/4.99 thf(fact_4003_order__less__le__subst2,axiom,
% 4.69/4.99 ! [A2: assn,B: assn,F: assn > assn,C: assn] :
% 4.69/4.99 ( ( ord_less_assn @ A2 @ B )
% 4.69/4.99 => ( ( ord_less_eq_assn @ ( F @ B ) @ C )
% 4.69/4.99 => ( ! [X3: assn,Y2: assn] :
% 4.69/4.99 ( ( ord_less_assn @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_assn @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_less_le_subst2
% 4.69/4.99 thf(fact_4004_order__less__le__subst2,axiom,
% 4.69/4.99 ! [A2: assn,B: assn,F: assn > code_integer,C: code_integer] :
% 4.69/4.99 ( ( ord_less_assn @ A2 @ B )
% 4.69/4.99 => ( ( ord_le3102999989581377725nteger @ ( F @ B ) @ C )
% 4.69/4.99 => ( ! [X3: assn,Y2: assn] :
% 4.69/4.99 ( ( ord_less_assn @ X3 @ Y2 )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_less_le_subst2
% 4.69/4.99 thf(fact_4005_order__less__le__subst2,axiom,
% 4.69/4.99 ! [A2: nat,B: nat,F: nat > assn,C: assn] :
% 4.69/4.99 ( ( ord_less_nat @ A2 @ B )
% 4.69/4.99 => ( ( ord_less_eq_assn @ ( F @ B ) @ C )
% 4.69/4.99 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.99 ( ( ord_less_nat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_assn @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_less_le_subst2
% 4.69/4.99 thf(fact_4006_order__less__le__subst2,axiom,
% 4.69/4.99 ! [A2: nat,B: nat,F: nat > code_integer,C: code_integer] :
% 4.69/4.99 ( ( ord_less_nat @ A2 @ B )
% 4.69/4.99 => ( ( ord_le3102999989581377725nteger @ ( F @ B ) @ C )
% 4.69/4.99 => ( ! [X3: nat,Y2: nat] :
% 4.69/4.99 ( ( ord_less_nat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_less_le_subst2
% 4.69/4.99 thf(fact_4007_order__less__le__subst2,axiom,
% 4.69/4.99 ! [A2: int,B: int,F: int > assn,C: assn] :
% 4.69/4.99 ( ( ord_less_int @ A2 @ B )
% 4.69/4.99 => ( ( ord_less_eq_assn @ ( F @ B ) @ C )
% 4.69/4.99 => ( ! [X3: int,Y2: int] :
% 4.69/4.99 ( ( ord_less_int @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_assn @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_less_le_subst2
% 4.69/4.99 thf(fact_4008_order__less__le__subst2,axiom,
% 4.69/4.99 ! [A2: int,B: int,F: int > code_integer,C: code_integer] :
% 4.69/4.99 ( ( ord_less_int @ A2 @ B )
% 4.69/4.99 => ( ( ord_le3102999989581377725nteger @ ( F @ B ) @ C )
% 4.69/4.99 => ( ! [X3: int,Y2: int] :
% 4.69/4.99 ( ( ord_less_int @ X3 @ Y2 )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_less_le_subst2
% 4.69/4.99 thf(fact_4009_order__less__le__subst2,axiom,
% 4.69/4.99 ! [A2: code_integer,B: code_integer,F: code_integer > assn,C: assn] :
% 4.69/4.99 ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/4.99 => ( ( ord_less_eq_assn @ ( F @ B ) @ C )
% 4.69/4.99 => ( ! [X3: code_integer,Y2: code_integer] :
% 4.69/4.99 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_assn @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_less_le_subst2
% 4.69/4.99 thf(fact_4010_order__less__le__subst2,axiom,
% 4.69/4.99 ! [A2: code_integer,B: code_integer,F: code_integer > code_integer,C: code_integer] :
% 4.69/4.99 ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/4.99 => ( ( ord_le3102999989581377725nteger @ ( F @ B ) @ C )
% 4.69/4.99 => ( ! [X3: code_integer,Y2: code_integer] :
% 4.69/4.99 ( ( ord_le6747313008572928689nteger @ X3 @ Y2 )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_less_le_subst2
% 4.69/4.99 thf(fact_4011_order__less__le__subst2,axiom,
% 4.69/4.99 ! [A2: rat,B: rat,F: rat > assn,C: assn] :
% 4.69/4.99 ( ( ord_less_rat @ A2 @ B )
% 4.69/4.99 => ( ( ord_less_eq_assn @ ( F @ B ) @ C )
% 4.69/4.99 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.99 ( ( ord_less_rat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_less_assn @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_less_le_subst2
% 4.69/4.99 thf(fact_4012_order__less__le__subst2,axiom,
% 4.69/4.99 ! [A2: rat,B: rat,F: rat > code_integer,C: code_integer] :
% 4.69/4.99 ( ( ord_less_rat @ A2 @ B )
% 4.69/4.99 => ( ( ord_le3102999989581377725nteger @ ( F @ B ) @ C )
% 4.69/4.99 => ( ! [X3: rat,Y2: rat] :
% 4.69/4.99 ( ( ord_less_rat @ X3 @ Y2 )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ ( F @ A2 ) @ C ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_less_le_subst2
% 4.69/4.99 thf(fact_4013_linorder__le__less__linear,axiom,
% 4.69/4.99 ! [X: code_integer,Y: code_integer] :
% 4.69/4.99 ( ( ord_le3102999989581377725nteger @ X @ Y )
% 4.69/4.99 | ( ord_le6747313008572928689nteger @ Y @ X ) ) ).
% 4.69/4.99
% 4.69/4.99 % linorder_le_less_linear
% 4.69/4.99 thf(fact_4014_linorder__le__less__linear,axiom,
% 4.69/4.99 ! [X: rat,Y: rat] :
% 4.69/4.99 ( ( ord_less_eq_rat @ X @ Y )
% 4.69/4.99 | ( ord_less_rat @ Y @ X ) ) ).
% 4.69/4.99
% 4.69/4.99 % linorder_le_less_linear
% 4.69/4.99 thf(fact_4015_linorder__le__less__linear,axiom,
% 4.69/4.99 ! [X: nat,Y: nat] :
% 4.69/4.99 ( ( ord_less_eq_nat @ X @ Y )
% 4.69/4.99 | ( ord_less_nat @ Y @ X ) ) ).
% 4.69/4.99
% 4.69/4.99 % linorder_le_less_linear
% 4.69/4.99 thf(fact_4016_linorder__le__less__linear,axiom,
% 4.69/4.99 ! [X: int,Y: int] :
% 4.69/4.99 ( ( ord_less_eq_int @ X @ Y )
% 4.69/4.99 | ( ord_less_int @ Y @ X ) ) ).
% 4.69/4.99
% 4.69/4.99 % linorder_le_less_linear
% 4.69/4.99 thf(fact_4017_order__le__imp__less__or__eq,axiom,
% 4.69/4.99 ! [X: assn,Y: assn] :
% 4.69/4.99 ( ( ord_less_eq_assn @ X @ Y )
% 4.69/4.99 => ( ( ord_less_assn @ X @ Y )
% 4.69/4.99 | ( X = Y ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_imp_less_or_eq
% 4.69/4.99 thf(fact_4018_order__le__imp__less__or__eq,axiom,
% 4.69/4.99 ! [X: code_integer,Y: code_integer] :
% 4.69/4.99 ( ( ord_le3102999989581377725nteger @ X @ Y )
% 4.69/4.99 => ( ( ord_le6747313008572928689nteger @ X @ Y )
% 4.69/4.99 | ( X = Y ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_imp_less_or_eq
% 4.69/4.99 thf(fact_4019_order__le__imp__less__or__eq,axiom,
% 4.69/4.99 ! [X: filter_nat,Y: filter_nat] :
% 4.69/4.99 ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 4.69/4.99 => ( ( ord_less_filter_nat @ X @ Y )
% 4.69/4.99 | ( X = Y ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_imp_less_or_eq
% 4.69/4.99 thf(fact_4020_order__le__imp__less__or__eq,axiom,
% 4.69/4.99 ! [X: set_nat,Y: set_nat] :
% 4.69/4.99 ( ( ord_less_eq_set_nat @ X @ Y )
% 4.69/4.99 => ( ( ord_less_set_nat @ X @ Y )
% 4.69/4.99 | ( X = Y ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_imp_less_or_eq
% 4.69/4.99 thf(fact_4021_order__le__imp__less__or__eq,axiom,
% 4.69/4.99 ! [X: rat,Y: rat] :
% 4.69/4.99 ( ( ord_less_eq_rat @ X @ Y )
% 4.69/4.99 => ( ( ord_less_rat @ X @ Y )
% 4.69/4.99 | ( X = Y ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_imp_less_or_eq
% 4.69/4.99 thf(fact_4022_order__le__imp__less__or__eq,axiom,
% 4.69/4.99 ! [X: nat,Y: nat] :
% 4.69/4.99 ( ( ord_less_eq_nat @ X @ Y )
% 4.69/4.99 => ( ( ord_less_nat @ X @ Y )
% 4.69/4.99 | ( X = Y ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_imp_less_or_eq
% 4.69/4.99 thf(fact_4023_order__le__imp__less__or__eq,axiom,
% 4.69/4.99 ! [X: int,Y: int] :
% 4.69/4.99 ( ( ord_less_eq_int @ X @ Y )
% 4.69/4.99 => ( ( ord_less_int @ X @ Y )
% 4.69/4.99 | ( X = Y ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % order_le_imp_less_or_eq
% 4.69/4.99 thf(fact_4024_less__numeral__extra_I4_J,axiom,
% 4.69/4.99 ~ ( ord_le5570908160329646204atural @ one_one_Code_natural @ one_one_Code_natural ) ).
% 4.69/4.99
% 4.69/4.99 % less_numeral_extra(4)
% 4.69/4.99 thf(fact_4025_less__numeral__extra_I4_J,axiom,
% 4.69/4.99 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 4.69/4.99
% 4.69/4.99 % less_numeral_extra(4)
% 4.69/4.99 thf(fact_4026_less__numeral__extra_I4_J,axiom,
% 4.69/4.99 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 4.69/4.99
% 4.69/4.99 % less_numeral_extra(4)
% 4.69/4.99 thf(fact_4027_less__numeral__extra_I4_J,axiom,
% 4.69/4.99 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 4.69/4.99
% 4.69/4.99 % less_numeral_extra(4)
% 4.69/4.99 thf(fact_4028_less__numeral__extra_I4_J,axiom,
% 4.69/4.99 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 4.69/4.99
% 4.69/4.99 % less_numeral_extra(4)
% 4.69/4.99 thf(fact_4029_diff__strict__mono,axiom,
% 4.69/4.99 ! [A2: int,B: int,D2: int,C: int] :
% 4.69/4.99 ( ( ord_less_int @ A2 @ B )
% 4.69/4.99 => ( ( ord_less_int @ D2 @ C )
% 4.69/4.99 => ( ord_less_int @ ( minus_minus_int @ A2 @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % diff_strict_mono
% 4.69/4.99 thf(fact_4030_diff__strict__mono,axiom,
% 4.69/4.99 ! [A2: code_integer,B: code_integer,D2: code_integer,C: code_integer] :
% 4.69/4.99 ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/4.99 => ( ( ord_le6747313008572928689nteger @ D2 @ C )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A2 @ C ) @ ( minus_8373710615458151222nteger @ B @ D2 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % diff_strict_mono
% 4.69/4.99 thf(fact_4031_diff__strict__mono,axiom,
% 4.69/4.99 ! [A2: rat,B: rat,D2: rat,C: rat] :
% 4.69/4.99 ( ( ord_less_rat @ A2 @ B )
% 4.69/4.99 => ( ( ord_less_rat @ D2 @ C )
% 4.69/4.99 => ( ord_less_rat @ ( minus_minus_rat @ A2 @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % diff_strict_mono
% 4.69/4.99 thf(fact_4032_diff__eq__diff__less,axiom,
% 4.69/4.99 ! [A2: int,B: int,C: int,D2: int] :
% 4.69/4.99 ( ( ( minus_minus_int @ A2 @ B )
% 4.69/4.99 = ( minus_minus_int @ C @ D2 ) )
% 4.69/4.99 => ( ( ord_less_int @ A2 @ B )
% 4.69/4.99 = ( ord_less_int @ C @ D2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % diff_eq_diff_less
% 4.69/4.99 thf(fact_4033_diff__eq__diff__less,axiom,
% 4.69/4.99 ! [A2: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 4.69/4.99 ( ( ( minus_8373710615458151222nteger @ A2 @ B )
% 4.69/4.99 = ( minus_8373710615458151222nteger @ C @ D2 ) )
% 4.69/4.99 => ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/4.99 = ( ord_le6747313008572928689nteger @ C @ D2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % diff_eq_diff_less
% 4.69/4.99 thf(fact_4034_diff__eq__diff__less,axiom,
% 4.69/4.99 ! [A2: rat,B: rat,C: rat,D2: rat] :
% 4.69/4.99 ( ( ( minus_minus_rat @ A2 @ B )
% 4.69/4.99 = ( minus_minus_rat @ C @ D2 ) )
% 4.69/4.99 => ( ( ord_less_rat @ A2 @ B )
% 4.69/4.99 = ( ord_less_rat @ C @ D2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % diff_eq_diff_less
% 4.69/4.99 thf(fact_4035_diff__strict__left__mono,axiom,
% 4.69/4.99 ! [B: int,A2: int,C: int] :
% 4.69/4.99 ( ( ord_less_int @ B @ A2 )
% 4.69/4.99 => ( ord_less_int @ ( minus_minus_int @ C @ A2 ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % diff_strict_left_mono
% 4.69/4.99 thf(fact_4036_diff__strict__left__mono,axiom,
% 4.69/4.99 ! [B: code_integer,A2: code_integer,C: code_integer] :
% 4.69/4.99 ( ( ord_le6747313008572928689nteger @ B @ A2 )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ C @ A2 ) @ ( minus_8373710615458151222nteger @ C @ B ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % diff_strict_left_mono
% 4.69/4.99 thf(fact_4037_diff__strict__left__mono,axiom,
% 4.69/4.99 ! [B: rat,A2: rat,C: rat] :
% 4.69/4.99 ( ( ord_less_rat @ B @ A2 )
% 4.69/4.99 => ( ord_less_rat @ ( minus_minus_rat @ C @ A2 ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % diff_strict_left_mono
% 4.69/4.99 thf(fact_4038_diff__strict__right__mono,axiom,
% 4.69/4.99 ! [A2: int,B: int,C: int] :
% 4.69/4.99 ( ( ord_less_int @ A2 @ B )
% 4.69/4.99 => ( ord_less_int @ ( minus_minus_int @ A2 @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % diff_strict_right_mono
% 4.69/4.99 thf(fact_4039_diff__strict__right__mono,axiom,
% 4.69/4.99 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/4.99 ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A2 @ C ) @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % diff_strict_right_mono
% 4.69/4.99 thf(fact_4040_diff__strict__right__mono,axiom,
% 4.69/4.99 ! [A2: rat,B: rat,C: rat] :
% 4.69/4.99 ( ( ord_less_rat @ A2 @ B )
% 4.69/4.99 => ( ord_less_rat @ ( minus_minus_rat @ A2 @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % diff_strict_right_mono
% 4.69/4.99 thf(fact_4041_bot_Oextremum__strict,axiom,
% 4.69/4.99 ! [A2: set_Product_unit] :
% 4.69/4.99 ~ ( ord_le8056459307392131481t_unit @ A2 @ bot_bo3957492148770167129t_unit ) ).
% 4.69/4.99
% 4.69/4.99 % bot.extremum_strict
% 4.69/4.99 thf(fact_4042_bot_Oextremum__strict,axiom,
% 4.69/4.99 ! [A2: set_o] :
% 4.69/4.99 ~ ( ord_less_set_o @ A2 @ bot_bot_set_o ) ).
% 4.69/4.99
% 4.69/4.99 % bot.extremum_strict
% 4.69/4.99 thf(fact_4043_bot_Oextremum__strict,axiom,
% 4.69/4.99 ! [A2: set_nat] :
% 4.69/4.99 ~ ( ord_less_set_nat @ A2 @ bot_bot_set_nat ) ).
% 4.69/4.99
% 4.69/4.99 % bot.extremum_strict
% 4.69/4.99 thf(fact_4044_bot_Oextremum__strict,axiom,
% 4.69/4.99 ! [A2: set_int] :
% 4.69/4.99 ~ ( ord_less_set_int @ A2 @ bot_bot_set_int ) ).
% 4.69/4.99
% 4.69/4.99 % bot.extremum_strict
% 4.69/4.99 thf(fact_4045_bot_Oextremum__strict,axiom,
% 4.69/4.99 ! [A2: set_Pr4532377907799695533_nat_o] :
% 4.69/4.99 ~ ( ord_le2453136405763929_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ).
% 4.69/4.99
% 4.69/4.99 % bot.extremum_strict
% 4.69/4.99 thf(fact_4046_bot_Oextremum__strict,axiom,
% 4.69/4.99 ! [A2: assn] :
% 4.69/4.99 ~ ( ord_less_assn @ A2 @ bot_bot_assn ) ).
% 4.69/4.99
% 4.69/4.99 % bot.extremum_strict
% 4.69/4.99 thf(fact_4047_bot_Oextremum__strict,axiom,
% 4.69/4.99 ! [A2: nat] :
% 4.69/4.99 ~ ( ord_less_nat @ A2 @ bot_bot_nat ) ).
% 4.69/4.99
% 4.69/4.99 % bot.extremum_strict
% 4.69/4.99 thf(fact_4048_bot_Onot__eq__extremum,axiom,
% 4.69/4.99 ! [A2: set_Product_unit] :
% 4.69/4.99 ( ( A2 != bot_bo3957492148770167129t_unit )
% 4.69/4.99 = ( ord_le8056459307392131481t_unit @ bot_bo3957492148770167129t_unit @ A2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % bot.not_eq_extremum
% 4.69/4.99 thf(fact_4049_bot_Onot__eq__extremum,axiom,
% 4.69/4.99 ! [A2: set_o] :
% 4.69/4.99 ( ( A2 != bot_bot_set_o )
% 4.69/4.99 = ( ord_less_set_o @ bot_bot_set_o @ A2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % bot.not_eq_extremum
% 4.69/4.99 thf(fact_4050_bot_Onot__eq__extremum,axiom,
% 4.69/4.99 ! [A2: set_nat] :
% 4.69/4.99 ( ( A2 != bot_bot_set_nat )
% 4.69/4.99 = ( ord_less_set_nat @ bot_bot_set_nat @ A2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % bot.not_eq_extremum
% 4.69/4.99 thf(fact_4051_bot_Onot__eq__extremum,axiom,
% 4.69/4.99 ! [A2: set_int] :
% 4.69/4.99 ( ( A2 != bot_bot_set_int )
% 4.69/4.99 = ( ord_less_set_int @ bot_bot_set_int @ A2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % bot.not_eq_extremum
% 4.69/4.99 thf(fact_4052_bot_Onot__eq__extremum,axiom,
% 4.69/4.99 ! [A2: set_Pr4532377907799695533_nat_o] :
% 4.69/4.99 ( ( A2 != bot_bo7824918357723582233_nat_o )
% 4.69/4.99 = ( ord_le2453136405763929_nat_o @ bot_bo7824918357723582233_nat_o @ A2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % bot.not_eq_extremum
% 4.69/4.99 thf(fact_4053_bot_Onot__eq__extremum,axiom,
% 4.69/4.99 ! [A2: assn] :
% 4.69/4.99 ( ( A2 != bot_bot_assn )
% 4.69/4.99 = ( ord_less_assn @ bot_bot_assn @ A2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % bot.not_eq_extremum
% 4.69/4.99 thf(fact_4054_bot_Onot__eq__extremum,axiom,
% 4.69/4.99 ! [A2: nat] :
% 4.69/4.99 ( ( A2 != bot_bot_nat )
% 4.69/4.99 = ( ord_less_nat @ bot_bot_nat @ A2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % bot.not_eq_extremum
% 4.69/4.99 thf(fact_4055_not__psubset__empty,axiom,
% 4.69/4.99 ! [A: set_Product_unit] :
% 4.69/4.99 ~ ( ord_le8056459307392131481t_unit @ A @ bot_bo3957492148770167129t_unit ) ).
% 4.69/4.99
% 4.69/4.99 % not_psubset_empty
% 4.69/4.99 thf(fact_4056_not__psubset__empty,axiom,
% 4.69/4.99 ! [A: set_o] :
% 4.69/4.99 ~ ( ord_less_set_o @ A @ bot_bot_set_o ) ).
% 4.69/4.99
% 4.69/4.99 % not_psubset_empty
% 4.69/4.99 thf(fact_4057_not__psubset__empty,axiom,
% 4.69/4.99 ! [A: set_nat] :
% 4.69/4.99 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 4.69/4.99
% 4.69/4.99 % not_psubset_empty
% 4.69/4.99 thf(fact_4058_not__psubset__empty,axiom,
% 4.69/4.99 ! [A: set_int] :
% 4.69/4.99 ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 4.69/4.99
% 4.69/4.99 % not_psubset_empty
% 4.69/4.99 thf(fact_4059_not__psubset__empty,axiom,
% 4.69/4.99 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.99 ~ ( ord_le2453136405763929_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ).
% 4.69/4.99
% 4.69/4.99 % not_psubset_empty
% 4.69/4.99 thf(fact_4060_psubsetE,axiom,
% 4.69/4.99 ! [A: set_nat,B4: set_nat] :
% 4.69/4.99 ( ( ord_less_set_nat @ A @ B4 )
% 4.69/4.99 => ~ ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.99 => ( ord_less_eq_set_nat @ B4 @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % psubsetE
% 4.69/4.99 thf(fact_4061_psubset__eq,axiom,
% 4.69/4.99 ( ord_less_set_nat
% 4.69/4.99 = ( ^ [A3: set_nat,B7: set_nat] :
% 4.69/4.99 ( ( ord_less_eq_set_nat @ A3 @ B7 )
% 4.69/4.99 & ( A3 != B7 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % psubset_eq
% 4.69/4.99 thf(fact_4062_psubset__imp__subset,axiom,
% 4.69/4.99 ! [A: set_nat,B4: set_nat] :
% 4.69/4.99 ( ( ord_less_set_nat @ A @ B4 )
% 4.69/4.99 => ( ord_less_eq_set_nat @ A @ B4 ) ) ).
% 4.69/4.99
% 4.69/4.99 % psubset_imp_subset
% 4.69/4.99 thf(fact_4063_psubset__subset__trans,axiom,
% 4.69/4.99 ! [A: set_nat,B4: set_nat,C5: set_nat] :
% 4.69/4.99 ( ( ord_less_set_nat @ A @ B4 )
% 4.69/4.99 => ( ( ord_less_eq_set_nat @ B4 @ C5 )
% 4.69/4.99 => ( ord_less_set_nat @ A @ C5 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % psubset_subset_trans
% 4.69/4.99 thf(fact_4064_subset__not__subset__eq,axiom,
% 4.69/4.99 ( ord_less_set_nat
% 4.69/4.99 = ( ^ [A3: set_nat,B7: set_nat] :
% 4.69/4.99 ( ( ord_less_eq_set_nat @ A3 @ B7 )
% 4.69/4.99 & ~ ( ord_less_eq_set_nat @ B7 @ A3 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % subset_not_subset_eq
% 4.69/4.99 thf(fact_4065_subset__psubset__trans,axiom,
% 4.69/4.99 ! [A: set_nat,B4: set_nat,C5: set_nat] :
% 4.69/4.99 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/4.99 => ( ( ord_less_set_nat @ B4 @ C5 )
% 4.69/4.99 => ( ord_less_set_nat @ A @ C5 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % subset_psubset_trans
% 4.69/4.99 thf(fact_4066_subset__iff__psubset__eq,axiom,
% 4.69/4.99 ( ord_less_eq_set_nat
% 4.69/4.99 = ( ^ [A3: set_nat,B7: set_nat] :
% 4.69/4.99 ( ( ord_less_set_nat @ A3 @ B7 )
% 4.69/4.99 | ( A3 = B7 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % subset_iff_psubset_eq
% 4.69/4.99 thf(fact_4067_rangeI,axiom,
% 4.69/4.99 ! [F: code_integer > code_integer,X: code_integer] : ( member_Code_integer @ ( F @ X ) @ ( image_4470545334726330049nteger @ F @ top_to4645266643341252675nteger ) ) ).
% 4.69/4.99
% 4.69/4.99 % rangeI
% 4.69/4.99 thf(fact_4068_rangeI,axiom,
% 4.69/4.99 ! [F: product_unit > nat,X: product_unit] : ( member_nat @ ( F @ X ) @ ( image_875570014554754200it_nat @ F @ top_to1996260823553986621t_unit ) ) ).
% 4.69/4.99
% 4.69/4.99 % rangeI
% 4.69/4.99 thf(fact_4069_rangeI,axiom,
% 4.69/4.99 ! [F: product_unit > int,X: product_unit] : ( member_int @ ( F @ X ) @ ( image_873079544045703924it_int @ F @ top_to1996260823553986621t_unit ) ) ).
% 4.69/4.99
% 4.69/4.99 % rangeI
% 4.69/4.99 thf(fact_4070_rangeI,axiom,
% 4.69/4.99 ! [F: product_unit > $o,X: product_unit] : ( member_o @ ( F @ X ) @ ( image_Product_unit_o2 @ F @ top_to1996260823553986621t_unit ) ) ).
% 4.69/4.99
% 4.69/4.99 % rangeI
% 4.69/4.99 thf(fact_4071_rangeI,axiom,
% 4.69/4.99 ! [F: product_unit > product_unit,X: product_unit] : ( member_Product_unit @ ( F @ X ) @ ( image_405062704495631173t_unit @ F @ top_to1996260823553986621t_unit ) ) ).
% 4.69/4.99
% 4.69/4.99 % rangeI
% 4.69/4.99 thf(fact_4072_rangeI,axiom,
% 4.69/4.99 ! [F: $o > nat,X: $o] : ( member_nat @ ( F @ X ) @ ( image_o_nat2 @ F @ top_top_set_o ) ) ).
% 4.69/4.99
% 4.69/4.99 % rangeI
% 4.69/4.99 thf(fact_4073_rangeI,axiom,
% 4.69/4.99 ! [F: $o > int,X: $o] : ( member_int @ ( F @ X ) @ ( image_o_int2 @ F @ top_top_set_o ) ) ).
% 4.69/4.99
% 4.69/4.99 % rangeI
% 4.69/4.99 thf(fact_4074_rangeI,axiom,
% 4.69/4.99 ! [F: $o > $o,X: $o] : ( member_o @ ( F @ X ) @ ( image_o_o2 @ F @ top_top_set_o ) ) ).
% 4.69/4.99
% 4.69/4.99 % rangeI
% 4.69/4.99 thf(fact_4075_rangeI,axiom,
% 4.69/4.99 ! [F: $o > product_unit,X: $o] : ( member_Product_unit @ ( F @ X ) @ ( image_o_Product_unit2 @ F @ top_top_set_o ) ) ).
% 4.69/4.99
% 4.69/4.99 % rangeI
% 4.69/4.99 thf(fact_4076_rangeI,axiom,
% 4.69/4.99 ! [F: nat > code_integer,X: nat] : ( member_Code_integer @ ( F @ X ) @ ( image_1215581382706833972nteger @ F @ top_top_set_nat ) ) ).
% 4.69/4.99
% 4.69/4.99 % rangeI
% 4.69/4.99 thf(fact_4077_range__eqI,axiom,
% 4.69/4.99 ! [B: code_integer,F: code_integer > code_integer,X: code_integer] :
% 4.69/4.99 ( ( B
% 4.69/4.99 = ( F @ X ) )
% 4.69/4.99 => ( member_Code_integer @ B @ ( image_4470545334726330049nteger @ F @ top_to4645266643341252675nteger ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_eqI
% 4.69/4.99 thf(fact_4078_range__eqI,axiom,
% 4.69/4.99 ! [B: nat,F: product_unit > nat,X: product_unit] :
% 4.69/4.99 ( ( B
% 4.69/4.99 = ( F @ X ) )
% 4.69/4.99 => ( member_nat @ B @ ( image_875570014554754200it_nat @ F @ top_to1996260823553986621t_unit ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_eqI
% 4.69/4.99 thf(fact_4079_range__eqI,axiom,
% 4.69/4.99 ! [B: int,F: product_unit > int,X: product_unit] :
% 4.69/4.99 ( ( B
% 4.69/4.99 = ( F @ X ) )
% 4.69/4.99 => ( member_int @ B @ ( image_873079544045703924it_int @ F @ top_to1996260823553986621t_unit ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_eqI
% 4.69/4.99 thf(fact_4080_range__eqI,axiom,
% 4.69/4.99 ! [B: $o,F: product_unit > $o,X: product_unit] :
% 4.69/4.99 ( ( B
% 4.69/4.99 = ( F @ X ) )
% 4.69/4.99 => ( member_o @ B @ ( image_Product_unit_o2 @ F @ top_to1996260823553986621t_unit ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_eqI
% 4.69/4.99 thf(fact_4081_range__eqI,axiom,
% 4.69/4.99 ! [B: product_unit,F: product_unit > product_unit,X: product_unit] :
% 4.69/4.99 ( ( B
% 4.69/4.99 = ( F @ X ) )
% 4.69/4.99 => ( member_Product_unit @ B @ ( image_405062704495631173t_unit @ F @ top_to1996260823553986621t_unit ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_eqI
% 4.69/4.99 thf(fact_4082_range__eqI,axiom,
% 4.69/4.99 ! [B: nat,F: $o > nat,X: $o] :
% 4.69/4.99 ( ( B
% 4.69/4.99 = ( F @ X ) )
% 4.69/4.99 => ( member_nat @ B @ ( image_o_nat2 @ F @ top_top_set_o ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_eqI
% 4.69/4.99 thf(fact_4083_range__eqI,axiom,
% 4.69/4.99 ! [B: int,F: $o > int,X: $o] :
% 4.69/4.99 ( ( B
% 4.69/4.99 = ( F @ X ) )
% 4.69/4.99 => ( member_int @ B @ ( image_o_int2 @ F @ top_top_set_o ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_eqI
% 4.69/4.99 thf(fact_4084_range__eqI,axiom,
% 4.69/4.99 ! [B: $o,F: $o > $o,X: $o] :
% 4.69/4.99 ( ( B
% 4.69/4.99 = ( F @ X ) )
% 4.69/4.99 => ( member_o @ B @ ( image_o_o2 @ F @ top_top_set_o ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_eqI
% 4.69/4.99 thf(fact_4085_range__eqI,axiom,
% 4.69/4.99 ! [B: product_unit,F: $o > product_unit,X: $o] :
% 4.69/4.99 ( ( B
% 4.69/4.99 = ( F @ X ) )
% 4.69/4.99 => ( member_Product_unit @ B @ ( image_o_Product_unit2 @ F @ top_top_set_o ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_eqI
% 4.69/4.99 thf(fact_4086_range__eqI,axiom,
% 4.69/4.99 ! [B: code_integer,F: nat > code_integer,X: nat] :
% 4.69/4.99 ( ( B
% 4.69/4.99 = ( F @ X ) )
% 4.69/4.99 => ( member_Code_integer @ B @ ( image_1215581382706833972nteger @ F @ top_top_set_nat ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_eqI
% 4.69/4.99 thf(fact_4087_empty__not__UNIV,axiom,
% 4.69/4.99 bot_bo7824918357723582233_nat_o != top_to4869887016220417533_nat_o ).
% 4.69/4.99
% 4.69/4.99 % empty_not_UNIV
% 4.69/4.99 thf(fact_4088_empty__not__UNIV,axiom,
% 4.69/4.99 bot_bo3957492148770167129t_unit != top_to1996260823553986621t_unit ).
% 4.69/4.99
% 4.69/4.99 % empty_not_UNIV
% 4.69/4.99 thf(fact_4089_empty__not__UNIV,axiom,
% 4.69/4.99 bot_bot_set_o != top_top_set_o ).
% 4.69/4.99
% 4.69/4.99 % empty_not_UNIV
% 4.69/4.99 thf(fact_4090_empty__not__UNIV,axiom,
% 4.69/4.99 bot_bot_set_nat != top_top_set_nat ).
% 4.69/4.99
% 4.69/4.99 % empty_not_UNIV
% 4.69/4.99 thf(fact_4091_empty__not__UNIV,axiom,
% 4.69/4.99 bot_bot_set_int != top_top_set_int ).
% 4.69/4.99
% 4.69/4.99 % empty_not_UNIV
% 4.69/4.99 thf(fact_4092_subset__UNIV,axiom,
% 4.69/4.99 ! [A: set_Product_unit] : ( ord_le3507040750410214029t_unit @ A @ top_to1996260823553986621t_unit ) ).
% 4.69/4.99
% 4.69/4.99 % subset_UNIV
% 4.69/4.99 thf(fact_4093_subset__UNIV,axiom,
% 4.69/4.99 ! [A: set_o] : ( ord_less_eq_set_o @ A @ top_top_set_o ) ).
% 4.69/4.99
% 4.69/4.99 % subset_UNIV
% 4.69/4.99 thf(fact_4094_subset__UNIV,axiom,
% 4.69/4.99 ! [A: set_int] : ( ord_less_eq_set_int @ A @ top_top_set_int ) ).
% 4.69/4.99
% 4.69/4.99 % subset_UNIV
% 4.69/4.99 thf(fact_4095_subset__UNIV,axiom,
% 4.69/4.99 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ top_top_set_nat ) ).
% 4.69/4.99
% 4.69/4.99 % subset_UNIV
% 4.69/4.99 thf(fact_4096_psubset__imp__ex__mem,axiom,
% 4.69/4.99 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.99 ( ( ord_le2453136405763929_nat_o @ A @ B4 )
% 4.69/4.99 => ? [B2: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ B2 @ ( minus_1801376950450012436_nat_o @ B4 @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % psubset_imp_ex_mem
% 4.69/4.99 thf(fact_4097_psubset__imp__ex__mem,axiom,
% 4.69/4.99 ! [A: set_int,B4: set_int] :
% 4.69/4.99 ( ( ord_less_set_int @ A @ B4 )
% 4.69/4.99 => ? [B2: int] : ( member_int @ B2 @ ( minus_minus_set_int @ B4 @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % psubset_imp_ex_mem
% 4.69/4.99 thf(fact_4098_psubset__imp__ex__mem,axiom,
% 4.69/4.99 ! [A: set_o,B4: set_o] :
% 4.69/4.99 ( ( ord_less_set_o @ A @ B4 )
% 4.69/4.99 => ? [B2: $o] : ( member_o @ B2 @ ( minus_minus_set_o @ B4 @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % psubset_imp_ex_mem
% 4.69/4.99 thf(fact_4099_psubset__imp__ex__mem,axiom,
% 4.69/4.99 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.99 ( ( ord_le8056459307392131481t_unit @ A @ B4 )
% 4.69/4.99 => ? [B2: product_unit] : ( member_Product_unit @ B2 @ ( minus_6452836326544984404t_unit @ B4 @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % psubset_imp_ex_mem
% 4.69/4.99 thf(fact_4100_psubset__imp__ex__mem,axiom,
% 4.69/4.99 ! [A: set_nat,B4: set_nat] :
% 4.69/4.99 ( ( ord_less_set_nat @ A @ B4 )
% 4.69/4.99 => ? [B2: nat] : ( member_nat @ B2 @ ( minus_minus_set_nat @ B4 @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % psubset_imp_ex_mem
% 4.69/4.99 thf(fact_4101_insert__UNIV,axiom,
% 4.69/4.99 ! [X: product_unit] :
% 4.69/4.99 ( ( insert_Product_unit @ X @ top_to1996260823553986621t_unit )
% 4.69/4.99 = top_to1996260823553986621t_unit ) ).
% 4.69/4.99
% 4.69/4.99 % insert_UNIV
% 4.69/4.99 thf(fact_4102_insert__UNIV,axiom,
% 4.69/4.99 ! [X: $o] :
% 4.69/4.99 ( ( insert_o @ X @ top_top_set_o )
% 4.69/4.99 = top_top_set_o ) ).
% 4.69/4.99
% 4.69/4.99 % insert_UNIV
% 4.69/4.99 thf(fact_4103_insert__UNIV,axiom,
% 4.69/4.99 ! [X: nat] :
% 4.69/4.99 ( ( insert_nat @ X @ top_top_set_nat )
% 4.69/4.99 = top_top_set_nat ) ).
% 4.69/4.99
% 4.69/4.99 % insert_UNIV
% 4.69/4.99 thf(fact_4104_insert__UNIV,axiom,
% 4.69/4.99 ! [X: int] :
% 4.69/4.99 ( ( insert_int @ X @ top_top_set_int )
% 4.69/4.99 = top_top_set_int ) ).
% 4.69/4.99
% 4.69/4.99 % insert_UNIV
% 4.69/4.99 thf(fact_4105_Int__UNIV__left,axiom,
% 4.69/4.99 ! [B4: set_Product_unit] :
% 4.69/4.99 ( ( inf_in4660618365625256667t_unit @ top_to1996260823553986621t_unit @ B4 )
% 4.69/4.99 = B4 ) ).
% 4.69/4.99
% 4.69/4.99 % Int_UNIV_left
% 4.69/4.99 thf(fact_4106_Int__UNIV__left,axiom,
% 4.69/4.99 ! [B4: set_o] :
% 4.69/4.99 ( ( inf_inf_set_o @ top_top_set_o @ B4 )
% 4.69/4.99 = B4 ) ).
% 4.69/4.99
% 4.69/4.99 % Int_UNIV_left
% 4.69/4.99 thf(fact_4107_Int__UNIV__left,axiom,
% 4.69/4.99 ! [B4: set_nat] :
% 4.69/4.99 ( ( inf_inf_set_nat @ top_top_set_nat @ B4 )
% 4.69/4.99 = B4 ) ).
% 4.69/4.99
% 4.69/4.99 % Int_UNIV_left
% 4.69/4.99 thf(fact_4108_Int__UNIV__left,axiom,
% 4.69/4.99 ! [B4: set_int] :
% 4.69/4.99 ( ( inf_inf_set_int @ top_top_set_int @ B4 )
% 4.69/4.99 = B4 ) ).
% 4.69/4.99
% 4.69/4.99 % Int_UNIV_left
% 4.69/4.99 thf(fact_4109_Int__UNIV__right,axiom,
% 4.69/4.99 ! [A: set_Product_unit] :
% 4.69/4.99 ( ( inf_in4660618365625256667t_unit @ A @ top_to1996260823553986621t_unit )
% 4.69/4.99 = A ) ).
% 4.69/4.99
% 4.69/4.99 % Int_UNIV_right
% 4.69/4.99 thf(fact_4110_Int__UNIV__right,axiom,
% 4.69/4.99 ! [A: set_o] :
% 4.69/4.99 ( ( inf_inf_set_o @ A @ top_top_set_o )
% 4.69/4.99 = A ) ).
% 4.69/4.99
% 4.69/4.99 % Int_UNIV_right
% 4.69/4.99 thf(fact_4111_Int__UNIV__right,axiom,
% 4.69/4.99 ! [A: set_nat] :
% 4.69/4.99 ( ( inf_inf_set_nat @ A @ top_top_set_nat )
% 4.69/4.99 = A ) ).
% 4.69/4.99
% 4.69/4.99 % Int_UNIV_right
% 4.69/4.99 thf(fact_4112_Int__UNIV__right,axiom,
% 4.69/4.99 ! [A: set_int] :
% 4.69/4.99 ( ( inf_inf_set_int @ A @ top_top_set_int )
% 4.69/4.99 = A ) ).
% 4.69/4.99
% 4.69/4.99 % Int_UNIV_right
% 4.69/4.99 thf(fact_4113_Un__UNIV__left,axiom,
% 4.69/4.99 ! [B4: set_Product_unit] :
% 4.69/4.99 ( ( sup_su793286257634532545t_unit @ top_to1996260823553986621t_unit @ B4 )
% 4.69/4.99 = top_to1996260823553986621t_unit ) ).
% 4.69/4.99
% 4.69/4.99 % Un_UNIV_left
% 4.69/4.99 thf(fact_4114_Un__UNIV__left,axiom,
% 4.69/4.99 ! [B4: set_o] :
% 4.69/4.99 ( ( sup_sup_set_o @ top_top_set_o @ B4 )
% 4.69/4.99 = top_top_set_o ) ).
% 4.69/4.99
% 4.69/4.99 % Un_UNIV_left
% 4.69/4.99 thf(fact_4115_Un__UNIV__left,axiom,
% 4.69/4.99 ! [B4: set_nat] :
% 4.69/4.99 ( ( sup_sup_set_nat @ top_top_set_nat @ B4 )
% 4.69/4.99 = top_top_set_nat ) ).
% 4.69/4.99
% 4.69/4.99 % Un_UNIV_left
% 4.69/4.99 thf(fact_4116_Un__UNIV__left,axiom,
% 4.69/4.99 ! [B4: set_int] :
% 4.69/4.99 ( ( sup_sup_set_int @ top_top_set_int @ B4 )
% 4.69/4.99 = top_top_set_int ) ).
% 4.69/4.99
% 4.69/4.99 % Un_UNIV_left
% 4.69/4.99 thf(fact_4117_Un__UNIV__right,axiom,
% 4.69/4.99 ! [A: set_Product_unit] :
% 4.69/4.99 ( ( sup_su793286257634532545t_unit @ A @ top_to1996260823553986621t_unit )
% 4.69/4.99 = top_to1996260823553986621t_unit ) ).
% 4.69/4.99
% 4.69/4.99 % Un_UNIV_right
% 4.69/4.99 thf(fact_4118_Un__UNIV__right,axiom,
% 4.69/4.99 ! [A: set_o] :
% 4.69/4.99 ( ( sup_sup_set_o @ A @ top_top_set_o )
% 4.69/4.99 = top_top_set_o ) ).
% 4.69/4.99
% 4.69/4.99 % Un_UNIV_right
% 4.69/4.99 thf(fact_4119_Un__UNIV__right,axiom,
% 4.69/4.99 ! [A: set_nat] :
% 4.69/4.99 ( ( sup_sup_set_nat @ A @ top_top_set_nat )
% 4.69/4.99 = top_top_set_nat ) ).
% 4.69/4.99
% 4.69/4.99 % Un_UNIV_right
% 4.69/4.99 thf(fact_4120_Un__UNIV__right,axiom,
% 4.69/4.99 ! [A: set_int] :
% 4.69/4.99 ( ( sup_sup_set_int @ A @ top_top_set_int )
% 4.69/4.99 = top_top_set_int ) ).
% 4.69/4.99
% 4.69/4.99 % Un_UNIV_right
% 4.69/4.99 thf(fact_4121_type__copy__ex__RepI,axiom,
% 4.69/4.99 ! [Rep2: assn > produc3658429121746597890et_nat > $o,Abs2: ( produc3658429121746597890et_nat > $o ) > assn,F2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 4.69/4.99 ( ( type_d3909072315231072503_nat_o @ Rep2 @ Abs2 @ top_to4869887016220417533_nat_o )
% 4.69/4.99 => ( ( ? [X7: produc3658429121746597890et_nat > $o] : ( F2 @ X7 ) )
% 4.69/4.99 = ( ? [B6: assn] : ( F2 @ ( Rep2 @ B6 ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_ex_RepI
% 4.69/4.99 thf(fact_4122_type__copy__ex__RepI,axiom,
% 4.69/4.99 ! [Rep2: code_integer > int,Abs2: int > code_integer,F2: int > $o] :
% 4.69/4.99 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ top_top_set_int )
% 4.69/4.99 => ( ( ? [X7: int] : ( F2 @ X7 ) )
% 4.69/4.99 = ( ? [B6: code_integer] : ( F2 @ ( Rep2 @ B6 ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_ex_RepI
% 4.69/4.99 thf(fact_4123_type__copy__ex__RepI,axiom,
% 4.69/4.99 ! [Rep2: product_unit > $o,Abs2: $o > product_unit,F2: $o > $o] :
% 4.69/4.99 ( ( type_d6188575255521822967unit_o @ Rep2 @ Abs2 @ top_top_set_o )
% 4.69/4.99 => ( ( ? [X7: $o] : ( F2 @ X7 ) )
% 4.69/4.99 = ( ? [B6: product_unit] : ( F2 @ ( Rep2 @ B6 ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_ex_RepI
% 4.69/4.99 thf(fact_4124_type__copy__ex__RepI,axiom,
% 4.69/4.99 ! [Rep2: code_natural > nat,Abs2: nat > code_natural,F2: nat > $o] :
% 4.69/4.99 ( ( type_d4410041424927559462al_nat @ Rep2 @ Abs2 @ top_top_set_nat )
% 4.69/4.99 => ( ( ? [X7: nat] : ( F2 @ X7 ) )
% 4.69/4.99 = ( ? [B6: code_natural] : ( F2 @ ( Rep2 @ B6 ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_ex_RepI
% 4.69/4.99 thf(fact_4125_type__copy__obj__one__point__absE,axiom,
% 4.69/4.99 ! [Rep2: assn > produc3658429121746597890et_nat > $o,Abs2: ( produc3658429121746597890et_nat > $o ) > assn,S2: assn] :
% 4.69/4.99 ( ( type_d3909072315231072503_nat_o @ Rep2 @ Abs2 @ top_to4869887016220417533_nat_o )
% 4.69/4.99 => ~ ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.99 ( S2
% 4.69/4.99 != ( Abs2 @ X3 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_obj_one_point_absE
% 4.69/4.99 thf(fact_4126_type__copy__obj__one__point__absE,axiom,
% 4.69/4.99 ! [Rep2: code_integer > int,Abs2: int > code_integer,S2: code_integer] :
% 4.69/4.99 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ top_top_set_int )
% 4.69/4.99 => ~ ! [X3: int] :
% 4.69/4.99 ( S2
% 4.69/4.99 != ( Abs2 @ X3 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_obj_one_point_absE
% 4.69/4.99 thf(fact_4127_type__copy__obj__one__point__absE,axiom,
% 4.69/4.99 ! [Rep2: product_unit > $o,Abs2: $o > product_unit,S2: product_unit] :
% 4.69/4.99 ( ( type_d6188575255521822967unit_o @ Rep2 @ Abs2 @ top_top_set_o )
% 4.69/4.99 => ~ ! [X3: $o] :
% 4.69/4.99 ( S2
% 4.69/4.99 != ( Abs2 @ X3 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_obj_one_point_absE
% 4.69/4.99 thf(fact_4128_type__copy__obj__one__point__absE,axiom,
% 4.69/4.99 ! [Rep2: code_natural > nat,Abs2: nat > code_natural,S2: code_natural] :
% 4.69/4.99 ( ( type_d4410041424927559462al_nat @ Rep2 @ Abs2 @ top_top_set_nat )
% 4.69/4.99 => ~ ! [X3: nat] :
% 4.69/4.99 ( S2
% 4.69/4.99 != ( Abs2 @ X3 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_obj_one_point_absE
% 4.69/4.99 thf(fact_4129_less__1__mult,axiom,
% 4.69/4.99 ! [M4: code_natural,N2: code_natural] :
% 4.69/4.99 ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ M4 )
% 4.69/4.99 => ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ N2 )
% 4.69/4.99 => ( ord_le5570908160329646204atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ M4 @ N2 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % less_1_mult
% 4.69/4.99 thf(fact_4130_less__1__mult,axiom,
% 4.69/4.99 ! [M4: nat,N2: nat] :
% 4.69/4.99 ( ( ord_less_nat @ one_one_nat @ M4 )
% 4.69/4.99 => ( ( ord_less_nat @ one_one_nat @ N2 )
% 4.69/4.99 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M4 @ N2 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % less_1_mult
% 4.69/4.99 thf(fact_4131_less__1__mult,axiom,
% 4.69/4.99 ! [M4: int,N2: int] :
% 4.69/4.99 ( ( ord_less_int @ one_one_int @ M4 )
% 4.69/4.99 => ( ( ord_less_int @ one_one_int @ N2 )
% 4.69/4.99 => ( ord_less_int @ one_one_int @ ( times_times_int @ M4 @ N2 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % less_1_mult
% 4.69/4.99 thf(fact_4132_less__1__mult,axiom,
% 4.69/4.99 ! [M4: code_integer,N2: code_integer] :
% 4.69/4.99 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ M4 )
% 4.69/4.99 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ N2 )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ M4 @ N2 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % less_1_mult
% 4.69/4.99 thf(fact_4133_less__1__mult,axiom,
% 4.69/4.99 ! [M4: rat,N2: rat] :
% 4.69/4.99 ( ( ord_less_rat @ one_one_rat @ M4 )
% 4.69/4.99 => ( ( ord_less_rat @ one_one_rat @ N2 )
% 4.69/4.99 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M4 @ N2 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % less_1_mult
% 4.69/4.99 thf(fact_4134_infinite__growing,axiom,
% 4.69/4.99 ! [X4: set_Product_unit] :
% 4.69/4.99 ( ( X4 != bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ( ! [X3: product_unit] :
% 4.69/4.99 ( ( member_Product_unit @ X3 @ X4 )
% 4.69/4.99 => ? [Xa2: product_unit] :
% 4.69/4.99 ( ( member_Product_unit @ Xa2 @ X4 )
% 4.69/4.99 & ( ord_le361264281704409273t_unit @ X3 @ Xa2 ) ) )
% 4.69/4.99 => ~ ( finite4290736615968046902t_unit @ X4 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % infinite_growing
% 4.69/4.99 thf(fact_4135_infinite__growing,axiom,
% 4.69/4.99 ! [X4: set_o] :
% 4.69/4.99 ( ( X4 != bot_bot_set_o )
% 4.69/4.99 => ( ! [X3: $o] :
% 4.69/4.99 ( ( member_o @ X3 @ X4 )
% 4.69/4.99 => ? [Xa2: $o] :
% 4.69/4.99 ( ( member_o @ Xa2 @ X4 )
% 4.69/4.99 & ( ord_less_o @ X3 @ Xa2 ) ) )
% 4.69/4.99 => ~ ( finite_finite_o @ X4 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % infinite_growing
% 4.69/4.99 thf(fact_4136_infinite__growing,axiom,
% 4.69/4.99 ! [X4: set_nat] :
% 4.69/4.99 ( ( X4 != bot_bot_set_nat )
% 4.69/4.99 => ( ! [X3: nat] :
% 4.69/4.99 ( ( member_nat @ X3 @ X4 )
% 4.69/4.99 => ? [Xa2: nat] :
% 4.69/4.99 ( ( member_nat @ Xa2 @ X4 )
% 4.69/4.99 & ( ord_less_nat @ X3 @ Xa2 ) ) )
% 4.69/4.99 => ~ ( finite_finite_nat @ X4 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % infinite_growing
% 4.69/4.99 thf(fact_4137_infinite__growing,axiom,
% 4.69/4.99 ! [X4: set_int] :
% 4.69/4.99 ( ( X4 != bot_bot_set_int )
% 4.69/4.99 => ( ! [X3: int] :
% 4.69/4.99 ( ( member_int @ X3 @ X4 )
% 4.69/4.99 => ? [Xa2: int] :
% 4.69/4.99 ( ( member_int @ Xa2 @ X4 )
% 4.69/4.99 & ( ord_less_int @ X3 @ Xa2 ) ) )
% 4.69/4.99 => ~ ( finite_finite_int @ X4 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % infinite_growing
% 4.69/4.99 thf(fact_4138_infinite__growing,axiom,
% 4.69/4.99 ! [X4: set_Code_integer] :
% 4.69/4.99 ( ( X4 != bot_bo3990330152332043303nteger )
% 4.69/4.99 => ( ! [X3: code_integer] :
% 4.69/4.99 ( ( member_Code_integer @ X3 @ X4 )
% 4.69/4.99 => ? [Xa2: code_integer] :
% 4.69/4.99 ( ( member_Code_integer @ Xa2 @ X4 )
% 4.69/4.99 & ( ord_le6747313008572928689nteger @ X3 @ Xa2 ) ) )
% 4.69/4.99 => ~ ( finite6017078050557962740nteger @ X4 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % infinite_growing
% 4.69/4.99 thf(fact_4139_infinite__growing,axiom,
% 4.69/4.99 ! [X4: set_rat] :
% 4.69/4.99 ( ( X4 != bot_bot_set_rat )
% 4.69/4.99 => ( ! [X3: rat] :
% 4.69/4.99 ( ( member_rat @ X3 @ X4 )
% 4.69/4.99 => ? [Xa2: rat] :
% 4.69/4.99 ( ( member_rat @ Xa2 @ X4 )
% 4.69/4.99 & ( ord_less_rat @ X3 @ Xa2 ) ) )
% 4.69/4.99 => ~ ( finite_finite_rat @ X4 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % infinite_growing
% 4.69/4.99 thf(fact_4140_ex__min__if__finite,axiom,
% 4.69/4.99 ! [S: set_Product_unit] :
% 4.69/4.99 ( ( finite4290736615968046902t_unit @ S )
% 4.69/4.99 => ( ( S != bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ? [X3: product_unit] :
% 4.69/4.99 ( ( member_Product_unit @ X3 @ S )
% 4.69/4.99 & ~ ? [Xa2: product_unit] :
% 4.69/4.99 ( ( member_Product_unit @ Xa2 @ S )
% 4.69/4.99 & ( ord_le361264281704409273t_unit @ Xa2 @ X3 ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % ex_min_if_finite
% 4.69/4.99 thf(fact_4141_ex__min__if__finite,axiom,
% 4.69/4.99 ! [S: set_o] :
% 4.69/4.99 ( ( finite_finite_o @ S )
% 4.69/4.99 => ( ( S != bot_bot_set_o )
% 4.69/4.99 => ? [X3: $o] :
% 4.69/4.99 ( ( member_o @ X3 @ S )
% 4.69/4.99 & ~ ? [Xa2: $o] :
% 4.69/4.99 ( ( member_o @ Xa2 @ S )
% 4.69/4.99 & ( ord_less_o @ Xa2 @ X3 ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % ex_min_if_finite
% 4.69/4.99 thf(fact_4142_ex__min__if__finite,axiom,
% 4.69/4.99 ! [S: set_Pr4532377907799695533_nat_o] :
% 4.69/4.99 ( ( finite3252695134891459830_nat_o @ S )
% 4.69/4.99 => ( ( S != bot_bo7824918357723582233_nat_o )
% 4.69/4.99 => ? [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.99 ( ( member6576561426505652726_nat_o @ X3 @ S )
% 4.69/4.99 & ~ ? [Xa2: produc3658429121746597890et_nat > $o] :
% 4.69/4.99 ( ( member6576561426505652726_nat_o @ Xa2 @ S )
% 4.69/4.99 & ( ord_le8176553561544679545_nat_o @ Xa2 @ X3 ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % ex_min_if_finite
% 4.69/4.99 thf(fact_4143_ex__min__if__finite,axiom,
% 4.69/4.99 ! [S: set_assn] :
% 4.69/4.99 ( ( finite_finite_assn @ S )
% 4.69/4.99 => ( ( S != bot_bot_set_assn )
% 4.69/4.99 => ? [X3: assn] :
% 4.69/4.99 ( ( member_assn @ X3 @ S )
% 4.69/4.99 & ~ ? [Xa2: assn] :
% 4.69/4.99 ( ( member_assn @ Xa2 @ S )
% 4.69/4.99 & ( ord_less_assn @ Xa2 @ X3 ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % ex_min_if_finite
% 4.69/4.99 thf(fact_4144_ex__min__if__finite,axiom,
% 4.69/4.99 ! [S: set_nat] :
% 4.69/4.99 ( ( finite_finite_nat @ S )
% 4.69/4.99 => ( ( S != bot_bot_set_nat )
% 4.69/4.99 => ? [X3: nat] :
% 4.69/4.99 ( ( member_nat @ X3 @ S )
% 4.69/4.99 & ~ ? [Xa2: nat] :
% 4.69/4.99 ( ( member_nat @ Xa2 @ S )
% 4.69/4.99 & ( ord_less_nat @ Xa2 @ X3 ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % ex_min_if_finite
% 4.69/4.99 thf(fact_4145_ex__min__if__finite,axiom,
% 4.69/4.99 ! [S: set_int] :
% 4.69/4.99 ( ( finite_finite_int @ S )
% 4.69/4.99 => ( ( S != bot_bot_set_int )
% 4.69/4.99 => ? [X3: int] :
% 4.69/4.99 ( ( member_int @ X3 @ S )
% 4.69/4.99 & ~ ? [Xa2: int] :
% 4.69/4.99 ( ( member_int @ Xa2 @ S )
% 4.69/4.99 & ( ord_less_int @ Xa2 @ X3 ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % ex_min_if_finite
% 4.69/4.99 thf(fact_4146_ex__min__if__finite,axiom,
% 4.69/4.99 ! [S: set_Code_integer] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ S )
% 4.69/4.99 => ( ( S != bot_bo3990330152332043303nteger )
% 4.69/4.99 => ? [X3: code_integer] :
% 4.69/4.99 ( ( member_Code_integer @ X3 @ S )
% 4.69/4.99 & ~ ? [Xa2: code_integer] :
% 4.69/4.99 ( ( member_Code_integer @ Xa2 @ S )
% 4.69/4.99 & ( ord_le6747313008572928689nteger @ Xa2 @ X3 ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % ex_min_if_finite
% 4.69/4.99 thf(fact_4147_ex__min__if__finite,axiom,
% 4.69/4.99 ! [S: set_rat] :
% 4.69/4.99 ( ( finite_finite_rat @ S )
% 4.69/4.99 => ( ( S != bot_bot_set_rat )
% 4.69/4.99 => ? [X3: rat] :
% 4.69/4.99 ( ( member_rat @ X3 @ S )
% 4.69/4.99 & ~ ? [Xa2: rat] :
% 4.69/4.99 ( ( member_rat @ Xa2 @ S )
% 4.69/4.99 & ( ord_less_rat @ Xa2 @ X3 ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % ex_min_if_finite
% 4.69/4.99 thf(fact_4148_less__cSupD,axiom,
% 4.69/4.99 ! [X4: set_int,Z: int] :
% 4.69/4.99 ( ( X4 != bot_bot_set_int )
% 4.69/4.99 => ( ( ord_less_int @ Z @ ( complete_Sup_Sup_int @ X4 ) )
% 4.69/4.99 => ? [X3: int] :
% 4.69/4.99 ( ( member_int @ X3 @ X4 )
% 4.69/4.99 & ( ord_less_int @ Z @ X3 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % less_cSupD
% 4.69/4.99 thf(fact_4149_less__cSupD,axiom,
% 4.69/4.99 ! [X4: set_nat,Z: nat] :
% 4.69/4.99 ( ( X4 != bot_bot_set_nat )
% 4.69/4.99 => ( ( ord_less_nat @ Z @ ( complete_Sup_Sup_nat @ X4 ) )
% 4.69/4.99 => ? [X3: nat] :
% 4.69/4.99 ( ( member_nat @ X3 @ X4 )
% 4.69/4.99 & ( ord_less_nat @ Z @ X3 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % less_cSupD
% 4.69/4.99 thf(fact_4150_less__cSupD,axiom,
% 4.69/4.99 ! [X4: set_Product_unit,Z: product_unit] :
% 4.69/4.99 ( ( X4 != bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ( ( ord_le361264281704409273t_unit @ Z @ ( comple4687483117567863418t_unit @ X4 ) )
% 4.69/4.99 => ? [X3: product_unit] :
% 4.69/4.99 ( ( member_Product_unit @ X3 @ X4 )
% 4.69/4.99 & ( ord_le361264281704409273t_unit @ Z @ X3 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % less_cSupD
% 4.69/4.99 thf(fact_4151_less__cSupE,axiom,
% 4.69/4.99 ! [Y: int,X4: set_int] :
% 4.69/4.99 ( ( ord_less_int @ Y @ ( complete_Sup_Sup_int @ X4 ) )
% 4.69/4.99 => ( ( X4 != bot_bot_set_int )
% 4.69/4.99 => ~ ! [X3: int] :
% 4.69/4.99 ( ( member_int @ X3 @ X4 )
% 4.69/4.99 => ~ ( ord_less_int @ Y @ X3 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % less_cSupE
% 4.69/4.99 thf(fact_4152_less__cSupE,axiom,
% 4.69/4.99 ! [Y: nat,X4: set_nat] :
% 4.69/4.99 ( ( ord_less_nat @ Y @ ( complete_Sup_Sup_nat @ X4 ) )
% 4.69/4.99 => ( ( X4 != bot_bot_set_nat )
% 4.69/4.99 => ~ ! [X3: nat] :
% 4.69/4.99 ( ( member_nat @ X3 @ X4 )
% 4.69/4.99 => ~ ( ord_less_nat @ Y @ X3 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % less_cSupE
% 4.69/4.99 thf(fact_4153_less__cSupE,axiom,
% 4.69/4.99 ! [Y: product_unit,X4: set_Product_unit] :
% 4.69/4.99 ( ( ord_le361264281704409273t_unit @ Y @ ( comple4687483117567863418t_unit @ X4 ) )
% 4.69/4.99 => ( ( X4 != bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ~ ! [X3: product_unit] :
% 4.69/4.99 ( ( member_Product_unit @ X3 @ X4 )
% 4.69/4.99 => ~ ( ord_le361264281704409273t_unit @ Y @ X3 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % less_cSupE
% 4.69/4.99 thf(fact_4154_Max__in,axiom,
% 4.69/4.99 ! [A: set_Code_integer] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.99 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/4.99 => ( member_Code_integer @ ( lattic4901227151466704046nteger @ A ) @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_in
% 4.69/4.99 thf(fact_4155_Max__in,axiom,
% 4.69/4.99 ! [A: set_Product_unit] :
% 4.69/4.99 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.99 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ( member_Product_unit @ ( lattic1210392890313158908t_unit @ A ) @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_in
% 4.69/4.99 thf(fact_4156_Max__in,axiom,
% 4.69/4.99 ! [A: set_o] :
% 4.69/4.99 ( ( finite_finite_o @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_o )
% 4.69/4.99 => ( member_o @ ( lattic1921953407002678535_Max_o @ A ) @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_in
% 4.69/4.99 thf(fact_4157_Max__in,axiom,
% 4.69/4.99 ! [A: set_int] :
% 4.69/4.99 ( ( finite_finite_int @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_int )
% 4.69/4.99 => ( member_int @ ( lattic8263393255366662781ax_int @ A ) @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_in
% 4.69/4.99 thf(fact_4158_Max__in,axiom,
% 4.69/4.99 ! [A: set_nat] :
% 4.69/4.99 ( ( finite_finite_nat @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_nat )
% 4.69/4.99 => ( member_nat @ ( lattic8265883725875713057ax_nat @ A ) @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_in
% 4.69/4.99 thf(fact_4159_range__subsetD,axiom,
% 4.69/4.99 ! [F: code_integer > code_integer,B4: set_Code_integer,I2: code_integer] :
% 4.69/4.99 ( ( ord_le7084787975880047091nteger @ ( image_4470545334726330049nteger @ F @ top_to4645266643341252675nteger ) @ B4 )
% 4.69/4.99 => ( member_Code_integer @ ( F @ I2 ) @ B4 ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_subsetD
% 4.69/4.99 thf(fact_4160_range__subsetD,axiom,
% 4.69/4.99 ! [F: product_unit > int,B4: set_int,I2: product_unit] :
% 4.69/4.99 ( ( ord_less_eq_set_int @ ( image_873079544045703924it_int @ F @ top_to1996260823553986621t_unit ) @ B4 )
% 4.69/4.99 => ( member_int @ ( F @ I2 ) @ B4 ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_subsetD
% 4.69/4.99 thf(fact_4161_range__subsetD,axiom,
% 4.69/4.99 ! [F: product_unit > $o,B4: set_o,I2: product_unit] :
% 4.69/4.99 ( ( ord_less_eq_set_o @ ( image_Product_unit_o2 @ F @ top_to1996260823553986621t_unit ) @ B4 )
% 4.69/4.99 => ( member_o @ ( F @ I2 ) @ B4 ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_subsetD
% 4.69/4.99 thf(fact_4162_range__subsetD,axiom,
% 4.69/4.99 ! [F: product_unit > product_unit,B4: set_Product_unit,I2: product_unit] :
% 4.69/4.99 ( ( ord_le3507040750410214029t_unit @ ( image_405062704495631173t_unit @ F @ top_to1996260823553986621t_unit ) @ B4 )
% 4.69/4.99 => ( member_Product_unit @ ( F @ I2 ) @ B4 ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_subsetD
% 4.69/4.99 thf(fact_4163_range__subsetD,axiom,
% 4.69/4.99 ! [F: $o > int,B4: set_int,I2: $o] :
% 4.69/4.99 ( ( ord_less_eq_set_int @ ( image_o_int2 @ F @ top_top_set_o ) @ B4 )
% 4.69/4.99 => ( member_int @ ( F @ I2 ) @ B4 ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_subsetD
% 4.69/4.99 thf(fact_4164_range__subsetD,axiom,
% 4.69/4.99 ! [F: $o > $o,B4: set_o,I2: $o] :
% 4.69/4.99 ( ( ord_less_eq_set_o @ ( image_o_o2 @ F @ top_top_set_o ) @ B4 )
% 4.69/4.99 => ( member_o @ ( F @ I2 ) @ B4 ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_subsetD
% 4.69/4.99 thf(fact_4165_range__subsetD,axiom,
% 4.69/4.99 ! [F: $o > product_unit,B4: set_Product_unit,I2: $o] :
% 4.69/4.99 ( ( ord_le3507040750410214029t_unit @ ( image_o_Product_unit2 @ F @ top_top_set_o ) @ B4 )
% 4.69/4.99 => ( member_Product_unit @ ( F @ I2 ) @ B4 ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_subsetD
% 4.69/4.99 thf(fact_4166_range__subsetD,axiom,
% 4.69/4.99 ! [F: nat > code_integer,B4: set_Code_integer,I2: nat] :
% 4.69/4.99 ( ( ord_le7084787975880047091nteger @ ( image_1215581382706833972nteger @ F @ top_top_set_nat ) @ B4 )
% 4.69/4.99 => ( member_Code_integer @ ( F @ I2 ) @ B4 ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_subsetD
% 4.69/4.99 thf(fact_4167_range__subsetD,axiom,
% 4.69/4.99 ! [F: nat > int,B4: set_int,I2: nat] :
% 4.69/4.99 ( ( ord_less_eq_set_int @ ( image_nat_int2 @ F @ top_top_set_nat ) @ B4 )
% 4.69/4.99 => ( member_int @ ( F @ I2 ) @ B4 ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_subsetD
% 4.69/4.99 thf(fact_4168_range__subsetD,axiom,
% 4.69/4.99 ! [F: nat > $o,B4: set_o,I2: nat] :
% 4.69/4.99 ( ( ord_less_eq_set_o @ ( image_nat_o2 @ F @ top_top_set_nat ) @ B4 )
% 4.69/4.99 => ( member_o @ ( F @ I2 ) @ B4 ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_subsetD
% 4.69/4.99 thf(fact_4169_surj__vimage__empty,axiom,
% 4.69/4.99 ! [F: code_integer > code_integer,A: set_Code_integer] :
% 4.69/4.99 ( ( ( image_4470545334726330049nteger @ F @ top_to4645266643341252675nteger )
% 4.69/4.99 = top_to4645266643341252675nteger )
% 4.69/4.99 => ( ( ( vimage1318793397690208119nteger @ F @ A )
% 4.69/4.99 = bot_bo3990330152332043303nteger )
% 4.69/4.99 = ( A = bot_bo3990330152332043303nteger ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % surj_vimage_empty
% 4.69/4.99 thf(fact_4170_surj__vimage__empty,axiom,
% 4.69/4.99 ! [F: product_unit > product_unit,A: set_Product_unit] :
% 4.69/4.99 ( ( ( image_405062704495631173t_unit @ F @ top_to1996260823553986621t_unit )
% 4.69/4.99 = top_to1996260823553986621t_unit )
% 4.69/4.99 => ( ( ( vimage7995052115951654139t_unit @ F @ A )
% 4.69/4.99 = bot_bo3957492148770167129t_unit )
% 4.69/4.99 = ( A = bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % surj_vimage_empty
% 4.69/4.99 thf(fact_4171_surj__vimage__empty,axiom,
% 4.69/4.99 ! [F: product_unit > $o,A: set_o] :
% 4.69/4.99 ( ( ( image_Product_unit_o2 @ F @ top_to1996260823553986621t_unit )
% 4.69/4.99 = top_top_set_o )
% 4.69/4.99 => ( ( ( vimage8808348054653608838unit_o @ F @ A )
% 4.69/4.99 = bot_bo3957492148770167129t_unit )
% 4.69/4.99 = ( A = bot_bot_set_o ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % surj_vimage_empty
% 4.69/4.99 thf(fact_4172_surj__vimage__empty,axiom,
% 4.69/4.99 ! [F: product_unit > nat,A: set_nat] :
% 4.69/4.99 ( ( ( image_875570014554754200it_nat @ F @ top_to1996260823553986621t_unit )
% 4.69/4.99 = top_top_set_nat )
% 4.69/4.99 => ( ( ( vimage6253328473476588386it_nat @ F @ A )
% 4.69/4.99 = bot_bo3957492148770167129t_unit )
% 4.69/4.99 = ( A = bot_bot_set_nat ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % surj_vimage_empty
% 4.69/4.99 thf(fact_4173_surj__vimage__empty,axiom,
% 4.69/4.99 ! [F: product_unit > int,A: set_int] :
% 4.69/4.99 ( ( ( image_873079544045703924it_int @ F @ top_to1996260823553986621t_unit )
% 4.69/4.99 = top_top_set_int )
% 4.69/4.99 => ( ( ( vimage6250838002967538110it_int @ F @ A )
% 4.69/4.99 = bot_bo3957492148770167129t_unit )
% 4.69/4.99 = ( A = bot_bot_set_int ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % surj_vimage_empty
% 4.69/4.99 thf(fact_4174_surj__vimage__empty,axiom,
% 4.69/4.99 ! [F: $o > product_unit,A: set_Product_unit] :
% 4.69/4.99 ( ( ( image_o_Product_unit2 @ F @ top_top_set_o )
% 4.69/4.99 = top_to1996260823553986621t_unit )
% 4.69/4.99 => ( ( ( vimage4222377557387472176t_unit @ F @ A )
% 4.69/4.99 = bot_bot_set_o )
% 4.69/4.99 = ( A = bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % surj_vimage_empty
% 4.69/4.99 thf(fact_4175_surj__vimage__empty,axiom,
% 4.69/4.99 ! [F: $o > $o,A: set_o] :
% 4.69/4.99 ( ( ( image_o_o2 @ F @ top_top_set_o )
% 4.69/4.99 = top_top_set_o )
% 4.69/4.99 => ( ( ( vimage_o_o @ F @ A )
% 4.69/4.99 = bot_bot_set_o )
% 4.69/4.99 = ( A = bot_bot_set_o ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % surj_vimage_empty
% 4.69/4.99 thf(fact_4176_surj__vimage__empty,axiom,
% 4.69/4.99 ! [F: $o > nat,A: set_nat] :
% 4.69/4.99 ( ( ( image_o_nat2 @ F @ top_top_set_o )
% 4.69/4.99 = top_top_set_nat )
% 4.69/4.99 => ( ( ( vimage_o_nat @ F @ A )
% 4.69/4.99 = bot_bot_set_o )
% 4.69/4.99 = ( A = bot_bot_set_nat ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % surj_vimage_empty
% 4.69/4.99 thf(fact_4177_surj__vimage__empty,axiom,
% 4.69/4.99 ! [F: $o > int,A: set_int] :
% 4.69/4.99 ( ( ( image_o_int2 @ F @ top_top_set_o )
% 4.69/4.99 = top_top_set_int )
% 4.69/4.99 => ( ( ( vimage_o_int @ F @ A )
% 4.69/4.99 = bot_bot_set_o )
% 4.69/4.99 = ( A = bot_bot_set_int ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % surj_vimage_empty
% 4.69/4.99 thf(fact_4178_surj__vimage__empty,axiom,
% 4.69/4.99 ! [F: nat > code_integer,A: set_Code_integer] :
% 4.69/4.99 ( ( ( image_1215581382706833972nteger @ F @ top_top_set_nat )
% 4.69/4.99 = top_to4645266643341252675nteger )
% 4.69/4.99 => ( ( ( vimage6104394758324456170nteger @ F @ A )
% 4.69/4.99 = bot_bot_set_nat )
% 4.69/4.99 = ( A = bot_bo3990330152332043303nteger ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % surj_vimage_empty
% 4.69/4.99 thf(fact_4179_acyclicI__order,axiom,
% 4.69/4.99 ! [R2: set_Pr1261947904930325089at_nat,F: nat > assn] :
% 4.69/4.99 ( ! [A4: nat,B2: nat] :
% 4.69/4.99 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A4 @ B2 ) @ R2 )
% 4.69/4.99 => ( ord_less_assn @ ( F @ B2 ) @ ( F @ A4 ) ) )
% 4.69/4.99 => ( transi3139058337892597825ic_nat @ R2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % acyclicI_order
% 4.69/4.99 thf(fact_4180_acyclicI__order,axiom,
% 4.69/4.99 ! [R2: set_Pr958786334691620121nt_int,F: int > assn] :
% 4.69/4.99 ( ! [A4: int,B2: int] :
% 4.69/4.99 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A4 @ B2 ) @ R2 )
% 4.69/4.99 => ( ord_less_assn @ ( F @ B2 ) @ ( F @ A4 ) ) )
% 4.69/4.99 => ( transi3136567867383547549ic_int @ R2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % acyclicI_order
% 4.69/4.99 thf(fact_4181_acyclicI__order,axiom,
% 4.69/4.99 ! [R2: set_Pr1261947904930325089at_nat,F: nat > nat] :
% 4.69/4.99 ( ! [A4: nat,B2: nat] :
% 4.69/4.99 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A4 @ B2 ) @ R2 )
% 4.69/4.99 => ( ord_less_nat @ ( F @ B2 ) @ ( F @ A4 ) ) )
% 4.69/4.99 => ( transi3139058337892597825ic_nat @ R2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % acyclicI_order
% 4.69/4.99 thf(fact_4182_acyclicI__order,axiom,
% 4.69/4.99 ! [R2: set_Pr958786334691620121nt_int,F: int > nat] :
% 4.69/4.99 ( ! [A4: int,B2: int] :
% 4.69/4.99 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A4 @ B2 ) @ R2 )
% 4.69/4.99 => ( ord_less_nat @ ( F @ B2 ) @ ( F @ A4 ) ) )
% 4.69/4.99 => ( transi3136567867383547549ic_int @ R2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % acyclicI_order
% 4.69/4.99 thf(fact_4183_acyclicI__order,axiom,
% 4.69/4.99 ! [R2: set_Pr1261947904930325089at_nat,F: nat > int] :
% 4.69/4.99 ( ! [A4: nat,B2: nat] :
% 4.69/4.99 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A4 @ B2 ) @ R2 )
% 4.69/4.99 => ( ord_less_int @ ( F @ B2 ) @ ( F @ A4 ) ) )
% 4.69/4.99 => ( transi3139058337892597825ic_nat @ R2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % acyclicI_order
% 4.69/4.99 thf(fact_4184_acyclicI__order,axiom,
% 4.69/4.99 ! [R2: set_Pr958786334691620121nt_int,F: int > int] :
% 4.69/4.99 ( ! [A4: int,B2: int] :
% 4.69/4.99 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A4 @ B2 ) @ R2 )
% 4.69/4.99 => ( ord_less_int @ ( F @ B2 ) @ ( F @ A4 ) ) )
% 4.69/4.99 => ( transi3136567867383547549ic_int @ R2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % acyclicI_order
% 4.69/4.99 thf(fact_4185_acyclicI__order,axiom,
% 4.69/4.99 ! [R2: set_Pr1261947904930325089at_nat,F: nat > code_integer] :
% 4.69/4.99 ( ! [A4: nat,B2: nat] :
% 4.69/4.99 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A4 @ B2 ) @ R2 )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ ( F @ B2 ) @ ( F @ A4 ) ) )
% 4.69/4.99 => ( transi3139058337892597825ic_nat @ R2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % acyclicI_order
% 4.69/4.99 thf(fact_4186_acyclicI__order,axiom,
% 4.69/4.99 ! [R2: set_Pr958786334691620121nt_int,F: int > code_integer] :
% 4.69/4.99 ( ! [A4: int,B2: int] :
% 4.69/4.99 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A4 @ B2 ) @ R2 )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ ( F @ B2 ) @ ( F @ A4 ) ) )
% 4.69/4.99 => ( transi3136567867383547549ic_int @ R2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % acyclicI_order
% 4.69/4.99 thf(fact_4187_acyclicI__order,axiom,
% 4.69/4.99 ! [R2: set_Pr1261947904930325089at_nat,F: nat > rat] :
% 4.69/4.99 ( ! [A4: nat,B2: nat] :
% 4.69/4.99 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A4 @ B2 ) @ R2 )
% 4.69/4.99 => ( ord_less_rat @ ( F @ B2 ) @ ( F @ A4 ) ) )
% 4.69/4.99 => ( transi3139058337892597825ic_nat @ R2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % acyclicI_order
% 4.69/4.99 thf(fact_4188_acyclicI__order,axiom,
% 4.69/4.99 ! [R2: set_Pr958786334691620121nt_int,F: int > rat] :
% 4.69/4.99 ( ! [A4: int,B2: int] :
% 4.69/4.99 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A4 @ B2 ) @ R2 )
% 4.69/4.99 => ( ord_less_rat @ ( F @ B2 ) @ ( F @ A4 ) ) )
% 4.69/4.99 => ( transi3136567867383547549ic_int @ R2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % acyclicI_order
% 4.69/4.99 thf(fact_4189_type__definition_OAbs__image,axiom,
% 4.69/4.99 ! [Rep2: set_nat > nat,Abs2: nat > set_nat,A: set_nat] :
% 4.69/4.99 ( ( type_d202864840109488260at_nat @ Rep2 @ Abs2 @ A )
% 4.69/4.99 => ( ( image_nat_set_nat @ Abs2 @ A )
% 4.69/4.99 = top_top_set_set_nat ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_definition.Abs_image
% 4.69/4.99 thf(fact_4190_type__definition_OAbs__image,axiom,
% 4.69/4.99 ! [Rep2: code_integer > code_integer,Abs2: code_integer > code_integer,A: set_Code_integer] :
% 4.69/4.99 ( ( type_d4796611474492816872nteger @ Rep2 @ Abs2 @ A )
% 4.69/4.99 => ( ( image_4470545334726330049nteger @ Abs2 @ A )
% 4.69/4.99 = top_to4645266643341252675nteger ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_definition.Abs_image
% 4.69/4.99 thf(fact_4191_type__definition_OAbs__image,axiom,
% 4.69/4.99 ! [Rep2: code_integer > nat,Abs2: nat > code_integer,A: set_nat] :
% 4.69/4.99 ( ( type_d8368584451094728027er_nat @ Rep2 @ Abs2 @ A )
% 4.69/4.99 => ( ( image_1215581382706833972nteger @ Abs2 @ A )
% 4.69/4.99 = top_to4645266643341252675nteger ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_definition.Abs_image
% 4.69/4.99 thf(fact_4192_type__definition_OAbs__image,axiom,
% 4.69/4.99 ! [Rep2: nat > nat,Abs2: nat > nat,A: set_nat] :
% 4.69/4.99 ( ( type_d6250493948777748686at_nat @ Rep2 @ Abs2 @ A )
% 4.69/4.99 => ( ( image_nat_nat2 @ Abs2 @ A )
% 4.69/4.99 = top_top_set_nat ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_definition.Abs_image
% 4.69/4.99 thf(fact_4193_type__definition_OAbs__image,axiom,
% 4.69/4.99 ! [Rep2: assn > produc3658429121746597890et_nat > $o,Abs2: ( produc3658429121746597890et_nat > $o ) > assn,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.99 ( ( type_d3909072315231072503_nat_o @ Rep2 @ Abs2 @ A )
% 4.69/4.99 => ( ( image_6451031022632655280o_assn @ Abs2 @ A )
% 4.69/4.99 = top_top_set_assn ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_definition.Abs_image
% 4.69/4.99 thf(fact_4194_type__definition_OAbs__image,axiom,
% 4.69/4.99 ! [Rep2: code_integer > int,Abs2: int > code_integer,A: set_int] :
% 4.69/4.99 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ A )
% 4.69/4.99 => ( ( image_1587234942943678608nteger @ Abs2 @ A )
% 4.69/4.99 = top_to4645266643341252675nteger ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_definition.Abs_image
% 4.69/4.99 thf(fact_4195_type__definition_OAbs__image,axiom,
% 4.69/4.99 ! [Rep2: product_unit > $o,Abs2: $o > product_unit,A: set_o] :
% 4.69/4.99 ( ( type_d6188575255521822967unit_o @ Rep2 @ Abs2 @ A )
% 4.69/4.99 => ( ( image_o_Product_unit2 @ Abs2 @ A )
% 4.69/4.99 = top_to1996260823553986621t_unit ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_definition.Abs_image
% 4.69/4.99 thf(fact_4196_type__definition_OAbs__image,axiom,
% 4.69/4.99 ! [Rep2: code_natural > nat,Abs2: nat > code_natural,A: set_nat] :
% 4.69/4.99 ( ( type_d4410041424927559462al_nat @ Rep2 @ Abs2 @ A )
% 4.69/4.99 => ( ( image_39176534463551487atural @ Abs2 @ A )
% 4.69/4.99 = top_to9103716463852441742atural ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_definition.Abs_image
% 4.69/4.99 thf(fact_4197_type__definition_ORep__range,axiom,
% 4.69/4.99 ! [Rep2: code_integer > code_integer,Abs2: code_integer > code_integer,A: set_Code_integer] :
% 4.69/4.99 ( ( type_d4796611474492816872nteger @ Rep2 @ Abs2 @ A )
% 4.69/4.99 => ( ( image_4470545334726330049nteger @ Rep2 @ top_to4645266643341252675nteger )
% 4.69/4.99 = A ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_definition.Rep_range
% 4.69/4.99 thf(fact_4198_type__definition_ORep__range,axiom,
% 4.69/4.99 ! [Rep2: nat > set_nat,Abs2: set_nat > nat,A: set_set_nat] :
% 4.69/4.99 ( ( type_d3768499744764857476et_nat @ Rep2 @ Abs2 @ A )
% 4.69/4.99 => ( ( image_nat_set_nat @ Rep2 @ top_top_set_nat )
% 4.69/4.99 = A ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_definition.Rep_range
% 4.69/4.99 thf(fact_4199_type__definition_ORep__range,axiom,
% 4.69/4.99 ! [Rep2: nat > nat,Abs2: nat > nat,A: set_nat] :
% 4.69/4.99 ( ( type_d6250493948777748686at_nat @ Rep2 @ Abs2 @ A )
% 4.69/4.99 => ( ( image_nat_nat2 @ Rep2 @ top_top_set_nat )
% 4.69/4.99 = A ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_definition.Rep_range
% 4.69/4.99 thf(fact_4200_type__definition_ORep__range,axiom,
% 4.69/4.99 ! [Rep2: nat > code_integer,Abs2: code_integer > nat,A: set_Code_integer] :
% 4.69/4.99 ( ( type_d8633139899873770843nteger @ Rep2 @ Abs2 @ A )
% 4.69/4.99 => ( ( image_1215581382706833972nteger @ Rep2 @ top_top_set_nat )
% 4.69/4.99 = A ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_definition.Rep_range
% 4.69/4.99 thf(fact_4201_type__definition_ORep__range,axiom,
% 4.69/4.99 ! [Rep2: assn > produc3658429121746597890et_nat > $o,Abs2: ( produc3658429121746597890et_nat > $o ) > assn,A: set_Pr4532377907799695533_nat_o] :
% 4.69/4.99 ( ( type_d3909072315231072503_nat_o @ Rep2 @ Abs2 @ A )
% 4.69/4.99 => ( ( image_5465535159827709278_nat_o @ Rep2 @ top_top_set_assn )
% 4.69/4.99 = A ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_definition.Rep_range
% 4.69/4.99 thf(fact_4202_type__definition_ORep__range,axiom,
% 4.69/4.99 ! [Rep2: code_integer > int,Abs2: int > code_integer,A: set_int] :
% 4.69/4.99 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ A )
% 4.69/4.99 => ( ( image_948535463418740880er_int @ Rep2 @ top_to4645266643341252675nteger )
% 4.69/4.99 = A ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_definition.Rep_range
% 4.69/4.99 thf(fact_4203_type__definition_ORep__range,axiom,
% 4.69/4.99 ! [Rep2: product_unit > $o,Abs2: $o > product_unit,A: set_o] :
% 4.69/4.99 ( ( type_d6188575255521822967unit_o @ Rep2 @ Abs2 @ A )
% 4.69/4.99 => ( ( image_Product_unit_o2 @ Rep2 @ top_to1996260823553986621t_unit )
% 4.69/4.99 = A ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_definition.Rep_range
% 4.69/4.99 thf(fact_4204_type__definition_ORep__range,axiom,
% 4.69/4.99 ! [Rep2: code_natural > nat,Abs2: nat > code_natural,A: set_nat] :
% 4.69/4.99 ( ( type_d4410041424927559462al_nat @ Rep2 @ Abs2 @ A )
% 4.69/4.99 => ( ( image_6215854944615398399al_nat @ Rep2 @ top_to9103716463852441742atural )
% 4.69/4.99 = A ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_definition.Rep_range
% 4.69/4.99 thf(fact_4205_refl__Id,axiom,
% 4.69/4.99 refl_on_Product_unit @ top_to1996260823553986621t_unit @ id_Product_unit ).
% 4.69/4.99
% 4.69/4.99 % refl_Id
% 4.69/4.99 thf(fact_4206_refl__Id,axiom,
% 4.69/4.99 refl_on_o @ top_top_set_o @ id_o2 ).
% 4.69/4.99
% 4.69/4.99 % refl_Id
% 4.69/4.99 thf(fact_4207_refl__Id,axiom,
% 4.69/4.99 refl_on_nat @ top_top_set_nat @ id_nat ).
% 4.69/4.99
% 4.69/4.99 % refl_Id
% 4.69/4.99 thf(fact_4208_refl__Id,axiom,
% 4.69/4.99 refl_on_int @ top_top_set_int @ id_int ).
% 4.69/4.99
% 4.69/4.99 % refl_Id
% 4.69/4.99 thf(fact_4209_boolean__algebra_Ocomplement__unique,axiom,
% 4.69/4.99 ! [A2: product_unit,X: product_unit,Y: product_unit] :
% 4.69/4.99 ( ( ( inf_inf_Product_unit @ A2 @ X )
% 4.69/4.99 = bot_bot_Product_unit )
% 4.69/4.99 => ( ( ( sup_sup_Product_unit @ A2 @ X )
% 4.69/4.99 = top_top_Product_unit )
% 4.69/4.99 => ( ( ( inf_inf_Product_unit @ A2 @ Y )
% 4.69/4.99 = bot_bot_Product_unit )
% 4.69/4.99 => ( ( ( sup_sup_Product_unit @ A2 @ Y )
% 4.69/4.99 = top_top_Product_unit )
% 4.69/4.99 => ( X = Y ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % boolean_algebra.complement_unique
% 4.69/4.99 thf(fact_4210_boolean__algebra_Ocomplement__unique,axiom,
% 4.69/4.99 ! [A2: set_Pr4532377907799695533_nat_o,X: set_Pr4532377907799695533_nat_o,Y: set_Pr4532377907799695533_nat_o] :
% 4.69/4.99 ( ( ( inf_in1906310914598751387_nat_o @ A2 @ X )
% 4.69/4.99 = bot_bo7824918357723582233_nat_o )
% 4.69/4.99 => ( ( ( sup_su5209123915105501825_nat_o @ A2 @ X )
% 4.69/4.99 = top_to4869887016220417533_nat_o )
% 4.69/4.99 => ( ( ( inf_in1906310914598751387_nat_o @ A2 @ Y )
% 4.69/4.99 = bot_bo7824918357723582233_nat_o )
% 4.69/4.99 => ( ( ( sup_su5209123915105501825_nat_o @ A2 @ Y )
% 4.69/4.99 = top_to4869887016220417533_nat_o )
% 4.69/4.99 => ( X = Y ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % boolean_algebra.complement_unique
% 4.69/4.99 thf(fact_4211_boolean__algebra_Ocomplement__unique,axiom,
% 4.69/4.99 ! [A2: assn,X: assn,Y: assn] :
% 4.69/4.99 ( ( ( inf_inf_assn @ A2 @ X )
% 4.69/4.99 = bot_bot_assn )
% 4.69/4.99 => ( ( ( sup_sup_assn @ A2 @ X )
% 4.69/4.99 = top_top_assn )
% 4.69/4.99 => ( ( ( inf_inf_assn @ A2 @ Y )
% 4.69/4.99 = bot_bot_assn )
% 4.69/4.99 => ( ( ( sup_sup_assn @ A2 @ Y )
% 4.69/4.99 = top_top_assn )
% 4.69/4.99 => ( X = Y ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % boolean_algebra.complement_unique
% 4.69/4.99 thf(fact_4212_boolean__algebra_Ocomplement__unique,axiom,
% 4.69/4.99 ! [A2: set_Product_unit,X: set_Product_unit,Y: set_Product_unit] :
% 4.69/4.99 ( ( ( inf_in4660618365625256667t_unit @ A2 @ X )
% 4.69/4.99 = bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ( ( ( sup_su793286257634532545t_unit @ A2 @ X )
% 4.69/4.99 = top_to1996260823553986621t_unit )
% 4.69/4.99 => ( ( ( inf_in4660618365625256667t_unit @ A2 @ Y )
% 4.69/4.99 = bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ( ( ( sup_su793286257634532545t_unit @ A2 @ Y )
% 4.69/4.99 = top_to1996260823553986621t_unit )
% 4.69/4.99 => ( X = Y ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % boolean_algebra.complement_unique
% 4.69/4.99 thf(fact_4213_boolean__algebra_Ocomplement__unique,axiom,
% 4.69/4.99 ! [A2: set_o,X: set_o,Y: set_o] :
% 4.69/4.99 ( ( ( inf_inf_set_o @ A2 @ X )
% 4.69/4.99 = bot_bot_set_o )
% 4.69/4.99 => ( ( ( sup_sup_set_o @ A2 @ X )
% 4.69/4.99 = top_top_set_o )
% 4.69/4.99 => ( ( ( inf_inf_set_o @ A2 @ Y )
% 4.69/4.99 = bot_bot_set_o )
% 4.69/4.99 => ( ( ( sup_sup_set_o @ A2 @ Y )
% 4.69/4.99 = top_top_set_o )
% 4.69/4.99 => ( X = Y ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % boolean_algebra.complement_unique
% 4.69/4.99 thf(fact_4214_boolean__algebra_Ocomplement__unique,axiom,
% 4.69/4.99 ! [A2: set_nat,X: set_nat,Y: set_nat] :
% 4.69/4.99 ( ( ( inf_inf_set_nat @ A2 @ X )
% 4.69/4.99 = bot_bot_set_nat )
% 4.69/4.99 => ( ( ( sup_sup_set_nat @ A2 @ X )
% 4.69/4.99 = top_top_set_nat )
% 4.69/4.99 => ( ( ( inf_inf_set_nat @ A2 @ Y )
% 4.69/4.99 = bot_bot_set_nat )
% 4.69/4.99 => ( ( ( sup_sup_set_nat @ A2 @ Y )
% 4.69/4.99 = top_top_set_nat )
% 4.69/4.99 => ( X = Y ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % boolean_algebra.complement_unique
% 4.69/4.99 thf(fact_4215_boolean__algebra_Ocomplement__unique,axiom,
% 4.69/4.99 ! [A2: set_int,X: set_int,Y: set_int] :
% 4.69/4.99 ( ( ( inf_inf_set_int @ A2 @ X )
% 4.69/4.99 = bot_bot_set_int )
% 4.69/4.99 => ( ( ( sup_sup_set_int @ A2 @ X )
% 4.69/4.99 = top_top_set_int )
% 4.69/4.99 => ( ( ( inf_inf_set_int @ A2 @ Y )
% 4.69/4.99 = bot_bot_set_int )
% 4.69/4.99 => ( ( ( sup_sup_set_int @ A2 @ Y )
% 4.69/4.99 = top_top_set_int )
% 4.69/4.99 => ( X = Y ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % boolean_algebra.complement_unique
% 4.69/4.99 thf(fact_4216_union__fold__insert,axiom,
% 4.69/4.99 ! [A: set_int,B4: set_int] :
% 4.69/4.99 ( ( finite_finite_int @ A )
% 4.69/4.99 => ( ( sup_sup_set_int @ A @ B4 )
% 4.69/4.99 = ( finite1723285575846220376et_int @ insert_int @ B4 @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % union_fold_insert
% 4.69/4.99 thf(fact_4217_union__fold__insert,axiom,
% 4.69/4.99 ! [A: set_o,B4: set_o] :
% 4.69/4.99 ( ( finite_finite_o @ A )
% 4.69/4.99 => ( ( sup_sup_set_o @ A @ B4 )
% 4.69/4.99 = ( finite_fold_o_set_o @ insert_o @ B4 @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % union_fold_insert
% 4.69/4.99 thf(fact_4218_union__fold__insert,axiom,
% 4.69/4.99 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.99 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.99 => ( ( sup_su793286257634532545t_unit @ A @ B4 )
% 4.69/4.99 = ( finite2740360166580943592t_unit @ insert_Product_unit @ B4 @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % union_fold_insert
% 4.69/4.99 thf(fact_4219_union__fold__insert,axiom,
% 4.69/4.99 ! [A: set_Code_integer,B4: set_Code_integer] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.99 => ( ( sup_su848401254843788991nteger @ A @ B4 )
% 4.69/4.99 = ( finite7486036041278456378nteger @ insert_Code_integer @ B4 @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % union_fold_insert
% 4.69/4.99 thf(fact_4220_union__fold__insert,axiom,
% 4.69/4.99 ! [A: set_nat,B4: set_nat] :
% 4.69/4.99 ( ( finite_finite_nat @ A )
% 4.69/4.99 => ( ( sup_sup_set_nat @ A @ B4 )
% 4.69/4.99 = ( finite5529483035118572448et_nat @ insert_nat @ B4 @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % union_fold_insert
% 4.69/4.99 thf(fact_4221_finite__linorder__min__induct,axiom,
% 4.69/4.99 ! [A: set_Product_unit,P: set_Product_unit > $o] :
% 4.69/4.99 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.99 => ( ( P @ bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ( ! [B2: product_unit,A9: set_Product_unit] :
% 4.69/4.99 ( ( finite4290736615968046902t_unit @ A9 )
% 4.69/4.99 => ( ! [X6: product_unit] :
% 4.69/4.99 ( ( member_Product_unit @ X6 @ A9 )
% 4.69/4.99 => ( ord_le361264281704409273t_unit @ B2 @ X6 ) )
% 4.69/4.99 => ( ( P @ A9 )
% 4.69/4.99 => ( P @ ( insert_Product_unit @ B2 @ A9 ) ) ) ) )
% 4.69/4.99 => ( P @ A ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % finite_linorder_min_induct
% 4.69/4.99 thf(fact_4222_finite__linorder__min__induct,axiom,
% 4.69/4.99 ! [A: set_o,P: set_o > $o] :
% 4.69/4.99 ( ( finite_finite_o @ A )
% 4.69/4.99 => ( ( P @ bot_bot_set_o )
% 4.69/4.99 => ( ! [B2: $o,A9: set_o] :
% 4.69/4.99 ( ( finite_finite_o @ A9 )
% 4.69/4.99 => ( ! [X6: $o] :
% 4.69/4.99 ( ( member_o @ X6 @ A9 )
% 4.69/4.99 => ( ord_less_o @ B2 @ X6 ) )
% 4.69/4.99 => ( ( P @ A9 )
% 4.69/4.99 => ( P @ ( insert_o @ B2 @ A9 ) ) ) ) )
% 4.69/4.99 => ( P @ A ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % finite_linorder_min_induct
% 4.69/4.99 thf(fact_4223_finite__linorder__min__induct,axiom,
% 4.69/4.99 ! [A: set_nat,P: set_nat > $o] :
% 4.69/4.99 ( ( finite_finite_nat @ A )
% 4.69/4.99 => ( ( P @ bot_bot_set_nat )
% 4.69/4.99 => ( ! [B2: nat,A9: set_nat] :
% 4.69/4.99 ( ( finite_finite_nat @ A9 )
% 4.69/4.99 => ( ! [X6: nat] :
% 4.69/4.99 ( ( member_nat @ X6 @ A9 )
% 4.69/4.99 => ( ord_less_nat @ B2 @ X6 ) )
% 4.69/4.99 => ( ( P @ A9 )
% 4.69/4.99 => ( P @ ( insert_nat @ B2 @ A9 ) ) ) ) )
% 4.69/4.99 => ( P @ A ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % finite_linorder_min_induct
% 4.69/4.99 thf(fact_4224_finite__linorder__min__induct,axiom,
% 4.69/4.99 ! [A: set_int,P: set_int > $o] :
% 4.69/4.99 ( ( finite_finite_int @ A )
% 4.69/4.99 => ( ( P @ bot_bot_set_int )
% 4.69/4.99 => ( ! [B2: int,A9: set_int] :
% 4.69/4.99 ( ( finite_finite_int @ A9 )
% 4.69/4.99 => ( ! [X6: int] :
% 4.69/4.99 ( ( member_int @ X6 @ A9 )
% 4.69/4.99 => ( ord_less_int @ B2 @ X6 ) )
% 4.69/4.99 => ( ( P @ A9 )
% 4.69/4.99 => ( P @ ( insert_int @ B2 @ A9 ) ) ) ) )
% 4.69/4.99 => ( P @ A ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % finite_linorder_min_induct
% 4.69/4.99 thf(fact_4225_finite__linorder__min__induct,axiom,
% 4.69/4.99 ! [A: set_Code_integer,P: set_Code_integer > $o] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.99 => ( ( P @ bot_bo3990330152332043303nteger )
% 4.69/4.99 => ( ! [B2: code_integer,A9: set_Code_integer] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ A9 )
% 4.69/4.99 => ( ! [X6: code_integer] :
% 4.69/4.99 ( ( member_Code_integer @ X6 @ A9 )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ B2 @ X6 ) )
% 4.69/4.99 => ( ( P @ A9 )
% 4.69/4.99 => ( P @ ( insert_Code_integer @ B2 @ A9 ) ) ) ) )
% 4.69/4.99 => ( P @ A ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % finite_linorder_min_induct
% 4.69/4.99 thf(fact_4226_finite__linorder__min__induct,axiom,
% 4.69/4.99 ! [A: set_rat,P: set_rat > $o] :
% 4.69/4.99 ( ( finite_finite_rat @ A )
% 4.69/4.99 => ( ( P @ bot_bot_set_rat )
% 4.69/4.99 => ( ! [B2: rat,A9: set_rat] :
% 4.69/4.99 ( ( finite_finite_rat @ A9 )
% 4.69/4.99 => ( ! [X6: rat] :
% 4.69/4.99 ( ( member_rat @ X6 @ A9 )
% 4.69/4.99 => ( ord_less_rat @ B2 @ X6 ) )
% 4.69/4.99 => ( ( P @ A9 )
% 4.69/4.99 => ( P @ ( insert_rat @ B2 @ A9 ) ) ) ) )
% 4.69/4.99 => ( P @ A ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % finite_linorder_min_induct
% 4.69/4.99 thf(fact_4227_finite__linorder__max__induct,axiom,
% 4.69/4.99 ! [A: set_Product_unit,P: set_Product_unit > $o] :
% 4.69/4.99 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.99 => ( ( P @ bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ( ! [B2: product_unit,A9: set_Product_unit] :
% 4.69/4.99 ( ( finite4290736615968046902t_unit @ A9 )
% 4.69/4.99 => ( ! [X6: product_unit] :
% 4.69/4.99 ( ( member_Product_unit @ X6 @ A9 )
% 4.69/4.99 => ( ord_le361264281704409273t_unit @ X6 @ B2 ) )
% 4.69/4.99 => ( ( P @ A9 )
% 4.69/4.99 => ( P @ ( insert_Product_unit @ B2 @ A9 ) ) ) ) )
% 4.69/4.99 => ( P @ A ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % finite_linorder_max_induct
% 4.69/4.99 thf(fact_4228_finite__linorder__max__induct,axiom,
% 4.69/4.99 ! [A: set_o,P: set_o > $o] :
% 4.69/4.99 ( ( finite_finite_o @ A )
% 4.69/4.99 => ( ( P @ bot_bot_set_o )
% 4.69/4.99 => ( ! [B2: $o,A9: set_o] :
% 4.69/4.99 ( ( finite_finite_o @ A9 )
% 4.69/4.99 => ( ! [X6: $o] :
% 4.69/4.99 ( ( member_o @ X6 @ A9 )
% 4.69/4.99 => ( ord_less_o @ X6 @ B2 ) )
% 4.69/4.99 => ( ( P @ A9 )
% 4.69/4.99 => ( P @ ( insert_o @ B2 @ A9 ) ) ) ) )
% 4.69/4.99 => ( P @ A ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % finite_linorder_max_induct
% 4.69/4.99 thf(fact_4229_finite__linorder__max__induct,axiom,
% 4.69/4.99 ! [A: set_nat,P: set_nat > $o] :
% 4.69/4.99 ( ( finite_finite_nat @ A )
% 4.69/4.99 => ( ( P @ bot_bot_set_nat )
% 4.69/4.99 => ( ! [B2: nat,A9: set_nat] :
% 4.69/4.99 ( ( finite_finite_nat @ A9 )
% 4.69/4.99 => ( ! [X6: nat] :
% 4.69/4.99 ( ( member_nat @ X6 @ A9 )
% 4.69/4.99 => ( ord_less_nat @ X6 @ B2 ) )
% 4.69/4.99 => ( ( P @ A9 )
% 4.69/4.99 => ( P @ ( insert_nat @ B2 @ A9 ) ) ) ) )
% 4.69/4.99 => ( P @ A ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % finite_linorder_max_induct
% 4.69/4.99 thf(fact_4230_finite__linorder__max__induct,axiom,
% 4.69/4.99 ! [A: set_int,P: set_int > $o] :
% 4.69/4.99 ( ( finite_finite_int @ A )
% 4.69/4.99 => ( ( P @ bot_bot_set_int )
% 4.69/4.99 => ( ! [B2: int,A9: set_int] :
% 4.69/4.99 ( ( finite_finite_int @ A9 )
% 4.69/4.99 => ( ! [X6: int] :
% 4.69/4.99 ( ( member_int @ X6 @ A9 )
% 4.69/4.99 => ( ord_less_int @ X6 @ B2 ) )
% 4.69/4.99 => ( ( P @ A9 )
% 4.69/4.99 => ( P @ ( insert_int @ B2 @ A9 ) ) ) ) )
% 4.69/4.99 => ( P @ A ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % finite_linorder_max_induct
% 4.69/4.99 thf(fact_4231_finite__linorder__max__induct,axiom,
% 4.69/4.99 ! [A: set_Code_integer,P: set_Code_integer > $o] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.99 => ( ( P @ bot_bo3990330152332043303nteger )
% 4.69/4.99 => ( ! [B2: code_integer,A9: set_Code_integer] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ A9 )
% 4.69/4.99 => ( ! [X6: code_integer] :
% 4.69/4.99 ( ( member_Code_integer @ X6 @ A9 )
% 4.69/4.99 => ( ord_le6747313008572928689nteger @ X6 @ B2 ) )
% 4.69/4.99 => ( ( P @ A9 )
% 4.69/4.99 => ( P @ ( insert_Code_integer @ B2 @ A9 ) ) ) ) )
% 4.69/4.99 => ( P @ A ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % finite_linorder_max_induct
% 4.69/4.99 thf(fact_4232_finite__linorder__max__induct,axiom,
% 4.69/4.99 ! [A: set_rat,P: set_rat > $o] :
% 4.69/4.99 ( ( finite_finite_rat @ A )
% 4.69/4.99 => ( ( P @ bot_bot_set_rat )
% 4.69/4.99 => ( ! [B2: rat,A9: set_rat] :
% 4.69/4.99 ( ( finite_finite_rat @ A9 )
% 4.69/4.99 => ( ! [X6: rat] :
% 4.69/4.99 ( ( member_rat @ X6 @ A9 )
% 4.69/4.99 => ( ord_less_rat @ X6 @ B2 ) )
% 4.69/4.99 => ( ( P @ A9 )
% 4.69/4.99 => ( P @ ( insert_rat @ B2 @ A9 ) ) ) ) )
% 4.69/4.99 => ( P @ A ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % finite_linorder_max_induct
% 4.69/4.99 thf(fact_4233_finite__Sup__less__iff,axiom,
% 4.69/4.99 ! [X4: set_int,A2: int] :
% 4.69/4.99 ( ( finite_finite_int @ X4 )
% 4.69/4.99 => ( ( X4 != bot_bot_set_int )
% 4.69/4.99 => ( ( ord_less_int @ ( complete_Sup_Sup_int @ X4 ) @ A2 )
% 4.69/4.99 = ( ! [X2: int] :
% 4.69/4.99 ( ( member_int @ X2 @ X4 )
% 4.69/4.99 => ( ord_less_int @ X2 @ A2 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % finite_Sup_less_iff
% 4.69/4.99 thf(fact_4234_finite__Sup__less__iff,axiom,
% 4.69/4.99 ! [X4: set_nat,A2: nat] :
% 4.69/4.99 ( ( finite_finite_nat @ X4 )
% 4.69/4.99 => ( ( X4 != bot_bot_set_nat )
% 4.69/4.99 => ( ( ord_less_nat @ ( complete_Sup_Sup_nat @ X4 ) @ A2 )
% 4.69/4.99 = ( ! [X2: nat] :
% 4.69/4.99 ( ( member_nat @ X2 @ X4 )
% 4.69/4.99 => ( ord_less_nat @ X2 @ A2 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % finite_Sup_less_iff
% 4.69/4.99 thf(fact_4235_finite__Sup__less__iff,axiom,
% 4.69/4.99 ! [X4: set_Product_unit,A2: product_unit] :
% 4.69/4.99 ( ( finite4290736615968046902t_unit @ X4 )
% 4.69/4.99 => ( ( X4 != bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ( ( ord_le361264281704409273t_unit @ ( comple4687483117567863418t_unit @ X4 ) @ A2 )
% 4.69/4.99 = ( ! [X2: product_unit] :
% 4.69/4.99 ( ( member_Product_unit @ X2 @ X4 )
% 4.69/4.99 => ( ord_le361264281704409273t_unit @ X2 @ A2 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % finite_Sup_less_iff
% 4.69/4.99 thf(fact_4236_Max__eq__iff,axiom,
% 4.69/4.99 ! [A: set_Code_integer,M4: code_integer] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.99 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/4.99 => ( ( ( lattic4901227151466704046nteger @ A )
% 4.69/4.99 = M4 )
% 4.69/4.99 = ( ( member_Code_integer @ M4 @ A )
% 4.69/4.99 & ! [X2: code_integer] :
% 4.69/4.99 ( ( member_Code_integer @ X2 @ A )
% 4.69/4.99 => ( ord_le3102999989581377725nteger @ X2 @ M4 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_eq_iff
% 4.69/4.99 thf(fact_4237_Max__eq__iff,axiom,
% 4.69/4.99 ! [A: set_Product_unit,M4: product_unit] :
% 4.69/4.99 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.99 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ( ( ( lattic1210392890313158908t_unit @ A )
% 4.69/4.99 = M4 )
% 4.69/4.99 = ( ( member_Product_unit @ M4 @ A )
% 4.69/4.99 & ! [X2: product_unit] :
% 4.69/4.99 ( ( member_Product_unit @ X2 @ A )
% 4.69/4.99 => ( ord_le3221252021190050221t_unit @ X2 @ M4 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_eq_iff
% 4.69/4.99 thf(fact_4238_Max__eq__iff,axiom,
% 4.69/4.99 ! [A: set_o,M4: $o] :
% 4.69/4.99 ( ( finite_finite_o @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_o )
% 4.69/4.99 => ( ( ( lattic1921953407002678535_Max_o @ A )
% 4.69/4.99 = M4 )
% 4.69/4.99 = ( ( member_o @ M4 @ A )
% 4.69/4.99 & ! [X2: $o] :
% 4.69/4.99 ( ( member_o @ X2 @ A )
% 4.69/4.99 => ( ord_less_eq_o @ X2 @ M4 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_eq_iff
% 4.69/4.99 thf(fact_4239_Max__eq__iff,axiom,
% 4.69/4.99 ! [A: set_rat,M4: rat] :
% 4.69/4.99 ( ( finite_finite_rat @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_rat )
% 4.69/4.99 => ( ( ( lattic7630753665789217321ax_rat @ A )
% 4.69/4.99 = M4 )
% 4.69/4.99 = ( ( member_rat @ M4 @ A )
% 4.69/4.99 & ! [X2: rat] :
% 4.69/4.99 ( ( member_rat @ X2 @ A )
% 4.69/4.99 => ( ord_less_eq_rat @ X2 @ M4 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_eq_iff
% 4.69/4.99 thf(fact_4240_Max__eq__iff,axiom,
% 4.69/4.99 ! [A: set_int,M4: int] :
% 4.69/4.99 ( ( finite_finite_int @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_int )
% 4.69/4.99 => ( ( ( lattic8263393255366662781ax_int @ A )
% 4.69/4.99 = M4 )
% 4.69/4.99 = ( ( member_int @ M4 @ A )
% 4.69/4.99 & ! [X2: int] :
% 4.69/4.99 ( ( member_int @ X2 @ A )
% 4.69/4.99 => ( ord_less_eq_int @ X2 @ M4 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_eq_iff
% 4.69/4.99 thf(fact_4241_Max__eq__iff,axiom,
% 4.69/4.99 ! [A: set_nat,M4: nat] :
% 4.69/4.99 ( ( finite_finite_nat @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_nat )
% 4.69/4.99 => ( ( ( lattic8265883725875713057ax_nat @ A )
% 4.69/4.99 = M4 )
% 4.69/4.99 = ( ( member_nat @ M4 @ A )
% 4.69/4.99 & ! [X2: nat] :
% 4.69/4.99 ( ( member_nat @ X2 @ A )
% 4.69/4.99 => ( ord_less_eq_nat @ X2 @ M4 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_eq_iff
% 4.69/4.99 thf(fact_4242_Max__ge__iff,axiom,
% 4.69/4.99 ! [A: set_Code_integer,X: code_integer] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.99 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/4.99 => ( ( ord_le3102999989581377725nteger @ X @ ( lattic4901227151466704046nteger @ A ) )
% 4.69/4.99 = ( ? [X2: code_integer] :
% 4.69/4.99 ( ( member_Code_integer @ X2 @ A )
% 4.69/4.99 & ( ord_le3102999989581377725nteger @ X @ X2 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_ge_iff
% 4.69/4.99 thf(fact_4243_Max__ge__iff,axiom,
% 4.69/4.99 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.99 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.99 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ( ( ord_le3221252021190050221t_unit @ X @ ( lattic1210392890313158908t_unit @ A ) )
% 4.69/4.99 = ( ? [X2: product_unit] :
% 4.69/4.99 ( ( member_Product_unit @ X2 @ A )
% 4.69/4.99 & ( ord_le3221252021190050221t_unit @ X @ X2 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_ge_iff
% 4.69/4.99 thf(fact_4244_Max__ge__iff,axiom,
% 4.69/4.99 ! [A: set_o,X: $o] :
% 4.69/4.99 ( ( finite_finite_o @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_o )
% 4.69/4.99 => ( ( ord_less_eq_o @ X @ ( lattic1921953407002678535_Max_o @ A ) )
% 4.69/4.99 = ( ? [X2: $o] :
% 4.69/4.99 ( ( member_o @ X2 @ A )
% 4.69/4.99 & ( ord_less_eq_o @ X @ X2 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_ge_iff
% 4.69/4.99 thf(fact_4245_Max__ge__iff,axiom,
% 4.69/4.99 ! [A: set_rat,X: rat] :
% 4.69/4.99 ( ( finite_finite_rat @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_rat )
% 4.69/4.99 => ( ( ord_less_eq_rat @ X @ ( lattic7630753665789217321ax_rat @ A ) )
% 4.69/4.99 = ( ? [X2: rat] :
% 4.69/4.99 ( ( member_rat @ X2 @ A )
% 4.69/4.99 & ( ord_less_eq_rat @ X @ X2 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_ge_iff
% 4.69/4.99 thf(fact_4246_Max__ge__iff,axiom,
% 4.69/4.99 ! [A: set_int,X: int] :
% 4.69/4.99 ( ( finite_finite_int @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_int )
% 4.69/4.99 => ( ( ord_less_eq_int @ X @ ( lattic8263393255366662781ax_int @ A ) )
% 4.69/4.99 = ( ? [X2: int] :
% 4.69/4.99 ( ( member_int @ X2 @ A )
% 4.69/4.99 & ( ord_less_eq_int @ X @ X2 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_ge_iff
% 4.69/4.99 thf(fact_4247_Max__ge__iff,axiom,
% 4.69/4.99 ! [A: set_nat,X: nat] :
% 4.69/4.99 ( ( finite_finite_nat @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_nat )
% 4.69/4.99 => ( ( ord_less_eq_nat @ X @ ( lattic8265883725875713057ax_nat @ A ) )
% 4.69/4.99 = ( ? [X2: nat] :
% 4.69/4.99 ( ( member_nat @ X2 @ A )
% 4.69/4.99 & ( ord_less_eq_nat @ X @ X2 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_ge_iff
% 4.69/4.99 thf(fact_4248_eq__Max__iff,axiom,
% 4.69/4.99 ! [A: set_Code_integer,M4: code_integer] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.99 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/4.99 => ( ( M4
% 4.69/4.99 = ( lattic4901227151466704046nteger @ A ) )
% 4.69/4.99 = ( ( member_Code_integer @ M4 @ A )
% 4.69/4.99 & ! [X2: code_integer] :
% 4.69/4.99 ( ( member_Code_integer @ X2 @ A )
% 4.69/4.99 => ( ord_le3102999989581377725nteger @ X2 @ M4 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % eq_Max_iff
% 4.69/4.99 thf(fact_4249_eq__Max__iff,axiom,
% 4.69/4.99 ! [A: set_Product_unit,M4: product_unit] :
% 4.69/4.99 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.99 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ( ( M4
% 4.69/4.99 = ( lattic1210392890313158908t_unit @ A ) )
% 4.69/4.99 = ( ( member_Product_unit @ M4 @ A )
% 4.69/4.99 & ! [X2: product_unit] :
% 4.69/4.99 ( ( member_Product_unit @ X2 @ A )
% 4.69/4.99 => ( ord_le3221252021190050221t_unit @ X2 @ M4 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % eq_Max_iff
% 4.69/4.99 thf(fact_4250_eq__Max__iff,axiom,
% 4.69/4.99 ! [A: set_o,M4: $o] :
% 4.69/4.99 ( ( finite_finite_o @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_o )
% 4.69/4.99 => ( ( M4
% 4.69/4.99 = ( lattic1921953407002678535_Max_o @ A ) )
% 4.69/4.99 = ( ( member_o @ M4 @ A )
% 4.69/4.99 & ! [X2: $o] :
% 4.69/4.99 ( ( member_o @ X2 @ A )
% 4.69/4.99 => ( ord_less_eq_o @ X2 @ M4 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % eq_Max_iff
% 4.69/4.99 thf(fact_4251_eq__Max__iff,axiom,
% 4.69/4.99 ! [A: set_rat,M4: rat] :
% 4.69/4.99 ( ( finite_finite_rat @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_rat )
% 4.69/4.99 => ( ( M4
% 4.69/4.99 = ( lattic7630753665789217321ax_rat @ A ) )
% 4.69/4.99 = ( ( member_rat @ M4 @ A )
% 4.69/4.99 & ! [X2: rat] :
% 4.69/4.99 ( ( member_rat @ X2 @ A )
% 4.69/4.99 => ( ord_less_eq_rat @ X2 @ M4 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % eq_Max_iff
% 4.69/4.99 thf(fact_4252_eq__Max__iff,axiom,
% 4.69/4.99 ! [A: set_int,M4: int] :
% 4.69/4.99 ( ( finite_finite_int @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_int )
% 4.69/4.99 => ( ( M4
% 4.69/4.99 = ( lattic8263393255366662781ax_int @ A ) )
% 4.69/4.99 = ( ( member_int @ M4 @ A )
% 4.69/4.99 & ! [X2: int] :
% 4.69/4.99 ( ( member_int @ X2 @ A )
% 4.69/4.99 => ( ord_less_eq_int @ X2 @ M4 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % eq_Max_iff
% 4.69/4.99 thf(fact_4253_eq__Max__iff,axiom,
% 4.69/4.99 ! [A: set_nat,M4: nat] :
% 4.69/4.99 ( ( finite_finite_nat @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_nat )
% 4.69/4.99 => ( ( M4
% 4.69/4.99 = ( lattic8265883725875713057ax_nat @ A ) )
% 4.69/4.99 = ( ( member_nat @ M4 @ A )
% 4.69/4.99 & ! [X2: nat] :
% 4.69/4.99 ( ( member_nat @ X2 @ A )
% 4.69/4.99 => ( ord_less_eq_nat @ X2 @ M4 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % eq_Max_iff
% 4.69/4.99 thf(fact_4254_Max_OboundedE,axiom,
% 4.69/4.99 ! [A: set_Code_integer,X: code_integer] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.99 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/4.99 => ( ( ord_le3102999989581377725nteger @ ( lattic4901227151466704046nteger @ A ) @ X )
% 4.69/4.99 => ! [A10: code_integer] :
% 4.69/4.99 ( ( member_Code_integer @ A10 @ A )
% 4.69/4.99 => ( ord_le3102999989581377725nteger @ A10 @ X ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max.boundedE
% 4.69/4.99 thf(fact_4255_Max_OboundedE,axiom,
% 4.69/4.99 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.99 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.99 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ( ( ord_le3221252021190050221t_unit @ ( lattic1210392890313158908t_unit @ A ) @ X )
% 4.69/4.99 => ! [A10: product_unit] :
% 4.69/4.99 ( ( member_Product_unit @ A10 @ A )
% 4.69/4.99 => ( ord_le3221252021190050221t_unit @ A10 @ X ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max.boundedE
% 4.69/4.99 thf(fact_4256_Max_OboundedE,axiom,
% 4.69/4.99 ! [A: set_o,X: $o] :
% 4.69/4.99 ( ( finite_finite_o @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_o )
% 4.69/4.99 => ( ( ord_less_eq_o @ ( lattic1921953407002678535_Max_o @ A ) @ X )
% 4.69/4.99 => ! [A10: $o] :
% 4.69/4.99 ( ( member_o @ A10 @ A )
% 4.69/4.99 => ( ord_less_eq_o @ A10 @ X ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max.boundedE
% 4.69/4.99 thf(fact_4257_Max_OboundedE,axiom,
% 4.69/4.99 ! [A: set_rat,X: rat] :
% 4.69/4.99 ( ( finite_finite_rat @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_rat )
% 4.69/4.99 => ( ( ord_less_eq_rat @ ( lattic7630753665789217321ax_rat @ A ) @ X )
% 4.69/4.99 => ! [A10: rat] :
% 4.69/4.99 ( ( member_rat @ A10 @ A )
% 4.69/4.99 => ( ord_less_eq_rat @ A10 @ X ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max.boundedE
% 4.69/4.99 thf(fact_4258_Max_OboundedE,axiom,
% 4.69/4.99 ! [A: set_int,X: int] :
% 4.69/4.99 ( ( finite_finite_int @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_int )
% 4.69/4.99 => ( ( ord_less_eq_int @ ( lattic8263393255366662781ax_int @ A ) @ X )
% 4.69/4.99 => ! [A10: int] :
% 4.69/4.99 ( ( member_int @ A10 @ A )
% 4.69/4.99 => ( ord_less_eq_int @ A10 @ X ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max.boundedE
% 4.69/4.99 thf(fact_4259_Max_OboundedE,axiom,
% 4.69/4.99 ! [A: set_nat,X: nat] :
% 4.69/4.99 ( ( finite_finite_nat @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_nat )
% 4.69/4.99 => ( ( ord_less_eq_nat @ ( lattic8265883725875713057ax_nat @ A ) @ X )
% 4.69/4.99 => ! [A10: nat] :
% 4.69/4.99 ( ( member_nat @ A10 @ A )
% 4.69/4.99 => ( ord_less_eq_nat @ A10 @ X ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max.boundedE
% 4.69/4.99 thf(fact_4260_Max_OboundedI,axiom,
% 4.69/4.99 ! [A: set_Code_integer,X: code_integer] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.99 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/4.99 => ( ! [A4: code_integer] :
% 4.69/4.99 ( ( member_Code_integer @ A4 @ A )
% 4.69/4.99 => ( ord_le3102999989581377725nteger @ A4 @ X ) )
% 4.69/4.99 => ( ord_le3102999989581377725nteger @ ( lattic4901227151466704046nteger @ A ) @ X ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max.boundedI
% 4.69/4.99 thf(fact_4261_Max_OboundedI,axiom,
% 4.69/4.99 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.99 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.99 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ( ! [A4: product_unit] :
% 4.69/4.99 ( ( member_Product_unit @ A4 @ A )
% 4.69/4.99 => ( ord_le3221252021190050221t_unit @ A4 @ X ) )
% 4.69/4.99 => ( ord_le3221252021190050221t_unit @ ( lattic1210392890313158908t_unit @ A ) @ X ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max.boundedI
% 4.69/4.99 thf(fact_4262_Max_OboundedI,axiom,
% 4.69/4.99 ! [A: set_o,X: $o] :
% 4.69/4.99 ( ( finite_finite_o @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_o )
% 4.69/4.99 => ( ! [A4: $o] :
% 4.69/4.99 ( ( member_o @ A4 @ A )
% 4.69/4.99 => ( ord_less_eq_o @ A4 @ X ) )
% 4.69/4.99 => ( ord_less_eq_o @ ( lattic1921953407002678535_Max_o @ A ) @ X ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max.boundedI
% 4.69/4.99 thf(fact_4263_Max_OboundedI,axiom,
% 4.69/4.99 ! [A: set_rat,X: rat] :
% 4.69/4.99 ( ( finite_finite_rat @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_rat )
% 4.69/4.99 => ( ! [A4: rat] :
% 4.69/4.99 ( ( member_rat @ A4 @ A )
% 4.69/4.99 => ( ord_less_eq_rat @ A4 @ X ) )
% 4.69/4.99 => ( ord_less_eq_rat @ ( lattic7630753665789217321ax_rat @ A ) @ X ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max.boundedI
% 4.69/4.99 thf(fact_4264_Max_OboundedI,axiom,
% 4.69/4.99 ! [A: set_int,X: int] :
% 4.69/4.99 ( ( finite_finite_int @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_int )
% 4.69/4.99 => ( ! [A4: int] :
% 4.69/4.99 ( ( member_int @ A4 @ A )
% 4.69/4.99 => ( ord_less_eq_int @ A4 @ X ) )
% 4.69/4.99 => ( ord_less_eq_int @ ( lattic8263393255366662781ax_int @ A ) @ X ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max.boundedI
% 4.69/4.99 thf(fact_4265_Max_OboundedI,axiom,
% 4.69/4.99 ! [A: set_nat,X: nat] :
% 4.69/4.99 ( ( finite_finite_nat @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_nat )
% 4.69/4.99 => ( ! [A4: nat] :
% 4.69/4.99 ( ( member_nat @ A4 @ A )
% 4.69/4.99 => ( ord_less_eq_nat @ A4 @ X ) )
% 4.69/4.99 => ( ord_less_eq_nat @ ( lattic8265883725875713057ax_nat @ A ) @ X ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max.boundedI
% 4.69/4.99 thf(fact_4266_Max__insert2,axiom,
% 4.69/4.99 ! [A: set_o,A2: $o] :
% 4.69/4.99 ( ( finite_finite_o @ A )
% 4.69/4.99 => ( ! [B2: $o] :
% 4.69/4.99 ( ( member_o @ B2 @ A )
% 4.69/4.99 => ( ord_less_eq_o @ B2 @ A2 ) )
% 4.69/4.99 => ( ( lattic1921953407002678535_Max_o @ ( insert_o @ A2 @ A ) )
% 4.69/4.99 = A2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_insert2
% 4.69/4.99 thf(fact_4267_Max__insert2,axiom,
% 4.69/4.99 ! [A: set_Product_unit,A2: product_unit] :
% 4.69/4.99 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.99 => ( ! [B2: product_unit] :
% 4.69/4.99 ( ( member_Product_unit @ B2 @ A )
% 4.69/4.99 => ( ord_le3221252021190050221t_unit @ B2 @ A2 ) )
% 4.69/4.99 => ( ( lattic1210392890313158908t_unit @ ( insert_Product_unit @ A2 @ A ) )
% 4.69/4.99 = A2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_insert2
% 4.69/4.99 thf(fact_4268_Max__insert2,axiom,
% 4.69/4.99 ! [A: set_Code_integer,A2: code_integer] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.99 => ( ! [B2: code_integer] :
% 4.69/4.99 ( ( member_Code_integer @ B2 @ A )
% 4.69/4.99 => ( ord_le3102999989581377725nteger @ B2 @ A2 ) )
% 4.69/4.99 => ( ( lattic4901227151466704046nteger @ ( insert_Code_integer @ A2 @ A ) )
% 4.69/4.99 = A2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_insert2
% 4.69/4.99 thf(fact_4269_Max__insert2,axiom,
% 4.69/4.99 ! [A: set_rat,A2: rat] :
% 4.69/4.99 ( ( finite_finite_rat @ A )
% 4.69/4.99 => ( ! [B2: rat] :
% 4.69/4.99 ( ( member_rat @ B2 @ A )
% 4.69/4.99 => ( ord_less_eq_rat @ B2 @ A2 ) )
% 4.69/4.99 => ( ( lattic7630753665789217321ax_rat @ ( insert_rat @ A2 @ A ) )
% 4.69/4.99 = A2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_insert2
% 4.69/4.99 thf(fact_4270_Max__insert2,axiom,
% 4.69/4.99 ! [A: set_int,A2: int] :
% 4.69/4.99 ( ( finite_finite_int @ A )
% 4.69/4.99 => ( ! [B2: int] :
% 4.69/4.99 ( ( member_int @ B2 @ A )
% 4.69/4.99 => ( ord_less_eq_int @ B2 @ A2 ) )
% 4.69/4.99 => ( ( lattic8263393255366662781ax_int @ ( insert_int @ A2 @ A ) )
% 4.69/4.99 = A2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_insert2
% 4.69/4.99 thf(fact_4271_Max__insert2,axiom,
% 4.69/4.99 ! [A: set_nat,A2: nat] :
% 4.69/4.99 ( ( finite_finite_nat @ A )
% 4.69/4.99 => ( ! [B2: nat] :
% 4.69/4.99 ( ( member_nat @ B2 @ A )
% 4.69/4.99 => ( ord_less_eq_nat @ B2 @ A2 ) )
% 4.69/4.99 => ( ( lattic8265883725875713057ax_nat @ ( insert_nat @ A2 @ A ) )
% 4.69/4.99 = A2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_insert2
% 4.69/4.99 thf(fact_4272_remove__subset,axiom,
% 4.69/4.99 ! [X: product_unit,S: set_Product_unit] :
% 4.69/4.99 ( ( member_Product_unit @ X @ S )
% 4.69/4.99 => ( ord_le8056459307392131481t_unit @ ( minus_6452836326544984404t_unit @ S @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) @ S ) ) ).
% 4.69/4.99
% 4.69/4.99 % remove_subset
% 4.69/4.99 thf(fact_4273_remove__subset,axiom,
% 4.69/4.99 ! [X: $o,S: set_o] :
% 4.69/4.99 ( ( member_o @ X @ S )
% 4.69/4.99 => ( ord_less_set_o @ ( minus_minus_set_o @ S @ ( insert_o @ X @ bot_bot_set_o ) ) @ S ) ) ).
% 4.69/4.99
% 4.69/4.99 % remove_subset
% 4.69/4.99 thf(fact_4274_remove__subset,axiom,
% 4.69/4.99 ! [X: int,S: set_int] :
% 4.69/4.99 ( ( member_int @ X @ S )
% 4.69/4.99 => ( ord_less_set_int @ ( minus_minus_set_int @ S @ ( insert_int @ X @ bot_bot_set_int ) ) @ S ) ) ).
% 4.69/4.99
% 4.69/4.99 % remove_subset
% 4.69/4.99 thf(fact_4275_remove__subset,axiom,
% 4.69/4.99 ! [X: produc3658429121746597890et_nat > $o,S: set_Pr4532377907799695533_nat_o] :
% 4.69/4.99 ( ( member6576561426505652726_nat_o @ X @ S )
% 4.69/4.99 => ( ord_le2453136405763929_nat_o @ ( minus_1801376950450012436_nat_o @ S @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) @ S ) ) ).
% 4.69/4.99
% 4.69/4.99 % remove_subset
% 4.69/4.99 thf(fact_4276_remove__subset,axiom,
% 4.69/4.99 ! [X: nat,S: set_nat] :
% 4.69/4.99 ( ( member_nat @ X @ S )
% 4.69/4.99 => ( ord_less_set_nat @ ( minus_minus_set_nat @ S @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ S ) ) ).
% 4.69/4.99
% 4.69/4.99 % remove_subset
% 4.69/4.99 thf(fact_4277_cSup__eq__Max,axiom,
% 4.69/4.99 ! [X4: set_int] :
% 4.69/4.99 ( ( finite_finite_int @ X4 )
% 4.69/4.99 => ( ( X4 != bot_bot_set_int )
% 4.69/4.99 => ( ( complete_Sup_Sup_int @ X4 )
% 4.69/4.99 = ( lattic8263393255366662781ax_int @ X4 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % cSup_eq_Max
% 4.69/4.99 thf(fact_4278_cSup__eq__Max,axiom,
% 4.69/4.99 ! [X4: set_Product_unit] :
% 4.69/4.99 ( ( finite4290736615968046902t_unit @ X4 )
% 4.69/4.99 => ( ( X4 != bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ( ( comple4687483117567863418t_unit @ X4 )
% 4.69/4.99 = ( lattic1210392890313158908t_unit @ X4 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % cSup_eq_Max
% 4.69/4.99 thf(fact_4279_cSup__eq__Max,axiom,
% 4.69/4.99 ! [X4: set_nat] :
% 4.69/4.99 ( ( finite_finite_nat @ X4 )
% 4.69/4.99 => ( ( X4 != bot_bot_set_nat )
% 4.69/4.99 => ( ( complete_Sup_Sup_nat @ X4 )
% 4.69/4.99 = ( lattic8265883725875713057ax_nat @ X4 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % cSup_eq_Max
% 4.69/4.99 thf(fact_4280_Max__Sup,axiom,
% 4.69/4.99 ! [A: set_Product_unit] :
% 4.69/4.99 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.99 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ( ( lattic1210392890313158908t_unit @ A )
% 4.69/4.99 = ( comple4687483117567863418t_unit @ A ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_Sup
% 4.69/4.99 thf(fact_4281_disjoint__alt__simp3,axiom,
% 4.69/4.99 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/4.99 ( ( ord_le8056459307392131481t_unit @ ( minus_6452836326544984404t_unit @ A @ B4 ) @ A )
% 4.69/4.99 = ( ( inf_in4660618365625256667t_unit @ A @ B4 )
% 4.69/4.99 != bot_bo3957492148770167129t_unit ) ) ).
% 4.69/4.99
% 4.69/4.99 % disjoint_alt_simp3
% 4.69/4.99 thf(fact_4282_disjoint__alt__simp3,axiom,
% 4.69/4.99 ! [A: set_o,B4: set_o] :
% 4.69/4.99 ( ( ord_less_set_o @ ( minus_minus_set_o @ A @ B4 ) @ A )
% 4.69/4.99 = ( ( inf_inf_set_o @ A @ B4 )
% 4.69/4.99 != bot_bot_set_o ) ) ).
% 4.69/4.99
% 4.69/4.99 % disjoint_alt_simp3
% 4.69/4.99 thf(fact_4283_disjoint__alt__simp3,axiom,
% 4.69/4.99 ! [A: set_int,B4: set_int] :
% 4.69/4.99 ( ( ord_less_set_int @ ( minus_minus_set_int @ A @ B4 ) @ A )
% 4.69/4.99 = ( ( inf_inf_set_int @ A @ B4 )
% 4.69/4.99 != bot_bot_set_int ) ) ).
% 4.69/4.99
% 4.69/4.99 % disjoint_alt_simp3
% 4.69/4.99 thf(fact_4284_disjoint__alt__simp3,axiom,
% 4.69/4.99 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/4.99 ( ( ord_le2453136405763929_nat_o @ ( minus_1801376950450012436_nat_o @ A @ B4 ) @ A )
% 4.69/4.99 = ( ( inf_in1906310914598751387_nat_o @ A @ B4 )
% 4.69/4.99 != bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/4.99
% 4.69/4.99 % disjoint_alt_simp3
% 4.69/4.99 thf(fact_4285_disjoint__alt__simp3,axiom,
% 4.69/4.99 ! [A: set_nat,B4: set_nat] :
% 4.69/4.99 ( ( ord_less_set_nat @ ( minus_minus_set_nat @ A @ B4 ) @ A )
% 4.69/4.99 = ( ( inf_inf_set_nat @ A @ B4 )
% 4.69/4.99 != bot_bot_set_nat ) ) ).
% 4.69/4.99
% 4.69/4.99 % disjoint_alt_simp3
% 4.69/4.99 thf(fact_4286_range__eq__singletonD,axiom,
% 4.69/4.99 ! [F: code_integer > code_integer,A2: code_integer,X: code_integer] :
% 4.69/4.99 ( ( ( image_4470545334726330049nteger @ F @ top_to4645266643341252675nteger )
% 4.69/4.99 = ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) )
% 4.69/4.99 => ( ( F @ X )
% 4.69/4.99 = A2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_eq_singletonD
% 4.69/4.99 thf(fact_4287_range__eq__singletonD,axiom,
% 4.69/4.99 ! [F: product_unit > product_unit,A2: product_unit,X: product_unit] :
% 4.69/4.99 ( ( ( image_405062704495631173t_unit @ F @ top_to1996260823553986621t_unit )
% 4.69/4.99 = ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.99 => ( ( F @ X )
% 4.69/4.99 = A2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_eq_singletonD
% 4.69/4.99 thf(fact_4288_range__eq__singletonD,axiom,
% 4.69/4.99 ! [F: product_unit > $o,A2: $o,X: product_unit] :
% 4.69/4.99 ( ( ( image_Product_unit_o2 @ F @ top_to1996260823553986621t_unit )
% 4.69/4.99 = ( insert_o @ A2 @ bot_bot_set_o ) )
% 4.69/4.99 => ( ( F @ X )
% 4.69/4.99 = A2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_eq_singletonD
% 4.69/4.99 thf(fact_4289_range__eq__singletonD,axiom,
% 4.69/4.99 ! [F: product_unit > nat,A2: nat,X: product_unit] :
% 4.69/4.99 ( ( ( image_875570014554754200it_nat @ F @ top_to1996260823553986621t_unit )
% 4.69/4.99 = ( insert_nat @ A2 @ bot_bot_set_nat ) )
% 4.69/4.99 => ( ( F @ X )
% 4.69/4.99 = A2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_eq_singletonD
% 4.69/4.99 thf(fact_4290_range__eq__singletonD,axiom,
% 4.69/4.99 ! [F: product_unit > int,A2: int,X: product_unit] :
% 4.69/4.99 ( ( ( image_873079544045703924it_int @ F @ top_to1996260823553986621t_unit )
% 4.69/4.99 = ( insert_int @ A2 @ bot_bot_set_int ) )
% 4.69/4.99 => ( ( F @ X )
% 4.69/4.99 = A2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_eq_singletonD
% 4.69/4.99 thf(fact_4291_range__eq__singletonD,axiom,
% 4.69/4.99 ! [F: $o > product_unit,A2: product_unit,X: $o] :
% 4.69/4.99 ( ( ( image_o_Product_unit2 @ F @ top_top_set_o )
% 4.69/4.99 = ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.99 => ( ( F @ X )
% 4.69/4.99 = A2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_eq_singletonD
% 4.69/4.99 thf(fact_4292_range__eq__singletonD,axiom,
% 4.69/4.99 ! [F: $o > $o,A2: $o,X: $o] :
% 4.69/4.99 ( ( ( image_o_o2 @ F @ top_top_set_o )
% 4.69/4.99 = ( insert_o @ A2 @ bot_bot_set_o ) )
% 4.69/4.99 => ( ( F @ X )
% 4.69/4.99 = A2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_eq_singletonD
% 4.69/4.99 thf(fact_4293_range__eq__singletonD,axiom,
% 4.69/4.99 ! [F: $o > nat,A2: nat,X: $o] :
% 4.69/4.99 ( ( ( image_o_nat2 @ F @ top_top_set_o )
% 4.69/4.99 = ( insert_nat @ A2 @ bot_bot_set_nat ) )
% 4.69/4.99 => ( ( F @ X )
% 4.69/4.99 = A2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_eq_singletonD
% 4.69/4.99 thf(fact_4294_range__eq__singletonD,axiom,
% 4.69/4.99 ! [F: $o > int,A2: int,X: $o] :
% 4.69/4.99 ( ( ( image_o_int2 @ F @ top_top_set_o )
% 4.69/4.99 = ( insert_int @ A2 @ bot_bot_set_int ) )
% 4.69/4.99 => ( ( F @ X )
% 4.69/4.99 = A2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_eq_singletonD
% 4.69/4.99 thf(fact_4295_range__eq__singletonD,axiom,
% 4.69/4.99 ! [F: nat > code_integer,A2: code_integer,X: nat] :
% 4.69/4.99 ( ( ( image_1215581382706833972nteger @ F @ top_top_set_nat )
% 4.69/4.99 = ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) )
% 4.69/4.99 => ( ( F @ X )
% 4.69/4.99 = A2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % range_eq_singletonD
% 4.69/4.99 thf(fact_4296_less__cSup__iff,axiom,
% 4.69/4.99 ! [X4: set_int,Y: int] :
% 4.69/4.99 ( ( X4 != bot_bot_set_int )
% 4.69/4.99 => ( ( condit2212336002400062152ve_int @ X4 )
% 4.69/4.99 => ( ( ord_less_int @ Y @ ( complete_Sup_Sup_int @ X4 ) )
% 4.69/4.99 = ( ? [X2: int] :
% 4.69/4.99 ( ( member_int @ X2 @ X4 )
% 4.69/4.99 & ( ord_less_int @ Y @ X2 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % less_cSup_iff
% 4.69/4.99 thf(fact_4297_less__cSup__iff,axiom,
% 4.69/4.99 ! [X4: set_nat,Y: nat] :
% 4.69/4.99 ( ( X4 != bot_bot_set_nat )
% 4.69/4.99 => ( ( condit2214826472909112428ve_nat @ X4 )
% 4.69/4.99 => ( ( ord_less_nat @ Y @ ( complete_Sup_Sup_nat @ X4 ) )
% 4.69/4.99 = ( ? [X2: nat] :
% 4.69/4.99 ( ( member_nat @ X2 @ X4 )
% 4.69/4.99 & ( ord_less_nat @ Y @ X2 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % less_cSup_iff
% 4.69/4.99 thf(fact_4298_less__cSup__iff,axiom,
% 4.69/4.99 ! [X4: set_Product_unit,Y: product_unit] :
% 4.69/4.99 ( ( X4 != bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ( ( condit2080475194861589617t_unit @ X4 )
% 4.69/4.99 => ( ( ord_le361264281704409273t_unit @ Y @ ( comple4687483117567863418t_unit @ X4 ) )
% 4.69/4.99 = ( ? [X2: product_unit] :
% 4.69/4.99 ( ( member_Product_unit @ X2 @ X4 )
% 4.69/4.99 & ( ord_le361264281704409273t_unit @ Y @ X2 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % less_cSup_iff
% 4.69/4.99 thf(fact_4299_underS__Field3,axiom,
% 4.69/4.99 ! [R2: set_Pr5094982260447487303t_unit,A2: product_unit] :
% 4.69/4.99 ( ( ( field_Product_unit @ R2 )
% 4.69/4.99 != bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ( ord_le8056459307392131481t_unit @ ( order_5809128134054296019t_unit @ R2 @ A2 ) @ ( field_Product_unit @ R2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % underS_Field3
% 4.69/4.99 thf(fact_4300_underS__Field3,axiom,
% 4.69/4.99 ! [R2: set_Product_prod_o_o,A2: $o] :
% 4.69/4.99 ( ( ( field_o @ R2 )
% 4.69/4.99 != bot_bot_set_o )
% 4.69/4.99 => ( ord_less_set_o @ ( order_underS_o @ R2 @ A2 ) @ ( field_o @ R2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % underS_Field3
% 4.69/4.99 thf(fact_4301_underS__Field3,axiom,
% 4.69/4.99 ! [R2: set_Pr1261947904930325089at_nat,A2: nat] :
% 4.69/4.99 ( ( ( field_nat @ R2 )
% 4.69/4.99 != bot_bot_set_nat )
% 4.69/4.99 => ( ord_less_set_nat @ ( order_underS_nat @ R2 @ A2 ) @ ( field_nat @ R2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % underS_Field3
% 4.69/4.99 thf(fact_4302_underS__Field3,axiom,
% 4.69/4.99 ! [R2: set_Pr958786334691620121nt_int,A2: int] :
% 4.69/4.99 ( ( ( field_int @ R2 )
% 4.69/4.99 != bot_bot_set_int )
% 4.69/4.99 => ( ord_less_set_int @ ( order_underS_int @ R2 @ A2 ) @ ( field_int @ R2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % underS_Field3
% 4.69/4.99 thf(fact_4303_underS__Field3,axiom,
% 4.69/4.99 ! [R2: set_Pr2161125870931222855_nat_o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/4.99 ( ( ( field_81821745747897882_nat_o @ R2 )
% 4.69/4.99 != bot_bo7824918357723582233_nat_o )
% 4.69/4.99 => ( ord_le2453136405763929_nat_o @ ( order_7262550146012401043_nat_o @ R2 @ A2 ) @ ( field_81821745747897882_nat_o @ R2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % underS_Field3
% 4.69/4.99 thf(fact_4304_arg__min__if__finite_I2_J,axiom,
% 4.69/4.99 ! [S: set_Code_integer,F: code_integer > assn] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ S )
% 4.69/4.99 => ( ( S != bot_bo3990330152332043303nteger )
% 4.69/4.99 => ~ ? [X6: code_integer] :
% 4.69/4.99 ( ( member_Code_integer @ X6 @ S )
% 4.69/4.99 & ( ord_less_assn @ ( F @ X6 ) @ ( F @ ( lattic4682378690128378784r_assn @ F @ S ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % arg_min_if_finite(2)
% 4.69/4.99 thf(fact_4305_arg__min__if__finite_I2_J,axiom,
% 4.69/4.99 ! [S: set_Product_unit,F: product_unit > assn] :
% 4.69/4.99 ( ( finite4290736615968046902t_unit @ S )
% 4.69/4.99 => ( ( S != bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ~ ? [X6: product_unit] :
% 4.69/4.99 ( ( member_Product_unit @ X6 @ S )
% 4.69/4.99 & ( ord_less_assn @ ( F @ X6 ) @ ( F @ ( lattic4376901495776413404t_assn @ F @ S ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % arg_min_if_finite(2)
% 4.69/4.99 thf(fact_4306_arg__min__if__finite_I2_J,axiom,
% 4.69/4.99 ! [S: set_o,F: $o > assn] :
% 4.69/4.99 ( ( finite_finite_o @ S )
% 4.69/4.99 => ( ( S != bot_bot_set_o )
% 4.69/4.99 => ~ ? [X6: $o] :
% 4.69/4.99 ( ( member_o @ X6 @ S )
% 4.69/4.99 & ( ord_less_assn @ ( F @ X6 ) @ ( F @ ( lattic7708394068118247271o_assn @ F @ S ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % arg_min_if_finite(2)
% 4.69/4.99 thf(fact_4307_arg__min__if__finite_I2_J,axiom,
% 4.69/4.99 ! [S: set_nat,F: nat > assn] :
% 4.69/4.99 ( ( finite_finite_nat @ S )
% 4.69/4.99 => ( ( S != bot_bot_set_nat )
% 4.69/4.99 => ~ ? [X6: nat] :
% 4.69/4.99 ( ( member_nat @ X6 @ S )
% 4.69/4.99 & ( ord_less_assn @ ( F @ X6 ) @ ( F @ ( lattic2187264146484958483t_assn @ F @ S ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % arg_min_if_finite(2)
% 4.69/4.99 thf(fact_4308_arg__min__if__finite_I2_J,axiom,
% 4.69/4.99 ! [S: set_int,F: int > assn] :
% 4.69/4.99 ( ( finite_finite_int @ S )
% 4.69/4.99 => ( ( S != bot_bot_set_int )
% 4.69/4.99 => ~ ? [X6: int] :
% 4.69/4.99 ( ( member_int @ X6 @ S )
% 4.69/4.99 & ( ord_less_assn @ ( F @ X6 ) @ ( F @ ( lattic3162799611691135855t_assn @ F @ S ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % arg_min_if_finite(2)
% 4.69/4.99 thf(fact_4309_arg__min__if__finite_I2_J,axiom,
% 4.69/4.99 ! [S: set_Code_integer,F: code_integer > nat] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ S )
% 4.69/4.99 => ( ( S != bot_bo3990330152332043303nteger )
% 4.69/4.99 => ~ ? [X6: code_integer] :
% 4.69/4.99 ( ( member_Code_integer @ X6 @ S )
% 4.69/4.99 & ( ord_less_nat @ ( F @ X6 ) @ ( F @ ( lattic6074936555552774728er_nat @ F @ S ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % arg_min_if_finite(2)
% 4.69/4.99 thf(fact_4310_arg__min__if__finite_I2_J,axiom,
% 4.69/4.99 ! [S: set_Product_unit,F: product_unit > nat] :
% 4.69/4.99 ( ( finite4290736615968046902t_unit @ S )
% 4.69/4.99 => ( ( S != bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ~ ? [X6: product_unit] :
% 4.69/4.99 ( ( member_Product_unit @ X6 @ S )
% 4.69/4.99 & ( ord_less_nat @ ( F @ X6 ) @ ( F @ ( lattic1360832392136924548it_nat @ F @ S ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % arg_min_if_finite(2)
% 4.69/4.99 thf(fact_4311_arg__min__if__finite_I2_J,axiom,
% 4.69/4.99 ! [S: set_o,F: $o > nat] :
% 4.69/4.99 ( ( finite_finite_o @ S )
% 4.69/4.99 => ( ( S != bot_bot_set_o )
% 4.69/4.99 => ~ ? [X6: $o] :
% 4.69/4.99 ( ( member_o @ X6 @ S )
% 4.69/4.99 & ( ord_less_nat @ ( F @ X6 ) @ ( F @ ( lattic2775856028456453135_o_nat @ F @ S ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % arg_min_if_finite(2)
% 4.69/4.99 thf(fact_4312_arg__min__if__finite_I2_J,axiom,
% 4.69/4.99 ! [S: set_nat,F: nat > nat] :
% 4.69/4.99 ( ( finite_finite_nat @ S )
% 4.69/4.99 => ( ( S != bot_bot_set_nat )
% 4.69/4.99 => ~ ? [X6: nat] :
% 4.69/4.99 ( ( member_nat @ X6 @ S )
% 4.69/4.99 & ( ord_less_nat @ ( F @ X6 ) @ ( F @ ( lattic7446932960582359483at_nat @ F @ S ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % arg_min_if_finite(2)
% 4.69/4.99 thf(fact_4313_arg__min__if__finite_I2_J,axiom,
% 4.69/4.99 ! [S: set_int,F: int > nat] :
% 4.69/4.99 ( ( finite_finite_int @ S )
% 4.69/4.99 => ( ( S != bot_bot_set_int )
% 4.69/4.99 => ~ ? [X6: int] :
% 4.69/4.99 ( ( member_int @ X6 @ S )
% 4.69/4.99 & ( ord_less_nat @ ( F @ X6 ) @ ( F @ ( lattic8446286672483414039nt_nat @ F @ S ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % arg_min_if_finite(2)
% 4.69/4.99 thf(fact_4314_Sup__fold__sup,axiom,
% 4.69/4.99 ! [A: set_set_Product_unit] :
% 4.69/4.99 ( ( finite1772178364199683094t_unit @ A )
% 4.69/4.99 => ( ( comple3349607820504768346t_unit @ A )
% 4.69/4.99 = ( finite4243028863286625800t_unit @ sup_su793286257634532545t_unit @ bot_bo3957492148770167129t_unit @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Sup_fold_sup
% 4.69/4.99 thf(fact_4315_Sup__fold__sup,axiom,
% 4.69/4.99 ! [A: set_set_o] :
% 4.69/4.99 ( ( finite_finite_set_o @ A )
% 4.69/4.99 => ( ( comple90263536869209701_set_o @ A )
% 4.69/4.99 = ( finite4337638375924247368_set_o @ sup_sup_set_o @ bot_bot_set_o @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Sup_fold_sup
% 4.69/4.99 thf(fact_4316_Sup__fold__sup,axiom,
% 4.69/4.99 ! [A: set_set_nat] :
% 4.69/4.99 ( ( finite1152437895449049373et_nat @ A )
% 4.69/4.99 => ( ( comple7399068483239264473et_nat @ A )
% 4.69/4.99 = ( finite677925301803182934et_nat @ sup_sup_set_nat @ bot_bot_set_nat @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Sup_fold_sup
% 4.69/4.99 thf(fact_4317_Sup__fold__sup,axiom,
% 4.69/4.99 ! [A: set_set_int] :
% 4.69/4.99 ( ( finite6197958912794628473et_int @ A )
% 4.69/4.99 => ( ( comple3221217463730067765et_int @ A )
% 4.69/4.99 = ( finite2508883933289561102et_int @ sup_sup_set_int @ bot_bot_set_int @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Sup_fold_sup
% 4.69/4.99 thf(fact_4318_Sup__fold__sup,axiom,
% 4.69/4.99 ! [A: set_se1353816476878259085_nat_o] :
% 4.69/4.99 ( ( finite6069017635265841110_nat_o @ A )
% 4.69/4.99 => ( ( comple3382087578465172250_nat_o @ A )
% 4.69/4.99 = ( finite8456856254070787592_nat_o @ sup_su5209123915105501825_nat_o @ bot_bo7824918357723582233_nat_o @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Sup_fold_sup
% 4.69/4.99 thf(fact_4319_Sup__fold__sup,axiom,
% 4.69/4.99 ! [A: set_Product_unit] :
% 4.69/4.99 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.99 => ( ( comple4687483117567863418t_unit @ A )
% 4.69/4.99 = ( finite8834431295148555784t_unit @ sup_sup_Product_unit @ bot_bot_Product_unit @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Sup_fold_sup
% 4.69/4.99 thf(fact_4320_SUP__fold__sup,axiom,
% 4.69/4.99 ! [A: set_nat,F: nat > product_unit] :
% 4.69/4.99 ( ( finite_finite_nat @ A )
% 4.69/4.99 => ( ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A ) )
% 4.69/4.99 = ( finite6602901031542678131t_unit @ ( comp_P6204500334276302049it_nat @ sup_sup_Product_unit @ F ) @ bot_bot_Product_unit @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % SUP_fold_sup
% 4.69/4.99 thf(fact_4321_SUP__fold__sup,axiom,
% 4.69/4.99 ! [A: set_Code_integer,F: code_integer > product_unit] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.99 => ( ( comple4687483117567863418t_unit @ ( image_7182656606676592809t_unit @ F @ A ) )
% 4.69/4.99 = ( finite2281032298429728806t_unit @ ( comp_P4558236313141964142nteger @ sup_sup_Product_unit @ F ) @ bot_bot_Product_unit @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % SUP_fold_sup
% 4.69/4.99 thf(fact_4322_SUP__fold__sup,axiom,
% 4.69/4.99 ! [A: set_nat,F: nat > set_Product_unit] :
% 4.69/4.99 ( ( finite_finite_nat @ A )
% 4.69/4.99 => ( ( comple3349607820504768346t_unit @ ( image_4824033694279209942t_unit @ F @ A ) )
% 4.69/4.99 = ( finite9145781422887121747t_unit @ ( comp_s6943286182646368705it_nat @ sup_su793286257634532545t_unit @ F ) @ bot_bo3957492148770167129t_unit @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % SUP_fold_sup
% 4.69/4.99 thf(fact_4323_SUP__fold__sup,axiom,
% 4.69/4.99 ! [A: set_Code_integer,F: code_integer > set_Product_unit] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.99 => ( ( comple3349607820504768346t_unit @ ( image_5870443399019143561t_unit @ F @ A ) )
% 4.69/4.99 = ( finite3687622995246107910t_unit @ ( comp_s3199726385246003790nteger @ sup_su793286257634532545t_unit @ F ) @ bot_bo3957492148770167129t_unit @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % SUP_fold_sup
% 4.69/4.99 thf(fact_4324_SUP__fold__sup,axiom,
% 4.69/4.99 ! [A: set_nat,F: nat > set_o] :
% 4.69/4.99 ( ( finite_finite_nat @ A )
% 4.69/4.99 => ( ( comple90263536869209701_set_o @ ( image_nat_set_o @ F @ A ) )
% 4.69/4.99 = ( finite3217087857726763998_set_o @ ( comp_s4424444925706540684_o_nat @ sup_sup_set_o @ F ) @ bot_bot_set_o @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % SUP_fold_sup
% 4.69/4.99 thf(fact_4325_SUP__fold__sup,axiom,
% 4.69/4.99 ! [A: set_Code_integer,F: code_integer > set_o] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.99 => ( ( comple90263536869209701_set_o @ ( image_1867029960091478804_set_o @ F @ A ) )
% 4.69/4.99 = ( finite1928688952044918289_set_o @ ( comp_s90868338361139993nteger @ sup_sup_set_o @ F ) @ bot_bot_set_o @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % SUP_fold_sup
% 4.69/4.99 thf(fact_4326_SUP__fold__sup,axiom,
% 4.69/4.99 ! [A: set_nat,F: nat > set_nat] :
% 4.69/4.99 ( ( finite_finite_nat @ A )
% 4.69/4.99 => ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ F @ A ) )
% 4.69/4.99 = ( finite5529483035118572448et_nat @ ( comp_s2351873599094224870at_nat @ sup_sup_set_nat @ F ) @ bot_bot_set_nat @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % SUP_fold_sup
% 4.69/4.99 thf(fact_4327_SUP__fold__sup,axiom,
% 4.69/4.99 ! [A: set_Code_integer,F: code_integer > set_nat] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.99 => ( ( comple7399068483239264473et_nat @ ( image_8829277216472192490et_nat @ F @ A ) )
% 4.69/4.99 = ( finite1590314701948642349et_nat @ ( comp_s3169385134670675059nteger @ sup_sup_set_nat @ F ) @ bot_bot_set_nat @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % SUP_fold_sup
% 4.69/4.99 thf(fact_4328_SUP__fold__sup,axiom,
% 4.69/4.99 ! [A: set_nat,F: nat > set_int] :
% 4.69/4.99 ( ( finite_finite_nat @ A )
% 4.69/4.99 => ( ( comple3221217463730067765et_int @ ( image_nat_set_int @ F @ A ) )
% 4.69/4.99 = ( finite1351632015609375740et_int @ ( comp_s6689493721604790522nt_nat @ sup_sup_set_int @ F ) @ bot_bot_set_int @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % SUP_fold_sup
% 4.69/4.99 thf(fact_4329_SUP__fold__sup,axiom,
% 4.69/4.99 ! [A: set_Code_integer,F: code_integer > set_int] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.99 => ( ( comple3221217463730067765et_int @ ( image_4651426196962995782et_int @ F @ A ) )
% 4.69/4.99 = ( finite6635835719294221449et_int @ ( comp_s3634918272309710215nteger @ sup_sup_set_int @ F ) @ bot_bot_set_int @ A ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % SUP_fold_sup
% 4.69/4.99 thf(fact_4330_finite__subset__Union__chain,axiom,
% 4.69/4.99 ! [A: set_Code_integer,B9: set_set_Code_integer,A11: set_set_Code_integer] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.99 => ( ( ord_le7084787975880047091nteger @ A @ ( comple739944243200306918nteger @ B9 ) )
% 4.69/4.99 => ( ( B9 != bot_bo9204850693367297629nteger )
% 4.69/4.99 => ( ( pred_c5891848916688490280nteger @ A11 @ ord_le1307284697595431911nteger @ B9 )
% 4.69/4.99 => ~ ! [B5: set_Code_integer] :
% 4.69/4.99 ( ( member1834298987299537450nteger @ B5 @ B9 )
% 4.69/4.99 => ~ ( ord_le7084787975880047091nteger @ A @ B5 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % finite_subset_Union_chain
% 4.69/4.99 thf(fact_4331_finite__subset__Union__chain,axiom,
% 4.69/4.99 ! [A: set_nat,B9: set_set_nat,A11: set_set_nat] :
% 4.69/4.99 ( ( finite_finite_nat @ A )
% 4.69/4.99 => ( ( ord_less_eq_set_nat @ A @ ( comple7399068483239264473et_nat @ B9 ) )
% 4.69/4.99 => ( ( B9 != bot_bot_set_set_nat )
% 4.69/4.99 => ( ( pred_chain_set_nat @ A11 @ ord_less_set_nat @ B9 )
% 4.69/4.99 => ~ ! [B5: set_nat] :
% 4.69/4.99 ( ( member_set_nat @ B5 @ B9 )
% 4.69/4.99 => ~ ( ord_less_eq_set_nat @ A @ B5 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % finite_subset_Union_chain
% 4.69/4.99 thf(fact_4332_merge__true__star,axiom,
% 4.69/4.99 ( ( times_times_assn @ top_top_assn @ top_top_assn )
% 4.69/4.99 = top_top_assn ) ).
% 4.69/4.99
% 4.69/4.99 % merge_true_star
% 4.69/4.99 thf(fact_4333_assn__basic__inequalities_I5_J,axiom,
% 4.69/4.99 top_top_assn != bot_bot_assn ).
% 4.69/4.99
% 4.69/4.99 % assn_basic_inequalities(5)
% 4.69/4.99 thf(fact_4334_assn__basic__inequalities_I1_J,axiom,
% 4.69/4.99 top_top_assn != one_one_assn ).
% 4.69/4.99
% 4.69/4.99 % assn_basic_inequalities(1)
% 4.69/4.99 thf(fact_4335_mod__true,axiom,
% 4.69/4.99 ! [H2: produc3658429121746597890et_nat] :
% 4.69/4.99 ( ( rep_assn @ top_top_assn @ H2 )
% 4.69/4.99 = ( in_range @ H2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % mod_true
% 4.69/4.99 thf(fact_4336_fun__comp__eq__conv,axiom,
% 4.69/4.99 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,Fg: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 4.69/4.99 ( ( ( comp_C1593894019821074884nteger @ F @ G )
% 4.69/4.99 = Fg )
% 4.69/4.99 = ( ! [X2: code_integer] :
% 4.69/4.99 ( ( F @ ( G @ X2 ) )
% 4.69/4.99 = ( Fg @ X2 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % fun_comp_eq_conv
% 4.69/4.99 thf(fact_4337_fun__comp__eq__conv,axiom,
% 4.69/4.99 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,Fg: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 4.69/4.99 ( ( ( comp_C8797469213163452608nteger @ F @ G )
% 4.69/4.99 = Fg )
% 4.69/4.99 = ( ! [X2: code_integer] :
% 4.69/4.99 ( ( F @ ( G @ X2 ) )
% 4.69/4.99 = ( Fg @ X2 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % fun_comp_eq_conv
% 4.69/4.99 thf(fact_4338_comp__cong__right,axiom,
% 4.69/4.99 ! [X: code_integer > code_integer,Y: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 4.69/4.99 ( ( X = Y )
% 4.69/4.99 => ( ( comp_C1593894019821074884nteger @ F @ X )
% 4.69/4.99 = ( comp_C1593894019821074884nteger @ F @ Y ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % comp_cong_right
% 4.69/4.99 thf(fact_4339_comp__cong__right,axiom,
% 4.69/4.99 ! [X: code_integer > code_integer > code_integer,Y: code_integer > code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 4.69/4.99 ( ( X = Y )
% 4.69/4.99 => ( ( comp_C8797469213163452608nteger @ F @ X )
% 4.69/4.99 = ( comp_C8797469213163452608nteger @ F @ Y ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % comp_cong_right
% 4.69/4.99 thf(fact_4340_comp__cong__left,axiom,
% 4.69/4.99 ! [X: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,Y: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer] :
% 4.69/4.99 ( ( X = Y )
% 4.69/4.99 => ( ( comp_C1593894019821074884nteger @ X @ F )
% 4.69/4.99 = ( comp_C1593894019821074884nteger @ Y @ F ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % comp_cong_left
% 4.69/4.99 thf(fact_4341_comp__cong__left,axiom,
% 4.69/4.99 ! [X: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,Y: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F: code_integer > code_integer > code_integer] :
% 4.69/4.99 ( ( X = Y )
% 4.69/4.99 => ( ( comp_C8797469213163452608nteger @ X @ F )
% 4.69/4.99 = ( comp_C8797469213163452608nteger @ Y @ F ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % comp_cong_left
% 4.69/4.99 thf(fact_4342_comp__apply__eq,axiom,
% 4.69/4.99 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,X: code_integer,H2: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,K3: code_integer > code_integer] :
% 4.69/4.99 ( ( ( F @ ( G @ X ) )
% 4.69/4.99 = ( H2 @ ( K3 @ X ) ) )
% 4.69/4.99 => ( ( comp_C1593894019821074884nteger @ F @ G @ X )
% 4.69/4.99 = ( comp_C1593894019821074884nteger @ H2 @ K3 @ X ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % comp_apply_eq
% 4.69/4.99 thf(fact_4343_comp__apply__eq,axiom,
% 4.69/4.99 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,X: code_integer,H2: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,K3: code_integer > code_integer > code_integer] :
% 4.69/4.99 ( ( ( F @ ( G @ X ) )
% 4.69/4.99 = ( H2 @ ( K3 @ X ) ) )
% 4.69/4.99 => ( ( comp_C1593894019821074884nteger @ F @ G @ X )
% 4.69/4.99 = ( comp_C8797469213163452608nteger @ H2 @ K3 @ X ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % comp_apply_eq
% 4.69/4.99 thf(fact_4344_comp__apply__eq,axiom,
% 4.69/4.99 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X: code_integer,H2: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,K3: code_integer > code_integer] :
% 4.69/4.99 ( ( ( F @ ( G @ X ) )
% 4.69/4.99 = ( H2 @ ( K3 @ X ) ) )
% 4.69/4.99 => ( ( comp_C8797469213163452608nteger @ F @ G @ X )
% 4.69/4.99 = ( comp_C1593894019821074884nteger @ H2 @ K3 @ X ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % comp_apply_eq
% 4.69/4.99 thf(fact_4345_comp__apply__eq,axiom,
% 4.69/4.99 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer > code_integer,X: code_integer,H2: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,K3: code_integer > code_integer > code_integer] :
% 4.69/4.99 ( ( ( F @ ( G @ X ) )
% 4.69/4.99 = ( H2 @ ( K3 @ X ) ) )
% 4.69/4.99 => ( ( comp_C8797469213163452608nteger @ F @ G @ X )
% 4.69/4.99 = ( comp_C8797469213163452608nteger @ H2 @ K3 @ X ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % comp_apply_eq
% 4.69/4.99 thf(fact_4346_type__copy__set__map0,axiom,
% 4.69/4.99 ! [Rep2: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer,Abs2: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,S: code_integer > set_nat,M: code_integer > code_integer,F: nat > nat,S4: code_integer > set_nat,G: code_integer > code_integer] :
% 4.69/4.99 ( ( type_d6544512618915850416nteger @ Rep2 @ Abs2 @ top_to4645266643341252675nteger )
% 4.69/4.99 => ( ( ( comp_C6537567860429791781nteger @ S @ M )
% 4.69/4.99 = ( comp_s4605850120322998606nteger @ ( image_nat_nat2 @ F ) @ S4 ) )
% 4.69/4.99 => ( ( comp_P8262219321096090349nteger @ ( comp_C3184339336801759213nteger @ S @ Rep2 ) @ ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ Abs2 @ M ) @ G ) )
% 4.69/4.99 = ( comp_s4605850120322998606nteger @ ( image_nat_nat2 @ F ) @ ( comp_C6537567860429791781nteger @ S4 @ G ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_set_map0
% 4.69/4.99 thf(fact_4347_type__copy__set__map0,axiom,
% 4.69/4.99 ! [Rep2: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer,Abs2: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,S: code_integer > set_Code_integer,M: code_integer > code_integer,F: code_integer > code_integer,S4: code_integer > set_Code_integer,G: code_integer > code_integer] :
% 4.69/4.99 ( ( type_d6544512618915850416nteger @ Rep2 @ Abs2 @ top_to4645266643341252675nteger )
% 4.69/4.99 => ( ( ( comp_C8186931911283765298nteger @ S @ M )
% 4.69/4.99 = ( comp_s956550612328592744nteger @ ( image_4470545334726330049nteger @ F ) @ S4 ) )
% 4.69/4.99 => ( ( comp_P4885729792186999034nteger @ ( comp_C6344129587964912378nteger @ S @ Rep2 ) @ ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ Abs2 @ M ) @ G ) )
% 4.69/4.99 = ( comp_s956550612328592744nteger @ ( image_4470545334726330049nteger @ F ) @ ( comp_C8186931911283765298nteger @ S4 @ G ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_set_map0
% 4.69/4.99 thf(fact_4348_type__copy__set__map0,axiom,
% 4.69/4.99 ! [Rep2: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > code_integer,Abs2: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,S: code_integer > set_Code_integer,M: code_integer > code_integer,F: nat > code_integer,S4: code_integer > set_nat,G: code_integer > code_integer] :
% 4.69/4.99 ( ( type_d6544512618915850416nteger @ Rep2 @ Abs2 @ top_to4645266643341252675nteger )
% 4.69/4.99 => ( ( ( comp_C8186931911283765298nteger @ S @ M )
% 4.69/4.99 = ( comp_s8292494440407567195nteger @ ( image_1215581382706833972nteger @ F ) @ S4 ) )
% 4.69/4.99 => ( ( comp_P4885729792186999034nteger @ ( comp_C6344129587964912378nteger @ S @ Rep2 ) @ ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ Abs2 @ M ) @ G ) )
% 4.69/4.99 = ( comp_s8292494440407567195nteger @ ( image_1215581382706833972nteger @ F ) @ ( comp_C6537567860429791781nteger @ S4 @ G ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_set_map0
% 4.69/4.99 thf(fact_4349_type__copy__set__map0,axiom,
% 4.69/4.99 ! [Rep2: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > product_unit,Abs2: product_unit > produc8923325533196201883nteger > produc8923325533196201883nteger,S: product_unit > set_nat,M: code_integer > product_unit,F: nat > nat,S4: code_integer > set_nat,G: code_integer > code_integer] :
% 4.69/4.99 ( ( type_d6996789741066924922t_unit @ Rep2 @ Abs2 @ top_to1996260823553986621t_unit )
% 4.69/4.99 => ( ( ( comp_P5878433733084393551nteger @ S @ M )
% 4.69/4.99 = ( comp_s4605850120322998606nteger @ ( image_nat_nat2 @ F ) @ S4 ) )
% 4.69/4.99 => ( ( comp_P8262219321096090349nteger @ ( comp_P6101996899264665623nteger @ S @ Rep2 ) @ ( comp_C1593894019821074884nteger @ ( comp_P4511551582283981294nteger @ Abs2 @ M ) @ G ) )
% 4.69/4.99 = ( comp_s4605850120322998606nteger @ ( image_nat_nat2 @ F ) @ ( comp_C6537567860429791781nteger @ S4 @ G ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_set_map0
% 4.69/4.99 thf(fact_4350_type__copy__set__map0,axiom,
% 4.69/4.99 ! [Rep2: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > product_unit,Abs2: product_unit > produc8923325533196201883nteger > produc8923325533196201883nteger,S: product_unit > set_Code_integer,M: code_integer > product_unit,F: code_integer > code_integer,S4: code_integer > set_Code_integer,G: code_integer > code_integer] :
% 4.69/4.99 ( ( type_d6996789741066924922t_unit @ Rep2 @ Abs2 @ top_to1996260823553986621t_unit )
% 4.69/4.99 => ( ( ( comp_P4767411901762164316nteger @ S @ M )
% 4.69/4.99 = ( comp_s956550612328592744nteger @ ( image_4470545334726330049nteger @ F ) @ S4 ) )
% 4.69/4.99 => ( ( comp_P4885729792186999034nteger @ ( comp_P4635212033913086756nteger @ S @ Rep2 ) @ ( comp_C1593894019821074884nteger @ ( comp_P4511551582283981294nteger @ Abs2 @ M ) @ G ) )
% 4.69/4.99 = ( comp_s956550612328592744nteger @ ( image_4470545334726330049nteger @ F ) @ ( comp_C8186931911283765298nteger @ S4 @ G ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_set_map0
% 4.69/4.99 thf(fact_4351_type__copy__set__map0,axiom,
% 4.69/4.99 ! [Rep2: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > product_unit,Abs2: product_unit > produc8923325533196201883nteger > produc8923325533196201883nteger,S: product_unit > set_Code_integer,M: code_integer > product_unit,F: nat > code_integer,S4: code_integer > set_nat,G: code_integer > code_integer] :
% 4.69/4.99 ( ( type_d6996789741066924922t_unit @ Rep2 @ Abs2 @ top_to1996260823553986621t_unit )
% 4.69/4.99 => ( ( ( comp_P4767411901762164316nteger @ S @ M )
% 4.69/4.99 = ( comp_s8292494440407567195nteger @ ( image_1215581382706833972nteger @ F ) @ S4 ) )
% 4.69/4.99 => ( ( comp_P4885729792186999034nteger @ ( comp_P4635212033913086756nteger @ S @ Rep2 ) @ ( comp_C1593894019821074884nteger @ ( comp_P4511551582283981294nteger @ Abs2 @ M ) @ G ) )
% 4.69/4.99 = ( comp_s8292494440407567195nteger @ ( image_1215581382706833972nteger @ F ) @ ( comp_C6537567860429791781nteger @ S4 @ G ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_set_map0
% 4.69/4.99 thf(fact_4352_type__copy__set__map0,axiom,
% 4.69/4.99 ! [Rep2: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o,Abs2: $o > produc8923325533196201883nteger > produc8923325533196201883nteger,S: $o > set_nat,M: code_integer > $o,F: nat > nat,S4: code_integer > set_nat,G: code_integer > code_integer] :
% 4.69/4.99 ( ( type_d5661033022651575429eger_o @ Rep2 @ Abs2 @ top_top_set_o )
% 4.69/4.99 => ( ( ( comp_o172754640513974618nteger @ S @ M )
% 4.69/4.99 = ( comp_s4605850120322998606nteger @ ( image_nat_nat2 @ F ) @ S4 ) )
% 4.69/4.99 => ( ( comp_P8262219321096090349nteger @ ( comp_o1289984117834210338nteger @ S @ Rep2 ) @ ( comp_C1593894019821074884nteger @ ( comp_o8922910837708301817nteger @ Abs2 @ M ) @ G ) )
% 4.69/4.99 = ( comp_s4605850120322998606nteger @ ( image_nat_nat2 @ F ) @ ( comp_C6537567860429791781nteger @ S4 @ G ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_set_map0
% 4.69/4.99 thf(fact_4353_type__copy__set__map0,axiom,
% 4.69/4.99 ! [Rep2: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o,Abs2: $o > produc8923325533196201883nteger > produc8923325533196201883nteger,S: $o > set_Code_integer,M: code_integer > $o,F: code_integer > code_integer,S4: code_integer > set_Code_integer,G: code_integer > code_integer] :
% 4.69/4.99 ( ( type_d5661033022651575429eger_o @ Rep2 @ Abs2 @ top_top_set_o )
% 4.69/4.99 => ( ( ( comp_o4291842030903409511nteger @ S @ M )
% 4.69/4.99 = ( comp_s956550612328592744nteger @ ( image_4470545334726330049nteger @ F ) @ S4 ) )
% 4.69/4.99 => ( ( comp_P4885729792186999034nteger @ ( comp_o7929101295636871983nteger @ S @ Rep2 ) @ ( comp_C1593894019821074884nteger @ ( comp_o8922910837708301817nteger @ Abs2 @ M ) @ G ) )
% 4.69/4.99 = ( comp_s956550612328592744nteger @ ( image_4470545334726330049nteger @ F ) @ ( comp_C8186931911283765298nteger @ S4 @ G ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_set_map0
% 4.69/4.99 thf(fact_4354_type__copy__set__map0,axiom,
% 4.69/4.99 ! [Rep2: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > $o,Abs2: $o > produc8923325533196201883nteger > produc8923325533196201883nteger,S: $o > set_Code_integer,M: code_integer > $o,F: nat > code_integer,S4: code_integer > set_nat,G: code_integer > code_integer] :
% 4.69/4.99 ( ( type_d5661033022651575429eger_o @ Rep2 @ Abs2 @ top_top_set_o )
% 4.69/4.99 => ( ( ( comp_o4291842030903409511nteger @ S @ M )
% 4.69/4.99 = ( comp_s8292494440407567195nteger @ ( image_1215581382706833972nteger @ F ) @ S4 ) )
% 4.69/4.99 => ( ( comp_P4885729792186999034nteger @ ( comp_o7929101295636871983nteger @ S @ Rep2 ) @ ( comp_C1593894019821074884nteger @ ( comp_o8922910837708301817nteger @ Abs2 @ M ) @ G ) )
% 4.69/4.99 = ( comp_s8292494440407567195nteger @ ( image_1215581382706833972nteger @ F ) @ ( comp_C6537567860429791781nteger @ S4 @ G ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_set_map0
% 4.69/4.99 thf(fact_4355_type__copy__set__map0,axiom,
% 4.69/4.99 ! [Rep2: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > nat,Abs2: nat > produc8923325533196201883nteger > produc8923325533196201883nteger,S: nat > set_nat,M: code_integer > nat,F: nat > nat,S4: code_integer > set_nat,G: code_integer > code_integer] :
% 4.69/4.99 ( ( type_d6278479724763174947er_nat @ Rep2 @ Abs2 @ top_top_set_nat )
% 4.69/4.99 => ( ( ( comp_n5963683855531483544nteger @ S @ M )
% 4.69/4.99 = ( comp_s4605850120322998606nteger @ ( image_nat_nat2 @ F ) @ S4 ) )
% 4.69/4.99 => ( ( comp_P8262219321096090349nteger @ ( comp_n3623798160786426464nteger @ S @ Rep2 ) @ ( comp_C1593894019821074884nteger @ ( comp_n2033352843805742135nteger @ Abs2 @ M ) @ G ) )
% 4.69/4.99 = ( comp_s4605850120322998606nteger @ ( image_nat_nat2 @ F ) @ ( comp_C6537567860429791781nteger @ S4 @ G ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_set_map0
% 4.69/4.99 thf(fact_4356_top__empty__eq,axiom,
% 4.69/4.99 ( top_to2462227307520033056at_o_o
% 4.69/4.99 = ( ^ [X2: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X2 @ top_to4869887016220417533_nat_o ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % top_empty_eq
% 4.69/4.99 thf(fact_4357_top__empty__eq,axiom,
% 4.69/4.99 ( top_to2465898995584390880unit_o
% 4.69/4.99 = ( ^ [X2: product_unit] : ( member_Product_unit @ X2 @ top_to1996260823553986621t_unit ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % top_empty_eq
% 4.69/4.99 thf(fact_4358_top__empty__eq,axiom,
% 4.69/4.99 ( top_top_o_o
% 4.69/4.99 = ( ^ [X2: $o] : ( member_o @ X2 @ top_top_set_o ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % top_empty_eq
% 4.69/4.99 thf(fact_4359_top__empty__eq,axiom,
% 4.69/4.99 ( top_top_nat_o
% 4.69/4.99 = ( ^ [X2: nat] : ( member_nat @ X2 @ top_top_set_nat ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % top_empty_eq
% 4.69/4.99 thf(fact_4360_top__empty__eq,axiom,
% 4.69/4.99 ( top_top_int_o
% 4.69/4.99 = ( ^ [X2: int] : ( member_int @ X2 @ top_top_set_int ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % top_empty_eq
% 4.69/4.99 thf(fact_4361_top__set__def,axiom,
% 4.69/4.99 ( top_to4869887016220417533_nat_o
% 4.69/4.99 = ( collec939566748876313656_nat_o @ top_to2462227307520033056at_o_o ) ) ).
% 4.69/4.99
% 4.69/4.99 % top_set_def
% 4.69/4.99 thf(fact_4362_top__set__def,axiom,
% 4.69/4.99 ( top_to1996260823553986621t_unit
% 4.69/4.99 = ( collect_Product_unit @ top_to2465898995584390880unit_o ) ) ).
% 4.69/4.99
% 4.69/4.99 % top_set_def
% 4.69/4.99 thf(fact_4363_top__set__def,axiom,
% 4.69/4.99 ( top_top_set_o
% 4.69/4.99 = ( collect_o @ top_top_o_o ) ) ).
% 4.69/4.99
% 4.69/4.99 % top_set_def
% 4.69/4.99 thf(fact_4364_top__set__def,axiom,
% 4.69/4.99 ( top_top_set_nat
% 4.69/4.99 = ( collect_nat @ top_top_nat_o ) ) ).
% 4.69/4.99
% 4.69/4.99 % top_set_def
% 4.69/4.99 thf(fact_4365_top__set__def,axiom,
% 4.69/4.99 ( top_top_set_int
% 4.69/4.99 = ( collect_int @ top_top_int_o ) ) ).
% 4.69/4.99
% 4.69/4.99 % top_set_def
% 4.69/4.99 thf(fact_4366_pred__on_Ochain__empty,axiom,
% 4.69/4.99 ! [A: set_Product_unit,P: product_unit > product_unit > $o] : ( pred_c6915491785556283576t_unit @ A @ P @ bot_bo3957492148770167129t_unit ) ).
% 4.69/4.99
% 4.69/4.99 % pred_on.chain_empty
% 4.69/4.99 thf(fact_4367_pred__on_Ochain__empty,axiom,
% 4.69/4.99 ! [A: set_o,P: $o > $o > $o] : ( pred_chain_o @ A @ P @ bot_bot_set_o ) ).
% 4.69/4.99
% 4.69/4.99 % pred_on.chain_empty
% 4.69/4.99 thf(fact_4368_pred__on_Ochain__empty,axiom,
% 4.69/4.99 ! [A: set_nat,P: nat > nat > $o] : ( pred_chain_nat @ A @ P @ bot_bot_set_nat ) ).
% 4.69/4.99
% 4.69/4.99 % pred_on.chain_empty
% 4.69/4.99 thf(fact_4369_pred__on_Ochain__empty,axiom,
% 4.69/4.99 ! [A: set_int,P: int > int > $o] : ( pred_chain_int @ A @ P @ bot_bot_set_int ) ).
% 4.69/4.99
% 4.69/4.99 % pred_on.chain_empty
% 4.69/4.99 thf(fact_4370_pred__on_Ochain__empty,axiom,
% 4.69/4.99 ! [A: set_Pr4532377907799695533_nat_o,P: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o] : ( pred_c177362287423414904_nat_o @ A @ P @ bot_bo7824918357723582233_nat_o ) ).
% 4.69/4.99
% 4.69/4.99 % pred_on.chain_empty
% 4.69/4.99 thf(fact_4371_surj__fun__eq,axiom,
% 4.69/4.99 ! [F: code_integer > code_integer > code_integer,X4: set_Code_integer,G1: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G2: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 4.69/4.99 ( ( ( image_2177946750938214461nteger @ F @ X4 )
% 4.69/4.99 = top_to3804862627464599871nteger )
% 4.69/4.99 => ( ! [X3: code_integer] :
% 4.69/4.99 ( ( member_Code_integer @ X3 @ X4 )
% 4.69/4.99 => ( ( comp_C8797469213163452608nteger @ G1 @ F @ X3 )
% 4.69/4.99 = ( comp_C8797469213163452608nteger @ G2 @ F @ X3 ) ) )
% 4.69/4.99 => ( G1 = G2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % surj_fun_eq
% 4.69/4.99 thf(fact_4372_surj__fun__eq,axiom,
% 4.69/4.99 ! [F: code_integer > code_integer,X4: set_Code_integer,G1: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G2: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger] :
% 4.69/4.99 ( ( ( image_4470545334726330049nteger @ F @ X4 )
% 4.69/4.99 = top_to4645266643341252675nteger )
% 4.69/4.99 => ( ! [X3: code_integer] :
% 4.69/4.99 ( ( member_Code_integer @ X3 @ X4 )
% 4.69/4.99 => ( ( comp_C1593894019821074884nteger @ G1 @ F @ X3 )
% 4.69/4.99 = ( comp_C1593894019821074884nteger @ G2 @ F @ X3 ) ) )
% 4.69/4.99 => ( G1 = G2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % surj_fun_eq
% 4.69/4.99 thf(fact_4373_type__copy__map__comp0,axiom,
% 4.69/4.99 ! [Rep2: code_integer > code_integer,Abs2: code_integer > code_integer,M: code_integer > code_integer,M1: code_integer > code_integer,M22: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer] :
% 4.69/4.99 ( ( type_d4796611474492816872nteger @ Rep2 @ Abs2 @ top_to4645266643341252675nteger )
% 4.69/4.99 => ( ( M
% 4.69/4.99 = ( comp_C7449957260575251196nteger @ M1 @ M22 ) )
% 4.69/4.99 => ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ M ) @ G )
% 4.69/4.99 = ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ M1 ) @ Rep2 ) @ ( comp_C7449957260575251196nteger @ ( comp_C7449957260575251196nteger @ Abs2 @ M22 ) @ G ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_map_comp0
% 4.69/4.99 thf(fact_4374_type__copy__map__comp0,axiom,
% 4.69/4.99 ! [Rep2: code_integer > product_unit,Abs2: product_unit > code_integer,M: code_integer > code_integer,M1: product_unit > code_integer,M22: code_integer > product_unit,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer] :
% 4.69/4.99 ( ( type_d9006111508436661314t_unit @ Rep2 @ Abs2 @ top_to1996260823553986621t_unit )
% 4.69/4.99 => ( ( M
% 4.69/4.99 = ( comp_P6790823133229852966nteger @ M1 @ M22 ) )
% 4.69/4.99 => ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ M ) @ G )
% 4.69/4.99 = ( comp_C1593894019821074884nteger @ ( comp_P4511551582283981294nteger @ ( comp_C5854136495726678886t_unit @ F @ M1 ) @ Rep2 ) @ ( comp_C7449957260575251196nteger @ ( comp_P6790823133229852966nteger @ Abs2 @ M22 ) @ G ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_map_comp0
% 4.69/4.99 thf(fact_4375_type__copy__map__comp0,axiom,
% 4.69/4.99 ! [Rep2: code_integer > $o,Abs2: $o > code_integer,M: code_integer > code_integer,M1: $o > code_integer,M22: code_integer > $o,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer] :
% 4.69/4.99 ( ( type_d6812736842639505741eger_o @ Rep2 @ Abs2 @ top_top_set_o )
% 4.69/4.99 => ( ( M
% 4.69/4.99 = ( comp_o1085144040659434033nteger @ M1 @ M22 ) )
% 4.69/4.99 => ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ M ) @ G )
% 4.69/4.99 = ( comp_C1593894019821074884nteger @ ( comp_o8922910837708301817nteger @ ( comp_C5733264393235242609eger_o @ F @ M1 ) @ Rep2 ) @ ( comp_C7449957260575251196nteger @ ( comp_o1085144040659434033nteger @ Abs2 @ M22 ) @ G ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_map_comp0
% 4.69/4.99 thf(fact_4376_type__copy__map__comp0,axiom,
% 4.69/4.99 ! [Rep2: code_integer > nat,Abs2: nat > code_integer,M: code_integer > code_integer,M1: nat > code_integer,M22: code_integer > nat,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer] :
% 4.69/4.99 ( ( type_d8368584451094728027er_nat @ Rep2 @ Abs2 @ top_top_set_nat )
% 4.69/4.99 => ( ( M
% 4.69/4.99 = ( comp_n6876073255676942959nteger @ M1 @ M22 ) )
% 4.69/4.99 => ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ M ) @ G )
% 4.69/4.99 = ( comp_C1593894019821074884nteger @ ( comp_n2033352843805742135nteger @ ( comp_C836733381939181879er_nat @ F @ M1 ) @ Rep2 ) @ ( comp_C7449957260575251196nteger @ ( comp_n6876073255676942959nteger @ Abs2 @ M22 ) @ G ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_map_comp0
% 4.69/4.99 thf(fact_4377_type__copy__map__comp0,axiom,
% 4.69/4.99 ! [Rep2: code_integer > int,Abs2: int > code_integer,M: code_integer > code_integer,M1: int > code_integer,M22: code_integer > int,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer] :
% 4.69/4.99 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ top_top_set_int )
% 4.69/4.99 => ( ( M
% 4.69/4.99 = ( comp_i6014793192326455499nteger @ M1 @ M22 ) )
% 4.69/4.99 => ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ M ) @ G )
% 4.69/4.99 = ( comp_C1593894019821074884nteger @ ( comp_i2874689474467862163nteger @ ( comp_C834242911430131603er_int @ F @ M1 ) @ Rep2 ) @ ( comp_C7449957260575251196nteger @ ( comp_i6014793192326455499nteger @ Abs2 @ M22 ) @ G ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_map_comp0
% 4.69/4.99 thf(fact_4378_type__copy__map__comp0,axiom,
% 4.69/4.99 ! [Rep2: product_unit > $o,Abs2: $o > product_unit,M: code_integer > code_integer,M1: $o > code_integer,M22: code_integer > $o,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer] :
% 4.69/4.99 ( ( type_d6188575255521822967unit_o @ Rep2 @ Abs2 @ top_top_set_o )
% 4.69/4.99 => ( ( M
% 4.69/4.99 = ( comp_o1085144040659434033nteger @ M1 @ M22 ) )
% 4.69/4.99 => ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ M ) @ G )
% 4.69/4.99 = ( comp_P4511551582283981294nteger @ ( comp_o6961622296474427249t_unit @ ( comp_C5733264393235242609eger_o @ F @ M1 ) @ Rep2 ) @ ( comp_C8146212659816229034nteger @ ( comp_o6635994240230588853nteger @ Abs2 @ M22 ) @ G ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_map_comp0
% 4.69/4.99 thf(fact_4379_type__copy__map__comp0,axiom,
% 4.69/4.99 ! [Rep2: code_natural > nat,Abs2: nat > code_natural,M: code_integer > code_integer,M1: nat > code_integer,M22: code_integer > nat,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer] :
% 4.69/4.99 ( ( type_d4410041424927559462al_nat @ Rep2 @ Abs2 @ top_top_set_nat )
% 4.69/4.99 => ( ( M
% 4.69/4.99 = ( comp_n6876073255676942959nteger @ M1 @ M22 ) )
% 4.69/4.99 => ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ M ) @ G )
% 4.69/4.99 = ( comp_C456341964420721295nteger @ ( comp_n856947995562459650atural @ ( comp_C836733381939181879er_nat @ F @ M1 ) @ Rep2 ) @ ( comp_C1891057325546811591nteger @ ( comp_n1317173320648503354nteger @ Abs2 @ M22 ) @ G ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_map_comp0
% 4.69/4.99 thf(fact_4380_type__copy__map__comp0,axiom,
% 4.69/4.99 ! [Rep2: code_integer > code_integer > code_integer,Abs2: ( code_integer > code_integer ) > code_integer,M: code_integer > code_integer,M1: ( code_integer > code_integer ) > code_integer,M22: code_integer > code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer] :
% 4.69/4.99 ( ( type_d669523880323286244nteger @ Rep2 @ Abs2 @ top_to3804862627464599871nteger )
% 4.69/4.99 => ( ( M
% 4.69/4.99 = ( comp_C5076291335850163704nteger @ M1 @ M22 ) )
% 4.69/4.99 => ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ M ) @ G )
% 4.69/4.99 = ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ ( comp_C95226695241045696nteger @ F @ M1 ) @ Rep2 ) @ ( comp_C7449957260575251196nteger @ ( comp_C5076291335850163704nteger @ Abs2 @ M22 ) @ G ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_map_comp0
% 4.69/4.99 thf(fact_4381_type__copy__map__comp0,axiom,
% 4.69/4.99 ! [Rep2: ( code_integer > code_integer ) > code_integer,Abs2: code_integer > code_integer > code_integer,M: code_integer > code_integer,M1: code_integer > code_integer,M22: code_integer > code_integer,F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer] :
% 4.69/4.99 ( ( type_d5515310227294319076nteger @ Rep2 @ Abs2 @ top_to4645266643341252675nteger )
% 4.69/4.99 => ( ( M
% 4.69/4.99 = ( comp_C7449957260575251196nteger @ M1 @ M22 ) )
% 4.69/4.99 => ( ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ F @ M ) @ G )
% 4.69/4.99 = ( comp_C8797469213163452608nteger @ ( comp_C95226695241045696nteger @ ( comp_C1593894019821074884nteger @ F @ M1 ) @ Rep2 ) @ ( comp_C2931745410781319416nteger @ ( comp_C2931745410781319416nteger @ Abs2 @ M22 ) @ G ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_map_comp0
% 4.69/4.99 thf(fact_4382_type__copy__map__comp0,axiom,
% 4.69/4.99 ! [Rep2: code_integer > code_integer,Abs2: code_integer > code_integer,M: code_integer > code_integer > code_integer,M1: code_integer > code_integer > code_integer,M22: code_integer > code_integer,F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer] :
% 4.69/4.99 ( ( type_d4796611474492816872nteger @ Rep2 @ Abs2 @ top_to4645266643341252675nteger )
% 4.69/4.99 => ( ( M
% 4.69/4.99 = ( comp_C2931745410781319416nteger @ M1 @ M22 ) )
% 4.69/4.99 => ( ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ F @ M ) @ G )
% 4.69/4.99 = ( comp_C1593894019821074884nteger @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ F @ M1 ) @ Rep2 ) @ ( comp_C7449957260575251196nteger @ ( comp_C7449957260575251196nteger @ Abs2 @ M22 ) @ G ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_map_comp0
% 4.69/4.99 thf(fact_4383_type__copy__map__comp0__undo,axiom,
% 4.69/4.99 ! [Rep2: code_integer > int,Abs2: int > code_integer,Rep3: code_integer > int,Abs3: int > code_integer,Rep4: code_integer > int,Abs4: int > code_integer,M: int > int,M1: int > int,M22: int > int] :
% 4.69/4.99 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ top_top_set_int )
% 4.69/4.99 => ( ( type_d8366093980585677751er_int @ Rep3 @ Abs3 @ top_top_set_int )
% 4.69/4.99 => ( ( type_d8366093980585677751er_int @ Rep4 @ Abs4 @ top_top_set_int )
% 4.69/4.99 => ( ( ( comp_i6014793192326455499nteger @ ( comp_i1585864551200866970er_int @ Abs3 @ M ) @ Rep4 )
% 4.69/4.99 = ( comp_C7449957260575251196nteger @ ( comp_i6014793192326455499nteger @ ( comp_i1585864551200866970er_int @ Abs3 @ M1 ) @ Rep2 ) @ ( comp_i6014793192326455499nteger @ ( comp_i1585864551200866970er_int @ Abs2 @ M22 ) @ Rep4 ) ) )
% 4.69/4.99 => ( ( comp_int_int_int @ M1 @ M22 )
% 4.69/4.99 = M ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_map_comp0_undo
% 4.69/4.99 thf(fact_4384_type__copy__map__comp0__undo,axiom,
% 4.69/4.99 ! [Rep2: code_integer > int,Abs2: int > code_integer,Rep3: code_integer > int,Abs3: int > code_integer,Rep4: product_unit > $o,Abs4: $o > product_unit,M: $o > int,M1: int > int,M22: $o > int] :
% 4.69/4.99 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ top_top_set_int )
% 4.69/4.99 => ( ( type_d8366093980585677751er_int @ Rep3 @ Abs3 @ top_top_set_int )
% 4.69/4.99 => ( ( type_d6188575255521822967unit_o @ Rep4 @ Abs4 @ top_top_set_o )
% 4.69/4.99 => ( ( ( comp_o780160699970281785t_unit @ ( comp_i5286552343147518890eger_o @ Abs3 @ M ) @ Rep4 )
% 4.69/4.99 = ( comp_C2290379119555921966t_unit @ ( comp_i6014793192326455499nteger @ ( comp_i1585864551200866970er_int @ Abs3 @ M1 ) @ Rep2 ) @ ( comp_o780160699970281785t_unit @ ( comp_i5286552343147518890eger_o @ Abs2 @ M22 ) @ Rep4 ) ) )
% 4.69/4.99 => ( ( comp_int_int_o @ M1 @ M22 )
% 4.69/4.99 = M ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_map_comp0_undo
% 4.69/4.99 thf(fact_4385_type__copy__map__comp0__undo,axiom,
% 4.69/4.99 ! [Rep2: code_integer > int,Abs2: int > code_integer,Rep3: code_integer > int,Abs3: int > code_integer,Rep4: code_natural > nat,Abs4: nat > code_natural,M: nat > int,M1: int > int,M22: nat > int] :
% 4.69/4.99 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ top_top_set_int )
% 4.69/4.99 => ( ( type_d8366093980585677751er_int @ Rep3 @ Abs3 @ top_top_set_int )
% 4.69/4.99 => ( ( type_d4410041424927559462al_nat @ Rep4 @ Abs4 @ top_top_set_nat )
% 4.69/4.99 => ( ( ( comp_n5699668407433660474atural @ ( comp_i1588355021709917246er_nat @ Abs3 @ M ) @ Rep4 )
% 4.69/4.99 = ( comp_C6273552412331968711atural @ ( comp_i6014793192326455499nteger @ ( comp_i1585864551200866970er_int @ Abs3 @ M1 ) @ Rep2 ) @ ( comp_n5699668407433660474atural @ ( comp_i1588355021709917246er_nat @ Abs2 @ M22 ) @ Rep4 ) ) )
% 4.69/4.99 => ( ( comp_int_int_nat @ M1 @ M22 )
% 4.69/4.99 = M ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_map_comp0_undo
% 4.69/4.99 thf(fact_4386_type__copy__map__comp0__undo,axiom,
% 4.69/4.99 ! [Rep2: code_integer > int,Abs2: int > code_integer,Rep3: product_unit > $o,Abs3: $o > product_unit,Rep4: code_integer > int,Abs4: int > code_integer,M: int > $o,M1: int > $o,M22: int > int] :
% 4.69/4.99 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ top_top_set_int )
% 4.69/4.99 => ( ( type_d6188575255521822967unit_o @ Rep3 @ Abs3 @ top_top_set_o )
% 4.69/4.99 => ( ( type_d8366093980585677751er_int @ Rep4 @ Abs4 @ top_top_set_int )
% 4.69/4.99 => ( ( ( comp_i8439899303502915483nteger @ ( comp_o7049022088938261380it_int @ Abs3 @ M ) @ Rep4 )
% 4.69/4.99 = ( comp_C8146212659816229034nteger @ ( comp_i8439899303502915483nteger @ ( comp_o7049022088938261380it_int @ Abs3 @ M1 ) @ Rep2 ) @ ( comp_i6014793192326455499nteger @ ( comp_i1585864551200866970er_int @ Abs2 @ M22 ) @ Rep4 ) ) )
% 4.69/4.99 => ( ( comp_int_o_int @ M1 @ M22 )
% 4.69/4.99 = M ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_map_comp0_undo
% 4.69/4.99 thf(fact_4387_type__copy__map__comp0__undo,axiom,
% 4.69/4.99 ! [Rep2: code_integer > int,Abs2: int > code_integer,Rep3: product_unit > $o,Abs3: $o > product_unit,Rep4: product_unit > $o,Abs4: $o > product_unit,M: $o > $o,M1: int > $o,M22: $o > int] :
% 4.69/4.99 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ top_top_set_int )
% 4.69/4.99 => ( ( type_d6188575255521822967unit_o @ Rep3 @ Abs3 @ top_top_set_o )
% 4.69/4.99 => ( ( type_d6188575255521822967unit_o @ Rep4 @ Abs4 @ top_top_set_o )
% 4.69/4.99 => ( ( ( comp_o7724735231917782709t_unit @ ( comp_o3916225744453444672unit_o @ Abs3 @ M ) @ Rep4 )
% 4.69/4.99 = ( comp_C2408090164605745152t_unit @ ( comp_i8439899303502915483nteger @ ( comp_o7049022088938261380it_int @ Abs3 @ M1 ) @ Rep2 ) @ ( comp_o780160699970281785t_unit @ ( comp_i5286552343147518890eger_o @ Abs2 @ M22 ) @ Rep4 ) ) )
% 4.69/4.99 => ( ( comp_int_o_o @ M1 @ M22 )
% 4.69/4.99 = M ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_map_comp0_undo
% 4.69/4.99 thf(fact_4388_type__copy__map__comp0__undo,axiom,
% 4.69/4.99 ! [Rep2: code_integer > int,Abs2: int > code_integer,Rep3: product_unit > $o,Abs3: $o > product_unit,Rep4: code_natural > nat,Abs4: nat > code_natural,M: nat > $o,M1: int > $o,M22: nat > int] :
% 4.69/4.99 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ top_top_set_int )
% 4.69/4.99 => ( ( type_d6188575255521822967unit_o @ Rep3 @ Abs3 @ top_top_set_o )
% 4.69/4.99 => ( ( type_d4410041424927559462al_nat @ Rep4 @ Abs4 @ top_top_set_nat )
% 4.69/4.99 => ( ( ( comp_n8360577435903631554atural @ ( comp_o7051512559447311656it_nat @ Abs3 @ M ) @ Rep4 )
% 4.69/4.99 = ( comp_C6969807811572946549atural @ ( comp_i8439899303502915483nteger @ ( comp_o7049022088938261380it_int @ Abs3 @ M1 ) @ Rep2 ) @ ( comp_n5699668407433660474atural @ ( comp_i1588355021709917246er_nat @ Abs2 @ M22 ) @ Rep4 ) ) )
% 4.69/4.99 => ( ( comp_int_o_nat @ M1 @ M22 )
% 4.69/4.99 = M ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_map_comp0_undo
% 4.69/4.99 thf(fact_4389_type__copy__map__comp0__undo,axiom,
% 4.69/4.99 ! [Rep2: code_integer > int,Abs2: int > code_integer,Rep3: code_natural > nat,Abs3: nat > code_natural,Rep4: code_integer > int,Abs4: int > code_integer,M: int > nat,M1: int > nat,M22: int > int] :
% 4.69/4.99 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ top_top_set_int )
% 4.69/4.99 => ( ( type_d4410041424927559462al_nat @ Rep3 @ Abs3 @ top_top_set_nat )
% 4.69/4.99 => ( ( type_d8366093980585677751er_int @ Rep4 @ Abs4 @ top_top_set_int )
% 4.69/4.99 => ( ( ( comp_i455893257298015894nteger @ ( comp_n9160511493981425161al_int @ Abs3 @ M ) @ Rep4 )
% 4.69/4.99 = ( comp_C1891057325546811591nteger @ ( comp_i455893257298015894nteger @ ( comp_n9160511493981425161al_int @ Abs3 @ M1 ) @ Rep2 ) @ ( comp_i6014793192326455499nteger @ ( comp_i1585864551200866970er_int @ Abs2 @ M22 ) @ Rep4 ) ) )
% 4.69/4.99 => ( ( comp_int_nat_int @ M1 @ M22 )
% 4.69/4.99 = M ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_map_comp0_undo
% 4.69/4.99 thf(fact_4390_type__copy__map__comp0__undo,axiom,
% 4.69/4.99 ! [Rep2: code_integer > int,Abs2: int > code_integer,Rep3: code_natural > nat,Abs3: nat > code_natural,Rep4: product_unit > $o,Abs4: $o > product_unit,M: $o > nat,M1: int > nat,M22: $o > int] :
% 4.69/4.99 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ top_top_set_int )
% 4.69/4.99 => ( ( type_d4410041424927559462al_nat @ Rep3 @ Abs3 @ top_top_set_nat )
% 4.69/4.99 => ( ( type_d6188575255521822967unit_o @ Rep4 @ Abs4 @ top_top_set_o )
% 4.69/4.99 => ( ( ( comp_o2643362028263920430t_unit @ ( comp_n2857367870785791611ural_o @ Abs3 @ M ) @ Rep4 )
% 4.69/4.99 = ( comp_C4153580447849560611t_unit @ ( comp_i455893257298015894nteger @ ( comp_n9160511493981425161al_int @ Abs3 @ M1 ) @ Rep2 ) @ ( comp_o780160699970281785t_unit @ ( comp_i5286552343147518890eger_o @ Abs2 @ M22 ) @ Rep4 ) ) )
% 4.69/4.99 => ( ( comp_int_nat_o @ M1 @ M22 )
% 4.69/4.99 = M ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_map_comp0_undo
% 4.69/4.99 thf(fact_4391_type__copy__map__comp0__undo,axiom,
% 4.69/4.99 ! [Rep2: code_integer > int,Abs2: int > code_integer,Rep3: code_natural > nat,Abs3: nat > code_natural,Rep4: code_natural > nat,Abs4: nat > code_natural,M: nat > nat,M1: int > nat,M22: nat > int] :
% 4.69/4.99 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ top_top_set_int )
% 4.69/4.99 => ( ( type_d4410041424927559462al_nat @ Rep3 @ Abs3 @ top_top_set_nat )
% 4.69/4.99 => ( ( type_d4410041424927559462al_nat @ Rep4 @ Abs4 @ top_top_set_nat )
% 4.69/4.99 => ( ( ( comp_n140768472405220869atural @ ( comp_n9163001964490475437al_nat @ Abs3 @ M ) @ Rep4 )
% 4.69/4.99 = ( comp_C714652477303529106atural @ ( comp_i455893257298015894nteger @ ( comp_n9160511493981425161al_int @ Abs3 @ M1 ) @ Rep2 ) @ ( comp_n5699668407433660474atural @ ( comp_i1588355021709917246er_nat @ Abs2 @ M22 ) @ Rep4 ) ) )
% 4.69/4.99 => ( ( comp_int_nat_nat @ M1 @ M22 )
% 4.69/4.99 = M ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_map_comp0_undo
% 4.69/4.99 thf(fact_4392_type__copy__map__comp0__undo,axiom,
% 4.69/4.99 ! [Rep2: product_unit > $o,Abs2: $o > product_unit,Rep3: code_integer > int,Abs3: int > code_integer,Rep4: code_integer > int,Abs4: int > code_integer,M: int > int,M1: $o > int,M22: int > $o] :
% 4.69/4.99 ( ( type_d6188575255521822967unit_o @ Rep2 @ Abs2 @ top_top_set_o )
% 4.69/4.99 => ( ( type_d8366093980585677751er_int @ Rep3 @ Abs3 @ top_top_set_int )
% 4.69/4.99 => ( ( type_d8366093980585677751er_int @ Rep4 @ Abs4 @ top_top_set_int )
% 4.69/4.99 => ( ( ( comp_i6014793192326455499nteger @ ( comp_i1585864551200866970er_int @ Abs3 @ M ) @ Rep4 )
% 4.69/4.99 = ( comp_P6790823133229852966nteger @ ( comp_o780160699970281785t_unit @ ( comp_i5286552343147518890eger_o @ Abs3 @ M1 ) @ Rep2 ) @ ( comp_i8439899303502915483nteger @ ( comp_o7049022088938261380it_int @ Abs2 @ M22 ) @ Rep4 ) ) )
% 4.69/4.99 => ( ( comp_o_int_int @ M1 @ M22 )
% 4.69/4.99 = M ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_map_comp0_undo
% 4.69/4.99 thf(fact_4393_wf__bounded__measure,axiom,
% 4.69/4.99 ! [R2: set_Pr1261947904930325089at_nat,Ub: nat > nat,F: nat > nat] :
% 4.69/4.99 ( ! [A4: nat,B2: nat] :
% 4.69/4.99 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B2 @ A4 ) @ R2 )
% 4.69/4.99 => ( ( ord_less_eq_nat @ ( Ub @ B2 ) @ ( Ub @ A4 ) )
% 4.69/4.99 & ( ord_less_eq_nat @ ( F @ B2 ) @ ( Ub @ A4 ) )
% 4.69/4.99 & ( ord_less_nat @ ( F @ A4 ) @ ( F @ B2 ) ) ) )
% 4.69/4.99 => ( wf_nat @ R2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % wf_bounded_measure
% 4.69/4.99 thf(fact_4394_wf__bounded__measure,axiom,
% 4.69/4.99 ! [R2: set_Pr958786334691620121nt_int,Ub: int > nat,F: int > nat] :
% 4.69/4.99 ( ! [A4: int,B2: int] :
% 4.69/4.99 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B2 @ A4 ) @ R2 )
% 4.69/4.99 => ( ( ord_less_eq_nat @ ( Ub @ B2 ) @ ( Ub @ A4 ) )
% 4.69/4.99 & ( ord_less_eq_nat @ ( F @ B2 ) @ ( Ub @ A4 ) )
% 4.69/4.99 & ( ord_less_nat @ ( F @ A4 ) @ ( F @ B2 ) ) ) )
% 4.69/4.99 => ( wf_int @ R2 ) ) ).
% 4.69/4.99
% 4.69/4.99 % wf_bounded_measure
% 4.69/4.99 thf(fact_4395_less__assn__def,axiom,
% 4.69/4.99 ( ord_less_assn
% 4.69/4.99 = ( ^ [A6: assn,B6: assn] :
% 4.69/4.99 ( ( ord_less_eq_assn @ A6 @ B6 )
% 4.69/4.99 & ( A6 != B6 ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % less_assn_def
% 4.69/4.99 thf(fact_4396_top__assn__def,axiom,
% 4.69/4.99 ( top_top_assn
% 4.69/4.99 = ( abs_assn @ in_range ) ) ).
% 4.69/4.99
% 4.69/4.99 % top_assn_def
% 4.69/4.99 thf(fact_4397_pred__on_Ochain__extend,axiom,
% 4.69/4.99 ! [A: set_Product_unit,P: product_unit > product_unit > $o,C5: set_Product_unit,Z: product_unit] :
% 4.69/4.99 ( ( pred_c6915491785556283576t_unit @ A @ P @ C5 )
% 4.69/4.99 => ( ( member_Product_unit @ Z @ A )
% 4.69/4.99 => ( ! [X3: product_unit] :
% 4.69/4.99 ( ( member_Product_unit @ X3 @ C5 )
% 4.69/4.99 => ( sup_su3411595859437804162unit_o @ P
% 4.69/4.99 @ ^ [Y4: product_unit,Z4: product_unit] : ( Y4 = Z4 )
% 4.69/4.99 @ X3
% 4.69/4.99 @ Z ) )
% 4.69/4.99 => ( pred_c6915491785556283576t_unit @ A @ P @ ( sup_su793286257634532545t_unit @ ( insert_Product_unit @ Z @ bot_bo3957492148770167129t_unit ) @ C5 ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % pred_on.chain_extend
% 4.69/4.99 thf(fact_4398_pred__on_Ochain__extend,axiom,
% 4.69/4.99 ! [A: set_o,P: $o > $o > $o,C5: set_o,Z: $o] :
% 4.69/4.99 ( ( pred_chain_o @ A @ P @ C5 )
% 4.69/4.99 => ( ( member_o @ Z @ A )
% 4.69/4.99 => ( ! [X3: $o] :
% 4.69/4.99 ( ( member_o @ X3 @ C5 )
% 4.69/4.99 => ( sup_sup_o_o_o @ P
% 4.69/4.99 @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 4.69/4.99 @ X3
% 4.69/4.99 @ Z ) )
% 4.69/4.99 => ( pred_chain_o @ A @ P @ ( sup_sup_set_o @ ( insert_o @ Z @ bot_bot_set_o ) @ C5 ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % pred_on.chain_extend
% 4.69/4.99 thf(fact_4399_pred__on_Ochain__extend,axiom,
% 4.69/4.99 ! [A: set_nat,P: nat > nat > $o,C5: set_nat,Z: nat] :
% 4.69/4.99 ( ( pred_chain_nat @ A @ P @ C5 )
% 4.69/4.99 => ( ( member_nat @ Z @ A )
% 4.69/4.99 => ( ! [X3: nat] :
% 4.69/4.99 ( ( member_nat @ X3 @ C5 )
% 4.69/4.99 => ( sup_sup_nat_nat_o @ P
% 4.69/4.99 @ ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 )
% 4.69/4.99 @ X3
% 4.69/4.99 @ Z ) )
% 4.69/4.99 => ( pred_chain_nat @ A @ P @ ( sup_sup_set_nat @ ( insert_nat @ Z @ bot_bot_set_nat ) @ C5 ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % pred_on.chain_extend
% 4.69/4.99 thf(fact_4400_pred__on_Ochain__extend,axiom,
% 4.69/4.99 ! [A: set_int,P: int > int > $o,C5: set_int,Z: int] :
% 4.69/4.99 ( ( pred_chain_int @ A @ P @ C5 )
% 4.69/4.99 => ( ( member_int @ Z @ A )
% 4.69/4.99 => ( ! [X3: int] :
% 4.69/4.99 ( ( member_int @ X3 @ C5 )
% 4.69/4.99 => ( sup_sup_int_int_o @ P
% 4.69/4.99 @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 4.69/4.99 @ X3
% 4.69/4.99 @ Z ) )
% 4.69/4.99 => ( pred_chain_int @ A @ P @ ( sup_sup_set_int @ ( insert_int @ Z @ bot_bot_set_int ) @ C5 ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % pred_on.chain_extend
% 4.69/4.99 thf(fact_4401_pred__on_Ochain__extend,axiom,
% 4.69/4.99 ! [A: set_Pr4532377907799695533_nat_o,P: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o,C5: set_Pr4532377907799695533_nat_o,Z: produc3658429121746597890et_nat > $o] :
% 4.69/4.99 ( ( pred_c177362287423414904_nat_o @ A @ P @ C5 )
% 4.69/4.99 => ( ( member6576561426505652726_nat_o @ Z @ A )
% 4.69/4.99 => ( ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/4.99 ( ( member6576561426505652726_nat_o @ X3 @ C5 )
% 4.69/4.99 => ( sup_su1942872429929737346at_o_o @ P
% 4.69/4.99 @ ^ [Y4: produc3658429121746597890et_nat > $o,Z4: produc3658429121746597890et_nat > $o] : ( Y4 = Z4 )
% 4.69/4.99 @ X3
% 4.69/4.99 @ Z ) )
% 4.69/4.99 => ( pred_c177362287423414904_nat_o @ A @ P @ ( sup_su5209123915105501825_nat_o @ ( insert5175938949040314269_nat_o @ Z @ bot_bo7824918357723582233_nat_o ) @ C5 ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % pred_on.chain_extend
% 4.69/4.99 thf(fact_4402_subset__Zorn__nonempty,axiom,
% 4.69/4.99 ! [A11: set_set_nat] :
% 4.69/4.99 ( ( A11 != bot_bot_set_set_nat )
% 4.69/4.99 => ( ! [C7: set_set_nat] :
% 4.69/4.99 ( ( C7 != bot_bot_set_set_nat )
% 4.69/4.99 => ( ( pred_chain_set_nat @ A11 @ ord_less_set_nat @ C7 )
% 4.69/4.99 => ( member_set_nat @ ( comple7399068483239264473et_nat @ C7 ) @ A11 ) ) )
% 4.69/4.99 => ? [X3: set_nat] :
% 4.69/4.99 ( ( member_set_nat @ X3 @ A11 )
% 4.69/4.99 & ! [Xa2: set_nat] :
% 4.69/4.99 ( ( member_set_nat @ Xa2 @ A11 )
% 4.69/4.99 => ( ( ord_less_eq_set_nat @ X3 @ Xa2 )
% 4.69/4.99 => ( Xa2 = X3 ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % subset_Zorn_nonempty
% 4.69/4.99 thf(fact_4403_in__measure,axiom,
% 4.69/4.99 ! [X: nat,Y: nat,F: nat > nat] :
% 4.69/4.99 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measure_nat @ F ) )
% 4.69/4.99 = ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % in_measure
% 4.69/4.99 thf(fact_4404_in__measure,axiom,
% 4.69/4.99 ! [X: int,Y: int,F: int > nat] :
% 4.69/4.99 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measure_int @ F ) )
% 4.69/4.99 = ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % in_measure
% 4.69/4.99 thf(fact_4405_top_Oordering__top__axioms,axiom,
% 4.69/4.99 orderi2935705153647960990t_unit @ ord_le3507040750410214029t_unit @ ord_le8056459307392131481t_unit @ top_to1996260823553986621t_unit ).
% 4.69/4.99
% 4.69/4.99 % top.ordering_top_axioms
% 4.69/4.99 thf(fact_4406_top_Oordering__top__axioms,axiom,
% 4.69/4.99 ordering_top_set_o @ ord_less_eq_set_o @ ord_less_set_o @ top_top_set_o ).
% 4.69/4.99
% 4.69/4.99 % top.ordering_top_axioms
% 4.69/4.99 thf(fact_4407_top_Oordering__top__axioms,axiom,
% 4.69/4.99 ordering_top_set_int @ ord_less_eq_set_int @ ord_less_set_int @ top_top_set_int ).
% 4.69/4.99
% 4.69/4.99 % top.ordering_top_axioms
% 4.69/4.99 thf(fact_4408_top_Oordering__top__axioms,axiom,
% 4.69/4.99 ordering_top_assn @ ord_less_eq_assn @ ord_less_assn @ top_top_assn ).
% 4.69/4.99
% 4.69/4.99 % top.ordering_top_axioms
% 4.69/4.99 thf(fact_4409_top_Oordering__top__axioms,axiom,
% 4.69/4.99 orderi2807725203697798511er_nat @ ord_le2510731241096832064er_nat @ ord_less_filter_nat @ top_top_filter_nat ).
% 4.69/4.99
% 4.69/4.99 % top.ordering_top_axioms
% 4.69/4.99 thf(fact_4410_top_Oordering__top__axioms,axiom,
% 4.69/4.99 ordering_top_set_nat @ ord_less_eq_set_nat @ ord_less_set_nat @ top_top_set_nat ).
% 4.69/4.99
% 4.69/4.99 % top.ordering_top_axioms
% 4.69/4.99 thf(fact_4411_Max_Oinsert__remove,axiom,
% 4.69/4.99 ! [A: set_Code_integer,X: code_integer] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.99 => ( ( ( ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) )
% 4.69/4.99 = bot_bo3990330152332043303nteger )
% 4.69/4.99 => ( ( lattic4901227151466704046nteger @ ( insert_Code_integer @ X @ A ) )
% 4.69/4.99 = X ) )
% 4.69/4.99 & ( ( ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) )
% 4.69/4.99 != bot_bo3990330152332043303nteger )
% 4.69/4.99 => ( ( lattic4901227151466704046nteger @ ( insert_Code_integer @ X @ A ) )
% 4.69/4.99 = ( ord_max_Code_integer @ X @ ( lattic4901227151466704046nteger @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max.insert_remove
% 4.69/4.99 thf(fact_4412_Max_Oinsert__remove,axiom,
% 4.69/4.99 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.99 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.99 => ( ( ( ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.99 = bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ( ( lattic1210392890313158908t_unit @ ( insert_Product_unit @ X @ A ) )
% 4.69/4.99 = X ) )
% 4.69/4.99 & ( ( ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.99 != bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ( ( lattic1210392890313158908t_unit @ ( insert_Product_unit @ X @ A ) )
% 4.69/4.99 = ( ord_max_Product_unit @ X @ ( lattic1210392890313158908t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max.insert_remove
% 4.69/4.99 thf(fact_4413_Max_Oinsert__remove,axiom,
% 4.69/4.99 ! [A: set_o,X: $o] :
% 4.69/4.99 ( ( finite_finite_o @ A )
% 4.69/4.99 => ( ( lattic1921953407002678535_Max_o @ ( insert_o @ X @ A ) )
% 4.69/4.99 = ( ( ( ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.99 = bot_bot_set_o )
% 4.69/4.99 => X )
% 4.69/4.99 & ( ( ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.99 != bot_bot_set_o )
% 4.69/4.99 => ( ord_max_o @ X @ ( lattic1921953407002678535_Max_o @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max.insert_remove
% 4.69/4.99 thf(fact_4414_Max_Oinsert__remove,axiom,
% 4.69/4.99 ! [A: set_int,X: int] :
% 4.69/4.99 ( ( finite_finite_int @ A )
% 4.69/4.99 => ( ( ( ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.99 = bot_bot_set_int )
% 4.69/4.99 => ( ( lattic8263393255366662781ax_int @ ( insert_int @ X @ A ) )
% 4.69/4.99 = X ) )
% 4.69/4.99 & ( ( ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.99 != bot_bot_set_int )
% 4.69/4.99 => ( ( lattic8263393255366662781ax_int @ ( insert_int @ X @ A ) )
% 4.69/4.99 = ( ord_max_int @ X @ ( lattic8263393255366662781ax_int @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max.insert_remove
% 4.69/4.99 thf(fact_4415_Max_Oinsert__remove,axiom,
% 4.69/4.99 ! [A: set_nat,X: nat] :
% 4.69/4.99 ( ( finite_finite_nat @ A )
% 4.69/4.99 => ( ( ( ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.99 = bot_bot_set_nat )
% 4.69/4.99 => ( ( lattic8265883725875713057ax_nat @ ( insert_nat @ X @ A ) )
% 4.69/4.99 = X ) )
% 4.69/4.99 & ( ( ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.99 != bot_bot_set_nat )
% 4.69/4.99 => ( ( lattic8265883725875713057ax_nat @ ( insert_nat @ X @ A ) )
% 4.69/4.99 = ( ord_max_nat @ X @ ( lattic8265883725875713057ax_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max.insert_remove
% 4.69/4.99 thf(fact_4416_Max_Oremove,axiom,
% 4.69/4.99 ! [A: set_Code_integer,X: code_integer] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.99 => ( ( member_Code_integer @ X @ A )
% 4.69/4.99 => ( ( ( ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) )
% 4.69/4.99 = bot_bo3990330152332043303nteger )
% 4.69/4.99 => ( ( lattic4901227151466704046nteger @ A )
% 4.69/4.99 = X ) )
% 4.69/4.99 & ( ( ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) )
% 4.69/4.99 != bot_bo3990330152332043303nteger )
% 4.69/4.99 => ( ( lattic4901227151466704046nteger @ A )
% 4.69/4.99 = ( ord_max_Code_integer @ X @ ( lattic4901227151466704046nteger @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max.remove
% 4.69/4.99 thf(fact_4417_Max_Oremove,axiom,
% 4.69/4.99 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.99 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.99 => ( ( member_Product_unit @ X @ A )
% 4.69/4.99 => ( ( ( ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.99 = bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ( ( lattic1210392890313158908t_unit @ A )
% 4.69/4.99 = X ) )
% 4.69/4.99 & ( ( ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/4.99 != bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ( ( lattic1210392890313158908t_unit @ A )
% 4.69/4.99 = ( ord_max_Product_unit @ X @ ( lattic1210392890313158908t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max.remove
% 4.69/4.99 thf(fact_4418_Max_Oremove,axiom,
% 4.69/4.99 ! [A: set_o,X: $o] :
% 4.69/4.99 ( ( finite_finite_o @ A )
% 4.69/4.99 => ( ( member_o @ X @ A )
% 4.69/4.99 => ( ( lattic1921953407002678535_Max_o @ A )
% 4.69/4.99 = ( ( ( ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.99 = bot_bot_set_o )
% 4.69/4.99 => X )
% 4.69/4.99 & ( ( ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/4.99 != bot_bot_set_o )
% 4.69/4.99 => ( ord_max_o @ X @ ( lattic1921953407002678535_Max_o @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max.remove
% 4.69/4.99 thf(fact_4419_Max_Oremove,axiom,
% 4.69/4.99 ! [A: set_int,X: int] :
% 4.69/4.99 ( ( finite_finite_int @ A )
% 4.69/4.99 => ( ( member_int @ X @ A )
% 4.69/4.99 => ( ( ( ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.99 = bot_bot_set_int )
% 4.69/4.99 => ( ( lattic8263393255366662781ax_int @ A )
% 4.69/4.99 = X ) )
% 4.69/4.99 & ( ( ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/4.99 != bot_bot_set_int )
% 4.69/4.99 => ( ( lattic8263393255366662781ax_int @ A )
% 4.69/4.99 = ( ord_max_int @ X @ ( lattic8263393255366662781ax_int @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max.remove
% 4.69/4.99 thf(fact_4420_Max_Oremove,axiom,
% 4.69/4.99 ! [A: set_nat,X: nat] :
% 4.69/4.99 ( ( finite_finite_nat @ A )
% 4.69/4.99 => ( ( member_nat @ X @ A )
% 4.69/4.99 => ( ( ( ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.99 = bot_bot_set_nat )
% 4.69/4.99 => ( ( lattic8265883725875713057ax_nat @ A )
% 4.69/4.99 = X ) )
% 4.69/4.99 & ( ( ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/4.99 != bot_bot_set_nat )
% 4.69/4.99 => ( ( lattic8265883725875713057ax_nat @ A )
% 4.69/4.99 = ( ord_max_nat @ X @ ( lattic8265883725875713057ax_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max.remove
% 4.69/4.99 thf(fact_4421_inj__on__Un,axiom,
% 4.69/4.99 ! [F: code_integer > code_integer,A: set_Code_integer,B4: set_Code_integer] :
% 4.69/4.99 ( ( inj_on1158064722259180589nteger @ F @ ( sup_su848401254843788991nteger @ A @ B4 ) )
% 4.69/4.99 = ( ( inj_on1158064722259180589nteger @ F @ A )
% 4.69/4.99 & ( inj_on1158064722259180589nteger @ F @ B4 )
% 4.69/4.99 & ( ( inf_in1364745209274528805nteger @ ( image_4470545334726330049nteger @ F @ ( minus_2355218937544613996nteger @ A @ B4 ) ) @ ( image_4470545334726330049nteger @ F @ ( minus_2355218937544613996nteger @ B4 @ A ) ) )
% 4.69/4.99 = bot_bo3990330152332043303nteger ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_on_Un
% 4.69/4.99 thf(fact_4422_inj__on__Un,axiom,
% 4.69/4.99 ! [F: nat > set_nat,A: set_nat,B4: set_nat] :
% 4.69/4.99 ( ( inj_on_nat_set_nat @ F @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.99 = ( ( inj_on_nat_set_nat @ F @ A )
% 4.69/4.99 & ( inj_on_nat_set_nat @ F @ B4 )
% 4.69/4.99 & ( ( inf_inf_set_set_nat @ ( image_nat_set_nat @ F @ ( minus_minus_set_nat @ A @ B4 ) ) @ ( image_nat_set_nat @ F @ ( minus_minus_set_nat @ B4 @ A ) ) )
% 4.69/4.99 = bot_bot_set_set_nat ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_on_Un
% 4.69/4.99 thf(fact_4423_inj__on__Un,axiom,
% 4.69/4.99 ! [F: nat > code_integer,A: set_nat,B4: set_nat] :
% 4.69/4.99 ( ( inj_on2245834603434889120nteger @ F @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.99 = ( ( inj_on2245834603434889120nteger @ F @ A )
% 4.69/4.99 & ( inj_on2245834603434889120nteger @ F @ B4 )
% 4.69/4.99 & ( ( inf_in1364745209274528805nteger @ ( image_1215581382706833972nteger @ F @ ( minus_minus_set_nat @ A @ B4 ) ) @ ( image_1215581382706833972nteger @ F @ ( minus_minus_set_nat @ B4 @ A ) ) )
% 4.69/4.99 = bot_bo3990330152332043303nteger ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_on_Un
% 4.69/4.99 thf(fact_4424_inj__on__Un,axiom,
% 4.69/4.99 ! [F: nat > product_unit,A: set_nat,B4: set_nat] :
% 4.69/4.99 ( ( inj_on7061601236592826506t_unit @ F @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.99 = ( ( inj_on7061601236592826506t_unit @ F @ A )
% 4.69/4.99 & ( inj_on7061601236592826506t_unit @ F @ B4 )
% 4.69/4.99 & ( ( inf_in4660618365625256667t_unit @ ( image_8730104196221521654t_unit @ F @ ( minus_minus_set_nat @ A @ B4 ) ) @ ( image_8730104196221521654t_unit @ F @ ( minus_minus_set_nat @ B4 @ A ) ) )
% 4.69/4.99 = bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_on_Un
% 4.69/4.99 thf(fact_4425_inj__on__Un,axiom,
% 4.69/4.99 ! [F: nat > $o,A: set_nat,B4: set_nat] :
% 4.69/4.99 ( ( inj_on_nat_o @ F @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.99 = ( ( inj_on_nat_o @ F @ A )
% 4.69/4.99 & ( inj_on_nat_o @ F @ B4 )
% 4.69/4.99 & ( ( inf_inf_set_o @ ( image_nat_o2 @ F @ ( minus_minus_set_nat @ A @ B4 ) ) @ ( image_nat_o2 @ F @ ( minus_minus_set_nat @ B4 @ A ) ) )
% 4.69/4.99 = bot_bot_set_o ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_on_Un
% 4.69/4.99 thf(fact_4426_inj__on__Un,axiom,
% 4.69/4.99 ! [F: nat > nat,A: set_nat,B4: set_nat] :
% 4.69/4.99 ( ( inj_on_nat_nat @ F @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.99 = ( ( inj_on_nat_nat @ F @ A )
% 4.69/4.99 & ( inj_on_nat_nat @ F @ B4 )
% 4.69/4.99 & ( ( inf_inf_set_nat @ ( image_nat_nat2 @ F @ ( minus_minus_set_nat @ A @ B4 ) ) @ ( image_nat_nat2 @ F @ ( minus_minus_set_nat @ B4 @ A ) ) )
% 4.69/4.99 = bot_bot_set_nat ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_on_Un
% 4.69/4.99 thf(fact_4427_inj__on__Un,axiom,
% 4.69/4.99 ! [F: nat > int,A: set_nat,B4: set_nat] :
% 4.69/4.99 ( ( inj_on_nat_int @ F @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.99 = ( ( inj_on_nat_int @ F @ A )
% 4.69/4.99 & ( inj_on_nat_int @ F @ B4 )
% 4.69/4.99 & ( ( inf_inf_set_int @ ( image_nat_int2 @ F @ ( minus_minus_set_nat @ A @ B4 ) ) @ ( image_nat_int2 @ F @ ( minus_minus_set_nat @ B4 @ A ) ) )
% 4.69/4.99 = bot_bot_set_int ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_on_Un
% 4.69/4.99 thf(fact_4428_inj__on__Un,axiom,
% 4.69/4.99 ! [F: nat > produc3658429121746597890et_nat > $o,A: set_nat,B4: set_nat] :
% 4.69/4.99 ( ( inj_on7779444506608719434_nat_o @ F @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/4.99 = ( ( inj_on7779444506608719434_nat_o @ F @ A )
% 4.69/4.99 & ( inj_on7779444506608719434_nat_o @ F @ B4 )
% 4.69/4.99 & ( ( inf_in1906310914598751387_nat_o @ ( image_4682239675366380726_nat_o @ F @ ( minus_minus_set_nat @ A @ B4 ) ) @ ( image_4682239675366380726_nat_o @ F @ ( minus_minus_set_nat @ B4 @ A ) ) )
% 4.69/4.99 = bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_on_Un
% 4.69/4.99 thf(fact_4429_Max__insert,axiom,
% 4.69/4.99 ! [A: set_Code_integer,X: code_integer] :
% 4.69/4.99 ( ( finite6017078050557962740nteger @ A )
% 4.69/4.99 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/4.99 => ( ( lattic4901227151466704046nteger @ ( insert_Code_integer @ X @ A ) )
% 4.69/4.99 = ( ord_max_Code_integer @ X @ ( lattic4901227151466704046nteger @ A ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_insert
% 4.69/4.99 thf(fact_4430_Max__insert,axiom,
% 4.69/4.99 ! [A: set_Product_unit,X: product_unit] :
% 4.69/4.99 ( ( finite4290736615968046902t_unit @ A )
% 4.69/4.99 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/4.99 => ( ( lattic1210392890313158908t_unit @ ( insert_Product_unit @ X @ A ) )
% 4.69/4.99 = ( ord_max_Product_unit @ X @ ( lattic1210392890313158908t_unit @ A ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_insert
% 4.69/4.99 thf(fact_4431_Max__insert,axiom,
% 4.69/4.99 ! [A: set_o,X: $o] :
% 4.69/4.99 ( ( finite_finite_o @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_o )
% 4.69/4.99 => ( ( lattic1921953407002678535_Max_o @ ( insert_o @ X @ A ) )
% 4.69/4.99 = ( ord_max_o @ X @ ( lattic1921953407002678535_Max_o @ A ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_insert
% 4.69/4.99 thf(fact_4432_Max__insert,axiom,
% 4.69/4.99 ! [A: set_int,X: int] :
% 4.69/4.99 ( ( finite_finite_int @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_int )
% 4.69/4.99 => ( ( lattic8263393255366662781ax_int @ ( insert_int @ X @ A ) )
% 4.69/4.99 = ( ord_max_int @ X @ ( lattic8263393255366662781ax_int @ A ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_insert
% 4.69/4.99 thf(fact_4433_Max__insert,axiom,
% 4.69/4.99 ! [A: set_nat,X: nat] :
% 4.69/4.99 ( ( finite_finite_nat @ A )
% 4.69/4.99 => ( ( A != bot_bot_set_nat )
% 4.69/4.99 => ( ( lattic8265883725875713057ax_nat @ ( insert_nat @ X @ A ) )
% 4.69/4.99 = ( ord_max_nat @ X @ ( lattic8265883725875713057ax_nat @ A ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % Max_insert
% 4.69/4.99 thf(fact_4434_map__prod__surj,axiom,
% 4.69/4.99 ! [F: code_integer > code_integer,G: code_integer > code_integer] :
% 4.69/4.99 ( ( ( image_4470545334726330049nteger @ F @ top_to4645266643341252675nteger )
% 4.69/4.99 = top_to4645266643341252675nteger )
% 4.69/4.99 => ( ( ( image_4470545334726330049nteger @ G @ top_to4645266643341252675nteger )
% 4.69/4.99 = top_to4645266643341252675nteger )
% 4.69/4.99 => ( ( image_7082141833288935621nteger @ ( produc1802105962441033582nteger @ F @ G ) @ top_to2363841527343591755nteger )
% 4.69/4.99 = top_to2363841527343591755nteger ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_surj
% 4.69/4.99 thf(fact_4435_map__prod__surj,axiom,
% 4.69/4.99 ! [F: code_integer > code_integer,G: product_unit > product_unit] :
% 4.69/4.99 ( ( ( image_4470545334726330049nteger @ F @ top_to4645266643341252675nteger )
% 4.69/4.99 = top_to4645266643341252675nteger )
% 4.69/4.99 => ( ( ( image_405062704495631173t_unit @ G @ top_to1996260823553986621t_unit )
% 4.69/4.99 = top_to1996260823553986621t_unit )
% 4.69/4.99 => ( ( image_3456600171786721233t_unit @ ( produc3346700480963112818t_unit @ F @ G ) @ top_to3244471725241573579t_unit )
% 4.69/4.99 = top_to3244471725241573579t_unit ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_surj
% 4.69/4.99 thf(fact_4436_map__prod__surj,axiom,
% 4.69/4.99 ! [F: code_integer > code_integer,G: product_unit > $o] :
% 4.69/4.99 ( ( ( image_4470545334726330049nteger @ F @ top_to4645266643341252675nteger )
% 4.69/4.99 = top_to4645266643341252675nteger )
% 4.69/4.99 => ( ( ( image_Product_unit_o2 @ G @ top_to1996260823553986621t_unit )
% 4.69/4.99 = top_top_set_o )
% 4.69/4.99 => ( ( image_7060974388358999388eger_o @ ( produc8116347370398923901unit_o @ F @ G ) @ top_to3244471725241573579t_unit )
% 4.69/4.99 = top_to2658285827425157974eger_o ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_surj
% 4.69/4.99 thf(fact_4437_map__prod__surj,axiom,
% 4.69/4.99 ! [F: code_integer > code_integer,G: product_unit > nat] :
% 4.69/4.99 ( ( ( image_4470545334726330049nteger @ F @ top_to4645266643341252675nteger )
% 4.69/4.99 = top_to4645266643341252675nteger )
% 4.69/4.99 => ( ( ( image_875570014554754200it_nat @ G @ top_to1996260823553986621t_unit )
% 4.69/4.99 = top_top_set_nat )
% 4.69/4.99 => ( ( image_8236373689398998434er_nat @ ( produc4022400886476617259it_nat @ F @ G ) @ top_to3244471725241573579t_unit )
% 4.69/4.99 = top_to8760411888770933182er_nat ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_surj
% 4.69/4.99 thf(fact_4438_map__prod__surj,axiom,
% 4.69/4.99 ! [F: code_integer > code_integer,G: product_unit > int] :
% 4.69/4.99 ( ( ( image_4470545334726330049nteger @ F @ top_to4645266643341252675nteger )
% 4.69/4.99 = top_to4645266643341252675nteger )
% 4.69/4.99 => ( ( ( image_873079544045703924it_int @ G @ top_to1996260823553986621t_unit )
% 4.69/4.99 = top_top_set_int )
% 4.69/4.99 => ( ( image_4058522669889801726er_int @ ( produc4019910415967566983it_int @ F @ G ) @ top_to3244471725241573579t_unit )
% 4.69/4.99 = top_to6270328743839206426er_int ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_surj
% 4.69/4.99 thf(fact_4439_map__prod__surj,axiom,
% 4.69/4.99 ! [F: code_integer > code_integer,G: $o > product_unit] :
% 4.69/4.99 ( ( ( image_4470545334726330049nteger @ F @ top_to4645266643341252675nteger )
% 4.69/4.99 = top_to4645266643341252675nteger )
% 4.69/4.99 => ( ( ( image_o_Product_unit2 @ G @ top_top_set_o )
% 4.69/4.99 = top_to1996260823553986621t_unit )
% 4.69/4.99 => ( ( image_2425804817718344284t_unit @ ( produc3530376873132787239t_unit @ F @ G ) @ top_to2658285827425157974eger_o )
% 4.69/4.99 = top_to3244471725241573579t_unit ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_surj
% 4.69/4.99 thf(fact_4440_map__prod__surj,axiom,
% 4.69/4.99 ! [F: code_integer > code_integer,G: $o > $o] :
% 4.69/4.99 ( ( ( image_4470545334726330049nteger @ F @ top_to4645266643341252675nteger )
% 4.69/4.99 = top_to4645266643341252675nteger )
% 4.69/4.99 => ( ( ( image_o_o2 @ G @ top_top_set_o )
% 4.69/4.99 = top_top_set_o )
% 4.69/4.99 => ( ( image_227735840630799463eger_o @ ( produc1084426483498010290er_o_o @ F @ G ) @ top_to2658285827425157974eger_o )
% 4.69/4.99 = top_to2658285827425157974eger_o ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_surj
% 4.69/4.99 thf(fact_4441_map__prod__surj,axiom,
% 4.69/4.99 ! [F: code_integer > code_integer,G: $o > nat] :
% 4.69/4.99 ( ( ( image_4470545334726330049nteger @ F @ top_to4645266643341252675nteger )
% 4.69/4.99 = top_to4645266643341252675nteger )
% 4.69/4.99 => ( ( ( image_o_nat2 @ G @ top_top_set_o )
% 4.69/4.99 = top_top_set_nat )
% 4.69/4.99 => ( ( image_1252617143230709591er_nat @ ( produc7550393335539917622_o_nat @ F @ G ) @ top_to2658285827425157974eger_o )
% 4.69/4.99 = top_to8760411888770933182er_nat ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_surj
% 4.69/4.99 thf(fact_4442_map__prod__surj,axiom,
% 4.69/4.99 ! [F: code_integer > code_integer,G: $o > int] :
% 4.69/4.99 ( ( ( image_4470545334726330049nteger @ F @ top_to4645266643341252675nteger )
% 4.69/4.99 = top_to4645266643341252675nteger )
% 4.69/4.99 => ( ( ( image_o_int2 @ G @ top_top_set_o )
% 4.69/4.99 = top_top_set_int )
% 4.69/4.99 => ( ( image_6298138160576288691er_int @ ( produc7547902865030867346_o_int @ F @ G ) @ top_to2658285827425157974eger_o )
% 4.69/4.99 = top_to6270328743839206426er_int ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_surj
% 4.69/4.99 thf(fact_4443_map__prod__surj,axiom,
% 4.69/4.99 ! [F: code_integer > code_integer,G: nat > code_integer] :
% 4.69/4.99 ( ( ( image_4470545334726330049nteger @ F @ top_to4645266643341252675nteger )
% 4.69/4.99 = top_to4645266643341252675nteger )
% 4.69/4.99 => ( ( ( image_1215581382706833972nteger @ G @ top_top_set_nat )
% 4.69/4.99 = top_to4645266643341252675nteger )
% 4.69/4.99 => ( ( image_4921214744877245202nteger @ ( produc1622059938646302433nteger @ F @ G ) @ top_to8760411888770933182er_nat )
% 4.69/4.99 = top_to2363841527343591755nteger ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_surj
% 4.69/4.99 thf(fact_4444_inj__on__insert,axiom,
% 4.69/4.99 ! [F: code_integer > code_integer,A2: code_integer,A: set_Code_integer] :
% 4.69/4.99 ( ( inj_on1158064722259180589nteger @ F @ ( insert_Code_integer @ A2 @ A ) )
% 4.69/4.99 = ( ( inj_on1158064722259180589nteger @ F @ A )
% 4.69/4.99 & ~ ( member_Code_integer @ ( F @ A2 ) @ ( image_4470545334726330049nteger @ F @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_on_insert
% 4.69/4.99 thf(fact_4445_inj__on__insert,axiom,
% 4.69/4.99 ! [F: product_unit > nat,A2: product_unit,A: set_Product_unit] :
% 4.69/4.99 ( ( inj_on8430439091780834860it_nat @ F @ ( insert_Product_unit @ A2 @ A ) )
% 4.69/4.99 = ( ( inj_on8430439091780834860it_nat @ F @ A )
% 4.69/4.99 & ~ ( member_nat @ ( F @ A2 ) @ ( image_875570014554754200it_nat @ F @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_on_insert
% 4.69/4.99 thf(fact_4446_inj__on__insert,axiom,
% 4.69/4.99 ! [F: product_unit > int,A2: product_unit,A: set_Product_unit] :
% 4.69/4.99 ( ( inj_on8427948621271784584it_int @ F @ ( insert_Product_unit @ A2 @ A ) )
% 4.69/4.99 = ( ( inj_on8427948621271784584it_int @ F @ A )
% 4.69/4.99 & ~ ( member_int @ ( F @ A2 ) @ ( image_873079544045703924it_int @ F @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_on_insert
% 4.69/4.99 thf(fact_4447_inj__on__insert,axiom,
% 4.69/4.99 ! [F: product_unit > $o,A2: product_unit,A: set_Product_unit] :
% 4.69/4.99 ( ( inj_on8854722734121536060unit_o @ F @ ( insert_Product_unit @ A2 @ A ) )
% 4.69/4.99 = ( ( inj_on8854722734121536060unit_o @ F @ A )
% 4.69/4.99 & ~ ( member_o @ ( F @ A2 ) @ ( image_Product_unit_o2 @ F @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_on_insert
% 4.69/4.99 thf(fact_4448_inj__on__insert,axiom,
% 4.69/4.99 ! [F: product_unit > product_unit,A2: product_unit,A: set_Product_unit] :
% 4.69/4.99 ( ( inj_on8151373323710067377t_unit @ F @ ( insert_Product_unit @ A2 @ A ) )
% 4.69/4.99 = ( ( inj_on8151373323710067377t_unit @ F @ A )
% 4.69/4.99 & ~ ( member_Product_unit @ ( F @ A2 ) @ ( image_405062704495631173t_unit @ F @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_on_insert
% 4.69/4.99 thf(fact_4449_inj__on__insert,axiom,
% 4.69/4.99 ! [F: $o > nat,A2: $o,A: set_o] :
% 4.69/4.99 ( ( inj_on_o_nat @ F @ ( insert_o @ A2 @ A ) )
% 4.69/4.99 = ( ( inj_on_o_nat @ F @ A )
% 4.69/4.99 & ~ ( member_nat @ ( F @ A2 ) @ ( image_o_nat2 @ F @ ( minus_minus_set_o @ A @ ( insert_o @ A2 @ bot_bot_set_o ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_on_insert
% 4.69/4.99 thf(fact_4450_inj__on__insert,axiom,
% 4.69/4.99 ! [F: $o > int,A2: $o,A: set_o] :
% 4.69/4.99 ( ( inj_on_o_int @ F @ ( insert_o @ A2 @ A ) )
% 4.69/4.99 = ( ( inj_on_o_int @ F @ A )
% 4.69/4.99 & ~ ( member_int @ ( F @ A2 ) @ ( image_o_int2 @ F @ ( minus_minus_set_o @ A @ ( insert_o @ A2 @ bot_bot_set_o ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_on_insert
% 4.69/4.99 thf(fact_4451_inj__on__insert,axiom,
% 4.69/4.99 ! [F: $o > $o,A2: $o,A: set_o] :
% 4.69/4.99 ( ( inj_on_o_o @ F @ ( insert_o @ A2 @ A ) )
% 4.69/4.99 = ( ( inj_on_o_o @ F @ A )
% 4.69/4.99 & ~ ( member_o @ ( F @ A2 ) @ ( image_o_o2 @ F @ ( minus_minus_set_o @ A @ ( insert_o @ A2 @ bot_bot_set_o ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_on_insert
% 4.69/4.99 thf(fact_4452_inj__on__insert,axiom,
% 4.69/4.99 ! [F: $o > product_unit,A2: $o,A: set_o] :
% 4.69/4.99 ( ( inj_on4268752236855399398t_unit @ F @ ( insert_o @ A2 @ A ) )
% 4.69/4.99 = ( ( inj_on4268752236855399398t_unit @ F @ A )
% 4.69/4.99 & ~ ( member_Product_unit @ ( F @ A2 ) @ ( image_o_Product_unit2 @ F @ ( minus_minus_set_o @ A @ ( insert_o @ A2 @ bot_bot_set_o ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_on_insert
% 4.69/4.99 thf(fact_4453_inj__on__insert,axiom,
% 4.69/4.99 ! [F: int > nat,A2: int,A: set_int] :
% 4.69/4.99 ( ( inj_on_int_nat @ F @ ( insert_int @ A2 @ A ) )
% 4.69/4.99 = ( ( inj_on_int_nat @ F @ A )
% 4.69/4.99 & ~ ( member_nat @ ( F @ A2 ) @ ( image_int_nat2 @ F @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ bot_bot_set_int ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_on_insert
% 4.69/4.99 thf(fact_4454_max__bot,axiom,
% 4.69/4.99 ! [X: set_Product_unit] :
% 4.69/4.99 ( ( ord_ma508538259134630082t_unit @ bot_bo3957492148770167129t_unit @ X )
% 4.69/4.99 = X ) ).
% 4.69/4.99
% 4.69/4.99 % max_bot
% 4.69/4.99 thf(fact_4455_max__bot,axiom,
% 4.69/4.99 ! [X: set_o] :
% 4.69/4.99 ( ( ord_max_set_o @ bot_bot_set_o @ X )
% 4.69/4.99 = X ) ).
% 4.69/4.99
% 4.69/4.99 % max_bot
% 4.69/4.99 thf(fact_4456_max__bot,axiom,
% 4.69/4.99 ! [X: set_nat] :
% 4.69/4.99 ( ( ord_max_set_nat @ bot_bot_set_nat @ X )
% 4.69/4.99 = X ) ).
% 4.69/4.99
% 4.69/4.99 % max_bot
% 4.69/4.99 thf(fact_4457_max__bot,axiom,
% 4.69/4.99 ! [X: set_int] :
% 4.69/4.99 ( ( ord_max_set_int @ bot_bot_set_int @ X )
% 4.69/4.99 = X ) ).
% 4.69/4.99
% 4.69/4.99 % max_bot
% 4.69/4.99 thf(fact_4458_max__bot,axiom,
% 4.69/4.99 ! [X: set_Pr4532377907799695533_nat_o] :
% 4.69/4.99 ( ( ord_ma8206644353667601538_nat_o @ bot_bo7824918357723582233_nat_o @ X )
% 4.69/4.99 = X ) ).
% 4.69/4.99
% 4.69/4.99 % max_bot
% 4.69/4.99 thf(fact_4459_max__bot,axiom,
% 4.69/4.99 ! [X: nat] :
% 4.69/4.99 ( ( ord_max_nat @ bot_bot_nat @ X )
% 4.69/4.99 = X ) ).
% 4.69/4.99
% 4.69/4.99 % max_bot
% 4.69/4.99 thf(fact_4460_max__bot2,axiom,
% 4.69/4.99 ! [X: set_Product_unit] :
% 4.69/4.99 ( ( ord_ma508538259134630082t_unit @ X @ bot_bo3957492148770167129t_unit )
% 4.69/4.99 = X ) ).
% 4.69/4.99
% 4.69/4.99 % max_bot2
% 4.69/4.99 thf(fact_4461_max__bot2,axiom,
% 4.69/4.99 ! [X: set_o] :
% 4.69/4.99 ( ( ord_max_set_o @ X @ bot_bot_set_o )
% 4.69/4.99 = X ) ).
% 4.69/4.99
% 4.69/4.99 % max_bot2
% 4.69/4.99 thf(fact_4462_max__bot2,axiom,
% 4.69/4.99 ! [X: set_nat] :
% 4.69/4.99 ( ( ord_max_set_nat @ X @ bot_bot_set_nat )
% 4.69/4.99 = X ) ).
% 4.69/4.99
% 4.69/4.99 % max_bot2
% 4.69/4.99 thf(fact_4463_max__bot2,axiom,
% 4.69/4.99 ! [X: set_int] :
% 4.69/4.99 ( ( ord_max_set_int @ X @ bot_bot_set_int )
% 4.69/4.99 = X ) ).
% 4.69/4.99
% 4.69/4.99 % max_bot2
% 4.69/4.99 thf(fact_4464_max__bot2,axiom,
% 4.69/4.99 ! [X: set_Pr4532377907799695533_nat_o] :
% 4.69/4.99 ( ( ord_ma8206644353667601538_nat_o @ X @ bot_bo7824918357723582233_nat_o )
% 4.69/4.99 = X ) ).
% 4.69/4.99
% 4.69/4.99 % max_bot2
% 4.69/4.99 thf(fact_4465_max__bot2,axiom,
% 4.69/4.99 ! [X: nat] :
% 4.69/4.99 ( ( ord_max_nat @ X @ bot_bot_nat )
% 4.69/4.99 = X ) ).
% 4.69/4.99
% 4.69/4.99 % max_bot2
% 4.69/4.99 thf(fact_4466_max__top,axiom,
% 4.69/4.99 ! [X: assn] :
% 4.69/4.99 ( ( ord_max_assn @ top_top_assn @ X )
% 4.69/4.99 = top_top_assn ) ).
% 4.69/4.99
% 4.69/4.99 % max_top
% 4.69/4.99 thf(fact_4467_max__top,axiom,
% 4.69/4.99 ! [X: set_Product_unit] :
% 4.69/4.99 ( ( ord_ma508538259134630082t_unit @ top_to1996260823553986621t_unit @ X )
% 4.69/4.99 = top_to1996260823553986621t_unit ) ).
% 4.69/4.99
% 4.69/4.99 % max_top
% 4.69/4.99 thf(fact_4468_max__top,axiom,
% 4.69/4.99 ! [X: set_o] :
% 4.69/4.99 ( ( ord_max_set_o @ top_top_set_o @ X )
% 4.69/4.99 = top_top_set_o ) ).
% 4.69/4.99
% 4.69/4.99 % max_top
% 4.69/4.99 thf(fact_4469_max__top,axiom,
% 4.69/4.99 ! [X: set_nat] :
% 4.69/4.99 ( ( ord_max_set_nat @ top_top_set_nat @ X )
% 4.69/4.99 = top_top_set_nat ) ).
% 4.69/4.99
% 4.69/4.99 % max_top
% 4.69/4.99 thf(fact_4470_max__top,axiom,
% 4.69/4.99 ! [X: set_int] :
% 4.69/4.99 ( ( ord_max_set_int @ top_top_set_int @ X )
% 4.69/4.99 = top_top_set_int ) ).
% 4.69/4.99
% 4.69/4.99 % max_top
% 4.69/4.99 thf(fact_4471_max__top2,axiom,
% 4.69/4.99 ! [X: assn] :
% 4.69/4.99 ( ( ord_max_assn @ X @ top_top_assn )
% 4.69/4.99 = top_top_assn ) ).
% 4.69/4.99
% 4.69/4.99 % max_top2
% 4.69/4.99 thf(fact_4472_max__top2,axiom,
% 4.69/4.99 ! [X: set_Product_unit] :
% 4.69/4.99 ( ( ord_ma508538259134630082t_unit @ X @ top_to1996260823553986621t_unit )
% 4.69/4.99 = top_to1996260823553986621t_unit ) ).
% 4.69/4.99
% 4.69/4.99 % max_top2
% 4.69/4.99 thf(fact_4473_max__top2,axiom,
% 4.69/4.99 ! [X: set_o] :
% 4.69/4.99 ( ( ord_max_set_o @ X @ top_top_set_o )
% 4.69/4.99 = top_top_set_o ) ).
% 4.69/4.99
% 4.69/4.99 % max_top2
% 4.69/4.99 thf(fact_4474_max__top2,axiom,
% 4.69/4.99 ! [X: set_nat] :
% 4.69/4.99 ( ( ord_max_set_nat @ X @ top_top_set_nat )
% 4.69/4.99 = top_top_set_nat ) ).
% 4.69/4.99
% 4.69/4.99 % max_top2
% 4.69/4.99 thf(fact_4475_max__top2,axiom,
% 4.69/4.99 ! [X: set_int] :
% 4.69/4.99 ( ( ord_max_set_int @ X @ top_top_set_int )
% 4.69/4.99 = top_top_set_int ) ).
% 4.69/4.99
% 4.69/4.99 % max_top2
% 4.69/4.99 thf(fact_4476_map__prod__simp,axiom,
% 4.69/4.99 ! [F: nat > nat,G: nat > nat,A2: nat,B: nat] :
% 4.69/4.99 ( ( produc6977886695330630970at_nat @ F @ G @ ( product_Pair_nat_nat @ A2 @ B ) )
% 4.69/4.99 = ( product_Pair_nat_nat @ ( F @ A2 ) @ ( G @ B ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_simp
% 4.69/4.99 thf(fact_4477_map__prod__simp,axiom,
% 4.69/4.99 ! [F: nat > int,G: nat > int,A2: nat,B: nat] :
% 4.69/4.99 ( ( produc7347049785058425330at_int @ F @ G @ ( product_Pair_nat_nat @ A2 @ B ) )
% 4.69/4.99 = ( product_Pair_int_int @ ( F @ A2 ) @ ( G @ B ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_simp
% 4.69/4.99 thf(fact_4478_map__prod__simp,axiom,
% 4.69/4.99 ! [F: int > nat,G: int > nat,A2: int,B: int] :
% 4.69/4.99 ( ( produc5667422475138734578nt_nat @ F @ G @ ( product_Pair_int_int @ A2 @ B ) )
% 4.69/4.99 = ( product_Pair_nat_nat @ ( F @ A2 ) @ ( G @ B ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_simp
% 4.69/4.99 thf(fact_4479_map__prod__simp,axiom,
% 4.69/4.99 ! [F: int > int,G: int > int,A2: int,B: int] :
% 4.69/4.99 ( ( produc6036585564866528938nt_int @ F @ G @ ( product_Pair_int_int @ A2 @ B ) )
% 4.69/4.99 = ( product_Pair_int_int @ ( F @ A2 ) @ ( G @ B ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_simp
% 4.69/4.99 thf(fact_4480_map__prod__simp,axiom,
% 4.69/4.99 ! [F: heap_e7401611519738050253t_unit > nat,G: set_nat > nat,A2: heap_e7401611519738050253t_unit,B: set_nat] :
% 4.69/4.99 ( ( produc8285742784527409791at_nat @ F @ G @ ( produc7507926704131184380et_nat @ A2 @ B ) )
% 4.69/4.99 = ( product_Pair_nat_nat @ ( F @ A2 ) @ ( G @ B ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_simp
% 4.69/4.99 thf(fact_4481_map__prod__simp,axiom,
% 4.69/4.99 ! [F: heap_e7401611519738050253t_unit > int,G: set_nat > int,A2: heap_e7401611519738050253t_unit,B: set_nat] :
% 4.69/4.99 ( ( produc5973434381925408567at_int @ F @ G @ ( produc7507926704131184380et_nat @ A2 @ B ) )
% 4.69/4.99 = ( product_Pair_int_int @ ( F @ A2 ) @ ( G @ B ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_simp
% 4.69/4.99 thf(fact_4482_map__prod__simp,axiom,
% 4.69/4.99 ! [F: nat > heap_e7401611519738050253t_unit,G: nat > set_nat,A2: nat,B: nat] :
% 4.69/4.99 ( ( produc2064153442785501et_nat @ F @ G @ ( product_Pair_nat_nat @ A2 @ B ) )
% 4.69/4.99 = ( produc7507926704131184380et_nat @ ( F @ A2 ) @ ( G @ B ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_simp
% 4.69/4.99 thf(fact_4483_map__prod__simp,axiom,
% 4.69/4.99 ! [F: int > heap_e7401611519738050253t_unit,G: int > set_nat,A2: int,B: int] :
% 4.69/4.99 ( ( produc3152090231653401565et_nat @ F @ G @ ( product_Pair_int_int @ A2 @ B ) )
% 4.69/4.99 = ( produc7507926704131184380et_nat @ ( F @ A2 ) @ ( G @ B ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_simp
% 4.69/4.99 thf(fact_4484_map__prod__simp,axiom,
% 4.69/4.99 ! [F: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit,G: set_nat > set_nat,A2: heap_e7401611519738050253t_unit,B: set_nat] :
% 4.69/4.99 ( ( produc8234977478398262212et_nat @ F @ G @ ( produc7507926704131184380et_nat @ A2 @ B ) )
% 4.69/4.99 = ( produc7507926704131184380et_nat @ ( F @ A2 ) @ ( G @ B ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_simp
% 4.69/4.99 thf(fact_4485_map__prod__simp,axiom,
% 4.69/4.99 ! [F: nat > produc3658429121746597890et_nat > $o,G: nat > produc3658429121746597890et_nat,A2: nat,B: nat] :
% 4.69/4.99 ( ( produc79747477514316377et_nat @ F @ G @ ( product_Pair_nat_nat @ A2 @ B ) )
% 4.69/4.99 = ( produc5001842942810119800et_nat @ ( F @ A2 ) @ ( G @ B ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_simp
% 4.69/4.99 thf(fact_4486_snd__comp__map__prod,axiom,
% 4.69/4.99 ! [F: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit,G: set_nat > set_nat] :
% 4.69/4.99 ( ( comp_P2930521774885306735et_nat @ produc8586169260539613262et_nat @ ( produc8234977478398262212et_nat @ F @ G ) )
% 4.69/4.99 = ( comp_s5696514601250091763et_nat @ G @ produc8586169260539613262et_nat ) ) ).
% 4.69/4.99
% 4.69/4.99 % snd_comp_map_prod
% 4.69/4.99 thf(fact_4487_snd__comp__map__prod,axiom,
% 4.69/4.99 ! [F: int > heap_e7401611519738050253t_unit,G: int > set_nat] :
% 4.69/4.99 ( ( comp_P8606889026643445772nt_int @ produc8586169260539613262et_nat @ ( produc3152090231653401565et_nat @ F @ G ) )
% 4.69/4.99 = ( comp_i6200299785623974754nt_int @ G @ product_snd_int_int ) ) ).
% 4.69/4.99
% 4.69/4.99 % snd_comp_map_prod
% 4.69/4.99 thf(fact_4488_snd__comp__map__prod,axiom,
% 4.69/4.99 ! [F: heap_e7401611519738050253t_unit > int,G: set_nat > int] :
% 4.69/4.99 ( ( comp_P8308861049717174982et_nat @ product_snd_int_int @ ( produc5973434381925408567at_int @ F @ G ) )
% 4.69/4.99 = ( comp_s1601710177542341017et_nat @ G @ produc8586169260539613262et_nat ) ) ).
% 4.69/4.99
% 4.69/4.99 % snd_comp_map_prod
% 4.69/4.99 thf(fact_4489_snd__comp__map__prod,axiom,
% 4.69/4.99 ! [F: int > int,G: int > int] :
% 4.69/4.99 ( ( comp_P5356232565778667509nt_int @ product_snd_int_int @ ( produc6036585564866528938nt_int @ F @ G ) )
% 4.69/4.99 = ( comp_i4330622015127193916nt_int @ G @ product_snd_int_int ) ) ).
% 4.69/4.99
% 4.69/4.99 % snd_comp_map_prod
% 4.69/4.99 thf(fact_4490_snd__map__prod,axiom,
% 4.69/4.99 ! [F: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit,G: set_nat > set_nat,X: produc3658429121746597890et_nat] :
% 4.69/4.99 ( ( produc8586169260539613262et_nat @ ( produc8234977478398262212et_nat @ F @ G @ X ) )
% 4.69/4.99 = ( G @ ( produc8586169260539613262et_nat @ X ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % snd_map_prod
% 4.69/4.99 thf(fact_4491_snd__map__prod,axiom,
% 4.69/4.99 ! [F: int > heap_e7401611519738050253t_unit,G: int > set_nat,X: product_prod_int_int] :
% 4.69/4.99 ( ( produc8586169260539613262et_nat @ ( produc3152090231653401565et_nat @ F @ G @ X ) )
% 4.69/4.99 = ( G @ ( product_snd_int_int @ X ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % snd_map_prod
% 4.69/4.99 thf(fact_4492_snd__map__prod,axiom,
% 4.69/4.99 ! [F: heap_e7401611519738050253t_unit > int,G: set_nat > int,X: produc3658429121746597890et_nat] :
% 4.69/4.99 ( ( product_snd_int_int @ ( produc5973434381925408567at_int @ F @ G @ X ) )
% 4.69/4.99 = ( G @ ( produc8586169260539613262et_nat @ X ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % snd_map_prod
% 4.69/4.99 thf(fact_4493_snd__map__prod,axiom,
% 4.69/4.99 ! [F: int > int,G: int > int,X: product_prod_int_int] :
% 4.69/4.99 ( ( product_snd_int_int @ ( produc6036585564866528938nt_int @ F @ G @ X ) )
% 4.69/4.99 = ( G @ ( product_snd_int_int @ X ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % snd_map_prod
% 4.69/4.99 thf(fact_4494_map__prod__imageI,axiom,
% 4.69/4.99 ! [A2: nat,B: nat,R3: set_Pr1261947904930325089at_nat,F: nat > nat,G: nat > nat] :
% 4.69/4.99 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R3 )
% 4.69/4.99 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ A2 ) @ ( G @ B ) ) @ ( image_5168914502847457605at_nat @ ( produc6977886695330630970at_nat @ F @ G ) @ R3 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_imageI
% 4.69/4.99 thf(fact_4495_map__prod__imageI,axiom,
% 4.69/4.99 ! [A2: nat,B: nat,R3: set_Pr1261947904930325089at_nat,F: nat > int,G: nat > int] :
% 4.69/4.99 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R3 )
% 4.69/4.99 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F @ A2 ) @ ( G @ B ) ) @ ( image_1990417195239315453nt_int @ ( produc7347049785058425330at_int @ F @ G ) @ R3 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_imageI
% 4.69/4.99 thf(fact_4496_map__prod__imageI,axiom,
% 4.69/4.99 ! [A2: int,B: int,R3: set_Pr958786334691620121nt_int,F: int > nat,G: int > nat] :
% 4.69/4.99 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R3 )
% 4.69/4.99 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ A2 ) @ ( G @ B ) ) @ ( image_5831868185956570253at_nat @ ( produc5667422475138734578nt_nat @ F @ G ) @ R3 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_imageI
% 4.69/4.99 thf(fact_4497_map__prod__imageI,axiom,
% 4.69/4.99 ! [A2: int,B: int,R3: set_Pr958786334691620121nt_int,F: int > int,G: int > int] :
% 4.69/4.99 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R3 )
% 4.69/4.99 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F @ A2 ) @ ( G @ B ) ) @ ( image_2653370878348428101nt_int @ ( produc6036585564866528938nt_int @ F @ G ) @ R3 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_imageI
% 4.69/4.99 thf(fact_4498_map__prod__imageI,axiom,
% 4.69/4.99 ! [A2: heap_e7401611519738050253t_unit,B: set_nat,R3: set_Pr3948176798113811640et_nat,F: heap_e7401611519738050253t_unit > nat,G: set_nat > nat] :
% 4.69/4.99 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ B ) @ R3 )
% 4.69/4.99 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ A2 ) @ ( G @ B ) ) @ ( image_7757775281999735736at_nat @ ( produc8285742784527409791at_nat @ F @ G ) @ R3 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_imageI
% 4.69/4.99 thf(fact_4499_map__prod__imageI,axiom,
% 4.69/4.99 ! [A2: heap_e7401611519738050253t_unit,B: set_nat,R3: set_Pr3948176798113811640et_nat,F: heap_e7401611519738050253t_unit > int,G: set_nat > int] :
% 4.69/4.99 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ B ) @ R3 )
% 4.69/4.99 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F @ A2 ) @ ( G @ B ) ) @ ( image_4579277974391593584nt_int @ ( produc5973434381925408567at_int @ F @ G ) @ R3 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_imageI
% 4.69/4.99 thf(fact_4500_map__prod__imageI,axiom,
% 4.69/4.99 ! [A2: nat,B: nat,R3: set_Pr1261947904930325089at_nat,F: nat > heap_e7401611519738050253t_unit,G: nat > set_nat] :
% 4.69/4.99 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R3 )
% 4.69/4.99 => ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ ( F @ A2 ) @ ( G @ B ) ) @ ( image_9068448769188195518et_nat @ ( produc2064153442785501et_nat @ F @ G ) @ R3 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_imageI
% 4.69/4.99 thf(fact_4501_map__prod__imageI,axiom,
% 4.69/4.99 ! [A2: int,B: int,R3: set_Pr958786334691620121nt_int,F: int > heap_e7401611519738050253t_unit,G: int > set_nat] :
% 4.69/4.99 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ R3 )
% 4.69/4.99 => ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ ( F @ A2 ) @ ( G @ B ) ) @ ( image_2127501072796355446et_nat @ ( produc3152090231653401565et_nat @ F @ G ) @ R3 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_imageI
% 4.69/4.99 thf(fact_4502_map__prod__imageI,axiom,
% 4.69/4.99 ! [A2: heap_e7401611519738050253t_unit,B: set_nat,R3: set_Pr3948176798113811640et_nat,F: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit,G: set_nat > set_nat] :
% 4.69/4.99 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ B ) @ R3 )
% 4.69/4.99 => ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ ( F @ A2 ) @ ( G @ B ) ) @ ( image_7426123528223433739et_nat @ ( produc8234977478398262212et_nat @ F @ G ) @ R3 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_imageI
% 4.69/4.99 thf(fact_4503_map__prod__imageI,axiom,
% 4.69/4.99 ! [A2: nat,B: nat,R3: set_Pr1261947904930325089at_nat,F: nat > produc3658429121746597890et_nat > $o,G: nat > produc3658429121746597890et_nat] :
% 4.69/4.99 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ R3 )
% 4.69/4.99 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ ( F @ A2 ) @ ( G @ B ) ) @ ( image_5744643625575355962et_nat @ ( produc79747477514316377et_nat @ F @ G ) @ R3 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_imageI
% 4.69/4.99 thf(fact_4504_exists__leI,axiom,
% 4.69/4.99 ! [N2: nat,P: nat > $o] :
% 4.69/4.99 ( ( ! [N5: nat] :
% 4.69/4.99 ( ( ord_less_nat @ N5 @ N2 )
% 4.69/4.99 => ~ ( P @ N5 ) )
% 4.69/4.99 => ( P @ N2 ) )
% 4.69/4.99 => ? [N6: nat] :
% 4.69/4.99 ( ( ord_less_eq_nat @ N6 @ N2 )
% 4.69/4.99 & ( P @ N6 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % exists_leI
% 4.69/4.99 thf(fact_4505_max__def,axiom,
% 4.69/4.99 ( ord_max_filter_nat
% 4.69/4.99 = ( ^ [A6: filter_nat,B6: filter_nat] : ( if_filter_nat @ ( ord_le2510731241096832064er_nat @ A6 @ B6 ) @ B6 @ A6 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % max_def
% 4.69/4.99 thf(fact_4506_max__def,axiom,
% 4.69/4.99 ( ord_max_set_nat
% 4.69/4.99 = ( ^ [A6: set_nat,B6: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A6 @ B6 ) @ B6 @ A6 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % max_def
% 4.69/4.99 thf(fact_4507_max__def,axiom,
% 4.69/4.99 ( ord_max_rat
% 4.69/4.99 = ( ^ [A6: rat,B6: rat] : ( if_rat @ ( ord_less_eq_rat @ A6 @ B6 ) @ B6 @ A6 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % max_def
% 4.69/4.99 thf(fact_4508_max__def,axiom,
% 4.69/4.99 ( ord_max_nat
% 4.69/4.99 = ( ^ [A6: nat,B6: nat] : ( if_nat @ ( ord_less_eq_nat @ A6 @ B6 ) @ B6 @ A6 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % max_def
% 4.69/4.99 thf(fact_4509_max__def,axiom,
% 4.69/4.99 ( ord_max_int
% 4.69/4.99 = ( ^ [A6: int,B6: int] : ( if_int @ ( ord_less_eq_int @ A6 @ B6 ) @ B6 @ A6 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % max_def
% 4.69/4.99 thf(fact_4510_max__absorb1,axiom,
% 4.69/4.99 ! [Y: filter_nat,X: filter_nat] :
% 4.69/4.99 ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 4.69/4.99 => ( ( ord_max_filter_nat @ X @ Y )
% 4.69/4.99 = X ) ) ).
% 4.69/4.99
% 4.69/4.99 % max_absorb1
% 4.69/4.99 thf(fact_4511_max__absorb1,axiom,
% 4.69/4.99 ! [Y: set_nat,X: set_nat] :
% 4.69/4.99 ( ( ord_less_eq_set_nat @ Y @ X )
% 4.69/4.99 => ( ( ord_max_set_nat @ X @ Y )
% 4.69/4.99 = X ) ) ).
% 4.69/4.99
% 4.69/4.99 % max_absorb1
% 4.69/4.99 thf(fact_4512_max__absorb1,axiom,
% 4.69/4.99 ! [Y: rat,X: rat] :
% 4.69/4.99 ( ( ord_less_eq_rat @ Y @ X )
% 4.69/4.99 => ( ( ord_max_rat @ X @ Y )
% 4.69/4.99 = X ) ) ).
% 4.69/4.99
% 4.69/4.99 % max_absorb1
% 4.69/4.99 thf(fact_4513_max__absorb1,axiom,
% 4.69/4.99 ! [Y: nat,X: nat] :
% 4.69/4.99 ( ( ord_less_eq_nat @ Y @ X )
% 4.69/4.99 => ( ( ord_max_nat @ X @ Y )
% 4.69/4.99 = X ) ) ).
% 4.69/4.99
% 4.69/4.99 % max_absorb1
% 4.69/4.99 thf(fact_4514_max__absorb1,axiom,
% 4.69/4.99 ! [Y: int,X: int] :
% 4.69/4.99 ( ( ord_less_eq_int @ Y @ X )
% 4.69/4.99 => ( ( ord_max_int @ X @ Y )
% 4.69/4.99 = X ) ) ).
% 4.69/4.99
% 4.69/4.99 % max_absorb1
% 4.69/4.99 thf(fact_4515_max__absorb2,axiom,
% 4.69/4.99 ! [X: filter_nat,Y: filter_nat] :
% 4.69/4.99 ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 4.69/4.99 => ( ( ord_max_filter_nat @ X @ Y )
% 4.69/4.99 = Y ) ) ).
% 4.69/4.99
% 4.69/4.99 % max_absorb2
% 4.69/4.99 thf(fact_4516_max__absorb2,axiom,
% 4.69/4.99 ! [X: set_nat,Y: set_nat] :
% 4.69/4.99 ( ( ord_less_eq_set_nat @ X @ Y )
% 4.69/4.99 => ( ( ord_max_set_nat @ X @ Y )
% 4.69/4.99 = Y ) ) ).
% 4.69/4.99
% 4.69/4.99 % max_absorb2
% 4.69/4.99 thf(fact_4517_max__absorb2,axiom,
% 4.69/4.99 ! [X: rat,Y: rat] :
% 4.69/4.99 ( ( ord_less_eq_rat @ X @ Y )
% 4.69/4.99 => ( ( ord_max_rat @ X @ Y )
% 4.69/4.99 = Y ) ) ).
% 4.69/4.99
% 4.69/4.99 % max_absorb2
% 4.69/4.99 thf(fact_4518_max__absorb2,axiom,
% 4.69/4.99 ! [X: nat,Y: nat] :
% 4.69/4.99 ( ( ord_less_eq_nat @ X @ Y )
% 4.69/4.99 => ( ( ord_max_nat @ X @ Y )
% 4.69/4.99 = Y ) ) ).
% 4.69/4.99
% 4.69/4.99 % max_absorb2
% 4.69/4.99 thf(fact_4519_max__absorb2,axiom,
% 4.69/4.99 ! [X: int,Y: int] :
% 4.69/4.99 ( ( ord_less_eq_int @ X @ Y )
% 4.69/4.99 => ( ( ord_max_int @ X @ Y )
% 4.69/4.99 = Y ) ) ).
% 4.69/4.99
% 4.69/4.99 % max_absorb2
% 4.69/4.99 thf(fact_4520_max__diff__distrib__left,axiom,
% 4.69/4.99 ! [X: rat,Y: rat,Z: rat] :
% 4.69/4.99 ( ( minus_minus_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 4.69/4.99 = ( ord_max_rat @ ( minus_minus_rat @ X @ Z ) @ ( minus_minus_rat @ Y @ Z ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % max_diff_distrib_left
% 4.69/4.99 thf(fact_4521_max__diff__distrib__left,axiom,
% 4.69/4.99 ! [X: int,Y: int,Z: int] :
% 4.69/4.99 ( ( minus_minus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 4.69/4.99 = ( ord_max_int @ ( minus_minus_int @ X @ Z ) @ ( minus_minus_int @ Y @ Z ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % max_diff_distrib_left
% 4.69/4.99 thf(fact_4522_map__prod_Ocomp,axiom,
% 4.69/4.99 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,H2: code_integer > code_integer,I2: code_integer > code_integer] :
% 4.69/4.99 ( ( comp_P234064951390806312nteger @ ( produc5081366107664765182nteger @ F @ G ) @ ( produc1802105962441033582nteger @ H2 @ I2 ) )
% 4.69/4.99 = ( produc5081366107664765182nteger @ ( comp_C1593894019821074884nteger @ F @ H2 ) @ ( comp_C1593894019821074884nteger @ G @ I2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod.comp
% 4.69/4.99 thf(fact_4523_map__prod_Ocomp,axiom,
% 4.69/4.99 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,H2: code_integer > code_integer,I2: code_integer > code_integer > code_integer] :
% 4.69/4.99 ( ( comp_P6312383820422015140nteger @ ( produc3090791198996863994nteger @ F @ G ) @ ( produc6023007152014423402nteger @ H2 @ I2 ) )
% 4.69/4.99 = ( produc5081366107664765182nteger @ ( comp_C1593894019821074884nteger @ F @ H2 ) @ ( comp_C8797469213163452608nteger @ G @ I2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod.comp
% 4.69/4.99 thf(fact_4524_map__prod_Ocomp,axiom,
% 4.69/4.99 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,H2: code_integer > code_integer > code_integer,I2: code_integer > code_integer] :
% 4.69/4.99 ( ( comp_P1414880308642389412nteger @ ( produc6158254626097298938nteger @ F @ G ) @ ( produc3789967387199524714nteger @ H2 @ I2 ) )
% 4.69/4.99 = ( produc5081366107664765182nteger @ ( comp_C8797469213163452608nteger @ F @ H2 ) @ ( comp_C1593894019821074884nteger @ G @ I2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod.comp
% 4.69/4.99 thf(fact_4525_map__prod_Ocomp,axiom,
% 4.69/4.99 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,H2: code_integer > code_integer > code_integer,I2: code_integer > code_integer > code_integer] :
% 4.69/4.99 ( ( comp_P5544053077415136032nteger @ ( produc4724772261320961782nteger @ F @ G ) @ ( produc7818937854452556646nteger @ H2 @ I2 ) )
% 4.69/4.99 = ( produc5081366107664765182nteger @ ( comp_C8797469213163452608nteger @ F @ H2 ) @ ( comp_C8797469213163452608nteger @ G @ I2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod.comp
% 4.69/4.99 thf(fact_4526_map__prod_Ocompositionality,axiom,
% 4.69/4.99 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,H2: code_integer > code_integer,I2: code_integer > code_integer,Prod: produc8923325533196201883nteger] :
% 4.69/4.99 ( ( produc5081366107664765182nteger @ F @ G @ ( produc1802105962441033582nteger @ H2 @ I2 @ Prod ) )
% 4.69/4.99 = ( produc5081366107664765182nteger @ ( comp_C1593894019821074884nteger @ F @ H2 ) @ ( comp_C1593894019821074884nteger @ G @ I2 ) @ Prod ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod.compositionality
% 4.69/4.99 thf(fact_4527_map__prod_Ocompositionality,axiom,
% 4.69/4.99 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,H2: code_integer > code_integer,I2: code_integer > code_integer > code_integer,Prod: produc8923325533196201883nteger] :
% 4.69/4.99 ( ( produc3090791198996863994nteger @ F @ G @ ( produc6023007152014423402nteger @ H2 @ I2 @ Prod ) )
% 4.69/4.99 = ( produc5081366107664765182nteger @ ( comp_C1593894019821074884nteger @ F @ H2 ) @ ( comp_C8797469213163452608nteger @ G @ I2 ) @ Prod ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod.compositionality
% 4.69/4.99 thf(fact_4528_map__prod_Ocompositionality,axiom,
% 4.69/4.99 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,H2: code_integer > code_integer > code_integer,I2: code_integer > code_integer,Prod: produc8923325533196201883nteger] :
% 4.69/4.99 ( ( produc6158254626097298938nteger @ F @ G @ ( produc3789967387199524714nteger @ H2 @ I2 @ Prod ) )
% 4.69/4.99 = ( produc5081366107664765182nteger @ ( comp_C8797469213163452608nteger @ F @ H2 ) @ ( comp_C1593894019821074884nteger @ G @ I2 ) @ Prod ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod.compositionality
% 4.69/4.99 thf(fact_4529_map__prod_Ocompositionality,axiom,
% 4.69/4.99 ! [F: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,H2: code_integer > code_integer > code_integer,I2: code_integer > code_integer > code_integer,Prod: produc8923325533196201883nteger] :
% 4.69/4.99 ( ( produc4724772261320961782nteger @ F @ G @ ( produc7818937854452556646nteger @ H2 @ I2 @ Prod ) )
% 4.69/4.99 = ( produc5081366107664765182nteger @ ( comp_C8797469213163452608nteger @ F @ H2 ) @ ( comp_C8797469213163452608nteger @ G @ I2 ) @ Prod ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod.compositionality
% 4.69/4.99 thf(fact_4530_map__prod__compose,axiom,
% 4.69/4.99 ! [F1: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,F22: code_integer > code_integer,G1: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G2: code_integer > code_integer] :
% 4.69/4.99 ( ( produc5081366107664765182nteger @ ( comp_C1593894019821074884nteger @ F1 @ F22 ) @ ( comp_C1593894019821074884nteger @ G1 @ G2 ) )
% 4.69/4.99 = ( comp_P234064951390806312nteger @ ( produc5081366107664765182nteger @ F1 @ G1 ) @ ( produc1802105962441033582nteger @ F22 @ G2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_compose
% 4.69/4.99 thf(fact_4531_map__prod__compose,axiom,
% 4.69/4.99 ! [F1: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,F22: code_integer > code_integer,G1: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G2: code_integer > code_integer > code_integer] :
% 4.69/4.99 ( ( produc5081366107664765182nteger @ ( comp_C1593894019821074884nteger @ F1 @ F22 ) @ ( comp_C8797469213163452608nteger @ G1 @ G2 ) )
% 4.69/4.99 = ( comp_P6312383820422015140nteger @ ( produc3090791198996863994nteger @ F1 @ G1 ) @ ( produc6023007152014423402nteger @ F22 @ G2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_compose
% 4.69/4.99 thf(fact_4532_map__prod__compose,axiom,
% 4.69/4.99 ! [F1: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F22: code_integer > code_integer > code_integer,G1: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G2: code_integer > code_integer] :
% 4.69/4.99 ( ( produc5081366107664765182nteger @ ( comp_C8797469213163452608nteger @ F1 @ F22 ) @ ( comp_C1593894019821074884nteger @ G1 @ G2 ) )
% 4.69/4.99 = ( comp_P1414880308642389412nteger @ ( produc6158254626097298938nteger @ F1 @ G1 ) @ ( produc3789967387199524714nteger @ F22 @ G2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_compose
% 4.69/4.99 thf(fact_4533_map__prod__compose,axiom,
% 4.69/4.99 ! [F1: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,F22: code_integer > code_integer > code_integer,G1: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger,G2: code_integer > code_integer > code_integer] :
% 4.69/4.99 ( ( produc5081366107664765182nteger @ ( comp_C8797469213163452608nteger @ F1 @ F22 ) @ ( comp_C8797469213163452608nteger @ G1 @ G2 ) )
% 4.69/4.99 = ( comp_P5544053077415136032nteger @ ( produc4724772261320961782nteger @ F1 @ G1 ) @ ( produc7818937854452556646nteger @ F22 @ G2 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % map_prod_compose
% 4.69/4.99 thf(fact_4534_inj__img__insertE,axiom,
% 4.69/4.99 ! [F: code_integer > code_integer,A: set_Code_integer,X: code_integer,B4: set_Code_integer] :
% 4.69/4.99 ( ( inj_on1158064722259180589nteger @ F @ A )
% 4.69/4.99 => ( ~ ( member_Code_integer @ X @ B4 )
% 4.69/4.99 => ( ( ( insert_Code_integer @ X @ B4 )
% 4.69/4.99 = ( image_4470545334726330049nteger @ F @ A ) )
% 4.69/4.99 => ~ ! [X10: code_integer,A7: set_Code_integer] :
% 4.69/4.99 ( ~ ( member_Code_integer @ X10 @ A7 )
% 4.69/4.99 => ( ( A
% 4.69/4.99 = ( insert_Code_integer @ X10 @ A7 ) )
% 4.69/4.99 => ( ( X
% 4.69/4.99 = ( F @ X10 ) )
% 4.69/4.99 => ( B4
% 4.69/4.99 != ( image_4470545334726330049nteger @ F @ A7 ) ) ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_img_insertE
% 4.69/4.99 thf(fact_4535_inj__img__insertE,axiom,
% 4.69/4.99 ! [F: nat > code_integer,A: set_nat,X: code_integer,B4: set_Code_integer] :
% 4.69/4.99 ( ( inj_on2245834603434889120nteger @ F @ A )
% 4.69/4.99 => ( ~ ( member_Code_integer @ X @ B4 )
% 4.69/4.99 => ( ( ( insert_Code_integer @ X @ B4 )
% 4.69/4.99 = ( image_1215581382706833972nteger @ F @ A ) )
% 4.69/4.99 => ~ ! [X10: nat,A7: set_nat] :
% 4.69/4.99 ( ~ ( member_nat @ X10 @ A7 )
% 4.69/4.99 => ( ( A
% 4.69/4.99 = ( insert_nat @ X10 @ A7 ) )
% 4.69/4.99 => ( ( X
% 4.69/4.99 = ( F @ X10 ) )
% 4.69/4.99 => ( B4
% 4.69/4.99 != ( image_1215581382706833972nteger @ F @ A7 ) ) ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_img_insertE
% 4.69/4.99 thf(fact_4536_inj__img__insertE,axiom,
% 4.69/4.99 ! [F: nat > nat,A: set_nat,X: nat,B4: set_nat] :
% 4.69/4.99 ( ( inj_on_nat_nat @ F @ A )
% 4.69/4.99 => ( ~ ( member_nat @ X @ B4 )
% 4.69/4.99 => ( ( ( insert_nat @ X @ B4 )
% 4.69/4.99 = ( image_nat_nat2 @ F @ A ) )
% 4.69/4.99 => ~ ! [X10: nat,A7: set_nat] :
% 4.69/4.99 ( ~ ( member_nat @ X10 @ A7 )
% 4.69/4.99 => ( ( A
% 4.69/4.99 = ( insert_nat @ X10 @ A7 ) )
% 4.69/4.99 => ( ( X
% 4.69/4.99 = ( F @ X10 ) )
% 4.69/4.99 => ( B4
% 4.69/4.99 != ( image_nat_nat2 @ F @ A7 ) ) ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_img_insertE
% 4.69/4.99 thf(fact_4537_inj__img__insertE,axiom,
% 4.69/4.99 ! [F: int > nat,A: set_int,X: nat,B4: set_nat] :
% 4.69/4.99 ( ( inj_on_int_nat @ F @ A )
% 4.69/4.99 => ( ~ ( member_nat @ X @ B4 )
% 4.69/4.99 => ( ( ( insert_nat @ X @ B4 )
% 4.69/4.99 = ( image_int_nat2 @ F @ A ) )
% 4.69/4.99 => ~ ! [X10: int,A7: set_int] :
% 4.69/4.99 ( ~ ( member_int @ X10 @ A7 )
% 4.69/4.99 => ( ( A
% 4.69/4.99 = ( insert_int @ X10 @ A7 ) )
% 4.69/4.99 => ( ( X
% 4.69/4.99 = ( F @ X10 ) )
% 4.69/4.99 => ( B4
% 4.69/4.99 != ( image_int_nat2 @ F @ A7 ) ) ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_img_insertE
% 4.69/4.99 thf(fact_4538_inj__img__insertE,axiom,
% 4.69/4.99 ! [F: $o > nat,A: set_o,X: nat,B4: set_nat] :
% 4.69/4.99 ( ( inj_on_o_nat @ F @ A )
% 4.69/4.99 => ( ~ ( member_nat @ X @ B4 )
% 4.69/4.99 => ( ( ( insert_nat @ X @ B4 )
% 4.69/4.99 = ( image_o_nat2 @ F @ A ) )
% 4.69/4.99 => ~ ! [X10: $o,A7: set_o] :
% 4.69/4.99 ( ~ ( member_o @ X10 @ A7 )
% 4.69/4.99 => ( ( A
% 4.69/4.99 = ( insert_o @ X10 @ A7 ) )
% 4.69/4.99 => ( ( X
% 4.69/4.99 = ( F @ X10 ) )
% 4.69/4.99 => ( B4
% 4.69/4.99 != ( image_o_nat2 @ F @ A7 ) ) ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_img_insertE
% 4.69/4.99 thf(fact_4539_inj__img__insertE,axiom,
% 4.69/4.99 ! [F: product_unit > nat,A: set_Product_unit,X: nat,B4: set_nat] :
% 4.69/4.99 ( ( inj_on8430439091780834860it_nat @ F @ A )
% 4.69/4.99 => ( ~ ( member_nat @ X @ B4 )
% 4.69/4.99 => ( ( ( insert_nat @ X @ B4 )
% 4.69/4.99 = ( image_875570014554754200it_nat @ F @ A ) )
% 4.69/4.99 => ~ ! [X10: product_unit,A7: set_Product_unit] :
% 4.69/4.99 ( ~ ( member_Product_unit @ X10 @ A7 )
% 4.69/4.99 => ( ( A
% 4.69/4.99 = ( insert_Product_unit @ X10 @ A7 ) )
% 4.69/4.99 => ( ( X
% 4.69/4.99 = ( F @ X10 ) )
% 4.69/4.99 => ( B4
% 4.69/4.99 != ( image_875570014554754200it_nat @ F @ A7 ) ) ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_img_insertE
% 4.69/4.99 thf(fact_4540_inj__img__insertE,axiom,
% 4.69/4.99 ! [F: nat > int,A: set_nat,X: int,B4: set_int] :
% 4.69/4.99 ( ( inj_on_nat_int @ F @ A )
% 4.69/4.99 => ( ~ ( member_int @ X @ B4 )
% 4.69/4.99 => ( ( ( insert_int @ X @ B4 )
% 4.69/4.99 = ( image_nat_int2 @ F @ A ) )
% 4.69/4.99 => ~ ! [X10: nat,A7: set_nat] :
% 4.69/4.99 ( ~ ( member_nat @ X10 @ A7 )
% 4.69/4.99 => ( ( A
% 4.69/4.99 = ( insert_nat @ X10 @ A7 ) )
% 4.69/4.99 => ( ( X
% 4.69/4.99 = ( F @ X10 ) )
% 4.69/4.99 => ( B4
% 4.69/4.99 != ( image_nat_int2 @ F @ A7 ) ) ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_img_insertE
% 4.69/4.99 thf(fact_4541_inj__img__insertE,axiom,
% 4.69/4.99 ! [F: int > int,A: set_int,X: int,B4: set_int] :
% 4.69/4.99 ( ( inj_on_int_int @ F @ A )
% 4.69/4.99 => ( ~ ( member_int @ X @ B4 )
% 4.69/4.99 => ( ( ( insert_int @ X @ B4 )
% 4.69/4.99 = ( image_int_int2 @ F @ A ) )
% 4.69/4.99 => ~ ! [X10: int,A7: set_int] :
% 4.69/4.99 ( ~ ( member_int @ X10 @ A7 )
% 4.69/4.99 => ( ( A
% 4.69/4.99 = ( insert_int @ X10 @ A7 ) )
% 4.69/4.99 => ( ( X
% 4.69/4.99 = ( F @ X10 ) )
% 4.69/4.99 => ( B4
% 4.69/4.99 != ( image_int_int2 @ F @ A7 ) ) ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_img_insertE
% 4.69/4.99 thf(fact_4542_inj__img__insertE,axiom,
% 4.69/4.99 ! [F: $o > int,A: set_o,X: int,B4: set_int] :
% 4.69/4.99 ( ( inj_on_o_int @ F @ A )
% 4.69/4.99 => ( ~ ( member_int @ X @ B4 )
% 4.69/4.99 => ( ( ( insert_int @ X @ B4 )
% 4.69/4.99 = ( image_o_int2 @ F @ A ) )
% 4.69/4.99 => ~ ! [X10: $o,A7: set_o] :
% 4.69/4.99 ( ~ ( member_o @ X10 @ A7 )
% 4.69/4.99 => ( ( A
% 4.69/4.99 = ( insert_o @ X10 @ A7 ) )
% 4.69/4.99 => ( ( X
% 4.69/4.99 = ( F @ X10 ) )
% 4.69/4.99 => ( B4
% 4.69/4.99 != ( image_o_int2 @ F @ A7 ) ) ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_img_insertE
% 4.69/4.99 thf(fact_4543_inj__img__insertE,axiom,
% 4.69/4.99 ! [F: product_unit > int,A: set_Product_unit,X: int,B4: set_int] :
% 4.69/4.99 ( ( inj_on8427948621271784584it_int @ F @ A )
% 4.69/4.99 => ( ~ ( member_int @ X @ B4 )
% 4.69/4.99 => ( ( ( insert_int @ X @ B4 )
% 4.69/4.99 = ( image_873079544045703924it_int @ F @ A ) )
% 4.69/4.99 => ~ ! [X10: product_unit,A7: set_Product_unit] :
% 4.69/4.99 ( ~ ( member_Product_unit @ X10 @ A7 )
% 4.69/4.99 => ( ( A
% 4.69/4.99 = ( insert_Product_unit @ X10 @ A7 ) )
% 4.69/4.99 => ( ( X
% 4.69/4.99 = ( F @ X10 ) )
% 4.69/4.99 => ( B4
% 4.69/4.99 != ( image_873079544045703924it_int @ F @ A7 ) ) ) ) ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % inj_img_insertE
% 4.69/4.99 thf(fact_4544_type__copy__wit,axiom,
% 4.69/4.99 ! [Rep2: code_integer > int,Abs2: int > code_integer,X: nat,S: int > set_nat,Y: int] :
% 4.69/4.99 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ top_top_set_int )
% 4.69/4.99 => ( ( member_nat @ X @ ( comp_i5102403792180996084nteger @ S @ Rep2 @ ( Abs2 @ Y ) ) )
% 4.69/4.99 => ( member_nat @ X @ ( S @ Y ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_wit
% 4.69/4.99 thf(fact_4545_type__copy__wit,axiom,
% 4.69/4.99 ! [Rep2: code_integer > int,Abs2: int > code_integer,X: int,S: int > set_int,Y: int] :
% 4.69/4.99 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ top_top_set_int )
% 4.69/4.99 => ( ( member_int @ X @ ( comp_i1887841406321795152nteger @ S @ Rep2 @ ( Abs2 @ Y ) ) )
% 4.69/4.99 => ( member_int @ X @ ( S @ Y ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_wit
% 4.69/4.99 thf(fact_4546_type__copy__wit,axiom,
% 4.69/4.99 ! [Rep2: code_integer > int,Abs2: int > code_integer,X: $o,S: int > set_o,Y: int] :
% 4.69/4.99 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ top_top_set_int )
% 4.69/4.99 => ( ( member_o @ X @ ( comp_i5479505385629679622nteger @ S @ Rep2 @ ( Abs2 @ Y ) ) )
% 4.69/4.99 => ( member_o @ X @ ( S @ Y ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_wit
% 4.69/4.99 thf(fact_4547_type__copy__wit,axiom,
% 4.69/4.99 ! [Rep2: code_integer > int,Abs2: int > code_integer,X: product_unit,S: int > set_Product_unit,Y: int] :
% 4.69/4.99 ( ( type_d8366093980585677751er_int @ Rep2 @ Abs2 @ top_top_set_int )
% 4.69/4.99 => ( ( member_Product_unit @ X @ ( comp_i3319814986458681467nteger @ S @ Rep2 @ ( Abs2 @ Y ) ) )
% 4.69/4.99 => ( member_Product_unit @ X @ ( S @ Y ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_wit
% 4.69/4.99 thf(fact_4548_type__copy__wit,axiom,
% 4.69/4.99 ! [Rep2: product_unit > $o,Abs2: $o > product_unit,X: nat,S: $o > set_nat,Y: $o] :
% 4.69/4.99 ( ( type_d6188575255521822967unit_o @ Rep2 @ Abs2 @ top_top_set_o )
% 4.69/4.99 => ( ( member_nat @ X @ ( comp_o9190160103024335696t_unit @ S @ Rep2 @ ( Abs2 @ Y ) ) )
% 4.69/4.99 => ( member_nat @ X @ ( S @ Y ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_wit
% 4.69/4.99 thf(fact_4549_type__copy__wit,axiom,
% 4.69/4.99 ! [Rep2: product_unit > $o,Abs2: $o > product_unit,X: int,S: $o > set_int,Y: $o] :
% 4.69/4.99 ( ( type_d6188575255521822967unit_o @ Rep2 @ Abs2 @ top_top_set_o )
% 4.69/4.99 => ( ( member_int @ X @ ( comp_o1521574261646630388t_unit @ S @ Rep2 @ ( Abs2 @ Y ) ) )
% 4.69/4.99 => ( member_int @ X @ ( S @ Y ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_wit
% 4.69/4.99 thf(fact_4550_type__copy__wit,axiom,
% 4.69/4.99 ! [Rep2: product_unit > $o,Abs2: $o > product_unit,X: $o,S: $o > set_o,Y: $o] :
% 4.69/4.99 ( ( type_d6188575255521822967unit_o @ Rep2 @ Abs2 @ top_top_set_o )
% 4.69/4.99 => ( ( member_o @ X @ ( comp_o6895741221744486154t_unit @ S @ Rep2 @ ( Abs2 @ Y ) ) )
% 4.69/4.99 => ( member_o @ X @ ( S @ Y ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_wit
% 4.69/4.99 thf(fact_4551_type__copy__wit,axiom,
% 4.69/4.99 ! [Rep2: product_unit > $o,Abs2: $o > product_unit,X: product_unit,S: $o > set_Product_unit,Y: $o] :
% 4.69/4.99 ( ( type_d6188575255521822967unit_o @ Rep2 @ Abs2 @ top_top_set_o )
% 4.69/4.99 => ( ( member_Product_unit @ X @ ( comp_o2086126948152544725t_unit @ S @ Rep2 @ ( Abs2 @ Y ) ) )
% 4.69/4.99 => ( member_Product_unit @ X @ ( S @ Y ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_wit
% 4.69/4.99 thf(fact_4552_type__copy__wit,axiom,
% 4.69/4.99 ! [Rep2: code_natural > nat,Abs2: nat > code_natural,X: nat,S: nat > set_nat,Y: nat] :
% 4.69/4.99 ( ( type_d4410041424927559462al_nat @ Rep2 @ Abs2 @ top_top_set_nat )
% 4.69/4.99 => ( ( member_nat @ X @ ( comp_n4787279007288201059atural @ S @ Rep2 @ ( Abs2 @ Y ) ) )
% 4.69/4.99 => ( member_nat @ X @ ( S @ Y ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_wit
% 4.69/4.99 thf(fact_4553_type__copy__wit,axiom,
% 4.69/4.99 ! [Rep2: code_natural > nat,Abs2: nat > code_natural,X: int,S: nat > set_int,Y: nat] :
% 4.69/4.99 ( ( type_d4410041424927559462al_nat @ Rep2 @ Abs2 @ top_top_set_nat )
% 4.69/4.99 => ( ( member_int @ X @ ( comp_n1572716621429000127atural @ S @ Rep2 @ ( Abs2 @ Y ) ) )
% 4.69/4.99 => ( member_int @ X @ ( S @ Y ) ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % type_copy_wit
% 4.69/4.99 thf(fact_4554_prod__fun__imageE,axiom,
% 4.69/4.99 ! [C: product_prod_nat_nat,F: nat > nat,G: nat > nat,R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.99 ( ( member8440522571783428010at_nat @ C @ ( image_5168914502847457605at_nat @ ( produc6977886695330630970at_nat @ F @ G ) @ R3 ) )
% 4.69/4.99 => ~ ! [X3: nat,Y2: nat] :
% 4.69/4.99 ( ( C
% 4.69/4.99 = ( product_Pair_nat_nat @ ( F @ X3 ) @ ( G @ Y2 ) ) )
% 4.69/4.99 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ R3 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % prod_fun_imageE
% 4.69/4.99 thf(fact_4555_prod__fun__imageE,axiom,
% 4.69/4.99 ! [C: product_prod_nat_nat,F: int > nat,G: int > nat,R3: set_Pr958786334691620121nt_int] :
% 4.69/4.99 ( ( member8440522571783428010at_nat @ C @ ( image_5831868185956570253at_nat @ ( produc5667422475138734578nt_nat @ F @ G ) @ R3 ) )
% 4.69/4.99 => ~ ! [X3: int,Y2: int] :
% 4.69/4.99 ( ( C
% 4.69/4.99 = ( product_Pair_nat_nat @ ( F @ X3 ) @ ( G @ Y2 ) ) )
% 4.69/4.99 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y2 ) @ R3 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % prod_fun_imageE
% 4.69/4.99 thf(fact_4556_prod__fun__imageE,axiom,
% 4.69/4.99 ! [C: product_prod_int_int,F: nat > int,G: nat > int,R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.99 ( ( member5262025264175285858nt_int @ C @ ( image_1990417195239315453nt_int @ ( produc7347049785058425330at_int @ F @ G ) @ R3 ) )
% 4.69/4.99 => ~ ! [X3: nat,Y2: nat] :
% 4.69/4.99 ( ( C
% 4.69/4.99 = ( product_Pair_int_int @ ( F @ X3 ) @ ( G @ Y2 ) ) )
% 4.69/4.99 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ R3 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % prod_fun_imageE
% 4.69/4.99 thf(fact_4557_prod__fun__imageE,axiom,
% 4.69/4.99 ! [C: product_prod_int_int,F: int > int,G: int > int,R3: set_Pr958786334691620121nt_int] :
% 4.69/4.99 ( ( member5262025264175285858nt_int @ C @ ( image_2653370878348428101nt_int @ ( produc6036585564866528938nt_int @ F @ G ) @ R3 ) )
% 4.69/4.99 => ~ ! [X3: int,Y2: int] :
% 4.69/4.99 ( ( C
% 4.69/4.99 = ( product_Pair_int_int @ ( F @ X3 ) @ ( G @ Y2 ) ) )
% 4.69/4.99 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y2 ) @ R3 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % prod_fun_imageE
% 4.69/4.99 thf(fact_4558_prod__fun__imageE,axiom,
% 4.69/4.99 ! [C: produc3658429121746597890et_nat,F: nat > heap_e7401611519738050253t_unit,G: nat > set_nat,R3: set_Pr1261947904930325089at_nat] :
% 4.69/4.99 ( ( member6260224972018164377et_nat @ C @ ( image_9068448769188195518et_nat @ ( produc2064153442785501et_nat @ F @ G ) @ R3 ) )
% 4.69/4.99 => ~ ! [X3: nat,Y2: nat] :
% 4.69/4.99 ( ( C
% 4.69/4.99 = ( produc7507926704131184380et_nat @ ( F @ X3 ) @ ( G @ Y2 ) ) )
% 4.69/4.99 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y2 ) @ R3 ) ) ) ).
% 4.69/4.99
% 4.69/4.99 % prod_fun_imageE
% 4.69/4.99 thf(fact_4559_prod__fun__imageE,axiom,
% 4.69/4.99 ! [C: produc3658429121746597890et_nat,F: int > heap_e7401611519738050253t_unit,G: int > set_nat,R3: set_Pr958786334691620121nt_int] :
% 4.69/4.99 ( ( member6260224972018164377et_nat @ C @ ( image_2127501072796355446et_nat @ ( produc3152090231653401565et_nat @ F @ G ) @ R3 ) )
% 4.69/4.99 => ~ ! [X3: int,Y2: int] :
% 4.69/4.99 ( ( C
% 4.69/4.99 = ( produc7507926704131184380et_nat @ ( F @ X3 ) @ ( G @ Y2 ) ) )
% 4.69/4.99 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y2 ) @ R3 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod_fun_imageE
% 4.69/5.00 thf(fact_4560_prod__fun__imageE,axiom,
% 4.69/5.00 ! [C: product_prod_nat_nat,F: heap_e7401611519738050253t_unit > nat,G: set_nat > nat,R3: set_Pr3948176798113811640et_nat] :
% 4.69/5.00 ( ( member8440522571783428010at_nat @ C @ ( image_7757775281999735736at_nat @ ( produc8285742784527409791at_nat @ F @ G ) @ R3 ) )
% 4.69/5.00 => ~ ! [X3: heap_e7401611519738050253t_unit,Y2: set_nat] :
% 4.69/5.00 ( ( C
% 4.69/5.00 = ( product_Pair_nat_nat @ ( F @ X3 ) @ ( G @ Y2 ) ) )
% 4.69/5.00 => ~ ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X3 @ Y2 ) @ R3 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod_fun_imageE
% 4.69/5.00 thf(fact_4561_prod__fun__imageE,axiom,
% 4.69/5.00 ! [C: product_prod_int_int,F: heap_e7401611519738050253t_unit > int,G: set_nat > int,R3: set_Pr3948176798113811640et_nat] :
% 4.69/5.00 ( ( member5262025264175285858nt_int @ C @ ( image_4579277974391593584nt_int @ ( produc5973434381925408567at_int @ F @ G ) @ R3 ) )
% 4.69/5.00 => ~ ! [X3: heap_e7401611519738050253t_unit,Y2: set_nat] :
% 4.69/5.00 ( ( C
% 4.69/5.00 = ( product_Pair_int_int @ ( F @ X3 ) @ ( G @ Y2 ) ) )
% 4.69/5.00 => ~ ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X3 @ Y2 ) @ R3 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod_fun_imageE
% 4.69/5.00 thf(fact_4562_prod__fun__imageE,axiom,
% 4.69/5.00 ! [C: produc3658429121746597890et_nat,F: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit,G: set_nat > set_nat,R3: set_Pr3948176798113811640et_nat] :
% 4.69/5.00 ( ( member6260224972018164377et_nat @ C @ ( image_7426123528223433739et_nat @ ( produc8234977478398262212et_nat @ F @ G ) @ R3 ) )
% 4.69/5.00 => ~ ! [X3: heap_e7401611519738050253t_unit,Y2: set_nat] :
% 4.69/5.00 ( ( C
% 4.69/5.00 = ( produc7507926704131184380et_nat @ ( F @ X3 ) @ ( G @ Y2 ) ) )
% 4.69/5.00 => ~ ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X3 @ Y2 ) @ R3 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod_fun_imageE
% 4.69/5.00 thf(fact_4563_prod__fun__imageE,axiom,
% 4.69/5.00 ! [C: product_prod_nat_nat,F: ( produc3658429121746597890et_nat > $o ) > nat,G: produc3658429121746597890et_nat > nat,R3: set_Pr3286484037609594932et_nat] :
% 4.69/5.00 ( ( member8440522571783428010at_nat @ C @ ( image_7073998564157519676at_nat @ ( produc2784369760062397435at_nat @ F @ G ) @ R3 ) )
% 4.69/5.00 => ~ ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( C
% 4.69/5.00 = ( product_Pair_nat_nat @ ( F @ X3 ) @ ( G @ Y2 ) ) )
% 4.69/5.00 => ~ ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y2 ) @ R3 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod_fun_imageE
% 4.69/5.00 thf(fact_4564_inj__on__iff__surj,axiom,
% 4.69/5.00 ! [A: set_Code_integer,A8: set_Code_integer] :
% 4.69/5.00 ( ( A != bot_bo3990330152332043303nteger )
% 4.69/5.00 => ( ( ? [F4: code_integer > code_integer] :
% 4.69/5.00 ( ( inj_on1158064722259180589nteger @ F4 @ A )
% 4.69/5.00 & ( ord_le7084787975880047091nteger @ ( image_4470545334726330049nteger @ F4 @ A ) @ A8 ) ) )
% 4.69/5.00 = ( ? [G3: code_integer > code_integer] :
% 4.69/5.00 ( ( image_4470545334726330049nteger @ G3 @ A8 )
% 4.69/5.00 = A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % inj_on_iff_surj
% 4.69/5.00 thf(fact_4565_inj__on__iff__surj,axiom,
% 4.69/5.00 ! [A: set_nat,A8: set_set_nat] :
% 4.69/5.00 ( ( A != bot_bot_set_nat )
% 4.69/5.00 => ( ( ? [F4: nat > set_nat] :
% 4.69/5.00 ( ( inj_on_nat_set_nat @ F4 @ A )
% 4.69/5.00 & ( ord_le6893508408891458716et_nat @ ( image_nat_set_nat @ F4 @ A ) @ A8 ) ) )
% 4.69/5.00 = ( ? [G3: set_nat > nat] :
% 4.69/5.00 ( ( image_set_nat_nat @ G3 @ A8 )
% 4.69/5.00 = A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % inj_on_iff_surj
% 4.69/5.00 thf(fact_4566_inj__on__iff__surj,axiom,
% 4.69/5.00 ! [A: set_nat,A8: set_Code_integer] :
% 4.69/5.00 ( ( A != bot_bot_set_nat )
% 4.69/5.00 => ( ( ? [F4: nat > code_integer] :
% 4.69/5.00 ( ( inj_on2245834603434889120nteger @ F4 @ A )
% 4.69/5.00 & ( ord_le7084787975880047091nteger @ ( image_1215581382706833972nteger @ F4 @ A ) @ A8 ) ) )
% 4.69/5.00 = ( ? [G3: code_integer > nat] :
% 4.69/5.00 ( ( image_951025933927791156er_nat @ G3 @ A8 )
% 4.69/5.00 = A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % inj_on_iff_surj
% 4.69/5.00 thf(fact_4567_inj__on__iff__surj,axiom,
% 4.69/5.00 ! [A: set_set_nat,A8: set_nat] :
% 4.69/5.00 ( ( A != bot_bot_set_set_nat )
% 4.69/5.00 => ( ( ? [F4: set_nat > nat] :
% 4.69/5.00 ( ( inj_on_set_nat_nat @ F4 @ A )
% 4.69/5.00 & ( ord_less_eq_set_nat @ ( image_set_nat_nat @ F4 @ A ) @ A8 ) ) )
% 4.69/5.00 = ( ? [G3: nat > set_nat] :
% 4.69/5.00 ( ( image_nat_set_nat @ G3 @ A8 )
% 4.69/5.00 = A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % inj_on_iff_surj
% 4.69/5.00 thf(fact_4568_inj__on__iff__surj,axiom,
% 4.69/5.00 ! [A: set_Code_integer,A8: set_nat] :
% 4.69/5.00 ( ( A != bot_bo3990330152332043303nteger )
% 4.69/5.00 => ( ( ? [F4: code_integer > nat] :
% 4.69/5.00 ( ( inj_on1981279154655846304er_nat @ F4 @ A )
% 4.69/5.00 & ( ord_less_eq_set_nat @ ( image_951025933927791156er_nat @ F4 @ A ) @ A8 ) ) )
% 4.69/5.00 = ( ? [G3: nat > code_integer] :
% 4.69/5.00 ( ( image_1215581382706833972nteger @ G3 @ A8 )
% 4.69/5.00 = A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % inj_on_iff_surj
% 4.69/5.00 thf(fact_4569_inj__on__iff__surj,axiom,
% 4.69/5.00 ! [A: set_Product_unit,A8: set_nat] :
% 4.69/5.00 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ( ? [F4: product_unit > nat] :
% 4.69/5.00 ( ( inj_on8430439091780834860it_nat @ F4 @ A )
% 4.69/5.00 & ( ord_less_eq_set_nat @ ( image_875570014554754200it_nat @ F4 @ A ) @ A8 ) ) )
% 4.69/5.00 = ( ? [G3: nat > product_unit] :
% 4.69/5.00 ( ( image_8730104196221521654t_unit @ G3 @ A8 )
% 4.69/5.00 = A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % inj_on_iff_surj
% 4.69/5.00 thf(fact_4570_inj__on__iff__surj,axiom,
% 4.69/5.00 ! [A: set_o,A8: set_nat] :
% 4.69/5.00 ( ( A != bot_bot_set_o )
% 4.69/5.00 => ( ( ? [F4: $o > nat] :
% 4.69/5.00 ( ( inj_on_o_nat @ F4 @ A )
% 4.69/5.00 & ( ord_less_eq_set_nat @ ( image_o_nat2 @ F4 @ A ) @ A8 ) ) )
% 4.69/5.00 = ( ? [G3: nat > $o] :
% 4.69/5.00 ( ( image_nat_o2 @ G3 @ A8 )
% 4.69/5.00 = A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % inj_on_iff_surj
% 4.69/5.00 thf(fact_4571_inj__on__iff__surj,axiom,
% 4.69/5.00 ! [A: set_nat,A8: set_nat] :
% 4.69/5.00 ( ( A != bot_bot_set_nat )
% 4.69/5.00 => ( ( ? [F4: nat > nat] :
% 4.69/5.00 ( ( inj_on_nat_nat @ F4 @ A )
% 4.69/5.00 & ( ord_less_eq_set_nat @ ( image_nat_nat2 @ F4 @ A ) @ A8 ) ) )
% 4.69/5.00 = ( ? [G3: nat > nat] :
% 4.69/5.00 ( ( image_nat_nat2 @ G3 @ A8 )
% 4.69/5.00 = A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % inj_on_iff_surj
% 4.69/5.00 thf(fact_4572_inj__on__iff__surj,axiom,
% 4.69/5.00 ! [A: set_int,A8: set_nat] :
% 4.69/5.00 ( ( A != bot_bot_set_int )
% 4.69/5.00 => ( ( ? [F4: int > nat] :
% 4.69/5.00 ( ( inj_on_int_nat @ F4 @ A )
% 4.69/5.00 & ( ord_less_eq_set_nat @ ( image_int_nat2 @ F4 @ A ) @ A8 ) ) )
% 4.69/5.00 = ( ? [G3: nat > int] :
% 4.69/5.00 ( ( image_nat_int2 @ G3 @ A8 )
% 4.69/5.00 = A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % inj_on_iff_surj
% 4.69/5.00 thf(fact_4573_inj__on__iff__surj,axiom,
% 4.69/5.00 ! [A: set_Pr4532377907799695533_nat_o,A8: set_nat] :
% 4.69/5.00 ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/5.00 => ( ( ? [F4: ( produc3658429121746597890et_nat > $o ) > nat] :
% 4.69/5.00 ( ( inj_on5271586719803267564_o_nat @ F4 @ A )
% 4.69/5.00 & ( ord_less_eq_set_nat @ ( image_2174381888560928856_o_nat @ F4 @ A ) @ A8 ) ) )
% 4.69/5.00 = ( ? [G3: nat > produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ( image_4682239675366380726_nat_o @ G3 @ A8 )
% 4.69/5.00 = A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % inj_on_iff_surj
% 4.69/5.00 thf(fact_4574_Sup__insert__finite,axiom,
% 4.69/5.00 ! [S: set_int,X: int] :
% 4.69/5.00 ( ( finite_finite_int @ S )
% 4.69/5.00 => ( ( ( S = bot_bot_set_int )
% 4.69/5.00 => ( ( complete_Sup_Sup_int @ ( insert_int @ X @ S ) )
% 4.69/5.00 = X ) )
% 4.69/5.00 & ( ( S != bot_bot_set_int )
% 4.69/5.00 => ( ( complete_Sup_Sup_int @ ( insert_int @ X @ S ) )
% 4.69/5.00 = ( ord_max_int @ X @ ( complete_Sup_Sup_int @ S ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Sup_insert_finite
% 4.69/5.00 thf(fact_4575_Sup__insert__finite,axiom,
% 4.69/5.00 ! [S: set_nat,X: nat] :
% 4.69/5.00 ( ( finite_finite_nat @ S )
% 4.69/5.00 => ( ( ( S = bot_bot_set_nat )
% 4.69/5.00 => ( ( complete_Sup_Sup_nat @ ( insert_nat @ X @ S ) )
% 4.69/5.00 = X ) )
% 4.69/5.00 & ( ( S != bot_bot_set_nat )
% 4.69/5.00 => ( ( complete_Sup_Sup_nat @ ( insert_nat @ X @ S ) )
% 4.69/5.00 = ( ord_max_nat @ X @ ( complete_Sup_Sup_nat @ S ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Sup_insert_finite
% 4.69/5.00 thf(fact_4576_Sup__insert__finite,axiom,
% 4.69/5.00 ! [S: set_Product_unit,X: product_unit] :
% 4.69/5.00 ( ( finite4290736615968046902t_unit @ S )
% 4.69/5.00 => ( ( ( S = bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ( comple4687483117567863418t_unit @ ( insert_Product_unit @ X @ S ) )
% 4.69/5.00 = X ) )
% 4.69/5.00 & ( ( S != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ( comple4687483117567863418t_unit @ ( insert_Product_unit @ X @ S ) )
% 4.69/5.00 = ( ord_max_Product_unit @ X @ ( comple4687483117567863418t_unit @ S ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Sup_insert_finite
% 4.69/5.00 thf(fact_4577_hom__Max__commute,axiom,
% 4.69/5.00 ! [H2: code_integer > code_integer,N: set_Code_integer] :
% 4.69/5.00 ( ! [X3: code_integer,Y2: code_integer] :
% 4.69/5.00 ( ( H2 @ ( ord_max_Code_integer @ X3 @ Y2 ) )
% 4.69/5.00 = ( ord_max_Code_integer @ ( H2 @ X3 ) @ ( H2 @ Y2 ) ) )
% 4.69/5.00 => ( ( finite6017078050557962740nteger @ N )
% 4.69/5.00 => ( ( N != bot_bo3990330152332043303nteger )
% 4.69/5.00 => ( ( H2 @ ( lattic4901227151466704046nteger @ N ) )
% 4.69/5.00 = ( lattic4901227151466704046nteger @ ( image_4470545334726330049nteger @ H2 @ N ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % hom_Max_commute
% 4.69/5.00 thf(fact_4578_hom__Max__commute,axiom,
% 4.69/5.00 ! [H2: product_unit > product_unit,N: set_Product_unit] :
% 4.69/5.00 ( ! [X3: product_unit,Y2: product_unit] :
% 4.69/5.00 ( ( H2 @ ( ord_max_Product_unit @ X3 @ Y2 ) )
% 4.69/5.00 = ( ord_max_Product_unit @ ( H2 @ X3 ) @ ( H2 @ Y2 ) ) )
% 4.69/5.00 => ( ( finite4290736615968046902t_unit @ N )
% 4.69/5.00 => ( ( N != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ( H2 @ ( lattic1210392890313158908t_unit @ N ) )
% 4.69/5.00 = ( lattic1210392890313158908t_unit @ ( image_405062704495631173t_unit @ H2 @ N ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % hom_Max_commute
% 4.69/5.00 thf(fact_4579_hom__Max__commute,axiom,
% 4.69/5.00 ! [H2: $o > $o,N: set_o] :
% 4.69/5.00 ( ! [X3: $o,Y2: $o] :
% 4.69/5.00 ( ( H2 @ ( ord_max_o @ X3 @ Y2 ) )
% 4.69/5.00 = ( ord_max_o @ ( H2 @ X3 ) @ ( H2 @ Y2 ) ) )
% 4.69/5.00 => ( ( finite_finite_o @ N )
% 4.69/5.00 => ( ( N != bot_bot_set_o )
% 4.69/5.00 => ( ( H2 @ ( lattic1921953407002678535_Max_o @ N ) )
% 4.69/5.00 = ( lattic1921953407002678535_Max_o @ ( image_o_o2 @ H2 @ N ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % hom_Max_commute
% 4.69/5.00 thf(fact_4580_hom__Max__commute,axiom,
% 4.69/5.00 ! [H2: int > int,N: set_int] :
% 4.69/5.00 ( ! [X3: int,Y2: int] :
% 4.69/5.00 ( ( H2 @ ( ord_max_int @ X3 @ Y2 ) )
% 4.69/5.00 = ( ord_max_int @ ( H2 @ X3 ) @ ( H2 @ Y2 ) ) )
% 4.69/5.00 => ( ( finite_finite_int @ N )
% 4.69/5.00 => ( ( N != bot_bot_set_int )
% 4.69/5.00 => ( ( H2 @ ( lattic8263393255366662781ax_int @ N ) )
% 4.69/5.00 = ( lattic8263393255366662781ax_int @ ( image_int_int2 @ H2 @ N ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % hom_Max_commute
% 4.69/5.00 thf(fact_4581_hom__Max__commute,axiom,
% 4.69/5.00 ! [H2: nat > nat,N: set_nat] :
% 4.69/5.00 ( ! [X3: nat,Y2: nat] :
% 4.69/5.00 ( ( H2 @ ( ord_max_nat @ X3 @ Y2 ) )
% 4.69/5.00 = ( ord_max_nat @ ( H2 @ X3 ) @ ( H2 @ Y2 ) ) )
% 4.69/5.00 => ( ( finite_finite_nat @ N )
% 4.69/5.00 => ( ( N != bot_bot_set_nat )
% 4.69/5.00 => ( ( H2 @ ( lattic8265883725875713057ax_nat @ N ) )
% 4.69/5.00 = ( lattic8265883725875713057ax_nat @ ( image_nat_nat2 @ H2 @ N ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % hom_Max_commute
% 4.69/5.00 thf(fact_4582_Max_Osubset,axiom,
% 4.69/5.00 ! [A: set_Code_integer,B4: set_Code_integer] :
% 4.69/5.00 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.00 => ( ( B4 != bot_bo3990330152332043303nteger )
% 4.69/5.00 => ( ( ord_le7084787975880047091nteger @ B4 @ A )
% 4.69/5.00 => ( ( ord_max_Code_integer @ ( lattic4901227151466704046nteger @ B4 ) @ ( lattic4901227151466704046nteger @ A ) )
% 4.69/5.00 = ( lattic4901227151466704046nteger @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.subset
% 4.69/5.00 thf(fact_4583_Max_Osubset,axiom,
% 4.69/5.00 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/5.00 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.00 => ( ( B4 != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ( ord_le3507040750410214029t_unit @ B4 @ A )
% 4.69/5.00 => ( ( ord_max_Product_unit @ ( lattic1210392890313158908t_unit @ B4 ) @ ( lattic1210392890313158908t_unit @ A ) )
% 4.69/5.00 = ( lattic1210392890313158908t_unit @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.subset
% 4.69/5.00 thf(fact_4584_Max_Osubset,axiom,
% 4.69/5.00 ! [A: set_o,B4: set_o] :
% 4.69/5.00 ( ( finite_finite_o @ A )
% 4.69/5.00 => ( ( B4 != bot_bot_set_o )
% 4.69/5.00 => ( ( ord_less_eq_set_o @ B4 @ A )
% 4.69/5.00 => ( ( ord_max_o @ ( lattic1921953407002678535_Max_o @ B4 ) @ ( lattic1921953407002678535_Max_o @ A ) )
% 4.69/5.00 = ( lattic1921953407002678535_Max_o @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.subset
% 4.69/5.00 thf(fact_4585_Max_Osubset,axiom,
% 4.69/5.00 ! [A: set_int,B4: set_int] :
% 4.69/5.00 ( ( finite_finite_int @ A )
% 4.69/5.00 => ( ( B4 != bot_bot_set_int )
% 4.69/5.00 => ( ( ord_less_eq_set_int @ B4 @ A )
% 4.69/5.00 => ( ( ord_max_int @ ( lattic8263393255366662781ax_int @ B4 ) @ ( lattic8263393255366662781ax_int @ A ) )
% 4.69/5.00 = ( lattic8263393255366662781ax_int @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.subset
% 4.69/5.00 thf(fact_4586_Max_Osubset,axiom,
% 4.69/5.00 ! [A: set_nat,B4: set_nat] :
% 4.69/5.00 ( ( finite_finite_nat @ A )
% 4.69/5.00 => ( ( B4 != bot_bot_set_nat )
% 4.69/5.00 => ( ( ord_less_eq_set_nat @ B4 @ A )
% 4.69/5.00 => ( ( ord_max_nat @ ( lattic8265883725875713057ax_nat @ B4 ) @ ( lattic8265883725875713057ax_nat @ A ) )
% 4.69/5.00 = ( lattic8265883725875713057ax_nat @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.subset
% 4.69/5.00 thf(fact_4587_Max_Oinsert__not__elem,axiom,
% 4.69/5.00 ! [A: set_Code_integer,X: code_integer] :
% 4.69/5.00 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.00 => ( ~ ( member_Code_integer @ X @ A )
% 4.69/5.00 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/5.00 => ( ( lattic4901227151466704046nteger @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.00 = ( ord_max_Code_integer @ X @ ( lattic4901227151466704046nteger @ A ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.insert_not_elem
% 4.69/5.00 thf(fact_4588_Max_Oinsert__not__elem,axiom,
% 4.69/5.00 ! [A: set_Product_unit,X: product_unit] :
% 4.69/5.00 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.00 => ( ~ ( member_Product_unit @ X @ A )
% 4.69/5.00 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ( lattic1210392890313158908t_unit @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.00 = ( ord_max_Product_unit @ X @ ( lattic1210392890313158908t_unit @ A ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.insert_not_elem
% 4.69/5.00 thf(fact_4589_Max_Oinsert__not__elem,axiom,
% 4.69/5.00 ! [A: set_o,X: $o] :
% 4.69/5.00 ( ( finite_finite_o @ A )
% 4.69/5.00 => ( ~ ( member_o @ X @ A )
% 4.69/5.00 => ( ( A != bot_bot_set_o )
% 4.69/5.00 => ( ( lattic1921953407002678535_Max_o @ ( insert_o @ X @ A ) )
% 4.69/5.00 = ( ord_max_o @ X @ ( lattic1921953407002678535_Max_o @ A ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.insert_not_elem
% 4.69/5.00 thf(fact_4590_Max_Oinsert__not__elem,axiom,
% 4.69/5.00 ! [A: set_int,X: int] :
% 4.69/5.00 ( ( finite_finite_int @ A )
% 4.69/5.00 => ( ~ ( member_int @ X @ A )
% 4.69/5.00 => ( ( A != bot_bot_set_int )
% 4.69/5.00 => ( ( lattic8263393255366662781ax_int @ ( insert_int @ X @ A ) )
% 4.69/5.00 = ( ord_max_int @ X @ ( lattic8263393255366662781ax_int @ A ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.insert_not_elem
% 4.69/5.00 thf(fact_4591_Max_Oinsert__not__elem,axiom,
% 4.69/5.00 ! [A: set_nat,X: nat] :
% 4.69/5.00 ( ( finite_finite_nat @ A )
% 4.69/5.00 => ( ~ ( member_nat @ X @ A )
% 4.69/5.00 => ( ( A != bot_bot_set_nat )
% 4.69/5.00 => ( ( lattic8265883725875713057ax_nat @ ( insert_nat @ X @ A ) )
% 4.69/5.00 = ( ord_max_nat @ X @ ( lattic8265883725875713057ax_nat @ A ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.insert_not_elem
% 4.69/5.00 thf(fact_4592_Max_Oclosed,axiom,
% 4.69/5.00 ! [A: set_Code_integer] :
% 4.69/5.00 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.00 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/5.00 => ( ! [X3: code_integer,Y2: code_integer] : ( member_Code_integer @ ( ord_max_Code_integer @ X3 @ Y2 ) @ ( insert_Code_integer @ X3 @ ( insert_Code_integer @ Y2 @ bot_bo3990330152332043303nteger ) ) )
% 4.69/5.00 => ( member_Code_integer @ ( lattic4901227151466704046nteger @ A ) @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.closed
% 4.69/5.00 thf(fact_4593_Max_Oclosed,axiom,
% 4.69/5.00 ! [A: set_Product_unit] :
% 4.69/5.00 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.00 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ! [X3: product_unit,Y2: product_unit] : ( member_Product_unit @ ( ord_max_Product_unit @ X3 @ Y2 ) @ ( insert_Product_unit @ X3 @ ( insert_Product_unit @ Y2 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/5.00 => ( member_Product_unit @ ( lattic1210392890313158908t_unit @ A ) @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.closed
% 4.69/5.00 thf(fact_4594_Max_Oclosed,axiom,
% 4.69/5.00 ! [A: set_o] :
% 4.69/5.00 ( ( finite_finite_o @ A )
% 4.69/5.00 => ( ( A != bot_bot_set_o )
% 4.69/5.00 => ( ! [X3: $o,Y2: $o] : ( member_o @ ( ord_max_o @ X3 @ Y2 ) @ ( insert_o @ X3 @ ( insert_o @ Y2 @ bot_bot_set_o ) ) )
% 4.69/5.00 => ( member_o @ ( lattic1921953407002678535_Max_o @ A ) @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.closed
% 4.69/5.00 thf(fact_4595_Max_Oclosed,axiom,
% 4.69/5.00 ! [A: set_int] :
% 4.69/5.00 ( ( finite_finite_int @ A )
% 4.69/5.00 => ( ( A != bot_bot_set_int )
% 4.69/5.00 => ( ! [X3: int,Y2: int] : ( member_int @ ( ord_max_int @ X3 @ Y2 ) @ ( insert_int @ X3 @ ( insert_int @ Y2 @ bot_bot_set_int ) ) )
% 4.69/5.00 => ( member_int @ ( lattic8263393255366662781ax_int @ A ) @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.closed
% 4.69/5.00 thf(fact_4596_Max_Oclosed,axiom,
% 4.69/5.00 ! [A: set_nat] :
% 4.69/5.00 ( ( finite_finite_nat @ A )
% 4.69/5.00 => ( ( A != bot_bot_set_nat )
% 4.69/5.00 => ( ! [X3: nat,Y2: nat] : ( member_nat @ ( ord_max_nat @ X3 @ Y2 ) @ ( insert_nat @ X3 @ ( insert_nat @ Y2 @ bot_bot_set_nat ) ) )
% 4.69/5.00 => ( member_nat @ ( lattic8265883725875713057ax_nat @ A ) @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.closed
% 4.69/5.00 thf(fact_4597_Max_Ounion,axiom,
% 4.69/5.00 ! [A: set_Code_integer,B4: set_Code_integer] :
% 4.69/5.00 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.00 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/5.00 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.00 => ( ( B4 != bot_bo3990330152332043303nteger )
% 4.69/5.00 => ( ( lattic4901227151466704046nteger @ ( sup_su848401254843788991nteger @ A @ B4 ) )
% 4.69/5.00 = ( ord_max_Code_integer @ ( lattic4901227151466704046nteger @ A ) @ ( lattic4901227151466704046nteger @ B4 ) ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.union
% 4.69/5.00 thf(fact_4598_Max_Ounion,axiom,
% 4.69/5.00 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/5.00 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.00 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ( finite4290736615968046902t_unit @ B4 )
% 4.69/5.00 => ( ( B4 != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ( lattic1210392890313158908t_unit @ ( sup_su793286257634532545t_unit @ A @ B4 ) )
% 4.69/5.00 = ( ord_max_Product_unit @ ( lattic1210392890313158908t_unit @ A ) @ ( lattic1210392890313158908t_unit @ B4 ) ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.union
% 4.69/5.00 thf(fact_4599_Max_Ounion,axiom,
% 4.69/5.00 ! [A: set_o,B4: set_o] :
% 4.69/5.00 ( ( finite_finite_o @ A )
% 4.69/5.00 => ( ( A != bot_bot_set_o )
% 4.69/5.00 => ( ( finite_finite_o @ B4 )
% 4.69/5.00 => ( ( B4 != bot_bot_set_o )
% 4.69/5.00 => ( ( lattic1921953407002678535_Max_o @ ( sup_sup_set_o @ A @ B4 ) )
% 4.69/5.00 = ( ord_max_o @ ( lattic1921953407002678535_Max_o @ A ) @ ( lattic1921953407002678535_Max_o @ B4 ) ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.union
% 4.69/5.00 thf(fact_4600_Max_Ounion,axiom,
% 4.69/5.00 ! [A: set_int,B4: set_int] :
% 4.69/5.00 ( ( finite_finite_int @ A )
% 4.69/5.00 => ( ( A != bot_bot_set_int )
% 4.69/5.00 => ( ( finite_finite_int @ B4 )
% 4.69/5.00 => ( ( B4 != bot_bot_set_int )
% 4.69/5.00 => ( ( lattic8263393255366662781ax_int @ ( sup_sup_set_int @ A @ B4 ) )
% 4.69/5.00 = ( ord_max_int @ ( lattic8263393255366662781ax_int @ A ) @ ( lattic8263393255366662781ax_int @ B4 ) ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.union
% 4.69/5.00 thf(fact_4601_Max_Ounion,axiom,
% 4.69/5.00 ! [A: set_nat,B4: set_nat] :
% 4.69/5.00 ( ( finite_finite_nat @ A )
% 4.69/5.00 => ( ( A != bot_bot_set_nat )
% 4.69/5.00 => ( ( finite_finite_nat @ B4 )
% 4.69/5.00 => ( ( B4 != bot_bot_set_nat )
% 4.69/5.00 => ( ( lattic8265883725875713057ax_nat @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/5.00 = ( ord_max_nat @ ( lattic8265883725875713057ax_nat @ A ) @ ( lattic8265883725875713057ax_nat @ B4 ) ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.union
% 4.69/5.00 thf(fact_4602_Max_Oeq__fold,axiom,
% 4.69/5.00 ! [A: set_o,X: $o] :
% 4.69/5.00 ( ( finite_finite_o @ A )
% 4.69/5.00 => ( ( lattic1921953407002678535_Max_o @ ( insert_o @ X @ A ) )
% 4.69/5.00 = ( finite_fold_o_o @ ord_max_o @ X @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.eq_fold
% 4.69/5.00 thf(fact_4603_Max_Oeq__fold,axiom,
% 4.69/5.00 ! [A: set_Product_unit,X: product_unit] :
% 4.69/5.00 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.00 => ( ( lattic1210392890313158908t_unit @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.00 = ( finite8834431295148555784t_unit @ ord_max_Product_unit @ X @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.eq_fold
% 4.69/5.00 thf(fact_4604_Max_Oeq__fold,axiom,
% 4.69/5.00 ! [A: set_Code_integer,X: code_integer] :
% 4.69/5.00 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.00 => ( ( lattic4901227151466704046nteger @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.00 = ( finite6454954857057555716nteger @ ord_max_Code_integer @ X @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.eq_fold
% 4.69/5.00 thf(fact_4605_Max_Oeq__fold,axiom,
% 4.69/5.00 ! [A: set_int,X: int] :
% 4.69/5.00 ( ( finite_finite_int @ A )
% 4.69/5.00 => ( ( lattic8263393255366662781ax_int @ ( insert_int @ X @ A ) )
% 4.69/5.00 = ( finite_fold_int_int @ ord_max_int @ X @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.eq_fold
% 4.69/5.00 thf(fact_4606_Max_Oeq__fold,axiom,
% 4.69/5.00 ! [A: set_nat,X: nat] :
% 4.69/5.00 ( ( finite_finite_nat @ A )
% 4.69/5.00 => ( ( lattic8265883725875713057ax_nat @ ( insert_nat @ X @ A ) )
% 4.69/5.00 = ( finite_fold_nat_nat @ ord_max_nat @ X @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Max.eq_fold
% 4.69/5.00 thf(fact_4607_finite__range__prod,axiom,
% 4.69/5.00 ! [F: code_integer > produc2591615631378489102nteger] :
% 4.69/5.00 ( ( finite_finite_nat @ ( image_951025933927791156er_nat @ ( comp_P5725896914063526938nteger @ produc8897218493789310642nteger @ F ) @ top_to4645266643341252675nteger ) )
% 4.69/5.00 => ( ( finite6017078050557962740nteger @ ( image_4470545334726330049nteger @ ( comp_P6122662217367900327nteger @ produc1781891006948753140nteger @ F ) @ top_to4645266643341252675nteger ) )
% 4.69/5.00 => ( finite1154042800025562295nteger @ ( image_3408592110290467754nteger @ F @ top_to4645266643341252675nteger ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % finite_range_prod
% 4.69/5.00 thf(fact_4608_finite__range__prod,axiom,
% 4.69/5.00 ! [F: code_integer > produc6433947425880249742er_nat] :
% 4.69/5.00 ( ( finite6017078050557962740nteger @ ( image_4470545334726330049nteger @ ( comp_P7101464685127059239nteger @ produc8632663045010267826er_nat @ F ) @ top_to4645266643341252675nteger ) )
% 4.69/5.00 => ( ( finite_finite_nat @ ( image_951025933927791156er_nat @ ( comp_P5964733648194011802nteger @ produc1517335558169710324er_nat @ F ) @ top_to4645266643341252675nteger ) )
% 4.69/5.00 => ( finite4996374594527322935er_nat @ ( image_7250923904792228394er_nat @ F @ top_to4645266643341252675nteger ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % finite_range_prod
% 4.69/5.00 thf(fact_4609_finite__range__prod,axiom,
% 4.69/5.00 ! [F: code_integer > produc8923325533196201883nteger] :
% 4.69/5.00 ( ( finite6017078050557962740nteger @ ( image_4470545334726330049nteger @ ( comp_P7111796090210262324nteger @ produc8508995932063986495nteger @ F ) @ top_to4645266643341252675nteger ) )
% 4.69/5.00 => ( ( finite6017078050557962740nteger @ ( image_4470545334726330049nteger @ ( comp_P7111796090210262324nteger @ produc6174133586879617921nteger @ F ) @ top_to4645266643341252675nteger ) )
% 4.69/5.00 => ( finite2154694888287295812nteger @ ( image_8049062792287394871nteger @ F @ top_to4645266643341252675nteger ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % finite_range_prod
% 4.69/5.00 thf(fact_4610_finite__range__prod,axiom,
% 4.69/5.00 ! [F: product_unit > product_prod_nat_nat] :
% 4.69/5.00 ( ( finite_finite_nat @ ( image_875570014554754200it_nat @ ( comp_P2980510830910040157t_unit @ product_fst_nat_nat @ F ) @ top_to1996260823553986621t_unit ) )
% 4.69/5.00 => ( ( finite_finite_nat @ ( image_875570014554754200it_nat @ ( comp_P2980510830910040157t_unit @ product_snd_nat_nat @ F ) @ top_to1996260823553986621t_unit ) )
% 4.69/5.00 => ( finite6177210948735845034at_nat @ ( image_7281959405765017145at_nat @ F @ top_to1996260823553986621t_unit ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % finite_range_prod
% 4.69/5.00 thf(fact_4611_finite__range__prod,axiom,
% 4.69/5.00 ! [F: product_unit > produc2591615631378489102nteger] :
% 4.69/5.00 ( ( finite_finite_nat @ ( image_875570014554754200it_nat @ ( comp_P7621350044865347728t_unit @ produc8897218493789310642nteger @ F ) @ top_to1996260823553986621t_unit ) )
% 4.69/5.00 => ( ( finite6017078050557962740nteger @ ( image_3815118110082124069nteger @ ( comp_P7320554561093743171t_unit @ produc1781891006948753140nteger @ F ) @ top_to1996260823553986621t_unit ) )
% 4.69/5.00 => ( finite1154042800025562295nteger @ ( image_4946983642536848454nteger @ F @ top_to1996260823553986621t_unit ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % finite_range_prod
% 4.69/5.00 thf(fact_4612_finite__range__prod,axiom,
% 4.69/5.00 ! [F: product_unit > produc6433947425880249742er_nat] :
% 4.69/5.00 ( ( finite6017078050557962740nteger @ ( image_3815118110082124069nteger @ ( comp_P7581484221039074243t_unit @ produc8632663045010267826er_nat @ F ) @ top_to1996260823553986621t_unit ) )
% 4.69/5.00 => ( ( finite_finite_nat @ ( image_875570014554754200it_nat @ ( comp_P6821003776282389008t_unit @ produc1517335558169710324er_nat @ F ) @ top_to1996260823553986621t_unit ) )
% 4.69/5.00 => ( finite4996374594527322935er_nat @ ( image_8789315437038609094er_nat @ F @ top_to1996260823553986621t_unit ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % finite_range_prod
% 4.69/5.00 thf(fact_4613_finite__range__prod,axiom,
% 4.69/5.00 ! [F: product_unit > produc8923325533196201883nteger] :
% 4.69/5.00 ( ( finite6017078050557962740nteger @ ( image_3815118110082124069nteger @ ( comp_P659088277599099894t_unit @ produc8508995932063986495nteger @ F ) @ top_to1996260823553986621t_unit ) )
% 4.69/5.00 => ( ( finite6017078050557962740nteger @ ( image_3815118110082124069nteger @ ( comp_P659088277599099894t_unit @ produc6174133586879617921nteger @ F ) @ top_to1996260823553986621t_unit ) )
% 4.69/5.00 => ( finite2154694888287295812nteger @ ( image_8089323762101378259nteger @ F @ top_to1996260823553986621t_unit ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % finite_range_prod
% 4.69/5.00 thf(fact_4614_finite__range__prod,axiom,
% 4.69/5.00 ! [F: product_unit > product_prod_int_int] :
% 4.69/5.00 ( ( finite_finite_int @ ( image_873079544045703924it_int @ ( comp_P6796073005956588617t_unit @ product_fst_int_int @ F ) @ top_to1996260823553986621t_unit ) )
% 4.69/5.00 => ( ( finite_finite_int @ ( image_873079544045703924it_int @ ( comp_P6796073005956588617t_unit @ product_snd_int_int @ F ) @ top_to1996260823553986621t_unit ) )
% 4.69/5.00 => ( finite2998713641127702882nt_int @ ( image_4103462098156874993nt_int @ F @ top_to1996260823553986621t_unit ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % finite_range_prod
% 4.69/5.00 thf(fact_4615_finite__range__prod,axiom,
% 4.69/5.00 ! [F: $o > product_prod_nat_nat] :
% 4.69/5.00 ( ( finite_finite_nat @ ( image_o_nat2 @ ( comp_P4394204175247225320_nat_o @ product_fst_nat_nat @ F ) @ top_top_set_o ) )
% 4.69/5.00 => ( ( finite_finite_nat @ ( image_o_nat2 @ ( comp_P4394204175247225320_nat_o @ product_snd_nat_nat @ F ) @ top_top_set_o ) )
% 4.69/5.00 => ( finite6177210948735845034at_nat @ ( image_3855930084881510382at_nat @ F @ top_top_set_o ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % finite_range_prod
% 4.69/5.00 thf(fact_4616_finite__range__prod,axiom,
% 4.69/5.00 ! [F: $o > produc2591615631378489102nteger] :
% 4.69/5.00 ( ( finite_finite_nat @ ( image_o_nat2 @ ( comp_P7179991235626930843_nat_o @ produc8897218493789310642nteger @ F ) @ top_top_set_o ) )
% 4.69/5.00 => ( ( finite6017078050557962740nteger @ ( image_o_Code_integer @ ( comp_P7177471617286032590eger_o @ produc1781891006948753140nteger @ F ) @ top_top_set_o ) )
% 4.69/5.00 => ( finite1154042800025562295nteger @ ( image_8407096251609565691nteger @ F @ top_top_set_o ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % finite_range_prod
% 4.69/5.00 thf(fact_4617_inj__apsnd,axiom,
% 4.69/5.00 ! [F: code_integer > code_integer] :
% 4.69/5.00 ( ( inj_on20428373856169009nteger @ ( produc6499014454317279255nteger @ F ) @ top_to2363841527343591755nteger )
% 4.69/5.00 = ( inj_on1158064722259180589nteger @ F @ top_to4645266643341252675nteger ) ) ).
% 4.69/5.00
% 4.69/5.00 % inj_apsnd
% 4.69/5.00 thf(fact_4618_total__inv__image,axiom,
% 4.69/5.00 ! [F: product_unit > product_unit,R2: set_Pr5094982260447487303t_unit] :
% 4.69/5.00 ( ( inj_on8151373323710067377t_unit @ F @ top_to1996260823553986621t_unit )
% 4.69/5.00 => ( ( total_5665700600833547665t_unit @ top_to1996260823553986621t_unit @ R2 )
% 4.69/5.00 => ( total_5665700600833547665t_unit @ top_to1996260823553986621t_unit @ ( inv_im8770536620514187154t_unit @ R2 @ F ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % total_inv_image
% 4.69/5.00 thf(fact_4619_total__inv__image,axiom,
% 4.69/5.00 ! [F: product_unit > $o,R2: set_Product_prod_o_o] :
% 4.69/5.00 ( ( inj_on8854722734121536060unit_o @ F @ top_to1996260823553986621t_unit )
% 4.69/5.00 => ( ( total_on_o @ top_top_set_o @ R2 )
% 4.69/5.00 => ( total_5665700600833547665t_unit @ top_to1996260823553986621t_unit @ ( inv_im4602722609573551687t_unit @ R2 @ F ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % total_inv_image
% 4.69/5.00 thf(fact_4620_total__inv__image,axiom,
% 4.69/5.00 ! [F: product_unit > nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/5.00 ( ( inj_on8430439091780834860it_nat @ F @ top_to1996260823553986621t_unit )
% 4.69/5.00 => ( ( total_on_nat @ top_top_set_nat @ R2 )
% 4.69/5.00 => ( total_5665700600833547665t_unit @ top_to1996260823553986621t_unit @ ( inv_im7624054837341743209t_unit @ R2 @ F ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % total_inv_image
% 4.69/5.00 thf(fact_4621_total__inv__image,axiom,
% 4.69/5.00 ! [F: product_unit > int,R2: set_Pr958786334691620121nt_int] :
% 4.69/5.00 ( ( inj_on8427948621271784584it_int @ F @ top_to1996260823553986621t_unit )
% 4.69/5.00 => ( ( total_on_int @ top_top_set_int @ R2 )
% 4.69/5.00 => ( total_5665700600833547665t_unit @ top_to1996260823553986621t_unit @ ( inv_im4740476784543923469t_unit @ R2 @ F ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % total_inv_image
% 4.69/5.00 thf(fact_4622_total__inv__image,axiom,
% 4.69/5.00 ! [F: $o > product_unit,R2: set_Pr5094982260447487303t_unit] :
% 4.69/5.00 ( ( inj_on4268752236855399398t_unit @ F @ top_top_set_o )
% 4.69/5.00 => ( ( total_5665700600833547665t_unit @ top_to1996260823553986621t_unit @ R2 )
% 4.69/5.00 => ( total_on_o @ top_top_set_o @ ( inv_im9188693106839688349unit_o @ R2 @ F ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % total_inv_image
% 4.69/5.00 thf(fact_4623_total__inv__image,axiom,
% 4.69/5.00 ! [F: $o > $o,R2: set_Product_prod_o_o] :
% 4.69/5.00 ( ( inj_on_o_o @ F @ top_top_set_o )
% 4.69/5.00 => ( ( total_on_o @ top_top_set_o @ R2 )
% 4.69/5.00 => ( total_on_o @ top_top_set_o @ ( inv_image_o_o @ R2 @ F ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % total_inv_image
% 4.69/5.00 thf(fact_4624_total__inv__image,axiom,
% 4.69/5.00 ! [F: $o > nat,R2: set_Pr1261947904930325089at_nat] :
% 4.69/5.00 ( ( inj_on_o_nat @ F @ top_top_set_o )
% 4.69/5.00 => ( ( total_on_nat @ top_top_set_nat @ R2 )
% 4.69/5.00 => ( total_on_o @ top_top_set_o @ ( inv_image_nat_o @ R2 @ F ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % total_inv_image
% 4.69/5.00 thf(fact_4625_total__inv__image,axiom,
% 4.69/5.00 ! [F: $o > int,R2: set_Pr958786334691620121nt_int] :
% 4.69/5.00 ( ( inj_on_o_int @ F @ top_top_set_o )
% 4.69/5.00 => ( ( total_on_int @ top_top_set_int @ R2 )
% 4.69/5.00 => ( total_on_o @ top_top_set_o @ ( inv_image_int_o @ R2 @ F ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % total_inv_image
% 4.69/5.00 thf(fact_4626_total__inv__image,axiom,
% 4.69/5.00 ! [F: nat > product_unit,R2: set_Pr5094982260447487303t_unit] :
% 4.69/5.00 ( ( inj_on7061601236592826506t_unit @ F @ top_top_set_nat )
% 4.69/5.00 => ( ( total_5665700600833547665t_unit @ top_to1996260823553986621t_unit @ R2 )
% 4.69/5.00 => ( total_on_nat @ top_top_set_nat @ ( inv_im8992892692529751563it_nat @ R2 @ F ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % total_inv_image
% 4.69/5.00 thf(fact_4627_total__inv__image,axiom,
% 4.69/5.00 ! [F: nat > $o,R2: set_Product_prod_o_o] :
% 4.69/5.00 ( ( inj_on_nat_o @ F @ top_top_set_nat )
% 4.69/5.00 => ( ( total_on_o @ top_top_set_o @ R2 )
% 4.69/5.00 => ( total_on_nat @ top_top_set_nat @ ( inv_image_o_nat @ R2 @ F ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % total_inv_image
% 4.69/5.00 thf(fact_4628_card__Diff1__less,axiom,
% 4.69/5.00 ! [A: set_Code_integer,X: code_integer] :
% 4.69/5.00 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.00 => ( ( member_Code_integer @ X @ A )
% 4.69/5.00 => ( ord_less_nat @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) @ ( finite4902975817058060853nteger @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff1_less
% 4.69/5.00 thf(fact_4629_card__Diff1__less,axiom,
% 4.69/5.00 ! [A: set_Product_unit,X: product_unit] :
% 4.69/5.00 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.00 => ( ( member_Product_unit @ X @ A )
% 4.69/5.00 => ( ord_less_nat @ ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) @ ( finite410649719033368117t_unit @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff1_less
% 4.69/5.00 thf(fact_4630_card__Diff1__less,axiom,
% 4.69/5.00 ! [A: set_o,X: $o] :
% 4.69/5.00 ( ( finite_finite_o @ A )
% 4.69/5.00 => ( ( member_o @ X @ A )
% 4.69/5.00 => ( ord_less_nat @ ( finite_card_o @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) @ ( finite_card_o @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff1_less
% 4.69/5.00 thf(fact_4631_card__Diff1__less,axiom,
% 4.69/5.00 ! [A: set_int,X: int] :
% 4.69/5.00 ( ( finite_finite_int @ A )
% 4.69/5.00 => ( ( member_int @ X @ A )
% 4.69/5.00 => ( ord_less_nat @ ( finite_card_int @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) ) @ ( finite_card_int @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff1_less
% 4.69/5.00 thf(fact_4632_card__Diff1__less,axiom,
% 4.69/5.00 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/5.00 => ( ( member6576561426505652726_nat_o @ X @ A )
% 4.69/5.00 => ( ord_less_nat @ ( finite1363419556375932405_nat_o @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) ) @ ( finite1363419556375932405_nat_o @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff1_less
% 4.69/5.00 thf(fact_4633_card__Diff1__less,axiom,
% 4.69/5.00 ! [A: set_nat,X: nat] :
% 4.69/5.00 ( ( finite_finite_nat @ A )
% 4.69/5.00 => ( ( member_nat @ X @ A )
% 4.69/5.00 => ( ord_less_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) @ ( finite_card_nat @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff1_less
% 4.69/5.00 thf(fact_4634_card__Diff2__less,axiom,
% 4.69/5.00 ! [A: set_Code_integer,X: code_integer,Y: code_integer] :
% 4.69/5.00 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.00 => ( ( member_Code_integer @ X @ A )
% 4.69/5.00 => ( ( member_Code_integer @ Y @ A )
% 4.69/5.00 => ( ord_less_nat @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) @ ( insert_Code_integer @ Y @ bot_bo3990330152332043303nteger ) ) ) @ ( finite4902975817058060853nteger @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff2_less
% 4.69/5.00 thf(fact_4635_card__Diff2__less,axiom,
% 4.69/5.00 ! [A: set_Product_unit,X: product_unit,Y: product_unit] :
% 4.69/5.00 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.00 => ( ( member_Product_unit @ X @ A )
% 4.69/5.00 => ( ( member_Product_unit @ Y @ A )
% 4.69/5.00 => ( ord_less_nat @ ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) @ ( insert_Product_unit @ Y @ bot_bo3957492148770167129t_unit ) ) ) @ ( finite410649719033368117t_unit @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff2_less
% 4.69/5.00 thf(fact_4636_card__Diff2__less,axiom,
% 4.69/5.00 ! [A: set_o,X: $o,Y: $o] :
% 4.69/5.00 ( ( finite_finite_o @ A )
% 4.69/5.00 => ( ( member_o @ X @ A )
% 4.69/5.00 => ( ( member_o @ Y @ A )
% 4.69/5.00 => ( ord_less_nat @ ( finite_card_o @ ( minus_minus_set_o @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) @ ( insert_o @ Y @ bot_bot_set_o ) ) ) @ ( finite_card_o @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff2_less
% 4.69/5.00 thf(fact_4637_card__Diff2__less,axiom,
% 4.69/5.00 ! [A: set_int,X: int,Y: int] :
% 4.69/5.00 ( ( finite_finite_int @ A )
% 4.69/5.00 => ( ( member_int @ X @ A )
% 4.69/5.00 => ( ( member_int @ Y @ A )
% 4.69/5.00 => ( ord_less_nat @ ( finite_card_int @ ( minus_minus_set_int @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) @ ( insert_int @ Y @ bot_bot_set_int ) ) ) @ ( finite_card_int @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff2_less
% 4.69/5.00 thf(fact_4638_card__Diff2__less,axiom,
% 4.69/5.00 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/5.00 => ( ( member6576561426505652726_nat_o @ X @ A )
% 4.69/5.00 => ( ( member6576561426505652726_nat_o @ Y @ A )
% 4.69/5.00 => ( ord_less_nat @ ( finite1363419556375932405_nat_o @ ( minus_1801376950450012436_nat_o @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) @ ( insert5175938949040314269_nat_o @ Y @ bot_bo7824918357723582233_nat_o ) ) ) @ ( finite1363419556375932405_nat_o @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff2_less
% 4.69/5.00 thf(fact_4639_card__Diff2__less,axiom,
% 4.69/5.00 ! [A: set_nat,X: nat,Y: nat] :
% 4.69/5.00 ( ( finite_finite_nat @ A )
% 4.69/5.00 => ( ( member_nat @ X @ A )
% 4.69/5.00 => ( ( member_nat @ Y @ A )
% 4.69/5.00 => ( ord_less_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ ( insert_nat @ Y @ bot_bot_set_nat ) ) ) @ ( finite_card_nat @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff2_less
% 4.69/5.00 thf(fact_4640_card__Diff1__less__iff,axiom,
% 4.69/5.00 ! [A: set_Code_integer,X: code_integer] :
% 4.69/5.00 ( ( ord_less_nat @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) @ ( finite4902975817058060853nteger @ A ) )
% 4.69/5.00 = ( ( finite6017078050557962740nteger @ A )
% 4.69/5.00 & ( member_Code_integer @ X @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff1_less_iff
% 4.69/5.00 thf(fact_4641_card__Diff1__less__iff,axiom,
% 4.69/5.00 ! [A: set_Product_unit,X: product_unit] :
% 4.69/5.00 ( ( ord_less_nat @ ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) @ ( finite410649719033368117t_unit @ A ) )
% 4.69/5.00 = ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.00 & ( member_Product_unit @ X @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff1_less_iff
% 4.69/5.00 thf(fact_4642_card__Diff1__less__iff,axiom,
% 4.69/5.00 ! [A: set_o,X: $o] :
% 4.69/5.00 ( ( ord_less_nat @ ( finite_card_o @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) @ ( finite_card_o @ A ) )
% 4.69/5.00 = ( ( finite_finite_o @ A )
% 4.69/5.00 & ( member_o @ X @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff1_less_iff
% 4.69/5.00 thf(fact_4643_card__Diff1__less__iff,axiom,
% 4.69/5.00 ! [A: set_int,X: int] :
% 4.69/5.00 ( ( ord_less_nat @ ( finite_card_int @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) ) @ ( finite_card_int @ A ) )
% 4.69/5.00 = ( ( finite_finite_int @ A )
% 4.69/5.00 & ( member_int @ X @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff1_less_iff
% 4.69/5.00 thf(fact_4644_card__Diff1__less__iff,axiom,
% 4.69/5.00 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ( ord_less_nat @ ( finite1363419556375932405_nat_o @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) ) @ ( finite1363419556375932405_nat_o @ A ) )
% 4.69/5.00 = ( ( finite3252695134891459830_nat_o @ A )
% 4.69/5.00 & ( member6576561426505652726_nat_o @ X @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff1_less_iff
% 4.69/5.00 thf(fact_4645_card__Diff1__less__iff,axiom,
% 4.69/5.00 ! [A: set_nat,X: nat] :
% 4.69/5.00 ( ( ord_less_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) @ ( finite_card_nat @ A ) )
% 4.69/5.00 = ( ( finite_finite_nat @ A )
% 4.69/5.00 & ( member_nat @ X @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff1_less_iff
% 4.69/5.00 thf(fact_4646_Inter__in__chain,axiom,
% 4.69/5.00 ! [B9: set_set_nat,A11: set_set_nat] :
% 4.69/5.00 ( ( finite1152437895449049373et_nat @ B9 )
% 4.69/5.00 => ( ( B9 != bot_bot_set_set_nat )
% 4.69/5.00 => ( ( pred_chain_set_nat @ A11 @ ord_less_set_nat @ B9 )
% 4.69/5.00 => ( member_set_nat @ ( comple7806235888213564991et_nat @ B9 ) @ B9 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Inter_in_chain
% 4.69/5.00 thf(fact_4647_card__eq__UNIV2,axiom,
% 4.69/5.00 ! [S: set_Product_unit] :
% 4.69/5.00 ( ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 4.69/5.00 = ( finite410649719033368117t_unit @ S ) )
% 4.69/5.00 = ( S = top_to1996260823553986621t_unit ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_eq_UNIV2
% 4.69/5.00 thf(fact_4648_card__eq__UNIV2,axiom,
% 4.69/5.00 ! [S: set_o] :
% 4.69/5.00 ( ( ( finite_card_o @ top_top_set_o )
% 4.69/5.00 = ( finite_card_o @ S ) )
% 4.69/5.00 = ( S = top_top_set_o ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_eq_UNIV2
% 4.69/5.00 thf(fact_4649_card__eq__UNIV,axiom,
% 4.69/5.00 ! [S: set_Product_unit] :
% 4.69/5.00 ( ( ( finite410649719033368117t_unit @ S )
% 4.69/5.00 = ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit ) )
% 4.69/5.00 = ( S = top_to1996260823553986621t_unit ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_eq_UNIV
% 4.69/5.00 thf(fact_4650_card__eq__UNIV,axiom,
% 4.69/5.00 ! [S: set_o] :
% 4.69/5.00 ( ( ( finite_card_o @ S )
% 4.69/5.00 = ( finite_card_o @ top_top_set_o ) )
% 4.69/5.00 = ( S = top_top_set_o ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_eq_UNIV
% 4.69/5.00 thf(fact_4651_fst__map__prod,axiom,
% 4.69/5.00 ! [F: int > int,G: int > int,X: product_prod_int_int] :
% 4.69/5.00 ( ( product_fst_int_int @ ( produc6036585564866528938nt_int @ F @ G @ X ) )
% 4.69/5.00 = ( F @ ( product_fst_int_int @ X ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % fst_map_prod
% 4.69/5.00 thf(fact_4652_apfst__conv,axiom,
% 4.69/5.00 ! [F: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit,X: heap_e7401611519738050253t_unit,Y: set_nat] :
% 4.69/5.00 ( ( produc4172003873565521026et_nat @ F @ ( produc7507926704131184380et_nat @ X @ Y ) )
% 4.69/5.00 = ( produc7507926704131184380et_nat @ ( F @ X ) @ Y ) ) ).
% 4.69/5.00
% 4.69/5.00 % apfst_conv
% 4.69/5.00 thf(fact_4653_apfst__conv,axiom,
% 4.69/5.00 ! [F: nat > nat,X: nat,Y: nat] :
% 4.69/5.00 ( ( produc986720760941809198at_nat @ F @ ( product_Pair_nat_nat @ X @ Y ) )
% 4.69/5.00 = ( product_Pair_nat_nat @ ( F @ X ) @ Y ) ) ).
% 4.69/5.00
% 4.69/5.00 % apfst_conv
% 4.69/5.00 thf(fact_4654_apfst__conv,axiom,
% 4.69/5.00 ! [F: int > int,X: int,Y: int] :
% 4.69/5.00 ( ( produc2355237562570658114nt_int @ F @ ( product_Pair_int_int @ X @ Y ) )
% 4.69/5.00 = ( product_Pair_int_int @ ( F @ X ) @ Y ) ) ).
% 4.69/5.00
% 4.69/5.00 % apfst_conv
% 4.69/5.00 thf(fact_4655_apfst__conv,axiom,
% 4.69/5.00 ! [F: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( produc3198230245617193214et_nat @ F @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 4.69/5.00 = ( produc5001842942810119800et_nat @ ( F @ X ) @ Y ) ) ).
% 4.69/5.00
% 4.69/5.00 % apfst_conv
% 4.69/5.00 thf(fact_4656_apfst__conv,axiom,
% 4.69/5.00 ! [F: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 4.69/5.00 ( ( produc1442628905706551930et_nat @ F @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 4.69/5.00 = ( produc2245416461498447860et_nat @ ( F @ X ) @ Y ) ) ).
% 4.69/5.00
% 4.69/5.00 % apfst_conv
% 4.69/5.00 thf(fact_4657_apsnd__conv,axiom,
% 4.69/5.00 ! [F: set_nat > set_nat,X: heap_e7401611519738050253t_unit,Y: set_nat] :
% 4.69/5.00 ( ( produc3286488329990770625t_unit @ F @ ( produc7507926704131184380et_nat @ X @ Y ) )
% 4.69/5.00 = ( produc7507926704131184380et_nat @ X @ ( F @ Y ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apsnd_conv
% 4.69/5.00 thf(fact_4658_apsnd__conv,axiom,
% 4.69/5.00 ! [F: nat > nat,X: nat,Y: nat] :
% 4.69/5.00 ( ( produc3094765310956027504at_nat @ F @ ( product_Pair_nat_nat @ X @ Y ) )
% 4.69/5.00 = ( product_Pair_nat_nat @ X @ ( F @ Y ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apsnd_conv
% 4.69/5.00 thf(fact_4659_apsnd__conv,axiom,
% 4.69/5.00 ! [F: int > int,X: int,Y: int] :
% 4.69/5.00 ( ( produc4463282112584876420nt_int @ F @ ( product_Pair_int_int @ X @ Y ) )
% 4.69/5.00 = ( product_Pair_int_int @ X @ ( F @ Y ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apsnd_conv
% 4.69/5.00 thf(fact_4660_apsnd__conv,axiom,
% 4.69/5.00 ! [F: produc3658429121746597890et_nat > produc3658429121746597890et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( produc8750854537940449737_nat_o @ F @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 4.69/5.00 = ( produc5001842942810119800et_nat @ X @ ( F @ Y ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apsnd_conv
% 4.69/5.00 thf(fact_4661_apsnd__conv,axiom,
% 4.69/5.00 ! [F: produc3658429121746597890et_nat > produc3925858234332021118et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( produc7714581247149323085_nat_o @ F @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 4.69/5.00 = ( produc2245416461498447860et_nat @ X @ ( F @ Y ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apsnd_conv
% 4.69/5.00 thf(fact_4662_apsnd__conv,axiom,
% 4.69/5.00 ! [F: produc3925858234332021118et_nat > produc3658429121746597890et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 4.69/5.00 ( ( produc1515462096303866701_nat_o @ F @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 4.69/5.00 = ( produc5001842942810119800et_nat @ X @ ( F @ Y ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apsnd_conv
% 4.69/5.00 thf(fact_4663_apsnd__conv,axiom,
% 4.69/5.00 ! [F: produc3925858234332021118et_nat > produc3925858234332021118et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 4.69/5.00 ( ( produc969530845752564945_nat_o @ F @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 4.69/5.00 = ( produc2245416461498447860et_nat @ X @ ( F @ Y ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apsnd_conv
% 4.69/5.00 thf(fact_4664_apsnd__conv,axiom,
% 4.69/5.00 ! [F: code_integer > code_integer,X: code_integer,Y: code_integer] :
% 4.69/5.00 ( ( produc6499014454317279255nteger @ F @ ( produc1086072967326762835nteger @ X @ Y ) )
% 4.69/5.00 = ( produc1086072967326762835nteger @ X @ ( F @ Y ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apsnd_conv
% 4.69/5.00 thf(fact_4665_fst__apfst,axiom,
% 4.69/5.00 ! [F: int > int,X: product_prod_int_int] :
% 4.69/5.00 ( ( product_fst_int_int @ ( produc2355237562570658114nt_int @ F @ X ) )
% 4.69/5.00 = ( F @ ( product_fst_int_int @ X ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % fst_apfst
% 4.69/5.00 thf(fact_4666_snd__apfst,axiom,
% 4.69/5.00 ! [F: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit,X: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( produc8586169260539613262et_nat @ ( produc4172003873565521026et_nat @ F @ X ) )
% 4.69/5.00 = ( produc8586169260539613262et_nat @ X ) ) ).
% 4.69/5.00
% 4.69/5.00 % snd_apfst
% 4.69/5.00 thf(fact_4667_snd__apfst,axiom,
% 4.69/5.00 ! [F: int > int,X: product_prod_int_int] :
% 4.69/5.00 ( ( product_snd_int_int @ ( produc2355237562570658114nt_int @ F @ X ) )
% 4.69/5.00 = ( product_snd_int_int @ X ) ) ).
% 4.69/5.00
% 4.69/5.00 % snd_apfst
% 4.69/5.00 thf(fact_4668_in__inv__image,axiom,
% 4.69/5.00 ! [X: nat,Y: nat,R2: set_Pr1261947904930325089at_nat,F: nat > nat] :
% 4.69/5.00 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( inv_image_nat_nat @ R2 @ F ) )
% 4.69/5.00 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ X ) @ ( F @ Y ) ) @ R2 ) ) ).
% 4.69/5.00
% 4.69/5.00 % in_inv_image
% 4.69/5.00 thf(fact_4669_in__inv__image,axiom,
% 4.69/5.00 ! [X: nat,Y: nat,R2: set_Pr958786334691620121nt_int,F: nat > int] :
% 4.69/5.00 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( inv_image_int_nat @ R2 @ F ) )
% 4.69/5.00 = ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F @ X ) @ ( F @ Y ) ) @ R2 ) ) ).
% 4.69/5.00
% 4.69/5.00 % in_inv_image
% 4.69/5.00 thf(fact_4670_in__inv__image,axiom,
% 4.69/5.00 ! [X: int,Y: int,R2: set_Pr1261947904930325089at_nat,F: int > nat] :
% 4.69/5.00 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( inv_image_nat_int @ R2 @ F ) )
% 4.69/5.00 = ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ X ) @ ( F @ Y ) ) @ R2 ) ) ).
% 4.69/5.00
% 4.69/5.00 % in_inv_image
% 4.69/5.00 thf(fact_4671_in__inv__image,axiom,
% 4.69/5.00 ! [X: int,Y: int,R2: set_Pr958786334691620121nt_int,F: int > int] :
% 4.69/5.00 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( inv_image_int_int @ R2 @ F ) )
% 4.69/5.00 = ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F @ X ) @ ( F @ Y ) ) @ R2 ) ) ).
% 4.69/5.00
% 4.69/5.00 % in_inv_image
% 4.69/5.00 thf(fact_4672_fst__apsnd,axiom,
% 4.69/5.00 ! [F: code_integer > code_integer,X: produc8923325533196201883nteger] :
% 4.69/5.00 ( ( produc8508995932063986495nteger @ ( produc6499014454317279255nteger @ F @ X ) )
% 4.69/5.00 = ( produc8508995932063986495nteger @ X ) ) ).
% 4.69/5.00
% 4.69/5.00 % fst_apsnd
% 4.69/5.00 thf(fact_4673_fst__apsnd,axiom,
% 4.69/5.00 ! [F: int > int,X: product_prod_int_int] :
% 4.69/5.00 ( ( product_fst_int_int @ ( produc4463282112584876420nt_int @ F @ X ) )
% 4.69/5.00 = ( product_fst_int_int @ X ) ) ).
% 4.69/5.00
% 4.69/5.00 % fst_apsnd
% 4.69/5.00 thf(fact_4674_apsnd__eq__conv,axiom,
% 4.69/5.00 ! [F: code_integer > code_integer,X: produc8923325533196201883nteger,G: code_integer > code_integer] :
% 4.69/5.00 ( ( ( produc6499014454317279255nteger @ F @ X )
% 4.69/5.00 = ( produc6499014454317279255nteger @ G @ X ) )
% 4.69/5.00 = ( ( F @ ( produc6174133586879617921nteger @ X ) )
% 4.69/5.00 = ( G @ ( produc6174133586879617921nteger @ X ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apsnd_eq_conv
% 4.69/5.00 thf(fact_4675_snd__apsnd,axiom,
% 4.69/5.00 ! [F: code_integer > code_integer,X: produc8923325533196201883nteger] :
% 4.69/5.00 ( ( produc6174133586879617921nteger @ ( produc6499014454317279255nteger @ F @ X ) )
% 4.69/5.00 = ( F @ ( produc6174133586879617921nteger @ X ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % snd_apsnd
% 4.69/5.00 thf(fact_4676_snd__apsnd,axiom,
% 4.69/5.00 ! [F: set_nat > set_nat,X: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( produc8586169260539613262et_nat @ ( produc3286488329990770625t_unit @ F @ X ) )
% 4.69/5.00 = ( F @ ( produc8586169260539613262et_nat @ X ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % snd_apsnd
% 4.69/5.00 thf(fact_4677_snd__apsnd,axiom,
% 4.69/5.00 ! [F: int > int,X: product_prod_int_int] :
% 4.69/5.00 ( ( product_snd_int_int @ ( produc4463282112584876420nt_int @ F @ X ) )
% 4.69/5.00 = ( F @ ( product_snd_int_int @ X ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % snd_apsnd
% 4.69/5.00 thf(fact_4678_Inf__eq__bot__iff,axiom,
% 4.69/5.00 ! [A: set_Product_unit] :
% 4.69/5.00 ( ( ( comple2584293577114468500t_unit @ A )
% 4.69/5.00 = bot_bot_Product_unit )
% 4.69/5.00 = ( ! [X2: product_unit] :
% 4.69/5.00 ( ( ord_le361264281704409273t_unit @ bot_bot_Product_unit @ X2 )
% 4.69/5.00 => ? [Y3: product_unit] :
% 4.69/5.00 ( ( member_Product_unit @ Y3 @ A )
% 4.69/5.00 & ( ord_le361264281704409273t_unit @ Y3 @ X2 ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_eq_bot_iff
% 4.69/5.00 thf(fact_4679_Inf__empty,axiom,
% 4.69/5.00 ( ( complete_Inf_Inf_o @ bot_bot_set_o )
% 4.69/5.00 = top_top_o ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_empty
% 4.69/5.00 thf(fact_4680_Inf__empty,axiom,
% 4.69/5.00 ( ( comple90455603224345172_nat_o @ bot_bo7824918357723582233_nat_o )
% 4.69/5.00 = top_to5213382387105117981_nat_o ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_empty
% 4.69/5.00 thf(fact_4681_Inf__empty,axiom,
% 4.69/5.00 ( ( comple7216939928495492468t_unit @ bot_bo6284674557190688313t_unit )
% 4.69/5.00 = top_to1996260823553986621t_unit ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_empty
% 4.69/5.00 thf(fact_4682_Inf__empty,axiom,
% 4.69/5.00 ( ( comple3063163877087187839_set_o @ bot_bot_set_set_o )
% 4.69/5.00 = top_top_set_o ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_empty
% 4.69/5.00 thf(fact_4683_Inf__empty,axiom,
% 4.69/5.00 ( ( comple3628384868704368283et_int @ bot_bot_set_set_int )
% 4.69/5.00 = top_top_set_int ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_empty
% 4.69/5.00 thf(fact_4684_Inf__empty,axiom,
% 4.69/5.00 ( ( comple7806235888213564991et_nat @ bot_bot_set_set_nat )
% 4.69/5.00 = top_top_set_nat ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_empty
% 4.69/5.00 thf(fact_4685_Inf__empty,axiom,
% 4.69/5.00 ( ( comple2584293577114468500t_unit @ bot_bo3957492148770167129t_unit )
% 4.69/5.00 = top_top_Product_unit ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_empty
% 4.69/5.00 thf(fact_4686_Inf__UNIV,axiom,
% 4.69/5.00 ( ( comple7216939928495492468t_unit @ top_to1767297665138865437t_unit )
% 4.69/5.00 = bot_bo3957492148770167129t_unit ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_UNIV
% 4.69/5.00 thf(fact_4687_Inf__UNIV,axiom,
% 4.69/5.00 ( ( comple3063163877087187839_set_o @ top_top_set_set_o )
% 4.69/5.00 = bot_bot_set_o ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_UNIV
% 4.69/5.00 thf(fact_4688_Inf__UNIV,axiom,
% 4.69/5.00 ( ( comple3628384868704368283et_int @ top_top_set_set_int )
% 4.69/5.00 = bot_bot_set_int ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_UNIV
% 4.69/5.00 thf(fact_4689_Inf__UNIV,axiom,
% 4.69/5.00 ( ( comple79274577958421812_nat_o @ top_to8515903933492314333_nat_o )
% 4.69/5.00 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_UNIV
% 4.69/5.00 thf(fact_4690_Inf__UNIV,axiom,
% 4.69/5.00 ( ( complete_Inf_Inf_o @ top_top_set_o )
% 4.69/5.00 = bot_bot_o ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_UNIV
% 4.69/5.00 thf(fact_4691_Inf__UNIV,axiom,
% 4.69/5.00 ( ( comple7806235888213564991et_nat @ top_top_set_set_nat )
% 4.69/5.00 = bot_bot_set_nat ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_UNIV
% 4.69/5.00 thf(fact_4692_Inf__UNIV,axiom,
% 4.69/5.00 ( ( comple2584293577114468500t_unit @ top_to1996260823553986621t_unit )
% 4.69/5.00 = bot_bot_Product_unit ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_UNIV
% 4.69/5.00 thf(fact_4693_cInf__singleton,axiom,
% 4.69/5.00 ! [X: $o] :
% 4.69/5.00 ( ( complete_Inf_Inf_o @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/5.00 = X ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_singleton
% 4.69/5.00 thf(fact_4694_cInf__singleton,axiom,
% 4.69/5.00 ! [X: int] :
% 4.69/5.00 ( ( complete_Inf_Inf_int @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/5.00 = X ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_singleton
% 4.69/5.00 thf(fact_4695_cInf__singleton,axiom,
% 4.69/5.00 ! [X: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ( comple90455603224345172_nat_o @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 4.69/5.00 = X ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_singleton
% 4.69/5.00 thf(fact_4696_cInf__singleton,axiom,
% 4.69/5.00 ! [X: nat] :
% 4.69/5.00 ( ( complete_Inf_Inf_nat @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/5.00 = X ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_singleton
% 4.69/5.00 thf(fact_4697_cInf__singleton,axiom,
% 4.69/5.00 ! [X: set_nat] :
% 4.69/5.00 ( ( comple7806235888213564991et_nat @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 4.69/5.00 = X ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_singleton
% 4.69/5.00 thf(fact_4698_cInf__singleton,axiom,
% 4.69/5.00 ! [X: product_unit] :
% 4.69/5.00 ( ( comple2584293577114468500t_unit @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/5.00 = X ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_singleton
% 4.69/5.00 thf(fact_4699_Inf__insert,axiom,
% 4.69/5.00 ! [A2: $o,A: set_o] :
% 4.69/5.00 ( ( complete_Inf_Inf_o @ ( insert_o @ A2 @ A ) )
% 4.69/5.00 = ( inf_inf_o @ A2 @ ( complete_Inf_Inf_o @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_insert
% 4.69/5.00 thf(fact_4700_Inf__insert,axiom,
% 4.69/5.00 ! [A2: set_nat,A: set_set_nat] :
% 4.69/5.00 ( ( comple7806235888213564991et_nat @ ( insert_set_nat @ A2 @ A ) )
% 4.69/5.00 = ( inf_inf_set_nat @ A2 @ ( comple7806235888213564991et_nat @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_insert
% 4.69/5.00 thf(fact_4701_Inf__insert,axiom,
% 4.69/5.00 ! [A2: product_unit,A: set_Product_unit] :
% 4.69/5.00 ( ( comple2584293577114468500t_unit @ ( insert_Product_unit @ A2 @ A ) )
% 4.69/5.00 = ( inf_inf_Product_unit @ A2 @ ( comple2584293577114468500t_unit @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_insert
% 4.69/5.00 thf(fact_4702_prod_Ocollapse,axiom,
% 4.69/5.00 ! [Prod: product_prod_nat_nat] :
% 4.69/5.00 ( ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) )
% 4.69/5.00 = Prod ) ).
% 4.69/5.00
% 4.69/5.00 % prod.collapse
% 4.69/5.00 thf(fact_4703_prod_Ocollapse,axiom,
% 4.69/5.00 ! [Prod: produc3925858234332021118et_nat] :
% 4.69/5.00 ( ( produc5001842942810119800et_nat @ ( produc995936583742144908et_nat @ Prod ) @ ( produc4011572625026189258et_nat @ Prod ) )
% 4.69/5.00 = Prod ) ).
% 4.69/5.00
% 4.69/5.00 % prod.collapse
% 4.69/5.00 thf(fact_4704_prod_Ocollapse,axiom,
% 4.69/5.00 ! [Prod: produc2732055786443039994et_nat] :
% 4.69/5.00 ( ( produc2245416461498447860et_nat @ ( produc180342877477747464et_nat @ Prod ) @ ( produc5374455773327741254et_nat @ Prod ) )
% 4.69/5.00 = Prod ) ).
% 4.69/5.00
% 4.69/5.00 % prod.collapse
% 4.69/5.00 thf(fact_4705_prod_Ocollapse,axiom,
% 4.69/5.00 ! [Prod: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( produc7507926704131184380et_nat @ ( produc1824681642469235216et_nat @ Prod ) @ ( produc8586169260539613262et_nat @ Prod ) )
% 4.69/5.00 = Prod ) ).
% 4.69/5.00
% 4.69/5.00 % prod.collapse
% 4.69/5.00 thf(fact_4706_prod_Ocollapse,axiom,
% 4.69/5.00 ! [Prod: product_prod_int_int] :
% 4.69/5.00 ( ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) )
% 4.69/5.00 = Prod ) ).
% 4.69/5.00
% 4.69/5.00 % prod.collapse
% 4.69/5.00 thf(fact_4707_card__ge__UNIV,axiom,
% 4.69/5.00 ! [S: set_Product_unit] :
% 4.69/5.00 ( ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit ) @ ( finite410649719033368117t_unit @ S ) )
% 4.69/5.00 = ( S = top_to1996260823553986621t_unit ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_ge_UNIV
% 4.69/5.00 thf(fact_4708_card__ge__UNIV,axiom,
% 4.69/5.00 ! [S: set_o] :
% 4.69/5.00 ( ( ord_less_eq_nat @ ( finite_card_o @ top_top_set_o ) @ ( finite_card_o @ S ) )
% 4.69/5.00 = ( S = top_top_set_o ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_ge_UNIV
% 4.69/5.00 thf(fact_4709_card__Diff__insert,axiom,
% 4.69/5.00 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/5.00 ( ( member6576561426505652726_nat_o @ A2 @ A )
% 4.69/5.00 => ( ~ ( member6576561426505652726_nat_o @ A2 @ B4 )
% 4.69/5.00 => ( ( finite1363419556375932405_nat_o @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ A2 @ B4 ) ) )
% 4.69/5.00 = ( minus_minus_nat @ ( finite1363419556375932405_nat_o @ ( minus_1801376950450012436_nat_o @ A @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff_insert
% 4.69/5.00 thf(fact_4710_card__Diff__insert,axiom,
% 4.69/5.00 ! [A2: int,A: set_int,B4: set_int] :
% 4.69/5.00 ( ( member_int @ A2 @ A )
% 4.69/5.00 => ( ~ ( member_int @ A2 @ B4 )
% 4.69/5.00 => ( ( finite_card_int @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ B4 ) ) )
% 4.69/5.00 = ( minus_minus_nat @ ( finite_card_int @ ( minus_minus_set_int @ A @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff_insert
% 4.69/5.00 thf(fact_4711_card__Diff__insert,axiom,
% 4.69/5.00 ! [A2: $o,A: set_o,B4: set_o] :
% 4.69/5.00 ( ( member_o @ A2 @ A )
% 4.69/5.00 => ( ~ ( member_o @ A2 @ B4 )
% 4.69/5.00 => ( ( finite_card_o @ ( minus_minus_set_o @ A @ ( insert_o @ A2 @ B4 ) ) )
% 4.69/5.00 = ( minus_minus_nat @ ( finite_card_o @ ( minus_minus_set_o @ A @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff_insert
% 4.69/5.00 thf(fact_4712_card__Diff__insert,axiom,
% 4.69/5.00 ! [A2: product_unit,A: set_Product_unit,B4: set_Product_unit] :
% 4.69/5.00 ( ( member_Product_unit @ A2 @ A )
% 4.69/5.00 => ( ~ ( member_Product_unit @ A2 @ B4 )
% 4.69/5.00 => ( ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ A2 @ B4 ) ) )
% 4.69/5.00 = ( minus_minus_nat @ ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff_insert
% 4.69/5.00 thf(fact_4713_card__Diff__insert,axiom,
% 4.69/5.00 ! [A2: nat,A: set_nat,B4: set_nat] :
% 4.69/5.00 ( ( member_nat @ A2 @ A )
% 4.69/5.00 => ( ~ ( member_nat @ A2 @ B4 )
% 4.69/5.00 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ B4 ) ) )
% 4.69/5.00 = ( minus_minus_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff_insert
% 4.69/5.00 thf(fact_4714_img__fst,axiom,
% 4.69/5.00 ! [A2: heap_e7401611519738050253t_unit,B: set_nat,S: set_Pr3948176798113811640et_nat] :
% 4.69/5.00 ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ A2 @ B ) @ S )
% 4.69/5.00 => ( member242389114213480694t_unit @ A2 @ ( image_6824039242672219652t_unit @ produc1824681642469235216et_nat @ S ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % img_fst
% 4.69/5.00 thf(fact_4715_img__fst,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,S: set_Pr1261947904930325089at_nat] :
% 4.69/5.00 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A2 @ B ) @ S )
% 4.69/5.00 => ( member_nat @ A2 @ ( image_2486076414777270412at_nat @ product_fst_nat_nat @ S ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % img_fst
% 4.69/5.00 thf(fact_4716_img__fst,axiom,
% 4.69/5.00 ! [A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,S: set_Pr3286484037609594932et_nat] :
% 4.69/5.00 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A2 @ B ) @ S )
% 4.69/5.00 => ( member6576561426505652726_nat_o @ A2 @ ( image_6802380912191114376_nat_o @ produc995936583742144908et_nat @ S ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % img_fst
% 4.69/5.00 thf(fact_4717_img__fst,axiom,
% 4.69/5.00 ! [A2: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,S: set_Pr8536935166611901872et_nat] :
% 4.69/5.00 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A2 @ B ) @ S )
% 4.69/5.00 => ( member6576561426505652726_nat_o @ A2 @ ( image_2517677226577294348_nat_o @ produc180342877477747464et_nat @ S ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % img_fst
% 4.69/5.00 thf(fact_4718_img__fst,axiom,
% 4.69/5.00 ! [A2: int,B: int,S: set_Pr958786334691620121nt_int] :
% 4.69/5.00 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A2 @ B ) @ S )
% 4.69/5.00 => ( member_int @ A2 @ ( image_5042161079198086560nt_int @ product_fst_int_int @ S ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % img_fst
% 4.69/5.00 thf(fact_4719_fst__swap,axiom,
% 4.69/5.00 ! [X: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( produc6012101397789842562t_unit @ ( produc6300697153377358172et_nat @ X ) )
% 4.69/5.00 = ( produc8586169260539613262et_nat @ X ) ) ).
% 4.69/5.00
% 4.69/5.00 % fst_swap
% 4.69/5.00 thf(fact_4720_fst__swap,axiom,
% 4.69/5.00 ! [X: product_prod_int_int] :
% 4.69/5.00 ( ( product_fst_int_int @ ( product_swap_int_int @ X ) )
% 4.69/5.00 = ( product_snd_int_int @ X ) ) ).
% 4.69/5.00
% 4.69/5.00 % fst_swap
% 4.69/5.00 thf(fact_4721_snd__swap,axiom,
% 4.69/5.00 ! [X: produc7348995623955488188t_unit] :
% 4.69/5.00 ( ( produc8586169260539613262et_nat @ ( produc1264744871843189710t_unit @ X ) )
% 4.69/5.00 = ( produc6012101397789842562t_unit @ X ) ) ).
% 4.69/5.00
% 4.69/5.00 % snd_swap
% 4.69/5.00 thf(fact_4722_snd__swap,axiom,
% 4.69/5.00 ! [X: product_prod_int_int] :
% 4.69/5.00 ( ( product_snd_int_int @ ( product_swap_int_int @ X ) )
% 4.69/5.00 = ( product_fst_int_int @ X ) ) ).
% 4.69/5.00
% 4.69/5.00 % snd_swap
% 4.69/5.00 thf(fact_4723_snd__comp__apfst,axiom,
% 4.69/5.00 ! [F: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit] :
% 4.69/5.00 ( ( comp_P2930521774885306735et_nat @ produc8586169260539613262et_nat @ ( produc4172003873565521026et_nat @ F ) )
% 4.69/5.00 = produc8586169260539613262et_nat ) ).
% 4.69/5.00
% 4.69/5.00 % snd_comp_apfst
% 4.69/5.00 thf(fact_4724_snd__comp__apfst,axiom,
% 4.69/5.00 ! [F: int > int] :
% 4.69/5.00 ( ( comp_P5356232565778667509nt_int @ product_snd_int_int @ ( produc2355237562570658114nt_int @ F ) )
% 4.69/5.00 = product_snd_int_int ) ).
% 4.69/5.00
% 4.69/5.00 % snd_comp_apfst
% 4.69/5.00 thf(fact_4725_fst__comp__apsnd,axiom,
% 4.69/5.00 ! [F: code_integer > code_integer] :
% 4.69/5.00 ( ( comp_P3428181540658402820nteger @ produc8508995932063986495nteger @ ( produc6499014454317279255nteger @ F ) )
% 4.69/5.00 = produc8508995932063986495nteger ) ).
% 4.69/5.00
% 4.69/5.00 % fst_comp_apsnd
% 4.69/5.00 thf(fact_4726_fst__comp__apsnd,axiom,
% 4.69/5.00 ! [F: int > int] :
% 4.69/5.00 ( ( comp_P5356232565778667509nt_int @ product_fst_int_int @ ( produc4463282112584876420nt_int @ F ) )
% 4.69/5.00 = product_fst_int_int ) ).
% 4.69/5.00
% 4.69/5.00 % fst_comp_apsnd
% 4.69/5.00 thf(fact_4727_range__fst,axiom,
% 4.69/5.00 ( ( image_5042161079198086560nt_int @ product_fst_int_int @ top_to4366644338036079209nt_int )
% 4.69/5.00 = top_top_set_int ) ).
% 4.69/5.00
% 4.69/5.00 % range_fst
% 4.69/5.00 thf(fact_4728_fst__comp__map__prod,axiom,
% 4.69/5.00 ! [F: int > int,G: int > int] :
% 4.69/5.00 ( ( comp_P5356232565778667509nt_int @ product_fst_int_int @ ( produc6036585564866528938nt_int @ F @ G ) )
% 4.69/5.00 = ( comp_i4330622015127193916nt_int @ F @ product_fst_int_int ) ) ).
% 4.69/5.00
% 4.69/5.00 % fst_comp_map_prod
% 4.69/5.00 thf(fact_4729_fst__comp__apfst,axiom,
% 4.69/5.00 ! [F: int > int] :
% 4.69/5.00 ( ( comp_P5356232565778667509nt_int @ product_fst_int_int @ ( produc2355237562570658114nt_int @ F ) )
% 4.69/5.00 = ( comp_i4330622015127193916nt_int @ F @ product_fst_int_int ) ) ).
% 4.69/5.00
% 4.69/5.00 % fst_comp_apfst
% 4.69/5.00 thf(fact_4730_snd__comp__apsnd,axiom,
% 4.69/5.00 ! [F: code_integer > code_integer] :
% 4.69/5.00 ( ( comp_P3428181540658402820nteger @ produc6174133586879617921nteger @ ( produc6499014454317279255nteger @ F ) )
% 4.69/5.00 = ( comp_C1043215000170864188nteger @ F @ produc6174133586879617921nteger ) ) ).
% 4.69/5.00
% 4.69/5.00 % snd_comp_apsnd
% 4.69/5.00 thf(fact_4731_snd__comp__apsnd,axiom,
% 4.69/5.00 ! [F: set_nat > set_nat] :
% 4.69/5.00 ( ( comp_P2930521774885306735et_nat @ produc8586169260539613262et_nat @ ( produc3286488329990770625t_unit @ F ) )
% 4.69/5.00 = ( comp_s5696514601250091763et_nat @ F @ produc8586169260539613262et_nat ) ) ).
% 4.69/5.00
% 4.69/5.00 % snd_comp_apsnd
% 4.69/5.00 thf(fact_4732_snd__comp__apsnd,axiom,
% 4.69/5.00 ! [F: int > int] :
% 4.69/5.00 ( ( comp_P5356232565778667509nt_int @ product_snd_int_int @ ( produc4463282112584876420nt_int @ F ) )
% 4.69/5.00 = ( comp_i4330622015127193916nt_int @ F @ product_snd_int_int ) ) ).
% 4.69/5.00
% 4.69/5.00 % snd_comp_apsnd
% 4.69/5.00 thf(fact_4733_apfst__apsnd,axiom,
% 4.69/5.00 ! [F: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit,G: set_nat > set_nat,X: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( produc4172003873565521026et_nat @ F @ ( produc3286488329990770625t_unit @ G @ X ) )
% 4.69/5.00 = ( produc7507926704131184380et_nat @ ( F @ ( produc1824681642469235216et_nat @ X ) ) @ ( G @ ( produc8586169260539613262et_nat @ X ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apfst_apsnd
% 4.69/5.00 thf(fact_4734_apfst__apsnd,axiom,
% 4.69/5.00 ! [F: heap_e7401611519738050253t_unit > nat,G: set_nat > nat,X: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( produc8233931525780029747at_nat @ F @ ( produc8442695800884449271t_unit @ G @ X ) )
% 4.69/5.00 = ( product_Pair_nat_nat @ ( F @ ( produc1824681642469235216et_nat @ X ) ) @ ( G @ ( produc8586169260539613262et_nat @ X ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apfst_apsnd
% 4.69/5.00 thf(fact_4735_apfst__apsnd,axiom,
% 4.69/5.00 ! [F: heap_e7401611519738050253t_unit > int,G: set_nat > int,X: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( produc7422730317258219nt_int @ F @ ( produc7345612820240450715t_unit @ G @ X ) )
% 4.69/5.00 = ( product_Pair_int_int @ ( F @ ( produc1824681642469235216et_nat @ X ) ) @ ( G @ ( produc8586169260539613262et_nat @ X ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apfst_apsnd
% 4.69/5.00 thf(fact_4736_apfst__apsnd,axiom,
% 4.69/5.00 ! [F: heap_e7401611519738050253t_unit > produc3658429121746597890et_nat > $o,G: set_nat > produc3658429121746597890et_nat,X: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( produc6095824665904122878et_nat @ F @ ( produc7441988914112407621t_unit @ G @ X ) )
% 4.69/5.00 = ( produc5001842942810119800et_nat @ ( F @ ( produc1824681642469235216et_nat @ X ) ) @ ( G @ ( produc8586169260539613262et_nat @ X ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apfst_apsnd
% 4.69/5.00 thf(fact_4737_apfst__apsnd,axiom,
% 4.69/5.00 ! [F: heap_e7401611519738050253t_unit > produc3658429121746597890et_nat > $o,G: set_nat > produc3925858234332021118et_nat,X: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( produc4273547285574235514et_nat @ F @ ( produc7176435795764513225t_unit @ G @ X ) )
% 4.69/5.00 = ( produc2245416461498447860et_nat @ ( F @ ( produc1824681642469235216et_nat @ X ) ) @ ( G @ ( produc8586169260539613262et_nat @ X ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apfst_apsnd
% 4.69/5.00 thf(fact_4738_apfst__apsnd,axiom,
% 4.69/5.00 ! [F: int > heap_e7401611519738050253t_unit,G: int > set_nat,X: product_prod_int_int] :
% 4.69/5.00 ( ( produc7086134074927288299et_nat @ F @ ( produc1253519502038700766at_int @ G @ X ) )
% 4.69/5.00 = ( produc7507926704131184380et_nat @ ( F @ ( product_fst_int_int @ X ) ) @ ( G @ ( product_snd_int_int @ X ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apfst_apsnd
% 4.69/5.00 thf(fact_4739_apfst__apsnd,axiom,
% 4.69/5.00 ! [F: int > nat,G: int > nat,X: product_prod_int_int] :
% 4.69/5.00 ( ( produc1358374321178653834at_nat @ F @ ( produc3463928400683821864at_int @ G @ X ) )
% 4.69/5.00 = ( product_Pair_nat_nat @ ( F @ ( product_fst_int_int @ X ) ) @ ( G @ ( product_snd_int_int @ X ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apfst_apsnd
% 4.69/5.00 thf(fact_4740_apfst__apsnd,axiom,
% 4.69/5.00 ! [F: int > int,G: int > int,X: product_prod_int_int] :
% 4.69/5.00 ( ( produc2355237562570658114nt_int @ F @ ( produc4463282112584876420nt_int @ G @ X ) )
% 4.69/5.00 = ( product_Pair_int_int @ ( F @ ( product_fst_int_int @ X ) ) @ ( G @ ( product_snd_int_int @ X ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apfst_apsnd
% 4.69/5.00 thf(fact_4741_apfst__apsnd,axiom,
% 4.69/5.00 ! [F: int > produc3658429121746597890et_nat > $o,G: int > produc3658429121746597890et_nat,X: product_prod_int_int] :
% 4.69/5.00 ( ( produc5259063908904861543et_nat @ F @ ( produc9121118195053341018at_int @ G @ X ) )
% 4.69/5.00 = ( produc5001842942810119800et_nat @ ( F @ ( product_fst_int_int @ X ) ) @ ( G @ ( product_snd_int_int @ X ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apfst_apsnd
% 4.69/5.00 thf(fact_4742_apfst__apsnd,axiom,
% 4.69/5.00 ! [F: int > produc3658429121746597890et_nat > $o,G: int > produc3925858234332021118et_nat,X: product_prod_int_int] :
% 4.69/5.00 ( ( produc3602029435013415139et_nat @ F @ ( produc2878475440847162070at_int @ G @ X ) )
% 4.69/5.00 = ( produc2245416461498447860et_nat @ ( F @ ( product_fst_int_int @ X ) ) @ ( G @ ( product_snd_int_int @ X ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apfst_apsnd
% 4.69/5.00 thf(fact_4743_apsnd__apfst,axiom,
% 4.69/5.00 ! [F: set_nat > set_nat,G: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit,X: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( produc3286488329990770625t_unit @ F @ ( produc4172003873565521026et_nat @ G @ X ) )
% 4.69/5.00 = ( produc7507926704131184380et_nat @ ( G @ ( produc1824681642469235216et_nat @ X ) ) @ ( F @ ( produc8586169260539613262et_nat @ X ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apsnd_apfst
% 4.69/5.00 thf(fact_4744_apsnd__apfst,axiom,
% 4.69/5.00 ! [F: set_nat > nat,G: heap_e7401611519738050253t_unit > nat,X: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( produc1747169720485888550at_nat @ F @ ( produc2974404638222180585et_nat @ G @ X ) )
% 4.69/5.00 = ( product_Pair_nat_nat @ ( G @ ( produc1824681642469235216et_nat @ X ) ) @ ( F @ ( produc8586169260539613262et_nat @ X ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apsnd_apfst
% 4.69/5.00 thf(fact_4745_apsnd__apfst,axiom,
% 4.69/5.00 ! [F: set_nat > int,G: heap_e7401611519738050253t_unit > int,X: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( produc2744032961877892830nt_int @ F @ ( produc3346058198459025221et_nat @ G @ X ) )
% 4.69/5.00 = ( product_Pair_int_int @ ( G @ ( produc1824681642469235216et_nat @ X ) ) @ ( F @ ( produc8586169260539613262et_nat @ X ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apsnd_apfst
% 4.69/5.00 thf(fact_4746_apsnd__apfst,axiom,
% 4.69/5.00 ! [F: set_nat > produc3658429121746597890et_nat,G: heap_e7401611519738050253t_unit > produc3658429121746597890et_nat > $o,X: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( produc1718959742329256773_nat_o @ F @ ( produc962520821680634754et_nat @ G @ X ) )
% 4.69/5.00 = ( produc5001842942810119800et_nat @ ( G @ ( produc1824681642469235216et_nat @ X ) ) @ ( F @ ( produc8586169260539613262et_nat @ X ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apsnd_apfst
% 4.69/5.00 thf(fact_4747_apsnd__apfst,axiom,
% 4.69/5.00 ! [F: set_nat > produc3925858234332021118et_nat,G: heap_e7401611519738050253t_unit > produc3658429121746597890et_nat > $o,X: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( produc3009152965630989513_nat_o @ F @ ( produc962520821680634754et_nat @ G @ X ) )
% 4.69/5.00 = ( produc2245416461498447860et_nat @ ( G @ ( produc1824681642469235216et_nat @ X ) ) @ ( F @ ( produc8586169260539613262et_nat @ X ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apsnd_apfst
% 4.69/5.00 thf(fact_4748_apsnd__apfst,axiom,
% 4.69/5.00 ! [F: int > set_nat,G: int > heap_e7401611519738050253t_unit,X: product_prod_int_int] :
% 4.69/5.00 ( ( produc2122153897363312795t_unit @ F @ ( produc1158806734383251089it_int @ G @ X ) )
% 4.69/5.00 = ( produc7507926704131184380et_nat @ ( G @ ( product_fst_int_int @ X ) ) @ ( F @ ( product_snd_int_int @ X ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apsnd_apfst
% 4.69/5.00 thf(fact_4749_apsnd__apfst,axiom,
% 4.69/5.00 ! [F: int > nat,G: int > nat,X: product_prod_int_int] :
% 4.69/5.00 ( ( produc3466418871192872140at_nat @ F @ ( produc1355883850669603558at_int @ G @ X ) )
% 4.69/5.00 = ( product_Pair_nat_nat @ ( G @ ( product_fst_int_int @ X ) ) @ ( F @ ( product_snd_int_int @ X ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apsnd_apfst
% 4.69/5.00 thf(fact_4750_apsnd__apfst,axiom,
% 4.69/5.00 ! [F: int > int,G: int > int,X: product_prod_int_int] :
% 4.69/5.00 ( ( produc4463282112584876420nt_int @ F @ ( produc2355237562570658114nt_int @ G @ X ) )
% 4.69/5.00 = ( product_Pair_int_int @ ( G @ ( product_fst_int_int @ X ) ) @ ( F @ ( product_snd_int_int @ X ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apsnd_apfst
% 4.69/5.00 thf(fact_4751_apsnd__apfst,axiom,
% 4.69/5.00 ! [F: int > produc3658429121746597890et_nat,G: int > produc3658429121746597890et_nat > $o,X: product_prod_int_int] :
% 4.69/5.00 ( ( produc3447581998352395295_nat_o @ F @ ( produc1933289243015553937_o_int @ G @ X ) )
% 4.69/5.00 = ( produc5001842942810119800et_nat @ ( G @ ( product_fst_int_int @ X ) ) @ ( F @ ( product_snd_int_int @ X ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apsnd_apfst
% 4.69/5.00 thf(fact_4752_apsnd__apfst,axiom,
% 4.69/5.00 ! [F: int > produc3925858234332021118et_nat,G: int > produc3658429121746597890et_nat > $o,X: product_prod_int_int] :
% 4.69/5.00 ( ( produc1783401272518604195_nat_o @ F @ ( produc1933289243015553937_o_int @ G @ X ) )
% 4.69/5.00 = ( produc2245416461498447860et_nat @ ( G @ ( product_fst_int_int @ X ) ) @ ( F @ ( product_snd_int_int @ X ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apsnd_apfst
% 4.69/5.00 thf(fact_4753_apsnd__apfst__commute,axiom,
% 4.69/5.00 ! [F: code_integer > code_integer,G: code_integer > code_integer,P3: produc8923325533196201883nteger] :
% 4.69/5.00 ( ( produc6499014454317279255nteger @ F @ ( produc3195571438000033749nteger @ G @ P3 ) )
% 4.69/5.00 = ( produc3195571438000033749nteger @ G @ ( produc6499014454317279255nteger @ F @ P3 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apsnd_apfst_commute
% 4.69/5.00 thf(fact_4754_fstI,axiom,
% 4.69/5.00 ! [X: produc3658429121746597890et_nat,Y: heap_e7401611519738050253t_unit,Z: set_nat] :
% 4.69/5.00 ( ( X
% 4.69/5.00 = ( produc7507926704131184380et_nat @ Y @ Z ) )
% 4.69/5.00 => ( ( produc1824681642469235216et_nat @ X )
% 4.69/5.00 = Y ) ) ).
% 4.69/5.00
% 4.69/5.00 % fstI
% 4.69/5.00 thf(fact_4755_fstI,axiom,
% 4.69/5.00 ! [X: product_prod_nat_nat,Y: nat,Z: nat] :
% 4.69/5.00 ( ( X
% 4.69/5.00 = ( product_Pair_nat_nat @ Y @ Z ) )
% 4.69/5.00 => ( ( product_fst_nat_nat @ X )
% 4.69/5.00 = Y ) ) ).
% 4.69/5.00
% 4.69/5.00 % fstI
% 4.69/5.00 thf(fact_4756_fstI,axiom,
% 4.69/5.00 ! [X: produc3925858234332021118et_nat,Y: produc3658429121746597890et_nat > $o,Z: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( X
% 4.69/5.00 = ( produc5001842942810119800et_nat @ Y @ Z ) )
% 4.69/5.00 => ( ( produc995936583742144908et_nat @ X )
% 4.69/5.00 = Y ) ) ).
% 4.69/5.00
% 4.69/5.00 % fstI
% 4.69/5.00 thf(fact_4757_fstI,axiom,
% 4.69/5.00 ! [X: produc2732055786443039994et_nat,Y: produc3658429121746597890et_nat > $o,Z: produc3925858234332021118et_nat] :
% 4.69/5.00 ( ( X
% 4.69/5.00 = ( produc2245416461498447860et_nat @ Y @ Z ) )
% 4.69/5.00 => ( ( produc180342877477747464et_nat @ X )
% 4.69/5.00 = Y ) ) ).
% 4.69/5.00
% 4.69/5.00 % fstI
% 4.69/5.00 thf(fact_4758_fstI,axiom,
% 4.69/5.00 ! [X: product_prod_int_int,Y: int,Z: int] :
% 4.69/5.00 ( ( X
% 4.69/5.00 = ( product_Pair_int_int @ Y @ Z ) )
% 4.69/5.00 => ( ( product_fst_int_int @ X )
% 4.69/5.00 = Y ) ) ).
% 4.69/5.00
% 4.69/5.00 % fstI
% 4.69/5.00 thf(fact_4759_fst__eqD,axiom,
% 4.69/5.00 ! [X: heap_e7401611519738050253t_unit,Y: set_nat,A2: heap_e7401611519738050253t_unit] :
% 4.69/5.00 ( ( ( produc1824681642469235216et_nat @ ( produc7507926704131184380et_nat @ X @ Y ) )
% 4.69/5.00 = A2 )
% 4.69/5.00 => ( X = A2 ) ) ).
% 4.69/5.00
% 4.69/5.00 % fst_eqD
% 4.69/5.00 thf(fact_4760_fst__eqD,axiom,
% 4.69/5.00 ! [X: nat,Y: nat,A2: nat] :
% 4.69/5.00 ( ( ( product_fst_nat_nat @ ( product_Pair_nat_nat @ X @ Y ) )
% 4.69/5.00 = A2 )
% 4.69/5.00 => ( X = A2 ) ) ).
% 4.69/5.00
% 4.69/5.00 % fst_eqD
% 4.69/5.00 thf(fact_4761_fst__eqD,axiom,
% 4.69/5.00 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat,A2: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ( ( produc995936583742144908et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 4.69/5.00 = A2 )
% 4.69/5.00 => ( X = A2 ) ) ).
% 4.69/5.00
% 4.69/5.00 % fst_eqD
% 4.69/5.00 thf(fact_4762_fst__eqD,axiom,
% 4.69/5.00 ! [X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat,A2: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ( ( produc180342877477747464et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 4.69/5.00 = A2 )
% 4.69/5.00 => ( X = A2 ) ) ).
% 4.69/5.00
% 4.69/5.00 % fst_eqD
% 4.69/5.00 thf(fact_4763_fst__eqD,axiom,
% 4.69/5.00 ! [X: int,Y: int,A2: int] :
% 4.69/5.00 ( ( ( product_fst_int_int @ ( product_Pair_int_int @ X @ Y ) )
% 4.69/5.00 = A2 )
% 4.69/5.00 => ( X = A2 ) ) ).
% 4.69/5.00
% 4.69/5.00 % fst_eqD
% 4.69/5.00 thf(fact_4764_fst__conv,axiom,
% 4.69/5.00 ! [X1: heap_e7401611519738050253t_unit,X22: set_nat] :
% 4.69/5.00 ( ( produc1824681642469235216et_nat @ ( produc7507926704131184380et_nat @ X1 @ X22 ) )
% 4.69/5.00 = X1 ) ).
% 4.69/5.00
% 4.69/5.00 % fst_conv
% 4.69/5.00 thf(fact_4765_fst__conv,axiom,
% 4.69/5.00 ! [X1: nat,X22: nat] :
% 4.69/5.00 ( ( product_fst_nat_nat @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 4.69/5.00 = X1 ) ).
% 4.69/5.00
% 4.69/5.00 % fst_conv
% 4.69/5.00 thf(fact_4766_fst__conv,axiom,
% 4.69/5.00 ! [X1: produc3658429121746597890et_nat > $o,X22: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( produc995936583742144908et_nat @ ( produc5001842942810119800et_nat @ X1 @ X22 ) )
% 4.69/5.00 = X1 ) ).
% 4.69/5.00
% 4.69/5.00 % fst_conv
% 4.69/5.00 thf(fact_4767_fst__conv,axiom,
% 4.69/5.00 ! [X1: produc3658429121746597890et_nat > $o,X22: produc3925858234332021118et_nat] :
% 4.69/5.00 ( ( produc180342877477747464et_nat @ ( produc2245416461498447860et_nat @ X1 @ X22 ) )
% 4.69/5.00 = X1 ) ).
% 4.69/5.00
% 4.69/5.00 % fst_conv
% 4.69/5.00 thf(fact_4768_fst__conv,axiom,
% 4.69/5.00 ! [X1: int,X22: int] :
% 4.69/5.00 ( ( product_fst_int_int @ ( product_Pair_int_int @ X1 @ X22 ) )
% 4.69/5.00 = X1 ) ).
% 4.69/5.00
% 4.69/5.00 % fst_conv
% 4.69/5.00 thf(fact_4769_eq__fst__iff,axiom,
% 4.69/5.00 ! [A2: heap_e7401611519738050253t_unit,P3: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( A2
% 4.69/5.00 = ( produc1824681642469235216et_nat @ P3 ) )
% 4.69/5.00 = ( ? [B6: set_nat] :
% 4.69/5.00 ( P3
% 4.69/5.00 = ( produc7507926704131184380et_nat @ A2 @ B6 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % eq_fst_iff
% 4.69/5.00 thf(fact_4770_eq__fst__iff,axiom,
% 4.69/5.00 ! [A2: nat,P3: product_prod_nat_nat] :
% 4.69/5.00 ( ( A2
% 4.69/5.00 = ( product_fst_nat_nat @ P3 ) )
% 4.69/5.00 = ( ? [B6: nat] :
% 4.69/5.00 ( P3
% 4.69/5.00 = ( product_Pair_nat_nat @ A2 @ B6 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % eq_fst_iff
% 4.69/5.00 thf(fact_4771_eq__fst__iff,axiom,
% 4.69/5.00 ! [A2: produc3658429121746597890et_nat > $o,P3: produc3925858234332021118et_nat] :
% 4.69/5.00 ( ( A2
% 4.69/5.00 = ( produc995936583742144908et_nat @ P3 ) )
% 4.69/5.00 = ( ? [B6: produc3658429121746597890et_nat] :
% 4.69/5.00 ( P3
% 4.69/5.00 = ( produc5001842942810119800et_nat @ A2 @ B6 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % eq_fst_iff
% 4.69/5.00 thf(fact_4772_eq__fst__iff,axiom,
% 4.69/5.00 ! [A2: produc3658429121746597890et_nat > $o,P3: produc2732055786443039994et_nat] :
% 4.69/5.00 ( ( A2
% 4.69/5.00 = ( produc180342877477747464et_nat @ P3 ) )
% 4.69/5.00 = ( ? [B6: produc3925858234332021118et_nat] :
% 4.69/5.00 ( P3
% 4.69/5.00 = ( produc2245416461498447860et_nat @ A2 @ B6 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % eq_fst_iff
% 4.69/5.00 thf(fact_4773_eq__fst__iff,axiom,
% 4.69/5.00 ! [A2: int,P3: product_prod_int_int] :
% 4.69/5.00 ( ( A2
% 4.69/5.00 = ( product_fst_int_int @ P3 ) )
% 4.69/5.00 = ( ? [B6: int] :
% 4.69/5.00 ( P3
% 4.69/5.00 = ( product_Pair_int_int @ A2 @ B6 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % eq_fst_iff
% 4.69/5.00 thf(fact_4774_fstE,axiom,
% 4.69/5.00 ! [X: produc3658429121746597890et_nat,A2: heap_e7401611519738050253t_unit,B: set_nat,P: heap_e7401611519738050253t_unit > $o] :
% 4.69/5.00 ( ( X
% 4.69/5.00 = ( produc7507926704131184380et_nat @ A2 @ B ) )
% 4.69/5.00 => ( ( P @ ( produc1824681642469235216et_nat @ X ) )
% 4.69/5.00 => ( P @ A2 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % fstE
% 4.69/5.00 thf(fact_4775_fstE,axiom,
% 4.69/5.00 ! [X: product_prod_nat_nat,A2: nat,B: nat,P: nat > $o] :
% 4.69/5.00 ( ( X
% 4.69/5.00 = ( product_Pair_nat_nat @ A2 @ B ) )
% 4.69/5.00 => ( ( P @ ( product_fst_nat_nat @ X ) )
% 4.69/5.00 => ( P @ A2 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % fstE
% 4.69/5.00 thf(fact_4776_fstE,axiom,
% 4.69/5.00 ! [X: produc3925858234332021118et_nat,A2: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 4.69/5.00 ( ( X
% 4.69/5.00 = ( produc5001842942810119800et_nat @ A2 @ B ) )
% 4.69/5.00 => ( ( P @ ( produc995936583742144908et_nat @ X ) )
% 4.69/5.00 => ( P @ A2 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % fstE
% 4.69/5.00 thf(fact_4777_fstE,axiom,
% 4.69/5.00 ! [X: produc2732055786443039994et_nat,A2: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 4.69/5.00 ( ( X
% 4.69/5.00 = ( produc2245416461498447860et_nat @ A2 @ B ) )
% 4.69/5.00 => ( ( P @ ( produc180342877477747464et_nat @ X ) )
% 4.69/5.00 => ( P @ A2 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % fstE
% 4.69/5.00 thf(fact_4778_fstE,axiom,
% 4.69/5.00 ! [X: product_prod_int_int,A2: int,B: int,P: int > $o] :
% 4.69/5.00 ( ( X
% 4.69/5.00 = ( product_Pair_int_int @ A2 @ B ) )
% 4.69/5.00 => ( ( P @ ( product_fst_int_int @ X ) )
% 4.69/5.00 => ( P @ A2 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % fstE
% 4.69/5.00 thf(fact_4779_prod__eq__iff,axiom,
% 4.69/5.00 ( ( ^ [Y4: produc3658429121746597890et_nat,Z4: produc3658429121746597890et_nat] : ( Y4 = Z4 ) )
% 4.69/5.00 = ( ^ [S7: produc3658429121746597890et_nat,T: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( ( produc1824681642469235216et_nat @ S7 )
% 4.69/5.00 = ( produc1824681642469235216et_nat @ T ) )
% 4.69/5.00 & ( ( produc8586169260539613262et_nat @ S7 )
% 4.69/5.00 = ( produc8586169260539613262et_nat @ T ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod_eq_iff
% 4.69/5.00 thf(fact_4780_prod__eq__iff,axiom,
% 4.69/5.00 ( ( ^ [Y4: product_prod_int_int,Z4: product_prod_int_int] : ( Y4 = Z4 ) )
% 4.69/5.00 = ( ^ [S7: product_prod_int_int,T: product_prod_int_int] :
% 4.69/5.00 ( ( ( product_fst_int_int @ S7 )
% 4.69/5.00 = ( product_fst_int_int @ T ) )
% 4.69/5.00 & ( ( product_snd_int_int @ S7 )
% 4.69/5.00 = ( product_snd_int_int @ T ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod_eq_iff
% 4.69/5.00 thf(fact_4781_prod__eqI,axiom,
% 4.69/5.00 ! [P3: produc3658429121746597890et_nat,Q4: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( ( produc1824681642469235216et_nat @ P3 )
% 4.69/5.00 = ( produc1824681642469235216et_nat @ Q4 ) )
% 4.69/5.00 => ( ( ( produc8586169260539613262et_nat @ P3 )
% 4.69/5.00 = ( produc8586169260539613262et_nat @ Q4 ) )
% 4.69/5.00 => ( P3 = Q4 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod_eqI
% 4.69/5.00 thf(fact_4782_prod__eqI,axiom,
% 4.69/5.00 ! [P3: product_prod_int_int,Q4: product_prod_int_int] :
% 4.69/5.00 ( ( ( product_fst_int_int @ P3 )
% 4.69/5.00 = ( product_fst_int_int @ Q4 ) )
% 4.69/5.00 => ( ( ( product_snd_int_int @ P3 )
% 4.69/5.00 = ( product_snd_int_int @ Q4 ) )
% 4.69/5.00 => ( P3 = Q4 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod_eqI
% 4.69/5.00 thf(fact_4783_prod_Oexpand,axiom,
% 4.69/5.00 ! [Prod: produc3658429121746597890et_nat,Prod2: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( ( ( produc1824681642469235216et_nat @ Prod )
% 4.69/5.00 = ( produc1824681642469235216et_nat @ Prod2 ) )
% 4.69/5.00 & ( ( produc8586169260539613262et_nat @ Prod )
% 4.69/5.00 = ( produc8586169260539613262et_nat @ Prod2 ) ) )
% 4.69/5.00 => ( Prod = Prod2 ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod.expand
% 4.69/5.00 thf(fact_4784_prod_Oexpand,axiom,
% 4.69/5.00 ! [Prod: product_prod_int_int,Prod2: product_prod_int_int] :
% 4.69/5.00 ( ( ( ( product_fst_int_int @ Prod )
% 4.69/5.00 = ( product_fst_int_int @ Prod2 ) )
% 4.69/5.00 & ( ( product_snd_int_int @ Prod )
% 4.69/5.00 = ( product_snd_int_int @ Prod2 ) ) )
% 4.69/5.00 => ( Prod = Prod2 ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod.expand
% 4.69/5.00 thf(fact_4785_All__prod__contract,axiom,
% 4.69/5.00 ! [P: heap_e7401611519738050253t_unit > set_nat > $o] :
% 4.69/5.00 ( ( ! [A6: heap_e7401611519738050253t_unit,X7: set_nat] : ( P @ A6 @ X7 ) )
% 4.69/5.00 = ( ! [Z2: produc3658429121746597890et_nat] : ( P @ ( produc1824681642469235216et_nat @ Z2 ) @ ( produc8586169260539613262et_nat @ Z2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % All_prod_contract
% 4.69/5.00 thf(fact_4786_All__prod__contract,axiom,
% 4.69/5.00 ! [P: int > int > $o] :
% 4.69/5.00 ( ( ! [A6: int,X7: int] : ( P @ A6 @ X7 ) )
% 4.69/5.00 = ( ! [Z2: product_prod_int_int] : ( P @ ( product_fst_int_int @ Z2 ) @ ( product_snd_int_int @ Z2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % All_prod_contract
% 4.69/5.00 thf(fact_4787_Ex__prod__contract,axiom,
% 4.69/5.00 ! [P: heap_e7401611519738050253t_unit > set_nat > $o] :
% 4.69/5.00 ( ( ? [A6: heap_e7401611519738050253t_unit,X7: set_nat] : ( P @ A6 @ X7 ) )
% 4.69/5.00 = ( ? [Z2: produc3658429121746597890et_nat] : ( P @ ( produc1824681642469235216et_nat @ Z2 ) @ ( produc8586169260539613262et_nat @ Z2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Ex_prod_contract
% 4.69/5.00 thf(fact_4788_Ex__prod__contract,axiom,
% 4.69/5.00 ! [P: int > int > $o] :
% 4.69/5.00 ( ( ? [A6: int,X7: int] : ( P @ A6 @ X7 ) )
% 4.69/5.00 = ( ? [Z2: product_prod_int_int] : ( P @ ( product_fst_int_int @ Z2 ) @ ( product_snd_int_int @ Z2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Ex_prod_contract
% 4.69/5.00 thf(fact_4789_apsnd__compose,axiom,
% 4.69/5.00 ! [F: code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger,G: code_integer > code_integer,X: produc8923325533196201883nteger] :
% 4.69/5.00 ( ( produc9020447175693601247nteger @ F @ ( produc6499014454317279255nteger @ G @ X ) )
% 4.69/5.00 = ( produc9020447175693601247nteger @ ( comp_C1593894019821074884nteger @ F @ G ) @ X ) ) ).
% 4.69/5.00
% 4.69/5.00 % apsnd_compose
% 4.69/5.00 thf(fact_4790_apsnd__compose,axiom,
% 4.69/5.00 ! [F: code_integer > code_integer,G: code_integer > code_integer,X: produc8923325533196201883nteger] :
% 4.69/5.00 ( ( produc6499014454317279255nteger @ F @ ( produc6499014454317279255nteger @ G @ X ) )
% 4.69/5.00 = ( produc6499014454317279255nteger @ ( comp_C7449957260575251196nteger @ F @ G ) @ X ) ) ).
% 4.69/5.00
% 4.69/5.00 % apsnd_compose
% 4.69/5.00 thf(fact_4791_refl__on__INTER,axiom,
% 4.69/5.00 ! [S: set_nat,A: nat > set_nat,R2: nat > set_Pr1261947904930325089at_nat] :
% 4.69/5.00 ( ! [X3: nat] :
% 4.69/5.00 ( ( member_nat @ X3 @ S )
% 4.69/5.00 => ( refl_on_nat @ ( A @ X3 ) @ ( R2 @ X3 ) ) )
% 4.69/5.00 => ( refl_on_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ A @ S ) ) @ ( comple1930127330929219688at_nat @ ( image_7178329752028323786at_nat @ R2 @ S ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % refl_on_INTER
% 4.69/5.00 thf(fact_4792_cInf__eq__non__empty,axiom,
% 4.69/5.00 ! [X4: set_o,A2: $o] :
% 4.69/5.00 ( ( X4 != bot_bot_set_o )
% 4.69/5.00 => ( ! [X3: $o] :
% 4.69/5.00 ( ( member_o @ X3 @ X4 )
% 4.69/5.00 => ( ord_less_eq_o @ A2 @ X3 ) )
% 4.69/5.00 => ( ! [Y2: $o] :
% 4.69/5.00 ( ! [X6: $o] :
% 4.69/5.00 ( ( member_o @ X6 @ X4 )
% 4.69/5.00 => ( ord_less_eq_o @ Y2 @ X6 ) )
% 4.69/5.00 => ( ord_less_eq_o @ Y2 @ A2 ) )
% 4.69/5.00 => ( ( complete_Inf_Inf_o @ X4 )
% 4.69/5.00 = A2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_eq_non_empty
% 4.69/5.00 thf(fact_4793_cInf__eq__non__empty,axiom,
% 4.69/5.00 ! [X4: set_Pr4532377907799695533_nat_o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ( X4 != bot_bo7824918357723582233_nat_o )
% 4.69/5.00 => ( ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ( member6576561426505652726_nat_o @ X3 @ X4 )
% 4.69/5.00 => ( ord_le729326519192465773_nat_o @ A2 @ X3 ) )
% 4.69/5.00 => ( ! [Y2: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ! [X6: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ( member6576561426505652726_nat_o @ X6 @ X4 )
% 4.69/5.00 => ( ord_le729326519192465773_nat_o @ Y2 @ X6 ) )
% 4.69/5.00 => ( ord_le729326519192465773_nat_o @ Y2 @ A2 ) )
% 4.69/5.00 => ( ( comple90455603224345172_nat_o @ X4 )
% 4.69/5.00 = A2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_eq_non_empty
% 4.69/5.00 thf(fact_4794_cInf__eq__non__empty,axiom,
% 4.69/5.00 ! [X4: set_filter_nat,A2: filter_nat] :
% 4.69/5.00 ( ( X4 != bot_bo498966703094740906er_nat )
% 4.69/5.00 => ( ! [X3: filter_nat] :
% 4.69/5.00 ( ( member_filter_nat @ X3 @ X4 )
% 4.69/5.00 => ( ord_le2510731241096832064er_nat @ A2 @ X3 ) )
% 4.69/5.00 => ( ! [Y2: filter_nat] :
% 4.69/5.00 ( ! [X6: filter_nat] :
% 4.69/5.00 ( ( member_filter_nat @ X6 @ X4 )
% 4.69/5.00 => ( ord_le2510731241096832064er_nat @ Y2 @ X6 ) )
% 4.69/5.00 => ( ord_le2510731241096832064er_nat @ Y2 @ A2 ) )
% 4.69/5.00 => ( ( comple6612786467464916249er_nat @ X4 )
% 4.69/5.00 = A2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_eq_non_empty
% 4.69/5.00 thf(fact_4795_cInf__eq__non__empty,axiom,
% 4.69/5.00 ! [X4: set_int,A2: int] :
% 4.69/5.00 ( ( X4 != bot_bot_set_int )
% 4.69/5.00 => ( ! [X3: int] :
% 4.69/5.00 ( ( member_int @ X3 @ X4 )
% 4.69/5.00 => ( ord_less_eq_int @ A2 @ X3 ) )
% 4.69/5.00 => ( ! [Y2: int] :
% 4.69/5.00 ( ! [X6: int] :
% 4.69/5.00 ( ( member_int @ X6 @ X4 )
% 4.69/5.00 => ( ord_less_eq_int @ Y2 @ X6 ) )
% 4.69/5.00 => ( ord_less_eq_int @ Y2 @ A2 ) )
% 4.69/5.00 => ( ( complete_Inf_Inf_int @ X4 )
% 4.69/5.00 = A2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_eq_non_empty
% 4.69/5.00 thf(fact_4796_cInf__eq__non__empty,axiom,
% 4.69/5.00 ! [X4: set_nat,A2: nat] :
% 4.69/5.00 ( ( X4 != bot_bot_set_nat )
% 4.69/5.00 => ( ! [X3: nat] :
% 4.69/5.00 ( ( member_nat @ X3 @ X4 )
% 4.69/5.00 => ( ord_less_eq_nat @ A2 @ X3 ) )
% 4.69/5.00 => ( ! [Y2: nat] :
% 4.69/5.00 ( ! [X6: nat] :
% 4.69/5.00 ( ( member_nat @ X6 @ X4 )
% 4.69/5.00 => ( ord_less_eq_nat @ Y2 @ X6 ) )
% 4.69/5.00 => ( ord_less_eq_nat @ Y2 @ A2 ) )
% 4.69/5.00 => ( ( complete_Inf_Inf_nat @ X4 )
% 4.69/5.00 = A2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_eq_non_empty
% 4.69/5.00 thf(fact_4797_cInf__eq__non__empty,axiom,
% 4.69/5.00 ! [X4: set_set_nat,A2: set_nat] :
% 4.69/5.00 ( ( X4 != bot_bot_set_set_nat )
% 4.69/5.00 => ( ! [X3: set_nat] :
% 4.69/5.00 ( ( member_set_nat @ X3 @ X4 )
% 4.69/5.00 => ( ord_less_eq_set_nat @ A2 @ X3 ) )
% 4.69/5.00 => ( ! [Y2: set_nat] :
% 4.69/5.00 ( ! [X6: set_nat] :
% 4.69/5.00 ( ( member_set_nat @ X6 @ X4 )
% 4.69/5.00 => ( ord_less_eq_set_nat @ Y2 @ X6 ) )
% 4.69/5.00 => ( ord_less_eq_set_nat @ Y2 @ A2 ) )
% 4.69/5.00 => ( ( comple7806235888213564991et_nat @ X4 )
% 4.69/5.00 = A2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_eq_non_empty
% 4.69/5.00 thf(fact_4798_cInf__eq__non__empty,axiom,
% 4.69/5.00 ! [X4: set_Product_unit,A2: product_unit] :
% 4.69/5.00 ( ( X4 != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ! [X3: product_unit] :
% 4.69/5.00 ( ( member_Product_unit @ X3 @ X4 )
% 4.69/5.00 => ( ord_le3221252021190050221t_unit @ A2 @ X3 ) )
% 4.69/5.00 => ( ! [Y2: product_unit] :
% 4.69/5.00 ( ! [X6: product_unit] :
% 4.69/5.00 ( ( member_Product_unit @ X6 @ X4 )
% 4.69/5.00 => ( ord_le3221252021190050221t_unit @ Y2 @ X6 ) )
% 4.69/5.00 => ( ord_le3221252021190050221t_unit @ Y2 @ A2 ) )
% 4.69/5.00 => ( ( comple2584293577114468500t_unit @ X4 )
% 4.69/5.00 = A2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_eq_non_empty
% 4.69/5.00 thf(fact_4799_cInf__greatest,axiom,
% 4.69/5.00 ! [X4: set_o,Z: $o] :
% 4.69/5.00 ( ( X4 != bot_bot_set_o )
% 4.69/5.00 => ( ! [X3: $o] :
% 4.69/5.00 ( ( member_o @ X3 @ X4 )
% 4.69/5.00 => ( ord_less_eq_o @ Z @ X3 ) )
% 4.69/5.00 => ( ord_less_eq_o @ Z @ ( complete_Inf_Inf_o @ X4 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_greatest
% 4.69/5.00 thf(fact_4800_cInf__greatest,axiom,
% 4.69/5.00 ! [X4: set_Pr4532377907799695533_nat_o,Z: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ( X4 != bot_bo7824918357723582233_nat_o )
% 4.69/5.00 => ( ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ( member6576561426505652726_nat_o @ X3 @ X4 )
% 4.69/5.00 => ( ord_le729326519192465773_nat_o @ Z @ X3 ) )
% 4.69/5.00 => ( ord_le729326519192465773_nat_o @ Z @ ( comple90455603224345172_nat_o @ X4 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_greatest
% 4.69/5.00 thf(fact_4801_cInf__greatest,axiom,
% 4.69/5.00 ! [X4: set_filter_nat,Z: filter_nat] :
% 4.69/5.00 ( ( X4 != bot_bo498966703094740906er_nat )
% 4.69/5.00 => ( ! [X3: filter_nat] :
% 4.69/5.00 ( ( member_filter_nat @ X3 @ X4 )
% 4.69/5.00 => ( ord_le2510731241096832064er_nat @ Z @ X3 ) )
% 4.69/5.00 => ( ord_le2510731241096832064er_nat @ Z @ ( comple6612786467464916249er_nat @ X4 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_greatest
% 4.69/5.00 thf(fact_4802_cInf__greatest,axiom,
% 4.69/5.00 ! [X4: set_int,Z: int] :
% 4.69/5.00 ( ( X4 != bot_bot_set_int )
% 4.69/5.00 => ( ! [X3: int] :
% 4.69/5.00 ( ( member_int @ X3 @ X4 )
% 4.69/5.00 => ( ord_less_eq_int @ Z @ X3 ) )
% 4.69/5.00 => ( ord_less_eq_int @ Z @ ( complete_Inf_Inf_int @ X4 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_greatest
% 4.69/5.00 thf(fact_4803_cInf__greatest,axiom,
% 4.69/5.00 ! [X4: set_nat,Z: nat] :
% 4.69/5.00 ( ( X4 != bot_bot_set_nat )
% 4.69/5.00 => ( ! [X3: nat] :
% 4.69/5.00 ( ( member_nat @ X3 @ X4 )
% 4.69/5.00 => ( ord_less_eq_nat @ Z @ X3 ) )
% 4.69/5.00 => ( ord_less_eq_nat @ Z @ ( complete_Inf_Inf_nat @ X4 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_greatest
% 4.69/5.00 thf(fact_4804_cInf__greatest,axiom,
% 4.69/5.00 ! [X4: set_set_nat,Z: set_nat] :
% 4.69/5.00 ( ( X4 != bot_bot_set_set_nat )
% 4.69/5.00 => ( ! [X3: set_nat] :
% 4.69/5.00 ( ( member_set_nat @ X3 @ X4 )
% 4.69/5.00 => ( ord_less_eq_set_nat @ Z @ X3 ) )
% 4.69/5.00 => ( ord_less_eq_set_nat @ Z @ ( comple7806235888213564991et_nat @ X4 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_greatest
% 4.69/5.00 thf(fact_4805_cInf__greatest,axiom,
% 4.69/5.00 ! [X4: set_Product_unit,Z: product_unit] :
% 4.69/5.00 ( ( X4 != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ! [X3: product_unit] :
% 4.69/5.00 ( ( member_Product_unit @ X3 @ X4 )
% 4.69/5.00 => ( ord_le3221252021190050221t_unit @ Z @ X3 ) )
% 4.69/5.00 => ( ord_le3221252021190050221t_unit @ Z @ ( comple2584293577114468500t_unit @ X4 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_greatest
% 4.69/5.00 thf(fact_4806_Inf__less__eq,axiom,
% 4.69/5.00 ! [A: set_o,U: $o] :
% 4.69/5.00 ( ! [V3: $o] :
% 4.69/5.00 ( ( member_o @ V3 @ A )
% 4.69/5.00 => ( ord_less_eq_o @ V3 @ U ) )
% 4.69/5.00 => ( ( A != bot_bot_set_o )
% 4.69/5.00 => ( ord_less_eq_o @ ( complete_Inf_Inf_o @ A ) @ U ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_less_eq
% 4.69/5.00 thf(fact_4807_Inf__less__eq,axiom,
% 4.69/5.00 ! [A: set_Pr4532377907799695533_nat_o,U: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ! [V3: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ( member6576561426505652726_nat_o @ V3 @ A )
% 4.69/5.00 => ( ord_le729326519192465773_nat_o @ V3 @ U ) )
% 4.69/5.00 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/5.00 => ( ord_le729326519192465773_nat_o @ ( comple90455603224345172_nat_o @ A ) @ U ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_less_eq
% 4.69/5.00 thf(fact_4808_Inf__less__eq,axiom,
% 4.69/5.00 ! [A: set_filter_nat,U: filter_nat] :
% 4.69/5.00 ( ! [V3: filter_nat] :
% 4.69/5.00 ( ( member_filter_nat @ V3 @ A )
% 4.69/5.00 => ( ord_le2510731241096832064er_nat @ V3 @ U ) )
% 4.69/5.00 => ( ( A != bot_bo498966703094740906er_nat )
% 4.69/5.00 => ( ord_le2510731241096832064er_nat @ ( comple6612786467464916249er_nat @ A ) @ U ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_less_eq
% 4.69/5.00 thf(fact_4809_Inf__less__eq,axiom,
% 4.69/5.00 ! [A: set_set_nat,U: set_nat] :
% 4.69/5.00 ( ! [V3: set_nat] :
% 4.69/5.00 ( ( member_set_nat @ V3 @ A )
% 4.69/5.00 => ( ord_less_eq_set_nat @ V3 @ U ) )
% 4.69/5.00 => ( ( A != bot_bot_set_set_nat )
% 4.69/5.00 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ A ) @ U ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_less_eq
% 4.69/5.00 thf(fact_4810_Inf__less__eq,axiom,
% 4.69/5.00 ! [A: set_Product_unit,U: product_unit] :
% 4.69/5.00 ( ! [V3: product_unit] :
% 4.69/5.00 ( ( member_Product_unit @ V3 @ A )
% 4.69/5.00 => ( ord_le3221252021190050221t_unit @ V3 @ U ) )
% 4.69/5.00 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ A ) @ U ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_less_eq
% 4.69/5.00 thf(fact_4811_cInf__lessD,axiom,
% 4.69/5.00 ! [X4: set_int,Z: int] :
% 4.69/5.00 ( ( X4 != bot_bot_set_int )
% 4.69/5.00 => ( ( ord_less_int @ ( complete_Inf_Inf_int @ X4 ) @ Z )
% 4.69/5.00 => ? [X3: int] :
% 4.69/5.00 ( ( member_int @ X3 @ X4 )
% 4.69/5.00 & ( ord_less_int @ X3 @ Z ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_lessD
% 4.69/5.00 thf(fact_4812_cInf__lessD,axiom,
% 4.69/5.00 ! [X4: set_nat,Z: nat] :
% 4.69/5.00 ( ( X4 != bot_bot_set_nat )
% 4.69/5.00 => ( ( ord_less_nat @ ( complete_Inf_Inf_nat @ X4 ) @ Z )
% 4.69/5.00 => ? [X3: nat] :
% 4.69/5.00 ( ( member_nat @ X3 @ X4 )
% 4.69/5.00 & ( ord_less_nat @ X3 @ Z ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_lessD
% 4.69/5.00 thf(fact_4813_cInf__lessD,axiom,
% 4.69/5.00 ! [X4: set_Product_unit,Z: product_unit] :
% 4.69/5.00 ( ( X4 != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ( ord_le361264281704409273t_unit @ ( comple2584293577114468500t_unit @ X4 ) @ Z )
% 4.69/5.00 => ? [X3: product_unit] :
% 4.69/5.00 ( ( member_Product_unit @ X3 @ X4 )
% 4.69/5.00 & ( ord_le361264281704409273t_unit @ X3 @ Z ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_lessD
% 4.69/5.00 thf(fact_4814_INF__eq__const,axiom,
% 4.69/5.00 ! [I: set_Product_unit,F: product_unit > set_nat,X: set_nat] :
% 4.69/5.00 ( ( I != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ! [I3: product_unit] :
% 4.69/5.00 ( ( member_Product_unit @ I3 @ I )
% 4.69/5.00 => ( ( F @ I3 )
% 4.69/5.00 = X ) )
% 4.69/5.00 => ( ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ I ) )
% 4.69/5.00 = X ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_eq_const
% 4.69/5.00 thf(fact_4815_INF__eq__const,axiom,
% 4.69/5.00 ! [I: set_o,F: $o > set_nat,X: set_nat] :
% 4.69/5.00 ( ( I != bot_bot_set_o )
% 4.69/5.00 => ( ! [I3: $o] :
% 4.69/5.00 ( ( member_o @ I3 @ I )
% 4.69/5.00 => ( ( F @ I3 )
% 4.69/5.00 = X ) )
% 4.69/5.00 => ( ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ I ) )
% 4.69/5.00 = X ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_eq_const
% 4.69/5.00 thf(fact_4816_INF__eq__const,axiom,
% 4.69/5.00 ! [I: set_nat,F: nat > set_nat,X: set_nat] :
% 4.69/5.00 ( ( I != bot_bot_set_nat )
% 4.69/5.00 => ( ! [I3: nat] :
% 4.69/5.00 ( ( member_nat @ I3 @ I )
% 4.69/5.00 => ( ( F @ I3 )
% 4.69/5.00 = X ) )
% 4.69/5.00 => ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ I ) )
% 4.69/5.00 = X ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_eq_const
% 4.69/5.00 thf(fact_4817_INF__eq__const,axiom,
% 4.69/5.00 ! [I: set_int,F: int > set_nat,X: set_nat] :
% 4.69/5.00 ( ( I != bot_bot_set_int )
% 4.69/5.00 => ( ! [I3: int] :
% 4.69/5.00 ( ( member_int @ I3 @ I )
% 4.69/5.00 => ( ( F @ I3 )
% 4.69/5.00 = X ) )
% 4.69/5.00 => ( ( comple7806235888213564991et_nat @ ( image_int_set_nat @ F @ I ) )
% 4.69/5.00 = X ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_eq_const
% 4.69/5.00 thf(fact_4818_INF__eq__const,axiom,
% 4.69/5.00 ! [I: set_Pr4532377907799695533_nat_o,F: ( produc3658429121746597890et_nat > $o ) > set_nat,X: set_nat] :
% 4.69/5.00 ( ( I != bot_bo7824918357723582233_nat_o )
% 4.69/5.00 => ( ! [I3: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ( member6576561426505652726_nat_o @ I3 @ I )
% 4.69/5.00 => ( ( F @ I3 )
% 4.69/5.00 = X ) )
% 4.69/5.00 => ( ( comple7806235888213564991et_nat @ ( image_6888641473154130958et_nat @ F @ I ) )
% 4.69/5.00 = X ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_eq_const
% 4.69/5.00 thf(fact_4819_INF__eq__const,axiom,
% 4.69/5.00 ! [I: set_Product_unit,F: product_unit > product_unit,X: product_unit] :
% 4.69/5.00 ( ( I != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ! [I3: product_unit] :
% 4.69/5.00 ( ( member_Product_unit @ I3 @ I )
% 4.69/5.00 => ( ( F @ I3 )
% 4.69/5.00 = X ) )
% 4.69/5.00 => ( ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ I ) )
% 4.69/5.00 = X ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_eq_const
% 4.69/5.00 thf(fact_4820_INF__eq__const,axiom,
% 4.69/5.00 ! [I: set_o,F: $o > product_unit,X: product_unit] :
% 4.69/5.00 ( ( I != bot_bot_set_o )
% 4.69/5.00 => ( ! [I3: $o] :
% 4.69/5.00 ( ( member_o @ I3 @ I )
% 4.69/5.00 => ( ( F @ I3 )
% 4.69/5.00 = X ) )
% 4.69/5.00 => ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit2 @ F @ I ) )
% 4.69/5.00 = X ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_eq_const
% 4.69/5.00 thf(fact_4821_INF__eq__const,axiom,
% 4.69/5.00 ! [I: set_nat,F: nat > product_unit,X: product_unit] :
% 4.69/5.00 ( ( I != bot_bot_set_nat )
% 4.69/5.00 => ( ! [I3: nat] :
% 4.69/5.00 ( ( member_nat @ I3 @ I )
% 4.69/5.00 => ( ( F @ I3 )
% 4.69/5.00 = X ) )
% 4.69/5.00 => ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ I ) )
% 4.69/5.00 = X ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_eq_const
% 4.69/5.00 thf(fact_4822_INF__eq__const,axiom,
% 4.69/5.00 ! [I: set_int,F: int > product_unit,X: product_unit] :
% 4.69/5.00 ( ( I != bot_bot_set_int )
% 4.69/5.00 => ( ! [I3: int] :
% 4.69/5.00 ( ( member_int @ I3 @ I )
% 4.69/5.00 => ( ( F @ I3 )
% 4.69/5.00 = X ) )
% 4.69/5.00 => ( ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ I ) )
% 4.69/5.00 = X ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_eq_const
% 4.69/5.00 thf(fact_4823_INF__eq__const,axiom,
% 4.69/5.00 ! [I: set_Pr4532377907799695533_nat_o,F: ( produc3658429121746597890et_nat > $o ) > product_unit,X: product_unit] :
% 4.69/5.00 ( ( I != bot_bo7824918357723582233_nat_o )
% 4.69/5.00 => ( ! [I3: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ( member6576561426505652726_nat_o @ I3 @ I )
% 4.69/5.00 => ( ( F @ I3 )
% 4.69/5.00 = X ) )
% 4.69/5.00 => ( ( comple2584293577114468500t_unit @ ( image_8451000719036923781t_unit @ F @ I ) )
% 4.69/5.00 = X ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_eq_const
% 4.69/5.00 thf(fact_4824_card__1__singletonE,axiom,
% 4.69/5.00 ! [A: set_Product_unit] :
% 4.69/5.00 ( ( ( finite410649719033368117t_unit @ A )
% 4.69/5.00 = one_one_nat )
% 4.69/5.00 => ~ ! [X3: product_unit] :
% 4.69/5.00 ( A
% 4.69/5.00 != ( insert_Product_unit @ X3 @ bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_1_singletonE
% 4.69/5.00 thf(fact_4825_card__1__singletonE,axiom,
% 4.69/5.00 ! [A: set_o] :
% 4.69/5.00 ( ( ( finite_card_o @ A )
% 4.69/5.00 = one_one_nat )
% 4.69/5.00 => ~ ! [X3: $o] :
% 4.69/5.00 ( A
% 4.69/5.00 != ( insert_o @ X3 @ bot_bot_set_o ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_1_singletonE
% 4.69/5.00 thf(fact_4826_card__1__singletonE,axiom,
% 4.69/5.00 ! [A: set_nat] :
% 4.69/5.00 ( ( ( finite_card_nat @ A )
% 4.69/5.00 = one_one_nat )
% 4.69/5.00 => ~ ! [X3: nat] :
% 4.69/5.00 ( A
% 4.69/5.00 != ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_1_singletonE
% 4.69/5.00 thf(fact_4827_card__1__singletonE,axiom,
% 4.69/5.00 ! [A: set_int] :
% 4.69/5.00 ( ( ( finite_card_int @ A )
% 4.69/5.00 = one_one_nat )
% 4.69/5.00 => ~ ! [X3: int] :
% 4.69/5.00 ( A
% 4.69/5.00 != ( insert_int @ X3 @ bot_bot_set_int ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_1_singletonE
% 4.69/5.00 thf(fact_4828_card__1__singletonE,axiom,
% 4.69/5.00 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/5.00 ( ( ( finite1363419556375932405_nat_o @ A )
% 4.69/5.00 = one_one_nat )
% 4.69/5.00 => ~ ! [X3: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( A
% 4.69/5.00 != ( insert5175938949040314269_nat_o @ X3 @ bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_1_singletonE
% 4.69/5.00 thf(fact_4829_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 4.69/5.00 ! [P: nat > nat > $o,X: nat,Y: nat,A2: product_prod_nat_nat] :
% 4.69/5.00 ( ( P @ X @ Y )
% 4.69/5.00 => ( ( A2
% 4.69/5.00 = ( product_Pair_nat_nat @ X @ Y ) )
% 4.69/5.00 => ( P @ ( product_fst_nat_nat @ A2 ) @ ( product_snd_nat_nat @ A2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % BNF_Greatest_Fixpoint.subst_Pair
% 4.69/5.00 thf(fact_4830_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 4.69/5.00 ! [P: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat,A2: produc3925858234332021118et_nat] :
% 4.69/5.00 ( ( P @ X @ Y )
% 4.69/5.00 => ( ( A2
% 4.69/5.00 = ( produc5001842942810119800et_nat @ X @ Y ) )
% 4.69/5.00 => ( P @ ( produc995936583742144908et_nat @ A2 ) @ ( produc4011572625026189258et_nat @ A2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % BNF_Greatest_Fixpoint.subst_Pair
% 4.69/5.00 thf(fact_4831_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 4.69/5.00 ! [P: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat,A2: produc2732055786443039994et_nat] :
% 4.69/5.00 ( ( P @ X @ Y )
% 4.69/5.00 => ( ( A2
% 4.69/5.00 = ( produc2245416461498447860et_nat @ X @ Y ) )
% 4.69/5.00 => ( P @ ( produc180342877477747464et_nat @ A2 ) @ ( produc5374455773327741254et_nat @ A2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % BNF_Greatest_Fixpoint.subst_Pair
% 4.69/5.00 thf(fact_4832_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 4.69/5.00 ! [P: heap_e7401611519738050253t_unit > set_nat > $o,X: heap_e7401611519738050253t_unit,Y: set_nat,A2: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( P @ X @ Y )
% 4.69/5.00 => ( ( A2
% 4.69/5.00 = ( produc7507926704131184380et_nat @ X @ Y ) )
% 4.69/5.00 => ( P @ ( produc1824681642469235216et_nat @ A2 ) @ ( produc8586169260539613262et_nat @ A2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % BNF_Greatest_Fixpoint.subst_Pair
% 4.69/5.00 thf(fact_4833_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 4.69/5.00 ! [P: int > int > $o,X: int,Y: int,A2: product_prod_int_int] :
% 4.69/5.00 ( ( P @ X @ Y )
% 4.69/5.00 => ( ( A2
% 4.69/5.00 = ( product_Pair_int_int @ X @ Y ) )
% 4.69/5.00 => ( P @ ( product_fst_int_int @ A2 ) @ ( product_snd_int_int @ A2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % BNF_Greatest_Fixpoint.subst_Pair
% 4.69/5.00 thf(fact_4834_prod_Oexhaust__sel,axiom,
% 4.69/5.00 ! [Prod: product_prod_nat_nat] :
% 4.69/5.00 ( Prod
% 4.69/5.00 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ Prod ) @ ( product_snd_nat_nat @ Prod ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod.exhaust_sel
% 4.69/5.00 thf(fact_4835_prod_Oexhaust__sel,axiom,
% 4.69/5.00 ! [Prod: produc3925858234332021118et_nat] :
% 4.69/5.00 ( Prod
% 4.69/5.00 = ( produc5001842942810119800et_nat @ ( produc995936583742144908et_nat @ Prod ) @ ( produc4011572625026189258et_nat @ Prod ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod.exhaust_sel
% 4.69/5.00 thf(fact_4836_prod_Oexhaust__sel,axiom,
% 4.69/5.00 ! [Prod: produc2732055786443039994et_nat] :
% 4.69/5.00 ( Prod
% 4.69/5.00 = ( produc2245416461498447860et_nat @ ( produc180342877477747464et_nat @ Prod ) @ ( produc5374455773327741254et_nat @ Prod ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod.exhaust_sel
% 4.69/5.00 thf(fact_4837_prod_Oexhaust__sel,axiom,
% 4.69/5.00 ! [Prod: produc3658429121746597890et_nat] :
% 4.69/5.00 ( Prod
% 4.69/5.00 = ( produc7507926704131184380et_nat @ ( produc1824681642469235216et_nat @ Prod ) @ ( produc8586169260539613262et_nat @ Prod ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod.exhaust_sel
% 4.69/5.00 thf(fact_4838_prod_Oexhaust__sel,axiom,
% 4.69/5.00 ! [Prod: product_prod_int_int] :
% 4.69/5.00 ( Prod
% 4.69/5.00 = ( product_Pair_int_int @ ( product_fst_int_int @ Prod ) @ ( product_snd_int_int @ Prod ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod.exhaust_sel
% 4.69/5.00 thf(fact_4839_surjective__pairing,axiom,
% 4.69/5.00 ! [T4: product_prod_nat_nat] :
% 4.69/5.00 ( T4
% 4.69/5.00 = ( product_Pair_nat_nat @ ( product_fst_nat_nat @ T4 ) @ ( product_snd_nat_nat @ T4 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % surjective_pairing
% 4.69/5.00 thf(fact_4840_surjective__pairing,axiom,
% 4.69/5.00 ! [T4: produc3925858234332021118et_nat] :
% 4.69/5.00 ( T4
% 4.69/5.00 = ( produc5001842942810119800et_nat @ ( produc995936583742144908et_nat @ T4 ) @ ( produc4011572625026189258et_nat @ T4 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % surjective_pairing
% 4.69/5.00 thf(fact_4841_surjective__pairing,axiom,
% 4.69/5.00 ! [T4: produc2732055786443039994et_nat] :
% 4.69/5.00 ( T4
% 4.69/5.00 = ( produc2245416461498447860et_nat @ ( produc180342877477747464et_nat @ T4 ) @ ( produc5374455773327741254et_nat @ T4 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % surjective_pairing
% 4.69/5.00 thf(fact_4842_surjective__pairing,axiom,
% 4.69/5.00 ! [T4: produc3658429121746597890et_nat] :
% 4.69/5.00 ( T4
% 4.69/5.00 = ( produc7507926704131184380et_nat @ ( produc1824681642469235216et_nat @ T4 ) @ ( produc8586169260539613262et_nat @ T4 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % surjective_pairing
% 4.69/5.00 thf(fact_4843_surjective__pairing,axiom,
% 4.69/5.00 ! [T4: product_prod_int_int] :
% 4.69/5.00 ( T4
% 4.69/5.00 = ( product_Pair_int_int @ ( product_fst_int_int @ T4 ) @ ( product_snd_int_int @ T4 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % surjective_pairing
% 4.69/5.00 thf(fact_4844_card__insert__le,axiom,
% 4.69/5.00 ! [A: set_nat,X: nat] : ( ord_less_eq_nat @ ( finite_card_nat @ A ) @ ( finite_card_nat @ ( insert_nat @ X @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_insert_le
% 4.69/5.00 thf(fact_4845_card__insert__le,axiom,
% 4.69/5.00 ! [A: set_int,X: int] : ( ord_less_eq_nat @ ( finite_card_int @ A ) @ ( finite_card_int @ ( insert_int @ X @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_insert_le
% 4.69/5.00 thf(fact_4846_card__insert__le,axiom,
% 4.69/5.00 ! [A: set_o,X: $o] : ( ord_less_eq_nat @ ( finite_card_o @ A ) @ ( finite_card_o @ ( insert_o @ X @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_insert_le
% 4.69/5.00 thf(fact_4847_card__insert__le,axiom,
% 4.69/5.00 ! [A: set_Product_unit,X: product_unit] : ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ A ) @ ( finite410649719033368117t_unit @ ( insert_Product_unit @ X @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_insert_le
% 4.69/5.00 thf(fact_4848_in__fst__imageE,axiom,
% 4.69/5.00 ! [X: heap_e7401611519738050253t_unit,S: set_Pr3948176798113811640et_nat] :
% 4.69/5.00 ( ( member242389114213480694t_unit @ X @ ( image_6824039242672219652t_unit @ produc1824681642469235216et_nat @ S ) )
% 4.69/5.00 => ~ ! [Y2: set_nat] :
% 4.69/5.00 ~ ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X @ Y2 ) @ S ) ) ).
% 4.69/5.00
% 4.69/5.00 % in_fst_imageE
% 4.69/5.00 thf(fact_4849_in__fst__imageE,axiom,
% 4.69/5.00 ! [X: nat,S: set_Pr1261947904930325089at_nat] :
% 4.69/5.00 ( ( member_nat @ X @ ( image_2486076414777270412at_nat @ product_fst_nat_nat @ S ) )
% 4.69/5.00 => ~ ! [Y2: nat] :
% 4.69/5.00 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y2 ) @ S ) ) ).
% 4.69/5.00
% 4.69/5.00 % in_fst_imageE
% 4.69/5.00 thf(fact_4850_in__fst__imageE,axiom,
% 4.69/5.00 ! [X: produc3658429121746597890et_nat > $o,S: set_Pr3286484037609594932et_nat] :
% 4.69/5.00 ( ( member6576561426505652726_nat_o @ X @ ( image_6802380912191114376_nat_o @ produc995936583742144908et_nat @ S ) )
% 4.69/5.00 => ~ ! [Y2: produc3658429121746597890et_nat] :
% 4.69/5.00 ~ ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X @ Y2 ) @ S ) ) ).
% 4.69/5.00
% 4.69/5.00 % in_fst_imageE
% 4.69/5.00 thf(fact_4851_in__fst__imageE,axiom,
% 4.69/5.00 ! [X: produc3658429121746597890et_nat > $o,S: set_Pr8536935166611901872et_nat] :
% 4.69/5.00 ( ( member6576561426505652726_nat_o @ X @ ( image_2517677226577294348_nat_o @ produc180342877477747464et_nat @ S ) )
% 4.69/5.00 => ~ ! [Y2: produc3925858234332021118et_nat] :
% 4.69/5.00 ~ ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X @ Y2 ) @ S ) ) ).
% 4.69/5.00
% 4.69/5.00 % in_fst_imageE
% 4.69/5.00 thf(fact_4852_in__fst__imageE,axiom,
% 4.69/5.00 ! [X: int,S: set_Pr958786334691620121nt_int] :
% 4.69/5.00 ( ( member_int @ X @ ( image_5042161079198086560nt_int @ product_fst_int_int @ S ) )
% 4.69/5.00 => ~ ! [Y2: int] :
% 4.69/5.00 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y2 ) @ S ) ) ).
% 4.69/5.00
% 4.69/5.00 % in_fst_imageE
% 4.69/5.00 thf(fact_4853_Inter__subset,axiom,
% 4.69/5.00 ! [A: set_set_nat,B4: set_nat] :
% 4.69/5.00 ( ! [X8: set_nat] :
% 4.69/5.00 ( ( member_set_nat @ X8 @ A )
% 4.69/5.00 => ( ord_less_eq_set_nat @ X8 @ B4 ) )
% 4.69/5.00 => ( ( A != bot_bot_set_set_nat )
% 4.69/5.00 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ A ) @ B4 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Inter_subset
% 4.69/5.00 thf(fact_4854_Inter__empty,axiom,
% 4.69/5.00 ( ( comple7216939928495492468t_unit @ bot_bo6284674557190688313t_unit )
% 4.69/5.00 = top_to1996260823553986621t_unit ) ).
% 4.69/5.00
% 4.69/5.00 % Inter_empty
% 4.69/5.00 thf(fact_4855_Inter__empty,axiom,
% 4.69/5.00 ( ( comple3063163877087187839_set_o @ bot_bot_set_set_o )
% 4.69/5.00 = top_top_set_o ) ).
% 4.69/5.00
% 4.69/5.00 % Inter_empty
% 4.69/5.00 thf(fact_4856_Inter__empty,axiom,
% 4.69/5.00 ( ( comple3628384868704368283et_int @ bot_bot_set_set_int )
% 4.69/5.00 = top_top_set_int ) ).
% 4.69/5.00
% 4.69/5.00 % Inter_empty
% 4.69/5.00 thf(fact_4857_Inter__empty,axiom,
% 4.69/5.00 ( ( comple7806235888213564991et_nat @ bot_bot_set_set_nat )
% 4.69/5.00 = top_top_set_nat ) ).
% 4.69/5.00
% 4.69/5.00 % Inter_empty
% 4.69/5.00 thf(fact_4858_fst__eq__Domain,axiom,
% 4.69/5.00 ! [R3: set_Pr958786334691620121nt_int] :
% 4.69/5.00 ( ( image_5042161079198086560nt_int @ product_fst_int_int @ R3 )
% 4.69/5.00 = ( domain_int_int @ R3 ) ) ).
% 4.69/5.00
% 4.69/5.00 % fst_eq_Domain
% 4.69/5.00 thf(fact_4859_Domain__fst,axiom,
% 4.69/5.00 ( domain_int_int
% 4.69/5.00 = ( image_5042161079198086560nt_int @ product_fst_int_int ) ) ).
% 4.69/5.00
% 4.69/5.00 % Domain_fst
% 4.69/5.00 thf(fact_4860_card__partition,axiom,
% 4.69/5.00 ! [C5: set_set_Code_integer,K3: nat] :
% 4.69/5.00 ( ( finite6931041176100689706nteger @ C5 )
% 4.69/5.00 => ( ( finite6017078050557962740nteger @ ( comple739944243200306918nteger @ C5 ) )
% 4.69/5.00 => ( ! [C2: set_Code_integer] :
% 4.69/5.00 ( ( member1834298987299537450nteger @ C2 @ C5 )
% 4.69/5.00 => ( ( finite4902975817058060853nteger @ C2 )
% 4.69/5.00 = K3 ) )
% 4.69/5.00 => ( ! [C1: set_Code_integer,C22: set_Code_integer] :
% 4.69/5.00 ( ( member1834298987299537450nteger @ C1 @ C5 )
% 4.69/5.00 => ( ( member1834298987299537450nteger @ C22 @ C5 )
% 4.69/5.00 => ( ( C1 != C22 )
% 4.69/5.00 => ( ( inf_in1364745209274528805nteger @ C1 @ C22 )
% 4.69/5.00 = bot_bo3990330152332043303nteger ) ) ) )
% 4.69/5.00 => ( ( times_times_nat @ K3 @ ( finite1340570857867686763nteger @ C5 ) )
% 4.69/5.00 = ( finite4902975817058060853nteger @ ( comple739944243200306918nteger @ C5 ) ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_partition
% 4.69/5.00 thf(fact_4861_card__partition,axiom,
% 4.69/5.00 ! [C5: set_set_Product_unit,K3: nat] :
% 4.69/5.00 ( ( finite1772178364199683094t_unit @ C5 )
% 4.69/5.00 => ( ( finite4290736615968046902t_unit @ ( comple3349607820504768346t_unit @ C5 ) )
% 4.69/5.00 => ( ! [C2: set_Product_unit] :
% 4.69/5.00 ( ( member5877623283571906838t_unit @ C2 @ C5 )
% 4.69/5.00 => ( ( finite410649719033368117t_unit @ C2 )
% 4.69/5.00 = K3 ) )
% 4.69/5.00 => ( ! [C1: set_Product_unit,C22: set_Product_unit] :
% 4.69/5.00 ( ( member5877623283571906838t_unit @ C1 @ C5 )
% 4.69/5.00 => ( ( member5877623283571906838t_unit @ C22 @ C5 )
% 4.69/5.00 => ( ( C1 != C22 )
% 4.69/5.00 => ( ( inf_in4660618365625256667t_unit @ C1 @ C22 )
% 4.69/5.00 = bot_bo3957492148770167129t_unit ) ) ) )
% 4.69/5.00 => ( ( times_times_nat @ K3 @ ( finite22775419188893461t_unit @ C5 ) )
% 4.69/5.00 = ( finite410649719033368117t_unit @ ( comple3349607820504768346t_unit @ C5 ) ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_partition
% 4.69/5.00 thf(fact_4862_card__partition,axiom,
% 4.69/5.00 ! [C5: set_set_o,K3: nat] :
% 4.69/5.00 ( ( finite_finite_set_o @ C5 )
% 4.69/5.00 => ( ( finite_finite_o @ ( comple90263536869209701_set_o @ C5 ) )
% 4.69/5.00 => ( ! [C2: set_o] :
% 4.69/5.00 ( ( member_set_o @ C2 @ C5 )
% 4.69/5.00 => ( ( finite_card_o @ C2 )
% 4.69/5.00 = K3 ) )
% 4.69/5.00 => ( ! [C1: set_o,C22: set_o] :
% 4.69/5.00 ( ( member_set_o @ C1 @ C5 )
% 4.69/5.00 => ( ( member_set_o @ C22 @ C5 )
% 4.69/5.00 => ( ( C1 != C22 )
% 4.69/5.00 => ( ( inf_inf_set_o @ C1 @ C22 )
% 4.69/5.00 = bot_bot_set_o ) ) ) )
% 4.69/5.00 => ( ( times_times_nat @ K3 @ ( finite_card_set_o @ C5 ) )
% 4.69/5.00 = ( finite_card_o @ ( comple90263536869209701_set_o @ C5 ) ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_partition
% 4.69/5.00 thf(fact_4863_card__partition,axiom,
% 4.69/5.00 ! [C5: set_set_nat,K3: nat] :
% 4.69/5.00 ( ( finite1152437895449049373et_nat @ C5 )
% 4.69/5.00 => ( ( finite_finite_nat @ ( comple7399068483239264473et_nat @ C5 ) )
% 4.69/5.00 => ( ! [C2: set_nat] :
% 4.69/5.00 ( ( member_set_nat @ C2 @ C5 )
% 4.69/5.00 => ( ( finite_card_nat @ C2 )
% 4.69/5.00 = K3 ) )
% 4.69/5.00 => ( ! [C1: set_nat,C22: set_nat] :
% 4.69/5.00 ( ( member_set_nat @ C1 @ C5 )
% 4.69/5.00 => ( ( member_set_nat @ C22 @ C5 )
% 4.69/5.00 => ( ( C1 != C22 )
% 4.69/5.00 => ( ( inf_inf_set_nat @ C1 @ C22 )
% 4.69/5.00 = bot_bot_set_nat ) ) ) )
% 4.69/5.00 => ( ( times_times_nat @ K3 @ ( finite_card_set_nat @ C5 ) )
% 4.69/5.00 = ( finite_card_nat @ ( comple7399068483239264473et_nat @ C5 ) ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_partition
% 4.69/5.00 thf(fact_4864_card__partition,axiom,
% 4.69/5.00 ! [C5: set_set_int,K3: nat] :
% 4.69/5.00 ( ( finite6197958912794628473et_int @ C5 )
% 4.69/5.00 => ( ( finite_finite_int @ ( comple3221217463730067765et_int @ C5 ) )
% 4.69/5.00 => ( ! [C2: set_int] :
% 4.69/5.00 ( ( member_set_int @ C2 @ C5 )
% 4.69/5.00 => ( ( finite_card_int @ C2 )
% 4.69/5.00 = K3 ) )
% 4.69/5.00 => ( ! [C1: set_int,C22: set_int] :
% 4.69/5.00 ( ( member_set_int @ C1 @ C5 )
% 4.69/5.00 => ( ( member_set_int @ C22 @ C5 )
% 4.69/5.00 => ( ( C1 != C22 )
% 4.69/5.00 => ( ( inf_inf_set_int @ C1 @ C22 )
% 4.69/5.00 = bot_bot_set_int ) ) ) )
% 4.69/5.00 => ( ( times_times_nat @ K3 @ ( finite_card_set_int @ C5 ) )
% 4.69/5.00 = ( finite_card_int @ ( comple3221217463730067765et_int @ C5 ) ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_partition
% 4.69/5.00 thf(fact_4865_card__partition,axiom,
% 4.69/5.00 ! [C5: set_se1353816476878259085_nat_o,K3: nat] :
% 4.69/5.00 ( ( finite6069017635265841110_nat_o @ C5 )
% 4.69/5.00 => ( ( finite3252695134891459830_nat_o @ ( comple3382087578465172250_nat_o @ C5 ) )
% 4.69/5.00 => ( ! [C2: set_Pr4532377907799695533_nat_o] :
% 4.69/5.00 ( ( member1452989533377600726_nat_o @ C2 @ C5 )
% 4.69/5.00 => ( ( finite1363419556375932405_nat_o @ C2 )
% 4.69/5.00 = K3 ) )
% 4.69/5.00 => ( ! [C1: set_Pr4532377907799695533_nat_o,C22: set_Pr4532377907799695533_nat_o] :
% 4.69/5.00 ( ( member1452989533377600726_nat_o @ C1 @ C5 )
% 4.69/5.00 => ( ( member1452989533377600726_nat_o @ C22 @ C5 )
% 4.69/5.00 => ( ( C1 != C22 )
% 4.69/5.00 => ( ( inf_in1906310914598751387_nat_o @ C1 @ C22 )
% 4.69/5.00 = bot_bo7824918357723582233_nat_o ) ) ) )
% 4.69/5.00 => ( ( times_times_nat @ K3 @ ( finite4731484169140532437_nat_o @ C5 ) )
% 4.69/5.00 = ( finite1363419556375932405_nat_o @ ( comple3382087578465172250_nat_o @ C5 ) ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_partition
% 4.69/5.00 thf(fact_4866_Inter__UNIV,axiom,
% 4.69/5.00 ( ( comple7216939928495492468t_unit @ top_to1767297665138865437t_unit )
% 4.69/5.00 = bot_bo3957492148770167129t_unit ) ).
% 4.69/5.00
% 4.69/5.00 % Inter_UNIV
% 4.69/5.00 thf(fact_4867_Inter__UNIV,axiom,
% 4.69/5.00 ( ( comple3063163877087187839_set_o @ top_top_set_set_o )
% 4.69/5.00 = bot_bot_set_o ) ).
% 4.69/5.00
% 4.69/5.00 % Inter_UNIV
% 4.69/5.00 thf(fact_4868_Inter__UNIV,axiom,
% 4.69/5.00 ( ( comple3628384868704368283et_int @ top_top_set_set_int )
% 4.69/5.00 = bot_bot_set_int ) ).
% 4.69/5.00
% 4.69/5.00 % Inter_UNIV
% 4.69/5.00 thf(fact_4869_Inter__UNIV,axiom,
% 4.69/5.00 ( ( comple79274577958421812_nat_o @ top_to8515903933492314333_nat_o )
% 4.69/5.00 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/5.00
% 4.69/5.00 % Inter_UNIV
% 4.69/5.00 thf(fact_4870_Inter__UNIV,axiom,
% 4.69/5.00 ( ( comple7806235888213564991et_nat @ top_top_set_set_nat )
% 4.69/5.00 = bot_bot_set_nat ) ).
% 4.69/5.00
% 4.69/5.00 % Inter_UNIV
% 4.69/5.00 thf(fact_4871_inv__on__f__range,axiom,
% 4.69/5.00 ! [Y: code_integer,F: code_integer > code_integer,A: set_Code_integer] :
% 4.69/5.00 ( ( member_Code_integer @ Y @ ( image_4470545334726330049nteger @ F @ A ) )
% 4.69/5.00 => ( member_Code_integer @ ( inv_on4869000451854154612nteger @ F @ A @ Y ) @ A ) ) ).
% 4.69/5.00
% 4.69/5.00 % inv_on_f_range
% 4.69/5.00 thf(fact_4872_inv__on__f__range,axiom,
% 4.69/5.00 ! [Y: code_integer,F: nat > code_integer,A: set_nat] :
% 4.69/5.00 ( ( member_Code_integer @ Y @ ( image_1215581382706833972nteger @ F @ A ) )
% 4.69/5.00 => ( member_nat @ ( inv_on1369624593536199399nteger @ F @ A @ Y ) @ A ) ) ).
% 4.69/5.00
% 4.69/5.00 % inv_on_f_range
% 4.69/5.00 thf(fact_4873_inv__on__f__range,axiom,
% 4.69/5.00 ! [Y: nat,F: nat > nat,A: set_nat] :
% 4.69/5.00 ( ( member_nat @ Y @ ( image_nat_nat2 @ F @ A ) )
% 4.69/5.00 => ( member_nat @ ( inv_on_nat_nat @ F @ A @ Y ) @ A ) ) ).
% 4.69/5.00
% 4.69/5.00 % inv_on_f_range
% 4.69/5.00 thf(fact_4874_inv__on__f__range,axiom,
% 4.69/5.00 ! [Y: nat,F: int > nat,A: set_int] :
% 4.69/5.00 ( ( member_nat @ Y @ ( image_int_nat2 @ F @ A ) )
% 4.69/5.00 => ( member_int @ ( inv_on_int_nat @ F @ A @ Y ) @ A ) ) ).
% 4.69/5.00
% 4.69/5.00 % inv_on_f_range
% 4.69/5.00 thf(fact_4875_inv__on__f__range,axiom,
% 4.69/5.00 ! [Y: nat,F: $o > nat,A: set_o] :
% 4.69/5.00 ( ( member_nat @ Y @ ( image_o_nat2 @ F @ A ) )
% 4.69/5.00 => ( member_o @ ( inv_on_o_nat @ F @ A @ Y ) @ A ) ) ).
% 4.69/5.00
% 4.69/5.00 % inv_on_f_range
% 4.69/5.00 thf(fact_4876_inv__on__f__range,axiom,
% 4.69/5.00 ! [Y: nat,F: product_unit > nat,A: set_Product_unit] :
% 4.69/5.00 ( ( member_nat @ Y @ ( image_875570014554754200it_nat @ F @ A ) )
% 4.69/5.00 => ( member_Product_unit @ ( inv_on7727615724625388965it_nat @ F @ A @ Y ) @ A ) ) ).
% 4.69/5.00
% 4.69/5.00 % inv_on_f_range
% 4.69/5.00 thf(fact_4877_inv__on__f__range,axiom,
% 4.69/5.00 ! [Y: int,F: nat > int,A: set_nat] :
% 4.69/5.00 ( ( member_int @ Y @ ( image_nat_int2 @ F @ A ) )
% 4.69/5.00 => ( member_nat @ ( inv_on_nat_int @ F @ A @ Y ) @ A ) ) ).
% 4.69/5.00
% 4.69/5.00 % inv_on_f_range
% 4.69/5.00 thf(fact_4878_inv__on__f__range,axiom,
% 4.69/5.00 ! [Y: int,F: int > int,A: set_int] :
% 4.69/5.00 ( ( member_int @ Y @ ( image_int_int2 @ F @ A ) )
% 4.69/5.00 => ( member_int @ ( inv_on_int_int @ F @ A @ Y ) @ A ) ) ).
% 4.69/5.00
% 4.69/5.00 % inv_on_f_range
% 4.69/5.00 thf(fact_4879_inv__on__f__range,axiom,
% 4.69/5.00 ! [Y: int,F: $o > int,A: set_o] :
% 4.69/5.00 ( ( member_int @ Y @ ( image_o_int2 @ F @ A ) )
% 4.69/5.00 => ( member_o @ ( inv_on_o_int @ F @ A @ Y ) @ A ) ) ).
% 4.69/5.00
% 4.69/5.00 % inv_on_f_range
% 4.69/5.00 thf(fact_4880_inv__on__f__range,axiom,
% 4.69/5.00 ! [Y: int,F: product_unit > int,A: set_Product_unit] :
% 4.69/5.00 ( ( member_int @ Y @ ( image_873079544045703924it_int @ F @ A ) )
% 4.69/5.00 => ( member_Product_unit @ ( inv_on7725125254116338689it_int @ F @ A @ Y ) @ A ) ) ).
% 4.69/5.00
% 4.69/5.00 % inv_on_f_range
% 4.69/5.00 thf(fact_4881_f__inv__on__f,axiom,
% 4.69/5.00 ! [Y: set_nat,F: nat > set_nat,A: set_nat] :
% 4.69/5.00 ( ( member_set_nat @ Y @ ( image_nat_set_nat @ F @ A ) )
% 4.69/5.00 => ( ( F @ ( inv_on_nat_set_nat @ F @ A @ Y ) )
% 4.69/5.00 = Y ) ) ).
% 4.69/5.00
% 4.69/5.00 % f_inv_on_f
% 4.69/5.00 thf(fact_4882_f__inv__on__f,axiom,
% 4.69/5.00 ! [Y: code_integer,F: code_integer > code_integer,A: set_Code_integer] :
% 4.69/5.00 ( ( member_Code_integer @ Y @ ( image_4470545334726330049nteger @ F @ A ) )
% 4.69/5.00 => ( ( F @ ( inv_on4869000451854154612nteger @ F @ A @ Y ) )
% 4.69/5.00 = Y ) ) ).
% 4.69/5.00
% 4.69/5.00 % f_inv_on_f
% 4.69/5.00 thf(fact_4883_f__inv__on__f,axiom,
% 4.69/5.00 ! [Y: code_integer,F: nat > code_integer,A: set_nat] :
% 4.69/5.00 ( ( member_Code_integer @ Y @ ( image_1215581382706833972nteger @ F @ A ) )
% 4.69/5.00 => ( ( F @ ( inv_on1369624593536199399nteger @ F @ A @ Y ) )
% 4.69/5.00 = Y ) ) ).
% 4.69/5.00
% 4.69/5.00 % f_inv_on_f
% 4.69/5.00 thf(fact_4884_f__inv__on__f,axiom,
% 4.69/5.00 ! [Y: nat,F: nat > nat,A: set_nat] :
% 4.69/5.00 ( ( member_nat @ Y @ ( image_nat_nat2 @ F @ A ) )
% 4.69/5.00 => ( ( F @ ( inv_on_nat_nat @ F @ A @ Y ) )
% 4.69/5.00 = Y ) ) ).
% 4.69/5.00
% 4.69/5.00 % f_inv_on_f
% 4.69/5.00 thf(fact_4885_cINF__greatest,axiom,
% 4.69/5.00 ! [A: set_Product_unit,M4: int,F: product_unit > int] :
% 4.69/5.00 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ! [X3: product_unit] :
% 4.69/5.00 ( ( member_Product_unit @ X3 @ A )
% 4.69/5.00 => ( ord_less_eq_int @ M4 @ ( F @ X3 ) ) )
% 4.69/5.00 => ( ord_less_eq_int @ M4 @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cINF_greatest
% 4.69/5.00 thf(fact_4886_cINF__greatest,axiom,
% 4.69/5.00 ! [A: set_o,M4: int,F: $o > int] :
% 4.69/5.00 ( ( A != bot_bot_set_o )
% 4.69/5.00 => ( ! [X3: $o] :
% 4.69/5.00 ( ( member_o @ X3 @ A )
% 4.69/5.00 => ( ord_less_eq_int @ M4 @ ( F @ X3 ) ) )
% 4.69/5.00 => ( ord_less_eq_int @ M4 @ ( complete_Inf_Inf_int @ ( image_o_int2 @ F @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cINF_greatest
% 4.69/5.00 thf(fact_4887_cINF__greatest,axiom,
% 4.69/5.00 ! [A: set_nat,M4: int,F: nat > int] :
% 4.69/5.00 ( ( A != bot_bot_set_nat )
% 4.69/5.00 => ( ! [X3: nat] :
% 4.69/5.00 ( ( member_nat @ X3 @ A )
% 4.69/5.00 => ( ord_less_eq_int @ M4 @ ( F @ X3 ) ) )
% 4.69/5.00 => ( ord_less_eq_int @ M4 @ ( complete_Inf_Inf_int @ ( image_nat_int2 @ F @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cINF_greatest
% 4.69/5.00 thf(fact_4888_cINF__greatest,axiom,
% 4.69/5.00 ! [A: set_int,M4: int,F: int > int] :
% 4.69/5.00 ( ( A != bot_bot_set_int )
% 4.69/5.00 => ( ! [X3: int] :
% 4.69/5.00 ( ( member_int @ X3 @ A )
% 4.69/5.00 => ( ord_less_eq_int @ M4 @ ( F @ X3 ) ) )
% 4.69/5.00 => ( ord_less_eq_int @ M4 @ ( complete_Inf_Inf_int @ ( image_int_int2 @ F @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cINF_greatest
% 4.69/5.00 thf(fact_4889_cINF__greatest,axiom,
% 4.69/5.00 ! [A: set_Product_unit,M4: nat,F: product_unit > nat] :
% 4.69/5.00 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ! [X3: product_unit] :
% 4.69/5.00 ( ( member_Product_unit @ X3 @ A )
% 4.69/5.00 => ( ord_less_eq_nat @ M4 @ ( F @ X3 ) ) )
% 4.69/5.00 => ( ord_less_eq_nat @ M4 @ ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ F @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cINF_greatest
% 4.69/5.00 thf(fact_4890_cINF__greatest,axiom,
% 4.69/5.00 ! [A: set_o,M4: nat,F: $o > nat] :
% 4.69/5.00 ( ( A != bot_bot_set_o )
% 4.69/5.00 => ( ! [X3: $o] :
% 4.69/5.00 ( ( member_o @ X3 @ A )
% 4.69/5.00 => ( ord_less_eq_nat @ M4 @ ( F @ X3 ) ) )
% 4.69/5.00 => ( ord_less_eq_nat @ M4 @ ( complete_Inf_Inf_nat @ ( image_o_nat2 @ F @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cINF_greatest
% 4.69/5.00 thf(fact_4891_cINF__greatest,axiom,
% 4.69/5.00 ! [A: set_nat,M4: nat,F: nat > nat] :
% 4.69/5.00 ( ( A != bot_bot_set_nat )
% 4.69/5.00 => ( ! [X3: nat] :
% 4.69/5.00 ( ( member_nat @ X3 @ A )
% 4.69/5.00 => ( ord_less_eq_nat @ M4 @ ( F @ X3 ) ) )
% 4.69/5.00 => ( ord_less_eq_nat @ M4 @ ( complete_Inf_Inf_nat @ ( image_nat_nat2 @ F @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cINF_greatest
% 4.69/5.00 thf(fact_4892_cINF__greatest,axiom,
% 4.69/5.00 ! [A: set_int,M4: nat,F: int > nat] :
% 4.69/5.00 ( ( A != bot_bot_set_int )
% 4.69/5.00 => ( ! [X3: int] :
% 4.69/5.00 ( ( member_int @ X3 @ A )
% 4.69/5.00 => ( ord_less_eq_nat @ M4 @ ( F @ X3 ) ) )
% 4.69/5.00 => ( ord_less_eq_nat @ M4 @ ( complete_Inf_Inf_nat @ ( image_int_nat2 @ F @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cINF_greatest
% 4.69/5.00 thf(fact_4893_cINF__greatest,axiom,
% 4.69/5.00 ! [A: set_Product_unit,M4: product_unit,F: product_unit > product_unit] :
% 4.69/5.00 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ! [X3: product_unit] :
% 4.69/5.00 ( ( member_Product_unit @ X3 @ A )
% 4.69/5.00 => ( ord_le3221252021190050221t_unit @ M4 @ ( F @ X3 ) ) )
% 4.69/5.00 => ( ord_le3221252021190050221t_unit @ M4 @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cINF_greatest
% 4.69/5.00 thf(fact_4894_cINF__greatest,axiom,
% 4.69/5.00 ! [A: set_o,M4: product_unit,F: $o > product_unit] :
% 4.69/5.00 ( ( A != bot_bot_set_o )
% 4.69/5.00 => ( ! [X3: $o] :
% 4.69/5.00 ( ( member_o @ X3 @ A )
% 4.69/5.00 => ( ord_le3221252021190050221t_unit @ M4 @ ( F @ X3 ) ) )
% 4.69/5.00 => ( ord_le3221252021190050221t_unit @ M4 @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit2 @ F @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cINF_greatest
% 4.69/5.00 thf(fact_4895_INF__eq__iff,axiom,
% 4.69/5.00 ! [I: set_Product_unit,F: product_unit > product_unit,C: product_unit] :
% 4.69/5.00 ( ( I != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ! [I3: product_unit] :
% 4.69/5.00 ( ( member_Product_unit @ I3 @ I )
% 4.69/5.00 => ( ord_le3221252021190050221t_unit @ ( F @ I3 ) @ C ) )
% 4.69/5.00 => ( ( ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ I ) )
% 4.69/5.00 = C )
% 4.69/5.00 = ( ! [X2: product_unit] :
% 4.69/5.00 ( ( member_Product_unit @ X2 @ I )
% 4.69/5.00 => ( ( F @ X2 )
% 4.69/5.00 = C ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_eq_iff
% 4.69/5.00 thf(fact_4896_INF__eq__iff,axiom,
% 4.69/5.00 ! [I: set_o,F: $o > product_unit,C: product_unit] :
% 4.69/5.00 ( ( I != bot_bot_set_o )
% 4.69/5.00 => ( ! [I3: $o] :
% 4.69/5.00 ( ( member_o @ I3 @ I )
% 4.69/5.00 => ( ord_le3221252021190050221t_unit @ ( F @ I3 ) @ C ) )
% 4.69/5.00 => ( ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit2 @ F @ I ) )
% 4.69/5.00 = C )
% 4.69/5.00 = ( ! [X2: $o] :
% 4.69/5.00 ( ( member_o @ X2 @ I )
% 4.69/5.00 => ( ( F @ X2 )
% 4.69/5.00 = C ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_eq_iff
% 4.69/5.00 thf(fact_4897_INF__eq__iff,axiom,
% 4.69/5.00 ! [I: set_nat,F: nat > product_unit,C: product_unit] :
% 4.69/5.00 ( ( I != bot_bot_set_nat )
% 4.69/5.00 => ( ! [I3: nat] :
% 4.69/5.00 ( ( member_nat @ I3 @ I )
% 4.69/5.00 => ( ord_le3221252021190050221t_unit @ ( F @ I3 ) @ C ) )
% 4.69/5.00 => ( ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ I ) )
% 4.69/5.00 = C )
% 4.69/5.00 = ( ! [X2: nat] :
% 4.69/5.00 ( ( member_nat @ X2 @ I )
% 4.69/5.00 => ( ( F @ X2 )
% 4.69/5.00 = C ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_eq_iff
% 4.69/5.00 thf(fact_4898_INF__eq__iff,axiom,
% 4.69/5.00 ! [I: set_int,F: int > product_unit,C: product_unit] :
% 4.69/5.00 ( ( I != bot_bot_set_int )
% 4.69/5.00 => ( ! [I3: int] :
% 4.69/5.00 ( ( member_int @ I3 @ I )
% 4.69/5.00 => ( ord_le3221252021190050221t_unit @ ( F @ I3 ) @ C ) )
% 4.69/5.00 => ( ( ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ I ) )
% 4.69/5.00 = C )
% 4.69/5.00 = ( ! [X2: int] :
% 4.69/5.00 ( ( member_int @ X2 @ I )
% 4.69/5.00 => ( ( F @ X2 )
% 4.69/5.00 = C ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_eq_iff
% 4.69/5.00 thf(fact_4899_INF__eq__iff,axiom,
% 4.69/5.00 ! [I: set_Product_unit,F: product_unit > filter_nat,C: filter_nat] :
% 4.69/5.00 ( ( I != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ! [I3: product_unit] :
% 4.69/5.00 ( ( member_Product_unit @ I3 @ I )
% 4.69/5.00 => ( ord_le2510731241096832064er_nat @ ( F @ I3 ) @ C ) )
% 4.69/5.00 => ( ( ( comple6612786467464916249er_nat @ ( image_1853478764106424488er_nat @ F @ I ) )
% 4.69/5.00 = C )
% 4.69/5.00 = ( ! [X2: product_unit] :
% 4.69/5.00 ( ( member_Product_unit @ X2 @ I )
% 4.69/5.00 => ( ( F @ X2 )
% 4.69/5.00 = C ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_eq_iff
% 4.69/5.00 thf(fact_4900_INF__eq__iff,axiom,
% 4.69/5.00 ! [I: set_o,F: $o > filter_nat,C: filter_nat] :
% 4.69/5.00 ( ( I != bot_bot_set_o )
% 4.69/5.00 => ( ! [I3: $o] :
% 4.69/5.00 ( ( member_o @ I3 @ I )
% 4.69/5.00 => ( ord_le2510731241096832064er_nat @ ( F @ I3 ) @ C ) )
% 4.69/5.00 => ( ( ( comple6612786467464916249er_nat @ ( image_o_filter_nat @ F @ I ) )
% 4.69/5.00 = C )
% 4.69/5.00 = ( ! [X2: $o] :
% 4.69/5.00 ( ( member_o @ X2 @ I )
% 4.69/5.00 => ( ( F @ X2 )
% 4.69/5.00 = C ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_eq_iff
% 4.69/5.00 thf(fact_4901_INF__eq__iff,axiom,
% 4.69/5.00 ! [I: set_nat,F: nat > filter_nat,C: filter_nat] :
% 4.69/5.00 ( ( I != bot_bot_set_nat )
% 4.69/5.00 => ( ! [I3: nat] :
% 4.69/5.00 ( ( member_nat @ I3 @ I )
% 4.69/5.00 => ( ord_le2510731241096832064er_nat @ ( F @ I3 ) @ C ) )
% 4.69/5.00 => ( ( ( comple6612786467464916249er_nat @ ( image_nat_filter_nat @ F @ I ) )
% 4.69/5.00 = C )
% 4.69/5.00 = ( ! [X2: nat] :
% 4.69/5.00 ( ( member_nat @ X2 @ I )
% 4.69/5.00 => ( ( F @ X2 )
% 4.69/5.00 = C ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_eq_iff
% 4.69/5.00 thf(fact_4902_INF__eq__iff,axiom,
% 4.69/5.00 ! [I: set_int,F: int > filter_nat,C: filter_nat] :
% 4.69/5.00 ( ( I != bot_bot_set_int )
% 4.69/5.00 => ( ! [I3: int] :
% 4.69/5.00 ( ( member_int @ I3 @ I )
% 4.69/5.00 => ( ord_le2510731241096832064er_nat @ ( F @ I3 ) @ C ) )
% 4.69/5.00 => ( ( ( comple6612786467464916249er_nat @ ( image_int_filter_nat @ F @ I ) )
% 4.69/5.00 = C )
% 4.69/5.00 = ( ! [X2: int] :
% 4.69/5.00 ( ( member_int @ X2 @ I )
% 4.69/5.00 => ( ( F @ X2 )
% 4.69/5.00 = C ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_eq_iff
% 4.69/5.00 thf(fact_4903_INF__eq__iff,axiom,
% 4.69/5.00 ! [I: set_Product_unit,F: product_unit > set_nat,C: set_nat] :
% 4.69/5.00 ( ( I != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ! [I3: product_unit] :
% 4.69/5.00 ( ( member_Product_unit @ I3 @ I )
% 4.69/5.00 => ( ord_less_eq_set_nat @ ( F @ I3 ) @ C ) )
% 4.69/5.00 => ( ( ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ I ) )
% 4.69/5.00 = C )
% 4.69/5.00 = ( ! [X2: product_unit] :
% 4.69/5.00 ( ( member_Product_unit @ X2 @ I )
% 4.69/5.00 => ( ( F @ X2 )
% 4.69/5.00 = C ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_eq_iff
% 4.69/5.00 thf(fact_4904_INF__eq__iff,axiom,
% 4.69/5.00 ! [I: set_o,F: $o > set_nat,C: set_nat] :
% 4.69/5.00 ( ( I != bot_bot_set_o )
% 4.69/5.00 => ( ! [I3: $o] :
% 4.69/5.00 ( ( member_o @ I3 @ I )
% 4.69/5.00 => ( ord_less_eq_set_nat @ ( F @ I3 ) @ C ) )
% 4.69/5.00 => ( ( ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ I ) )
% 4.69/5.00 = C )
% 4.69/5.00 = ( ! [X2: $o] :
% 4.69/5.00 ( ( member_o @ X2 @ I )
% 4.69/5.00 => ( ( F @ X2 )
% 4.69/5.00 = C ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_eq_iff
% 4.69/5.00 thf(fact_4905_finite__less__Inf__iff,axiom,
% 4.69/5.00 ! [X4: set_int,A2: int] :
% 4.69/5.00 ( ( finite_finite_int @ X4 )
% 4.69/5.00 => ( ( X4 != bot_bot_set_int )
% 4.69/5.00 => ( ( ord_less_int @ A2 @ ( complete_Inf_Inf_int @ X4 ) )
% 4.69/5.00 = ( ! [X2: int] :
% 4.69/5.00 ( ( member_int @ X2 @ X4 )
% 4.69/5.00 => ( ord_less_int @ A2 @ X2 ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % finite_less_Inf_iff
% 4.69/5.00 thf(fact_4906_finite__less__Inf__iff,axiom,
% 4.69/5.00 ! [X4: set_nat,A2: nat] :
% 4.69/5.00 ( ( finite_finite_nat @ X4 )
% 4.69/5.00 => ( ( X4 != bot_bot_set_nat )
% 4.69/5.00 => ( ( ord_less_nat @ A2 @ ( complete_Inf_Inf_nat @ X4 ) )
% 4.69/5.00 = ( ! [X2: nat] :
% 4.69/5.00 ( ( member_nat @ X2 @ X4 )
% 4.69/5.00 => ( ord_less_nat @ A2 @ X2 ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % finite_less_Inf_iff
% 4.69/5.00 thf(fact_4907_finite__less__Inf__iff,axiom,
% 4.69/5.00 ! [X4: set_Product_unit,A2: product_unit] :
% 4.69/5.00 ( ( finite4290736615968046902t_unit @ X4 )
% 4.69/5.00 => ( ( X4 != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ( ord_le361264281704409273t_unit @ A2 @ ( comple2584293577114468500t_unit @ X4 ) )
% 4.69/5.00 = ( ! [X2: product_unit] :
% 4.69/5.00 ( ( member_Product_unit @ X2 @ X4 )
% 4.69/5.00 => ( ord_le361264281704409273t_unit @ A2 @ X2 ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % finite_less_Inf_iff
% 4.69/5.00 thf(fact_4908_Inf__le__Sup,axiom,
% 4.69/5.00 ! [A: set_o] :
% 4.69/5.00 ( ( A != bot_bot_set_o )
% 4.69/5.00 => ( ord_less_eq_o @ ( complete_Inf_Inf_o @ A ) @ ( complete_Sup_Sup_o @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_le_Sup
% 4.69/5.00 thf(fact_4909_Inf__le__Sup,axiom,
% 4.69/5.00 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/5.00 ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/5.00 => ( ord_le729326519192465773_nat_o @ ( comple90455603224345172_nat_o @ A ) @ ( comple4225350640907012154_nat_o @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_le_Sup
% 4.69/5.00 thf(fact_4910_Inf__le__Sup,axiom,
% 4.69/5.00 ! [A: set_filter_nat] :
% 4.69/5.00 ( ( A != bot_bo498966703094740906er_nat )
% 4.69/5.00 => ( ord_le2510731241096832064er_nat @ ( comple6612786467464916249er_nat @ A ) @ ( comple2454491259644266675er_nat @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_le_Sup
% 4.69/5.00 thf(fact_4911_Inf__le__Sup,axiom,
% 4.69/5.00 ! [A: set_set_nat] :
% 4.69/5.00 ( ( A != bot_bot_set_set_nat )
% 4.69/5.00 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ A ) @ ( comple7399068483239264473et_nat @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_le_Sup
% 4.69/5.00 thf(fact_4912_Inf__le__Sup,axiom,
% 4.69/5.00 ! [A: set_Product_unit] :
% 4.69/5.00 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ A ) @ ( comple4687483117567863418t_unit @ A ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_le_Sup
% 4.69/5.00 thf(fact_4913_finite__Inf__in,axiom,
% 4.69/5.00 ! [A: set_o] :
% 4.69/5.00 ( ( finite_finite_o @ A )
% 4.69/5.00 => ( ( A != bot_bot_set_o )
% 4.69/5.00 => ( ! [X3: $o,Y2: $o] :
% 4.69/5.00 ( ( member_o @ X3 @ A )
% 4.69/5.00 => ( ( member_o @ Y2 @ A )
% 4.69/5.00 => ( member_o @ ( inf_inf_o @ X3 @ Y2 ) @ A ) ) )
% 4.69/5.00 => ( member_o @ ( complete_Inf_Inf_o @ A ) @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % finite_Inf_in
% 4.69/5.00 thf(fact_4914_finite__Inf__in,axiom,
% 4.69/5.00 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/5.00 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/5.00 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/5.00 => ( ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ( member6576561426505652726_nat_o @ X3 @ A )
% 4.69/5.00 => ( ( member6576561426505652726_nat_o @ Y2 @ A )
% 4.69/5.00 => ( member6576561426505652726_nat_o @ ( inf_in1318976480646536635_nat_o @ X3 @ Y2 ) @ A ) ) )
% 4.69/5.00 => ( member6576561426505652726_nat_o @ ( comple90455603224345172_nat_o @ A ) @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % finite_Inf_in
% 4.69/5.00 thf(fact_4915_finite__Inf__in,axiom,
% 4.69/5.00 ! [A: set_set_nat] :
% 4.69/5.00 ( ( finite1152437895449049373et_nat @ A )
% 4.69/5.00 => ( ( A != bot_bot_set_set_nat )
% 4.69/5.00 => ( ! [X3: set_nat,Y2: set_nat] :
% 4.69/5.00 ( ( member_set_nat @ X3 @ A )
% 4.69/5.00 => ( ( member_set_nat @ Y2 @ A )
% 4.69/5.00 => ( member_set_nat @ ( inf_inf_set_nat @ X3 @ Y2 ) @ A ) ) )
% 4.69/5.00 => ( member_set_nat @ ( comple7806235888213564991et_nat @ A ) @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % finite_Inf_in
% 4.69/5.00 thf(fact_4916_finite__Inf__in,axiom,
% 4.69/5.00 ! [A: set_Product_unit] :
% 4.69/5.00 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.00 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ! [X3: product_unit,Y2: product_unit] :
% 4.69/5.00 ( ( member_Product_unit @ X3 @ A )
% 4.69/5.00 => ( ( member_Product_unit @ Y2 @ A )
% 4.69/5.00 => ( member_Product_unit @ ( inf_inf_Product_unit @ X3 @ Y2 ) @ A ) ) )
% 4.69/5.00 => ( member_Product_unit @ ( comple2584293577114468500t_unit @ A ) @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % finite_Inf_in
% 4.69/5.00 thf(fact_4917_card__1__singletonI,axiom,
% 4.69/5.00 ! [S: set_Code_integer,X: code_integer] :
% 4.69/5.00 ( ( finite6017078050557962740nteger @ S )
% 4.69/5.00 => ( ( ( finite4902975817058060853nteger @ S )
% 4.69/5.00 = one_one_nat )
% 4.69/5.00 => ( ( member_Code_integer @ X @ S )
% 4.69/5.00 => ( S
% 4.69/5.00 = ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_1_singletonI
% 4.69/5.00 thf(fact_4918_card__1__singletonI,axiom,
% 4.69/5.00 ! [S: set_Product_unit,X: product_unit] :
% 4.69/5.00 ( ( finite4290736615968046902t_unit @ S )
% 4.69/5.00 => ( ( ( finite410649719033368117t_unit @ S )
% 4.69/5.00 = one_one_nat )
% 4.69/5.00 => ( ( member_Product_unit @ X @ S )
% 4.69/5.00 => ( S
% 4.69/5.00 = ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_1_singletonI
% 4.69/5.00 thf(fact_4919_card__1__singletonI,axiom,
% 4.69/5.00 ! [S: set_o,X: $o] :
% 4.69/5.00 ( ( finite_finite_o @ S )
% 4.69/5.00 => ( ( ( finite_card_o @ S )
% 4.69/5.00 = one_one_nat )
% 4.69/5.00 => ( ( member_o @ X @ S )
% 4.69/5.00 => ( S
% 4.69/5.00 = ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_1_singletonI
% 4.69/5.00 thf(fact_4920_card__1__singletonI,axiom,
% 4.69/5.00 ! [S: set_nat,X: nat] :
% 4.69/5.00 ( ( finite_finite_nat @ S )
% 4.69/5.00 => ( ( ( finite_card_nat @ S )
% 4.69/5.00 = one_one_nat )
% 4.69/5.00 => ( ( member_nat @ X @ S )
% 4.69/5.00 => ( S
% 4.69/5.00 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_1_singletonI
% 4.69/5.00 thf(fact_4921_card__1__singletonI,axiom,
% 4.69/5.00 ! [S: set_int,X: int] :
% 4.69/5.00 ( ( finite_finite_int @ S )
% 4.69/5.00 => ( ( ( finite_card_int @ S )
% 4.69/5.00 = one_one_nat )
% 4.69/5.00 => ( ( member_int @ X @ S )
% 4.69/5.00 => ( S
% 4.69/5.00 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_1_singletonI
% 4.69/5.00 thf(fact_4922_card__1__singletonI,axiom,
% 4.69/5.00 ! [S: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ( finite3252695134891459830_nat_o @ S )
% 4.69/5.00 => ( ( ( finite1363419556375932405_nat_o @ S )
% 4.69/5.00 = one_one_nat )
% 4.69/5.00 => ( ( member6576561426505652726_nat_o @ X @ S )
% 4.69/5.00 => ( S
% 4.69/5.00 = ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_1_singletonI
% 4.69/5.00 thf(fact_4923_card__Diff__singleton__if,axiom,
% 4.69/5.00 ! [X: product_unit,A: set_Product_unit] :
% 4.69/5.00 ( ( ( member_Product_unit @ X @ A )
% 4.69/5.00 => ( ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/5.00 = ( minus_minus_nat @ ( finite410649719033368117t_unit @ A ) @ one_one_nat ) ) )
% 4.69/5.00 & ( ~ ( member_Product_unit @ X @ A )
% 4.69/5.00 => ( ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/5.00 = ( finite410649719033368117t_unit @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff_singleton_if
% 4.69/5.00 thf(fact_4924_card__Diff__singleton__if,axiom,
% 4.69/5.00 ! [X: $o,A: set_o] :
% 4.69/5.00 ( ( ( member_o @ X @ A )
% 4.69/5.00 => ( ( finite_card_o @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) )
% 4.69/5.00 = ( minus_minus_nat @ ( finite_card_o @ A ) @ one_one_nat ) ) )
% 4.69/5.00 & ( ~ ( member_o @ X @ A )
% 4.69/5.00 => ( ( finite_card_o @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) )
% 4.69/5.00 = ( finite_card_o @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff_singleton_if
% 4.69/5.00 thf(fact_4925_card__Diff__singleton__if,axiom,
% 4.69/5.00 ! [X: int,A: set_int] :
% 4.69/5.00 ( ( ( member_int @ X @ A )
% 4.69/5.00 => ( ( finite_card_int @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) )
% 4.69/5.00 = ( minus_minus_nat @ ( finite_card_int @ A ) @ one_one_nat ) ) )
% 4.69/5.00 & ( ~ ( member_int @ X @ A )
% 4.69/5.00 => ( ( finite_card_int @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) )
% 4.69/5.00 = ( finite_card_int @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff_singleton_if
% 4.69/5.00 thf(fact_4926_card__Diff__singleton__if,axiom,
% 4.69/5.00 ! [X: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/5.00 ( ( ( member6576561426505652726_nat_o @ X @ A )
% 4.69/5.00 => ( ( finite1363419556375932405_nat_o @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/5.00 = ( minus_minus_nat @ ( finite1363419556375932405_nat_o @ A ) @ one_one_nat ) ) )
% 4.69/5.00 & ( ~ ( member6576561426505652726_nat_o @ X @ A )
% 4.69/5.00 => ( ( finite1363419556375932405_nat_o @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/5.00 = ( finite1363419556375932405_nat_o @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff_singleton_if
% 4.69/5.00 thf(fact_4927_card__Diff__singleton__if,axiom,
% 4.69/5.00 ! [X: nat,A: set_nat] :
% 4.69/5.00 ( ( ( member_nat @ X @ A )
% 4.69/5.00 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 4.69/5.00 = ( minus_minus_nat @ ( finite_card_nat @ A ) @ one_one_nat ) ) )
% 4.69/5.00 & ( ~ ( member_nat @ X @ A )
% 4.69/5.00 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 4.69/5.00 = ( finite_card_nat @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff_singleton_if
% 4.69/5.00 thf(fact_4928_card__Diff__singleton,axiom,
% 4.69/5.00 ! [X: product_unit,A: set_Product_unit] :
% 4.69/5.00 ( ( member_Product_unit @ X @ A )
% 4.69/5.00 => ( ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/5.00 = ( minus_minus_nat @ ( finite410649719033368117t_unit @ A ) @ one_one_nat ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff_singleton
% 4.69/5.00 thf(fact_4929_card__Diff__singleton,axiom,
% 4.69/5.00 ! [X: $o,A: set_o] :
% 4.69/5.00 ( ( member_o @ X @ A )
% 4.69/5.00 => ( ( finite_card_o @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) )
% 4.69/5.00 = ( minus_minus_nat @ ( finite_card_o @ A ) @ one_one_nat ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff_singleton
% 4.69/5.00 thf(fact_4930_card__Diff__singleton,axiom,
% 4.69/5.00 ! [X: int,A: set_int] :
% 4.69/5.00 ( ( member_int @ X @ A )
% 4.69/5.00 => ( ( finite_card_int @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) )
% 4.69/5.00 = ( minus_minus_nat @ ( finite_card_int @ A ) @ one_one_nat ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff_singleton
% 4.69/5.00 thf(fact_4931_card__Diff__singleton,axiom,
% 4.69/5.00 ! [X: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/5.00 ( ( member6576561426505652726_nat_o @ X @ A )
% 4.69/5.00 => ( ( finite1363419556375932405_nat_o @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/5.00 = ( minus_minus_nat @ ( finite1363419556375932405_nat_o @ A ) @ one_one_nat ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff_singleton
% 4.69/5.00 thf(fact_4932_card__Diff__singleton,axiom,
% 4.69/5.00 ! [X: nat,A: set_nat] :
% 4.69/5.00 ( ( member_nat @ X @ A )
% 4.69/5.00 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 4.69/5.00 = ( minus_minus_nat @ ( finite_card_nat @ A ) @ one_one_nat ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff_singleton
% 4.69/5.00 thf(fact_4933_fst__image__mp,axiom,
% 4.69/5.00 ! [A: set_Pr3948176798113811640et_nat,B4: set_he8644174446132254637t_unit,X: heap_e7401611519738050253t_unit,Y: set_nat] :
% 4.69/5.00 ( ( ord_le4903435234951335757t_unit @ ( image_6824039242672219652t_unit @ produc1824681642469235216et_nat @ A ) @ B4 )
% 4.69/5.00 => ( ( member6260224972018164377et_nat @ ( produc7507926704131184380et_nat @ X @ Y ) @ A )
% 4.69/5.00 => ( member242389114213480694t_unit @ X @ B4 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % fst_image_mp
% 4.69/5.00 thf(fact_4934_fst__image__mp,axiom,
% 4.69/5.00 ! [A: set_Pr3286484037609594932et_nat,B4: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( ord_le2965882846123202637_nat_o @ ( image_6802380912191114376_nat_o @ produc995936583742144908et_nat @ A ) @ B4 )
% 4.69/5.00 => ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) @ A )
% 4.69/5.00 => ( member6576561426505652726_nat_o @ X @ B4 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % fst_image_mp
% 4.69/5.00 thf(fact_4935_fst__image__mp,axiom,
% 4.69/5.00 ! [A: set_Pr8536935166611901872et_nat,B4: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 4.69/5.00 ( ( ord_le2965882846123202637_nat_o @ ( image_2517677226577294348_nat_o @ produc180342877477747464et_nat @ A ) @ B4 )
% 4.69/5.00 => ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) @ A )
% 4.69/5.00 => ( member6576561426505652726_nat_o @ X @ B4 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % fst_image_mp
% 4.69/5.00 thf(fact_4936_fst__image__mp,axiom,
% 4.69/5.00 ! [A: set_Pr958786334691620121nt_int,B4: set_int,X: int,Y: int] :
% 4.69/5.00 ( ( ord_less_eq_set_int @ ( image_5042161079198086560nt_int @ product_fst_int_int @ A ) @ B4 )
% 4.69/5.00 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ A )
% 4.69/5.00 => ( member_int @ X @ B4 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % fst_image_mp
% 4.69/5.00 thf(fact_4937_fst__image__mp,axiom,
% 4.69/5.00 ! [A: set_Pr1261947904930325089at_nat,B4: set_nat,X: nat,Y: nat] :
% 4.69/5.00 ( ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ product_fst_nat_nat @ A ) @ B4 )
% 4.69/5.00 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ A )
% 4.69/5.00 => ( member_nat @ X @ B4 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % fst_image_mp
% 4.69/5.00 thf(fact_4938_fst__in__Field,axiom,
% 4.69/5.00 ! [R3: set_Pr958786334691620121nt_int] : ( ord_less_eq_set_int @ ( image_5042161079198086560nt_int @ product_fst_int_int @ R3 ) @ ( field_int @ R3 ) ) ).
% 4.69/5.00
% 4.69/5.00 % fst_in_Field
% 4.69/5.00 thf(fact_4939_fst__in__Field,axiom,
% 4.69/5.00 ! [R3: set_Pr1261947904930325089at_nat] : ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ product_fst_nat_nat @ R3 ) @ ( field_nat @ R3 ) ) ).
% 4.69/5.00
% 4.69/5.00 % fst_in_Field
% 4.69/5.00 thf(fact_4940_Inf__fin__Inf,axiom,
% 4.69/5.00 ! [A: set_o] :
% 4.69/5.00 ( ( finite_finite_o @ A )
% 4.69/5.00 => ( ( A != bot_bot_set_o )
% 4.69/5.00 => ( ( lattic4107685809792843317_fin_o @ A )
% 4.69/5.00 = ( complete_Inf_Inf_o @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_fin_Inf
% 4.69/5.00 thf(fact_4941_Inf__fin__Inf,axiom,
% 4.69/5.00 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/5.00 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/5.00 => ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/5.00 => ( ( lattic956194824204696298_nat_o @ A )
% 4.69/5.00 = ( comple90455603224345172_nat_o @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_fin_Inf
% 4.69/5.00 thf(fact_4942_Inf__fin__Inf,axiom,
% 4.69/5.00 ! [A: set_set_nat] :
% 4.69/5.00 ( ( finite1152437895449049373et_nat @ A )
% 4.69/5.00 => ( ( A != bot_bot_set_set_nat )
% 4.69/5.00 => ( ( lattic3014633134055518761et_nat @ A )
% 4.69/5.00 = ( comple7806235888213564991et_nat @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_fin_Inf
% 4.69/5.00 thf(fact_4943_Inf__fin__Inf,axiom,
% 4.69/5.00 ! [A: set_Product_unit] :
% 4.69/5.00 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.00 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ( lattic1263872656861969706t_unit @ A )
% 4.69/5.00 = ( comple2584293577114468500t_unit @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_fin_Inf
% 4.69/5.00 thf(fact_4944_cInf__eq__Inf__fin,axiom,
% 4.69/5.00 ! [X4: set_o] :
% 4.69/5.00 ( ( finite_finite_o @ X4 )
% 4.69/5.00 => ( ( X4 != bot_bot_set_o )
% 4.69/5.00 => ( ( complete_Inf_Inf_o @ X4 )
% 4.69/5.00 = ( lattic4107685809792843317_fin_o @ X4 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_eq_Inf_fin
% 4.69/5.00 thf(fact_4945_cInf__eq__Inf__fin,axiom,
% 4.69/5.00 ! [X4: set_int] :
% 4.69/5.00 ( ( finite_finite_int @ X4 )
% 4.69/5.00 => ( ( X4 != bot_bot_set_int )
% 4.69/5.00 => ( ( complete_Inf_Inf_int @ X4 )
% 4.69/5.00 = ( lattic5235898064620869839in_int @ X4 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_eq_Inf_fin
% 4.69/5.00 thf(fact_4946_cInf__eq__Inf__fin,axiom,
% 4.69/5.00 ! [X4: set_Pr4532377907799695533_nat_o] :
% 4.69/5.00 ( ( finite3252695134891459830_nat_o @ X4 )
% 4.69/5.00 => ( ( X4 != bot_bo7824918357723582233_nat_o )
% 4.69/5.00 => ( ( comple90455603224345172_nat_o @ X4 )
% 4.69/5.00 = ( lattic956194824204696298_nat_o @ X4 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_eq_Inf_fin
% 4.69/5.00 thf(fact_4947_cInf__eq__Inf__fin,axiom,
% 4.69/5.00 ! [X4: set_nat] :
% 4.69/5.00 ( ( finite_finite_nat @ X4 )
% 4.69/5.00 => ( ( X4 != bot_bot_set_nat )
% 4.69/5.00 => ( ( complete_Inf_Inf_nat @ X4 )
% 4.69/5.00 = ( lattic5238388535129920115in_nat @ X4 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_eq_Inf_fin
% 4.69/5.00 thf(fact_4948_cInf__eq__Inf__fin,axiom,
% 4.69/5.00 ! [X4: set_set_nat] :
% 4.69/5.00 ( ( finite1152437895449049373et_nat @ X4 )
% 4.69/5.00 => ( ( X4 != bot_bot_set_set_nat )
% 4.69/5.00 => ( ( comple7806235888213564991et_nat @ X4 )
% 4.69/5.00 = ( lattic3014633134055518761et_nat @ X4 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_eq_Inf_fin
% 4.69/5.00 thf(fact_4949_cInf__eq__Inf__fin,axiom,
% 4.69/5.00 ! [X4: set_Product_unit] :
% 4.69/5.00 ( ( finite4290736615968046902t_unit @ X4 )
% 4.69/5.00 => ( ( X4 != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ( comple2584293577114468500t_unit @ X4 )
% 4.69/5.00 = ( lattic1263872656861969706t_unit @ X4 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % cInf_eq_Inf_fin
% 4.69/5.00 thf(fact_4950_prod__set__defs_I1_J,axiom,
% 4.69/5.00 ( basic_fsts_int_int
% 4.69/5.00 = ( ^ [P5: product_prod_int_int] : ( insert_int @ ( product_fst_int_int @ P5 ) @ bot_bot_set_int ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod_set_defs(1)
% 4.69/5.00 thf(fact_4951_prod_Oswap__def,axiom,
% 4.69/5.00 ( produc1264744871843189710t_unit
% 4.69/5.00 = ( ^ [P5: produc7348995623955488188t_unit] : ( produc7507926704131184380et_nat @ ( produc3550216979005444800t_unit @ P5 ) @ ( produc6012101397789842562t_unit @ P5 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod.swap_def
% 4.69/5.00 thf(fact_4952_prod_Oswap__def,axiom,
% 4.69/5.00 ( product_swap_nat_nat
% 4.69/5.00 = ( ^ [P5: product_prod_nat_nat] : ( product_Pair_nat_nat @ ( product_snd_nat_nat @ P5 ) @ ( product_fst_nat_nat @ P5 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod.swap_def
% 4.69/5.00 thf(fact_4953_prod_Oswap__def,axiom,
% 4.69/5.00 ( produc1078497009909708626_nat_o
% 4.69/5.00 = ( ^ [P5: produc6907119039986491712_nat_o] : ( produc5001842942810119800et_nat @ ( produc1838968430882301508_nat_o @ P5 ) @ ( produc8046704426453032966_nat_o @ P5 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod.swap_def
% 4.69/5.00 thf(fact_4954_prod_Oswap__def,axiom,
% 4.69/5.00 ( produc2580581461503396054_nat_o
% 4.69/5.00 = ( ^ [P5: produc4962441903510821572_nat_o] : ( produc2245416461498447860et_nat @ ( produc6803565743942592456_nat_o @ P5 ) @ ( produc1609452848092598666_nat_o @ P5 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod.swap_def
% 4.69/5.00 thf(fact_4955_prod_Oswap__def,axiom,
% 4.69/5.00 ( produc6300697153377358172et_nat
% 4.69/5.00 = ( ^ [P5: produc3658429121746597890et_nat] : ( produc2471974422597015918t_unit @ ( produc8586169260539613262et_nat @ P5 ) @ ( produc1824681642469235216et_nat @ P5 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod.swap_def
% 4.69/5.00 thf(fact_4956_prod_Oswap__def,axiom,
% 4.69/5.00 ( product_swap_int_int
% 4.69/5.00 = ( ^ [P5: product_prod_int_int] : ( product_Pair_int_int @ ( product_snd_int_int @ P5 ) @ ( product_fst_int_int @ P5 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % prod.swap_def
% 4.69/5.00 thf(fact_4957_equiv__proj,axiom,
% 4.69/5.00 ! [A: set_int,R3: set_Pr958786334691620121nt_int,Z: product_prod_int_int] :
% 4.69/5.00 ( ( equiv_equiv_int @ A @ R3 )
% 4.69/5.00 => ( ( member5262025264175285858nt_int @ Z @ R3 )
% 4.69/5.00 => ( ( comp_i5103216804979976198nt_int @ ( equiv_proj_int_int @ R3 ) @ product_fst_int_int @ Z )
% 4.69/5.00 = ( comp_i5103216804979976198nt_int @ ( equiv_proj_int_int @ R3 ) @ product_snd_int_int @ Z ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % equiv_proj
% 4.69/5.00 thf(fact_4958_INF__le__SUP,axiom,
% 4.69/5.00 ! [A: set_Product_unit,F: product_unit > product_unit] :
% 4.69/5.00 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A ) ) @ ( comple4687483117567863418t_unit @ ( image_405062704495631173t_unit @ F @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_le_SUP
% 4.69/5.00 thf(fact_4959_INF__le__SUP,axiom,
% 4.69/5.00 ! [A: set_o,F: $o > product_unit] :
% 4.69/5.00 ( ( A != bot_bot_set_o )
% 4.69/5.00 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit2 @ F @ A ) ) @ ( comple4687483117567863418t_unit @ ( image_o_Product_unit2 @ F @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_le_SUP
% 4.69/5.00 thf(fact_4960_INF__le__SUP,axiom,
% 4.69/5.00 ! [A: set_nat,F: nat > product_unit] :
% 4.69/5.00 ( ( A != bot_bot_set_nat )
% 4.69/5.00 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A ) ) @ ( comple4687483117567863418t_unit @ ( image_8730104196221521654t_unit @ F @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_le_SUP
% 4.69/5.00 thf(fact_4961_INF__le__SUP,axiom,
% 4.69/5.00 ! [A: set_int,F: int > product_unit] :
% 4.69/5.00 ( ( A != bot_bot_set_int )
% 4.69/5.00 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A ) ) @ ( comple4687483117567863418t_unit @ ( image_5846526143423701914t_unit @ F @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_le_SUP
% 4.69/5.00 thf(fact_4962_INF__le__SUP,axiom,
% 4.69/5.00 ! [A: set_Product_unit,F: product_unit > filter_nat] :
% 4.69/5.00 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ord_le2510731241096832064er_nat @ ( comple6612786467464916249er_nat @ ( image_1853478764106424488er_nat @ F @ A ) ) @ ( comple2454491259644266675er_nat @ ( image_1853478764106424488er_nat @ F @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_le_SUP
% 4.69/5.00 thf(fact_4963_INF__le__SUP,axiom,
% 4.69/5.00 ! [A: set_o,F: $o > filter_nat] :
% 4.69/5.00 ( ( A != bot_bot_set_o )
% 4.69/5.00 => ( ord_le2510731241096832064er_nat @ ( comple6612786467464916249er_nat @ ( image_o_filter_nat @ F @ A ) ) @ ( comple2454491259644266675er_nat @ ( image_o_filter_nat @ F @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_le_SUP
% 4.69/5.00 thf(fact_4964_INF__le__SUP,axiom,
% 4.69/5.00 ! [A: set_nat,F: nat > filter_nat] :
% 4.69/5.00 ( ( A != bot_bot_set_nat )
% 4.69/5.00 => ( ord_le2510731241096832064er_nat @ ( comple6612786467464916249er_nat @ ( image_nat_filter_nat @ F @ A ) ) @ ( comple2454491259644266675er_nat @ ( image_nat_filter_nat @ F @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_le_SUP
% 4.69/5.00 thf(fact_4965_INF__le__SUP,axiom,
% 4.69/5.00 ! [A: set_int,F: int > filter_nat] :
% 4.69/5.00 ( ( A != bot_bot_set_int )
% 4.69/5.00 => ( ord_le2510731241096832064er_nat @ ( comple6612786467464916249er_nat @ ( image_int_filter_nat @ F @ A ) ) @ ( comple2454491259644266675er_nat @ ( image_int_filter_nat @ F @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_le_SUP
% 4.69/5.00 thf(fact_4966_INF__le__SUP,axiom,
% 4.69/5.00 ! [A: set_Product_unit,F: product_unit > set_nat] :
% 4.69/5.00 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ A ) ) @ ( comple7399068483239264473et_nat @ ( image_8173849991827986510et_nat @ F @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_le_SUP
% 4.69/5.00 thf(fact_4967_INF__le__SUP,axiom,
% 4.69/5.00 ! [A: set_o,F: $o > set_nat] :
% 4.69/5.00 ( ( A != bot_bot_set_o )
% 4.69/5.00 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A ) ) @ ( comple7399068483239264473et_nat @ ( image_o_set_nat @ F @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % INF_le_SUP
% 4.69/5.00 thf(fact_4968_card__Diff1__le,axiom,
% 4.69/5.00 ! [A: set_Product_unit,X: product_unit] : ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) @ ( finite410649719033368117t_unit @ A ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff1_le
% 4.69/5.00 thf(fact_4969_card__Diff1__le,axiom,
% 4.69/5.00 ! [A: set_o,X: $o] : ( ord_less_eq_nat @ ( finite_card_o @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) @ ( finite_card_o @ A ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff1_le
% 4.69/5.00 thf(fact_4970_card__Diff1__le,axiom,
% 4.69/5.00 ! [A: set_int,X: int] : ( ord_less_eq_nat @ ( finite_card_int @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) ) @ ( finite_card_int @ A ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff1_le
% 4.69/5.00 thf(fact_4971_card__Diff1__le,axiom,
% 4.69/5.00 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] : ( ord_less_eq_nat @ ( finite1363419556375932405_nat_o @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) ) @ ( finite1363419556375932405_nat_o @ A ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff1_le
% 4.69/5.00 thf(fact_4972_card__Diff1__le,axiom,
% 4.69/5.00 ! [A: set_nat,X: nat] : ( ord_less_eq_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) @ ( finite_card_nat @ A ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Diff1_le
% 4.69/5.00 thf(fact_4973_exI__realizer,axiom,
% 4.69/5.00 ! [P: nat > nat > $o,Y: nat,X: nat] :
% 4.69/5.00 ( ( P @ Y @ X )
% 4.69/5.00 => ( P @ ( product_snd_nat_nat @ ( product_Pair_nat_nat @ X @ Y ) ) @ ( product_fst_nat_nat @ ( product_Pair_nat_nat @ X @ Y ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % exI_realizer
% 4.69/5.00 thf(fact_4974_exI__realizer,axiom,
% 4.69/5.00 ! [P: produc3658429121746597890et_nat > ( produc3658429121746597890et_nat > $o ) > $o,Y: produc3658429121746597890et_nat,X: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ( P @ Y @ X )
% 4.69/5.00 => ( P @ ( produc4011572625026189258et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) ) @ ( produc995936583742144908et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % exI_realizer
% 4.69/5.00 thf(fact_4975_exI__realizer,axiom,
% 4.69/5.00 ! [P: produc3925858234332021118et_nat > ( produc3658429121746597890et_nat > $o ) > $o,Y: produc3925858234332021118et_nat,X: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ( P @ Y @ X )
% 4.69/5.00 => ( P @ ( produc5374455773327741254et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) ) @ ( produc180342877477747464et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % exI_realizer
% 4.69/5.00 thf(fact_4976_exI__realizer,axiom,
% 4.69/5.00 ! [P: set_nat > heap_e7401611519738050253t_unit > $o,Y: set_nat,X: heap_e7401611519738050253t_unit] :
% 4.69/5.00 ( ( P @ Y @ X )
% 4.69/5.00 => ( P @ ( produc8586169260539613262et_nat @ ( produc7507926704131184380et_nat @ X @ Y ) ) @ ( produc1824681642469235216et_nat @ ( produc7507926704131184380et_nat @ X @ Y ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % exI_realizer
% 4.69/5.00 thf(fact_4977_exI__realizer,axiom,
% 4.69/5.00 ! [P: int > int > $o,Y: int,X: int] :
% 4.69/5.00 ( ( P @ Y @ X )
% 4.69/5.00 => ( P @ ( product_snd_int_int @ ( product_Pair_int_int @ X @ Y ) ) @ ( product_fst_int_int @ ( product_Pair_int_int @ X @ Y ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % exI_realizer
% 4.69/5.00 thf(fact_4978_conjI__realizer,axiom,
% 4.69/5.00 ! [P: nat > $o,P3: nat,Q2: nat > $o,Q4: nat] :
% 4.69/5.00 ( ( P @ P3 )
% 4.69/5.00 => ( ( Q2 @ Q4 )
% 4.69/5.00 => ( ( P @ ( product_fst_nat_nat @ ( product_Pair_nat_nat @ P3 @ Q4 ) ) )
% 4.69/5.00 & ( Q2 @ ( product_snd_nat_nat @ ( product_Pair_nat_nat @ P3 @ Q4 ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % conjI_realizer
% 4.69/5.00 thf(fact_4979_conjI__realizer,axiom,
% 4.69/5.00 ! [P: ( produc3658429121746597890et_nat > $o ) > $o,P3: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o,Q4: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( P @ P3 )
% 4.69/5.00 => ( ( Q2 @ Q4 )
% 4.69/5.00 => ( ( P @ ( produc995936583742144908et_nat @ ( produc5001842942810119800et_nat @ P3 @ Q4 ) ) )
% 4.69/5.00 & ( Q2 @ ( produc4011572625026189258et_nat @ ( produc5001842942810119800et_nat @ P3 @ Q4 ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % conjI_realizer
% 4.69/5.00 thf(fact_4980_conjI__realizer,axiom,
% 4.69/5.00 ! [P: ( produc3658429121746597890et_nat > $o ) > $o,P3: produc3658429121746597890et_nat > $o,Q2: produc3925858234332021118et_nat > $o,Q4: produc3925858234332021118et_nat] :
% 4.69/5.00 ( ( P @ P3 )
% 4.69/5.00 => ( ( Q2 @ Q4 )
% 4.69/5.00 => ( ( P @ ( produc180342877477747464et_nat @ ( produc2245416461498447860et_nat @ P3 @ Q4 ) ) )
% 4.69/5.00 & ( Q2 @ ( produc5374455773327741254et_nat @ ( produc2245416461498447860et_nat @ P3 @ Q4 ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % conjI_realizer
% 4.69/5.00 thf(fact_4981_conjI__realizer,axiom,
% 4.69/5.00 ! [P: heap_e7401611519738050253t_unit > $o,P3: heap_e7401611519738050253t_unit,Q2: set_nat > $o,Q4: set_nat] :
% 4.69/5.00 ( ( P @ P3 )
% 4.69/5.00 => ( ( Q2 @ Q4 )
% 4.69/5.00 => ( ( P @ ( produc1824681642469235216et_nat @ ( produc7507926704131184380et_nat @ P3 @ Q4 ) ) )
% 4.69/5.00 & ( Q2 @ ( produc8586169260539613262et_nat @ ( produc7507926704131184380et_nat @ P3 @ Q4 ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % conjI_realizer
% 4.69/5.00 thf(fact_4982_conjI__realizer,axiom,
% 4.69/5.00 ! [P: int > $o,P3: int,Q2: int > $o,Q4: int] :
% 4.69/5.00 ( ( P @ P3 )
% 4.69/5.00 => ( ( Q2 @ Q4 )
% 4.69/5.00 => ( ( P @ ( product_fst_int_int @ ( product_Pair_int_int @ P3 @ Q4 ) ) )
% 4.69/5.00 & ( Q2 @ ( product_snd_int_int @ ( product_Pair_int_int @ P3 @ Q4 ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % conjI_realizer
% 4.69/5.00 thf(fact_4983_apfst__convE,axiom,
% 4.69/5.00 ! [Q4: produc3658429121746597890et_nat,F: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit,P3: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( Q4
% 4.69/5.00 = ( produc4172003873565521026et_nat @ F @ P3 ) )
% 4.69/5.00 => ~ ! [X3: heap_e7401611519738050253t_unit,Y2: set_nat] :
% 4.69/5.00 ( ( P3
% 4.69/5.00 = ( produc7507926704131184380et_nat @ X3 @ Y2 ) )
% 4.69/5.00 => ( Q4
% 4.69/5.00 != ( produc7507926704131184380et_nat @ ( F @ X3 ) @ Y2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apfst_convE
% 4.69/5.00 thf(fact_4984_apfst__convE,axiom,
% 4.69/5.00 ! [Q4: product_prod_nat_nat,F: nat > nat,P3: product_prod_nat_nat] :
% 4.69/5.00 ( ( Q4
% 4.69/5.00 = ( produc986720760941809198at_nat @ F @ P3 ) )
% 4.69/5.00 => ~ ! [X3: nat,Y2: nat] :
% 4.69/5.00 ( ( P3
% 4.69/5.00 = ( product_Pair_nat_nat @ X3 @ Y2 ) )
% 4.69/5.00 => ( Q4
% 4.69/5.00 != ( product_Pair_nat_nat @ ( F @ X3 ) @ Y2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apfst_convE
% 4.69/5.00 thf(fact_4985_apfst__convE,axiom,
% 4.69/5.00 ! [Q4: product_prod_int_int,F: int > int,P3: product_prod_int_int] :
% 4.69/5.00 ( ( Q4
% 4.69/5.00 = ( produc2355237562570658114nt_int @ F @ P3 ) )
% 4.69/5.00 => ~ ! [X3: int,Y2: int] :
% 4.69/5.00 ( ( P3
% 4.69/5.00 = ( product_Pair_int_int @ X3 @ Y2 ) )
% 4.69/5.00 => ( Q4
% 4.69/5.00 != ( product_Pair_int_int @ ( F @ X3 ) @ Y2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apfst_convE
% 4.69/5.00 thf(fact_4986_apfst__convE,axiom,
% 4.69/5.00 ! [Q4: produc3925858234332021118et_nat,F: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,P3: produc3925858234332021118et_nat] :
% 4.69/5.00 ( ( Q4
% 4.69/5.00 = ( produc3198230245617193214et_nat @ F @ P3 ) )
% 4.69/5.00 => ~ ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( P3
% 4.69/5.00 = ( produc5001842942810119800et_nat @ X3 @ Y2 ) )
% 4.69/5.00 => ( Q4
% 4.69/5.00 != ( produc5001842942810119800et_nat @ ( F @ X3 ) @ Y2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apfst_convE
% 4.69/5.00 thf(fact_4987_apfst__convE,axiom,
% 4.69/5.00 ! [Q4: produc2732055786443039994et_nat,F: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,P3: produc2732055786443039994et_nat] :
% 4.69/5.00 ( ( Q4
% 4.69/5.00 = ( produc1442628905706551930et_nat @ F @ P3 ) )
% 4.69/5.00 => ~ ! [X3: produc3658429121746597890et_nat > $o,Y2: produc3925858234332021118et_nat] :
% 4.69/5.00 ( ( P3
% 4.69/5.00 = ( produc2245416461498447860et_nat @ X3 @ Y2 ) )
% 4.69/5.00 => ( Q4
% 4.69/5.00 != ( produc2245416461498447860et_nat @ ( F @ X3 ) @ Y2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % apfst_convE
% 4.69/5.00 thf(fact_4988_exE__realizer_H,axiom,
% 4.69/5.00 ! [P: set_nat > heap_e7401611519738050253t_unit > $o,P3: produc3658429121746597890et_nat] :
% 4.69/5.00 ( ( P @ ( produc8586169260539613262et_nat @ P3 ) @ ( produc1824681642469235216et_nat @ P3 ) )
% 4.69/5.00 => ~ ! [X3: heap_e7401611519738050253t_unit,Y2: set_nat] :
% 4.69/5.00 ~ ( P @ Y2 @ X3 ) ) ).
% 4.69/5.00
% 4.69/5.00 % exE_realizer'
% 4.69/5.00 thf(fact_4989_exE__realizer_H,axiom,
% 4.69/5.00 ! [P: int > int > $o,P3: product_prod_int_int] :
% 4.69/5.00 ( ( P @ ( product_snd_int_int @ P3 ) @ ( product_fst_int_int @ P3 ) )
% 4.69/5.00 => ~ ! [X3: int,Y2: int] :
% 4.69/5.00 ~ ( P @ Y2 @ X3 ) ) ).
% 4.69/5.00
% 4.69/5.00 % exE_realizer'
% 4.69/5.00 thf(fact_4990_snd__sndOp,axiom,
% 4.69/5.00 ! [P: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o,Q2: heap_e7401611519738050253t_unit > set_nat > $o] :
% 4.69/5.00 ( produc8586169260539613262et_nat
% 4.69/5.00 = ( comp_P2930521774885306735et_nat @ produc8586169260539613262et_nat @ ( bNF_sn4039337771197282234et_nat @ P @ Q2 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % snd_sndOp
% 4.69/5.00 thf(fact_4991_snd__sndOp,axiom,
% 4.69/5.00 ! [P: int > int > $o,Q2: int > int > $o] :
% 4.69/5.00 ( product_snd_int_int
% 4.69/5.00 = ( comp_P5356232565778667509nt_int @ product_snd_int_int @ ( bNF_sn1062102010912252026nt_int @ P @ Q2 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % snd_sndOp
% 4.69/5.00 thf(fact_4992_fst__fstOp,axiom,
% 4.69/5.00 ! [P: int > int > $o,Q2: int > int > $o] :
% 4.69/5.00 ( product_fst_int_int
% 4.69/5.00 = ( comp_P5356232565778667509nt_int @ product_fst_int_int @ ( bNF_fs8167890477030535480nt_int @ P @ Q2 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % fst_fstOp
% 4.69/5.00 thf(fact_4993_card__Un__disjoint,axiom,
% 4.69/5.00 ! [A: set_Code_integer,B4: set_Code_integer] :
% 4.69/5.00 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.00 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.00 => ( ( ( inf_in1364745209274528805nteger @ A @ B4 )
% 4.69/5.00 = bot_bo3990330152332043303nteger )
% 4.69/5.00 => ( ( finite4902975817058060853nteger @ ( sup_su848401254843788991nteger @ A @ B4 ) )
% 4.69/5.00 = ( plus_plus_nat @ ( finite4902975817058060853nteger @ A ) @ ( finite4902975817058060853nteger @ B4 ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Un_disjoint
% 4.69/5.00 thf(fact_4994_card__Un__disjoint,axiom,
% 4.69/5.00 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/5.00 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.00 => ( ( finite4290736615968046902t_unit @ B4 )
% 4.69/5.00 => ( ( ( inf_in4660618365625256667t_unit @ A @ B4 )
% 4.69/5.00 = bot_bo3957492148770167129t_unit )
% 4.69/5.00 => ( ( finite410649719033368117t_unit @ ( sup_su793286257634532545t_unit @ A @ B4 ) )
% 4.69/5.00 = ( plus_plus_nat @ ( finite410649719033368117t_unit @ A ) @ ( finite410649719033368117t_unit @ B4 ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Un_disjoint
% 4.69/5.00 thf(fact_4995_card__Un__disjoint,axiom,
% 4.69/5.00 ! [A: set_o,B4: set_o] :
% 4.69/5.00 ( ( finite_finite_o @ A )
% 4.69/5.00 => ( ( finite_finite_o @ B4 )
% 4.69/5.00 => ( ( ( inf_inf_set_o @ A @ B4 )
% 4.69/5.00 = bot_bot_set_o )
% 4.69/5.00 => ( ( finite_card_o @ ( sup_sup_set_o @ A @ B4 ) )
% 4.69/5.00 = ( plus_plus_nat @ ( finite_card_o @ A ) @ ( finite_card_o @ B4 ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Un_disjoint
% 4.69/5.00 thf(fact_4996_card__Un__disjoint,axiom,
% 4.69/5.00 ! [A: set_nat,B4: set_nat] :
% 4.69/5.00 ( ( finite_finite_nat @ A )
% 4.69/5.00 => ( ( finite_finite_nat @ B4 )
% 4.69/5.00 => ( ( ( inf_inf_set_nat @ A @ B4 )
% 4.69/5.00 = bot_bot_set_nat )
% 4.69/5.00 => ( ( finite_card_nat @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/5.00 = ( plus_plus_nat @ ( finite_card_nat @ A ) @ ( finite_card_nat @ B4 ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Un_disjoint
% 4.69/5.00 thf(fact_4997_card__Un__disjoint,axiom,
% 4.69/5.00 ! [A: set_int,B4: set_int] :
% 4.69/5.00 ( ( finite_finite_int @ A )
% 4.69/5.00 => ( ( finite_finite_int @ B4 )
% 4.69/5.00 => ( ( ( inf_inf_set_int @ A @ B4 )
% 4.69/5.00 = bot_bot_set_int )
% 4.69/5.00 => ( ( finite_card_int @ ( sup_sup_set_int @ A @ B4 ) )
% 4.69/5.00 = ( plus_plus_nat @ ( finite_card_int @ A ) @ ( finite_card_int @ B4 ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Un_disjoint
% 4.69/5.00 thf(fact_4998_card__Un__disjoint,axiom,
% 4.69/5.00 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/5.00 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/5.00 => ( ( finite3252695134891459830_nat_o @ B4 )
% 4.69/5.00 => ( ( ( inf_in1906310914598751387_nat_o @ A @ B4 )
% 4.69/5.00 = bot_bo7824918357723582233_nat_o )
% 4.69/5.00 => ( ( finite1363419556375932405_nat_o @ ( sup_su5209123915105501825_nat_o @ A @ B4 ) )
% 4.69/5.00 = ( plus_plus_nat @ ( finite1363419556375932405_nat_o @ A ) @ ( finite1363419556375932405_nat_o @ B4 ) ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Un_disjoint
% 4.69/5.00 thf(fact_4999_card__Suc__Diff1,axiom,
% 4.69/5.00 ! [A: set_Code_integer,X: code_integer] :
% 4.69/5.00 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.00 => ( ( member_Code_integer @ X @ A )
% 4.69/5.00 => ( ( suc @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) )
% 4.69/5.00 = ( finite4902975817058060853nteger @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Suc_Diff1
% 4.69/5.00 thf(fact_5000_card__Suc__Diff1,axiom,
% 4.69/5.00 ! [A: set_Product_unit,X: product_unit] :
% 4.69/5.00 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.00 => ( ( member_Product_unit @ X @ A )
% 4.69/5.00 => ( ( suc @ ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) )
% 4.69/5.00 = ( finite410649719033368117t_unit @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Suc_Diff1
% 4.69/5.00 thf(fact_5001_card__Suc__Diff1,axiom,
% 4.69/5.00 ! [A: set_o,X: $o] :
% 4.69/5.00 ( ( finite_finite_o @ A )
% 4.69/5.00 => ( ( member_o @ X @ A )
% 4.69/5.00 => ( ( suc @ ( finite_card_o @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) )
% 4.69/5.00 = ( finite_card_o @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Suc_Diff1
% 4.69/5.00 thf(fact_5002_card__Suc__Diff1,axiom,
% 4.69/5.00 ! [A: set_int,X: int] :
% 4.69/5.00 ( ( finite_finite_int @ A )
% 4.69/5.00 => ( ( member_int @ X @ A )
% 4.69/5.00 => ( ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) ) )
% 4.69/5.00 = ( finite_card_int @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Suc_Diff1
% 4.69/5.00 thf(fact_5003_card__Suc__Diff1,axiom,
% 4.69/5.00 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/5.00 => ( ( member6576561426505652726_nat_o @ X @ A )
% 4.69/5.00 => ( ( suc @ ( finite1363419556375932405_nat_o @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) ) )
% 4.69/5.00 = ( finite1363419556375932405_nat_o @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Suc_Diff1
% 4.69/5.00 thf(fact_5004_card__Suc__Diff1,axiom,
% 4.69/5.00 ! [A: set_nat,X: nat] :
% 4.69/5.00 ( ( finite_finite_nat @ A )
% 4.69/5.00 => ( ( member_nat @ X @ A )
% 4.69/5.00 => ( ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) )
% 4.69/5.00 = ( finite_card_nat @ A ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_Suc_Diff1
% 4.69/5.00 thf(fact_5005_add__left__cancel,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.00 ( ( ( plus_p5714425477246183910nteger @ A2 @ B )
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ A2 @ C ) )
% 4.69/5.00 = ( B = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_left_cancel
% 4.69/5.00 thf(fact_5006_add__left__cancel,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.00 ( ( ( plus_plus_rat @ A2 @ B )
% 4.69/5.00 = ( plus_plus_rat @ A2 @ C ) )
% 4.69/5.00 = ( B = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_left_cancel
% 4.69/5.00 thf(fact_5007_add__left__cancel,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.00 ( ( ( plus_plus_nat @ A2 @ B )
% 4.69/5.00 = ( plus_plus_nat @ A2 @ C ) )
% 4.69/5.00 = ( B = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_left_cancel
% 4.69/5.00 thf(fact_5008_add__left__cancel,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int] :
% 4.69/5.00 ( ( ( plus_plus_int @ A2 @ B )
% 4.69/5.00 = ( plus_plus_int @ A2 @ C ) )
% 4.69/5.00 = ( B = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_left_cancel
% 4.69/5.00 thf(fact_5009_add__right__cancel,axiom,
% 4.69/5.00 ! [B: code_integer,A2: code_integer,C: code_integer] :
% 4.69/5.00 ( ( ( plus_p5714425477246183910nteger @ B @ A2 )
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ C @ A2 ) )
% 4.69/5.00 = ( B = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_right_cancel
% 4.69/5.00 thf(fact_5010_add__right__cancel,axiom,
% 4.69/5.00 ! [B: rat,A2: rat,C: rat] :
% 4.69/5.00 ( ( ( plus_plus_rat @ B @ A2 )
% 4.69/5.00 = ( plus_plus_rat @ C @ A2 ) )
% 4.69/5.00 = ( B = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_right_cancel
% 4.69/5.00 thf(fact_5011_add__right__cancel,axiom,
% 4.69/5.00 ! [B: nat,A2: nat,C: nat] :
% 4.69/5.00 ( ( ( plus_plus_nat @ B @ A2 )
% 4.69/5.00 = ( plus_plus_nat @ C @ A2 ) )
% 4.69/5.00 = ( B = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_right_cancel
% 4.69/5.00 thf(fact_5012_add__right__cancel,axiom,
% 4.69/5.00 ! [B: int,A2: int,C: int] :
% 4.69/5.00 ( ( ( plus_plus_int @ B @ A2 )
% 4.69/5.00 = ( plus_plus_int @ C @ A2 ) )
% 4.69/5.00 = ( B = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_right_cancel
% 4.69/5.00 thf(fact_5013_add__le__cancel__left,axiom,
% 4.69/5.00 ! [C: code_integer,A2: code_integer,B: code_integer] :
% 4.69/5.00 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ C @ A2 ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 4.69/5.00 = ( ord_le3102999989581377725nteger @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_le_cancel_left
% 4.69/5.00 thf(fact_5014_add__le__cancel__left,axiom,
% 4.69/5.00 ! [C: rat,A2: rat,B: rat] :
% 4.69/5.00 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A2 ) @ ( plus_plus_rat @ C @ B ) )
% 4.69/5.00 = ( ord_less_eq_rat @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_le_cancel_left
% 4.69/5.00 thf(fact_5015_add__le__cancel__left,axiom,
% 4.69/5.00 ! [C: nat,A2: nat,B: nat] :
% 4.69/5.00 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A2 ) @ ( plus_plus_nat @ C @ B ) )
% 4.69/5.00 = ( ord_less_eq_nat @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_le_cancel_left
% 4.69/5.00 thf(fact_5016_add__le__cancel__left,axiom,
% 4.69/5.00 ! [C: int,A2: int,B: int] :
% 4.69/5.00 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A2 ) @ ( plus_plus_int @ C @ B ) )
% 4.69/5.00 = ( ord_less_eq_int @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_le_cancel_left
% 4.69/5.00 thf(fact_5017_add__le__cancel__right,axiom,
% 4.69/5.00 ! [A2: code_integer,C: code_integer,B: code_integer] :
% 4.69/5.00 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 4.69/5.00 = ( ord_le3102999989581377725nteger @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_le_cancel_right
% 4.69/5.00 thf(fact_5018_add__le__cancel__right,axiom,
% 4.69/5.00 ! [A2: rat,C: rat,B: rat] :
% 4.69/5.00 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B @ C ) )
% 4.69/5.00 = ( ord_less_eq_rat @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_le_cancel_right
% 4.69/5.00 thf(fact_5019_add__le__cancel__right,axiom,
% 4.69/5.00 ! [A2: nat,C: nat,B: nat] :
% 4.69/5.00 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B @ C ) )
% 4.69/5.00 = ( ord_less_eq_nat @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_le_cancel_right
% 4.69/5.00 thf(fact_5020_add__le__cancel__right,axiom,
% 4.69/5.00 ! [A2: int,C: int,B: int] :
% 4.69/5.00 ( ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B @ C ) )
% 4.69/5.00 = ( ord_less_eq_int @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_le_cancel_right
% 4.69/5.00 thf(fact_5021_add__less__cancel__left,axiom,
% 4.69/5.00 ! [C: nat,A2: nat,B: nat] :
% 4.69/5.00 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A2 ) @ ( plus_plus_nat @ C @ B ) )
% 4.69/5.00 = ( ord_less_nat @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_less_cancel_left
% 4.69/5.00 thf(fact_5022_add__less__cancel__left,axiom,
% 4.69/5.00 ! [C: int,A2: int,B: int] :
% 4.69/5.00 ( ( ord_less_int @ ( plus_plus_int @ C @ A2 ) @ ( plus_plus_int @ C @ B ) )
% 4.69/5.00 = ( ord_less_int @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_less_cancel_left
% 4.69/5.00 thf(fact_5023_add__less__cancel__left,axiom,
% 4.69/5.00 ! [C: code_integer,A2: code_integer,B: code_integer] :
% 4.69/5.00 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ C @ A2 ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 4.69/5.00 = ( ord_le6747313008572928689nteger @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_less_cancel_left
% 4.69/5.00 thf(fact_5024_add__less__cancel__left,axiom,
% 4.69/5.00 ! [C: rat,A2: rat,B: rat] :
% 4.69/5.00 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A2 ) @ ( plus_plus_rat @ C @ B ) )
% 4.69/5.00 = ( ord_less_rat @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_less_cancel_left
% 4.69/5.00 thf(fact_5025_add__less__cancel__right,axiom,
% 4.69/5.00 ! [A2: nat,C: nat,B: nat] :
% 4.69/5.00 ( ( ord_less_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B @ C ) )
% 4.69/5.00 = ( ord_less_nat @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_less_cancel_right
% 4.69/5.00 thf(fact_5026_add__less__cancel__right,axiom,
% 4.69/5.00 ! [A2: int,C: int,B: int] :
% 4.69/5.00 ( ( ord_less_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B @ C ) )
% 4.69/5.00 = ( ord_less_int @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_less_cancel_right
% 4.69/5.00 thf(fact_5027_add__less__cancel__right,axiom,
% 4.69/5.00 ! [A2: code_integer,C: code_integer,B: code_integer] :
% 4.69/5.00 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 4.69/5.00 = ( ord_le6747313008572928689nteger @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_less_cancel_right
% 4.69/5.00 thf(fact_5028_add__less__cancel__right,axiom,
% 4.69/5.00 ! [A2: rat,C: rat,B: rat] :
% 4.69/5.00 ( ( ord_less_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B @ C ) )
% 4.69/5.00 = ( ord_less_rat @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_less_cancel_right
% 4.69/5.00 thf(fact_5029_add__diff__cancel,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer] :
% 4.69/5.00 ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) @ B )
% 4.69/5.00 = A2 ) ).
% 4.69/5.00
% 4.69/5.00 % add_diff_cancel
% 4.69/5.00 thf(fact_5030_add__diff__cancel,axiom,
% 4.69/5.00 ! [A2: rat,B: rat] :
% 4.69/5.00 ( ( minus_minus_rat @ ( plus_plus_rat @ A2 @ B ) @ B )
% 4.69/5.00 = A2 ) ).
% 4.69/5.00
% 4.69/5.00 % add_diff_cancel
% 4.69/5.00 thf(fact_5031_add__diff__cancel,axiom,
% 4.69/5.00 ! [A2: int,B: int] :
% 4.69/5.00 ( ( minus_minus_int @ ( plus_plus_int @ A2 @ B ) @ B )
% 4.69/5.00 = A2 ) ).
% 4.69/5.00
% 4.69/5.00 % add_diff_cancel
% 4.69/5.00 thf(fact_5032_diff__add__cancel,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer] :
% 4.69/5.00 ( ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ A2 @ B ) @ B )
% 4.69/5.00 = A2 ) ).
% 4.69/5.00
% 4.69/5.00 % diff_add_cancel
% 4.69/5.00 thf(fact_5033_diff__add__cancel,axiom,
% 4.69/5.00 ! [A2: rat,B: rat] :
% 4.69/5.00 ( ( plus_plus_rat @ ( minus_minus_rat @ A2 @ B ) @ B )
% 4.69/5.00 = A2 ) ).
% 4.69/5.00
% 4.69/5.00 % diff_add_cancel
% 4.69/5.00 thf(fact_5034_diff__add__cancel,axiom,
% 4.69/5.00 ! [A2: int,B: int] :
% 4.69/5.00 ( ( plus_plus_int @ ( minus_minus_int @ A2 @ B ) @ B )
% 4.69/5.00 = A2 ) ).
% 4.69/5.00
% 4.69/5.00 % diff_add_cancel
% 4.69/5.00 thf(fact_5035_add__diff__cancel__left,axiom,
% 4.69/5.00 ! [C: code_integer,A2: code_integer,B: code_integer] :
% 4.69/5.00 ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ C @ A2 ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 4.69/5.00 = ( minus_8373710615458151222nteger @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_diff_cancel_left
% 4.69/5.00 thf(fact_5036_add__diff__cancel__left,axiom,
% 4.69/5.00 ! [C: rat,A2: rat,B: rat] :
% 4.69/5.00 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A2 ) @ ( plus_plus_rat @ C @ B ) )
% 4.69/5.00 = ( minus_minus_rat @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_diff_cancel_left
% 4.69/5.00 thf(fact_5037_add__diff__cancel__left,axiom,
% 4.69/5.00 ! [C: nat,A2: nat,B: nat] :
% 4.69/5.00 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A2 ) @ ( plus_plus_nat @ C @ B ) )
% 4.69/5.00 = ( minus_minus_nat @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_diff_cancel_left
% 4.69/5.00 thf(fact_5038_add__diff__cancel__left,axiom,
% 4.69/5.00 ! [C: int,A2: int,B: int] :
% 4.69/5.00 ( ( minus_minus_int @ ( plus_plus_int @ C @ A2 ) @ ( plus_plus_int @ C @ B ) )
% 4.69/5.00 = ( minus_minus_int @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_diff_cancel_left
% 4.69/5.00 thf(fact_5039_add__diff__cancel__left_H,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer] :
% 4.69/5.00 ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) @ A2 )
% 4.69/5.00 = B ) ).
% 4.69/5.00
% 4.69/5.00 % add_diff_cancel_left'
% 4.69/5.00 thf(fact_5040_add__diff__cancel__left_H,axiom,
% 4.69/5.00 ! [A2: rat,B: rat] :
% 4.69/5.00 ( ( minus_minus_rat @ ( plus_plus_rat @ A2 @ B ) @ A2 )
% 4.69/5.00 = B ) ).
% 4.69/5.00
% 4.69/5.00 % add_diff_cancel_left'
% 4.69/5.00 thf(fact_5041_add__diff__cancel__left_H,axiom,
% 4.69/5.00 ! [A2: nat,B: nat] :
% 4.69/5.00 ( ( minus_minus_nat @ ( plus_plus_nat @ A2 @ B ) @ A2 )
% 4.69/5.00 = B ) ).
% 4.69/5.00
% 4.69/5.00 % add_diff_cancel_left'
% 4.69/5.00 thf(fact_5042_add__diff__cancel__left_H,axiom,
% 4.69/5.00 ! [A2: int,B: int] :
% 4.69/5.00 ( ( minus_minus_int @ ( plus_plus_int @ A2 @ B ) @ A2 )
% 4.69/5.00 = B ) ).
% 4.69/5.00
% 4.69/5.00 % add_diff_cancel_left'
% 4.69/5.00 thf(fact_5043_add__diff__cancel__right,axiom,
% 4.69/5.00 ! [A2: code_integer,C: code_integer,B: code_integer] :
% 4.69/5.00 ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 4.69/5.00 = ( minus_8373710615458151222nteger @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_diff_cancel_right
% 4.69/5.00 thf(fact_5044_add__diff__cancel__right,axiom,
% 4.69/5.00 ! [A2: rat,C: rat,B: rat] :
% 4.69/5.00 ( ( minus_minus_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B @ C ) )
% 4.69/5.00 = ( minus_minus_rat @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_diff_cancel_right
% 4.69/5.00 thf(fact_5045_add__diff__cancel__right,axiom,
% 4.69/5.00 ! [A2: nat,C: nat,B: nat] :
% 4.69/5.00 ( ( minus_minus_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B @ C ) )
% 4.69/5.00 = ( minus_minus_nat @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_diff_cancel_right
% 4.69/5.00 thf(fact_5046_add__diff__cancel__right,axiom,
% 4.69/5.00 ! [A2: int,C: int,B: int] :
% 4.69/5.00 ( ( minus_minus_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B @ C ) )
% 4.69/5.00 = ( minus_minus_int @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_diff_cancel_right
% 4.69/5.00 thf(fact_5047_add__diff__cancel__right_H,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer] :
% 4.69/5.00 ( ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) @ B )
% 4.69/5.00 = A2 ) ).
% 4.69/5.00
% 4.69/5.00 % add_diff_cancel_right'
% 4.69/5.00 thf(fact_5048_add__diff__cancel__right_H,axiom,
% 4.69/5.00 ! [A2: rat,B: rat] :
% 4.69/5.00 ( ( minus_minus_rat @ ( plus_plus_rat @ A2 @ B ) @ B )
% 4.69/5.00 = A2 ) ).
% 4.69/5.00
% 4.69/5.00 % add_diff_cancel_right'
% 4.69/5.00 thf(fact_5049_add__diff__cancel__right_H,axiom,
% 4.69/5.00 ! [A2: nat,B: nat] :
% 4.69/5.00 ( ( minus_minus_nat @ ( plus_plus_nat @ A2 @ B ) @ B )
% 4.69/5.00 = A2 ) ).
% 4.69/5.00
% 4.69/5.00 % add_diff_cancel_right'
% 4.69/5.00 thf(fact_5050_add__diff__cancel__right_H,axiom,
% 4.69/5.00 ! [A2: int,B: int] :
% 4.69/5.00 ( ( minus_minus_int @ ( plus_plus_int @ A2 @ B ) @ B )
% 4.69/5.00 = A2 ) ).
% 4.69/5.00
% 4.69/5.00 % add_diff_cancel_right'
% 4.69/5.00 thf(fact_5051_card__insert__disjoint,axiom,
% 4.69/5.00 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/5.00 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/5.00 => ( ~ ( member6576561426505652726_nat_o @ X @ A )
% 4.69/5.00 => ( ( finite1363419556375932405_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) )
% 4.69/5.00 = ( suc @ ( finite1363419556375932405_nat_o @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_insert_disjoint
% 4.69/5.00 thf(fact_5052_card__insert__disjoint,axiom,
% 4.69/5.00 ! [A: set_int,X: int] :
% 4.69/5.00 ( ( finite_finite_int @ A )
% 4.69/5.00 => ( ~ ( member_int @ X @ A )
% 4.69/5.00 => ( ( finite_card_int @ ( insert_int @ X @ A ) )
% 4.69/5.00 = ( suc @ ( finite_card_int @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_insert_disjoint
% 4.69/5.00 thf(fact_5053_card__insert__disjoint,axiom,
% 4.69/5.00 ! [A: set_o,X: $o] :
% 4.69/5.00 ( ( finite_finite_o @ A )
% 4.69/5.00 => ( ~ ( member_o @ X @ A )
% 4.69/5.00 => ( ( finite_card_o @ ( insert_o @ X @ A ) )
% 4.69/5.00 = ( suc @ ( finite_card_o @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_insert_disjoint
% 4.69/5.00 thf(fact_5054_card__insert__disjoint,axiom,
% 4.69/5.00 ! [A: set_Product_unit,X: product_unit] :
% 4.69/5.00 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.00 => ( ~ ( member_Product_unit @ X @ A )
% 4.69/5.00 => ( ( finite410649719033368117t_unit @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.00 = ( suc @ ( finite410649719033368117t_unit @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_insert_disjoint
% 4.69/5.00 thf(fact_5055_card__insert__disjoint,axiom,
% 4.69/5.00 ! [A: set_nat,X: nat] :
% 4.69/5.00 ( ( finite_finite_nat @ A )
% 4.69/5.00 => ( ~ ( member_nat @ X @ A )
% 4.69/5.00 => ( ( finite_card_nat @ ( insert_nat @ X @ A ) )
% 4.69/5.00 = ( suc @ ( finite_card_nat @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_insert_disjoint
% 4.69/5.00 thf(fact_5056_card__insert__disjoint,axiom,
% 4.69/5.00 ! [A: set_Code_integer,X: code_integer] :
% 4.69/5.00 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.00 => ( ~ ( member_Code_integer @ X @ A )
% 4.69/5.00 => ( ( finite4902975817058060853nteger @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.00 = ( suc @ ( finite4902975817058060853nteger @ A ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % card_insert_disjoint
% 4.69/5.00 thf(fact_5057_Suc__diff,axiom,
% 4.69/5.00 ! [M4: nat,N2: nat] :
% 4.69/5.00 ( ( ord_less_eq_nat @ M4 @ N2 )
% 4.69/5.00 => ( ( ord_less_eq_nat @ one_one_nat @ M4 )
% 4.69/5.00 => ( ( suc @ ( minus_minus_nat @ N2 @ M4 ) )
% 4.69/5.00 = ( minus_minus_nat @ N2 @ ( minus_minus_nat @ M4 @ one_one_nat ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Suc_diff
% 4.69/5.00 thf(fact_5058_add__mono__thms__linordered__semiring_I4_J,axiom,
% 4.69/5.00 ! [I2: code_integer,J: code_integer,K3: code_integer,L: code_integer] :
% 4.69/5.00 ( ( ( I2 = J )
% 4.69/5.00 & ( K3 = L ) )
% 4.69/5.00 => ( ( plus_p5714425477246183910nteger @ I2 @ K3 )
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_semiring(4)
% 4.69/5.00 thf(fact_5059_add__mono__thms__linordered__semiring_I4_J,axiom,
% 4.69/5.00 ! [I2: rat,J: rat,K3: rat,L: rat] :
% 4.69/5.00 ( ( ( I2 = J )
% 4.69/5.00 & ( K3 = L ) )
% 4.69/5.00 => ( ( plus_plus_rat @ I2 @ K3 )
% 4.69/5.00 = ( plus_plus_rat @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_semiring(4)
% 4.69/5.00 thf(fact_5060_add__mono__thms__linordered__semiring_I4_J,axiom,
% 4.69/5.00 ! [I2: nat,J: nat,K3: nat,L: nat] :
% 4.69/5.00 ( ( ( I2 = J )
% 4.69/5.00 & ( K3 = L ) )
% 4.69/5.00 => ( ( plus_plus_nat @ I2 @ K3 )
% 4.69/5.00 = ( plus_plus_nat @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_semiring(4)
% 4.69/5.00 thf(fact_5061_add__mono__thms__linordered__semiring_I4_J,axiom,
% 4.69/5.00 ! [I2: int,J: int,K3: int,L: int] :
% 4.69/5.00 ( ( ( I2 = J )
% 4.69/5.00 & ( K3 = L ) )
% 4.69/5.00 => ( ( plus_plus_int @ I2 @ K3 )
% 4.69/5.00 = ( plus_plus_int @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_semiring(4)
% 4.69/5.00 thf(fact_5062_group__cancel_Oadd1,axiom,
% 4.69/5.00 ! [A: code_integer,K3: code_integer,A2: code_integer,B: code_integer] :
% 4.69/5.00 ( ( A
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ K3 @ A2 ) )
% 4.69/5.00 => ( ( plus_p5714425477246183910nteger @ A @ B )
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ K3 @ ( plus_p5714425477246183910nteger @ A2 @ B ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % group_cancel.add1
% 4.69/5.00 thf(fact_5063_group__cancel_Oadd1,axiom,
% 4.69/5.00 ! [A: rat,K3: rat,A2: rat,B: rat] :
% 4.69/5.00 ( ( A
% 4.69/5.00 = ( plus_plus_rat @ K3 @ A2 ) )
% 4.69/5.00 => ( ( plus_plus_rat @ A @ B )
% 4.69/5.00 = ( plus_plus_rat @ K3 @ ( plus_plus_rat @ A2 @ B ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % group_cancel.add1
% 4.69/5.00 thf(fact_5064_group__cancel_Oadd1,axiom,
% 4.69/5.00 ! [A: nat,K3: nat,A2: nat,B: nat] :
% 4.69/5.00 ( ( A
% 4.69/5.00 = ( plus_plus_nat @ K3 @ A2 ) )
% 4.69/5.00 => ( ( plus_plus_nat @ A @ B )
% 4.69/5.00 = ( plus_plus_nat @ K3 @ ( plus_plus_nat @ A2 @ B ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % group_cancel.add1
% 4.69/5.00 thf(fact_5065_group__cancel_Oadd1,axiom,
% 4.69/5.00 ! [A: int,K3: int,A2: int,B: int] :
% 4.69/5.00 ( ( A
% 4.69/5.00 = ( plus_plus_int @ K3 @ A2 ) )
% 4.69/5.00 => ( ( plus_plus_int @ A @ B )
% 4.69/5.00 = ( plus_plus_int @ K3 @ ( plus_plus_int @ A2 @ B ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % group_cancel.add1
% 4.69/5.00 thf(fact_5066_group__cancel_Oadd2,axiom,
% 4.69/5.00 ! [B4: code_integer,K3: code_integer,B: code_integer,A2: code_integer] :
% 4.69/5.00 ( ( B4
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ K3 @ B ) )
% 4.69/5.00 => ( ( plus_p5714425477246183910nteger @ A2 @ B4 )
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ K3 @ ( plus_p5714425477246183910nteger @ A2 @ B ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % group_cancel.add2
% 4.69/5.00 thf(fact_5067_group__cancel_Oadd2,axiom,
% 4.69/5.00 ! [B4: rat,K3: rat,B: rat,A2: rat] :
% 4.69/5.00 ( ( B4
% 4.69/5.00 = ( plus_plus_rat @ K3 @ B ) )
% 4.69/5.00 => ( ( plus_plus_rat @ A2 @ B4 )
% 4.69/5.00 = ( plus_plus_rat @ K3 @ ( plus_plus_rat @ A2 @ B ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % group_cancel.add2
% 4.69/5.00 thf(fact_5068_group__cancel_Oadd2,axiom,
% 4.69/5.00 ! [B4: nat,K3: nat,B: nat,A2: nat] :
% 4.69/5.00 ( ( B4
% 4.69/5.00 = ( plus_plus_nat @ K3 @ B ) )
% 4.69/5.00 => ( ( plus_plus_nat @ A2 @ B4 )
% 4.69/5.00 = ( plus_plus_nat @ K3 @ ( plus_plus_nat @ A2 @ B ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % group_cancel.add2
% 4.69/5.00 thf(fact_5069_group__cancel_Oadd2,axiom,
% 4.69/5.00 ! [B4: int,K3: int,B: int,A2: int] :
% 4.69/5.00 ( ( B4
% 4.69/5.00 = ( plus_plus_int @ K3 @ B ) )
% 4.69/5.00 => ( ( plus_plus_int @ A2 @ B4 )
% 4.69/5.00 = ( plus_plus_int @ K3 @ ( plus_plus_int @ A2 @ B ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % group_cancel.add2
% 4.69/5.00 thf(fact_5070_add_Oassoc,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.00 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) @ C )
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ A2 @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add.assoc
% 4.69/5.00 thf(fact_5071_add_Oassoc,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.00 ( ( plus_plus_rat @ ( plus_plus_rat @ A2 @ B ) @ C )
% 4.69/5.00 = ( plus_plus_rat @ A2 @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add.assoc
% 4.69/5.00 thf(fact_5072_add_Oassoc,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.00 ( ( plus_plus_nat @ ( plus_plus_nat @ A2 @ B ) @ C )
% 4.69/5.00 = ( plus_plus_nat @ A2 @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add.assoc
% 4.69/5.00 thf(fact_5073_add_Oassoc,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int] :
% 4.69/5.00 ( ( plus_plus_int @ ( plus_plus_int @ A2 @ B ) @ C )
% 4.69/5.00 = ( plus_plus_int @ A2 @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add.assoc
% 4.69/5.00 thf(fact_5074_add_Oleft__cancel,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.00 ( ( ( plus_p5714425477246183910nteger @ A2 @ B )
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ A2 @ C ) )
% 4.69/5.00 = ( B = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add.left_cancel
% 4.69/5.00 thf(fact_5075_add_Oleft__cancel,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.00 ( ( ( plus_plus_rat @ A2 @ B )
% 4.69/5.00 = ( plus_plus_rat @ A2 @ C ) )
% 4.69/5.00 = ( B = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add.left_cancel
% 4.69/5.00 thf(fact_5076_add_Oleft__cancel,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int] :
% 4.69/5.00 ( ( ( plus_plus_int @ A2 @ B )
% 4.69/5.00 = ( plus_plus_int @ A2 @ C ) )
% 4.69/5.00 = ( B = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add.left_cancel
% 4.69/5.00 thf(fact_5077_add_Oright__cancel,axiom,
% 4.69/5.00 ! [B: code_integer,A2: code_integer,C: code_integer] :
% 4.69/5.00 ( ( ( plus_p5714425477246183910nteger @ B @ A2 )
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ C @ A2 ) )
% 4.69/5.00 = ( B = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add.right_cancel
% 4.69/5.00 thf(fact_5078_add_Oright__cancel,axiom,
% 4.69/5.00 ! [B: rat,A2: rat,C: rat] :
% 4.69/5.00 ( ( ( plus_plus_rat @ B @ A2 )
% 4.69/5.00 = ( plus_plus_rat @ C @ A2 ) )
% 4.69/5.00 = ( B = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add.right_cancel
% 4.69/5.00 thf(fact_5079_add_Oright__cancel,axiom,
% 4.69/5.00 ! [B: int,A2: int,C: int] :
% 4.69/5.00 ( ( ( plus_plus_int @ B @ A2 )
% 4.69/5.00 = ( plus_plus_int @ C @ A2 ) )
% 4.69/5.00 = ( B = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add.right_cancel
% 4.69/5.00 thf(fact_5080_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 4.69/5.00 ( plus_p5714425477246183910nteger
% 4.69/5.00 = ( ^ [A6: code_integer,B6: code_integer] : ( plus_p5714425477246183910nteger @ B6 @ A6 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % ab_semigroup_add_class.add.commute
% 4.69/5.00 thf(fact_5081_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 4.69/5.00 ( plus_plus_rat
% 4.69/5.00 = ( ^ [A6: rat,B6: rat] : ( plus_plus_rat @ B6 @ A6 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % ab_semigroup_add_class.add.commute
% 4.69/5.00 thf(fact_5082_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 4.69/5.00 ( plus_plus_nat
% 4.69/5.00 = ( ^ [A6: nat,B6: nat] : ( plus_plus_nat @ B6 @ A6 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % ab_semigroup_add_class.add.commute
% 4.69/5.00 thf(fact_5083_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 4.69/5.00 ( plus_plus_int
% 4.69/5.00 = ( ^ [A6: int,B6: int] : ( plus_plus_int @ B6 @ A6 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % ab_semigroup_add_class.add.commute
% 4.69/5.00 thf(fact_5084_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 4.69/5.00 ! [B: code_integer,A2: code_integer,C: code_integer] :
% 4.69/5.00 ( ( plus_p5714425477246183910nteger @ B @ ( plus_p5714425477246183910nteger @ A2 @ C ) )
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ A2 @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % ab_semigroup_add_class.add.left_commute
% 4.69/5.00 thf(fact_5085_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 4.69/5.00 ! [B: rat,A2: rat,C: rat] :
% 4.69/5.00 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A2 @ C ) )
% 4.69/5.00 = ( plus_plus_rat @ A2 @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % ab_semigroup_add_class.add.left_commute
% 4.69/5.00 thf(fact_5086_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 4.69/5.00 ! [B: nat,A2: nat,C: nat] :
% 4.69/5.00 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A2 @ C ) )
% 4.69/5.00 = ( plus_plus_nat @ A2 @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % ab_semigroup_add_class.add.left_commute
% 4.69/5.00 thf(fact_5087_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 4.69/5.00 ! [B: int,A2: int,C: int] :
% 4.69/5.00 ( ( plus_plus_int @ B @ ( plus_plus_int @ A2 @ C ) )
% 4.69/5.00 = ( plus_plus_int @ A2 @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % ab_semigroup_add_class.add.left_commute
% 4.69/5.00 thf(fact_5088_add__left__imp__eq,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.00 ( ( ( plus_p5714425477246183910nteger @ A2 @ B )
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ A2 @ C ) )
% 4.69/5.00 => ( B = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_left_imp_eq
% 4.69/5.00 thf(fact_5089_add__left__imp__eq,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.00 ( ( ( plus_plus_rat @ A2 @ B )
% 4.69/5.00 = ( plus_plus_rat @ A2 @ C ) )
% 4.69/5.00 => ( B = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_left_imp_eq
% 4.69/5.00 thf(fact_5090_add__left__imp__eq,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.00 ( ( ( plus_plus_nat @ A2 @ B )
% 4.69/5.00 = ( plus_plus_nat @ A2 @ C ) )
% 4.69/5.00 => ( B = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_left_imp_eq
% 4.69/5.00 thf(fact_5091_add__left__imp__eq,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int] :
% 4.69/5.00 ( ( ( plus_plus_int @ A2 @ B )
% 4.69/5.00 = ( plus_plus_int @ A2 @ C ) )
% 4.69/5.00 => ( B = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_left_imp_eq
% 4.69/5.00 thf(fact_5092_add__right__imp__eq,axiom,
% 4.69/5.00 ! [B: code_integer,A2: code_integer,C: code_integer] :
% 4.69/5.00 ( ( ( plus_p5714425477246183910nteger @ B @ A2 )
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ C @ A2 ) )
% 4.69/5.00 => ( B = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_right_imp_eq
% 4.69/5.00 thf(fact_5093_add__right__imp__eq,axiom,
% 4.69/5.00 ! [B: rat,A2: rat,C: rat] :
% 4.69/5.00 ( ( ( plus_plus_rat @ B @ A2 )
% 4.69/5.00 = ( plus_plus_rat @ C @ A2 ) )
% 4.69/5.00 => ( B = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_right_imp_eq
% 4.69/5.00 thf(fact_5094_add__right__imp__eq,axiom,
% 4.69/5.00 ! [B: nat,A2: nat,C: nat] :
% 4.69/5.00 ( ( ( plus_plus_nat @ B @ A2 )
% 4.69/5.00 = ( plus_plus_nat @ C @ A2 ) )
% 4.69/5.00 => ( B = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_right_imp_eq
% 4.69/5.00 thf(fact_5095_add__right__imp__eq,axiom,
% 4.69/5.00 ! [B: int,A2: int,C: int] :
% 4.69/5.00 ( ( ( plus_plus_int @ B @ A2 )
% 4.69/5.00 = ( plus_plus_int @ C @ A2 ) )
% 4.69/5.00 => ( B = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_right_imp_eq
% 4.69/5.00 thf(fact_5096_add__mono__thms__linordered__semiring_I3_J,axiom,
% 4.69/5.00 ! [I2: code_integer,J: code_integer,K3: code_integer,L: code_integer] :
% 4.69/5.00 ( ( ( ord_le3102999989581377725nteger @ I2 @ J )
% 4.69/5.00 & ( K3 = L ) )
% 4.69/5.00 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I2 @ K3 ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_semiring(3)
% 4.69/5.00 thf(fact_5097_add__mono__thms__linordered__semiring_I3_J,axiom,
% 4.69/5.00 ! [I2: rat,J: rat,K3: rat,L: rat] :
% 4.69/5.00 ( ( ( ord_less_eq_rat @ I2 @ J )
% 4.69/5.00 & ( K3 = L ) )
% 4.69/5.00 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K3 ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_semiring(3)
% 4.69/5.00 thf(fact_5098_add__mono__thms__linordered__semiring_I3_J,axiom,
% 4.69/5.00 ! [I2: nat,J: nat,K3: nat,L: nat] :
% 4.69/5.00 ( ( ( ord_less_eq_nat @ I2 @ J )
% 4.69/5.00 & ( K3 = L ) )
% 4.69/5.00 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K3 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_semiring(3)
% 4.69/5.00 thf(fact_5099_add__mono__thms__linordered__semiring_I3_J,axiom,
% 4.69/5.00 ! [I2: int,J: int,K3: int,L: int] :
% 4.69/5.00 ( ( ( ord_less_eq_int @ I2 @ J )
% 4.69/5.00 & ( K3 = L ) )
% 4.69/5.00 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K3 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_semiring(3)
% 4.69/5.00 thf(fact_5100_add__mono__thms__linordered__semiring_I2_J,axiom,
% 4.69/5.00 ! [I2: code_integer,J: code_integer,K3: code_integer,L: code_integer] :
% 4.69/5.00 ( ( ( I2 = J )
% 4.69/5.00 & ( ord_le3102999989581377725nteger @ K3 @ L ) )
% 4.69/5.00 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I2 @ K3 ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_semiring(2)
% 4.69/5.00 thf(fact_5101_add__mono__thms__linordered__semiring_I2_J,axiom,
% 4.69/5.00 ! [I2: rat,J: rat,K3: rat,L: rat] :
% 4.69/5.00 ( ( ( I2 = J )
% 4.69/5.00 & ( ord_less_eq_rat @ K3 @ L ) )
% 4.69/5.00 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K3 ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_semiring(2)
% 4.69/5.00 thf(fact_5102_add__mono__thms__linordered__semiring_I2_J,axiom,
% 4.69/5.00 ! [I2: nat,J: nat,K3: nat,L: nat] :
% 4.69/5.00 ( ( ( I2 = J )
% 4.69/5.00 & ( ord_less_eq_nat @ K3 @ L ) )
% 4.69/5.00 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K3 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_semiring(2)
% 4.69/5.00 thf(fact_5103_add__mono__thms__linordered__semiring_I2_J,axiom,
% 4.69/5.00 ! [I2: int,J: int,K3: int,L: int] :
% 4.69/5.00 ( ( ( I2 = J )
% 4.69/5.00 & ( ord_less_eq_int @ K3 @ L ) )
% 4.69/5.00 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K3 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_semiring(2)
% 4.69/5.00 thf(fact_5104_add__mono__thms__linordered__semiring_I1_J,axiom,
% 4.69/5.00 ! [I2: code_integer,J: code_integer,K3: code_integer,L: code_integer] :
% 4.69/5.00 ( ( ( ord_le3102999989581377725nteger @ I2 @ J )
% 4.69/5.00 & ( ord_le3102999989581377725nteger @ K3 @ L ) )
% 4.69/5.00 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ I2 @ K3 ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_semiring(1)
% 4.69/5.00 thf(fact_5105_add__mono__thms__linordered__semiring_I1_J,axiom,
% 4.69/5.00 ! [I2: rat,J: rat,K3: rat,L: rat] :
% 4.69/5.00 ( ( ( ord_less_eq_rat @ I2 @ J )
% 4.69/5.00 & ( ord_less_eq_rat @ K3 @ L ) )
% 4.69/5.00 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K3 ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_semiring(1)
% 4.69/5.00 thf(fact_5106_add__mono__thms__linordered__semiring_I1_J,axiom,
% 4.69/5.00 ! [I2: nat,J: nat,K3: nat,L: nat] :
% 4.69/5.00 ( ( ( ord_less_eq_nat @ I2 @ J )
% 4.69/5.00 & ( ord_less_eq_nat @ K3 @ L ) )
% 4.69/5.00 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K3 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_semiring(1)
% 4.69/5.00 thf(fact_5107_add__mono__thms__linordered__semiring_I1_J,axiom,
% 4.69/5.00 ! [I2: int,J: int,K3: int,L: int] :
% 4.69/5.00 ( ( ( ord_less_eq_int @ I2 @ J )
% 4.69/5.00 & ( ord_less_eq_int @ K3 @ L ) )
% 4.69/5.00 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K3 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_semiring(1)
% 4.69/5.00 thf(fact_5108_add__mono,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 4.69/5.00 ( ( ord_le3102999989581377725nteger @ A2 @ B )
% 4.69/5.00 => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 4.69/5.00 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ ( plus_p5714425477246183910nteger @ B @ D2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono
% 4.69/5.00 thf(fact_5109_add__mono,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat,D2: rat] :
% 4.69/5.00 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/5.00 => ( ( ord_less_eq_rat @ C @ D2 )
% 4.69/5.00 => ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono
% 4.69/5.00 thf(fact_5110_add__mono,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat,D2: nat] :
% 4.69/5.00 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.00 => ( ( ord_less_eq_nat @ C @ D2 )
% 4.69/5.00 => ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono
% 4.69/5.00 thf(fact_5111_add__mono,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int,D2: int] :
% 4.69/5.00 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/5.00 => ( ( ord_less_eq_int @ C @ D2 )
% 4.69/5.00 => ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono
% 4.69/5.00 thf(fact_5112_add__left__mono,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.00 ( ( ord_le3102999989581377725nteger @ A2 @ B )
% 4.69/5.00 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ C @ A2 ) @ ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_left_mono
% 4.69/5.00 thf(fact_5113_add__left__mono,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.00 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/5.00 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A2 ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_left_mono
% 4.69/5.00 thf(fact_5114_add__left__mono,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.00 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.00 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A2 ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_left_mono
% 4.69/5.00 thf(fact_5115_add__left__mono,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int] :
% 4.69/5.00 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/5.00 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A2 ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_left_mono
% 4.69/5.00 thf(fact_5116_less__eqE,axiom,
% 4.69/5.00 ! [A2: nat,B: nat] :
% 4.69/5.00 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.00 => ~ ! [C2: nat] :
% 4.69/5.00 ( B
% 4.69/5.00 != ( plus_plus_nat @ A2 @ C2 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % less_eqE
% 4.69/5.00 thf(fact_5117_add__right__mono,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.00 ( ( ord_le3102999989581377725nteger @ A2 @ B )
% 4.69/5.00 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_right_mono
% 4.69/5.00 thf(fact_5118_add__right__mono,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.00 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/5.00 => ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_right_mono
% 4.69/5.00 thf(fact_5119_add__right__mono,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.00 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.00 => ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_right_mono
% 4.69/5.00 thf(fact_5120_add__right__mono,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int] :
% 4.69/5.00 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/5.00 => ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_right_mono
% 4.69/5.00 thf(fact_5121_le__iff__add,axiom,
% 4.69/5.00 ( ord_less_eq_nat
% 4.69/5.00 = ( ^ [A6: nat,B6: nat] :
% 4.69/5.00 ? [C4: nat] :
% 4.69/5.00 ( B6
% 4.69/5.00 = ( plus_plus_nat @ A6 @ C4 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % le_iff_add
% 4.69/5.00 thf(fact_5122_add__le__imp__le__left,axiom,
% 4.69/5.00 ! [C: code_integer,A2: code_integer,B: code_integer] :
% 4.69/5.00 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ C @ A2 ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 4.69/5.00 => ( ord_le3102999989581377725nteger @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_le_imp_le_left
% 4.69/5.00 thf(fact_5123_add__le__imp__le__left,axiom,
% 4.69/5.00 ! [C: rat,A2: rat,B: rat] :
% 4.69/5.00 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A2 ) @ ( plus_plus_rat @ C @ B ) )
% 4.69/5.00 => ( ord_less_eq_rat @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_le_imp_le_left
% 4.69/5.00 thf(fact_5124_add__le__imp__le__left,axiom,
% 4.69/5.00 ! [C: nat,A2: nat,B: nat] :
% 4.69/5.00 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A2 ) @ ( plus_plus_nat @ C @ B ) )
% 4.69/5.00 => ( ord_less_eq_nat @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_le_imp_le_left
% 4.69/5.00 thf(fact_5125_add__le__imp__le__left,axiom,
% 4.69/5.00 ! [C: int,A2: int,B: int] :
% 4.69/5.00 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A2 ) @ ( plus_plus_int @ C @ B ) )
% 4.69/5.00 => ( ord_less_eq_int @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_le_imp_le_left
% 4.69/5.00 thf(fact_5126_add__le__imp__le__right,axiom,
% 4.69/5.00 ! [A2: code_integer,C: code_integer,B: code_integer] :
% 4.69/5.00 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 4.69/5.00 => ( ord_le3102999989581377725nteger @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_le_imp_le_right
% 4.69/5.00 thf(fact_5127_add__le__imp__le__right,axiom,
% 4.69/5.00 ! [A2: rat,C: rat,B: rat] :
% 4.69/5.00 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B @ C ) )
% 4.69/5.00 => ( ord_less_eq_rat @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_le_imp_le_right
% 4.69/5.00 thf(fact_5128_add__le__imp__le__right,axiom,
% 4.69/5.00 ! [A2: nat,C: nat,B: nat] :
% 4.69/5.00 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B @ C ) )
% 4.69/5.00 => ( ord_less_eq_nat @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_le_imp_le_right
% 4.69/5.00 thf(fact_5129_add__le__imp__le__right,axiom,
% 4.69/5.00 ! [A2: int,C: int,B: int] :
% 4.69/5.00 ( ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B @ C ) )
% 4.69/5.00 => ( ord_less_eq_int @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_le_imp_le_right
% 4.69/5.00 thf(fact_5130_add__mono__thms__linordered__field_I5_J,axiom,
% 4.69/5.00 ! [I2: nat,J: nat,K3: nat,L: nat] :
% 4.69/5.00 ( ( ( ord_less_nat @ I2 @ J )
% 4.69/5.00 & ( ord_less_nat @ K3 @ L ) )
% 4.69/5.00 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K3 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_field(5)
% 4.69/5.00 thf(fact_5131_add__mono__thms__linordered__field_I5_J,axiom,
% 4.69/5.00 ! [I2: int,J: int,K3: int,L: int] :
% 4.69/5.00 ( ( ( ord_less_int @ I2 @ J )
% 4.69/5.00 & ( ord_less_int @ K3 @ L ) )
% 4.69/5.00 => ( ord_less_int @ ( plus_plus_int @ I2 @ K3 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_field(5)
% 4.69/5.00 thf(fact_5132_add__mono__thms__linordered__field_I5_J,axiom,
% 4.69/5.00 ! [I2: code_integer,J: code_integer,K3: code_integer,L: code_integer] :
% 4.69/5.00 ( ( ( ord_le6747313008572928689nteger @ I2 @ J )
% 4.69/5.00 & ( ord_le6747313008572928689nteger @ K3 @ L ) )
% 4.69/5.00 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I2 @ K3 ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_field(5)
% 4.69/5.00 thf(fact_5133_add__mono__thms__linordered__field_I5_J,axiom,
% 4.69/5.00 ! [I2: rat,J: rat,K3: rat,L: rat] :
% 4.69/5.00 ( ( ( ord_less_rat @ I2 @ J )
% 4.69/5.00 & ( ord_less_rat @ K3 @ L ) )
% 4.69/5.00 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K3 ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_field(5)
% 4.69/5.00 thf(fact_5134_add__mono__thms__linordered__field_I2_J,axiom,
% 4.69/5.00 ! [I2: nat,J: nat,K3: nat,L: nat] :
% 4.69/5.00 ( ( ( I2 = J )
% 4.69/5.00 & ( ord_less_nat @ K3 @ L ) )
% 4.69/5.00 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K3 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_field(2)
% 4.69/5.00 thf(fact_5135_add__mono__thms__linordered__field_I2_J,axiom,
% 4.69/5.00 ! [I2: int,J: int,K3: int,L: int] :
% 4.69/5.00 ( ( ( I2 = J )
% 4.69/5.00 & ( ord_less_int @ K3 @ L ) )
% 4.69/5.00 => ( ord_less_int @ ( plus_plus_int @ I2 @ K3 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_field(2)
% 4.69/5.00 thf(fact_5136_add__mono__thms__linordered__field_I2_J,axiom,
% 4.69/5.00 ! [I2: code_integer,J: code_integer,K3: code_integer,L: code_integer] :
% 4.69/5.00 ( ( ( I2 = J )
% 4.69/5.00 & ( ord_le6747313008572928689nteger @ K3 @ L ) )
% 4.69/5.00 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I2 @ K3 ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_field(2)
% 4.69/5.00 thf(fact_5137_add__mono__thms__linordered__field_I2_J,axiom,
% 4.69/5.00 ! [I2: rat,J: rat,K3: rat,L: rat] :
% 4.69/5.00 ( ( ( I2 = J )
% 4.69/5.00 & ( ord_less_rat @ K3 @ L ) )
% 4.69/5.00 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K3 ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_field(2)
% 4.69/5.00 thf(fact_5138_add__mono__thms__linordered__field_I1_J,axiom,
% 4.69/5.00 ! [I2: nat,J: nat,K3: nat,L: nat] :
% 4.69/5.00 ( ( ( ord_less_nat @ I2 @ J )
% 4.69/5.00 & ( K3 = L ) )
% 4.69/5.00 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K3 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_field(1)
% 4.69/5.00 thf(fact_5139_add__mono__thms__linordered__field_I1_J,axiom,
% 4.69/5.00 ! [I2: int,J: int,K3: int,L: int] :
% 4.69/5.00 ( ( ( ord_less_int @ I2 @ J )
% 4.69/5.00 & ( K3 = L ) )
% 4.69/5.00 => ( ord_less_int @ ( plus_plus_int @ I2 @ K3 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_field(1)
% 4.69/5.00 thf(fact_5140_add__mono__thms__linordered__field_I1_J,axiom,
% 4.69/5.00 ! [I2: code_integer,J: code_integer,K3: code_integer,L: code_integer] :
% 4.69/5.00 ( ( ( ord_le6747313008572928689nteger @ I2 @ J )
% 4.69/5.00 & ( K3 = L ) )
% 4.69/5.00 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I2 @ K3 ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_field(1)
% 4.69/5.00 thf(fact_5141_add__mono__thms__linordered__field_I1_J,axiom,
% 4.69/5.00 ! [I2: rat,J: rat,K3: rat,L: rat] :
% 4.69/5.00 ( ( ( ord_less_rat @ I2 @ J )
% 4.69/5.00 & ( K3 = L ) )
% 4.69/5.00 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K3 ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_field(1)
% 4.69/5.00 thf(fact_5142_add__strict__mono,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat,D2: nat] :
% 4.69/5.00 ( ( ord_less_nat @ A2 @ B )
% 4.69/5.00 => ( ( ord_less_nat @ C @ D2 )
% 4.69/5.00 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_strict_mono
% 4.69/5.00 thf(fact_5143_add__strict__mono,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int,D2: int] :
% 4.69/5.00 ( ( ord_less_int @ A2 @ B )
% 4.69/5.00 => ( ( ord_less_int @ C @ D2 )
% 4.69/5.00 => ( ord_less_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_strict_mono
% 4.69/5.00 thf(fact_5144_add__strict__mono,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 4.69/5.00 ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/5.00 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 4.69/5.00 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ ( plus_p5714425477246183910nteger @ B @ D2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_strict_mono
% 4.69/5.00 thf(fact_5145_add__strict__mono,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat,D2: rat] :
% 4.69/5.00 ( ( ord_less_rat @ A2 @ B )
% 4.69/5.00 => ( ( ord_less_rat @ C @ D2 )
% 4.69/5.00 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_strict_mono
% 4.69/5.00 thf(fact_5146_add__strict__left__mono,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.00 ( ( ord_less_nat @ A2 @ B )
% 4.69/5.00 => ( ord_less_nat @ ( plus_plus_nat @ C @ A2 ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_strict_left_mono
% 4.69/5.00 thf(fact_5147_add__strict__left__mono,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int] :
% 4.69/5.00 ( ( ord_less_int @ A2 @ B )
% 4.69/5.00 => ( ord_less_int @ ( plus_plus_int @ C @ A2 ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_strict_left_mono
% 4.69/5.00 thf(fact_5148_add__strict__left__mono,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.00 ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/5.00 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ C @ A2 ) @ ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_strict_left_mono
% 4.69/5.00 thf(fact_5149_add__strict__left__mono,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.00 ( ( ord_less_rat @ A2 @ B )
% 4.69/5.00 => ( ord_less_rat @ ( plus_plus_rat @ C @ A2 ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_strict_left_mono
% 4.69/5.00 thf(fact_5150_add__strict__right__mono,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.00 ( ( ord_less_nat @ A2 @ B )
% 4.69/5.00 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_strict_right_mono
% 4.69/5.00 thf(fact_5151_add__strict__right__mono,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int] :
% 4.69/5.00 ( ( ord_less_int @ A2 @ B )
% 4.69/5.00 => ( ord_less_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_strict_right_mono
% 4.69/5.00 thf(fact_5152_add__strict__right__mono,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.00 ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/5.00 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_strict_right_mono
% 4.69/5.00 thf(fact_5153_add__strict__right__mono,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.00 ( ( ord_less_rat @ A2 @ B )
% 4.69/5.00 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_strict_right_mono
% 4.69/5.00 thf(fact_5154_add__less__imp__less__left,axiom,
% 4.69/5.00 ! [C: nat,A2: nat,B: nat] :
% 4.69/5.00 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A2 ) @ ( plus_plus_nat @ C @ B ) )
% 4.69/5.00 => ( ord_less_nat @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_less_imp_less_left
% 4.69/5.00 thf(fact_5155_add__less__imp__less__left,axiom,
% 4.69/5.00 ! [C: int,A2: int,B: int] :
% 4.69/5.00 ( ( ord_less_int @ ( plus_plus_int @ C @ A2 ) @ ( plus_plus_int @ C @ B ) )
% 4.69/5.00 => ( ord_less_int @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_less_imp_less_left
% 4.69/5.00 thf(fact_5156_add__less__imp__less__left,axiom,
% 4.69/5.00 ! [C: code_integer,A2: code_integer,B: code_integer] :
% 4.69/5.00 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ C @ A2 ) @ ( plus_p5714425477246183910nteger @ C @ B ) )
% 4.69/5.00 => ( ord_le6747313008572928689nteger @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_less_imp_less_left
% 4.69/5.00 thf(fact_5157_add__less__imp__less__left,axiom,
% 4.69/5.00 ! [C: rat,A2: rat,B: rat] :
% 4.69/5.00 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A2 ) @ ( plus_plus_rat @ C @ B ) )
% 4.69/5.00 => ( ord_less_rat @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_less_imp_less_left
% 4.69/5.00 thf(fact_5158_add__less__imp__less__right,axiom,
% 4.69/5.00 ! [A2: nat,C: nat,B: nat] :
% 4.69/5.00 ( ( ord_less_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B @ C ) )
% 4.69/5.00 => ( ord_less_nat @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_less_imp_less_right
% 4.69/5.00 thf(fact_5159_add__less__imp__less__right,axiom,
% 4.69/5.00 ! [A2: int,C: int,B: int] :
% 4.69/5.00 ( ( ord_less_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B @ C ) )
% 4.69/5.00 => ( ord_less_int @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_less_imp_less_right
% 4.69/5.00 thf(fact_5160_add__less__imp__less__right,axiom,
% 4.69/5.00 ! [A2: code_integer,C: code_integer,B: code_integer] :
% 4.69/5.00 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 4.69/5.00 => ( ord_le6747313008572928689nteger @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_less_imp_less_right
% 4.69/5.00 thf(fact_5161_add__less__imp__less__right,axiom,
% 4.69/5.00 ! [A2: rat,C: rat,B: rat] :
% 4.69/5.00 ( ( ord_less_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B @ C ) )
% 4.69/5.00 => ( ord_less_rat @ A2 @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_less_imp_less_right
% 4.69/5.00 thf(fact_5162_combine__common__factor,axiom,
% 4.69/5.00 ! [A2: code_integer,E2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.00 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ E2 ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ C ) )
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) @ E2 ) @ C ) ) ).
% 4.69/5.00
% 4.69/5.00 % combine_common_factor
% 4.69/5.00 thf(fact_5163_combine__common__factor,axiom,
% 4.69/5.00 ! [A2: rat,E2: rat,B: rat,C: rat] :
% 4.69/5.00 ( ( plus_plus_rat @ ( times_times_rat @ A2 @ E2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ C ) )
% 4.69/5.00 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A2 @ B ) @ E2 ) @ C ) ) ).
% 4.69/5.00
% 4.69/5.00 % combine_common_factor
% 4.69/5.00 thf(fact_5164_combine__common__factor,axiom,
% 4.69/5.00 ! [A2: nat,E2: nat,B: nat,C: nat] :
% 4.69/5.00 ( ( plus_plus_nat @ ( times_times_nat @ A2 @ E2 ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E2 ) @ C ) )
% 4.69/5.00 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A2 @ B ) @ E2 ) @ C ) ) ).
% 4.69/5.00
% 4.69/5.00 % combine_common_factor
% 4.69/5.00 thf(fact_5165_combine__common__factor,axiom,
% 4.69/5.00 ! [A2: int,E2: int,B: int,C: int] :
% 4.69/5.00 ( ( plus_plus_int @ ( times_times_int @ A2 @ E2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ C ) )
% 4.69/5.00 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A2 @ B ) @ E2 ) @ C ) ) ).
% 4.69/5.00
% 4.69/5.00 % combine_common_factor
% 4.69/5.00 thf(fact_5166_distrib__right,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.00 ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) @ C )
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % distrib_right
% 4.69/5.00 thf(fact_5167_distrib__right,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.00 ( ( times_times_rat @ ( plus_plus_rat @ A2 @ B ) @ C )
% 4.69/5.00 = ( plus_plus_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % distrib_right
% 4.69/5.00 thf(fact_5168_distrib__right,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.00 ( ( times_times_nat @ ( plus_plus_nat @ A2 @ B ) @ C )
% 4.69/5.00 = ( plus_plus_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % distrib_right
% 4.69/5.00 thf(fact_5169_distrib__right,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int] :
% 4.69/5.00 ( ( times_times_int @ ( plus_plus_int @ A2 @ B ) @ C )
% 4.69/5.00 = ( plus_plus_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % distrib_right
% 4.69/5.00 thf(fact_5170_distrib__left,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.00 ( ( times_3573771949741848930nteger @ A2 @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ B ) @ ( times_3573771949741848930nteger @ A2 @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % distrib_left
% 4.69/5.00 thf(fact_5171_distrib__left,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.00 ( ( times_times_rat @ A2 @ ( plus_plus_rat @ B @ C ) )
% 4.69/5.00 = ( plus_plus_rat @ ( times_times_rat @ A2 @ B ) @ ( times_times_rat @ A2 @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % distrib_left
% 4.69/5.00 thf(fact_5172_distrib__left,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.00 ( ( times_times_nat @ A2 @ ( plus_plus_nat @ B @ C ) )
% 4.69/5.00 = ( plus_plus_nat @ ( times_times_nat @ A2 @ B ) @ ( times_times_nat @ A2 @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % distrib_left
% 4.69/5.00 thf(fact_5173_distrib__left,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int] :
% 4.69/5.00 ( ( times_times_int @ A2 @ ( plus_plus_int @ B @ C ) )
% 4.69/5.00 = ( plus_plus_int @ ( times_times_int @ A2 @ B ) @ ( times_times_int @ A2 @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % distrib_left
% 4.69/5.00 thf(fact_5174_comm__semiring__class_Odistrib,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.00 ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) @ C )
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % comm_semiring_class.distrib
% 4.69/5.00 thf(fact_5175_comm__semiring__class_Odistrib,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.00 ( ( times_times_rat @ ( plus_plus_rat @ A2 @ B ) @ C )
% 4.69/5.00 = ( plus_plus_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % comm_semiring_class.distrib
% 4.69/5.00 thf(fact_5176_comm__semiring__class_Odistrib,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.00 ( ( times_times_nat @ ( plus_plus_nat @ A2 @ B ) @ C )
% 4.69/5.00 = ( plus_plus_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % comm_semiring_class.distrib
% 4.69/5.00 thf(fact_5177_comm__semiring__class_Odistrib,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int] :
% 4.69/5.00 ( ( times_times_int @ ( plus_plus_int @ A2 @ B ) @ C )
% 4.69/5.00 = ( plus_plus_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % comm_semiring_class.distrib
% 4.69/5.00 thf(fact_5178_ring__class_Oring__distribs_I1_J,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.00 ( ( times_3573771949741848930nteger @ A2 @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ B ) @ ( times_3573771949741848930nteger @ A2 @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % ring_class.ring_distribs(1)
% 4.69/5.00 thf(fact_5179_ring__class_Oring__distribs_I1_J,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.00 ( ( times_times_rat @ A2 @ ( plus_plus_rat @ B @ C ) )
% 4.69/5.00 = ( plus_plus_rat @ ( times_times_rat @ A2 @ B ) @ ( times_times_rat @ A2 @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % ring_class.ring_distribs(1)
% 4.69/5.00 thf(fact_5180_ring__class_Oring__distribs_I1_J,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int] :
% 4.69/5.00 ( ( times_times_int @ A2 @ ( plus_plus_int @ B @ C ) )
% 4.69/5.00 = ( plus_plus_int @ ( times_times_int @ A2 @ B ) @ ( times_times_int @ A2 @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % ring_class.ring_distribs(1)
% 4.69/5.00 thf(fact_5181_ring__class_Oring__distribs_I2_J,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.00 ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) @ C )
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % ring_class.ring_distribs(2)
% 4.69/5.00 thf(fact_5182_ring__class_Oring__distribs_I2_J,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.00 ( ( times_times_rat @ ( plus_plus_rat @ A2 @ B ) @ C )
% 4.69/5.00 = ( plus_plus_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % ring_class.ring_distribs(2)
% 4.69/5.00 thf(fact_5183_ring__class_Oring__distribs_I2_J,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int] :
% 4.69/5.00 ( ( times_times_int @ ( plus_plus_int @ A2 @ B ) @ C )
% 4.69/5.00 = ( plus_plus_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % ring_class.ring_distribs(2)
% 4.69/5.00 thf(fact_5184_group__cancel_Osub1,axiom,
% 4.69/5.00 ! [A: code_integer,K3: code_integer,A2: code_integer,B: code_integer] :
% 4.69/5.00 ( ( A
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ K3 @ A2 ) )
% 4.69/5.00 => ( ( minus_8373710615458151222nteger @ A @ B )
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ K3 @ ( minus_8373710615458151222nteger @ A2 @ B ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % group_cancel.sub1
% 4.69/5.00 thf(fact_5185_group__cancel_Osub1,axiom,
% 4.69/5.00 ! [A: rat,K3: rat,A2: rat,B: rat] :
% 4.69/5.00 ( ( A
% 4.69/5.00 = ( plus_plus_rat @ K3 @ A2 ) )
% 4.69/5.00 => ( ( minus_minus_rat @ A @ B )
% 4.69/5.00 = ( plus_plus_rat @ K3 @ ( minus_minus_rat @ A2 @ B ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % group_cancel.sub1
% 4.69/5.00 thf(fact_5186_group__cancel_Osub1,axiom,
% 4.69/5.00 ! [A: int,K3: int,A2: int,B: int] :
% 4.69/5.00 ( ( A
% 4.69/5.00 = ( plus_plus_int @ K3 @ A2 ) )
% 4.69/5.00 => ( ( minus_minus_int @ A @ B )
% 4.69/5.00 = ( plus_plus_int @ K3 @ ( minus_minus_int @ A2 @ B ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % group_cancel.sub1
% 4.69/5.00 thf(fact_5187_diff__eq__eq,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.00 ( ( ( minus_8373710615458151222nteger @ A2 @ B )
% 4.69/5.00 = C )
% 4.69/5.00 = ( A2
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % diff_eq_eq
% 4.69/5.00 thf(fact_5188_diff__eq__eq,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.00 ( ( ( minus_minus_rat @ A2 @ B )
% 4.69/5.00 = C )
% 4.69/5.00 = ( A2
% 4.69/5.00 = ( plus_plus_rat @ C @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % diff_eq_eq
% 4.69/5.00 thf(fact_5189_diff__eq__eq,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int] :
% 4.69/5.00 ( ( ( minus_minus_int @ A2 @ B )
% 4.69/5.00 = C )
% 4.69/5.00 = ( A2
% 4.69/5.00 = ( plus_plus_int @ C @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % diff_eq_eq
% 4.69/5.00 thf(fact_5190_eq__diff__eq,axiom,
% 4.69/5.00 ! [A2: code_integer,C: code_integer,B: code_integer] :
% 4.69/5.00 ( ( A2
% 4.69/5.00 = ( minus_8373710615458151222nteger @ C @ B ) )
% 4.69/5.00 = ( ( plus_p5714425477246183910nteger @ A2 @ B )
% 4.69/5.00 = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % eq_diff_eq
% 4.69/5.00 thf(fact_5191_eq__diff__eq,axiom,
% 4.69/5.00 ! [A2: rat,C: rat,B: rat] :
% 4.69/5.00 ( ( A2
% 4.69/5.00 = ( minus_minus_rat @ C @ B ) )
% 4.69/5.00 = ( ( plus_plus_rat @ A2 @ B )
% 4.69/5.00 = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % eq_diff_eq
% 4.69/5.00 thf(fact_5192_eq__diff__eq,axiom,
% 4.69/5.00 ! [A2: int,C: int,B: int] :
% 4.69/5.00 ( ( A2
% 4.69/5.00 = ( minus_minus_int @ C @ B ) )
% 4.69/5.00 = ( ( plus_plus_int @ A2 @ B )
% 4.69/5.00 = C ) ) ).
% 4.69/5.00
% 4.69/5.00 % eq_diff_eq
% 4.69/5.00 thf(fact_5193_add__diff__eq,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.00 ( ( plus_p5714425477246183910nteger @ A2 @ ( minus_8373710615458151222nteger @ B @ C ) )
% 4.69/5.00 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) @ C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_diff_eq
% 4.69/5.00 thf(fact_5194_add__diff__eq,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.00 ( ( plus_plus_rat @ A2 @ ( minus_minus_rat @ B @ C ) )
% 4.69/5.00 = ( minus_minus_rat @ ( plus_plus_rat @ A2 @ B ) @ C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_diff_eq
% 4.69/5.00 thf(fact_5195_add__diff__eq,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int] :
% 4.69/5.00 ( ( plus_plus_int @ A2 @ ( minus_minus_int @ B @ C ) )
% 4.69/5.00 = ( minus_minus_int @ ( plus_plus_int @ A2 @ B ) @ C ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_diff_eq
% 4.69/5.00 thf(fact_5196_diff__diff__eq2,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.00 ( ( minus_8373710615458151222nteger @ A2 @ ( minus_8373710615458151222nteger @ B @ C ) )
% 4.69/5.00 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % diff_diff_eq2
% 4.69/5.00 thf(fact_5197_diff__diff__eq2,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.00 ( ( minus_minus_rat @ A2 @ ( minus_minus_rat @ B @ C ) )
% 4.69/5.00 = ( minus_minus_rat @ ( plus_plus_rat @ A2 @ C ) @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % diff_diff_eq2
% 4.69/5.00 thf(fact_5198_diff__diff__eq2,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int] :
% 4.69/5.00 ( ( minus_minus_int @ A2 @ ( minus_minus_int @ B @ C ) )
% 4.69/5.00 = ( minus_minus_int @ ( plus_plus_int @ A2 @ C ) @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % diff_diff_eq2
% 4.69/5.00 thf(fact_5199_diff__add__eq,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.00 ( ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ A2 @ B ) @ C )
% 4.69/5.00 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % diff_add_eq
% 4.69/5.00 thf(fact_5200_diff__add__eq,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.00 ( ( plus_plus_rat @ ( minus_minus_rat @ A2 @ B ) @ C )
% 4.69/5.00 = ( minus_minus_rat @ ( plus_plus_rat @ A2 @ C ) @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % diff_add_eq
% 4.69/5.00 thf(fact_5201_diff__add__eq,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int] :
% 4.69/5.00 ( ( plus_plus_int @ ( minus_minus_int @ A2 @ B ) @ C )
% 4.69/5.00 = ( minus_minus_int @ ( plus_plus_int @ A2 @ C ) @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % diff_add_eq
% 4.69/5.00 thf(fact_5202_diff__add__eq__diff__diff__swap,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.00 ( ( minus_8373710615458151222nteger @ A2 @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 4.69/5.00 = ( minus_8373710615458151222nteger @ ( minus_8373710615458151222nteger @ A2 @ C ) @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % diff_add_eq_diff_diff_swap
% 4.69/5.00 thf(fact_5203_diff__add__eq__diff__diff__swap,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.00 ( ( minus_minus_rat @ A2 @ ( plus_plus_rat @ B @ C ) )
% 4.69/5.00 = ( minus_minus_rat @ ( minus_minus_rat @ A2 @ C ) @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % diff_add_eq_diff_diff_swap
% 4.69/5.00 thf(fact_5204_diff__add__eq__diff__diff__swap,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int] :
% 4.69/5.00 ( ( minus_minus_int @ A2 @ ( plus_plus_int @ B @ C ) )
% 4.69/5.00 = ( minus_minus_int @ ( minus_minus_int @ A2 @ C ) @ B ) ) ).
% 4.69/5.00
% 4.69/5.00 % diff_add_eq_diff_diff_swap
% 4.69/5.00 thf(fact_5205_add__implies__diff,axiom,
% 4.69/5.00 ! [C: code_integer,B: code_integer,A2: code_integer] :
% 4.69/5.00 ( ( ( plus_p5714425477246183910nteger @ C @ B )
% 4.69/5.00 = A2 )
% 4.69/5.00 => ( C
% 4.69/5.00 = ( minus_8373710615458151222nteger @ A2 @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_implies_diff
% 4.69/5.00 thf(fact_5206_add__implies__diff,axiom,
% 4.69/5.00 ! [C: rat,B: rat,A2: rat] :
% 4.69/5.00 ( ( ( plus_plus_rat @ C @ B )
% 4.69/5.00 = A2 )
% 4.69/5.00 => ( C
% 4.69/5.00 = ( minus_minus_rat @ A2 @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_implies_diff
% 4.69/5.00 thf(fact_5207_add__implies__diff,axiom,
% 4.69/5.00 ! [C: nat,B: nat,A2: nat] :
% 4.69/5.00 ( ( ( plus_plus_nat @ C @ B )
% 4.69/5.00 = A2 )
% 4.69/5.00 => ( C
% 4.69/5.00 = ( minus_minus_nat @ A2 @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_implies_diff
% 4.69/5.00 thf(fact_5208_add__implies__diff,axiom,
% 4.69/5.00 ! [C: int,B: int,A2: int] :
% 4.69/5.00 ( ( ( plus_plus_int @ C @ B )
% 4.69/5.00 = A2 )
% 4.69/5.00 => ( C
% 4.69/5.00 = ( minus_minus_int @ A2 @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_implies_diff
% 4.69/5.00 thf(fact_5209_diff__diff__eq,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.00 ( ( minus_8373710615458151222nteger @ ( minus_8373710615458151222nteger @ A2 @ B ) @ C )
% 4.69/5.00 = ( minus_8373710615458151222nteger @ A2 @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % diff_diff_eq
% 4.69/5.00 thf(fact_5210_diff__diff__eq,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.00 ( ( minus_minus_rat @ ( minus_minus_rat @ A2 @ B ) @ C )
% 4.69/5.00 = ( minus_minus_rat @ A2 @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % diff_diff_eq
% 4.69/5.00 thf(fact_5211_diff__diff__eq,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.00 ( ( minus_minus_nat @ ( minus_minus_nat @ A2 @ B ) @ C )
% 4.69/5.00 = ( minus_minus_nat @ A2 @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % diff_diff_eq
% 4.69/5.00 thf(fact_5212_diff__diff__eq,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int] :
% 4.69/5.00 ( ( minus_minus_int @ ( minus_minus_int @ A2 @ B ) @ C )
% 4.69/5.00 = ( minus_minus_int @ A2 @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % diff_diff_eq
% 4.69/5.00 thf(fact_5213_mlex__bound,axiom,
% 4.69/5.00 ! [A2: nat,A: nat,B: nat,N: nat] :
% 4.69/5.00 ( ( ord_less_nat @ A2 @ A )
% 4.69/5.00 => ( ( ord_less_nat @ B @ N )
% 4.69/5.00 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N ) @ B ) @ ( times_times_nat @ A @ N ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % mlex_bound
% 4.69/5.00 thf(fact_5214_mlex__fst__decrI,axiom,
% 4.69/5.00 ! [A2: nat,A5: nat,B: nat,N: nat,B3: nat] :
% 4.69/5.00 ( ( ord_less_nat @ A2 @ A5 )
% 4.69/5.00 => ( ( ord_less_nat @ B @ N )
% 4.69/5.00 => ( ( ord_less_nat @ B3 @ N )
% 4.69/5.00 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A5 @ N ) @ B3 ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % mlex_fst_decrI
% 4.69/5.00 thf(fact_5215_mlex__snd__decrI,axiom,
% 4.69/5.00 ! [A2: nat,A5: nat,B: nat,B3: nat,N: nat] :
% 4.69/5.00 ( ( A2 = A5 )
% 4.69/5.00 => ( ( ord_less_nat @ B @ B3 )
% 4.69/5.00 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A5 @ N ) @ B3 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % mlex_snd_decrI
% 4.69/5.00 thf(fact_5216_mlex__leI,axiom,
% 4.69/5.00 ! [A2: nat,A5: nat,B: nat,B3: nat,N: nat] :
% 4.69/5.00 ( ( ord_less_eq_nat @ A2 @ A5 )
% 4.69/5.00 => ( ( ord_less_eq_nat @ B @ B3 )
% 4.69/5.00 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A5 @ N ) @ B3 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % mlex_leI
% 4.69/5.00 thf(fact_5217_Inf__nat__def1,axiom,
% 4.69/5.00 ! [K4: set_nat] :
% 4.69/5.00 ( ( K4 != bot_bot_set_nat )
% 4.69/5.00 => ( member_nat @ ( complete_Inf_Inf_nat @ K4 ) @ K4 ) ) ).
% 4.69/5.00
% 4.69/5.00 % Inf_nat_def1
% 4.69/5.00 thf(fact_5218_max__add__distrib__left,axiom,
% 4.69/5.00 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 4.69/5.00 ( ( plus_p5714425477246183910nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 4.69/5.00 = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Z ) @ ( plus_p5714425477246183910nteger @ Y @ Z ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % max_add_distrib_left
% 4.69/5.00 thf(fact_5219_max__add__distrib__left,axiom,
% 4.69/5.00 ! [X: rat,Y: rat,Z: rat] :
% 4.69/5.00 ( ( plus_plus_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 4.69/5.00 = ( ord_max_rat @ ( plus_plus_rat @ X @ Z ) @ ( plus_plus_rat @ Y @ Z ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % max_add_distrib_left
% 4.69/5.00 thf(fact_5220_max__add__distrib__left,axiom,
% 4.69/5.00 ! [X: nat,Y: nat,Z: nat] :
% 4.69/5.00 ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 4.69/5.00 = ( ord_max_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % max_add_distrib_left
% 4.69/5.00 thf(fact_5221_max__add__distrib__left,axiom,
% 4.69/5.00 ! [X: int,Y: int,Z: int] :
% 4.69/5.00 ( ( plus_plus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 4.69/5.00 = ( ord_max_int @ ( plus_plus_int @ X @ Z ) @ ( plus_plus_int @ Y @ Z ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % max_add_distrib_left
% 4.69/5.00 thf(fact_5222_max__add__distrib__right,axiom,
% 4.69/5.00 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 4.69/5.00 ( ( plus_p5714425477246183910nteger @ X @ ( ord_max_Code_integer @ Y @ Z ) )
% 4.69/5.00 = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( plus_p5714425477246183910nteger @ X @ Z ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % max_add_distrib_right
% 4.69/5.00 thf(fact_5223_max__add__distrib__right,axiom,
% 4.69/5.00 ! [X: rat,Y: rat,Z: rat] :
% 4.69/5.00 ( ( plus_plus_rat @ X @ ( ord_max_rat @ Y @ Z ) )
% 4.69/5.00 = ( ord_max_rat @ ( plus_plus_rat @ X @ Y ) @ ( plus_plus_rat @ X @ Z ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % max_add_distrib_right
% 4.69/5.00 thf(fact_5224_max__add__distrib__right,axiom,
% 4.69/5.00 ! [X: nat,Y: nat,Z: nat] :
% 4.69/5.00 ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z ) )
% 4.69/5.00 = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % max_add_distrib_right
% 4.69/5.00 thf(fact_5225_max__add__distrib__right,axiom,
% 4.69/5.00 ! [X: int,Y: int,Z: int] :
% 4.69/5.00 ( ( plus_plus_int @ X @ ( ord_max_int @ Y @ Z ) )
% 4.69/5.00 = ( ord_max_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % max_add_distrib_right
% 4.69/5.00 thf(fact_5226_add__mono__thms__linordered__field_I4_J,axiom,
% 4.69/5.00 ! [I2: code_integer,J: code_integer,K3: code_integer,L: code_integer] :
% 4.69/5.00 ( ( ( ord_le3102999989581377725nteger @ I2 @ J )
% 4.69/5.00 & ( ord_le6747313008572928689nteger @ K3 @ L ) )
% 4.69/5.00 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I2 @ K3 ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_field(4)
% 4.69/5.00 thf(fact_5227_add__mono__thms__linordered__field_I4_J,axiom,
% 4.69/5.00 ! [I2: rat,J: rat,K3: rat,L: rat] :
% 4.69/5.00 ( ( ( ord_less_eq_rat @ I2 @ J )
% 4.69/5.00 & ( ord_less_rat @ K3 @ L ) )
% 4.69/5.00 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K3 ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_field(4)
% 4.69/5.00 thf(fact_5228_add__mono__thms__linordered__field_I4_J,axiom,
% 4.69/5.00 ! [I2: nat,J: nat,K3: nat,L: nat] :
% 4.69/5.00 ( ( ( ord_less_eq_nat @ I2 @ J )
% 4.69/5.00 & ( ord_less_nat @ K3 @ L ) )
% 4.69/5.00 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K3 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_field(4)
% 4.69/5.00 thf(fact_5229_add__mono__thms__linordered__field_I4_J,axiom,
% 4.69/5.00 ! [I2: int,J: int,K3: int,L: int] :
% 4.69/5.00 ( ( ( ord_less_eq_int @ I2 @ J )
% 4.69/5.00 & ( ord_less_int @ K3 @ L ) )
% 4.69/5.00 => ( ord_less_int @ ( plus_plus_int @ I2 @ K3 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_field(4)
% 4.69/5.00 thf(fact_5230_add__mono__thms__linordered__field_I3_J,axiom,
% 4.69/5.00 ! [I2: code_integer,J: code_integer,K3: code_integer,L: code_integer] :
% 4.69/5.00 ( ( ( ord_le6747313008572928689nteger @ I2 @ J )
% 4.69/5.00 & ( ord_le3102999989581377725nteger @ K3 @ L ) )
% 4.69/5.00 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ I2 @ K3 ) @ ( plus_p5714425477246183910nteger @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_field(3)
% 4.69/5.00 thf(fact_5231_add__mono__thms__linordered__field_I3_J,axiom,
% 4.69/5.00 ! [I2: rat,J: rat,K3: rat,L: rat] :
% 4.69/5.00 ( ( ( ord_less_rat @ I2 @ J )
% 4.69/5.00 & ( ord_less_eq_rat @ K3 @ L ) )
% 4.69/5.00 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K3 ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_field(3)
% 4.69/5.00 thf(fact_5232_add__mono__thms__linordered__field_I3_J,axiom,
% 4.69/5.00 ! [I2: nat,J: nat,K3: nat,L: nat] :
% 4.69/5.00 ( ( ( ord_less_nat @ I2 @ J )
% 4.69/5.00 & ( ord_less_eq_nat @ K3 @ L ) )
% 4.69/5.00 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K3 ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_field(3)
% 4.69/5.00 thf(fact_5233_add__mono__thms__linordered__field_I3_J,axiom,
% 4.69/5.00 ! [I2: int,J: int,K3: int,L: int] :
% 4.69/5.00 ( ( ( ord_less_int @ I2 @ J )
% 4.69/5.00 & ( ord_less_eq_int @ K3 @ L ) )
% 4.69/5.00 => ( ord_less_int @ ( plus_plus_int @ I2 @ K3 ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono_thms_linordered_field(3)
% 4.69/5.00 thf(fact_5234_add__le__less__mono,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 4.69/5.00 ( ( ord_le3102999989581377725nteger @ A2 @ B )
% 4.69/5.00 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 4.69/5.00 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ ( plus_p5714425477246183910nteger @ B @ D2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_le_less_mono
% 4.69/5.00 thf(fact_5235_add__le__less__mono,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat,D2: rat] :
% 4.69/5.00 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/5.00 => ( ( ord_less_rat @ C @ D2 )
% 4.69/5.00 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_le_less_mono
% 4.69/5.00 thf(fact_5236_add__le__less__mono,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat,D2: nat] :
% 4.69/5.00 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.00 => ( ( ord_less_nat @ C @ D2 )
% 4.69/5.00 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_le_less_mono
% 4.69/5.00 thf(fact_5237_add__le__less__mono,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int,D2: int] :
% 4.69/5.00 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/5.00 => ( ( ord_less_int @ C @ D2 )
% 4.69/5.00 => ( ord_less_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_le_less_mono
% 4.69/5.00 thf(fact_5238_add__less__le__mono,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 4.69/5.00 ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/5.00 => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 4.69/5.00 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ ( plus_p5714425477246183910nteger @ B @ D2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_less_le_mono
% 4.69/5.00 thf(fact_5239_add__less__le__mono,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat,D2: rat] :
% 4.69/5.00 ( ( ord_less_rat @ A2 @ B )
% 4.69/5.00 => ( ( ord_less_eq_rat @ C @ D2 )
% 4.69/5.00 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_less_le_mono
% 4.69/5.00 thf(fact_5240_add__less__le__mono,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat,D2: nat] :
% 4.69/5.00 ( ( ord_less_nat @ A2 @ B )
% 4.69/5.00 => ( ( ord_less_eq_nat @ C @ D2 )
% 4.69/5.00 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_less_le_mono
% 4.69/5.00 thf(fact_5241_add__less__le__mono,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int,D2: int] :
% 4.69/5.00 ( ( ord_less_int @ A2 @ B )
% 4.69/5.00 => ( ( ord_less_eq_int @ C @ D2 )
% 4.69/5.00 => ( ord_less_int @ ( plus_plus_int @ A2 @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_less_le_mono
% 4.69/5.00 thf(fact_5242_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.00 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.00 => ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.00 => ( ( ( minus_minus_nat @ B @ A2 )
% 4.69/5.00 = C )
% 4.69/5.00 = ( B
% 4.69/5.00 = ( plus_plus_nat @ C @ A2 ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 4.69/5.00 thf(fact_5243_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 4.69/5.00 ! [A2: nat,B: nat] :
% 4.69/5.00 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.00 => ( ( plus_plus_nat @ A2 @ ( minus_minus_nat @ B @ A2 ) )
% 4.69/5.00 = B ) ) ).
% 4.69/5.00
% 4.69/5.00 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 4.69/5.00 thf(fact_5244_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.00 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.00 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A2 ) )
% 4.69/5.00 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A2 ) @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 4.69/5.00 thf(fact_5245_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.00 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.00 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A2 )
% 4.69/5.00 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A2 ) @ C ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 4.69/5.00 thf(fact_5246_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.00 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.00 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A2 ) @ C )
% 4.69/5.00 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A2 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 4.69/5.00 thf(fact_5247_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.00 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.00 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A2 )
% 4.69/5.00 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A2 ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 4.69/5.00 thf(fact_5248_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.00 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.00 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A2 ) )
% 4.69/5.00 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A2 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 4.69/5.00 thf(fact_5249_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.00 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.00 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A2 ) )
% 4.69/5.00 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A2 ) @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 4.69/5.00 thf(fact_5250_le__add__diff,axiom,
% 4.69/5.00 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.00 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.00 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A2 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % le_add_diff
% 4.69/5.00 thf(fact_5251_ordered__cancel__comm__monoid__diff__class_Odiff__add,axiom,
% 4.69/5.00 ! [A2: nat,B: nat] :
% 4.69/5.00 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.00 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A2 ) @ A2 )
% 4.69/5.00 = B ) ) ).
% 4.69/5.00
% 4.69/5.00 % ordered_cancel_comm_monoid_diff_class.diff_add
% 4.69/5.00 thf(fact_5252_le__diff__eq,axiom,
% 4.69/5.00 ! [A2: code_integer,C: code_integer,B: code_integer] :
% 4.69/5.00 ( ( ord_le3102999989581377725nteger @ A2 @ ( minus_8373710615458151222nteger @ C @ B ) )
% 4.69/5.00 = ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) @ C ) ) ).
% 4.69/5.00
% 4.69/5.00 % le_diff_eq
% 4.69/5.00 thf(fact_5253_le__diff__eq,axiom,
% 4.69/5.00 ! [A2: rat,C: rat,B: rat] :
% 4.69/5.00 ( ( ord_less_eq_rat @ A2 @ ( minus_minus_rat @ C @ B ) )
% 4.69/5.00 = ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ B ) @ C ) ) ).
% 4.69/5.00
% 4.69/5.00 % le_diff_eq
% 4.69/5.00 thf(fact_5254_le__diff__eq,axiom,
% 4.69/5.00 ! [A2: int,C: int,B: int] :
% 4.69/5.00 ( ( ord_less_eq_int @ A2 @ ( minus_minus_int @ C @ B ) )
% 4.69/5.00 = ( ord_less_eq_int @ ( plus_plus_int @ A2 @ B ) @ C ) ) ).
% 4.69/5.00
% 4.69/5.00 % le_diff_eq
% 4.69/5.00 thf(fact_5255_diff__le__eq,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.00 ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A2 @ B ) @ C )
% 4.69/5.00 = ( ord_le3102999989581377725nteger @ A2 @ ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % diff_le_eq
% 4.69/5.00 thf(fact_5256_diff__le__eq,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.00 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A2 @ B ) @ C )
% 4.69/5.00 = ( ord_less_eq_rat @ A2 @ ( plus_plus_rat @ C @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % diff_le_eq
% 4.69/5.00 thf(fact_5257_diff__le__eq,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int] :
% 4.69/5.00 ( ( ord_less_eq_int @ ( minus_minus_int @ A2 @ B ) @ C )
% 4.69/5.00 = ( ord_less_eq_int @ A2 @ ( plus_plus_int @ C @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % diff_le_eq
% 4.69/5.00 thf(fact_5258_less__add__one,axiom,
% 4.69/5.00 ! [A2: code_natural] : ( ord_le5570908160329646204atural @ A2 @ ( plus_p4538020629002901425atural @ A2 @ one_one_Code_natural ) ) ).
% 4.69/5.00
% 4.69/5.00 % less_add_one
% 4.69/5.00 thf(fact_5259_less__add__one,axiom,
% 4.69/5.00 ! [A2: nat] : ( ord_less_nat @ A2 @ ( plus_plus_nat @ A2 @ one_one_nat ) ) ).
% 4.69/5.00
% 4.69/5.00 % less_add_one
% 4.69/5.00 thf(fact_5260_less__add__one,axiom,
% 4.69/5.00 ! [A2: int] : ( ord_less_int @ A2 @ ( plus_plus_int @ A2 @ one_one_int ) ) ).
% 4.69/5.00
% 4.69/5.00 % less_add_one
% 4.69/5.00 thf(fact_5261_less__add__one,axiom,
% 4.69/5.00 ! [A2: code_integer] : ( ord_le6747313008572928689nteger @ A2 @ ( plus_p5714425477246183910nteger @ A2 @ one_one_Code_integer ) ) ).
% 4.69/5.00
% 4.69/5.00 % less_add_one
% 4.69/5.00 thf(fact_5262_less__add__one,axiom,
% 4.69/5.00 ! [A2: rat] : ( ord_less_rat @ A2 @ ( plus_plus_rat @ A2 @ one_one_rat ) ) ).
% 4.69/5.00
% 4.69/5.00 % less_add_one
% 4.69/5.00 thf(fact_5263_add__mono1,axiom,
% 4.69/5.00 ! [A2: code_natural,B: code_natural] :
% 4.69/5.00 ( ( ord_le5570908160329646204atural @ A2 @ B )
% 4.69/5.00 => ( ord_le5570908160329646204atural @ ( plus_p4538020629002901425atural @ A2 @ one_one_Code_natural ) @ ( plus_p4538020629002901425atural @ B @ one_one_Code_natural ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono1
% 4.69/5.00 thf(fact_5264_add__mono1,axiom,
% 4.69/5.00 ! [A2: nat,B: nat] :
% 4.69/5.00 ( ( ord_less_nat @ A2 @ B )
% 4.69/5.00 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono1
% 4.69/5.00 thf(fact_5265_add__mono1,axiom,
% 4.69/5.00 ! [A2: int,B: int] :
% 4.69/5.00 ( ( ord_less_int @ A2 @ B )
% 4.69/5.00 => ( ord_less_int @ ( plus_plus_int @ A2 @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono1
% 4.69/5.00 thf(fact_5266_add__mono1,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer] :
% 4.69/5.00 ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/5.00 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ B @ one_one_Code_integer ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono1
% 4.69/5.00 thf(fact_5267_add__mono1,axiom,
% 4.69/5.00 ! [A2: rat,B: rat] :
% 4.69/5.00 ( ( ord_less_rat @ A2 @ B )
% 4.69/5.00 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % add_mono1
% 4.69/5.00 thf(fact_5268_diff__less__eq,axiom,
% 4.69/5.00 ! [A2: int,B: int,C: int] :
% 4.69/5.00 ( ( ord_less_int @ ( minus_minus_int @ A2 @ B ) @ C )
% 4.69/5.00 = ( ord_less_int @ A2 @ ( plus_plus_int @ C @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % diff_less_eq
% 4.69/5.00 thf(fact_5269_diff__less__eq,axiom,
% 4.69/5.00 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.00 ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A2 @ B ) @ C )
% 4.69/5.00 = ( ord_le6747313008572928689nteger @ A2 @ ( plus_p5714425477246183910nteger @ C @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % diff_less_eq
% 4.69/5.00 thf(fact_5270_diff__less__eq,axiom,
% 4.69/5.00 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.00 ( ( ord_less_rat @ ( minus_minus_rat @ A2 @ B ) @ C )
% 4.69/5.00 = ( ord_less_rat @ A2 @ ( plus_plus_rat @ C @ B ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % diff_less_eq
% 4.69/5.00 thf(fact_5271_less__diff__eq,axiom,
% 4.69/5.00 ! [A2: int,C: int,B: int] :
% 4.69/5.00 ( ( ord_less_int @ A2 @ ( minus_minus_int @ C @ B ) )
% 4.69/5.00 = ( ord_less_int @ ( plus_plus_int @ A2 @ B ) @ C ) ) ).
% 4.69/5.00
% 4.69/5.00 % less_diff_eq
% 4.69/5.00 thf(fact_5272_less__diff__eq,axiom,
% 4.69/5.00 ! [A2: code_integer,C: code_integer,B: code_integer] :
% 4.69/5.00 ( ( ord_le6747313008572928689nteger @ A2 @ ( minus_8373710615458151222nteger @ C @ B ) )
% 4.69/5.00 = ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) @ C ) ) ).
% 4.69/5.00
% 4.69/5.00 % less_diff_eq
% 4.69/5.00 thf(fact_5273_less__diff__eq,axiom,
% 4.69/5.00 ! [A2: rat,C: rat,B: rat] :
% 4.69/5.00 ( ( ord_less_rat @ A2 @ ( minus_minus_rat @ C @ B ) )
% 4.69/5.00 = ( ord_less_rat @ ( plus_plus_rat @ A2 @ B ) @ C ) ) ).
% 4.69/5.00
% 4.69/5.00 % less_diff_eq
% 4.69/5.00 thf(fact_5274_square__diff__square__factored,axiom,
% 4.69/5.00 ! [X: code_integer,Y: code_integer] :
% 4.69/5.00 ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 4.69/5.00 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( minus_8373710615458151222nteger @ X @ Y ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % square_diff_square_factored
% 4.69/5.00 thf(fact_5275_square__diff__square__factored,axiom,
% 4.69/5.00 ! [X: rat,Y: rat] :
% 4.69/5.00 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 4.69/5.00 = ( times_times_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_rat @ X @ Y ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % square_diff_square_factored
% 4.69/5.00 thf(fact_5276_square__diff__square__factored,axiom,
% 4.69/5.00 ! [X: int,Y: int] :
% 4.69/5.00 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 4.69/5.00 = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % square_diff_square_factored
% 4.69/5.00 thf(fact_5277_eq__add__iff2,axiom,
% 4.69/5.00 ! [A2: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 4.69/5.00 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ E2 ) @ C )
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 4.69/5.00 = ( C
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A2 ) @ E2 ) @ D2 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % eq_add_iff2
% 4.69/5.00 thf(fact_5278_eq__add__iff2,axiom,
% 4.69/5.00 ! [A2: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 4.69/5.00 ( ( ( plus_plus_rat @ ( times_times_rat @ A2 @ E2 ) @ C )
% 4.69/5.00 = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 4.69/5.00 = ( C
% 4.69/5.00 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A2 ) @ E2 ) @ D2 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % eq_add_iff2
% 4.69/5.00 thf(fact_5279_eq__add__iff2,axiom,
% 4.69/5.00 ! [A2: int,E2: int,C: int,B: int,D2: int] :
% 4.69/5.00 ( ( ( plus_plus_int @ ( times_times_int @ A2 @ E2 ) @ C )
% 4.69/5.00 = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 4.69/5.00 = ( C
% 4.69/5.00 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A2 ) @ E2 ) @ D2 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % eq_add_iff2
% 4.69/5.00 thf(fact_5280_eq__add__iff1,axiom,
% 4.69/5.00 ! [A2: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 4.69/5.00 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ E2 ) @ C )
% 4.69/5.00 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 4.69/5.00 = ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A2 @ B ) @ E2 ) @ C )
% 4.69/5.00 = D2 ) ) ).
% 4.69/5.00
% 4.69/5.00 % eq_add_iff1
% 4.69/5.00 thf(fact_5281_eq__add__iff1,axiom,
% 4.69/5.00 ! [A2: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 4.69/5.00 ( ( ( plus_plus_rat @ ( times_times_rat @ A2 @ E2 ) @ C )
% 4.69/5.00 = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 4.69/5.00 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A2 @ B ) @ E2 ) @ C )
% 4.69/5.00 = D2 ) ) ).
% 4.69/5.00
% 4.69/5.00 % eq_add_iff1
% 4.69/5.00 thf(fact_5282_eq__add__iff1,axiom,
% 4.69/5.00 ! [A2: int,E2: int,C: int,B: int,D2: int] :
% 4.69/5.00 ( ( ( plus_plus_int @ ( times_times_int @ A2 @ E2 ) @ C )
% 4.69/5.00 = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 4.69/5.00 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A2 @ B ) @ E2 ) @ C )
% 4.69/5.00 = D2 ) ) ).
% 4.69/5.00
% 4.69/5.00 % eq_add_iff1
% 4.69/5.00 thf(fact_5283_Suc__n__minus__m__eq,axiom,
% 4.69/5.00 ! [M4: nat,N2: nat] :
% 4.69/5.00 ( ( ord_less_eq_nat @ M4 @ N2 )
% 4.69/5.00 => ( ( ord_less_nat @ one_one_nat @ M4 )
% 4.69/5.00 => ( ( suc @ ( minus_minus_nat @ N2 @ M4 ) )
% 4.69/5.00 = ( minus_minus_nat @ N2 @ ( minus_minus_nat @ M4 @ one_one_nat ) ) ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % Suc_n_minus_m_eq
% 4.69/5.00 thf(fact_5284_nat__in__between__eq_I1_J,axiom,
% 4.69/5.00 ! [A2: nat,B: nat] :
% 4.69/5.00 ( ( ( ord_less_nat @ A2 @ B )
% 4.69/5.00 & ( ord_less_eq_nat @ B @ ( suc @ A2 ) ) )
% 4.69/5.00 = ( B
% 4.69/5.00 = ( suc @ A2 ) ) ) ).
% 4.69/5.00
% 4.69/5.00 % nat_in_between_eq(1)
% 4.69/5.00 thf(fact_5285_nat__in__between__eq_I2_J,axiom,
% 4.69/5.00 ! [A2: nat,B: nat] :
% 4.69/5.00 ( ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.00 & ( ord_less_nat @ B @ ( suc @ A2 ) ) )
% 4.69/5.00 = ( B = A2 ) ) ).
% 4.69/5.00
% 4.69/5.00 % nat_in_between_eq(2)
% 4.69/5.00 thf(fact_5286_wf__no__infinite__down__chainE,axiom,
% 4.69/5.00 ! [R2: set_Pr1261947904930325089at_nat,F: nat > nat] :
% 4.69/5.00 ( ( wf_nat @ R2 )
% 4.69/5.00 => ~ ! [K: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F @ ( suc @ K ) ) @ ( F @ K ) ) @ R2 ) ) ).
% 4.69/5.00
% 4.69/5.00 % wf_no_infinite_down_chainE
% 4.69/5.00 thf(fact_5287_wf__no__infinite__down__chainE,axiom,
% 4.69/5.00 ! [R2: set_Pr958786334691620121nt_int,F: nat > int] :
% 4.69/5.01 ( ( wf_int @ R2 )
% 4.69/5.01 => ~ ! [K: nat] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F @ ( suc @ K ) ) @ ( F @ K ) ) @ R2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % wf_no_infinite_down_chainE
% 4.69/5.01 thf(fact_5288_wf__iff__no__infinite__down__chain,axiom,
% 4.69/5.01 ( wf_nat
% 4.69/5.01 = ( ^ [R4: set_Pr1261947904930325089at_nat] :
% 4.69/5.01 ~ ? [F4: nat > nat] :
% 4.69/5.01 ! [I4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( F4 @ ( suc @ I4 ) ) @ ( F4 @ I4 ) ) @ R4 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % wf_iff_no_infinite_down_chain
% 4.69/5.01 thf(fact_5289_wf__iff__no__infinite__down__chain,axiom,
% 4.69/5.01 ( wf_int
% 4.69/5.01 = ( ^ [R4: set_Pr958786334691620121nt_int] :
% 4.69/5.01 ~ ? [F4: nat > int] :
% 4.69/5.01 ! [I4: nat] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( F4 @ ( suc @ I4 ) ) @ ( F4 @ I4 ) ) @ R4 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % wf_iff_no_infinite_down_chain
% 4.69/5.01 thf(fact_5290_Inf__INT__eq,axiom,
% 4.69/5.01 ( comple4605987646318907561at_o_o
% 4.69/5.01 = ( ^ [S6: set_Pr6409761941060870310at_o_o,X2: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X2 @ ( comple79274577958421812_nat_o @ ( image_8639947063239330806_nat_o @ collec939566748876313656_nat_o @ S6 ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % Inf_INT_eq
% 4.69/5.01 thf(fact_5291_Inf__INT__eq,axiom,
% 4.69/5.01 ( comple4393433247856107946_int_o
% 4.69/5.01 = ( ^ [S6: set_int_o,X2: int] : ( member_int @ X2 @ ( comple3628384868704368283et_int @ ( image_int_o_set_int @ collect_int @ S6 ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % Inf_INT_eq
% 4.69/5.01 thf(fact_5292_Inf__INT__eq,axiom,
% 4.69/5.01 ( complete_Inf_Inf_o_o
% 4.69/5.01 = ( ^ [S6: set_o_o,X2: $o] : ( member_o @ X2 @ ( comple3063163877087187839_set_o @ ( image_o_o_set_o @ collect_o @ S6 ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % Inf_INT_eq
% 4.69/5.01 thf(fact_5293_Inf__INT__eq,axiom,
% 4.69/5.01 ( comple2092403528524206185unit_o
% 4.69/5.01 = ( ^ [S6: set_Product_unit_o,X2: product_unit] : ( member_Product_unit @ X2 @ ( comple7216939928495492468t_unit @ ( image_5138372075374782070t_unit @ collect_Product_unit @ S6 ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % Inf_INT_eq
% 4.69/5.01 thf(fact_5294_Inf__INT__eq,axiom,
% 4.69/5.01 ( comple6214475593288795910_nat_o
% 4.69/5.01 = ( ^ [S6: set_nat_o,X2: nat] : ( member_nat @ X2 @ ( comple7806235888213564991et_nat @ ( image_nat_o_set_nat @ collect_nat @ S6 ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % Inf_INT_eq
% 4.69/5.01 thf(fact_5295_le__add__iff2,axiom,
% 4.69/5.01 ! [A2: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ E2 ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 4.69/5.01 = ( ord_le3102999989581377725nteger @ C @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A2 ) @ E2 ) @ D2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % le_add_iff2
% 4.69/5.01 thf(fact_5296_le__add__iff2,axiom,
% 4.69/5.01 ! [A2: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A2 @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 4.69/5.01 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A2 ) @ E2 ) @ D2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % le_add_iff2
% 4.69/5.01 thf(fact_5297_le__add__iff2,axiom,
% 4.69/5.01 ! [A2: int,E2: int,C: int,B: int,D2: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A2 @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 4.69/5.01 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A2 ) @ E2 ) @ D2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % le_add_iff2
% 4.69/5.01 thf(fact_5298_le__add__iff1,axiom,
% 4.69/5.01 ! [A2: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ E2 ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 4.69/5.01 = ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A2 @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % le_add_iff1
% 4.69/5.01 thf(fact_5299_le__add__iff1,axiom,
% 4.69/5.01 ! [A2: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A2 @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 4.69/5.01 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A2 @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % le_add_iff1
% 4.69/5.01 thf(fact_5300_le__add__iff1,axiom,
% 4.69/5.01 ! [A2: int,E2: int,C: int,B: int,D2: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A2 @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 4.69/5.01 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A2 @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % le_add_iff1
% 4.69/5.01 thf(fact_5301_less__add__iff2,axiom,
% 4.69/5.01 ! [A2: int,E2: int,C: int,B: int,D2: int] :
% 4.69/5.01 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A2 @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 4.69/5.01 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A2 ) @ E2 ) @ D2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % less_add_iff2
% 4.69/5.01 thf(fact_5302_less__add__iff2,axiom,
% 4.69/5.01 ! [A2: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ E2 ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 4.69/5.01 = ( ord_le6747313008572928689nteger @ C @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A2 ) @ E2 ) @ D2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % less_add_iff2
% 4.69/5.01 thf(fact_5303_less__add__iff2,axiom,
% 4.69/5.01 ! [A2: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 4.69/5.01 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A2 @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 4.69/5.01 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A2 ) @ E2 ) @ D2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % less_add_iff2
% 4.69/5.01 thf(fact_5304_less__add__iff1,axiom,
% 4.69/5.01 ! [A2: int,E2: int,C: int,B: int,D2: int] :
% 4.69/5.01 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A2 @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 4.69/5.01 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A2 @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % less_add_iff1
% 4.69/5.01 thf(fact_5305_less__add__iff1,axiom,
% 4.69/5.01 ! [A2: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ E2 ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 4.69/5.01 = ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A2 @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % less_add_iff1
% 4.69/5.01 thf(fact_5306_less__add__iff1,axiom,
% 4.69/5.01 ! [A2: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 4.69/5.01 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A2 @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 4.69/5.01 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A2 @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % less_add_iff1
% 4.69/5.01 thf(fact_5307_square__diff__one__factored,axiom,
% 4.69/5.01 ! [X: code_integer] :
% 4.69/5.01 ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ X ) @ one_one_Code_integer )
% 4.69/5.01 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ X @ one_one_Code_integer ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % square_diff_one_factored
% 4.69/5.01 thf(fact_5308_square__diff__one__factored,axiom,
% 4.69/5.01 ! [X: rat] :
% 4.69/5.01 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 4.69/5.01 = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % square_diff_one_factored
% 4.69/5.01 thf(fact_5309_square__diff__one__factored,axiom,
% 4.69/5.01 ! [X: int] :
% 4.69/5.01 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 4.69/5.01 = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % square_diff_one_factored
% 4.69/5.01 thf(fact_5310_card__Suc__eq__finite,axiom,
% 4.69/5.01 ! [A: set_Pr4532377907799695533_nat_o,K3: nat] :
% 4.69/5.01 ( ( ( finite1363419556375932405_nat_o @ A )
% 4.69/5.01 = ( suc @ K3 ) )
% 4.69/5.01 = ( ? [B6: produc3658429121746597890et_nat > $o,B7: set_Pr4532377907799695533_nat_o] :
% 4.69/5.01 ( ( A
% 4.69/5.01 = ( insert5175938949040314269_nat_o @ B6 @ B7 ) )
% 4.69/5.01 & ~ ( member6576561426505652726_nat_o @ B6 @ B7 )
% 4.69/5.01 & ( ( finite1363419556375932405_nat_o @ B7 )
% 4.69/5.01 = K3 )
% 4.69/5.01 & ( finite3252695134891459830_nat_o @ B7 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_Suc_eq_finite
% 4.69/5.01 thf(fact_5311_card__Suc__eq__finite,axiom,
% 4.69/5.01 ! [A: set_int,K3: nat] :
% 4.69/5.01 ( ( ( finite_card_int @ A )
% 4.69/5.01 = ( suc @ K3 ) )
% 4.69/5.01 = ( ? [B6: int,B7: set_int] :
% 4.69/5.01 ( ( A
% 4.69/5.01 = ( insert_int @ B6 @ B7 ) )
% 4.69/5.01 & ~ ( member_int @ B6 @ B7 )
% 4.69/5.01 & ( ( finite_card_int @ B7 )
% 4.69/5.01 = K3 )
% 4.69/5.01 & ( finite_finite_int @ B7 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_Suc_eq_finite
% 4.69/5.01 thf(fact_5312_card__Suc__eq__finite,axiom,
% 4.69/5.01 ! [A: set_o,K3: nat] :
% 4.69/5.01 ( ( ( finite_card_o @ A )
% 4.69/5.01 = ( suc @ K3 ) )
% 4.69/5.01 = ( ? [B6: $o,B7: set_o] :
% 4.69/5.01 ( ( A
% 4.69/5.01 = ( insert_o @ B6 @ B7 ) )
% 4.69/5.01 & ~ ( member_o @ B6 @ B7 )
% 4.69/5.01 & ( ( finite_card_o @ B7 )
% 4.69/5.01 = K3 )
% 4.69/5.01 & ( finite_finite_o @ B7 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_Suc_eq_finite
% 4.69/5.01 thf(fact_5313_card__Suc__eq__finite,axiom,
% 4.69/5.01 ! [A: set_Product_unit,K3: nat] :
% 4.69/5.01 ( ( ( finite410649719033368117t_unit @ A )
% 4.69/5.01 = ( suc @ K3 ) )
% 4.69/5.01 = ( ? [B6: product_unit,B7: set_Product_unit] :
% 4.69/5.01 ( ( A
% 4.69/5.01 = ( insert_Product_unit @ B6 @ B7 ) )
% 4.69/5.01 & ~ ( member_Product_unit @ B6 @ B7 )
% 4.69/5.01 & ( ( finite410649719033368117t_unit @ B7 )
% 4.69/5.01 = K3 )
% 4.69/5.01 & ( finite4290736615968046902t_unit @ B7 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_Suc_eq_finite
% 4.69/5.01 thf(fact_5314_card__Suc__eq__finite,axiom,
% 4.69/5.01 ! [A: set_nat,K3: nat] :
% 4.69/5.01 ( ( ( finite_card_nat @ A )
% 4.69/5.01 = ( suc @ K3 ) )
% 4.69/5.01 = ( ? [B6: nat,B7: set_nat] :
% 4.69/5.01 ( ( A
% 4.69/5.01 = ( insert_nat @ B6 @ B7 ) )
% 4.69/5.01 & ~ ( member_nat @ B6 @ B7 )
% 4.69/5.01 & ( ( finite_card_nat @ B7 )
% 4.69/5.01 = K3 )
% 4.69/5.01 & ( finite_finite_nat @ B7 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_Suc_eq_finite
% 4.69/5.01 thf(fact_5315_card__Suc__eq__finite,axiom,
% 4.69/5.01 ! [A: set_Code_integer,K3: nat] :
% 4.69/5.01 ( ( ( finite4902975817058060853nteger @ A )
% 4.69/5.01 = ( suc @ K3 ) )
% 4.69/5.01 = ( ? [B6: code_integer,B7: set_Code_integer] :
% 4.69/5.01 ( ( A
% 4.69/5.01 = ( insert_Code_integer @ B6 @ B7 ) )
% 4.69/5.01 & ~ ( member_Code_integer @ B6 @ B7 )
% 4.69/5.01 & ( ( finite4902975817058060853nteger @ B7 )
% 4.69/5.01 = K3 )
% 4.69/5.01 & ( finite6017078050557962740nteger @ B7 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_Suc_eq_finite
% 4.69/5.01 thf(fact_5316_card__insert__if,axiom,
% 4.69/5.01 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/5.01 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/5.01 => ( ( ( member6576561426505652726_nat_o @ X @ A )
% 4.69/5.01 => ( ( finite1363419556375932405_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) )
% 4.69/5.01 = ( finite1363419556375932405_nat_o @ A ) ) )
% 4.69/5.01 & ( ~ ( member6576561426505652726_nat_o @ X @ A )
% 4.69/5.01 => ( ( finite1363419556375932405_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) )
% 4.69/5.01 = ( suc @ ( finite1363419556375932405_nat_o @ A ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_insert_if
% 4.69/5.01 thf(fact_5317_card__insert__if,axiom,
% 4.69/5.01 ! [A: set_int,X: int] :
% 4.69/5.01 ( ( finite_finite_int @ A )
% 4.69/5.01 => ( ( ( member_int @ X @ A )
% 4.69/5.01 => ( ( finite_card_int @ ( insert_int @ X @ A ) )
% 4.69/5.01 = ( finite_card_int @ A ) ) )
% 4.69/5.01 & ( ~ ( member_int @ X @ A )
% 4.69/5.01 => ( ( finite_card_int @ ( insert_int @ X @ A ) )
% 4.69/5.01 = ( suc @ ( finite_card_int @ A ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_insert_if
% 4.69/5.01 thf(fact_5318_card__insert__if,axiom,
% 4.69/5.01 ! [A: set_o,X: $o] :
% 4.69/5.01 ( ( finite_finite_o @ A )
% 4.69/5.01 => ( ( ( member_o @ X @ A )
% 4.69/5.01 => ( ( finite_card_o @ ( insert_o @ X @ A ) )
% 4.69/5.01 = ( finite_card_o @ A ) ) )
% 4.69/5.01 & ( ~ ( member_o @ X @ A )
% 4.69/5.01 => ( ( finite_card_o @ ( insert_o @ X @ A ) )
% 4.69/5.01 = ( suc @ ( finite_card_o @ A ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_insert_if
% 4.69/5.01 thf(fact_5319_card__insert__if,axiom,
% 4.69/5.01 ! [A: set_Product_unit,X: product_unit] :
% 4.69/5.01 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.01 => ( ( ( member_Product_unit @ X @ A )
% 4.69/5.01 => ( ( finite410649719033368117t_unit @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.01 = ( finite410649719033368117t_unit @ A ) ) )
% 4.69/5.01 & ( ~ ( member_Product_unit @ X @ A )
% 4.69/5.01 => ( ( finite410649719033368117t_unit @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.01 = ( suc @ ( finite410649719033368117t_unit @ A ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_insert_if
% 4.69/5.01 thf(fact_5320_card__insert__if,axiom,
% 4.69/5.01 ! [A: set_nat,X: nat] :
% 4.69/5.01 ( ( finite_finite_nat @ A )
% 4.69/5.01 => ( ( ( member_nat @ X @ A )
% 4.69/5.01 => ( ( finite_card_nat @ ( insert_nat @ X @ A ) )
% 4.69/5.01 = ( finite_card_nat @ A ) ) )
% 4.69/5.01 & ( ~ ( member_nat @ X @ A )
% 4.69/5.01 => ( ( finite_card_nat @ ( insert_nat @ X @ A ) )
% 4.69/5.01 = ( suc @ ( finite_card_nat @ A ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_insert_if
% 4.69/5.01 thf(fact_5321_card__insert__if,axiom,
% 4.69/5.01 ! [A: set_Code_integer,X: code_integer] :
% 4.69/5.01 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.01 => ( ( ( member_Code_integer @ X @ A )
% 4.69/5.01 => ( ( finite4902975817058060853nteger @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.01 = ( finite4902975817058060853nteger @ A ) ) )
% 4.69/5.01 & ( ~ ( member_Code_integer @ X @ A )
% 4.69/5.01 => ( ( finite4902975817058060853nteger @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.01 = ( suc @ ( finite4902975817058060853nteger @ A ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_insert_if
% 4.69/5.01 thf(fact_5322_card__le__Suc__iff,axiom,
% 4.69/5.01 ! [N2: nat,A: set_Pr4532377907799695533_nat_o] :
% 4.69/5.01 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( finite1363419556375932405_nat_o @ A ) )
% 4.69/5.01 = ( ? [A6: produc3658429121746597890et_nat > $o,B7: set_Pr4532377907799695533_nat_o] :
% 4.69/5.01 ( ( A
% 4.69/5.01 = ( insert5175938949040314269_nat_o @ A6 @ B7 ) )
% 4.69/5.01 & ~ ( member6576561426505652726_nat_o @ A6 @ B7 )
% 4.69/5.01 & ( ord_less_eq_nat @ N2 @ ( finite1363419556375932405_nat_o @ B7 ) )
% 4.69/5.01 & ( finite3252695134891459830_nat_o @ B7 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_le_Suc_iff
% 4.69/5.01 thf(fact_5323_card__le__Suc__iff,axiom,
% 4.69/5.01 ! [N2: nat,A: set_int] :
% 4.69/5.01 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( finite_card_int @ A ) )
% 4.69/5.01 = ( ? [A6: int,B7: set_int] :
% 4.69/5.01 ( ( A
% 4.69/5.01 = ( insert_int @ A6 @ B7 ) )
% 4.69/5.01 & ~ ( member_int @ A6 @ B7 )
% 4.69/5.01 & ( ord_less_eq_nat @ N2 @ ( finite_card_int @ B7 ) )
% 4.69/5.01 & ( finite_finite_int @ B7 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_le_Suc_iff
% 4.69/5.01 thf(fact_5324_card__le__Suc__iff,axiom,
% 4.69/5.01 ! [N2: nat,A: set_o] :
% 4.69/5.01 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( finite_card_o @ A ) )
% 4.69/5.01 = ( ? [A6: $o,B7: set_o] :
% 4.69/5.01 ( ( A
% 4.69/5.01 = ( insert_o @ A6 @ B7 ) )
% 4.69/5.01 & ~ ( member_o @ A6 @ B7 )
% 4.69/5.01 & ( ord_less_eq_nat @ N2 @ ( finite_card_o @ B7 ) )
% 4.69/5.01 & ( finite_finite_o @ B7 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_le_Suc_iff
% 4.69/5.01 thf(fact_5325_card__le__Suc__iff,axiom,
% 4.69/5.01 ! [N2: nat,A: set_Product_unit] :
% 4.69/5.01 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( finite410649719033368117t_unit @ A ) )
% 4.69/5.01 = ( ? [A6: product_unit,B7: set_Product_unit] :
% 4.69/5.01 ( ( A
% 4.69/5.01 = ( insert_Product_unit @ A6 @ B7 ) )
% 4.69/5.01 & ~ ( member_Product_unit @ A6 @ B7 )
% 4.69/5.01 & ( ord_less_eq_nat @ N2 @ ( finite410649719033368117t_unit @ B7 ) )
% 4.69/5.01 & ( finite4290736615968046902t_unit @ B7 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_le_Suc_iff
% 4.69/5.01 thf(fact_5326_card__le__Suc__iff,axiom,
% 4.69/5.01 ! [N2: nat,A: set_nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( finite_card_nat @ A ) )
% 4.69/5.01 = ( ? [A6: nat,B7: set_nat] :
% 4.69/5.01 ( ( A
% 4.69/5.01 = ( insert_nat @ A6 @ B7 ) )
% 4.69/5.01 & ~ ( member_nat @ A6 @ B7 )
% 4.69/5.01 & ( ord_less_eq_nat @ N2 @ ( finite_card_nat @ B7 ) )
% 4.69/5.01 & ( finite_finite_nat @ B7 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_le_Suc_iff
% 4.69/5.01 thf(fact_5327_card__le__Suc__iff,axiom,
% 4.69/5.01 ! [N2: nat,A: set_Code_integer] :
% 4.69/5.01 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( finite4902975817058060853nteger @ A ) )
% 4.69/5.01 = ( ? [A6: code_integer,B7: set_Code_integer] :
% 4.69/5.01 ( ( A
% 4.69/5.01 = ( insert_Code_integer @ A6 @ B7 ) )
% 4.69/5.01 & ~ ( member_Code_integer @ A6 @ B7 )
% 4.69/5.01 & ( ord_less_eq_nat @ N2 @ ( finite4902975817058060853nteger @ B7 ) )
% 4.69/5.01 & ( finite6017078050557962740nteger @ B7 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_le_Suc_iff
% 4.69/5.01 thf(fact_5328_card_Oremove,axiom,
% 4.69/5.01 ! [A: set_Code_integer,X: code_integer] :
% 4.69/5.01 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.01 => ( ( member_Code_integer @ X @ A )
% 4.69/5.01 => ( ( finite4902975817058060853nteger @ A )
% 4.69/5.01 = ( suc @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card.remove
% 4.69/5.01 thf(fact_5329_card_Oremove,axiom,
% 4.69/5.01 ! [A: set_Product_unit,X: product_unit] :
% 4.69/5.01 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.01 => ( ( member_Product_unit @ X @ A )
% 4.69/5.01 => ( ( finite410649719033368117t_unit @ A )
% 4.69/5.01 = ( suc @ ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card.remove
% 4.69/5.01 thf(fact_5330_card_Oremove,axiom,
% 4.69/5.01 ! [A: set_o,X: $o] :
% 4.69/5.01 ( ( finite_finite_o @ A )
% 4.69/5.01 => ( ( member_o @ X @ A )
% 4.69/5.01 => ( ( finite_card_o @ A )
% 4.69/5.01 = ( suc @ ( finite_card_o @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card.remove
% 4.69/5.01 thf(fact_5331_card_Oremove,axiom,
% 4.69/5.01 ! [A: set_int,X: int] :
% 4.69/5.01 ( ( finite_finite_int @ A )
% 4.69/5.01 => ( ( member_int @ X @ A )
% 4.69/5.01 => ( ( finite_card_int @ A )
% 4.69/5.01 = ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card.remove
% 4.69/5.01 thf(fact_5332_card_Oremove,axiom,
% 4.69/5.01 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/5.01 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/5.01 => ( ( member6576561426505652726_nat_o @ X @ A )
% 4.69/5.01 => ( ( finite1363419556375932405_nat_o @ A )
% 4.69/5.01 = ( suc @ ( finite1363419556375932405_nat_o @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card.remove
% 4.69/5.01 thf(fact_5333_card_Oremove,axiom,
% 4.69/5.01 ! [A: set_nat,X: nat] :
% 4.69/5.01 ( ( finite_finite_nat @ A )
% 4.69/5.01 => ( ( member_nat @ X @ A )
% 4.69/5.01 => ( ( finite_card_nat @ A )
% 4.69/5.01 = ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card.remove
% 4.69/5.01 thf(fact_5334_card_Oinsert__remove,axiom,
% 4.69/5.01 ! [A: set_Code_integer,X: code_integer] :
% 4.69/5.01 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.01 => ( ( finite4902975817058060853nteger @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.01 = ( suc @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card.insert_remove
% 4.69/5.01 thf(fact_5335_card_Oinsert__remove,axiom,
% 4.69/5.01 ! [A: set_Product_unit,X: product_unit] :
% 4.69/5.01 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.01 => ( ( finite410649719033368117t_unit @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.01 = ( suc @ ( finite410649719033368117t_unit @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card.insert_remove
% 4.69/5.01 thf(fact_5336_card_Oinsert__remove,axiom,
% 4.69/5.01 ! [A: set_o,X: $o] :
% 4.69/5.01 ( ( finite_finite_o @ A )
% 4.69/5.01 => ( ( finite_card_o @ ( insert_o @ X @ A ) )
% 4.69/5.01 = ( suc @ ( finite_card_o @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card.insert_remove
% 4.69/5.01 thf(fact_5337_card_Oinsert__remove,axiom,
% 4.69/5.01 ! [A: set_int,X: int] :
% 4.69/5.01 ( ( finite_finite_int @ A )
% 4.69/5.01 => ( ( finite_card_int @ ( insert_int @ X @ A ) )
% 4.69/5.01 = ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card.insert_remove
% 4.69/5.01 thf(fact_5338_card_Oinsert__remove,axiom,
% 4.69/5.01 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/5.01 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/5.01 => ( ( finite1363419556375932405_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) )
% 4.69/5.01 = ( suc @ ( finite1363419556375932405_nat_o @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card.insert_remove
% 4.69/5.01 thf(fact_5339_card_Oinsert__remove,axiom,
% 4.69/5.01 ! [A: set_nat,X: nat] :
% 4.69/5.01 ( ( finite_finite_nat @ A )
% 4.69/5.01 => ( ( finite_card_nat @ ( insert_nat @ X @ A ) )
% 4.69/5.01 = ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card.insert_remove
% 4.69/5.01 thf(fact_5340_mult__Suc__right,axiom,
% 4.69/5.01 ! [M4: nat,N2: nat] :
% 4.69/5.01 ( ( times_times_nat @ M4 @ ( suc @ N2 ) )
% 4.69/5.01 = ( plus_plus_nat @ M4 @ ( times_times_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_Suc_right
% 4.69/5.01 thf(fact_5341_nat__mult__eq__1__iff,axiom,
% 4.69/5.01 ! [M4: nat,N2: nat] :
% 4.69/5.01 ( ( ( times_times_nat @ M4 @ N2 )
% 4.69/5.01 = one_one_nat )
% 4.69/5.01 = ( ( M4 = one_one_nat )
% 4.69/5.01 & ( N2 = one_one_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % nat_mult_eq_1_iff
% 4.69/5.01 thf(fact_5342_nat__1__eq__mult__iff,axiom,
% 4.69/5.01 ! [M4: nat,N2: nat] :
% 4.69/5.01 ( ( one_one_nat
% 4.69/5.01 = ( times_times_nat @ M4 @ N2 ) )
% 4.69/5.01 = ( ( M4 = one_one_nat )
% 4.69/5.01 & ( N2 = one_one_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % nat_1_eq_mult_iff
% 4.69/5.01 thf(fact_5343_nat__less__add__iff1,axiom,
% 4.69/5.01 ! [J: nat,I2: nat,U: nat,M4: nat,N2: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ J @ I2 )
% 4.69/5.01 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M4 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 4.69/5.01 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M4 ) @ N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % nat_less_add_iff1
% 4.69/5.01 thf(fact_5344_nat__less__add__iff2,axiom,
% 4.69/5.01 ! [I2: nat,J: nat,U: nat,M4: nat,N2: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ I2 @ J )
% 4.69/5.01 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M4 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 4.69/5.01 = ( ord_less_nat @ M4 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % nat_less_add_iff2
% 4.69/5.01 thf(fact_5345_nat__diff__add__eq2,axiom,
% 4.69/5.01 ! [I2: nat,J: nat,U: nat,M4: nat,N2: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ I2 @ J )
% 4.69/5.01 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M4 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 4.69/5.01 = ( minus_minus_nat @ M4 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % nat_diff_add_eq2
% 4.69/5.01 thf(fact_5346_nat__diff__add__eq1,axiom,
% 4.69/5.01 ! [J: nat,I2: nat,U: nat,M4: nat,N2: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ J @ I2 )
% 4.69/5.01 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M4 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 4.69/5.01 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M4 ) @ N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % nat_diff_add_eq1
% 4.69/5.01 thf(fact_5347_nat__le__add__iff2,axiom,
% 4.69/5.01 ! [I2: nat,J: nat,U: nat,M4: nat,N2: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ I2 @ J )
% 4.69/5.01 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M4 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 4.69/5.01 = ( ord_less_eq_nat @ M4 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % nat_le_add_iff2
% 4.69/5.01 thf(fact_5348_nat__mult__max__right,axiom,
% 4.69/5.01 ! [M4: nat,N2: nat,Q4: nat] :
% 4.69/5.01 ( ( times_times_nat @ M4 @ ( ord_max_nat @ N2 @ Q4 ) )
% 4.69/5.01 = ( ord_max_nat @ ( times_times_nat @ M4 @ N2 ) @ ( times_times_nat @ M4 @ Q4 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % nat_mult_max_right
% 4.69/5.01 thf(fact_5349_nat__mult__max__left,axiom,
% 4.69/5.01 ! [M4: nat,N2: nat,Q4: nat] :
% 4.69/5.01 ( ( times_times_nat @ ( ord_max_nat @ M4 @ N2 ) @ Q4 )
% 4.69/5.01 = ( ord_max_nat @ ( times_times_nat @ M4 @ Q4 ) @ ( times_times_nat @ N2 @ Q4 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % nat_mult_max_left
% 4.69/5.01 thf(fact_5350_Suc__mult__cancel1,axiom,
% 4.69/5.01 ! [K3: nat,M4: nat,N2: nat] :
% 4.69/5.01 ( ( ( times_times_nat @ ( suc @ K3 ) @ M4 )
% 4.69/5.01 = ( times_times_nat @ ( suc @ K3 ) @ N2 ) )
% 4.69/5.01 = ( M4 = N2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % Suc_mult_cancel1
% 4.69/5.01 thf(fact_5351_mult__le__mono2,axiom,
% 4.69/5.01 ! [I2: nat,J: nat,K3: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ I2 @ J )
% 4.69/5.01 => ( ord_less_eq_nat @ ( times_times_nat @ K3 @ I2 ) @ ( times_times_nat @ K3 @ J ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_mono2
% 4.69/5.01 thf(fact_5352_mult__le__mono1,axiom,
% 4.69/5.01 ! [I2: nat,J: nat,K3: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ I2 @ J )
% 4.69/5.01 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K3 ) @ ( times_times_nat @ J @ K3 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_mono1
% 4.69/5.01 thf(fact_5353_mult__le__mono,axiom,
% 4.69/5.01 ! [I2: nat,J: nat,K3: nat,L: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ I2 @ J )
% 4.69/5.01 => ( ( ord_less_eq_nat @ K3 @ L )
% 4.69/5.01 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K3 ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_mono
% 4.69/5.01 thf(fact_5354_le__square,axiom,
% 4.69/5.01 ! [M4: nat] : ( ord_less_eq_nat @ M4 @ ( times_times_nat @ M4 @ M4 ) ) ).
% 4.69/5.01
% 4.69/5.01 % le_square
% 4.69/5.01 thf(fact_5355_le__cube,axiom,
% 4.69/5.01 ! [M4: nat] : ( ord_less_eq_nat @ M4 @ ( times_times_nat @ M4 @ ( times_times_nat @ M4 @ M4 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % le_cube
% 4.69/5.01 thf(fact_5356_add__mult__distrib,axiom,
% 4.69/5.01 ! [M4: nat,N2: nat,K3: nat] :
% 4.69/5.01 ( ( times_times_nat @ ( plus_plus_nat @ M4 @ N2 ) @ K3 )
% 4.69/5.01 = ( plus_plus_nat @ ( times_times_nat @ M4 @ K3 ) @ ( times_times_nat @ N2 @ K3 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_mult_distrib
% 4.69/5.01 thf(fact_5357_add__mult__distrib2,axiom,
% 4.69/5.01 ! [K3: nat,M4: nat,N2: nat] :
% 4.69/5.01 ( ( times_times_nat @ K3 @ ( plus_plus_nat @ M4 @ N2 ) )
% 4.69/5.01 = ( plus_plus_nat @ ( times_times_nat @ K3 @ M4 ) @ ( times_times_nat @ K3 @ N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_mult_distrib2
% 4.69/5.01 thf(fact_5358_left__add__mult__distrib,axiom,
% 4.69/5.01 ! [I2: nat,U: nat,J: nat,K3: nat] :
% 4.69/5.01 ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K3 ) )
% 4.69/5.01 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I2 @ J ) @ U ) @ K3 ) ) ).
% 4.69/5.01
% 4.69/5.01 % left_add_mult_distrib
% 4.69/5.01 thf(fact_5359_diff__mult__distrib,axiom,
% 4.69/5.01 ! [M4: nat,N2: nat,K3: nat] :
% 4.69/5.01 ( ( times_times_nat @ ( minus_minus_nat @ M4 @ N2 ) @ K3 )
% 4.69/5.01 = ( minus_minus_nat @ ( times_times_nat @ M4 @ K3 ) @ ( times_times_nat @ N2 @ K3 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % diff_mult_distrib
% 4.69/5.01 thf(fact_5360_diff__mult__distrib2,axiom,
% 4.69/5.01 ! [K3: nat,M4: nat,N2: nat] :
% 4.69/5.01 ( ( times_times_nat @ K3 @ ( minus_minus_nat @ M4 @ N2 ) )
% 4.69/5.01 = ( minus_minus_nat @ ( times_times_nat @ K3 @ M4 ) @ ( times_times_nat @ K3 @ N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % diff_mult_distrib2
% 4.69/5.01 thf(fact_5361_nat__mult__1,axiom,
% 4.69/5.01 ! [N2: nat] :
% 4.69/5.01 ( ( times_times_nat @ one_one_nat @ N2 )
% 4.69/5.01 = N2 ) ).
% 4.69/5.01
% 4.69/5.01 % nat_mult_1
% 4.69/5.01 thf(fact_5362_nat__mult__1__right,axiom,
% 4.69/5.01 ! [N2: nat] :
% 4.69/5.01 ( ( times_times_nat @ N2 @ one_one_nat )
% 4.69/5.01 = N2 ) ).
% 4.69/5.01
% 4.69/5.01 % nat_mult_1_right
% 4.69/5.01 thf(fact_5363_Suc__mult__less__cancel1,axiom,
% 4.69/5.01 ! [K3: nat,M4: nat,N2: nat] :
% 4.69/5.01 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K3 ) @ M4 ) @ ( times_times_nat @ ( suc @ K3 ) @ N2 ) )
% 4.69/5.01 = ( ord_less_nat @ M4 @ N2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % Suc_mult_less_cancel1
% 4.69/5.01 thf(fact_5364_Suc__mult__le__cancel1,axiom,
% 4.69/5.01 ! [K3: nat,M4: nat,N2: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K3 ) @ M4 ) @ ( times_times_nat @ ( suc @ K3 ) @ N2 ) )
% 4.69/5.01 = ( ord_less_eq_nat @ M4 @ N2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % Suc_mult_le_cancel1
% 4.69/5.01 thf(fact_5365_mult__Suc,axiom,
% 4.69/5.01 ! [M4: nat,N2: nat] :
% 4.69/5.01 ( ( times_times_nat @ ( suc @ M4 ) @ N2 )
% 4.69/5.01 = ( plus_plus_nat @ N2 @ ( times_times_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_Suc
% 4.69/5.01 thf(fact_5366_nat__eq__add__iff1,axiom,
% 4.69/5.01 ! [J: nat,I2: nat,U: nat,M4: nat,N2: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ J @ I2 )
% 4.69/5.01 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M4 )
% 4.69/5.01 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 4.69/5.01 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M4 )
% 4.69/5.01 = N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % nat_eq_add_iff1
% 4.69/5.01 thf(fact_5367_nat__eq__add__iff2,axiom,
% 4.69/5.01 ! [I2: nat,J: nat,U: nat,M4: nat,N2: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ I2 @ J )
% 4.69/5.01 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M4 )
% 4.69/5.01 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 4.69/5.01 = ( M4
% 4.69/5.01 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % nat_eq_add_iff2
% 4.69/5.01 thf(fact_5368_nat__le__add__iff1,axiom,
% 4.69/5.01 ! [J: nat,I2: nat,U: nat,M4: nat,N2: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ J @ I2 )
% 4.69/5.01 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M4 ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 4.69/5.01 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M4 ) @ N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % nat_le_add_iff1
% 4.69/5.01 thf(fact_5369_discrete,axiom,
% 4.69/5.01 ( ord_le6747313008572928689nteger
% 4.69/5.01 = ( ^ [A6: code_integer] : ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A6 @ one_one_Code_integer ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % discrete
% 4.69/5.01 thf(fact_5370_discrete,axiom,
% 4.69/5.01 ( ord_less_nat
% 4.69/5.01 = ( ^ [A6: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A6 @ one_one_nat ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % discrete
% 4.69/5.01 thf(fact_5371_discrete,axiom,
% 4.69/5.01 ( ord_less_int
% 4.69/5.01 = ( ^ [A6: int] : ( ord_less_eq_int @ ( plus_plus_int @ A6 @ one_one_int ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % discrete
% 4.69/5.01 thf(fact_5372_fstOp__def,axiom,
% 4.69/5.01 ( bNF_fs3871268833404974121et_nat
% 4.69/5.01 = ( ^ [P2: heap_e7401611519738050253t_unit > set_nat > $o,Q: set_nat > set_nat > $o,Ac: produc3658429121746597890et_nat] : ( produc7507926704131184380et_nat @ ( produc1824681642469235216et_nat @ Ac ) @ ( bNF_pi4042512755101277815et_nat @ P2 @ Q @ ( produc1824681642469235216et_nat @ Ac ) @ ( produc8586169260539613262et_nat @ Ac ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % fstOp_def
% 4.69/5.01 thf(fact_5373_fstOp__def,axiom,
% 4.69/5.01 ( bNF_fs8167890477030535480nt_int
% 4.69/5.01 = ( ^ [P2: int > int > $o,Q: int > int > $o,Ac: product_prod_int_int] : ( product_Pair_int_int @ ( product_fst_int_int @ Ac ) @ ( bNF_pi8853482479757052266nt_int @ P2 @ Q @ ( product_fst_int_int @ Ac ) @ ( product_snd_int_int @ Ac ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % fstOp_def
% 4.69/5.01 thf(fact_5374_sndOp__def,axiom,
% 4.69/5.01 ( bNF_sn4039337771197282234et_nat
% 4.69/5.01 = ( ^ [P2: heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o,Q: heap_e7401611519738050253t_unit > set_nat > $o,Ac: produc3658429121746597890et_nat] : ( produc7507926704131184380et_nat @ ( bNF_pi3450177011487049898et_nat @ P2 @ Q @ ( produc1824681642469235216et_nat @ Ac ) @ ( produc8586169260539613262et_nat @ Ac ) ) @ ( produc8586169260539613262et_nat @ Ac ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % sndOp_def
% 4.69/5.01 thf(fact_5375_sndOp__def,axiom,
% 4.69/5.01 ( bNF_sn1062102010912252026nt_int
% 4.69/5.01 = ( ^ [P2: int > int > $o,Q: int > int > $o,Ac: product_prod_int_int] : ( product_Pair_int_int @ ( bNF_pi8853482479757052266nt_int @ P2 @ Q @ ( product_fst_int_int @ Ac ) @ ( product_snd_int_int @ Ac ) ) @ ( product_snd_int_int @ Ac ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % sndOp_def
% 4.69/5.01 thf(fact_5376_card__insert__le__m1,axiom,
% 4.69/5.01 ! [N2: nat,Y: set_nat,X: nat] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.01 => ( ( ord_less_eq_nat @ ( finite_card_nat @ Y ) @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 4.69/5.01 => ( ord_less_eq_nat @ ( finite_card_nat @ ( insert_nat @ X @ Y ) ) @ N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_insert_le_m1
% 4.69/5.01 thf(fact_5377_card__insert__le__m1,axiom,
% 4.69/5.01 ! [N2: nat,Y: set_int,X: int] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.01 => ( ( ord_less_eq_nat @ ( finite_card_int @ Y ) @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 4.69/5.01 => ( ord_less_eq_nat @ ( finite_card_int @ ( insert_int @ X @ Y ) ) @ N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_insert_le_m1
% 4.69/5.01 thf(fact_5378_card__insert__le__m1,axiom,
% 4.69/5.01 ! [N2: nat,Y: set_o,X: $o] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.01 => ( ( ord_less_eq_nat @ ( finite_card_o @ Y ) @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 4.69/5.01 => ( ord_less_eq_nat @ ( finite_card_o @ ( insert_o @ X @ Y ) ) @ N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_insert_le_m1
% 4.69/5.01 thf(fact_5379_card__insert__le__m1,axiom,
% 4.69/5.01 ! [N2: nat,Y: set_Product_unit,X: product_unit] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.01 => ( ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ Y ) @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 4.69/5.01 => ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ ( insert_Product_unit @ X @ Y ) ) @ N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_insert_le_m1
% 4.69/5.01 thf(fact_5380_crossproduct__noteq,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 4.69/5.01 ( ( ( A2 != B )
% 4.69/5.01 & ( C != D2 ) )
% 4.69/5.01 = ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) )
% 4.69/5.01 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A2 @ D2 ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % crossproduct_noteq
% 4.69/5.01 thf(fact_5381_crossproduct__noteq,axiom,
% 4.69/5.01 ! [A2: rat,B: rat,C: rat,D2: rat] :
% 4.69/5.01 ( ( ( A2 != B )
% 4.69/5.01 & ( C != D2 ) )
% 4.69/5.01 = ( ( plus_plus_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B @ D2 ) )
% 4.69/5.01 != ( plus_plus_rat @ ( times_times_rat @ A2 @ D2 ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % crossproduct_noteq
% 4.69/5.01 thf(fact_5382_crossproduct__noteq,axiom,
% 4.69/5.01 ! [A2: nat,B: nat,C: nat,D2: nat] :
% 4.69/5.01 ( ( ( A2 != B )
% 4.69/5.01 & ( C != D2 ) )
% 4.69/5.01 = ( ( plus_plus_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ D2 ) )
% 4.69/5.01 != ( plus_plus_nat @ ( times_times_nat @ A2 @ D2 ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % crossproduct_noteq
% 4.69/5.01 thf(fact_5383_crossproduct__noteq,axiom,
% 4.69/5.01 ! [A2: int,B: int,C: int,D2: int] :
% 4.69/5.01 ( ( ( A2 != B )
% 4.69/5.01 & ( C != D2 ) )
% 4.69/5.01 = ( ( plus_plus_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ D2 ) )
% 4.69/5.01 != ( plus_plus_int @ ( times_times_int @ A2 @ D2 ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % crossproduct_noteq
% 4.69/5.01 thf(fact_5384_crossproduct__eq,axiom,
% 4.69/5.01 ! [W: code_integer,Y: code_integer,X: code_integer,Z: code_integer] :
% 4.69/5.01 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ W @ Y ) @ ( times_3573771949741848930nteger @ X @ Z ) )
% 4.69/5.01 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ W @ Z ) @ ( times_3573771949741848930nteger @ X @ Y ) ) )
% 4.69/5.01 = ( ( W = X )
% 4.69/5.01 | ( Y = Z ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % crossproduct_eq
% 4.69/5.01 thf(fact_5385_crossproduct__eq,axiom,
% 4.69/5.01 ! [W: rat,Y: rat,X: rat,Z: rat] :
% 4.69/5.01 ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y ) @ ( times_times_rat @ X @ Z ) )
% 4.69/5.01 = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X @ Y ) ) )
% 4.69/5.01 = ( ( W = X )
% 4.69/5.01 | ( Y = Z ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % crossproduct_eq
% 4.69/5.01 thf(fact_5386_crossproduct__eq,axiom,
% 4.69/5.01 ! [W: nat,Y: nat,X: nat,Z: nat] :
% 4.69/5.01 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X @ Z ) )
% 4.69/5.01 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y ) ) )
% 4.69/5.01 = ( ( W = X )
% 4.69/5.01 | ( Y = Z ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % crossproduct_eq
% 4.69/5.01 thf(fact_5387_crossproduct__eq,axiom,
% 4.69/5.01 ! [W: int,Y: int,X: int,Z: int] :
% 4.69/5.01 ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X @ Z ) )
% 4.69/5.01 = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X @ Y ) ) )
% 4.69/5.01 = ( ( W = X )
% 4.69/5.01 | ( Y = Z ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % crossproduct_eq
% 4.69/5.01 thf(fact_5388_dbl__dec__def,axiom,
% 4.69/5.01 ( neg_nu7757733837767384882nteger
% 4.69/5.01 = ( ^ [X2: code_integer] : ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ X2 @ X2 ) @ one_one_Code_integer ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % dbl_dec_def
% 4.69/5.01 thf(fact_5389_dbl__dec__def,axiom,
% 4.69/5.01 ( neg_nu3179335615603231917ec_rat
% 4.69/5.01 = ( ^ [X2: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % dbl_dec_def
% 4.69/5.01 thf(fact_5390_dbl__dec__def,axiom,
% 4.69/5.01 ( neg_nu3811975205180677377ec_int
% 4.69/5.01 = ( ^ [X2: int] : ( minus_minus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % dbl_dec_def
% 4.69/5.01 thf(fact_5391_card__insert__disjoint_H,axiom,
% 4.69/5.01 ! [A: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o] :
% 4.69/5.01 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/5.01 => ( ~ ( member6576561426505652726_nat_o @ X @ A )
% 4.69/5.01 => ( ( minus_minus_nat @ ( finite1363419556375932405_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) ) @ ( suc @ zero_zero_nat ) )
% 4.69/5.01 = ( finite1363419556375932405_nat_o @ A ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_insert_disjoint'
% 4.69/5.01 thf(fact_5392_card__insert__disjoint_H,axiom,
% 4.69/5.01 ! [A: set_int,X: int] :
% 4.69/5.01 ( ( finite_finite_int @ A )
% 4.69/5.01 => ( ~ ( member_int @ X @ A )
% 4.69/5.01 => ( ( minus_minus_nat @ ( finite_card_int @ ( insert_int @ X @ A ) ) @ ( suc @ zero_zero_nat ) )
% 4.69/5.01 = ( finite_card_int @ A ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_insert_disjoint'
% 4.69/5.01 thf(fact_5393_card__insert__disjoint_H,axiom,
% 4.69/5.01 ! [A: set_o,X: $o] :
% 4.69/5.01 ( ( finite_finite_o @ A )
% 4.69/5.01 => ( ~ ( member_o @ X @ A )
% 4.69/5.01 => ( ( minus_minus_nat @ ( finite_card_o @ ( insert_o @ X @ A ) ) @ ( suc @ zero_zero_nat ) )
% 4.69/5.01 = ( finite_card_o @ A ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_insert_disjoint'
% 4.69/5.01 thf(fact_5394_card__insert__disjoint_H,axiom,
% 4.69/5.01 ! [A: set_Product_unit,X: product_unit] :
% 4.69/5.01 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.01 => ( ~ ( member_Product_unit @ X @ A )
% 4.69/5.01 => ( ( minus_minus_nat @ ( finite410649719033368117t_unit @ ( insert_Product_unit @ X @ A ) ) @ ( suc @ zero_zero_nat ) )
% 4.69/5.01 = ( finite410649719033368117t_unit @ A ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_insert_disjoint'
% 4.69/5.01 thf(fact_5395_card__insert__disjoint_H,axiom,
% 4.69/5.01 ! [A: set_nat,X: nat] :
% 4.69/5.01 ( ( finite_finite_nat @ A )
% 4.69/5.01 => ( ~ ( member_nat @ X @ A )
% 4.69/5.01 => ( ( minus_minus_nat @ ( finite_card_nat @ ( insert_nat @ X @ A ) ) @ ( suc @ zero_zero_nat ) )
% 4.69/5.01 = ( finite_card_nat @ A ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_insert_disjoint'
% 4.69/5.01 thf(fact_5396_card__insert__disjoint_H,axiom,
% 4.69/5.01 ! [A: set_Code_integer,X: code_integer] :
% 4.69/5.01 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.01 => ( ~ ( member_Code_integer @ X @ A )
% 4.69/5.01 => ( ( minus_minus_nat @ ( finite4902975817058060853nteger @ ( insert_Code_integer @ X @ A ) ) @ ( suc @ zero_zero_nat ) )
% 4.69/5.01 = ( finite4902975817058060853nteger @ A ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_insert_disjoint'
% 4.69/5.01 thf(fact_5397_le__zero__eq,axiom,
% 4.69/5.01 ! [N2: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 4.69/5.01 = ( N2 = zero_zero_nat ) ) ).
% 4.69/5.01
% 4.69/5.01 % le_zero_eq
% 4.69/5.01 thf(fact_5398_not__gr__zero,axiom,
% 4.69/5.01 ! [N2: nat] :
% 4.69/5.01 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 4.69/5.01 = ( N2 = zero_zero_nat ) ) ).
% 4.69/5.01
% 4.69/5.01 % not_gr_zero
% 4.69/5.01 thf(fact_5399_add_Oright__neutral,axiom,
% 4.69/5.01 ! [A2: rat] :
% 4.69/5.01 ( ( plus_plus_rat @ A2 @ zero_zero_rat )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % add.right_neutral
% 4.69/5.01 thf(fact_5400_add_Oright__neutral,axiom,
% 4.69/5.01 ! [A2: nat] :
% 4.69/5.01 ( ( plus_plus_nat @ A2 @ zero_zero_nat )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % add.right_neutral
% 4.69/5.01 thf(fact_5401_add_Oright__neutral,axiom,
% 4.69/5.01 ! [A2: int] :
% 4.69/5.01 ( ( plus_plus_int @ A2 @ zero_zero_int )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % add.right_neutral
% 4.69/5.01 thf(fact_5402_add_Oright__neutral,axiom,
% 4.69/5.01 ! [A2: code_integer] :
% 4.69/5.01 ( ( plus_p5714425477246183910nteger @ A2 @ zero_z3403309356797280102nteger )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % add.right_neutral
% 4.69/5.01 thf(fact_5403_double__zero__sym,axiom,
% 4.69/5.01 ! [A2: rat] :
% 4.69/5.01 ( ( zero_zero_rat
% 4.69/5.01 = ( plus_plus_rat @ A2 @ A2 ) )
% 4.69/5.01 = ( A2 = zero_zero_rat ) ) ).
% 4.69/5.01
% 4.69/5.01 % double_zero_sym
% 4.69/5.01 thf(fact_5404_double__zero__sym,axiom,
% 4.69/5.01 ! [A2: int] :
% 4.69/5.01 ( ( zero_zero_int
% 4.69/5.01 = ( plus_plus_int @ A2 @ A2 ) )
% 4.69/5.01 = ( A2 = zero_zero_int ) ) ).
% 4.69/5.01
% 4.69/5.01 % double_zero_sym
% 4.69/5.01 thf(fact_5405_double__zero__sym,axiom,
% 4.69/5.01 ! [A2: code_integer] :
% 4.69/5.01 ( ( zero_z3403309356797280102nteger
% 4.69/5.01 = ( plus_p5714425477246183910nteger @ A2 @ A2 ) )
% 4.69/5.01 = ( A2 = zero_z3403309356797280102nteger ) ) ).
% 4.69/5.01
% 4.69/5.01 % double_zero_sym
% 4.69/5.01 thf(fact_5406_add__cancel__left__left,axiom,
% 4.69/5.01 ! [B: rat,A2: rat] :
% 4.69/5.01 ( ( ( plus_plus_rat @ B @ A2 )
% 4.69/5.01 = A2 )
% 4.69/5.01 = ( B = zero_zero_rat ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_cancel_left_left
% 4.69/5.01 thf(fact_5407_add__cancel__left__left,axiom,
% 4.69/5.01 ! [B: nat,A2: nat] :
% 4.69/5.01 ( ( ( plus_plus_nat @ B @ A2 )
% 4.69/5.01 = A2 )
% 4.69/5.01 = ( B = zero_zero_nat ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_cancel_left_left
% 4.69/5.01 thf(fact_5408_add__cancel__left__left,axiom,
% 4.69/5.01 ! [B: int,A2: int] :
% 4.69/5.01 ( ( ( plus_plus_int @ B @ A2 )
% 4.69/5.01 = A2 )
% 4.69/5.01 = ( B = zero_zero_int ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_cancel_left_left
% 4.69/5.01 thf(fact_5409_add__cancel__left__left,axiom,
% 4.69/5.01 ! [B: code_integer,A2: code_integer] :
% 4.69/5.01 ( ( ( plus_p5714425477246183910nteger @ B @ A2 )
% 4.69/5.01 = A2 )
% 4.69/5.01 = ( B = zero_z3403309356797280102nteger ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_cancel_left_left
% 4.69/5.01 thf(fact_5410_add__cancel__left__right,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ( plus_plus_rat @ A2 @ B )
% 4.69/5.01 = A2 )
% 4.69/5.01 = ( B = zero_zero_rat ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_cancel_left_right
% 4.69/5.01 thf(fact_5411_add__cancel__left__right,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ( plus_plus_nat @ A2 @ B )
% 4.69/5.01 = A2 )
% 4.69/5.01 = ( B = zero_zero_nat ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_cancel_left_right
% 4.69/5.01 thf(fact_5412_add__cancel__left__right,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ( plus_plus_int @ A2 @ B )
% 4.69/5.01 = A2 )
% 4.69/5.01 = ( B = zero_zero_int ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_cancel_left_right
% 4.69/5.01 thf(fact_5413_add__cancel__left__right,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ( plus_p5714425477246183910nteger @ A2 @ B )
% 4.69/5.01 = A2 )
% 4.69/5.01 = ( B = zero_z3403309356797280102nteger ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_cancel_left_right
% 4.69/5.01 thf(fact_5414_add__cancel__right__left,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( A2
% 4.69/5.01 = ( plus_plus_rat @ B @ A2 ) )
% 4.69/5.01 = ( B = zero_zero_rat ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_cancel_right_left
% 4.69/5.01 thf(fact_5415_add__cancel__right__left,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( A2
% 4.69/5.01 = ( plus_plus_nat @ B @ A2 ) )
% 4.69/5.01 = ( B = zero_zero_nat ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_cancel_right_left
% 4.69/5.01 thf(fact_5416_add__cancel__right__left,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( A2
% 4.69/5.01 = ( plus_plus_int @ B @ A2 ) )
% 4.69/5.01 = ( B = zero_zero_int ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_cancel_right_left
% 4.69/5.01 thf(fact_5417_add__cancel__right__left,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( A2
% 4.69/5.01 = ( plus_p5714425477246183910nteger @ B @ A2 ) )
% 4.69/5.01 = ( B = zero_z3403309356797280102nteger ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_cancel_right_left
% 4.69/5.01 thf(fact_5418_add__cancel__right__right,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( A2
% 4.69/5.01 = ( plus_plus_rat @ A2 @ B ) )
% 4.69/5.01 = ( B = zero_zero_rat ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_cancel_right_right
% 4.69/5.01 thf(fact_5419_add__cancel__right__right,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( A2
% 4.69/5.01 = ( plus_plus_nat @ A2 @ B ) )
% 4.69/5.01 = ( B = zero_zero_nat ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_cancel_right_right
% 4.69/5.01 thf(fact_5420_add__cancel__right__right,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( A2
% 4.69/5.01 = ( plus_plus_int @ A2 @ B ) )
% 4.69/5.01 = ( B = zero_zero_int ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_cancel_right_right
% 4.69/5.01 thf(fact_5421_add__cancel__right__right,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( A2
% 4.69/5.01 = ( plus_p5714425477246183910nteger @ A2 @ B ) )
% 4.69/5.01 = ( B = zero_z3403309356797280102nteger ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_cancel_right_right
% 4.69/5.01 thf(fact_5422_add__eq__0__iff__both__eq__0,axiom,
% 4.69/5.01 ! [X: nat,Y: nat] :
% 4.69/5.01 ( ( ( plus_plus_nat @ X @ Y )
% 4.69/5.01 = zero_zero_nat )
% 4.69/5.01 = ( ( X = zero_zero_nat )
% 4.69/5.01 & ( Y = zero_zero_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_eq_0_iff_both_eq_0
% 4.69/5.01 thf(fact_5423_zero__eq__add__iff__both__eq__0,axiom,
% 4.69/5.01 ! [X: nat,Y: nat] :
% 4.69/5.01 ( ( zero_zero_nat
% 4.69/5.01 = ( plus_plus_nat @ X @ Y ) )
% 4.69/5.01 = ( ( X = zero_zero_nat )
% 4.69/5.01 & ( Y = zero_zero_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_eq_add_iff_both_eq_0
% 4.69/5.01 thf(fact_5424_add__0,axiom,
% 4.69/5.01 ! [A2: rat] :
% 4.69/5.01 ( ( plus_plus_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % add_0
% 4.69/5.01 thf(fact_5425_add__0,axiom,
% 4.69/5.01 ! [A2: nat] :
% 4.69/5.01 ( ( plus_plus_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % add_0
% 4.69/5.01 thf(fact_5426_add__0,axiom,
% 4.69/5.01 ! [A2: int] :
% 4.69/5.01 ( ( plus_plus_int @ zero_zero_int @ A2 )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % add_0
% 4.69/5.01 thf(fact_5427_add__0,axiom,
% 4.69/5.01 ! [A2: code_integer] :
% 4.69/5.01 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % add_0
% 4.69/5.01 thf(fact_5428_mult__cancel__right,axiom,
% 4.69/5.01 ! [A2: code_integer,C: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ( times_3573771949741848930nteger @ A2 @ C )
% 4.69/5.01 = ( times_3573771949741848930nteger @ B @ C ) )
% 4.69/5.01 = ( ( C = zero_z3403309356797280102nteger )
% 4.69/5.01 | ( A2 = B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_cancel_right
% 4.69/5.01 thf(fact_5429_mult__cancel__right,axiom,
% 4.69/5.01 ! [A2: rat,C: rat,B: rat] :
% 4.69/5.01 ( ( ( times_times_rat @ A2 @ C )
% 4.69/5.01 = ( times_times_rat @ B @ C ) )
% 4.69/5.01 = ( ( C = zero_zero_rat )
% 4.69/5.01 | ( A2 = B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_cancel_right
% 4.69/5.01 thf(fact_5430_mult__cancel__right,axiom,
% 4.69/5.01 ! [A2: nat,C: nat,B: nat] :
% 4.69/5.01 ( ( ( times_times_nat @ A2 @ C )
% 4.69/5.01 = ( times_times_nat @ B @ C ) )
% 4.69/5.01 = ( ( C = zero_zero_nat )
% 4.69/5.01 | ( A2 = B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_cancel_right
% 4.69/5.01 thf(fact_5431_mult__cancel__right,axiom,
% 4.69/5.01 ! [A2: int,C: int,B: int] :
% 4.69/5.01 ( ( ( times_times_int @ A2 @ C )
% 4.69/5.01 = ( times_times_int @ B @ C ) )
% 4.69/5.01 = ( ( C = zero_zero_int )
% 4.69/5.01 | ( A2 = B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_cancel_right
% 4.69/5.01 thf(fact_5432_mult__cancel__left,axiom,
% 4.69/5.01 ! [C: code_integer,A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ( times_3573771949741848930nteger @ C @ A2 )
% 4.69/5.01 = ( times_3573771949741848930nteger @ C @ B ) )
% 4.69/5.01 = ( ( C = zero_z3403309356797280102nteger )
% 4.69/5.01 | ( A2 = B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_cancel_left
% 4.69/5.01 thf(fact_5433_mult__cancel__left,axiom,
% 4.69/5.01 ! [C: rat,A2: rat,B: rat] :
% 4.69/5.01 ( ( ( times_times_rat @ C @ A2 )
% 4.69/5.01 = ( times_times_rat @ C @ B ) )
% 4.69/5.01 = ( ( C = zero_zero_rat )
% 4.69/5.01 | ( A2 = B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_cancel_left
% 4.69/5.01 thf(fact_5434_mult__cancel__left,axiom,
% 4.69/5.01 ! [C: nat,A2: nat,B: nat] :
% 4.69/5.01 ( ( ( times_times_nat @ C @ A2 )
% 4.69/5.01 = ( times_times_nat @ C @ B ) )
% 4.69/5.01 = ( ( C = zero_zero_nat )
% 4.69/5.01 | ( A2 = B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_cancel_left
% 4.69/5.01 thf(fact_5435_mult__cancel__left,axiom,
% 4.69/5.01 ! [C: int,A2: int,B: int] :
% 4.69/5.01 ( ( ( times_times_int @ C @ A2 )
% 4.69/5.01 = ( times_times_int @ C @ B ) )
% 4.69/5.01 = ( ( C = zero_zero_int )
% 4.69/5.01 | ( A2 = B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_cancel_left
% 4.69/5.01 thf(fact_5436_mult__eq__0__iff,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ( times_3573771949741848930nteger @ A2 @ B )
% 4.69/5.01 = zero_z3403309356797280102nteger )
% 4.69/5.01 = ( ( A2 = zero_z3403309356797280102nteger )
% 4.69/5.01 | ( B = zero_z3403309356797280102nteger ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_eq_0_iff
% 4.69/5.01 thf(fact_5437_mult__eq__0__iff,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ( times_times_rat @ A2 @ B )
% 4.69/5.01 = zero_zero_rat )
% 4.69/5.01 = ( ( A2 = zero_zero_rat )
% 4.69/5.01 | ( B = zero_zero_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_eq_0_iff
% 4.69/5.01 thf(fact_5438_mult__eq__0__iff,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ( times_times_nat @ A2 @ B )
% 4.69/5.01 = zero_zero_nat )
% 4.69/5.01 = ( ( A2 = zero_zero_nat )
% 4.69/5.01 | ( B = zero_zero_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_eq_0_iff
% 4.69/5.01 thf(fact_5439_mult__eq__0__iff,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ( times_times_int @ A2 @ B )
% 4.69/5.01 = zero_zero_int )
% 4.69/5.01 = ( ( A2 = zero_zero_int )
% 4.69/5.01 | ( B = zero_zero_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_eq_0_iff
% 4.69/5.01 thf(fact_5440_mult__zero__right,axiom,
% 4.69/5.01 ! [A2: code_integer] :
% 4.69/5.01 ( ( times_3573771949741848930nteger @ A2 @ zero_z3403309356797280102nteger )
% 4.69/5.01 = zero_z3403309356797280102nteger ) ).
% 4.69/5.01
% 4.69/5.01 % mult_zero_right
% 4.69/5.01 thf(fact_5441_mult__zero__right,axiom,
% 4.69/5.01 ! [A2: rat] :
% 4.69/5.01 ( ( times_times_rat @ A2 @ zero_zero_rat )
% 4.69/5.01 = zero_zero_rat ) ).
% 4.69/5.01
% 4.69/5.01 % mult_zero_right
% 4.69/5.01 thf(fact_5442_mult__zero__right,axiom,
% 4.69/5.01 ! [A2: nat] :
% 4.69/5.01 ( ( times_times_nat @ A2 @ zero_zero_nat )
% 4.69/5.01 = zero_zero_nat ) ).
% 4.69/5.01
% 4.69/5.01 % mult_zero_right
% 4.69/5.01 thf(fact_5443_mult__zero__right,axiom,
% 4.69/5.01 ! [A2: int] :
% 4.69/5.01 ( ( times_times_int @ A2 @ zero_zero_int )
% 4.69/5.01 = zero_zero_int ) ).
% 4.69/5.01
% 4.69/5.01 % mult_zero_right
% 4.69/5.01 thf(fact_5444_mult__zero__left,axiom,
% 4.69/5.01 ! [A2: code_integer] :
% 4.69/5.01 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 = zero_z3403309356797280102nteger ) ).
% 4.69/5.01
% 4.69/5.01 % mult_zero_left
% 4.69/5.01 thf(fact_5445_mult__zero__left,axiom,
% 4.69/5.01 ! [A2: rat] :
% 4.69/5.01 ( ( times_times_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 = zero_zero_rat ) ).
% 4.69/5.01
% 4.69/5.01 % mult_zero_left
% 4.69/5.01 thf(fact_5446_mult__zero__left,axiom,
% 4.69/5.01 ! [A2: nat] :
% 4.69/5.01 ( ( times_times_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 = zero_zero_nat ) ).
% 4.69/5.01
% 4.69/5.01 % mult_zero_left
% 4.69/5.01 thf(fact_5447_mult__zero__left,axiom,
% 4.69/5.01 ! [A2: int] :
% 4.69/5.01 ( ( times_times_int @ zero_zero_int @ A2 )
% 4.69/5.01 = zero_zero_int ) ).
% 4.69/5.01
% 4.69/5.01 % mult_zero_left
% 4.69/5.01 thf(fact_5448_diff__self,axiom,
% 4.69/5.01 ! [A2: code_integer] :
% 4.69/5.01 ( ( minus_8373710615458151222nteger @ A2 @ A2 )
% 4.69/5.01 = zero_z3403309356797280102nteger ) ).
% 4.69/5.01
% 4.69/5.01 % diff_self
% 4.69/5.01 thf(fact_5449_diff__self,axiom,
% 4.69/5.01 ! [A2: rat] :
% 4.69/5.01 ( ( minus_minus_rat @ A2 @ A2 )
% 4.69/5.01 = zero_zero_rat ) ).
% 4.69/5.01
% 4.69/5.01 % diff_self
% 4.69/5.01 thf(fact_5450_diff__self,axiom,
% 4.69/5.01 ! [A2: int] :
% 4.69/5.01 ( ( minus_minus_int @ A2 @ A2 )
% 4.69/5.01 = zero_zero_int ) ).
% 4.69/5.01
% 4.69/5.01 % diff_self
% 4.69/5.01 thf(fact_5451_diff__0__right,axiom,
% 4.69/5.01 ! [A2: code_integer] :
% 4.69/5.01 ( ( minus_8373710615458151222nteger @ A2 @ zero_z3403309356797280102nteger )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % diff_0_right
% 4.69/5.01 thf(fact_5452_diff__0__right,axiom,
% 4.69/5.01 ! [A2: rat] :
% 4.69/5.01 ( ( minus_minus_rat @ A2 @ zero_zero_rat )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % diff_0_right
% 4.69/5.01 thf(fact_5453_diff__0__right,axiom,
% 4.69/5.01 ! [A2: int] :
% 4.69/5.01 ( ( minus_minus_int @ A2 @ zero_zero_int )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % diff_0_right
% 4.69/5.01 thf(fact_5454_zero__diff,axiom,
% 4.69/5.01 ! [A2: nat] :
% 4.69/5.01 ( ( minus_minus_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 = zero_zero_nat ) ).
% 4.69/5.01
% 4.69/5.01 % zero_diff
% 4.69/5.01 thf(fact_5455_diff__zero,axiom,
% 4.69/5.01 ! [A2: code_integer] :
% 4.69/5.01 ( ( minus_8373710615458151222nteger @ A2 @ zero_z3403309356797280102nteger )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % diff_zero
% 4.69/5.01 thf(fact_5456_diff__zero,axiom,
% 4.69/5.01 ! [A2: rat] :
% 4.69/5.01 ( ( minus_minus_rat @ A2 @ zero_zero_rat )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % diff_zero
% 4.69/5.01 thf(fact_5457_diff__zero,axiom,
% 4.69/5.01 ! [A2: nat] :
% 4.69/5.01 ( ( minus_minus_nat @ A2 @ zero_zero_nat )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % diff_zero
% 4.69/5.01 thf(fact_5458_diff__zero,axiom,
% 4.69/5.01 ! [A2: int] :
% 4.69/5.01 ( ( minus_minus_int @ A2 @ zero_zero_int )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % diff_zero
% 4.69/5.01 thf(fact_5459_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 4.69/5.01 ! [A2: code_integer] :
% 4.69/5.01 ( ( minus_8373710615458151222nteger @ A2 @ A2 )
% 4.69/5.01 = zero_z3403309356797280102nteger ) ).
% 4.69/5.01
% 4.69/5.01 % cancel_comm_monoid_add_class.diff_cancel
% 4.69/5.01 thf(fact_5460_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 4.69/5.01 ! [A2: rat] :
% 4.69/5.01 ( ( minus_minus_rat @ A2 @ A2 )
% 4.69/5.01 = zero_zero_rat ) ).
% 4.69/5.01
% 4.69/5.01 % cancel_comm_monoid_add_class.diff_cancel
% 4.69/5.01 thf(fact_5461_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 4.69/5.01 ! [A2: nat] :
% 4.69/5.01 ( ( minus_minus_nat @ A2 @ A2 )
% 4.69/5.01 = zero_zero_nat ) ).
% 4.69/5.01
% 4.69/5.01 % cancel_comm_monoid_add_class.diff_cancel
% 4.69/5.01 thf(fact_5462_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 4.69/5.01 ! [A2: int] :
% 4.69/5.01 ( ( minus_minus_int @ A2 @ A2 )
% 4.69/5.01 = zero_zero_int ) ).
% 4.69/5.01
% 4.69/5.01 % cancel_comm_monoid_add_class.diff_cancel
% 4.69/5.01 thf(fact_5463_mult__cancel2,axiom,
% 4.69/5.01 ! [M4: nat,K3: nat,N2: nat] :
% 4.69/5.01 ( ( ( times_times_nat @ M4 @ K3 )
% 4.69/5.01 = ( times_times_nat @ N2 @ K3 ) )
% 4.69/5.01 = ( ( M4 = N2 )
% 4.69/5.01 | ( K3 = zero_zero_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_cancel2
% 4.69/5.01 thf(fact_5464_mult__cancel1,axiom,
% 4.69/5.01 ! [K3: nat,M4: nat,N2: nat] :
% 4.69/5.01 ( ( ( times_times_nat @ K3 @ M4 )
% 4.69/5.01 = ( times_times_nat @ K3 @ N2 ) )
% 4.69/5.01 = ( ( M4 = N2 )
% 4.69/5.01 | ( K3 = zero_zero_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_cancel1
% 4.69/5.01 thf(fact_5465_mult__0__right,axiom,
% 4.69/5.01 ! [M4: nat] :
% 4.69/5.01 ( ( times_times_nat @ M4 @ zero_zero_nat )
% 4.69/5.01 = zero_zero_nat ) ).
% 4.69/5.01
% 4.69/5.01 % mult_0_right
% 4.69/5.01 thf(fact_5466_mult__is__0,axiom,
% 4.69/5.01 ! [M4: nat,N2: nat] :
% 4.69/5.01 ( ( ( times_times_nat @ M4 @ N2 )
% 4.69/5.01 = zero_zero_nat )
% 4.69/5.01 = ( ( M4 = zero_zero_nat )
% 4.69/5.01 | ( N2 = zero_zero_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_is_0
% 4.69/5.01 thf(fact_5467_Sup__nat__empty,axiom,
% 4.69/5.01 ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 4.69/5.01 = zero_zero_nat ) ).
% 4.69/5.01
% 4.69/5.01 % Sup_nat_empty
% 4.69/5.01 thf(fact_5468_dbl__dec__simps_I3_J,axiom,
% 4.69/5.01 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 4.69/5.01 = one_one_int ) ).
% 4.69/5.01
% 4.69/5.01 % dbl_dec_simps(3)
% 4.69/5.01 thf(fact_5469_dbl__dec__simps_I3_J,axiom,
% 4.69/5.01 ( ( neg_nu7757733837767384882nteger @ one_one_Code_integer )
% 4.69/5.01 = one_one_Code_integer ) ).
% 4.69/5.01
% 4.69/5.01 % dbl_dec_simps(3)
% 4.69/5.01 thf(fact_5470_zero__le__double__add__iff__zero__le__single__add,axiom,
% 4.69/5.01 ! [A2: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A2 @ A2 ) )
% 4.69/5.01 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_le_double_add_iff_zero_le_single_add
% 4.69/5.01 thf(fact_5471_zero__le__double__add__iff__zero__le__single__add,axiom,
% 4.69/5.01 ! [A2: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ A2 ) )
% 4.69/5.01 = ( ord_less_eq_rat @ zero_zero_rat @ A2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_le_double_add_iff_zero_le_single_add
% 4.69/5.01 thf(fact_5472_zero__le__double__add__iff__zero__le__single__add,axiom,
% 4.69/5.01 ! [A2: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A2 @ A2 ) )
% 4.69/5.01 = ( ord_less_eq_int @ zero_zero_int @ A2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_le_double_add_iff_zero_le_single_add
% 4.69/5.01 thf(fact_5473_double__add__le__zero__iff__single__add__le__zero,axiom,
% 4.69/5.01 ! [A2: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A2 @ A2 ) @ zero_z3403309356797280102nteger )
% 4.69/5.01 = ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 4.69/5.01
% 4.69/5.01 % double_add_le_zero_iff_single_add_le_zero
% 4.69/5.01 thf(fact_5474_double__add__le__zero__iff__single__add__le__zero,axiom,
% 4.69/5.01 ! [A2: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ A2 ) @ zero_zero_rat )
% 4.69/5.01 = ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ).
% 4.69/5.01
% 4.69/5.01 % double_add_le_zero_iff_single_add_le_zero
% 4.69/5.01 thf(fact_5475_double__add__le__zero__iff__single__add__le__zero,axiom,
% 4.69/5.01 ! [A2: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ ( plus_plus_int @ A2 @ A2 ) @ zero_zero_int )
% 4.69/5.01 = ( ord_less_eq_int @ A2 @ zero_zero_int ) ) ).
% 4.69/5.01
% 4.69/5.01 % double_add_le_zero_iff_single_add_le_zero
% 4.69/5.01 thf(fact_5476_le__add__same__cancel2,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ A2 @ ( plus_p5714425477246183910nteger @ B @ A2 ) )
% 4.69/5.01 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 4.69/5.01
% 4.69/5.01 % le_add_same_cancel2
% 4.69/5.01 thf(fact_5477_le__add__same__cancel2,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ A2 @ ( plus_plus_rat @ B @ A2 ) )
% 4.69/5.01 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 4.69/5.01
% 4.69/5.01 % le_add_same_cancel2
% 4.69/5.01 thf(fact_5478_le__add__same__cancel2,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ A2 @ ( plus_plus_nat @ B @ A2 ) )
% 4.69/5.01 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 4.69/5.01
% 4.69/5.01 % le_add_same_cancel2
% 4.69/5.01 thf(fact_5479_le__add__same__cancel2,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ A2 @ ( plus_plus_int @ B @ A2 ) )
% 4.69/5.01 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 4.69/5.01
% 4.69/5.01 % le_add_same_cancel2
% 4.69/5.01 thf(fact_5480_le__add__same__cancel1,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ A2 @ ( plus_p5714425477246183910nteger @ A2 @ B ) )
% 4.69/5.01 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 4.69/5.01
% 4.69/5.01 % le_add_same_cancel1
% 4.69/5.01 thf(fact_5481_le__add__same__cancel1,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ A2 @ ( plus_plus_rat @ A2 @ B ) )
% 4.69/5.01 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 4.69/5.01
% 4.69/5.01 % le_add_same_cancel1
% 4.69/5.01 thf(fact_5482_le__add__same__cancel1,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ A2 @ ( plus_plus_nat @ A2 @ B ) )
% 4.69/5.01 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 4.69/5.01
% 4.69/5.01 % le_add_same_cancel1
% 4.69/5.01 thf(fact_5483_le__add__same__cancel1,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ A2 @ ( plus_plus_int @ A2 @ B ) )
% 4.69/5.01 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 4.69/5.01
% 4.69/5.01 % le_add_same_cancel1
% 4.69/5.01 thf(fact_5484_add__le__same__cancel2,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) @ B )
% 4.69/5.01 = ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_le_same_cancel2
% 4.69/5.01 thf(fact_5485_add__le__same__cancel2,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ B ) @ B )
% 4.69/5.01 = ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_le_same_cancel2
% 4.69/5.01 thf(fact_5486_add__le__same__cancel2,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ B ) @ B )
% 4.69/5.01 = ( ord_less_eq_nat @ A2 @ zero_zero_nat ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_le_same_cancel2
% 4.69/5.01 thf(fact_5487_add__le__same__cancel2,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ ( plus_plus_int @ A2 @ B ) @ B )
% 4.69/5.01 = ( ord_less_eq_int @ A2 @ zero_zero_int ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_le_same_cancel2
% 4.69/5.01 thf(fact_5488_add__le__same__cancel1,axiom,
% 4.69/5.01 ! [B: code_integer,A2: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ B @ A2 ) @ B )
% 4.69/5.01 = ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_le_same_cancel1
% 4.69/5.01 thf(fact_5489_add__le__same__cancel1,axiom,
% 4.69/5.01 ! [B: rat,A2: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A2 ) @ B )
% 4.69/5.01 = ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_le_same_cancel1
% 4.69/5.01 thf(fact_5490_add__le__same__cancel1,axiom,
% 4.69/5.01 ! [B: nat,A2: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A2 ) @ B )
% 4.69/5.01 = ( ord_less_eq_nat @ A2 @ zero_zero_nat ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_le_same_cancel1
% 4.69/5.01 thf(fact_5491_add__le__same__cancel1,axiom,
% 4.69/5.01 ! [B: int,A2: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A2 ) @ B )
% 4.69/5.01 = ( ord_less_eq_int @ A2 @ zero_zero_int ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_le_same_cancel1
% 4.69/5.01 thf(fact_5492_diff__ge__0__iff__ge,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A2 @ B ) )
% 4.69/5.01 = ( ord_le3102999989581377725nteger @ B @ A2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % diff_ge_0_iff_ge
% 4.69/5.01 thf(fact_5493_diff__ge__0__iff__ge,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A2 @ B ) )
% 4.69/5.01 = ( ord_less_eq_rat @ B @ A2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % diff_ge_0_iff_ge
% 4.69/5.01 thf(fact_5494_diff__ge__0__iff__ge,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A2 @ B ) )
% 4.69/5.01 = ( ord_less_eq_int @ B @ A2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % diff_ge_0_iff_ge
% 4.69/5.01 thf(fact_5495_zero__comp__diff__simps_I1_J,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A2 @ B ) )
% 4.69/5.01 = ( ord_le3102999989581377725nteger @ B @ A2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_comp_diff_simps(1)
% 4.69/5.01 thf(fact_5496_zero__comp__diff__simps_I1_J,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A2 @ B ) )
% 4.69/5.01 = ( ord_less_eq_rat @ B @ A2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_comp_diff_simps(1)
% 4.69/5.01 thf(fact_5497_zero__comp__diff__simps_I1_J,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A2 @ B ) )
% 4.69/5.01 = ( ord_less_eq_int @ B @ A2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_comp_diff_simps(1)
% 4.69/5.01 thf(fact_5498_zero__less__double__add__iff__zero__less__single__add,axiom,
% 4.69/5.01 ! [A2: int] :
% 4.69/5.01 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A2 @ A2 ) )
% 4.69/5.01 = ( ord_less_int @ zero_zero_int @ A2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_less_double_add_iff_zero_less_single_add
% 4.69/5.01 thf(fact_5499_zero__less__double__add__iff__zero__less__single__add,axiom,
% 4.69/5.01 ! [A2: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A2 @ A2 ) )
% 4.69/5.01 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_less_double_add_iff_zero_less_single_add
% 4.69/5.01 thf(fact_5500_zero__less__double__add__iff__zero__less__single__add,axiom,
% 4.69/5.01 ! [A2: rat] :
% 4.69/5.01 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ A2 ) )
% 4.69/5.01 = ( ord_less_rat @ zero_zero_rat @ A2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_less_double_add_iff_zero_less_single_add
% 4.69/5.01 thf(fact_5501_double__add__less__zero__iff__single__add__less__zero,axiom,
% 4.69/5.01 ! [A2: int] :
% 4.69/5.01 ( ( ord_less_int @ ( plus_plus_int @ A2 @ A2 ) @ zero_zero_int )
% 4.69/5.01 = ( ord_less_int @ A2 @ zero_zero_int ) ) ).
% 4.69/5.01
% 4.69/5.01 % double_add_less_zero_iff_single_add_less_zero
% 4.69/5.01 thf(fact_5502_double__add__less__zero__iff__single__add__less__zero,axiom,
% 4.69/5.01 ! [A2: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ A2 ) @ zero_z3403309356797280102nteger )
% 4.69/5.01 = ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 4.69/5.01
% 4.69/5.01 % double_add_less_zero_iff_single_add_less_zero
% 4.69/5.01 thf(fact_5503_double__add__less__zero__iff__single__add__less__zero,axiom,
% 4.69/5.01 ! [A2: rat] :
% 4.69/5.01 ( ( ord_less_rat @ ( plus_plus_rat @ A2 @ A2 ) @ zero_zero_rat )
% 4.69/5.01 = ( ord_less_rat @ A2 @ zero_zero_rat ) ) ).
% 4.69/5.01
% 4.69/5.01 % double_add_less_zero_iff_single_add_less_zero
% 4.69/5.01 thf(fact_5504_less__add__same__cancel2,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_nat @ A2 @ ( plus_plus_nat @ B @ A2 ) )
% 4.69/5.01 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 4.69/5.01
% 4.69/5.01 % less_add_same_cancel2
% 4.69/5.01 thf(fact_5505_less__add__same__cancel2,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ A2 @ ( plus_plus_int @ B @ A2 ) )
% 4.69/5.01 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 4.69/5.01
% 4.69/5.01 % less_add_same_cancel2
% 4.69/5.01 thf(fact_5506_less__add__same__cancel2,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ A2 @ ( plus_p5714425477246183910nteger @ B @ A2 ) )
% 4.69/5.01 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 4.69/5.01
% 4.69/5.01 % less_add_same_cancel2
% 4.69/5.01 thf(fact_5507_less__add__same__cancel2,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ A2 @ ( plus_plus_rat @ B @ A2 ) )
% 4.69/5.01 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 4.69/5.01
% 4.69/5.01 % less_add_same_cancel2
% 4.69/5.01 thf(fact_5508_less__add__same__cancel1,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_nat @ A2 @ ( plus_plus_nat @ A2 @ B ) )
% 4.69/5.01 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 4.69/5.01
% 4.69/5.01 % less_add_same_cancel1
% 4.69/5.01 thf(fact_5509_less__add__same__cancel1,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ A2 @ ( plus_plus_int @ A2 @ B ) )
% 4.69/5.01 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 4.69/5.01
% 4.69/5.01 % less_add_same_cancel1
% 4.69/5.01 thf(fact_5510_less__add__same__cancel1,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ A2 @ ( plus_p5714425477246183910nteger @ A2 @ B ) )
% 4.69/5.01 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 4.69/5.01
% 4.69/5.01 % less_add_same_cancel1
% 4.69/5.01 thf(fact_5511_less__add__same__cancel1,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ A2 @ ( plus_plus_rat @ A2 @ B ) )
% 4.69/5.01 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 4.69/5.01
% 4.69/5.01 % less_add_same_cancel1
% 4.69/5.01 thf(fact_5512_add__less__same__cancel2,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_nat @ ( plus_plus_nat @ A2 @ B ) @ B )
% 4.69/5.01 = ( ord_less_nat @ A2 @ zero_zero_nat ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_less_same_cancel2
% 4.69/5.01 thf(fact_5513_add__less__same__cancel2,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ ( plus_plus_int @ A2 @ B ) @ B )
% 4.69/5.01 = ( ord_less_int @ A2 @ zero_zero_int ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_less_same_cancel2
% 4.69/5.01 thf(fact_5514_add__less__same__cancel2,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) @ B )
% 4.69/5.01 = ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_less_same_cancel2
% 4.69/5.01 thf(fact_5515_add__less__same__cancel2,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ ( plus_plus_rat @ A2 @ B ) @ B )
% 4.69/5.01 = ( ord_less_rat @ A2 @ zero_zero_rat ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_less_same_cancel2
% 4.69/5.01 thf(fact_5516_add__less__same__cancel1,axiom,
% 4.69/5.01 ! [B: nat,A2: nat] :
% 4.69/5.01 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A2 ) @ B )
% 4.69/5.01 = ( ord_less_nat @ A2 @ zero_zero_nat ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_less_same_cancel1
% 4.69/5.01 thf(fact_5517_add__less__same__cancel1,axiom,
% 4.69/5.01 ! [B: int,A2: int] :
% 4.69/5.01 ( ( ord_less_int @ ( plus_plus_int @ B @ A2 ) @ B )
% 4.69/5.01 = ( ord_less_int @ A2 @ zero_zero_int ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_less_same_cancel1
% 4.69/5.01 thf(fact_5518_add__less__same__cancel1,axiom,
% 4.69/5.01 ! [B: code_integer,A2: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ B @ A2 ) @ B )
% 4.69/5.01 = ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_less_same_cancel1
% 4.69/5.01 thf(fact_5519_add__less__same__cancel1,axiom,
% 4.69/5.01 ! [B: rat,A2: rat] :
% 4.69/5.01 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A2 ) @ B )
% 4.69/5.01 = ( ord_less_rat @ A2 @ zero_zero_rat ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_less_same_cancel1
% 4.69/5.01 thf(fact_5520_zero__comp__diff__simps_I2_J,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A2 @ B ) )
% 4.69/5.01 = ( ord_less_int @ B @ A2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_comp_diff_simps(2)
% 4.69/5.01 thf(fact_5521_zero__comp__diff__simps_I2_J,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A2 @ B ) )
% 4.69/5.01 = ( ord_le6747313008572928689nteger @ B @ A2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_comp_diff_simps(2)
% 4.69/5.01 thf(fact_5522_zero__comp__diff__simps_I2_J,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A2 @ B ) )
% 4.69/5.01 = ( ord_less_rat @ B @ A2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_comp_diff_simps(2)
% 4.69/5.01 thf(fact_5523_diff__gt__0__iff__gt,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A2 @ B ) )
% 4.69/5.01 = ( ord_less_int @ B @ A2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % diff_gt_0_iff_gt
% 4.69/5.01 thf(fact_5524_diff__gt__0__iff__gt,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A2 @ B ) )
% 4.69/5.01 = ( ord_le6747313008572928689nteger @ B @ A2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % diff_gt_0_iff_gt
% 4.69/5.01 thf(fact_5525_diff__gt__0__iff__gt,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A2 @ B ) )
% 4.69/5.01 = ( ord_less_rat @ B @ A2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % diff_gt_0_iff_gt
% 4.69/5.01 thf(fact_5526_diff__add__zero,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( minus_minus_nat @ A2 @ ( plus_plus_nat @ A2 @ B ) )
% 4.69/5.01 = zero_zero_nat ) ).
% 4.69/5.01
% 4.69/5.01 % diff_add_zero
% 4.69/5.01 thf(fact_5527_mult__cancel__right2,axiom,
% 4.69/5.01 ! [A2: code_integer,C: code_integer] :
% 4.69/5.01 ( ( ( times_3573771949741848930nteger @ A2 @ C )
% 4.69/5.01 = C )
% 4.69/5.01 = ( ( C = zero_z3403309356797280102nteger )
% 4.69/5.01 | ( A2 = one_one_Code_integer ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_cancel_right2
% 4.69/5.01 thf(fact_5528_mult__cancel__right2,axiom,
% 4.69/5.01 ! [A2: rat,C: rat] :
% 4.69/5.01 ( ( ( times_times_rat @ A2 @ C )
% 4.69/5.01 = C )
% 4.69/5.01 = ( ( C = zero_zero_rat )
% 4.69/5.01 | ( A2 = one_one_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_cancel_right2
% 4.69/5.01 thf(fact_5529_mult__cancel__right2,axiom,
% 4.69/5.01 ! [A2: int,C: int] :
% 4.69/5.01 ( ( ( times_times_int @ A2 @ C )
% 4.69/5.01 = C )
% 4.69/5.01 = ( ( C = zero_zero_int )
% 4.69/5.01 | ( A2 = one_one_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_cancel_right2
% 4.69/5.01 thf(fact_5530_mult__cancel__right1,axiom,
% 4.69/5.01 ! [C: code_integer,B: code_integer] :
% 4.69/5.01 ( ( C
% 4.69/5.01 = ( times_3573771949741848930nteger @ B @ C ) )
% 4.69/5.01 = ( ( C = zero_z3403309356797280102nteger )
% 4.69/5.01 | ( B = one_one_Code_integer ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_cancel_right1
% 4.69/5.01 thf(fact_5531_mult__cancel__right1,axiom,
% 4.69/5.01 ! [C: rat,B: rat] :
% 4.69/5.01 ( ( C
% 4.69/5.01 = ( times_times_rat @ B @ C ) )
% 4.69/5.01 = ( ( C = zero_zero_rat )
% 4.69/5.01 | ( B = one_one_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_cancel_right1
% 4.69/5.01 thf(fact_5532_mult__cancel__right1,axiom,
% 4.69/5.01 ! [C: int,B: int] :
% 4.69/5.01 ( ( C
% 4.69/5.01 = ( times_times_int @ B @ C ) )
% 4.69/5.01 = ( ( C = zero_zero_int )
% 4.69/5.01 | ( B = one_one_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_cancel_right1
% 4.69/5.01 thf(fact_5533_mult__cancel__left2,axiom,
% 4.69/5.01 ! [C: code_integer,A2: code_integer] :
% 4.69/5.01 ( ( ( times_3573771949741848930nteger @ C @ A2 )
% 4.69/5.01 = C )
% 4.69/5.01 = ( ( C = zero_z3403309356797280102nteger )
% 4.69/5.01 | ( A2 = one_one_Code_integer ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_cancel_left2
% 4.69/5.01 thf(fact_5534_mult__cancel__left2,axiom,
% 4.69/5.01 ! [C: rat,A2: rat] :
% 4.69/5.01 ( ( ( times_times_rat @ C @ A2 )
% 4.69/5.01 = C )
% 4.69/5.01 = ( ( C = zero_zero_rat )
% 4.69/5.01 | ( A2 = one_one_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_cancel_left2
% 4.69/5.01 thf(fact_5535_mult__cancel__left2,axiom,
% 4.69/5.01 ! [C: int,A2: int] :
% 4.69/5.01 ( ( ( times_times_int @ C @ A2 )
% 4.69/5.01 = C )
% 4.69/5.01 = ( ( C = zero_zero_int )
% 4.69/5.01 | ( A2 = one_one_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_cancel_left2
% 4.69/5.01 thf(fact_5536_mult__cancel__left1,axiom,
% 4.69/5.01 ! [C: code_integer,B: code_integer] :
% 4.69/5.01 ( ( C
% 4.69/5.01 = ( times_3573771949741848930nteger @ C @ B ) )
% 4.69/5.01 = ( ( C = zero_z3403309356797280102nteger )
% 4.69/5.01 | ( B = one_one_Code_integer ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_cancel_left1
% 4.69/5.01 thf(fact_5537_mult__cancel__left1,axiom,
% 4.69/5.01 ! [C: rat,B: rat] :
% 4.69/5.01 ( ( C
% 4.69/5.01 = ( times_times_rat @ C @ B ) )
% 4.69/5.01 = ( ( C = zero_zero_rat )
% 4.69/5.01 | ( B = one_one_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_cancel_left1
% 4.69/5.01 thf(fact_5538_mult__cancel__left1,axiom,
% 4.69/5.01 ! [C: int,B: int] :
% 4.69/5.01 ( ( C
% 4.69/5.01 = ( times_times_int @ C @ B ) )
% 4.69/5.01 = ( ( C = zero_zero_int )
% 4.69/5.01 | ( B = one_one_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_cancel_left1
% 4.69/5.01 thf(fact_5539_image__add__0,axiom,
% 4.69/5.01 ! [S: set_rat] :
% 4.69/5.01 ( ( image_rat_rat @ ( plus_plus_rat @ zero_zero_rat ) @ S )
% 4.69/5.01 = S ) ).
% 4.69/5.01
% 4.69/5.01 % image_add_0
% 4.69/5.01 thf(fact_5540_image__add__0,axiom,
% 4.69/5.01 ! [S: set_nat] :
% 4.69/5.01 ( ( image_nat_nat2 @ ( plus_plus_nat @ zero_zero_nat ) @ S )
% 4.69/5.01 = S ) ).
% 4.69/5.01
% 4.69/5.01 % image_add_0
% 4.69/5.01 thf(fact_5541_image__add__0,axiom,
% 4.69/5.01 ! [S: set_int] :
% 4.69/5.01 ( ( image_int_int2 @ ( plus_plus_int @ zero_zero_int ) @ S )
% 4.69/5.01 = S ) ).
% 4.69/5.01
% 4.69/5.01 % image_add_0
% 4.69/5.01 thf(fact_5542_image__add__0,axiom,
% 4.69/5.01 ! [S: set_Code_integer] :
% 4.69/5.01 ( ( image_4470545334726330049nteger @ ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger ) @ S )
% 4.69/5.01 = S ) ).
% 4.69/5.01
% 4.69/5.01 % image_add_0
% 4.69/5.01 thf(fact_5543_diff__numeral__special_I9_J,axiom,
% 4.69/5.01 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ one_one_Code_integer )
% 4.69/5.01 = zero_z3403309356797280102nteger ) ).
% 4.69/5.01
% 4.69/5.01 % diff_numeral_special(9)
% 4.69/5.01 thf(fact_5544_diff__numeral__special_I9_J,axiom,
% 4.69/5.01 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 4.69/5.01 = zero_zero_rat ) ).
% 4.69/5.01
% 4.69/5.01 % diff_numeral_special(9)
% 4.69/5.01 thf(fact_5545_diff__numeral__special_I9_J,axiom,
% 4.69/5.01 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 4.69/5.01 = zero_zero_int ) ).
% 4.69/5.01
% 4.69/5.01 % diff_numeral_special(9)
% 4.69/5.01 thf(fact_5546_max__0__1_I2_J,axiom,
% 4.69/5.01 ( ( ord_max_Code_natural @ one_one_Code_natural @ zero_z2226904508553997617atural )
% 4.69/5.01 = one_one_Code_natural ) ).
% 4.69/5.01
% 4.69/5.01 % max_0_1(2)
% 4.69/5.01 thf(fact_5547_max__0__1_I2_J,axiom,
% 4.69/5.01 ( ( ord_max_Code_integer @ one_one_Code_integer @ zero_z3403309356797280102nteger )
% 4.69/5.01 = one_one_Code_integer ) ).
% 4.69/5.01
% 4.69/5.01 % max_0_1(2)
% 4.69/5.01 thf(fact_5548_max__0__1_I2_J,axiom,
% 4.69/5.01 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 4.69/5.01 = one_one_nat ) ).
% 4.69/5.01
% 4.69/5.01 % max_0_1(2)
% 4.69/5.01 thf(fact_5549_max__0__1_I2_J,axiom,
% 4.69/5.01 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 4.69/5.01 = one_one_int ) ).
% 4.69/5.01
% 4.69/5.01 % max_0_1(2)
% 4.69/5.01 thf(fact_5550_max__0__1_I1_J,axiom,
% 4.69/5.01 ( ( ord_max_Code_natural @ zero_z2226904508553997617atural @ one_one_Code_natural )
% 4.69/5.01 = one_one_Code_natural ) ).
% 4.69/5.01
% 4.69/5.01 % max_0_1(1)
% 4.69/5.01 thf(fact_5551_max__0__1_I1_J,axiom,
% 4.69/5.01 ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer )
% 4.69/5.01 = one_one_Code_integer ) ).
% 4.69/5.01
% 4.69/5.01 % max_0_1(1)
% 4.69/5.01 thf(fact_5552_max__0__1_I1_J,axiom,
% 4.69/5.01 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 4.69/5.01 = one_one_nat ) ).
% 4.69/5.01
% 4.69/5.01 % max_0_1(1)
% 4.69/5.01 thf(fact_5553_max__0__1_I1_J,axiom,
% 4.69/5.01 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 4.69/5.01 = one_one_int ) ).
% 4.69/5.01
% 4.69/5.01 % max_0_1(1)
% 4.69/5.01 thf(fact_5554_card_Oempty,axiom,
% 4.69/5.01 ( ( finite410649719033368117t_unit @ bot_bo3957492148770167129t_unit )
% 4.69/5.01 = zero_zero_nat ) ).
% 4.69/5.01
% 4.69/5.01 % card.empty
% 4.69/5.01 thf(fact_5555_card_Oempty,axiom,
% 4.69/5.01 ( ( finite_card_o @ bot_bot_set_o )
% 4.69/5.01 = zero_zero_nat ) ).
% 4.69/5.01
% 4.69/5.01 % card.empty
% 4.69/5.01 thf(fact_5556_card_Oempty,axiom,
% 4.69/5.01 ( ( finite_card_nat @ bot_bot_set_nat )
% 4.69/5.01 = zero_zero_nat ) ).
% 4.69/5.01
% 4.69/5.01 % card.empty
% 4.69/5.01 thf(fact_5557_card_Oempty,axiom,
% 4.69/5.01 ( ( finite_card_int @ bot_bot_set_int )
% 4.69/5.01 = zero_zero_nat ) ).
% 4.69/5.01
% 4.69/5.01 % card.empty
% 4.69/5.01 thf(fact_5558_card_Oempty,axiom,
% 4.69/5.01 ( ( finite1363419556375932405_nat_o @ bot_bo7824918357723582233_nat_o )
% 4.69/5.01 = zero_zero_nat ) ).
% 4.69/5.01
% 4.69/5.01 % card.empty
% 4.69/5.01 thf(fact_5559_one__eq__mult__iff,axiom,
% 4.69/5.01 ! [M4: nat,N2: nat] :
% 4.69/5.01 ( ( ( suc @ zero_zero_nat )
% 4.69/5.01 = ( times_times_nat @ M4 @ N2 ) )
% 4.69/5.01 = ( ( M4
% 4.69/5.01 = ( suc @ zero_zero_nat ) )
% 4.69/5.01 & ( N2
% 4.69/5.01 = ( suc @ zero_zero_nat ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % one_eq_mult_iff
% 4.69/5.01 thf(fact_5560_mult__eq__1__iff,axiom,
% 4.69/5.01 ! [M4: nat,N2: nat] :
% 4.69/5.01 ( ( ( times_times_nat @ M4 @ N2 )
% 4.69/5.01 = ( suc @ zero_zero_nat ) )
% 4.69/5.01 = ( ( M4
% 4.69/5.01 = ( suc @ zero_zero_nat ) )
% 4.69/5.01 & ( N2
% 4.69/5.01 = ( suc @ zero_zero_nat ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_eq_1_iff
% 4.69/5.01 thf(fact_5561_nat__mult__less__cancel__disj,axiom,
% 4.69/5.01 ! [K3: nat,M4: nat,N2: nat] :
% 4.69/5.01 ( ( ord_less_nat @ ( times_times_nat @ K3 @ M4 ) @ ( times_times_nat @ K3 @ N2 ) )
% 4.69/5.01 = ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 4.69/5.01 & ( ord_less_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % nat_mult_less_cancel_disj
% 4.69/5.01 thf(fact_5562_nat__0__less__mult__iff,axiom,
% 4.69/5.01 ! [M4: nat,N2: nat] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M4 @ N2 ) )
% 4.69/5.01 = ( ( ord_less_nat @ zero_zero_nat @ M4 )
% 4.69/5.01 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % nat_0_less_mult_iff
% 4.69/5.01 thf(fact_5563_mult__less__cancel2,axiom,
% 4.69/5.01 ! [M4: nat,K3: nat,N2: nat] :
% 4.69/5.01 ( ( ord_less_nat @ ( times_times_nat @ M4 @ K3 ) @ ( times_times_nat @ N2 @ K3 ) )
% 4.69/5.01 = ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 4.69/5.01 & ( ord_less_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel2
% 4.69/5.01 thf(fact_5564_card__0__eq,axiom,
% 4.69/5.01 ! [A: set_Code_integer] :
% 4.69/5.01 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.01 => ( ( ( finite4902975817058060853nteger @ A )
% 4.69/5.01 = zero_zero_nat )
% 4.69/5.01 = ( A = bot_bo3990330152332043303nteger ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_0_eq
% 4.69/5.01 thf(fact_5565_card__0__eq,axiom,
% 4.69/5.01 ! [A: set_Product_unit] :
% 4.69/5.01 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.01 => ( ( ( finite410649719033368117t_unit @ A )
% 4.69/5.01 = zero_zero_nat )
% 4.69/5.01 = ( A = bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_0_eq
% 4.69/5.01 thf(fact_5566_card__0__eq,axiom,
% 4.69/5.01 ! [A: set_o] :
% 4.69/5.01 ( ( finite_finite_o @ A )
% 4.69/5.01 => ( ( ( finite_card_o @ A )
% 4.69/5.01 = zero_zero_nat )
% 4.69/5.01 = ( A = bot_bot_set_o ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_0_eq
% 4.69/5.01 thf(fact_5567_card__0__eq,axiom,
% 4.69/5.01 ! [A: set_nat] :
% 4.69/5.01 ( ( finite_finite_nat @ A )
% 4.69/5.01 => ( ( ( finite_card_nat @ A )
% 4.69/5.01 = zero_zero_nat )
% 4.69/5.01 = ( A = bot_bot_set_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_0_eq
% 4.69/5.01 thf(fact_5568_card__0__eq,axiom,
% 4.69/5.01 ! [A: set_int] :
% 4.69/5.01 ( ( finite_finite_int @ A )
% 4.69/5.01 => ( ( ( finite_card_int @ A )
% 4.69/5.01 = zero_zero_nat )
% 4.69/5.01 = ( A = bot_bot_set_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_0_eq
% 4.69/5.01 thf(fact_5569_card__0__eq,axiom,
% 4.69/5.01 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/5.01 ( ( finite3252695134891459830_nat_o @ A )
% 4.69/5.01 => ( ( ( finite1363419556375932405_nat_o @ A )
% 4.69/5.01 = zero_zero_nat )
% 4.69/5.01 = ( A = bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_0_eq
% 4.69/5.01 thf(fact_5570_one__le__mult__iff,axiom,
% 4.69/5.01 ! [M4: nat,N2: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M4 @ N2 ) )
% 4.69/5.01 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M4 )
% 4.69/5.01 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % one_le_mult_iff
% 4.69/5.01 thf(fact_5571_mult__le__cancel2,axiom,
% 4.69/5.01 ! [M4: nat,K3: nat,N2: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ ( times_times_nat @ M4 @ K3 ) @ ( times_times_nat @ N2 @ K3 ) )
% 4.69/5.01 = ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 4.69/5.01 => ( ord_less_eq_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel2
% 4.69/5.01 thf(fact_5572_nat__mult__le__cancel__disj,axiom,
% 4.69/5.01 ! [K3: nat,M4: nat,N2: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ ( times_times_nat @ K3 @ M4 ) @ ( times_times_nat @ K3 @ N2 ) )
% 4.69/5.01 = ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 4.69/5.01 => ( ord_less_eq_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % nat_mult_le_cancel_disj
% 4.69/5.01 thf(fact_5573_bot__nat__def,axiom,
% 4.69/5.01 bot_bot_nat = zero_zero_nat ).
% 4.69/5.01
% 4.69/5.01 % bot_nat_def
% 4.69/5.01 thf(fact_5574_zero__reorient,axiom,
% 4.69/5.01 ! [X: nat] :
% 4.69/5.01 ( ( zero_zero_nat = X )
% 4.69/5.01 = ( X = zero_zero_nat ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_reorient
% 4.69/5.01 thf(fact_5575_zero__reorient,axiom,
% 4.69/5.01 ! [X: int] :
% 4.69/5.01 ( ( zero_zero_int = X )
% 4.69/5.01 = ( X = zero_zero_int ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_reorient
% 4.69/5.01 thf(fact_5576_zero__reorient,axiom,
% 4.69/5.01 ! [X: code_integer] :
% 4.69/5.01 ( ( zero_z3403309356797280102nteger = X )
% 4.69/5.01 = ( X = zero_z3403309356797280102nteger ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_reorient
% 4.69/5.01 thf(fact_5577_zero__le,axiom,
% 4.69/5.01 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 4.69/5.01
% 4.69/5.01 % zero_le
% 4.69/5.01 thf(fact_5578_gr__zeroI,axiom,
% 4.69/5.01 ! [N2: nat] :
% 4.69/5.01 ( ( N2 != zero_zero_nat )
% 4.69/5.01 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % gr_zeroI
% 4.69/5.01 thf(fact_5579_not__less__zero,axiom,
% 4.69/5.01 ! [N2: nat] :
% 4.69/5.01 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 4.69/5.01
% 4.69/5.01 % not_less_zero
% 4.69/5.01 thf(fact_5580_gr__implies__not__zero,axiom,
% 4.69/5.01 ! [M4: nat,N2: nat] :
% 4.69/5.01 ( ( ord_less_nat @ M4 @ N2 )
% 4.69/5.01 => ( N2 != zero_zero_nat ) ) ).
% 4.69/5.01
% 4.69/5.01 % gr_implies_not_zero
% 4.69/5.01 thf(fact_5581_zero__less__iff__neq__zero,axiom,
% 4.69/5.01 ! [N2: nat] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.01 = ( N2 != zero_zero_nat ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_less_iff_neq_zero
% 4.69/5.01 thf(fact_5582_comm__monoid__add__class_Oadd__0,axiom,
% 4.69/5.01 ! [A2: rat] :
% 4.69/5.01 ( ( plus_plus_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % comm_monoid_add_class.add_0
% 4.69/5.01 thf(fact_5583_comm__monoid__add__class_Oadd__0,axiom,
% 4.69/5.01 ! [A2: nat] :
% 4.69/5.01 ( ( plus_plus_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % comm_monoid_add_class.add_0
% 4.69/5.01 thf(fact_5584_comm__monoid__add__class_Oadd__0,axiom,
% 4.69/5.01 ! [A2: int] :
% 4.69/5.01 ( ( plus_plus_int @ zero_zero_int @ A2 )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % comm_monoid_add_class.add_0
% 4.69/5.01 thf(fact_5585_comm__monoid__add__class_Oadd__0,axiom,
% 4.69/5.01 ! [A2: code_integer] :
% 4.69/5.01 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % comm_monoid_add_class.add_0
% 4.69/5.01 thf(fact_5586_add_Ocomm__neutral,axiom,
% 4.69/5.01 ! [A2: rat] :
% 4.69/5.01 ( ( plus_plus_rat @ A2 @ zero_zero_rat )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % add.comm_neutral
% 4.69/5.01 thf(fact_5587_add_Ocomm__neutral,axiom,
% 4.69/5.01 ! [A2: nat] :
% 4.69/5.01 ( ( plus_plus_nat @ A2 @ zero_zero_nat )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % add.comm_neutral
% 4.69/5.01 thf(fact_5588_add_Ocomm__neutral,axiom,
% 4.69/5.01 ! [A2: int] :
% 4.69/5.01 ( ( plus_plus_int @ A2 @ zero_zero_int )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % add.comm_neutral
% 4.69/5.01 thf(fact_5589_add_Ocomm__neutral,axiom,
% 4.69/5.01 ! [A2: code_integer] :
% 4.69/5.01 ( ( plus_p5714425477246183910nteger @ A2 @ zero_z3403309356797280102nteger )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % add.comm_neutral
% 4.69/5.01 thf(fact_5590_add_Ogroup__left__neutral,axiom,
% 4.69/5.01 ! [A2: rat] :
% 4.69/5.01 ( ( plus_plus_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % add.group_left_neutral
% 4.69/5.01 thf(fact_5591_add_Ogroup__left__neutral,axiom,
% 4.69/5.01 ! [A2: int] :
% 4.69/5.01 ( ( plus_plus_int @ zero_zero_int @ A2 )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % add.group_left_neutral
% 4.69/5.01 thf(fact_5592_add_Ogroup__left__neutral,axiom,
% 4.69/5.01 ! [A2: code_integer] :
% 4.69/5.01 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 = A2 ) ).
% 4.69/5.01
% 4.69/5.01 % add.group_left_neutral
% 4.69/5.01 thf(fact_5593_mult__right__cancel,axiom,
% 4.69/5.01 ! [C: code_integer,A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( C != zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ( ( times_3573771949741848930nteger @ A2 @ C )
% 4.69/5.01 = ( times_3573771949741848930nteger @ B @ C ) )
% 4.69/5.01 = ( A2 = B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_right_cancel
% 4.69/5.01 thf(fact_5594_mult__right__cancel,axiom,
% 4.69/5.01 ! [C: rat,A2: rat,B: rat] :
% 4.69/5.01 ( ( C != zero_zero_rat )
% 4.69/5.01 => ( ( ( times_times_rat @ A2 @ C )
% 4.69/5.01 = ( times_times_rat @ B @ C ) )
% 4.69/5.01 = ( A2 = B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_right_cancel
% 4.69/5.01 thf(fact_5595_mult__right__cancel,axiom,
% 4.69/5.01 ! [C: nat,A2: nat,B: nat] :
% 4.69/5.01 ( ( C != zero_zero_nat )
% 4.69/5.01 => ( ( ( times_times_nat @ A2 @ C )
% 4.69/5.01 = ( times_times_nat @ B @ C ) )
% 4.69/5.01 = ( A2 = B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_right_cancel
% 4.69/5.01 thf(fact_5596_mult__right__cancel,axiom,
% 4.69/5.01 ! [C: int,A2: int,B: int] :
% 4.69/5.01 ( ( C != zero_zero_int )
% 4.69/5.01 => ( ( ( times_times_int @ A2 @ C )
% 4.69/5.01 = ( times_times_int @ B @ C ) )
% 4.69/5.01 = ( A2 = B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_right_cancel
% 4.69/5.01 thf(fact_5597_mult__left__cancel,axiom,
% 4.69/5.01 ! [C: code_integer,A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( C != zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ( ( times_3573771949741848930nteger @ C @ A2 )
% 4.69/5.01 = ( times_3573771949741848930nteger @ C @ B ) )
% 4.69/5.01 = ( A2 = B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_cancel
% 4.69/5.01 thf(fact_5598_mult__left__cancel,axiom,
% 4.69/5.01 ! [C: rat,A2: rat,B: rat] :
% 4.69/5.01 ( ( C != zero_zero_rat )
% 4.69/5.01 => ( ( ( times_times_rat @ C @ A2 )
% 4.69/5.01 = ( times_times_rat @ C @ B ) )
% 4.69/5.01 = ( A2 = B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_cancel
% 4.69/5.01 thf(fact_5599_mult__left__cancel,axiom,
% 4.69/5.01 ! [C: nat,A2: nat,B: nat] :
% 4.69/5.01 ( ( C != zero_zero_nat )
% 4.69/5.01 => ( ( ( times_times_nat @ C @ A2 )
% 4.69/5.01 = ( times_times_nat @ C @ B ) )
% 4.69/5.01 = ( A2 = B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_cancel
% 4.69/5.01 thf(fact_5600_mult__left__cancel,axiom,
% 4.69/5.01 ! [C: int,A2: int,B: int] :
% 4.69/5.01 ( ( C != zero_zero_int )
% 4.69/5.01 => ( ( ( times_times_int @ C @ A2 )
% 4.69/5.01 = ( times_times_int @ C @ B ) )
% 4.69/5.01 = ( A2 = B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_cancel
% 4.69/5.01 thf(fact_5601_no__zero__divisors,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( A2 != zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ( B != zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ( times_3573771949741848930nteger @ A2 @ B )
% 4.69/5.01 != zero_z3403309356797280102nteger ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % no_zero_divisors
% 4.69/5.01 thf(fact_5602_no__zero__divisors,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( A2 != zero_zero_rat )
% 4.69/5.01 => ( ( B != zero_zero_rat )
% 4.69/5.01 => ( ( times_times_rat @ A2 @ B )
% 4.69/5.01 != zero_zero_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % no_zero_divisors
% 4.69/5.01 thf(fact_5603_no__zero__divisors,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( A2 != zero_zero_nat )
% 4.69/5.01 => ( ( B != zero_zero_nat )
% 4.69/5.01 => ( ( times_times_nat @ A2 @ B )
% 4.69/5.01 != zero_zero_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % no_zero_divisors
% 4.69/5.01 thf(fact_5604_no__zero__divisors,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( A2 != zero_zero_int )
% 4.69/5.01 => ( ( B != zero_zero_int )
% 4.69/5.01 => ( ( times_times_int @ A2 @ B )
% 4.69/5.01 != zero_zero_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % no_zero_divisors
% 4.69/5.01 thf(fact_5605_divisors__zero,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ( times_3573771949741848930nteger @ A2 @ B )
% 4.69/5.01 = zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ( A2 = zero_z3403309356797280102nteger )
% 4.69/5.01 | ( B = zero_z3403309356797280102nteger ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % divisors_zero
% 4.69/5.01 thf(fact_5606_divisors__zero,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ( times_times_rat @ A2 @ B )
% 4.69/5.01 = zero_zero_rat )
% 4.69/5.01 => ( ( A2 = zero_zero_rat )
% 4.69/5.01 | ( B = zero_zero_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % divisors_zero
% 4.69/5.01 thf(fact_5607_divisors__zero,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ( times_times_nat @ A2 @ B )
% 4.69/5.01 = zero_zero_nat )
% 4.69/5.01 => ( ( A2 = zero_zero_nat )
% 4.69/5.01 | ( B = zero_zero_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % divisors_zero
% 4.69/5.01 thf(fact_5608_divisors__zero,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ( times_times_int @ A2 @ B )
% 4.69/5.01 = zero_zero_int )
% 4.69/5.01 => ( ( A2 = zero_zero_int )
% 4.69/5.01 | ( B = zero_zero_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % divisors_zero
% 4.69/5.01 thf(fact_5609_mult__not__zero,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ( times_3573771949741848930nteger @ A2 @ B )
% 4.69/5.01 != zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ( A2 != zero_z3403309356797280102nteger )
% 4.69/5.01 & ( B != zero_z3403309356797280102nteger ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_not_zero
% 4.69/5.01 thf(fact_5610_mult__not__zero,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ( times_times_rat @ A2 @ B )
% 4.69/5.01 != zero_zero_rat )
% 4.69/5.01 => ( ( A2 != zero_zero_rat )
% 4.69/5.01 & ( B != zero_zero_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_not_zero
% 4.69/5.01 thf(fact_5611_mult__not__zero,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ( times_times_nat @ A2 @ B )
% 4.69/5.01 != zero_zero_nat )
% 4.69/5.01 => ( ( A2 != zero_zero_nat )
% 4.69/5.01 & ( B != zero_zero_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_not_zero
% 4.69/5.01 thf(fact_5612_mult__not__zero,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ( times_times_int @ A2 @ B )
% 4.69/5.01 != zero_zero_int )
% 4.69/5.01 => ( ( A2 != zero_zero_int )
% 4.69/5.01 & ( B != zero_zero_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_not_zero
% 4.69/5.01 thf(fact_5613_zero__neq__one,axiom,
% 4.69/5.01 zero_z2226904508553997617atural != one_one_Code_natural ).
% 4.69/5.01
% 4.69/5.01 % zero_neq_one
% 4.69/5.01 thf(fact_5614_zero__neq__one,axiom,
% 4.69/5.01 zero_zero_nat != one_one_nat ).
% 4.69/5.01
% 4.69/5.01 % zero_neq_one
% 4.69/5.01 thf(fact_5615_zero__neq__one,axiom,
% 4.69/5.01 zero_zero_int != one_one_int ).
% 4.69/5.01
% 4.69/5.01 % zero_neq_one
% 4.69/5.01 thf(fact_5616_zero__neq__one,axiom,
% 4.69/5.01 zero_z3403309356797280102nteger != one_one_Code_integer ).
% 4.69/5.01
% 4.69/5.01 % zero_neq_one
% 4.69/5.01 thf(fact_5617_eq__iff__diff__eq__0,axiom,
% 4.69/5.01 ( ( ^ [Y4: code_integer,Z4: code_integer] : ( Y4 = Z4 ) )
% 4.69/5.01 = ( ^ [A6: code_integer,B6: code_integer] :
% 4.69/5.01 ( ( minus_8373710615458151222nteger @ A6 @ B6 )
% 4.69/5.01 = zero_z3403309356797280102nteger ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % eq_iff_diff_eq_0
% 4.69/5.01 thf(fact_5618_eq__iff__diff__eq__0,axiom,
% 4.69/5.01 ( ( ^ [Y4: rat,Z4: rat] : ( Y4 = Z4 ) )
% 4.69/5.01 = ( ^ [A6: rat,B6: rat] :
% 4.69/5.01 ( ( minus_minus_rat @ A6 @ B6 )
% 4.69/5.01 = zero_zero_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % eq_iff_diff_eq_0
% 4.69/5.01 thf(fact_5619_eq__iff__diff__eq__0,axiom,
% 4.69/5.01 ( ( ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 4.69/5.01 = ( ^ [A6: int,B6: int] :
% 4.69/5.01 ( ( minus_minus_int @ A6 @ B6 )
% 4.69/5.01 = zero_zero_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % eq_iff_diff_eq_0
% 4.69/5.01 thf(fact_5620_mult__0,axiom,
% 4.69/5.01 ! [N2: nat] :
% 4.69/5.01 ( ( times_times_nat @ zero_zero_nat @ N2 )
% 4.69/5.01 = zero_zero_nat ) ).
% 4.69/5.01
% 4.69/5.01 % mult_0
% 4.69/5.01 thf(fact_5621_nat__mult__eq__cancel__disj,axiom,
% 4.69/5.01 ! [K3: nat,M4: nat,N2: nat] :
% 4.69/5.01 ( ( ( times_times_nat @ K3 @ M4 )
% 4.69/5.01 = ( times_times_nat @ K3 @ N2 ) )
% 4.69/5.01 = ( ( K3 = zero_zero_nat )
% 4.69/5.01 | ( M4 = N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % nat_mult_eq_cancel_disj
% 4.69/5.01 thf(fact_5622_add__scale__eq__noteq,axiom,
% 4.69/5.01 ! [R2: code_integer,A2: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 4.69/5.01 ( ( R2 != zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ( ( A2 = B )
% 4.69/5.01 & ( C != D2 ) )
% 4.69/5.01 => ( ( plus_p5714425477246183910nteger @ A2 @ ( times_3573771949741848930nteger @ R2 @ C ) )
% 4.69/5.01 != ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ R2 @ D2 ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_scale_eq_noteq
% 4.69/5.01 thf(fact_5623_add__scale__eq__noteq,axiom,
% 4.69/5.01 ! [R2: rat,A2: rat,B: rat,C: rat,D2: rat] :
% 4.69/5.01 ( ( R2 != zero_zero_rat )
% 4.69/5.01 => ( ( ( A2 = B )
% 4.69/5.01 & ( C != D2 ) )
% 4.69/5.01 => ( ( plus_plus_rat @ A2 @ ( times_times_rat @ R2 @ C ) )
% 4.69/5.01 != ( plus_plus_rat @ B @ ( times_times_rat @ R2 @ D2 ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_scale_eq_noteq
% 4.69/5.01 thf(fact_5624_add__scale__eq__noteq,axiom,
% 4.69/5.01 ! [R2: nat,A2: nat,B: nat,C: nat,D2: nat] :
% 4.69/5.01 ( ( R2 != zero_zero_nat )
% 4.69/5.01 => ( ( ( A2 = B )
% 4.69/5.01 & ( C != D2 ) )
% 4.69/5.01 => ( ( plus_plus_nat @ A2 @ ( times_times_nat @ R2 @ C ) )
% 4.69/5.01 != ( plus_plus_nat @ B @ ( times_times_nat @ R2 @ D2 ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_scale_eq_noteq
% 4.69/5.01 thf(fact_5625_add__scale__eq__noteq,axiom,
% 4.69/5.01 ! [R2: int,A2: int,B: int,C: int,D2: int] :
% 4.69/5.01 ( ( R2 != zero_zero_int )
% 4.69/5.01 => ( ( ( A2 = B )
% 4.69/5.01 & ( C != D2 ) )
% 4.69/5.01 => ( ( plus_plus_int @ A2 @ ( times_times_int @ R2 @ C ) )
% 4.69/5.01 != ( plus_plus_int @ B @ ( times_times_int @ R2 @ D2 ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_scale_eq_noteq
% 4.69/5.01 thf(fact_5626_Sup__nat__def,axiom,
% 4.69/5.01 ( complete_Sup_Sup_nat
% 4.69/5.01 = ( ^ [X7: set_nat] : ( if_nat @ ( X7 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X7 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % Sup_nat_def
% 4.69/5.01 thf(fact_5627_add__decreasing,axiom,
% 4.69/5.01 ! [A2: code_integer,C: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ C @ B )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_decreasing
% 4.69/5.01 thf(fact_5628_add__decreasing,axiom,
% 4.69/5.01 ! [A2: rat,C: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 4.69/5.01 => ( ( ord_less_eq_rat @ C @ B )
% 4.69/5.01 => ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C ) @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_decreasing
% 4.69/5.01 thf(fact_5629_add__decreasing,axiom,
% 4.69/5.01 ! [A2: nat,C: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 4.69/5.01 => ( ( ord_less_eq_nat @ C @ B )
% 4.69/5.01 => ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C ) @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_decreasing
% 4.69/5.01 thf(fact_5630_add__decreasing,axiom,
% 4.69/5.01 ! [A2: int,C: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 4.69/5.01 => ( ( ord_less_eq_int @ C @ B )
% 4.69/5.01 => ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C ) @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_decreasing
% 4.69/5.01 thf(fact_5631_add__increasing,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ B @ C )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ B @ ( plus_p5714425477246183910nteger @ A2 @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_increasing
% 4.69/5.01 thf(fact_5632_add__increasing,axiom,
% 4.69/5.01 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_rat @ B @ C )
% 4.69/5.01 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A2 @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_increasing
% 4.69/5.01 thf(fact_5633_add__increasing,axiom,
% 4.69/5.01 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_nat @ B @ C )
% 4.69/5.01 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A2 @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_increasing
% 4.69/5.01 thf(fact_5634_add__increasing,axiom,
% 4.69/5.01 ! [A2: int,B: int,C: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_int @ B @ C )
% 4.69/5.01 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A2 @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_increasing
% 4.69/5.01 thf(fact_5635_add__decreasing2,axiom,
% 4.69/5.01 ! [C: code_integer,A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ A2 @ B )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A2 @ C ) @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_decreasing2
% 4.69/5.01 thf(fact_5636_add__decreasing2,axiom,
% 4.69/5.01 ! [C: rat,A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.69/5.01 => ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/5.01 => ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ C ) @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_decreasing2
% 4.69/5.01 thf(fact_5637_add__decreasing2,axiom,
% 4.69/5.01 ! [C: nat,A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 4.69/5.01 => ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.01 => ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ C ) @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_decreasing2
% 4.69/5.01 thf(fact_5638_add__decreasing2,axiom,
% 4.69/5.01 ! [C: int,A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.69/5.01 => ( ( ord_less_eq_int @ A2 @ B )
% 4.69/5.01 => ( ord_less_eq_int @ ( plus_plus_int @ A2 @ C ) @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_decreasing2
% 4.69/5.01 thf(fact_5639_add__increasing2,axiom,
% 4.69/5.01 ! [C: code_integer,B: code_integer,A2: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ B @ A2 )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ B @ ( plus_p5714425477246183910nteger @ A2 @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_increasing2
% 4.69/5.01 thf(fact_5640_add__increasing2,axiom,
% 4.69/5.01 ! [C: rat,B: rat,A2: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ( ord_less_eq_rat @ B @ A2 )
% 4.69/5.01 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A2 @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_increasing2
% 4.69/5.01 thf(fact_5641_add__increasing2,axiom,
% 4.69/5.01 ! [C: nat,B: nat,A2: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.69/5.01 => ( ( ord_less_eq_nat @ B @ A2 )
% 4.69/5.01 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A2 @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_increasing2
% 4.69/5.01 thf(fact_5642_add__increasing2,axiom,
% 4.69/5.01 ! [C: int,B: int,A2: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ( ord_less_eq_int @ B @ A2 )
% 4.69/5.01 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A2 @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_increasing2
% 4.69/5.01 thf(fact_5643_add__nonneg__nonneg,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonneg_nonneg
% 4.69/5.01 thf(fact_5644_add__nonneg__nonneg,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.69/5.01 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonneg_nonneg
% 4.69/5.01 thf(fact_5645_add__nonneg__nonneg,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.69/5.01 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonneg_nonneg
% 4.69/5.01 thf(fact_5646_add__nonneg__nonneg,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.69/5.01 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonneg_nonneg
% 4.69/5.01 thf(fact_5647_add__nonpos__nonpos,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonpos_nonpos
% 4.69/5.01 thf(fact_5648_add__nonpos__nonpos,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 4.69/5.01 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_eq_rat @ ( plus_plus_rat @ A2 @ B ) @ zero_zero_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonpos_nonpos
% 4.69/5.01 thf(fact_5649_add__nonpos__nonpos,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 4.69/5.01 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 4.69/5.01 => ( ord_less_eq_nat @ ( plus_plus_nat @ A2 @ B ) @ zero_zero_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonpos_nonpos
% 4.69/5.01 thf(fact_5650_add__nonpos__nonpos,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 4.69/5.01 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 4.69/5.01 => ( ord_less_eq_int @ ( plus_plus_int @ A2 @ B ) @ zero_zero_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonpos_nonpos
% 4.69/5.01 thf(fact_5651_add__nonneg__eq__0__iff,axiom,
% 4.69/5.01 ! [X: code_integer,Y: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 4.69/5.01 => ( ( ( plus_p5714425477246183910nteger @ X @ Y )
% 4.69/5.01 = zero_z3403309356797280102nteger )
% 4.69/5.01 = ( ( X = zero_z3403309356797280102nteger )
% 4.69/5.01 & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonneg_eq_0_iff
% 4.69/5.01 thf(fact_5652_add__nonneg__eq__0__iff,axiom,
% 4.69/5.01 ! [X: rat,Y: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.69/5.01 => ( ( ( plus_plus_rat @ X @ Y )
% 4.69/5.01 = zero_zero_rat )
% 4.69/5.01 = ( ( X = zero_zero_rat )
% 4.69/5.01 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonneg_eq_0_iff
% 4.69/5.01 thf(fact_5653_add__nonneg__eq__0__iff,axiom,
% 4.69/5.01 ! [X: nat,Y: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 4.69/5.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 4.69/5.01 => ( ( ( plus_plus_nat @ X @ Y )
% 4.69/5.01 = zero_zero_nat )
% 4.69/5.01 = ( ( X = zero_zero_nat )
% 4.69/5.01 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonneg_eq_0_iff
% 4.69/5.01 thf(fact_5654_add__nonneg__eq__0__iff,axiom,
% 4.69/5.01 ! [X: int,Y: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.69/5.01 => ( ( ( plus_plus_int @ X @ Y )
% 4.69/5.01 = zero_zero_int )
% 4.69/5.01 = ( ( X = zero_zero_int )
% 4.69/5.01 & ( Y = zero_zero_int ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonneg_eq_0_iff
% 4.69/5.01 thf(fact_5655_add__nonpos__eq__0__iff,axiom,
% 4.69/5.01 ! [X: code_integer,Y: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ X @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ Y @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ( ( plus_p5714425477246183910nteger @ X @ Y )
% 4.69/5.01 = zero_z3403309356797280102nteger )
% 4.69/5.01 = ( ( X = zero_z3403309356797280102nteger )
% 4.69/5.01 & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonpos_eq_0_iff
% 4.69/5.01 thf(fact_5656_add__nonpos__eq__0__iff,axiom,
% 4.69/5.01 ! [X: rat,Y: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 4.69/5.01 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 4.69/5.01 => ( ( ( plus_plus_rat @ X @ Y )
% 4.69/5.01 = zero_zero_rat )
% 4.69/5.01 = ( ( X = zero_zero_rat )
% 4.69/5.01 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonpos_eq_0_iff
% 4.69/5.01 thf(fact_5657_add__nonpos__eq__0__iff,axiom,
% 4.69/5.01 ! [X: nat,Y: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 4.69/5.01 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 4.69/5.01 => ( ( ( plus_plus_nat @ X @ Y )
% 4.69/5.01 = zero_zero_nat )
% 4.69/5.01 = ( ( X = zero_zero_nat )
% 4.69/5.01 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonpos_eq_0_iff
% 4.69/5.01 thf(fact_5658_add__nonpos__eq__0__iff,axiom,
% 4.69/5.01 ! [X: int,Y: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 4.69/5.01 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 4.69/5.01 => ( ( ( plus_plus_int @ X @ Y )
% 4.69/5.01 = zero_zero_int )
% 4.69/5.01 = ( ( X = zero_zero_int )
% 4.69/5.01 & ( Y = zero_zero_int ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonpos_eq_0_iff
% 4.69/5.01 thf(fact_5659_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ A2 @ B )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % ordered_comm_semiring_class.comm_mult_left_mono
% 4.69/5.01 thf(fact_5660_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 4.69/5.01 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % ordered_comm_semiring_class.comm_mult_left_mono
% 4.69/5.01 thf(fact_5661_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 4.69/5.01 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.69/5.01 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % ordered_comm_semiring_class.comm_mult_left_mono
% 4.69/5.01 thf(fact_5662_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 4.69/5.01 ! [A2: int,B: int,C: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % ordered_comm_semiring_class.comm_mult_left_mono
% 4.69/5.01 thf(fact_5663_zero__le__mult__iff,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A2 @ B ) )
% 4.69/5.01 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) )
% 4.69/5.01 | ( ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger )
% 4.69/5.01 & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_le_mult_iff
% 4.69/5.01 thf(fact_5664_zero__le__mult__iff,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B ) )
% 4.69/5.01 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 4.69/5.01 | ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 4.69/5.01 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_le_mult_iff
% 4.69/5.01 thf(fact_5665_zero__le__mult__iff,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A2 @ B ) )
% 4.69/5.01 = ( ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 4.69/5.01 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 4.69/5.01 | ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 4.69/5.01 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_le_mult_iff
% 4.69/5.01 thf(fact_5666_mult__nonneg__nonpos2,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ B @ A2 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_nonneg_nonpos2
% 4.69/5.01 thf(fact_5667_mult__nonneg__nonpos2,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A2 ) @ zero_zero_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_nonneg_nonpos2
% 4.69/5.01 thf(fact_5668_mult__nonneg__nonpos2,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 4.69/5.01 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A2 ) @ zero_zero_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_nonneg_nonpos2
% 4.69/5.01 thf(fact_5669_mult__nonneg__nonpos2,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 4.69/5.01 => ( ord_less_eq_int @ ( times_times_int @ B @ A2 ) @ zero_zero_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_nonneg_nonpos2
% 4.69/5.01 thf(fact_5670_mult__nonpos__nonneg,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_nonpos_nonneg
% 4.69/5.01 thf(fact_5671_mult__nonpos__nonneg,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.69/5.01 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ B ) @ zero_zero_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_nonpos_nonneg
% 4.69/5.01 thf(fact_5672_mult__nonpos__nonneg,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 4.69/5.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.69/5.01 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B ) @ zero_zero_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_nonpos_nonneg
% 4.69/5.01 thf(fact_5673_mult__nonpos__nonneg,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.69/5.01 => ( ord_less_eq_int @ ( times_times_int @ A2 @ B ) @ zero_zero_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_nonpos_nonneg
% 4.69/5.01 thf(fact_5674_mult__nonneg__nonpos,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_nonneg_nonpos
% 4.69/5.01 thf(fact_5675_mult__nonneg__nonpos,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ B ) @ zero_zero_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_nonneg_nonpos
% 4.69/5.01 thf(fact_5676_mult__nonneg__nonpos,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 4.69/5.01 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B ) @ zero_zero_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_nonneg_nonpos
% 4.69/5.01 thf(fact_5677_mult__nonneg__nonpos,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 4.69/5.01 => ( ord_less_eq_int @ ( times_times_int @ A2 @ B ) @ zero_zero_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_nonneg_nonpos
% 4.69/5.01 thf(fact_5678_mult__nonneg__nonneg,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_nonneg_nonneg
% 4.69/5.01 thf(fact_5679_mult__nonneg__nonneg,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.69/5.01 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_nonneg_nonneg
% 4.69/5.01 thf(fact_5680_mult__nonneg__nonneg,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.69/5.01 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_nonneg_nonneg
% 4.69/5.01 thf(fact_5681_mult__nonneg__nonneg,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.69/5.01 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_nonneg_nonneg
% 4.69/5.01 thf(fact_5682_split__mult__neg__le,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) )
% 4.69/5.01 | ( ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger )
% 4.69/5.01 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ B ) @ zero_z3403309356797280102nteger ) ) ).
% 4.69/5.01
% 4.69/5.01 % split_mult_neg_le
% 4.69/5.01 thf(fact_5683_split__mult__neg__le,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 4.69/5.01 | ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 4.69/5.01 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 4.69/5.01 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ B ) @ zero_zero_rat ) ) ).
% 4.69/5.01
% 4.69/5.01 % split_mult_neg_le
% 4.69/5.01 thf(fact_5684_split__mult__neg__le,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 4.69/5.01 | ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 4.69/5.01 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 4.69/5.01 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B ) @ zero_zero_nat ) ) ).
% 4.69/5.01
% 4.69/5.01 % split_mult_neg_le
% 4.69/5.01 thf(fact_5685_split__mult__neg__le,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 4.69/5.01 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 4.69/5.01 | ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 4.69/5.01 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 4.69/5.01 => ( ord_less_eq_int @ ( times_times_int @ A2 @ B ) @ zero_zero_int ) ) ).
% 4.69/5.01
% 4.69/5.01 % split_mult_neg_le
% 4.69/5.01 thf(fact_5686_mult__le__0__iff,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ B ) @ zero_z3403309356797280102nteger )
% 4.69/5.01 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) )
% 4.69/5.01 | ( ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger )
% 4.69/5.01 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_0_iff
% 4.69/5.01 thf(fact_5687_mult__le__0__iff,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ ( times_times_rat @ A2 @ B ) @ zero_zero_rat )
% 4.69/5.01 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 4.69/5.01 | ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 4.69/5.01 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_0_iff
% 4.69/5.01 thf(fact_5688_mult__le__0__iff,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ ( times_times_int @ A2 @ B ) @ zero_zero_int )
% 4.69/5.01 = ( ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 4.69/5.01 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 4.69/5.01 | ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 4.69/5.01 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_0_iff
% 4.69/5.01 thf(fact_5689_mult__right__mono,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ A2 @ B )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_right_mono
% 4.69/5.01 thf(fact_5690_mult__right__mono,axiom,
% 4.69/5.01 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_right_mono
% 4.69/5.01 thf(fact_5691_mult__right__mono,axiom,
% 4.69/5.01 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.69/5.01 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_right_mono
% 4.69/5.01 thf(fact_5692_mult__right__mono,axiom,
% 4.69/5.01 ! [A2: int,B: int,C: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_right_mono
% 4.69/5.01 thf(fact_5693_mult__right__mono__neg,axiom,
% 4.69/5.01 ! [B: code_integer,A2: code_integer,C: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ B @ A2 )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_right_mono_neg
% 4.69/5.01 thf(fact_5694_mult__right__mono__neg,axiom,
% 4.69/5.01 ! [B: rat,A2: rat,C: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ B @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_right_mono_neg
% 4.69/5.01 thf(fact_5695_mult__right__mono__neg,axiom,
% 4.69/5.01 ! [B: int,A2: int,C: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ B @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.69/5.01 => ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_right_mono_neg
% 4.69/5.01 thf(fact_5696_mult__left__mono,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ A2 @ B )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_mono
% 4.69/5.01 thf(fact_5697_mult__left__mono,axiom,
% 4.69/5.01 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_mono
% 4.69/5.01 thf(fact_5698_mult__left__mono,axiom,
% 4.69/5.01 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.69/5.01 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_mono
% 4.69/5.01 thf(fact_5699_mult__left__mono,axiom,
% 4.69/5.01 ! [A2: int,B: int,C: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_mono
% 4.69/5.01 thf(fact_5700_mult__nonpos__nonpos,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_nonpos_nonpos
% 4.69/5.01 thf(fact_5701_mult__nonpos__nonpos,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 4.69/5.01 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_nonpos_nonpos
% 4.69/5.01 thf(fact_5702_mult__nonpos__nonpos,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 4.69/5.01 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 4.69/5.01 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_nonpos_nonpos
% 4.69/5.01 thf(fact_5703_mult__left__mono__neg,axiom,
% 4.69/5.01 ! [B: code_integer,A2: code_integer,C: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ B @ A2 )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_mono_neg
% 4.69/5.01 thf(fact_5704_mult__left__mono__neg,axiom,
% 4.69/5.01 ! [B: rat,A2: rat,C: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ B @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_mono_neg
% 4.69/5.01 thf(fact_5705_mult__left__mono__neg,axiom,
% 4.69/5.01 ! [B: int,A2: int,C: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ B @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.69/5.01 => ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_mono_neg
% 4.69/5.01 thf(fact_5706_split__mult__pos__le,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) )
% 4.69/5.01 | ( ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger )
% 4.69/5.01 & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % split_mult_pos_le
% 4.69/5.01 thf(fact_5707_split__mult__pos__le,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 4.69/5.01 | ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 4.69/5.01 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 4.69/5.01 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % split_mult_pos_le
% 4.69/5.01 thf(fact_5708_split__mult__pos__le,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 4.69/5.01 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 4.69/5.01 | ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 4.69/5.01 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 4.69/5.01 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % split_mult_pos_le
% 4.69/5.01 thf(fact_5709_zero__le__square,axiom,
% 4.69/5.01 ! [A2: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A2 @ A2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_le_square
% 4.69/5.01 thf(fact_5710_zero__le__square,axiom,
% 4.69/5.01 ! [A2: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ A2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_le_square
% 4.69/5.01 thf(fact_5711_zero__le__square,axiom,
% 4.69/5.01 ! [A2: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A2 @ A2 ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_le_square
% 4.69/5.01 thf(fact_5712_mult__mono_H,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ A2 @ B )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_mono'
% 4.69/5.01 thf(fact_5713_mult__mono_H,axiom,
% 4.69/5.01 ! [A2: rat,B: rat,C: rat,D2: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_eq_rat @ C @ D2 )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_mono'
% 4.69/5.01 thf(fact_5714_mult__mono_H,axiom,
% 4.69/5.01 ! [A2: nat,B: nat,C: nat,D2: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_eq_nat @ C @ D2 )
% 4.69/5.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.69/5.01 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_mono'
% 4.69/5.01 thf(fact_5715_mult__mono_H,axiom,
% 4.69/5.01 ! [A2: int,B: int,C: int,D2: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_eq_int @ C @ D2 )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_mono'
% 4.69/5.01 thf(fact_5716_mult__mono,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ A2 @ B )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_mono
% 4.69/5.01 thf(fact_5717_mult__mono,axiom,
% 4.69/5.01 ! [A2: rat,B: rat,C: rat,D2: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_eq_rat @ C @ D2 )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_mono
% 4.69/5.01 thf(fact_5718_mult__mono,axiom,
% 4.69/5.01 ! [A2: nat,B: nat,C: nat,D2: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_eq_nat @ C @ D2 )
% 4.69/5.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.69/5.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.69/5.01 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_mono
% 4.69/5.01 thf(fact_5719_mult__mono,axiom,
% 4.69/5.01 ! [A2: int,B: int,C: int,D2: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_eq_int @ C @ D2 )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_mono
% 4.69/5.01 thf(fact_5720_not__one__le__zero,axiom,
% 4.69/5.01 ~ ( ord_le1926595141338095240atural @ one_one_Code_natural @ zero_z2226904508553997617atural ) ).
% 4.69/5.01
% 4.69/5.01 % not_one_le_zero
% 4.69/5.01 thf(fact_5721_not__one__le__zero,axiom,
% 4.69/5.01 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 4.69/5.01
% 4.69/5.01 % not_one_le_zero
% 4.69/5.01 thf(fact_5722_not__one__le__zero,axiom,
% 4.69/5.01 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 4.69/5.01
% 4.69/5.01 % not_one_le_zero
% 4.69/5.01 thf(fact_5723_not__one__le__zero,axiom,
% 4.69/5.01 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 4.69/5.01
% 4.69/5.01 % not_one_le_zero
% 4.69/5.01 thf(fact_5724_not__one__le__zero,axiom,
% 4.69/5.01 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 4.69/5.01
% 4.69/5.01 % not_one_le_zero
% 4.69/5.01 thf(fact_5725_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 4.69/5.01 ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ one_one_Code_natural ).
% 4.69/5.01
% 4.69/5.01 % linordered_nonzero_semiring_class.zero_le_one
% 4.69/5.01 thf(fact_5726_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 4.69/5.01 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 4.69/5.01
% 4.69/5.01 % linordered_nonzero_semiring_class.zero_le_one
% 4.69/5.01 thf(fact_5727_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 4.69/5.01 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 4.69/5.01
% 4.69/5.01 % linordered_nonzero_semiring_class.zero_le_one
% 4.69/5.01 thf(fact_5728_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 4.69/5.01 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 4.69/5.01
% 4.69/5.01 % linordered_nonzero_semiring_class.zero_le_one
% 4.69/5.01 thf(fact_5729_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 4.69/5.01 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 4.69/5.01
% 4.69/5.01 % linordered_nonzero_semiring_class.zero_le_one
% 4.69/5.01 thf(fact_5730_zero__less__one__class_Ozero__le__one,axiom,
% 4.69/5.01 ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ one_one_Code_natural ).
% 4.69/5.01
% 4.69/5.01 % zero_less_one_class.zero_le_one
% 4.69/5.01 thf(fact_5731_zero__less__one__class_Ozero__le__one,axiom,
% 4.69/5.01 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 4.69/5.01
% 4.69/5.01 % zero_less_one_class.zero_le_one
% 4.69/5.01 thf(fact_5732_zero__less__one__class_Ozero__le__one,axiom,
% 4.69/5.01 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 4.69/5.01
% 4.69/5.01 % zero_less_one_class.zero_le_one
% 4.69/5.01 thf(fact_5733_zero__less__one__class_Ozero__le__one,axiom,
% 4.69/5.01 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 4.69/5.01
% 4.69/5.01 % zero_less_one_class.zero_le_one
% 4.69/5.01 thf(fact_5734_zero__less__one__class_Ozero__le__one,axiom,
% 4.69/5.01 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 4.69/5.01
% 4.69/5.01 % zero_less_one_class.zero_le_one
% 4.69/5.01 thf(fact_5735_le__iff__diff__le__0,axiom,
% 4.69/5.01 ( ord_le3102999989581377725nteger
% 4.69/5.01 = ( ^ [A6: code_integer,B6: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A6 @ B6 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % le_iff_diff_le_0
% 4.69/5.01 thf(fact_5736_le__iff__diff__le__0,axiom,
% 4.69/5.01 ( ord_less_eq_rat
% 4.69/5.01 = ( ^ [A6: rat,B6: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A6 @ B6 ) @ zero_zero_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % le_iff_diff_le_0
% 4.69/5.01 thf(fact_5737_le__iff__diff__le__0,axiom,
% 4.69/5.01 ( ord_less_eq_int
% 4.69/5.01 = ( ^ [A6: int,B6: int] : ( ord_less_eq_int @ ( minus_minus_int @ A6 @ B6 ) @ zero_zero_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % le_iff_diff_le_0
% 4.69/5.01 thf(fact_5738_pos__add__strict,axiom,
% 4.69/5.01 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 => ( ( ord_less_nat @ B @ C )
% 4.69/5.01 => ( ord_less_nat @ B @ ( plus_plus_nat @ A2 @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % pos_add_strict
% 4.69/5.01 thf(fact_5739_pos__add__strict,axiom,
% 4.69/5.01 ! [A2: int,B: int,C: int] :
% 4.69/5.01 ( ( ord_less_int @ zero_zero_int @ A2 )
% 4.69/5.01 => ( ( ord_less_int @ B @ C )
% 4.69/5.01 => ( ord_less_int @ B @ ( plus_plus_int @ A2 @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % pos_add_strict
% 4.69/5.01 thf(fact_5740_pos__add__strict,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ B @ C )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A2 @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % pos_add_strict
% 4.69/5.01 thf(fact_5741_pos__add__strict,axiom,
% 4.69/5.01 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.01 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 => ( ( ord_less_rat @ B @ C )
% 4.69/5.01 => ( ord_less_rat @ B @ ( plus_plus_rat @ A2 @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % pos_add_strict
% 4.69/5.01 thf(fact_5742_canonically__ordered__monoid__add__class_OlessE,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_nat @ A2 @ B )
% 4.69/5.01 => ~ ! [C2: nat] :
% 4.69/5.01 ( ( B
% 4.69/5.01 = ( plus_plus_nat @ A2 @ C2 ) )
% 4.69/5.01 => ( C2 = zero_zero_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % canonically_ordered_monoid_add_class.lessE
% 4.69/5.01 thf(fact_5743_add__pos__pos,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.69/5.01 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_pos_pos
% 4.69/5.01 thf(fact_5744_add__pos__pos,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ zero_zero_int @ A2 )
% 4.69/5.01 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.69/5.01 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_pos_pos
% 4.69/5.01 thf(fact_5745_add__pos__pos,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_pos_pos
% 4.69/5.01 thf(fact_5746_add__pos__pos,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.69/5.01 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_pos_pos
% 4.69/5.01 thf(fact_5747_add__neg__neg,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_nat @ A2 @ zero_zero_nat )
% 4.69/5.01 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 4.69/5.01 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ B ) @ zero_zero_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_neg_neg
% 4.69/5.01 thf(fact_5748_add__neg__neg,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ A2 @ zero_zero_int )
% 4.69/5.01 => ( ( ord_less_int @ B @ zero_zero_int )
% 4.69/5.01 => ( ord_less_int @ ( plus_plus_int @ A2 @ B ) @ zero_zero_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_neg_neg
% 4.69/5.01 thf(fact_5749_add__neg__neg,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_neg_neg
% 4.69/5.01 thf(fact_5750_add__neg__neg,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 4.69/5.01 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ B ) @ zero_zero_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_neg_neg
% 4.69/5.01 thf(fact_5751_mult__neg__neg,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ A2 @ zero_zero_int )
% 4.69/5.01 => ( ( ord_less_int @ B @ zero_zero_int )
% 4.69/5.01 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_neg_neg
% 4.69/5.01 thf(fact_5752_mult__neg__neg,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_neg_neg
% 4.69/5.01 thf(fact_5753_mult__neg__neg,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 4.69/5.01 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_neg_neg
% 4.69/5.01 thf(fact_5754_not__square__less__zero,axiom,
% 4.69/5.01 ! [A2: int] :
% 4.69/5.01 ~ ( ord_less_int @ ( times_times_int @ A2 @ A2 ) @ zero_zero_int ) ).
% 4.69/5.01
% 4.69/5.01 % not_square_less_zero
% 4.69/5.01 thf(fact_5755_not__square__less__zero,axiom,
% 4.69/5.01 ! [A2: code_integer] :
% 4.69/5.01 ~ ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ A2 ) @ zero_z3403309356797280102nteger ) ).
% 4.69/5.01
% 4.69/5.01 % not_square_less_zero
% 4.69/5.01 thf(fact_5756_not__square__less__zero,axiom,
% 4.69/5.01 ! [A2: rat] :
% 4.69/5.01 ~ ( ord_less_rat @ ( times_times_rat @ A2 @ A2 ) @ zero_zero_rat ) ).
% 4.69/5.01
% 4.69/5.01 % not_square_less_zero
% 4.69/5.01 thf(fact_5757_mult__less__0__iff,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ ( times_times_int @ A2 @ B ) @ zero_zero_int )
% 4.69/5.01 = ( ( ( ord_less_int @ zero_zero_int @ A2 )
% 4.69/5.01 & ( ord_less_int @ B @ zero_zero_int ) )
% 4.69/5.01 | ( ( ord_less_int @ A2 @ zero_zero_int )
% 4.69/5.01 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_0_iff
% 4.69/5.01 thf(fact_5758_mult__less__0__iff,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ B ) @ zero_z3403309356797280102nteger )
% 4.69/5.01 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 & ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger ) )
% 4.69/5.01 | ( ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger )
% 4.69/5.01 & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_0_iff
% 4.69/5.01 thf(fact_5759_mult__less__0__iff,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ ( times_times_rat @ A2 @ B ) @ zero_zero_rat )
% 4.69/5.01 = ( ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 4.69/5.01 | ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 4.69/5.01 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_0_iff
% 4.69/5.01 thf(fact_5760_mult__neg__pos,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_nat @ A2 @ zero_zero_nat )
% 4.69/5.01 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.69/5.01 => ( ord_less_nat @ ( times_times_nat @ A2 @ B ) @ zero_zero_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_neg_pos
% 4.69/5.01 thf(fact_5761_mult__neg__pos,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ A2 @ zero_zero_int )
% 4.69/5.01 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.69/5.01 => ( ord_less_int @ ( times_times_int @ A2 @ B ) @ zero_zero_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_neg_pos
% 4.69/5.01 thf(fact_5762_mult__neg__pos,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_neg_pos
% 4.69/5.01 thf(fact_5763_mult__neg__pos,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 4.69/5.01 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.69/5.01 => ( ord_less_rat @ ( times_times_rat @ A2 @ B ) @ zero_zero_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_neg_pos
% 4.69/5.01 thf(fact_5764_mult__pos__neg,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 4.69/5.01 => ( ord_less_nat @ ( times_times_nat @ A2 @ B ) @ zero_zero_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_pos_neg
% 4.69/5.01 thf(fact_5765_mult__pos__neg,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ zero_zero_int @ A2 )
% 4.69/5.01 => ( ( ord_less_int @ B @ zero_zero_int )
% 4.69/5.01 => ( ord_less_int @ ( times_times_int @ A2 @ B ) @ zero_zero_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_pos_neg
% 4.69/5.01 thf(fact_5766_mult__pos__neg,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_pos_neg
% 4.69/5.01 thf(fact_5767_mult__pos__neg,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_rat @ ( times_times_rat @ A2 @ B ) @ zero_zero_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_pos_neg
% 4.69/5.01 thf(fact_5768_mult__pos__pos,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.69/5.01 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_pos_pos
% 4.69/5.01 thf(fact_5769_mult__pos__pos,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ zero_zero_int @ A2 )
% 4.69/5.01 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.69/5.01 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_pos_pos
% 4.69/5.01 thf(fact_5770_mult__pos__pos,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_pos_pos
% 4.69/5.01 thf(fact_5771_mult__pos__pos,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.69/5.01 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_pos_pos
% 4.69/5.01 thf(fact_5772_mult__pos__neg2,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 4.69/5.01 => ( ord_less_nat @ ( times_times_nat @ B @ A2 ) @ zero_zero_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_pos_neg2
% 4.69/5.01 thf(fact_5773_mult__pos__neg2,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ zero_zero_int @ A2 )
% 4.69/5.01 => ( ( ord_less_int @ B @ zero_zero_int )
% 4.69/5.01 => ( ord_less_int @ ( times_times_int @ B @ A2 ) @ zero_zero_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_pos_neg2
% 4.69/5.01 thf(fact_5774_mult__pos__neg2,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ B @ A2 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_pos_neg2
% 4.69/5.01 thf(fact_5775_mult__pos__neg2,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_rat @ ( times_times_rat @ B @ A2 ) @ zero_zero_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_pos_neg2
% 4.69/5.01 thf(fact_5776_zero__less__mult__iff,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A2 @ B ) )
% 4.69/5.01 = ( ( ( ord_less_int @ zero_zero_int @ A2 )
% 4.69/5.01 & ( ord_less_int @ zero_zero_int @ B ) )
% 4.69/5.01 | ( ( ord_less_int @ A2 @ zero_zero_int )
% 4.69/5.01 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_less_mult_iff
% 4.69/5.01 thf(fact_5777_zero__less__mult__iff,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A2 @ B ) )
% 4.69/5.01 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) )
% 4.69/5.01 | ( ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger )
% 4.69/5.01 & ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_less_mult_iff
% 4.69/5.01 thf(fact_5778_zero__less__mult__iff,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B ) )
% 4.69/5.01 = ( ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 4.69/5.01 | ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 4.69/5.01 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_less_mult_iff
% 4.69/5.01 thf(fact_5779_zero__less__mult__pos,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A2 @ B ) )
% 4.69/5.01 => ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_less_mult_pos
% 4.69/5.01 thf(fact_5780_zero__less__mult__pos,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A2 @ B ) )
% 4.69/5.01 => ( ( ord_less_int @ zero_zero_int @ A2 )
% 4.69/5.01 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_less_mult_pos
% 4.69/5.01 thf(fact_5781_zero__less__mult__pos,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A2 @ B ) )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_less_mult_pos
% 4.69/5.01 thf(fact_5782_zero__less__mult__pos,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A2 @ B ) )
% 4.69/5.01 => ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_less_mult_pos
% 4.69/5.01 thf(fact_5783_zero__less__mult__pos2,axiom,
% 4.69/5.01 ! [B: nat,A2: nat] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A2 ) )
% 4.69/5.01 => ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_less_mult_pos2
% 4.69/5.01 thf(fact_5784_zero__less__mult__pos2,axiom,
% 4.69/5.01 ! [B: int,A2: int] :
% 4.69/5.01 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A2 ) )
% 4.69/5.01 => ( ( ord_less_int @ zero_zero_int @ A2 )
% 4.69/5.01 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_less_mult_pos2
% 4.69/5.01 thf(fact_5785_zero__less__mult__pos2,axiom,
% 4.69/5.01 ! [B: code_integer,A2: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ B @ A2 ) )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_less_mult_pos2
% 4.69/5.01 thf(fact_5786_zero__less__mult__pos2,axiom,
% 4.69/5.01 ! [B: rat,A2: rat] :
% 4.69/5.01 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A2 ) )
% 4.69/5.01 => ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % zero_less_mult_pos2
% 4.69/5.01 thf(fact_5787_mult__less__cancel__left__neg,axiom,
% 4.69/5.01 ! [C: int,A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ C @ zero_zero_int )
% 4.69/5.01 => ( ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B ) )
% 4.69/5.01 = ( ord_less_int @ B @ A2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_left_neg
% 4.69/5.01 thf(fact_5788_mult__less__cancel__left__neg,axiom,
% 4.69/5.01 ! [C: code_integer,A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 4.69/5.01 = ( ord_le6747313008572928689nteger @ B @ A2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_left_neg
% 4.69/5.01 thf(fact_5789_mult__less__cancel__left__neg,axiom,
% 4.69/5.01 ! [C: rat,A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.69/5.01 => ( ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B ) )
% 4.69/5.01 = ( ord_less_rat @ B @ A2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_left_neg
% 4.69/5.01 thf(fact_5790_mult__less__cancel__left__pos,axiom,
% 4.69/5.01 ! [C: int,A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B ) )
% 4.69/5.01 = ( ord_less_int @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_left_pos
% 4.69/5.01 thf(fact_5791_mult__less__cancel__left__pos,axiom,
% 4.69/5.01 ! [C: code_integer,A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 4.69/5.01 = ( ord_le6747313008572928689nteger @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_left_pos
% 4.69/5.01 thf(fact_5792_mult__less__cancel__left__pos,axiom,
% 4.69/5.01 ! [C: rat,A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B ) )
% 4.69/5.01 = ( ord_less_rat @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_left_pos
% 4.69/5.01 thf(fact_5793_mult__strict__left__mono__neg,axiom,
% 4.69/5.01 ! [B: int,A2: int,C: int] :
% 4.69/5.01 ( ( ord_less_int @ B @ A2 )
% 4.69/5.01 => ( ( ord_less_int @ C @ zero_zero_int )
% 4.69/5.01 => ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_strict_left_mono_neg
% 4.69/5.01 thf(fact_5794_mult__strict__left__mono__neg,axiom,
% 4.69/5.01 ! [B: code_integer,A2: code_integer,C: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ B @ A2 )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_strict_left_mono_neg
% 4.69/5.01 thf(fact_5795_mult__strict__left__mono__neg,axiom,
% 4.69/5.01 ! [B: rat,A2: rat,C: rat] :
% 4.69/5.01 ( ( ord_less_rat @ B @ A2 )
% 4.69/5.01 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_strict_left_mono_neg
% 4.69/5.01 thf(fact_5796_mult__strict__left__mono,axiom,
% 4.69/5.01 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.01 ( ( ord_less_nat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 4.69/5.01 => ( ord_less_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_strict_left_mono
% 4.69/5.01 thf(fact_5797_mult__strict__left__mono,axiom,
% 4.69/5.01 ! [A2: int,B: int,C: int] :
% 4.69/5.01 ( ( ord_less_int @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_strict_left_mono
% 4.69/5.01 thf(fact_5798_mult__strict__left__mono,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_strict_left_mono
% 4.69/5.01 thf(fact_5799_mult__strict__left__mono,axiom,
% 4.69/5.01 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.01 ( ( ord_less_rat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_strict_left_mono
% 4.69/5.01 thf(fact_5800_mult__less__cancel__left__disj,axiom,
% 4.69/5.01 ! [C: int,A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B ) )
% 4.69/5.01 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.69/5.01 & ( ord_less_int @ A2 @ B ) )
% 4.69/5.01 | ( ( ord_less_int @ C @ zero_zero_int )
% 4.69/5.01 & ( ord_less_int @ B @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_left_disj
% 4.69/5.01 thf(fact_5801_mult__less__cancel__left__disj,axiom,
% 4.69/5.01 ! [C: code_integer,A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 4.69/5.01 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 & ( ord_le6747313008572928689nteger @ A2 @ B ) )
% 4.69/5.01 | ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 4.69/5.01 & ( ord_le6747313008572928689nteger @ B @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_left_disj
% 4.69/5.01 thf(fact_5802_mult__less__cancel__left__disj,axiom,
% 4.69/5.01 ! [C: rat,A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B ) )
% 4.69/5.01 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.69/5.01 & ( ord_less_rat @ A2 @ B ) )
% 4.69/5.01 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.69/5.01 & ( ord_less_rat @ B @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_left_disj
% 4.69/5.01 thf(fact_5803_mult__strict__right__mono__neg,axiom,
% 4.69/5.01 ! [B: int,A2: int,C: int] :
% 4.69/5.01 ( ( ord_less_int @ B @ A2 )
% 4.69/5.01 => ( ( ord_less_int @ C @ zero_zero_int )
% 4.69/5.01 => ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_strict_right_mono_neg
% 4.69/5.01 thf(fact_5804_mult__strict__right__mono__neg,axiom,
% 4.69/5.01 ! [B: code_integer,A2: code_integer,C: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ B @ A2 )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_strict_right_mono_neg
% 4.69/5.01 thf(fact_5805_mult__strict__right__mono__neg,axiom,
% 4.69/5.01 ! [B: rat,A2: rat,C: rat] :
% 4.69/5.01 ( ( ord_less_rat @ B @ A2 )
% 4.69/5.01 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_strict_right_mono_neg
% 4.69/5.01 thf(fact_5806_mult__strict__right__mono,axiom,
% 4.69/5.01 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.01 ( ( ord_less_nat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 4.69/5.01 => ( ord_less_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_strict_right_mono
% 4.69/5.01 thf(fact_5807_mult__strict__right__mono,axiom,
% 4.69/5.01 ! [A2: int,B: int,C: int] :
% 4.69/5.01 ( ( ord_less_int @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_strict_right_mono
% 4.69/5.01 thf(fact_5808_mult__strict__right__mono,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_strict_right_mono
% 4.69/5.01 thf(fact_5809_mult__strict__right__mono,axiom,
% 4.69/5.01 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.01 ( ( ord_less_rat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_strict_right_mono
% 4.69/5.01 thf(fact_5810_mult__less__cancel__right__disj,axiom,
% 4.69/5.01 ! [A2: int,C: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ C ) )
% 4.69/5.01 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.69/5.01 & ( ord_less_int @ A2 @ B ) )
% 4.69/5.01 | ( ( ord_less_int @ C @ zero_zero_int )
% 4.69/5.01 & ( ord_less_int @ B @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_right_disj
% 4.69/5.01 thf(fact_5811_mult__less__cancel__right__disj,axiom,
% 4.69/5.01 ! [A2: code_integer,C: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 4.69/5.01 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 & ( ord_le6747313008572928689nteger @ A2 @ B ) )
% 4.69/5.01 | ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 4.69/5.01 & ( ord_le6747313008572928689nteger @ B @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_right_disj
% 4.69/5.01 thf(fact_5812_mult__less__cancel__right__disj,axiom,
% 4.69/5.01 ! [A2: rat,C: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B @ C ) )
% 4.69/5.01 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.69/5.01 & ( ord_less_rat @ A2 @ B ) )
% 4.69/5.01 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.69/5.01 & ( ord_less_rat @ B @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_right_disj
% 4.69/5.01 thf(fact_5813_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 4.69/5.01 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.01 ( ( ord_less_nat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 4.69/5.01 => ( ord_less_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 4.69/5.01 thf(fact_5814_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 4.69/5.01 ! [A2: int,B: int,C: int] :
% 4.69/5.01 ( ( ord_less_int @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 4.69/5.01 thf(fact_5815_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 4.69/5.01 thf(fact_5816_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 4.69/5.01 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.01 ( ( ord_less_rat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 4.69/5.01 thf(fact_5817_less__numeral__extra_I1_J,axiom,
% 4.69/5.01 ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ one_one_Code_natural ).
% 4.69/5.01
% 4.69/5.01 % less_numeral_extra(1)
% 4.69/5.01 thf(fact_5818_less__numeral__extra_I1_J,axiom,
% 4.69/5.01 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 4.69/5.01
% 4.69/5.01 % less_numeral_extra(1)
% 4.69/5.01 thf(fact_5819_less__numeral__extra_I1_J,axiom,
% 4.69/5.01 ord_less_int @ zero_zero_int @ one_one_int ).
% 4.69/5.01
% 4.69/5.01 % less_numeral_extra(1)
% 4.69/5.01 thf(fact_5820_less__numeral__extra_I1_J,axiom,
% 4.69/5.01 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 4.69/5.01
% 4.69/5.01 % less_numeral_extra(1)
% 4.69/5.01 thf(fact_5821_less__numeral__extra_I1_J,axiom,
% 4.69/5.01 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 4.69/5.01
% 4.69/5.01 % less_numeral_extra(1)
% 4.69/5.01 thf(fact_5822_zero__less__one,axiom,
% 4.69/5.01 ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ one_one_Code_natural ).
% 4.69/5.01
% 4.69/5.01 % zero_less_one
% 4.69/5.01 thf(fact_5823_zero__less__one,axiom,
% 4.69/5.01 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 4.69/5.01
% 4.69/5.01 % zero_less_one
% 4.69/5.01 thf(fact_5824_zero__less__one,axiom,
% 4.69/5.01 ord_less_int @ zero_zero_int @ one_one_int ).
% 4.69/5.01
% 4.69/5.01 % zero_less_one
% 4.69/5.01 thf(fact_5825_zero__less__one,axiom,
% 4.69/5.01 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 4.69/5.01
% 4.69/5.01 % zero_less_one
% 4.69/5.01 thf(fact_5826_zero__less__one,axiom,
% 4.69/5.01 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 4.69/5.01
% 4.69/5.01 % zero_less_one
% 4.69/5.01 thf(fact_5827_not__one__less__zero,axiom,
% 4.69/5.01 ~ ( ord_le5570908160329646204atural @ one_one_Code_natural @ zero_z2226904508553997617atural ) ).
% 4.69/5.01
% 4.69/5.01 % not_one_less_zero
% 4.69/5.01 thf(fact_5828_not__one__less__zero,axiom,
% 4.69/5.01 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 4.69/5.01
% 4.69/5.01 % not_one_less_zero
% 4.69/5.01 thf(fact_5829_not__one__less__zero,axiom,
% 4.69/5.01 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 4.69/5.01
% 4.69/5.01 % not_one_less_zero
% 4.69/5.01 thf(fact_5830_not__one__less__zero,axiom,
% 4.69/5.01 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 4.69/5.01
% 4.69/5.01 % not_one_less_zero
% 4.69/5.01 thf(fact_5831_not__one__less__zero,axiom,
% 4.69/5.01 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 4.69/5.01
% 4.69/5.01 % not_one_less_zero
% 4.69/5.01 thf(fact_5832_less__iff__diff__less__0,axiom,
% 4.69/5.01 ( ord_less_int
% 4.69/5.01 = ( ^ [A6: int,B6: int] : ( ord_less_int @ ( minus_minus_int @ A6 @ B6 ) @ zero_zero_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % less_iff_diff_less_0
% 4.69/5.01 thf(fact_5833_less__iff__diff__less__0,axiom,
% 4.69/5.01 ( ord_le6747313008572928689nteger
% 4.69/5.01 = ( ^ [A6: code_integer,B6: code_integer] : ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A6 @ B6 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % less_iff_diff_less_0
% 4.69/5.01 thf(fact_5834_less__iff__diff__less__0,axiom,
% 4.69/5.01 ( ord_less_rat
% 4.69/5.01 = ( ^ [A6: rat,B6: rat] : ( ord_less_rat @ ( minus_minus_rat @ A6 @ B6 ) @ zero_zero_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % less_iff_diff_less_0
% 4.69/5.01 thf(fact_5835_inj__on__mult,axiom,
% 4.69/5.01 ! [A2: code_integer,A: set_Code_integer] :
% 4.69/5.01 ( ( A2 != zero_z3403309356797280102nteger )
% 4.69/5.01 => ( inj_on1158064722259180589nteger @ ( times_3573771949741848930nteger @ A2 ) @ A ) ) ).
% 4.69/5.01
% 4.69/5.01 % inj_on_mult
% 4.69/5.01 thf(fact_5836_inj__on__mult,axiom,
% 4.69/5.01 ! [A2: rat,A: set_rat] :
% 4.69/5.01 ( ( A2 != zero_zero_rat )
% 4.69/5.01 => ( inj_on_rat_rat @ ( times_times_rat @ A2 ) @ A ) ) ).
% 4.69/5.01
% 4.69/5.01 % inj_on_mult
% 4.69/5.01 thf(fact_5837_inj__on__mult,axiom,
% 4.69/5.01 ! [A2: nat,A: set_nat] :
% 4.69/5.01 ( ( A2 != zero_zero_nat )
% 4.69/5.01 => ( inj_on_nat_nat @ ( times_times_nat @ A2 ) @ A ) ) ).
% 4.69/5.01
% 4.69/5.01 % inj_on_mult
% 4.69/5.01 thf(fact_5838_inj__on__mult,axiom,
% 4.69/5.01 ! [A2: int,A: set_int] :
% 4.69/5.01 ( ( A2 != zero_zero_int )
% 4.69/5.01 => ( inj_on_int_int @ ( times_times_int @ A2 ) @ A ) ) ).
% 4.69/5.01
% 4.69/5.01 % inj_on_mult
% 4.69/5.01 thf(fact_5839_nat__compl__induct,axiom,
% 4.69/5.01 ! [P: nat > $o,N2: nat] :
% 4.69/5.01 ( ( P @ zero_zero_nat )
% 4.69/5.01 => ( ! [N3: nat] :
% 4.69/5.01 ( ! [Nn: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ Nn @ N3 )
% 4.69/5.01 => ( P @ Nn ) )
% 4.69/5.01 => ( P @ ( suc @ N3 ) ) )
% 4.69/5.01 => ( P @ N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % nat_compl_induct
% 4.69/5.01 thf(fact_5840_nat__compl__induct_H,axiom,
% 4.69/5.01 ! [P: nat > $o,N2: nat] :
% 4.69/5.01 ( ( P @ zero_zero_nat )
% 4.69/5.01 => ( ! [N3: nat] :
% 4.69/5.01 ( ! [Nn: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ Nn @ N3 )
% 4.69/5.01 => ( P @ Nn ) )
% 4.69/5.01 => ( P @ ( suc @ N3 ) ) )
% 4.69/5.01 => ( P @ N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % nat_compl_induct'
% 4.69/5.01 thf(fact_5841_Suc__to__right,axiom,
% 4.69/5.01 ! [N2: nat,M4: nat] :
% 4.69/5.01 ( ( ( suc @ N2 )
% 4.69/5.01 = M4 )
% 4.69/5.01 => ( N2
% 4.69/5.01 = ( minus_minus_nat @ M4 @ ( suc @ zero_zero_nat ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % Suc_to_right
% 4.69/5.01 thf(fact_5842_mult__less__mono1,axiom,
% 4.69/5.01 ! [I2: nat,J: nat,K3: nat] :
% 4.69/5.01 ( ( ord_less_nat @ I2 @ J )
% 4.69/5.01 => ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 4.69/5.01 => ( ord_less_nat @ ( times_times_nat @ I2 @ K3 ) @ ( times_times_nat @ J @ K3 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_mono1
% 4.69/5.01 thf(fact_5843_mult__less__mono2,axiom,
% 4.69/5.01 ! [I2: nat,J: nat,K3: nat] :
% 4.69/5.01 ( ( ord_less_nat @ I2 @ J )
% 4.69/5.01 => ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 4.69/5.01 => ( ord_less_nat @ ( times_times_nat @ K3 @ I2 ) @ ( times_times_nat @ K3 @ J ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_mono2
% 4.69/5.01 thf(fact_5844_nat__mult__eq__cancel1,axiom,
% 4.69/5.01 ! [K3: nat,M4: nat,N2: nat] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 4.69/5.01 => ( ( ( times_times_nat @ K3 @ M4 )
% 4.69/5.01 = ( times_times_nat @ K3 @ N2 ) )
% 4.69/5.01 = ( M4 = N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % nat_mult_eq_cancel1
% 4.69/5.01 thf(fact_5845_nat__mult__less__cancel1,axiom,
% 4.69/5.01 ! [K3: nat,M4: nat,N2: nat] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 4.69/5.01 => ( ( ord_less_nat @ ( times_times_nat @ K3 @ M4 ) @ ( times_times_nat @ K3 @ N2 ) )
% 4.69/5.01 = ( ord_less_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % nat_mult_less_cancel1
% 4.69/5.01 thf(fact_5846_nat__geq__1__eq__neqz,axiom,
% 4.69/5.01 ! [X: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ one_one_nat @ X )
% 4.69/5.01 = ( X != zero_zero_nat ) ) ).
% 4.69/5.01
% 4.69/5.01 % nat_geq_1_eq_neqz
% 4.69/5.01 thf(fact_5847_mult__eq__self__implies__10,axiom,
% 4.69/5.01 ! [M4: nat,N2: nat] :
% 4.69/5.01 ( ( M4
% 4.69/5.01 = ( times_times_nat @ M4 @ N2 ) )
% 4.69/5.01 => ( ( N2 = one_one_nat )
% 4.69/5.01 | ( M4 = zero_zero_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_eq_self_implies_10
% 4.69/5.01 thf(fact_5848_add__strict__increasing2,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ B @ C )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A2 @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_strict_increasing2
% 4.69/5.01 thf(fact_5849_add__strict__increasing2,axiom,
% 4.69/5.01 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 => ( ( ord_less_rat @ B @ C )
% 4.69/5.01 => ( ord_less_rat @ B @ ( plus_plus_rat @ A2 @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_strict_increasing2
% 4.69/5.01 thf(fact_5850_add__strict__increasing2,axiom,
% 4.69/5.01 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 => ( ( ord_less_nat @ B @ C )
% 4.69/5.01 => ( ord_less_nat @ B @ ( plus_plus_nat @ A2 @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_strict_increasing2
% 4.69/5.01 thf(fact_5851_add__strict__increasing2,axiom,
% 4.69/5.01 ! [A2: int,B: int,C: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 4.69/5.01 => ( ( ord_less_int @ B @ C )
% 4.69/5.01 => ( ord_less_int @ B @ ( plus_plus_int @ A2 @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_strict_increasing2
% 4.69/5.01 thf(fact_5852_add__strict__increasing,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ B @ C )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A2 @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_strict_increasing
% 4.69/5.01 thf(fact_5853_add__strict__increasing,axiom,
% 4.69/5.01 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.01 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_rat @ B @ C )
% 4.69/5.01 => ( ord_less_rat @ B @ ( plus_plus_rat @ A2 @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_strict_increasing
% 4.69/5.01 thf(fact_5854_add__strict__increasing,axiom,
% 4.69/5.01 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_nat @ B @ C )
% 4.69/5.01 => ( ord_less_nat @ B @ ( plus_plus_nat @ A2 @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_strict_increasing
% 4.69/5.01 thf(fact_5855_add__strict__increasing,axiom,
% 4.69/5.01 ! [A2: int,B: int,C: int] :
% 4.69/5.01 ( ( ord_less_int @ zero_zero_int @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_int @ B @ C )
% 4.69/5.01 => ( ord_less_int @ B @ ( plus_plus_int @ A2 @ C ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_strict_increasing
% 4.69/5.01 thf(fact_5856_add__pos__nonneg,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_pos_nonneg
% 4.69/5.01 thf(fact_5857_add__pos__nonneg,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.69/5.01 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_pos_nonneg
% 4.69/5.01 thf(fact_5858_add__pos__nonneg,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.69/5.01 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_pos_nonneg
% 4.69/5.01 thf(fact_5859_add__pos__nonneg,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ zero_zero_int @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.69/5.01 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_pos_nonneg
% 4.69/5.01 thf(fact_5860_add__nonpos__neg,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonpos_neg
% 4.69/5.01 thf(fact_5861_add__nonpos__neg,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ A2 @ zero_zero_rat )
% 4.69/5.01 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ B ) @ zero_zero_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonpos_neg
% 4.69/5.01 thf(fact_5862_add__nonpos__neg,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
% 4.69/5.01 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 4.69/5.01 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ B ) @ zero_zero_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonpos_neg
% 4.69/5.01 thf(fact_5863_add__nonpos__neg,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 4.69/5.01 => ( ( ord_less_int @ B @ zero_zero_int )
% 4.69/5.01 => ( ord_less_int @ ( plus_plus_int @ A2 @ B ) @ zero_zero_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonpos_neg
% 4.69/5.01 thf(fact_5864_add__nonneg__pos,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonneg_pos
% 4.69/5.01 thf(fact_5865_add__nonneg__pos,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.69/5.01 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonneg_pos
% 4.69/5.01 thf(fact_5866_add__nonneg__pos,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.69/5.01 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonneg_pos
% 4.69/5.01 thf(fact_5867_add__nonneg__pos,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 4.69/5.01 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.69/5.01 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A2 @ B ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_nonneg_pos
% 4.69/5.01 thf(fact_5868_add__neg__nonpos,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_neg_nonpos
% 4.69/5.01 thf(fact_5869_add__neg__nonpos,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ A2 @ zero_zero_rat )
% 4.69/5.01 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_rat @ ( plus_plus_rat @ A2 @ B ) @ zero_zero_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_neg_nonpos
% 4.69/5.01 thf(fact_5870_add__neg__nonpos,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_nat @ A2 @ zero_zero_nat )
% 4.69/5.01 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 4.69/5.01 => ( ord_less_nat @ ( plus_plus_nat @ A2 @ B ) @ zero_zero_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_neg_nonpos
% 4.69/5.01 thf(fact_5871_add__neg__nonpos,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ A2 @ zero_zero_int )
% 4.69/5.01 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 4.69/5.01 => ( ord_less_int @ ( plus_plus_int @ A2 @ B ) @ zero_zero_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % add_neg_nonpos
% 4.69/5.01 thf(fact_5872_mult__less__le__imp__less,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_le_imp_less
% 4.69/5.01 thf(fact_5873_mult__less__le__imp__less,axiom,
% 4.69/5.01 ! [A2: rat,B: rat,C: rat,D2: rat] :
% 4.69/5.01 ( ( ord_less_rat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_eq_rat @ C @ D2 )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_le_imp_less
% 4.69/5.01 thf(fact_5874_mult__less__le__imp__less,axiom,
% 4.69/5.01 ! [A2: nat,B: nat,C: nat,D2: nat] :
% 4.69/5.01 ( ( ord_less_nat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_eq_nat @ C @ D2 )
% 4.69/5.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 4.69/5.01 => ( ord_less_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_le_imp_less
% 4.69/5.01 thf(fact_5875_mult__less__le__imp__less,axiom,
% 4.69/5.01 ! [A2: int,B: int,C: int,D2: int] :
% 4.69/5.01 ( ( ord_less_int @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_eq_int @ C @ D2 )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 4.69/5.01 => ( ( ord_less_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_le_imp_less
% 4.69/5.01 thf(fact_5876_mult__le__less__imp__less,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ A2 @ B )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_less_imp_less
% 4.69/5.01 thf(fact_5877_mult__le__less__imp__less,axiom,
% 4.69/5.01 ! [A2: rat,B: rat,C: rat,D2: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_rat @ C @ D2 )
% 4.69/5.01 => ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_less_imp_less
% 4.69/5.01 thf(fact_5878_mult__le__less__imp__less,axiom,
% 4.69/5.01 ! [A2: nat,B: nat,C: nat,D2: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_nat @ C @ D2 )
% 4.69/5.01 => ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.69/5.01 => ( ord_less_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_less_imp_less
% 4.69/5.01 thf(fact_5879_mult__le__less__imp__less,axiom,
% 4.69/5.01 ! [A2: int,B: int,C: int,D2: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_int @ C @ D2 )
% 4.69/5.01 => ( ( ord_less_int @ zero_zero_int @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_less_imp_less
% 4.69/5.01 thf(fact_5880_mult__right__le__imp__le,axiom,
% 4.69/5.01 ! [A2: code_integer,C: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_right_le_imp_le
% 4.69/5.01 thf(fact_5881_mult__right__le__imp__le,axiom,
% 4.69/5.01 ! [A2: rat,C: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B @ C ) )
% 4.69/5.01 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_eq_rat @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_right_le_imp_le
% 4.69/5.01 thf(fact_5882_mult__right__le__imp__le,axiom,
% 4.69/5.01 ! [A2: nat,C: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ C ) )
% 4.69/5.01 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 4.69/5.01 => ( ord_less_eq_nat @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_right_le_imp_le
% 4.69/5.01 thf(fact_5883_mult__right__le__imp__le,axiom,
% 4.69/5.01 ! [A2: int,C: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ C ) )
% 4.69/5.01 => ( ( ord_less_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_eq_int @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_right_le_imp_le
% 4.69/5.01 thf(fact_5884_mult__left__le__imp__le,axiom,
% 4.69/5.01 ! [C: code_integer,A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_le_imp_le
% 4.69/5.01 thf(fact_5885_mult__left__le__imp__le,axiom,
% 4.69/5.01 ! [C: rat,A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B ) )
% 4.69/5.01 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_eq_rat @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_le_imp_le
% 4.69/5.01 thf(fact_5886_mult__left__le__imp__le,axiom,
% 4.69/5.01 ! [C: nat,A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B ) )
% 4.69/5.01 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 4.69/5.01 => ( ord_less_eq_nat @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_le_imp_le
% 4.69/5.01 thf(fact_5887_mult__left__le__imp__le,axiom,
% 4.69/5.01 ! [C: int,A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B ) )
% 4.69/5.01 => ( ( ord_less_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_eq_int @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_le_imp_le
% 4.69/5.01 thf(fact_5888_mult__le__cancel__left__pos,axiom,
% 4.69/5.01 ! [C: code_integer,A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 4.69/5.01 = ( ord_le3102999989581377725nteger @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_left_pos
% 4.69/5.01 thf(fact_5889_mult__le__cancel__left__pos,axiom,
% 4.69/5.01 ! [C: rat,A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B ) )
% 4.69/5.01 = ( ord_less_eq_rat @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_left_pos
% 4.69/5.01 thf(fact_5890_mult__le__cancel__left__pos,axiom,
% 4.69/5.01 ! [C: int,A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B ) )
% 4.69/5.01 = ( ord_less_eq_int @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_left_pos
% 4.69/5.01 thf(fact_5891_mult__le__cancel__left__neg,axiom,
% 4.69/5.01 ! [C: code_integer,A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 4.69/5.01 = ( ord_le3102999989581377725nteger @ B @ A2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_left_neg
% 4.69/5.01 thf(fact_5892_mult__le__cancel__left__neg,axiom,
% 4.69/5.01 ! [C: rat,A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.69/5.01 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B ) )
% 4.69/5.01 = ( ord_less_eq_rat @ B @ A2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_left_neg
% 4.69/5.01 thf(fact_5893_mult__le__cancel__left__neg,axiom,
% 4.69/5.01 ! [C: int,A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ C @ zero_zero_int )
% 4.69/5.01 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B ) )
% 4.69/5.01 = ( ord_less_eq_int @ B @ A2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_left_neg
% 4.69/5.01 thf(fact_5894_mult__less__cancel__right,axiom,
% 4.69/5.01 ! [A2: code_integer,C: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 4.69/5.01 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ A2 @ B ) )
% 4.69/5.01 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ B @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_right
% 4.69/5.01 thf(fact_5895_mult__less__cancel__right,axiom,
% 4.69/5.01 ! [A2: rat,C: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B @ C ) )
% 4.69/5.01 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_rat @ A2 @ B ) )
% 4.69/5.01 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_rat @ B @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_right
% 4.69/5.01 thf(fact_5896_mult__less__cancel__right,axiom,
% 4.69/5.01 ! [A2: int,C: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ C ) )
% 4.69/5.01 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_int @ A2 @ B ) )
% 4.69/5.01 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.69/5.01 => ( ord_less_int @ B @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_right
% 4.69/5.01 thf(fact_5897_mult__strict__mono_H,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_strict_mono'
% 4.69/5.01 thf(fact_5898_mult__strict__mono_H,axiom,
% 4.69/5.01 ! [A2: rat,B: rat,C: rat,D2: rat] :
% 4.69/5.01 ( ( ord_less_rat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_rat @ C @ D2 )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_strict_mono'
% 4.69/5.01 thf(fact_5899_mult__strict__mono_H,axiom,
% 4.69/5.01 ! [A2: nat,B: nat,C: nat,D2: nat] :
% 4.69/5.01 ( ( ord_less_nat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_nat @ C @ D2 )
% 4.69/5.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.69/5.01 => ( ord_less_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_strict_mono'
% 4.69/5.01 thf(fact_5900_mult__strict__mono_H,axiom,
% 4.69/5.01 ! [A2: int,B: int,C: int,D2: int] :
% 4.69/5.01 ( ( ord_less_int @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_int @ C @ D2 )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_strict_mono'
% 4.69/5.01 thf(fact_5901_mult__right__less__imp__less,axiom,
% 4.69/5.01 ! [A2: code_integer,C: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_right_less_imp_less
% 4.69/5.01 thf(fact_5902_mult__right__less__imp__less,axiom,
% 4.69/5.01 ! [A2: rat,C: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B @ C ) )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_rat @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_right_less_imp_less
% 4.69/5.01 thf(fact_5903_mult__right__less__imp__less,axiom,
% 4.69/5.01 ! [A2: nat,C: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ C ) )
% 4.69/5.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.69/5.01 => ( ord_less_nat @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_right_less_imp_less
% 4.69/5.01 thf(fact_5904_mult__right__less__imp__less,axiom,
% 4.69/5.01 ! [A2: int,C: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ C ) )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_int @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_right_less_imp_less
% 4.69/5.01 thf(fact_5905_mult__less__cancel__left,axiom,
% 4.69/5.01 ! [C: code_integer,A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 4.69/5.01 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ A2 @ B ) )
% 4.69/5.01 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ B @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_left
% 4.69/5.01 thf(fact_5906_mult__less__cancel__left,axiom,
% 4.69/5.01 ! [C: rat,A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B ) )
% 4.69/5.01 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_rat @ A2 @ B ) )
% 4.69/5.01 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_rat @ B @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_left
% 4.69/5.01 thf(fact_5907_mult__less__cancel__left,axiom,
% 4.69/5.01 ! [C: int,A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B ) )
% 4.69/5.01 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_int @ A2 @ B ) )
% 4.69/5.01 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.69/5.01 => ( ord_less_int @ B @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_left
% 4.69/5.01 thf(fact_5908_mult__strict__mono,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ A2 @ B )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_strict_mono
% 4.69/5.01 thf(fact_5909_mult__strict__mono,axiom,
% 4.69/5.01 ! [A2: rat,B: rat,C: rat,D2: rat] :
% 4.69/5.01 ( ( ord_less_rat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_rat @ C @ D2 )
% 4.69/5.01 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_strict_mono
% 4.69/5.01 thf(fact_5910_mult__strict__mono,axiom,
% 4.69/5.01 ! [A2: nat,B: nat,C: nat,D2: nat] :
% 4.69/5.01 ( ( ord_less_nat @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_nat @ C @ D2 )
% 4.69/5.01 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.69/5.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.69/5.01 => ( ord_less_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_strict_mono
% 4.69/5.01 thf(fact_5911_mult__strict__mono,axiom,
% 4.69/5.01 ! [A2: int,B: int,C: int,D2: int] :
% 4.69/5.01 ( ( ord_less_int @ A2 @ B )
% 4.69/5.01 => ( ( ord_less_int @ C @ D2 )
% 4.69/5.01 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_strict_mono
% 4.69/5.01 thf(fact_5912_mult__left__less__imp__less,axiom,
% 4.69/5.01 ! [C: code_integer,A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_less_imp_less
% 4.69/5.01 thf(fact_5913_mult__left__less__imp__less,axiom,
% 4.69/5.01 ! [C: rat,A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B ) )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_rat @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_less_imp_less
% 4.69/5.01 thf(fact_5914_mult__left__less__imp__less,axiom,
% 4.69/5.01 ! [C: nat,A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_nat @ ( times_times_nat @ C @ A2 ) @ ( times_times_nat @ C @ B ) )
% 4.69/5.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.69/5.01 => ( ord_less_nat @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_less_imp_less
% 4.69/5.01 thf(fact_5915_mult__left__less__imp__less,axiom,
% 4.69/5.01 ! [C: int,A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B ) )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_int @ A2 @ B ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_less_imp_less
% 4.69/5.01 thf(fact_5916_mult__le__cancel__right,axiom,
% 4.69/5.01 ! [A2: code_integer,C: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 4.69/5.01 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ A2 @ B ) )
% 4.69/5.01 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ B @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_right
% 4.69/5.01 thf(fact_5917_mult__le__cancel__right,axiom,
% 4.69/5.01 ! [A2: rat,C: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B @ C ) )
% 4.69/5.01 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_eq_rat @ A2 @ B ) )
% 4.69/5.01 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_eq_rat @ B @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_right
% 4.69/5.01 thf(fact_5918_mult__le__cancel__right,axiom,
% 4.69/5.01 ! [A2: int,C: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ C ) )
% 4.69/5.01 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_eq_int @ A2 @ B ) )
% 4.69/5.01 & ( ( ord_less_int @ C @ zero_zero_int )
% 4.69/5.01 => ( ord_less_eq_int @ B @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_right
% 4.69/5.01 thf(fact_5919_mult__le__cancel__left,axiom,
% 4.69/5.01 ! [C: code_integer,A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 4.69/5.01 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ A2 @ B ) )
% 4.69/5.01 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ B @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_left
% 4.69/5.01 thf(fact_5920_mult__le__cancel__left,axiom,
% 4.69/5.01 ! [C: rat,A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B ) )
% 4.69/5.01 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_eq_rat @ A2 @ B ) )
% 4.69/5.01 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_eq_rat @ B @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_left
% 4.69/5.01 thf(fact_5921_mult__le__cancel__left,axiom,
% 4.69/5.01 ! [C: int,A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B ) )
% 4.69/5.01 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_eq_int @ A2 @ B ) )
% 4.69/5.01 & ( ( ord_less_int @ C @ zero_zero_int )
% 4.69/5.01 => ( ord_less_eq_int @ B @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_left
% 4.69/5.01 thf(fact_5922_sum__squares__ge__zero,axiom,
% 4.69/5.01 ! [X: code_integer,Y: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % sum_squares_ge_zero
% 4.69/5.01 thf(fact_5923_sum__squares__ge__zero,axiom,
% 4.69/5.01 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % sum_squares_ge_zero
% 4.69/5.01 thf(fact_5924_sum__squares__ge__zero,axiom,
% 4.69/5.01 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % sum_squares_ge_zero
% 4.69/5.01 thf(fact_5925_mult__left__le,axiom,
% 4.69/5.01 ! [C: code_natural,A2: code_natural] :
% 4.69/5.01 ( ( ord_le1926595141338095240atural @ C @ one_one_Code_natural )
% 4.69/5.01 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A2 )
% 4.69/5.01 => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A2 @ C ) @ A2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_le
% 4.69/5.01 thf(fact_5926_mult__left__le,axiom,
% 4.69/5.01 ! [C: code_integer,A2: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ C @ one_one_Code_integer )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ A2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_le
% 4.69/5.01 thf(fact_5927_mult__left__le,axiom,
% 4.69/5.01 ! [C: rat,A2: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 4.69/5.01 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ A2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_le
% 4.69/5.01 thf(fact_5928_mult__left__le,axiom,
% 4.69/5.01 ! [C: nat,A2: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 4.69/5.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 4.69/5.01 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ C ) @ A2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_le
% 4.69/5.01 thf(fact_5929_mult__left__le,axiom,
% 4.69/5.01 ! [C: int,A2: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ C @ one_one_int )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 4.69/5.01 => ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ A2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_le
% 4.69/5.01 thf(fact_5930_mult__le__one,axiom,
% 4.69/5.01 ! [A2: code_natural,B: code_natural] :
% 4.69/5.01 ( ( ord_le1926595141338095240atural @ A2 @ one_one_Code_natural )
% 4.69/5.01 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ B )
% 4.69/5.01 => ( ( ord_le1926595141338095240atural @ B @ one_one_Code_natural )
% 4.69/5.01 => ( ord_le1926595141338095240atural @ ( times_2397367101498566445atural @ A2 @ B ) @ one_one_Code_natural ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_one
% 4.69/5.01 thf(fact_5931_mult__le__one,axiom,
% 4.69/5.01 ! [A2: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ A2 @ one_one_Code_integer )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ B ) @ one_one_Code_integer ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_one
% 4.69/5.01 thf(fact_5932_mult__le__one,axiom,
% 4.69/5.01 ! [A2: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ A2 @ one_one_rat )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.69/5.01 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 4.69/5.01 => ( ord_less_eq_rat @ ( times_times_rat @ A2 @ B ) @ one_one_rat ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_one
% 4.69/5.01 thf(fact_5933_mult__le__one,axiom,
% 4.69/5.01 ! [A2: nat,B: nat] :
% 4.69/5.01 ( ( ord_less_eq_nat @ A2 @ one_one_nat )
% 4.69/5.01 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.69/5.01 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 4.69/5.01 => ( ord_less_eq_nat @ ( times_times_nat @ A2 @ B ) @ one_one_nat ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_one
% 4.69/5.01 thf(fact_5934_mult__le__one,axiom,
% 4.69/5.01 ! [A2: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ A2 @ one_one_int )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.69/5.01 => ( ( ord_less_eq_int @ B @ one_one_int )
% 4.69/5.01 => ( ord_less_eq_int @ ( times_times_int @ A2 @ B ) @ one_one_int ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_one
% 4.69/5.01 thf(fact_5935_mult__right__le__one__le,axiom,
% 4.69/5.01 ! [X: code_integer,Y: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X @ Y ) @ X ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_right_le_one_le
% 4.69/5.01 thf(fact_5936_mult__right__le__one__le,axiom,
% 4.69/5.01 ! [X: rat,Y: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.69/5.01 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 4.69/5.01 => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y ) @ X ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_right_le_one_le
% 4.69/5.01 thf(fact_5937_mult__right__le__one__le,axiom,
% 4.69/5.01 ! [X: int,Y: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.69/5.01 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 4.69/5.01 => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_right_le_one_le
% 4.69/5.01 thf(fact_5938_mult__left__le__one__le,axiom,
% 4.69/5.01 ! [X: code_integer,Y: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Y @ X ) @ X ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_le_one_le
% 4.69/5.01 thf(fact_5939_mult__left__le__one__le,axiom,
% 4.69/5.01 ! [X: rat,Y: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.69/5.01 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 4.69/5.01 => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X ) @ X ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_le_one_le
% 4.69/5.01 thf(fact_5940_mult__left__le__one__le,axiom,
% 4.69/5.01 ! [X: int,Y: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.69/5.01 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 4.69/5.01 => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_left_le_one_le
% 4.69/5.01 thf(fact_5941_not__sum__squares__lt__zero,axiom,
% 4.69/5.01 ! [X: int,Y: int] :
% 4.69/5.01 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 4.69/5.01
% 4.69/5.01 % not_sum_squares_lt_zero
% 4.69/5.01 thf(fact_5942_not__sum__squares__lt__zero,axiom,
% 4.69/5.01 ! [X: code_integer,Y: code_integer] :
% 4.69/5.01 ~ ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger ) ).
% 4.69/5.01
% 4.69/5.01 % not_sum_squares_lt_zero
% 4.69/5.01 thf(fact_5943_not__sum__squares__lt__zero,axiom,
% 4.69/5.01 ! [X: rat,Y: rat] :
% 4.69/5.01 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 4.69/5.01
% 4.69/5.01 % not_sum_squares_lt_zero
% 4.69/5.01 thf(fact_5944_zero__less__two,axiom,
% 4.69/5.01 ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ one_one_Code_natural ) ).
% 4.69/5.01
% 4.69/5.01 % zero_less_two
% 4.69/5.01 thf(fact_5945_zero__less__two,axiom,
% 4.69/5.01 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 4.69/5.01
% 4.69/5.01 % zero_less_two
% 4.69/5.01 thf(fact_5946_zero__less__two,axiom,
% 4.69/5.01 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 4.69/5.01
% 4.69/5.01 % zero_less_two
% 4.69/5.01 thf(fact_5947_zero__less__two,axiom,
% 4.69/5.01 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 4.69/5.01
% 4.69/5.01 % zero_less_two
% 4.69/5.01 thf(fact_5948_zero__less__two,axiom,
% 4.69/5.01 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 4.69/5.01
% 4.69/5.01 % zero_less_two
% 4.69/5.01 thf(fact_5949_card__eq__0__iff,axiom,
% 4.69/5.01 ! [A: set_Code_integer] :
% 4.69/5.01 ( ( ( finite4902975817058060853nteger @ A )
% 4.69/5.01 = zero_zero_nat )
% 4.69/5.01 = ( ( A = bot_bo3990330152332043303nteger )
% 4.69/5.01 | ~ ( finite6017078050557962740nteger @ A ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_eq_0_iff
% 4.69/5.01 thf(fact_5950_card__eq__0__iff,axiom,
% 4.69/5.01 ! [A: set_Product_unit] :
% 4.69/5.01 ( ( ( finite410649719033368117t_unit @ A )
% 4.69/5.01 = zero_zero_nat )
% 4.69/5.01 = ( ( A = bot_bo3957492148770167129t_unit )
% 4.69/5.01 | ~ ( finite4290736615968046902t_unit @ A ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_eq_0_iff
% 4.69/5.01 thf(fact_5951_card__eq__0__iff,axiom,
% 4.69/5.01 ! [A: set_o] :
% 4.69/5.01 ( ( ( finite_card_o @ A )
% 4.69/5.01 = zero_zero_nat )
% 4.69/5.01 = ( ( A = bot_bot_set_o )
% 4.69/5.01 | ~ ( finite_finite_o @ A ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_eq_0_iff
% 4.69/5.01 thf(fact_5952_card__eq__0__iff,axiom,
% 4.69/5.01 ! [A: set_nat] :
% 4.69/5.01 ( ( ( finite_card_nat @ A )
% 4.69/5.01 = zero_zero_nat )
% 4.69/5.01 = ( ( A = bot_bot_set_nat )
% 4.69/5.01 | ~ ( finite_finite_nat @ A ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_eq_0_iff
% 4.69/5.01 thf(fact_5953_card__eq__0__iff,axiom,
% 4.69/5.01 ! [A: set_int] :
% 4.69/5.01 ( ( ( finite_card_int @ A )
% 4.69/5.01 = zero_zero_nat )
% 4.69/5.01 = ( ( A = bot_bot_set_int )
% 4.69/5.01 | ~ ( finite_finite_int @ A ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_eq_0_iff
% 4.69/5.01 thf(fact_5954_card__eq__0__iff,axiom,
% 4.69/5.01 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/5.01 ( ( ( finite1363419556375932405_nat_o @ A )
% 4.69/5.01 = zero_zero_nat )
% 4.69/5.01 = ( ( A = bot_bo7824918357723582233_nat_o )
% 4.69/5.01 | ~ ( finite3252695134891459830_nat_o @ A ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_eq_0_iff
% 4.69/5.01 thf(fact_5955_one__less__mult,axiom,
% 4.69/5.01 ! [N2: nat,M4: nat] :
% 4.69/5.01 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 4.69/5.01 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M4 )
% 4.69/5.01 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M4 @ N2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % one_less_mult
% 4.69/5.01 thf(fact_5956_n__less__m__mult__n,axiom,
% 4.69/5.01 ! [N2: nat,M4: nat] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.01 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M4 )
% 4.69/5.01 => ( ord_less_nat @ N2 @ ( times_times_nat @ M4 @ N2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % n_less_m_mult_n
% 4.69/5.01 thf(fact_5957_n__less__n__mult__m,axiom,
% 4.69/5.01 ! [N2: nat,M4: nat] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.01 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M4 )
% 4.69/5.01 => ( ord_less_nat @ N2 @ ( times_times_nat @ N2 @ M4 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % n_less_n_mult_m
% 4.69/5.01 thf(fact_5958_nat__mult__le__cancel1,axiom,
% 4.69/5.01 ! [K3: nat,M4: nat,N2: nat] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 4.69/5.01 => ( ( ord_less_eq_nat @ ( times_times_nat @ K3 @ M4 ) @ ( times_times_nat @ K3 @ N2 ) )
% 4.69/5.01 = ( ord_less_eq_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % nat_mult_le_cancel1
% 4.69/5.01 thf(fact_5959_mult__le__cancel__left1,axiom,
% 4.69/5.01 ! [C: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ C @ ( times_3573771949741848930nteger @ C @ B ) )
% 4.69/5.01 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 4.69/5.01 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_left1
% 4.69/5.01 thf(fact_5960_mult__le__cancel__left1,axiom,
% 4.69/5.01 ! [C: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 4.69/5.01 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 4.69/5.01 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_left1
% 4.69/5.01 thf(fact_5961_mult__le__cancel__left1,axiom,
% 4.69/5.01 ! [C: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 4.69/5.01 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_eq_int @ one_one_int @ B ) )
% 4.69/5.01 & ( ( ord_less_int @ C @ zero_zero_int )
% 4.69/5.01 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_left1
% 4.69/5.01 thf(fact_5962_mult__le__cancel__left2,axiom,
% 4.69/5.01 ! [C: code_integer,A2: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ C )
% 4.69/5.01 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ A2 @ one_one_Code_integer ) )
% 4.69/5.01 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_left2
% 4.69/5.01 thf(fact_5963_mult__le__cancel__left2,axiom,
% 4.69/5.01 ! [C: rat,A2: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A2 ) @ C )
% 4.69/5.01 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_eq_rat @ A2 @ one_one_rat ) )
% 4.69/5.01 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_eq_rat @ one_one_rat @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_left2
% 4.69/5.01 thf(fact_5964_mult__le__cancel__left2,axiom,
% 4.69/5.01 ! [C: int,A2: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ ( times_times_int @ C @ A2 ) @ C )
% 4.69/5.01 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_eq_int @ A2 @ one_one_int ) )
% 4.69/5.01 & ( ( ord_less_int @ C @ zero_zero_int )
% 4.69/5.01 => ( ord_less_eq_int @ one_one_int @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_left2
% 4.69/5.01 thf(fact_5965_mult__le__cancel__right1,axiom,
% 4.69/5.01 ! [C: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ C @ ( times_3573771949741848930nteger @ B @ C ) )
% 4.69/5.01 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 4.69/5.01 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_right1
% 4.69/5.01 thf(fact_5966_mult__le__cancel__right1,axiom,
% 4.69/5.01 ! [C: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 4.69/5.01 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 4.69/5.01 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_right1
% 4.69/5.01 thf(fact_5967_mult__le__cancel__right1,axiom,
% 4.69/5.01 ! [C: int,B: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 4.69/5.01 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_eq_int @ one_one_int @ B ) )
% 4.69/5.01 & ( ( ord_less_int @ C @ zero_zero_int )
% 4.69/5.01 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_right1
% 4.69/5.01 thf(fact_5968_mult__le__cancel__right2,axiom,
% 4.69/5.01 ! [A2: code_integer,C: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ C )
% 4.69/5.01 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ A2 @ one_one_Code_integer ) )
% 4.69/5.01 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_right2
% 4.69/5.01 thf(fact_5969_mult__le__cancel__right2,axiom,
% 4.69/5.01 ! [A2: rat,C: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ ( times_times_rat @ A2 @ C ) @ C )
% 4.69/5.01 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_eq_rat @ A2 @ one_one_rat ) )
% 4.69/5.01 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_eq_rat @ one_one_rat @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_right2
% 4.69/5.01 thf(fact_5970_mult__le__cancel__right2,axiom,
% 4.69/5.01 ! [A2: int,C: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ ( times_times_int @ A2 @ C ) @ C )
% 4.69/5.01 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_eq_int @ A2 @ one_one_int ) )
% 4.69/5.01 & ( ( ord_less_int @ C @ zero_zero_int )
% 4.69/5.01 => ( ord_less_eq_int @ one_one_int @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_right2
% 4.69/5.01 thf(fact_5971_mult__less__cancel__left1,axiom,
% 4.69/5.01 ! [C: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ C @ ( times_3573771949741848930nteger @ C @ B ) )
% 4.69/5.01 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 4.69/5.01 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_left1
% 4.69/5.01 thf(fact_5972_mult__less__cancel__left1,axiom,
% 4.69/5.01 ! [C: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 4.69/5.01 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_rat @ one_one_rat @ B ) )
% 4.69/5.01 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_left1
% 4.69/5.01 thf(fact_5973_mult__less__cancel__left1,axiom,
% 4.69/5.01 ! [C: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 4.69/5.01 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_int @ one_one_int @ B ) )
% 4.69/5.01 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.69/5.01 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_left1
% 4.69/5.01 thf(fact_5974_mult__less__cancel__left2,axiom,
% 4.69/5.01 ! [C: code_integer,A2: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ C )
% 4.69/5.01 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ A2 @ one_one_Code_integer ) )
% 4.69/5.01 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_left2
% 4.69/5.01 thf(fact_5975_mult__less__cancel__left2,axiom,
% 4.69/5.01 ! [C: rat,A2: rat] :
% 4.69/5.01 ( ( ord_less_rat @ ( times_times_rat @ C @ A2 ) @ C )
% 4.69/5.01 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_rat @ A2 @ one_one_rat ) )
% 4.69/5.01 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_rat @ one_one_rat @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_left2
% 4.69/5.01 thf(fact_5976_mult__less__cancel__left2,axiom,
% 4.69/5.01 ! [C: int,A2: int] :
% 4.69/5.01 ( ( ord_less_int @ ( times_times_int @ C @ A2 ) @ C )
% 4.69/5.01 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_int @ A2 @ one_one_int ) )
% 4.69/5.01 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.69/5.01 => ( ord_less_int @ one_one_int @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_left2
% 4.69/5.01 thf(fact_5977_mult__less__cancel__right1,axiom,
% 4.69/5.01 ! [C: code_integer,B: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ C @ ( times_3573771949741848930nteger @ B @ C ) )
% 4.69/5.01 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 4.69/5.01 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_right1
% 4.69/5.01 thf(fact_5978_mult__less__cancel__right1,axiom,
% 4.69/5.01 ! [C: rat,B: rat] :
% 4.69/5.01 ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 4.69/5.01 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_rat @ one_one_rat @ B ) )
% 4.69/5.01 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_right1
% 4.69/5.01 thf(fact_5979_mult__less__cancel__right1,axiom,
% 4.69/5.01 ! [C: int,B: int] :
% 4.69/5.01 ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 4.69/5.01 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_int @ one_one_int @ B ) )
% 4.69/5.01 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.69/5.01 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_right1
% 4.69/5.01 thf(fact_5980_mult__less__cancel__right2,axiom,
% 4.69/5.01 ! [A2: code_integer,C: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ C ) @ C )
% 4.69/5.01 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ A2 @ one_one_Code_integer ) )
% 4.69/5.01 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_right2
% 4.69/5.01 thf(fact_5981_mult__less__cancel__right2,axiom,
% 4.69/5.01 ! [A2: rat,C: rat] :
% 4.69/5.01 ( ( ord_less_rat @ ( times_times_rat @ A2 @ C ) @ C )
% 4.69/5.01 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.69/5.01 => ( ord_less_rat @ A2 @ one_one_rat ) )
% 4.69/5.01 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.69/5.01 => ( ord_less_rat @ one_one_rat @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_right2
% 4.69/5.01 thf(fact_5982_mult__less__cancel__right2,axiom,
% 4.69/5.01 ! [A2: int,C: int] :
% 4.69/5.01 ( ( ord_less_int @ ( times_times_int @ A2 @ C ) @ C )
% 4.69/5.01 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.69/5.01 => ( ord_less_int @ A2 @ one_one_int ) )
% 4.69/5.01 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.69/5.01 => ( ord_less_int @ one_one_int @ A2 ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_less_cancel_right2
% 4.69/5.01 thf(fact_5983_convex__bound__le,axiom,
% 4.69/5.01 ! [X: code_integer,A2: code_integer,Y: code_integer,U: code_integer,V: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ X @ A2 )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ Y @ A2 )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V )
% 4.69/5.01 => ( ( ( plus_p5714425477246183910nteger @ U @ V )
% 4.69/5.01 = one_one_Code_integer )
% 4.69/5.01 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V @ Y ) ) @ A2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % convex_bound_le
% 4.69/5.01 thf(fact_5984_convex__bound__le,axiom,
% 4.69/5.01 ! [X: rat,A2: rat,Y: rat,U: rat,V: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ X @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_rat @ Y @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 4.69/5.01 => ( ( ( plus_plus_rat @ U @ V )
% 4.69/5.01 = one_one_rat )
% 4.69/5.01 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % convex_bound_le
% 4.69/5.01 thf(fact_5985_convex__bound__le,axiom,
% 4.69/5.01 ! [X: int,A2: int,Y: int,U: int,V: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ X @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_int @ Y @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 4.69/5.01 => ( ( ( plus_plus_int @ U @ V )
% 4.69/5.01 = one_one_int )
% 4.69/5.01 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % convex_bound_le
% 4.69/5.01 thf(fact_5986_card__gt__0__iff,axiom,
% 4.69/5.01 ! [A: set_Code_integer] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ ( finite4902975817058060853nteger @ A ) )
% 4.69/5.01 = ( ( A != bot_bo3990330152332043303nteger )
% 4.69/5.01 & ( finite6017078050557962740nteger @ A ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_gt_0_iff
% 4.69/5.01 thf(fact_5987_card__gt__0__iff,axiom,
% 4.69/5.01 ! [A: set_Product_unit] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ ( finite410649719033368117t_unit @ A ) )
% 4.69/5.01 = ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.01 & ( finite4290736615968046902t_unit @ A ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_gt_0_iff
% 4.69/5.01 thf(fact_5988_card__gt__0__iff,axiom,
% 4.69/5.01 ! [A: set_o] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_o @ A ) )
% 4.69/5.01 = ( ( A != bot_bot_set_o )
% 4.69/5.01 & ( finite_finite_o @ A ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_gt_0_iff
% 4.69/5.01 thf(fact_5989_card__gt__0__iff,axiom,
% 4.69/5.01 ! [A: set_nat] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A ) )
% 4.69/5.01 = ( ( A != bot_bot_set_nat )
% 4.69/5.01 & ( finite_finite_nat @ A ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_gt_0_iff
% 4.69/5.01 thf(fact_5990_card__gt__0__iff,axiom,
% 4.69/5.01 ! [A: set_int] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A ) )
% 4.69/5.01 = ( ( A != bot_bot_set_int )
% 4.69/5.01 & ( finite_finite_int @ A ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_gt_0_iff
% 4.69/5.01 thf(fact_5991_card__gt__0__iff,axiom,
% 4.69/5.01 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ ( finite1363419556375932405_nat_o @ A ) )
% 4.69/5.01 = ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/5.01 & ( finite3252695134891459830_nat_o @ A ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_gt_0_iff
% 4.69/5.01 thf(fact_5992_card__1__singleton__iff,axiom,
% 4.69/5.01 ! [A: set_Product_unit] :
% 4.69/5.01 ( ( ( finite410649719033368117t_unit @ A )
% 4.69/5.01 = ( suc @ zero_zero_nat ) )
% 4.69/5.01 = ( ? [X2: product_unit] :
% 4.69/5.01 ( A
% 4.69/5.01 = ( insert_Product_unit @ X2 @ bot_bo3957492148770167129t_unit ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_1_singleton_iff
% 4.69/5.01 thf(fact_5993_card__1__singleton__iff,axiom,
% 4.69/5.01 ! [A: set_o] :
% 4.69/5.01 ( ( ( finite_card_o @ A )
% 4.69/5.01 = ( suc @ zero_zero_nat ) )
% 4.69/5.01 = ( ? [X2: $o] :
% 4.69/5.01 ( A
% 4.69/5.01 = ( insert_o @ X2 @ bot_bot_set_o ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_1_singleton_iff
% 4.69/5.01 thf(fact_5994_card__1__singleton__iff,axiom,
% 4.69/5.01 ! [A: set_nat] :
% 4.69/5.01 ( ( ( finite_card_nat @ A )
% 4.69/5.01 = ( suc @ zero_zero_nat ) )
% 4.69/5.01 = ( ? [X2: nat] :
% 4.69/5.01 ( A
% 4.69/5.01 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_1_singleton_iff
% 4.69/5.01 thf(fact_5995_card__1__singleton__iff,axiom,
% 4.69/5.01 ! [A: set_int] :
% 4.69/5.01 ( ( ( finite_card_int @ A )
% 4.69/5.01 = ( suc @ zero_zero_nat ) )
% 4.69/5.01 = ( ? [X2: int] :
% 4.69/5.01 ( A
% 4.69/5.01 = ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_1_singleton_iff
% 4.69/5.01 thf(fact_5996_card__1__singleton__iff,axiom,
% 4.69/5.01 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/5.01 ( ( ( finite1363419556375932405_nat_o @ A )
% 4.69/5.01 = ( suc @ zero_zero_nat ) )
% 4.69/5.01 = ( ? [X2: produc3658429121746597890et_nat > $o] :
% 4.69/5.01 ( A
% 4.69/5.01 = ( insert5175938949040314269_nat_o @ X2 @ bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_1_singleton_iff
% 4.69/5.01 thf(fact_5997_card__eq__SucD,axiom,
% 4.69/5.01 ! [A: set_Product_unit,K3: nat] :
% 4.69/5.01 ( ( ( finite410649719033368117t_unit @ A )
% 4.69/5.01 = ( suc @ K3 ) )
% 4.69/5.01 => ? [B2: product_unit,B5: set_Product_unit] :
% 4.69/5.01 ( ( A
% 4.69/5.01 = ( insert_Product_unit @ B2 @ B5 ) )
% 4.69/5.01 & ~ ( member_Product_unit @ B2 @ B5 )
% 4.69/5.01 & ( ( finite410649719033368117t_unit @ B5 )
% 4.69/5.01 = K3 )
% 4.69/5.01 & ( ( K3 = zero_zero_nat )
% 4.69/5.01 => ( B5 = bot_bo3957492148770167129t_unit ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_eq_SucD
% 4.69/5.01 thf(fact_5998_card__eq__SucD,axiom,
% 4.69/5.01 ! [A: set_o,K3: nat] :
% 4.69/5.01 ( ( ( finite_card_o @ A )
% 4.69/5.01 = ( suc @ K3 ) )
% 4.69/5.01 => ? [B2: $o,B5: set_o] :
% 4.69/5.01 ( ( A
% 4.69/5.01 = ( insert_o @ B2 @ B5 ) )
% 4.69/5.01 & ~ ( member_o @ B2 @ B5 )
% 4.69/5.01 & ( ( finite_card_o @ B5 )
% 4.69/5.01 = K3 )
% 4.69/5.01 & ( ( K3 = zero_zero_nat )
% 4.69/5.01 => ( B5 = bot_bot_set_o ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_eq_SucD
% 4.69/5.01 thf(fact_5999_card__eq__SucD,axiom,
% 4.69/5.01 ! [A: set_nat,K3: nat] :
% 4.69/5.01 ( ( ( finite_card_nat @ A )
% 4.69/5.01 = ( suc @ K3 ) )
% 4.69/5.01 => ? [B2: nat,B5: set_nat] :
% 4.69/5.01 ( ( A
% 4.69/5.01 = ( insert_nat @ B2 @ B5 ) )
% 4.69/5.01 & ~ ( member_nat @ B2 @ B5 )
% 4.69/5.01 & ( ( finite_card_nat @ B5 )
% 4.69/5.01 = K3 )
% 4.69/5.01 & ( ( K3 = zero_zero_nat )
% 4.69/5.01 => ( B5 = bot_bot_set_nat ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_eq_SucD
% 4.69/5.01 thf(fact_6000_card__eq__SucD,axiom,
% 4.69/5.01 ! [A: set_int,K3: nat] :
% 4.69/5.01 ( ( ( finite_card_int @ A )
% 4.69/5.01 = ( suc @ K3 ) )
% 4.69/5.01 => ? [B2: int,B5: set_int] :
% 4.69/5.01 ( ( A
% 4.69/5.01 = ( insert_int @ B2 @ B5 ) )
% 4.69/5.01 & ~ ( member_int @ B2 @ B5 )
% 4.69/5.01 & ( ( finite_card_int @ B5 )
% 4.69/5.01 = K3 )
% 4.69/5.01 & ( ( K3 = zero_zero_nat )
% 4.69/5.01 => ( B5 = bot_bot_set_int ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_eq_SucD
% 4.69/5.01 thf(fact_6001_card__eq__SucD,axiom,
% 4.69/5.01 ! [A: set_Pr4532377907799695533_nat_o,K3: nat] :
% 4.69/5.01 ( ( ( finite1363419556375932405_nat_o @ A )
% 4.69/5.01 = ( suc @ K3 ) )
% 4.69/5.01 => ? [B2: produc3658429121746597890et_nat > $o,B5: set_Pr4532377907799695533_nat_o] :
% 4.69/5.01 ( ( A
% 4.69/5.01 = ( insert5175938949040314269_nat_o @ B2 @ B5 ) )
% 4.69/5.01 & ~ ( member6576561426505652726_nat_o @ B2 @ B5 )
% 4.69/5.01 & ( ( finite1363419556375932405_nat_o @ B5 )
% 4.69/5.01 = K3 )
% 4.69/5.01 & ( ( K3 = zero_zero_nat )
% 4.69/5.01 => ( B5 = bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_eq_SucD
% 4.69/5.01 thf(fact_6002_card__Suc__eq,axiom,
% 4.69/5.01 ! [A: set_Product_unit,K3: nat] :
% 4.69/5.01 ( ( ( finite410649719033368117t_unit @ A )
% 4.69/5.01 = ( suc @ K3 ) )
% 4.69/5.01 = ( ? [B6: product_unit,B7: set_Product_unit] :
% 4.69/5.01 ( ( A
% 4.69/5.01 = ( insert_Product_unit @ B6 @ B7 ) )
% 4.69/5.01 & ~ ( member_Product_unit @ B6 @ B7 )
% 4.69/5.01 & ( ( finite410649719033368117t_unit @ B7 )
% 4.69/5.01 = K3 )
% 4.69/5.01 & ( ( K3 = zero_zero_nat )
% 4.69/5.01 => ( B7 = bot_bo3957492148770167129t_unit ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_Suc_eq
% 4.69/5.01 thf(fact_6003_card__Suc__eq,axiom,
% 4.69/5.01 ! [A: set_o,K3: nat] :
% 4.69/5.01 ( ( ( finite_card_o @ A )
% 4.69/5.01 = ( suc @ K3 ) )
% 4.69/5.01 = ( ? [B6: $o,B7: set_o] :
% 4.69/5.01 ( ( A
% 4.69/5.01 = ( insert_o @ B6 @ B7 ) )
% 4.69/5.01 & ~ ( member_o @ B6 @ B7 )
% 4.69/5.01 & ( ( finite_card_o @ B7 )
% 4.69/5.01 = K3 )
% 4.69/5.01 & ( ( K3 = zero_zero_nat )
% 4.69/5.01 => ( B7 = bot_bot_set_o ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_Suc_eq
% 4.69/5.01 thf(fact_6004_card__Suc__eq,axiom,
% 4.69/5.01 ! [A: set_nat,K3: nat] :
% 4.69/5.01 ( ( ( finite_card_nat @ A )
% 4.69/5.01 = ( suc @ K3 ) )
% 4.69/5.01 = ( ? [B6: nat,B7: set_nat] :
% 4.69/5.01 ( ( A
% 4.69/5.01 = ( insert_nat @ B6 @ B7 ) )
% 4.69/5.01 & ~ ( member_nat @ B6 @ B7 )
% 4.69/5.01 & ( ( finite_card_nat @ B7 )
% 4.69/5.01 = K3 )
% 4.69/5.01 & ( ( K3 = zero_zero_nat )
% 4.69/5.01 => ( B7 = bot_bot_set_nat ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_Suc_eq
% 4.69/5.01 thf(fact_6005_card__Suc__eq,axiom,
% 4.69/5.01 ! [A: set_int,K3: nat] :
% 4.69/5.01 ( ( ( finite_card_int @ A )
% 4.69/5.01 = ( suc @ K3 ) )
% 4.69/5.01 = ( ? [B6: int,B7: set_int] :
% 4.69/5.01 ( ( A
% 4.69/5.01 = ( insert_int @ B6 @ B7 ) )
% 4.69/5.01 & ~ ( member_int @ B6 @ B7 )
% 4.69/5.01 & ( ( finite_card_int @ B7 )
% 4.69/5.01 = K3 )
% 4.69/5.01 & ( ( K3 = zero_zero_nat )
% 4.69/5.01 => ( B7 = bot_bot_set_int ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_Suc_eq
% 4.69/5.01 thf(fact_6006_card__Suc__eq,axiom,
% 4.69/5.01 ! [A: set_Pr4532377907799695533_nat_o,K3: nat] :
% 4.69/5.01 ( ( ( finite1363419556375932405_nat_o @ A )
% 4.69/5.01 = ( suc @ K3 ) )
% 4.69/5.01 = ( ? [B6: produc3658429121746597890et_nat > $o,B7: set_Pr4532377907799695533_nat_o] :
% 4.69/5.01 ( ( A
% 4.69/5.01 = ( insert5175938949040314269_nat_o @ B6 @ B7 ) )
% 4.69/5.01 & ~ ( member6576561426505652726_nat_o @ B6 @ B7 )
% 4.69/5.01 & ( ( finite1363419556375932405_nat_o @ B7 )
% 4.69/5.01 = K3 )
% 4.69/5.01 & ( ( K3 = zero_zero_nat )
% 4.69/5.01 => ( B7 = bot_bo7824918357723582233_nat_o ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % card_Suc_eq
% 4.69/5.01 thf(fact_6007_nz__le__conv__less,axiom,
% 4.69/5.01 ! [K3: nat,M4: nat] :
% 4.69/5.01 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 4.69/5.01 => ( ( ord_less_eq_nat @ K3 @ M4 )
% 4.69/5.01 => ( ord_less_nat @ ( minus_minus_nat @ K3 @ ( suc @ zero_zero_nat ) ) @ M4 ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % nz_le_conv_less
% 4.69/5.01 thf(fact_6008_mult__eq__if,axiom,
% 4.69/5.01 ( times_times_nat
% 4.69/5.01 = ( ^ [M3: nat,N4: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N4 @ ( times_times_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N4 ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_eq_if
% 4.69/5.01 thf(fact_6009_convex__bound__lt,axiom,
% 4.69/5.01 ! [X: code_integer,A2: code_integer,Y: code_integer,U: code_integer,V: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ X @ A2 )
% 4.69/5.01 => ( ( ord_le6747313008572928689nteger @ Y @ A2 )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V )
% 4.69/5.01 => ( ( ( plus_p5714425477246183910nteger @ U @ V )
% 4.69/5.01 = one_one_Code_integer )
% 4.69/5.01 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V @ Y ) ) @ A2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % convex_bound_lt
% 4.69/5.01 thf(fact_6010_convex__bound__lt,axiom,
% 4.69/5.01 ! [X: rat,A2: rat,Y: rat,U: rat,V: rat] :
% 4.69/5.01 ( ( ord_less_rat @ X @ A2 )
% 4.69/5.01 => ( ( ord_less_rat @ Y @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 4.69/5.01 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 4.69/5.01 => ( ( ( plus_plus_rat @ U @ V )
% 4.69/5.01 = one_one_rat )
% 4.69/5.01 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % convex_bound_lt
% 4.69/5.01 thf(fact_6011_convex__bound__lt,axiom,
% 4.69/5.01 ! [X: int,A2: int,Y: int,U: int,V: int] :
% 4.69/5.01 ( ( ord_less_int @ X @ A2 )
% 4.69/5.01 => ( ( ord_less_int @ Y @ A2 )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 4.69/5.01 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 4.69/5.01 => ( ( ( plus_plus_int @ U @ V )
% 4.69/5.01 = one_one_int )
% 4.69/5.01 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A2 ) ) ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % convex_bound_lt
% 4.69/5.01 thf(fact_6012_inj__mult__left,axiom,
% 4.69/5.01 ! [A2: code_integer] :
% 4.69/5.01 ( ( inj_on1158064722259180589nteger @ ( times_3573771949741848930nteger @ A2 ) @ top_to4645266643341252675nteger )
% 4.69/5.01 = ( A2 != zero_z3403309356797280102nteger ) ) ).
% 4.69/5.01
% 4.69/5.01 % inj_mult_left
% 4.69/5.01 thf(fact_6013_inj__mult__left,axiom,
% 4.69/5.01 ! [A2: rat] :
% 4.69/5.01 ( ( inj_on_rat_rat @ ( times_times_rat @ A2 ) @ top_top_set_rat )
% 4.69/5.01 = ( A2 != zero_zero_rat ) ) ).
% 4.69/5.01
% 4.69/5.01 % inj_mult_left
% 4.69/5.01 thf(fact_6014_inj__mult__left,axiom,
% 4.69/5.01 ! [A2: int] :
% 4.69/5.01 ( ( inj_on_int_int @ ( times_times_int @ A2 ) @ top_top_set_int )
% 4.69/5.01 = ( A2 != zero_zero_int ) ) ).
% 4.69/5.01
% 4.69/5.01 % inj_mult_left
% 4.69/5.01 thf(fact_6015_field__le__mult__one__interval,axiom,
% 4.69/5.01 ! [X: rat,Y: rat] :
% 4.69/5.01 ( ! [Z3: rat] :
% 4.69/5.01 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 4.69/5.01 => ( ( ord_less_rat @ Z3 @ one_one_rat )
% 4.69/5.01 => ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ X ) @ Y ) ) )
% 4.69/5.01 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 4.69/5.01
% 4.69/5.01 % field_le_mult_one_interval
% 4.69/5.01 thf(fact_6016_size__prod__simp,axiom,
% 4.69/5.01 ( basic_5567952622663070111et_nat
% 4.69/5.01 = ( ^ [F4: heap_e7401611519738050253t_unit > nat,G3: set_nat > nat,P5: produc3658429121746597890et_nat] : ( plus_plus_nat @ ( plus_plus_nat @ ( F4 @ ( produc1824681642469235216et_nat @ P5 ) ) @ ( G3 @ ( produc8586169260539613262et_nat @ P5 ) ) ) @ ( suc @ zero_zero_nat ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % size_prod_simp
% 4.69/5.01 thf(fact_6017_size__prod__simp,axiom,
% 4.69/5.01 ( basic_1872990034501187214nt_int
% 4.69/5.01 = ( ^ [F4: int > nat,G3: int > nat,P5: product_prod_int_int] : ( plus_plus_nat @ ( plus_plus_nat @ ( F4 @ ( product_fst_int_int @ P5 ) ) @ ( G3 @ ( product_snd_int_int @ P5 ) ) ) @ ( suc @ zero_zero_nat ) ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % size_prod_simp
% 4.69/5.01 thf(fact_6018_sum__squares__gt__zero__iff,axiom,
% 4.69/5.01 ! [X: int,Y: int] :
% 4.69/5.01 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 4.69/5.01 = ( ( X != zero_zero_int )
% 4.69/5.01 | ( Y != zero_zero_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % sum_squares_gt_zero_iff
% 4.69/5.01 thf(fact_6019_sum__squares__gt__zero__iff,axiom,
% 4.69/5.01 ! [X: code_integer,Y: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) )
% 4.69/5.01 = ( ( X != zero_z3403309356797280102nteger )
% 4.69/5.01 | ( Y != zero_z3403309356797280102nteger ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % sum_squares_gt_zero_iff
% 4.69/5.01 thf(fact_6020_sum__squares__gt__zero__iff,axiom,
% 4.69/5.01 ! [X: rat,Y: rat] :
% 4.69/5.01 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) )
% 4.69/5.01 = ( ( X != zero_zero_rat )
% 4.69/5.01 | ( Y != zero_zero_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % sum_squares_gt_zero_iff
% 4.69/5.01 thf(fact_6021_sum__squares__le__zero__iff,axiom,
% 4.69/5.01 ! [X: code_integer,Y: code_integer] :
% 4.69/5.01 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger )
% 4.69/5.01 = ( ( X = zero_z3403309356797280102nteger )
% 4.69/5.01 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % sum_squares_le_zero_iff
% 4.69/5.01 thf(fact_6022_sum__squares__le__zero__iff,axiom,
% 4.69/5.01 ! [X: rat,Y: rat] :
% 4.69/5.01 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 4.69/5.01 = ( ( X = zero_zero_rat )
% 4.69/5.01 & ( Y = zero_zero_rat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % sum_squares_le_zero_iff
% 4.69/5.01 thf(fact_6023_sum__squares__le__zero__iff,axiom,
% 4.69/5.01 ! [X: int,Y: int] :
% 4.69/5.01 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 4.69/5.01 = ( ( X = zero_zero_int )
% 4.69/5.01 & ( Y = zero_zero_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % sum_squares_le_zero_iff
% 4.69/5.01 thf(fact_6024_mult__le__cancel__iff2,axiom,
% 4.69/5.01 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Z @ X ) @ ( times_3573771949741848930nteger @ Z @ Y ) )
% 4.69/5.01 = ( ord_le3102999989581377725nteger @ X @ Y ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_iff2
% 4.69/5.01 thf(fact_6025_mult__le__cancel__iff2,axiom,
% 4.69/5.01 ! [Z: rat,X: rat,Y: rat] :
% 4.69/5.01 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 4.69/5.01 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ ( times_times_rat @ Z @ Y ) )
% 4.69/5.01 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_iff2
% 4.69/5.01 thf(fact_6026_mult__le__cancel__iff2,axiom,
% 4.69/5.01 ! [Z: int,X: int,Y: int] :
% 4.69/5.01 ( ( ord_less_int @ zero_zero_int @ Z )
% 4.69/5.01 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X ) @ ( times_times_int @ Z @ Y ) )
% 4.69/5.01 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_iff2
% 4.69/5.01 thf(fact_6027_mult__le__cancel__iff1,axiom,
% 4.69/5.01 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 4.69/5.01 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z )
% 4.69/5.01 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X @ Z ) @ ( times_3573771949741848930nteger @ Y @ Z ) )
% 4.69/5.01 = ( ord_le3102999989581377725nteger @ X @ Y ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_iff1
% 4.69/5.01 thf(fact_6028_mult__le__cancel__iff1,axiom,
% 4.69/5.01 ! [Z: rat,X: rat,Y: rat] :
% 4.69/5.01 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 4.69/5.01 => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 4.69/5.01 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_iff1
% 4.69/5.01 thf(fact_6029_mult__le__cancel__iff1,axiom,
% 4.69/5.01 ! [Z: int,X: int,Y: int] :
% 4.69/5.01 ( ( ord_less_int @ zero_zero_int @ Z )
% 4.69/5.01 => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 4.69/5.01 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % mult_le_cancel_iff1
% 4.69/5.01 thf(fact_6030_divides__aux__eq,axiom,
% 4.69/5.01 ! [Q4: nat,R2: nat] :
% 4.69/5.01 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q4 @ R2 ) )
% 4.69/5.01 = ( R2 = zero_zero_nat ) ) ).
% 4.69/5.01
% 4.69/5.01 % divides_aux_eq
% 4.69/5.01 thf(fact_6031_divides__aux__eq,axiom,
% 4.69/5.01 ! [Q4: int,R2: int] :
% 4.69/5.01 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q4 @ R2 ) )
% 4.69/5.01 = ( R2 = zero_zero_int ) ) ).
% 4.69/5.01
% 4.69/5.01 % divides_aux_eq
% 4.69/5.01 thf(fact_6032_divides__aux__eq,axiom,
% 4.69/5.01 ! [Q4: code_integer,R2: code_integer] :
% 4.69/5.01 ( ( unique5706413561485394159nteger @ ( produc1086072967326762835nteger @ Q4 @ R2 ) )
% 4.69/5.01 = ( R2 = zero_z3403309356797280102nteger ) ) ).
% 4.69/5.01
% 4.69/5.01 % divides_aux_eq
% 4.69/5.01 thf(fact_6033_divides__aux__def,axiom,
% 4.69/5.01 ( unique6322359934112328802ux_nat
% 4.69/5.01 = ( ^ [Qr: product_prod_nat_nat] :
% 4.69/5.01 ( ( product_snd_nat_nat @ Qr )
% 4.69/5.01 = zero_zero_nat ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % divides_aux_def
% 4.69/5.01 thf(fact_6034_divides__aux__def,axiom,
% 4.69/5.01 ( unique6319869463603278526ux_int
% 4.69/5.01 = ( ^ [Qr: product_prod_int_int] :
% 4.69/5.01 ( ( product_snd_int_int @ Qr )
% 4.69/5.01 = zero_zero_int ) ) ) ).
% 4.69/5.01
% 4.69/5.01 % divides_aux_def
% 4.69/5.01 thf(fact_6035_divides__aux__def,axiom,
% 4.69/5.01 ( unique5706413561485394159nteger
% 4.69/5.01 = ( ^ [Qr: produc8923325533196201883nteger] :
% 4.69/5.01 ( ( produc6174133586879617921nteger @ Qr )
% 4.69/5.01 = zero_z3403309356797280102nteger ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % divides_aux_def
% 4.69/5.02 thf(fact_6036_mult__less__iff1,axiom,
% 4.69/5.02 ! [Z: int,X: int,Y: int] :
% 4.69/5.02 ( ( ord_less_int @ zero_zero_int @ Z )
% 4.69/5.02 => ( ( ord_less_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 4.69/5.02 = ( ord_less_int @ X @ Y ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % mult_less_iff1
% 4.69/5.02 thf(fact_6037_mult__less__iff1,axiom,
% 4.69/5.02 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 4.69/5.02 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z )
% 4.69/5.02 => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ X @ Z ) @ ( times_3573771949741848930nteger @ Y @ Z ) )
% 4.69/5.02 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % mult_less_iff1
% 4.69/5.02 thf(fact_6038_mult__less__iff1,axiom,
% 4.69/5.02 ! [Z: rat,X: rat,Y: rat] :
% 4.69/5.02 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 4.69/5.02 => ( ( ord_less_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 4.69/5.02 = ( ord_less_rat @ X @ Y ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % mult_less_iff1
% 4.69/5.02 thf(fact_6039_sum__squares__eq__zero__iff,axiom,
% 4.69/5.02 ! [X: code_integer,Y: code_integer] :
% 4.69/5.02 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 4.69/5.02 = zero_z3403309356797280102nteger )
% 4.69/5.02 = ( ( X = zero_z3403309356797280102nteger )
% 4.69/5.02 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_squares_eq_zero_iff
% 4.69/5.02 thf(fact_6040_sum__squares__eq__zero__iff,axiom,
% 4.69/5.02 ! [X: rat,Y: rat] :
% 4.69/5.02 ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 4.69/5.02 = zero_zero_rat )
% 4.69/5.02 = ( ( X = zero_zero_rat )
% 4.69/5.02 & ( Y = zero_zero_rat ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_squares_eq_zero_iff
% 4.69/5.02 thf(fact_6041_sum__squares__eq__zero__iff,axiom,
% 4.69/5.02 ! [X: int,Y: int] :
% 4.69/5.02 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 4.69/5.02 = zero_zero_int )
% 4.69/5.02 = ( ( X = zero_zero_int )
% 4.69/5.02 & ( Y = zero_zero_int ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_squares_eq_zero_iff
% 4.69/5.02 thf(fact_6042_dbl__inc__simps_I2_J,axiom,
% 4.69/5.02 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 4.69/5.02 = one_one_int ) ).
% 4.69/5.02
% 4.69/5.02 % dbl_inc_simps(2)
% 4.69/5.02 thf(fact_6043_dbl__inc__simps_I2_J,axiom,
% 4.69/5.02 ( ( neg_nu5831290666863070958nteger @ zero_z3403309356797280102nteger )
% 4.69/5.02 = one_one_Code_integer ) ).
% 4.69/5.02
% 4.69/5.02 % dbl_inc_simps(2)
% 4.69/5.02 thf(fact_6044_enumerate__Suc_H,axiom,
% 4.69/5.02 ! [S: set_Product_unit,N2: nat] :
% 4.69/5.02 ( ( infini7930543730640340914t_unit @ S @ ( suc @ N2 ) )
% 4.69/5.02 = ( infini7930543730640340914t_unit @ ( minus_6452836326544984404t_unit @ S @ ( insert_Product_unit @ ( infini7930543730640340914t_unit @ S @ zero_zero_nat ) @ bot_bo3957492148770167129t_unit ) ) @ N2 ) ) ).
% 4.69/5.02
% 4.69/5.02 % enumerate_Suc'
% 4.69/5.02 thf(fact_6045_enumerate__Suc_H,axiom,
% 4.69/5.02 ! [S: set_nat,N2: nat] :
% 4.69/5.02 ( ( infini8530281810654367211te_nat @ S @ ( suc @ N2 ) )
% 4.69/5.02 = ( infini8530281810654367211te_nat @ ( minus_minus_set_nat @ S @ ( insert_nat @ ( infini8530281810654367211te_nat @ S @ zero_zero_nat ) @ bot_bot_set_nat ) ) @ N2 ) ) ).
% 4.69/5.02
% 4.69/5.02 % enumerate_Suc'
% 4.69/5.02 thf(fact_6046_power__decreasing__iff,axiom,
% 4.69/5.02 ! [B: code_natural,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 4.69/5.02 => ( ( ord_le5570908160329646204atural @ B @ one_one_Code_natural )
% 4.69/5.02 => ( ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ B @ M4 ) @ ( power_7079662738309270450atural @ B @ N2 ) )
% 4.69/5.02 = ( ord_less_eq_nat @ N2 @ M4 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_decreasing_iff
% 4.69/5.02 thf(fact_6047_power__decreasing__iff,axiom,
% 4.69/5.02 ! [B: code_integer,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 4.69/5.02 => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 4.69/5.02 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ M4 ) @ ( power_8256067586552552935nteger @ B @ N2 ) )
% 4.69/5.02 = ( ord_less_eq_nat @ N2 @ M4 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_decreasing_iff
% 4.69/5.02 thf(fact_6048_power__decreasing__iff,axiom,
% 4.69/5.02 ! [B: rat,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.69/5.02 => ( ( ord_less_rat @ B @ one_one_rat )
% 4.69/5.02 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M4 ) @ ( power_power_rat @ B @ N2 ) )
% 4.69/5.02 = ( ord_less_eq_nat @ N2 @ M4 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_decreasing_iff
% 4.69/5.02 thf(fact_6049_power__decreasing__iff,axiom,
% 4.69/5.02 ! [B: nat,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.69/5.02 => ( ( ord_less_nat @ B @ one_one_nat )
% 4.69/5.02 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M4 ) @ ( power_power_nat @ B @ N2 ) )
% 4.69/5.02 = ( ord_less_eq_nat @ N2 @ M4 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_decreasing_iff
% 4.69/5.02 thf(fact_6050_power__decreasing__iff,axiom,
% 4.69/5.02 ! [B: int,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_int @ zero_zero_int @ B )
% 4.69/5.02 => ( ( ord_less_int @ B @ one_one_int )
% 4.69/5.02 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M4 ) @ ( power_power_int @ B @ N2 ) )
% 4.69/5.02 = ( ord_less_eq_nat @ N2 @ M4 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_decreasing_iff
% 4.69/5.02 thf(fact_6051_dvd__partition,axiom,
% 4.69/5.02 ! [C5: set_set_Code_integer,K3: nat] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ ( comple739944243200306918nteger @ C5 ) )
% 4.69/5.02 => ( ! [X3: set_Code_integer] :
% 4.69/5.02 ( ( member1834298987299537450nteger @ X3 @ C5 )
% 4.69/5.02 => ( dvd_dvd_nat @ K3 @ ( finite4902975817058060853nteger @ X3 ) ) )
% 4.69/5.02 => ( ! [X3: set_Code_integer] :
% 4.69/5.02 ( ( member1834298987299537450nteger @ X3 @ C5 )
% 4.69/5.02 => ! [Xa3: set_Code_integer] :
% 4.69/5.02 ( ( member1834298987299537450nteger @ Xa3 @ C5 )
% 4.69/5.02 => ( ( X3 != Xa3 )
% 4.69/5.02 => ( ( inf_in1364745209274528805nteger @ X3 @ Xa3 )
% 4.69/5.02 = bot_bo3990330152332043303nteger ) ) ) )
% 4.69/5.02 => ( dvd_dvd_nat @ K3 @ ( finite4902975817058060853nteger @ ( comple739944243200306918nteger @ C5 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_partition
% 4.69/5.02 thf(fact_6052_dvd__partition,axiom,
% 4.69/5.02 ! [C5: set_set_Product_unit,K3: nat] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ ( comple3349607820504768346t_unit @ C5 ) )
% 4.69/5.02 => ( ! [X3: set_Product_unit] :
% 4.69/5.02 ( ( member5877623283571906838t_unit @ X3 @ C5 )
% 4.69/5.02 => ( dvd_dvd_nat @ K3 @ ( finite410649719033368117t_unit @ X3 ) ) )
% 4.69/5.02 => ( ! [X3: set_Product_unit] :
% 4.69/5.02 ( ( member5877623283571906838t_unit @ X3 @ C5 )
% 4.69/5.02 => ! [Xa3: set_Product_unit] :
% 4.69/5.02 ( ( member5877623283571906838t_unit @ Xa3 @ C5 )
% 4.69/5.02 => ( ( X3 != Xa3 )
% 4.69/5.02 => ( ( inf_in4660618365625256667t_unit @ X3 @ Xa3 )
% 4.69/5.02 = bot_bo3957492148770167129t_unit ) ) ) )
% 4.69/5.02 => ( dvd_dvd_nat @ K3 @ ( finite410649719033368117t_unit @ ( comple3349607820504768346t_unit @ C5 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_partition
% 4.69/5.02 thf(fact_6053_dvd__partition,axiom,
% 4.69/5.02 ! [C5: set_set_o,K3: nat] :
% 4.69/5.02 ( ( finite_finite_o @ ( comple90263536869209701_set_o @ C5 ) )
% 4.69/5.02 => ( ! [X3: set_o] :
% 4.69/5.02 ( ( member_set_o @ X3 @ C5 )
% 4.69/5.02 => ( dvd_dvd_nat @ K3 @ ( finite_card_o @ X3 ) ) )
% 4.69/5.02 => ( ! [X3: set_o] :
% 4.69/5.02 ( ( member_set_o @ X3 @ C5 )
% 4.69/5.02 => ! [Xa3: set_o] :
% 4.69/5.02 ( ( member_set_o @ Xa3 @ C5 )
% 4.69/5.02 => ( ( X3 != Xa3 )
% 4.69/5.02 => ( ( inf_inf_set_o @ X3 @ Xa3 )
% 4.69/5.02 = bot_bot_set_o ) ) ) )
% 4.69/5.02 => ( dvd_dvd_nat @ K3 @ ( finite_card_o @ ( comple90263536869209701_set_o @ C5 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_partition
% 4.69/5.02 thf(fact_6054_dvd__partition,axiom,
% 4.69/5.02 ! [C5: set_set_nat,K3: nat] :
% 4.69/5.02 ( ( finite_finite_nat @ ( comple7399068483239264473et_nat @ C5 ) )
% 4.69/5.02 => ( ! [X3: set_nat] :
% 4.69/5.02 ( ( member_set_nat @ X3 @ C5 )
% 4.69/5.02 => ( dvd_dvd_nat @ K3 @ ( finite_card_nat @ X3 ) ) )
% 4.69/5.02 => ( ! [X3: set_nat] :
% 4.69/5.02 ( ( member_set_nat @ X3 @ C5 )
% 4.69/5.02 => ! [Xa3: set_nat] :
% 4.69/5.02 ( ( member_set_nat @ Xa3 @ C5 )
% 4.69/5.02 => ( ( X3 != Xa3 )
% 4.69/5.02 => ( ( inf_inf_set_nat @ X3 @ Xa3 )
% 4.69/5.02 = bot_bot_set_nat ) ) ) )
% 4.69/5.02 => ( dvd_dvd_nat @ K3 @ ( finite_card_nat @ ( comple7399068483239264473et_nat @ C5 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_partition
% 4.69/5.02 thf(fact_6055_dvd__partition,axiom,
% 4.69/5.02 ! [C5: set_set_int,K3: nat] :
% 4.69/5.02 ( ( finite_finite_int @ ( comple3221217463730067765et_int @ C5 ) )
% 4.69/5.02 => ( ! [X3: set_int] :
% 4.69/5.02 ( ( member_set_int @ X3 @ C5 )
% 4.69/5.02 => ( dvd_dvd_nat @ K3 @ ( finite_card_int @ X3 ) ) )
% 4.69/5.02 => ( ! [X3: set_int] :
% 4.69/5.02 ( ( member_set_int @ X3 @ C5 )
% 4.69/5.02 => ! [Xa3: set_int] :
% 4.69/5.02 ( ( member_set_int @ Xa3 @ C5 )
% 4.69/5.02 => ( ( X3 != Xa3 )
% 4.69/5.02 => ( ( inf_inf_set_int @ X3 @ Xa3 )
% 4.69/5.02 = bot_bot_set_int ) ) ) )
% 4.69/5.02 => ( dvd_dvd_nat @ K3 @ ( finite_card_int @ ( comple3221217463730067765et_int @ C5 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_partition
% 4.69/5.02 thf(fact_6056_dvd__partition,axiom,
% 4.69/5.02 ! [C5: set_se1353816476878259085_nat_o,K3: nat] :
% 4.69/5.02 ( ( finite3252695134891459830_nat_o @ ( comple3382087578465172250_nat_o @ C5 ) )
% 4.69/5.02 => ( ! [X3: set_Pr4532377907799695533_nat_o] :
% 4.69/5.02 ( ( member1452989533377600726_nat_o @ X3 @ C5 )
% 4.69/5.02 => ( dvd_dvd_nat @ K3 @ ( finite1363419556375932405_nat_o @ X3 ) ) )
% 4.69/5.02 => ( ! [X3: set_Pr4532377907799695533_nat_o] :
% 4.69/5.02 ( ( member1452989533377600726_nat_o @ X3 @ C5 )
% 4.69/5.02 => ! [Xa3: set_Pr4532377907799695533_nat_o] :
% 4.69/5.02 ( ( member1452989533377600726_nat_o @ Xa3 @ C5 )
% 4.69/5.02 => ( ( X3 != Xa3 )
% 4.69/5.02 => ( ( inf_in1906310914598751387_nat_o @ X3 @ Xa3 )
% 4.69/5.02 = bot_bo7824918357723582233_nat_o ) ) ) )
% 4.69/5.02 => ( dvd_dvd_nat @ K3 @ ( finite1363419556375932405_nat_o @ ( comple3382087578465172250_nat_o @ C5 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_partition
% 4.69/5.02 thf(fact_6057_cInf__le__cSup,axiom,
% 4.69/5.02 ! [A: set_o] :
% 4.69/5.02 ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( condit5488710616941104124bove_o @ A )
% 4.69/5.02 => ( ( condit5413489452508810728elow_o @ A )
% 4.69/5.02 => ( ord_less_eq_o @ ( complete_Inf_Inf_o @ A ) @ ( complete_Sup_Sup_o @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_le_cSup
% 4.69/5.02 thf(fact_6058_cInf__le__cSup,axiom,
% 4.69/5.02 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/5.02 ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/5.02 => ( ( condit4352657709669162033_nat_o @ A )
% 4.69/5.02 => ( ( condit8399017556247434269_nat_o @ A )
% 4.69/5.02 => ( ord_le729326519192465773_nat_o @ ( comple90455603224345172_nat_o @ A ) @ ( comple4225350640907012154_nat_o @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_le_cSup
% 4.69/5.02 thf(fact_6059_cInf__le__cSup,axiom,
% 4.69/5.02 ! [A: set_filter_nat] :
% 4.69/5.02 ( ( A != bot_bo498966703094740906er_nat )
% 4.69/5.02 => ( ( condit4029664723990530684er_nat @ A )
% 4.69/5.02 => ( ( condit3133331395780078992er_nat @ A )
% 4.69/5.02 => ( ord_le2510731241096832064er_nat @ ( comple6612786467464916249er_nat @ A ) @ ( comple2454491259644266675er_nat @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_le_cSup
% 4.69/5.02 thf(fact_6060_cInf__le__cSup,axiom,
% 4.69/5.02 ! [A: set_int] :
% 4.69/5.02 ( ( A != bot_bot_set_int )
% 4.69/5.02 => ( ( condit2212336002400062152ve_int @ A )
% 4.69/5.02 => ( ( condit1735850657277959132ow_int @ A )
% 4.69/5.02 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ A ) @ ( complete_Sup_Sup_int @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_le_cSup
% 4.69/5.02 thf(fact_6061_cInf__le__cSup,axiom,
% 4.69/5.02 ! [A: set_set_nat] :
% 4.69/5.02 ( ( A != bot_bot_set_set_nat )
% 4.69/5.02 => ( ( condit5477540289124974626et_nat @ A )
% 4.69/5.02 => ( ( condit68592940725977398et_nat @ A )
% 4.69/5.02 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ A ) @ ( comple7399068483239264473et_nat @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_le_cSup
% 4.69/5.02 thf(fact_6062_cInf__le__cSup,axiom,
% 4.69/5.02 ! [A: set_nat] :
% 4.69/5.02 ( ( A != bot_bot_set_nat )
% 4.69/5.02 => ( ( condit2214826472909112428ve_nat @ A )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ A )
% 4.69/5.02 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ A ) @ ( complete_Sup_Sup_nat @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_le_cSup
% 4.69/5.02 thf(fact_6063_cInf__le__cSup,axiom,
% 4.69/5.02 ! [A: set_Product_unit] :
% 4.69/5.02 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit2080475194861589617t_unit @ A )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ A )
% 4.69/5.02 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ A ) @ ( comple4687483117567863418t_unit @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_le_cSup
% 4.69/5.02 thf(fact_6064_sum__le__card__Max,axiom,
% 4.69/5.02 ! [A: set_Code_integer,F: code_integer > nat] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ord_less_eq_nat @ ( groups7237345082560585321er_nat @ F @ A ) @ ( times_times_nat @ ( finite4902975817058060853nteger @ A ) @ ( lattic8265883725875713057ax_nat @ ( image_951025933927791156er_nat @ F @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_le_card_Max
% 4.69/5.02 thf(fact_6065_sum__le__card__Max,axiom,
% 4.69/5.02 ! [A: set_nat,F: nat > nat] :
% 4.69/5.02 ( ( finite_finite_nat @ A )
% 4.69/5.02 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ A ) @ ( times_times_nat @ ( finite_card_nat @ A ) @ ( lattic8265883725875713057ax_nat @ ( image_nat_nat2 @ F @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_le_card_Max
% 4.69/5.02 thf(fact_6066_gbinomial__reduce__nat,axiom,
% 4.69/5.02 ! [K3: nat,A2: rat] :
% 4.69/5.02 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 4.69/5.02 => ( ( gbinomial_rat @ A2 @ K3 )
% 4.69/5.02 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A2 @ one_one_rat ) @ ( minus_minus_nat @ K3 @ one_one_nat ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A2 @ one_one_rat ) @ K3 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % gbinomial_reduce_nat
% 4.69/5.02 thf(fact_6067_power__one,axiom,
% 4.69/5.02 ! [N2: nat] :
% 4.69/5.02 ( ( power_power_assn @ one_one_assn @ N2 )
% 4.69/5.02 = one_one_assn ) ).
% 4.69/5.02
% 4.69/5.02 % power_one
% 4.69/5.02 thf(fact_6068_power__one,axiom,
% 4.69/5.02 ! [N2: nat] :
% 4.69/5.02 ( ( power_8256067586552552935nteger @ one_one_Code_integer @ N2 )
% 4.69/5.02 = one_one_Code_integer ) ).
% 4.69/5.02
% 4.69/5.02 % power_one
% 4.69/5.02 thf(fact_6069_power__one,axiom,
% 4.69/5.02 ! [N2: nat] :
% 4.69/5.02 ( ( power_7079662738309270450atural @ one_one_Code_natural @ N2 )
% 4.69/5.02 = one_one_Code_natural ) ).
% 4.69/5.02
% 4.69/5.02 % power_one
% 4.69/5.02 thf(fact_6070_power__one,axiom,
% 4.69/5.02 ! [N2: nat] :
% 4.69/5.02 ( ( power_power_int @ one_one_int @ N2 )
% 4.69/5.02 = one_one_int ) ).
% 4.69/5.02
% 4.69/5.02 % power_one
% 4.69/5.02 thf(fact_6071_power__one,axiom,
% 4.69/5.02 ! [N2: nat] :
% 4.69/5.02 ( ( power_power_nat @ one_one_nat @ N2 )
% 4.69/5.02 = one_one_nat ) ).
% 4.69/5.02
% 4.69/5.02 % power_one
% 4.69/5.02 thf(fact_6072_bdd__below__empty,axiom,
% 4.69/5.02 condit9161856309968323677t_unit @ bot_bo3957492148770167129t_unit ).
% 4.69/5.02
% 4.69/5.02 % bdd_below_empty
% 4.69/5.02 thf(fact_6073_bdd__below__empty,axiom,
% 4.69/5.02 condit5413489452508810728elow_o @ bot_bot_set_o ).
% 4.69/5.02
% 4.69/5.02 % bdd_below_empty
% 4.69/5.02 thf(fact_6074_bdd__below__empty,axiom,
% 4.69/5.02 condit1738341127787009408ow_nat @ bot_bot_set_nat ).
% 4.69/5.02
% 4.69/5.02 % bdd_below_empty
% 4.69/5.02 thf(fact_6075_bdd__below__empty,axiom,
% 4.69/5.02 condit1735850657277959132ow_int @ bot_bot_set_int ).
% 4.69/5.02
% 4.69/5.02 % bdd_below_empty
% 4.69/5.02 thf(fact_6076_bdd__below__empty,axiom,
% 4.69/5.02 condit8399017556247434269_nat_o @ bot_bo7824918357723582233_nat_o ).
% 4.69/5.02
% 4.69/5.02 % bdd_below_empty
% 4.69/5.02 thf(fact_6077_bdd__below__insert,axiom,
% 4.69/5.02 ! [A2: nat,A: set_nat] :
% 4.69/5.02 ( ( condit1738341127787009408ow_nat @ ( insert_nat @ A2 @ A ) )
% 4.69/5.02 = ( condit1738341127787009408ow_nat @ A ) ) ).
% 4.69/5.02
% 4.69/5.02 % bdd_below_insert
% 4.69/5.02 thf(fact_6078_bdd__below__insert,axiom,
% 4.69/5.02 ! [A2: int,A: set_int] :
% 4.69/5.02 ( ( condit1735850657277959132ow_int @ ( insert_int @ A2 @ A ) )
% 4.69/5.02 = ( condit1735850657277959132ow_int @ A ) ) ).
% 4.69/5.02
% 4.69/5.02 % bdd_below_insert
% 4.69/5.02 thf(fact_6079_bdd__below__insert,axiom,
% 4.69/5.02 ! [A2: $o,A: set_o] :
% 4.69/5.02 ( ( condit5413489452508810728elow_o @ ( insert_o @ A2 @ A ) )
% 4.69/5.02 = ( condit5413489452508810728elow_o @ A ) ) ).
% 4.69/5.02
% 4.69/5.02 % bdd_below_insert
% 4.69/5.02 thf(fact_6080_bdd__below__insert,axiom,
% 4.69/5.02 ! [A2: product_unit,A: set_Product_unit] :
% 4.69/5.02 ( ( condit9161856309968323677t_unit @ ( insert_Product_unit @ A2 @ A ) )
% 4.69/5.02 = ( condit9161856309968323677t_unit @ A ) ) ).
% 4.69/5.02
% 4.69/5.02 % bdd_below_insert
% 4.69/5.02 thf(fact_6081_dvd__times__right__cancel__iff,axiom,
% 4.69/5.02 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.02 ( ( A2 != zero_z3403309356797280102nteger )
% 4.69/5.02 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A2 ) @ ( times_3573771949741848930nteger @ C @ A2 ) )
% 4.69/5.02 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_times_right_cancel_iff
% 4.69/5.02 thf(fact_6082_dvd__times__right__cancel__iff,axiom,
% 4.69/5.02 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.02 ( ( A2 != zero_zero_nat )
% 4.69/5.02 => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A2 ) @ ( times_times_nat @ C @ A2 ) )
% 4.69/5.02 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_times_right_cancel_iff
% 4.69/5.02 thf(fact_6083_dvd__times__right__cancel__iff,axiom,
% 4.69/5.02 ! [A2: int,B: int,C: int] :
% 4.69/5.02 ( ( A2 != zero_zero_int )
% 4.69/5.02 => ( ( dvd_dvd_int @ ( times_times_int @ B @ A2 ) @ ( times_times_int @ C @ A2 ) )
% 4.69/5.02 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_times_right_cancel_iff
% 4.69/5.02 thf(fact_6084_dvd__times__left__cancel__iff,axiom,
% 4.69/5.02 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.02 ( ( A2 != zero_z3403309356797280102nteger )
% 4.69/5.02 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A2 @ B ) @ ( times_3573771949741848930nteger @ A2 @ C ) )
% 4.69/5.02 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_times_left_cancel_iff
% 4.69/5.02 thf(fact_6085_dvd__times__left__cancel__iff,axiom,
% 4.69/5.02 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.02 ( ( A2 != zero_zero_nat )
% 4.69/5.02 => ( ( dvd_dvd_nat @ ( times_times_nat @ A2 @ B ) @ ( times_times_nat @ A2 @ C ) )
% 4.69/5.02 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_times_left_cancel_iff
% 4.69/5.02 thf(fact_6086_dvd__times__left__cancel__iff,axiom,
% 4.69/5.02 ! [A2: int,B: int,C: int] :
% 4.69/5.02 ( ( A2 != zero_zero_int )
% 4.69/5.02 => ( ( dvd_dvd_int @ ( times_times_int @ A2 @ B ) @ ( times_times_int @ A2 @ C ) )
% 4.69/5.02 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_times_left_cancel_iff
% 4.69/5.02 thf(fact_6087_dvd__mult__cancel__right,axiom,
% 4.69/5.02 ! [A2: code_integer,C: code_integer,B: code_integer] :
% 4.69/5.02 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A2 @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 4.69/5.02 = ( ( C = zero_z3403309356797280102nteger )
% 4.69/5.02 | ( dvd_dvd_Code_integer @ A2 @ B ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_cancel_right
% 4.69/5.02 thf(fact_6088_dvd__mult__cancel__right,axiom,
% 4.69/5.02 ! [A2: rat,C: rat,B: rat] :
% 4.69/5.02 ( ( dvd_dvd_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B @ C ) )
% 4.69/5.02 = ( ( C = zero_zero_rat )
% 4.69/5.02 | ( dvd_dvd_rat @ A2 @ B ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_cancel_right
% 4.69/5.02 thf(fact_6089_dvd__mult__cancel__right,axiom,
% 4.69/5.02 ! [A2: int,C: int,B: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ C ) )
% 4.69/5.02 = ( ( C = zero_zero_int )
% 4.69/5.02 | ( dvd_dvd_int @ A2 @ B ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_cancel_right
% 4.69/5.02 thf(fact_6090_dvd__mult__cancel__left,axiom,
% 4.69/5.02 ! [C: code_integer,A2: code_integer,B: code_integer] :
% 4.69/5.02 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A2 ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 4.69/5.02 = ( ( C = zero_z3403309356797280102nteger )
% 4.69/5.02 | ( dvd_dvd_Code_integer @ A2 @ B ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_cancel_left
% 4.69/5.02 thf(fact_6091_dvd__mult__cancel__left,axiom,
% 4.69/5.02 ! [C: rat,A2: rat,B: rat] :
% 4.69/5.02 ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A2 ) @ ( times_times_rat @ C @ B ) )
% 4.69/5.02 = ( ( C = zero_zero_rat )
% 4.69/5.02 | ( dvd_dvd_rat @ A2 @ B ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_cancel_left
% 4.69/5.02 thf(fact_6092_dvd__mult__cancel__left,axiom,
% 4.69/5.02 ! [C: int,A2: int,B: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B ) )
% 4.69/5.02 = ( ( C = zero_zero_int )
% 4.69/5.02 | ( dvd_dvd_int @ A2 @ B ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_cancel_left
% 4.69/5.02 thf(fact_6093_dvd__add__times__triv__left__iff,axiom,
% 4.69/5.02 ! [A2: code_integer,C: code_integer,B: code_integer] :
% 4.69/5.02 ( ( dvd_dvd_Code_integer @ A2 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A2 ) @ B ) )
% 4.69/5.02 = ( dvd_dvd_Code_integer @ A2 @ B ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_add_times_triv_left_iff
% 4.69/5.02 thf(fact_6094_dvd__add__times__triv__left__iff,axiom,
% 4.69/5.02 ! [A2: rat,C: rat,B: rat] :
% 4.69/5.02 ( ( dvd_dvd_rat @ A2 @ ( plus_plus_rat @ ( times_times_rat @ C @ A2 ) @ B ) )
% 4.69/5.02 = ( dvd_dvd_rat @ A2 @ B ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_add_times_triv_left_iff
% 4.69/5.02 thf(fact_6095_dvd__add__times__triv__left__iff,axiom,
% 4.69/5.02 ! [A2: nat,C: nat,B: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ A2 @ ( plus_plus_nat @ ( times_times_nat @ C @ A2 ) @ B ) )
% 4.69/5.02 = ( dvd_dvd_nat @ A2 @ B ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_add_times_triv_left_iff
% 4.69/5.02 thf(fact_6096_dvd__add__times__triv__left__iff,axiom,
% 4.69/5.02 ! [A2: int,C: int,B: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ A2 @ ( plus_plus_int @ ( times_times_int @ C @ A2 ) @ B ) )
% 4.69/5.02 = ( dvd_dvd_int @ A2 @ B ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_add_times_triv_left_iff
% 4.69/5.02 thf(fact_6097_dvd__add__times__triv__right__iff,axiom,
% 4.69/5.02 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.02 ( ( dvd_dvd_Code_integer @ A2 @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A2 ) ) )
% 4.69/5.02 = ( dvd_dvd_Code_integer @ A2 @ B ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_add_times_triv_right_iff
% 4.69/5.02 thf(fact_6098_dvd__add__times__triv__right__iff,axiom,
% 4.69/5.02 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.02 ( ( dvd_dvd_rat @ A2 @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A2 ) ) )
% 4.69/5.02 = ( dvd_dvd_rat @ A2 @ B ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_add_times_triv_right_iff
% 4.69/5.02 thf(fact_6099_dvd__add__times__triv__right__iff,axiom,
% 4.69/5.02 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ A2 @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A2 ) ) )
% 4.69/5.02 = ( dvd_dvd_nat @ A2 @ B ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_add_times_triv_right_iff
% 4.69/5.02 thf(fact_6100_dvd__add__times__triv__right__iff,axiom,
% 4.69/5.02 ! [A2: int,B: int,C: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ A2 @ ( plus_plus_int @ B @ ( times_times_int @ C @ A2 ) ) )
% 4.69/5.02 = ( dvd_dvd_int @ A2 @ B ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_add_times_triv_right_iff
% 4.69/5.02 thf(fact_6101_unit__prod,axiom,
% 4.69/5.02 ! [A2: code_integer,B: code_integer] :
% 4.69/5.02 ( ( dvd_dvd_Code_integer @ A2 @ one_one_Code_integer )
% 4.69/5.02 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 4.69/5.02 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A2 @ B ) @ one_one_Code_integer ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % unit_prod
% 4.69/5.02 thf(fact_6102_unit__prod,axiom,
% 4.69/5.02 ! [A2: code_natural,B: code_natural] :
% 4.69/5.02 ( ( dvd_dvd_Code_natural @ A2 @ one_one_Code_natural )
% 4.69/5.02 => ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 4.69/5.02 => ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ A2 @ B ) @ one_one_Code_natural ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % unit_prod
% 4.69/5.02 thf(fact_6103_unit__prod,axiom,
% 4.69/5.02 ! [A2: nat,B: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ A2 @ one_one_nat )
% 4.69/5.02 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 4.69/5.02 => ( dvd_dvd_nat @ ( times_times_nat @ A2 @ B ) @ one_one_nat ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % unit_prod
% 4.69/5.02 thf(fact_6104_unit__prod,axiom,
% 4.69/5.02 ! [A2: int,B: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ A2 @ one_one_int )
% 4.69/5.02 => ( ( dvd_dvd_int @ B @ one_one_int )
% 4.69/5.02 => ( dvd_dvd_int @ ( times_times_int @ A2 @ B ) @ one_one_int ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % unit_prod
% 4.69/5.02 thf(fact_6105_power__inject__exp,axiom,
% 4.69/5.02 ! [A2: code_natural,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A2 )
% 4.69/5.02 => ( ( ( power_7079662738309270450atural @ A2 @ M4 )
% 4.69/5.02 = ( power_7079662738309270450atural @ A2 @ N2 ) )
% 4.69/5.02 = ( M4 = N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_inject_exp
% 4.69/5.02 thf(fact_6106_power__inject__exp,axiom,
% 4.69/5.02 ! [A2: nat,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_nat @ one_one_nat @ A2 )
% 4.69/5.02 => ( ( ( power_power_nat @ A2 @ M4 )
% 4.69/5.02 = ( power_power_nat @ A2 @ N2 ) )
% 4.69/5.02 = ( M4 = N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_inject_exp
% 4.69/5.02 thf(fact_6107_power__inject__exp,axiom,
% 4.69/5.02 ! [A2: int,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_int @ one_one_int @ A2 )
% 4.69/5.02 => ( ( ( power_power_int @ A2 @ M4 )
% 4.69/5.02 = ( power_power_int @ A2 @ N2 ) )
% 4.69/5.02 = ( M4 = N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_inject_exp
% 4.69/5.02 thf(fact_6108_power__inject__exp,axiom,
% 4.69/5.02 ! [A2: code_integer,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A2 )
% 4.69/5.02 => ( ( ( power_8256067586552552935nteger @ A2 @ M4 )
% 4.69/5.02 = ( power_8256067586552552935nteger @ A2 @ N2 ) )
% 4.69/5.02 = ( M4 = N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_inject_exp
% 4.69/5.02 thf(fact_6109_power__inject__exp,axiom,
% 4.69/5.02 ! [A2: rat,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_rat @ one_one_rat @ A2 )
% 4.69/5.02 => ( ( ( power_power_rat @ A2 @ M4 )
% 4.69/5.02 = ( power_power_rat @ A2 @ N2 ) )
% 4.69/5.02 = ( M4 = N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_inject_exp
% 4.69/5.02 thf(fact_6110_nat__mult__dvd__cancel__disj,axiom,
% 4.69/5.02 ! [K3: nat,M4: nat,N2: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ ( times_times_nat @ K3 @ M4 ) @ ( times_times_nat @ K3 @ N2 ) )
% 4.69/5.02 = ( ( K3 = zero_zero_nat )
% 4.69/5.02 | ( dvd_dvd_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % nat_mult_dvd_cancel_disj
% 4.69/5.02 thf(fact_6111_gbinomial__0_I1_J,axiom,
% 4.69/5.02 ! [A2: nat] :
% 4.69/5.02 ( ( gbinomial_nat @ A2 @ zero_zero_nat )
% 4.69/5.02 = one_one_nat ) ).
% 4.69/5.02
% 4.69/5.02 % gbinomial_0(1)
% 4.69/5.02 thf(fact_6112_gbinomial__0_I1_J,axiom,
% 4.69/5.02 ! [A2: int] :
% 4.69/5.02 ( ( gbinomial_int @ A2 @ zero_zero_nat )
% 4.69/5.02 = one_one_int ) ).
% 4.69/5.02
% 4.69/5.02 % gbinomial_0(1)
% 4.69/5.02 thf(fact_6113_gbinomial__0_I1_J,axiom,
% 4.69/5.02 ! [A2: code_integer] :
% 4.69/5.02 ( ( gbinom8545251970709558553nteger @ A2 @ zero_zero_nat )
% 4.69/5.02 = one_one_Code_integer ) ).
% 4.69/5.02
% 4.69/5.02 % gbinomial_0(1)
% 4.69/5.02 thf(fact_6114_gbinomial__0_I1_J,axiom,
% 4.69/5.02 ! [A2: code_natural] :
% 4.69/5.02 ( ( gbinom7368847122466276068atural @ A2 @ zero_zero_nat )
% 4.69/5.02 = one_one_Code_natural ) ).
% 4.69/5.02
% 4.69/5.02 % gbinomial_0(1)
% 4.69/5.02 thf(fact_6115_power__strict__increasing__iff,axiom,
% 4.69/5.02 ! [B: code_natural,X: nat,Y: nat] :
% 4.69/5.02 ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ B )
% 4.69/5.02 => ( ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ B @ X ) @ ( power_7079662738309270450atural @ B @ Y ) )
% 4.69/5.02 = ( ord_less_nat @ X @ Y ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_strict_increasing_iff
% 4.69/5.02 thf(fact_6116_power__strict__increasing__iff,axiom,
% 4.69/5.02 ! [B: nat,X: nat,Y: nat] :
% 4.69/5.02 ( ( ord_less_nat @ one_one_nat @ B )
% 4.69/5.02 => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 4.69/5.02 = ( ord_less_nat @ X @ Y ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_strict_increasing_iff
% 4.69/5.02 thf(fact_6117_power__strict__increasing__iff,axiom,
% 4.69/5.02 ! [B: int,X: nat,Y: nat] :
% 4.69/5.02 ( ( ord_less_int @ one_one_int @ B )
% 4.69/5.02 => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 4.69/5.02 = ( ord_less_nat @ X @ Y ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_strict_increasing_iff
% 4.69/5.02 thf(fact_6118_power__strict__increasing__iff,axiom,
% 4.69/5.02 ! [B: code_integer,X: nat,Y: nat] :
% 4.69/5.02 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 4.69/5.02 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ X ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 4.69/5.02 = ( ord_less_nat @ X @ Y ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_strict_increasing_iff
% 4.69/5.02 thf(fact_6119_power__strict__increasing__iff,axiom,
% 4.69/5.02 ! [B: rat,X: nat,Y: nat] :
% 4.69/5.02 ( ( ord_less_rat @ one_one_rat @ B )
% 4.69/5.02 => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 4.69/5.02 = ( ord_less_nat @ X @ Y ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_strict_increasing_iff
% 4.69/5.02 thf(fact_6120_power__strict__decreasing__iff,axiom,
% 4.69/5.02 ! [B: code_natural,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ B )
% 4.69/5.02 => ( ( ord_le5570908160329646204atural @ B @ one_one_Code_natural )
% 4.69/5.02 => ( ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ B @ M4 ) @ ( power_7079662738309270450atural @ B @ N2 ) )
% 4.69/5.02 = ( ord_less_nat @ N2 @ M4 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_strict_decreasing_iff
% 4.69/5.02 thf(fact_6121_power__strict__decreasing__iff,axiom,
% 4.69/5.02 ! [B: nat,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.69/5.02 => ( ( ord_less_nat @ B @ one_one_nat )
% 4.69/5.02 => ( ( ord_less_nat @ ( power_power_nat @ B @ M4 ) @ ( power_power_nat @ B @ N2 ) )
% 4.69/5.02 = ( ord_less_nat @ N2 @ M4 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_strict_decreasing_iff
% 4.69/5.02 thf(fact_6122_power__strict__decreasing__iff,axiom,
% 4.69/5.02 ! [B: int,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_int @ zero_zero_int @ B )
% 4.69/5.02 => ( ( ord_less_int @ B @ one_one_int )
% 4.69/5.02 => ( ( ord_less_int @ ( power_power_int @ B @ M4 ) @ ( power_power_int @ B @ N2 ) )
% 4.69/5.02 = ( ord_less_nat @ N2 @ M4 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_strict_decreasing_iff
% 4.69/5.02 thf(fact_6123_power__strict__decreasing__iff,axiom,
% 4.69/5.02 ! [B: code_integer,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 4.69/5.02 => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 4.69/5.02 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ M4 ) @ ( power_8256067586552552935nteger @ B @ N2 ) )
% 4.69/5.02 = ( ord_less_nat @ N2 @ M4 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_strict_decreasing_iff
% 4.69/5.02 thf(fact_6124_power__strict__decreasing__iff,axiom,
% 4.69/5.02 ! [B: rat,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.69/5.02 => ( ( ord_less_rat @ B @ one_one_rat )
% 4.69/5.02 => ( ( ord_less_rat @ ( power_power_rat @ B @ M4 ) @ ( power_power_rat @ B @ N2 ) )
% 4.69/5.02 = ( ord_less_nat @ N2 @ M4 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_strict_decreasing_iff
% 4.69/5.02 thf(fact_6125_power__increasing__iff,axiom,
% 4.69/5.02 ! [B: code_natural,X: nat,Y: nat] :
% 4.69/5.02 ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ B )
% 4.69/5.02 => ( ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ B @ X ) @ ( power_7079662738309270450atural @ B @ Y ) )
% 4.69/5.02 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_increasing_iff
% 4.69/5.02 thf(fact_6126_power__increasing__iff,axiom,
% 4.69/5.02 ! [B: code_integer,X: nat,Y: nat] :
% 4.69/5.02 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 4.69/5.02 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ X ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 4.69/5.02 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_increasing_iff
% 4.69/5.02 thf(fact_6127_power__increasing__iff,axiom,
% 4.69/5.02 ! [B: rat,X: nat,Y: nat] :
% 4.69/5.02 ( ( ord_less_rat @ one_one_rat @ B )
% 4.69/5.02 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 4.69/5.02 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_increasing_iff
% 4.69/5.02 thf(fact_6128_power__increasing__iff,axiom,
% 4.69/5.02 ! [B: nat,X: nat,Y: nat] :
% 4.69/5.02 ( ( ord_less_nat @ one_one_nat @ B )
% 4.69/5.02 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 4.69/5.02 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_increasing_iff
% 4.69/5.02 thf(fact_6129_power__increasing__iff,axiom,
% 4.69/5.02 ! [B: int,X: nat,Y: nat] :
% 4.69/5.02 ( ( ord_less_int @ one_one_int @ B )
% 4.69/5.02 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 4.69/5.02 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_increasing_iff
% 4.69/5.02 thf(fact_6130_is__unit__power__iff,axiom,
% 4.69/5.02 ! [A2: code_integer,N2: nat] :
% 4.69/5.02 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A2 @ N2 ) @ one_one_Code_integer )
% 4.69/5.02 = ( ( dvd_dvd_Code_integer @ A2 @ one_one_Code_integer )
% 4.69/5.02 | ( N2 = zero_zero_nat ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % is_unit_power_iff
% 4.69/5.02 thf(fact_6131_is__unit__power__iff,axiom,
% 4.69/5.02 ! [A2: code_natural,N2: nat] :
% 4.69/5.02 ( ( dvd_dvd_Code_natural @ ( power_7079662738309270450atural @ A2 @ N2 ) @ one_one_Code_natural )
% 4.69/5.02 = ( ( dvd_dvd_Code_natural @ A2 @ one_one_Code_natural )
% 4.69/5.02 | ( N2 = zero_zero_nat ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % is_unit_power_iff
% 4.69/5.02 thf(fact_6132_is__unit__power__iff,axiom,
% 4.69/5.02 ! [A2: int,N2: nat] :
% 4.69/5.02 ( ( dvd_dvd_int @ ( power_power_int @ A2 @ N2 ) @ one_one_int )
% 4.69/5.02 = ( ( dvd_dvd_int @ A2 @ one_one_int )
% 4.69/5.02 | ( N2 = zero_zero_nat ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % is_unit_power_iff
% 4.69/5.02 thf(fact_6133_is__unit__power__iff,axiom,
% 4.69/5.02 ! [A2: nat,N2: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ ( power_power_nat @ A2 @ N2 ) @ one_one_nat )
% 4.69/5.02 = ( ( dvd_dvd_nat @ A2 @ one_one_nat )
% 4.69/5.02 | ( N2 = zero_zero_nat ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % is_unit_power_iff
% 4.69/5.02 thf(fact_6134_power__commuting__commutes,axiom,
% 4.69/5.02 ! [X: assn,Y: assn,N2: nat] :
% 4.69/5.02 ( ( ( times_times_assn @ X @ Y )
% 4.69/5.02 = ( times_times_assn @ Y @ X ) )
% 4.69/5.02 => ( ( times_times_assn @ ( power_power_assn @ X @ N2 ) @ Y )
% 4.69/5.02 = ( times_times_assn @ Y @ ( power_power_assn @ X @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_commuting_commutes
% 4.69/5.02 thf(fact_6135_power__commuting__commutes,axiom,
% 4.69/5.02 ! [X: rat,Y: rat,N2: nat] :
% 4.69/5.02 ( ( ( times_times_rat @ X @ Y )
% 4.69/5.02 = ( times_times_rat @ Y @ X ) )
% 4.69/5.02 => ( ( times_times_rat @ ( power_power_rat @ X @ N2 ) @ Y )
% 4.69/5.02 = ( times_times_rat @ Y @ ( power_power_rat @ X @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_commuting_commutes
% 4.69/5.02 thf(fact_6136_power__commuting__commutes,axiom,
% 4.69/5.02 ! [X: nat,Y: nat,N2: nat] :
% 4.69/5.02 ( ( ( times_times_nat @ X @ Y )
% 4.69/5.02 = ( times_times_nat @ Y @ X ) )
% 4.69/5.02 => ( ( times_times_nat @ ( power_power_nat @ X @ N2 ) @ Y )
% 4.69/5.02 = ( times_times_nat @ Y @ ( power_power_nat @ X @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_commuting_commutes
% 4.69/5.02 thf(fact_6137_power__commuting__commutes,axiom,
% 4.69/5.02 ! [X: int,Y: int,N2: nat] :
% 4.69/5.02 ( ( ( times_times_int @ X @ Y )
% 4.69/5.02 = ( times_times_int @ Y @ X ) )
% 4.69/5.02 => ( ( times_times_int @ ( power_power_int @ X @ N2 ) @ Y )
% 4.69/5.02 = ( times_times_int @ Y @ ( power_power_int @ X @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_commuting_commutes
% 4.69/5.02 thf(fact_6138_power__mult__distrib,axiom,
% 4.69/5.02 ! [A2: assn,B: assn,N2: nat] :
% 4.69/5.02 ( ( power_power_assn @ ( times_times_assn @ A2 @ B ) @ N2 )
% 4.69/5.02 = ( times_times_assn @ ( power_power_assn @ A2 @ N2 ) @ ( power_power_assn @ B @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_mult_distrib
% 4.69/5.02 thf(fact_6139_power__mult__distrib,axiom,
% 4.69/5.02 ! [A2: rat,B: rat,N2: nat] :
% 4.69/5.02 ( ( power_power_rat @ ( times_times_rat @ A2 @ B ) @ N2 )
% 4.69/5.02 = ( times_times_rat @ ( power_power_rat @ A2 @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_mult_distrib
% 4.69/5.02 thf(fact_6140_power__mult__distrib,axiom,
% 4.69/5.02 ! [A2: nat,B: nat,N2: nat] :
% 4.69/5.02 ( ( power_power_nat @ ( times_times_nat @ A2 @ B ) @ N2 )
% 4.69/5.02 = ( times_times_nat @ ( power_power_nat @ A2 @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_mult_distrib
% 4.69/5.02 thf(fact_6141_power__mult__distrib,axiom,
% 4.69/5.02 ! [A2: int,B: int,N2: nat] :
% 4.69/5.02 ( ( power_power_int @ ( times_times_int @ A2 @ B ) @ N2 )
% 4.69/5.02 = ( times_times_int @ ( power_power_int @ A2 @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_mult_distrib
% 4.69/5.02 thf(fact_6142_power__commutes,axiom,
% 4.69/5.02 ! [A2: assn,N2: nat] :
% 4.69/5.02 ( ( times_times_assn @ ( power_power_assn @ A2 @ N2 ) @ A2 )
% 4.69/5.02 = ( times_times_assn @ A2 @ ( power_power_assn @ A2 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_commutes
% 4.69/5.02 thf(fact_6143_power__commutes,axiom,
% 4.69/5.02 ! [A2: rat,N2: nat] :
% 4.69/5.02 ( ( times_times_rat @ ( power_power_rat @ A2 @ N2 ) @ A2 )
% 4.69/5.02 = ( times_times_rat @ A2 @ ( power_power_rat @ A2 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_commutes
% 4.69/5.02 thf(fact_6144_power__commutes,axiom,
% 4.69/5.02 ! [A2: nat,N2: nat] :
% 4.69/5.02 ( ( times_times_nat @ ( power_power_nat @ A2 @ N2 ) @ A2 )
% 4.69/5.02 = ( times_times_nat @ A2 @ ( power_power_nat @ A2 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_commutes
% 4.69/5.02 thf(fact_6145_power__commutes,axiom,
% 4.69/5.02 ! [A2: int,N2: nat] :
% 4.69/5.02 ( ( times_times_int @ ( power_power_int @ A2 @ N2 ) @ A2 )
% 4.69/5.02 = ( times_times_int @ A2 @ ( power_power_int @ A2 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_commutes
% 4.69/5.02 thf(fact_6146_dvd__triv__right,axiom,
% 4.69/5.02 ! [A2: assn,B: assn] : ( dvd_dvd_assn @ A2 @ ( times_times_assn @ B @ A2 ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_triv_right
% 4.69/5.02 thf(fact_6147_dvd__triv__right,axiom,
% 4.69/5.02 ! [A2: rat,B: rat] : ( dvd_dvd_rat @ A2 @ ( times_times_rat @ B @ A2 ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_triv_right
% 4.69/5.02 thf(fact_6148_dvd__triv__right,axiom,
% 4.69/5.02 ! [A2: nat,B: nat] : ( dvd_dvd_nat @ A2 @ ( times_times_nat @ B @ A2 ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_triv_right
% 4.69/5.02 thf(fact_6149_dvd__triv__right,axiom,
% 4.69/5.02 ! [A2: int,B: int] : ( dvd_dvd_int @ A2 @ ( times_times_int @ B @ A2 ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_triv_right
% 4.69/5.02 thf(fact_6150_dvd__mult__right,axiom,
% 4.69/5.02 ! [A2: assn,B: assn,C: assn] :
% 4.69/5.02 ( ( dvd_dvd_assn @ ( times_times_assn @ A2 @ B ) @ C )
% 4.69/5.02 => ( dvd_dvd_assn @ B @ C ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_right
% 4.69/5.02 thf(fact_6151_dvd__mult__right,axiom,
% 4.69/5.02 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.02 ( ( dvd_dvd_rat @ ( times_times_rat @ A2 @ B ) @ C )
% 4.69/5.02 => ( dvd_dvd_rat @ B @ C ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_right
% 4.69/5.02 thf(fact_6152_dvd__mult__right,axiom,
% 4.69/5.02 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ ( times_times_nat @ A2 @ B ) @ C )
% 4.69/5.02 => ( dvd_dvd_nat @ B @ C ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_right
% 4.69/5.02 thf(fact_6153_dvd__mult__right,axiom,
% 4.69/5.02 ! [A2: int,B: int,C: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ ( times_times_int @ A2 @ B ) @ C )
% 4.69/5.02 => ( dvd_dvd_int @ B @ C ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_right
% 4.69/5.02 thf(fact_6154_mult__dvd__mono,axiom,
% 4.69/5.02 ! [A2: assn,B: assn,C: assn,D2: assn] :
% 4.69/5.02 ( ( dvd_dvd_assn @ A2 @ B )
% 4.69/5.02 => ( ( dvd_dvd_assn @ C @ D2 )
% 4.69/5.02 => ( dvd_dvd_assn @ ( times_times_assn @ A2 @ C ) @ ( times_times_assn @ B @ D2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % mult_dvd_mono
% 4.69/5.02 thf(fact_6155_mult__dvd__mono,axiom,
% 4.69/5.02 ! [A2: rat,B: rat,C: rat,D2: rat] :
% 4.69/5.02 ( ( dvd_dvd_rat @ A2 @ B )
% 4.69/5.02 => ( ( dvd_dvd_rat @ C @ D2 )
% 4.69/5.02 => ( dvd_dvd_rat @ ( times_times_rat @ A2 @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % mult_dvd_mono
% 4.69/5.02 thf(fact_6156_mult__dvd__mono,axiom,
% 4.69/5.02 ! [A2: nat,B: nat,C: nat,D2: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ A2 @ B )
% 4.69/5.02 => ( ( dvd_dvd_nat @ C @ D2 )
% 4.69/5.02 => ( dvd_dvd_nat @ ( times_times_nat @ A2 @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % mult_dvd_mono
% 4.69/5.02 thf(fact_6157_mult__dvd__mono,axiom,
% 4.69/5.02 ! [A2: int,B: int,C: int,D2: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ A2 @ B )
% 4.69/5.02 => ( ( dvd_dvd_int @ C @ D2 )
% 4.69/5.02 => ( dvd_dvd_int @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % mult_dvd_mono
% 4.69/5.02 thf(fact_6158_dvd__triv__left,axiom,
% 4.69/5.02 ! [A2: assn,B: assn] : ( dvd_dvd_assn @ A2 @ ( times_times_assn @ A2 @ B ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_triv_left
% 4.69/5.02 thf(fact_6159_dvd__triv__left,axiom,
% 4.69/5.02 ! [A2: rat,B: rat] : ( dvd_dvd_rat @ A2 @ ( times_times_rat @ A2 @ B ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_triv_left
% 4.69/5.02 thf(fact_6160_dvd__triv__left,axiom,
% 4.69/5.02 ! [A2: nat,B: nat] : ( dvd_dvd_nat @ A2 @ ( times_times_nat @ A2 @ B ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_triv_left
% 4.69/5.02 thf(fact_6161_dvd__triv__left,axiom,
% 4.69/5.02 ! [A2: int,B: int] : ( dvd_dvd_int @ A2 @ ( times_times_int @ A2 @ B ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_triv_left
% 4.69/5.02 thf(fact_6162_dvd__mult__left,axiom,
% 4.69/5.02 ! [A2: assn,B: assn,C: assn] :
% 4.69/5.02 ( ( dvd_dvd_assn @ ( times_times_assn @ A2 @ B ) @ C )
% 4.69/5.02 => ( dvd_dvd_assn @ A2 @ C ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_left
% 4.69/5.02 thf(fact_6163_dvd__mult__left,axiom,
% 4.69/5.02 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.02 ( ( dvd_dvd_rat @ ( times_times_rat @ A2 @ B ) @ C )
% 4.69/5.02 => ( dvd_dvd_rat @ A2 @ C ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_left
% 4.69/5.02 thf(fact_6164_dvd__mult__left,axiom,
% 4.69/5.02 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ ( times_times_nat @ A2 @ B ) @ C )
% 4.69/5.02 => ( dvd_dvd_nat @ A2 @ C ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_left
% 4.69/5.02 thf(fact_6165_dvd__mult__left,axiom,
% 4.69/5.02 ! [A2: int,B: int,C: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ ( times_times_int @ A2 @ B ) @ C )
% 4.69/5.02 => ( dvd_dvd_int @ A2 @ C ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_left
% 4.69/5.02 thf(fact_6166_dvd__mult2,axiom,
% 4.69/5.02 ! [A2: assn,B: assn,C: assn] :
% 4.69/5.02 ( ( dvd_dvd_assn @ A2 @ B )
% 4.69/5.02 => ( dvd_dvd_assn @ A2 @ ( times_times_assn @ B @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult2
% 4.69/5.02 thf(fact_6167_dvd__mult2,axiom,
% 4.69/5.02 ! [A2: rat,B: rat,C: rat] :
% 4.69/5.02 ( ( dvd_dvd_rat @ A2 @ B )
% 4.69/5.02 => ( dvd_dvd_rat @ A2 @ ( times_times_rat @ B @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult2
% 4.69/5.02 thf(fact_6168_dvd__mult2,axiom,
% 4.69/5.02 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ A2 @ B )
% 4.69/5.02 => ( dvd_dvd_nat @ A2 @ ( times_times_nat @ B @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult2
% 4.69/5.02 thf(fact_6169_dvd__mult2,axiom,
% 4.69/5.02 ! [A2: int,B: int,C: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ A2 @ B )
% 4.69/5.02 => ( dvd_dvd_int @ A2 @ ( times_times_int @ B @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult2
% 4.69/5.02 thf(fact_6170_dvd__mult,axiom,
% 4.69/5.02 ! [A2: assn,C: assn,B: assn] :
% 4.69/5.02 ( ( dvd_dvd_assn @ A2 @ C )
% 4.69/5.02 => ( dvd_dvd_assn @ A2 @ ( times_times_assn @ B @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult
% 4.69/5.02 thf(fact_6171_dvd__mult,axiom,
% 4.69/5.02 ! [A2: rat,C: rat,B: rat] :
% 4.69/5.02 ( ( dvd_dvd_rat @ A2 @ C )
% 4.69/5.02 => ( dvd_dvd_rat @ A2 @ ( times_times_rat @ B @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult
% 4.69/5.02 thf(fact_6172_dvd__mult,axiom,
% 4.69/5.02 ! [A2: nat,C: nat,B: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ A2 @ C )
% 4.69/5.02 => ( dvd_dvd_nat @ A2 @ ( times_times_nat @ B @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult
% 4.69/5.02 thf(fact_6173_dvd__mult,axiom,
% 4.69/5.02 ! [A2: int,C: int,B: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ A2 @ C )
% 4.69/5.02 => ( dvd_dvd_int @ A2 @ ( times_times_int @ B @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult
% 4.69/5.02 thf(fact_6174_dvd__def,axiom,
% 4.69/5.02 ( dvd_dvd_assn
% 4.69/5.02 = ( ^ [B6: assn,A6: assn] :
% 4.69/5.02 ? [K5: assn] :
% 4.69/5.02 ( A6
% 4.69/5.02 = ( times_times_assn @ B6 @ K5 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_def
% 4.69/5.02 thf(fact_6175_dvd__def,axiom,
% 4.69/5.02 ( dvd_dvd_rat
% 4.69/5.02 = ( ^ [B6: rat,A6: rat] :
% 4.69/5.02 ? [K5: rat] :
% 4.69/5.02 ( A6
% 4.69/5.02 = ( times_times_rat @ B6 @ K5 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_def
% 4.69/5.02 thf(fact_6176_dvd__def,axiom,
% 4.69/5.02 ( dvd_dvd_nat
% 4.69/5.02 = ( ^ [B6: nat,A6: nat] :
% 4.69/5.02 ? [K5: nat] :
% 4.69/5.02 ( A6
% 4.69/5.02 = ( times_times_nat @ B6 @ K5 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_def
% 4.69/5.02 thf(fact_6177_dvd__def,axiom,
% 4.69/5.02 ( dvd_dvd_int
% 4.69/5.02 = ( ^ [B6: int,A6: int] :
% 4.69/5.02 ? [K5: int] :
% 4.69/5.02 ( A6
% 4.69/5.02 = ( times_times_int @ B6 @ K5 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_def
% 4.69/5.02 thf(fact_6178_dvdI,axiom,
% 4.69/5.02 ! [A2: assn,B: assn,K3: assn] :
% 4.69/5.02 ( ( A2
% 4.69/5.02 = ( times_times_assn @ B @ K3 ) )
% 4.69/5.02 => ( dvd_dvd_assn @ B @ A2 ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvdI
% 4.69/5.02 thf(fact_6179_dvdI,axiom,
% 4.69/5.02 ! [A2: rat,B: rat,K3: rat] :
% 4.69/5.02 ( ( A2
% 4.69/5.02 = ( times_times_rat @ B @ K3 ) )
% 4.69/5.02 => ( dvd_dvd_rat @ B @ A2 ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvdI
% 4.69/5.02 thf(fact_6180_dvdI,axiom,
% 4.69/5.02 ! [A2: nat,B: nat,K3: nat] :
% 4.69/5.02 ( ( A2
% 4.69/5.02 = ( times_times_nat @ B @ K3 ) )
% 4.69/5.02 => ( dvd_dvd_nat @ B @ A2 ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvdI
% 4.69/5.02 thf(fact_6181_dvdI,axiom,
% 4.69/5.02 ! [A2: int,B: int,K3: int] :
% 4.69/5.02 ( ( A2
% 4.69/5.02 = ( times_times_int @ B @ K3 ) )
% 4.69/5.02 => ( dvd_dvd_int @ B @ A2 ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvdI
% 4.69/5.02 thf(fact_6182_dvdE,axiom,
% 4.69/5.02 ! [B: assn,A2: assn] :
% 4.69/5.02 ( ( dvd_dvd_assn @ B @ A2 )
% 4.69/5.02 => ~ ! [K: assn] :
% 4.69/5.02 ( A2
% 4.69/5.02 != ( times_times_assn @ B @ K ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvdE
% 4.69/5.02 thf(fact_6183_dvdE,axiom,
% 4.69/5.02 ! [B: rat,A2: rat] :
% 4.69/5.02 ( ( dvd_dvd_rat @ B @ A2 )
% 4.69/5.02 => ~ ! [K: rat] :
% 4.69/5.02 ( A2
% 4.69/5.02 != ( times_times_rat @ B @ K ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvdE
% 4.69/5.02 thf(fact_6184_dvdE,axiom,
% 4.69/5.02 ! [B: nat,A2: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ B @ A2 )
% 4.69/5.02 => ~ ! [K: nat] :
% 4.69/5.02 ( A2
% 4.69/5.02 != ( times_times_nat @ B @ K ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvdE
% 4.69/5.02 thf(fact_6185_dvdE,axiom,
% 4.69/5.02 ! [B: int,A2: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ B @ A2 )
% 4.69/5.02 => ~ ! [K: int] :
% 4.69/5.02 ( A2
% 4.69/5.02 != ( times_times_int @ B @ K ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvdE
% 4.69/5.02 thf(fact_6186_dvd__unit__imp__unit,axiom,
% 4.69/5.02 ! [A2: nat,B: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ A2 @ B )
% 4.69/5.02 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 4.69/5.02 => ( dvd_dvd_nat @ A2 @ one_one_nat ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_unit_imp_unit
% 4.69/5.02 thf(fact_6187_dvd__unit__imp__unit,axiom,
% 4.69/5.02 ! [A2: int,B: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ A2 @ B )
% 4.69/5.02 => ( ( dvd_dvd_int @ B @ one_one_int )
% 4.69/5.02 => ( dvd_dvd_int @ A2 @ one_one_int ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_unit_imp_unit
% 4.69/5.02 thf(fact_6188_dvd__unit__imp__unit,axiom,
% 4.69/5.02 ! [A2: code_integer,B: code_integer] :
% 4.69/5.02 ( ( dvd_dvd_Code_integer @ A2 @ B )
% 4.69/5.02 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 4.69/5.02 => ( dvd_dvd_Code_integer @ A2 @ one_one_Code_integer ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_unit_imp_unit
% 4.69/5.02 thf(fact_6189_dvd__unit__imp__unit,axiom,
% 4.69/5.02 ! [A2: code_natural,B: code_natural] :
% 4.69/5.02 ( ( dvd_dvd_Code_natural @ A2 @ B )
% 4.69/5.02 => ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 4.69/5.02 => ( dvd_dvd_Code_natural @ A2 @ one_one_Code_natural ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_unit_imp_unit
% 4.69/5.02 thf(fact_6190_unit__imp__dvd,axiom,
% 4.69/5.02 ! [B: nat,A2: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 4.69/5.02 => ( dvd_dvd_nat @ B @ A2 ) ) ).
% 4.69/5.02
% 4.69/5.02 % unit_imp_dvd
% 4.69/5.02 thf(fact_6191_unit__imp__dvd,axiom,
% 4.69/5.02 ! [B: int,A2: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ B @ one_one_int )
% 4.69/5.02 => ( dvd_dvd_int @ B @ A2 ) ) ).
% 4.69/5.02
% 4.69/5.02 % unit_imp_dvd
% 4.69/5.02 thf(fact_6192_unit__imp__dvd,axiom,
% 4.69/5.02 ! [B: code_integer,A2: code_integer] :
% 4.69/5.02 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 4.69/5.02 => ( dvd_dvd_Code_integer @ B @ A2 ) ) ).
% 4.69/5.02
% 4.69/5.02 % unit_imp_dvd
% 4.69/5.02 thf(fact_6193_unit__imp__dvd,axiom,
% 4.69/5.02 ! [B: code_natural,A2: code_natural] :
% 4.69/5.02 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 4.69/5.02 => ( dvd_dvd_Code_natural @ B @ A2 ) ) ).
% 4.69/5.02
% 4.69/5.02 % unit_imp_dvd
% 4.69/5.02 thf(fact_6194_one__dvd,axiom,
% 4.69/5.02 ! [A2: assn] : ( dvd_dvd_assn @ one_one_assn @ A2 ) ).
% 4.69/5.02
% 4.69/5.02 % one_dvd
% 4.69/5.02 thf(fact_6195_one__dvd,axiom,
% 4.69/5.02 ! [A2: nat] : ( dvd_dvd_nat @ one_one_nat @ A2 ) ).
% 4.69/5.02
% 4.69/5.02 % one_dvd
% 4.69/5.02 thf(fact_6196_one__dvd,axiom,
% 4.69/5.02 ! [A2: int] : ( dvd_dvd_int @ one_one_int @ A2 ) ).
% 4.69/5.02
% 4.69/5.02 % one_dvd
% 4.69/5.02 thf(fact_6197_one__dvd,axiom,
% 4.69/5.02 ! [A2: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A2 ) ).
% 4.69/5.02
% 4.69/5.02 % one_dvd
% 4.69/5.02 thf(fact_6198_one__dvd,axiom,
% 4.69/5.02 ! [A2: code_natural] : ( dvd_dvd_Code_natural @ one_one_Code_natural @ A2 ) ).
% 4.69/5.02
% 4.69/5.02 % one_dvd
% 4.69/5.02 thf(fact_6199_power__mult,axiom,
% 4.69/5.02 ! [A2: int,M4: nat,N2: nat] :
% 4.69/5.02 ( ( power_power_int @ A2 @ ( times_times_nat @ M4 @ N2 ) )
% 4.69/5.02 = ( power_power_int @ ( power_power_int @ A2 @ M4 ) @ N2 ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_mult
% 4.69/5.02 thf(fact_6200_power__mult,axiom,
% 4.69/5.02 ! [A2: nat,M4: nat,N2: nat] :
% 4.69/5.02 ( ( power_power_nat @ A2 @ ( times_times_nat @ M4 @ N2 ) )
% 4.69/5.02 = ( power_power_nat @ ( power_power_nat @ A2 @ M4 ) @ N2 ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_mult
% 4.69/5.02 thf(fact_6201_dvd__power__iff,axiom,
% 4.69/5.02 ! [X: code_natural,M4: nat,N2: nat] :
% 4.69/5.02 ( ( X != zero_z2226904508553997617atural )
% 4.69/5.02 => ( ( dvd_dvd_Code_natural @ ( power_7079662738309270450atural @ X @ M4 ) @ ( power_7079662738309270450atural @ X @ N2 ) )
% 4.69/5.02 = ( ( dvd_dvd_Code_natural @ X @ one_one_Code_natural )
% 4.69/5.02 | ( ord_less_eq_nat @ M4 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_power_iff
% 4.69/5.02 thf(fact_6202_dvd__power__iff,axiom,
% 4.69/5.02 ! [X: code_integer,M4: nat,N2: nat] :
% 4.69/5.02 ( ( X != zero_z3403309356797280102nteger )
% 4.69/5.02 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M4 ) @ ( power_8256067586552552935nteger @ X @ N2 ) )
% 4.69/5.02 = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 4.69/5.02 | ( ord_less_eq_nat @ M4 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_power_iff
% 4.69/5.02 thf(fact_6203_dvd__power__iff,axiom,
% 4.69/5.02 ! [X: int,M4: nat,N2: nat] :
% 4.69/5.02 ( ( X != zero_zero_int )
% 4.69/5.02 => ( ( dvd_dvd_int @ ( power_power_int @ X @ M4 ) @ ( power_power_int @ X @ N2 ) )
% 4.69/5.02 = ( ( dvd_dvd_int @ X @ one_one_int )
% 4.69/5.02 | ( ord_less_eq_nat @ M4 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_power_iff
% 4.69/5.02 thf(fact_6204_dvd__power__iff,axiom,
% 4.69/5.02 ! [X: nat,M4: nat,N2: nat] :
% 4.69/5.02 ( ( X != zero_zero_nat )
% 4.69/5.02 => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M4 ) @ ( power_power_nat @ X @ N2 ) )
% 4.69/5.02 = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 4.69/5.02 | ( ord_less_eq_nat @ M4 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_power_iff
% 4.69/5.02 thf(fact_6205_dvd__power,axiom,
% 4.69/5.02 ! [N2: nat,X: code_integer] :
% 4.69/5.02 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.02 | ( X = one_one_Code_integer ) )
% 4.69/5.02 => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_power
% 4.69/5.02 thf(fact_6206_dvd__power,axiom,
% 4.69/5.02 ! [N2: nat,X: code_natural] :
% 4.69/5.02 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.02 | ( X = one_one_Code_natural ) )
% 4.69/5.02 => ( dvd_dvd_Code_natural @ X @ ( power_7079662738309270450atural @ X @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_power
% 4.69/5.02 thf(fact_6207_dvd__power,axiom,
% 4.69/5.02 ! [N2: nat,X: int] :
% 4.69/5.02 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.02 | ( X = one_one_int ) )
% 4.69/5.02 => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_power
% 4.69/5.02 thf(fact_6208_dvd__power,axiom,
% 4.69/5.02 ! [N2: nat,X: nat] :
% 4.69/5.02 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.02 | ( X = one_one_nat ) )
% 4.69/5.02 => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_power
% 4.69/5.02 thf(fact_6209_gbinomial__Suc__Suc,axiom,
% 4.69/5.02 ! [A2: rat,K3: nat] :
% 4.69/5.02 ( ( gbinomial_rat @ ( plus_plus_rat @ A2 @ one_one_rat ) @ ( suc @ K3 ) )
% 4.69/5.02 = ( plus_plus_rat @ ( gbinomial_rat @ A2 @ K3 ) @ ( gbinomial_rat @ A2 @ ( suc @ K3 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % gbinomial_Suc_Suc
% 4.69/5.02 thf(fact_6210_one__le__power,axiom,
% 4.69/5.02 ! [A2: code_integer,N2: nat] :
% 4.69/5.02 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A2 )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A2 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % one_le_power
% 4.69/5.02 thf(fact_6211_one__le__power,axiom,
% 4.69/5.02 ! [A2: code_natural,N2: nat] :
% 4.69/5.02 ( ( ord_le1926595141338095240atural @ one_one_Code_natural @ A2 )
% 4.69/5.02 => ( ord_le1926595141338095240atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ A2 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % one_le_power
% 4.69/5.02 thf(fact_6212_one__le__power,axiom,
% 4.69/5.02 ! [A2: rat,N2: nat] :
% 4.69/5.02 ( ( ord_less_eq_rat @ one_one_rat @ A2 )
% 4.69/5.02 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A2 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % one_le_power
% 4.69/5.02 thf(fact_6213_one__le__power,axiom,
% 4.69/5.02 ! [A2: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_eq_nat @ one_one_nat @ A2 )
% 4.69/5.02 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A2 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % one_le_power
% 4.69/5.02 thf(fact_6214_one__le__power,axiom,
% 4.69/5.02 ! [A2: int,N2: nat] :
% 4.69/5.02 ( ( ord_less_eq_int @ one_one_int @ A2 )
% 4.69/5.02 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A2 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % one_le_power
% 4.69/5.02 thf(fact_6215_not__is__unit__0,axiom,
% 4.69/5.02 ~ ( dvd_dvd_Code_natural @ zero_z2226904508553997617atural @ one_one_Code_natural ) ).
% 4.69/5.02
% 4.69/5.02 % not_is_unit_0
% 4.69/5.02 thf(fact_6216_not__is__unit__0,axiom,
% 4.69/5.02 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 4.69/5.02
% 4.69/5.02 % not_is_unit_0
% 4.69/5.02 thf(fact_6217_not__is__unit__0,axiom,
% 4.69/5.02 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 4.69/5.02
% 4.69/5.02 % not_is_unit_0
% 4.69/5.02 thf(fact_6218_not__is__unit__0,axiom,
% 4.69/5.02 ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 4.69/5.02
% 4.69/5.02 % not_is_unit_0
% 4.69/5.02 thf(fact_6219_left__right__inverse__power,axiom,
% 4.69/5.02 ! [X: code_integer,Y: code_integer,N2: nat] :
% 4.69/5.02 ( ( ( times_3573771949741848930nteger @ X @ Y )
% 4.69/5.02 = one_one_Code_integer )
% 4.69/5.02 => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ N2 ) @ ( power_8256067586552552935nteger @ Y @ N2 ) )
% 4.69/5.02 = one_one_Code_integer ) ) ).
% 4.69/5.02
% 4.69/5.02 % left_right_inverse_power
% 4.69/5.02 thf(fact_6220_left__right__inverse__power,axiom,
% 4.69/5.02 ! [X: code_natural,Y: code_natural,N2: nat] :
% 4.69/5.02 ( ( ( times_2397367101498566445atural @ X @ Y )
% 4.69/5.02 = one_one_Code_natural )
% 4.69/5.02 => ( ( times_2397367101498566445atural @ ( power_7079662738309270450atural @ X @ N2 ) @ ( power_7079662738309270450atural @ Y @ N2 ) )
% 4.69/5.02 = one_one_Code_natural ) ) ).
% 4.69/5.02
% 4.69/5.02 % left_right_inverse_power
% 4.69/5.02 thf(fact_6221_left__right__inverse__power,axiom,
% 4.69/5.02 ! [X: assn,Y: assn,N2: nat] :
% 4.69/5.02 ( ( ( times_times_assn @ X @ Y )
% 4.69/5.02 = one_one_assn )
% 4.69/5.02 => ( ( times_times_assn @ ( power_power_assn @ X @ N2 ) @ ( power_power_assn @ Y @ N2 ) )
% 4.69/5.02 = one_one_assn ) ) ).
% 4.69/5.02
% 4.69/5.02 % left_right_inverse_power
% 4.69/5.02 thf(fact_6222_left__right__inverse__power,axiom,
% 4.69/5.02 ! [X: rat,Y: rat,N2: nat] :
% 4.69/5.02 ( ( ( times_times_rat @ X @ Y )
% 4.69/5.02 = one_one_rat )
% 4.69/5.02 => ( ( times_times_rat @ ( power_power_rat @ X @ N2 ) @ ( power_power_rat @ Y @ N2 ) )
% 4.69/5.02 = one_one_rat ) ) ).
% 4.69/5.02
% 4.69/5.02 % left_right_inverse_power
% 4.69/5.02 thf(fact_6223_left__right__inverse__power,axiom,
% 4.69/5.02 ! [X: nat,Y: nat,N2: nat] :
% 4.69/5.02 ( ( ( times_times_nat @ X @ Y )
% 4.69/5.02 = one_one_nat )
% 4.69/5.02 => ( ( times_times_nat @ ( power_power_nat @ X @ N2 ) @ ( power_power_nat @ Y @ N2 ) )
% 4.69/5.02 = one_one_nat ) ) ).
% 4.69/5.02
% 4.69/5.02 % left_right_inverse_power
% 4.69/5.02 thf(fact_6224_left__right__inverse__power,axiom,
% 4.69/5.02 ! [X: int,Y: int,N2: nat] :
% 4.69/5.02 ( ( ( times_times_int @ X @ Y )
% 4.69/5.02 = one_one_int )
% 4.69/5.02 => ( ( times_times_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 4.69/5.02 = one_one_int ) ) ).
% 4.69/5.02
% 4.69/5.02 % left_right_inverse_power
% 4.69/5.02 thf(fact_6225_power__Suc2,axiom,
% 4.69/5.02 ! [A2: assn,N2: nat] :
% 4.69/5.02 ( ( power_power_assn @ A2 @ ( suc @ N2 ) )
% 4.69/5.02 = ( times_times_assn @ ( power_power_assn @ A2 @ N2 ) @ A2 ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc2
% 4.69/5.02 thf(fact_6226_power__Suc2,axiom,
% 4.69/5.02 ! [A2: rat,N2: nat] :
% 4.69/5.02 ( ( power_power_rat @ A2 @ ( suc @ N2 ) )
% 4.69/5.02 = ( times_times_rat @ ( power_power_rat @ A2 @ N2 ) @ A2 ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc2
% 4.69/5.02 thf(fact_6227_power__Suc2,axiom,
% 4.69/5.02 ! [A2: nat,N2: nat] :
% 4.69/5.02 ( ( power_power_nat @ A2 @ ( suc @ N2 ) )
% 4.69/5.02 = ( times_times_nat @ ( power_power_nat @ A2 @ N2 ) @ A2 ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc2
% 4.69/5.02 thf(fact_6228_power__Suc2,axiom,
% 4.69/5.02 ! [A2: int,N2: nat] :
% 4.69/5.02 ( ( power_power_int @ A2 @ ( suc @ N2 ) )
% 4.69/5.02 = ( times_times_int @ ( power_power_int @ A2 @ N2 ) @ A2 ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc2
% 4.69/5.02 thf(fact_6229_power__Suc,axiom,
% 4.69/5.02 ! [A2: assn,N2: nat] :
% 4.69/5.02 ( ( power_power_assn @ A2 @ ( suc @ N2 ) )
% 4.69/5.02 = ( times_times_assn @ A2 @ ( power_power_assn @ A2 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc
% 4.69/5.02 thf(fact_6230_power__Suc,axiom,
% 4.69/5.02 ! [A2: rat,N2: nat] :
% 4.69/5.02 ( ( power_power_rat @ A2 @ ( suc @ N2 ) )
% 4.69/5.02 = ( times_times_rat @ A2 @ ( power_power_rat @ A2 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc
% 4.69/5.02 thf(fact_6231_power__Suc,axiom,
% 4.69/5.02 ! [A2: nat,N2: nat] :
% 4.69/5.02 ( ( power_power_nat @ A2 @ ( suc @ N2 ) )
% 4.69/5.02 = ( times_times_nat @ A2 @ ( power_power_nat @ A2 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc
% 4.69/5.02 thf(fact_6232_power__Suc,axiom,
% 4.69/5.02 ! [A2: int,N2: nat] :
% 4.69/5.02 ( ( power_power_int @ A2 @ ( suc @ N2 ) )
% 4.69/5.02 = ( times_times_int @ A2 @ ( power_power_int @ A2 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc
% 4.69/5.02 thf(fact_6233_unit__mult__right__cancel,axiom,
% 4.69/5.02 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.02 ( ( dvd_dvd_Code_integer @ A2 @ one_one_Code_integer )
% 4.69/5.02 => ( ( ( times_3573771949741848930nteger @ B @ A2 )
% 4.69/5.02 = ( times_3573771949741848930nteger @ C @ A2 ) )
% 4.69/5.02 = ( B = C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % unit_mult_right_cancel
% 4.69/5.02 thf(fact_6234_unit__mult__right__cancel,axiom,
% 4.69/5.02 ! [A2: code_natural,B: code_natural,C: code_natural] :
% 4.69/5.02 ( ( dvd_dvd_Code_natural @ A2 @ one_one_Code_natural )
% 4.69/5.02 => ( ( ( times_2397367101498566445atural @ B @ A2 )
% 4.69/5.02 = ( times_2397367101498566445atural @ C @ A2 ) )
% 4.69/5.02 = ( B = C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % unit_mult_right_cancel
% 4.69/5.02 thf(fact_6235_unit__mult__right__cancel,axiom,
% 4.69/5.02 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ A2 @ one_one_nat )
% 4.69/5.02 => ( ( ( times_times_nat @ B @ A2 )
% 4.69/5.02 = ( times_times_nat @ C @ A2 ) )
% 4.69/5.02 = ( B = C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % unit_mult_right_cancel
% 4.69/5.02 thf(fact_6236_unit__mult__right__cancel,axiom,
% 4.69/5.02 ! [A2: int,B: int,C: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ A2 @ one_one_int )
% 4.69/5.02 => ( ( ( times_times_int @ B @ A2 )
% 4.69/5.02 = ( times_times_int @ C @ A2 ) )
% 4.69/5.02 = ( B = C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % unit_mult_right_cancel
% 4.69/5.02 thf(fact_6237_unit__mult__left__cancel,axiom,
% 4.69/5.02 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.02 ( ( dvd_dvd_Code_integer @ A2 @ one_one_Code_integer )
% 4.69/5.02 => ( ( ( times_3573771949741848930nteger @ A2 @ B )
% 4.69/5.02 = ( times_3573771949741848930nteger @ A2 @ C ) )
% 4.69/5.02 = ( B = C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % unit_mult_left_cancel
% 4.69/5.02 thf(fact_6238_unit__mult__left__cancel,axiom,
% 4.69/5.02 ! [A2: code_natural,B: code_natural,C: code_natural] :
% 4.69/5.02 ( ( dvd_dvd_Code_natural @ A2 @ one_one_Code_natural )
% 4.69/5.02 => ( ( ( times_2397367101498566445atural @ A2 @ B )
% 4.69/5.02 = ( times_2397367101498566445atural @ A2 @ C ) )
% 4.69/5.02 = ( B = C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % unit_mult_left_cancel
% 4.69/5.02 thf(fact_6239_unit__mult__left__cancel,axiom,
% 4.69/5.02 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ A2 @ one_one_nat )
% 4.69/5.02 => ( ( ( times_times_nat @ A2 @ B )
% 4.69/5.02 = ( times_times_nat @ A2 @ C ) )
% 4.69/5.02 = ( B = C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % unit_mult_left_cancel
% 4.69/5.02 thf(fact_6240_unit__mult__left__cancel,axiom,
% 4.69/5.02 ! [A2: int,B: int,C: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ A2 @ one_one_int )
% 4.69/5.02 => ( ( ( times_times_int @ A2 @ B )
% 4.69/5.02 = ( times_times_int @ A2 @ C ) )
% 4.69/5.02 = ( B = C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % unit_mult_left_cancel
% 4.69/5.02 thf(fact_6241_mult__unit__dvd__iff_H,axiom,
% 4.69/5.02 ! [A2: code_integer,B: code_integer,C: code_integer] :
% 4.69/5.02 ( ( dvd_dvd_Code_integer @ A2 @ one_one_Code_integer )
% 4.69/5.02 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A2 @ B ) @ C )
% 4.69/5.02 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % mult_unit_dvd_iff'
% 4.69/5.02 thf(fact_6242_mult__unit__dvd__iff_H,axiom,
% 4.69/5.02 ! [A2: code_natural,B: code_natural,C: code_natural] :
% 4.69/5.02 ( ( dvd_dvd_Code_natural @ A2 @ one_one_Code_natural )
% 4.69/5.02 => ( ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ A2 @ B ) @ C )
% 4.69/5.02 = ( dvd_dvd_Code_natural @ B @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % mult_unit_dvd_iff'
% 4.69/5.02 thf(fact_6243_mult__unit__dvd__iff_H,axiom,
% 4.69/5.02 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ A2 @ one_one_nat )
% 4.69/5.02 => ( ( dvd_dvd_nat @ ( times_times_nat @ A2 @ B ) @ C )
% 4.69/5.02 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % mult_unit_dvd_iff'
% 4.69/5.02 thf(fact_6244_mult__unit__dvd__iff_H,axiom,
% 4.69/5.02 ! [A2: int,B: int,C: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ A2 @ one_one_int )
% 4.69/5.02 => ( ( dvd_dvd_int @ ( times_times_int @ A2 @ B ) @ C )
% 4.69/5.02 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % mult_unit_dvd_iff'
% 4.69/5.02 thf(fact_6245_dvd__mult__unit__iff_H,axiom,
% 4.69/5.02 ! [B: code_integer,A2: code_integer,C: code_integer] :
% 4.69/5.02 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 4.69/5.02 => ( ( dvd_dvd_Code_integer @ A2 @ ( times_3573771949741848930nteger @ B @ C ) )
% 4.69/5.02 = ( dvd_dvd_Code_integer @ A2 @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_unit_iff'
% 4.69/5.02 thf(fact_6246_dvd__mult__unit__iff_H,axiom,
% 4.69/5.02 ! [B: code_natural,A2: code_natural,C: code_natural] :
% 4.69/5.02 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 4.69/5.02 => ( ( dvd_dvd_Code_natural @ A2 @ ( times_2397367101498566445atural @ B @ C ) )
% 4.69/5.02 = ( dvd_dvd_Code_natural @ A2 @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_unit_iff'
% 4.69/5.02 thf(fact_6247_dvd__mult__unit__iff_H,axiom,
% 4.69/5.02 ! [B: nat,A2: nat,C: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 4.69/5.02 => ( ( dvd_dvd_nat @ A2 @ ( times_times_nat @ B @ C ) )
% 4.69/5.02 = ( dvd_dvd_nat @ A2 @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_unit_iff'
% 4.69/5.02 thf(fact_6248_dvd__mult__unit__iff_H,axiom,
% 4.69/5.02 ! [B: int,A2: int,C: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ B @ one_one_int )
% 4.69/5.02 => ( ( dvd_dvd_int @ A2 @ ( times_times_int @ B @ C ) )
% 4.69/5.02 = ( dvd_dvd_int @ A2 @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_unit_iff'
% 4.69/5.02 thf(fact_6249_mult__unit__dvd__iff,axiom,
% 4.69/5.02 ! [B: code_integer,A2: code_integer,C: code_integer] :
% 4.69/5.02 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 4.69/5.02 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A2 @ B ) @ C )
% 4.69/5.02 = ( dvd_dvd_Code_integer @ A2 @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % mult_unit_dvd_iff
% 4.69/5.02 thf(fact_6250_mult__unit__dvd__iff,axiom,
% 4.69/5.02 ! [B: code_natural,A2: code_natural,C: code_natural] :
% 4.69/5.02 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 4.69/5.02 => ( ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ A2 @ B ) @ C )
% 4.69/5.02 = ( dvd_dvd_Code_natural @ A2 @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % mult_unit_dvd_iff
% 4.69/5.02 thf(fact_6251_mult__unit__dvd__iff,axiom,
% 4.69/5.02 ! [B: nat,A2: nat,C: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 4.69/5.02 => ( ( dvd_dvd_nat @ ( times_times_nat @ A2 @ B ) @ C )
% 4.69/5.02 = ( dvd_dvd_nat @ A2 @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % mult_unit_dvd_iff
% 4.69/5.02 thf(fact_6252_mult__unit__dvd__iff,axiom,
% 4.69/5.02 ! [B: int,A2: int,C: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ B @ one_one_int )
% 4.69/5.02 => ( ( dvd_dvd_int @ ( times_times_int @ A2 @ B ) @ C )
% 4.69/5.02 = ( dvd_dvd_int @ A2 @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % mult_unit_dvd_iff
% 4.69/5.02 thf(fact_6253_dvd__mult__unit__iff,axiom,
% 4.69/5.02 ! [B: code_integer,A2: code_integer,C: code_integer] :
% 4.69/5.02 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 4.69/5.02 => ( ( dvd_dvd_Code_integer @ A2 @ ( times_3573771949741848930nteger @ C @ B ) )
% 4.69/5.02 = ( dvd_dvd_Code_integer @ A2 @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_unit_iff
% 4.69/5.02 thf(fact_6254_dvd__mult__unit__iff,axiom,
% 4.69/5.02 ! [B: code_natural,A2: code_natural,C: code_natural] :
% 4.69/5.02 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 4.69/5.02 => ( ( dvd_dvd_Code_natural @ A2 @ ( times_2397367101498566445atural @ C @ B ) )
% 4.69/5.02 = ( dvd_dvd_Code_natural @ A2 @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_unit_iff
% 4.69/5.02 thf(fact_6255_dvd__mult__unit__iff,axiom,
% 4.69/5.02 ! [B: nat,A2: nat,C: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 4.69/5.02 => ( ( dvd_dvd_nat @ A2 @ ( times_times_nat @ C @ B ) )
% 4.69/5.02 = ( dvd_dvd_nat @ A2 @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_unit_iff
% 4.69/5.02 thf(fact_6256_dvd__mult__unit__iff,axiom,
% 4.69/5.02 ! [B: int,A2: int,C: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ B @ one_one_int )
% 4.69/5.02 => ( ( dvd_dvd_int @ A2 @ ( times_times_int @ C @ B ) )
% 4.69/5.02 = ( dvd_dvd_int @ A2 @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_unit_iff
% 4.69/5.02 thf(fact_6257_is__unit__mult__iff,axiom,
% 4.69/5.02 ! [A2: code_integer,B: code_integer] :
% 4.69/5.02 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A2 @ B ) @ one_one_Code_integer )
% 4.69/5.02 = ( ( dvd_dvd_Code_integer @ A2 @ one_one_Code_integer )
% 4.69/5.02 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % is_unit_mult_iff
% 4.69/5.02 thf(fact_6258_is__unit__mult__iff,axiom,
% 4.69/5.02 ! [A2: code_natural,B: code_natural] :
% 4.69/5.02 ( ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ A2 @ B ) @ one_one_Code_natural )
% 4.69/5.02 = ( ( dvd_dvd_Code_natural @ A2 @ one_one_Code_natural )
% 4.69/5.02 & ( dvd_dvd_Code_natural @ B @ one_one_Code_natural ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % is_unit_mult_iff
% 4.69/5.02 thf(fact_6259_is__unit__mult__iff,axiom,
% 4.69/5.02 ! [A2: nat,B: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ ( times_times_nat @ A2 @ B ) @ one_one_nat )
% 4.69/5.02 = ( ( dvd_dvd_nat @ A2 @ one_one_nat )
% 4.69/5.02 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % is_unit_mult_iff
% 4.69/5.02 thf(fact_6260_is__unit__mult__iff,axiom,
% 4.69/5.02 ! [A2: int,B: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ ( times_times_int @ A2 @ B ) @ one_one_int )
% 4.69/5.02 = ( ( dvd_dvd_int @ A2 @ one_one_int )
% 4.69/5.02 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % is_unit_mult_iff
% 4.69/5.02 thf(fact_6261_power__0,axiom,
% 4.69/5.02 ! [A2: assn] :
% 4.69/5.02 ( ( power_power_assn @ A2 @ zero_zero_nat )
% 4.69/5.02 = one_one_assn ) ).
% 4.69/5.02
% 4.69/5.02 % power_0
% 4.69/5.02 thf(fact_6262_power__0,axiom,
% 4.69/5.02 ! [A2: code_integer] :
% 4.69/5.02 ( ( power_8256067586552552935nteger @ A2 @ zero_zero_nat )
% 4.69/5.02 = one_one_Code_integer ) ).
% 4.69/5.02
% 4.69/5.02 % power_0
% 4.69/5.02 thf(fact_6263_power__0,axiom,
% 4.69/5.02 ! [A2: code_natural] :
% 4.69/5.02 ( ( power_7079662738309270450atural @ A2 @ zero_zero_nat )
% 4.69/5.02 = one_one_Code_natural ) ).
% 4.69/5.02
% 4.69/5.02 % power_0
% 4.69/5.02 thf(fact_6264_power__0,axiom,
% 4.69/5.02 ! [A2: int] :
% 4.69/5.02 ( ( power_power_int @ A2 @ zero_zero_nat )
% 4.69/5.02 = one_one_int ) ).
% 4.69/5.02
% 4.69/5.02 % power_0
% 4.69/5.02 thf(fact_6265_power__0,axiom,
% 4.69/5.02 ! [A2: nat] :
% 4.69/5.02 ( ( power_power_nat @ A2 @ zero_zero_nat )
% 4.69/5.02 = one_one_nat ) ).
% 4.69/5.02
% 4.69/5.02 % power_0
% 4.69/5.02 thf(fact_6266_power__add,axiom,
% 4.69/5.02 ! [A2: assn,M4: nat,N2: nat] :
% 4.69/5.02 ( ( power_power_assn @ A2 @ ( plus_plus_nat @ M4 @ N2 ) )
% 4.69/5.02 = ( times_times_assn @ ( power_power_assn @ A2 @ M4 ) @ ( power_power_assn @ A2 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_add
% 4.69/5.02 thf(fact_6267_power__add,axiom,
% 4.69/5.02 ! [A2: rat,M4: nat,N2: nat] :
% 4.69/5.02 ( ( power_power_rat @ A2 @ ( plus_plus_nat @ M4 @ N2 ) )
% 4.69/5.02 = ( times_times_rat @ ( power_power_rat @ A2 @ M4 ) @ ( power_power_rat @ A2 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_add
% 4.69/5.02 thf(fact_6268_power__add,axiom,
% 4.69/5.02 ! [A2: nat,M4: nat,N2: nat] :
% 4.69/5.02 ( ( power_power_nat @ A2 @ ( plus_plus_nat @ M4 @ N2 ) )
% 4.69/5.02 = ( times_times_nat @ ( power_power_nat @ A2 @ M4 ) @ ( power_power_nat @ A2 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_add
% 4.69/5.02 thf(fact_6269_power__add,axiom,
% 4.69/5.02 ! [A2: int,M4: nat,N2: nat] :
% 4.69/5.02 ( ( power_power_int @ A2 @ ( plus_plus_nat @ M4 @ N2 ) )
% 4.69/5.02 = ( times_times_int @ ( power_power_int @ A2 @ M4 ) @ ( power_power_int @ A2 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_add
% 4.69/5.02 thf(fact_6270_gbinomial__addition__formula,axiom,
% 4.69/5.02 ! [A2: rat,K3: nat] :
% 4.69/5.02 ( ( gbinomial_rat @ A2 @ ( suc @ K3 ) )
% 4.69/5.02 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A2 @ one_one_rat ) @ ( suc @ K3 ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A2 @ one_one_rat ) @ K3 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % gbinomial_addition_formula
% 4.69/5.02 thf(fact_6271_power__le__one,axiom,
% 4.69/5.02 ! [A2: code_natural,N2: nat] :
% 4.69/5.02 ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A2 )
% 4.69/5.02 => ( ( ord_le1926595141338095240atural @ A2 @ one_one_Code_natural )
% 4.69/5.02 => ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A2 @ N2 ) @ one_one_Code_natural ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_le_one
% 4.69/5.02 thf(fact_6272_power__le__one,axiom,
% 4.69/5.02 ! [A2: code_integer,N2: nat] :
% 4.69/5.02 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.02 => ( ( ord_le3102999989581377725nteger @ A2 @ one_one_Code_integer )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A2 @ N2 ) @ one_one_Code_integer ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_le_one
% 4.69/5.02 thf(fact_6273_power__le__one,axiom,
% 4.69/5.02 ! [A2: rat,N2: nat] :
% 4.69/5.02 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 4.69/5.02 => ( ( ord_less_eq_rat @ A2 @ one_one_rat )
% 4.69/5.02 => ( ord_less_eq_rat @ ( power_power_rat @ A2 @ N2 ) @ one_one_rat ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_le_one
% 4.69/5.02 thf(fact_6274_power__le__one,axiom,
% 4.69/5.02 ! [A2: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 4.69/5.02 => ( ( ord_less_eq_nat @ A2 @ one_one_nat )
% 4.69/5.02 => ( ord_less_eq_nat @ ( power_power_nat @ A2 @ N2 ) @ one_one_nat ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_le_one
% 4.69/5.02 thf(fact_6275_power__le__one,axiom,
% 4.69/5.02 ! [A2: int,N2: nat] :
% 4.69/5.02 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 4.69/5.02 => ( ( ord_less_eq_int @ A2 @ one_one_int )
% 4.69/5.02 => ( ord_less_eq_int @ ( power_power_int @ A2 @ N2 ) @ one_one_int ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_le_one
% 4.69/5.02 thf(fact_6276_power__less__power__Suc,axiom,
% 4.69/5.02 ! [A2: code_natural,N2: nat] :
% 4.69/5.02 ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A2 )
% 4.69/5.02 => ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ A2 @ N2 ) @ ( times_2397367101498566445atural @ A2 @ ( power_7079662738309270450atural @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_less_power_Suc
% 4.69/5.02 thf(fact_6277_power__less__power__Suc,axiom,
% 4.69/5.02 ! [A2: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_nat @ one_one_nat @ A2 )
% 4.69/5.02 => ( ord_less_nat @ ( power_power_nat @ A2 @ N2 ) @ ( times_times_nat @ A2 @ ( power_power_nat @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_less_power_Suc
% 4.69/5.02 thf(fact_6278_power__less__power__Suc,axiom,
% 4.69/5.02 ! [A2: int,N2: nat] :
% 4.69/5.02 ( ( ord_less_int @ one_one_int @ A2 )
% 4.69/5.02 => ( ord_less_int @ ( power_power_int @ A2 @ N2 ) @ ( times_times_int @ A2 @ ( power_power_int @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_less_power_Suc
% 4.69/5.02 thf(fact_6279_power__less__power__Suc,axiom,
% 4.69/5.02 ! [A2: code_integer,N2: nat] :
% 4.69/5.02 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A2 )
% 4.69/5.02 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A2 @ N2 ) @ ( times_3573771949741848930nteger @ A2 @ ( power_8256067586552552935nteger @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_less_power_Suc
% 4.69/5.02 thf(fact_6280_power__less__power__Suc,axiom,
% 4.69/5.02 ! [A2: rat,N2: nat] :
% 4.69/5.02 ( ( ord_less_rat @ one_one_rat @ A2 )
% 4.69/5.02 => ( ord_less_rat @ ( power_power_rat @ A2 @ N2 ) @ ( times_times_rat @ A2 @ ( power_power_rat @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_less_power_Suc
% 4.69/5.02 thf(fact_6281_power__gt1__lemma,axiom,
% 4.69/5.02 ! [A2: code_natural,N2: nat] :
% 4.69/5.02 ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A2 )
% 4.69/5.02 => ( ord_le5570908160329646204atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ A2 @ ( power_7079662738309270450atural @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_gt1_lemma
% 4.69/5.02 thf(fact_6282_power__gt1__lemma,axiom,
% 4.69/5.02 ! [A2: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_nat @ one_one_nat @ A2 )
% 4.69/5.02 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A2 @ ( power_power_nat @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_gt1_lemma
% 4.69/5.02 thf(fact_6283_power__gt1__lemma,axiom,
% 4.69/5.02 ! [A2: int,N2: nat] :
% 4.69/5.02 ( ( ord_less_int @ one_one_int @ A2 )
% 4.69/5.02 => ( ord_less_int @ one_one_int @ ( times_times_int @ A2 @ ( power_power_int @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_gt1_lemma
% 4.69/5.02 thf(fact_6284_power__gt1__lemma,axiom,
% 4.69/5.02 ! [A2: code_integer,N2: nat] :
% 4.69/5.02 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A2 )
% 4.69/5.02 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ A2 @ ( power_8256067586552552935nteger @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_gt1_lemma
% 4.69/5.02 thf(fact_6285_power__gt1__lemma,axiom,
% 4.69/5.02 ! [A2: rat,N2: nat] :
% 4.69/5.02 ( ( ord_less_rat @ one_one_rat @ A2 )
% 4.69/5.02 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A2 @ ( power_power_rat @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_gt1_lemma
% 4.69/5.02 thf(fact_6286_unity__coeff__ex,axiom,
% 4.69/5.02 ! [P: code_integer > $o,L: code_integer] :
% 4.69/5.02 ( ( ? [X2: code_integer] : ( P @ ( times_3573771949741848930nteger @ L @ X2 ) ) )
% 4.69/5.02 = ( ? [X2: code_integer] :
% 4.69/5.02 ( ( dvd_dvd_Code_integer @ L @ ( plus_p5714425477246183910nteger @ X2 @ zero_z3403309356797280102nteger ) )
% 4.69/5.02 & ( P @ X2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % unity_coeff_ex
% 4.69/5.02 thf(fact_6287_unity__coeff__ex,axiom,
% 4.69/5.02 ! [P: rat > $o,L: rat] :
% 4.69/5.02 ( ( ? [X2: rat] : ( P @ ( times_times_rat @ L @ X2 ) ) )
% 4.69/5.02 = ( ? [X2: rat] :
% 4.69/5.02 ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X2 @ zero_zero_rat ) )
% 4.69/5.02 & ( P @ X2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % unity_coeff_ex
% 4.69/5.02 thf(fact_6288_unity__coeff__ex,axiom,
% 4.69/5.02 ! [P: nat > $o,L: nat] :
% 4.69/5.02 ( ( ? [X2: nat] : ( P @ ( times_times_nat @ L @ X2 ) ) )
% 4.69/5.02 = ( ? [X2: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X2 @ zero_zero_nat ) )
% 4.69/5.02 & ( P @ X2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % unity_coeff_ex
% 4.69/5.02 thf(fact_6289_unity__coeff__ex,axiom,
% 4.69/5.02 ! [P: int > $o,L: int] :
% 4.69/5.02 ( ( ? [X2: int] : ( P @ ( times_times_int @ L @ X2 ) ) )
% 4.69/5.02 = ( ? [X2: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X2 @ zero_zero_int ) )
% 4.69/5.02 & ( P @ X2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % unity_coeff_ex
% 4.69/5.02 thf(fact_6290_power__0__left,axiom,
% 4.69/5.02 ! [N2: nat] :
% 4.69/5.02 ( ( ( N2 = zero_zero_nat )
% 4.69/5.02 => ( ( power_7079662738309270450atural @ zero_z2226904508553997617atural @ N2 )
% 4.69/5.02 = one_one_Code_natural ) )
% 4.69/5.02 & ( ( N2 != zero_zero_nat )
% 4.69/5.02 => ( ( power_7079662738309270450atural @ zero_z2226904508553997617atural @ N2 )
% 4.69/5.02 = zero_z2226904508553997617atural ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_0_left
% 4.69/5.02 thf(fact_6291_power__0__left,axiom,
% 4.69/5.02 ! [N2: nat] :
% 4.69/5.02 ( ( ( N2 = zero_zero_nat )
% 4.69/5.02 => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N2 )
% 4.69/5.02 = one_one_Code_integer ) )
% 4.69/5.02 & ( ( N2 != zero_zero_nat )
% 4.69/5.02 => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N2 )
% 4.69/5.02 = zero_z3403309356797280102nteger ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_0_left
% 4.69/5.02 thf(fact_6292_power__0__left,axiom,
% 4.69/5.02 ! [N2: nat] :
% 4.69/5.02 ( ( ( N2 = zero_zero_nat )
% 4.69/5.02 => ( ( power_power_int @ zero_zero_int @ N2 )
% 4.69/5.02 = one_one_int ) )
% 4.69/5.02 & ( ( N2 != zero_zero_nat )
% 4.69/5.02 => ( ( power_power_int @ zero_zero_int @ N2 )
% 4.69/5.02 = zero_zero_int ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_0_left
% 4.69/5.02 thf(fact_6293_power__0__left,axiom,
% 4.69/5.02 ! [N2: nat] :
% 4.69/5.02 ( ( ( N2 = zero_zero_nat )
% 4.69/5.02 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 4.69/5.02 = one_one_nat ) )
% 4.69/5.02 & ( ( N2 != zero_zero_nat )
% 4.69/5.02 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 4.69/5.02 = zero_zero_nat ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_0_left
% 4.69/5.02 thf(fact_6294_unit__dvdE,axiom,
% 4.69/5.02 ! [A2: code_natural,B: code_natural] :
% 4.69/5.02 ( ( dvd_dvd_Code_natural @ A2 @ one_one_Code_natural )
% 4.69/5.02 => ~ ( ( A2 != zero_z2226904508553997617atural )
% 4.69/5.02 => ! [C2: code_natural] :
% 4.69/5.02 ( B
% 4.69/5.02 != ( times_2397367101498566445atural @ A2 @ C2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % unit_dvdE
% 4.69/5.02 thf(fact_6295_unit__dvdE,axiom,
% 4.69/5.02 ! [A2: code_integer,B: code_integer] :
% 4.69/5.02 ( ( dvd_dvd_Code_integer @ A2 @ one_one_Code_integer )
% 4.69/5.02 => ~ ( ( A2 != zero_z3403309356797280102nteger )
% 4.69/5.02 => ! [C2: code_integer] :
% 4.69/5.02 ( B
% 4.69/5.02 != ( times_3573771949741848930nteger @ A2 @ C2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % unit_dvdE
% 4.69/5.02 thf(fact_6296_unit__dvdE,axiom,
% 4.69/5.02 ! [A2: nat,B: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ A2 @ one_one_nat )
% 4.69/5.02 => ~ ( ( A2 != zero_zero_nat )
% 4.69/5.02 => ! [C2: nat] :
% 4.69/5.02 ( B
% 4.69/5.02 != ( times_times_nat @ A2 @ C2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % unit_dvdE
% 4.69/5.02 thf(fact_6297_unit__dvdE,axiom,
% 4.69/5.02 ! [A2: int,B: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ A2 @ one_one_int )
% 4.69/5.02 => ~ ( ( A2 != zero_zero_int )
% 4.69/5.02 => ! [C2: int] :
% 4.69/5.02 ( B
% 4.69/5.02 != ( times_times_int @ A2 @ C2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % unit_dvdE
% 4.69/5.02 thf(fact_6298_power__gt1,axiom,
% 4.69/5.02 ! [A2: code_natural,N2: nat] :
% 4.69/5.02 ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A2 )
% 4.69/5.02 => ( ord_le5570908160329646204atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ A2 @ ( suc @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_gt1
% 4.69/5.02 thf(fact_6299_power__gt1,axiom,
% 4.69/5.02 ! [A2: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_nat @ one_one_nat @ A2 )
% 4.69/5.02 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A2 @ ( suc @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_gt1
% 4.69/5.02 thf(fact_6300_power__gt1,axiom,
% 4.69/5.02 ! [A2: int,N2: nat] :
% 4.69/5.02 ( ( ord_less_int @ one_one_int @ A2 )
% 4.69/5.02 => ( ord_less_int @ one_one_int @ ( power_power_int @ A2 @ ( suc @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_gt1
% 4.69/5.02 thf(fact_6301_power__gt1,axiom,
% 4.69/5.02 ! [A2: code_integer,N2: nat] :
% 4.69/5.02 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A2 )
% 4.69/5.02 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A2 @ ( suc @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_gt1
% 4.69/5.02 thf(fact_6302_power__gt1,axiom,
% 4.69/5.02 ! [A2: rat,N2: nat] :
% 4.69/5.02 ( ( ord_less_rat @ one_one_rat @ A2 )
% 4.69/5.02 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A2 @ ( suc @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_gt1
% 4.69/5.02 thf(fact_6303_power__strict__increasing,axiom,
% 4.69/5.02 ! [N2: nat,N: nat,A2: code_natural] :
% 4.69/5.02 ( ( ord_less_nat @ N2 @ N )
% 4.69/5.02 => ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A2 )
% 4.69/5.02 => ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ A2 @ N2 ) @ ( power_7079662738309270450atural @ A2 @ N ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_strict_increasing
% 4.69/5.02 thf(fact_6304_power__strict__increasing,axiom,
% 4.69/5.02 ! [N2: nat,N: nat,A2: nat] :
% 4.69/5.02 ( ( ord_less_nat @ N2 @ N )
% 4.69/5.02 => ( ( ord_less_nat @ one_one_nat @ A2 )
% 4.69/5.02 => ( ord_less_nat @ ( power_power_nat @ A2 @ N2 ) @ ( power_power_nat @ A2 @ N ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_strict_increasing
% 4.69/5.02 thf(fact_6305_power__strict__increasing,axiom,
% 4.69/5.02 ! [N2: nat,N: nat,A2: int] :
% 4.69/5.02 ( ( ord_less_nat @ N2 @ N )
% 4.69/5.02 => ( ( ord_less_int @ one_one_int @ A2 )
% 4.69/5.02 => ( ord_less_int @ ( power_power_int @ A2 @ N2 ) @ ( power_power_int @ A2 @ N ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_strict_increasing
% 4.69/5.02 thf(fact_6306_power__strict__increasing,axiom,
% 4.69/5.02 ! [N2: nat,N: nat,A2: code_integer] :
% 4.69/5.02 ( ( ord_less_nat @ N2 @ N )
% 4.69/5.02 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A2 )
% 4.69/5.02 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A2 @ N2 ) @ ( power_8256067586552552935nteger @ A2 @ N ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_strict_increasing
% 4.69/5.02 thf(fact_6307_power__strict__increasing,axiom,
% 4.69/5.02 ! [N2: nat,N: nat,A2: rat] :
% 4.69/5.02 ( ( ord_less_nat @ N2 @ N )
% 4.69/5.02 => ( ( ord_less_rat @ one_one_rat @ A2 )
% 4.69/5.02 => ( ord_less_rat @ ( power_power_rat @ A2 @ N2 ) @ ( power_power_rat @ A2 @ N ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_strict_increasing
% 4.69/5.02 thf(fact_6308_power__less__imp__less__exp,axiom,
% 4.69/5.02 ! [A2: code_natural,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A2 )
% 4.69/5.02 => ( ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ A2 @ M4 ) @ ( power_7079662738309270450atural @ A2 @ N2 ) )
% 4.69/5.02 => ( ord_less_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_less_imp_less_exp
% 4.69/5.02 thf(fact_6309_power__less__imp__less__exp,axiom,
% 4.69/5.02 ! [A2: nat,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_nat @ one_one_nat @ A2 )
% 4.69/5.02 => ( ( ord_less_nat @ ( power_power_nat @ A2 @ M4 ) @ ( power_power_nat @ A2 @ N2 ) )
% 4.69/5.02 => ( ord_less_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_less_imp_less_exp
% 4.69/5.02 thf(fact_6310_power__less__imp__less__exp,axiom,
% 4.69/5.02 ! [A2: int,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_int @ one_one_int @ A2 )
% 4.69/5.02 => ( ( ord_less_int @ ( power_power_int @ A2 @ M4 ) @ ( power_power_int @ A2 @ N2 ) )
% 4.69/5.02 => ( ord_less_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_less_imp_less_exp
% 4.69/5.02 thf(fact_6311_power__less__imp__less__exp,axiom,
% 4.69/5.02 ! [A2: code_integer,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A2 )
% 4.69/5.02 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A2 @ M4 ) @ ( power_8256067586552552935nteger @ A2 @ N2 ) )
% 4.69/5.02 => ( ord_less_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_less_imp_less_exp
% 4.69/5.02 thf(fact_6312_power__less__imp__less__exp,axiom,
% 4.69/5.02 ! [A2: rat,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_rat @ one_one_rat @ A2 )
% 4.69/5.02 => ( ( ord_less_rat @ ( power_power_rat @ A2 @ M4 ) @ ( power_power_rat @ A2 @ N2 ) )
% 4.69/5.02 => ( ord_less_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_less_imp_less_exp
% 4.69/5.02 thf(fact_6313_power__increasing,axiom,
% 4.69/5.02 ! [N2: nat,N: nat,A2: code_integer] :
% 4.69/5.02 ( ( ord_less_eq_nat @ N2 @ N )
% 4.69/5.02 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A2 )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A2 @ N2 ) @ ( power_8256067586552552935nteger @ A2 @ N ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_increasing
% 4.69/5.02 thf(fact_6314_power__increasing,axiom,
% 4.69/5.02 ! [N2: nat,N: nat,A2: code_natural] :
% 4.69/5.02 ( ( ord_less_eq_nat @ N2 @ N )
% 4.69/5.02 => ( ( ord_le1926595141338095240atural @ one_one_Code_natural @ A2 )
% 4.69/5.02 => ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A2 @ N2 ) @ ( power_7079662738309270450atural @ A2 @ N ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_increasing
% 4.69/5.02 thf(fact_6315_power__increasing,axiom,
% 4.69/5.02 ! [N2: nat,N: nat,A2: rat] :
% 4.69/5.02 ( ( ord_less_eq_nat @ N2 @ N )
% 4.69/5.02 => ( ( ord_less_eq_rat @ one_one_rat @ A2 )
% 4.69/5.02 => ( ord_less_eq_rat @ ( power_power_rat @ A2 @ N2 ) @ ( power_power_rat @ A2 @ N ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_increasing
% 4.69/5.02 thf(fact_6316_power__increasing,axiom,
% 4.69/5.02 ! [N2: nat,N: nat,A2: nat] :
% 4.69/5.02 ( ( ord_less_eq_nat @ N2 @ N )
% 4.69/5.02 => ( ( ord_less_eq_nat @ one_one_nat @ A2 )
% 4.69/5.02 => ( ord_less_eq_nat @ ( power_power_nat @ A2 @ N2 ) @ ( power_power_nat @ A2 @ N ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_increasing
% 4.69/5.02 thf(fact_6317_power__increasing,axiom,
% 4.69/5.02 ! [N2: nat,N: nat,A2: int] :
% 4.69/5.02 ( ( ord_less_eq_nat @ N2 @ N )
% 4.69/5.02 => ( ( ord_less_eq_int @ one_one_int @ A2 )
% 4.69/5.02 => ( ord_less_eq_int @ ( power_power_int @ A2 @ N2 ) @ ( power_power_int @ A2 @ N ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_increasing
% 4.69/5.02 thf(fact_6318_inf__period_I3_J,axiom,
% 4.69/5.02 ! [D2: code_integer,D3: code_integer,T4: code_integer] :
% 4.69/5.02 ( ( dvd_dvd_Code_integer @ D2 @ D3 )
% 4.69/5.02 => ! [X6: code_integer,K2: code_integer] :
% 4.69/5.02 ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X6 @ T4 ) )
% 4.69/5.02 = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X6 @ ( times_3573771949741848930nteger @ K2 @ D3 ) ) @ T4 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % inf_period(3)
% 4.69/5.02 thf(fact_6319_inf__period_I3_J,axiom,
% 4.69/5.02 ! [D2: rat,D3: rat,T4: rat] :
% 4.69/5.02 ( ( dvd_dvd_rat @ D2 @ D3 )
% 4.69/5.02 => ! [X6: rat,K2: rat] :
% 4.69/5.02 ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X6 @ T4 ) )
% 4.69/5.02 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K2 @ D3 ) ) @ T4 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % inf_period(3)
% 4.69/5.02 thf(fact_6320_inf__period_I3_J,axiom,
% 4.69/5.02 ! [D2: int,D3: int,T4: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ D2 @ D3 )
% 4.69/5.02 => ! [X6: int,K2: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ T4 ) )
% 4.69/5.02 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X6 @ ( times_times_int @ K2 @ D3 ) ) @ T4 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % inf_period(3)
% 4.69/5.02 thf(fact_6321_inf__period_I4_J,axiom,
% 4.69/5.02 ! [D2: code_integer,D3: code_integer,T4: code_integer] :
% 4.69/5.02 ( ( dvd_dvd_Code_integer @ D2 @ D3 )
% 4.69/5.02 => ! [X6: code_integer,K2: code_integer] :
% 4.69/5.02 ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X6 @ T4 ) ) )
% 4.69/5.02 = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X6 @ ( times_3573771949741848930nteger @ K2 @ D3 ) ) @ T4 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % inf_period(4)
% 4.69/5.02 thf(fact_6322_inf__period_I4_J,axiom,
% 4.69/5.02 ! [D2: rat,D3: rat,T4: rat] :
% 4.69/5.02 ( ( dvd_dvd_rat @ D2 @ D3 )
% 4.69/5.02 => ! [X6: rat,K2: rat] :
% 4.69/5.02 ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X6 @ T4 ) ) )
% 4.69/5.02 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K2 @ D3 ) ) @ T4 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % inf_period(4)
% 4.69/5.02 thf(fact_6323_inf__period_I4_J,axiom,
% 4.69/5.02 ! [D2: int,D3: int,T4: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ D2 @ D3 )
% 4.69/5.02 => ! [X6: int,K2: int] :
% 4.69/5.02 ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X6 @ T4 ) ) )
% 4.69/5.02 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X6 @ ( times_times_int @ K2 @ D3 ) ) @ T4 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % inf_period(4)
% 4.69/5.02 thf(fact_6324_cInf__mono,axiom,
% 4.69/5.02 ! [B4: set_o,A: set_o] :
% 4.69/5.02 ( ( B4 != bot_bot_set_o )
% 4.69/5.02 => ( ( condit5413489452508810728elow_o @ A )
% 4.69/5.02 => ( ! [B2: $o] :
% 4.69/5.02 ( ( member_o @ B2 @ B4 )
% 4.69/5.02 => ? [X6: $o] :
% 4.69/5.02 ( ( member_o @ X6 @ A )
% 4.69/5.02 & ( ord_less_eq_o @ X6 @ B2 ) ) )
% 4.69/5.02 => ( ord_less_eq_o @ ( complete_Inf_Inf_o @ A ) @ ( complete_Inf_Inf_o @ B4 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_mono
% 4.69/5.02 thf(fact_6325_cInf__mono,axiom,
% 4.69/5.02 ! [B4: set_Pr4532377907799695533_nat_o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/5.02 ( ( B4 != bot_bo7824918357723582233_nat_o )
% 4.69/5.02 => ( ( condit8399017556247434269_nat_o @ A )
% 4.69/5.02 => ( ! [B2: produc3658429121746597890et_nat > $o] :
% 4.69/5.02 ( ( member6576561426505652726_nat_o @ B2 @ B4 )
% 4.69/5.02 => ? [X6: produc3658429121746597890et_nat > $o] :
% 4.69/5.02 ( ( member6576561426505652726_nat_o @ X6 @ A )
% 4.69/5.02 & ( ord_le729326519192465773_nat_o @ X6 @ B2 ) ) )
% 4.69/5.02 => ( ord_le729326519192465773_nat_o @ ( comple90455603224345172_nat_o @ A ) @ ( comple90455603224345172_nat_o @ B4 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_mono
% 4.69/5.02 thf(fact_6326_cInf__mono,axiom,
% 4.69/5.02 ! [B4: set_filter_nat,A: set_filter_nat] :
% 4.69/5.02 ( ( B4 != bot_bo498966703094740906er_nat )
% 4.69/5.02 => ( ( condit3133331395780078992er_nat @ A )
% 4.69/5.02 => ( ! [B2: filter_nat] :
% 4.69/5.02 ( ( member_filter_nat @ B2 @ B4 )
% 4.69/5.02 => ? [X6: filter_nat] :
% 4.69/5.02 ( ( member_filter_nat @ X6 @ A )
% 4.69/5.02 & ( ord_le2510731241096832064er_nat @ X6 @ B2 ) ) )
% 4.69/5.02 => ( ord_le2510731241096832064er_nat @ ( comple6612786467464916249er_nat @ A ) @ ( comple6612786467464916249er_nat @ B4 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_mono
% 4.69/5.02 thf(fact_6327_cInf__mono,axiom,
% 4.69/5.02 ! [B4: set_int,A: set_int] :
% 4.69/5.02 ( ( B4 != bot_bot_set_int )
% 4.69/5.02 => ( ( condit1735850657277959132ow_int @ A )
% 4.69/5.02 => ( ! [B2: int] :
% 4.69/5.02 ( ( member_int @ B2 @ B4 )
% 4.69/5.02 => ? [X6: int] :
% 4.69/5.02 ( ( member_int @ X6 @ A )
% 4.69/5.02 & ( ord_less_eq_int @ X6 @ B2 ) ) )
% 4.69/5.02 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ A ) @ ( complete_Inf_Inf_int @ B4 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_mono
% 4.69/5.02 thf(fact_6328_cInf__mono,axiom,
% 4.69/5.02 ! [B4: set_nat,A: set_nat] :
% 4.69/5.02 ( ( B4 != bot_bot_set_nat )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ A )
% 4.69/5.02 => ( ! [B2: nat] :
% 4.69/5.02 ( ( member_nat @ B2 @ B4 )
% 4.69/5.02 => ? [X6: nat] :
% 4.69/5.02 ( ( member_nat @ X6 @ A )
% 4.69/5.02 & ( ord_less_eq_nat @ X6 @ B2 ) ) )
% 4.69/5.02 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ A ) @ ( complete_Inf_Inf_nat @ B4 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_mono
% 4.69/5.02 thf(fact_6329_cInf__mono,axiom,
% 4.69/5.02 ! [B4: set_set_nat,A: set_set_nat] :
% 4.69/5.02 ( ( B4 != bot_bot_set_set_nat )
% 4.69/5.02 => ( ( condit68592940725977398et_nat @ A )
% 4.69/5.02 => ( ! [B2: set_nat] :
% 4.69/5.02 ( ( member_set_nat @ B2 @ B4 )
% 4.69/5.02 => ? [X6: set_nat] :
% 4.69/5.02 ( ( member_set_nat @ X6 @ A )
% 4.69/5.02 & ( ord_less_eq_set_nat @ X6 @ B2 ) ) )
% 4.69/5.02 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ A ) @ ( comple7806235888213564991et_nat @ B4 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_mono
% 4.69/5.02 thf(fact_6330_cInf__mono,axiom,
% 4.69/5.02 ! [B4: set_Product_unit,A: set_Product_unit] :
% 4.69/5.02 ( ( B4 != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ A )
% 4.69/5.02 => ( ! [B2: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ B2 @ B4 )
% 4.69/5.02 => ? [X6: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ X6 @ A )
% 4.69/5.02 & ( ord_le3221252021190050221t_unit @ X6 @ B2 ) ) )
% 4.69/5.02 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ A ) @ ( comple2584293577114468500t_unit @ B4 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_mono
% 4.69/5.02 thf(fact_6331_le__cInf__iff,axiom,
% 4.69/5.02 ! [S: set_o,A2: $o] :
% 4.69/5.02 ( ( S != bot_bot_set_o )
% 4.69/5.02 => ( ( condit5413489452508810728elow_o @ S )
% 4.69/5.02 => ( ( ord_less_eq_o @ A2 @ ( complete_Inf_Inf_o @ S ) )
% 4.69/5.02 = ( ! [X2: $o] :
% 4.69/5.02 ( ( member_o @ X2 @ S )
% 4.69/5.02 => ( ord_less_eq_o @ A2 @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % le_cInf_iff
% 4.69/5.02 thf(fact_6332_le__cInf__iff,axiom,
% 4.69/5.02 ! [S: set_Pr4532377907799695533_nat_o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/5.02 ( ( S != bot_bo7824918357723582233_nat_o )
% 4.69/5.02 => ( ( condit8399017556247434269_nat_o @ S )
% 4.69/5.02 => ( ( ord_le729326519192465773_nat_o @ A2 @ ( comple90455603224345172_nat_o @ S ) )
% 4.69/5.02 = ( ! [X2: produc3658429121746597890et_nat > $o] :
% 4.69/5.02 ( ( member6576561426505652726_nat_o @ X2 @ S )
% 4.69/5.02 => ( ord_le729326519192465773_nat_o @ A2 @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % le_cInf_iff
% 4.69/5.02 thf(fact_6333_le__cInf__iff,axiom,
% 4.69/5.02 ! [S: set_filter_nat,A2: filter_nat] :
% 4.69/5.02 ( ( S != bot_bo498966703094740906er_nat )
% 4.69/5.02 => ( ( condit3133331395780078992er_nat @ S )
% 4.69/5.02 => ( ( ord_le2510731241096832064er_nat @ A2 @ ( comple6612786467464916249er_nat @ S ) )
% 4.69/5.02 = ( ! [X2: filter_nat] :
% 4.69/5.02 ( ( member_filter_nat @ X2 @ S )
% 4.69/5.02 => ( ord_le2510731241096832064er_nat @ A2 @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % le_cInf_iff
% 4.69/5.02 thf(fact_6334_le__cInf__iff,axiom,
% 4.69/5.02 ! [S: set_int,A2: int] :
% 4.69/5.02 ( ( S != bot_bot_set_int )
% 4.69/5.02 => ( ( condit1735850657277959132ow_int @ S )
% 4.69/5.02 => ( ( ord_less_eq_int @ A2 @ ( complete_Inf_Inf_int @ S ) )
% 4.69/5.02 = ( ! [X2: int] :
% 4.69/5.02 ( ( member_int @ X2 @ S )
% 4.69/5.02 => ( ord_less_eq_int @ A2 @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % le_cInf_iff
% 4.69/5.02 thf(fact_6335_le__cInf__iff,axiom,
% 4.69/5.02 ! [S: set_nat,A2: nat] :
% 4.69/5.02 ( ( S != bot_bot_set_nat )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ S )
% 4.69/5.02 => ( ( ord_less_eq_nat @ A2 @ ( complete_Inf_Inf_nat @ S ) )
% 4.69/5.02 = ( ! [X2: nat] :
% 4.69/5.02 ( ( member_nat @ X2 @ S )
% 4.69/5.02 => ( ord_less_eq_nat @ A2 @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % le_cInf_iff
% 4.69/5.02 thf(fact_6336_le__cInf__iff,axiom,
% 4.69/5.02 ! [S: set_set_nat,A2: set_nat] :
% 4.69/5.02 ( ( S != bot_bot_set_set_nat )
% 4.69/5.02 => ( ( condit68592940725977398et_nat @ S )
% 4.69/5.02 => ( ( ord_less_eq_set_nat @ A2 @ ( comple7806235888213564991et_nat @ S ) )
% 4.69/5.02 = ( ! [X2: set_nat] :
% 4.69/5.02 ( ( member_set_nat @ X2 @ S )
% 4.69/5.02 => ( ord_less_eq_set_nat @ A2 @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % le_cInf_iff
% 4.69/5.02 thf(fact_6337_le__cInf__iff,axiom,
% 4.69/5.02 ! [S: set_Product_unit,A2: product_unit] :
% 4.69/5.02 ( ( S != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ S )
% 4.69/5.02 => ( ( ord_le3221252021190050221t_unit @ A2 @ ( comple2584293577114468500t_unit @ S ) )
% 4.69/5.02 = ( ! [X2: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ X2 @ S )
% 4.69/5.02 => ( ord_le3221252021190050221t_unit @ A2 @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % le_cInf_iff
% 4.69/5.02 thf(fact_6338_cInf__less__iff,axiom,
% 4.69/5.02 ! [X4: set_int,Y: int] :
% 4.69/5.02 ( ( X4 != bot_bot_set_int )
% 4.69/5.02 => ( ( condit1735850657277959132ow_int @ X4 )
% 4.69/5.02 => ( ( ord_less_int @ ( complete_Inf_Inf_int @ X4 ) @ Y )
% 4.69/5.02 = ( ? [X2: int] :
% 4.69/5.02 ( ( member_int @ X2 @ X4 )
% 4.69/5.02 & ( ord_less_int @ X2 @ Y ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_less_iff
% 4.69/5.02 thf(fact_6339_cInf__less__iff,axiom,
% 4.69/5.02 ! [X4: set_nat,Y: nat] :
% 4.69/5.02 ( ( X4 != bot_bot_set_nat )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ X4 )
% 4.69/5.02 => ( ( ord_less_nat @ ( complete_Inf_Inf_nat @ X4 ) @ Y )
% 4.69/5.02 = ( ? [X2: nat] :
% 4.69/5.02 ( ( member_nat @ X2 @ X4 )
% 4.69/5.02 & ( ord_less_nat @ X2 @ Y ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_less_iff
% 4.69/5.02 thf(fact_6340_cInf__less__iff,axiom,
% 4.69/5.02 ! [X4: set_Product_unit,Y: product_unit] :
% 4.69/5.02 ( ( X4 != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ X4 )
% 4.69/5.02 => ( ( ord_le361264281704409273t_unit @ ( comple2584293577114468500t_unit @ X4 ) @ Y )
% 4.69/5.02 = ( ? [X2: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ X2 @ X4 )
% 4.69/5.02 & ( ord_le361264281704409273t_unit @ X2 @ Y ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_less_iff
% 4.69/5.02 thf(fact_6341_dvd__mult__cancel,axiom,
% 4.69/5.02 ! [K3: nat,M4: nat,N2: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ ( times_times_nat @ K3 @ M4 ) @ ( times_times_nat @ K3 @ N2 ) )
% 4.69/5.02 => ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 4.69/5.02 => ( dvd_dvd_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_cancel
% 4.69/5.02 thf(fact_6342_nat__mult__dvd__cancel1,axiom,
% 4.69/5.02 ! [K3: nat,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 4.69/5.02 => ( ( dvd_dvd_nat @ ( times_times_nat @ K3 @ M4 ) @ ( times_times_nat @ K3 @ N2 ) )
% 4.69/5.02 = ( dvd_dvd_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % nat_mult_dvd_cancel1
% 4.69/5.02 thf(fact_6343_power__Suc__less,axiom,
% 4.69/5.02 ! [A2: code_natural,N2: nat] :
% 4.69/5.02 ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A2 )
% 4.69/5.02 => ( ( ord_le5570908160329646204atural @ A2 @ one_one_Code_natural )
% 4.69/5.02 => ( ord_le5570908160329646204atural @ ( times_2397367101498566445atural @ A2 @ ( power_7079662738309270450atural @ A2 @ N2 ) ) @ ( power_7079662738309270450atural @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc_less
% 4.69/5.02 thf(fact_6344_power__Suc__less,axiom,
% 4.69/5.02 ! [A2: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 4.69/5.02 => ( ( ord_less_nat @ A2 @ one_one_nat )
% 4.69/5.02 => ( ord_less_nat @ ( times_times_nat @ A2 @ ( power_power_nat @ A2 @ N2 ) ) @ ( power_power_nat @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc_less
% 4.69/5.02 thf(fact_6345_power__Suc__less,axiom,
% 4.69/5.02 ! [A2: int,N2: nat] :
% 4.69/5.02 ( ( ord_less_int @ zero_zero_int @ A2 )
% 4.69/5.02 => ( ( ord_less_int @ A2 @ one_one_int )
% 4.69/5.02 => ( ord_less_int @ ( times_times_int @ A2 @ ( power_power_int @ A2 @ N2 ) ) @ ( power_power_int @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc_less
% 4.69/5.02 thf(fact_6346_power__Suc__less,axiom,
% 4.69/5.02 ! [A2: code_integer,N2: nat] :
% 4.69/5.02 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.02 => ( ( ord_le6747313008572928689nteger @ A2 @ one_one_Code_integer )
% 4.69/5.02 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A2 @ ( power_8256067586552552935nteger @ A2 @ N2 ) ) @ ( power_8256067586552552935nteger @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc_less
% 4.69/5.02 thf(fact_6347_power__Suc__less,axiom,
% 4.69/5.02 ! [A2: rat,N2: nat] :
% 4.69/5.02 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 4.69/5.02 => ( ( ord_less_rat @ A2 @ one_one_rat )
% 4.69/5.02 => ( ord_less_rat @ ( times_times_rat @ A2 @ ( power_power_rat @ A2 @ N2 ) ) @ ( power_power_rat @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc_less
% 4.69/5.02 thf(fact_6348_power__Suc__le__self,axiom,
% 4.69/5.02 ! [A2: code_natural,N2: nat] :
% 4.69/5.02 ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A2 )
% 4.69/5.02 => ( ( ord_le1926595141338095240atural @ A2 @ one_one_Code_natural )
% 4.69/5.02 => ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A2 @ ( suc @ N2 ) ) @ A2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc_le_self
% 4.69/5.02 thf(fact_6349_power__Suc__le__self,axiom,
% 4.69/5.02 ! [A2: code_integer,N2: nat] :
% 4.69/5.02 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.02 => ( ( ord_le3102999989581377725nteger @ A2 @ one_one_Code_integer )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A2 @ ( suc @ N2 ) ) @ A2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc_le_self
% 4.69/5.02 thf(fact_6350_power__Suc__le__self,axiom,
% 4.69/5.02 ! [A2: rat,N2: nat] :
% 4.69/5.02 ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 4.69/5.02 => ( ( ord_less_eq_rat @ A2 @ one_one_rat )
% 4.69/5.02 => ( ord_less_eq_rat @ ( power_power_rat @ A2 @ ( suc @ N2 ) ) @ A2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc_le_self
% 4.69/5.02 thf(fact_6351_power__Suc__le__self,axiom,
% 4.69/5.02 ! [A2: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 4.69/5.02 => ( ( ord_less_eq_nat @ A2 @ one_one_nat )
% 4.69/5.02 => ( ord_less_eq_nat @ ( power_power_nat @ A2 @ ( suc @ N2 ) ) @ A2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc_le_self
% 4.69/5.02 thf(fact_6352_power__Suc__le__self,axiom,
% 4.69/5.02 ! [A2: int,N2: nat] :
% 4.69/5.02 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 4.69/5.02 => ( ( ord_less_eq_int @ A2 @ one_one_int )
% 4.69/5.02 => ( ord_less_eq_int @ ( power_power_int @ A2 @ ( suc @ N2 ) ) @ A2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc_le_self
% 4.69/5.02 thf(fact_6353_power__Suc__less__one,axiom,
% 4.69/5.02 ! [A2: code_natural,N2: nat] :
% 4.69/5.02 ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A2 )
% 4.69/5.02 => ( ( ord_le5570908160329646204atural @ A2 @ one_one_Code_natural )
% 4.69/5.02 => ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ A2 @ ( suc @ N2 ) ) @ one_one_Code_natural ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc_less_one
% 4.69/5.02 thf(fact_6354_power__Suc__less__one,axiom,
% 4.69/5.02 ! [A2: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 4.69/5.02 => ( ( ord_less_nat @ A2 @ one_one_nat )
% 4.69/5.02 => ( ord_less_nat @ ( power_power_nat @ A2 @ ( suc @ N2 ) ) @ one_one_nat ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc_less_one
% 4.69/5.02 thf(fact_6355_power__Suc__less__one,axiom,
% 4.69/5.02 ! [A2: int,N2: nat] :
% 4.69/5.02 ( ( ord_less_int @ zero_zero_int @ A2 )
% 4.69/5.02 => ( ( ord_less_int @ A2 @ one_one_int )
% 4.69/5.02 => ( ord_less_int @ ( power_power_int @ A2 @ ( suc @ N2 ) ) @ one_one_int ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc_less_one
% 4.69/5.02 thf(fact_6356_power__Suc__less__one,axiom,
% 4.69/5.02 ! [A2: code_integer,N2: nat] :
% 4.69/5.02 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.02 => ( ( ord_le6747313008572928689nteger @ A2 @ one_one_Code_integer )
% 4.69/5.02 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A2 @ ( suc @ N2 ) ) @ one_one_Code_integer ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc_less_one
% 4.69/5.02 thf(fact_6357_power__Suc__less__one,axiom,
% 4.69/5.02 ! [A2: rat,N2: nat] :
% 4.69/5.02 ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 4.69/5.02 => ( ( ord_less_rat @ A2 @ one_one_rat )
% 4.69/5.02 => ( ord_less_rat @ ( power_power_rat @ A2 @ ( suc @ N2 ) ) @ one_one_rat ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_Suc_less_one
% 4.69/5.02 thf(fact_6358_power__strict__decreasing,axiom,
% 4.69/5.02 ! [N2: nat,N: nat,A2: code_natural] :
% 4.69/5.02 ( ( ord_less_nat @ N2 @ N )
% 4.69/5.02 => ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ A2 )
% 4.69/5.02 => ( ( ord_le5570908160329646204atural @ A2 @ one_one_Code_natural )
% 4.69/5.02 => ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ A2 @ N ) @ ( power_7079662738309270450atural @ A2 @ N2 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_strict_decreasing
% 4.69/5.02 thf(fact_6359_power__strict__decreasing,axiom,
% 4.69/5.02 ! [N2: nat,N: nat,A2: nat] :
% 4.69/5.02 ( ( ord_less_nat @ N2 @ N )
% 4.69/5.02 => ( ( ord_less_nat @ zero_zero_nat @ A2 )
% 4.69/5.02 => ( ( ord_less_nat @ A2 @ one_one_nat )
% 4.69/5.02 => ( ord_less_nat @ ( power_power_nat @ A2 @ N ) @ ( power_power_nat @ A2 @ N2 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_strict_decreasing
% 4.69/5.02 thf(fact_6360_power__strict__decreasing,axiom,
% 4.69/5.02 ! [N2: nat,N: nat,A2: int] :
% 4.69/5.02 ( ( ord_less_nat @ N2 @ N )
% 4.69/5.02 => ( ( ord_less_int @ zero_zero_int @ A2 )
% 4.69/5.02 => ( ( ord_less_int @ A2 @ one_one_int )
% 4.69/5.02 => ( ord_less_int @ ( power_power_int @ A2 @ N ) @ ( power_power_int @ A2 @ N2 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_strict_decreasing
% 4.69/5.02 thf(fact_6361_power__strict__decreasing,axiom,
% 4.69/5.02 ! [N2: nat,N: nat,A2: code_integer] :
% 4.69/5.02 ( ( ord_less_nat @ N2 @ N )
% 4.69/5.02 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.02 => ( ( ord_le6747313008572928689nteger @ A2 @ one_one_Code_integer )
% 4.69/5.02 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ ( power_8256067586552552935nteger @ A2 @ N2 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_strict_decreasing
% 4.69/5.02 thf(fact_6362_power__strict__decreasing,axiom,
% 4.69/5.02 ! [N2: nat,N: nat,A2: rat] :
% 4.69/5.02 ( ( ord_less_nat @ N2 @ N )
% 4.69/5.02 => ( ( ord_less_rat @ zero_zero_rat @ A2 )
% 4.69/5.02 => ( ( ord_less_rat @ A2 @ one_one_rat )
% 4.69/5.02 => ( ord_less_rat @ ( power_power_rat @ A2 @ N ) @ ( power_power_rat @ A2 @ N2 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_strict_decreasing
% 4.69/5.02 thf(fact_6363_power__decreasing,axiom,
% 4.69/5.02 ! [N2: nat,N: nat,A2: code_natural] :
% 4.69/5.02 ( ( ord_less_eq_nat @ N2 @ N )
% 4.69/5.02 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ A2 )
% 4.69/5.02 => ( ( ord_le1926595141338095240atural @ A2 @ one_one_Code_natural )
% 4.69/5.02 => ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A2 @ N ) @ ( power_7079662738309270450atural @ A2 @ N2 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_decreasing
% 4.69/5.02 thf(fact_6364_power__decreasing,axiom,
% 4.69/5.02 ! [N2: nat,N: nat,A2: code_integer] :
% 4.69/5.02 ( ( ord_less_eq_nat @ N2 @ N )
% 4.69/5.02 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.02 => ( ( ord_le3102999989581377725nteger @ A2 @ one_one_Code_integer )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A2 @ N ) @ ( power_8256067586552552935nteger @ A2 @ N2 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_decreasing
% 4.69/5.02 thf(fact_6365_power__decreasing,axiom,
% 4.69/5.02 ! [N2: nat,N: nat,A2: rat] :
% 4.69/5.02 ( ( ord_less_eq_nat @ N2 @ N )
% 4.69/5.02 => ( ( ord_less_eq_rat @ zero_zero_rat @ A2 )
% 4.69/5.02 => ( ( ord_less_eq_rat @ A2 @ one_one_rat )
% 4.69/5.02 => ( ord_less_eq_rat @ ( power_power_rat @ A2 @ N ) @ ( power_power_rat @ A2 @ N2 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_decreasing
% 4.69/5.02 thf(fact_6366_power__decreasing,axiom,
% 4.69/5.02 ! [N2: nat,N: nat,A2: nat] :
% 4.69/5.02 ( ( ord_less_eq_nat @ N2 @ N )
% 4.69/5.02 => ( ( ord_less_eq_nat @ zero_zero_nat @ A2 )
% 4.69/5.02 => ( ( ord_less_eq_nat @ A2 @ one_one_nat )
% 4.69/5.02 => ( ord_less_eq_nat @ ( power_power_nat @ A2 @ N ) @ ( power_power_nat @ A2 @ N2 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_decreasing
% 4.69/5.02 thf(fact_6367_power__decreasing,axiom,
% 4.69/5.02 ! [N2: nat,N: nat,A2: int] :
% 4.69/5.02 ( ( ord_less_eq_nat @ N2 @ N )
% 4.69/5.02 => ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 4.69/5.02 => ( ( ord_less_eq_int @ A2 @ one_one_int )
% 4.69/5.02 => ( ord_less_eq_int @ ( power_power_int @ A2 @ N ) @ ( power_power_int @ A2 @ N2 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_decreasing
% 4.69/5.02 thf(fact_6368_power__le__imp__le__exp,axiom,
% 4.69/5.02 ! [A2: code_natural,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A2 )
% 4.69/5.02 => ( ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ A2 @ M4 ) @ ( power_7079662738309270450atural @ A2 @ N2 ) )
% 4.69/5.02 => ( ord_less_eq_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_le_imp_le_exp
% 4.69/5.02 thf(fact_6369_power__le__imp__le__exp,axiom,
% 4.69/5.02 ! [A2: code_integer,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A2 )
% 4.69/5.02 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A2 @ M4 ) @ ( power_8256067586552552935nteger @ A2 @ N2 ) )
% 4.69/5.02 => ( ord_less_eq_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_le_imp_le_exp
% 4.69/5.02 thf(fact_6370_power__le__imp__le__exp,axiom,
% 4.69/5.02 ! [A2: rat,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_rat @ one_one_rat @ A2 )
% 4.69/5.02 => ( ( ord_less_eq_rat @ ( power_power_rat @ A2 @ M4 ) @ ( power_power_rat @ A2 @ N2 ) )
% 4.69/5.02 => ( ord_less_eq_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_le_imp_le_exp
% 4.69/5.02 thf(fact_6371_power__le__imp__le__exp,axiom,
% 4.69/5.02 ! [A2: nat,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_nat @ one_one_nat @ A2 )
% 4.69/5.02 => ( ( ord_less_eq_nat @ ( power_power_nat @ A2 @ M4 ) @ ( power_power_nat @ A2 @ N2 ) )
% 4.69/5.02 => ( ord_less_eq_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_le_imp_le_exp
% 4.69/5.02 thf(fact_6372_power__le__imp__le__exp,axiom,
% 4.69/5.02 ! [A2: int,M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_int @ one_one_int @ A2 )
% 4.69/5.02 => ( ( ord_less_eq_int @ ( power_power_int @ A2 @ M4 ) @ ( power_power_int @ A2 @ N2 ) )
% 4.69/5.02 => ( ord_less_eq_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_le_imp_le_exp
% 4.69/5.02 thf(fact_6373_self__le__power,axiom,
% 4.69/5.02 ! [A2: code_integer,N2: nat] :
% 4.69/5.02 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A2 )
% 4.69/5.02 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ A2 @ ( power_8256067586552552935nteger @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % self_le_power
% 4.69/5.02 thf(fact_6374_self__le__power,axiom,
% 4.69/5.02 ! [A2: code_natural,N2: nat] :
% 4.69/5.02 ( ( ord_le1926595141338095240atural @ one_one_Code_natural @ A2 )
% 4.69/5.02 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.02 => ( ord_le1926595141338095240atural @ A2 @ ( power_7079662738309270450atural @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % self_le_power
% 4.69/5.02 thf(fact_6375_self__le__power,axiom,
% 4.69/5.02 ! [A2: rat,N2: nat] :
% 4.69/5.02 ( ( ord_less_eq_rat @ one_one_rat @ A2 )
% 4.69/5.02 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.02 => ( ord_less_eq_rat @ A2 @ ( power_power_rat @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % self_le_power
% 4.69/5.02 thf(fact_6376_self__le__power,axiom,
% 4.69/5.02 ! [A2: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_eq_nat @ one_one_nat @ A2 )
% 4.69/5.02 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.02 => ( ord_less_eq_nat @ A2 @ ( power_power_nat @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % self_le_power
% 4.69/5.02 thf(fact_6377_self__le__power,axiom,
% 4.69/5.02 ! [A2: int,N2: nat] :
% 4.69/5.02 ( ( ord_less_eq_int @ one_one_int @ A2 )
% 4.69/5.02 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.02 => ( ord_less_eq_int @ A2 @ ( power_power_int @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % self_le_power
% 4.69/5.02 thf(fact_6378_one__less__power,axiom,
% 4.69/5.02 ! [A2: code_natural,N2: nat] :
% 4.69/5.02 ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ A2 )
% 4.69/5.02 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.02 => ( ord_le5570908160329646204atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % one_less_power
% 4.69/5.02 thf(fact_6379_one__less__power,axiom,
% 4.69/5.02 ! [A2: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_nat @ one_one_nat @ A2 )
% 4.69/5.02 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.02 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % one_less_power
% 4.69/5.02 thf(fact_6380_one__less__power,axiom,
% 4.69/5.02 ! [A2: int,N2: nat] :
% 4.69/5.02 ( ( ord_less_int @ one_one_int @ A2 )
% 4.69/5.02 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.02 => ( ord_less_int @ one_one_int @ ( power_power_int @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % one_less_power
% 4.69/5.02 thf(fact_6381_one__less__power,axiom,
% 4.69/5.02 ! [A2: code_integer,N2: nat] :
% 4.69/5.02 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A2 )
% 4.69/5.02 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.02 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % one_less_power
% 4.69/5.02 thf(fact_6382_one__less__power,axiom,
% 4.69/5.02 ! [A2: rat,N2: nat] :
% 4.69/5.02 ( ( ord_less_rat @ one_one_rat @ A2 )
% 4.69/5.02 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.02 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A2 @ N2 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % one_less_power
% 4.69/5.02 thf(fact_6383_cINF__mono,axiom,
% 4.69/5.02 ! [B4: set_Product_unit,F: nat > nat,A: set_nat,G: product_unit > nat] :
% 4.69/5.02 ( ( B4 != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat2 @ F @ A ) )
% 4.69/5.02 => ( ! [M2: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ M2 @ B4 )
% 4.69/5.02 => ? [X6: nat] :
% 4.69/5.02 ( ( member_nat @ X6 @ A )
% 4.69/5.02 & ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ M2 ) ) ) )
% 4.69/5.02 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat2 @ F @ A ) ) @ ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_mono
% 4.69/5.02 thf(fact_6384_cINF__mono,axiom,
% 4.69/5.02 ! [B4: set_o,F: nat > nat,A: set_nat,G: $o > nat] :
% 4.69/5.02 ( ( B4 != bot_bot_set_o )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat2 @ F @ A ) )
% 4.69/5.02 => ( ! [M2: $o] :
% 4.69/5.02 ( ( member_o @ M2 @ B4 )
% 4.69/5.02 => ? [X6: nat] :
% 4.69/5.02 ( ( member_nat @ X6 @ A )
% 4.69/5.02 & ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ M2 ) ) ) )
% 4.69/5.02 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat2 @ F @ A ) ) @ ( complete_Inf_Inf_nat @ ( image_o_nat2 @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_mono
% 4.69/5.02 thf(fact_6385_cINF__mono,axiom,
% 4.69/5.02 ! [B4: set_nat,F: nat > nat,A: set_nat,G: nat > nat] :
% 4.69/5.02 ( ( B4 != bot_bot_set_nat )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat2 @ F @ A ) )
% 4.69/5.02 => ( ! [M2: nat] :
% 4.69/5.02 ( ( member_nat @ M2 @ B4 )
% 4.69/5.02 => ? [X6: nat] :
% 4.69/5.02 ( ( member_nat @ X6 @ A )
% 4.69/5.02 & ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ M2 ) ) ) )
% 4.69/5.02 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat2 @ F @ A ) ) @ ( complete_Inf_Inf_nat @ ( image_nat_nat2 @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_mono
% 4.69/5.02 thf(fact_6386_cINF__mono,axiom,
% 4.69/5.02 ! [B4: set_int,F: nat > nat,A: set_nat,G: int > nat] :
% 4.69/5.02 ( ( B4 != bot_bot_set_int )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat2 @ F @ A ) )
% 4.69/5.02 => ( ! [M2: int] :
% 4.69/5.02 ( ( member_int @ M2 @ B4 )
% 4.69/5.02 => ? [X6: nat] :
% 4.69/5.02 ( ( member_nat @ X6 @ A )
% 4.69/5.02 & ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ M2 ) ) ) )
% 4.69/5.02 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat2 @ F @ A ) ) @ ( complete_Inf_Inf_nat @ ( image_int_nat2 @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_mono
% 4.69/5.02 thf(fact_6387_cINF__mono,axiom,
% 4.69/5.02 ! [B4: set_Pr4532377907799695533_nat_o,F: nat > nat,A: set_nat,G: ( produc3658429121746597890et_nat > $o ) > nat] :
% 4.69/5.02 ( ( B4 != bot_bo7824918357723582233_nat_o )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat2 @ F @ A ) )
% 4.69/5.02 => ( ! [M2: produc3658429121746597890et_nat > $o] :
% 4.69/5.02 ( ( member6576561426505652726_nat_o @ M2 @ B4 )
% 4.69/5.02 => ? [X6: nat] :
% 4.69/5.02 ( ( member_nat @ X6 @ A )
% 4.69/5.02 & ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ M2 ) ) ) )
% 4.69/5.02 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat2 @ F @ A ) ) @ ( complete_Inf_Inf_nat @ ( image_2174381888560928856_o_nat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_mono
% 4.69/5.02 thf(fact_6388_cINF__mono,axiom,
% 4.69/5.02 ! [B4: set_Product_unit,F: nat > set_nat,A: set_nat,G: product_unit > set_nat] :
% 4.69/5.02 ( ( B4 != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit68592940725977398et_nat @ ( image_nat_set_nat @ F @ A ) )
% 4.69/5.02 => ( ! [M2: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ M2 @ B4 )
% 4.69/5.02 => ? [X6: nat] :
% 4.69/5.02 ( ( member_nat @ X6 @ A )
% 4.69/5.02 & ( ord_less_eq_set_nat @ ( F @ X6 ) @ ( G @ M2 ) ) ) )
% 4.69/5.02 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A ) ) @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_mono
% 4.69/5.02 thf(fact_6389_cINF__mono,axiom,
% 4.69/5.02 ! [B4: set_o,F: nat > set_nat,A: set_nat,G: $o > set_nat] :
% 4.69/5.02 ( ( B4 != bot_bot_set_o )
% 4.69/5.02 => ( ( condit68592940725977398et_nat @ ( image_nat_set_nat @ F @ A ) )
% 4.69/5.02 => ( ! [M2: $o] :
% 4.69/5.02 ( ( member_o @ M2 @ B4 )
% 4.69/5.02 => ? [X6: nat] :
% 4.69/5.02 ( ( member_nat @ X6 @ A )
% 4.69/5.02 & ( ord_less_eq_set_nat @ ( F @ X6 ) @ ( G @ M2 ) ) ) )
% 4.69/5.02 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A ) ) @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_mono
% 4.69/5.02 thf(fact_6390_cINF__mono,axiom,
% 4.69/5.02 ! [B4: set_nat,F: nat > set_nat,A: set_nat,G: nat > set_nat] :
% 4.69/5.02 ( ( B4 != bot_bot_set_nat )
% 4.69/5.02 => ( ( condit68592940725977398et_nat @ ( image_nat_set_nat @ F @ A ) )
% 4.69/5.02 => ( ! [M2: nat] :
% 4.69/5.02 ( ( member_nat @ M2 @ B4 )
% 4.69/5.02 => ? [X6: nat] :
% 4.69/5.02 ( ( member_nat @ X6 @ A )
% 4.69/5.02 & ( ord_less_eq_set_nat @ ( F @ X6 ) @ ( G @ M2 ) ) ) )
% 4.69/5.02 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A ) ) @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_mono
% 4.69/5.02 thf(fact_6391_cINF__mono,axiom,
% 4.69/5.02 ! [B4: set_int,F: nat > set_nat,A: set_nat,G: int > set_nat] :
% 4.69/5.02 ( ( B4 != bot_bot_set_int )
% 4.69/5.02 => ( ( condit68592940725977398et_nat @ ( image_nat_set_nat @ F @ A ) )
% 4.69/5.02 => ( ! [M2: int] :
% 4.69/5.02 ( ( member_int @ M2 @ B4 )
% 4.69/5.02 => ? [X6: nat] :
% 4.69/5.02 ( ( member_nat @ X6 @ A )
% 4.69/5.02 & ( ord_less_eq_set_nat @ ( F @ X6 ) @ ( G @ M2 ) ) ) )
% 4.69/5.02 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A ) ) @ ( comple7806235888213564991et_nat @ ( image_int_set_nat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_mono
% 4.69/5.02 thf(fact_6392_cINF__mono,axiom,
% 4.69/5.02 ! [B4: set_Pr4532377907799695533_nat_o,F: nat > set_nat,A: set_nat,G: ( produc3658429121746597890et_nat > $o ) > set_nat] :
% 4.69/5.02 ( ( B4 != bot_bo7824918357723582233_nat_o )
% 4.69/5.02 => ( ( condit68592940725977398et_nat @ ( image_nat_set_nat @ F @ A ) )
% 4.69/5.02 => ( ! [M2: produc3658429121746597890et_nat > $o] :
% 4.69/5.02 ( ( member6576561426505652726_nat_o @ M2 @ B4 )
% 4.69/5.02 => ? [X6: nat] :
% 4.69/5.02 ( ( member_nat @ X6 @ A )
% 4.69/5.02 & ( ord_less_eq_set_nat @ ( F @ X6 ) @ ( G @ M2 ) ) ) )
% 4.69/5.02 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ F @ A ) ) @ ( comple7806235888213564991et_nat @ ( image_6888641473154130958et_nat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_mono
% 4.69/5.02 thf(fact_6393_le__cINF__iff,axiom,
% 4.69/5.02 ! [A: set_Product_unit,F: product_unit > int,U: int] :
% 4.69/5.02 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit1735850657277959132ow_int @ ( image_873079544045703924it_int @ F @ A ) )
% 4.69/5.02 => ( ( ord_less_eq_int @ U @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ A ) ) )
% 4.69/5.02 = ( ! [X2: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ X2 @ A )
% 4.69/5.02 => ( ord_less_eq_int @ U @ ( F @ X2 ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % le_cINF_iff
% 4.69/5.02 thf(fact_6394_le__cINF__iff,axiom,
% 4.69/5.02 ! [A: set_o,F: $o > int,U: int] :
% 4.69/5.02 ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( condit1735850657277959132ow_int @ ( image_o_int2 @ F @ A ) )
% 4.69/5.02 => ( ( ord_less_eq_int @ U @ ( complete_Inf_Inf_int @ ( image_o_int2 @ F @ A ) ) )
% 4.69/5.02 = ( ! [X2: $o] :
% 4.69/5.02 ( ( member_o @ X2 @ A )
% 4.69/5.02 => ( ord_less_eq_int @ U @ ( F @ X2 ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % le_cINF_iff
% 4.69/5.02 thf(fact_6395_le__cINF__iff,axiom,
% 4.69/5.02 ! [A: set_nat,F: nat > int,U: int] :
% 4.69/5.02 ( ( A != bot_bot_set_nat )
% 4.69/5.02 => ( ( condit1735850657277959132ow_int @ ( image_nat_int2 @ F @ A ) )
% 4.69/5.02 => ( ( ord_less_eq_int @ U @ ( complete_Inf_Inf_int @ ( image_nat_int2 @ F @ A ) ) )
% 4.69/5.02 = ( ! [X2: nat] :
% 4.69/5.02 ( ( member_nat @ X2 @ A )
% 4.69/5.02 => ( ord_less_eq_int @ U @ ( F @ X2 ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % le_cINF_iff
% 4.69/5.02 thf(fact_6396_le__cINF__iff,axiom,
% 4.69/5.02 ! [A: set_int,F: int > int,U: int] :
% 4.69/5.02 ( ( A != bot_bot_set_int )
% 4.69/5.02 => ( ( condit1735850657277959132ow_int @ ( image_int_int2 @ F @ A ) )
% 4.69/5.02 => ( ( ord_less_eq_int @ U @ ( complete_Inf_Inf_int @ ( image_int_int2 @ F @ A ) ) )
% 4.69/5.02 = ( ! [X2: int] :
% 4.69/5.02 ( ( member_int @ X2 @ A )
% 4.69/5.02 => ( ord_less_eq_int @ U @ ( F @ X2 ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % le_cINF_iff
% 4.69/5.02 thf(fact_6397_le__cINF__iff,axiom,
% 4.69/5.02 ! [A: set_Product_unit,F: product_unit > nat,U: nat] :
% 4.69/5.02 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_875570014554754200it_nat @ F @ A ) )
% 4.69/5.02 => ( ( ord_less_eq_nat @ U @ ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ F @ A ) ) )
% 4.69/5.02 = ( ! [X2: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ X2 @ A )
% 4.69/5.02 => ( ord_less_eq_nat @ U @ ( F @ X2 ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % le_cINF_iff
% 4.69/5.02 thf(fact_6398_le__cINF__iff,axiom,
% 4.69/5.02 ! [A: set_o,F: $o > nat,U: nat] :
% 4.69/5.02 ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_o_nat2 @ F @ A ) )
% 4.69/5.02 => ( ( ord_less_eq_nat @ U @ ( complete_Inf_Inf_nat @ ( image_o_nat2 @ F @ A ) ) )
% 4.69/5.02 = ( ! [X2: $o] :
% 4.69/5.02 ( ( member_o @ X2 @ A )
% 4.69/5.02 => ( ord_less_eq_nat @ U @ ( F @ X2 ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % le_cINF_iff
% 4.69/5.02 thf(fact_6399_le__cINF__iff,axiom,
% 4.69/5.02 ! [A: set_nat,F: nat > nat,U: nat] :
% 4.69/5.02 ( ( A != bot_bot_set_nat )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat2 @ F @ A ) )
% 4.69/5.02 => ( ( ord_less_eq_nat @ U @ ( complete_Inf_Inf_nat @ ( image_nat_nat2 @ F @ A ) ) )
% 4.69/5.02 = ( ! [X2: nat] :
% 4.69/5.02 ( ( member_nat @ X2 @ A )
% 4.69/5.02 => ( ord_less_eq_nat @ U @ ( F @ X2 ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % le_cINF_iff
% 4.69/5.02 thf(fact_6400_le__cINF__iff,axiom,
% 4.69/5.02 ! [A: set_int,F: int > nat,U: nat] :
% 4.69/5.02 ( ( A != bot_bot_set_int )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat2 @ F @ A ) )
% 4.69/5.02 => ( ( ord_less_eq_nat @ U @ ( complete_Inf_Inf_nat @ ( image_int_nat2 @ F @ A ) ) )
% 4.69/5.02 = ( ! [X2: int] :
% 4.69/5.02 ( ( member_int @ X2 @ A )
% 4.69/5.02 => ( ord_less_eq_nat @ U @ ( F @ X2 ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % le_cINF_iff
% 4.69/5.02 thf(fact_6401_le__cINF__iff,axiom,
% 4.69/5.02 ! [A: set_Product_unit,F: product_unit > product_unit,U: product_unit] :
% 4.69/5.02 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ ( image_405062704495631173t_unit @ F @ A ) )
% 4.69/5.02 => ( ( ord_le3221252021190050221t_unit @ U @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A ) ) )
% 4.69/5.02 = ( ! [X2: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ X2 @ A )
% 4.69/5.02 => ( ord_le3221252021190050221t_unit @ U @ ( F @ X2 ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % le_cINF_iff
% 4.69/5.02 thf(fact_6402_le__cINF__iff,axiom,
% 4.69/5.02 ! [A: set_o,F: $o > product_unit,U: product_unit] :
% 4.69/5.02 ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit2 @ F @ A ) )
% 4.69/5.02 => ( ( ord_le3221252021190050221t_unit @ U @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit2 @ F @ A ) ) )
% 4.69/5.02 = ( ! [X2: $o] :
% 4.69/5.02 ( ( member_o @ X2 @ A )
% 4.69/5.02 => ( ord_le3221252021190050221t_unit @ U @ ( F @ X2 ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % le_cINF_iff
% 4.69/5.02 thf(fact_6403_cInf__superset__mono,axiom,
% 4.69/5.02 ! [A: set_o,B4: set_o] :
% 4.69/5.02 ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( condit5413489452508810728elow_o @ B4 )
% 4.69/5.02 => ( ( ord_less_eq_set_o @ A @ B4 )
% 4.69/5.02 => ( ord_less_eq_o @ ( complete_Inf_Inf_o @ B4 ) @ ( complete_Inf_Inf_o @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_superset_mono
% 4.69/5.02 thf(fact_6404_cInf__superset__mono,axiom,
% 4.69/5.02 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/5.02 ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/5.02 => ( ( condit8399017556247434269_nat_o @ B4 )
% 4.69/5.02 => ( ( ord_le2965882846123202637_nat_o @ A @ B4 )
% 4.69/5.02 => ( ord_le729326519192465773_nat_o @ ( comple90455603224345172_nat_o @ B4 ) @ ( comple90455603224345172_nat_o @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_superset_mono
% 4.69/5.02 thf(fact_6405_cInf__superset__mono,axiom,
% 4.69/5.02 ! [A: set_filter_nat,B4: set_filter_nat] :
% 4.69/5.02 ( ( A != bot_bo498966703094740906er_nat )
% 4.69/5.02 => ( ( condit3133331395780078992er_nat @ B4 )
% 4.69/5.02 => ( ( ord_le2426478655948331894er_nat @ A @ B4 )
% 4.69/5.02 => ( ord_le2510731241096832064er_nat @ ( comple6612786467464916249er_nat @ B4 ) @ ( comple6612786467464916249er_nat @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_superset_mono
% 4.69/5.02 thf(fact_6406_cInf__superset__mono,axiom,
% 4.69/5.02 ! [A: set_int,B4: set_int] :
% 4.69/5.02 ( ( A != bot_bot_set_int )
% 4.69/5.02 => ( ( condit1735850657277959132ow_int @ B4 )
% 4.69/5.02 => ( ( ord_less_eq_set_int @ A @ B4 )
% 4.69/5.02 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ B4 ) @ ( complete_Inf_Inf_int @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_superset_mono
% 4.69/5.02 thf(fact_6407_cInf__superset__mono,axiom,
% 4.69/5.02 ! [A: set_nat,B4: set_nat] :
% 4.69/5.02 ( ( A != bot_bot_set_nat )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ B4 )
% 4.69/5.02 => ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/5.02 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ B4 ) @ ( complete_Inf_Inf_nat @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_superset_mono
% 4.69/5.02 thf(fact_6408_cInf__superset__mono,axiom,
% 4.69/5.02 ! [A: set_set_nat,B4: set_set_nat] :
% 4.69/5.02 ( ( A != bot_bot_set_set_nat )
% 4.69/5.02 => ( ( condit68592940725977398et_nat @ B4 )
% 4.69/5.02 => ( ( ord_le6893508408891458716et_nat @ A @ B4 )
% 4.69/5.02 => ( ord_less_eq_set_nat @ ( comple7806235888213564991et_nat @ B4 ) @ ( comple7806235888213564991et_nat @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_superset_mono
% 4.69/5.02 thf(fact_6409_cInf__superset__mono,axiom,
% 4.69/5.02 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/5.02 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ B4 )
% 4.69/5.02 => ( ( ord_le3507040750410214029t_unit @ A @ B4 )
% 4.69/5.02 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ B4 ) @ ( comple2584293577114468500t_unit @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_superset_mono
% 4.69/5.02 thf(fact_6410_cInf__insert,axiom,
% 4.69/5.02 ! [X4: set_o,A2: $o] :
% 4.69/5.02 ( ( X4 != bot_bot_set_o )
% 4.69/5.02 => ( ( condit5413489452508810728elow_o @ X4 )
% 4.69/5.02 => ( ( complete_Inf_Inf_o @ ( insert_o @ A2 @ X4 ) )
% 4.69/5.02 = ( inf_inf_o @ A2 @ ( complete_Inf_Inf_o @ X4 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_insert
% 4.69/5.02 thf(fact_6411_cInf__insert,axiom,
% 4.69/5.02 ! [X4: set_int,A2: int] :
% 4.69/5.02 ( ( X4 != bot_bot_set_int )
% 4.69/5.02 => ( ( condit1735850657277959132ow_int @ X4 )
% 4.69/5.02 => ( ( complete_Inf_Inf_int @ ( insert_int @ A2 @ X4 ) )
% 4.69/5.02 = ( inf_inf_int @ A2 @ ( complete_Inf_Inf_int @ X4 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_insert
% 4.69/5.02 thf(fact_6412_cInf__insert,axiom,
% 4.69/5.02 ! [X4: set_Pr4532377907799695533_nat_o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/5.02 ( ( X4 != bot_bo7824918357723582233_nat_o )
% 4.69/5.02 => ( ( condit8399017556247434269_nat_o @ X4 )
% 4.69/5.02 => ( ( comple90455603224345172_nat_o @ ( insert5175938949040314269_nat_o @ A2 @ X4 ) )
% 4.69/5.02 = ( inf_in1318976480646536635_nat_o @ A2 @ ( comple90455603224345172_nat_o @ X4 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_insert
% 4.69/5.02 thf(fact_6413_cInf__insert,axiom,
% 4.69/5.02 ! [X4: set_nat,A2: nat] :
% 4.69/5.02 ( ( X4 != bot_bot_set_nat )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ X4 )
% 4.69/5.02 => ( ( complete_Inf_Inf_nat @ ( insert_nat @ A2 @ X4 ) )
% 4.69/5.02 = ( inf_inf_nat @ A2 @ ( complete_Inf_Inf_nat @ X4 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_insert
% 4.69/5.02 thf(fact_6414_cInf__insert,axiom,
% 4.69/5.02 ! [X4: set_set_nat,A2: set_nat] :
% 4.69/5.02 ( ( X4 != bot_bot_set_set_nat )
% 4.69/5.02 => ( ( condit68592940725977398et_nat @ X4 )
% 4.69/5.02 => ( ( comple7806235888213564991et_nat @ ( insert_set_nat @ A2 @ X4 ) )
% 4.69/5.02 = ( inf_inf_set_nat @ A2 @ ( comple7806235888213564991et_nat @ X4 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_insert
% 4.69/5.02 thf(fact_6415_cInf__insert,axiom,
% 4.69/5.02 ! [X4: set_Product_unit,A2: product_unit] :
% 4.69/5.02 ( ( X4 != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ X4 )
% 4.69/5.02 => ( ( comple2584293577114468500t_unit @ ( insert_Product_unit @ A2 @ X4 ) )
% 4.69/5.02 = ( inf_inf_Product_unit @ A2 @ ( comple2584293577114468500t_unit @ X4 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_insert
% 4.69/5.02 thf(fact_6416_cInf__insert__If,axiom,
% 4.69/5.02 ! [X4: set_o,A2: $o] :
% 4.69/5.02 ( ( condit5413489452508810728elow_o @ X4 )
% 4.69/5.02 => ( ( complete_Inf_Inf_o @ ( insert_o @ A2 @ X4 ) )
% 4.69/5.02 = ( ( ( X4 = bot_bot_set_o )
% 4.69/5.02 => A2 )
% 4.69/5.02 & ( ( X4 != bot_bot_set_o )
% 4.69/5.02 => ( inf_inf_o @ A2 @ ( complete_Inf_Inf_o @ X4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_insert_If
% 4.69/5.02 thf(fact_6417_cInf__insert__If,axiom,
% 4.69/5.02 ! [X4: set_int,A2: int] :
% 4.69/5.02 ( ( condit1735850657277959132ow_int @ X4 )
% 4.69/5.02 => ( ( ( X4 = bot_bot_set_int )
% 4.69/5.02 => ( ( complete_Inf_Inf_int @ ( insert_int @ A2 @ X4 ) )
% 4.69/5.02 = A2 ) )
% 4.69/5.02 & ( ( X4 != bot_bot_set_int )
% 4.69/5.02 => ( ( complete_Inf_Inf_int @ ( insert_int @ A2 @ X4 ) )
% 4.69/5.02 = ( inf_inf_int @ A2 @ ( complete_Inf_Inf_int @ X4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_insert_If
% 4.69/5.02 thf(fact_6418_cInf__insert__If,axiom,
% 4.69/5.02 ! [X4: set_Pr4532377907799695533_nat_o,A2: produc3658429121746597890et_nat > $o] :
% 4.69/5.02 ( ( condit8399017556247434269_nat_o @ X4 )
% 4.69/5.02 => ( ( ( X4 = bot_bo7824918357723582233_nat_o )
% 4.69/5.02 => ( ( comple90455603224345172_nat_o @ ( insert5175938949040314269_nat_o @ A2 @ X4 ) )
% 4.69/5.02 = A2 ) )
% 4.69/5.02 & ( ( X4 != bot_bo7824918357723582233_nat_o )
% 4.69/5.02 => ( ( comple90455603224345172_nat_o @ ( insert5175938949040314269_nat_o @ A2 @ X4 ) )
% 4.69/5.02 = ( inf_in1318976480646536635_nat_o @ A2 @ ( comple90455603224345172_nat_o @ X4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_insert_If
% 4.69/5.02 thf(fact_6419_cInf__insert__If,axiom,
% 4.69/5.02 ! [X4: set_nat,A2: nat] :
% 4.69/5.02 ( ( condit1738341127787009408ow_nat @ X4 )
% 4.69/5.02 => ( ( ( X4 = bot_bot_set_nat )
% 4.69/5.02 => ( ( complete_Inf_Inf_nat @ ( insert_nat @ A2 @ X4 ) )
% 4.69/5.02 = A2 ) )
% 4.69/5.02 & ( ( X4 != bot_bot_set_nat )
% 4.69/5.02 => ( ( complete_Inf_Inf_nat @ ( insert_nat @ A2 @ X4 ) )
% 4.69/5.02 = ( inf_inf_nat @ A2 @ ( complete_Inf_Inf_nat @ X4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_insert_If
% 4.69/5.02 thf(fact_6420_cInf__insert__If,axiom,
% 4.69/5.02 ! [X4: set_set_nat,A2: set_nat] :
% 4.69/5.02 ( ( condit68592940725977398et_nat @ X4 )
% 4.69/5.02 => ( ( ( X4 = bot_bot_set_set_nat )
% 4.69/5.02 => ( ( comple7806235888213564991et_nat @ ( insert_set_nat @ A2 @ X4 ) )
% 4.69/5.02 = A2 ) )
% 4.69/5.02 & ( ( X4 != bot_bot_set_set_nat )
% 4.69/5.02 => ( ( comple7806235888213564991et_nat @ ( insert_set_nat @ A2 @ X4 ) )
% 4.69/5.02 = ( inf_inf_set_nat @ A2 @ ( comple7806235888213564991et_nat @ X4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_insert_If
% 4.69/5.02 thf(fact_6421_cInf__insert__If,axiom,
% 4.69/5.02 ! [X4: set_Product_unit,A2: product_unit] :
% 4.69/5.02 ( ( condit9161856309968323677t_unit @ X4 )
% 4.69/5.02 => ( ( ( X4 = bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( comple2584293577114468500t_unit @ ( insert_Product_unit @ A2 @ X4 ) )
% 4.69/5.02 = A2 ) )
% 4.69/5.02 & ( ( X4 != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( comple2584293577114468500t_unit @ ( insert_Product_unit @ A2 @ X4 ) )
% 4.69/5.02 = ( inf_inf_Product_unit @ A2 @ ( comple2584293577114468500t_unit @ X4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_insert_If
% 4.69/5.02 thf(fact_6422_cInf__union__distrib,axiom,
% 4.69/5.02 ! [A: set_o,B4: set_o] :
% 4.69/5.02 ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( condit5413489452508810728elow_o @ A )
% 4.69/5.02 => ( ( B4 != bot_bot_set_o )
% 4.69/5.02 => ( ( condit5413489452508810728elow_o @ B4 )
% 4.69/5.02 => ( ( complete_Inf_Inf_o @ ( sup_sup_set_o @ A @ B4 ) )
% 4.69/5.02 = ( inf_inf_o @ ( complete_Inf_Inf_o @ A ) @ ( complete_Inf_Inf_o @ B4 ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_union_distrib
% 4.69/5.02 thf(fact_6423_cInf__union__distrib,axiom,
% 4.69/5.02 ! [A: set_int,B4: set_int] :
% 4.69/5.02 ( ( A != bot_bot_set_int )
% 4.69/5.02 => ( ( condit1735850657277959132ow_int @ A )
% 4.69/5.02 => ( ( B4 != bot_bot_set_int )
% 4.69/5.02 => ( ( condit1735850657277959132ow_int @ B4 )
% 4.69/5.02 => ( ( complete_Inf_Inf_int @ ( sup_sup_set_int @ A @ B4 ) )
% 4.69/5.02 = ( inf_inf_int @ ( complete_Inf_Inf_int @ A ) @ ( complete_Inf_Inf_int @ B4 ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_union_distrib
% 4.69/5.02 thf(fact_6424_cInf__union__distrib,axiom,
% 4.69/5.02 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/5.02 ( ( A != bot_bo7824918357723582233_nat_o )
% 4.69/5.02 => ( ( condit8399017556247434269_nat_o @ A )
% 4.69/5.02 => ( ( B4 != bot_bo7824918357723582233_nat_o )
% 4.69/5.02 => ( ( condit8399017556247434269_nat_o @ B4 )
% 4.69/5.02 => ( ( comple90455603224345172_nat_o @ ( sup_su5209123915105501825_nat_o @ A @ B4 ) )
% 4.69/5.02 = ( inf_in1318976480646536635_nat_o @ ( comple90455603224345172_nat_o @ A ) @ ( comple90455603224345172_nat_o @ B4 ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_union_distrib
% 4.69/5.02 thf(fact_6425_cInf__union__distrib,axiom,
% 4.69/5.02 ! [A: set_nat,B4: set_nat] :
% 4.69/5.02 ( ( A != bot_bot_set_nat )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ A )
% 4.69/5.02 => ( ( B4 != bot_bot_set_nat )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ B4 )
% 4.69/5.02 => ( ( complete_Inf_Inf_nat @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/5.02 = ( inf_inf_nat @ ( complete_Inf_Inf_nat @ A ) @ ( complete_Inf_Inf_nat @ B4 ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_union_distrib
% 4.69/5.02 thf(fact_6426_cInf__union__distrib,axiom,
% 4.69/5.02 ! [A: set_set_nat,B4: set_set_nat] :
% 4.69/5.02 ( ( A != bot_bot_set_set_nat )
% 4.69/5.02 => ( ( condit68592940725977398et_nat @ A )
% 4.69/5.02 => ( ( B4 != bot_bot_set_set_nat )
% 4.69/5.02 => ( ( condit68592940725977398et_nat @ B4 )
% 4.69/5.02 => ( ( comple7806235888213564991et_nat @ ( sup_sup_set_set_nat @ A @ B4 ) )
% 4.69/5.02 = ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ A ) @ ( comple7806235888213564991et_nat @ B4 ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_union_distrib
% 4.69/5.02 thf(fact_6427_cInf__union__distrib,axiom,
% 4.69/5.02 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/5.02 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ A )
% 4.69/5.02 => ( ( B4 != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ B4 )
% 4.69/5.02 => ( ( comple2584293577114468500t_unit @ ( sup_su793286257634532545t_unit @ A @ B4 ) )
% 4.69/5.02 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ A ) @ ( comple2584293577114468500t_unit @ B4 ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_union_distrib
% 4.69/5.02 thf(fact_6428_dbl__inc__def,axiom,
% 4.69/5.02 ( neg_nu5831290666863070958nteger
% 4.69/5.02 = ( ^ [X2: code_integer] : ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ X2 @ X2 ) @ one_one_Code_integer ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dbl_inc_def
% 4.69/5.02 thf(fact_6429_dbl__inc__def,axiom,
% 4.69/5.02 ( neg_nu5219082963157363817nc_rat
% 4.69/5.02 = ( ^ [X2: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X2 @ X2 ) @ one_one_rat ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dbl_inc_def
% 4.69/5.02 thf(fact_6430_dbl__inc__def,axiom,
% 4.69/5.02 ( neg_nu5851722552734809277nc_int
% 4.69/5.02 = ( ^ [X2: int] : ( plus_plus_int @ ( plus_plus_int @ X2 @ X2 ) @ one_one_int ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dbl_inc_def
% 4.69/5.02 thf(fact_6431_dvd__mult__cancel1,axiom,
% 4.69/5.02 ! [M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_nat @ zero_zero_nat @ M4 )
% 4.69/5.02 => ( ( dvd_dvd_nat @ ( times_times_nat @ M4 @ N2 ) @ M4 )
% 4.69/5.02 = ( N2 = one_one_nat ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_cancel1
% 4.69/5.02 thf(fact_6432_dvd__mult__cancel2,axiom,
% 4.69/5.02 ! [M4: nat,N2: nat] :
% 4.69/5.02 ( ( ord_less_nat @ zero_zero_nat @ M4 )
% 4.69/5.02 => ( ( dvd_dvd_nat @ ( times_times_nat @ N2 @ M4 ) @ M4 )
% 4.69/5.02 = ( N2 = one_one_nat ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_mult_cancel2
% 4.69/5.02 thf(fact_6433_dvd__minus__add,axiom,
% 4.69/5.02 ! [Q4: nat,N2: nat,R2: nat,M4: nat] :
% 4.69/5.02 ( ( ord_less_eq_nat @ Q4 @ N2 )
% 4.69/5.02 => ( ( ord_less_eq_nat @ Q4 @ ( times_times_nat @ R2 @ M4 ) )
% 4.69/5.02 => ( ( dvd_dvd_nat @ M4 @ ( minus_minus_nat @ N2 @ Q4 ) )
% 4.69/5.02 = ( dvd_dvd_nat @ M4 @ ( plus_plus_nat @ N2 @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M4 ) @ Q4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_minus_add
% 4.69/5.02 thf(fact_6434_cINF__superset__mono,axiom,
% 4.69/5.02 ! [A: set_Product_unit,G: product_unit > int,B4: set_Product_unit,F: product_unit > int] :
% 4.69/5.02 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit1735850657277959132ow_int @ ( image_873079544045703924it_int @ G @ B4 ) )
% 4.69/5.02 => ( ( ord_le3507040750410214029t_unit @ A @ B4 )
% 4.69/5.02 => ( ! [X3: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ X3 @ B4 )
% 4.69/5.02 => ( ord_less_eq_int @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 4.69/5.02 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ G @ B4 ) ) @ ( complete_Inf_Inf_int @ ( image_873079544045703924it_int @ F @ A ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_superset_mono
% 4.69/5.02 thf(fact_6435_cINF__superset__mono,axiom,
% 4.69/5.02 ! [A: set_o,G: $o > int,B4: set_o,F: $o > int] :
% 4.69/5.02 ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( condit1735850657277959132ow_int @ ( image_o_int2 @ G @ B4 ) )
% 4.69/5.02 => ( ( ord_less_eq_set_o @ A @ B4 )
% 4.69/5.02 => ( ! [X3: $o] :
% 4.69/5.02 ( ( member_o @ X3 @ B4 )
% 4.69/5.02 => ( ord_less_eq_int @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 4.69/5.02 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_o_int2 @ G @ B4 ) ) @ ( complete_Inf_Inf_int @ ( image_o_int2 @ F @ A ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_superset_mono
% 4.69/5.02 thf(fact_6436_cINF__superset__mono,axiom,
% 4.69/5.02 ! [A: set_int,G: int > int,B4: set_int,F: int > int] :
% 4.69/5.02 ( ( A != bot_bot_set_int )
% 4.69/5.02 => ( ( condit1735850657277959132ow_int @ ( image_int_int2 @ G @ B4 ) )
% 4.69/5.02 => ( ( ord_less_eq_set_int @ A @ B4 )
% 4.69/5.02 => ( ! [X3: int] :
% 4.69/5.02 ( ( member_int @ X3 @ B4 )
% 4.69/5.02 => ( ord_less_eq_int @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 4.69/5.02 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_int_int2 @ G @ B4 ) ) @ ( complete_Inf_Inf_int @ ( image_int_int2 @ F @ A ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_superset_mono
% 4.69/5.02 thf(fact_6437_cINF__superset__mono,axiom,
% 4.69/5.02 ! [A: set_nat,G: nat > int,B4: set_nat,F: nat > int] :
% 4.69/5.02 ( ( A != bot_bot_set_nat )
% 4.69/5.02 => ( ( condit1735850657277959132ow_int @ ( image_nat_int2 @ G @ B4 ) )
% 4.69/5.02 => ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/5.02 => ( ! [X3: nat] :
% 4.69/5.02 ( ( member_nat @ X3 @ B4 )
% 4.69/5.02 => ( ord_less_eq_int @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 4.69/5.02 => ( ord_less_eq_int @ ( complete_Inf_Inf_int @ ( image_nat_int2 @ G @ B4 ) ) @ ( complete_Inf_Inf_int @ ( image_nat_int2 @ F @ A ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_superset_mono
% 4.69/5.02 thf(fact_6438_cINF__superset__mono,axiom,
% 4.69/5.02 ! [A: set_Product_unit,G: product_unit > nat,B4: set_Product_unit,F: product_unit > nat] :
% 4.69/5.02 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_875570014554754200it_nat @ G @ B4 ) )
% 4.69/5.02 => ( ( ord_le3507040750410214029t_unit @ A @ B4 )
% 4.69/5.02 => ( ! [X3: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ X3 @ B4 )
% 4.69/5.02 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 4.69/5.02 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ G @ B4 ) ) @ ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ F @ A ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_superset_mono
% 4.69/5.02 thf(fact_6439_cINF__superset__mono,axiom,
% 4.69/5.02 ! [A: set_o,G: $o > nat,B4: set_o,F: $o > nat] :
% 4.69/5.02 ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_o_nat2 @ G @ B4 ) )
% 4.69/5.02 => ( ( ord_less_eq_set_o @ A @ B4 )
% 4.69/5.02 => ( ! [X3: $o] :
% 4.69/5.02 ( ( member_o @ X3 @ B4 )
% 4.69/5.02 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 4.69/5.02 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_o_nat2 @ G @ B4 ) ) @ ( complete_Inf_Inf_nat @ ( image_o_nat2 @ F @ A ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_superset_mono
% 4.69/5.02 thf(fact_6440_cINF__superset__mono,axiom,
% 4.69/5.02 ! [A: set_int,G: int > nat,B4: set_int,F: int > nat] :
% 4.69/5.02 ( ( A != bot_bot_set_int )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat2 @ G @ B4 ) )
% 4.69/5.02 => ( ( ord_less_eq_set_int @ A @ B4 )
% 4.69/5.02 => ( ! [X3: int] :
% 4.69/5.02 ( ( member_int @ X3 @ B4 )
% 4.69/5.02 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 4.69/5.02 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_int_nat2 @ G @ B4 ) ) @ ( complete_Inf_Inf_nat @ ( image_int_nat2 @ F @ A ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_superset_mono
% 4.69/5.02 thf(fact_6441_cINF__superset__mono,axiom,
% 4.69/5.02 ! [A: set_nat,G: nat > nat,B4: set_nat,F: nat > nat] :
% 4.69/5.02 ( ( A != bot_bot_set_nat )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat2 @ G @ B4 ) )
% 4.69/5.02 => ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/5.02 => ( ! [X3: nat] :
% 4.69/5.02 ( ( member_nat @ X3 @ B4 )
% 4.69/5.02 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 4.69/5.02 => ( ord_less_eq_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat2 @ G @ B4 ) ) @ ( complete_Inf_Inf_nat @ ( image_nat_nat2 @ F @ A ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_superset_mono
% 4.69/5.02 thf(fact_6442_cINF__superset__mono,axiom,
% 4.69/5.02 ! [A: set_Product_unit,G: product_unit > product_unit,B4: set_Product_unit,F: product_unit > product_unit] :
% 4.69/5.02 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ ( image_405062704495631173t_unit @ G @ B4 ) )
% 4.69/5.02 => ( ( ord_le3507040750410214029t_unit @ A @ B4 )
% 4.69/5.02 => ( ! [X3: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ X3 @ B4 )
% 4.69/5.02 => ( ord_le3221252021190050221t_unit @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 4.69/5.02 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ G @ B4 ) ) @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_superset_mono
% 4.69/5.02 thf(fact_6443_cINF__superset__mono,axiom,
% 4.69/5.02 ! [A: set_o,G: $o > product_unit,B4: set_o,F: $o > product_unit] :
% 4.69/5.02 ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit2 @ G @ B4 ) )
% 4.69/5.02 => ( ( ord_less_eq_set_o @ A @ B4 )
% 4.69/5.02 => ( ! [X3: $o] :
% 4.69/5.02 ( ( member_o @ X3 @ B4 )
% 4.69/5.02 => ( ord_le3221252021190050221t_unit @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 4.69/5.02 => ( ord_le3221252021190050221t_unit @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit2 @ G @ B4 ) ) @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit2 @ F @ A ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_superset_mono
% 4.69/5.02 thf(fact_6444_less__eq__cInf__inter,axiom,
% 4.69/5.02 ! [A: set_o,B4: set_o] :
% 4.69/5.02 ( ( condit5413489452508810728elow_o @ A )
% 4.69/5.02 => ( ( condit5413489452508810728elow_o @ B4 )
% 4.69/5.02 => ( ( ( inf_inf_set_o @ A @ B4 )
% 4.69/5.02 != bot_bot_set_o )
% 4.69/5.02 => ( ord_less_eq_o @ ( inf_inf_o @ ( complete_Inf_Inf_o @ A ) @ ( complete_Inf_Inf_o @ B4 ) ) @ ( complete_Inf_Inf_o @ ( inf_inf_set_o @ A @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % less_eq_cInf_inter
% 4.69/5.02 thf(fact_6445_less__eq__cInf__inter,axiom,
% 4.69/5.02 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/5.02 ( ( condit8399017556247434269_nat_o @ A )
% 4.69/5.02 => ( ( condit8399017556247434269_nat_o @ B4 )
% 4.69/5.02 => ( ( ( inf_in1906310914598751387_nat_o @ A @ B4 )
% 4.69/5.02 != bot_bo7824918357723582233_nat_o )
% 4.69/5.02 => ( ord_le729326519192465773_nat_o @ ( inf_in1318976480646536635_nat_o @ ( comple90455603224345172_nat_o @ A ) @ ( comple90455603224345172_nat_o @ B4 ) ) @ ( comple90455603224345172_nat_o @ ( inf_in1906310914598751387_nat_o @ A @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % less_eq_cInf_inter
% 4.69/5.02 thf(fact_6446_less__eq__cInf__inter,axiom,
% 4.69/5.02 ! [A: set_filter_nat,B4: set_filter_nat] :
% 4.69/5.02 ( ( condit3133331395780078992er_nat @ A )
% 4.69/5.02 => ( ( condit3133331395780078992er_nat @ B4 )
% 4.69/5.02 => ( ( ( inf_in7395780696554941096er_nat @ A @ B4 )
% 4.69/5.02 != bot_bo498966703094740906er_nat )
% 4.69/5.02 => ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ ( comple6612786467464916249er_nat @ A ) @ ( comple6612786467464916249er_nat @ B4 ) ) @ ( comple6612786467464916249er_nat @ ( inf_in7395780696554941096er_nat @ A @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % less_eq_cInf_inter
% 4.69/5.02 thf(fact_6447_less__eq__cInf__inter,axiom,
% 4.69/5.02 ! [A: set_int,B4: set_int] :
% 4.69/5.02 ( ( condit1735850657277959132ow_int @ A )
% 4.69/5.02 => ( ( condit1735850657277959132ow_int @ B4 )
% 4.69/5.02 => ( ( ( inf_inf_set_int @ A @ B4 )
% 4.69/5.02 != bot_bot_set_int )
% 4.69/5.02 => ( ord_less_eq_int @ ( inf_inf_int @ ( complete_Inf_Inf_int @ A ) @ ( complete_Inf_Inf_int @ B4 ) ) @ ( complete_Inf_Inf_int @ ( inf_inf_set_int @ A @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % less_eq_cInf_inter
% 4.69/5.02 thf(fact_6448_less__eq__cInf__inter,axiom,
% 4.69/5.02 ! [A: set_nat,B4: set_nat] :
% 4.69/5.02 ( ( condit1738341127787009408ow_nat @ A )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ B4 )
% 4.69/5.02 => ( ( ( inf_inf_set_nat @ A @ B4 )
% 4.69/5.02 != bot_bot_set_nat )
% 4.69/5.02 => ( ord_less_eq_nat @ ( inf_inf_nat @ ( complete_Inf_Inf_nat @ A ) @ ( complete_Inf_Inf_nat @ B4 ) ) @ ( complete_Inf_Inf_nat @ ( inf_inf_set_nat @ A @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % less_eq_cInf_inter
% 4.69/5.02 thf(fact_6449_less__eq__cInf__inter,axiom,
% 4.69/5.02 ! [A: set_set_nat,B4: set_set_nat] :
% 4.69/5.02 ( ( condit68592940725977398et_nat @ A )
% 4.69/5.02 => ( ( condit68592940725977398et_nat @ B4 )
% 4.69/5.02 => ( ( ( inf_inf_set_set_nat @ A @ B4 )
% 4.69/5.02 != bot_bot_set_set_nat )
% 4.69/5.02 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ A ) @ ( comple7806235888213564991et_nat @ B4 ) ) @ ( comple7806235888213564991et_nat @ ( inf_inf_set_set_nat @ A @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % less_eq_cInf_inter
% 4.69/5.02 thf(fact_6450_less__eq__cInf__inter,axiom,
% 4.69/5.02 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/5.02 ( ( condit9161856309968323677t_unit @ A )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ B4 )
% 4.69/5.02 => ( ( ( inf_in4660618365625256667t_unit @ A @ B4 )
% 4.69/5.02 != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ A ) @ ( comple2584293577114468500t_unit @ B4 ) ) @ ( comple2584293577114468500t_unit @ ( inf_in4660618365625256667t_unit @ A @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % less_eq_cInf_inter
% 4.69/5.02 thf(fact_6451_cINF__insert,axiom,
% 4.69/5.02 ! [A: set_Product_unit,F: product_unit > nat,A2: product_unit] :
% 4.69/5.02 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_875570014554754200it_nat @ F @ A ) )
% 4.69/5.02 => ( ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ F @ ( insert_Product_unit @ A2 @ A ) ) )
% 4.69/5.02 = ( inf_inf_nat @ ( F @ A2 ) @ ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ F @ A ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_insert
% 4.69/5.02 thf(fact_6452_cINF__insert,axiom,
% 4.69/5.02 ! [A: set_o,F: $o > nat,A2: $o] :
% 4.69/5.02 ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_o_nat2 @ F @ A ) )
% 4.69/5.02 => ( ( complete_Inf_Inf_nat @ ( image_o_nat2 @ F @ ( insert_o @ A2 @ A ) ) )
% 4.69/5.02 = ( inf_inf_nat @ ( F @ A2 ) @ ( complete_Inf_Inf_nat @ ( image_o_nat2 @ F @ A ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_insert
% 4.69/5.02 thf(fact_6453_cINF__insert,axiom,
% 4.69/5.02 ! [A: set_nat,F: nat > nat,A2: nat] :
% 4.69/5.02 ( ( A != bot_bot_set_nat )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat2 @ F @ A ) )
% 4.69/5.02 => ( ( complete_Inf_Inf_nat @ ( image_nat_nat2 @ F @ ( insert_nat @ A2 @ A ) ) )
% 4.69/5.02 = ( inf_inf_nat @ ( F @ A2 ) @ ( complete_Inf_Inf_nat @ ( image_nat_nat2 @ F @ A ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_insert
% 4.69/5.02 thf(fact_6454_cINF__insert,axiom,
% 4.69/5.02 ! [A: set_int,F: int > nat,A2: int] :
% 4.69/5.02 ( ( A != bot_bot_set_int )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat2 @ F @ A ) )
% 4.69/5.02 => ( ( complete_Inf_Inf_nat @ ( image_int_nat2 @ F @ ( insert_int @ A2 @ A ) ) )
% 4.69/5.02 = ( inf_inf_nat @ ( F @ A2 ) @ ( complete_Inf_Inf_nat @ ( image_int_nat2 @ F @ A ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_insert
% 4.69/5.02 thf(fact_6455_cINF__insert,axiom,
% 4.69/5.02 ! [A: set_Product_unit,F: product_unit > product_unit,A2: product_unit] :
% 4.69/5.02 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ ( image_405062704495631173t_unit @ F @ A ) )
% 4.69/5.02 => ( ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ ( insert_Product_unit @ A2 @ A ) ) )
% 4.69/5.02 = ( inf_inf_Product_unit @ ( F @ A2 ) @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_insert
% 4.69/5.02 thf(fact_6456_cINF__insert,axiom,
% 4.69/5.02 ! [A: set_o,F: $o > product_unit,A2: $o] :
% 4.69/5.02 ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit2 @ F @ A ) )
% 4.69/5.02 => ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit2 @ F @ ( insert_o @ A2 @ A ) ) )
% 4.69/5.02 = ( inf_inf_Product_unit @ ( F @ A2 ) @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit2 @ F @ A ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_insert
% 4.69/5.02 thf(fact_6457_cINF__insert,axiom,
% 4.69/5.02 ! [A: set_nat,F: nat > product_unit,A2: nat] :
% 4.69/5.02 ( ( A != bot_bot_set_nat )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ ( image_8730104196221521654t_unit @ F @ A ) )
% 4.69/5.02 => ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ ( insert_nat @ A2 @ A ) ) )
% 4.69/5.02 = ( inf_inf_Product_unit @ ( F @ A2 ) @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_insert
% 4.69/5.02 thf(fact_6458_cINF__insert,axiom,
% 4.69/5.02 ! [A: set_int,F: int > product_unit,A2: int] :
% 4.69/5.02 ( ( A != bot_bot_set_int )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ ( image_5846526143423701914t_unit @ F @ A ) )
% 4.69/5.02 => ( ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ ( insert_int @ A2 @ A ) ) )
% 4.69/5.02 = ( inf_inf_Product_unit @ ( F @ A2 ) @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_insert
% 4.69/5.02 thf(fact_6459_cINF__insert,axiom,
% 4.69/5.02 ! [A: set_Product_unit,F: product_unit > set_nat,A2: product_unit] :
% 4.69/5.02 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit68592940725977398et_nat @ ( image_8173849991827986510et_nat @ F @ A ) )
% 4.69/5.02 => ( ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ ( insert_Product_unit @ A2 @ A ) ) )
% 4.69/5.02 = ( inf_inf_set_nat @ ( F @ A2 ) @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ A ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_insert
% 4.69/5.02 thf(fact_6460_cINF__insert,axiom,
% 4.69/5.02 ! [A: set_o,F: $o > set_nat,A2: $o] :
% 4.69/5.02 ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( condit68592940725977398et_nat @ ( image_o_set_nat @ F @ A ) )
% 4.69/5.02 => ( ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ ( insert_o @ A2 @ A ) ) )
% 4.69/5.02 = ( inf_inf_set_nat @ ( F @ A2 ) @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_insert
% 4.69/5.02 thf(fact_6461_power__eq__if,axiom,
% 4.69/5.02 ( power_8256067586552552935nteger
% 4.69/5.02 = ( ^ [P5: code_integer,M3: nat] : ( if_Code_integer @ ( M3 = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ P5 @ ( power_8256067586552552935nteger @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_eq_if
% 4.69/5.02 thf(fact_6462_power__eq__if,axiom,
% 4.69/5.02 ( power_7079662738309270450atural
% 4.69/5.02 = ( ^ [P5: code_natural,M3: nat] : ( if_Code_natural @ ( M3 = zero_zero_nat ) @ one_one_Code_natural @ ( times_2397367101498566445atural @ P5 @ ( power_7079662738309270450atural @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_eq_if
% 4.69/5.02 thf(fact_6463_power__eq__if,axiom,
% 4.69/5.02 ( power_power_assn
% 4.69/5.02 = ( ^ [P5: assn,M3: nat] : ( if_assn @ ( M3 = zero_zero_nat ) @ one_one_assn @ ( times_times_assn @ P5 @ ( power_power_assn @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_eq_if
% 4.69/5.02 thf(fact_6464_power__eq__if,axiom,
% 4.69/5.02 ( power_power_rat
% 4.69/5.02 = ( ^ [P5: rat,M3: nat] : ( if_rat @ ( M3 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P5 @ ( power_power_rat @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_eq_if
% 4.69/5.02 thf(fact_6465_power__eq__if,axiom,
% 4.69/5.02 ( power_power_nat
% 4.69/5.02 = ( ^ [P5: nat,M3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P5 @ ( power_power_nat @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_eq_if
% 4.69/5.02 thf(fact_6466_power__eq__if,axiom,
% 4.69/5.02 ( power_power_int
% 4.69/5.02 = ( ^ [P5: int,M3: nat] : ( if_int @ ( M3 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P5 @ ( power_power_int @ P5 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_eq_if
% 4.69/5.02 thf(fact_6467_power__minus__mult,axiom,
% 4.69/5.02 ! [N2: nat,A2: assn] :
% 4.69/5.02 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.02 => ( ( times_times_assn @ ( power_power_assn @ A2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A2 )
% 4.69/5.02 = ( power_power_assn @ A2 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_minus_mult
% 4.69/5.02 thf(fact_6468_power__minus__mult,axiom,
% 4.69/5.02 ! [N2: nat,A2: rat] :
% 4.69/5.02 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.02 => ( ( times_times_rat @ ( power_power_rat @ A2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A2 )
% 4.69/5.02 = ( power_power_rat @ A2 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_minus_mult
% 4.69/5.02 thf(fact_6469_power__minus__mult,axiom,
% 4.69/5.02 ! [N2: nat,A2: nat] :
% 4.69/5.02 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.02 => ( ( times_times_nat @ ( power_power_nat @ A2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A2 )
% 4.69/5.02 = ( power_power_nat @ A2 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_minus_mult
% 4.69/5.02 thf(fact_6470_power__minus__mult,axiom,
% 4.69/5.02 ! [N2: nat,A2: int] :
% 4.69/5.02 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.02 => ( ( times_times_int @ ( power_power_int @ A2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A2 )
% 4.69/5.02 = ( power_power_int @ A2 @ N2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % power_minus_mult
% 4.69/5.02 thf(fact_6471_cINF__union,axiom,
% 4.69/5.02 ! [A: set_Product_unit,F: product_unit > nat,B4: set_Product_unit] :
% 4.69/5.02 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_875570014554754200it_nat @ F @ A ) )
% 4.69/5.02 => ( ( B4 != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_875570014554754200it_nat @ F @ B4 ) )
% 4.69/5.02 => ( ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ F @ ( sup_su793286257634532545t_unit @ A @ B4 ) ) )
% 4.69/5.02 = ( inf_inf_nat @ ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ F @ A ) ) @ ( complete_Inf_Inf_nat @ ( image_875570014554754200it_nat @ F @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_union
% 4.69/5.02 thf(fact_6472_cINF__union,axiom,
% 4.69/5.02 ! [A: set_o,F: $o > nat,B4: set_o] :
% 4.69/5.02 ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_o_nat2 @ F @ A ) )
% 4.69/5.02 => ( ( B4 != bot_bot_set_o )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_o_nat2 @ F @ B4 ) )
% 4.69/5.02 => ( ( complete_Inf_Inf_nat @ ( image_o_nat2 @ F @ ( sup_sup_set_o @ A @ B4 ) ) )
% 4.69/5.02 = ( inf_inf_nat @ ( complete_Inf_Inf_nat @ ( image_o_nat2 @ F @ A ) ) @ ( complete_Inf_Inf_nat @ ( image_o_nat2 @ F @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_union
% 4.69/5.02 thf(fact_6473_cINF__union,axiom,
% 4.69/5.02 ! [A: set_nat,F: nat > nat,B4: set_nat] :
% 4.69/5.02 ( ( A != bot_bot_set_nat )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat2 @ F @ A ) )
% 4.69/5.02 => ( ( B4 != bot_bot_set_nat )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_nat_nat2 @ F @ B4 ) )
% 4.69/5.02 => ( ( complete_Inf_Inf_nat @ ( image_nat_nat2 @ F @ ( sup_sup_set_nat @ A @ B4 ) ) )
% 4.69/5.02 = ( inf_inf_nat @ ( complete_Inf_Inf_nat @ ( image_nat_nat2 @ F @ A ) ) @ ( complete_Inf_Inf_nat @ ( image_nat_nat2 @ F @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_union
% 4.69/5.02 thf(fact_6474_cINF__union,axiom,
% 4.69/5.02 ! [A: set_int,F: int > nat,B4: set_int] :
% 4.69/5.02 ( ( A != bot_bot_set_int )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat2 @ F @ A ) )
% 4.69/5.02 => ( ( B4 != bot_bot_set_int )
% 4.69/5.02 => ( ( condit1738341127787009408ow_nat @ ( image_int_nat2 @ F @ B4 ) )
% 4.69/5.02 => ( ( complete_Inf_Inf_nat @ ( image_int_nat2 @ F @ ( sup_sup_set_int @ A @ B4 ) ) )
% 4.69/5.02 = ( inf_inf_nat @ ( complete_Inf_Inf_nat @ ( image_int_nat2 @ F @ A ) ) @ ( complete_Inf_Inf_nat @ ( image_int_nat2 @ F @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_union
% 4.69/5.02 thf(fact_6475_cINF__union,axiom,
% 4.69/5.02 ! [A: set_Product_unit,F: product_unit > product_unit,B4: set_Product_unit] :
% 4.69/5.02 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ ( image_405062704495631173t_unit @ F @ A ) )
% 4.69/5.02 => ( ( B4 != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ ( image_405062704495631173t_unit @ F @ B4 ) )
% 4.69/5.02 => ( ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ ( sup_su793286257634532545t_unit @ A @ B4 ) ) )
% 4.69/5.02 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ A ) ) @ ( comple2584293577114468500t_unit @ ( image_405062704495631173t_unit @ F @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_union
% 4.69/5.02 thf(fact_6476_cINF__union,axiom,
% 4.69/5.02 ! [A: set_o,F: $o > product_unit,B4: set_o] :
% 4.69/5.02 ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit2 @ F @ A ) )
% 4.69/5.02 => ( ( B4 != bot_bot_set_o )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ ( image_o_Product_unit2 @ F @ B4 ) )
% 4.69/5.02 => ( ( comple2584293577114468500t_unit @ ( image_o_Product_unit2 @ F @ ( sup_sup_set_o @ A @ B4 ) ) )
% 4.69/5.02 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit2 @ F @ A ) ) @ ( comple2584293577114468500t_unit @ ( image_o_Product_unit2 @ F @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_union
% 4.69/5.02 thf(fact_6477_cINF__union,axiom,
% 4.69/5.02 ! [A: set_nat,F: nat > product_unit,B4: set_nat] :
% 4.69/5.02 ( ( A != bot_bot_set_nat )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ ( image_8730104196221521654t_unit @ F @ A ) )
% 4.69/5.02 => ( ( B4 != bot_bot_set_nat )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ ( image_8730104196221521654t_unit @ F @ B4 ) )
% 4.69/5.02 => ( ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ ( sup_sup_set_nat @ A @ B4 ) ) )
% 4.69/5.02 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ A ) ) @ ( comple2584293577114468500t_unit @ ( image_8730104196221521654t_unit @ F @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_union
% 4.69/5.02 thf(fact_6478_cINF__union,axiom,
% 4.69/5.02 ! [A: set_int,F: int > product_unit,B4: set_int] :
% 4.69/5.02 ( ( A != bot_bot_set_int )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ ( image_5846526143423701914t_unit @ F @ A ) )
% 4.69/5.02 => ( ( B4 != bot_bot_set_int )
% 4.69/5.02 => ( ( condit9161856309968323677t_unit @ ( image_5846526143423701914t_unit @ F @ B4 ) )
% 4.69/5.02 => ( ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ ( sup_sup_set_int @ A @ B4 ) ) )
% 4.69/5.02 = ( inf_inf_Product_unit @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ A ) ) @ ( comple2584293577114468500t_unit @ ( image_5846526143423701914t_unit @ F @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_union
% 4.69/5.02 thf(fact_6479_cINF__union,axiom,
% 4.69/5.02 ! [A: set_Product_unit,F: product_unit > set_nat,B4: set_Product_unit] :
% 4.69/5.02 ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit68592940725977398et_nat @ ( image_8173849991827986510et_nat @ F @ A ) )
% 4.69/5.02 => ( ( B4 != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( condit68592940725977398et_nat @ ( image_8173849991827986510et_nat @ F @ B4 ) )
% 4.69/5.02 => ( ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ ( sup_su793286257634532545t_unit @ A @ B4 ) ) )
% 4.69/5.02 = ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ A ) ) @ ( comple7806235888213564991et_nat @ ( image_8173849991827986510et_nat @ F @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_union
% 4.69/5.02 thf(fact_6480_cINF__union,axiom,
% 4.69/5.02 ! [A: set_o,F: $o > set_nat,B4: set_o] :
% 4.69/5.02 ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( condit68592940725977398et_nat @ ( image_o_set_nat @ F @ A ) )
% 4.69/5.02 => ( ( B4 != bot_bot_set_o )
% 4.69/5.02 => ( ( condit68592940725977398et_nat @ ( image_o_set_nat @ F @ B4 ) )
% 4.69/5.02 => ( ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ ( sup_sup_set_o @ A @ B4 ) ) )
% 4.69/5.02 = ( inf_inf_set_nat @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ A ) ) @ ( comple7806235888213564991et_nat @ ( image_o_set_nat @ F @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cINF_union
% 4.69/5.02 thf(fact_6481_sum_Oinsert,axiom,
% 4.69/5.02 ! [A: set_int,X: int,G: int > code_integer] :
% 4.69/5.02 ( ( finite_finite_int @ A )
% 4.69/5.02 => ( ~ ( member_int @ X @ A )
% 4.69/5.02 => ( ( groups7873554091576472773nteger @ G @ ( insert_int @ X @ A ) )
% 4.69/5.02 = ( plus_p5714425477246183910nteger @ ( G @ X ) @ ( groups7873554091576472773nteger @ G @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert
% 4.69/5.02 thf(fact_6482_sum_Oinsert,axiom,
% 4.69/5.02 ! [A: set_o,X: $o,G: $o > code_integer] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ~ ( member_o @ X @ A )
% 4.69/5.02 => ( ( groups4406642042086082107nteger @ G @ ( insert_o @ X @ A ) )
% 4.69/5.02 = ( plus_p5714425477246183910nteger @ ( G @ X ) @ ( groups4406642042086082107nteger @ G @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert
% 4.69/5.02 thf(fact_6483_sum_Oinsert,axiom,
% 4.69/5.02 ! [A: set_Product_unit,X: product_unit,G: product_unit > code_integer] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ~ ( member_Product_unit @ X @ A )
% 4.69/5.02 => ( ( groups5393439102872367408nteger @ G @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.02 = ( plus_p5714425477246183910nteger @ ( G @ X ) @ ( groups5393439102872367408nteger @ G @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert
% 4.69/5.02 thf(fact_6484_sum_Oinsert,axiom,
% 4.69/5.02 ! [A: set_nat,X: nat,G: nat > code_integer] :
% 4.69/5.02 ( ( finite_finite_nat @ A )
% 4.69/5.02 => ( ~ ( member_nat @ X @ A )
% 4.69/5.02 => ( ( groups7501900531339628137nteger @ G @ ( insert_nat @ X @ A ) )
% 4.69/5.02 = ( plus_p5714425477246183910nteger @ ( G @ X ) @ ( groups7501900531339628137nteger @ G @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert
% 4.69/5.02 thf(fact_6485_sum_Oinsert,axiom,
% 4.69/5.02 ! [A: set_Code_integer,X: code_integer,G: code_integer > code_integer] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ~ ( member_Code_integer @ X @ A )
% 4.69/5.02 => ( ( groups879477027807139574nteger @ G @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.02 = ( plus_p5714425477246183910nteger @ ( G @ X ) @ ( groups879477027807139574nteger @ G @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert
% 4.69/5.02 thf(fact_6486_sum_Oinsert,axiom,
% 4.69/5.02 ! [A: set_int,X: int,G: int > rat] :
% 4.69/5.02 ( ( finite_finite_int @ A )
% 4.69/5.02 => ( ~ ( member_int @ X @ A )
% 4.69/5.02 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A ) )
% 4.69/5.02 = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert
% 4.69/5.02 thf(fact_6487_sum_Oinsert,axiom,
% 4.69/5.02 ! [A: set_o,X: $o,G: $o > rat] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ~ ( member_o @ X @ A )
% 4.69/5.02 => ( ( groups7872700643590313910_o_rat @ G @ ( insert_o @ X @ A ) )
% 4.69/5.02 = ( plus_plus_rat @ ( G @ X ) @ ( groups7872700643590313910_o_rat @ G @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert
% 4.69/5.02 thf(fact_6488_sum_Oinsert,axiom,
% 4.69/5.02 ! [A: set_Product_unit,X: product_unit,G: product_unit > rat] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ~ ( member_Product_unit @ X @ A )
% 4.69/5.02 => ( ( groups8131667117488461483it_rat @ G @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.02 = ( plus_plus_rat @ ( G @ X ) @ ( groups8131667117488461483it_rat @ G @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert
% 4.69/5.02 thf(fact_6489_sum_Oinsert,axiom,
% 4.69/5.02 ! [A: set_nat,X: nat,G: nat > rat] :
% 4.69/5.02 ( ( finite_finite_nat @ A )
% 4.69/5.02 => ( ~ ( member_nat @ X @ A )
% 4.69/5.02 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A ) )
% 4.69/5.02 = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert
% 4.69/5.02 thf(fact_6490_sum_Oinsert,axiom,
% 4.69/5.02 ! [A: set_Code_integer,X: code_integer,G: code_integer > rat] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ~ ( member_Code_integer @ X @ A )
% 4.69/5.02 => ( ( groups6602215022474089585er_rat @ G @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.02 = ( plus_plus_rat @ ( G @ X ) @ ( groups6602215022474089585er_rat @ G @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert
% 4.69/5.02 thf(fact_6491_sum_Oempty,axiom,
% 4.69/5.02 ! [G: product_unit > nat] :
% 4.69/5.02 ( ( groups8766797177574957219it_nat @ G @ bot_bo3957492148770167129t_unit )
% 4.69/5.02 = zero_zero_nat ) ).
% 4.69/5.02
% 4.69/5.02 % sum.empty
% 4.69/5.02 thf(fact_6492_sum_Oempty,axiom,
% 4.69/5.02 ! [G: product_unit > int] :
% 4.69/5.02 ( ( groups8764306707065906943it_int @ G @ bot_bo3957492148770167129t_unit )
% 4.69/5.02 = zero_zero_int ) ).
% 4.69/5.02
% 4.69/5.02 % sum.empty
% 4.69/5.02 thf(fact_6493_sum_Oempty,axiom,
% 4.69/5.02 ! [G: product_unit > code_integer] :
% 4.69/5.02 ( ( groups5393439102872367408nteger @ G @ bot_bo3957492148770167129t_unit )
% 4.69/5.02 = zero_z3403309356797280102nteger ) ).
% 4.69/5.02
% 4.69/5.02 % sum.empty
% 4.69/5.02 thf(fact_6494_sum_Oempty,axiom,
% 4.69/5.02 ! [G: $o > nat] :
% 4.69/5.02 ( ( groups8507830703676809646_o_nat @ G @ bot_bot_set_o )
% 4.69/5.02 = zero_zero_nat ) ).
% 4.69/5.02
% 4.69/5.02 % sum.empty
% 4.69/5.02 thf(fact_6495_sum_Oempty,axiom,
% 4.69/5.02 ! [G: $o > int] :
% 4.69/5.02 ( ( groups8505340233167759370_o_int @ G @ bot_bot_set_o )
% 4.69/5.02 = zero_zero_int ) ).
% 4.69/5.02
% 4.69/5.02 % sum.empty
% 4.69/5.02 thf(fact_6496_sum_Oempty,axiom,
% 4.69/5.02 ! [G: $o > code_integer] :
% 4.69/5.02 ( ( groups4406642042086082107nteger @ G @ bot_bot_set_o )
% 4.69/5.02 = zero_z3403309356797280102nteger ) ).
% 4.69/5.02
% 4.69/5.02 % sum.empty
% 4.69/5.02 thf(fact_6497_sum_Oempty,axiom,
% 4.69/5.02 ! [G: nat > int] :
% 4.69/5.02 ( ( groups3539618377306564664at_int @ G @ bot_bot_set_nat )
% 4.69/5.02 = zero_zero_int ) ).
% 4.69/5.02
% 4.69/5.02 % sum.empty
% 4.69/5.02 thf(fact_6498_sum_Oempty,axiom,
% 4.69/5.02 ! [G: nat > code_integer] :
% 4.69/5.02 ( ( groups7501900531339628137nteger @ G @ bot_bot_set_nat )
% 4.69/5.02 = zero_z3403309356797280102nteger ) ).
% 4.69/5.02
% 4.69/5.02 % sum.empty
% 4.69/5.02 thf(fact_6499_sum_Oempty,axiom,
% 4.69/5.02 ! [G: int > nat] :
% 4.69/5.02 ( ( groups4541462559716669496nt_nat @ G @ bot_bot_set_int )
% 4.69/5.02 = zero_zero_nat ) ).
% 4.69/5.02
% 4.69/5.02 % sum.empty
% 4.69/5.02 thf(fact_6500_sum_Oempty,axiom,
% 4.69/5.02 ! [G: int > code_integer] :
% 4.69/5.02 ( ( groups7873554091576472773nteger @ G @ bot_bot_set_int )
% 4.69/5.02 = zero_z3403309356797280102nteger ) ).
% 4.69/5.02
% 4.69/5.02 % sum.empty
% 4.69/5.02 thf(fact_6501_member__le__sum,axiom,
% 4.69/5.02 ! [I2: code_integer,A: set_Code_integer,F: code_integer > code_integer] :
% 4.69/5.02 ( ( member_Code_integer @ I2 @ A )
% 4.69/5.02 => ( ! [X3: code_integer] :
% 4.69/5.02 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ I2 @ bot_bo3990330152332043303nteger ) ) )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 4.69/5.02 => ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ ( groups879477027807139574nteger @ F @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % member_le_sum
% 4.69/5.02 thf(fact_6502_member__le__sum,axiom,
% 4.69/5.02 ! [I2: product_unit,A: set_Product_unit,F: product_unit > code_integer] :
% 4.69/5.02 ( ( member_Product_unit @ I2 @ A )
% 4.69/5.02 => ( ! [X3: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ X3 @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ I2 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 4.69/5.02 => ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ ( groups5393439102872367408nteger @ F @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % member_le_sum
% 4.69/5.02 thf(fact_6503_member__le__sum,axiom,
% 4.69/5.02 ! [I2: $o,A: set_o,F: $o > code_integer] :
% 4.69/5.02 ( ( member_o @ I2 @ A )
% 4.69/5.02 => ( ! [X3: $o] :
% 4.69/5.02 ( ( member_o @ X3 @ ( minus_minus_set_o @ A @ ( insert_o @ I2 @ bot_bot_set_o ) ) )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 4.69/5.02 => ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ ( groups4406642042086082107nteger @ F @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % member_le_sum
% 4.69/5.02 thf(fact_6504_member__le__sum,axiom,
% 4.69/5.02 ! [I2: int,A: set_int,F: int > code_integer] :
% 4.69/5.02 ( ( member_int @ I2 @ A )
% 4.69/5.02 => ( ! [X3: int] :
% 4.69/5.02 ( ( member_int @ X3 @ ( minus_minus_set_int @ A @ ( insert_int @ I2 @ bot_bot_set_int ) ) )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 4.69/5.02 => ( ( finite_finite_int @ A )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ ( groups7873554091576472773nteger @ F @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % member_le_sum
% 4.69/5.02 thf(fact_6505_member__le__sum,axiom,
% 4.69/5.02 ! [I2: nat,A: set_nat,F: nat > code_integer] :
% 4.69/5.02 ( ( member_nat @ I2 @ A )
% 4.69/5.02 => ( ! [X3: nat] :
% 4.69/5.02 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ A @ ( insert_nat @ I2 @ bot_bot_set_nat ) ) )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 4.69/5.02 => ( ( finite_finite_nat @ A )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ ( groups7501900531339628137nteger @ F @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % member_le_sum
% 4.69/5.02 thf(fact_6506_member__le__sum,axiom,
% 4.69/5.02 ! [I2: code_integer,A: set_Code_integer,F: code_integer > rat] :
% 4.69/5.02 ( ( member_Code_integer @ I2 @ A )
% 4.69/5.02 => ( ! [X3: code_integer] :
% 4.69/5.02 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ I2 @ bot_bo3990330152332043303nteger ) ) )
% 4.69/5.02 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 4.69/5.02 => ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( groups6602215022474089585er_rat @ F @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % member_le_sum
% 4.69/5.02 thf(fact_6507_member__le__sum,axiom,
% 4.69/5.02 ! [I2: product_unit,A: set_Product_unit,F: product_unit > rat] :
% 4.69/5.02 ( ( member_Product_unit @ I2 @ A )
% 4.69/5.02 => ( ! [X3: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ X3 @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ I2 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/5.02 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 4.69/5.02 => ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( groups8131667117488461483it_rat @ F @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % member_le_sum
% 4.69/5.02 thf(fact_6508_member__le__sum,axiom,
% 4.69/5.02 ! [I2: $o,A: set_o,F: $o > rat] :
% 4.69/5.02 ( ( member_o @ I2 @ A )
% 4.69/5.02 => ( ! [X3: $o] :
% 4.69/5.02 ( ( member_o @ X3 @ ( minus_minus_set_o @ A @ ( insert_o @ I2 @ bot_bot_set_o ) ) )
% 4.69/5.02 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 4.69/5.02 => ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( groups7872700643590313910_o_rat @ F @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % member_le_sum
% 4.69/5.02 thf(fact_6509_member__le__sum,axiom,
% 4.69/5.02 ! [I2: int,A: set_int,F: int > rat] :
% 4.69/5.02 ( ( member_int @ I2 @ A )
% 4.69/5.02 => ( ! [X3: int] :
% 4.69/5.02 ( ( member_int @ X3 @ ( minus_minus_set_int @ A @ ( insert_int @ I2 @ bot_bot_set_int ) ) )
% 4.69/5.02 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 4.69/5.02 => ( ( finite_finite_int @ A )
% 4.69/5.02 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( groups3906332499630173760nt_rat @ F @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % member_le_sum
% 4.69/5.02 thf(fact_6510_member__le__sum,axiom,
% 4.69/5.02 ! [I2: nat,A: set_nat,F: nat > rat] :
% 4.69/5.02 ( ( member_nat @ I2 @ A )
% 4.69/5.02 => ( ! [X3: nat] :
% 4.69/5.02 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ A @ ( insert_nat @ I2 @ bot_bot_set_nat ) ) )
% 4.69/5.02 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 4.69/5.02 => ( ( finite_finite_nat @ A )
% 4.69/5.02 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( groups2906978787729119204at_rat @ F @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % member_le_sum
% 4.69/5.02 thf(fact_6511_sum_Ounion__disjoint,axiom,
% 4.69/5.02 ! [A: set_Code_integer,B4: set_Code_integer,G: code_integer > code_integer] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.02 => ( ( ( inf_in1364745209274528805nteger @ A @ B4 )
% 4.69/5.02 = bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( ( groups879477027807139574nteger @ G @ ( sup_su848401254843788991nteger @ A @ B4 ) )
% 4.69/5.02 = ( plus_p5714425477246183910nteger @ ( groups879477027807139574nteger @ G @ A ) @ ( groups879477027807139574nteger @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.union_disjoint
% 4.69/5.02 thf(fact_6512_sum_Ounion__disjoint,axiom,
% 4.69/5.02 ! [A: set_Code_integer,B4: set_Code_integer,G: code_integer > rat] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.02 => ( ( ( inf_in1364745209274528805nteger @ A @ B4 )
% 4.69/5.02 = bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( ( groups6602215022474089585er_rat @ G @ ( sup_su848401254843788991nteger @ A @ B4 ) )
% 4.69/5.02 = ( plus_plus_rat @ ( groups6602215022474089585er_rat @ G @ A ) @ ( groups6602215022474089585er_rat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.union_disjoint
% 4.69/5.02 thf(fact_6513_sum_Ounion__disjoint,axiom,
% 4.69/5.02 ! [A: set_Code_integer,B4: set_Code_integer,G: code_integer > nat] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.02 => ( ( ( inf_in1364745209274528805nteger @ A @ B4 )
% 4.69/5.02 = bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( ( groups7237345082560585321er_nat @ G @ ( sup_su848401254843788991nteger @ A @ B4 ) )
% 4.69/5.02 = ( plus_plus_nat @ ( groups7237345082560585321er_nat @ G @ A ) @ ( groups7237345082560585321er_nat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.union_disjoint
% 4.69/5.02 thf(fact_6514_sum_Ounion__disjoint,axiom,
% 4.69/5.02 ! [A: set_Code_integer,B4: set_Code_integer,G: code_integer > int] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.02 => ( ( ( inf_in1364745209274528805nteger @ A @ B4 )
% 4.69/5.02 = bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( ( groups7234854612051535045er_int @ G @ ( sup_su848401254843788991nteger @ A @ B4 ) )
% 4.69/5.02 = ( plus_plus_int @ ( groups7234854612051535045er_int @ G @ A ) @ ( groups7234854612051535045er_int @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.union_disjoint
% 4.69/5.02 thf(fact_6515_sum_Ounion__disjoint,axiom,
% 4.69/5.02 ! [A: set_Product_unit,B4: set_Product_unit,G: product_unit > code_integer] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( finite4290736615968046902t_unit @ B4 )
% 4.69/5.02 => ( ( ( inf_in4660618365625256667t_unit @ A @ B4 )
% 4.69/5.02 = bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( groups5393439102872367408nteger @ G @ ( sup_su793286257634532545t_unit @ A @ B4 ) )
% 4.69/5.02 = ( plus_p5714425477246183910nteger @ ( groups5393439102872367408nteger @ G @ A ) @ ( groups5393439102872367408nteger @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.union_disjoint
% 4.69/5.02 thf(fact_6516_sum_Ounion__disjoint,axiom,
% 4.69/5.02 ! [A: set_Product_unit,B4: set_Product_unit,G: product_unit > rat] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( finite4290736615968046902t_unit @ B4 )
% 4.69/5.02 => ( ( ( inf_in4660618365625256667t_unit @ A @ B4 )
% 4.69/5.02 = bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( groups8131667117488461483it_rat @ G @ ( sup_su793286257634532545t_unit @ A @ B4 ) )
% 4.69/5.02 = ( plus_plus_rat @ ( groups8131667117488461483it_rat @ G @ A ) @ ( groups8131667117488461483it_rat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.union_disjoint
% 4.69/5.02 thf(fact_6517_sum_Ounion__disjoint,axiom,
% 4.69/5.02 ! [A: set_Product_unit,B4: set_Product_unit,G: product_unit > nat] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( finite4290736615968046902t_unit @ B4 )
% 4.69/5.02 => ( ( ( inf_in4660618365625256667t_unit @ A @ B4 )
% 4.69/5.02 = bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( groups8766797177574957219it_nat @ G @ ( sup_su793286257634532545t_unit @ A @ B4 ) )
% 4.69/5.02 = ( plus_plus_nat @ ( groups8766797177574957219it_nat @ G @ A ) @ ( groups8766797177574957219it_nat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.union_disjoint
% 4.69/5.02 thf(fact_6518_sum_Ounion__disjoint,axiom,
% 4.69/5.02 ! [A: set_Product_unit,B4: set_Product_unit,G: product_unit > int] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( finite4290736615968046902t_unit @ B4 )
% 4.69/5.02 => ( ( ( inf_in4660618365625256667t_unit @ A @ B4 )
% 4.69/5.02 = bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( groups8764306707065906943it_int @ G @ ( sup_su793286257634532545t_unit @ A @ B4 ) )
% 4.69/5.02 = ( plus_plus_int @ ( groups8764306707065906943it_int @ G @ A ) @ ( groups8764306707065906943it_int @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.union_disjoint
% 4.69/5.02 thf(fact_6519_sum_Ounion__disjoint,axiom,
% 4.69/5.02 ! [A: set_o,B4: set_o,G: $o > code_integer] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ( finite_finite_o @ B4 )
% 4.69/5.02 => ( ( ( inf_inf_set_o @ A @ B4 )
% 4.69/5.02 = bot_bot_set_o )
% 4.69/5.02 => ( ( groups4406642042086082107nteger @ G @ ( sup_sup_set_o @ A @ B4 ) )
% 4.69/5.02 = ( plus_p5714425477246183910nteger @ ( groups4406642042086082107nteger @ G @ A ) @ ( groups4406642042086082107nteger @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.union_disjoint
% 4.69/5.02 thf(fact_6520_sum_Ounion__disjoint,axiom,
% 4.69/5.02 ! [A: set_o,B4: set_o,G: $o > rat] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ( finite_finite_o @ B4 )
% 4.69/5.02 => ( ( ( inf_inf_set_o @ A @ B4 )
% 4.69/5.02 = bot_bot_set_o )
% 4.69/5.02 => ( ( groups7872700643590313910_o_rat @ G @ ( sup_sup_set_o @ A @ B4 ) )
% 4.69/5.02 = ( plus_plus_rat @ ( groups7872700643590313910_o_rat @ G @ A ) @ ( groups7872700643590313910_o_rat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.union_disjoint
% 4.69/5.02 thf(fact_6521_sum__diff1,axiom,
% 4.69/5.02 ! [A: set_Code_integer,A2: code_integer,F: code_integer > rat] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( ( member_Code_integer @ A2 @ A )
% 4.69/5.02 => ( ( groups6602215022474089585er_rat @ F @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) )
% 4.69/5.02 = ( minus_minus_rat @ ( groups6602215022474089585er_rat @ F @ A ) @ ( F @ A2 ) ) ) )
% 4.69/5.02 & ( ~ ( member_Code_integer @ A2 @ A )
% 4.69/5.02 => ( ( groups6602215022474089585er_rat @ F @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) )
% 4.69/5.02 = ( groups6602215022474089585er_rat @ F @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_diff1
% 4.69/5.02 thf(fact_6522_sum__diff1,axiom,
% 4.69/5.02 ! [A: set_Product_unit,A2: product_unit,F: product_unit > rat] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( ( member_Product_unit @ A2 @ A )
% 4.69/5.02 => ( ( groups8131667117488461483it_rat @ F @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/5.02 = ( minus_minus_rat @ ( groups8131667117488461483it_rat @ F @ A ) @ ( F @ A2 ) ) ) )
% 4.69/5.02 & ( ~ ( member_Product_unit @ A2 @ A )
% 4.69/5.02 => ( ( groups8131667117488461483it_rat @ F @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/5.02 = ( groups8131667117488461483it_rat @ F @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_diff1
% 4.69/5.02 thf(fact_6523_sum__diff1,axiom,
% 4.69/5.02 ! [A: set_o,A2: $o,F: $o > rat] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ( ( member_o @ A2 @ A )
% 4.69/5.02 => ( ( groups7872700643590313910_o_rat @ F @ ( minus_minus_set_o @ A @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 4.69/5.02 = ( minus_minus_rat @ ( groups7872700643590313910_o_rat @ F @ A ) @ ( F @ A2 ) ) ) )
% 4.69/5.02 & ( ~ ( member_o @ A2 @ A )
% 4.69/5.02 => ( ( groups7872700643590313910_o_rat @ F @ ( minus_minus_set_o @ A @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 4.69/5.02 = ( groups7872700643590313910_o_rat @ F @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_diff1
% 4.69/5.02 thf(fact_6524_sum__diff1,axiom,
% 4.69/5.02 ! [A: set_int,A2: int,F: int > rat] :
% 4.69/5.02 ( ( finite_finite_int @ A )
% 4.69/5.02 => ( ( ( member_int @ A2 @ A )
% 4.69/5.02 => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 4.69/5.02 = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A ) @ ( F @ A2 ) ) ) )
% 4.69/5.02 & ( ~ ( member_int @ A2 @ A )
% 4.69/5.02 => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 4.69/5.02 = ( groups3906332499630173760nt_rat @ F @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_diff1
% 4.69/5.02 thf(fact_6525_sum__diff1,axiom,
% 4.69/5.02 ! [A: set_Code_integer,A2: code_integer,F: code_integer > int] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( ( member_Code_integer @ A2 @ A )
% 4.69/5.02 => ( ( groups7234854612051535045er_int @ F @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) )
% 4.69/5.02 = ( minus_minus_int @ ( groups7234854612051535045er_int @ F @ A ) @ ( F @ A2 ) ) ) )
% 4.69/5.02 & ( ~ ( member_Code_integer @ A2 @ A )
% 4.69/5.02 => ( ( groups7234854612051535045er_int @ F @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ A2 @ bot_bo3990330152332043303nteger ) ) )
% 4.69/5.02 = ( groups7234854612051535045er_int @ F @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_diff1
% 4.69/5.02 thf(fact_6526_sum__diff1,axiom,
% 4.69/5.02 ! [A: set_Product_unit,A2: product_unit,F: product_unit > int] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( ( member_Product_unit @ A2 @ A )
% 4.69/5.02 => ( ( groups8764306707065906943it_int @ F @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/5.02 = ( minus_minus_int @ ( groups8764306707065906943it_int @ F @ A ) @ ( F @ A2 ) ) ) )
% 4.69/5.02 & ( ~ ( member_Product_unit @ A2 @ A )
% 4.69/5.02 => ( ( groups8764306707065906943it_int @ F @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/5.02 = ( groups8764306707065906943it_int @ F @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_diff1
% 4.69/5.02 thf(fact_6527_sum__diff1,axiom,
% 4.69/5.02 ! [A: set_o,A2: $o,F: $o > int] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ( ( member_o @ A2 @ A )
% 4.69/5.02 => ( ( groups8505340233167759370_o_int @ F @ ( minus_minus_set_o @ A @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 4.69/5.02 = ( minus_minus_int @ ( groups8505340233167759370_o_int @ F @ A ) @ ( F @ A2 ) ) ) )
% 4.69/5.02 & ( ~ ( member_o @ A2 @ A )
% 4.69/5.02 => ( ( groups8505340233167759370_o_int @ F @ ( minus_minus_set_o @ A @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 4.69/5.02 = ( groups8505340233167759370_o_int @ F @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_diff1
% 4.69/5.02 thf(fact_6528_sum__diff1,axiom,
% 4.69/5.02 ! [A: set_nat,A2: nat,F: nat > rat] :
% 4.69/5.02 ( ( finite_finite_nat @ A )
% 4.69/5.02 => ( ( ( member_nat @ A2 @ A )
% 4.69/5.02 => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 4.69/5.02 = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ A ) @ ( F @ A2 ) ) ) )
% 4.69/5.02 & ( ~ ( member_nat @ A2 @ A )
% 4.69/5.02 => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 4.69/5.02 = ( groups2906978787729119204at_rat @ F @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_diff1
% 4.69/5.02 thf(fact_6529_sum__diff1,axiom,
% 4.69/5.02 ! [A: set_nat,A2: nat,F: nat > int] :
% 4.69/5.02 ( ( finite_finite_nat @ A )
% 4.69/5.02 => ( ( ( member_nat @ A2 @ A )
% 4.69/5.02 => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 4.69/5.02 = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A ) @ ( F @ A2 ) ) ) )
% 4.69/5.02 & ( ~ ( member_nat @ A2 @ A )
% 4.69/5.02 => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 4.69/5.02 = ( groups3539618377306564664at_int @ F @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_diff1
% 4.69/5.02 thf(fact_6530_sum__diff1,axiom,
% 4.69/5.02 ! [A: set_int,A2: int,F: int > int] :
% 4.69/5.02 ( ( finite_finite_int @ A )
% 4.69/5.02 => ( ( ( member_int @ A2 @ A )
% 4.69/5.02 => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 4.69/5.02 = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A ) @ ( F @ A2 ) ) ) )
% 4.69/5.02 & ( ~ ( member_int @ A2 @ A )
% 4.69/5.02 => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 4.69/5.02 = ( groups4538972089207619220nt_int @ F @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_diff1
% 4.69/5.02 thf(fact_6531_sum_Oremove,axiom,
% 4.69/5.02 ! [A: set_Code_integer,X: code_integer,G: code_integer > code_integer] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( member_Code_integer @ X @ A )
% 4.69/5.02 => ( ( groups879477027807139574nteger @ G @ A )
% 4.69/5.02 = ( plus_p5714425477246183910nteger @ ( G @ X ) @ ( groups879477027807139574nteger @ G @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.remove
% 4.69/5.02 thf(fact_6532_sum_Oremove,axiom,
% 4.69/5.02 ! [A: set_Code_integer,X: code_integer,G: code_integer > rat] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( member_Code_integer @ X @ A )
% 4.69/5.02 => ( ( groups6602215022474089585er_rat @ G @ A )
% 4.69/5.02 = ( plus_plus_rat @ ( G @ X ) @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.remove
% 4.69/5.02 thf(fact_6533_sum_Oremove,axiom,
% 4.69/5.02 ! [A: set_Code_integer,X: code_integer,G: code_integer > nat] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( member_Code_integer @ X @ A )
% 4.69/5.02 => ( ( groups7237345082560585321er_nat @ G @ A )
% 4.69/5.02 = ( plus_plus_nat @ ( G @ X ) @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.remove
% 4.69/5.02 thf(fact_6534_sum_Oremove,axiom,
% 4.69/5.02 ! [A: set_Code_integer,X: code_integer,G: code_integer > int] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( member_Code_integer @ X @ A )
% 4.69/5.02 => ( ( groups7234854612051535045er_int @ G @ A )
% 4.69/5.02 = ( plus_plus_int @ ( G @ X ) @ ( groups7234854612051535045er_int @ G @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.remove
% 4.69/5.02 thf(fact_6535_sum_Oremove,axiom,
% 4.69/5.02 ! [A: set_Product_unit,X: product_unit,G: product_unit > code_integer] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( member_Product_unit @ X @ A )
% 4.69/5.02 => ( ( groups5393439102872367408nteger @ G @ A )
% 4.69/5.02 = ( plus_p5714425477246183910nteger @ ( G @ X ) @ ( groups5393439102872367408nteger @ G @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.remove
% 4.69/5.02 thf(fact_6536_sum_Oremove,axiom,
% 4.69/5.02 ! [A: set_Product_unit,X: product_unit,G: product_unit > rat] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( member_Product_unit @ X @ A )
% 4.69/5.02 => ( ( groups8131667117488461483it_rat @ G @ A )
% 4.69/5.02 = ( plus_plus_rat @ ( G @ X ) @ ( groups8131667117488461483it_rat @ G @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.remove
% 4.69/5.02 thf(fact_6537_sum_Oremove,axiom,
% 4.69/5.02 ! [A: set_Product_unit,X: product_unit,G: product_unit > nat] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( member_Product_unit @ X @ A )
% 4.69/5.02 => ( ( groups8766797177574957219it_nat @ G @ A )
% 4.69/5.02 = ( plus_plus_nat @ ( G @ X ) @ ( groups8766797177574957219it_nat @ G @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.remove
% 4.69/5.02 thf(fact_6538_sum_Oremove,axiom,
% 4.69/5.02 ! [A: set_Product_unit,X: product_unit,G: product_unit > int] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( member_Product_unit @ X @ A )
% 4.69/5.02 => ( ( groups8764306707065906943it_int @ G @ A )
% 4.69/5.02 = ( plus_plus_int @ ( G @ X ) @ ( groups8764306707065906943it_int @ G @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.remove
% 4.69/5.02 thf(fact_6539_sum_Oremove,axiom,
% 4.69/5.02 ! [A: set_o,X: $o,G: $o > code_integer] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ( member_o @ X @ A )
% 4.69/5.02 => ( ( groups4406642042086082107nteger @ G @ A )
% 4.69/5.02 = ( plus_p5714425477246183910nteger @ ( G @ X ) @ ( groups4406642042086082107nteger @ G @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.remove
% 4.69/5.02 thf(fact_6540_sum_Oremove,axiom,
% 4.69/5.02 ! [A: set_o,X: $o,G: $o > rat] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ( member_o @ X @ A )
% 4.69/5.02 => ( ( groups7872700643590313910_o_rat @ G @ A )
% 4.69/5.02 = ( plus_plus_rat @ ( G @ X ) @ ( groups7872700643590313910_o_rat @ G @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.remove
% 4.69/5.02 thf(fact_6541_sum_Oinsert__remove,axiom,
% 4.69/5.02 ! [A: set_Code_integer,G: code_integer > code_integer,X: code_integer] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( groups879477027807139574nteger @ G @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.02 = ( plus_p5714425477246183910nteger @ ( G @ X ) @ ( groups879477027807139574nteger @ G @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert_remove
% 4.69/5.02 thf(fact_6542_sum_Oinsert__remove,axiom,
% 4.69/5.02 ! [A: set_Code_integer,G: code_integer > rat,X: code_integer] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( groups6602215022474089585er_rat @ G @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.02 = ( plus_plus_rat @ ( G @ X ) @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert_remove
% 4.69/5.02 thf(fact_6543_sum_Oinsert__remove,axiom,
% 4.69/5.02 ! [A: set_Code_integer,G: code_integer > nat,X: code_integer] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( groups7237345082560585321er_nat @ G @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.02 = ( plus_plus_nat @ ( G @ X ) @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert_remove
% 4.69/5.02 thf(fact_6544_sum_Oinsert__remove,axiom,
% 4.69/5.02 ! [A: set_Code_integer,G: code_integer > int,X: code_integer] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( groups7234854612051535045er_int @ G @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.02 = ( plus_plus_int @ ( G @ X ) @ ( groups7234854612051535045er_int @ G @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert_remove
% 4.69/5.02 thf(fact_6545_sum_Oinsert__remove,axiom,
% 4.69/5.02 ! [A: set_Product_unit,G: product_unit > code_integer,X: product_unit] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( groups5393439102872367408nteger @ G @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.02 = ( plus_p5714425477246183910nteger @ ( G @ X ) @ ( groups5393439102872367408nteger @ G @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert_remove
% 4.69/5.02 thf(fact_6546_sum_Oinsert__remove,axiom,
% 4.69/5.02 ! [A: set_Product_unit,G: product_unit > rat,X: product_unit] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( groups8131667117488461483it_rat @ G @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.02 = ( plus_plus_rat @ ( G @ X ) @ ( groups8131667117488461483it_rat @ G @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert_remove
% 4.69/5.02 thf(fact_6547_sum_Oinsert__remove,axiom,
% 4.69/5.02 ! [A: set_Product_unit,G: product_unit > nat,X: product_unit] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( groups8766797177574957219it_nat @ G @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.02 = ( plus_plus_nat @ ( G @ X ) @ ( groups8766797177574957219it_nat @ G @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert_remove
% 4.69/5.02 thf(fact_6548_sum_Oinsert__remove,axiom,
% 4.69/5.02 ! [A: set_Product_unit,G: product_unit > int,X: product_unit] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( groups8764306707065906943it_int @ G @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.02 = ( plus_plus_int @ ( G @ X ) @ ( groups8764306707065906943it_int @ G @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert_remove
% 4.69/5.02 thf(fact_6549_sum_Oinsert__remove,axiom,
% 4.69/5.02 ! [A: set_o,G: $o > code_integer,X: $o] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ( groups4406642042086082107nteger @ G @ ( insert_o @ X @ A ) )
% 4.69/5.02 = ( plus_p5714425477246183910nteger @ ( G @ X ) @ ( groups4406642042086082107nteger @ G @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert_remove
% 4.69/5.02 thf(fact_6550_sum_Oinsert__remove,axiom,
% 4.69/5.02 ! [A: set_o,G: $o > rat,X: $o] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ( groups7872700643590313910_o_rat @ G @ ( insert_o @ X @ A ) )
% 4.69/5.02 = ( plus_plus_rat @ ( G @ X ) @ ( groups7872700643590313910_o_rat @ G @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert_remove
% 4.69/5.02 thf(fact_6551_sum__strict__mono,axiom,
% 4.69/5.02 ! [A: set_Code_integer,F: code_integer > nat,G: code_integer > nat] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( ! [X3: code_integer] :
% 4.69/5.02 ( ( member_Code_integer @ X3 @ A )
% 4.69/5.02 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 4.69/5.02 => ( ord_less_nat @ ( groups7237345082560585321er_nat @ F @ A ) @ ( groups7237345082560585321er_nat @ G @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_strict_mono
% 4.69/5.02 thf(fact_6552_sum__strict__mono,axiom,
% 4.69/5.02 ! [A: set_Product_unit,F: product_unit > nat,G: product_unit > nat] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ! [X3: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ X3 @ A )
% 4.69/5.02 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 4.69/5.02 => ( ord_less_nat @ ( groups8766797177574957219it_nat @ F @ A ) @ ( groups8766797177574957219it_nat @ G @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_strict_mono
% 4.69/5.02 thf(fact_6553_sum__strict__mono,axiom,
% 4.69/5.02 ! [A: set_o,F: $o > nat,G: $o > nat] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ! [X3: $o] :
% 4.69/5.02 ( ( member_o @ X3 @ A )
% 4.69/5.02 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 4.69/5.02 => ( ord_less_nat @ ( groups8507830703676809646_o_nat @ F @ A ) @ ( groups8507830703676809646_o_nat @ G @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_strict_mono
% 4.69/5.02 thf(fact_6554_sum__strict__mono,axiom,
% 4.69/5.02 ! [A: set_int,F: int > nat,G: int > nat] :
% 4.69/5.02 ( ( finite_finite_int @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_int )
% 4.69/5.02 => ( ! [X3: int] :
% 4.69/5.02 ( ( member_int @ X3 @ A )
% 4.69/5.02 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 4.69/5.02 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A ) @ ( groups4541462559716669496nt_nat @ G @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_strict_mono
% 4.69/5.02 thf(fact_6555_sum__strict__mono,axiom,
% 4.69/5.02 ! [A: set_Code_integer,F: code_integer > int,G: code_integer > int] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( ! [X3: code_integer] :
% 4.69/5.02 ( ( member_Code_integer @ X3 @ A )
% 4.69/5.02 => ( ord_less_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 4.69/5.02 => ( ord_less_int @ ( groups7234854612051535045er_int @ F @ A ) @ ( groups7234854612051535045er_int @ G @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_strict_mono
% 4.69/5.02 thf(fact_6556_sum__strict__mono,axiom,
% 4.69/5.02 ! [A: set_Product_unit,F: product_unit > int,G: product_unit > int] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ! [X3: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ X3 @ A )
% 4.69/5.02 => ( ord_less_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 4.69/5.02 => ( ord_less_int @ ( groups8764306707065906943it_int @ F @ A ) @ ( groups8764306707065906943it_int @ G @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_strict_mono
% 4.69/5.02 thf(fact_6557_sum__strict__mono,axiom,
% 4.69/5.02 ! [A: set_o,F: $o > int,G: $o > int] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ! [X3: $o] :
% 4.69/5.02 ( ( member_o @ X3 @ A )
% 4.69/5.02 => ( ord_less_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 4.69/5.02 => ( ord_less_int @ ( groups8505340233167759370_o_int @ F @ A ) @ ( groups8505340233167759370_o_int @ G @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_strict_mono
% 4.69/5.02 thf(fact_6558_sum__strict__mono,axiom,
% 4.69/5.02 ! [A: set_nat,F: nat > int,G: nat > int] :
% 4.69/5.02 ( ( finite_finite_nat @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_nat )
% 4.69/5.02 => ( ! [X3: nat] :
% 4.69/5.02 ( ( member_nat @ X3 @ A )
% 4.69/5.02 => ( ord_less_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 4.69/5.02 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A ) @ ( groups3539618377306564664at_int @ G @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_strict_mono
% 4.69/5.02 thf(fact_6559_sum__strict__mono,axiom,
% 4.69/5.02 ! [A: set_Code_integer,F: code_integer > code_integer,G: code_integer > code_integer] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( ! [X3: code_integer] :
% 4.69/5.02 ( ( member_Code_integer @ X3 @ A )
% 4.69/5.02 => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 4.69/5.02 => ( ord_le6747313008572928689nteger @ ( groups879477027807139574nteger @ F @ A ) @ ( groups879477027807139574nteger @ G @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_strict_mono
% 4.69/5.02 thf(fact_6560_sum__strict__mono,axiom,
% 4.69/5.02 ! [A: set_Product_unit,F: product_unit > code_integer,G: product_unit > code_integer] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ! [X3: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ X3 @ A )
% 4.69/5.02 => ( ord_le6747313008572928689nteger @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 4.69/5.02 => ( ord_le6747313008572928689nteger @ ( groups5393439102872367408nteger @ F @ A ) @ ( groups5393439102872367408nteger @ G @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_strict_mono
% 4.69/5.02 thf(fact_6561_sum_Oinsert__if,axiom,
% 4.69/5.02 ! [A: set_int,X: int,G: int > code_integer] :
% 4.69/5.02 ( ( finite_finite_int @ A )
% 4.69/5.02 => ( ( ( member_int @ X @ A )
% 4.69/5.02 => ( ( groups7873554091576472773nteger @ G @ ( insert_int @ X @ A ) )
% 4.69/5.02 = ( groups7873554091576472773nteger @ G @ A ) ) )
% 4.69/5.02 & ( ~ ( member_int @ X @ A )
% 4.69/5.02 => ( ( groups7873554091576472773nteger @ G @ ( insert_int @ X @ A ) )
% 4.69/5.02 = ( plus_p5714425477246183910nteger @ ( G @ X ) @ ( groups7873554091576472773nteger @ G @ A ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert_if
% 4.69/5.02 thf(fact_6562_sum_Oinsert__if,axiom,
% 4.69/5.02 ! [A: set_o,X: $o,G: $o > code_integer] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ( ( member_o @ X @ A )
% 4.69/5.02 => ( ( groups4406642042086082107nteger @ G @ ( insert_o @ X @ A ) )
% 4.69/5.02 = ( groups4406642042086082107nteger @ G @ A ) ) )
% 4.69/5.02 & ( ~ ( member_o @ X @ A )
% 4.69/5.02 => ( ( groups4406642042086082107nteger @ G @ ( insert_o @ X @ A ) )
% 4.69/5.02 = ( plus_p5714425477246183910nteger @ ( G @ X ) @ ( groups4406642042086082107nteger @ G @ A ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert_if
% 4.69/5.02 thf(fact_6563_sum_Oinsert__if,axiom,
% 4.69/5.02 ! [A: set_Product_unit,X: product_unit,G: product_unit > code_integer] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( ( member_Product_unit @ X @ A )
% 4.69/5.02 => ( ( groups5393439102872367408nteger @ G @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.02 = ( groups5393439102872367408nteger @ G @ A ) ) )
% 4.69/5.02 & ( ~ ( member_Product_unit @ X @ A )
% 4.69/5.02 => ( ( groups5393439102872367408nteger @ G @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.02 = ( plus_p5714425477246183910nteger @ ( G @ X ) @ ( groups5393439102872367408nteger @ G @ A ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert_if
% 4.69/5.02 thf(fact_6564_sum_Oinsert__if,axiom,
% 4.69/5.02 ! [A: set_nat,X: nat,G: nat > code_integer] :
% 4.69/5.02 ( ( finite_finite_nat @ A )
% 4.69/5.02 => ( ( ( member_nat @ X @ A )
% 4.69/5.02 => ( ( groups7501900531339628137nteger @ G @ ( insert_nat @ X @ A ) )
% 4.69/5.02 = ( groups7501900531339628137nteger @ G @ A ) ) )
% 4.69/5.02 & ( ~ ( member_nat @ X @ A )
% 4.69/5.02 => ( ( groups7501900531339628137nteger @ G @ ( insert_nat @ X @ A ) )
% 4.69/5.02 = ( plus_p5714425477246183910nteger @ ( G @ X ) @ ( groups7501900531339628137nteger @ G @ A ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert_if
% 4.69/5.02 thf(fact_6565_sum_Oinsert__if,axiom,
% 4.69/5.02 ! [A: set_Code_integer,X: code_integer,G: code_integer > code_integer] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( ( member_Code_integer @ X @ A )
% 4.69/5.02 => ( ( groups879477027807139574nteger @ G @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.02 = ( groups879477027807139574nteger @ G @ A ) ) )
% 4.69/5.02 & ( ~ ( member_Code_integer @ X @ A )
% 4.69/5.02 => ( ( groups879477027807139574nteger @ G @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.02 = ( plus_p5714425477246183910nteger @ ( G @ X ) @ ( groups879477027807139574nteger @ G @ A ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert_if
% 4.69/5.02 thf(fact_6566_sum_Oinsert__if,axiom,
% 4.69/5.02 ! [A: set_int,X: int,G: int > rat] :
% 4.69/5.02 ( ( finite_finite_int @ A )
% 4.69/5.02 => ( ( ( member_int @ X @ A )
% 4.69/5.02 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A ) )
% 4.69/5.02 = ( groups3906332499630173760nt_rat @ G @ A ) ) )
% 4.69/5.02 & ( ~ ( member_int @ X @ A )
% 4.69/5.02 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A ) )
% 4.69/5.02 = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ A ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert_if
% 4.69/5.02 thf(fact_6567_sum_Oinsert__if,axiom,
% 4.69/5.02 ! [A: set_o,X: $o,G: $o > rat] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ( ( member_o @ X @ A )
% 4.69/5.02 => ( ( groups7872700643590313910_o_rat @ G @ ( insert_o @ X @ A ) )
% 4.69/5.02 = ( groups7872700643590313910_o_rat @ G @ A ) ) )
% 4.69/5.02 & ( ~ ( member_o @ X @ A )
% 4.69/5.02 => ( ( groups7872700643590313910_o_rat @ G @ ( insert_o @ X @ A ) )
% 4.69/5.02 = ( plus_plus_rat @ ( G @ X ) @ ( groups7872700643590313910_o_rat @ G @ A ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert_if
% 4.69/5.02 thf(fact_6568_sum_Oinsert__if,axiom,
% 4.69/5.02 ! [A: set_Product_unit,X: product_unit,G: product_unit > rat] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( ( member_Product_unit @ X @ A )
% 4.69/5.02 => ( ( groups8131667117488461483it_rat @ G @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.02 = ( groups8131667117488461483it_rat @ G @ A ) ) )
% 4.69/5.02 & ( ~ ( member_Product_unit @ X @ A )
% 4.69/5.02 => ( ( groups8131667117488461483it_rat @ G @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.02 = ( plus_plus_rat @ ( G @ X ) @ ( groups8131667117488461483it_rat @ G @ A ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert_if
% 4.69/5.02 thf(fact_6569_sum_Oinsert__if,axiom,
% 4.69/5.02 ! [A: set_nat,X: nat,G: nat > rat] :
% 4.69/5.02 ( ( finite_finite_nat @ A )
% 4.69/5.02 => ( ( ( member_nat @ X @ A )
% 4.69/5.02 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A ) )
% 4.69/5.02 = ( groups2906978787729119204at_rat @ G @ A ) ) )
% 4.69/5.02 & ( ~ ( member_nat @ X @ A )
% 4.69/5.02 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A ) )
% 4.69/5.02 = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert_if
% 4.69/5.02 thf(fact_6570_sum_Oinsert__if,axiom,
% 4.69/5.02 ! [A: set_Code_integer,X: code_integer,G: code_integer > rat] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( ( member_Code_integer @ X @ A )
% 4.69/5.02 => ( ( groups6602215022474089585er_rat @ G @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.02 = ( groups6602215022474089585er_rat @ G @ A ) ) )
% 4.69/5.02 & ( ~ ( member_Code_integer @ X @ A )
% 4.69/5.02 => ( ( groups6602215022474089585er_rat @ G @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.02 = ( plus_plus_rat @ ( G @ X ) @ ( groups6602215022474089585er_rat @ G @ A ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.insert_if
% 4.69/5.02 thf(fact_6571_sum__pos,axiom,
% 4.69/5.02 ! [I: set_Code_integer,F: code_integer > nat] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ I )
% 4.69/5.02 => ( ( I != bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( ! [I3: code_integer] :
% 4.69/5.02 ( ( member_Code_integer @ I3 @ I )
% 4.69/5.02 => ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 4.69/5.02 => ( ord_less_nat @ zero_zero_nat @ ( groups7237345082560585321er_nat @ F @ I ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_pos
% 4.69/5.02 thf(fact_6572_sum__pos,axiom,
% 4.69/5.02 ! [I: set_Product_unit,F: product_unit > nat] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ I )
% 4.69/5.02 => ( ( I != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ! [I3: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ I3 @ I )
% 4.69/5.02 => ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 4.69/5.02 => ( ord_less_nat @ zero_zero_nat @ ( groups8766797177574957219it_nat @ F @ I ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_pos
% 4.69/5.02 thf(fact_6573_sum__pos,axiom,
% 4.69/5.02 ! [I: set_o,F: $o > nat] :
% 4.69/5.02 ( ( finite_finite_o @ I )
% 4.69/5.02 => ( ( I != bot_bot_set_o )
% 4.69/5.02 => ( ! [I3: $o] :
% 4.69/5.02 ( ( member_o @ I3 @ I )
% 4.69/5.02 => ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 4.69/5.02 => ( ord_less_nat @ zero_zero_nat @ ( groups8507830703676809646_o_nat @ F @ I ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_pos
% 4.69/5.02 thf(fact_6574_sum__pos,axiom,
% 4.69/5.02 ! [I: set_int,F: int > nat] :
% 4.69/5.02 ( ( finite_finite_int @ I )
% 4.69/5.02 => ( ( I != bot_bot_set_int )
% 4.69/5.02 => ( ! [I3: int] :
% 4.69/5.02 ( ( member_int @ I3 @ I )
% 4.69/5.02 => ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 4.69/5.02 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_pos
% 4.69/5.02 thf(fact_6575_sum__pos,axiom,
% 4.69/5.02 ! [I: set_Code_integer,F: code_integer > int] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ I )
% 4.69/5.02 => ( ( I != bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( ! [I3: code_integer] :
% 4.69/5.02 ( ( member_Code_integer @ I3 @ I )
% 4.69/5.02 => ( ord_less_int @ zero_zero_int @ ( F @ I3 ) ) )
% 4.69/5.02 => ( ord_less_int @ zero_zero_int @ ( groups7234854612051535045er_int @ F @ I ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_pos
% 4.69/5.02 thf(fact_6576_sum__pos,axiom,
% 4.69/5.02 ! [I: set_Product_unit,F: product_unit > int] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ I )
% 4.69/5.02 => ( ( I != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ! [I3: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ I3 @ I )
% 4.69/5.02 => ( ord_less_int @ zero_zero_int @ ( F @ I3 ) ) )
% 4.69/5.02 => ( ord_less_int @ zero_zero_int @ ( groups8764306707065906943it_int @ F @ I ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_pos
% 4.69/5.02 thf(fact_6577_sum__pos,axiom,
% 4.69/5.02 ! [I: set_o,F: $o > int] :
% 4.69/5.02 ( ( finite_finite_o @ I )
% 4.69/5.02 => ( ( I != bot_bot_set_o )
% 4.69/5.02 => ( ! [I3: $o] :
% 4.69/5.02 ( ( member_o @ I3 @ I )
% 4.69/5.02 => ( ord_less_int @ zero_zero_int @ ( F @ I3 ) ) )
% 4.69/5.02 => ( ord_less_int @ zero_zero_int @ ( groups8505340233167759370_o_int @ F @ I ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_pos
% 4.69/5.02 thf(fact_6578_sum__pos,axiom,
% 4.69/5.02 ! [I: set_nat,F: nat > int] :
% 4.69/5.02 ( ( finite_finite_nat @ I )
% 4.69/5.02 => ( ( I != bot_bot_set_nat )
% 4.69/5.02 => ( ! [I3: nat] :
% 4.69/5.02 ( ( member_nat @ I3 @ I )
% 4.69/5.02 => ( ord_less_int @ zero_zero_int @ ( F @ I3 ) ) )
% 4.69/5.02 => ( ord_less_int @ zero_zero_int @ ( groups3539618377306564664at_int @ F @ I ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_pos
% 4.69/5.02 thf(fact_6579_sum__pos,axiom,
% 4.69/5.02 ! [I: set_Code_integer,F: code_integer > code_integer] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ I )
% 4.69/5.02 => ( ( I != bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( ! [I3: code_integer] :
% 4.69/5.02 ( ( member_Code_integer @ I3 @ I )
% 4.69/5.02 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 4.69/5.02 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups879477027807139574nteger @ F @ I ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_pos
% 4.69/5.02 thf(fact_6580_sum__pos,axiom,
% 4.69/5.02 ! [I: set_Product_unit,F: product_unit > code_integer] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ I )
% 4.69/5.02 => ( ( I != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ! [I3: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ I3 @ I )
% 4.69/5.02 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 4.69/5.02 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups5393439102872367408nteger @ F @ I ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_pos
% 4.69/5.02 thf(fact_6581_sum_OUnion__disjoint,axiom,
% 4.69/5.02 ! [C5: set_set_nat,G: nat > nat] :
% 4.69/5.02 ( ! [X3: set_nat] :
% 4.69/5.02 ( ( member_set_nat @ X3 @ C5 )
% 4.69/5.02 => ( finite_finite_nat @ X3 ) )
% 4.69/5.02 => ( ! [X3: set_nat] :
% 4.69/5.02 ( ( member_set_nat @ X3 @ C5 )
% 4.69/5.02 => ! [Xa3: set_nat] :
% 4.69/5.02 ( ( member_set_nat @ Xa3 @ C5 )
% 4.69/5.02 => ( ( X3 != Xa3 )
% 4.69/5.02 => ( ( inf_inf_set_nat @ X3 @ Xa3 )
% 4.69/5.02 = bot_bot_set_nat ) ) ) )
% 4.69/5.02 => ( ( groups3542108847815614940at_nat @ G @ ( comple7399068483239264473et_nat @ C5 ) )
% 4.69/5.02 = ( comp_s5456809700045850692at_nat @ groups8294997508430121362at_nat @ groups3542108847815614940at_nat @ G @ C5 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.Union_disjoint
% 4.69/5.02 thf(fact_6582_sum_OUnion__disjoint,axiom,
% 4.69/5.02 ! [C5: set_set_int,G: int > int] :
% 4.69/5.02 ( ! [X3: set_int] :
% 4.69/5.02 ( ( member_set_int @ X3 @ C5 )
% 4.69/5.02 => ( finite_finite_int @ X3 ) )
% 4.69/5.02 => ( ! [X3: set_int] :
% 4.69/5.02 ( ( member_set_int @ X3 @ C5 )
% 4.69/5.02 => ! [Xa3: set_int] :
% 4.69/5.02 ( ( member_set_int @ Xa3 @ C5 )
% 4.69/5.02 => ( ( X3 != Xa3 )
% 4.69/5.02 => ( ( inf_inf_set_int @ X3 @ Xa3 )
% 4.69/5.02 = bot_bot_set_int ) ) ) )
% 4.69/5.02 => ( ( groups4538972089207619220nt_int @ G @ ( comple3221217463730067765et_int @ C5 ) )
% 4.69/5.02 = ( comp_s9098231955081793132nt_int @ groups1256056575759317066nt_int @ groups4538972089207619220nt_int @ G @ C5 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum.Union_disjoint
% 4.69/5.02 thf(fact_6583_sum__diff1__nat,axiom,
% 4.69/5.02 ! [A2: product_unit,A: set_Product_unit,F: product_unit > nat] :
% 4.69/5.02 ( ( ( member_Product_unit @ A2 @ A )
% 4.69/5.02 => ( ( groups8766797177574957219it_nat @ F @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/5.02 = ( minus_minus_nat @ ( groups8766797177574957219it_nat @ F @ A ) @ ( F @ A2 ) ) ) )
% 4.69/5.02 & ( ~ ( member_Product_unit @ A2 @ A )
% 4.69/5.02 => ( ( groups8766797177574957219it_nat @ F @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ A2 @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/5.02 = ( groups8766797177574957219it_nat @ F @ A ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_diff1_nat
% 4.69/5.02 thf(fact_6584_sum__diff1__nat,axiom,
% 4.69/5.02 ! [A2: $o,A: set_o,F: $o > nat] :
% 4.69/5.02 ( ( ( member_o @ A2 @ A )
% 4.69/5.02 => ( ( groups8507830703676809646_o_nat @ F @ ( minus_minus_set_o @ A @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 4.69/5.02 = ( minus_minus_nat @ ( groups8507830703676809646_o_nat @ F @ A ) @ ( F @ A2 ) ) ) )
% 4.69/5.02 & ( ~ ( member_o @ A2 @ A )
% 4.69/5.02 => ( ( groups8507830703676809646_o_nat @ F @ ( minus_minus_set_o @ A @ ( insert_o @ A2 @ bot_bot_set_o ) ) )
% 4.69/5.02 = ( groups8507830703676809646_o_nat @ F @ A ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_diff1_nat
% 4.69/5.02 thf(fact_6585_sum__diff1__nat,axiom,
% 4.69/5.02 ! [A2: int,A: set_int,F: int > nat] :
% 4.69/5.02 ( ( ( member_int @ A2 @ A )
% 4.69/5.02 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 4.69/5.02 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A ) @ ( F @ A2 ) ) ) )
% 4.69/5.02 & ( ~ ( member_int @ A2 @ A )
% 4.69/5.02 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A @ ( insert_int @ A2 @ bot_bot_set_int ) ) )
% 4.69/5.02 = ( groups4541462559716669496nt_nat @ F @ A ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_diff1_nat
% 4.69/5.02 thf(fact_6586_sum__diff1__nat,axiom,
% 4.69/5.02 ! [A2: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o,F: ( produc3658429121746597890et_nat > $o ) > nat] :
% 4.69/5.02 ( ( ( member6576561426505652726_nat_o @ A2 @ A )
% 4.69/5.02 => ( ( groups6742167275697360483_o_nat @ F @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/5.02 = ( minus_minus_nat @ ( groups6742167275697360483_o_nat @ F @ A ) @ ( F @ A2 ) ) ) )
% 4.69/5.02 & ( ~ ( member6576561426505652726_nat_o @ A2 @ A )
% 4.69/5.02 => ( ( groups6742167275697360483_o_nat @ F @ ( minus_1801376950450012436_nat_o @ A @ ( insert5175938949040314269_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/5.02 = ( groups6742167275697360483_o_nat @ F @ A ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_diff1_nat
% 4.69/5.02 thf(fact_6587_sum__diff1__nat,axiom,
% 4.69/5.02 ! [A2: nat,A: set_nat,F: nat > nat] :
% 4.69/5.02 ( ( ( member_nat @ A2 @ A )
% 4.69/5.02 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 4.69/5.02 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A ) @ ( F @ A2 ) ) ) )
% 4.69/5.02 & ( ~ ( member_nat @ A2 @ A )
% 4.69/5.02 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A @ ( insert_nat @ A2 @ bot_bot_set_nat ) ) )
% 4.69/5.02 = ( groups3542108847815614940at_nat @ F @ A ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_diff1_nat
% 4.69/5.02 thf(fact_6588_bezout__add__strong__nat,axiom,
% 4.69/5.02 ! [A2: nat,B: nat] :
% 4.69/5.02 ( ( A2 != zero_zero_nat )
% 4.69/5.02 => ? [D: nat,X3: nat,Y2: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ D @ A2 )
% 4.69/5.02 & ( dvd_dvd_nat @ D @ B )
% 4.69/5.02 & ( ( times_times_nat @ A2 @ X3 )
% 4.69/5.02 = ( plus_plus_nat @ ( times_times_nat @ B @ Y2 ) @ D ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % bezout_add_strong_nat
% 4.69/5.02 thf(fact_6589_bezout1__nat,axiom,
% 4.69/5.02 ! [A2: nat,B: nat] :
% 4.69/5.02 ? [D: nat,X3: nat,Y2: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ D @ A2 )
% 4.69/5.02 & ( dvd_dvd_nat @ D @ B )
% 4.69/5.02 & ( ( ( minus_minus_nat @ ( times_times_nat @ A2 @ X3 ) @ ( times_times_nat @ B @ Y2 ) )
% 4.69/5.02 = D )
% 4.69/5.02 | ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A2 @ Y2 ) )
% 4.69/5.02 = D ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % bezout1_nat
% 4.69/5.02 thf(fact_6590_bezout__add__nat,axiom,
% 4.69/5.02 ! [A2: nat,B: nat] :
% 4.69/5.02 ? [D: nat,X3: nat,Y2: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ D @ A2 )
% 4.69/5.02 & ( dvd_dvd_nat @ D @ B )
% 4.69/5.02 & ( ( ( times_times_nat @ A2 @ X3 )
% 4.69/5.02 = ( plus_plus_nat @ ( times_times_nat @ B @ Y2 ) @ D ) )
% 4.69/5.02 | ( ( times_times_nat @ B @ X3 )
% 4.69/5.02 = ( plus_plus_nat @ ( times_times_nat @ A2 @ Y2 ) @ D ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % bezout_add_nat
% 4.69/5.02 thf(fact_6591_bezout__lemma__nat,axiom,
% 4.69/5.02 ! [D2: nat,A2: nat,B: nat,X: nat,Y: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ D2 @ A2 )
% 4.69/5.02 => ( ( dvd_dvd_nat @ D2 @ B )
% 4.69/5.02 => ( ( ( ( times_times_nat @ A2 @ X )
% 4.69/5.02 = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D2 ) )
% 4.69/5.02 | ( ( times_times_nat @ B @ X )
% 4.69/5.02 = ( plus_plus_nat @ ( times_times_nat @ A2 @ Y ) @ D2 ) ) )
% 4.69/5.02 => ? [X3: nat,Y2: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ D2 @ A2 )
% 4.69/5.02 & ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ A2 @ B ) )
% 4.69/5.02 & ( ( ( times_times_nat @ A2 @ X3 )
% 4.69/5.02 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A2 @ B ) @ Y2 ) @ D2 ) )
% 4.69/5.02 | ( ( times_times_nat @ ( plus_plus_nat @ A2 @ B ) @ X3 )
% 4.69/5.02 = ( plus_plus_nat @ ( times_times_nat @ A2 @ Y2 ) @ D2 ) ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % bezout_lemma_nat
% 4.69/5.02 thf(fact_6592_dvd__productE,axiom,
% 4.69/5.02 ! [P3: nat,A2: nat,B: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ P3 @ ( times_times_nat @ A2 @ B ) )
% 4.69/5.02 => ~ ! [X3: nat,Y2: nat] :
% 4.69/5.02 ( ( P3
% 4.69/5.02 = ( times_times_nat @ X3 @ Y2 ) )
% 4.69/5.02 => ( ( dvd_dvd_nat @ X3 @ A2 )
% 4.69/5.02 => ~ ( dvd_dvd_nat @ Y2 @ B ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_productE
% 4.69/5.02 thf(fact_6593_dvd__productE,axiom,
% 4.69/5.02 ! [P3: int,A2: int,B: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ P3 @ ( times_times_int @ A2 @ B ) )
% 4.69/5.02 => ~ ! [X3: int,Y2: int] :
% 4.69/5.02 ( ( P3
% 4.69/5.02 = ( times_times_int @ X3 @ Y2 ) )
% 4.69/5.02 => ( ( dvd_dvd_int @ X3 @ A2 )
% 4.69/5.02 => ~ ( dvd_dvd_int @ Y2 @ B ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % dvd_productE
% 4.69/5.02 thf(fact_6594_division__decomp,axiom,
% 4.69/5.02 ! [A2: nat,B: nat,C: nat] :
% 4.69/5.02 ( ( dvd_dvd_nat @ A2 @ ( times_times_nat @ B @ C ) )
% 4.69/5.02 => ? [B10: nat,C8: nat] :
% 4.69/5.02 ( ( A2
% 4.69/5.02 = ( times_times_nat @ B10 @ C8 ) )
% 4.69/5.02 & ( dvd_dvd_nat @ B10 @ B )
% 4.69/5.02 & ( dvd_dvd_nat @ C8 @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % division_decomp
% 4.69/5.02 thf(fact_6595_division__decomp,axiom,
% 4.69/5.02 ! [A2: int,B: int,C: int] :
% 4.69/5.02 ( ( dvd_dvd_int @ A2 @ ( times_times_int @ B @ C ) )
% 4.69/5.02 => ? [B10: int,C8: int] :
% 4.69/5.02 ( ( A2
% 4.69/5.02 = ( times_times_int @ B10 @ C8 ) )
% 4.69/5.02 & ( dvd_dvd_int @ B10 @ B )
% 4.69/5.02 & ( dvd_dvd_int @ C8 @ C ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % division_decomp
% 4.69/5.02 thf(fact_6596_card__Min__le__sum,axiom,
% 4.69/5.02 ! [A: set_Code_integer,F: code_integer > nat] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ord_less_eq_nat @ ( times_times_nat @ ( finite4902975817058060853nteger @ A ) @ ( lattic8721135487736765967in_nat @ ( image_951025933927791156er_nat @ F @ A ) ) ) @ ( groups7237345082560585321er_nat @ F @ A ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % card_Min_le_sum
% 4.69/5.02 thf(fact_6597_card__Min__le__sum,axiom,
% 4.69/5.02 ! [A: set_nat,F: nat > nat] :
% 4.69/5.02 ( ( finite_finite_nat @ A )
% 4.69/5.02 => ( ord_less_eq_nat @ ( times_times_nat @ ( finite_card_nat @ A ) @ ( lattic8721135487736765967in_nat @ ( image_nat_nat2 @ F @ A ) ) ) @ ( groups3542108847815614940at_nat @ F @ A ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % card_Min_le_sum
% 4.69/5.02 thf(fact_6598_Min__singleton,axiom,
% 4.69/5.02 ! [X: product_unit] :
% 4.69/5.02 ( ( lattic8554435388794137742t_unit @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) )
% 4.69/5.02 = X ) ).
% 4.69/5.02
% 4.69/5.02 % Min_singleton
% 4.69/5.02 thf(fact_6599_Min__singleton,axiom,
% 4.69/5.02 ! [X: $o] :
% 4.69/5.02 ( ( lattic1973801136483472281_Min_o @ ( insert_o @ X @ bot_bot_set_o ) )
% 4.69/5.02 = X ) ).
% 4.69/5.02
% 4.69/5.02 % Min_singleton
% 4.69/5.02 thf(fact_6600_Min__singleton,axiom,
% 4.69/5.02 ! [X: nat] :
% 4.69/5.02 ( ( lattic8721135487736765967in_nat @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 4.69/5.02 = X ) ).
% 4.69/5.02
% 4.69/5.02 % Min_singleton
% 4.69/5.02 thf(fact_6601_Min__singleton,axiom,
% 4.69/5.02 ! [X: int] :
% 4.69/5.02 ( ( lattic8718645017227715691in_int @ ( insert_int @ X @ bot_bot_set_int ) )
% 4.69/5.02 = X ) ).
% 4.69/5.02
% 4.69/5.02 % Min_singleton
% 4.69/5.02 thf(fact_6602_Min_Obounded__iff,axiom,
% 4.69/5.02 ! [A: set_Code_integer,X: code_integer] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( ( ord_le3102999989581377725nteger @ X @ ( lattic1063845414844153500nteger @ A ) )
% 4.69/5.02 = ( ! [X2: code_integer] :
% 4.69/5.02 ( ( member_Code_integer @ X2 @ A )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ X @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.bounded_iff
% 4.69/5.02 thf(fact_6603_Min_Obounded__iff,axiom,
% 4.69/5.02 ! [A: set_Product_unit,X: product_unit] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( ord_le3221252021190050221t_unit @ X @ ( lattic8554435388794137742t_unit @ A ) )
% 4.69/5.02 = ( ! [X2: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ X2 @ A )
% 4.69/5.02 => ( ord_le3221252021190050221t_unit @ X @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.bounded_iff
% 4.69/5.02 thf(fact_6604_Min_Obounded__iff,axiom,
% 4.69/5.02 ! [A: set_o,X: $o] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( ord_less_eq_o @ X @ ( lattic1973801136483472281_Min_o @ A ) )
% 4.69/5.02 = ( ! [X2: $o] :
% 4.69/5.02 ( ( member_o @ X2 @ A )
% 4.69/5.02 => ( ord_less_eq_o @ X @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.bounded_iff
% 4.69/5.02 thf(fact_6605_Min_Obounded__iff,axiom,
% 4.69/5.02 ! [A: set_rat,X: rat] :
% 4.69/5.02 ( ( finite_finite_rat @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_rat )
% 4.69/5.02 => ( ( ord_less_eq_rat @ X @ ( lattic8086005427650270231in_rat @ A ) )
% 4.69/5.02 = ( ! [X2: rat] :
% 4.69/5.02 ( ( member_rat @ X2 @ A )
% 4.69/5.02 => ( ord_less_eq_rat @ X @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.bounded_iff
% 4.69/5.02 thf(fact_6606_Min_Obounded__iff,axiom,
% 4.69/5.02 ! [A: set_nat,X: nat] :
% 4.69/5.02 ( ( finite_finite_nat @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_nat )
% 4.69/5.02 => ( ( ord_less_eq_nat @ X @ ( lattic8721135487736765967in_nat @ A ) )
% 4.69/5.02 = ( ! [X2: nat] :
% 4.69/5.02 ( ( member_nat @ X2 @ A )
% 4.69/5.02 => ( ord_less_eq_nat @ X @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.bounded_iff
% 4.69/5.02 thf(fact_6607_Min_Obounded__iff,axiom,
% 4.69/5.02 ! [A: set_int,X: int] :
% 4.69/5.02 ( ( finite_finite_int @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_int )
% 4.69/5.02 => ( ( ord_less_eq_int @ X @ ( lattic8718645017227715691in_int @ A ) )
% 4.69/5.02 = ( ! [X2: int] :
% 4.69/5.02 ( ( member_int @ X2 @ A )
% 4.69/5.02 => ( ord_less_eq_int @ X @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.bounded_iff
% 4.69/5.02 thf(fact_6608_Min__gr__iff,axiom,
% 4.69/5.02 ! [A: set_Product_unit,X: product_unit] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( ord_le361264281704409273t_unit @ X @ ( lattic8554435388794137742t_unit @ A ) )
% 4.69/5.02 = ( ! [X2: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ X2 @ A )
% 4.69/5.02 => ( ord_le361264281704409273t_unit @ X @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_gr_iff
% 4.69/5.02 thf(fact_6609_Min__gr__iff,axiom,
% 4.69/5.02 ! [A: set_o,X: $o] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( ord_less_o @ X @ ( lattic1973801136483472281_Min_o @ A ) )
% 4.69/5.02 = ( ! [X2: $o] :
% 4.69/5.02 ( ( member_o @ X2 @ A )
% 4.69/5.02 => ( ord_less_o @ X @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_gr_iff
% 4.69/5.02 thf(fact_6610_Min__gr__iff,axiom,
% 4.69/5.02 ! [A: set_nat,X: nat] :
% 4.69/5.02 ( ( finite_finite_nat @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_nat )
% 4.69/5.02 => ( ( ord_less_nat @ X @ ( lattic8721135487736765967in_nat @ A ) )
% 4.69/5.02 = ( ! [X2: nat] :
% 4.69/5.02 ( ( member_nat @ X2 @ A )
% 4.69/5.02 => ( ord_less_nat @ X @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_gr_iff
% 4.69/5.02 thf(fact_6611_Min__gr__iff,axiom,
% 4.69/5.02 ! [A: set_int,X: int] :
% 4.69/5.02 ( ( finite_finite_int @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_int )
% 4.69/5.02 => ( ( ord_less_int @ X @ ( lattic8718645017227715691in_int @ A ) )
% 4.69/5.02 = ( ! [X2: int] :
% 4.69/5.02 ( ( member_int @ X2 @ A )
% 4.69/5.02 => ( ord_less_int @ X @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_gr_iff
% 4.69/5.02 thf(fact_6612_Min__gr__iff,axiom,
% 4.69/5.02 ! [A: set_Code_integer,X: code_integer] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( ( ord_le6747313008572928689nteger @ X @ ( lattic1063845414844153500nteger @ A ) )
% 4.69/5.02 = ( ! [X2: code_integer] :
% 4.69/5.02 ( ( member_Code_integer @ X2 @ A )
% 4.69/5.02 => ( ord_le6747313008572928689nteger @ X @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_gr_iff
% 4.69/5.02 thf(fact_6613_Min__gr__iff,axiom,
% 4.69/5.02 ! [A: set_rat,X: rat] :
% 4.69/5.02 ( ( finite_finite_rat @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_rat )
% 4.69/5.02 => ( ( ord_less_rat @ X @ ( lattic8086005427650270231in_rat @ A ) )
% 4.69/5.02 = ( ! [X2: rat] :
% 4.69/5.02 ( ( member_rat @ X2 @ A )
% 4.69/5.02 => ( ord_less_rat @ X @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_gr_iff
% 4.69/5.02 thf(fact_6614_Min__in,axiom,
% 4.69/5.02 ! [A: set_Code_integer] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( member_Code_integer @ ( lattic1063845414844153500nteger @ A ) @ A ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_in
% 4.69/5.02 thf(fact_6615_Min__in,axiom,
% 4.69/5.02 ! [A: set_Product_unit] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( member_Product_unit @ ( lattic8554435388794137742t_unit @ A ) @ A ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_in
% 4.69/5.02 thf(fact_6616_Min__in,axiom,
% 4.69/5.02 ! [A: set_o] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( member_o @ ( lattic1973801136483472281_Min_o @ A ) @ A ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_in
% 4.69/5.02 thf(fact_6617_Min__in,axiom,
% 4.69/5.02 ! [A: set_nat] :
% 4.69/5.02 ( ( finite_finite_nat @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_nat )
% 4.69/5.02 => ( member_nat @ ( lattic8721135487736765967in_nat @ A ) @ A ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_in
% 4.69/5.02 thf(fact_6618_Min__in,axiom,
% 4.69/5.02 ! [A: set_int] :
% 4.69/5.02 ( ( finite_finite_int @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_int )
% 4.69/5.02 => ( member_int @ ( lattic8718645017227715691in_int @ A ) @ A ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_in
% 4.69/5.02 thf(fact_6619_Min__eq__iff,axiom,
% 4.69/5.02 ! [A: set_Code_integer,M4: code_integer] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( ( ( lattic1063845414844153500nteger @ A )
% 4.69/5.02 = M4 )
% 4.69/5.02 = ( ( member_Code_integer @ M4 @ A )
% 4.69/5.02 & ! [X2: code_integer] :
% 4.69/5.02 ( ( member_Code_integer @ X2 @ A )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ M4 @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_eq_iff
% 4.69/5.02 thf(fact_6620_Min__eq__iff,axiom,
% 4.69/5.02 ! [A: set_Product_unit,M4: product_unit] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( ( lattic8554435388794137742t_unit @ A )
% 4.69/5.02 = M4 )
% 4.69/5.02 = ( ( member_Product_unit @ M4 @ A )
% 4.69/5.02 & ! [X2: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ X2 @ A )
% 4.69/5.02 => ( ord_le3221252021190050221t_unit @ M4 @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_eq_iff
% 4.69/5.02 thf(fact_6621_Min__eq__iff,axiom,
% 4.69/5.02 ! [A: set_o,M4: $o] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( ( lattic1973801136483472281_Min_o @ A )
% 4.69/5.02 = M4 )
% 4.69/5.02 = ( ( member_o @ M4 @ A )
% 4.69/5.02 & ! [X2: $o] :
% 4.69/5.02 ( ( member_o @ X2 @ A )
% 4.69/5.02 => ( ord_less_eq_o @ M4 @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_eq_iff
% 4.69/5.02 thf(fact_6622_Min__eq__iff,axiom,
% 4.69/5.02 ! [A: set_rat,M4: rat] :
% 4.69/5.02 ( ( finite_finite_rat @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_rat )
% 4.69/5.02 => ( ( ( lattic8086005427650270231in_rat @ A )
% 4.69/5.02 = M4 )
% 4.69/5.02 = ( ( member_rat @ M4 @ A )
% 4.69/5.02 & ! [X2: rat] :
% 4.69/5.02 ( ( member_rat @ X2 @ A )
% 4.69/5.02 => ( ord_less_eq_rat @ M4 @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_eq_iff
% 4.69/5.02 thf(fact_6623_Min__eq__iff,axiom,
% 4.69/5.02 ! [A: set_nat,M4: nat] :
% 4.69/5.02 ( ( finite_finite_nat @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_nat )
% 4.69/5.02 => ( ( ( lattic8721135487736765967in_nat @ A )
% 4.69/5.02 = M4 )
% 4.69/5.02 = ( ( member_nat @ M4 @ A )
% 4.69/5.02 & ! [X2: nat] :
% 4.69/5.02 ( ( member_nat @ X2 @ A )
% 4.69/5.02 => ( ord_less_eq_nat @ M4 @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_eq_iff
% 4.69/5.02 thf(fact_6624_Min__eq__iff,axiom,
% 4.69/5.02 ! [A: set_int,M4: int] :
% 4.69/5.02 ( ( finite_finite_int @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_int )
% 4.69/5.02 => ( ( ( lattic8718645017227715691in_int @ A )
% 4.69/5.02 = M4 )
% 4.69/5.02 = ( ( member_int @ M4 @ A )
% 4.69/5.02 & ! [X2: int] :
% 4.69/5.02 ( ( member_int @ X2 @ A )
% 4.69/5.02 => ( ord_less_eq_int @ M4 @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_eq_iff
% 4.69/5.02 thf(fact_6625_Min__le__iff,axiom,
% 4.69/5.02 ! [A: set_Code_integer,X: code_integer] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( ( ord_le3102999989581377725nteger @ ( lattic1063845414844153500nteger @ A ) @ X )
% 4.69/5.02 = ( ? [X2: code_integer] :
% 4.69/5.02 ( ( member_Code_integer @ X2 @ A )
% 4.69/5.02 & ( ord_le3102999989581377725nteger @ X2 @ X ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_le_iff
% 4.69/5.02 thf(fact_6626_Min__le__iff,axiom,
% 4.69/5.02 ! [A: set_Product_unit,X: product_unit] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( ord_le3221252021190050221t_unit @ ( lattic8554435388794137742t_unit @ A ) @ X )
% 4.69/5.02 = ( ? [X2: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ X2 @ A )
% 4.69/5.02 & ( ord_le3221252021190050221t_unit @ X2 @ X ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_le_iff
% 4.69/5.02 thf(fact_6627_Min__le__iff,axiom,
% 4.69/5.02 ! [A: set_o,X: $o] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( ord_less_eq_o @ ( lattic1973801136483472281_Min_o @ A ) @ X )
% 4.69/5.02 = ( ? [X2: $o] :
% 4.69/5.02 ( ( member_o @ X2 @ A )
% 4.69/5.02 & ( ord_less_eq_o @ X2 @ X ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_le_iff
% 4.69/5.02 thf(fact_6628_Min__le__iff,axiom,
% 4.69/5.02 ! [A: set_rat,X: rat] :
% 4.69/5.02 ( ( finite_finite_rat @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_rat )
% 4.69/5.02 => ( ( ord_less_eq_rat @ ( lattic8086005427650270231in_rat @ A ) @ X )
% 4.69/5.02 = ( ? [X2: rat] :
% 4.69/5.02 ( ( member_rat @ X2 @ A )
% 4.69/5.02 & ( ord_less_eq_rat @ X2 @ X ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_le_iff
% 4.69/5.02 thf(fact_6629_Min__le__iff,axiom,
% 4.69/5.02 ! [A: set_nat,X: nat] :
% 4.69/5.02 ( ( finite_finite_nat @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_nat )
% 4.69/5.02 => ( ( ord_less_eq_nat @ ( lattic8721135487736765967in_nat @ A ) @ X )
% 4.69/5.02 = ( ? [X2: nat] :
% 4.69/5.02 ( ( member_nat @ X2 @ A )
% 4.69/5.02 & ( ord_less_eq_nat @ X2 @ X ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_le_iff
% 4.69/5.02 thf(fact_6630_Min__le__iff,axiom,
% 4.69/5.02 ! [A: set_int,X: int] :
% 4.69/5.02 ( ( finite_finite_int @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_int )
% 4.69/5.02 => ( ( ord_less_eq_int @ ( lattic8718645017227715691in_int @ A ) @ X )
% 4.69/5.02 = ( ? [X2: int] :
% 4.69/5.02 ( ( member_int @ X2 @ A )
% 4.69/5.02 & ( ord_less_eq_int @ X2 @ X ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_le_iff
% 4.69/5.02 thf(fact_6631_eq__Min__iff,axiom,
% 4.69/5.02 ! [A: set_Code_integer,M4: code_integer] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( ( M4
% 4.69/5.02 = ( lattic1063845414844153500nteger @ A ) )
% 4.69/5.02 = ( ( member_Code_integer @ M4 @ A )
% 4.69/5.02 & ! [X2: code_integer] :
% 4.69/5.02 ( ( member_Code_integer @ X2 @ A )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ M4 @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % eq_Min_iff
% 4.69/5.02 thf(fact_6632_eq__Min__iff,axiom,
% 4.69/5.02 ! [A: set_Product_unit,M4: product_unit] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( M4
% 4.69/5.02 = ( lattic8554435388794137742t_unit @ A ) )
% 4.69/5.02 = ( ( member_Product_unit @ M4 @ A )
% 4.69/5.02 & ! [X2: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ X2 @ A )
% 4.69/5.02 => ( ord_le3221252021190050221t_unit @ M4 @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % eq_Min_iff
% 4.69/5.02 thf(fact_6633_eq__Min__iff,axiom,
% 4.69/5.02 ! [A: set_o,M4: $o] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( M4
% 4.69/5.02 = ( lattic1973801136483472281_Min_o @ A ) )
% 4.69/5.02 = ( ( member_o @ M4 @ A )
% 4.69/5.02 & ! [X2: $o] :
% 4.69/5.02 ( ( member_o @ X2 @ A )
% 4.69/5.02 => ( ord_less_eq_o @ M4 @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % eq_Min_iff
% 4.69/5.02 thf(fact_6634_eq__Min__iff,axiom,
% 4.69/5.02 ! [A: set_rat,M4: rat] :
% 4.69/5.02 ( ( finite_finite_rat @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_rat )
% 4.69/5.02 => ( ( M4
% 4.69/5.02 = ( lattic8086005427650270231in_rat @ A ) )
% 4.69/5.02 = ( ( member_rat @ M4 @ A )
% 4.69/5.02 & ! [X2: rat] :
% 4.69/5.02 ( ( member_rat @ X2 @ A )
% 4.69/5.02 => ( ord_less_eq_rat @ M4 @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % eq_Min_iff
% 4.69/5.02 thf(fact_6635_eq__Min__iff,axiom,
% 4.69/5.02 ! [A: set_nat,M4: nat] :
% 4.69/5.02 ( ( finite_finite_nat @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_nat )
% 4.69/5.02 => ( ( M4
% 4.69/5.02 = ( lattic8721135487736765967in_nat @ A ) )
% 4.69/5.02 = ( ( member_nat @ M4 @ A )
% 4.69/5.02 & ! [X2: nat] :
% 4.69/5.02 ( ( member_nat @ X2 @ A )
% 4.69/5.02 => ( ord_less_eq_nat @ M4 @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % eq_Min_iff
% 4.69/5.02 thf(fact_6636_eq__Min__iff,axiom,
% 4.69/5.02 ! [A: set_int,M4: int] :
% 4.69/5.02 ( ( finite_finite_int @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_int )
% 4.69/5.02 => ( ( M4
% 4.69/5.02 = ( lattic8718645017227715691in_int @ A ) )
% 4.69/5.02 = ( ( member_int @ M4 @ A )
% 4.69/5.02 & ! [X2: int] :
% 4.69/5.02 ( ( member_int @ X2 @ A )
% 4.69/5.02 => ( ord_less_eq_int @ M4 @ X2 ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % eq_Min_iff
% 4.69/5.02 thf(fact_6637_Min_OboundedE,axiom,
% 4.69/5.02 ! [A: set_Code_integer,X: code_integer] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( ( ord_le3102999989581377725nteger @ X @ ( lattic1063845414844153500nteger @ A ) )
% 4.69/5.02 => ! [A10: code_integer] :
% 4.69/5.02 ( ( member_Code_integer @ A10 @ A )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ X @ A10 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.boundedE
% 4.69/5.02 thf(fact_6638_Min_OboundedE,axiom,
% 4.69/5.02 ! [A: set_Product_unit,X: product_unit] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( ord_le3221252021190050221t_unit @ X @ ( lattic8554435388794137742t_unit @ A ) )
% 4.69/5.02 => ! [A10: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ A10 @ A )
% 4.69/5.02 => ( ord_le3221252021190050221t_unit @ X @ A10 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.boundedE
% 4.69/5.02 thf(fact_6639_Min_OboundedE,axiom,
% 4.69/5.02 ! [A: set_o,X: $o] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( ord_less_eq_o @ X @ ( lattic1973801136483472281_Min_o @ A ) )
% 4.69/5.02 => ! [A10: $o] :
% 4.69/5.02 ( ( member_o @ A10 @ A )
% 4.69/5.02 => ( ord_less_eq_o @ X @ A10 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.boundedE
% 4.69/5.02 thf(fact_6640_Min_OboundedE,axiom,
% 4.69/5.02 ! [A: set_rat,X: rat] :
% 4.69/5.02 ( ( finite_finite_rat @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_rat )
% 4.69/5.02 => ( ( ord_less_eq_rat @ X @ ( lattic8086005427650270231in_rat @ A ) )
% 4.69/5.02 => ! [A10: rat] :
% 4.69/5.02 ( ( member_rat @ A10 @ A )
% 4.69/5.02 => ( ord_less_eq_rat @ X @ A10 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.boundedE
% 4.69/5.02 thf(fact_6641_Min_OboundedE,axiom,
% 4.69/5.02 ! [A: set_nat,X: nat] :
% 4.69/5.02 ( ( finite_finite_nat @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_nat )
% 4.69/5.02 => ( ( ord_less_eq_nat @ X @ ( lattic8721135487736765967in_nat @ A ) )
% 4.69/5.02 => ! [A10: nat] :
% 4.69/5.02 ( ( member_nat @ A10 @ A )
% 4.69/5.02 => ( ord_less_eq_nat @ X @ A10 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.boundedE
% 4.69/5.02 thf(fact_6642_Min_OboundedE,axiom,
% 4.69/5.02 ! [A: set_int,X: int] :
% 4.69/5.02 ( ( finite_finite_int @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_int )
% 4.69/5.02 => ( ( ord_less_eq_int @ X @ ( lattic8718645017227715691in_int @ A ) )
% 4.69/5.02 => ! [A10: int] :
% 4.69/5.02 ( ( member_int @ A10 @ A )
% 4.69/5.02 => ( ord_less_eq_int @ X @ A10 ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.boundedE
% 4.69/5.02 thf(fact_6643_Min_OboundedI,axiom,
% 4.69/5.02 ! [A: set_Code_integer,X: code_integer] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( ! [A4: code_integer] :
% 4.69/5.02 ( ( member_Code_integer @ A4 @ A )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ X @ A4 ) )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ X @ ( lattic1063845414844153500nteger @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.boundedI
% 4.69/5.02 thf(fact_6644_Min_OboundedI,axiom,
% 4.69/5.02 ! [A: set_Product_unit,X: product_unit] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ! [A4: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ A4 @ A )
% 4.69/5.02 => ( ord_le3221252021190050221t_unit @ X @ A4 ) )
% 4.69/5.02 => ( ord_le3221252021190050221t_unit @ X @ ( lattic8554435388794137742t_unit @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.boundedI
% 4.69/5.02 thf(fact_6645_Min_OboundedI,axiom,
% 4.69/5.02 ! [A: set_o,X: $o] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ! [A4: $o] :
% 4.69/5.02 ( ( member_o @ A4 @ A )
% 4.69/5.02 => ( ord_less_eq_o @ X @ A4 ) )
% 4.69/5.02 => ( ord_less_eq_o @ X @ ( lattic1973801136483472281_Min_o @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.boundedI
% 4.69/5.02 thf(fact_6646_Min_OboundedI,axiom,
% 4.69/5.02 ! [A: set_rat,X: rat] :
% 4.69/5.02 ( ( finite_finite_rat @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_rat )
% 4.69/5.02 => ( ! [A4: rat] :
% 4.69/5.02 ( ( member_rat @ A4 @ A )
% 4.69/5.02 => ( ord_less_eq_rat @ X @ A4 ) )
% 4.69/5.02 => ( ord_less_eq_rat @ X @ ( lattic8086005427650270231in_rat @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.boundedI
% 4.69/5.02 thf(fact_6647_Min_OboundedI,axiom,
% 4.69/5.02 ! [A: set_nat,X: nat] :
% 4.69/5.02 ( ( finite_finite_nat @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_nat )
% 4.69/5.02 => ( ! [A4: nat] :
% 4.69/5.02 ( ( member_nat @ A4 @ A )
% 4.69/5.02 => ( ord_less_eq_nat @ X @ A4 ) )
% 4.69/5.02 => ( ord_less_eq_nat @ X @ ( lattic8721135487736765967in_nat @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.boundedI
% 4.69/5.02 thf(fact_6648_Min_OboundedI,axiom,
% 4.69/5.02 ! [A: set_int,X: int] :
% 4.69/5.02 ( ( finite_finite_int @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_int )
% 4.69/5.02 => ( ! [A4: int] :
% 4.69/5.02 ( ( member_int @ A4 @ A )
% 4.69/5.02 => ( ord_less_eq_int @ X @ A4 ) )
% 4.69/5.02 => ( ord_less_eq_int @ X @ ( lattic8718645017227715691in_int @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.boundedI
% 4.69/5.02 thf(fact_6649_Min__less__iff,axiom,
% 4.69/5.02 ! [A: set_Product_unit,X: product_unit] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( ord_le361264281704409273t_unit @ ( lattic8554435388794137742t_unit @ A ) @ X )
% 4.69/5.02 = ( ? [X2: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ X2 @ A )
% 4.69/5.02 & ( ord_le361264281704409273t_unit @ X2 @ X ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_less_iff
% 4.69/5.02 thf(fact_6650_Min__less__iff,axiom,
% 4.69/5.02 ! [A: set_o,X: $o] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( ord_less_o @ ( lattic1973801136483472281_Min_o @ A ) @ X )
% 4.69/5.02 = ( ? [X2: $o] :
% 4.69/5.02 ( ( member_o @ X2 @ A )
% 4.69/5.02 & ( ord_less_o @ X2 @ X ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_less_iff
% 4.69/5.02 thf(fact_6651_Min__less__iff,axiom,
% 4.69/5.02 ! [A: set_nat,X: nat] :
% 4.69/5.02 ( ( finite_finite_nat @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_nat )
% 4.69/5.02 => ( ( ord_less_nat @ ( lattic8721135487736765967in_nat @ A ) @ X )
% 4.69/5.02 = ( ? [X2: nat] :
% 4.69/5.02 ( ( member_nat @ X2 @ A )
% 4.69/5.02 & ( ord_less_nat @ X2 @ X ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_less_iff
% 4.69/5.02 thf(fact_6652_Min__less__iff,axiom,
% 4.69/5.02 ! [A: set_int,X: int] :
% 4.69/5.02 ( ( finite_finite_int @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_int )
% 4.69/5.02 => ( ( ord_less_int @ ( lattic8718645017227715691in_int @ A ) @ X )
% 4.69/5.02 = ( ? [X2: int] :
% 4.69/5.02 ( ( member_int @ X2 @ A )
% 4.69/5.02 & ( ord_less_int @ X2 @ X ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_less_iff
% 4.69/5.02 thf(fact_6653_Min__less__iff,axiom,
% 4.69/5.02 ! [A: set_Code_integer,X: code_integer] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( ( ord_le6747313008572928689nteger @ ( lattic1063845414844153500nteger @ A ) @ X )
% 4.69/5.02 = ( ? [X2: code_integer] :
% 4.69/5.02 ( ( member_Code_integer @ X2 @ A )
% 4.69/5.02 & ( ord_le6747313008572928689nteger @ X2 @ X ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_less_iff
% 4.69/5.02 thf(fact_6654_Min__less__iff,axiom,
% 4.69/5.02 ! [A: set_rat,X: rat] :
% 4.69/5.02 ( ( finite_finite_rat @ A )
% 4.69/5.02 => ( ( A != bot_bot_set_rat )
% 4.69/5.02 => ( ( ord_less_rat @ ( lattic8086005427650270231in_rat @ A ) @ X )
% 4.69/5.02 = ( ? [X2: rat] :
% 4.69/5.02 ( ( member_rat @ X2 @ A )
% 4.69/5.02 & ( ord_less_rat @ X2 @ X ) ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_less_iff
% 4.69/5.02 thf(fact_6655_Min__insert2,axiom,
% 4.69/5.02 ! [A: set_o,A2: $o] :
% 4.69/5.02 ( ( finite_finite_o @ A )
% 4.69/5.02 => ( ! [B2: $o] :
% 4.69/5.02 ( ( member_o @ B2 @ A )
% 4.69/5.02 => ( ord_less_eq_o @ A2 @ B2 ) )
% 4.69/5.02 => ( ( lattic1973801136483472281_Min_o @ ( insert_o @ A2 @ A ) )
% 4.69/5.02 = A2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_insert2
% 4.69/5.02 thf(fact_6656_Min__insert2,axiom,
% 4.69/5.02 ! [A: set_Product_unit,A2: product_unit] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ! [B2: product_unit] :
% 4.69/5.02 ( ( member_Product_unit @ B2 @ A )
% 4.69/5.02 => ( ord_le3221252021190050221t_unit @ A2 @ B2 ) )
% 4.69/5.02 => ( ( lattic8554435388794137742t_unit @ ( insert_Product_unit @ A2 @ A ) )
% 4.69/5.02 = A2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_insert2
% 4.69/5.02 thf(fact_6657_Min__insert2,axiom,
% 4.69/5.02 ! [A: set_Code_integer,A2: code_integer] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.02 => ( ! [B2: code_integer] :
% 4.69/5.02 ( ( member_Code_integer @ B2 @ A )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ A2 @ B2 ) )
% 4.69/5.02 => ( ( lattic1063845414844153500nteger @ ( insert_Code_integer @ A2 @ A ) )
% 4.69/5.02 = A2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_insert2
% 4.69/5.02 thf(fact_6658_Min__insert2,axiom,
% 4.69/5.02 ! [A: set_rat,A2: rat] :
% 4.69/5.02 ( ( finite_finite_rat @ A )
% 4.69/5.02 => ( ! [B2: rat] :
% 4.69/5.02 ( ( member_rat @ B2 @ A )
% 4.69/5.02 => ( ord_less_eq_rat @ A2 @ B2 ) )
% 4.69/5.02 => ( ( lattic8086005427650270231in_rat @ ( insert_rat @ A2 @ A ) )
% 4.69/5.02 = A2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_insert2
% 4.69/5.02 thf(fact_6659_Min__insert2,axiom,
% 4.69/5.02 ! [A: set_nat,A2: nat] :
% 4.69/5.02 ( ( finite_finite_nat @ A )
% 4.69/5.02 => ( ! [B2: nat] :
% 4.69/5.02 ( ( member_nat @ B2 @ A )
% 4.69/5.02 => ( ord_less_eq_nat @ A2 @ B2 ) )
% 4.69/5.02 => ( ( lattic8721135487736765967in_nat @ ( insert_nat @ A2 @ A ) )
% 4.69/5.02 = A2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_insert2
% 4.69/5.02 thf(fact_6660_Min__insert2,axiom,
% 4.69/5.02 ! [A: set_int,A2: int] :
% 4.69/5.02 ( ( finite_finite_int @ A )
% 4.69/5.02 => ( ! [B2: int] :
% 4.69/5.02 ( ( member_int @ B2 @ A )
% 4.69/5.02 => ( ord_less_eq_int @ A2 @ B2 ) )
% 4.69/5.02 => ( ( lattic8718645017227715691in_int @ ( insert_int @ A2 @ A ) )
% 4.69/5.02 = A2 ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_insert2
% 4.69/5.02 thf(fact_6661_cInf__eq__Min,axiom,
% 4.69/5.02 ! [X4: set_int] :
% 4.69/5.02 ( ( finite_finite_int @ X4 )
% 4.69/5.02 => ( ( X4 != bot_bot_set_int )
% 4.69/5.02 => ( ( complete_Inf_Inf_int @ X4 )
% 4.69/5.02 = ( lattic8718645017227715691in_int @ X4 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_eq_Min
% 4.69/5.02 thf(fact_6662_cInf__eq__Min,axiom,
% 4.69/5.02 ! [X4: set_nat] :
% 4.69/5.02 ( ( finite_finite_nat @ X4 )
% 4.69/5.02 => ( ( X4 != bot_bot_set_nat )
% 4.69/5.02 => ( ( complete_Inf_Inf_nat @ X4 )
% 4.69/5.02 = ( lattic8721135487736765967in_nat @ X4 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_eq_Min
% 4.69/5.02 thf(fact_6663_cInf__eq__Min,axiom,
% 4.69/5.02 ! [X4: set_Product_unit] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ X4 )
% 4.69/5.02 => ( ( X4 != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( comple2584293577114468500t_unit @ X4 )
% 4.69/5.02 = ( lattic8554435388794137742t_unit @ X4 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % cInf_eq_Min
% 4.69/5.02 thf(fact_6664_Min__Inf,axiom,
% 4.69/5.02 ! [A: set_Product_unit] :
% 4.69/5.02 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.02 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( lattic8554435388794137742t_unit @ A )
% 4.69/5.02 = ( comple2584293577114468500t_unit @ A ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_Inf
% 4.69/5.02 thf(fact_6665_Min__antimono,axiom,
% 4.69/5.02 ! [M: set_Code_integer,N: set_Code_integer] :
% 4.69/5.02 ( ( ord_le7084787975880047091nteger @ M @ N )
% 4.69/5.02 => ( ( M != bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( ( finite6017078050557962740nteger @ N )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ ( lattic1063845414844153500nteger @ N ) @ ( lattic1063845414844153500nteger @ M ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_antimono
% 4.69/5.02 thf(fact_6666_Min__antimono,axiom,
% 4.69/5.02 ! [M: set_Product_unit,N: set_Product_unit] :
% 4.69/5.02 ( ( ord_le3507040750410214029t_unit @ M @ N )
% 4.69/5.02 => ( ( M != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( finite4290736615968046902t_unit @ N )
% 4.69/5.02 => ( ord_le3221252021190050221t_unit @ ( lattic8554435388794137742t_unit @ N ) @ ( lattic8554435388794137742t_unit @ M ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_antimono
% 4.69/5.02 thf(fact_6667_Min__antimono,axiom,
% 4.69/5.02 ! [M: set_o,N: set_o] :
% 4.69/5.02 ( ( ord_less_eq_set_o @ M @ N )
% 4.69/5.02 => ( ( M != bot_bot_set_o )
% 4.69/5.02 => ( ( finite_finite_o @ N )
% 4.69/5.02 => ( ord_less_eq_o @ ( lattic1973801136483472281_Min_o @ N ) @ ( lattic1973801136483472281_Min_o @ M ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_antimono
% 4.69/5.02 thf(fact_6668_Min__antimono,axiom,
% 4.69/5.02 ! [M: set_rat,N: set_rat] :
% 4.69/5.02 ( ( ord_less_eq_set_rat @ M @ N )
% 4.69/5.02 => ( ( M != bot_bot_set_rat )
% 4.69/5.02 => ( ( finite_finite_rat @ N )
% 4.69/5.02 => ( ord_less_eq_rat @ ( lattic8086005427650270231in_rat @ N ) @ ( lattic8086005427650270231in_rat @ M ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_antimono
% 4.69/5.02 thf(fact_6669_Min__antimono,axiom,
% 4.69/5.02 ! [M: set_int,N: set_int] :
% 4.69/5.02 ( ( ord_less_eq_set_int @ M @ N )
% 4.69/5.02 => ( ( M != bot_bot_set_int )
% 4.69/5.02 => ( ( finite_finite_int @ N )
% 4.69/5.02 => ( ord_less_eq_int @ ( lattic8718645017227715691in_int @ N ) @ ( lattic8718645017227715691in_int @ M ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_antimono
% 4.69/5.02 thf(fact_6670_Min__antimono,axiom,
% 4.69/5.02 ! [M: set_nat,N: set_nat] :
% 4.69/5.02 ( ( ord_less_eq_set_nat @ M @ N )
% 4.69/5.02 => ( ( M != bot_bot_set_nat )
% 4.69/5.02 => ( ( finite_finite_nat @ N )
% 4.69/5.02 => ( ord_less_eq_nat @ ( lattic8721135487736765967in_nat @ N ) @ ( lattic8721135487736765967in_nat @ M ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min_antimono
% 4.69/5.02 thf(fact_6671_Min_Osubset__imp,axiom,
% 4.69/5.02 ! [A: set_Code_integer,B4: set_Code_integer] :
% 4.69/5.02 ( ( ord_le7084787975880047091nteger @ A @ B4 )
% 4.69/5.02 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.02 => ( ord_le3102999989581377725nteger @ ( lattic1063845414844153500nteger @ B4 ) @ ( lattic1063845414844153500nteger @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.subset_imp
% 4.69/5.02 thf(fact_6672_Min_Osubset__imp,axiom,
% 4.69/5.02 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/5.02 ( ( ord_le3507040750410214029t_unit @ A @ B4 )
% 4.69/5.02 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.02 => ( ( finite4290736615968046902t_unit @ B4 )
% 4.69/5.02 => ( ord_le3221252021190050221t_unit @ ( lattic8554435388794137742t_unit @ B4 ) @ ( lattic8554435388794137742t_unit @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.subset_imp
% 4.69/5.02 thf(fact_6673_Min_Osubset__imp,axiom,
% 4.69/5.02 ! [A: set_o,B4: set_o] :
% 4.69/5.02 ( ( ord_less_eq_set_o @ A @ B4 )
% 4.69/5.02 => ( ( A != bot_bot_set_o )
% 4.69/5.02 => ( ( finite_finite_o @ B4 )
% 4.69/5.02 => ( ord_less_eq_o @ ( lattic1973801136483472281_Min_o @ B4 ) @ ( lattic1973801136483472281_Min_o @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.subset_imp
% 4.69/5.02 thf(fact_6674_Min_Osubset__imp,axiom,
% 4.69/5.02 ! [A: set_rat,B4: set_rat] :
% 4.69/5.02 ( ( ord_less_eq_set_rat @ A @ B4 )
% 4.69/5.02 => ( ( A != bot_bot_set_rat )
% 4.69/5.02 => ( ( finite_finite_rat @ B4 )
% 4.69/5.02 => ( ord_less_eq_rat @ ( lattic8086005427650270231in_rat @ B4 ) @ ( lattic8086005427650270231in_rat @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.subset_imp
% 4.69/5.02 thf(fact_6675_Min_Osubset__imp,axiom,
% 4.69/5.02 ! [A: set_int,B4: set_int] :
% 4.69/5.02 ( ( ord_less_eq_set_int @ A @ B4 )
% 4.69/5.02 => ( ( A != bot_bot_set_int )
% 4.69/5.02 => ( ( finite_finite_int @ B4 )
% 4.69/5.02 => ( ord_less_eq_int @ ( lattic8718645017227715691in_int @ B4 ) @ ( lattic8718645017227715691in_int @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.subset_imp
% 4.69/5.02 thf(fact_6676_Min_Osubset__imp,axiom,
% 4.69/5.02 ! [A: set_nat,B4: set_nat] :
% 4.69/5.02 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/5.02 => ( ( A != bot_bot_set_nat )
% 4.69/5.02 => ( ( finite_finite_nat @ B4 )
% 4.69/5.02 => ( ord_less_eq_nat @ ( lattic8721135487736765967in_nat @ B4 ) @ ( lattic8721135487736765967in_nat @ A ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Min.subset_imp
% 4.69/5.02 thf(fact_6677_minus__Min__eq__Max,axiom,
% 4.69/5.02 ! [S: set_int] :
% 4.69/5.02 ( ( finite_finite_int @ S )
% 4.69/5.02 => ( ( S != bot_bot_set_int )
% 4.69/5.02 => ( ( uminus_uminus_int @ ( lattic8718645017227715691in_int @ S ) )
% 4.69/5.02 = ( lattic8263393255366662781ax_int @ ( image_int_int2 @ uminus_uminus_int @ S ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % minus_Min_eq_Max
% 4.69/5.02 thf(fact_6678_minus__Min__eq__Max,axiom,
% 4.69/5.02 ! [S: set_Code_integer] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ S )
% 4.69/5.02 => ( ( S != bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( ( uminus1351360451143612070nteger @ ( lattic1063845414844153500nteger @ S ) )
% 4.69/5.02 = ( lattic4901227151466704046nteger @ ( image_4470545334726330049nteger @ uminus1351360451143612070nteger @ S ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % minus_Min_eq_Max
% 4.69/5.02 thf(fact_6679_minus__Max__eq__Min,axiom,
% 4.69/5.02 ! [S: set_int] :
% 4.69/5.02 ( ( finite_finite_int @ S )
% 4.69/5.02 => ( ( S != bot_bot_set_int )
% 4.69/5.02 => ( ( uminus_uminus_int @ ( lattic8263393255366662781ax_int @ S ) )
% 4.69/5.02 = ( lattic8718645017227715691in_int @ ( image_int_int2 @ uminus_uminus_int @ S ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % minus_Max_eq_Min
% 4.69/5.02 thf(fact_6680_minus__Max__eq__Min,axiom,
% 4.69/5.02 ! [S: set_Code_integer] :
% 4.69/5.02 ( ( finite6017078050557962740nteger @ S )
% 4.69/5.02 => ( ( S != bot_bo3990330152332043303nteger )
% 4.69/5.02 => ( ( uminus1351360451143612070nteger @ ( lattic4901227151466704046nteger @ S ) )
% 4.69/5.02 = ( lattic1063845414844153500nteger @ ( image_4470545334726330049nteger @ uminus1351360451143612070nteger @ S ) ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % minus_Max_eq_Min
% 4.69/5.02 thf(fact_6681_Gcd__0__iff,axiom,
% 4.69/5.02 ! [A: set_int] :
% 4.69/5.02 ( ( ( gcd_Gcd_int @ A )
% 4.69/5.02 = zero_zero_int )
% 4.69/5.02 = ( ord_less_eq_set_int @ A @ ( insert_int @ zero_zero_int @ bot_bot_set_int ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Gcd_0_iff
% 4.69/5.02 thf(fact_6682_Gcd__0__iff,axiom,
% 4.69/5.02 ! [A: set_nat] :
% 4.69/5.02 ( ( ( gcd_Gcd_nat @ A )
% 4.69/5.02 = zero_zero_nat )
% 4.69/5.02 = ( ord_less_eq_set_nat @ A @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Gcd_0_iff
% 4.69/5.02 thf(fact_6683_Gcd__fin__0__iff,axiom,
% 4.69/5.02 ! [A: set_int] :
% 4.69/5.02 ( ( ( semiri4256215615220890538in_int @ A )
% 4.69/5.02 = zero_zero_int )
% 4.69/5.02 = ( ( ord_less_eq_set_int @ A @ ( insert_int @ zero_zero_int @ bot_bot_set_int ) )
% 4.69/5.02 & ( finite_finite_int @ A ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Gcd_fin_0_iff
% 4.69/5.02 thf(fact_6684_Gcd__fin__0__iff,axiom,
% 4.69/5.02 ! [A: set_nat] :
% 4.69/5.02 ( ( ( semiri4258706085729940814in_nat @ A )
% 4.69/5.02 = zero_zero_nat )
% 4.69/5.02 = ( ( ord_less_eq_set_nat @ A @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
% 4.69/5.02 & ( finite_finite_nat @ A ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % Gcd_fin_0_iff
% 4.69/5.02 thf(fact_6685_sum__bounded__above__strict,axiom,
% 4.69/5.02 ! [A: set_nat,F: nat > rat,K4: rat] :
% 4.69/5.02 ( ! [I3: nat] :
% 4.69/5.02 ( ( member_nat @ I3 @ A )
% 4.69/5.02 => ( ord_less_rat @ ( F @ I3 ) @ K4 ) )
% 4.69/5.02 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A ) )
% 4.69/5.02 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A ) ) @ K4 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_bounded_above_strict
% 4.69/5.02 thf(fact_6686_sum__bounded__above__strict,axiom,
% 4.69/5.02 ! [A: set_int,F: int > rat,K4: rat] :
% 4.69/5.02 ( ! [I3: int] :
% 4.69/5.02 ( ( member_int @ I3 @ A )
% 4.69/5.02 => ( ord_less_rat @ ( F @ I3 ) @ K4 ) )
% 4.69/5.02 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A ) )
% 4.69/5.02 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A ) ) @ K4 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_bounded_above_strict
% 4.69/5.02 thf(fact_6687_sum__bounded__above__strict,axiom,
% 4.69/5.02 ! [A: set_o,F: $o > rat,K4: rat] :
% 4.69/5.02 ( ! [I3: $o] :
% 4.69/5.02 ( ( member_o @ I3 @ A )
% 4.69/5.02 => ( ord_less_rat @ ( F @ I3 ) @ K4 ) )
% 4.69/5.02 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_o @ A ) )
% 4.69/5.02 => ( ord_less_rat @ ( groups7872700643590313910_o_rat @ F @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_o @ A ) ) @ K4 ) ) ) ) ).
% 4.69/5.02
% 4.69/5.02 % sum_bounded_above_strict
% 4.69/5.03 thf(fact_6688_sum__bounded__above__strict,axiom,
% 4.69/5.03 ! [A: set_Product_unit,F: product_unit > rat,K4: rat] :
% 4.69/5.03 ( ! [I3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ I3 @ A )
% 4.69/5.03 => ( ord_less_rat @ ( F @ I3 ) @ K4 ) )
% 4.69/5.03 => ( ( ord_less_nat @ zero_zero_nat @ ( finite410649719033368117t_unit @ A ) )
% 4.69/5.03 => ( ord_less_rat @ ( groups8131667117488461483it_rat @ F @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite410649719033368117t_unit @ A ) ) @ K4 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % sum_bounded_above_strict
% 4.69/5.03 thf(fact_6689_sum__bounded__above__strict,axiom,
% 4.69/5.03 ! [A: set_nat,F: nat > int,K4: int] :
% 4.69/5.03 ( ! [I3: nat] :
% 4.69/5.03 ( ( member_nat @ I3 @ A )
% 4.69/5.03 => ( ord_less_int @ ( F @ I3 ) @ K4 ) )
% 4.69/5.03 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A ) )
% 4.69/5.03 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_nat @ A ) ) @ K4 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % sum_bounded_above_strict
% 4.69/5.03 thf(fact_6690_sum__bounded__above__strict,axiom,
% 4.69/5.03 ! [A: set_o,F: $o > int,K4: int] :
% 4.69/5.03 ( ! [I3: $o] :
% 4.69/5.03 ( ( member_o @ I3 @ A )
% 4.69/5.03 => ( ord_less_int @ ( F @ I3 ) @ K4 ) )
% 4.69/5.03 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_o @ A ) )
% 4.69/5.03 => ( ord_less_int @ ( groups8505340233167759370_o_int @ F @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_o @ A ) ) @ K4 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % sum_bounded_above_strict
% 4.69/5.03 thf(fact_6691_sum__bounded__above__strict,axiom,
% 4.69/5.03 ! [A: set_Product_unit,F: product_unit > int,K4: int] :
% 4.69/5.03 ( ! [I3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ I3 @ A )
% 4.69/5.03 => ( ord_less_int @ ( F @ I3 ) @ K4 ) )
% 4.69/5.03 => ( ( ord_less_nat @ zero_zero_nat @ ( finite410649719033368117t_unit @ A ) )
% 4.69/5.03 => ( ord_less_int @ ( groups8764306707065906943it_int @ F @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite410649719033368117t_unit @ A ) ) @ K4 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % sum_bounded_above_strict
% 4.69/5.03 thf(fact_6692_sum__bounded__above__strict,axiom,
% 4.69/5.03 ! [A: set_int,F: int > nat,K4: nat] :
% 4.69/5.03 ( ! [I3: int] :
% 4.69/5.03 ( ( member_int @ I3 @ A )
% 4.69/5.03 => ( ord_less_nat @ ( F @ I3 ) @ K4 ) )
% 4.69/5.03 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A ) )
% 4.69/5.03 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_int @ A ) ) @ K4 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % sum_bounded_above_strict
% 4.69/5.03 thf(fact_6693_sum__bounded__above__strict,axiom,
% 4.69/5.03 ! [A: set_o,F: $o > nat,K4: nat] :
% 4.69/5.03 ( ! [I3: $o] :
% 4.69/5.03 ( ( member_o @ I3 @ A )
% 4.69/5.03 => ( ord_less_nat @ ( F @ I3 ) @ K4 ) )
% 4.69/5.03 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_o @ A ) )
% 4.69/5.03 => ( ord_less_nat @ ( groups8507830703676809646_o_nat @ F @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_o @ A ) ) @ K4 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % sum_bounded_above_strict
% 4.69/5.03 thf(fact_6694_sum__bounded__above__strict,axiom,
% 4.69/5.03 ! [A: set_Product_unit,F: product_unit > nat,K4: nat] :
% 4.69/5.03 ( ! [I3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ I3 @ A )
% 4.69/5.03 => ( ord_less_nat @ ( F @ I3 ) @ K4 ) )
% 4.69/5.03 => ( ( ord_less_nat @ zero_zero_nat @ ( finite410649719033368117t_unit @ A ) )
% 4.69/5.03 => ( ord_less_nat @ ( groups8766797177574957219it_nat @ F @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite410649719033368117t_unit @ A ) ) @ K4 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % sum_bounded_above_strict
% 4.69/5.03 thf(fact_6695_prod__le__power,axiom,
% 4.69/5.03 ! [A: set_nat,F: nat > code_natural,N2: code_natural,K3: nat] :
% 4.69/5.03 ( ! [I3: nat] :
% 4.69/5.03 ( ( member_nat @ I3 @ A )
% 4.69/5.03 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( F @ I3 ) )
% 4.69/5.03 & ( ord_le1926595141338095240atural @ ( F @ I3 ) @ N2 ) ) )
% 4.69/5.03 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A ) @ K3 )
% 4.69/5.03 => ( ( ord_le1926595141338095240atural @ one_one_Code_natural @ N2 )
% 4.69/5.03 => ( ord_le1926595141338095240atural @ ( groups2279045934846249631atural @ F @ A ) @ ( power_7079662738309270450atural @ N2 @ K3 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_le_power
% 4.69/5.03 thf(fact_6696_prod__le__power,axiom,
% 4.69/5.03 ! [A: set_int,F: int > code_natural,N2: code_natural,K3: nat] :
% 4.69/5.03 ( ! [I3: int] :
% 4.69/5.03 ( ( member_int @ I3 @ A )
% 4.69/5.03 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( F @ I3 ) )
% 4.69/5.03 & ( ord_le1926595141338095240atural @ ( F @ I3 ) @ N2 ) ) )
% 4.69/5.03 => ( ( ord_less_eq_nat @ ( finite_card_int @ A ) @ K3 )
% 4.69/5.03 => ( ( ord_le1926595141338095240atural @ one_one_Code_natural @ N2 )
% 4.69/5.03 => ( ord_le1926595141338095240atural @ ( groups2650699495083094267atural @ F @ A ) @ ( power_7079662738309270450atural @ N2 @ K3 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_le_power
% 4.69/5.03 thf(fact_6697_prod__le__power,axiom,
% 4.69/5.03 ! [A: set_o,F: $o > code_natural,N2: code_natural,K3: nat] :
% 4.69/5.03 ( ! [I3: $o] :
% 4.69/5.03 ( ( member_o @ I3 @ A )
% 4.69/5.03 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( F @ I3 ) )
% 4.69/5.03 & ( ord_le1926595141338095240atural @ ( F @ I3 ) @ N2 ) ) )
% 4.69/5.03 => ( ( ord_less_eq_nat @ ( finite_card_o @ A ) @ K3 )
% 4.69/5.03 => ( ( ord_le1926595141338095240atural @ one_one_Code_natural @ N2 )
% 4.69/5.03 => ( ord_le1926595141338095240atural @ ( groups6518289543945209051atural @ F @ A ) @ ( power_7079662738309270450atural @ N2 @ K3 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_le_power
% 4.69/5.03 thf(fact_6698_prod__le__power,axiom,
% 4.69/5.03 ! [A: set_Product_unit,F: product_unit > code_natural,N2: code_natural,K3: nat] :
% 4.69/5.03 ( ! [I3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ I3 @ A )
% 4.69/5.03 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( F @ I3 ) )
% 4.69/5.03 & ( ord_le1926595141338095240atural @ ( F @ I3 ) @ N2 ) ) )
% 4.69/5.03 => ( ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ A ) @ K3 )
% 4.69/5.03 => ( ( ord_le1926595141338095240atural @ one_one_Code_natural @ N2 )
% 4.69/5.03 => ( ord_le1926595141338095240atural @ ( groups7008954963700796496atural @ F @ A ) @ ( power_7079662738309270450atural @ N2 @ K3 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_le_power
% 4.69/5.03 thf(fact_6699_prod__le__power,axiom,
% 4.69/5.03 ! [A: set_nat,F: nat > code_integer,N2: code_integer,K3: nat] :
% 4.69/5.03 ( ! [I3: nat] :
% 4.69/5.03 ( ( member_nat @ I3 @ A )
% 4.69/5.03 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 4.69/5.03 & ( ord_le3102999989581377725nteger @ ( F @ I3 ) @ N2 ) ) )
% 4.69/5.03 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A ) @ K3 )
% 4.69/5.03 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N2 )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F @ A ) @ ( power_8256067586552552935nteger @ N2 @ K3 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_le_power
% 4.69/5.03 thf(fact_6700_prod__le__power,axiom,
% 4.69/5.03 ! [A: set_int,F: int > code_integer,N2: code_integer,K3: nat] :
% 4.69/5.03 ( ! [I3: int] :
% 4.69/5.03 ( ( member_int @ I3 @ A )
% 4.69/5.03 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 4.69/5.03 & ( ord_le3102999989581377725nteger @ ( F @ I3 ) @ N2 ) ) )
% 4.69/5.03 => ( ( ord_less_eq_nat @ ( finite_card_int @ A ) @ K3 )
% 4.69/5.03 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N2 )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F @ A ) @ ( power_8256067586552552935nteger @ N2 @ K3 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_le_power
% 4.69/5.03 thf(fact_6701_prod__le__power,axiom,
% 4.69/5.03 ! [A: set_o,F: $o > code_integer,N2: code_integer,K3: nat] :
% 4.69/5.03 ( ! [I3: $o] :
% 4.69/5.03 ( ( member_o @ I3 @ A )
% 4.69/5.03 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 4.69/5.03 & ( ord_le3102999989581377725nteger @ ( F @ I3 ) @ N2 ) ) )
% 4.69/5.03 => ( ( ord_less_eq_nat @ ( finite_card_o @ A ) @ K3 )
% 4.69/5.03 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N2 )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ ( groups7694694392188491536nteger @ F @ A ) @ ( power_8256067586552552935nteger @ N2 @ K3 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_le_power
% 4.69/5.03 thf(fact_6702_prod__le__power,axiom,
% 4.69/5.03 ! [A: set_Product_unit,F: product_unit > code_integer,N2: code_integer,K3: nat] :
% 4.69/5.03 ( ! [I3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ I3 @ A )
% 4.69/5.03 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 4.69/5.03 & ( ord_le3102999989581377725nteger @ ( F @ I3 ) @ N2 ) ) )
% 4.69/5.03 => ( ( ord_less_eq_nat @ ( finite410649719033368117t_unit @ A ) @ K3 )
% 4.69/5.03 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N2 )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ ( groups8185359811944078981nteger @ F @ A ) @ ( power_8256067586552552935nteger @ N2 @ K3 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_le_power
% 4.69/5.03 thf(fact_6703_prod__le__power,axiom,
% 4.69/5.03 ! [A: set_nat,F: nat > rat,N2: rat,K3: nat] :
% 4.69/5.03 ( ! [I3: nat] :
% 4.69/5.03 ( ( member_nat @ I3 @ A )
% 4.69/5.03 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 4.69/5.03 & ( ord_less_eq_rat @ ( F @ I3 ) @ N2 ) ) )
% 4.69/5.03 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A ) @ K3 )
% 4.69/5.03 => ( ( ord_less_eq_rat @ one_one_rat @ N2 )
% 4.69/5.03 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A ) @ ( power_power_rat @ N2 @ K3 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_le_power
% 4.69/5.03 thf(fact_6704_prod__le__power,axiom,
% 4.69/5.03 ! [A: set_int,F: int > rat,N2: rat,K3: nat] :
% 4.69/5.03 ( ! [I3: int] :
% 4.69/5.03 ( ( member_int @ I3 @ A )
% 4.69/5.03 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 4.69/5.03 & ( ord_less_eq_rat @ ( F @ I3 ) @ N2 ) ) )
% 4.69/5.03 => ( ( ord_less_eq_nat @ ( finite_card_int @ A ) @ K3 )
% 4.69/5.03 => ( ( ord_less_eq_rat @ one_one_rat @ N2 )
% 4.69/5.03 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A ) @ ( power_power_rat @ N2 @ K3 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_le_power
% 4.69/5.03 thf(fact_6705_prod__mono2,axiom,
% 4.69/5.03 ! [B4: set_int,A: set_int,F: int > code_integer] :
% 4.69/5.03 ( ( finite_finite_int @ B4 )
% 4.69/5.03 => ( ( ord_less_eq_set_int @ A @ B4 )
% 4.69/5.03 => ( ! [B2: int] :
% 4.69/5.03 ( ( member_int @ B2 @ ( minus_minus_set_int @ B4 @ A ) )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ B2 ) ) )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ A )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ A4 ) ) )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F @ A ) @ ( groups3827104343326376752nteger @ F @ B4 ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_mono2
% 4.69/5.03 thf(fact_6706_prod__mono2,axiom,
% 4.69/5.03 ! [B4: set_o,A: set_o,F: $o > code_integer] :
% 4.69/5.03 ( ( finite_finite_o @ B4 )
% 4.69/5.03 => ( ( ord_less_eq_set_o @ A @ B4 )
% 4.69/5.03 => ( ! [B2: $o] :
% 4.69/5.03 ( ( member_o @ B2 @ ( minus_minus_set_o @ B4 @ A ) )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ B2 ) ) )
% 4.69/5.03 => ( ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ A )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ A4 ) ) )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ ( groups7694694392188491536nteger @ F @ A ) @ ( groups7694694392188491536nteger @ F @ B4 ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_mono2
% 4.69/5.03 thf(fact_6707_prod__mono2,axiom,
% 4.69/5.03 ! [B4: set_Product_unit,A: set_Product_unit,F: product_unit > code_integer] :
% 4.69/5.03 ( ( finite4290736615968046902t_unit @ B4 )
% 4.69/5.03 => ( ( ord_le3507040750410214029t_unit @ A @ B4 )
% 4.69/5.03 => ( ! [B2: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ B2 @ ( minus_6452836326544984404t_unit @ B4 @ A ) )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ B2 ) ) )
% 4.69/5.03 => ( ! [A4: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ A4 @ A )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ A4 ) ) )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ ( groups8185359811944078981nteger @ F @ A ) @ ( groups8185359811944078981nteger @ F @ B4 ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_mono2
% 4.69/5.03 thf(fact_6708_prod__mono2,axiom,
% 4.69/5.03 ! [B4: set_Code_integer,A: set_Code_integer,F: code_integer > code_integer] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ A @ B4 )
% 4.69/5.03 => ( ! [B2: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ B4 @ A ) )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ B2 ) ) )
% 4.69/5.03 => ( ! [A4: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ A4 @ A )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ A4 ) ) )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ ( groups3674199335183972705nteger @ F @ A ) @ ( groups3674199335183972705nteger @ F @ B4 ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_mono2
% 4.69/5.03 thf(fact_6709_prod__mono2,axiom,
% 4.69/5.03 ! [B4: set_int,A: set_int,F: int > rat] :
% 4.69/5.03 ( ( finite_finite_int @ B4 )
% 4.69/5.03 => ( ( ord_less_eq_set_int @ A @ B4 )
% 4.69/5.03 => ( ! [B2: int] :
% 4.69/5.03 ( ( member_int @ B2 @ ( minus_minus_set_int @ B4 @ A ) )
% 4.69/5.03 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ A )
% 4.69/5.03 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 4.69/5.03 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A ) @ ( groups1072433553688619179nt_rat @ F @ B4 ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_mono2
% 4.69/5.03 thf(fact_6710_prod__mono2,axiom,
% 4.69/5.03 ! [B4: set_o,A: set_o,F: $o > rat] :
% 4.69/5.03 ( ( finite_finite_o @ B4 )
% 4.69/5.03 => ( ( ord_less_eq_set_o @ A @ B4 )
% 4.69/5.03 => ( ! [B2: $o] :
% 4.69/5.03 ( ( member_o @ B2 @ ( minus_minus_set_o @ B4 @ A ) )
% 4.69/5.03 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 4.69/5.03 => ( ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ A )
% 4.69/5.03 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 4.69/5.03 => ( ord_less_eq_rat @ ( groups2869687844427037835_o_rat @ F @ A ) @ ( groups2869687844427037835_o_rat @ F @ B4 ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_mono2
% 4.69/5.03 thf(fact_6711_prod__mono2,axiom,
% 4.69/5.03 ! [B4: set_Product_unit,A: set_Product_unit,F: product_unit > rat] :
% 4.69/5.03 ( ( finite4290736615968046902t_unit @ B4 )
% 4.69/5.03 => ( ( ord_le3507040750410214029t_unit @ A @ B4 )
% 4.69/5.03 => ( ! [B2: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ B2 @ ( minus_6452836326544984404t_unit @ B4 @ A ) )
% 4.69/5.03 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 4.69/5.03 => ( ! [A4: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ A4 @ A )
% 4.69/5.03 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 4.69/5.03 => ( ord_less_eq_rat @ ( groups8984663225794451456it_rat @ F @ A ) @ ( groups8984663225794451456it_rat @ F @ B4 ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_mono2
% 4.69/5.03 thf(fact_6712_prod__mono2,axiom,
% 4.69/5.03 ! [B4: set_Code_integer,A: set_Code_integer,F: code_integer > rat] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ A @ B4 )
% 4.69/5.03 => ( ! [B2: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ B4 @ A ) )
% 4.69/5.03 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B2 ) ) )
% 4.69/5.03 => ( ! [A4: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ A4 @ A )
% 4.69/5.03 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 4.69/5.03 => ( ord_less_eq_rat @ ( groups2555765274223993564er_rat @ F @ A ) @ ( groups2555765274223993564er_rat @ F @ B4 ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_mono2
% 4.69/5.03 thf(fact_6713_prod__mono2,axiom,
% 4.69/5.03 ! [B4: set_int,A: set_int,F: int > int] :
% 4.69/5.03 ( ( finite_finite_int @ B4 )
% 4.69/5.03 => ( ( ord_less_eq_set_int @ A @ B4 )
% 4.69/5.03 => ( ! [B2: int] :
% 4.69/5.03 ( ( member_int @ B2 @ ( minus_minus_set_int @ B4 @ A ) )
% 4.69/5.03 => ( ord_less_eq_int @ one_one_int @ ( F @ B2 ) ) )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ A )
% 4.69/5.03 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A4 ) ) )
% 4.69/5.03 => ( ord_less_eq_int @ ( groups1705073143266064639nt_int @ F @ A ) @ ( groups1705073143266064639nt_int @ F @ B4 ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_mono2
% 4.69/5.03 thf(fact_6714_prod__mono2,axiom,
% 4.69/5.03 ! [B4: set_o,A: set_o,F: $o > int] :
% 4.69/5.03 ( ( finite_finite_o @ B4 )
% 4.69/5.03 => ( ( ord_less_eq_set_o @ A @ B4 )
% 4.69/5.03 => ( ! [B2: $o] :
% 4.69/5.03 ( ( member_o @ B2 @ ( minus_minus_set_o @ B4 @ A ) )
% 4.69/5.03 => ( ord_less_eq_int @ one_one_int @ ( F @ B2 ) ) )
% 4.69/5.03 => ( ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ A )
% 4.69/5.03 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A4 ) ) )
% 4.69/5.03 => ( ord_less_eq_int @ ( groups3502327434004483295_o_int @ F @ A ) @ ( groups3502327434004483295_o_int @ F @ B4 ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_mono2
% 4.69/5.03 thf(fact_6715_neg__equal__iff__equal,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( ( uminus_uminus_int @ A2 )
% 4.69/5.03 = ( uminus_uminus_int @ B ) )
% 4.69/5.03 = ( A2 = B ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_equal_iff_equal
% 4.69/5.03 thf(fact_6716_neg__equal__iff__equal,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( ( uminus1351360451143612070nteger @ A2 )
% 4.69/5.03 = ( uminus1351360451143612070nteger @ B ) )
% 4.69/5.03 = ( A2 = B ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_equal_iff_equal
% 4.69/5.03 thf(fact_6717_add_Oinverse__inverse,axiom,
% 4.69/5.03 ! [A2: int] :
% 4.69/5.03 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A2 ) )
% 4.69/5.03 = A2 ) ).
% 4.69/5.03
% 4.69/5.03 % add.inverse_inverse
% 4.69/5.03 thf(fact_6718_add_Oinverse__inverse,axiom,
% 4.69/5.03 ! [A2: code_integer] :
% 4.69/5.03 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A2 ) )
% 4.69/5.03 = A2 ) ).
% 4.69/5.03
% 4.69/5.03 % add.inverse_inverse
% 4.69/5.03 thf(fact_6719_Compl__subset__Compl__iff,axiom,
% 4.69/5.03 ! [A: set_nat,B4: set_nat] :
% 4.69/5.03 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ A ) @ ( uminus5710092332889474511et_nat @ B4 ) )
% 4.69/5.03 = ( ord_less_eq_set_nat @ B4 @ A ) ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_subset_Compl_iff
% 4.69/5.03 thf(fact_6720_Compl__anti__mono,axiom,
% 4.69/5.03 ! [A: set_nat,B4: set_nat] :
% 4.69/5.03 ( ( ord_less_eq_set_nat @ A @ B4 )
% 4.69/5.03 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ B4 ) @ ( uminus5710092332889474511et_nat @ A ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_anti_mono
% 4.69/5.03 thf(fact_6721_neg__le__iff__le,axiom,
% 4.69/5.03 ! [B: code_integer,A2: code_integer] :
% 4.69/5.03 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A2 ) )
% 4.69/5.03 = ( ord_le3102999989581377725nteger @ A2 @ B ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_le_iff_le
% 4.69/5.03 thf(fact_6722_neg__le__iff__le,axiom,
% 4.69/5.03 ! [B: rat,A2: rat] :
% 4.69/5.03 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A2 ) )
% 4.69/5.03 = ( ord_less_eq_rat @ A2 @ B ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_le_iff_le
% 4.69/5.03 thf(fact_6723_neg__le__iff__le,axiom,
% 4.69/5.03 ! [B: int,A2: int] :
% 4.69/5.03 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A2 ) )
% 4.69/5.03 = ( ord_less_eq_int @ A2 @ B ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_le_iff_le
% 4.69/5.03 thf(fact_6724_neg__equal__zero,axiom,
% 4.69/5.03 ! [A2: int] :
% 4.69/5.03 ( ( ( uminus_uminus_int @ A2 )
% 4.69/5.03 = A2 )
% 4.69/5.03 = ( A2 = zero_zero_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_equal_zero
% 4.69/5.03 thf(fact_6725_neg__equal__zero,axiom,
% 4.69/5.03 ! [A2: code_integer] :
% 4.69/5.03 ( ( ( uminus1351360451143612070nteger @ A2 )
% 4.69/5.03 = A2 )
% 4.69/5.03 = ( A2 = zero_z3403309356797280102nteger ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_equal_zero
% 4.69/5.03 thf(fact_6726_equal__neg__zero,axiom,
% 4.69/5.03 ! [A2: int] :
% 4.69/5.03 ( ( A2
% 4.69/5.03 = ( uminus_uminus_int @ A2 ) )
% 4.69/5.03 = ( A2 = zero_zero_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % equal_neg_zero
% 4.69/5.03 thf(fact_6727_equal__neg__zero,axiom,
% 4.69/5.03 ! [A2: code_integer] :
% 4.69/5.03 ( ( A2
% 4.69/5.03 = ( uminus1351360451143612070nteger @ A2 ) )
% 4.69/5.03 = ( A2 = zero_z3403309356797280102nteger ) ) ).
% 4.69/5.03
% 4.69/5.03 % equal_neg_zero
% 4.69/5.03 thf(fact_6728_neg__equal__0__iff__equal,axiom,
% 4.69/5.03 ! [A2: int] :
% 4.69/5.03 ( ( ( uminus_uminus_int @ A2 )
% 4.69/5.03 = zero_zero_int )
% 4.69/5.03 = ( A2 = zero_zero_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_equal_0_iff_equal
% 4.69/5.03 thf(fact_6729_neg__equal__0__iff__equal,axiom,
% 4.69/5.03 ! [A2: code_integer] :
% 4.69/5.03 ( ( ( uminus1351360451143612070nteger @ A2 )
% 4.69/5.03 = zero_z3403309356797280102nteger )
% 4.69/5.03 = ( A2 = zero_z3403309356797280102nteger ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_equal_0_iff_equal
% 4.69/5.03 thf(fact_6730_neg__0__equal__iff__equal,axiom,
% 4.69/5.03 ! [A2: int] :
% 4.69/5.03 ( ( zero_zero_int
% 4.69/5.03 = ( uminus_uminus_int @ A2 ) )
% 4.69/5.03 = ( zero_zero_int = A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_0_equal_iff_equal
% 4.69/5.03 thf(fact_6731_neg__0__equal__iff__equal,axiom,
% 4.69/5.03 ! [A2: code_integer] :
% 4.69/5.03 ( ( zero_z3403309356797280102nteger
% 4.69/5.03 = ( uminus1351360451143612070nteger @ A2 ) )
% 4.69/5.03 = ( zero_z3403309356797280102nteger = A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_0_equal_iff_equal
% 4.69/5.03 thf(fact_6732_add_Oinverse__neutral,axiom,
% 4.69/5.03 ( ( uminus_uminus_int @ zero_zero_int )
% 4.69/5.03 = zero_zero_int ) ).
% 4.69/5.03
% 4.69/5.03 % add.inverse_neutral
% 4.69/5.03 thf(fact_6733_add_Oinverse__neutral,axiom,
% 4.69/5.03 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 4.69/5.03 = zero_z3403309356797280102nteger ) ).
% 4.69/5.03
% 4.69/5.03 % add.inverse_neutral
% 4.69/5.03 thf(fact_6734_neg__less__iff__less,axiom,
% 4.69/5.03 ! [B: rat,A2: rat] :
% 4.69/5.03 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A2 ) )
% 4.69/5.03 = ( ord_less_rat @ A2 @ B ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_less_iff_less
% 4.69/5.03 thf(fact_6735_neg__less__iff__less,axiom,
% 4.69/5.03 ! [B: int,A2: int] :
% 4.69/5.03 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A2 ) )
% 4.69/5.03 = ( ord_less_int @ A2 @ B ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_less_iff_less
% 4.69/5.03 thf(fact_6736_neg__less__iff__less,axiom,
% 4.69/5.03 ! [B: code_integer,A2: code_integer] :
% 4.69/5.03 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A2 ) )
% 4.69/5.03 = ( ord_le6747313008572928689nteger @ A2 @ B ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_less_iff_less
% 4.69/5.03 thf(fact_6737_minus__add__distrib,axiom,
% 4.69/5.03 ! [A2: rat,B: rat] :
% 4.69/5.03 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A2 @ B ) )
% 4.69/5.03 = ( plus_plus_rat @ ( uminus_uminus_rat @ A2 ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_add_distrib
% 4.69/5.03 thf(fact_6738_minus__add__distrib,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( uminus_uminus_int @ ( plus_plus_int @ A2 @ B ) )
% 4.69/5.03 = ( plus_plus_int @ ( uminus_uminus_int @ A2 ) @ ( uminus_uminus_int @ B ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_add_distrib
% 4.69/5.03 thf(fact_6739_minus__add__distrib,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) )
% 4.69/5.03 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A2 ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_add_distrib
% 4.69/5.03 thf(fact_6740_minus__add__cancel,axiom,
% 4.69/5.03 ! [A2: rat,B: rat] :
% 4.69/5.03 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A2 ) @ ( plus_plus_rat @ A2 @ B ) )
% 4.69/5.03 = B ) ).
% 4.69/5.03
% 4.69/5.03 % minus_add_cancel
% 4.69/5.03 thf(fact_6741_minus__add__cancel,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( plus_plus_int @ ( uminus_uminus_int @ A2 ) @ ( plus_plus_int @ A2 @ B ) )
% 4.69/5.03 = B ) ).
% 4.69/5.03
% 4.69/5.03 % minus_add_cancel
% 4.69/5.03 thf(fact_6742_minus__add__cancel,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A2 ) @ ( plus_p5714425477246183910nteger @ A2 @ B ) )
% 4.69/5.03 = B ) ).
% 4.69/5.03
% 4.69/5.03 % minus_add_cancel
% 4.69/5.03 thf(fact_6743_add__minus__cancel,axiom,
% 4.69/5.03 ! [A2: rat,B: rat] :
% 4.69/5.03 ( ( plus_plus_rat @ A2 @ ( plus_plus_rat @ ( uminus_uminus_rat @ A2 ) @ B ) )
% 4.69/5.03 = B ) ).
% 4.69/5.03
% 4.69/5.03 % add_minus_cancel
% 4.69/5.03 thf(fact_6744_add__minus__cancel,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( plus_plus_int @ A2 @ ( plus_plus_int @ ( uminus_uminus_int @ A2 ) @ B ) )
% 4.69/5.03 = B ) ).
% 4.69/5.03
% 4.69/5.03 % add_minus_cancel
% 4.69/5.03 thf(fact_6745_add__minus__cancel,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( plus_p5714425477246183910nteger @ A2 @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A2 ) @ B ) )
% 4.69/5.03 = B ) ).
% 4.69/5.03
% 4.69/5.03 % add_minus_cancel
% 4.69/5.03 thf(fact_6746_mult__minus__left,axiom,
% 4.69/5.03 ! [A2: rat,B: rat] :
% 4.69/5.03 ( ( times_times_rat @ ( uminus_uminus_rat @ A2 ) @ B )
% 4.69/5.03 = ( uminus_uminus_rat @ ( times_times_rat @ A2 @ B ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % mult_minus_left
% 4.69/5.03 thf(fact_6747_mult__minus__left,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( times_times_int @ ( uminus_uminus_int @ A2 ) @ B )
% 4.69/5.03 = ( uminus_uminus_int @ ( times_times_int @ A2 @ B ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % mult_minus_left
% 4.69/5.03 thf(fact_6748_mult__minus__left,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A2 ) @ B )
% 4.69/5.03 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A2 @ B ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % mult_minus_left
% 4.69/5.03 thf(fact_6749_minus__mult__minus,axiom,
% 4.69/5.03 ! [A2: rat,B: rat] :
% 4.69/5.03 ( ( times_times_rat @ ( uminus_uminus_rat @ A2 ) @ ( uminus_uminus_rat @ B ) )
% 4.69/5.03 = ( times_times_rat @ A2 @ B ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_mult_minus
% 4.69/5.03 thf(fact_6750_minus__mult__minus,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( times_times_int @ ( uminus_uminus_int @ A2 ) @ ( uminus_uminus_int @ B ) )
% 4.69/5.03 = ( times_times_int @ A2 @ B ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_mult_minus
% 4.69/5.03 thf(fact_6751_minus__mult__minus,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A2 ) @ ( uminus1351360451143612070nteger @ B ) )
% 4.69/5.03 = ( times_3573771949741848930nteger @ A2 @ B ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_mult_minus
% 4.69/5.03 thf(fact_6752_mult__minus__right,axiom,
% 4.69/5.03 ! [A2: rat,B: rat] :
% 4.69/5.03 ( ( times_times_rat @ A2 @ ( uminus_uminus_rat @ B ) )
% 4.69/5.03 = ( uminus_uminus_rat @ ( times_times_rat @ A2 @ B ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % mult_minus_right
% 4.69/5.03 thf(fact_6753_mult__minus__right,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( times_times_int @ A2 @ ( uminus_uminus_int @ B ) )
% 4.69/5.03 = ( uminus_uminus_int @ ( times_times_int @ A2 @ B ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % mult_minus_right
% 4.69/5.03 thf(fact_6754_mult__minus__right,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( times_3573771949741848930nteger @ A2 @ ( uminus1351360451143612070nteger @ B ) )
% 4.69/5.03 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A2 @ B ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % mult_minus_right
% 4.69/5.03 thf(fact_6755_minus__diff__eq,axiom,
% 4.69/5.03 ! [A2: rat,B: rat] :
% 4.69/5.03 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A2 @ B ) )
% 4.69/5.03 = ( minus_minus_rat @ B @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_diff_eq
% 4.69/5.03 thf(fact_6756_minus__diff__eq,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( uminus_uminus_int @ ( minus_minus_int @ A2 @ B ) )
% 4.69/5.03 = ( minus_minus_int @ B @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_diff_eq
% 4.69/5.03 thf(fact_6757_minus__diff__eq,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A2 @ B ) )
% 4.69/5.03 = ( minus_8373710615458151222nteger @ B @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_diff_eq
% 4.69/5.03 thf(fact_6758_Compl__disjoint,axiom,
% 4.69/5.03 ! [A: set_Product_unit] :
% 4.69/5.03 ( ( inf_in4660618365625256667t_unit @ A @ ( uminus5944136376168626660t_unit @ A ) )
% 4.69/5.03 = bot_bo3957492148770167129t_unit ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_disjoint
% 4.69/5.03 thf(fact_6759_Compl__disjoint,axiom,
% 4.69/5.03 ! [A: set_o] :
% 4.69/5.03 ( ( inf_inf_set_o @ A @ ( uminus_uminus_set_o @ A ) )
% 4.69/5.03 = bot_bot_set_o ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_disjoint
% 4.69/5.03 thf(fact_6760_Compl__disjoint,axiom,
% 4.69/5.03 ! [A: set_nat] :
% 4.69/5.03 ( ( inf_inf_set_nat @ A @ ( uminus5710092332889474511et_nat @ A ) )
% 4.69/5.03 = bot_bot_set_nat ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_disjoint
% 4.69/5.03 thf(fact_6761_Compl__disjoint,axiom,
% 4.69/5.03 ! [A: set_int] :
% 4.69/5.03 ( ( inf_inf_set_int @ A @ ( uminus1532241313380277803et_int @ A ) )
% 4.69/5.03 = bot_bot_set_int ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_disjoint
% 4.69/5.03 thf(fact_6762_Compl__disjoint,axiom,
% 4.69/5.03 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/5.03 ( ( inf_in1906310914598751387_nat_o @ A @ ( uminus5254974436814262692_nat_o @ A ) )
% 4.69/5.03 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_disjoint
% 4.69/5.03 thf(fact_6763_Compl__disjoint2,axiom,
% 4.69/5.03 ! [A: set_Product_unit] :
% 4.69/5.03 ( ( inf_in4660618365625256667t_unit @ ( uminus5944136376168626660t_unit @ A ) @ A )
% 4.69/5.03 = bot_bo3957492148770167129t_unit ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_disjoint2
% 4.69/5.03 thf(fact_6764_Compl__disjoint2,axiom,
% 4.69/5.03 ! [A: set_o] :
% 4.69/5.03 ( ( inf_inf_set_o @ ( uminus_uminus_set_o @ A ) @ A )
% 4.69/5.03 = bot_bot_set_o ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_disjoint2
% 4.69/5.03 thf(fact_6765_Compl__disjoint2,axiom,
% 4.69/5.03 ! [A: set_nat] :
% 4.69/5.03 ( ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A ) @ A )
% 4.69/5.03 = bot_bot_set_nat ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_disjoint2
% 4.69/5.03 thf(fact_6766_Compl__disjoint2,axiom,
% 4.69/5.03 ! [A: set_int] :
% 4.69/5.03 ( ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ A ) @ A )
% 4.69/5.03 = bot_bot_set_int ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_disjoint2
% 4.69/5.03 thf(fact_6767_Compl__disjoint2,axiom,
% 4.69/5.03 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/5.03 ( ( inf_in1906310914598751387_nat_o @ ( uminus5254974436814262692_nat_o @ A ) @ A )
% 4.69/5.03 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_disjoint2
% 4.69/5.03 thf(fact_6768_inter__compl__diff__conv,axiom,
% 4.69/5.03 ! [A: set_nat,B4: set_nat] :
% 4.69/5.03 ( ( inf_inf_set_nat @ A @ ( uminus5710092332889474511et_nat @ B4 ) )
% 4.69/5.03 = ( minus_minus_set_nat @ A @ B4 ) ) ).
% 4.69/5.03
% 4.69/5.03 % inter_compl_diff_conv
% 4.69/5.03 thf(fact_6769_Diff__Compl,axiom,
% 4.69/5.03 ! [A: set_nat,B4: set_nat] :
% 4.69/5.03 ( ( minus_minus_set_nat @ A @ ( uminus5710092332889474511et_nat @ B4 ) )
% 4.69/5.03 = ( inf_inf_set_nat @ A @ B4 ) ) ).
% 4.69/5.03
% 4.69/5.03 % Diff_Compl
% 4.69/5.03 thf(fact_6770_Compl__Diff__eq,axiom,
% 4.69/5.03 ! [A: set_nat,B4: set_nat] :
% 4.69/5.03 ( ( uminus5710092332889474511et_nat @ ( minus_minus_set_nat @ A @ B4 ) )
% 4.69/5.03 = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ A ) @ B4 ) ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_Diff_eq
% 4.69/5.03 thf(fact_6771_neg__0__le__iff__le,axiom,
% 4.69/5.03 ! [A2: code_integer] :
% 4.69/5.03 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A2 ) )
% 4.69/5.03 = ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_0_le_iff_le
% 4.69/5.03 thf(fact_6772_neg__0__le__iff__le,axiom,
% 4.69/5.03 ! [A2: rat] :
% 4.69/5.03 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A2 ) )
% 4.69/5.03 = ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_0_le_iff_le
% 4.69/5.03 thf(fact_6773_neg__0__le__iff__le,axiom,
% 4.69/5.03 ! [A2: int] :
% 4.69/5.03 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A2 ) )
% 4.69/5.03 = ( ord_less_eq_int @ A2 @ zero_zero_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_0_le_iff_le
% 4.69/5.03 thf(fact_6774_neg__le__0__iff__le,axiom,
% 4.69/5.03 ! [A2: code_integer] :
% 4.69/5.03 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A2 ) @ zero_z3403309356797280102nteger )
% 4.69/5.03 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_le_0_iff_le
% 4.69/5.03 thf(fact_6775_neg__le__0__iff__le,axiom,
% 4.69/5.03 ! [A2: rat] :
% 4.69/5.03 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A2 ) @ zero_zero_rat )
% 4.69/5.03 = ( ord_less_eq_rat @ zero_zero_rat @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_le_0_iff_le
% 4.69/5.03 thf(fact_6776_neg__le__0__iff__le,axiom,
% 4.69/5.03 ! [A2: int] :
% 4.69/5.03 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A2 ) @ zero_zero_int )
% 4.69/5.03 = ( ord_less_eq_int @ zero_zero_int @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_le_0_iff_le
% 4.69/5.03 thf(fact_6777_less__eq__neg__nonpos,axiom,
% 4.69/5.03 ! [A2: code_integer] :
% 4.69/5.03 ( ( ord_le3102999989581377725nteger @ A2 @ ( uminus1351360451143612070nteger @ A2 ) )
% 4.69/5.03 = ( ord_le3102999989581377725nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_eq_neg_nonpos
% 4.69/5.03 thf(fact_6778_less__eq__neg__nonpos,axiom,
% 4.69/5.03 ! [A2: rat] :
% 4.69/5.03 ( ( ord_less_eq_rat @ A2 @ ( uminus_uminus_rat @ A2 ) )
% 4.69/5.03 = ( ord_less_eq_rat @ A2 @ zero_zero_rat ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_eq_neg_nonpos
% 4.69/5.03 thf(fact_6779_less__eq__neg__nonpos,axiom,
% 4.69/5.03 ! [A2: int] :
% 4.69/5.03 ( ( ord_less_eq_int @ A2 @ ( uminus_uminus_int @ A2 ) )
% 4.69/5.03 = ( ord_less_eq_int @ A2 @ zero_zero_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_eq_neg_nonpos
% 4.69/5.03 thf(fact_6780_neg__less__eq__nonneg,axiom,
% 4.69/5.03 ! [A2: code_integer] :
% 4.69/5.03 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A2 ) @ A2 )
% 4.69/5.03 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_less_eq_nonneg
% 4.69/5.03 thf(fact_6781_neg__less__eq__nonneg,axiom,
% 4.69/5.03 ! [A2: rat] :
% 4.69/5.03 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A2 ) @ A2 )
% 4.69/5.03 = ( ord_less_eq_rat @ zero_zero_rat @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_less_eq_nonneg
% 4.69/5.03 thf(fact_6782_neg__less__eq__nonneg,axiom,
% 4.69/5.03 ! [A2: int] :
% 4.69/5.03 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A2 ) @ A2 )
% 4.69/5.03 = ( ord_less_eq_int @ zero_zero_int @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_less_eq_nonneg
% 4.69/5.03 thf(fact_6783_less__neg__neg,axiom,
% 4.69/5.03 ! [A2: rat] :
% 4.69/5.03 ( ( ord_less_rat @ A2 @ ( uminus_uminus_rat @ A2 ) )
% 4.69/5.03 = ( ord_less_rat @ A2 @ zero_zero_rat ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_neg_neg
% 4.69/5.03 thf(fact_6784_less__neg__neg,axiom,
% 4.69/5.03 ! [A2: int] :
% 4.69/5.03 ( ( ord_less_int @ A2 @ ( uminus_uminus_int @ A2 ) )
% 4.69/5.03 = ( ord_less_int @ A2 @ zero_zero_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_neg_neg
% 4.69/5.03 thf(fact_6785_less__neg__neg,axiom,
% 4.69/5.03 ! [A2: code_integer] :
% 4.69/5.03 ( ( ord_le6747313008572928689nteger @ A2 @ ( uminus1351360451143612070nteger @ A2 ) )
% 4.69/5.03 = ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_neg_neg
% 4.69/5.03 thf(fact_6786_neg__less__pos,axiom,
% 4.69/5.03 ! [A2: rat] :
% 4.69/5.03 ( ( ord_less_rat @ ( uminus_uminus_rat @ A2 ) @ A2 )
% 4.69/5.03 = ( ord_less_rat @ zero_zero_rat @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_less_pos
% 4.69/5.03 thf(fact_6787_neg__less__pos,axiom,
% 4.69/5.03 ! [A2: int] :
% 4.69/5.03 ( ( ord_less_int @ ( uminus_uminus_int @ A2 ) @ A2 )
% 4.69/5.03 = ( ord_less_int @ zero_zero_int @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_less_pos
% 4.69/5.03 thf(fact_6788_neg__less__pos,axiom,
% 4.69/5.03 ! [A2: code_integer] :
% 4.69/5.03 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A2 ) @ A2 )
% 4.69/5.03 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_less_pos
% 4.69/5.03 thf(fact_6789_neg__0__less__iff__less,axiom,
% 4.69/5.03 ! [A2: rat] :
% 4.69/5.03 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A2 ) )
% 4.69/5.03 = ( ord_less_rat @ A2 @ zero_zero_rat ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_0_less_iff_less
% 4.69/5.03 thf(fact_6790_neg__0__less__iff__less,axiom,
% 4.69/5.03 ! [A2: int] :
% 4.69/5.03 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A2 ) )
% 4.69/5.03 = ( ord_less_int @ A2 @ zero_zero_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_0_less_iff_less
% 4.69/5.03 thf(fact_6791_neg__0__less__iff__less,axiom,
% 4.69/5.03 ! [A2: code_integer] :
% 4.69/5.03 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A2 ) )
% 4.69/5.03 = ( ord_le6747313008572928689nteger @ A2 @ zero_z3403309356797280102nteger ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_0_less_iff_less
% 4.69/5.03 thf(fact_6792_neg__less__0__iff__less,axiom,
% 4.69/5.03 ! [A2: rat] :
% 4.69/5.03 ( ( ord_less_rat @ ( uminus_uminus_rat @ A2 ) @ zero_zero_rat )
% 4.69/5.03 = ( ord_less_rat @ zero_zero_rat @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_less_0_iff_less
% 4.69/5.03 thf(fact_6793_neg__less__0__iff__less,axiom,
% 4.69/5.03 ! [A2: int] :
% 4.69/5.03 ( ( ord_less_int @ ( uminus_uminus_int @ A2 ) @ zero_zero_int )
% 4.69/5.03 = ( ord_less_int @ zero_zero_int @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_less_0_iff_less
% 4.69/5.03 thf(fact_6794_neg__less__0__iff__less,axiom,
% 4.69/5.03 ! [A2: code_integer] :
% 4.69/5.03 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A2 ) @ zero_z3403309356797280102nteger )
% 4.69/5.03 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_less_0_iff_less
% 4.69/5.03 thf(fact_6795_ab__left__minus,axiom,
% 4.69/5.03 ! [A2: rat] :
% 4.69/5.03 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A2 ) @ A2 )
% 4.69/5.03 = zero_zero_rat ) ).
% 4.69/5.03
% 4.69/5.03 % ab_left_minus
% 4.69/5.03 thf(fact_6796_ab__left__minus,axiom,
% 4.69/5.03 ! [A2: int] :
% 4.69/5.03 ( ( plus_plus_int @ ( uminus_uminus_int @ A2 ) @ A2 )
% 4.69/5.03 = zero_zero_int ) ).
% 4.69/5.03
% 4.69/5.03 % ab_left_minus
% 4.69/5.03 thf(fact_6797_ab__left__minus,axiom,
% 4.69/5.03 ! [A2: code_integer] :
% 4.69/5.03 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A2 ) @ A2 )
% 4.69/5.03 = zero_z3403309356797280102nteger ) ).
% 4.69/5.03
% 4.69/5.03 % ab_left_minus
% 4.69/5.03 thf(fact_6798_add_Oright__inverse,axiom,
% 4.69/5.03 ! [A2: rat] :
% 4.69/5.03 ( ( plus_plus_rat @ A2 @ ( uminus_uminus_rat @ A2 ) )
% 4.69/5.03 = zero_zero_rat ) ).
% 4.69/5.03
% 4.69/5.03 % add.right_inverse
% 4.69/5.03 thf(fact_6799_add_Oright__inverse,axiom,
% 4.69/5.03 ! [A2: int] :
% 4.69/5.03 ( ( plus_plus_int @ A2 @ ( uminus_uminus_int @ A2 ) )
% 4.69/5.03 = zero_zero_int ) ).
% 4.69/5.03
% 4.69/5.03 % add.right_inverse
% 4.69/5.03 thf(fact_6800_add_Oright__inverse,axiom,
% 4.69/5.03 ! [A2: code_integer] :
% 4.69/5.03 ( ( plus_p5714425477246183910nteger @ A2 @ ( uminus1351360451143612070nteger @ A2 ) )
% 4.69/5.03 = zero_z3403309356797280102nteger ) ).
% 4.69/5.03
% 4.69/5.03 % add.right_inverse
% 4.69/5.03 thf(fact_6801_diff__0,axiom,
% 4.69/5.03 ! [A2: rat] :
% 4.69/5.03 ( ( minus_minus_rat @ zero_zero_rat @ A2 )
% 4.69/5.03 = ( uminus_uminus_rat @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % diff_0
% 4.69/5.03 thf(fact_6802_diff__0,axiom,
% 4.69/5.03 ! [A2: int] :
% 4.69/5.03 ( ( minus_minus_int @ zero_zero_int @ A2 )
% 4.69/5.03 = ( uminus_uminus_int @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % diff_0
% 4.69/5.03 thf(fact_6803_diff__0,axiom,
% 4.69/5.03 ! [A2: code_integer] :
% 4.69/5.03 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A2 )
% 4.69/5.03 = ( uminus1351360451143612070nteger @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % diff_0
% 4.69/5.03 thf(fact_6804_diff__minus__eq__add,axiom,
% 4.69/5.03 ! [A2: rat,B: rat] :
% 4.69/5.03 ( ( minus_minus_rat @ A2 @ ( uminus_uminus_rat @ B ) )
% 4.69/5.03 = ( plus_plus_rat @ A2 @ B ) ) ).
% 4.69/5.03
% 4.69/5.03 % diff_minus_eq_add
% 4.69/5.03 thf(fact_6805_diff__minus__eq__add,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( minus_minus_int @ A2 @ ( uminus_uminus_int @ B ) )
% 4.69/5.03 = ( plus_plus_int @ A2 @ B ) ) ).
% 4.69/5.03
% 4.69/5.03 % diff_minus_eq_add
% 4.69/5.03 thf(fact_6806_diff__minus__eq__add,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( minus_8373710615458151222nteger @ A2 @ ( uminus1351360451143612070nteger @ B ) )
% 4.69/5.03 = ( plus_p5714425477246183910nteger @ A2 @ B ) ) ).
% 4.69/5.03
% 4.69/5.03 % diff_minus_eq_add
% 4.69/5.03 thf(fact_6807_uminus__add__conv__diff,axiom,
% 4.69/5.03 ! [A2: rat,B: rat] :
% 4.69/5.03 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A2 ) @ B )
% 4.69/5.03 = ( minus_minus_rat @ B @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % uminus_add_conv_diff
% 4.69/5.03 thf(fact_6808_uminus__add__conv__diff,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( plus_plus_int @ ( uminus_uminus_int @ A2 ) @ B )
% 4.69/5.03 = ( minus_minus_int @ B @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % uminus_add_conv_diff
% 4.69/5.03 thf(fact_6809_uminus__add__conv__diff,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A2 ) @ B )
% 4.69/5.03 = ( minus_8373710615458151222nteger @ B @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % uminus_add_conv_diff
% 4.69/5.03 thf(fact_6810_mult__minus1,axiom,
% 4.69/5.03 ! [Z: rat] :
% 4.69/5.03 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 4.69/5.03 = ( uminus_uminus_rat @ Z ) ) ).
% 4.69/5.03
% 4.69/5.03 % mult_minus1
% 4.69/5.03 thf(fact_6811_mult__minus1,axiom,
% 4.69/5.03 ! [Z: int] :
% 4.69/5.03 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 4.69/5.03 = ( uminus_uminus_int @ Z ) ) ).
% 4.69/5.03
% 4.69/5.03 % mult_minus1
% 4.69/5.03 thf(fact_6812_mult__minus1,axiom,
% 4.69/5.03 ! [Z: code_integer] :
% 4.69/5.03 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 4.69/5.03 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 4.69/5.03
% 4.69/5.03 % mult_minus1
% 4.69/5.03 thf(fact_6813_mult__minus1__right,axiom,
% 4.69/5.03 ! [Z: rat] :
% 4.69/5.03 ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.69/5.03 = ( uminus_uminus_rat @ Z ) ) ).
% 4.69/5.03
% 4.69/5.03 % mult_minus1_right
% 4.69/5.03 thf(fact_6814_mult__minus1__right,axiom,
% 4.69/5.03 ! [Z: int] :
% 4.69/5.03 ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 4.69/5.03 = ( uminus_uminus_int @ Z ) ) ).
% 4.69/5.03
% 4.69/5.03 % mult_minus1_right
% 4.69/5.03 thf(fact_6815_mult__minus1__right,axiom,
% 4.69/5.03 ! [Z: code_integer] :
% 4.69/5.03 ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 4.69/5.03 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 4.69/5.03
% 4.69/5.03 % mult_minus1_right
% 4.69/5.03 thf(fact_6816_boolean__algebra_Ocompl__one,axiom,
% 4.69/5.03 ( ( uminus5254974436814262692_nat_o @ top_to4869887016220417533_nat_o )
% 4.69/5.03 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.compl_one
% 4.69/5.03 thf(fact_6817_boolean__algebra_Ocompl__one,axiom,
% 4.69/5.03 ( ( uminus5944136376168626660t_unit @ top_to1996260823553986621t_unit )
% 4.69/5.03 = bot_bo3957492148770167129t_unit ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.compl_one
% 4.69/5.03 thf(fact_6818_boolean__algebra_Ocompl__one,axiom,
% 4.69/5.03 ( ( uminus_uminus_set_o @ top_top_set_o )
% 4.69/5.03 = bot_bot_set_o ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.compl_one
% 4.69/5.03 thf(fact_6819_boolean__algebra_Ocompl__one,axiom,
% 4.69/5.03 ( ( uminus5710092332889474511et_nat @ top_top_set_nat )
% 4.69/5.03 = bot_bot_set_nat ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.compl_one
% 4.69/5.03 thf(fact_6820_boolean__algebra_Ocompl__one,axiom,
% 4.69/5.03 ( ( uminus1532241313380277803et_int @ top_top_set_int )
% 4.69/5.03 = bot_bot_set_int ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.compl_one
% 4.69/5.03 thf(fact_6821_boolean__algebra_Ocompl__one,axiom,
% 4.69/5.03 ( ( uminus_uminus_assn @ top_top_assn )
% 4.69/5.03 = bot_bot_assn ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.compl_one
% 4.69/5.03 thf(fact_6822_boolean__algebra_Ocompl__one,axiom,
% 4.69/5.03 ( ( uminus2952777764628376836t_unit @ top_top_Product_unit )
% 4.69/5.03 = bot_bot_Product_unit ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.compl_one
% 4.69/5.03 thf(fact_6823_boolean__algebra_Ocompl__zero,axiom,
% 4.69/5.03 ( ( uminus5254974436814262692_nat_o @ bot_bo7824918357723582233_nat_o )
% 4.69/5.03 = top_to4869887016220417533_nat_o ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.compl_zero
% 4.69/5.03 thf(fact_6824_boolean__algebra_Ocompl__zero,axiom,
% 4.69/5.03 ( ( uminus5944136376168626660t_unit @ bot_bo3957492148770167129t_unit )
% 4.69/5.03 = top_to1996260823553986621t_unit ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.compl_zero
% 4.69/5.03 thf(fact_6825_boolean__algebra_Ocompl__zero,axiom,
% 4.69/5.03 ( ( uminus_uminus_set_o @ bot_bot_set_o )
% 4.69/5.03 = top_top_set_o ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.compl_zero
% 4.69/5.03 thf(fact_6826_boolean__algebra_Ocompl__zero,axiom,
% 4.69/5.03 ( ( uminus5710092332889474511et_nat @ bot_bot_set_nat )
% 4.69/5.03 = top_top_set_nat ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.compl_zero
% 4.69/5.03 thf(fact_6827_boolean__algebra_Ocompl__zero,axiom,
% 4.69/5.03 ( ( uminus1532241313380277803et_int @ bot_bot_set_int )
% 4.69/5.03 = top_top_set_int ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.compl_zero
% 4.69/5.03 thf(fact_6828_boolean__algebra_Ocompl__zero,axiom,
% 4.69/5.03 ( ( uminus_uminus_assn @ bot_bot_assn )
% 4.69/5.03 = top_top_assn ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.compl_zero
% 4.69/5.03 thf(fact_6829_boolean__algebra_Ocompl__zero,axiom,
% 4.69/5.03 ( ( uminus2952777764628376836t_unit @ bot_bot_Product_unit )
% 4.69/5.03 = top_top_Product_unit ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.compl_zero
% 4.69/5.03 thf(fact_6830_boolean__algebra_Oconj__cancel__right,axiom,
% 4.69/5.03 ! [X: set_Product_unit] :
% 4.69/5.03 ( ( inf_in4660618365625256667t_unit @ X @ ( uminus5944136376168626660t_unit @ X ) )
% 4.69/5.03 = bot_bo3957492148770167129t_unit ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.conj_cancel_right
% 4.69/5.03 thf(fact_6831_boolean__algebra_Oconj__cancel__right,axiom,
% 4.69/5.03 ! [X: set_o] :
% 4.69/5.03 ( ( inf_inf_set_o @ X @ ( uminus_uminus_set_o @ X ) )
% 4.69/5.03 = bot_bot_set_o ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.conj_cancel_right
% 4.69/5.03 thf(fact_6832_boolean__algebra_Oconj__cancel__right,axiom,
% 4.69/5.03 ! [X: set_nat] :
% 4.69/5.03 ( ( inf_inf_set_nat @ X @ ( uminus5710092332889474511et_nat @ X ) )
% 4.69/5.03 = bot_bot_set_nat ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.conj_cancel_right
% 4.69/5.03 thf(fact_6833_boolean__algebra_Oconj__cancel__right,axiom,
% 4.69/5.03 ! [X: set_int] :
% 4.69/5.03 ( ( inf_inf_set_int @ X @ ( uminus1532241313380277803et_int @ X ) )
% 4.69/5.03 = bot_bot_set_int ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.conj_cancel_right
% 4.69/5.03 thf(fact_6834_boolean__algebra_Oconj__cancel__right,axiom,
% 4.69/5.03 ! [X: set_Pr4532377907799695533_nat_o] :
% 4.69/5.03 ( ( inf_in1906310914598751387_nat_o @ X @ ( uminus5254974436814262692_nat_o @ X ) )
% 4.69/5.03 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.conj_cancel_right
% 4.69/5.03 thf(fact_6835_boolean__algebra_Oconj__cancel__right,axiom,
% 4.69/5.03 ! [X: assn] :
% 4.69/5.03 ( ( inf_inf_assn @ X @ ( uminus_uminus_assn @ X ) )
% 4.69/5.03 = bot_bot_assn ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.conj_cancel_right
% 4.69/5.03 thf(fact_6836_boolean__algebra_Oconj__cancel__right,axiom,
% 4.69/5.03 ! [X: product_unit] :
% 4.69/5.03 ( ( inf_inf_Product_unit @ X @ ( uminus2952777764628376836t_unit @ X ) )
% 4.69/5.03 = bot_bot_Product_unit ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.conj_cancel_right
% 4.69/5.03 thf(fact_6837_boolean__algebra_Oconj__cancel__left,axiom,
% 4.69/5.03 ! [X: set_Product_unit] :
% 4.69/5.03 ( ( inf_in4660618365625256667t_unit @ ( uminus5944136376168626660t_unit @ X ) @ X )
% 4.69/5.03 = bot_bo3957492148770167129t_unit ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.conj_cancel_left
% 4.69/5.03 thf(fact_6838_boolean__algebra_Oconj__cancel__left,axiom,
% 4.69/5.03 ! [X: set_o] :
% 4.69/5.03 ( ( inf_inf_set_o @ ( uminus_uminus_set_o @ X ) @ X )
% 4.69/5.03 = bot_bot_set_o ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.conj_cancel_left
% 4.69/5.03 thf(fact_6839_boolean__algebra_Oconj__cancel__left,axiom,
% 4.69/5.03 ! [X: set_nat] :
% 4.69/5.03 ( ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ X )
% 4.69/5.03 = bot_bot_set_nat ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.conj_cancel_left
% 4.69/5.03 thf(fact_6840_boolean__algebra_Oconj__cancel__left,axiom,
% 4.69/5.03 ! [X: set_int] :
% 4.69/5.03 ( ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ X )
% 4.69/5.03 = bot_bot_set_int ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.conj_cancel_left
% 4.69/5.03 thf(fact_6841_boolean__algebra_Oconj__cancel__left,axiom,
% 4.69/5.03 ! [X: set_Pr4532377907799695533_nat_o] :
% 4.69/5.03 ( ( inf_in1906310914598751387_nat_o @ ( uminus5254974436814262692_nat_o @ X ) @ X )
% 4.69/5.03 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.conj_cancel_left
% 4.69/5.03 thf(fact_6842_boolean__algebra_Oconj__cancel__left,axiom,
% 4.69/5.03 ! [X: assn] :
% 4.69/5.03 ( ( inf_inf_assn @ ( uminus_uminus_assn @ X ) @ X )
% 4.69/5.03 = bot_bot_assn ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.conj_cancel_left
% 4.69/5.03 thf(fact_6843_boolean__algebra_Oconj__cancel__left,axiom,
% 4.69/5.03 ! [X: product_unit] :
% 4.69/5.03 ( ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ X )
% 4.69/5.03 = bot_bot_Product_unit ) ).
% 4.69/5.03
% 4.69/5.03 % boolean_algebra.conj_cancel_left
% 4.69/5.03 thf(fact_6844_inf__compl__bot__right,axiom,
% 4.69/5.03 ! [X: set_Product_unit,Y: set_Product_unit] :
% 4.69/5.03 ( ( inf_in4660618365625256667t_unit @ X @ ( inf_in4660618365625256667t_unit @ Y @ ( uminus5944136376168626660t_unit @ X ) ) )
% 4.69/5.03 = bot_bo3957492148770167129t_unit ) ).
% 4.69/5.03
% 4.69/5.03 % inf_compl_bot_right
% 4.69/5.03 thf(fact_6845_inf__compl__bot__right,axiom,
% 4.69/5.03 ! [X: set_o,Y: set_o] :
% 4.69/5.03 ( ( inf_inf_set_o @ X @ ( inf_inf_set_o @ Y @ ( uminus_uminus_set_o @ X ) ) )
% 4.69/5.03 = bot_bot_set_o ) ).
% 4.69/5.03
% 4.69/5.03 % inf_compl_bot_right
% 4.69/5.03 thf(fact_6846_inf__compl__bot__right,axiom,
% 4.69/5.03 ! [X: set_nat,Y: set_nat] :
% 4.69/5.03 ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ ( uminus5710092332889474511et_nat @ X ) ) )
% 4.69/5.03 = bot_bot_set_nat ) ).
% 4.69/5.03
% 4.69/5.03 % inf_compl_bot_right
% 4.69/5.03 thf(fact_6847_inf__compl__bot__right,axiom,
% 4.69/5.03 ! [X: set_int,Y: set_int] :
% 4.69/5.03 ( ( inf_inf_set_int @ X @ ( inf_inf_set_int @ Y @ ( uminus1532241313380277803et_int @ X ) ) )
% 4.69/5.03 = bot_bot_set_int ) ).
% 4.69/5.03
% 4.69/5.03 % inf_compl_bot_right
% 4.69/5.03 thf(fact_6848_inf__compl__bot__right,axiom,
% 4.69/5.03 ! [X: set_Pr4532377907799695533_nat_o,Y: set_Pr4532377907799695533_nat_o] :
% 4.69/5.03 ( ( inf_in1906310914598751387_nat_o @ X @ ( inf_in1906310914598751387_nat_o @ Y @ ( uminus5254974436814262692_nat_o @ X ) ) )
% 4.69/5.03 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/5.03
% 4.69/5.03 % inf_compl_bot_right
% 4.69/5.03 thf(fact_6849_inf__compl__bot__right,axiom,
% 4.69/5.03 ! [X: assn,Y: assn] :
% 4.69/5.03 ( ( inf_inf_assn @ X @ ( inf_inf_assn @ Y @ ( uminus_uminus_assn @ X ) ) )
% 4.69/5.03 = bot_bot_assn ) ).
% 4.69/5.03
% 4.69/5.03 % inf_compl_bot_right
% 4.69/5.03 thf(fact_6850_inf__compl__bot__right,axiom,
% 4.69/5.03 ! [X: product_unit,Y: product_unit] :
% 4.69/5.03 ( ( inf_inf_Product_unit @ X @ ( inf_inf_Product_unit @ Y @ ( uminus2952777764628376836t_unit @ X ) ) )
% 4.69/5.03 = bot_bot_Product_unit ) ).
% 4.69/5.03
% 4.69/5.03 % inf_compl_bot_right
% 4.69/5.03 thf(fact_6851_inf__compl__bot__left2,axiom,
% 4.69/5.03 ! [X: set_Product_unit,Y: set_Product_unit] :
% 4.69/5.03 ( ( inf_in4660618365625256667t_unit @ X @ ( inf_in4660618365625256667t_unit @ ( uminus5944136376168626660t_unit @ X ) @ Y ) )
% 4.69/5.03 = bot_bo3957492148770167129t_unit ) ).
% 4.69/5.03
% 4.69/5.03 % inf_compl_bot_left2
% 4.69/5.03 thf(fact_6852_inf__compl__bot__left2,axiom,
% 4.69/5.03 ! [X: set_o,Y: set_o] :
% 4.69/5.03 ( ( inf_inf_set_o @ X @ ( inf_inf_set_o @ ( uminus_uminus_set_o @ X ) @ Y ) )
% 4.69/5.03 = bot_bot_set_o ) ).
% 4.69/5.03
% 4.69/5.03 % inf_compl_bot_left2
% 4.69/5.03 thf(fact_6853_inf__compl__bot__left2,axiom,
% 4.69/5.03 ! [X: set_nat,Y: set_nat] :
% 4.69/5.03 ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ Y ) )
% 4.69/5.03 = bot_bot_set_nat ) ).
% 4.69/5.03
% 4.69/5.03 % inf_compl_bot_left2
% 4.69/5.03 thf(fact_6854_inf__compl__bot__left2,axiom,
% 4.69/5.03 ! [X: set_int,Y: set_int] :
% 4.69/5.03 ( ( inf_inf_set_int @ X @ ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ Y ) )
% 4.69/5.03 = bot_bot_set_int ) ).
% 4.69/5.03
% 4.69/5.03 % inf_compl_bot_left2
% 4.69/5.03 thf(fact_6855_inf__compl__bot__left2,axiom,
% 4.69/5.03 ! [X: set_Pr4532377907799695533_nat_o,Y: set_Pr4532377907799695533_nat_o] :
% 4.69/5.03 ( ( inf_in1906310914598751387_nat_o @ X @ ( inf_in1906310914598751387_nat_o @ ( uminus5254974436814262692_nat_o @ X ) @ Y ) )
% 4.69/5.03 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/5.03
% 4.69/5.03 % inf_compl_bot_left2
% 4.69/5.03 thf(fact_6856_inf__compl__bot__left2,axiom,
% 4.69/5.03 ! [X: assn,Y: assn] :
% 4.69/5.03 ( ( inf_inf_assn @ X @ ( inf_inf_assn @ ( uminus_uminus_assn @ X ) @ Y ) )
% 4.69/5.03 = bot_bot_assn ) ).
% 4.69/5.03
% 4.69/5.03 % inf_compl_bot_left2
% 4.69/5.03 thf(fact_6857_inf__compl__bot__left2,axiom,
% 4.69/5.03 ! [X: product_unit,Y: product_unit] :
% 4.69/5.03 ( ( inf_inf_Product_unit @ X @ ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ Y ) )
% 4.69/5.03 = bot_bot_Product_unit ) ).
% 4.69/5.03
% 4.69/5.03 % inf_compl_bot_left2
% 4.69/5.03 thf(fact_6858_inf__compl__bot__left1,axiom,
% 4.69/5.03 ! [X: set_Product_unit,Y: set_Product_unit] :
% 4.69/5.03 ( ( inf_in4660618365625256667t_unit @ ( uminus5944136376168626660t_unit @ X ) @ ( inf_in4660618365625256667t_unit @ X @ Y ) )
% 4.69/5.03 = bot_bo3957492148770167129t_unit ) ).
% 4.69/5.03
% 4.69/5.03 % inf_compl_bot_left1
% 4.69/5.03 thf(fact_6859_inf__compl__bot__left1,axiom,
% 4.69/5.03 ! [X: set_o,Y: set_o] :
% 4.69/5.03 ( ( inf_inf_set_o @ ( uminus_uminus_set_o @ X ) @ ( inf_inf_set_o @ X @ Y ) )
% 4.69/5.03 = bot_bot_set_o ) ).
% 4.69/5.03
% 4.69/5.03 % inf_compl_bot_left1
% 4.69/5.03 thf(fact_6860_inf__compl__bot__left1,axiom,
% 4.69/5.03 ! [X: set_nat,Y: set_nat] :
% 4.69/5.03 ( ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( inf_inf_set_nat @ X @ Y ) )
% 4.69/5.03 = bot_bot_set_nat ) ).
% 4.69/5.03
% 4.69/5.03 % inf_compl_bot_left1
% 4.69/5.03 thf(fact_6861_inf__compl__bot__left1,axiom,
% 4.69/5.03 ! [X: set_int,Y: set_int] :
% 4.69/5.03 ( ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ ( inf_inf_set_int @ X @ Y ) )
% 4.69/5.03 = bot_bot_set_int ) ).
% 4.69/5.03
% 4.69/5.03 % inf_compl_bot_left1
% 4.69/5.03 thf(fact_6862_inf__compl__bot__left1,axiom,
% 4.69/5.03 ! [X: set_Pr4532377907799695533_nat_o,Y: set_Pr4532377907799695533_nat_o] :
% 4.69/5.03 ( ( inf_in1906310914598751387_nat_o @ ( uminus5254974436814262692_nat_o @ X ) @ ( inf_in1906310914598751387_nat_o @ X @ Y ) )
% 4.69/5.03 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/5.03
% 4.69/5.03 % inf_compl_bot_left1
% 4.69/5.03 thf(fact_6863_inf__compl__bot__left1,axiom,
% 4.69/5.03 ! [X: assn,Y: assn] :
% 4.69/5.03 ( ( inf_inf_assn @ ( uminus_uminus_assn @ X ) @ ( inf_inf_assn @ X @ Y ) )
% 4.69/5.03 = bot_bot_assn ) ).
% 4.69/5.03
% 4.69/5.03 % inf_compl_bot_left1
% 4.69/5.03 thf(fact_6864_inf__compl__bot__left1,axiom,
% 4.69/5.03 ! [X: product_unit,Y: product_unit] :
% 4.69/5.03 ( ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ ( inf_inf_Product_unit @ X @ Y ) )
% 4.69/5.03 = bot_bot_Product_unit ) ).
% 4.69/5.03
% 4.69/5.03 % inf_compl_bot_left1
% 4.69/5.03 thf(fact_6865_subset__Compl__singleton,axiom,
% 4.69/5.03 ! [A: set_Product_unit,B: product_unit] :
% 4.69/5.03 ( ( ord_le3507040750410214029t_unit @ A @ ( uminus5944136376168626660t_unit @ ( insert_Product_unit @ B @ bot_bo3957492148770167129t_unit ) ) )
% 4.69/5.03 = ( ~ ( member_Product_unit @ B @ A ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % subset_Compl_singleton
% 4.69/5.03 thf(fact_6866_subset__Compl__singleton,axiom,
% 4.69/5.03 ! [A: set_o,B: $o] :
% 4.69/5.03 ( ( ord_less_eq_set_o @ A @ ( uminus_uminus_set_o @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 4.69/5.03 = ( ~ ( member_o @ B @ A ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % subset_Compl_singleton
% 4.69/5.03 thf(fact_6867_subset__Compl__singleton,axiom,
% 4.69/5.03 ! [A: set_int,B: int] :
% 4.69/5.03 ( ( ord_less_eq_set_int @ A @ ( uminus1532241313380277803et_int @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 4.69/5.03 = ( ~ ( member_int @ B @ A ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % subset_Compl_singleton
% 4.69/5.03 thf(fact_6868_subset__Compl__singleton,axiom,
% 4.69/5.03 ! [A: set_Pr4532377907799695533_nat_o,B: produc3658429121746597890et_nat > $o] :
% 4.69/5.03 ( ( ord_le2965882846123202637_nat_o @ A @ ( uminus5254974436814262692_nat_o @ ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o ) ) )
% 4.69/5.03 = ( ~ ( member6576561426505652726_nat_o @ B @ A ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % subset_Compl_singleton
% 4.69/5.03 thf(fact_6869_subset__Compl__singleton,axiom,
% 4.69/5.03 ! [A: set_nat,B: nat] :
% 4.69/5.03 ( ( ord_less_eq_set_nat @ A @ ( uminus5710092332889474511et_nat @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 4.69/5.03 = ( ~ ( member_nat @ B @ A ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % subset_Compl_singleton
% 4.69/5.03 thf(fact_6870_prod_Oempty,axiom,
% 4.69/5.03 ! [G: product_unit > assn] :
% 4.69/5.03 ( ( groups5360233303959380816t_assn @ G @ bot_bo3957492148770167129t_unit )
% 4.69/5.03 = one_one_assn ) ).
% 4.69/5.03
% 4.69/5.03 % prod.empty
% 4.69/5.03 thf(fact_6871_prod_Oempty,axiom,
% 4.69/5.03 ! [G: product_unit > nat] :
% 4.69/5.03 ( ( groups396421249026171384it_nat @ G @ bot_bo3957492148770167129t_unit )
% 4.69/5.03 = one_one_nat ) ).
% 4.69/5.03
% 4.69/5.03 % prod.empty
% 4.69/5.03 thf(fact_6872_prod_Oempty,axiom,
% 4.69/5.03 ! [G: product_unit > int] :
% 4.69/5.03 ( ( groups393930778517121108it_int @ G @ bot_bo3957492148770167129t_unit )
% 4.69/5.03 = one_one_int ) ).
% 4.69/5.03
% 4.69/5.03 % prod.empty
% 4.69/5.03 thf(fact_6873_prod_Oempty,axiom,
% 4.69/5.03 ! [G: product_unit > code_integer] :
% 4.69/5.03 ( ( groups8185359811944078981nteger @ G @ bot_bo3957492148770167129t_unit )
% 4.69/5.03 = one_one_Code_integer ) ).
% 4.69/5.03
% 4.69/5.03 % prod.empty
% 4.69/5.03 thf(fact_6874_prod_Oempty,axiom,
% 4.69/5.03 ! [G: product_unit > code_natural] :
% 4.69/5.03 ( ( groups7008954963700796496atural @ G @ bot_bo3957492148770167129t_unit )
% 4.69/5.03 = one_one_Code_natural ) ).
% 4.69/5.03
% 4.69/5.03 % prod.empty
% 4.69/5.03 thf(fact_6875_prod_Oempty,axiom,
% 4.69/5.03 ! [G: $o > assn] :
% 4.69/5.03 ( ( groups5301882518646026715o_assn @ G @ bot_bot_set_o )
% 4.69/5.03 = one_one_assn ) ).
% 4.69/5.03
% 4.69/5.03 % prod.empty
% 4.69/5.03 thf(fact_6876_prod_Oempty,axiom,
% 4.69/5.03 ! [G: $o > nat] :
% 4.69/5.03 ( ( groups3504817904513533571_o_nat @ G @ bot_bot_set_o )
% 4.69/5.03 = one_one_nat ) ).
% 4.69/5.03
% 4.69/5.03 % prod.empty
% 4.69/5.03 thf(fact_6877_prod_Oempty,axiom,
% 4.69/5.03 ! [G: $o > int] :
% 4.69/5.03 ( ( groups3502327434004483295_o_int @ G @ bot_bot_set_o )
% 4.69/5.03 = one_one_int ) ).
% 4.69/5.03
% 4.69/5.03 % prod.empty
% 4.69/5.03 thf(fact_6878_prod_Oempty,axiom,
% 4.69/5.03 ! [G: $o > code_integer] :
% 4.69/5.03 ( ( groups7694694392188491536nteger @ G @ bot_bot_set_o )
% 4.69/5.03 = one_one_Code_integer ) ).
% 4.69/5.03
% 4.69/5.03 % prod.empty
% 4.69/5.03 thf(fact_6879_prod_Oempty,axiom,
% 4.69/5.03 ! [G: $o > code_natural] :
% 4.69/5.03 ( ( groups6518289543945209051atural @ G @ bot_bot_set_o )
% 4.69/5.03 = one_one_Code_natural ) ).
% 4.69/5.03
% 4.69/5.03 % prod.empty
% 4.69/5.03 thf(fact_6880_prod_Oinfinite,axiom,
% 4.69/5.03 ! [A: set_nat,G: nat > assn] :
% 4.69/5.03 ( ~ ( finite_finite_nat @ A )
% 4.69/5.03 => ( ( groups6906906614972039071t_assn @ G @ A )
% 4.69/5.03 = one_one_assn ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.infinite
% 4.69/5.03 thf(fact_6881_prod_Oinfinite,axiom,
% 4.69/5.03 ! [A: set_Code_integer,G: code_integer > assn] :
% 4.69/5.03 ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ( groups1304777262505850412r_assn @ G @ A )
% 4.69/5.03 = one_one_assn ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.infinite
% 4.69/5.03 thf(fact_6882_prod_Oinfinite,axiom,
% 4.69/5.03 ! [A: set_Code_integer,G: code_integer > nat] :
% 4.69/5.03 ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ( groups3190895334310489300er_nat @ G @ A )
% 4.69/5.03 = one_one_nat ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.infinite
% 4.69/5.03 thf(fact_6883_prod_Oinfinite,axiom,
% 4.69/5.03 ! [A: set_nat,G: nat > int] :
% 4.69/5.03 ( ~ ( finite_finite_nat @ A )
% 4.69/5.03 => ( ( groups705719431365010083at_int @ G @ A )
% 4.69/5.03 = one_one_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.infinite
% 4.69/5.03 thf(fact_6884_prod_Oinfinite,axiom,
% 4.69/5.03 ! [A: set_Code_integer,G: code_integer > int] :
% 4.69/5.03 ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ( groups3188404863801439024er_int @ G @ A )
% 4.69/5.03 = one_one_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.infinite
% 4.69/5.03 thf(fact_6885_prod_Oinfinite,axiom,
% 4.69/5.03 ! [A: set_nat,G: nat > code_integer] :
% 4.69/5.03 ( ~ ( finite_finite_nat @ A )
% 4.69/5.03 => ( ( groups3455450783089532116nteger @ G @ A )
% 4.69/5.03 = one_one_Code_integer ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.infinite
% 4.69/5.03 thf(fact_6886_prod_Oinfinite,axiom,
% 4.69/5.03 ! [A: set_Code_integer,G: code_integer > code_integer] :
% 4.69/5.03 ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ( groups3674199335183972705nteger @ G @ A )
% 4.69/5.03 = one_one_Code_integer ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.infinite
% 4.69/5.03 thf(fact_6887_prod_Oinfinite,axiom,
% 4.69/5.03 ! [A: set_nat,G: nat > code_natural] :
% 4.69/5.03 ( ~ ( finite_finite_nat @ A )
% 4.69/5.03 => ( ( groups2279045934846249631atural @ G @ A )
% 4.69/5.03 = one_one_Code_natural ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.infinite
% 4.69/5.03 thf(fact_6888_prod_Oinfinite,axiom,
% 4.69/5.03 ! [A: set_Code_integer,G: code_integer > code_natural] :
% 4.69/5.03 ( ~ ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ( groups2497794486940690220atural @ G @ A )
% 4.69/5.03 = one_one_Code_natural ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.infinite
% 4.69/5.03 thf(fact_6889_prod_Oinfinite,axiom,
% 4.69/5.03 ! [A: set_nat,G: nat > nat] :
% 4.69/5.03 ( ~ ( finite_finite_nat @ A )
% 4.69/5.03 => ( ( groups708209901874060359at_nat @ G @ A )
% 4.69/5.03 = one_one_nat ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.infinite
% 4.69/5.03 thf(fact_6890_of__nat__mult,axiom,
% 4.69/5.03 ! [M4: nat,N2: nat] :
% 4.69/5.03 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M4 @ N2 ) )
% 4.69/5.03 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M4 ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % of_nat_mult
% 4.69/5.03 thf(fact_6891_of__nat__mult,axiom,
% 4.69/5.03 ! [M4: nat,N2: nat] :
% 4.69/5.03 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M4 @ N2 ) )
% 4.69/5.03 = ( times_times_int @ ( semiri1314217659103216013at_int @ M4 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % of_nat_mult
% 4.69/5.03 thf(fact_6892_of__nat__mult,axiom,
% 4.69/5.03 ! [M4: nat,N2: nat] :
% 4.69/5.03 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M4 @ N2 ) )
% 4.69/5.03 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M4 ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % of_nat_mult
% 4.69/5.03 thf(fact_6893_of__nat__mult,axiom,
% 4.69/5.03 ! [M4: nat,N2: nat] :
% 4.69/5.03 ( ( semiri4939895301339042750nteger @ ( times_times_nat @ M4 @ N2 ) )
% 4.69/5.03 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M4 ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % of_nat_mult
% 4.69/5.03 thf(fact_6894_of__nat__1,axiom,
% 4.69/5.03 ( ( semiri3763490453095760265atural @ one_one_nat )
% 4.69/5.03 = one_one_Code_natural ) ).
% 4.69/5.03
% 4.69/5.03 % of_nat_1
% 4.69/5.03 thf(fact_6895_of__nat__1,axiom,
% 4.69/5.03 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 4.69/5.03 = one_one_int ) ).
% 4.69/5.03
% 4.69/5.03 % of_nat_1
% 4.69/5.03 thf(fact_6896_of__nat__1,axiom,
% 4.69/5.03 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 4.69/5.03 = one_one_nat ) ).
% 4.69/5.03
% 4.69/5.03 % of_nat_1
% 4.69/5.03 thf(fact_6897_of__nat__1,axiom,
% 4.69/5.03 ( ( semiri4939895301339042750nteger @ one_one_nat )
% 4.69/5.03 = one_one_Code_integer ) ).
% 4.69/5.03
% 4.69/5.03 % of_nat_1
% 4.69/5.03 thf(fact_6898_of__nat__1__eq__iff,axiom,
% 4.69/5.03 ! [N2: nat] :
% 4.69/5.03 ( ( one_one_Code_natural
% 4.69/5.03 = ( semiri3763490453095760265atural @ N2 ) )
% 4.69/5.03 = ( N2 = one_one_nat ) ) ).
% 4.69/5.03
% 4.69/5.03 % of_nat_1_eq_iff
% 4.69/5.03 thf(fact_6899_of__nat__1__eq__iff,axiom,
% 4.69/5.03 ! [N2: nat] :
% 4.69/5.03 ( ( one_one_int
% 4.69/5.03 = ( semiri1314217659103216013at_int @ N2 ) )
% 4.69/5.03 = ( N2 = one_one_nat ) ) ).
% 4.69/5.03
% 4.69/5.03 % of_nat_1_eq_iff
% 4.69/5.03 thf(fact_6900_of__nat__1__eq__iff,axiom,
% 4.69/5.03 ! [N2: nat] :
% 4.69/5.03 ( ( one_one_nat
% 4.69/5.03 = ( semiri1316708129612266289at_nat @ N2 ) )
% 4.69/5.03 = ( N2 = one_one_nat ) ) ).
% 4.69/5.03
% 4.69/5.03 % of_nat_1_eq_iff
% 4.69/5.03 thf(fact_6901_of__nat__1__eq__iff,axiom,
% 4.69/5.03 ! [N2: nat] :
% 4.69/5.03 ( ( one_one_Code_integer
% 4.69/5.03 = ( semiri4939895301339042750nteger @ N2 ) )
% 4.69/5.03 = ( N2 = one_one_nat ) ) ).
% 4.69/5.03
% 4.69/5.03 % of_nat_1_eq_iff
% 4.69/5.03 thf(fact_6902_of__nat__eq__1__iff,axiom,
% 4.69/5.03 ! [N2: nat] :
% 4.69/5.03 ( ( ( semiri3763490453095760265atural @ N2 )
% 4.69/5.03 = one_one_Code_natural )
% 4.69/5.03 = ( N2 = one_one_nat ) ) ).
% 4.69/5.03
% 4.69/5.03 % of_nat_eq_1_iff
% 4.69/5.03 thf(fact_6903_of__nat__eq__1__iff,axiom,
% 4.69/5.03 ! [N2: nat] :
% 4.69/5.03 ( ( ( semiri1314217659103216013at_int @ N2 )
% 4.69/5.03 = one_one_int )
% 4.69/5.03 = ( N2 = one_one_nat ) ) ).
% 4.69/5.03
% 4.69/5.03 % of_nat_eq_1_iff
% 4.69/5.03 thf(fact_6904_of__nat__eq__1__iff,axiom,
% 4.69/5.03 ! [N2: nat] :
% 4.69/5.03 ( ( ( semiri1316708129612266289at_nat @ N2 )
% 4.69/5.03 = one_one_nat )
% 4.69/5.03 = ( N2 = one_one_nat ) ) ).
% 4.69/5.03
% 4.69/5.03 % of_nat_eq_1_iff
% 4.69/5.03 thf(fact_6905_of__nat__eq__1__iff,axiom,
% 4.69/5.03 ! [N2: nat] :
% 4.69/5.03 ( ( ( semiri4939895301339042750nteger @ N2 )
% 4.69/5.03 = one_one_Code_integer )
% 4.69/5.03 = ( N2 = one_one_nat ) ) ).
% 4.69/5.03
% 4.69/5.03 % of_nat_eq_1_iff
% 4.69/5.03 thf(fact_6906_Gcd__empty,axiom,
% 4.69/5.03 ( ( gcd_Gcd_nat @ bot_bot_set_nat )
% 4.69/5.03 = zero_zero_nat ) ).
% 4.69/5.03
% 4.69/5.03 % Gcd_empty
% 4.69/5.03 thf(fact_6907_Gcd__empty,axiom,
% 4.69/5.03 ( ( gcd_Gcd_int @ bot_bot_set_int )
% 4.69/5.03 = zero_zero_int ) ).
% 4.69/5.03
% 4.69/5.03 % Gcd_empty
% 4.69/5.03 thf(fact_6908_Gcd__UNIV,axiom,
% 4.69/5.03 ( ( gcd_Gcd_nat @ top_top_set_nat )
% 4.69/5.03 = one_one_nat ) ).
% 4.69/5.03
% 4.69/5.03 % Gcd_UNIV
% 4.69/5.03 thf(fact_6909_Gcd__UNIV,axiom,
% 4.69/5.03 ( ( gcd_Gcd_int @ top_top_set_int )
% 4.69/5.03 = one_one_int ) ).
% 4.69/5.03
% 4.69/5.03 % Gcd_UNIV
% 4.69/5.03 thf(fact_6910_Gcd__fin_Oempty,axiom,
% 4.69/5.03 ( ( semiri4258706085729940814in_nat @ bot_bot_set_nat )
% 4.69/5.03 = zero_zero_nat ) ).
% 4.69/5.03
% 4.69/5.03 % Gcd_fin.empty
% 4.69/5.03 thf(fact_6911_Gcd__fin_Oempty,axiom,
% 4.69/5.03 ( ( semiri4256215615220890538in_int @ bot_bot_set_int )
% 4.69/5.03 = zero_zero_int ) ).
% 4.69/5.03
% 4.69/5.03 % Gcd_fin.empty
% 4.69/5.03 thf(fact_6912_Gcd__fin_Oinfinite,axiom,
% 4.69/5.03 ! [A: set_nat] :
% 4.69/5.03 ( ~ ( finite_finite_nat @ A )
% 4.69/5.03 => ( ( semiri4258706085729940814in_nat @ A )
% 4.69/5.03 = one_one_nat ) ) ).
% 4.69/5.03
% 4.69/5.03 % Gcd_fin.infinite
% 4.69/5.03 thf(fact_6913_Gcd__fin_Oinfinite,axiom,
% 4.69/5.03 ! [A: set_int] :
% 4.69/5.03 ( ~ ( finite_finite_int @ A )
% 4.69/5.03 => ( ( semiri4256215615220890538in_int @ A )
% 4.69/5.03 = one_one_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % Gcd_fin.infinite
% 4.69/5.03 thf(fact_6914_is__unit__Gcd__fin__iff,axiom,
% 4.69/5.03 ! [A: set_nat] :
% 4.69/5.03 ( ( dvd_dvd_nat @ ( semiri4258706085729940814in_nat @ A ) @ one_one_nat )
% 4.69/5.03 = ( ( semiri4258706085729940814in_nat @ A )
% 4.69/5.03 = one_one_nat ) ) ).
% 4.69/5.03
% 4.69/5.03 % is_unit_Gcd_fin_iff
% 4.69/5.03 thf(fact_6915_is__unit__Gcd__fin__iff,axiom,
% 4.69/5.03 ! [A: set_int] :
% 4.69/5.03 ( ( dvd_dvd_int @ ( semiri4256215615220890538in_int @ A ) @ one_one_int )
% 4.69/5.03 = ( ( semiri4256215615220890538in_int @ A )
% 4.69/5.03 = one_one_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % is_unit_Gcd_fin_iff
% 4.69/5.03 thf(fact_6916_dbl__inc__simps_I4_J,axiom,
% 4.69/5.03 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 4.69/5.03 = ( uminus_uminus_int @ one_one_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % dbl_inc_simps(4)
% 4.69/5.03 thf(fact_6917_dbl__inc__simps_I4_J,axiom,
% 4.69/5.03 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 4.69/5.03 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.69/5.03
% 4.69/5.03 % dbl_inc_simps(4)
% 4.69/5.03 thf(fact_6918_add__neg__numeral__special_I7_J,axiom,
% 4.69/5.03 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.69/5.03 = zero_zero_rat ) ).
% 4.69/5.03
% 4.69/5.03 % add_neg_numeral_special(7)
% 4.69/5.03 thf(fact_6919_add__neg__numeral__special_I7_J,axiom,
% 4.69/5.03 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 4.69/5.03 = zero_zero_int ) ).
% 4.69/5.03
% 4.69/5.03 % add_neg_numeral_special(7)
% 4.69/5.03 thf(fact_6920_add__neg__numeral__special_I7_J,axiom,
% 4.69/5.03 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 4.69/5.03 = zero_z3403309356797280102nteger ) ).
% 4.69/5.03
% 4.69/5.03 % add_neg_numeral_special(7)
% 4.69/5.03 thf(fact_6921_add__neg__numeral__special_I8_J,axiom,
% 4.69/5.03 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 4.69/5.03 = zero_zero_rat ) ).
% 4.69/5.03
% 4.69/5.03 % add_neg_numeral_special(8)
% 4.69/5.03 thf(fact_6922_add__neg__numeral__special_I8_J,axiom,
% 4.69/5.03 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 4.69/5.03 = zero_zero_int ) ).
% 4.69/5.03
% 4.69/5.03 % add_neg_numeral_special(8)
% 4.69/5.03 thf(fact_6923_add__neg__numeral__special_I8_J,axiom,
% 4.69/5.03 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 4.69/5.03 = zero_z3403309356797280102nteger ) ).
% 4.69/5.03
% 4.69/5.03 % add_neg_numeral_special(8)
% 4.69/5.03 thf(fact_6924_diff__numeral__special_I12_J,axiom,
% 4.69/5.03 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 4.69/5.03 = zero_zero_rat ) ).
% 4.69/5.03
% 4.69/5.03 % diff_numeral_special(12)
% 4.69/5.03 thf(fact_6925_diff__numeral__special_I12_J,axiom,
% 4.69/5.03 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 4.69/5.03 = zero_zero_int ) ).
% 4.69/5.03
% 4.69/5.03 % diff_numeral_special(12)
% 4.69/5.03 thf(fact_6926_diff__numeral__special_I12_J,axiom,
% 4.69/5.03 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 4.69/5.03 = zero_z3403309356797280102nteger ) ).
% 4.69/5.03
% 4.69/5.03 % diff_numeral_special(12)
% 4.69/5.03 thf(fact_6927_minus__one__mult__self,axiom,
% 4.69/5.03 ! [N2: nat] :
% 4.69/5.03 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) )
% 4.69/5.03 = one_one_rat ) ).
% 4.69/5.03
% 4.69/5.03 % minus_one_mult_self
% 4.69/5.03 thf(fact_6928_minus__one__mult__self,axiom,
% 4.69/5.03 ! [N2: nat] :
% 4.69/5.03 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) )
% 4.69/5.03 = one_one_int ) ).
% 4.69/5.03
% 4.69/5.03 % minus_one_mult_self
% 4.69/5.03 thf(fact_6929_minus__one__mult__self,axiom,
% 4.69/5.03 ! [N2: nat] :
% 4.69/5.03 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) )
% 4.69/5.03 = one_one_Code_integer ) ).
% 4.69/5.03
% 4.69/5.03 % minus_one_mult_self
% 4.69/5.03 thf(fact_6930_left__minus__one__mult__self,axiom,
% 4.69/5.03 ! [N2: nat,A2: rat] :
% 4.69/5.03 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ A2 ) )
% 4.69/5.03 = A2 ) ).
% 4.69/5.03
% 4.69/5.03 % left_minus_one_mult_self
% 4.69/5.03 thf(fact_6931_left__minus__one__mult__self,axiom,
% 4.69/5.03 ! [N2: nat,A2: int] :
% 4.69/5.03 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ A2 ) )
% 4.69/5.03 = A2 ) ).
% 4.69/5.03
% 4.69/5.03 % left_minus_one_mult_self
% 4.69/5.03 thf(fact_6932_left__minus__one__mult__self,axiom,
% 4.69/5.03 ! [N2: nat,A2: code_integer] :
% 4.69/5.03 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ A2 ) )
% 4.69/5.03 = A2 ) ).
% 4.69/5.03
% 4.69/5.03 % left_minus_one_mult_self
% 4.69/5.03 thf(fact_6933_of__nat__Suc,axiom,
% 4.69/5.03 ! [M4: nat] :
% 4.69/5.03 ( ( semiri3763490453095760265atural @ ( suc @ M4 ) )
% 4.69/5.03 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( semiri3763490453095760265atural @ M4 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % of_nat_Suc
% 4.69/5.03 thf(fact_6934_of__nat__Suc,axiom,
% 4.69/5.03 ! [M4: nat] :
% 4.69/5.03 ( ( semiri681578069525770553at_rat @ ( suc @ M4 ) )
% 4.69/5.03 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M4 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % of_nat_Suc
% 4.69/5.03 thf(fact_6935_of__nat__Suc,axiom,
% 4.69/5.03 ! [M4: nat] :
% 4.69/5.03 ( ( semiri1314217659103216013at_int @ ( suc @ M4 ) )
% 4.69/5.03 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M4 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % of_nat_Suc
% 4.69/5.03 thf(fact_6936_of__nat__Suc,axiom,
% 4.69/5.03 ! [M4: nat] :
% 4.69/5.03 ( ( semiri1316708129612266289at_nat @ ( suc @ M4 ) )
% 4.69/5.03 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M4 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % of_nat_Suc
% 4.69/5.03 thf(fact_6937_of__nat__Suc,axiom,
% 4.69/5.03 ! [M4: nat] :
% 4.69/5.03 ( ( semiri4939895301339042750nteger @ ( suc @ M4 ) )
% 4.69/5.03 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( semiri4939895301339042750nteger @ M4 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % of_nat_Suc
% 4.69/5.03 thf(fact_6938_prod_Oinsert,axiom,
% 4.69/5.03 ! [A: set_int,X: int,G: int > assn] :
% 4.69/5.03 ( ( finite_finite_int @ A )
% 4.69/5.03 => ( ~ ( member_int @ X @ A )
% 4.69/5.03 => ( ( groups7882442080178216443t_assn @ G @ ( insert_int @ X @ A ) )
% 4.69/5.03 = ( times_times_assn @ ( G @ X ) @ ( groups7882442080178216443t_assn @ G @ A ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.insert
% 4.69/5.03 thf(fact_6939_prod_Oinsert,axiom,
% 4.69/5.03 ! [A: set_o,X: $o,G: $o > assn] :
% 4.69/5.03 ( ( finite_finite_o @ A )
% 4.69/5.03 => ( ~ ( member_o @ X @ A )
% 4.69/5.03 => ( ( groups5301882518646026715o_assn @ G @ ( insert_o @ X @ A ) )
% 4.69/5.03 = ( times_times_assn @ ( G @ X ) @ ( groups5301882518646026715o_assn @ G @ A ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.insert
% 4.69/5.03 thf(fact_6940_prod_Oinsert,axiom,
% 4.69/5.03 ! [A: set_Product_unit,X: product_unit,G: product_unit > assn] :
% 4.69/5.03 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.03 => ( ~ ( member_Product_unit @ X @ A )
% 4.69/5.03 => ( ( groups5360233303959380816t_assn @ G @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.03 = ( times_times_assn @ ( G @ X ) @ ( groups5360233303959380816t_assn @ G @ A ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.insert
% 4.69/5.03 thf(fact_6941_prod_Oinsert,axiom,
% 4.69/5.03 ! [A: set_nat,X: nat,G: nat > assn] :
% 4.69/5.03 ( ( finite_finite_nat @ A )
% 4.69/5.03 => ( ~ ( member_nat @ X @ A )
% 4.69/5.03 => ( ( groups6906906614972039071t_assn @ G @ ( insert_nat @ X @ A ) )
% 4.69/5.03 = ( times_times_assn @ ( G @ X ) @ ( groups6906906614972039071t_assn @ G @ A ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.insert
% 4.69/5.03 thf(fact_6942_prod_Oinsert,axiom,
% 4.69/5.03 ! [A: set_Code_integer,X: code_integer,G: code_integer > assn] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ~ ( member_Code_integer @ X @ A )
% 4.69/5.03 => ( ( groups1304777262505850412r_assn @ G @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.03 = ( times_times_assn @ ( G @ X ) @ ( groups1304777262505850412r_assn @ G @ A ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.insert
% 4.69/5.03 thf(fact_6943_prod_Oinsert,axiom,
% 4.69/5.03 ! [A: set_int,X: int,G: int > rat] :
% 4.69/5.03 ( ( finite_finite_int @ A )
% 4.69/5.03 => ( ~ ( member_int @ X @ A )
% 4.69/5.03 => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X @ A ) )
% 4.69/5.03 = ( times_times_rat @ ( G @ X ) @ ( groups1072433553688619179nt_rat @ G @ A ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.insert
% 4.69/5.03 thf(fact_6944_prod_Oinsert,axiom,
% 4.69/5.03 ! [A: set_o,X: $o,G: $o > rat] :
% 4.69/5.03 ( ( finite_finite_o @ A )
% 4.69/5.03 => ( ~ ( member_o @ X @ A )
% 4.69/5.03 => ( ( groups2869687844427037835_o_rat @ G @ ( insert_o @ X @ A ) )
% 4.69/5.03 = ( times_times_rat @ ( G @ X ) @ ( groups2869687844427037835_o_rat @ G @ A ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.insert
% 4.69/5.03 thf(fact_6945_prod_Oinsert,axiom,
% 4.69/5.03 ! [A: set_Product_unit,X: product_unit,G: product_unit > rat] :
% 4.69/5.03 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.03 => ( ~ ( member_Product_unit @ X @ A )
% 4.69/5.03 => ( ( groups8984663225794451456it_rat @ G @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.03 = ( times_times_rat @ ( G @ X ) @ ( groups8984663225794451456it_rat @ G @ A ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.insert
% 4.69/5.03 thf(fact_6946_prod_Oinsert,axiom,
% 4.69/5.03 ! [A: set_nat,X: nat,G: nat > rat] :
% 4.69/5.03 ( ( finite_finite_nat @ A )
% 4.69/5.03 => ( ~ ( member_nat @ X @ A )
% 4.69/5.03 => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X @ A ) )
% 4.69/5.03 = ( times_times_rat @ ( G @ X ) @ ( groups73079841787564623at_rat @ G @ A ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.insert
% 4.69/5.03 thf(fact_6947_prod_Oinsert,axiom,
% 4.69/5.03 ! [A: set_Code_integer,X: code_integer,G: code_integer > rat] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ~ ( member_Code_integer @ X @ A )
% 4.69/5.03 => ( ( groups2555765274223993564er_rat @ G @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.03 = ( times_times_rat @ ( G @ X ) @ ( groups2555765274223993564er_rat @ G @ A ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.insert
% 4.69/5.03 thf(fact_6948_dbl__dec__simps_I2_J,axiom,
% 4.69/5.03 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 4.69/5.03 = ( uminus_uminus_int @ one_one_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % dbl_dec_simps(2)
% 4.69/5.03 thf(fact_6949_dbl__dec__simps_I2_J,axiom,
% 4.69/5.03 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 4.69/5.03 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.69/5.03
% 4.69/5.03 % dbl_dec_simps(2)
% 4.69/5.03 thf(fact_6950_minus__equation__iff,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( ( uminus_uminus_int @ A2 )
% 4.69/5.03 = B )
% 4.69/5.03 = ( ( uminus_uminus_int @ B )
% 4.69/5.03 = A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_equation_iff
% 4.69/5.03 thf(fact_6951_minus__equation__iff,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( ( uminus1351360451143612070nteger @ A2 )
% 4.69/5.03 = B )
% 4.69/5.03 = ( ( uminus1351360451143612070nteger @ B )
% 4.69/5.03 = A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_equation_iff
% 4.69/5.03 thf(fact_6952_equation__minus__iff,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( A2
% 4.69/5.03 = ( uminus_uminus_int @ B ) )
% 4.69/5.03 = ( B
% 4.69/5.03 = ( uminus_uminus_int @ A2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % equation_minus_iff
% 4.69/5.03 thf(fact_6953_equation__minus__iff,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( A2
% 4.69/5.03 = ( uminus1351360451143612070nteger @ B ) )
% 4.69/5.03 = ( B
% 4.69/5.03 = ( uminus1351360451143612070nteger @ A2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % equation_minus_iff
% 4.69/5.03 thf(fact_6954_prod_Oneutral,axiom,
% 4.69/5.03 ! [A: set_nat,G: nat > nat] :
% 4.69/5.03 ( ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ A )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ( groups708209901874060359at_nat @ G @ A )
% 4.69/5.03 = one_one_nat ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.neutral
% 4.69/5.03 thf(fact_6955_prod_Onot__neutral__contains__not__neutral,axiom,
% 4.69/5.03 ! [G: nat > assn,A: set_nat] :
% 4.69/5.03 ( ( ( groups6906906614972039071t_assn @ G @ A )
% 4.69/5.03 != one_one_assn )
% 4.69/5.03 => ~ ! [A4: nat] :
% 4.69/5.03 ( ( member_nat @ A4 @ A )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_assn ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.not_neutral_contains_not_neutral
% 4.69/5.03 thf(fact_6956_prod_Onot__neutral__contains__not__neutral,axiom,
% 4.69/5.03 ! [G: int > assn,A: set_int] :
% 4.69/5.03 ( ( ( groups7882442080178216443t_assn @ G @ A )
% 4.69/5.03 != one_one_assn )
% 4.69/5.03 => ~ ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ A )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_assn ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.not_neutral_contains_not_neutral
% 4.69/5.03 thf(fact_6957_prod_Onot__neutral__contains__not__neutral,axiom,
% 4.69/5.03 ! [G: $o > assn,A: set_o] :
% 4.69/5.03 ( ( ( groups5301882518646026715o_assn @ G @ A )
% 4.69/5.03 != one_one_assn )
% 4.69/5.03 => ~ ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ A )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_assn ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.not_neutral_contains_not_neutral
% 4.69/5.03 thf(fact_6958_prod_Onot__neutral__contains__not__neutral,axiom,
% 4.69/5.03 ! [G: product_unit > assn,A: set_Product_unit] :
% 4.69/5.03 ( ( ( groups5360233303959380816t_assn @ G @ A )
% 4.69/5.03 != one_one_assn )
% 4.69/5.03 => ~ ! [A4: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ A4 @ A )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_assn ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.not_neutral_contains_not_neutral
% 4.69/5.03 thf(fact_6959_prod_Onot__neutral__contains__not__neutral,axiom,
% 4.69/5.03 ! [G: int > nat,A: set_int] :
% 4.69/5.03 ( ( ( groups1707563613775114915nt_nat @ G @ A )
% 4.69/5.03 != one_one_nat )
% 4.69/5.03 => ~ ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ A )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_nat ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.not_neutral_contains_not_neutral
% 4.69/5.03 thf(fact_6960_prod_Onot__neutral__contains__not__neutral,axiom,
% 4.69/5.03 ! [G: $o > nat,A: set_o] :
% 4.69/5.03 ( ( ( groups3504817904513533571_o_nat @ G @ A )
% 4.69/5.03 != one_one_nat )
% 4.69/5.03 => ~ ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ A )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_nat ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.not_neutral_contains_not_neutral
% 4.69/5.03 thf(fact_6961_prod_Onot__neutral__contains__not__neutral,axiom,
% 4.69/5.03 ! [G: product_unit > nat,A: set_Product_unit] :
% 4.69/5.03 ( ( ( groups396421249026171384it_nat @ G @ A )
% 4.69/5.03 != one_one_nat )
% 4.69/5.03 => ~ ! [A4: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ A4 @ A )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_nat ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.not_neutral_contains_not_neutral
% 4.69/5.03 thf(fact_6962_prod_Onot__neutral__contains__not__neutral,axiom,
% 4.69/5.03 ! [G: nat > int,A: set_nat] :
% 4.69/5.03 ( ( ( groups705719431365010083at_int @ G @ A )
% 4.69/5.03 != one_one_int )
% 4.69/5.03 => ~ ! [A4: nat] :
% 4.69/5.03 ( ( member_nat @ A4 @ A )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_int ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.not_neutral_contains_not_neutral
% 4.69/5.03 thf(fact_6963_prod_Onot__neutral__contains__not__neutral,axiom,
% 4.69/5.03 ! [G: int > int,A: set_int] :
% 4.69/5.03 ( ( ( groups1705073143266064639nt_int @ G @ A )
% 4.69/5.03 != one_one_int )
% 4.69/5.03 => ~ ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ A )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_int ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.not_neutral_contains_not_neutral
% 4.69/5.03 thf(fact_6964_prod_Onot__neutral__contains__not__neutral,axiom,
% 4.69/5.03 ! [G: $o > int,A: set_o] :
% 4.69/5.03 ( ( ( groups3502327434004483295_o_int @ G @ A )
% 4.69/5.03 != one_one_int )
% 4.69/5.03 => ~ ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ A )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_int ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.not_neutral_contains_not_neutral
% 4.69/5.03 thf(fact_6965_mult__of__nat__commute,axiom,
% 4.69/5.03 ! [X: nat,Y: rat] :
% 4.69/5.03 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X ) @ Y )
% 4.69/5.03 = ( times_times_rat @ Y @ ( semiri681578069525770553at_rat @ X ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % mult_of_nat_commute
% 4.69/5.03 thf(fact_6966_mult__of__nat__commute,axiom,
% 4.69/5.03 ! [X: nat,Y: int] :
% 4.69/5.03 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y )
% 4.69/5.03 = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % mult_of_nat_commute
% 4.69/5.03 thf(fact_6967_mult__of__nat__commute,axiom,
% 4.69/5.03 ! [X: nat,Y: nat] :
% 4.69/5.03 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
% 4.69/5.03 = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % mult_of_nat_commute
% 4.69/5.03 thf(fact_6968_mult__of__nat__commute,axiom,
% 4.69/5.03 ! [X: nat,Y: code_integer] :
% 4.69/5.03 ( ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ X ) @ Y )
% 4.69/5.03 = ( times_3573771949741848930nteger @ Y @ ( semiri4939895301339042750nteger @ X ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % mult_of_nat_commute
% 4.69/5.03 thf(fact_6969_le__imp__neg__le,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( ord_le3102999989581377725nteger @ A2 @ B )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % le_imp_neg_le
% 4.69/5.03 thf(fact_6970_le__imp__neg__le,axiom,
% 4.69/5.03 ! [A2: rat,B: rat] :
% 4.69/5.03 ( ( ord_less_eq_rat @ A2 @ B )
% 4.69/5.03 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % le_imp_neg_le
% 4.69/5.03 thf(fact_6971_le__imp__neg__le,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( ord_less_eq_int @ A2 @ B )
% 4.69/5.03 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % le_imp_neg_le
% 4.69/5.03 thf(fact_6972_minus__le__iff,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A2 ) @ B )
% 4.69/5.03 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_le_iff
% 4.69/5.03 thf(fact_6973_minus__le__iff,axiom,
% 4.69/5.03 ! [A2: rat,B: rat] :
% 4.69/5.03 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A2 ) @ B )
% 4.69/5.03 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_le_iff
% 4.69/5.03 thf(fact_6974_minus__le__iff,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A2 ) @ B )
% 4.69/5.03 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_le_iff
% 4.69/5.03 thf(fact_6975_le__minus__iff,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( ord_le3102999989581377725nteger @ A2 @ ( uminus1351360451143612070nteger @ B ) )
% 4.69/5.03 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % le_minus_iff
% 4.69/5.03 thf(fact_6976_le__minus__iff,axiom,
% 4.69/5.03 ! [A2: rat,B: rat] :
% 4.69/5.03 ( ( ord_less_eq_rat @ A2 @ ( uminus_uminus_rat @ B ) )
% 4.69/5.03 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % le_minus_iff
% 4.69/5.03 thf(fact_6977_le__minus__iff,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( ord_less_eq_int @ A2 @ ( uminus_uminus_int @ B ) )
% 4.69/5.03 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % le_minus_iff
% 4.69/5.03 thf(fact_6978_minus__less__iff,axiom,
% 4.69/5.03 ! [A2: rat,B: rat] :
% 4.69/5.03 ( ( ord_less_rat @ ( uminus_uminus_rat @ A2 ) @ B )
% 4.69/5.03 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_less_iff
% 4.69/5.03 thf(fact_6979_minus__less__iff,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( ord_less_int @ ( uminus_uminus_int @ A2 ) @ B )
% 4.69/5.03 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_less_iff
% 4.69/5.03 thf(fact_6980_minus__less__iff,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A2 ) @ B )
% 4.69/5.03 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A2 ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_less_iff
% 4.69/5.03 thf(fact_6981_less__minus__iff,axiom,
% 4.69/5.03 ! [A2: rat,B: rat] :
% 4.69/5.03 ( ( ord_less_rat @ A2 @ ( uminus_uminus_rat @ B ) )
% 4.69/5.03 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_minus_iff
% 4.69/5.03 thf(fact_6982_less__minus__iff,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( ord_less_int @ A2 @ ( uminus_uminus_int @ B ) )
% 4.69/5.03 = ( ord_less_int @ B @ ( uminus_uminus_int @ A2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_minus_iff
% 4.69/5.03 thf(fact_6983_less__minus__iff,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( ord_le6747313008572928689nteger @ A2 @ ( uminus1351360451143612070nteger @ B ) )
% 4.69/5.03 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_minus_iff
% 4.69/5.03 thf(fact_6984_add_Oinverse__distrib__swap,axiom,
% 4.69/5.03 ! [A2: rat,B: rat] :
% 4.69/5.03 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A2 @ B ) )
% 4.69/5.03 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % add.inverse_distrib_swap
% 4.69/5.03 thf(fact_6985_add_Oinverse__distrib__swap,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( uminus_uminus_int @ ( plus_plus_int @ A2 @ B ) )
% 4.69/5.03 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % add.inverse_distrib_swap
% 4.69/5.03 thf(fact_6986_add_Oinverse__distrib__swap,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A2 @ B ) )
% 4.69/5.03 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % add.inverse_distrib_swap
% 4.69/5.03 thf(fact_6987_group__cancel_Oneg1,axiom,
% 4.69/5.03 ! [A: rat,K3: rat,A2: rat] :
% 4.69/5.03 ( ( A
% 4.69/5.03 = ( plus_plus_rat @ K3 @ A2 ) )
% 4.69/5.03 => ( ( uminus_uminus_rat @ A )
% 4.69/5.03 = ( plus_plus_rat @ ( uminus_uminus_rat @ K3 ) @ ( uminus_uminus_rat @ A2 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % group_cancel.neg1
% 4.69/5.03 thf(fact_6988_group__cancel_Oneg1,axiom,
% 4.69/5.03 ! [A: int,K3: int,A2: int] :
% 4.69/5.03 ( ( A
% 4.69/5.03 = ( plus_plus_int @ K3 @ A2 ) )
% 4.69/5.03 => ( ( uminus_uminus_int @ A )
% 4.69/5.03 = ( plus_plus_int @ ( uminus_uminus_int @ K3 ) @ ( uminus_uminus_int @ A2 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % group_cancel.neg1
% 4.69/5.03 thf(fact_6989_group__cancel_Oneg1,axiom,
% 4.69/5.03 ! [A: code_integer,K3: code_integer,A2: code_integer] :
% 4.69/5.03 ( ( A
% 4.69/5.03 = ( plus_p5714425477246183910nteger @ K3 @ A2 ) )
% 4.69/5.03 => ( ( uminus1351360451143612070nteger @ A )
% 4.69/5.03 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K3 ) @ ( uminus1351360451143612070nteger @ A2 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % group_cancel.neg1
% 4.69/5.03 thf(fact_6990_square__eq__iff,axiom,
% 4.69/5.03 ! [A2: rat,B: rat] :
% 4.69/5.03 ( ( ( times_times_rat @ A2 @ A2 )
% 4.69/5.03 = ( times_times_rat @ B @ B ) )
% 4.69/5.03 = ( ( A2 = B )
% 4.69/5.03 | ( A2
% 4.69/5.03 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % square_eq_iff
% 4.69/5.03 thf(fact_6991_square__eq__iff,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( ( times_times_int @ A2 @ A2 )
% 4.69/5.03 = ( times_times_int @ B @ B ) )
% 4.69/5.03 = ( ( A2 = B )
% 4.69/5.03 | ( A2
% 4.69/5.03 = ( uminus_uminus_int @ B ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % square_eq_iff
% 4.69/5.03 thf(fact_6992_square__eq__iff,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( ( times_3573771949741848930nteger @ A2 @ A2 )
% 4.69/5.03 = ( times_3573771949741848930nteger @ B @ B ) )
% 4.69/5.03 = ( ( A2 = B )
% 4.69/5.03 | ( A2
% 4.69/5.03 = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % square_eq_iff
% 4.69/5.03 thf(fact_6993_minus__mult__commute,axiom,
% 4.69/5.03 ! [A2: rat,B: rat] :
% 4.69/5.03 ( ( times_times_rat @ ( uminus_uminus_rat @ A2 ) @ B )
% 4.69/5.03 = ( times_times_rat @ A2 @ ( uminus_uminus_rat @ B ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_mult_commute
% 4.69/5.03 thf(fact_6994_minus__mult__commute,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( times_times_int @ ( uminus_uminus_int @ A2 ) @ B )
% 4.69/5.03 = ( times_times_int @ A2 @ ( uminus_uminus_int @ B ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_mult_commute
% 4.69/5.03 thf(fact_6995_minus__mult__commute,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A2 ) @ B )
% 4.69/5.03 = ( times_3573771949741848930nteger @ A2 @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_mult_commute
% 4.69/5.03 thf(fact_6996_one__neq__neg__one,axiom,
% 4.69/5.03 ( one_one_int
% 4.69/5.03 != ( uminus_uminus_int @ one_one_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % one_neq_neg_one
% 4.69/5.03 thf(fact_6997_one__neq__neg__one,axiom,
% 4.69/5.03 ( one_one_Code_integer
% 4.69/5.03 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.69/5.03
% 4.69/5.03 % one_neq_neg_one
% 4.69/5.03 thf(fact_6998_minus__diff__commute,axiom,
% 4.69/5.03 ! [B: rat,A2: rat] :
% 4.69/5.03 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A2 )
% 4.69/5.03 = ( minus_minus_rat @ ( uminus_uminus_rat @ A2 ) @ B ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_diff_commute
% 4.69/5.03 thf(fact_6999_minus__diff__commute,axiom,
% 4.69/5.03 ! [B: int,A2: int] :
% 4.69/5.03 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A2 )
% 4.69/5.03 = ( minus_minus_int @ ( uminus_uminus_int @ A2 ) @ B ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_diff_commute
% 4.69/5.03 thf(fact_7000_minus__diff__commute,axiom,
% 4.69/5.03 ! [B: code_integer,A2: code_integer] :
% 4.69/5.03 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A2 )
% 4.69/5.03 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A2 ) @ B ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_diff_commute
% 4.69/5.03 thf(fact_7001_Gcd__1,axiom,
% 4.69/5.03 ! [A: set_nat] :
% 4.69/5.03 ( ( member_nat @ one_one_nat @ A )
% 4.69/5.03 => ( ( gcd_Gcd_nat @ A )
% 4.69/5.03 = one_one_nat ) ) ).
% 4.69/5.03
% 4.69/5.03 % Gcd_1
% 4.69/5.03 thf(fact_7002_Gcd__1,axiom,
% 4.69/5.03 ! [A: set_int] :
% 4.69/5.03 ( ( member_int @ one_one_int @ A )
% 4.69/5.03 => ( ( gcd_Gcd_int @ A )
% 4.69/5.03 = one_one_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % Gcd_1
% 4.69/5.03 thf(fact_7003_minus__assn__def,axiom,
% 4.69/5.03 ( minus_minus_assn
% 4.69/5.03 = ( ^ [A6: assn,B6: assn] : ( inf_inf_assn @ A6 @ ( uminus_uminus_assn @ B6 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % minus_assn_def
% 4.69/5.03 thf(fact_7004_prod__ge__1,axiom,
% 4.69/5.03 ! [A: set_nat,F: nat > code_integer] :
% 4.69/5.03 ( ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ A )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ X3 ) ) )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F @ A ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_ge_1
% 4.69/5.03 thf(fact_7005_prod__ge__1,axiom,
% 4.69/5.03 ! [A: set_int,F: int > code_integer] :
% 4.69/5.03 ( ! [X3: int] :
% 4.69/5.03 ( ( member_int @ X3 @ A )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ X3 ) ) )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F @ A ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_ge_1
% 4.69/5.03 thf(fact_7006_prod__ge__1,axiom,
% 4.69/5.03 ! [A: set_o,F: $o > code_integer] :
% 4.69/5.03 ( ! [X3: $o] :
% 4.69/5.03 ( ( member_o @ X3 @ A )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ X3 ) ) )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups7694694392188491536nteger @ F @ A ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_ge_1
% 4.69/5.03 thf(fact_7007_prod__ge__1,axiom,
% 4.69/5.03 ! [A: set_Product_unit,F: product_unit > code_integer] :
% 4.69/5.03 ( ! [X3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ X3 @ A )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ X3 ) ) )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups8185359811944078981nteger @ F @ A ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_ge_1
% 4.69/5.03 thf(fact_7008_prod__ge__1,axiom,
% 4.69/5.03 ! [A: set_nat,F: nat > code_natural] :
% 4.69/5.03 ( ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ A )
% 4.69/5.03 => ( ord_le1926595141338095240atural @ one_one_Code_natural @ ( F @ X3 ) ) )
% 4.69/5.03 => ( ord_le1926595141338095240atural @ one_one_Code_natural @ ( groups2279045934846249631atural @ F @ A ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_ge_1
% 4.69/5.03 thf(fact_7009_prod__ge__1,axiom,
% 4.69/5.03 ! [A: set_int,F: int > code_natural] :
% 4.69/5.03 ( ! [X3: int] :
% 4.69/5.03 ( ( member_int @ X3 @ A )
% 4.69/5.03 => ( ord_le1926595141338095240atural @ one_one_Code_natural @ ( F @ X3 ) ) )
% 4.69/5.03 => ( ord_le1926595141338095240atural @ one_one_Code_natural @ ( groups2650699495083094267atural @ F @ A ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_ge_1
% 4.69/5.03 thf(fact_7010_prod__ge__1,axiom,
% 4.69/5.03 ! [A: set_o,F: $o > code_natural] :
% 4.69/5.03 ( ! [X3: $o] :
% 4.69/5.03 ( ( member_o @ X3 @ A )
% 4.69/5.03 => ( ord_le1926595141338095240atural @ one_one_Code_natural @ ( F @ X3 ) ) )
% 4.69/5.03 => ( ord_le1926595141338095240atural @ one_one_Code_natural @ ( groups6518289543945209051atural @ F @ A ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_ge_1
% 4.69/5.03 thf(fact_7011_prod__ge__1,axiom,
% 4.69/5.03 ! [A: set_Product_unit,F: product_unit > code_natural] :
% 4.69/5.03 ( ! [X3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ X3 @ A )
% 4.69/5.03 => ( ord_le1926595141338095240atural @ one_one_Code_natural @ ( F @ X3 ) ) )
% 4.69/5.03 => ( ord_le1926595141338095240atural @ one_one_Code_natural @ ( groups7008954963700796496atural @ F @ A ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_ge_1
% 4.69/5.03 thf(fact_7012_prod__ge__1,axiom,
% 4.69/5.03 ! [A: set_nat,F: nat > rat] :
% 4.69/5.03 ( ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ A )
% 4.69/5.03 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 4.69/5.03 => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_ge_1
% 4.69/5.03 thf(fact_7013_prod__ge__1,axiom,
% 4.69/5.03 ! [A: set_int,F: int > rat] :
% 4.69/5.03 ( ! [X3: int] :
% 4.69/5.03 ( ( member_int @ X3 @ A )
% 4.69/5.03 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 4.69/5.03 => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_ge_1
% 4.69/5.03 thf(fact_7014_prod_OUnion__comp,axiom,
% 4.69/5.03 ! [B4: set_set_int,G: int > assn] :
% 4.69/5.03 ( ! [X3: set_int] :
% 4.69/5.03 ( ( member_set_int @ X3 @ B4 )
% 4.69/5.03 => ( finite_finite_int @ X3 ) )
% 4.69/5.03 => ( ! [A12: set_int] :
% 4.69/5.03 ( ( member_set_int @ A12 @ B4 )
% 4.69/5.03 => ! [A23: set_int] :
% 4.69/5.03 ( ( member_set_int @ A23 @ B4 )
% 4.69/5.03 => ( ( A12 != A23 )
% 4.69/5.03 => ! [X3: int] :
% 4.69/5.03 ( ( member_int @ X3 @ A12 )
% 4.69/5.03 => ( ( member_int @ X3 @ A23 )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_assn ) ) ) ) ) )
% 4.69/5.03 => ( ( groups7882442080178216443t_assn @ G @ ( comple3221217463730067765et_int @ B4 ) )
% 4.69/5.03 = ( comp_s4595925057662634336t_assn @ groups5950967880310095793t_assn @ groups7882442080178216443t_assn @ G @ B4 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.Union_comp
% 4.69/5.03 thf(fact_7015_prod_OUnion__comp,axiom,
% 4.69/5.03 ! [B4: set_set_o,G: $o > assn] :
% 4.69/5.03 ( ! [X3: set_o] :
% 4.69/5.03 ( ( member_set_o @ X3 @ B4 )
% 4.69/5.03 => ( finite_finite_o @ X3 ) )
% 4.69/5.03 => ( ! [A12: set_o] :
% 4.69/5.03 ( ( member_set_o @ A12 @ B4 )
% 4.69/5.03 => ! [A23: set_o] :
% 4.69/5.03 ( ( member_set_o @ A23 @ B4 )
% 4.69/5.03 => ( ( A12 != A23 )
% 4.69/5.03 => ! [X3: $o] :
% 4.69/5.03 ( ( member_o @ X3 @ A12 )
% 4.69/5.03 => ( ( member_o @ X3 @ A23 )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_assn ) ) ) ) ) )
% 4.69/5.03 => ( ( groups5301882518646026715o_assn @ G @ ( comple90263536869209701_set_o @ B4 ) )
% 4.69/5.03 = ( comp_s518380907012905326o_assn @ groups6963733262650904763o_assn @ groups5301882518646026715o_assn @ G @ B4 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.Union_comp
% 4.69/5.03 thf(fact_7016_prod_OUnion__comp,axiom,
% 4.69/5.03 ! [B4: set_set_Product_unit,G: product_unit > assn] :
% 4.69/5.03 ( ! [X3: set_Product_unit] :
% 4.69/5.03 ( ( member5877623283571906838t_unit @ X3 @ B4 )
% 4.69/5.03 => ( finite4290736615968046902t_unit @ X3 ) )
% 4.69/5.03 => ( ! [A12: set_Product_unit] :
% 4.69/5.03 ( ( member5877623283571906838t_unit @ A12 @ B4 )
% 4.69/5.03 => ! [A23: set_Product_unit] :
% 4.69/5.03 ( ( member5877623283571906838t_unit @ A23 @ B4 )
% 4.69/5.03 => ( ( A12 != A23 )
% 4.69/5.03 => ! [X3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ X3 @ A12 )
% 4.69/5.03 => ( ( member_Product_unit @ X3 @ A23 )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_assn ) ) ) ) ) )
% 4.69/5.03 => ( ( groups5360233303959380816t_assn @ G @ ( comple3349607820504768346t_unit @ B4 ) )
% 4.69/5.03 = ( comp_s8247530669214396195t_assn @ groups2392624107559085104t_assn @ groups5360233303959380816t_assn @ G @ B4 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.Union_comp
% 4.69/5.03 thf(fact_7017_prod_OUnion__comp,axiom,
% 4.69/5.03 ! [B4: set_set_nat,G: nat > assn] :
% 4.69/5.03 ( ! [X3: set_nat] :
% 4.69/5.03 ( ( member_set_nat @ X3 @ B4 )
% 4.69/5.03 => ( finite_finite_nat @ X3 ) )
% 4.69/5.03 => ( ! [A12: set_nat] :
% 4.69/5.03 ( ( member_set_nat @ A12 @ B4 )
% 4.69/5.03 => ! [A23: set_nat] :
% 4.69/5.03 ( ( member_set_nat @ A23 @ B4 )
% 4.69/5.03 => ( ( A12 != A23 )
% 4.69/5.03 => ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ A12 )
% 4.69/5.03 => ( ( member_nat @ X3 @ A23 )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_assn ) ) ) ) ) )
% 4.69/5.03 => ( ( groups6906906614972039071t_assn @ G @ ( comple7399068483239264473et_nat @ B4 ) )
% 4.69/5.03 = ( comp_s2451231738238893644t_assn @ groups1535173586962943829t_assn @ groups6906906614972039071t_assn @ G @ B4 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.Union_comp
% 4.69/5.03 thf(fact_7018_prod_OUnion__comp,axiom,
% 4.69/5.03 ! [B4: set_set_Code_integer,G: code_integer > assn] :
% 4.69/5.03 ( ! [X3: set_Code_integer] :
% 4.69/5.03 ( ( member1834298987299537450nteger @ X3 @ B4 )
% 4.69/5.03 => ( finite6017078050557962740nteger @ X3 ) )
% 4.69/5.03 => ( ! [A12: set_Code_integer] :
% 4.69/5.03 ( ( member1834298987299537450nteger @ A12 @ B4 )
% 4.69/5.03 => ! [A23: set_Code_integer] :
% 4.69/5.03 ( ( member1834298987299537450nteger @ A23 @ B4 )
% 4.69/5.03 => ( ( A12 != A23 )
% 4.69/5.03 => ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ A12 )
% 4.69/5.03 => ( ( member_Code_integer @ X3 @ A23 )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_assn ) ) ) ) ) )
% 4.69/5.03 => ( ( groups1304777262505850412r_assn @ G @ ( comple739944243200306918nteger @ B4 ) )
% 4.69/5.03 = ( comp_s3531641609786562035r_assn @ groups4245288774754739042r_assn @ groups1304777262505850412r_assn @ G @ B4 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.Union_comp
% 4.69/5.03 thf(fact_7019_prod_OUnion__comp,axiom,
% 4.69/5.03 ! [B4: set_set_int,G: int > nat] :
% 4.69/5.03 ( ! [X3: set_int] :
% 4.69/5.03 ( ( member_set_int @ X3 @ B4 )
% 4.69/5.03 => ( finite_finite_int @ X3 ) )
% 4.69/5.03 => ( ! [A12: set_int] :
% 4.69/5.03 ( ( member_set_int @ A12 @ B4 )
% 4.69/5.03 => ! [A23: set_int] :
% 4.69/5.03 ( ( member_set_int @ A23 @ B4 )
% 4.69/5.03 => ( ( A12 != A23 )
% 4.69/5.03 => ! [X3: int] :
% 4.69/5.03 ( ( member_int @ X3 @ A12 )
% 4.69/5.03 => ( ( member_int @ X3 @ A23 )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_nat ) ) ) ) ) )
% 4.69/5.03 => ( ( groups1707563613775114915nt_nat @ G @ ( comple3221217463730067765et_int @ B4 ) )
% 4.69/5.03 = ( comp_s3237642481825588056nt_nat @ groups6435469334873047129nt_nat @ groups1707563613775114915nt_nat @ G @ B4 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.Union_comp
% 4.69/5.03 thf(fact_7020_prod_OUnion__comp,axiom,
% 4.69/5.03 ! [B4: set_set_o,G: $o > nat] :
% 4.69/5.03 ( ! [X3: set_o] :
% 4.69/5.03 ( ( member_set_o @ X3 @ B4 )
% 4.69/5.03 => ( finite_finite_o @ X3 ) )
% 4.69/5.03 => ( ! [A12: set_o] :
% 4.69/5.03 ( ( member_set_o @ A12 @ B4 )
% 4.69/5.03 => ! [A23: set_o] :
% 4.69/5.03 ( ( member_set_o @ A23 @ B4 )
% 4.69/5.03 => ( ( A12 != A23 )
% 4.69/5.03 => ! [X3: $o] :
% 4.69/5.03 ( ( member_o @ X3 @ A12 )
% 4.69/5.03 => ( ( member_o @ X3 @ A23 )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_nat ) ) ) ) ) )
% 4.69/5.03 => ( ( groups3504817904513533571_o_nat @ G @ ( comple90263536869209701_set_o @ B4 ) )
% 4.69/5.03 = ( comp_s6084864194472624150_o_nat @ groups4868773677410035043_o_nat @ groups3504817904513533571_o_nat @ G @ B4 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.Union_comp
% 4.69/5.03 thf(fact_7021_prod_OUnion__comp,axiom,
% 4.69/5.03 ! [B4: set_set_Product_unit,G: product_unit > nat] :
% 4.69/5.03 ( ! [X3: set_Product_unit] :
% 4.69/5.03 ( ( member5877623283571906838t_unit @ X3 @ B4 )
% 4.69/5.03 => ( finite4290736615968046902t_unit @ X3 ) )
% 4.69/5.03 => ( ! [A12: set_Product_unit] :
% 4.69/5.03 ( ( member5877623283571906838t_unit @ A12 @ B4 )
% 4.69/5.03 => ! [A23: set_Product_unit] :
% 4.69/5.03 ( ( member5877623283571906838t_unit @ A23 @ B4 )
% 4.69/5.03 => ( ( A12 != A23 )
% 4.69/5.03 => ! [X3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ X3 @ A12 )
% 4.69/5.03 => ( ( member_Product_unit @ X3 @ A23 )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_nat ) ) ) ) ) )
% 4.69/5.03 => ( ( groups396421249026171384it_nat @ G @ ( comple3349607820504768346t_unit @ B4 ) )
% 4.69/5.03 = ( comp_s8928436226432208331it_nat @ groups8454329047868613336it_nat @ groups396421249026171384it_nat @ G @ B4 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.Union_comp
% 4.69/5.03 thf(fact_7022_prod_OUnion__comp,axiom,
% 4.69/5.03 ! [B4: set_set_Code_integer,G: code_integer > nat] :
% 4.69/5.03 ( ! [X3: set_Code_integer] :
% 4.69/5.03 ( ( member1834298987299537450nteger @ X3 @ B4 )
% 4.69/5.03 => ( finite6017078050557962740nteger @ X3 ) )
% 4.69/5.03 => ( ! [A12: set_Code_integer] :
% 4.69/5.03 ( ( member1834298987299537450nteger @ A12 @ B4 )
% 4.69/5.03 => ! [A23: set_Code_integer] :
% 4.69/5.03 ( ( member1834298987299537450nteger @ A23 @ B4 )
% 4.69/5.03 => ( ( A12 != A23 )
% 4.69/5.03 => ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ A12 )
% 4.69/5.03 => ( ( member_Code_integer @ X3 @ A23 )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_nat ) ) ) ) ) )
% 4.69/5.03 => ( ( groups3190895334310489300er_nat @ G @ ( comple739944243200306918nteger @ B4 ) )
% 4.69/5.03 = ( comp_s8759123648413916139er_nat @ groups6044384099095135754er_nat @ groups3190895334310489300er_nat @ G @ B4 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.Union_comp
% 4.69/5.03 thf(fact_7023_prod_OUnion__comp,axiom,
% 4.69/5.03 ! [B4: set_set_int,G: int > int] :
% 4.69/5.03 ( ! [X3: set_int] :
% 4.69/5.03 ( ( member_set_int @ X3 @ B4 )
% 4.69/5.03 => ( finite_finite_int @ X3 ) )
% 4.69/5.03 => ( ! [A12: set_int] :
% 4.69/5.03 ( ( member_set_int @ A12 @ B4 )
% 4.69/5.03 => ! [A23: set_int] :
% 4.69/5.03 ( ( member_set_int @ A23 @ B4 )
% 4.69/5.03 => ( ( A12 != A23 )
% 4.69/5.03 => ! [X3: int] :
% 4.69/5.03 ( ( member_int @ X3 @ A12 )
% 4.69/5.03 => ( ( member_int @ X3 @ A23 )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_int ) ) ) ) ) )
% 4.69/5.03 => ( ( groups1705073143266064639nt_int @ G @ ( comple3221217463730067765et_int @ B4 ) )
% 4.69/5.03 = ( comp_s9098231955081793132nt_int @ groups6432978864363996853nt_int @ groups1705073143266064639nt_int @ G @ B4 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.Union_comp
% 4.69/5.03 thf(fact_7024_neg__eq__iff__add__eq__0,axiom,
% 4.69/5.03 ! [A2: rat,B: rat] :
% 4.69/5.03 ( ( ( uminus_uminus_rat @ A2 )
% 4.69/5.03 = B )
% 4.69/5.03 = ( ( plus_plus_rat @ A2 @ B )
% 4.69/5.03 = zero_zero_rat ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_eq_iff_add_eq_0
% 4.69/5.03 thf(fact_7025_neg__eq__iff__add__eq__0,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( ( uminus_uminus_int @ A2 )
% 4.69/5.03 = B )
% 4.69/5.03 = ( ( plus_plus_int @ A2 @ B )
% 4.69/5.03 = zero_zero_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_eq_iff_add_eq_0
% 4.69/5.03 thf(fact_7026_neg__eq__iff__add__eq__0,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( ( uminus1351360451143612070nteger @ A2 )
% 4.69/5.03 = B )
% 4.69/5.03 = ( ( plus_p5714425477246183910nteger @ A2 @ B )
% 4.69/5.03 = zero_z3403309356797280102nteger ) ) ).
% 4.69/5.03
% 4.69/5.03 % neg_eq_iff_add_eq_0
% 4.69/5.03 thf(fact_7027_eq__neg__iff__add__eq__0,axiom,
% 4.69/5.03 ! [A2: rat,B: rat] :
% 4.69/5.03 ( ( A2
% 4.69/5.03 = ( uminus_uminus_rat @ B ) )
% 4.69/5.03 = ( ( plus_plus_rat @ A2 @ B )
% 4.69/5.03 = zero_zero_rat ) ) ).
% 4.69/5.03
% 4.69/5.03 % eq_neg_iff_add_eq_0
% 4.69/5.03 thf(fact_7028_eq__neg__iff__add__eq__0,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( A2
% 4.69/5.03 = ( uminus_uminus_int @ B ) )
% 4.69/5.03 = ( ( plus_plus_int @ A2 @ B )
% 4.69/5.03 = zero_zero_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % eq_neg_iff_add_eq_0
% 4.69/5.03 thf(fact_7029_eq__neg__iff__add__eq__0,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( A2
% 4.69/5.03 = ( uminus1351360451143612070nteger @ B ) )
% 4.69/5.03 = ( ( plus_p5714425477246183910nteger @ A2 @ B )
% 4.69/5.03 = zero_z3403309356797280102nteger ) ) ).
% 4.69/5.03
% 4.69/5.03 % eq_neg_iff_add_eq_0
% 4.69/5.03 thf(fact_7030_add_Oinverse__unique,axiom,
% 4.69/5.03 ! [A2: rat,B: rat] :
% 4.69/5.03 ( ( ( plus_plus_rat @ A2 @ B )
% 4.69/5.03 = zero_zero_rat )
% 4.69/5.03 => ( ( uminus_uminus_rat @ A2 )
% 4.69/5.03 = B ) ) ).
% 4.69/5.03
% 4.69/5.03 % add.inverse_unique
% 4.69/5.03 thf(fact_7031_add_Oinverse__unique,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( ( plus_plus_int @ A2 @ B )
% 4.69/5.03 = zero_zero_int )
% 4.69/5.03 => ( ( uminus_uminus_int @ A2 )
% 4.69/5.03 = B ) ) ).
% 4.69/5.03
% 4.69/5.03 % add.inverse_unique
% 4.69/5.03 thf(fact_7032_add_Oinverse__unique,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( ( plus_p5714425477246183910nteger @ A2 @ B )
% 4.69/5.03 = zero_z3403309356797280102nteger )
% 4.69/5.03 => ( ( uminus1351360451143612070nteger @ A2 )
% 4.69/5.03 = B ) ) ).
% 4.69/5.03
% 4.69/5.03 % add.inverse_unique
% 4.69/5.03 thf(fact_7033_ab__group__add__class_Oab__left__minus,axiom,
% 4.69/5.03 ! [A2: rat] :
% 4.69/5.03 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A2 ) @ A2 )
% 4.69/5.03 = zero_zero_rat ) ).
% 4.69/5.03
% 4.69/5.03 % ab_group_add_class.ab_left_minus
% 4.69/5.03 thf(fact_7034_ab__group__add__class_Oab__left__minus,axiom,
% 4.69/5.03 ! [A2: int] :
% 4.69/5.03 ( ( plus_plus_int @ ( uminus_uminus_int @ A2 ) @ A2 )
% 4.69/5.03 = zero_zero_int ) ).
% 4.69/5.03
% 4.69/5.03 % ab_group_add_class.ab_left_minus
% 4.69/5.03 thf(fact_7035_ab__group__add__class_Oab__left__minus,axiom,
% 4.69/5.03 ! [A2: code_integer] :
% 4.69/5.03 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A2 ) @ A2 )
% 4.69/5.03 = zero_z3403309356797280102nteger ) ).
% 4.69/5.03
% 4.69/5.03 % ab_group_add_class.ab_left_minus
% 4.69/5.03 thf(fact_7036_add__eq__0__iff,axiom,
% 4.69/5.03 ! [A2: rat,B: rat] :
% 4.69/5.03 ( ( ( plus_plus_rat @ A2 @ B )
% 4.69/5.03 = zero_zero_rat )
% 4.69/5.03 = ( B
% 4.69/5.03 = ( uminus_uminus_rat @ A2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % add_eq_0_iff
% 4.69/5.03 thf(fact_7037_add__eq__0__iff,axiom,
% 4.69/5.03 ! [A2: int,B: int] :
% 4.69/5.03 ( ( ( plus_plus_int @ A2 @ B )
% 4.69/5.03 = zero_zero_int )
% 4.69/5.03 = ( B
% 4.69/5.03 = ( uminus_uminus_int @ A2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % add_eq_0_iff
% 4.69/5.03 thf(fact_7038_add__eq__0__iff,axiom,
% 4.69/5.03 ! [A2: code_integer,B: code_integer] :
% 4.69/5.03 ( ( ( plus_p5714425477246183910nteger @ A2 @ B )
% 4.69/5.03 = zero_z3403309356797280102nteger )
% 4.69/5.03 = ( B
% 4.69/5.03 = ( uminus1351360451143612070nteger @ A2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % add_eq_0_iff
% 4.69/5.03 thf(fact_7039_le__minus__one__simps_I4_J,axiom,
% 4.69/5.03 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.69/5.03
% 4.69/5.03 % le_minus_one_simps(4)
% 4.69/5.03 thf(fact_7040_le__minus__one__simps_I4_J,axiom,
% 4.69/5.03 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.69/5.03
% 4.69/5.03 % le_minus_one_simps(4)
% 4.69/5.03 thf(fact_7041_le__minus__one__simps_I4_J,axiom,
% 4.69/5.03 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % le_minus_one_simps(4)
% 4.69/5.03 thf(fact_7042_le__minus__one__simps_I2_J,axiom,
% 4.69/5.03 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 4.69/5.03
% 4.69/5.03 % le_minus_one_simps(2)
% 4.69/5.03 thf(fact_7043_le__minus__one__simps_I2_J,axiom,
% 4.69/5.03 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 4.69/5.03
% 4.69/5.03 % le_minus_one_simps(2)
% 4.69/5.03 thf(fact_7044_le__minus__one__simps_I2_J,axiom,
% 4.69/5.03 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 4.69/5.03
% 4.69/5.03 % le_minus_one_simps(2)
% 4.69/5.03 thf(fact_7045_zero__neq__neg__one,axiom,
% 4.69/5.03 ( zero_zero_int
% 4.69/5.03 != ( uminus_uminus_int @ one_one_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % zero_neq_neg_one
% 4.69/5.03 thf(fact_7046_zero__neq__neg__one,axiom,
% 4.69/5.03 ( zero_z3403309356797280102nteger
% 4.69/5.03 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.69/5.03
% 4.69/5.03 % zero_neq_neg_one
% 4.69/5.03 thf(fact_7047_less__minus__one__simps_I2_J,axiom,
% 4.69/5.03 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 4.69/5.03
% 4.69/5.03 % less_minus_one_simps(2)
% 4.69/5.03 thf(fact_7048_less__minus__one__simps_I2_J,axiom,
% 4.69/5.03 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 4.69/5.03
% 4.69/5.03 % less_minus_one_simps(2)
% 4.69/5.03 thf(fact_7049_less__minus__one__simps_I2_J,axiom,
% 4.69/5.03 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 4.69/5.03
% 4.69/5.03 % less_minus_one_simps(2)
% 4.69/5.03 thf(fact_7050_less__minus__one__simps_I4_J,axiom,
% 4.69/5.03 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_minus_one_simps(4)
% 4.69/5.03 thf(fact_7051_less__minus__one__simps_I4_J,axiom,
% 4.69/5.03 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_minus_one_simps(4)
% 4.69/5.03 thf(fact_7052_less__minus__one__simps_I4_J,axiom,
% 4.69/5.03 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_minus_one_simps(4)
% 4.69/5.03 thf(fact_7053_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 4.69/5.03 ( minus_minus_rat
% 4.69/5.03 = ( ^ [A6: rat,B6: rat] : ( plus_plus_rat @ A6 @ ( uminus_uminus_rat @ B6 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % ab_group_add_class.ab_diff_conv_add_uminus
% 4.69/5.03 thf(fact_7054_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 4.69/5.03 ( minus_minus_int
% 4.69/5.03 = ( ^ [A6: int,B6: int] : ( plus_plus_int @ A6 @ ( uminus_uminus_int @ B6 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % ab_group_add_class.ab_diff_conv_add_uminus
% 4.69/5.03 thf(fact_7055_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 4.69/5.03 ( minus_8373710615458151222nteger
% 4.69/5.03 = ( ^ [A6: code_integer,B6: code_integer] : ( plus_p5714425477246183910nteger @ A6 @ ( uminus1351360451143612070nteger @ B6 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % ab_group_add_class.ab_diff_conv_add_uminus
% 4.69/5.03 thf(fact_7056_diff__conv__add__uminus,axiom,
% 4.69/5.03 ( minus_minus_rat
% 4.69/5.03 = ( ^ [A6: rat,B6: rat] : ( plus_plus_rat @ A6 @ ( uminus_uminus_rat @ B6 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % diff_conv_add_uminus
% 4.69/5.03 thf(fact_7057_diff__conv__add__uminus,axiom,
% 4.69/5.03 ( minus_minus_int
% 4.69/5.03 = ( ^ [A6: int,B6: int] : ( plus_plus_int @ A6 @ ( uminus_uminus_int @ B6 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % diff_conv_add_uminus
% 4.69/5.03 thf(fact_7058_diff__conv__add__uminus,axiom,
% 4.69/5.03 ( minus_8373710615458151222nteger
% 4.69/5.03 = ( ^ [A6: code_integer,B6: code_integer] : ( plus_p5714425477246183910nteger @ A6 @ ( uminus1351360451143612070nteger @ B6 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % diff_conv_add_uminus
% 4.69/5.03 thf(fact_7059_group__cancel_Osub2,axiom,
% 4.69/5.03 ! [B4: rat,K3: rat,B: rat,A2: rat] :
% 4.69/5.03 ( ( B4
% 4.69/5.03 = ( plus_plus_rat @ K3 @ B ) )
% 4.69/5.03 => ( ( minus_minus_rat @ A2 @ B4 )
% 4.69/5.03 = ( plus_plus_rat @ ( uminus_uminus_rat @ K3 ) @ ( minus_minus_rat @ A2 @ B ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % group_cancel.sub2
% 4.69/5.03 thf(fact_7060_group__cancel_Osub2,axiom,
% 4.69/5.03 ! [B4: int,K3: int,B: int,A2: int] :
% 4.69/5.03 ( ( B4
% 4.69/5.03 = ( plus_plus_int @ K3 @ B ) )
% 4.69/5.03 => ( ( minus_minus_int @ A2 @ B4 )
% 4.69/5.03 = ( plus_plus_int @ ( uminus_uminus_int @ K3 ) @ ( minus_minus_int @ A2 @ B ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % group_cancel.sub2
% 4.69/5.03 thf(fact_7061_group__cancel_Osub2,axiom,
% 4.69/5.03 ! [B4: code_integer,K3: code_integer,B: code_integer,A2: code_integer] :
% 4.69/5.03 ( ( B4
% 4.69/5.03 = ( plus_p5714425477246183910nteger @ K3 @ B ) )
% 4.69/5.03 => ( ( minus_8373710615458151222nteger @ A2 @ B4 )
% 4.69/5.03 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K3 ) @ ( minus_8373710615458151222nteger @ A2 @ B ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % group_cancel.sub2
% 4.69/5.03 thf(fact_7062_square__eq__1__iff,axiom,
% 4.69/5.03 ! [X: rat] :
% 4.69/5.03 ( ( ( times_times_rat @ X @ X )
% 4.69/5.03 = one_one_rat )
% 4.69/5.03 = ( ( X = one_one_rat )
% 4.69/5.03 | ( X
% 4.69/5.03 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % square_eq_1_iff
% 4.69/5.03 thf(fact_7063_square__eq__1__iff,axiom,
% 4.69/5.03 ! [X: int] :
% 4.69/5.03 ( ( ( times_times_int @ X @ X )
% 4.69/5.03 = one_one_int )
% 4.69/5.03 = ( ( X = one_one_int )
% 4.69/5.03 | ( X
% 4.69/5.03 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % square_eq_1_iff
% 4.69/5.03 thf(fact_7064_square__eq__1__iff,axiom,
% 4.69/5.03 ! [X: code_integer] :
% 4.69/5.03 ( ( ( times_3573771949741848930nteger @ X @ X )
% 4.69/5.03 = one_one_Code_integer )
% 4.69/5.03 = ( ( X = one_one_Code_integer )
% 4.69/5.03 | ( X
% 4.69/5.03 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % square_eq_1_iff
% 4.69/5.03 thf(fact_7065_inf__cancel__left2,axiom,
% 4.69/5.03 ! [X: set_Product_unit,A2: set_Product_unit,B: set_Product_unit] :
% 4.69/5.03 ( ( inf_in4660618365625256667t_unit @ ( inf_in4660618365625256667t_unit @ ( uminus5944136376168626660t_unit @ X ) @ A2 ) @ ( inf_in4660618365625256667t_unit @ X @ B ) )
% 4.69/5.03 = bot_bo3957492148770167129t_unit ) ).
% 4.69/5.03
% 4.69/5.03 % inf_cancel_left2
% 4.69/5.03 thf(fact_7066_inf__cancel__left2,axiom,
% 4.69/5.03 ! [X: set_o,A2: set_o,B: set_o] :
% 4.69/5.03 ( ( inf_inf_set_o @ ( inf_inf_set_o @ ( uminus_uminus_set_o @ X ) @ A2 ) @ ( inf_inf_set_o @ X @ B ) )
% 4.69/5.03 = bot_bot_set_o ) ).
% 4.69/5.03
% 4.69/5.03 % inf_cancel_left2
% 4.69/5.03 thf(fact_7067_inf__cancel__left2,axiom,
% 4.69/5.03 ! [X: set_nat,A2: set_nat,B: set_nat] :
% 4.69/5.03 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ A2 ) @ ( inf_inf_set_nat @ X @ B ) )
% 4.69/5.03 = bot_bot_set_nat ) ).
% 4.69/5.03
% 4.69/5.03 % inf_cancel_left2
% 4.69/5.03 thf(fact_7068_inf__cancel__left2,axiom,
% 4.69/5.03 ! [X: set_int,A2: set_int,B: set_int] :
% 4.69/5.03 ( ( inf_inf_set_int @ ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ A2 ) @ ( inf_inf_set_int @ X @ B ) )
% 4.69/5.03 = bot_bot_set_int ) ).
% 4.69/5.03
% 4.69/5.03 % inf_cancel_left2
% 4.69/5.03 thf(fact_7069_inf__cancel__left2,axiom,
% 4.69/5.03 ! [X: set_Pr4532377907799695533_nat_o,A2: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 4.69/5.03 ( ( inf_in1906310914598751387_nat_o @ ( inf_in1906310914598751387_nat_o @ ( uminus5254974436814262692_nat_o @ X ) @ A2 ) @ ( inf_in1906310914598751387_nat_o @ X @ B ) )
% 4.69/5.03 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/5.03
% 4.69/5.03 % inf_cancel_left2
% 4.69/5.03 thf(fact_7070_inf__cancel__left2,axiom,
% 4.69/5.03 ! [X: assn,A2: assn,B: assn] :
% 4.69/5.03 ( ( inf_inf_assn @ ( inf_inf_assn @ ( uminus_uminus_assn @ X ) @ A2 ) @ ( inf_inf_assn @ X @ B ) )
% 4.69/5.03 = bot_bot_assn ) ).
% 4.69/5.03
% 4.69/5.03 % inf_cancel_left2
% 4.69/5.03 thf(fact_7071_inf__cancel__left2,axiom,
% 4.69/5.03 ! [X: product_unit,A2: product_unit,B: product_unit] :
% 4.69/5.03 ( ( inf_inf_Product_unit @ ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ A2 ) @ ( inf_inf_Product_unit @ X @ B ) )
% 4.69/5.03 = bot_bot_Product_unit ) ).
% 4.69/5.03
% 4.69/5.03 % inf_cancel_left2
% 4.69/5.03 thf(fact_7072_inf__cancel__left1,axiom,
% 4.69/5.03 ! [X: set_Product_unit,A2: set_Product_unit,B: set_Product_unit] :
% 4.69/5.03 ( ( inf_in4660618365625256667t_unit @ ( inf_in4660618365625256667t_unit @ X @ A2 ) @ ( inf_in4660618365625256667t_unit @ ( uminus5944136376168626660t_unit @ X ) @ B ) )
% 4.69/5.03 = bot_bo3957492148770167129t_unit ) ).
% 4.69/5.03
% 4.69/5.03 % inf_cancel_left1
% 4.69/5.03 thf(fact_7073_inf__cancel__left1,axiom,
% 4.69/5.03 ! [X: set_o,A2: set_o,B: set_o] :
% 4.69/5.03 ( ( inf_inf_set_o @ ( inf_inf_set_o @ X @ A2 ) @ ( inf_inf_set_o @ ( uminus_uminus_set_o @ X ) @ B ) )
% 4.69/5.03 = bot_bot_set_o ) ).
% 4.69/5.03
% 4.69/5.03 % inf_cancel_left1
% 4.69/5.03 thf(fact_7074_inf__cancel__left1,axiom,
% 4.69/5.03 ! [X: set_nat,A2: set_nat,B: set_nat] :
% 4.69/5.03 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X @ A2 ) @ ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ B ) )
% 4.69/5.03 = bot_bot_set_nat ) ).
% 4.69/5.03
% 4.69/5.03 % inf_cancel_left1
% 4.69/5.03 thf(fact_7075_inf__cancel__left1,axiom,
% 4.69/5.03 ! [X: set_int,A2: set_int,B: set_int] :
% 4.69/5.03 ( ( inf_inf_set_int @ ( inf_inf_set_int @ X @ A2 ) @ ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ B ) )
% 4.69/5.03 = bot_bot_set_int ) ).
% 4.69/5.03
% 4.69/5.03 % inf_cancel_left1
% 4.69/5.03 thf(fact_7076_inf__cancel__left1,axiom,
% 4.69/5.03 ! [X: set_Pr4532377907799695533_nat_o,A2: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 4.69/5.03 ( ( inf_in1906310914598751387_nat_o @ ( inf_in1906310914598751387_nat_o @ X @ A2 ) @ ( inf_in1906310914598751387_nat_o @ ( uminus5254974436814262692_nat_o @ X ) @ B ) )
% 4.69/5.03 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/5.03
% 4.69/5.03 % inf_cancel_left1
% 4.69/5.03 thf(fact_7077_inf__cancel__left1,axiom,
% 4.69/5.03 ! [X: assn,A2: assn,B: assn] :
% 4.69/5.03 ( ( inf_inf_assn @ ( inf_inf_assn @ X @ A2 ) @ ( inf_inf_assn @ ( uminus_uminus_assn @ X ) @ B ) )
% 4.69/5.03 = bot_bot_assn ) ).
% 4.69/5.03
% 4.69/5.03 % inf_cancel_left1
% 4.69/5.03 thf(fact_7078_inf__cancel__left1,axiom,
% 4.69/5.03 ! [X: product_unit,A2: product_unit,B: product_unit] :
% 4.69/5.03 ( ( inf_inf_Product_unit @ ( inf_inf_Product_unit @ X @ A2 ) @ ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ B ) )
% 4.69/5.03 = bot_bot_Product_unit ) ).
% 4.69/5.03
% 4.69/5.03 % inf_cancel_left1
% 4.69/5.03 thf(fact_7079_subset__Compl__self__eq,axiom,
% 4.69/5.03 ! [A: set_Product_unit] :
% 4.69/5.03 ( ( ord_le3507040750410214029t_unit @ A @ ( uminus5944136376168626660t_unit @ A ) )
% 4.69/5.03 = ( A = bot_bo3957492148770167129t_unit ) ) ).
% 4.69/5.03
% 4.69/5.03 % subset_Compl_self_eq
% 4.69/5.03 thf(fact_7080_subset__Compl__self__eq,axiom,
% 4.69/5.03 ! [A: set_o] :
% 4.69/5.03 ( ( ord_less_eq_set_o @ A @ ( uminus_uminus_set_o @ A ) )
% 4.69/5.03 = ( A = bot_bot_set_o ) ) ).
% 4.69/5.03
% 4.69/5.03 % subset_Compl_self_eq
% 4.69/5.03 thf(fact_7081_subset__Compl__self__eq,axiom,
% 4.69/5.03 ! [A: set_int] :
% 4.69/5.03 ( ( ord_less_eq_set_int @ A @ ( uminus1532241313380277803et_int @ A ) )
% 4.69/5.03 = ( A = bot_bot_set_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % subset_Compl_self_eq
% 4.69/5.03 thf(fact_7082_subset__Compl__self__eq,axiom,
% 4.69/5.03 ! [A: set_Pr4532377907799695533_nat_o] :
% 4.69/5.03 ( ( ord_le2965882846123202637_nat_o @ A @ ( uminus5254974436814262692_nat_o @ A ) )
% 4.69/5.03 = ( A = bot_bo7824918357723582233_nat_o ) ) ).
% 4.69/5.03
% 4.69/5.03 % subset_Compl_self_eq
% 4.69/5.03 thf(fact_7083_subset__Compl__self__eq,axiom,
% 4.69/5.03 ! [A: set_nat] :
% 4.69/5.03 ( ( ord_less_eq_set_nat @ A @ ( uminus5710092332889474511et_nat @ A ) )
% 4.69/5.03 = ( A = bot_bot_set_nat ) ) ).
% 4.69/5.03
% 4.69/5.03 % subset_Compl_self_eq
% 4.69/5.03 thf(fact_7084_Compl__UNIV__eq,axiom,
% 4.69/5.03 ( ( uminus5254974436814262692_nat_o @ top_to4869887016220417533_nat_o )
% 4.69/5.03 = bot_bo7824918357723582233_nat_o ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_UNIV_eq
% 4.69/5.03 thf(fact_7085_Compl__UNIV__eq,axiom,
% 4.69/5.03 ( ( uminus5944136376168626660t_unit @ top_to1996260823553986621t_unit )
% 4.69/5.03 = bot_bo3957492148770167129t_unit ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_UNIV_eq
% 4.69/5.03 thf(fact_7086_Compl__UNIV__eq,axiom,
% 4.69/5.03 ( ( uminus_uminus_set_o @ top_top_set_o )
% 4.69/5.03 = bot_bot_set_o ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_UNIV_eq
% 4.69/5.03 thf(fact_7087_Compl__UNIV__eq,axiom,
% 4.69/5.03 ( ( uminus5710092332889474511et_nat @ top_top_set_nat )
% 4.69/5.03 = bot_bot_set_nat ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_UNIV_eq
% 4.69/5.03 thf(fact_7088_Compl__UNIV__eq,axiom,
% 4.69/5.03 ( ( uminus1532241313380277803et_int @ top_top_set_int )
% 4.69/5.03 = bot_bot_set_int ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_UNIV_eq
% 4.69/5.03 thf(fact_7089_Compl__empty__eq,axiom,
% 4.69/5.03 ( ( uminus5254974436814262692_nat_o @ bot_bo7824918357723582233_nat_o )
% 4.69/5.03 = top_to4869887016220417533_nat_o ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_empty_eq
% 4.69/5.03 thf(fact_7090_Compl__empty__eq,axiom,
% 4.69/5.03 ( ( uminus5944136376168626660t_unit @ bot_bo3957492148770167129t_unit )
% 4.69/5.03 = top_to1996260823553986621t_unit ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_empty_eq
% 4.69/5.03 thf(fact_7091_Compl__empty__eq,axiom,
% 4.69/5.03 ( ( uminus_uminus_set_o @ bot_bot_set_o )
% 4.69/5.03 = top_top_set_o ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_empty_eq
% 4.69/5.03 thf(fact_7092_Compl__empty__eq,axiom,
% 4.69/5.03 ( ( uminus5710092332889474511et_nat @ bot_bot_set_nat )
% 4.69/5.03 = top_top_set_nat ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_empty_eq
% 4.69/5.03 thf(fact_7093_Compl__empty__eq,axiom,
% 4.69/5.03 ( ( uminus1532241313380277803et_int @ bot_bot_set_int )
% 4.69/5.03 = top_top_set_int ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_empty_eq
% 4.69/5.03 thf(fact_7094_Compl__partition2,axiom,
% 4.69/5.03 ! [A: set_Product_unit] :
% 4.69/5.03 ( ( sup_su793286257634532545t_unit @ ( uminus5944136376168626660t_unit @ A ) @ A )
% 4.69/5.03 = top_to1996260823553986621t_unit ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_partition2
% 4.69/5.03 thf(fact_7095_Compl__partition2,axiom,
% 4.69/5.03 ! [A: set_o] :
% 4.69/5.03 ( ( sup_sup_set_o @ ( uminus_uminus_set_o @ A ) @ A )
% 4.69/5.03 = top_top_set_o ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_partition2
% 4.69/5.03 thf(fact_7096_Compl__partition2,axiom,
% 4.69/5.03 ! [A: set_nat] :
% 4.69/5.03 ( ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ A ) @ A )
% 4.69/5.03 = top_top_set_nat ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_partition2
% 4.69/5.03 thf(fact_7097_Compl__partition2,axiom,
% 4.69/5.03 ! [A: set_int] :
% 4.69/5.03 ( ( sup_sup_set_int @ ( uminus1532241313380277803et_int @ A ) @ A )
% 4.69/5.03 = top_top_set_int ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_partition2
% 4.69/5.03 thf(fact_7098_Compl__partition,axiom,
% 4.69/5.03 ! [A: set_Product_unit] :
% 4.69/5.03 ( ( sup_su793286257634532545t_unit @ A @ ( uminus5944136376168626660t_unit @ A ) )
% 4.69/5.03 = top_to1996260823553986621t_unit ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_partition
% 4.69/5.03 thf(fact_7099_Compl__partition,axiom,
% 4.69/5.03 ! [A: set_o] :
% 4.69/5.03 ( ( sup_sup_set_o @ A @ ( uminus_uminus_set_o @ A ) )
% 4.69/5.03 = top_top_set_o ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_partition
% 4.69/5.03 thf(fact_7100_Compl__partition,axiom,
% 4.69/5.03 ! [A: set_nat] :
% 4.69/5.03 ( ( sup_sup_set_nat @ A @ ( uminus5710092332889474511et_nat @ A ) )
% 4.69/5.03 = top_top_set_nat ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_partition
% 4.69/5.03 thf(fact_7101_Compl__partition,axiom,
% 4.69/5.03 ! [A: set_int] :
% 4.69/5.03 ( ( sup_sup_set_int @ A @ ( uminus1532241313380277803et_int @ A ) )
% 4.69/5.03 = top_top_set_int ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_partition
% 4.69/5.03 thf(fact_7102_Compl__eq__Diff__UNIV,axiom,
% 4.69/5.03 ( uminus5944136376168626660t_unit
% 4.69/5.03 = ( minus_6452836326544984404t_unit @ top_to1996260823553986621t_unit ) ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_eq_Diff_UNIV
% 4.69/5.03 thf(fact_7103_Compl__eq__Diff__UNIV,axiom,
% 4.69/5.03 ( uminus_uminus_set_o
% 4.69/5.03 = ( minus_minus_set_o @ top_top_set_o ) ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_eq_Diff_UNIV
% 4.69/5.03 thf(fact_7104_Compl__eq__Diff__UNIV,axiom,
% 4.69/5.03 ( uminus1532241313380277803et_int
% 4.69/5.03 = ( minus_minus_set_int @ top_top_set_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_eq_Diff_UNIV
% 4.69/5.03 thf(fact_7105_Compl__eq__Diff__UNIV,axiom,
% 4.69/5.03 ( uminus5710092332889474511et_nat
% 4.69/5.03 = ( minus_minus_set_nat @ top_top_set_nat ) ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_eq_Diff_UNIV
% 4.69/5.03 thf(fact_7106_Compl__Int,axiom,
% 4.69/5.03 ! [A: set_nat,B4: set_nat] :
% 4.69/5.03 ( ( uminus5710092332889474511et_nat @ ( inf_inf_set_nat @ A @ B4 ) )
% 4.69/5.03 = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ A ) @ ( uminus5710092332889474511et_nat @ B4 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_Int
% 4.69/5.03 thf(fact_7107_Compl__Un,axiom,
% 4.69/5.03 ! [A: set_nat,B4: set_nat] :
% 4.69/5.03 ( ( uminus5710092332889474511et_nat @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/5.03 = ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A ) @ ( uminus5710092332889474511et_nat @ B4 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_Un
% 4.69/5.03 thf(fact_7108_gbinomial__negated__upper,axiom,
% 4.69/5.03 ( gbinomial_rat
% 4.69/5.03 = ( ^ [A6: rat,K5: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K5 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K5 ) @ A6 ) @ one_one_rat ) @ K5 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % gbinomial_negated_upper
% 4.69/5.03 thf(fact_7109_gbinomial__index__swap,axiom,
% 4.69/5.03 ! [K3: nat,N2: nat] :
% 4.69/5.03 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ one_one_rat ) @ K3 ) )
% 4.69/5.03 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) @ one_one_rat ) @ N2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % gbinomial_index_swap
% 4.69/5.03 thf(fact_7110_prod_OUnion__disjoint,axiom,
% 4.69/5.03 ! [C5: set_set_nat,G: nat > nat] :
% 4.69/5.03 ( ! [X3: set_nat] :
% 4.69/5.03 ( ( member_set_nat @ X3 @ C5 )
% 4.69/5.03 => ( finite_finite_nat @ X3 ) )
% 4.69/5.03 => ( ! [X3: set_nat] :
% 4.69/5.03 ( ( member_set_nat @ X3 @ C5 )
% 4.69/5.03 => ! [Xa3: set_nat] :
% 4.69/5.03 ( ( member_set_nat @ Xa3 @ C5 )
% 4.69/5.03 => ( ( X3 != Xa3 )
% 4.69/5.03 => ( ( inf_inf_set_nat @ X3 @ Xa3 )
% 4.69/5.03 = bot_bot_set_nat ) ) ) )
% 4.69/5.03 => ( ( groups708209901874060359at_nat @ G @ ( comple7399068483239264473et_nat @ C5 ) )
% 4.69/5.03 = ( comp_s5456809700045850692at_nat @ groups4248547760180025341at_nat @ groups708209901874060359at_nat @ G @ C5 ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.Union_disjoint
% 4.69/5.03 thf(fact_7111_Gcd__remove0__nat,axiom,
% 4.69/5.03 ! [M: set_nat] :
% 4.69/5.03 ( ( finite_finite_nat @ M )
% 4.69/5.03 => ( ( gcd_Gcd_nat @ M )
% 4.69/5.03 = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % Gcd_remove0_nat
% 4.69/5.03 thf(fact_7112_Gcd__eq__1__I,axiom,
% 4.69/5.03 ! [A2: nat,A: set_nat] :
% 4.69/5.03 ( ( dvd_dvd_nat @ A2 @ one_one_nat )
% 4.69/5.03 => ( ( member_nat @ A2 @ A )
% 4.69/5.03 => ( ( gcd_Gcd_nat @ A )
% 4.69/5.03 = one_one_nat ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % Gcd_eq_1_I
% 4.69/5.03 thf(fact_7113_Gcd__eq__1__I,axiom,
% 4.69/5.03 ! [A2: int,A: set_int] :
% 4.69/5.03 ( ( dvd_dvd_int @ A2 @ one_one_int )
% 4.69/5.03 => ( ( member_int @ A2 @ A )
% 4.69/5.03 => ( ( gcd_Gcd_int @ A )
% 4.69/5.03 = one_one_int ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % Gcd_eq_1_I
% 4.69/5.03 thf(fact_7114_prod__le__1,axiom,
% 4.69/5.03 ! [A: set_nat,F: nat > code_natural] :
% 4.69/5.03 ( ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ A )
% 4.69/5.03 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( F @ X3 ) )
% 4.69/5.03 & ( ord_le1926595141338095240atural @ ( F @ X3 ) @ one_one_Code_natural ) ) )
% 4.69/5.03 => ( ord_le1926595141338095240atural @ ( groups2279045934846249631atural @ F @ A ) @ one_one_Code_natural ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_le_1
% 4.69/5.03 thf(fact_7115_prod__le__1,axiom,
% 4.69/5.03 ! [A: set_int,F: int > code_natural] :
% 4.69/5.03 ( ! [X3: int] :
% 4.69/5.03 ( ( member_int @ X3 @ A )
% 4.69/5.03 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( F @ X3 ) )
% 4.69/5.03 & ( ord_le1926595141338095240atural @ ( F @ X3 ) @ one_one_Code_natural ) ) )
% 4.69/5.03 => ( ord_le1926595141338095240atural @ ( groups2650699495083094267atural @ F @ A ) @ one_one_Code_natural ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_le_1
% 4.69/5.03 thf(fact_7116_prod__le__1,axiom,
% 4.69/5.03 ! [A: set_o,F: $o > code_natural] :
% 4.69/5.03 ( ! [X3: $o] :
% 4.69/5.03 ( ( member_o @ X3 @ A )
% 4.69/5.03 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( F @ X3 ) )
% 4.69/5.03 & ( ord_le1926595141338095240atural @ ( F @ X3 ) @ one_one_Code_natural ) ) )
% 4.69/5.03 => ( ord_le1926595141338095240atural @ ( groups6518289543945209051atural @ F @ A ) @ one_one_Code_natural ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_le_1
% 4.69/5.03 thf(fact_7117_prod__le__1,axiom,
% 4.69/5.03 ! [A: set_Product_unit,F: product_unit > code_natural] :
% 4.69/5.03 ( ! [X3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ X3 @ A )
% 4.69/5.03 => ( ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( F @ X3 ) )
% 4.69/5.03 & ( ord_le1926595141338095240atural @ ( F @ X3 ) @ one_one_Code_natural ) ) )
% 4.69/5.03 => ( ord_le1926595141338095240atural @ ( groups7008954963700796496atural @ F @ A ) @ one_one_Code_natural ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_le_1
% 4.69/5.03 thf(fact_7118_prod__le__1,axiom,
% 4.69/5.03 ! [A: set_nat,F: nat > code_integer] :
% 4.69/5.03 ( ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ A )
% 4.69/5.03 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) )
% 4.69/5.03 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ one_one_Code_integer ) ) )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F @ A ) @ one_one_Code_integer ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_le_1
% 4.69/5.03 thf(fact_7119_prod__le__1,axiom,
% 4.69/5.03 ! [A: set_int,F: int > code_integer] :
% 4.69/5.03 ( ! [X3: int] :
% 4.69/5.03 ( ( member_int @ X3 @ A )
% 4.69/5.03 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) )
% 4.69/5.03 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ one_one_Code_integer ) ) )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F @ A ) @ one_one_Code_integer ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_le_1
% 4.69/5.03 thf(fact_7120_prod__le__1,axiom,
% 4.69/5.03 ! [A: set_o,F: $o > code_integer] :
% 4.69/5.03 ( ! [X3: $o] :
% 4.69/5.03 ( ( member_o @ X3 @ A )
% 4.69/5.03 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) )
% 4.69/5.03 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ one_one_Code_integer ) ) )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ ( groups7694694392188491536nteger @ F @ A ) @ one_one_Code_integer ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_le_1
% 4.69/5.03 thf(fact_7121_prod__le__1,axiom,
% 4.69/5.03 ! [A: set_Product_unit,F: product_unit > code_integer] :
% 4.69/5.03 ( ! [X3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ X3 @ A )
% 4.69/5.03 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) )
% 4.69/5.03 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ one_one_Code_integer ) ) )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ ( groups8185359811944078981nteger @ F @ A ) @ one_one_Code_integer ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_le_1
% 4.69/5.03 thf(fact_7122_prod__le__1,axiom,
% 4.69/5.03 ! [A: set_nat,F: nat > rat] :
% 4.69/5.03 ( ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ A )
% 4.69/5.03 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 4.69/5.03 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 4.69/5.03 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A ) @ one_one_rat ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_le_1
% 4.69/5.03 thf(fact_7123_prod__le__1,axiom,
% 4.69/5.03 ! [A: set_int,F: int > rat] :
% 4.69/5.03 ( ! [X3: int] :
% 4.69/5.03 ( ( member_int @ X3 @ A )
% 4.69/5.03 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 4.69/5.03 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 4.69/5.03 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A ) @ one_one_rat ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod_le_1
% 4.69/5.03 thf(fact_7124_prod_Orelated,axiom,
% 4.69/5.03 ! [R3: code_integer > code_integer > $o,S: set_nat,H2: nat > code_integer,G: nat > code_integer] :
% 4.69/5.03 ( ( R3 @ one_one_Code_integer @ one_one_Code_integer )
% 4.69/5.03 => ( ! [X12: code_integer,Y12: code_integer,X23: code_integer,Y23: code_integer] :
% 4.69/5.03 ( ( ( R3 @ X12 @ X23 )
% 4.69/5.03 & ( R3 @ Y12 @ Y23 ) )
% 4.69/5.03 => ( R3 @ ( times_3573771949741848930nteger @ X12 @ Y12 ) @ ( times_3573771949741848930nteger @ X23 @ Y23 ) ) )
% 4.69/5.03 => ( ( finite_finite_nat @ S )
% 4.69/5.03 => ( ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ S )
% 4.69/5.03 => ( R3 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 4.69/5.03 => ( R3 @ ( groups3455450783089532116nteger @ H2 @ S ) @ ( groups3455450783089532116nteger @ G @ S ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.related
% 4.69/5.03 thf(fact_7125_prod_Orelated,axiom,
% 4.69/5.03 ! [R3: code_integer > code_integer > $o,S: set_Code_integer,H2: code_integer > code_integer,G: code_integer > code_integer] :
% 4.69/5.03 ( ( R3 @ one_one_Code_integer @ one_one_Code_integer )
% 4.69/5.03 => ( ! [X12: code_integer,Y12: code_integer,X23: code_integer,Y23: code_integer] :
% 4.69/5.03 ( ( ( R3 @ X12 @ X23 )
% 4.69/5.03 & ( R3 @ Y12 @ Y23 ) )
% 4.69/5.03 => ( R3 @ ( times_3573771949741848930nteger @ X12 @ Y12 ) @ ( times_3573771949741848930nteger @ X23 @ Y23 ) ) )
% 4.69/5.03 => ( ( finite6017078050557962740nteger @ S )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ S )
% 4.69/5.03 => ( R3 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 4.69/5.03 => ( R3 @ ( groups3674199335183972705nteger @ H2 @ S ) @ ( groups3674199335183972705nteger @ G @ S ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.related
% 4.69/5.03 thf(fact_7126_prod_Orelated,axiom,
% 4.69/5.03 ! [R3: code_natural > code_natural > $o,S: set_nat,H2: nat > code_natural,G: nat > code_natural] :
% 4.69/5.03 ( ( R3 @ one_one_Code_natural @ one_one_Code_natural )
% 4.69/5.03 => ( ! [X12: code_natural,Y12: code_natural,X23: code_natural,Y23: code_natural] :
% 4.69/5.03 ( ( ( R3 @ X12 @ X23 )
% 4.69/5.03 & ( R3 @ Y12 @ Y23 ) )
% 4.69/5.03 => ( R3 @ ( times_2397367101498566445atural @ X12 @ Y12 ) @ ( times_2397367101498566445atural @ X23 @ Y23 ) ) )
% 4.69/5.03 => ( ( finite_finite_nat @ S )
% 4.69/5.03 => ( ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ S )
% 4.69/5.03 => ( R3 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 4.69/5.03 => ( R3 @ ( groups2279045934846249631atural @ H2 @ S ) @ ( groups2279045934846249631atural @ G @ S ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.related
% 4.69/5.03 thf(fact_7127_prod_Orelated,axiom,
% 4.69/5.03 ! [R3: code_natural > code_natural > $o,S: set_Code_integer,H2: code_integer > code_natural,G: code_integer > code_natural] :
% 4.69/5.03 ( ( R3 @ one_one_Code_natural @ one_one_Code_natural )
% 4.69/5.03 => ( ! [X12: code_natural,Y12: code_natural,X23: code_natural,Y23: code_natural] :
% 4.69/5.03 ( ( ( R3 @ X12 @ X23 )
% 4.69/5.03 & ( R3 @ Y12 @ Y23 ) )
% 4.69/5.03 => ( R3 @ ( times_2397367101498566445atural @ X12 @ Y12 ) @ ( times_2397367101498566445atural @ X23 @ Y23 ) ) )
% 4.69/5.03 => ( ( finite6017078050557962740nteger @ S )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ S )
% 4.69/5.03 => ( R3 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 4.69/5.03 => ( R3 @ ( groups2497794486940690220atural @ H2 @ S ) @ ( groups2497794486940690220atural @ G @ S ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.related
% 4.69/5.03 thf(fact_7128_prod_Orelated,axiom,
% 4.69/5.03 ! [R3: assn > assn > $o,S: set_nat,H2: nat > assn,G: nat > assn] :
% 4.69/5.03 ( ( R3 @ one_one_assn @ one_one_assn )
% 4.69/5.03 => ( ! [X12: assn,Y12: assn,X23: assn,Y23: assn] :
% 4.69/5.03 ( ( ( R3 @ X12 @ X23 )
% 4.69/5.03 & ( R3 @ Y12 @ Y23 ) )
% 4.69/5.03 => ( R3 @ ( times_times_assn @ X12 @ Y12 ) @ ( times_times_assn @ X23 @ Y23 ) ) )
% 4.69/5.03 => ( ( finite_finite_nat @ S )
% 4.69/5.03 => ( ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ S )
% 4.69/5.03 => ( R3 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 4.69/5.03 => ( R3 @ ( groups6906906614972039071t_assn @ H2 @ S ) @ ( groups6906906614972039071t_assn @ G @ S ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.related
% 4.69/5.03 thf(fact_7129_prod_Orelated,axiom,
% 4.69/5.03 ! [R3: assn > assn > $o,S: set_Code_integer,H2: code_integer > assn,G: code_integer > assn] :
% 4.69/5.03 ( ( R3 @ one_one_assn @ one_one_assn )
% 4.69/5.03 => ( ! [X12: assn,Y12: assn,X23: assn,Y23: assn] :
% 4.69/5.03 ( ( ( R3 @ X12 @ X23 )
% 4.69/5.03 & ( R3 @ Y12 @ Y23 ) )
% 4.69/5.03 => ( R3 @ ( times_times_assn @ X12 @ Y12 ) @ ( times_times_assn @ X23 @ Y23 ) ) )
% 4.69/5.03 => ( ( finite6017078050557962740nteger @ S )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ S )
% 4.69/5.03 => ( R3 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 4.69/5.03 => ( R3 @ ( groups1304777262505850412r_assn @ H2 @ S ) @ ( groups1304777262505850412r_assn @ G @ S ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.related
% 4.69/5.03 thf(fact_7130_prod_Orelated,axiom,
% 4.69/5.03 ! [R3: rat > rat > $o,S: set_nat,H2: nat > rat,G: nat > rat] :
% 4.69/5.03 ( ( R3 @ one_one_rat @ one_one_rat )
% 4.69/5.03 => ( ! [X12: rat,Y12: rat,X23: rat,Y23: rat] :
% 4.69/5.03 ( ( ( R3 @ X12 @ X23 )
% 4.69/5.03 & ( R3 @ Y12 @ Y23 ) )
% 4.69/5.03 => ( R3 @ ( times_times_rat @ X12 @ Y12 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 4.69/5.03 => ( ( finite_finite_nat @ S )
% 4.69/5.03 => ( ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ S )
% 4.69/5.03 => ( R3 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 4.69/5.03 => ( R3 @ ( groups73079841787564623at_rat @ H2 @ S ) @ ( groups73079841787564623at_rat @ G @ S ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.related
% 4.69/5.03 thf(fact_7131_prod_Orelated,axiom,
% 4.69/5.03 ! [R3: rat > rat > $o,S: set_Code_integer,H2: code_integer > rat,G: code_integer > rat] :
% 4.69/5.03 ( ( R3 @ one_one_rat @ one_one_rat )
% 4.69/5.03 => ( ! [X12: rat,Y12: rat,X23: rat,Y23: rat] :
% 4.69/5.03 ( ( ( R3 @ X12 @ X23 )
% 4.69/5.03 & ( R3 @ Y12 @ Y23 ) )
% 4.69/5.03 => ( R3 @ ( times_times_rat @ X12 @ Y12 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 4.69/5.03 => ( ( finite6017078050557962740nteger @ S )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ S )
% 4.69/5.03 => ( R3 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 4.69/5.03 => ( R3 @ ( groups2555765274223993564er_rat @ H2 @ S ) @ ( groups2555765274223993564er_rat @ G @ S ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.related
% 4.69/5.03 thf(fact_7132_prod_Orelated,axiom,
% 4.69/5.03 ! [R3: nat > nat > $o,S: set_Code_integer,H2: code_integer > nat,G: code_integer > nat] :
% 4.69/5.03 ( ( R3 @ one_one_nat @ one_one_nat )
% 4.69/5.03 => ( ! [X12: nat,Y12: nat,X23: nat,Y23: nat] :
% 4.69/5.03 ( ( ( R3 @ X12 @ X23 )
% 4.69/5.03 & ( R3 @ Y12 @ Y23 ) )
% 4.69/5.03 => ( R3 @ ( times_times_nat @ X12 @ Y12 ) @ ( times_times_nat @ X23 @ Y23 ) ) )
% 4.69/5.03 => ( ( finite6017078050557962740nteger @ S )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ S )
% 4.69/5.03 => ( R3 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 4.69/5.03 => ( R3 @ ( groups3190895334310489300er_nat @ H2 @ S ) @ ( groups3190895334310489300er_nat @ G @ S ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.related
% 4.69/5.03 thf(fact_7133_prod_Orelated,axiom,
% 4.69/5.03 ! [R3: int > int > $o,S: set_nat,H2: nat > int,G: nat > int] :
% 4.69/5.03 ( ( R3 @ one_one_int @ one_one_int )
% 4.69/5.03 => ( ! [X12: int,Y12: int,X23: int,Y23: int] :
% 4.69/5.03 ( ( ( R3 @ X12 @ X23 )
% 4.69/5.03 & ( R3 @ Y12 @ Y23 ) )
% 4.69/5.03 => ( R3 @ ( times_times_int @ X12 @ Y12 ) @ ( times_times_int @ X23 @ Y23 ) ) )
% 4.69/5.03 => ( ( finite_finite_nat @ S )
% 4.69/5.03 => ( ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ S )
% 4.69/5.03 => ( R3 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 4.69/5.03 => ( R3 @ ( groups705719431365010083at_int @ H2 @ S ) @ ( groups705719431365010083at_int @ G @ S ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.related
% 4.69/5.03 thf(fact_7134_prod_Oinsert__if,axiom,
% 4.69/5.03 ! [A: set_int,X: int,G: int > assn] :
% 4.69/5.03 ( ( finite_finite_int @ A )
% 4.69/5.03 => ( ( ( member_int @ X @ A )
% 4.69/5.03 => ( ( groups7882442080178216443t_assn @ G @ ( insert_int @ X @ A ) )
% 4.69/5.03 = ( groups7882442080178216443t_assn @ G @ A ) ) )
% 4.69/5.03 & ( ~ ( member_int @ X @ A )
% 4.69/5.03 => ( ( groups7882442080178216443t_assn @ G @ ( insert_int @ X @ A ) )
% 4.69/5.03 = ( times_times_assn @ ( G @ X ) @ ( groups7882442080178216443t_assn @ G @ A ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.insert_if
% 4.69/5.03 thf(fact_7135_prod_Oinsert__if,axiom,
% 4.69/5.03 ! [A: set_o,X: $o,G: $o > assn] :
% 4.69/5.03 ( ( finite_finite_o @ A )
% 4.69/5.03 => ( ( ( member_o @ X @ A )
% 4.69/5.03 => ( ( groups5301882518646026715o_assn @ G @ ( insert_o @ X @ A ) )
% 4.69/5.03 = ( groups5301882518646026715o_assn @ G @ A ) ) )
% 4.69/5.03 & ( ~ ( member_o @ X @ A )
% 4.69/5.03 => ( ( groups5301882518646026715o_assn @ G @ ( insert_o @ X @ A ) )
% 4.69/5.03 = ( times_times_assn @ ( G @ X ) @ ( groups5301882518646026715o_assn @ G @ A ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.insert_if
% 4.69/5.03 thf(fact_7136_prod_Oinsert__if,axiom,
% 4.69/5.03 ! [A: set_Product_unit,X: product_unit,G: product_unit > assn] :
% 4.69/5.03 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.03 => ( ( ( member_Product_unit @ X @ A )
% 4.69/5.03 => ( ( groups5360233303959380816t_assn @ G @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.03 = ( groups5360233303959380816t_assn @ G @ A ) ) )
% 4.69/5.03 & ( ~ ( member_Product_unit @ X @ A )
% 4.69/5.03 => ( ( groups5360233303959380816t_assn @ G @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.03 = ( times_times_assn @ ( G @ X ) @ ( groups5360233303959380816t_assn @ G @ A ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.insert_if
% 4.69/5.03 thf(fact_7137_prod_Oinsert__if,axiom,
% 4.69/5.03 ! [A: set_nat,X: nat,G: nat > assn] :
% 4.69/5.03 ( ( finite_finite_nat @ A )
% 4.69/5.03 => ( ( ( member_nat @ X @ A )
% 4.69/5.03 => ( ( groups6906906614972039071t_assn @ G @ ( insert_nat @ X @ A ) )
% 4.69/5.03 = ( groups6906906614972039071t_assn @ G @ A ) ) )
% 4.69/5.03 & ( ~ ( member_nat @ X @ A )
% 4.69/5.03 => ( ( groups6906906614972039071t_assn @ G @ ( insert_nat @ X @ A ) )
% 4.69/5.03 = ( times_times_assn @ ( G @ X ) @ ( groups6906906614972039071t_assn @ G @ A ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.insert_if
% 4.69/5.03 thf(fact_7138_prod_Oinsert__if,axiom,
% 4.69/5.03 ! [A: set_Code_integer,X: code_integer,G: code_integer > assn] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ( ( member_Code_integer @ X @ A )
% 4.69/5.03 => ( ( groups1304777262505850412r_assn @ G @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.03 = ( groups1304777262505850412r_assn @ G @ A ) ) )
% 4.69/5.03 & ( ~ ( member_Code_integer @ X @ A )
% 4.69/5.03 => ( ( groups1304777262505850412r_assn @ G @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.03 = ( times_times_assn @ ( G @ X ) @ ( groups1304777262505850412r_assn @ G @ A ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.insert_if
% 4.69/5.03 thf(fact_7139_prod_Oinsert__if,axiom,
% 4.69/5.03 ! [A: set_int,X: int,G: int > rat] :
% 4.69/5.03 ( ( finite_finite_int @ A )
% 4.69/5.03 => ( ( ( member_int @ X @ A )
% 4.69/5.03 => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X @ A ) )
% 4.69/5.03 = ( groups1072433553688619179nt_rat @ G @ A ) ) )
% 4.69/5.03 & ( ~ ( member_int @ X @ A )
% 4.69/5.03 => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X @ A ) )
% 4.69/5.03 = ( times_times_rat @ ( G @ X ) @ ( groups1072433553688619179nt_rat @ G @ A ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.insert_if
% 4.69/5.03 thf(fact_7140_prod_Oinsert__if,axiom,
% 4.69/5.03 ! [A: set_o,X: $o,G: $o > rat] :
% 4.69/5.03 ( ( finite_finite_o @ A )
% 4.69/5.03 => ( ( ( member_o @ X @ A )
% 4.69/5.03 => ( ( groups2869687844427037835_o_rat @ G @ ( insert_o @ X @ A ) )
% 4.69/5.03 = ( groups2869687844427037835_o_rat @ G @ A ) ) )
% 4.69/5.03 & ( ~ ( member_o @ X @ A )
% 4.69/5.03 => ( ( groups2869687844427037835_o_rat @ G @ ( insert_o @ X @ A ) )
% 4.69/5.03 = ( times_times_rat @ ( G @ X ) @ ( groups2869687844427037835_o_rat @ G @ A ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.insert_if
% 4.69/5.03 thf(fact_7141_prod_Oinsert__if,axiom,
% 4.69/5.03 ! [A: set_Product_unit,X: product_unit,G: product_unit > rat] :
% 4.69/5.03 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.03 => ( ( ( member_Product_unit @ X @ A )
% 4.69/5.03 => ( ( groups8984663225794451456it_rat @ G @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.03 = ( groups8984663225794451456it_rat @ G @ A ) ) )
% 4.69/5.03 & ( ~ ( member_Product_unit @ X @ A )
% 4.69/5.03 => ( ( groups8984663225794451456it_rat @ G @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.03 = ( times_times_rat @ ( G @ X ) @ ( groups8984663225794451456it_rat @ G @ A ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.insert_if
% 4.69/5.03 thf(fact_7142_prod_Oinsert__if,axiom,
% 4.69/5.03 ! [A: set_nat,X: nat,G: nat > rat] :
% 4.69/5.03 ( ( finite_finite_nat @ A )
% 4.69/5.03 => ( ( ( member_nat @ X @ A )
% 4.69/5.03 => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X @ A ) )
% 4.69/5.03 = ( groups73079841787564623at_rat @ G @ A ) ) )
% 4.69/5.03 & ( ~ ( member_nat @ X @ A )
% 4.69/5.03 => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X @ A ) )
% 4.69/5.03 = ( times_times_rat @ ( G @ X ) @ ( groups73079841787564623at_rat @ G @ A ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.insert_if
% 4.69/5.03 thf(fact_7143_prod_Oinsert__if,axiom,
% 4.69/5.03 ! [A: set_Code_integer,X: code_integer,G: code_integer > rat] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ( ( member_Code_integer @ X @ A )
% 4.69/5.03 => ( ( groups2555765274223993564er_rat @ G @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.03 = ( groups2555765274223993564er_rat @ G @ A ) ) )
% 4.69/5.03 & ( ~ ( member_Code_integer @ X @ A )
% 4.69/5.03 => ( ( groups2555765274223993564er_rat @ G @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.03 = ( times_times_rat @ ( G @ X ) @ ( groups2555765274223993564er_rat @ G @ A ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.insert_if
% 4.69/5.03 thf(fact_7144_prod_Oreindex__bij__witness__not__neutral,axiom,
% 4.69/5.03 ! [S4: set_int,T5: set_int,S: set_int,I2: int > int,J: int > int,T2: set_int,G: int > assn,H2: int > assn] :
% 4.69/5.03 ( ( finite_finite_int @ S4 )
% 4.69/5.03 => ( ( finite_finite_int @ T5 )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ ( minus_minus_set_int @ S @ S4 ) )
% 4.69/5.03 => ( ( I2 @ ( J @ A4 ) )
% 4.69/5.03 = A4 ) )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ ( minus_minus_set_int @ S @ S4 ) )
% 4.69/5.03 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T2 @ T5 ) ) )
% 4.69/5.03 => ( ! [B2: int] :
% 4.69/5.03 ( ( member_int @ B2 @ ( minus_minus_set_int @ T2 @ T5 ) )
% 4.69/5.03 => ( ( J @ ( I2 @ B2 ) )
% 4.69/5.03 = B2 ) )
% 4.69/5.03 => ( ! [B2: int] :
% 4.69/5.03 ( ( member_int @ B2 @ ( minus_minus_set_int @ T2 @ T5 ) )
% 4.69/5.03 => ( member_int @ ( I2 @ B2 ) @ ( minus_minus_set_int @ S @ S4 ) ) )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ S4 )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [B2: int] :
% 4.69/5.03 ( ( member_int @ B2 @ T5 )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ S )
% 4.69/5.03 => ( ( H2 @ ( J @ A4 ) )
% 4.69/5.03 = ( G @ A4 ) ) )
% 4.69/5.03 => ( ( groups7882442080178216443t_assn @ G @ S )
% 4.69/5.03 = ( groups7882442080178216443t_assn @ H2 @ T2 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.reindex_bij_witness_not_neutral
% 4.69/5.03 thf(fact_7145_prod_Oreindex__bij__witness__not__neutral,axiom,
% 4.69/5.03 ! [S4: set_int,T5: set_o,S: set_int,I2: $o > int,J: int > $o,T2: set_o,G: int > assn,H2: $o > assn] :
% 4.69/5.03 ( ( finite_finite_int @ S4 )
% 4.69/5.03 => ( ( finite_finite_o @ T5 )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ ( minus_minus_set_int @ S @ S4 ) )
% 4.69/5.03 => ( ( I2 @ ( J @ A4 ) )
% 4.69/5.03 = A4 ) )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ ( minus_minus_set_int @ S @ S4 ) )
% 4.69/5.03 => ( member_o @ ( J @ A4 ) @ ( minus_minus_set_o @ T2 @ T5 ) ) )
% 4.69/5.03 => ( ! [B2: $o] :
% 4.69/5.03 ( ( member_o @ B2 @ ( minus_minus_set_o @ T2 @ T5 ) )
% 4.69/5.03 => ( ( J @ ( I2 @ B2 ) )
% 4.69/5.03 = B2 ) )
% 4.69/5.03 => ( ! [B2: $o] :
% 4.69/5.03 ( ( member_o @ B2 @ ( minus_minus_set_o @ T2 @ T5 ) )
% 4.69/5.03 => ( member_int @ ( I2 @ B2 ) @ ( minus_minus_set_int @ S @ S4 ) ) )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ S4 )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [B2: $o] :
% 4.69/5.03 ( ( member_o @ B2 @ T5 )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ S )
% 4.69/5.03 => ( ( H2 @ ( J @ A4 ) )
% 4.69/5.03 = ( G @ A4 ) ) )
% 4.69/5.03 => ( ( groups7882442080178216443t_assn @ G @ S )
% 4.69/5.03 = ( groups5301882518646026715o_assn @ H2 @ T2 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.reindex_bij_witness_not_neutral
% 4.69/5.03 thf(fact_7146_prod_Oreindex__bij__witness__not__neutral,axiom,
% 4.69/5.03 ! [S4: set_int,T5: set_Product_unit,S: set_int,I2: product_unit > int,J: int > product_unit,T2: set_Product_unit,G: int > assn,H2: product_unit > assn] :
% 4.69/5.03 ( ( finite_finite_int @ S4 )
% 4.69/5.03 => ( ( finite4290736615968046902t_unit @ T5 )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ ( minus_minus_set_int @ S @ S4 ) )
% 4.69/5.03 => ( ( I2 @ ( J @ A4 ) )
% 4.69/5.03 = A4 ) )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ ( minus_minus_set_int @ S @ S4 ) )
% 4.69/5.03 => ( member_Product_unit @ ( J @ A4 ) @ ( minus_6452836326544984404t_unit @ T2 @ T5 ) ) )
% 4.69/5.03 => ( ! [B2: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ B2 @ ( minus_6452836326544984404t_unit @ T2 @ T5 ) )
% 4.69/5.03 => ( ( J @ ( I2 @ B2 ) )
% 4.69/5.03 = B2 ) )
% 4.69/5.03 => ( ! [B2: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ B2 @ ( minus_6452836326544984404t_unit @ T2 @ T5 ) )
% 4.69/5.03 => ( member_int @ ( I2 @ B2 ) @ ( minus_minus_set_int @ S @ S4 ) ) )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ S4 )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [B2: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ B2 @ T5 )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ S )
% 4.69/5.03 => ( ( H2 @ ( J @ A4 ) )
% 4.69/5.03 = ( G @ A4 ) ) )
% 4.69/5.03 => ( ( groups7882442080178216443t_assn @ G @ S )
% 4.69/5.03 = ( groups5360233303959380816t_assn @ H2 @ T2 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.reindex_bij_witness_not_neutral
% 4.69/5.03 thf(fact_7147_prod_Oreindex__bij__witness__not__neutral,axiom,
% 4.69/5.03 ! [S4: set_o,T5: set_int,S: set_o,I2: int > $o,J: $o > int,T2: set_int,G: $o > assn,H2: int > assn] :
% 4.69/5.03 ( ( finite_finite_o @ S4 )
% 4.69/5.03 => ( ( finite_finite_int @ T5 )
% 4.69/5.03 => ( ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ ( minus_minus_set_o @ S @ S4 ) )
% 4.69/5.03 => ( ( I2 @ ( J @ A4 ) )
% 4.69/5.03 = A4 ) )
% 4.69/5.03 => ( ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ ( minus_minus_set_o @ S @ S4 ) )
% 4.69/5.03 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T2 @ T5 ) ) )
% 4.69/5.03 => ( ! [B2: int] :
% 4.69/5.03 ( ( member_int @ B2 @ ( minus_minus_set_int @ T2 @ T5 ) )
% 4.69/5.03 => ( ( J @ ( I2 @ B2 ) )
% 4.69/5.03 = B2 ) )
% 4.69/5.03 => ( ! [B2: int] :
% 4.69/5.03 ( ( member_int @ B2 @ ( minus_minus_set_int @ T2 @ T5 ) )
% 4.69/5.03 => ( member_o @ ( I2 @ B2 ) @ ( minus_minus_set_o @ S @ S4 ) ) )
% 4.69/5.03 => ( ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ S4 )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [B2: int] :
% 4.69/5.03 ( ( member_int @ B2 @ T5 )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ S )
% 4.69/5.03 => ( ( H2 @ ( J @ A4 ) )
% 4.69/5.03 = ( G @ A4 ) ) )
% 4.69/5.03 => ( ( groups5301882518646026715o_assn @ G @ S )
% 4.69/5.03 = ( groups7882442080178216443t_assn @ H2 @ T2 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.reindex_bij_witness_not_neutral
% 4.69/5.03 thf(fact_7148_prod_Oreindex__bij__witness__not__neutral,axiom,
% 4.69/5.03 ! [S4: set_o,T5: set_o,S: set_o,I2: $o > $o,J: $o > $o,T2: set_o,G: $o > assn,H2: $o > assn] :
% 4.69/5.03 ( ( finite_finite_o @ S4 )
% 4.69/5.03 => ( ( finite_finite_o @ T5 )
% 4.69/5.03 => ( ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ ( minus_minus_set_o @ S @ S4 ) )
% 4.69/5.03 => ( ( I2 @ ( J @ A4 ) )
% 4.69/5.03 = A4 ) )
% 4.69/5.03 => ( ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ ( minus_minus_set_o @ S @ S4 ) )
% 4.69/5.03 => ( member_o @ ( J @ A4 ) @ ( minus_minus_set_o @ T2 @ T5 ) ) )
% 4.69/5.03 => ( ! [B2: $o] :
% 4.69/5.03 ( ( member_o @ B2 @ ( minus_minus_set_o @ T2 @ T5 ) )
% 4.69/5.03 => ( ( J @ ( I2 @ B2 ) )
% 4.69/5.03 = B2 ) )
% 4.69/5.03 => ( ! [B2: $o] :
% 4.69/5.03 ( ( member_o @ B2 @ ( minus_minus_set_o @ T2 @ T5 ) )
% 4.69/5.03 => ( member_o @ ( I2 @ B2 ) @ ( minus_minus_set_o @ S @ S4 ) ) )
% 4.69/5.03 => ( ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ S4 )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [B2: $o] :
% 4.69/5.03 ( ( member_o @ B2 @ T5 )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ S )
% 4.69/5.03 => ( ( H2 @ ( J @ A4 ) )
% 4.69/5.03 = ( G @ A4 ) ) )
% 4.69/5.03 => ( ( groups5301882518646026715o_assn @ G @ S )
% 4.69/5.03 = ( groups5301882518646026715o_assn @ H2 @ T2 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.reindex_bij_witness_not_neutral
% 4.69/5.03 thf(fact_7149_prod_Oreindex__bij__witness__not__neutral,axiom,
% 4.69/5.03 ! [S4: set_o,T5: set_Product_unit,S: set_o,I2: product_unit > $o,J: $o > product_unit,T2: set_Product_unit,G: $o > assn,H2: product_unit > assn] :
% 4.69/5.03 ( ( finite_finite_o @ S4 )
% 4.69/5.03 => ( ( finite4290736615968046902t_unit @ T5 )
% 4.69/5.03 => ( ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ ( minus_minus_set_o @ S @ S4 ) )
% 4.69/5.03 => ( ( I2 @ ( J @ A4 ) )
% 4.69/5.03 = A4 ) )
% 4.69/5.03 => ( ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ ( minus_minus_set_o @ S @ S4 ) )
% 4.69/5.03 => ( member_Product_unit @ ( J @ A4 ) @ ( minus_6452836326544984404t_unit @ T2 @ T5 ) ) )
% 4.69/5.03 => ( ! [B2: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ B2 @ ( minus_6452836326544984404t_unit @ T2 @ T5 ) )
% 4.69/5.03 => ( ( J @ ( I2 @ B2 ) )
% 4.69/5.03 = B2 ) )
% 4.69/5.03 => ( ! [B2: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ B2 @ ( minus_6452836326544984404t_unit @ T2 @ T5 ) )
% 4.69/5.03 => ( member_o @ ( I2 @ B2 ) @ ( minus_minus_set_o @ S @ S4 ) ) )
% 4.69/5.03 => ( ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ S4 )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [B2: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ B2 @ T5 )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ S )
% 4.69/5.03 => ( ( H2 @ ( J @ A4 ) )
% 4.69/5.03 = ( G @ A4 ) ) )
% 4.69/5.03 => ( ( groups5301882518646026715o_assn @ G @ S )
% 4.69/5.03 = ( groups5360233303959380816t_assn @ H2 @ T2 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.reindex_bij_witness_not_neutral
% 4.69/5.03 thf(fact_7150_prod_Oreindex__bij__witness__not__neutral,axiom,
% 4.69/5.03 ! [S4: set_Product_unit,T5: set_int,S: set_Product_unit,I2: int > product_unit,J: product_unit > int,T2: set_int,G: product_unit > assn,H2: int > assn] :
% 4.69/5.03 ( ( finite4290736615968046902t_unit @ S4 )
% 4.69/5.03 => ( ( finite_finite_int @ T5 )
% 4.69/5.03 => ( ! [A4: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ A4 @ ( minus_6452836326544984404t_unit @ S @ S4 ) )
% 4.69/5.03 => ( ( I2 @ ( J @ A4 ) )
% 4.69/5.03 = A4 ) )
% 4.69/5.03 => ( ! [A4: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ A4 @ ( minus_6452836326544984404t_unit @ S @ S4 ) )
% 4.69/5.03 => ( member_int @ ( J @ A4 ) @ ( minus_minus_set_int @ T2 @ T5 ) ) )
% 4.69/5.03 => ( ! [B2: int] :
% 4.69/5.03 ( ( member_int @ B2 @ ( minus_minus_set_int @ T2 @ T5 ) )
% 4.69/5.03 => ( ( J @ ( I2 @ B2 ) )
% 4.69/5.03 = B2 ) )
% 4.69/5.03 => ( ! [B2: int] :
% 4.69/5.03 ( ( member_int @ B2 @ ( minus_minus_set_int @ T2 @ T5 ) )
% 4.69/5.03 => ( member_Product_unit @ ( I2 @ B2 ) @ ( minus_6452836326544984404t_unit @ S @ S4 ) ) )
% 4.69/5.03 => ( ! [A4: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ A4 @ S4 )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [B2: int] :
% 4.69/5.03 ( ( member_int @ B2 @ T5 )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [A4: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ A4 @ S )
% 4.69/5.03 => ( ( H2 @ ( J @ A4 ) )
% 4.69/5.03 = ( G @ A4 ) ) )
% 4.69/5.03 => ( ( groups5360233303959380816t_assn @ G @ S )
% 4.69/5.03 = ( groups7882442080178216443t_assn @ H2 @ T2 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.reindex_bij_witness_not_neutral
% 4.69/5.03 thf(fact_7151_prod_Oreindex__bij__witness__not__neutral,axiom,
% 4.69/5.03 ! [S4: set_Product_unit,T5: set_o,S: set_Product_unit,I2: $o > product_unit,J: product_unit > $o,T2: set_o,G: product_unit > assn,H2: $o > assn] :
% 4.69/5.03 ( ( finite4290736615968046902t_unit @ S4 )
% 4.69/5.03 => ( ( finite_finite_o @ T5 )
% 4.69/5.03 => ( ! [A4: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ A4 @ ( minus_6452836326544984404t_unit @ S @ S4 ) )
% 4.69/5.03 => ( ( I2 @ ( J @ A4 ) )
% 4.69/5.03 = A4 ) )
% 4.69/5.03 => ( ! [A4: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ A4 @ ( minus_6452836326544984404t_unit @ S @ S4 ) )
% 4.69/5.03 => ( member_o @ ( J @ A4 ) @ ( minus_minus_set_o @ T2 @ T5 ) ) )
% 4.69/5.03 => ( ! [B2: $o] :
% 4.69/5.03 ( ( member_o @ B2 @ ( minus_minus_set_o @ T2 @ T5 ) )
% 4.69/5.03 => ( ( J @ ( I2 @ B2 ) )
% 4.69/5.03 = B2 ) )
% 4.69/5.03 => ( ! [B2: $o] :
% 4.69/5.03 ( ( member_o @ B2 @ ( minus_minus_set_o @ T2 @ T5 ) )
% 4.69/5.03 => ( member_Product_unit @ ( I2 @ B2 ) @ ( minus_6452836326544984404t_unit @ S @ S4 ) ) )
% 4.69/5.03 => ( ! [A4: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ A4 @ S4 )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [B2: $o] :
% 4.69/5.03 ( ( member_o @ B2 @ T5 )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [A4: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ A4 @ S )
% 4.69/5.03 => ( ( H2 @ ( J @ A4 ) )
% 4.69/5.03 = ( G @ A4 ) ) )
% 4.69/5.03 => ( ( groups5360233303959380816t_assn @ G @ S )
% 4.69/5.03 = ( groups5301882518646026715o_assn @ H2 @ T2 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.reindex_bij_witness_not_neutral
% 4.69/5.03 thf(fact_7152_prod_Oreindex__bij__witness__not__neutral,axiom,
% 4.69/5.03 ! [S4: set_Product_unit,T5: set_Product_unit,S: set_Product_unit,I2: product_unit > product_unit,J: product_unit > product_unit,T2: set_Product_unit,G: product_unit > assn,H2: product_unit > assn] :
% 4.69/5.03 ( ( finite4290736615968046902t_unit @ S4 )
% 4.69/5.03 => ( ( finite4290736615968046902t_unit @ T5 )
% 4.69/5.03 => ( ! [A4: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ A4 @ ( minus_6452836326544984404t_unit @ S @ S4 ) )
% 4.69/5.03 => ( ( I2 @ ( J @ A4 ) )
% 4.69/5.03 = A4 ) )
% 4.69/5.03 => ( ! [A4: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ A4 @ ( minus_6452836326544984404t_unit @ S @ S4 ) )
% 4.69/5.03 => ( member_Product_unit @ ( J @ A4 ) @ ( minus_6452836326544984404t_unit @ T2 @ T5 ) ) )
% 4.69/5.03 => ( ! [B2: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ B2 @ ( minus_6452836326544984404t_unit @ T2 @ T5 ) )
% 4.69/5.03 => ( ( J @ ( I2 @ B2 ) )
% 4.69/5.03 = B2 ) )
% 4.69/5.03 => ( ! [B2: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ B2 @ ( minus_6452836326544984404t_unit @ T2 @ T5 ) )
% 4.69/5.03 => ( member_Product_unit @ ( I2 @ B2 ) @ ( minus_6452836326544984404t_unit @ S @ S4 ) ) )
% 4.69/5.03 => ( ! [A4: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ A4 @ S4 )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [B2: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ B2 @ T5 )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [A4: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ A4 @ S )
% 4.69/5.03 => ( ( H2 @ ( J @ A4 ) )
% 4.69/5.03 = ( G @ A4 ) ) )
% 4.69/5.03 => ( ( groups5360233303959380816t_assn @ G @ S )
% 4.69/5.03 = ( groups5360233303959380816t_assn @ H2 @ T2 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.reindex_bij_witness_not_neutral
% 4.69/5.03 thf(fact_7153_prod_Oreindex__bij__witness__not__neutral,axiom,
% 4.69/5.03 ! [S4: set_int,T5: set_Code_integer,S: set_int,I2: code_integer > int,J: int > code_integer,T2: set_Code_integer,G: int > assn,H2: code_integer > assn] :
% 4.69/5.03 ( ( finite_finite_int @ S4 )
% 4.69/5.03 => ( ( finite6017078050557962740nteger @ T5 )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ ( minus_minus_set_int @ S @ S4 ) )
% 4.69/5.03 => ( ( I2 @ ( J @ A4 ) )
% 4.69/5.03 = A4 ) )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ ( minus_minus_set_int @ S @ S4 ) )
% 4.69/5.03 => ( member_Code_integer @ ( J @ A4 ) @ ( minus_2355218937544613996nteger @ T2 @ T5 ) ) )
% 4.69/5.03 => ( ! [B2: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ T2 @ T5 ) )
% 4.69/5.03 => ( ( J @ ( I2 @ B2 ) )
% 4.69/5.03 = B2 ) )
% 4.69/5.03 => ( ! [B2: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ T2 @ T5 ) )
% 4.69/5.03 => ( member_int @ ( I2 @ B2 ) @ ( minus_minus_set_int @ S @ S4 ) ) )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ S4 )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [B2: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ B2 @ T5 )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ S )
% 4.69/5.03 => ( ( H2 @ ( J @ A4 ) )
% 4.69/5.03 = ( G @ A4 ) ) )
% 4.69/5.03 => ( ( groups7882442080178216443t_assn @ G @ S )
% 4.69/5.03 = ( groups1304777262505850412r_assn @ H2 @ T2 ) ) ) ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.reindex_bij_witness_not_neutral
% 4.69/5.03 thf(fact_7154_gbinomial__minus,axiom,
% 4.69/5.03 ! [A2: rat,K3: nat] :
% 4.69/5.03 ( ( gbinomial_rat @ ( uminus_uminus_rat @ A2 ) @ K3 )
% 4.69/5.03 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A2 @ ( semiri681578069525770553at_rat @ K3 ) ) @ one_one_rat ) @ K3 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % gbinomial_minus
% 4.69/5.03 thf(fact_7155_le__minus__one__simps_I3_J,axiom,
% 4.69/5.03 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.69/5.03
% 4.69/5.03 % le_minus_one_simps(3)
% 4.69/5.03 thf(fact_7156_le__minus__one__simps_I3_J,axiom,
% 4.69/5.03 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.69/5.03
% 4.69/5.03 % le_minus_one_simps(3)
% 4.69/5.03 thf(fact_7157_le__minus__one__simps_I3_J,axiom,
% 4.69/5.03 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % le_minus_one_simps(3)
% 4.69/5.03 thf(fact_7158_le__minus__one__simps_I1_J,axiom,
% 4.69/5.03 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 4.69/5.03
% 4.69/5.03 % le_minus_one_simps(1)
% 4.69/5.03 thf(fact_7159_le__minus__one__simps_I1_J,axiom,
% 4.69/5.03 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 4.69/5.03
% 4.69/5.03 % le_minus_one_simps(1)
% 4.69/5.03 thf(fact_7160_le__minus__one__simps_I1_J,axiom,
% 4.69/5.03 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 4.69/5.03
% 4.69/5.03 % le_minus_one_simps(1)
% 4.69/5.03 thf(fact_7161_less__minus__one__simps_I1_J,axiom,
% 4.69/5.03 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 4.69/5.03
% 4.69/5.03 % less_minus_one_simps(1)
% 4.69/5.03 thf(fact_7162_less__minus__one__simps_I1_J,axiom,
% 4.69/5.03 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 4.69/5.03
% 4.69/5.03 % less_minus_one_simps(1)
% 4.69/5.03 thf(fact_7163_less__minus__one__simps_I1_J,axiom,
% 4.69/5.03 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 4.69/5.03
% 4.69/5.03 % less_minus_one_simps(1)
% 4.69/5.03 thf(fact_7164_less__minus__one__simps_I3_J,axiom,
% 4.69/5.03 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_minus_one_simps(3)
% 4.69/5.03 thf(fact_7165_less__minus__one__simps_I3_J,axiom,
% 4.69/5.03 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_minus_one_simps(3)
% 4.69/5.03 thf(fact_7166_less__minus__one__simps_I3_J,axiom,
% 4.69/5.03 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_minus_one_simps(3)
% 4.69/5.03 thf(fact_7167_inf__shunt,axiom,
% 4.69/5.03 ! [X: set_Product_unit,Y: set_Product_unit] :
% 4.69/5.03 ( ( ( inf_in4660618365625256667t_unit @ X @ Y )
% 4.69/5.03 = bot_bo3957492148770167129t_unit )
% 4.69/5.03 = ( ord_le3507040750410214029t_unit @ X @ ( uminus5944136376168626660t_unit @ Y ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % inf_shunt
% 4.69/5.03 thf(fact_7168_inf__shunt,axiom,
% 4.69/5.03 ! [X: set_o,Y: set_o] :
% 4.69/5.03 ( ( ( inf_inf_set_o @ X @ Y )
% 4.69/5.03 = bot_bot_set_o )
% 4.69/5.03 = ( ord_less_eq_set_o @ X @ ( uminus_uminus_set_o @ Y ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % inf_shunt
% 4.69/5.03 thf(fact_7169_inf__shunt,axiom,
% 4.69/5.03 ! [X: set_int,Y: set_int] :
% 4.69/5.03 ( ( ( inf_inf_set_int @ X @ Y )
% 4.69/5.03 = bot_bot_set_int )
% 4.69/5.03 = ( ord_less_eq_set_int @ X @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % inf_shunt
% 4.69/5.03 thf(fact_7170_inf__shunt,axiom,
% 4.69/5.03 ! [X: set_Pr4532377907799695533_nat_o,Y: set_Pr4532377907799695533_nat_o] :
% 4.69/5.03 ( ( ( inf_in1906310914598751387_nat_o @ X @ Y )
% 4.69/5.03 = bot_bo7824918357723582233_nat_o )
% 4.69/5.03 = ( ord_le2965882846123202637_nat_o @ X @ ( uminus5254974436814262692_nat_o @ Y ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % inf_shunt
% 4.69/5.03 thf(fact_7171_inf__shunt,axiom,
% 4.69/5.03 ! [X: assn,Y: assn] :
% 4.69/5.03 ( ( ( inf_inf_assn @ X @ Y )
% 4.69/5.03 = bot_bot_assn )
% 4.69/5.03 = ( ord_less_eq_assn @ X @ ( uminus_uminus_assn @ Y ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % inf_shunt
% 4.69/5.03 thf(fact_7172_inf__shunt,axiom,
% 4.69/5.03 ! [X: product_unit,Y: product_unit] :
% 4.69/5.03 ( ( ( inf_inf_Product_unit @ X @ Y )
% 4.69/5.03 = bot_bot_Product_unit )
% 4.69/5.03 = ( ord_le3221252021190050221t_unit @ X @ ( uminus2952777764628376836t_unit @ Y ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % inf_shunt
% 4.69/5.03 thf(fact_7173_inf__shunt,axiom,
% 4.69/5.03 ! [X: set_nat,Y: set_nat] :
% 4.69/5.03 ( ( ( inf_inf_set_nat @ X @ Y )
% 4.69/5.03 = bot_bot_set_nat )
% 4.69/5.03 = ( ord_less_eq_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % inf_shunt
% 4.69/5.03 thf(fact_7174_power__minus,axiom,
% 4.69/5.03 ! [A2: rat,N2: nat] :
% 4.69/5.03 ( ( power_power_rat @ ( uminus_uminus_rat @ A2 ) @ N2 )
% 4.69/5.03 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ A2 @ N2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % power_minus
% 4.69/5.03 thf(fact_7175_power__minus,axiom,
% 4.69/5.03 ! [A2: int,N2: nat] :
% 4.69/5.03 ( ( power_power_int @ ( uminus_uminus_int @ A2 ) @ N2 )
% 4.69/5.03 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ A2 @ N2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % power_minus
% 4.69/5.03 thf(fact_7176_power__minus,axiom,
% 4.69/5.03 ! [A2: code_integer,N2: nat] :
% 4.69/5.03 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A2 ) @ N2 )
% 4.69/5.03 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ A2 @ N2 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % power_minus
% 4.69/5.03 thf(fact_7177_disjoint__eq__subset__Compl,axiom,
% 4.69/5.03 ! [A: set_Product_unit,B4: set_Product_unit] :
% 4.69/5.03 ( ( ( inf_in4660618365625256667t_unit @ A @ B4 )
% 4.69/5.03 = bot_bo3957492148770167129t_unit )
% 4.69/5.03 = ( ord_le3507040750410214029t_unit @ A @ ( uminus5944136376168626660t_unit @ B4 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % disjoint_eq_subset_Compl
% 4.69/5.03 thf(fact_7178_disjoint__eq__subset__Compl,axiom,
% 4.69/5.03 ! [A: set_o,B4: set_o] :
% 4.69/5.03 ( ( ( inf_inf_set_o @ A @ B4 )
% 4.69/5.03 = bot_bot_set_o )
% 4.69/5.03 = ( ord_less_eq_set_o @ A @ ( uminus_uminus_set_o @ B4 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % disjoint_eq_subset_Compl
% 4.69/5.03 thf(fact_7179_disjoint__eq__subset__Compl,axiom,
% 4.69/5.03 ! [A: set_int,B4: set_int] :
% 4.69/5.03 ( ( ( inf_inf_set_int @ A @ B4 )
% 4.69/5.03 = bot_bot_set_int )
% 4.69/5.03 = ( ord_less_eq_set_int @ A @ ( uminus1532241313380277803et_int @ B4 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % disjoint_eq_subset_Compl
% 4.69/5.03 thf(fact_7180_disjoint__eq__subset__Compl,axiom,
% 4.69/5.03 ! [A: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 4.69/5.03 ( ( ( inf_in1906310914598751387_nat_o @ A @ B4 )
% 4.69/5.03 = bot_bo7824918357723582233_nat_o )
% 4.69/5.03 = ( ord_le2965882846123202637_nat_o @ A @ ( uminus5254974436814262692_nat_o @ B4 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % disjoint_eq_subset_Compl
% 4.69/5.03 thf(fact_7181_disjoint__eq__subset__Compl,axiom,
% 4.69/5.03 ! [A: set_nat,B4: set_nat] :
% 4.69/5.03 ( ( ( inf_inf_set_nat @ A @ B4 )
% 4.69/5.03 = bot_bot_set_nat )
% 4.69/5.03 = ( ord_less_eq_set_nat @ A @ ( uminus5710092332889474511et_nat @ B4 ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % disjoint_eq_subset_Compl
% 4.69/5.03 thf(fact_7182_Compl__insert,axiom,
% 4.69/5.03 ! [X: product_unit,A: set_Product_unit] :
% 4.69/5.03 ( ( uminus5944136376168626660t_unit @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.03 = ( minus_6452836326544984404t_unit @ ( uminus5944136376168626660t_unit @ A ) @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_insert
% 4.69/5.03 thf(fact_7183_Compl__insert,axiom,
% 4.69/5.03 ! [X: $o,A: set_o] :
% 4.69/5.03 ( ( uminus_uminus_set_o @ ( insert_o @ X @ A ) )
% 4.69/5.03 = ( minus_minus_set_o @ ( uminus_uminus_set_o @ A ) @ ( insert_o @ X @ bot_bot_set_o ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_insert
% 4.69/5.03 thf(fact_7184_Compl__insert,axiom,
% 4.69/5.03 ! [X: int,A: set_int] :
% 4.69/5.03 ( ( uminus1532241313380277803et_int @ ( insert_int @ X @ A ) )
% 4.69/5.03 = ( minus_minus_set_int @ ( uminus1532241313380277803et_int @ A ) @ ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_insert
% 4.69/5.03 thf(fact_7185_Compl__insert,axiom,
% 4.69/5.03 ! [X: produc3658429121746597890et_nat > $o,A: set_Pr4532377907799695533_nat_o] :
% 4.69/5.03 ( ( uminus5254974436814262692_nat_o @ ( insert5175938949040314269_nat_o @ X @ A ) )
% 4.69/5.03 = ( minus_1801376950450012436_nat_o @ ( uminus5254974436814262692_nat_o @ A ) @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_insert
% 4.69/5.03 thf(fact_7186_Compl__insert,axiom,
% 4.69/5.03 ! [X: nat,A: set_nat] :
% 4.69/5.03 ( ( uminus5710092332889474511et_nat @ ( insert_nat @ X @ A ) )
% 4.69/5.03 = ( minus_minus_set_nat @ ( uminus5710092332889474511et_nat @ A ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % Compl_insert
% 4.69/5.03 thf(fact_7187_Image__subset__eq,axiom,
% 4.69/5.03 ! [R2: set_Pr1261947904930325089at_nat,A: set_nat,B4: set_nat] :
% 4.69/5.03 ( ( ord_less_eq_set_nat @ ( image_nat_nat @ R2 @ A ) @ B4 )
% 4.69/5.03 = ( ord_less_eq_set_nat @ A @ ( uminus5710092332889474511et_nat @ ( image_nat_nat @ ( converse_nat_nat @ R2 ) @ ( uminus5710092332889474511et_nat @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % Image_subset_eq
% 4.69/5.03 thf(fact_7188_less__1__prod2,axiom,
% 4.69/5.03 ! [I: set_int,I2: int,F: int > code_integer] :
% 4.69/5.03 ( ( finite_finite_int @ I )
% 4.69/5.03 => ( ( member_int @ I2 @ I )
% 4.69/5.03 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I2 ) )
% 4.69/5.03 => ( ! [I3: int] :
% 4.69/5.03 ( ( member_int @ I3 @ I )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 4.69/5.03 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F @ I ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_1_prod2
% 4.69/5.03 thf(fact_7189_less__1__prod2,axiom,
% 4.69/5.03 ! [I: set_o,I2: $o,F: $o > code_integer] :
% 4.69/5.03 ( ( finite_finite_o @ I )
% 4.69/5.03 => ( ( member_o @ I2 @ I )
% 4.69/5.03 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I2 ) )
% 4.69/5.03 => ( ! [I3: $o] :
% 4.69/5.03 ( ( member_o @ I3 @ I )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 4.69/5.03 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups7694694392188491536nteger @ F @ I ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_1_prod2
% 4.69/5.03 thf(fact_7190_less__1__prod2,axiom,
% 4.69/5.03 ! [I: set_Product_unit,I2: product_unit,F: product_unit > code_integer] :
% 4.69/5.03 ( ( finite4290736615968046902t_unit @ I )
% 4.69/5.03 => ( ( member_Product_unit @ I2 @ I )
% 4.69/5.03 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I2 ) )
% 4.69/5.03 => ( ! [I3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ I3 @ I )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 4.69/5.03 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups8185359811944078981nteger @ F @ I ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_1_prod2
% 4.69/5.03 thf(fact_7191_less__1__prod2,axiom,
% 4.69/5.03 ! [I: set_nat,I2: nat,F: nat > code_integer] :
% 4.69/5.03 ( ( finite_finite_nat @ I )
% 4.69/5.03 => ( ( member_nat @ I2 @ I )
% 4.69/5.03 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I2 ) )
% 4.69/5.03 => ( ! [I3: nat] :
% 4.69/5.03 ( ( member_nat @ I3 @ I )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 4.69/5.03 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F @ I ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_1_prod2
% 4.69/5.03 thf(fact_7192_less__1__prod2,axiom,
% 4.69/5.03 ! [I: set_Code_integer,I2: code_integer,F: code_integer > code_integer] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ I )
% 4.69/5.03 => ( ( member_Code_integer @ I2 @ I )
% 4.69/5.03 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I2 ) )
% 4.69/5.03 => ( ! [I3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ I3 @ I )
% 4.69/5.03 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 4.69/5.03 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3674199335183972705nteger @ F @ I ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_1_prod2
% 4.69/5.03 thf(fact_7193_less__1__prod2,axiom,
% 4.69/5.03 ! [I: set_int,I2: int,F: int > rat] :
% 4.69/5.03 ( ( finite_finite_int @ I )
% 4.69/5.03 => ( ( member_int @ I2 @ I )
% 4.69/5.03 => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 4.69/5.03 => ( ! [I3: int] :
% 4.69/5.03 ( ( member_int @ I3 @ I )
% 4.69/5.03 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 4.69/5.03 => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_1_prod2
% 4.69/5.03 thf(fact_7194_less__1__prod2,axiom,
% 4.69/5.03 ! [I: set_o,I2: $o,F: $o > rat] :
% 4.69/5.03 ( ( finite_finite_o @ I )
% 4.69/5.03 => ( ( member_o @ I2 @ I )
% 4.69/5.03 => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 4.69/5.03 => ( ! [I3: $o] :
% 4.69/5.03 ( ( member_o @ I3 @ I )
% 4.69/5.03 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 4.69/5.03 => ( ord_less_rat @ one_one_rat @ ( groups2869687844427037835_o_rat @ F @ I ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_1_prod2
% 4.69/5.03 thf(fact_7195_less__1__prod2,axiom,
% 4.69/5.03 ! [I: set_Product_unit,I2: product_unit,F: product_unit > rat] :
% 4.69/5.03 ( ( finite4290736615968046902t_unit @ I )
% 4.69/5.03 => ( ( member_Product_unit @ I2 @ I )
% 4.69/5.03 => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 4.69/5.03 => ( ! [I3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ I3 @ I )
% 4.69/5.03 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 4.69/5.03 => ( ord_less_rat @ one_one_rat @ ( groups8984663225794451456it_rat @ F @ I ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_1_prod2
% 4.69/5.03 thf(fact_7196_less__1__prod2,axiom,
% 4.69/5.03 ! [I: set_nat,I2: nat,F: nat > rat] :
% 4.69/5.03 ( ( finite_finite_nat @ I )
% 4.69/5.03 => ( ( member_nat @ I2 @ I )
% 4.69/5.03 => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 4.69/5.03 => ( ! [I3: nat] :
% 4.69/5.03 ( ( member_nat @ I3 @ I )
% 4.69/5.03 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 4.69/5.03 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_1_prod2
% 4.69/5.03 thf(fact_7197_less__1__prod2,axiom,
% 4.69/5.03 ! [I: set_Code_integer,I2: code_integer,F: code_integer > rat] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ I )
% 4.69/5.03 => ( ( member_Code_integer @ I2 @ I )
% 4.69/5.03 => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 4.69/5.03 => ( ! [I3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ I3 @ I )
% 4.69/5.03 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 4.69/5.03 => ( ord_less_rat @ one_one_rat @ ( groups2555765274223993564er_rat @ F @ I ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_1_prod2
% 4.69/5.03 thf(fact_7198_less__1__prod,axiom,
% 4.69/5.03 ! [I: set_Code_integer,F: code_integer > int] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ I )
% 4.69/5.03 => ( ( I != bot_bo3990330152332043303nteger )
% 4.69/5.03 => ( ! [I3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ I3 @ I )
% 4.69/5.03 => ( ord_less_int @ one_one_int @ ( F @ I3 ) ) )
% 4.69/5.03 => ( ord_less_int @ one_one_int @ ( groups3188404863801439024er_int @ F @ I ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_1_prod
% 4.69/5.03 thf(fact_7199_less__1__prod,axiom,
% 4.69/5.03 ! [I: set_Product_unit,F: product_unit > int] :
% 4.69/5.03 ( ( finite4290736615968046902t_unit @ I )
% 4.69/5.03 => ( ( I != bot_bo3957492148770167129t_unit )
% 4.69/5.03 => ( ! [I3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ I3 @ I )
% 4.69/5.03 => ( ord_less_int @ one_one_int @ ( F @ I3 ) ) )
% 4.69/5.03 => ( ord_less_int @ one_one_int @ ( groups393930778517121108it_int @ F @ I ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_1_prod
% 4.69/5.03 thf(fact_7200_less__1__prod,axiom,
% 4.69/5.03 ! [I: set_o,F: $o > int] :
% 4.69/5.03 ( ( finite_finite_o @ I )
% 4.69/5.03 => ( ( I != bot_bot_set_o )
% 4.69/5.03 => ( ! [I3: $o] :
% 4.69/5.03 ( ( member_o @ I3 @ I )
% 4.69/5.03 => ( ord_less_int @ one_one_int @ ( F @ I3 ) ) )
% 4.69/5.03 => ( ord_less_int @ one_one_int @ ( groups3502327434004483295_o_int @ F @ I ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_1_prod
% 4.69/5.03 thf(fact_7201_less__1__prod,axiom,
% 4.69/5.03 ! [I: set_nat,F: nat > int] :
% 4.69/5.03 ( ( finite_finite_nat @ I )
% 4.69/5.03 => ( ( I != bot_bot_set_nat )
% 4.69/5.03 => ( ! [I3: nat] :
% 4.69/5.03 ( ( member_nat @ I3 @ I )
% 4.69/5.03 => ( ord_less_int @ one_one_int @ ( F @ I3 ) ) )
% 4.69/5.03 => ( ord_less_int @ one_one_int @ ( groups705719431365010083at_int @ F @ I ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_1_prod
% 4.69/5.03 thf(fact_7202_less__1__prod,axiom,
% 4.69/5.03 ! [I: set_int,F: int > int] :
% 4.69/5.03 ( ( finite_finite_int @ I )
% 4.69/5.03 => ( ( I != bot_bot_set_int )
% 4.69/5.03 => ( ! [I3: int] :
% 4.69/5.03 ( ( member_int @ I3 @ I )
% 4.69/5.03 => ( ord_less_int @ one_one_int @ ( F @ I3 ) ) )
% 4.69/5.03 => ( ord_less_int @ one_one_int @ ( groups1705073143266064639nt_int @ F @ I ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_1_prod
% 4.69/5.03 thf(fact_7203_less__1__prod,axiom,
% 4.69/5.03 ! [I: set_Code_integer,F: code_integer > code_integer] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ I )
% 4.69/5.03 => ( ( I != bot_bo3990330152332043303nteger )
% 4.69/5.03 => ( ! [I3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ I3 @ I )
% 4.69/5.03 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 4.69/5.03 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3674199335183972705nteger @ F @ I ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_1_prod
% 4.69/5.03 thf(fact_7204_less__1__prod,axiom,
% 4.69/5.03 ! [I: set_Product_unit,F: product_unit > code_integer] :
% 4.69/5.03 ( ( finite4290736615968046902t_unit @ I )
% 4.69/5.03 => ( ( I != bot_bo3957492148770167129t_unit )
% 4.69/5.03 => ( ! [I3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ I3 @ I )
% 4.69/5.03 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 4.69/5.03 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups8185359811944078981nteger @ F @ I ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_1_prod
% 4.69/5.03 thf(fact_7205_less__1__prod,axiom,
% 4.69/5.03 ! [I: set_o,F: $o > code_integer] :
% 4.69/5.03 ( ( finite_finite_o @ I )
% 4.69/5.03 => ( ( I != bot_bot_set_o )
% 4.69/5.03 => ( ! [I3: $o] :
% 4.69/5.03 ( ( member_o @ I3 @ I )
% 4.69/5.03 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 4.69/5.03 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups7694694392188491536nteger @ F @ I ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_1_prod
% 4.69/5.03 thf(fact_7206_less__1__prod,axiom,
% 4.69/5.03 ! [I: set_nat,F: nat > code_integer] :
% 4.69/5.03 ( ( finite_finite_nat @ I )
% 4.69/5.03 => ( ( I != bot_bot_set_nat )
% 4.69/5.03 => ( ! [I3: nat] :
% 4.69/5.03 ( ( member_nat @ I3 @ I )
% 4.69/5.03 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 4.69/5.03 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F @ I ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_1_prod
% 4.69/5.03 thf(fact_7207_less__1__prod,axiom,
% 4.69/5.03 ! [I: set_int,F: int > code_integer] :
% 4.69/5.03 ( ( finite_finite_int @ I )
% 4.69/5.03 => ( ( I != bot_bot_set_int )
% 4.69/5.03 => ( ! [I3: int] :
% 4.69/5.03 ( ( member_int @ I3 @ I )
% 4.69/5.03 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 4.69/5.03 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F @ I ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % less_1_prod
% 4.69/5.03 thf(fact_7208_prod_Oreindex__nontrivial,axiom,
% 4.69/5.03 ! [A: set_nat,H2: nat > nat,G: nat > assn] :
% 4.69/5.03 ( ( finite_finite_nat @ A )
% 4.69/5.03 => ( ! [X3: nat,Y2: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ A )
% 4.69/5.03 => ( ( member_nat @ Y2 @ A )
% 4.69/5.03 => ( ( X3 != Y2 )
% 4.69/5.03 => ( ( ( H2 @ X3 )
% 4.69/5.03 = ( H2 @ Y2 ) )
% 4.69/5.03 => ( ( G @ ( H2 @ X3 ) )
% 4.69/5.03 = one_one_assn ) ) ) ) )
% 4.69/5.03 => ( ( groups6906906614972039071t_assn @ G @ ( image_nat_nat2 @ H2 @ A ) )
% 4.69/5.03 = ( groups6906906614972039071t_assn @ ( comp_nat_assn_nat @ G @ H2 ) @ A ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.reindex_nontrivial
% 4.69/5.03 thf(fact_7209_prod_Oreindex__nontrivial,axiom,
% 4.69/5.03 ! [A: set_nat,H2: nat > code_integer,G: code_integer > assn] :
% 4.69/5.03 ( ( finite_finite_nat @ A )
% 4.69/5.03 => ( ! [X3: nat,Y2: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ A )
% 4.69/5.03 => ( ( member_nat @ Y2 @ A )
% 4.69/5.03 => ( ( X3 != Y2 )
% 4.69/5.03 => ( ( ( H2 @ X3 )
% 4.69/5.03 = ( H2 @ Y2 ) )
% 4.69/5.03 => ( ( G @ ( H2 @ X3 ) )
% 4.69/5.03 = one_one_assn ) ) ) ) )
% 4.69/5.03 => ( ( groups1304777262505850412r_assn @ G @ ( image_1215581382706833972nteger @ H2 @ A ) )
% 4.69/5.03 = ( groups6906906614972039071t_assn @ ( comp_C8462447471145125178sn_nat @ G @ H2 ) @ A ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.reindex_nontrivial
% 4.69/5.03 thf(fact_7210_prod_Oreindex__nontrivial,axiom,
% 4.69/5.03 ! [A: set_Code_integer,H2: code_integer > code_integer,G: code_integer > assn] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ! [X3: code_integer,Y2: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ A )
% 4.69/5.03 => ( ( member_Code_integer @ Y2 @ A )
% 4.69/5.03 => ( ( X3 != Y2 )
% 4.69/5.03 => ( ( ( H2 @ X3 )
% 4.69/5.03 = ( H2 @ Y2 ) )
% 4.69/5.03 => ( ( G @ ( H2 @ X3 ) )
% 4.69/5.03 = one_one_assn ) ) ) ) )
% 4.69/5.03 => ( ( groups1304777262505850412r_assn @ G @ ( image_4470545334726330049nteger @ H2 @ A ) )
% 4.69/5.03 = ( groups1304777262505850412r_assn @ ( comp_C3026223900822616519nteger @ G @ H2 ) @ A ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.reindex_nontrivial
% 4.69/5.03 thf(fact_7211_prod_Oreindex__nontrivial,axiom,
% 4.69/5.03 ! [A: set_Code_integer,H2: code_integer > code_integer,G: code_integer > nat] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ! [X3: code_integer,Y2: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ A )
% 4.69/5.03 => ( ( member_Code_integer @ Y2 @ A )
% 4.69/5.03 => ( ( X3 != Y2 )
% 4.69/5.03 => ( ( ( H2 @ X3 )
% 4.69/5.03 = ( H2 @ Y2 ) )
% 4.69/5.03 => ( ( G @ ( H2 @ X3 ) )
% 4.69/5.03 = one_one_nat ) ) ) ) )
% 4.69/5.03 => ( ( groups3190895334310489300er_nat @ G @ ( image_4470545334726330049nteger @ H2 @ A ) )
% 4.69/5.03 = ( groups3190895334310489300er_nat @ ( comp_C7238605732685392495nteger @ G @ H2 ) @ A ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.reindex_nontrivial
% 4.69/5.03 thf(fact_7212_prod_Oreindex__nontrivial,axiom,
% 4.69/5.03 ! [A: set_nat,H2: nat > nat,G: nat > int] :
% 4.69/5.03 ( ( finite_finite_nat @ A )
% 4.69/5.03 => ( ! [X3: nat,Y2: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ A )
% 4.69/5.03 => ( ( member_nat @ Y2 @ A )
% 4.69/5.03 => ( ( X3 != Y2 )
% 4.69/5.03 => ( ( ( H2 @ X3 )
% 4.69/5.03 = ( H2 @ Y2 ) )
% 4.69/5.03 => ( ( G @ ( H2 @ X3 ) )
% 4.69/5.03 = one_one_int ) ) ) ) )
% 4.69/5.03 => ( ( groups705719431365010083at_int @ G @ ( image_nat_nat2 @ H2 @ A ) )
% 4.69/5.03 = ( groups705719431365010083at_int @ ( comp_nat_int_nat @ G @ H2 ) @ A ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.reindex_nontrivial
% 4.69/5.03 thf(fact_7213_prod_Oreindex__nontrivial,axiom,
% 4.69/5.03 ! [A: set_nat,H2: nat > code_integer,G: code_integer > int] :
% 4.69/5.03 ( ( finite_finite_nat @ A )
% 4.69/5.03 => ( ! [X3: nat,Y2: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ A )
% 4.69/5.03 => ( ( member_nat @ Y2 @ A )
% 4.69/5.03 => ( ( X3 != Y2 )
% 4.69/5.03 => ( ( ( H2 @ X3 )
% 4.69/5.03 = ( H2 @ Y2 ) )
% 4.69/5.03 => ( ( G @ ( H2 @ X3 ) )
% 4.69/5.03 = one_one_int ) ) ) ) )
% 4.69/5.03 => ( ( groups3188404863801439024er_int @ G @ ( image_1215581382706833972nteger @ H2 @ A ) )
% 4.69/5.03 = ( groups705719431365010083at_int @ ( comp_C5048910307564104766nt_nat @ G @ H2 ) @ A ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.reindex_nontrivial
% 4.69/5.03 thf(fact_7214_prod_Oreindex__nontrivial,axiom,
% 4.69/5.03 ! [A: set_Code_integer,H2: code_integer > code_integer,G: code_integer > int] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ! [X3: code_integer,Y2: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ A )
% 4.69/5.03 => ( ( member_Code_integer @ Y2 @ A )
% 4.69/5.03 => ( ( X3 != Y2 )
% 4.69/5.03 => ( ( ( H2 @ X3 )
% 4.69/5.03 = ( H2 @ Y2 ) )
% 4.69/5.03 => ( ( G @ ( H2 @ X3 ) )
% 4.69/5.03 = one_one_int ) ) ) ) )
% 4.69/5.03 => ( ( groups3188404863801439024er_int @ G @ ( image_4470545334726330049nteger @ H2 @ A ) )
% 4.69/5.03 = ( groups3188404863801439024er_int @ ( comp_C7610259292922237131nteger @ G @ H2 ) @ A ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.reindex_nontrivial
% 4.69/5.03 thf(fact_7215_prod_Oreindex__nontrivial,axiom,
% 4.69/5.03 ! [A: set_nat,H2: nat > nat,G: nat > code_integer] :
% 4.69/5.03 ( ( finite_finite_nat @ A )
% 4.69/5.03 => ( ! [X3: nat,Y2: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ A )
% 4.69/5.03 => ( ( member_nat @ Y2 @ A )
% 4.69/5.03 => ( ( X3 != Y2 )
% 4.69/5.03 => ( ( ( H2 @ X3 )
% 4.69/5.03 = ( H2 @ Y2 ) )
% 4.69/5.03 => ( ( G @ ( H2 @ X3 ) )
% 4.69/5.03 = one_one_Code_integer ) ) ) ) )
% 4.69/5.03 => ( ( groups3455450783089532116nteger @ G @ ( image_nat_nat2 @ H2 @ A ) )
% 4.69/5.03 = ( groups3455450783089532116nteger @ ( comp_n3898172953802868194er_nat @ G @ H2 ) @ A ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.reindex_nontrivial
% 4.69/5.03 thf(fact_7216_prod_Oreindex__nontrivial,axiom,
% 4.69/5.03 ! [A: set_nat,H2: nat > code_integer,G: code_integer > code_integer] :
% 4.69/5.03 ( ( finite_finite_nat @ A )
% 4.69/5.03 => ( ! [X3: nat,Y2: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ A )
% 4.69/5.03 => ( ( member_nat @ Y2 @ A )
% 4.69/5.03 => ( ( X3 != Y2 )
% 4.69/5.03 => ( ( ( H2 @ X3 )
% 4.69/5.03 = ( H2 @ Y2 ) )
% 4.69/5.03 => ( ( G @ ( H2 @ X3 ) )
% 4.69/5.03 = one_one_Code_integer ) ) ) ) )
% 4.69/5.03 => ( ( groups3674199335183972705nteger @ G @ ( image_1215581382706833972nteger @ H2 @ A ) )
% 4.69/5.03 = ( groups3455450783089532116nteger @ ( comp_C6974050283906349679er_nat @ G @ H2 ) @ A ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.reindex_nontrivial
% 4.69/5.03 thf(fact_7217_prod_Oreindex__nontrivial,axiom,
% 4.69/5.03 ! [A: set_Code_integer,H2: code_integer > code_integer,G: code_integer > code_integer] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ! [X3: code_integer,Y2: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ A )
% 4.69/5.03 => ( ( member_Code_integer @ Y2 @ A )
% 4.69/5.03 => ( ( X3 != Y2 )
% 4.69/5.03 => ( ( ( H2 @ X3 )
% 4.69/5.03 = ( H2 @ Y2 ) )
% 4.69/5.03 => ( ( G @ ( H2 @ X3 ) )
% 4.69/5.03 = one_one_Code_integer ) ) ) ) )
% 4.69/5.03 => ( ( groups3674199335183972705nteger @ G @ ( image_4470545334726330049nteger @ H2 @ A ) )
% 4.69/5.03 = ( groups3674199335183972705nteger @ ( comp_C7449957260575251196nteger @ G @ H2 ) @ A ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.reindex_nontrivial
% 4.69/5.03 thf(fact_7218_prod_Osubset__diff,axiom,
% 4.69/5.03 ! [B4: set_Code_integer,A: set_Code_integer,G: code_integer > assn] :
% 4.69/5.03 ( ( ord_le7084787975880047091nteger @ B4 @ A )
% 4.69/5.03 => ( ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ( groups1304777262505850412r_assn @ G @ A )
% 4.69/5.03 = ( times_times_assn @ ( groups1304777262505850412r_assn @ G @ ( minus_2355218937544613996nteger @ A @ B4 ) ) @ ( groups1304777262505850412r_assn @ G @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.subset_diff
% 4.69/5.03 thf(fact_7219_prod_Osubset__diff,axiom,
% 4.69/5.03 ! [B4: set_Code_integer,A: set_Code_integer,G: code_integer > rat] :
% 4.69/5.03 ( ( ord_le7084787975880047091nteger @ B4 @ A )
% 4.69/5.03 => ( ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ( groups2555765274223993564er_rat @ G @ A )
% 4.69/5.03 = ( times_times_rat @ ( groups2555765274223993564er_rat @ G @ ( minus_2355218937544613996nteger @ A @ B4 ) ) @ ( groups2555765274223993564er_rat @ G @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.subset_diff
% 4.69/5.03 thf(fact_7220_prod_Osubset__diff,axiom,
% 4.69/5.03 ! [B4: set_Code_integer,A: set_Code_integer,G: code_integer > nat] :
% 4.69/5.03 ( ( ord_le7084787975880047091nteger @ B4 @ A )
% 4.69/5.03 => ( ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ( groups3190895334310489300er_nat @ G @ A )
% 4.69/5.03 = ( times_times_nat @ ( groups3190895334310489300er_nat @ G @ ( minus_2355218937544613996nteger @ A @ B4 ) ) @ ( groups3190895334310489300er_nat @ G @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.subset_diff
% 4.69/5.03 thf(fact_7221_prod_Osubset__diff,axiom,
% 4.69/5.03 ! [B4: set_Code_integer,A: set_Code_integer,G: code_integer > int] :
% 4.69/5.03 ( ( ord_le7084787975880047091nteger @ B4 @ A )
% 4.69/5.03 => ( ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ( groups3188404863801439024er_int @ G @ A )
% 4.69/5.03 = ( times_times_int @ ( groups3188404863801439024er_int @ G @ ( minus_2355218937544613996nteger @ A @ B4 ) ) @ ( groups3188404863801439024er_int @ G @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.subset_diff
% 4.69/5.03 thf(fact_7222_prod_Osubset__diff,axiom,
% 4.69/5.03 ! [B4: set_nat,A: set_nat,G: nat > assn] :
% 4.69/5.03 ( ( ord_less_eq_set_nat @ B4 @ A )
% 4.69/5.03 => ( ( finite_finite_nat @ A )
% 4.69/5.03 => ( ( groups6906906614972039071t_assn @ G @ A )
% 4.69/5.03 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( minus_minus_set_nat @ A @ B4 ) ) @ ( groups6906906614972039071t_assn @ G @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.subset_diff
% 4.69/5.03 thf(fact_7223_prod_Osubset__diff,axiom,
% 4.69/5.03 ! [B4: set_nat,A: set_nat,G: nat > rat] :
% 4.69/5.03 ( ( ord_less_eq_set_nat @ B4 @ A )
% 4.69/5.03 => ( ( finite_finite_nat @ A )
% 4.69/5.03 => ( ( groups73079841787564623at_rat @ G @ A )
% 4.69/5.03 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A @ B4 ) ) @ ( groups73079841787564623at_rat @ G @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.subset_diff
% 4.69/5.03 thf(fact_7224_prod_Osubset__diff,axiom,
% 4.69/5.03 ! [B4: set_nat,A: set_nat,G: nat > int] :
% 4.69/5.03 ( ( ord_less_eq_set_nat @ B4 @ A )
% 4.69/5.03 => ( ( finite_finite_nat @ A )
% 4.69/5.03 => ( ( groups705719431365010083at_int @ G @ A )
% 4.69/5.03 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( minus_minus_set_nat @ A @ B4 ) ) @ ( groups705719431365010083at_int @ G @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.subset_diff
% 4.69/5.03 thf(fact_7225_prod_Osubset__diff,axiom,
% 4.69/5.03 ! [B4: set_nat,A: set_nat,G: nat > nat] :
% 4.69/5.03 ( ( ord_less_eq_set_nat @ B4 @ A )
% 4.69/5.03 => ( ( finite_finite_nat @ A )
% 4.69/5.03 => ( ( groups708209901874060359at_nat @ G @ A )
% 4.69/5.03 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( minus_minus_set_nat @ A @ B4 ) ) @ ( groups708209901874060359at_nat @ G @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.subset_diff
% 4.69/5.03 thf(fact_7226_prod_Osame__carrier,axiom,
% 4.69/5.03 ! [C5: set_int,A: set_int,B4: set_int,G: int > assn,H2: int > assn] :
% 4.69/5.03 ( ( finite_finite_int @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_int @ A @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_int @ B4 @ C5 )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ ( minus_minus_set_int @ C5 @ A ) )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [B2: int] :
% 4.69/5.03 ( ( member_int @ B2 @ ( minus_minus_set_int @ C5 @ B4 ) )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ( ( groups7882442080178216443t_assn @ G @ A )
% 4.69/5.03 = ( groups7882442080178216443t_assn @ H2 @ B4 ) )
% 4.69/5.03 = ( ( groups7882442080178216443t_assn @ G @ C5 )
% 4.69/5.03 = ( groups7882442080178216443t_assn @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.same_carrier
% 4.69/5.03 thf(fact_7227_prod_Osame__carrier,axiom,
% 4.69/5.03 ! [C5: set_o,A: set_o,B4: set_o,G: $o > assn,H2: $o > assn] :
% 4.69/5.03 ( ( finite_finite_o @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_o @ A @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_o @ B4 @ C5 )
% 4.69/5.03 => ( ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ ( minus_minus_set_o @ C5 @ A ) )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [B2: $o] :
% 4.69/5.03 ( ( member_o @ B2 @ ( minus_minus_set_o @ C5 @ B4 ) )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ( ( groups5301882518646026715o_assn @ G @ A )
% 4.69/5.03 = ( groups5301882518646026715o_assn @ H2 @ B4 ) )
% 4.69/5.03 = ( ( groups5301882518646026715o_assn @ G @ C5 )
% 4.69/5.03 = ( groups5301882518646026715o_assn @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.same_carrier
% 4.69/5.03 thf(fact_7228_prod_Osame__carrier,axiom,
% 4.69/5.03 ! [C5: set_Product_unit,A: set_Product_unit,B4: set_Product_unit,G: product_unit > assn,H2: product_unit > assn] :
% 4.69/5.03 ( ( finite4290736615968046902t_unit @ C5 )
% 4.69/5.03 => ( ( ord_le3507040750410214029t_unit @ A @ C5 )
% 4.69/5.03 => ( ( ord_le3507040750410214029t_unit @ B4 @ C5 )
% 4.69/5.03 => ( ! [A4: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ A4 @ ( minus_6452836326544984404t_unit @ C5 @ A ) )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [B2: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ B2 @ ( minus_6452836326544984404t_unit @ C5 @ B4 ) )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ( ( groups5360233303959380816t_assn @ G @ A )
% 4.69/5.03 = ( groups5360233303959380816t_assn @ H2 @ B4 ) )
% 4.69/5.03 = ( ( groups5360233303959380816t_assn @ G @ C5 )
% 4.69/5.03 = ( groups5360233303959380816t_assn @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.same_carrier
% 4.69/5.03 thf(fact_7229_prod_Osame__carrier,axiom,
% 4.69/5.03 ! [C5: set_Code_integer,A: set_Code_integer,B4: set_Code_integer,G: code_integer > assn,H2: code_integer > assn] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ C5 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ A @ C5 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ B4 @ C5 )
% 4.69/5.03 => ( ! [A4: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ A4 @ ( minus_2355218937544613996nteger @ C5 @ A ) )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [B2: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ C5 @ B4 ) )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ( ( groups1304777262505850412r_assn @ G @ A )
% 4.69/5.03 = ( groups1304777262505850412r_assn @ H2 @ B4 ) )
% 4.69/5.03 = ( ( groups1304777262505850412r_assn @ G @ C5 )
% 4.69/5.03 = ( groups1304777262505850412r_assn @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.same_carrier
% 4.69/5.03 thf(fact_7230_prod_Osame__carrier,axiom,
% 4.69/5.03 ! [C5: set_int,A: set_int,B4: set_int,G: int > nat,H2: int > nat] :
% 4.69/5.03 ( ( finite_finite_int @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_int @ A @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_int @ B4 @ C5 )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ ( minus_minus_set_int @ C5 @ A ) )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ! [B2: int] :
% 4.69/5.03 ( ( member_int @ B2 @ ( minus_minus_set_int @ C5 @ B4 ) )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ( ( groups1707563613775114915nt_nat @ G @ A )
% 4.69/5.03 = ( groups1707563613775114915nt_nat @ H2 @ B4 ) )
% 4.69/5.03 = ( ( groups1707563613775114915nt_nat @ G @ C5 )
% 4.69/5.03 = ( groups1707563613775114915nt_nat @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.same_carrier
% 4.69/5.03 thf(fact_7231_prod_Osame__carrier,axiom,
% 4.69/5.03 ! [C5: set_o,A: set_o,B4: set_o,G: $o > nat,H2: $o > nat] :
% 4.69/5.03 ( ( finite_finite_o @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_o @ A @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_o @ B4 @ C5 )
% 4.69/5.03 => ( ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ ( minus_minus_set_o @ C5 @ A ) )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ! [B2: $o] :
% 4.69/5.03 ( ( member_o @ B2 @ ( minus_minus_set_o @ C5 @ B4 ) )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ( ( groups3504817904513533571_o_nat @ G @ A )
% 4.69/5.03 = ( groups3504817904513533571_o_nat @ H2 @ B4 ) )
% 4.69/5.03 = ( ( groups3504817904513533571_o_nat @ G @ C5 )
% 4.69/5.03 = ( groups3504817904513533571_o_nat @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.same_carrier
% 4.69/5.03 thf(fact_7232_prod_Osame__carrier,axiom,
% 4.69/5.03 ! [C5: set_Product_unit,A: set_Product_unit,B4: set_Product_unit,G: product_unit > nat,H2: product_unit > nat] :
% 4.69/5.03 ( ( finite4290736615968046902t_unit @ C5 )
% 4.69/5.03 => ( ( ord_le3507040750410214029t_unit @ A @ C5 )
% 4.69/5.03 => ( ( ord_le3507040750410214029t_unit @ B4 @ C5 )
% 4.69/5.03 => ( ! [A4: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ A4 @ ( minus_6452836326544984404t_unit @ C5 @ A ) )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ! [B2: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ B2 @ ( minus_6452836326544984404t_unit @ C5 @ B4 ) )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ( ( groups396421249026171384it_nat @ G @ A )
% 4.69/5.03 = ( groups396421249026171384it_nat @ H2 @ B4 ) )
% 4.69/5.03 = ( ( groups396421249026171384it_nat @ G @ C5 )
% 4.69/5.03 = ( groups396421249026171384it_nat @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.same_carrier
% 4.69/5.03 thf(fact_7233_prod_Osame__carrier,axiom,
% 4.69/5.03 ! [C5: set_Code_integer,A: set_Code_integer,B4: set_Code_integer,G: code_integer > nat,H2: code_integer > nat] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ C5 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ A @ C5 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ B4 @ C5 )
% 4.69/5.03 => ( ! [A4: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ A4 @ ( minus_2355218937544613996nteger @ C5 @ A ) )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ! [B2: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ C5 @ B4 ) )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ( ( groups3190895334310489300er_nat @ G @ A )
% 4.69/5.03 = ( groups3190895334310489300er_nat @ H2 @ B4 ) )
% 4.69/5.03 = ( ( groups3190895334310489300er_nat @ G @ C5 )
% 4.69/5.03 = ( groups3190895334310489300er_nat @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.same_carrier
% 4.69/5.03 thf(fact_7234_prod_Osame__carrier,axiom,
% 4.69/5.03 ! [C5: set_int,A: set_int,B4: set_int,G: int > int,H2: int > int] :
% 4.69/5.03 ( ( finite_finite_int @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_int @ A @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_int @ B4 @ C5 )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ ( minus_minus_set_int @ C5 @ A ) )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_int ) )
% 4.69/5.03 => ( ! [B2: int] :
% 4.69/5.03 ( ( member_int @ B2 @ ( minus_minus_set_int @ C5 @ B4 ) )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_int ) )
% 4.69/5.03 => ( ( ( groups1705073143266064639nt_int @ G @ A )
% 4.69/5.03 = ( groups1705073143266064639nt_int @ H2 @ B4 ) )
% 4.69/5.03 = ( ( groups1705073143266064639nt_int @ G @ C5 )
% 4.69/5.03 = ( groups1705073143266064639nt_int @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.same_carrier
% 4.69/5.03 thf(fact_7235_prod_Osame__carrier,axiom,
% 4.69/5.03 ! [C5: set_o,A: set_o,B4: set_o,G: $o > int,H2: $o > int] :
% 4.69/5.03 ( ( finite_finite_o @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_o @ A @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_o @ B4 @ C5 )
% 4.69/5.03 => ( ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ ( minus_minus_set_o @ C5 @ A ) )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_int ) )
% 4.69/5.03 => ( ! [B2: $o] :
% 4.69/5.03 ( ( member_o @ B2 @ ( minus_minus_set_o @ C5 @ B4 ) )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_int ) )
% 4.69/5.03 => ( ( ( groups3502327434004483295_o_int @ G @ A )
% 4.69/5.03 = ( groups3502327434004483295_o_int @ H2 @ B4 ) )
% 4.69/5.03 = ( ( groups3502327434004483295_o_int @ G @ C5 )
% 4.69/5.03 = ( groups3502327434004483295_o_int @ H2 @ C5 ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.same_carrier
% 4.69/5.03 thf(fact_7236_prod_Osame__carrierI,axiom,
% 4.69/5.03 ! [C5: set_int,A: set_int,B4: set_int,G: int > assn,H2: int > assn] :
% 4.69/5.03 ( ( finite_finite_int @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_int @ A @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_int @ B4 @ C5 )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ ( minus_minus_set_int @ C5 @ A ) )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [B2: int] :
% 4.69/5.03 ( ( member_int @ B2 @ ( minus_minus_set_int @ C5 @ B4 ) )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ( ( groups7882442080178216443t_assn @ G @ C5 )
% 4.69/5.03 = ( groups7882442080178216443t_assn @ H2 @ C5 ) )
% 4.69/5.03 => ( ( groups7882442080178216443t_assn @ G @ A )
% 4.69/5.03 = ( groups7882442080178216443t_assn @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.same_carrierI
% 4.69/5.03 thf(fact_7237_prod_Osame__carrierI,axiom,
% 4.69/5.03 ! [C5: set_o,A: set_o,B4: set_o,G: $o > assn,H2: $o > assn] :
% 4.69/5.03 ( ( finite_finite_o @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_o @ A @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_o @ B4 @ C5 )
% 4.69/5.03 => ( ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ ( minus_minus_set_o @ C5 @ A ) )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [B2: $o] :
% 4.69/5.03 ( ( member_o @ B2 @ ( minus_minus_set_o @ C5 @ B4 ) )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ( ( groups5301882518646026715o_assn @ G @ C5 )
% 4.69/5.03 = ( groups5301882518646026715o_assn @ H2 @ C5 ) )
% 4.69/5.03 => ( ( groups5301882518646026715o_assn @ G @ A )
% 4.69/5.03 = ( groups5301882518646026715o_assn @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.same_carrierI
% 4.69/5.03 thf(fact_7238_prod_Osame__carrierI,axiom,
% 4.69/5.03 ! [C5: set_Product_unit,A: set_Product_unit,B4: set_Product_unit,G: product_unit > assn,H2: product_unit > assn] :
% 4.69/5.03 ( ( finite4290736615968046902t_unit @ C5 )
% 4.69/5.03 => ( ( ord_le3507040750410214029t_unit @ A @ C5 )
% 4.69/5.03 => ( ( ord_le3507040750410214029t_unit @ B4 @ C5 )
% 4.69/5.03 => ( ! [A4: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ A4 @ ( minus_6452836326544984404t_unit @ C5 @ A ) )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [B2: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ B2 @ ( minus_6452836326544984404t_unit @ C5 @ B4 ) )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ( ( groups5360233303959380816t_assn @ G @ C5 )
% 4.69/5.03 = ( groups5360233303959380816t_assn @ H2 @ C5 ) )
% 4.69/5.03 => ( ( groups5360233303959380816t_assn @ G @ A )
% 4.69/5.03 = ( groups5360233303959380816t_assn @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.same_carrierI
% 4.69/5.03 thf(fact_7239_prod_Osame__carrierI,axiom,
% 4.69/5.03 ! [C5: set_Code_integer,A: set_Code_integer,B4: set_Code_integer,G: code_integer > assn,H2: code_integer > assn] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ C5 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ A @ C5 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ B4 @ C5 )
% 4.69/5.03 => ( ! [A4: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ A4 @ ( minus_2355218937544613996nteger @ C5 @ A ) )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [B2: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ C5 @ B4 ) )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ( ( groups1304777262505850412r_assn @ G @ C5 )
% 4.69/5.03 = ( groups1304777262505850412r_assn @ H2 @ C5 ) )
% 4.69/5.03 => ( ( groups1304777262505850412r_assn @ G @ A )
% 4.69/5.03 = ( groups1304777262505850412r_assn @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.same_carrierI
% 4.69/5.03 thf(fact_7240_prod_Osame__carrierI,axiom,
% 4.69/5.03 ! [C5: set_int,A: set_int,B4: set_int,G: int > nat,H2: int > nat] :
% 4.69/5.03 ( ( finite_finite_int @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_int @ A @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_int @ B4 @ C5 )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ ( minus_minus_set_int @ C5 @ A ) )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ! [B2: int] :
% 4.69/5.03 ( ( member_int @ B2 @ ( minus_minus_set_int @ C5 @ B4 ) )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ( ( groups1707563613775114915nt_nat @ G @ C5 )
% 4.69/5.03 = ( groups1707563613775114915nt_nat @ H2 @ C5 ) )
% 4.69/5.03 => ( ( groups1707563613775114915nt_nat @ G @ A )
% 4.69/5.03 = ( groups1707563613775114915nt_nat @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.same_carrierI
% 4.69/5.03 thf(fact_7241_prod_Osame__carrierI,axiom,
% 4.69/5.03 ! [C5: set_o,A: set_o,B4: set_o,G: $o > nat,H2: $o > nat] :
% 4.69/5.03 ( ( finite_finite_o @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_o @ A @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_o @ B4 @ C5 )
% 4.69/5.03 => ( ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ ( minus_minus_set_o @ C5 @ A ) )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ! [B2: $o] :
% 4.69/5.03 ( ( member_o @ B2 @ ( minus_minus_set_o @ C5 @ B4 ) )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ( ( groups3504817904513533571_o_nat @ G @ C5 )
% 4.69/5.03 = ( groups3504817904513533571_o_nat @ H2 @ C5 ) )
% 4.69/5.03 => ( ( groups3504817904513533571_o_nat @ G @ A )
% 4.69/5.03 = ( groups3504817904513533571_o_nat @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.same_carrierI
% 4.69/5.03 thf(fact_7242_prod_Osame__carrierI,axiom,
% 4.69/5.03 ! [C5: set_Product_unit,A: set_Product_unit,B4: set_Product_unit,G: product_unit > nat,H2: product_unit > nat] :
% 4.69/5.03 ( ( finite4290736615968046902t_unit @ C5 )
% 4.69/5.03 => ( ( ord_le3507040750410214029t_unit @ A @ C5 )
% 4.69/5.03 => ( ( ord_le3507040750410214029t_unit @ B4 @ C5 )
% 4.69/5.03 => ( ! [A4: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ A4 @ ( minus_6452836326544984404t_unit @ C5 @ A ) )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ! [B2: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ B2 @ ( minus_6452836326544984404t_unit @ C5 @ B4 ) )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ( ( groups396421249026171384it_nat @ G @ C5 )
% 4.69/5.03 = ( groups396421249026171384it_nat @ H2 @ C5 ) )
% 4.69/5.03 => ( ( groups396421249026171384it_nat @ G @ A )
% 4.69/5.03 = ( groups396421249026171384it_nat @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.same_carrierI
% 4.69/5.03 thf(fact_7243_prod_Osame__carrierI,axiom,
% 4.69/5.03 ! [C5: set_Code_integer,A: set_Code_integer,B4: set_Code_integer,G: code_integer > nat,H2: code_integer > nat] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ C5 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ A @ C5 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ B4 @ C5 )
% 4.69/5.03 => ( ! [A4: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ A4 @ ( minus_2355218937544613996nteger @ C5 @ A ) )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ! [B2: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ B2 @ ( minus_2355218937544613996nteger @ C5 @ B4 ) )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ( ( groups3190895334310489300er_nat @ G @ C5 )
% 4.69/5.03 = ( groups3190895334310489300er_nat @ H2 @ C5 ) )
% 4.69/5.03 => ( ( groups3190895334310489300er_nat @ G @ A )
% 4.69/5.03 = ( groups3190895334310489300er_nat @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.same_carrierI
% 4.69/5.03 thf(fact_7244_prod_Osame__carrierI,axiom,
% 4.69/5.03 ! [C5: set_int,A: set_int,B4: set_int,G: int > int,H2: int > int] :
% 4.69/5.03 ( ( finite_finite_int @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_int @ A @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_int @ B4 @ C5 )
% 4.69/5.03 => ( ! [A4: int] :
% 4.69/5.03 ( ( member_int @ A4 @ ( minus_minus_set_int @ C5 @ A ) )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_int ) )
% 4.69/5.03 => ( ! [B2: int] :
% 4.69/5.03 ( ( member_int @ B2 @ ( minus_minus_set_int @ C5 @ B4 ) )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_int ) )
% 4.69/5.03 => ( ( ( groups1705073143266064639nt_int @ G @ C5 )
% 4.69/5.03 = ( groups1705073143266064639nt_int @ H2 @ C5 ) )
% 4.69/5.03 => ( ( groups1705073143266064639nt_int @ G @ A )
% 4.69/5.03 = ( groups1705073143266064639nt_int @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.same_carrierI
% 4.69/5.03 thf(fact_7245_prod_Osame__carrierI,axiom,
% 4.69/5.03 ! [C5: set_o,A: set_o,B4: set_o,G: $o > int,H2: $o > int] :
% 4.69/5.03 ( ( finite_finite_o @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_o @ A @ C5 )
% 4.69/5.03 => ( ( ord_less_eq_set_o @ B4 @ C5 )
% 4.69/5.03 => ( ! [A4: $o] :
% 4.69/5.03 ( ( member_o @ A4 @ ( minus_minus_set_o @ C5 @ A ) )
% 4.69/5.03 => ( ( G @ A4 )
% 4.69/5.03 = one_one_int ) )
% 4.69/5.03 => ( ! [B2: $o] :
% 4.69/5.03 ( ( member_o @ B2 @ ( minus_minus_set_o @ C5 @ B4 ) )
% 4.69/5.03 => ( ( H2 @ B2 )
% 4.69/5.03 = one_one_int ) )
% 4.69/5.03 => ( ( ( groups3502327434004483295_o_int @ G @ C5 )
% 4.69/5.03 = ( groups3502327434004483295_o_int @ H2 @ C5 ) )
% 4.69/5.03 => ( ( groups3502327434004483295_o_int @ G @ A )
% 4.69/5.03 = ( groups3502327434004483295_o_int @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.same_carrierI
% 4.69/5.03 thf(fact_7246_prod_Omono__neutral__left,axiom,
% 4.69/5.03 ! [T2: set_Code_integer,S: set_Code_integer,G: code_integer > assn] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ T2 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ S @ T2 )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ( groups1304777262505850412r_assn @ G @ S )
% 4.69/5.03 = ( groups1304777262505850412r_assn @ G @ T2 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_left
% 4.69/5.03 thf(fact_7247_prod_Omono__neutral__left,axiom,
% 4.69/5.03 ! [T2: set_Code_integer,S: set_Code_integer,G: code_integer > nat] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ T2 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ S @ T2 )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ( groups3190895334310489300er_nat @ G @ S )
% 4.69/5.03 = ( groups3190895334310489300er_nat @ G @ T2 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_left
% 4.69/5.03 thf(fact_7248_prod_Omono__neutral__left,axiom,
% 4.69/5.03 ! [T2: set_Code_integer,S: set_Code_integer,G: code_integer > int] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ T2 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ S @ T2 )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_int ) )
% 4.69/5.03 => ( ( groups3188404863801439024er_int @ G @ S )
% 4.69/5.03 = ( groups3188404863801439024er_int @ G @ T2 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_left
% 4.69/5.03 thf(fact_7249_prod_Omono__neutral__left,axiom,
% 4.69/5.03 ! [T2: set_Code_integer,S: set_Code_integer,G: code_integer > code_integer] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ T2 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ S @ T2 )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_Code_integer ) )
% 4.69/5.03 => ( ( groups3674199335183972705nteger @ G @ S )
% 4.69/5.03 = ( groups3674199335183972705nteger @ G @ T2 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_left
% 4.69/5.03 thf(fact_7250_prod_Omono__neutral__left,axiom,
% 4.69/5.03 ! [T2: set_Code_integer,S: set_Code_integer,G: code_integer > code_natural] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ T2 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ S @ T2 )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_Code_natural ) )
% 4.69/5.03 => ( ( groups2497794486940690220atural @ G @ S )
% 4.69/5.03 = ( groups2497794486940690220atural @ G @ T2 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_left
% 4.69/5.03 thf(fact_7251_prod_Omono__neutral__left,axiom,
% 4.69/5.03 ! [T2: set_nat,S: set_nat,G: nat > assn] :
% 4.69/5.03 ( ( finite_finite_nat @ T2 )
% 4.69/5.03 => ( ( ord_less_eq_set_nat @ S @ T2 )
% 4.69/5.03 => ( ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ( groups6906906614972039071t_assn @ G @ S )
% 4.69/5.03 = ( groups6906906614972039071t_assn @ G @ T2 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_left
% 4.69/5.03 thf(fact_7252_prod_Omono__neutral__left,axiom,
% 4.69/5.03 ! [T2: set_nat,S: set_nat,G: nat > int] :
% 4.69/5.03 ( ( finite_finite_nat @ T2 )
% 4.69/5.03 => ( ( ord_less_eq_set_nat @ S @ T2 )
% 4.69/5.03 => ( ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_int ) )
% 4.69/5.03 => ( ( groups705719431365010083at_int @ G @ S )
% 4.69/5.03 = ( groups705719431365010083at_int @ G @ T2 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_left
% 4.69/5.03 thf(fact_7253_prod_Omono__neutral__left,axiom,
% 4.69/5.03 ! [T2: set_nat,S: set_nat,G: nat > code_integer] :
% 4.69/5.03 ( ( finite_finite_nat @ T2 )
% 4.69/5.03 => ( ( ord_less_eq_set_nat @ S @ T2 )
% 4.69/5.03 => ( ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_Code_integer ) )
% 4.69/5.03 => ( ( groups3455450783089532116nteger @ G @ S )
% 4.69/5.03 = ( groups3455450783089532116nteger @ G @ T2 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_left
% 4.69/5.03 thf(fact_7254_prod_Omono__neutral__left,axiom,
% 4.69/5.03 ! [T2: set_nat,S: set_nat,G: nat > code_natural] :
% 4.69/5.03 ( ( finite_finite_nat @ T2 )
% 4.69/5.03 => ( ( ord_less_eq_set_nat @ S @ T2 )
% 4.69/5.03 => ( ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_Code_natural ) )
% 4.69/5.03 => ( ( groups2279045934846249631atural @ G @ S )
% 4.69/5.03 = ( groups2279045934846249631atural @ G @ T2 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_left
% 4.69/5.03 thf(fact_7255_prod_Omono__neutral__left,axiom,
% 4.69/5.03 ! [T2: set_nat,S: set_nat,G: nat > nat] :
% 4.69/5.03 ( ( finite_finite_nat @ T2 )
% 4.69/5.03 => ( ( ord_less_eq_set_nat @ S @ T2 )
% 4.69/5.03 => ( ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ( groups708209901874060359at_nat @ G @ S )
% 4.69/5.03 = ( groups708209901874060359at_nat @ G @ T2 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_left
% 4.69/5.03 thf(fact_7256_prod_Omono__neutral__right,axiom,
% 4.69/5.03 ! [T2: set_Code_integer,S: set_Code_integer,G: code_integer > assn] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ T2 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ S @ T2 )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ( groups1304777262505850412r_assn @ G @ T2 )
% 4.69/5.03 = ( groups1304777262505850412r_assn @ G @ S ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_right
% 4.69/5.03 thf(fact_7257_prod_Omono__neutral__right,axiom,
% 4.69/5.03 ! [T2: set_Code_integer,S: set_Code_integer,G: code_integer > nat] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ T2 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ S @ T2 )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ( groups3190895334310489300er_nat @ G @ T2 )
% 4.69/5.03 = ( groups3190895334310489300er_nat @ G @ S ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_right
% 4.69/5.03 thf(fact_7258_prod_Omono__neutral__right,axiom,
% 4.69/5.03 ! [T2: set_Code_integer,S: set_Code_integer,G: code_integer > int] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ T2 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ S @ T2 )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_int ) )
% 4.69/5.03 => ( ( groups3188404863801439024er_int @ G @ T2 )
% 4.69/5.03 = ( groups3188404863801439024er_int @ G @ S ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_right
% 4.69/5.03 thf(fact_7259_prod_Omono__neutral__right,axiom,
% 4.69/5.03 ! [T2: set_Code_integer,S: set_Code_integer,G: code_integer > code_integer] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ T2 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ S @ T2 )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_Code_integer ) )
% 4.69/5.03 => ( ( groups3674199335183972705nteger @ G @ T2 )
% 4.69/5.03 = ( groups3674199335183972705nteger @ G @ S ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_right
% 4.69/5.03 thf(fact_7260_prod_Omono__neutral__right,axiom,
% 4.69/5.03 ! [T2: set_Code_integer,S: set_Code_integer,G: code_integer > code_natural] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ T2 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ S @ T2 )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_Code_natural ) )
% 4.69/5.03 => ( ( groups2497794486940690220atural @ G @ T2 )
% 4.69/5.03 = ( groups2497794486940690220atural @ G @ S ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_right
% 4.69/5.03 thf(fact_7261_prod_Omono__neutral__right,axiom,
% 4.69/5.03 ! [T2: set_nat,S: set_nat,G: nat > assn] :
% 4.69/5.03 ( ( finite_finite_nat @ T2 )
% 4.69/5.03 => ( ( ord_less_eq_set_nat @ S @ T2 )
% 4.69/5.03 => ( ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ( groups6906906614972039071t_assn @ G @ T2 )
% 4.69/5.03 = ( groups6906906614972039071t_assn @ G @ S ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_right
% 4.69/5.03 thf(fact_7262_prod_Omono__neutral__right,axiom,
% 4.69/5.03 ! [T2: set_nat,S: set_nat,G: nat > int] :
% 4.69/5.03 ( ( finite_finite_nat @ T2 )
% 4.69/5.03 => ( ( ord_less_eq_set_nat @ S @ T2 )
% 4.69/5.03 => ( ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_int ) )
% 4.69/5.03 => ( ( groups705719431365010083at_int @ G @ T2 )
% 4.69/5.03 = ( groups705719431365010083at_int @ G @ S ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_right
% 4.69/5.03 thf(fact_7263_prod_Omono__neutral__right,axiom,
% 4.69/5.03 ! [T2: set_nat,S: set_nat,G: nat > code_integer] :
% 4.69/5.03 ( ( finite_finite_nat @ T2 )
% 4.69/5.03 => ( ( ord_less_eq_set_nat @ S @ T2 )
% 4.69/5.03 => ( ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_Code_integer ) )
% 4.69/5.03 => ( ( groups3455450783089532116nteger @ G @ T2 )
% 4.69/5.03 = ( groups3455450783089532116nteger @ G @ S ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_right
% 4.69/5.03 thf(fact_7264_prod_Omono__neutral__right,axiom,
% 4.69/5.03 ! [T2: set_nat,S: set_nat,G: nat > code_natural] :
% 4.69/5.03 ( ( finite_finite_nat @ T2 )
% 4.69/5.03 => ( ( ord_less_eq_set_nat @ S @ T2 )
% 4.69/5.03 => ( ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_Code_natural ) )
% 4.69/5.03 => ( ( groups2279045934846249631atural @ G @ T2 )
% 4.69/5.03 = ( groups2279045934846249631atural @ G @ S ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_right
% 4.69/5.03 thf(fact_7265_prod_Omono__neutral__right,axiom,
% 4.69/5.03 ! [T2: set_nat,S: set_nat,G: nat > nat] :
% 4.69/5.03 ( ( finite_finite_nat @ T2 )
% 4.69/5.03 => ( ( ord_less_eq_set_nat @ S @ T2 )
% 4.69/5.03 => ( ! [X3: nat] :
% 4.69/5.03 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ( groups708209901874060359at_nat @ G @ T2 )
% 4.69/5.03 = ( groups708209901874060359at_nat @ G @ S ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_right
% 4.69/5.03 thf(fact_7266_prod_Omono__neutral__cong__left,axiom,
% 4.69/5.03 ! [T2: set_int,S: set_int,H2: int > assn,G: int > assn] :
% 4.69/5.03 ( ( finite_finite_int @ T2 )
% 4.69/5.03 => ( ( ord_less_eq_set_int @ S @ T2 )
% 4.69/5.03 => ( ! [X3: int] :
% 4.69/5.03 ( ( member_int @ X3 @ ( minus_minus_set_int @ T2 @ S ) )
% 4.69/5.03 => ( ( H2 @ X3 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [X3: int] :
% 4.69/5.03 ( ( member_int @ X3 @ S )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = ( H2 @ X3 ) ) )
% 4.69/5.03 => ( ( groups7882442080178216443t_assn @ G @ S )
% 4.69/5.03 = ( groups7882442080178216443t_assn @ H2 @ T2 ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_cong_left
% 4.69/5.03 thf(fact_7267_prod_Omono__neutral__cong__left,axiom,
% 4.69/5.03 ! [T2: set_o,S: set_o,H2: $o > assn,G: $o > assn] :
% 4.69/5.03 ( ( finite_finite_o @ T2 )
% 4.69/5.03 => ( ( ord_less_eq_set_o @ S @ T2 )
% 4.69/5.03 => ( ! [X3: $o] :
% 4.69/5.03 ( ( member_o @ X3 @ ( minus_minus_set_o @ T2 @ S ) )
% 4.69/5.03 => ( ( H2 @ X3 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [X3: $o] :
% 4.69/5.03 ( ( member_o @ X3 @ S )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = ( H2 @ X3 ) ) )
% 4.69/5.03 => ( ( groups5301882518646026715o_assn @ G @ S )
% 4.69/5.03 = ( groups5301882518646026715o_assn @ H2 @ T2 ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_cong_left
% 4.69/5.03 thf(fact_7268_prod_Omono__neutral__cong__left,axiom,
% 4.69/5.03 ! [T2: set_Product_unit,S: set_Product_unit,H2: product_unit > assn,G: product_unit > assn] :
% 4.69/5.03 ( ( finite4290736615968046902t_unit @ T2 )
% 4.69/5.03 => ( ( ord_le3507040750410214029t_unit @ S @ T2 )
% 4.69/5.03 => ( ! [X3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ X3 @ ( minus_6452836326544984404t_unit @ T2 @ S ) )
% 4.69/5.03 => ( ( H2 @ X3 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [X3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ X3 @ S )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = ( H2 @ X3 ) ) )
% 4.69/5.03 => ( ( groups5360233303959380816t_assn @ G @ S )
% 4.69/5.03 = ( groups5360233303959380816t_assn @ H2 @ T2 ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_cong_left
% 4.69/5.03 thf(fact_7269_prod_Omono__neutral__cong__left,axiom,
% 4.69/5.03 ! [T2: set_Code_integer,S: set_Code_integer,H2: code_integer > assn,G: code_integer > assn] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ T2 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ S @ T2 )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T2 @ S ) )
% 4.69/5.03 => ( ( H2 @ X3 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ S )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = ( H2 @ X3 ) ) )
% 4.69/5.03 => ( ( groups1304777262505850412r_assn @ G @ S )
% 4.69/5.03 = ( groups1304777262505850412r_assn @ H2 @ T2 ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_cong_left
% 4.69/5.03 thf(fact_7270_prod_Omono__neutral__cong__left,axiom,
% 4.69/5.03 ! [T2: set_int,S: set_int,H2: int > nat,G: int > nat] :
% 4.69/5.03 ( ( finite_finite_int @ T2 )
% 4.69/5.03 => ( ( ord_less_eq_set_int @ S @ T2 )
% 4.69/5.03 => ( ! [X3: int] :
% 4.69/5.03 ( ( member_int @ X3 @ ( minus_minus_set_int @ T2 @ S ) )
% 4.69/5.03 => ( ( H2 @ X3 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ! [X3: int] :
% 4.69/5.03 ( ( member_int @ X3 @ S )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = ( H2 @ X3 ) ) )
% 4.69/5.03 => ( ( groups1707563613775114915nt_nat @ G @ S )
% 4.69/5.03 = ( groups1707563613775114915nt_nat @ H2 @ T2 ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_cong_left
% 4.69/5.03 thf(fact_7271_prod_Omono__neutral__cong__left,axiom,
% 4.69/5.03 ! [T2: set_o,S: set_o,H2: $o > nat,G: $o > nat] :
% 4.69/5.03 ( ( finite_finite_o @ T2 )
% 4.69/5.03 => ( ( ord_less_eq_set_o @ S @ T2 )
% 4.69/5.03 => ( ! [X3: $o] :
% 4.69/5.03 ( ( member_o @ X3 @ ( minus_minus_set_o @ T2 @ S ) )
% 4.69/5.03 => ( ( H2 @ X3 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ! [X3: $o] :
% 4.69/5.03 ( ( member_o @ X3 @ S )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = ( H2 @ X3 ) ) )
% 4.69/5.03 => ( ( groups3504817904513533571_o_nat @ G @ S )
% 4.69/5.03 = ( groups3504817904513533571_o_nat @ H2 @ T2 ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_cong_left
% 4.69/5.03 thf(fact_7272_prod_Omono__neutral__cong__left,axiom,
% 4.69/5.03 ! [T2: set_Product_unit,S: set_Product_unit,H2: product_unit > nat,G: product_unit > nat] :
% 4.69/5.03 ( ( finite4290736615968046902t_unit @ T2 )
% 4.69/5.03 => ( ( ord_le3507040750410214029t_unit @ S @ T2 )
% 4.69/5.03 => ( ! [X3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ X3 @ ( minus_6452836326544984404t_unit @ T2 @ S ) )
% 4.69/5.03 => ( ( H2 @ X3 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ! [X3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ X3 @ S )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = ( H2 @ X3 ) ) )
% 4.69/5.03 => ( ( groups396421249026171384it_nat @ G @ S )
% 4.69/5.03 = ( groups396421249026171384it_nat @ H2 @ T2 ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_cong_left
% 4.69/5.03 thf(fact_7273_prod_Omono__neutral__cong__left,axiom,
% 4.69/5.03 ! [T2: set_Code_integer,S: set_Code_integer,H2: code_integer > nat,G: code_integer > nat] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ T2 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ S @ T2 )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T2 @ S ) )
% 4.69/5.03 => ( ( H2 @ X3 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ S )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = ( H2 @ X3 ) ) )
% 4.69/5.03 => ( ( groups3190895334310489300er_nat @ G @ S )
% 4.69/5.03 = ( groups3190895334310489300er_nat @ H2 @ T2 ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_cong_left
% 4.69/5.03 thf(fact_7274_prod_Omono__neutral__cong__left,axiom,
% 4.69/5.03 ! [T2: set_int,S: set_int,H2: int > int,G: int > int] :
% 4.69/5.03 ( ( finite_finite_int @ T2 )
% 4.69/5.03 => ( ( ord_less_eq_set_int @ S @ T2 )
% 4.69/5.03 => ( ! [X3: int] :
% 4.69/5.03 ( ( member_int @ X3 @ ( minus_minus_set_int @ T2 @ S ) )
% 4.69/5.03 => ( ( H2 @ X3 )
% 4.69/5.03 = one_one_int ) )
% 4.69/5.03 => ( ! [X3: int] :
% 4.69/5.03 ( ( member_int @ X3 @ S )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = ( H2 @ X3 ) ) )
% 4.69/5.03 => ( ( groups1705073143266064639nt_int @ G @ S )
% 4.69/5.03 = ( groups1705073143266064639nt_int @ H2 @ T2 ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_cong_left
% 4.69/5.03 thf(fact_7275_prod_Omono__neutral__cong__left,axiom,
% 4.69/5.03 ! [T2: set_o,S: set_o,H2: $o > int,G: $o > int] :
% 4.69/5.03 ( ( finite_finite_o @ T2 )
% 4.69/5.03 => ( ( ord_less_eq_set_o @ S @ T2 )
% 4.69/5.03 => ( ! [X3: $o] :
% 4.69/5.03 ( ( member_o @ X3 @ ( minus_minus_set_o @ T2 @ S ) )
% 4.69/5.03 => ( ( H2 @ X3 )
% 4.69/5.03 = one_one_int ) )
% 4.69/5.03 => ( ! [X3: $o] :
% 4.69/5.03 ( ( member_o @ X3 @ S )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = ( H2 @ X3 ) ) )
% 4.69/5.03 => ( ( groups3502327434004483295_o_int @ G @ S )
% 4.69/5.03 = ( groups3502327434004483295_o_int @ H2 @ T2 ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_cong_left
% 4.69/5.03 thf(fact_7276_prod_Omono__neutral__cong__right,axiom,
% 4.69/5.03 ! [T2: set_int,S: set_int,G: int > assn,H2: int > assn] :
% 4.69/5.03 ( ( finite_finite_int @ T2 )
% 4.69/5.03 => ( ( ord_less_eq_set_int @ S @ T2 )
% 4.69/5.03 => ( ! [X3: int] :
% 4.69/5.03 ( ( member_int @ X3 @ ( minus_minus_set_int @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [X3: int] :
% 4.69/5.03 ( ( member_int @ X3 @ S )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = ( H2 @ X3 ) ) )
% 4.69/5.03 => ( ( groups7882442080178216443t_assn @ G @ T2 )
% 4.69/5.03 = ( groups7882442080178216443t_assn @ H2 @ S ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_cong_right
% 4.69/5.03 thf(fact_7277_prod_Omono__neutral__cong__right,axiom,
% 4.69/5.03 ! [T2: set_o,S: set_o,G: $o > assn,H2: $o > assn] :
% 4.69/5.03 ( ( finite_finite_o @ T2 )
% 4.69/5.03 => ( ( ord_less_eq_set_o @ S @ T2 )
% 4.69/5.03 => ( ! [X3: $o] :
% 4.69/5.03 ( ( member_o @ X3 @ ( minus_minus_set_o @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [X3: $o] :
% 4.69/5.03 ( ( member_o @ X3 @ S )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = ( H2 @ X3 ) ) )
% 4.69/5.03 => ( ( groups5301882518646026715o_assn @ G @ T2 )
% 4.69/5.03 = ( groups5301882518646026715o_assn @ H2 @ S ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_cong_right
% 4.69/5.03 thf(fact_7278_prod_Omono__neutral__cong__right,axiom,
% 4.69/5.03 ! [T2: set_Product_unit,S: set_Product_unit,G: product_unit > assn,H2: product_unit > assn] :
% 4.69/5.03 ( ( finite4290736615968046902t_unit @ T2 )
% 4.69/5.03 => ( ( ord_le3507040750410214029t_unit @ S @ T2 )
% 4.69/5.03 => ( ! [X3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ X3 @ ( minus_6452836326544984404t_unit @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [X3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ X3 @ S )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = ( H2 @ X3 ) ) )
% 4.69/5.03 => ( ( groups5360233303959380816t_assn @ G @ T2 )
% 4.69/5.03 = ( groups5360233303959380816t_assn @ H2 @ S ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_cong_right
% 4.69/5.03 thf(fact_7279_prod_Omono__neutral__cong__right,axiom,
% 4.69/5.03 ! [T2: set_Code_integer,S: set_Code_integer,G: code_integer > assn,H2: code_integer > assn] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ T2 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ S @ T2 )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ S )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = ( H2 @ X3 ) ) )
% 4.69/5.03 => ( ( groups1304777262505850412r_assn @ G @ T2 )
% 4.69/5.03 = ( groups1304777262505850412r_assn @ H2 @ S ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_cong_right
% 4.69/5.03 thf(fact_7280_prod_Omono__neutral__cong__right,axiom,
% 4.69/5.03 ! [T2: set_int,S: set_int,G: int > nat,H2: int > nat] :
% 4.69/5.03 ( ( finite_finite_int @ T2 )
% 4.69/5.03 => ( ( ord_less_eq_set_int @ S @ T2 )
% 4.69/5.03 => ( ! [X3: int] :
% 4.69/5.03 ( ( member_int @ X3 @ ( minus_minus_set_int @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ! [X3: int] :
% 4.69/5.03 ( ( member_int @ X3 @ S )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = ( H2 @ X3 ) ) )
% 4.69/5.03 => ( ( groups1707563613775114915nt_nat @ G @ T2 )
% 4.69/5.03 = ( groups1707563613775114915nt_nat @ H2 @ S ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_cong_right
% 4.69/5.03 thf(fact_7281_prod_Omono__neutral__cong__right,axiom,
% 4.69/5.03 ! [T2: set_o,S: set_o,G: $o > nat,H2: $o > nat] :
% 4.69/5.03 ( ( finite_finite_o @ T2 )
% 4.69/5.03 => ( ( ord_less_eq_set_o @ S @ T2 )
% 4.69/5.03 => ( ! [X3: $o] :
% 4.69/5.03 ( ( member_o @ X3 @ ( minus_minus_set_o @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ! [X3: $o] :
% 4.69/5.03 ( ( member_o @ X3 @ S )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = ( H2 @ X3 ) ) )
% 4.69/5.03 => ( ( groups3504817904513533571_o_nat @ G @ T2 )
% 4.69/5.03 = ( groups3504817904513533571_o_nat @ H2 @ S ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_cong_right
% 4.69/5.03 thf(fact_7282_prod_Omono__neutral__cong__right,axiom,
% 4.69/5.03 ! [T2: set_Product_unit,S: set_Product_unit,G: product_unit > nat,H2: product_unit > nat] :
% 4.69/5.03 ( ( finite4290736615968046902t_unit @ T2 )
% 4.69/5.03 => ( ( ord_le3507040750410214029t_unit @ S @ T2 )
% 4.69/5.03 => ( ! [X3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ X3 @ ( minus_6452836326544984404t_unit @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ! [X3: product_unit] :
% 4.69/5.03 ( ( member_Product_unit @ X3 @ S )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = ( H2 @ X3 ) ) )
% 4.69/5.03 => ( ( groups396421249026171384it_nat @ G @ T2 )
% 4.69/5.03 = ( groups396421249026171384it_nat @ H2 @ S ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_cong_right
% 4.69/5.03 thf(fact_7283_prod_Omono__neutral__cong__right,axiom,
% 4.69/5.03 ! [T2: set_Code_integer,S: set_Code_integer,G: code_integer > nat,H2: code_integer > nat] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ T2 )
% 4.69/5.03 => ( ( ord_le7084787975880047091nteger @ S @ T2 )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_nat ) )
% 4.69/5.03 => ( ! [X3: code_integer] :
% 4.69/5.03 ( ( member_Code_integer @ X3 @ S )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = ( H2 @ X3 ) ) )
% 4.69/5.03 => ( ( groups3190895334310489300er_nat @ G @ T2 )
% 4.69/5.03 = ( groups3190895334310489300er_nat @ H2 @ S ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_cong_right
% 4.69/5.03 thf(fact_7284_prod_Omono__neutral__cong__right,axiom,
% 4.69/5.03 ! [T2: set_int,S: set_int,G: int > int,H2: int > int] :
% 4.69/5.03 ( ( finite_finite_int @ T2 )
% 4.69/5.03 => ( ( ord_less_eq_set_int @ S @ T2 )
% 4.69/5.03 => ( ! [X3: int] :
% 4.69/5.03 ( ( member_int @ X3 @ ( minus_minus_set_int @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_int ) )
% 4.69/5.03 => ( ! [X3: int] :
% 4.69/5.03 ( ( member_int @ X3 @ S )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = ( H2 @ X3 ) ) )
% 4.69/5.03 => ( ( groups1705073143266064639nt_int @ G @ T2 )
% 4.69/5.03 = ( groups1705073143266064639nt_int @ H2 @ S ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_cong_right
% 4.69/5.03 thf(fact_7285_prod_Omono__neutral__cong__right,axiom,
% 4.69/5.03 ! [T2: set_o,S: set_o,G: $o > int,H2: $o > int] :
% 4.69/5.03 ( ( finite_finite_o @ T2 )
% 4.69/5.03 => ( ( ord_less_eq_set_o @ S @ T2 )
% 4.69/5.03 => ( ! [X3: $o] :
% 4.69/5.03 ( ( member_o @ X3 @ ( minus_minus_set_o @ T2 @ S ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = one_one_int ) )
% 4.69/5.03 => ( ! [X3: $o] :
% 4.69/5.03 ( ( member_o @ X3 @ S )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = ( H2 @ X3 ) ) )
% 4.69/5.03 => ( ( groups3502327434004483295_o_int @ G @ T2 )
% 4.69/5.03 = ( groups3502327434004483295_o_int @ H2 @ S ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_cong_right
% 4.69/5.03 thf(fact_7286_prod_Ounion__inter,axiom,
% 4.69/5.03 ! [A: set_Code_integer,B4: set_Code_integer,G: code_integer > assn] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.03 => ( ( times_times_assn @ ( groups1304777262505850412r_assn @ G @ ( sup_su848401254843788991nteger @ A @ B4 ) ) @ ( groups1304777262505850412r_assn @ G @ ( inf_in1364745209274528805nteger @ A @ B4 ) ) )
% 4.69/5.03 = ( times_times_assn @ ( groups1304777262505850412r_assn @ G @ A ) @ ( groups1304777262505850412r_assn @ G @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.union_inter
% 4.69/5.03 thf(fact_7287_prod_Ounion__inter,axiom,
% 4.69/5.03 ! [A: set_nat,B4: set_nat,G: nat > assn] :
% 4.69/5.03 ( ( finite_finite_nat @ A )
% 4.69/5.03 => ( ( finite_finite_nat @ B4 )
% 4.69/5.03 => ( ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( sup_sup_set_nat @ A @ B4 ) ) @ ( groups6906906614972039071t_assn @ G @ ( inf_inf_set_nat @ A @ B4 ) ) )
% 4.69/5.03 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ A ) @ ( groups6906906614972039071t_assn @ G @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.union_inter
% 4.69/5.03 thf(fact_7288_prod_Ounion__inter,axiom,
% 4.69/5.03 ! [A: set_Code_integer,B4: set_Code_integer,G: code_integer > rat] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.03 => ( ( times_times_rat @ ( groups2555765274223993564er_rat @ G @ ( sup_su848401254843788991nteger @ A @ B4 ) ) @ ( groups2555765274223993564er_rat @ G @ ( inf_in1364745209274528805nteger @ A @ B4 ) ) )
% 4.69/5.03 = ( times_times_rat @ ( groups2555765274223993564er_rat @ G @ A ) @ ( groups2555765274223993564er_rat @ G @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.union_inter
% 4.69/5.03 thf(fact_7289_prod_Ounion__inter,axiom,
% 4.69/5.03 ! [A: set_nat,B4: set_nat,G: nat > rat] :
% 4.69/5.03 ( ( finite_finite_nat @ A )
% 4.69/5.03 => ( ( finite_finite_nat @ B4 )
% 4.69/5.03 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( sup_sup_set_nat @ A @ B4 ) ) @ ( groups73079841787564623at_rat @ G @ ( inf_inf_set_nat @ A @ B4 ) ) )
% 4.69/5.03 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ A ) @ ( groups73079841787564623at_rat @ G @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.union_inter
% 4.69/5.03 thf(fact_7290_prod_Ounion__inter,axiom,
% 4.69/5.03 ! [A: set_Code_integer,B4: set_Code_integer,G: code_integer > nat] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.03 => ( ( times_times_nat @ ( groups3190895334310489300er_nat @ G @ ( sup_su848401254843788991nteger @ A @ B4 ) ) @ ( groups3190895334310489300er_nat @ G @ ( inf_in1364745209274528805nteger @ A @ B4 ) ) )
% 4.69/5.03 = ( times_times_nat @ ( groups3190895334310489300er_nat @ G @ A ) @ ( groups3190895334310489300er_nat @ G @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.union_inter
% 4.69/5.03 thf(fact_7291_prod_Ounion__inter,axiom,
% 4.69/5.03 ! [A: set_Code_integer,B4: set_Code_integer,G: code_integer > int] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.03 => ( ( times_times_int @ ( groups3188404863801439024er_int @ G @ ( sup_su848401254843788991nteger @ A @ B4 ) ) @ ( groups3188404863801439024er_int @ G @ ( inf_in1364745209274528805nteger @ A @ B4 ) ) )
% 4.69/5.03 = ( times_times_int @ ( groups3188404863801439024er_int @ G @ A ) @ ( groups3188404863801439024er_int @ G @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.union_inter
% 4.69/5.03 thf(fact_7292_prod_Ounion__inter,axiom,
% 4.69/5.03 ! [A: set_nat,B4: set_nat,G: nat > int] :
% 4.69/5.03 ( ( finite_finite_nat @ A )
% 4.69/5.03 => ( ( finite_finite_nat @ B4 )
% 4.69/5.03 => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( sup_sup_set_nat @ A @ B4 ) ) @ ( groups705719431365010083at_int @ G @ ( inf_inf_set_nat @ A @ B4 ) ) )
% 4.69/5.03 = ( times_times_int @ ( groups705719431365010083at_int @ G @ A ) @ ( groups705719431365010083at_int @ G @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.union_inter
% 4.69/5.03 thf(fact_7293_prod_Ounion__inter,axiom,
% 4.69/5.03 ! [A: set_nat,B4: set_nat,G: nat > nat] :
% 4.69/5.03 ( ( finite_finite_nat @ A )
% 4.69/5.03 => ( ( finite_finite_nat @ B4 )
% 4.69/5.03 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( sup_sup_set_nat @ A @ B4 ) ) @ ( groups708209901874060359at_nat @ G @ ( inf_inf_set_nat @ A @ B4 ) ) )
% 4.69/5.03 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ A ) @ ( groups708209901874060359at_nat @ G @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.union_inter
% 4.69/5.03 thf(fact_7294_prod_OInt__Diff,axiom,
% 4.69/5.03 ! [A: set_Code_integer,G: code_integer > assn,B4: set_Code_integer] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ( groups1304777262505850412r_assn @ G @ A )
% 4.69/5.03 = ( times_times_assn @ ( groups1304777262505850412r_assn @ G @ ( inf_in1364745209274528805nteger @ A @ B4 ) ) @ ( groups1304777262505850412r_assn @ G @ ( minus_2355218937544613996nteger @ A @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.Int_Diff
% 4.69/5.03 thf(fact_7295_prod_OInt__Diff,axiom,
% 4.69/5.03 ! [A: set_nat,G: nat > assn,B4: set_nat] :
% 4.69/5.03 ( ( finite_finite_nat @ A )
% 4.69/5.03 => ( ( groups6906906614972039071t_assn @ G @ A )
% 4.69/5.03 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( inf_inf_set_nat @ A @ B4 ) ) @ ( groups6906906614972039071t_assn @ G @ ( minus_minus_set_nat @ A @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.Int_Diff
% 4.69/5.03 thf(fact_7296_prod_OInt__Diff,axiom,
% 4.69/5.03 ! [A: set_Code_integer,G: code_integer > rat,B4: set_Code_integer] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ( groups2555765274223993564er_rat @ G @ A )
% 4.69/5.03 = ( times_times_rat @ ( groups2555765274223993564er_rat @ G @ ( inf_in1364745209274528805nteger @ A @ B4 ) ) @ ( groups2555765274223993564er_rat @ G @ ( minus_2355218937544613996nteger @ A @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.Int_Diff
% 4.69/5.03 thf(fact_7297_prod_OInt__Diff,axiom,
% 4.69/5.03 ! [A: set_nat,G: nat > rat,B4: set_nat] :
% 4.69/5.03 ( ( finite_finite_nat @ A )
% 4.69/5.03 => ( ( groups73079841787564623at_rat @ G @ A )
% 4.69/5.03 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( inf_inf_set_nat @ A @ B4 ) ) @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.Int_Diff
% 4.69/5.03 thf(fact_7298_prod_OInt__Diff,axiom,
% 4.69/5.03 ! [A: set_Code_integer,G: code_integer > nat,B4: set_Code_integer] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ( groups3190895334310489300er_nat @ G @ A )
% 4.69/5.03 = ( times_times_nat @ ( groups3190895334310489300er_nat @ G @ ( inf_in1364745209274528805nteger @ A @ B4 ) ) @ ( groups3190895334310489300er_nat @ G @ ( minus_2355218937544613996nteger @ A @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.Int_Diff
% 4.69/5.03 thf(fact_7299_prod_OInt__Diff,axiom,
% 4.69/5.03 ! [A: set_Code_integer,G: code_integer > int,B4: set_Code_integer] :
% 4.69/5.03 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.03 => ( ( groups3188404863801439024er_int @ G @ A )
% 4.69/5.03 = ( times_times_int @ ( groups3188404863801439024er_int @ G @ ( inf_in1364745209274528805nteger @ A @ B4 ) ) @ ( groups3188404863801439024er_int @ G @ ( minus_2355218937544613996nteger @ A @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.Int_Diff
% 4.69/5.03 thf(fact_7300_prod_OInt__Diff,axiom,
% 4.69/5.03 ! [A: set_nat,G: nat > int,B4: set_nat] :
% 4.69/5.03 ( ( finite_finite_nat @ A )
% 4.69/5.03 => ( ( groups705719431365010083at_int @ G @ A )
% 4.69/5.03 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( inf_inf_set_nat @ A @ B4 ) ) @ ( groups705719431365010083at_int @ G @ ( minus_minus_set_nat @ A @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.Int_Diff
% 4.69/5.03 thf(fact_7301_prod_OInt__Diff,axiom,
% 4.69/5.03 ! [A: set_nat,G: nat > nat,B4: set_nat] :
% 4.69/5.03 ( ( finite_finite_nat @ A )
% 4.69/5.03 => ( ( groups708209901874060359at_nat @ G @ A )
% 4.69/5.03 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( inf_inf_set_nat @ A @ B4 ) ) @ ( groups708209901874060359at_nat @ G @ ( minus_minus_set_nat @ A @ B4 ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.Int_Diff
% 4.69/5.03 thf(fact_7302_prod_Omono__neutral__cong,axiom,
% 4.69/5.03 ! [T2: set_int,S: set_int,H2: int > assn,G: int > assn] :
% 4.69/5.03 ( ( finite_finite_int @ T2 )
% 4.69/5.03 => ( ( finite_finite_int @ S )
% 4.69/5.03 => ( ! [I3: int] :
% 4.69/5.03 ( ( member_int @ I3 @ ( minus_minus_set_int @ T2 @ S ) )
% 4.69/5.03 => ( ( H2 @ I3 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [I3: int] :
% 4.69/5.03 ( ( member_int @ I3 @ ( minus_minus_set_int @ S @ T2 ) )
% 4.69/5.03 => ( ( G @ I3 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [X3: int] :
% 4.69/5.03 ( ( member_int @ X3 @ ( inf_inf_set_int @ S @ T2 ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = ( H2 @ X3 ) ) )
% 4.69/5.03 => ( ( groups7882442080178216443t_assn @ G @ S )
% 4.69/5.03 = ( groups7882442080178216443t_assn @ H2 @ T2 ) ) ) ) ) ) ) ).
% 4.69/5.03
% 4.69/5.03 % prod.mono_neutral_cong
% 4.69/5.03 thf(fact_7303_prod_Omono__neutral__cong,axiom,
% 4.69/5.03 ! [T2: set_o,S: set_o,H2: $o > assn,G: $o > assn] :
% 4.69/5.03 ( ( finite_finite_o @ T2 )
% 4.69/5.03 => ( ( finite_finite_o @ S )
% 4.69/5.03 => ( ! [I3: $o] :
% 4.69/5.03 ( ( member_o @ I3 @ ( minus_minus_set_o @ T2 @ S ) )
% 4.69/5.03 => ( ( H2 @ I3 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [I3: $o] :
% 4.69/5.03 ( ( member_o @ I3 @ ( minus_minus_set_o @ S @ T2 ) )
% 4.69/5.03 => ( ( G @ I3 )
% 4.69/5.03 = one_one_assn ) )
% 4.69/5.03 => ( ! [X3: $o] :
% 4.69/5.03 ( ( member_o @ X3 @ ( inf_inf_set_o @ S @ T2 ) )
% 4.69/5.03 => ( ( G @ X3 )
% 4.69/5.03 = ( H2 @ X3 ) ) )
% 4.69/5.03 => ( ( groups5301882518646026715o_assn @ G @ S )
% 4.69/5.04 = ( groups5301882518646026715o_assn @ H2 @ T2 ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.mono_neutral_cong
% 4.69/5.04 thf(fact_7304_prod_Omono__neutral__cong,axiom,
% 4.69/5.04 ! [T2: set_Product_unit,S: set_Product_unit,H2: product_unit > assn,G: product_unit > assn] :
% 4.69/5.04 ( ( finite4290736615968046902t_unit @ T2 )
% 4.69/5.04 => ( ( finite4290736615968046902t_unit @ S )
% 4.69/5.04 => ( ! [I3: product_unit] :
% 4.69/5.04 ( ( member_Product_unit @ I3 @ ( minus_6452836326544984404t_unit @ T2 @ S ) )
% 4.69/5.04 => ( ( H2 @ I3 )
% 4.69/5.04 = one_one_assn ) )
% 4.69/5.04 => ( ! [I3: product_unit] :
% 4.69/5.04 ( ( member_Product_unit @ I3 @ ( minus_6452836326544984404t_unit @ S @ T2 ) )
% 4.69/5.04 => ( ( G @ I3 )
% 4.69/5.04 = one_one_assn ) )
% 4.69/5.04 => ( ! [X3: product_unit] :
% 4.69/5.04 ( ( member_Product_unit @ X3 @ ( inf_in4660618365625256667t_unit @ S @ T2 ) )
% 4.69/5.04 => ( ( G @ X3 )
% 4.69/5.04 = ( H2 @ X3 ) ) )
% 4.69/5.04 => ( ( groups5360233303959380816t_assn @ G @ S )
% 4.69/5.04 = ( groups5360233303959380816t_assn @ H2 @ T2 ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.mono_neutral_cong
% 4.69/5.04 thf(fact_7305_prod_Omono__neutral__cong,axiom,
% 4.69/5.04 ! [T2: set_Code_integer,S: set_Code_integer,H2: code_integer > assn,G: code_integer > assn] :
% 4.69/5.04 ( ( finite6017078050557962740nteger @ T2 )
% 4.69/5.04 => ( ( finite6017078050557962740nteger @ S )
% 4.69/5.04 => ( ! [I3: code_integer] :
% 4.69/5.04 ( ( member_Code_integer @ I3 @ ( minus_2355218937544613996nteger @ T2 @ S ) )
% 4.69/5.04 => ( ( H2 @ I3 )
% 4.69/5.04 = one_one_assn ) )
% 4.69/5.04 => ( ! [I3: code_integer] :
% 4.69/5.04 ( ( member_Code_integer @ I3 @ ( minus_2355218937544613996nteger @ S @ T2 ) )
% 4.69/5.04 => ( ( G @ I3 )
% 4.69/5.04 = one_one_assn ) )
% 4.69/5.04 => ( ! [X3: code_integer] :
% 4.69/5.04 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ S @ T2 ) )
% 4.69/5.04 => ( ( G @ X3 )
% 4.69/5.04 = ( H2 @ X3 ) ) )
% 4.69/5.04 => ( ( groups1304777262505850412r_assn @ G @ S )
% 4.69/5.04 = ( groups1304777262505850412r_assn @ H2 @ T2 ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.mono_neutral_cong
% 4.69/5.04 thf(fact_7306_prod_Omono__neutral__cong,axiom,
% 4.69/5.04 ! [T2: set_int,S: set_int,H2: int > nat,G: int > nat] :
% 4.69/5.04 ( ( finite_finite_int @ T2 )
% 4.69/5.04 => ( ( finite_finite_int @ S )
% 4.69/5.04 => ( ! [I3: int] :
% 4.69/5.04 ( ( member_int @ I3 @ ( minus_minus_set_int @ T2 @ S ) )
% 4.69/5.04 => ( ( H2 @ I3 )
% 4.69/5.04 = one_one_nat ) )
% 4.69/5.04 => ( ! [I3: int] :
% 4.69/5.04 ( ( member_int @ I3 @ ( minus_minus_set_int @ S @ T2 ) )
% 4.69/5.04 => ( ( G @ I3 )
% 4.69/5.04 = one_one_nat ) )
% 4.69/5.04 => ( ! [X3: int] :
% 4.69/5.04 ( ( member_int @ X3 @ ( inf_inf_set_int @ S @ T2 ) )
% 4.69/5.04 => ( ( G @ X3 )
% 4.69/5.04 = ( H2 @ X3 ) ) )
% 4.69/5.04 => ( ( groups1707563613775114915nt_nat @ G @ S )
% 4.69/5.04 = ( groups1707563613775114915nt_nat @ H2 @ T2 ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.mono_neutral_cong
% 4.69/5.04 thf(fact_7307_prod_Omono__neutral__cong,axiom,
% 4.69/5.04 ! [T2: set_o,S: set_o,H2: $o > nat,G: $o > nat] :
% 4.69/5.04 ( ( finite_finite_o @ T2 )
% 4.69/5.04 => ( ( finite_finite_o @ S )
% 4.69/5.04 => ( ! [I3: $o] :
% 4.69/5.04 ( ( member_o @ I3 @ ( minus_minus_set_o @ T2 @ S ) )
% 4.69/5.04 => ( ( H2 @ I3 )
% 4.69/5.04 = one_one_nat ) )
% 4.69/5.04 => ( ! [I3: $o] :
% 4.69/5.04 ( ( member_o @ I3 @ ( minus_minus_set_o @ S @ T2 ) )
% 4.69/5.04 => ( ( G @ I3 )
% 4.69/5.04 = one_one_nat ) )
% 4.69/5.04 => ( ! [X3: $o] :
% 4.69/5.04 ( ( member_o @ X3 @ ( inf_inf_set_o @ S @ T2 ) )
% 4.69/5.04 => ( ( G @ X3 )
% 4.69/5.04 = ( H2 @ X3 ) ) )
% 4.69/5.04 => ( ( groups3504817904513533571_o_nat @ G @ S )
% 4.69/5.04 = ( groups3504817904513533571_o_nat @ H2 @ T2 ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.mono_neutral_cong
% 4.69/5.04 thf(fact_7308_prod_Omono__neutral__cong,axiom,
% 4.69/5.04 ! [T2: set_Product_unit,S: set_Product_unit,H2: product_unit > nat,G: product_unit > nat] :
% 4.69/5.04 ( ( finite4290736615968046902t_unit @ T2 )
% 4.69/5.04 => ( ( finite4290736615968046902t_unit @ S )
% 4.69/5.04 => ( ! [I3: product_unit] :
% 4.69/5.04 ( ( member_Product_unit @ I3 @ ( minus_6452836326544984404t_unit @ T2 @ S ) )
% 4.69/5.04 => ( ( H2 @ I3 )
% 4.69/5.04 = one_one_nat ) )
% 4.69/5.04 => ( ! [I3: product_unit] :
% 4.69/5.04 ( ( member_Product_unit @ I3 @ ( minus_6452836326544984404t_unit @ S @ T2 ) )
% 4.69/5.04 => ( ( G @ I3 )
% 4.69/5.04 = one_one_nat ) )
% 4.69/5.04 => ( ! [X3: product_unit] :
% 4.69/5.04 ( ( member_Product_unit @ X3 @ ( inf_in4660618365625256667t_unit @ S @ T2 ) )
% 4.69/5.04 => ( ( G @ X3 )
% 4.69/5.04 = ( H2 @ X3 ) ) )
% 4.69/5.04 => ( ( groups396421249026171384it_nat @ G @ S )
% 4.69/5.04 = ( groups396421249026171384it_nat @ H2 @ T2 ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.mono_neutral_cong
% 4.69/5.04 thf(fact_7309_prod_Omono__neutral__cong,axiom,
% 4.69/5.04 ! [T2: set_Code_integer,S: set_Code_integer,H2: code_integer > nat,G: code_integer > nat] :
% 4.69/5.04 ( ( finite6017078050557962740nteger @ T2 )
% 4.69/5.04 => ( ( finite6017078050557962740nteger @ S )
% 4.69/5.04 => ( ! [I3: code_integer] :
% 4.69/5.04 ( ( member_Code_integer @ I3 @ ( minus_2355218937544613996nteger @ T2 @ S ) )
% 4.69/5.04 => ( ( H2 @ I3 )
% 4.69/5.04 = one_one_nat ) )
% 4.69/5.04 => ( ! [I3: code_integer] :
% 4.69/5.04 ( ( member_Code_integer @ I3 @ ( minus_2355218937544613996nteger @ S @ T2 ) )
% 4.69/5.04 => ( ( G @ I3 )
% 4.69/5.04 = one_one_nat ) )
% 4.69/5.04 => ( ! [X3: code_integer] :
% 4.69/5.04 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ S @ T2 ) )
% 4.69/5.04 => ( ( G @ X3 )
% 4.69/5.04 = ( H2 @ X3 ) ) )
% 4.69/5.04 => ( ( groups3190895334310489300er_nat @ G @ S )
% 4.69/5.04 = ( groups3190895334310489300er_nat @ H2 @ T2 ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.mono_neutral_cong
% 4.69/5.04 thf(fact_7310_prod_Omono__neutral__cong,axiom,
% 4.69/5.04 ! [T2: set_int,S: set_int,H2: int > int,G: int > int] :
% 4.69/5.04 ( ( finite_finite_int @ T2 )
% 4.69/5.04 => ( ( finite_finite_int @ S )
% 4.69/5.04 => ( ! [I3: int] :
% 4.69/5.04 ( ( member_int @ I3 @ ( minus_minus_set_int @ T2 @ S ) )
% 4.69/5.04 => ( ( H2 @ I3 )
% 4.69/5.04 = one_one_int ) )
% 4.69/5.04 => ( ! [I3: int] :
% 4.69/5.04 ( ( member_int @ I3 @ ( minus_minus_set_int @ S @ T2 ) )
% 4.69/5.04 => ( ( G @ I3 )
% 4.69/5.04 = one_one_int ) )
% 4.69/5.04 => ( ! [X3: int] :
% 4.69/5.04 ( ( member_int @ X3 @ ( inf_inf_set_int @ S @ T2 ) )
% 4.69/5.04 => ( ( G @ X3 )
% 4.69/5.04 = ( H2 @ X3 ) ) )
% 4.69/5.04 => ( ( groups1705073143266064639nt_int @ G @ S )
% 4.69/5.04 = ( groups1705073143266064639nt_int @ H2 @ T2 ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.mono_neutral_cong
% 4.69/5.04 thf(fact_7311_prod_Omono__neutral__cong,axiom,
% 4.69/5.04 ! [T2: set_o,S: set_o,H2: $o > int,G: $o > int] :
% 4.69/5.04 ( ( finite_finite_o @ T2 )
% 4.69/5.04 => ( ( finite_finite_o @ S )
% 4.69/5.04 => ( ! [I3: $o] :
% 4.69/5.04 ( ( member_o @ I3 @ ( minus_minus_set_o @ T2 @ S ) )
% 4.69/5.04 => ( ( H2 @ I3 )
% 4.69/5.04 = one_one_int ) )
% 4.69/5.04 => ( ! [I3: $o] :
% 4.69/5.04 ( ( member_o @ I3 @ ( minus_minus_set_o @ S @ T2 ) )
% 4.69/5.04 => ( ( G @ I3 )
% 4.69/5.04 = one_one_int ) )
% 4.69/5.04 => ( ! [X3: $o] :
% 4.69/5.04 ( ( member_o @ X3 @ ( inf_inf_set_o @ S @ T2 ) )
% 4.69/5.04 => ( ( G @ X3 )
% 4.69/5.04 = ( H2 @ X3 ) ) )
% 4.69/5.04 => ( ( groups3502327434004483295_o_int @ G @ S )
% 4.69/5.04 = ( groups3502327434004483295_o_int @ H2 @ T2 ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.mono_neutral_cong
% 4.69/5.04 thf(fact_7312_prod_Oeq__fold,axiom,
% 4.69/5.04 ( groups708209901874060359at_nat
% 4.69/5.04 = ( ^ [G3: nat > nat] : ( finite_fold_nat_nat @ ( comp_nat_nat_nat_nat @ times_times_nat @ G3 ) @ one_one_nat ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.eq_fold
% 4.69/5.04 thf(fact_7313_sum__bounded__above,axiom,
% 4.69/5.04 ! [A: set_nat,F: nat > code_integer,K4: code_integer] :
% 4.69/5.04 ( ! [I3: nat] :
% 4.69/5.04 ( ( member_nat @ I3 @ A )
% 4.69/5.04 => ( ord_le3102999989581377725nteger @ ( F @ I3 ) @ K4 ) )
% 4.69/5.04 => ( ord_le3102999989581377725nteger @ ( groups7501900531339628137nteger @ F @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_nat @ A ) ) @ K4 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sum_bounded_above
% 4.69/5.04 thf(fact_7314_sum__bounded__above,axiom,
% 4.69/5.04 ! [A: set_int,F: int > code_integer,K4: code_integer] :
% 4.69/5.04 ( ! [I3: int] :
% 4.69/5.04 ( ( member_int @ I3 @ A )
% 4.69/5.04 => ( ord_le3102999989581377725nteger @ ( F @ I3 ) @ K4 ) )
% 4.69/5.04 => ( ord_le3102999989581377725nteger @ ( groups7873554091576472773nteger @ F @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_int @ A ) ) @ K4 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sum_bounded_above
% 4.69/5.04 thf(fact_7315_sum__bounded__above,axiom,
% 4.69/5.04 ! [A: set_o,F: $o > code_integer,K4: code_integer] :
% 4.69/5.04 ( ! [I3: $o] :
% 4.69/5.04 ( ( member_o @ I3 @ A )
% 4.69/5.04 => ( ord_le3102999989581377725nteger @ ( F @ I3 ) @ K4 ) )
% 4.69/5.04 => ( ord_le3102999989581377725nteger @ ( groups4406642042086082107nteger @ F @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_o @ A ) ) @ K4 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sum_bounded_above
% 4.69/5.04 thf(fact_7316_sum__bounded__above,axiom,
% 4.69/5.04 ! [A: set_Product_unit,F: product_unit > code_integer,K4: code_integer] :
% 4.69/5.04 ( ! [I3: product_unit] :
% 4.69/5.04 ( ( member_Product_unit @ I3 @ A )
% 4.69/5.04 => ( ord_le3102999989581377725nteger @ ( F @ I3 ) @ K4 ) )
% 4.69/5.04 => ( ord_le3102999989581377725nteger @ ( groups5393439102872367408nteger @ F @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite410649719033368117t_unit @ A ) ) @ K4 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sum_bounded_above
% 4.69/5.04 thf(fact_7317_sum__bounded__above,axiom,
% 4.69/5.04 ! [A: set_nat,F: nat > rat,K4: rat] :
% 4.69/5.04 ( ! [I3: nat] :
% 4.69/5.04 ( ( member_nat @ I3 @ A )
% 4.69/5.04 => ( ord_less_eq_rat @ ( F @ I3 ) @ K4 ) )
% 4.69/5.04 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A ) ) @ K4 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sum_bounded_above
% 4.69/5.04 thf(fact_7318_sum__bounded__above,axiom,
% 4.69/5.04 ! [A: set_int,F: int > rat,K4: rat] :
% 4.69/5.04 ( ! [I3: int] :
% 4.69/5.04 ( ( member_int @ I3 @ A )
% 4.69/5.04 => ( ord_less_eq_rat @ ( F @ I3 ) @ K4 ) )
% 4.69/5.04 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A ) ) @ K4 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sum_bounded_above
% 4.69/5.04 thf(fact_7319_sum__bounded__above,axiom,
% 4.69/5.04 ! [A: set_o,F: $o > rat,K4: rat] :
% 4.69/5.04 ( ! [I3: $o] :
% 4.69/5.04 ( ( member_o @ I3 @ A )
% 4.69/5.04 => ( ord_less_eq_rat @ ( F @ I3 ) @ K4 ) )
% 4.69/5.04 => ( ord_less_eq_rat @ ( groups7872700643590313910_o_rat @ F @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_o @ A ) ) @ K4 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sum_bounded_above
% 4.69/5.04 thf(fact_7320_sum__bounded__above,axiom,
% 4.69/5.04 ! [A: set_Product_unit,F: product_unit > rat,K4: rat] :
% 4.69/5.04 ( ! [I3: product_unit] :
% 4.69/5.04 ( ( member_Product_unit @ I3 @ A )
% 4.69/5.04 => ( ord_less_eq_rat @ ( F @ I3 ) @ K4 ) )
% 4.69/5.04 => ( ord_less_eq_rat @ ( groups8131667117488461483it_rat @ F @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite410649719033368117t_unit @ A ) ) @ K4 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sum_bounded_above
% 4.69/5.04 thf(fact_7321_sum__bounded__above,axiom,
% 4.69/5.04 ! [A: set_int,F: int > nat,K4: nat] :
% 4.69/5.04 ( ! [I3: int] :
% 4.69/5.04 ( ( member_int @ I3 @ A )
% 4.69/5.04 => ( ord_less_eq_nat @ ( F @ I3 ) @ K4 ) )
% 4.69/5.04 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_int @ A ) ) @ K4 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sum_bounded_above
% 4.69/5.04 thf(fact_7322_sum__bounded__above,axiom,
% 4.69/5.04 ! [A: set_o,F: $o > nat,K4: nat] :
% 4.69/5.04 ( ! [I3: $o] :
% 4.69/5.04 ( ( member_o @ I3 @ A )
% 4.69/5.04 => ( ord_less_eq_nat @ ( F @ I3 ) @ K4 ) )
% 4.69/5.04 => ( ord_less_eq_nat @ ( groups8507830703676809646_o_nat @ F @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_o @ A ) ) @ K4 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sum_bounded_above
% 4.69/5.04 thf(fact_7323_sum__bounded__below,axiom,
% 4.69/5.04 ! [A: set_nat,K4: code_integer,F: nat > code_integer] :
% 4.69/5.04 ( ! [I3: nat] :
% 4.69/5.04 ( ( member_nat @ I3 @ A )
% 4.69/5.04 => ( ord_le3102999989581377725nteger @ K4 @ ( F @ I3 ) ) )
% 4.69/5.04 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_nat @ A ) ) @ K4 ) @ ( groups7501900531339628137nteger @ F @ A ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sum_bounded_below
% 4.69/5.04 thf(fact_7324_sum__bounded__below,axiom,
% 4.69/5.04 ! [A: set_int,K4: code_integer,F: int > code_integer] :
% 4.69/5.04 ( ! [I3: int] :
% 4.69/5.04 ( ( member_int @ I3 @ A )
% 4.69/5.04 => ( ord_le3102999989581377725nteger @ K4 @ ( F @ I3 ) ) )
% 4.69/5.04 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_int @ A ) ) @ K4 ) @ ( groups7873554091576472773nteger @ F @ A ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sum_bounded_below
% 4.69/5.04 thf(fact_7325_sum__bounded__below,axiom,
% 4.69/5.04 ! [A: set_o,K4: code_integer,F: $o > code_integer] :
% 4.69/5.04 ( ! [I3: $o] :
% 4.69/5.04 ( ( member_o @ I3 @ A )
% 4.69/5.04 => ( ord_le3102999989581377725nteger @ K4 @ ( F @ I3 ) ) )
% 4.69/5.04 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_o @ A ) ) @ K4 ) @ ( groups4406642042086082107nteger @ F @ A ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sum_bounded_below
% 4.69/5.04 thf(fact_7326_sum__bounded__below,axiom,
% 4.69/5.04 ! [A: set_Product_unit,K4: code_integer,F: product_unit > code_integer] :
% 4.69/5.04 ( ! [I3: product_unit] :
% 4.69/5.04 ( ( member_Product_unit @ I3 @ A )
% 4.69/5.04 => ( ord_le3102999989581377725nteger @ K4 @ ( F @ I3 ) ) )
% 4.69/5.04 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite410649719033368117t_unit @ A ) ) @ K4 ) @ ( groups5393439102872367408nteger @ F @ A ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sum_bounded_below
% 4.69/5.04 thf(fact_7327_sum__bounded__below,axiom,
% 4.69/5.04 ! [A: set_nat,K4: rat,F: nat > rat] :
% 4.69/5.04 ( ! [I3: nat] :
% 4.69/5.04 ( ( member_nat @ I3 @ A )
% 4.69/5.04 => ( ord_less_eq_rat @ K4 @ ( F @ I3 ) ) )
% 4.69/5.04 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A ) ) @ K4 ) @ ( groups2906978787729119204at_rat @ F @ A ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sum_bounded_below
% 4.69/5.04 thf(fact_7328_sum__bounded__below,axiom,
% 4.69/5.04 ! [A: set_int,K4: rat,F: int > rat] :
% 4.69/5.04 ( ! [I3: int] :
% 4.69/5.04 ( ( member_int @ I3 @ A )
% 4.69/5.04 => ( ord_less_eq_rat @ K4 @ ( F @ I3 ) ) )
% 4.69/5.04 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A ) ) @ K4 ) @ ( groups3906332499630173760nt_rat @ F @ A ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sum_bounded_below
% 4.69/5.04 thf(fact_7329_sum__bounded__below,axiom,
% 4.69/5.04 ! [A: set_o,K4: rat,F: $o > rat] :
% 4.69/5.04 ( ! [I3: $o] :
% 4.69/5.04 ( ( member_o @ I3 @ A )
% 4.69/5.04 => ( ord_less_eq_rat @ K4 @ ( F @ I3 ) ) )
% 4.69/5.04 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_o @ A ) ) @ K4 ) @ ( groups7872700643590313910_o_rat @ F @ A ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sum_bounded_below
% 4.69/5.04 thf(fact_7330_sum__bounded__below,axiom,
% 4.69/5.04 ! [A: set_Product_unit,K4: rat,F: product_unit > rat] :
% 4.69/5.04 ( ! [I3: product_unit] :
% 4.69/5.04 ( ( member_Product_unit @ I3 @ A )
% 4.69/5.04 => ( ord_less_eq_rat @ K4 @ ( F @ I3 ) ) )
% 4.69/5.04 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite410649719033368117t_unit @ A ) ) @ K4 ) @ ( groups8131667117488461483it_rat @ F @ A ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sum_bounded_below
% 4.69/5.04 thf(fact_7331_sum__bounded__below,axiom,
% 4.69/5.04 ! [A: set_int,K4: nat,F: int > nat] :
% 4.69/5.04 ( ! [I3: int] :
% 4.69/5.04 ( ( member_int @ I3 @ A )
% 4.69/5.04 => ( ord_less_eq_nat @ K4 @ ( F @ I3 ) ) )
% 4.69/5.04 => ( ord_less_eq_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_int @ A ) ) @ K4 ) @ ( groups4541462559716669496nt_nat @ F @ A ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sum_bounded_below
% 4.69/5.04 thf(fact_7332_sum__bounded__below,axiom,
% 4.69/5.04 ! [A: set_o,K4: nat,F: $o > nat] :
% 4.69/5.04 ( ! [I3: $o] :
% 4.69/5.04 ( ( member_o @ I3 @ A )
% 4.69/5.04 => ( ord_less_eq_nat @ K4 @ ( F @ I3 ) ) )
% 4.69/5.04 => ( ord_less_eq_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_o @ A ) ) @ K4 ) @ ( groups8507830703676809646_o_nat @ F @ A ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sum_bounded_below
% 4.69/5.04 thf(fact_7333_gbinomial__absorb__comp,axiom,
% 4.69/5.04 ! [A2: rat,K3: nat] :
% 4.69/5.04 ( ( times_times_rat @ ( minus_minus_rat @ A2 @ ( semiri681578069525770553at_rat @ K3 ) ) @ ( gbinomial_rat @ A2 @ K3 ) )
% 4.69/5.04 = ( times_times_rat @ A2 @ ( gbinomial_rat @ ( minus_minus_rat @ A2 @ one_one_rat ) @ K3 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % gbinomial_absorb_comp
% 4.69/5.04 thf(fact_7334_gbinomial__mult__1,axiom,
% 4.69/5.04 ! [A2: rat,K3: nat] :
% 4.69/5.04 ( ( times_times_rat @ A2 @ ( gbinomial_rat @ A2 @ K3 ) )
% 4.69/5.04 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( gbinomial_rat @ A2 @ K3 ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K3 ) ) @ ( gbinomial_rat @ A2 @ ( suc @ K3 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % gbinomial_mult_1
% 4.69/5.04 thf(fact_7335_gbinomial__mult__1_H,axiom,
% 4.69/5.04 ! [A2: rat,K3: nat] :
% 4.69/5.04 ( ( times_times_rat @ ( gbinomial_rat @ A2 @ K3 ) @ A2 )
% 4.69/5.04 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( gbinomial_rat @ A2 @ K3 ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K3 ) ) @ ( gbinomial_rat @ A2 @ ( suc @ K3 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % gbinomial_mult_1'
% 4.69/5.04 thf(fact_7336_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 4.69/5.04 ! [X: set_Pr4532377907799695533_nat_o,Y: set_Pr4532377907799695533_nat_o] :
% 4.69/5.04 ( ( ( inf_in1906310914598751387_nat_o @ X @ Y )
% 4.69/5.04 = bot_bo7824918357723582233_nat_o )
% 4.69/5.04 => ( ( ( sup_su5209123915105501825_nat_o @ X @ Y )
% 4.69/5.04 = top_to4869887016220417533_nat_o )
% 4.69/5.04 => ( ( uminus5254974436814262692_nat_o @ X )
% 4.69/5.04 = Y ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % boolean_algebra_class.boolean_algebra.compl_unique
% 4.69/5.04 thf(fact_7337_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 4.69/5.04 ! [X: set_Product_unit,Y: set_Product_unit] :
% 4.69/5.04 ( ( ( inf_in4660618365625256667t_unit @ X @ Y )
% 4.69/5.04 = bot_bo3957492148770167129t_unit )
% 4.69/5.04 => ( ( ( sup_su793286257634532545t_unit @ X @ Y )
% 4.69/5.04 = top_to1996260823553986621t_unit )
% 4.69/5.04 => ( ( uminus5944136376168626660t_unit @ X )
% 4.69/5.04 = Y ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % boolean_algebra_class.boolean_algebra.compl_unique
% 4.69/5.04 thf(fact_7338_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 4.69/5.04 ! [X: set_o,Y: set_o] :
% 4.69/5.04 ( ( ( inf_inf_set_o @ X @ Y )
% 4.69/5.04 = bot_bot_set_o )
% 4.69/5.04 => ( ( ( sup_sup_set_o @ X @ Y )
% 4.69/5.04 = top_top_set_o )
% 4.69/5.04 => ( ( uminus_uminus_set_o @ X )
% 4.69/5.04 = Y ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % boolean_algebra_class.boolean_algebra.compl_unique
% 4.69/5.04 thf(fact_7339_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 4.69/5.04 ! [X: set_nat,Y: set_nat] :
% 4.69/5.04 ( ( ( inf_inf_set_nat @ X @ Y )
% 4.69/5.04 = bot_bot_set_nat )
% 4.69/5.04 => ( ( ( sup_sup_set_nat @ X @ Y )
% 4.69/5.04 = top_top_set_nat )
% 4.69/5.04 => ( ( uminus5710092332889474511et_nat @ X )
% 4.69/5.04 = Y ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % boolean_algebra_class.boolean_algebra.compl_unique
% 4.69/5.04 thf(fact_7340_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 4.69/5.04 ! [X: set_int,Y: set_int] :
% 4.69/5.04 ( ( ( inf_inf_set_int @ X @ Y )
% 4.69/5.04 = bot_bot_set_int )
% 4.69/5.04 => ( ( ( sup_sup_set_int @ X @ Y )
% 4.69/5.04 = top_top_set_int )
% 4.69/5.04 => ( ( uminus1532241313380277803et_int @ X )
% 4.69/5.04 = Y ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % boolean_algebra_class.boolean_algebra.compl_unique
% 4.69/5.04 thf(fact_7341_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 4.69/5.04 ! [X: assn,Y: assn] :
% 4.69/5.04 ( ( ( inf_inf_assn @ X @ Y )
% 4.69/5.04 = bot_bot_assn )
% 4.69/5.04 => ( ( ( sup_sup_assn @ X @ Y )
% 4.69/5.04 = top_top_assn )
% 4.69/5.04 => ( ( uminus_uminus_assn @ X )
% 4.69/5.04 = Y ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % boolean_algebra_class.boolean_algebra.compl_unique
% 4.69/5.04 thf(fact_7342_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 4.69/5.04 ! [X: product_unit,Y: product_unit] :
% 4.69/5.04 ( ( ( inf_inf_Product_unit @ X @ Y )
% 4.69/5.04 = bot_bot_Product_unit )
% 4.69/5.04 => ( ( ( sup_sup_Product_unit @ X @ Y )
% 4.69/5.04 = top_top_Product_unit )
% 4.69/5.04 => ( ( uminus2952777764628376836t_unit @ X )
% 4.69/5.04 = Y ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % boolean_algebra_class.boolean_algebra.compl_unique
% 4.69/5.04 thf(fact_7343_prod__mono__strict,axiom,
% 4.69/5.04 ! [A: set_Code_integer,F: code_integer > code_integer,G: code_integer > code_integer] :
% 4.69/5.04 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.04 => ( ! [I3: code_integer] :
% 4.69/5.04 ( ( member_Code_integer @ I3 @ A )
% 4.69/5.04 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 4.69/5.04 & ( ord_le6747313008572928689nteger @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 4.69/5.04 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/5.04 => ( ord_le6747313008572928689nteger @ ( groups3674199335183972705nteger @ F @ A ) @ ( groups3674199335183972705nteger @ G @ A ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod_mono_strict
% 4.69/5.04 thf(fact_7344_prod__mono__strict,axiom,
% 4.69/5.04 ! [A: set_Product_unit,F: product_unit > code_integer,G: product_unit > code_integer] :
% 4.69/5.04 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.04 => ( ! [I3: product_unit] :
% 4.69/5.04 ( ( member_Product_unit @ I3 @ A )
% 4.69/5.04 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 4.69/5.04 & ( ord_le6747313008572928689nteger @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 4.69/5.04 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.04 => ( ord_le6747313008572928689nteger @ ( groups8185359811944078981nteger @ F @ A ) @ ( groups8185359811944078981nteger @ G @ A ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod_mono_strict
% 4.69/5.04 thf(fact_7345_prod__mono__strict,axiom,
% 4.69/5.04 ! [A: set_o,F: $o > code_integer,G: $o > code_integer] :
% 4.69/5.04 ( ( finite_finite_o @ A )
% 4.69/5.04 => ( ! [I3: $o] :
% 4.69/5.04 ( ( member_o @ I3 @ A )
% 4.69/5.04 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 4.69/5.04 & ( ord_le6747313008572928689nteger @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 4.69/5.04 => ( ( A != bot_bot_set_o )
% 4.69/5.04 => ( ord_le6747313008572928689nteger @ ( groups7694694392188491536nteger @ F @ A ) @ ( groups7694694392188491536nteger @ G @ A ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod_mono_strict
% 4.69/5.04 thf(fact_7346_prod__mono__strict,axiom,
% 4.69/5.04 ! [A: set_nat,F: nat > code_integer,G: nat > code_integer] :
% 4.69/5.04 ( ( finite_finite_nat @ A )
% 4.69/5.04 => ( ! [I3: nat] :
% 4.69/5.04 ( ( member_nat @ I3 @ A )
% 4.69/5.04 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 4.69/5.04 & ( ord_le6747313008572928689nteger @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 4.69/5.04 => ( ( A != bot_bot_set_nat )
% 4.69/5.04 => ( ord_le6747313008572928689nteger @ ( groups3455450783089532116nteger @ F @ A ) @ ( groups3455450783089532116nteger @ G @ A ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod_mono_strict
% 4.69/5.04 thf(fact_7347_prod__mono__strict,axiom,
% 4.69/5.04 ! [A: set_int,F: int > code_integer,G: int > code_integer] :
% 4.69/5.04 ( ( finite_finite_int @ A )
% 4.69/5.04 => ( ! [I3: int] :
% 4.69/5.04 ( ( member_int @ I3 @ A )
% 4.69/5.04 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 4.69/5.04 & ( ord_le6747313008572928689nteger @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 4.69/5.04 => ( ( A != bot_bot_set_int )
% 4.69/5.04 => ( ord_le6747313008572928689nteger @ ( groups3827104343326376752nteger @ F @ A ) @ ( groups3827104343326376752nteger @ G @ A ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod_mono_strict
% 4.69/5.04 thf(fact_7348_prod__mono__strict,axiom,
% 4.69/5.04 ! [A: set_Code_integer,F: code_integer > rat,G: code_integer > rat] :
% 4.69/5.04 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.04 => ( ! [I3: code_integer] :
% 4.69/5.04 ( ( member_Code_integer @ I3 @ A )
% 4.69/5.04 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 4.69/5.04 & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 4.69/5.04 => ( ( A != bot_bo3990330152332043303nteger )
% 4.69/5.04 => ( ord_less_rat @ ( groups2555765274223993564er_rat @ F @ A ) @ ( groups2555765274223993564er_rat @ G @ A ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod_mono_strict
% 4.69/5.04 thf(fact_7349_prod__mono__strict,axiom,
% 4.69/5.04 ! [A: set_Product_unit,F: product_unit > rat,G: product_unit > rat] :
% 4.69/5.04 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.04 => ( ! [I3: product_unit] :
% 4.69/5.04 ( ( member_Product_unit @ I3 @ A )
% 4.69/5.04 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 4.69/5.04 & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 4.69/5.04 => ( ( A != bot_bo3957492148770167129t_unit )
% 4.69/5.04 => ( ord_less_rat @ ( groups8984663225794451456it_rat @ F @ A ) @ ( groups8984663225794451456it_rat @ G @ A ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod_mono_strict
% 4.69/5.04 thf(fact_7350_prod__mono__strict,axiom,
% 4.69/5.04 ! [A: set_o,F: $o > rat,G: $o > rat] :
% 4.69/5.04 ( ( finite_finite_o @ A )
% 4.69/5.04 => ( ! [I3: $o] :
% 4.69/5.04 ( ( member_o @ I3 @ A )
% 4.69/5.04 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 4.69/5.04 & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 4.69/5.04 => ( ( A != bot_bot_set_o )
% 4.69/5.04 => ( ord_less_rat @ ( groups2869687844427037835_o_rat @ F @ A ) @ ( groups2869687844427037835_o_rat @ G @ A ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod_mono_strict
% 4.69/5.04 thf(fact_7351_prod__mono__strict,axiom,
% 4.69/5.04 ! [A: set_nat,F: nat > rat,G: nat > rat] :
% 4.69/5.04 ( ( finite_finite_nat @ A )
% 4.69/5.04 => ( ! [I3: nat] :
% 4.69/5.04 ( ( member_nat @ I3 @ A )
% 4.69/5.04 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 4.69/5.04 & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 4.69/5.04 => ( ( A != bot_bot_set_nat )
% 4.69/5.04 => ( ord_less_rat @ ( groups73079841787564623at_rat @ F @ A ) @ ( groups73079841787564623at_rat @ G @ A ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod_mono_strict
% 4.69/5.04 thf(fact_7352_prod__mono__strict,axiom,
% 4.69/5.04 ! [A: set_int,F: int > rat,G: int > rat] :
% 4.69/5.04 ( ( finite_finite_int @ A )
% 4.69/5.04 => ( ! [I3: int] :
% 4.69/5.04 ( ( member_int @ I3 @ A )
% 4.69/5.04 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 4.69/5.04 & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 4.69/5.04 => ( ( A != bot_bot_set_int )
% 4.69/5.04 => ( ord_less_rat @ ( groups1072433553688619179nt_rat @ F @ A ) @ ( groups1072433553688619179nt_rat @ G @ A ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod_mono_strict
% 4.69/5.04 thf(fact_7353_prod_Oinsert__remove,axiom,
% 4.69/5.04 ! [A: set_Code_integer,G: code_integer > assn,X: code_integer] :
% 4.69/5.04 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.04 => ( ( groups1304777262505850412r_assn @ G @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.04 = ( times_times_assn @ ( G @ X ) @ ( groups1304777262505850412r_assn @ G @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.insert_remove
% 4.69/5.04 thf(fact_7354_prod_Oinsert__remove,axiom,
% 4.69/5.04 ! [A: set_Product_unit,G: product_unit > assn,X: product_unit] :
% 4.69/5.04 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.04 => ( ( groups5360233303959380816t_assn @ G @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.04 = ( times_times_assn @ ( G @ X ) @ ( groups5360233303959380816t_assn @ G @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.insert_remove
% 4.69/5.04 thf(fact_7355_prod_Oinsert__remove,axiom,
% 4.69/5.04 ! [A: set_o,G: $o > assn,X: $o] :
% 4.69/5.04 ( ( finite_finite_o @ A )
% 4.69/5.04 => ( ( groups5301882518646026715o_assn @ G @ ( insert_o @ X @ A ) )
% 4.69/5.04 = ( times_times_assn @ ( G @ X ) @ ( groups5301882518646026715o_assn @ G @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.insert_remove
% 4.69/5.04 thf(fact_7356_prod_Oinsert__remove,axiom,
% 4.69/5.04 ! [A: set_int,G: int > assn,X: int] :
% 4.69/5.04 ( ( finite_finite_int @ A )
% 4.69/5.04 => ( ( groups7882442080178216443t_assn @ G @ ( insert_int @ X @ A ) )
% 4.69/5.04 = ( times_times_assn @ ( G @ X ) @ ( groups7882442080178216443t_assn @ G @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.insert_remove
% 4.69/5.04 thf(fact_7357_prod_Oinsert__remove,axiom,
% 4.69/5.04 ! [A: set_nat,G: nat > assn,X: nat] :
% 4.69/5.04 ( ( finite_finite_nat @ A )
% 4.69/5.04 => ( ( groups6906906614972039071t_assn @ G @ ( insert_nat @ X @ A ) )
% 4.69/5.04 = ( times_times_assn @ ( G @ X ) @ ( groups6906906614972039071t_assn @ G @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.insert_remove
% 4.69/5.04 thf(fact_7358_prod_Oinsert__remove,axiom,
% 4.69/5.04 ! [A: set_Code_integer,G: code_integer > rat,X: code_integer] :
% 4.69/5.04 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.04 => ( ( groups2555765274223993564er_rat @ G @ ( insert_Code_integer @ X @ A ) )
% 4.69/5.04 = ( times_times_rat @ ( G @ X ) @ ( groups2555765274223993564er_rat @ G @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.insert_remove
% 4.69/5.04 thf(fact_7359_prod_Oinsert__remove,axiom,
% 4.69/5.04 ! [A: set_Product_unit,G: product_unit > rat,X: product_unit] :
% 4.69/5.04 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.04 => ( ( groups8984663225794451456it_rat @ G @ ( insert_Product_unit @ X @ A ) )
% 4.69/5.04 = ( times_times_rat @ ( G @ X ) @ ( groups8984663225794451456it_rat @ G @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.insert_remove
% 4.69/5.04 thf(fact_7360_prod_Oinsert__remove,axiom,
% 4.69/5.04 ! [A: set_o,G: $o > rat,X: $o] :
% 4.69/5.04 ( ( finite_finite_o @ A )
% 4.69/5.04 => ( ( groups2869687844427037835_o_rat @ G @ ( insert_o @ X @ A ) )
% 4.69/5.04 = ( times_times_rat @ ( G @ X ) @ ( groups2869687844427037835_o_rat @ G @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.insert_remove
% 4.69/5.04 thf(fact_7361_prod_Oinsert__remove,axiom,
% 4.69/5.04 ! [A: set_int,G: int > rat,X: int] :
% 4.69/5.04 ( ( finite_finite_int @ A )
% 4.69/5.04 => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X @ A ) )
% 4.69/5.04 = ( times_times_rat @ ( G @ X ) @ ( groups1072433553688619179nt_rat @ G @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.insert_remove
% 4.69/5.04 thf(fact_7362_prod_Oinsert__remove,axiom,
% 4.69/5.04 ! [A: set_nat,G: nat > rat,X: nat] :
% 4.69/5.04 ( ( finite_finite_nat @ A )
% 4.69/5.04 => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X @ A ) )
% 4.69/5.04 = ( times_times_rat @ ( G @ X ) @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.insert_remove
% 4.69/5.04 thf(fact_7363_prod_Oremove,axiom,
% 4.69/5.04 ! [A: set_Code_integer,X: code_integer,G: code_integer > assn] :
% 4.69/5.04 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.04 => ( ( member_Code_integer @ X @ A )
% 4.69/5.04 => ( ( groups1304777262505850412r_assn @ G @ A )
% 4.69/5.04 = ( times_times_assn @ ( G @ X ) @ ( groups1304777262505850412r_assn @ G @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.remove
% 4.69/5.04 thf(fact_7364_prod_Oremove,axiom,
% 4.69/5.04 ! [A: set_Product_unit,X: product_unit,G: product_unit > assn] :
% 4.69/5.04 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.04 => ( ( member_Product_unit @ X @ A )
% 4.69/5.04 => ( ( groups5360233303959380816t_assn @ G @ A )
% 4.69/5.04 = ( times_times_assn @ ( G @ X ) @ ( groups5360233303959380816t_assn @ G @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.remove
% 4.69/5.04 thf(fact_7365_prod_Oremove,axiom,
% 4.69/5.04 ! [A: set_o,X: $o,G: $o > assn] :
% 4.69/5.04 ( ( finite_finite_o @ A )
% 4.69/5.04 => ( ( member_o @ X @ A )
% 4.69/5.04 => ( ( groups5301882518646026715o_assn @ G @ A )
% 4.69/5.04 = ( times_times_assn @ ( G @ X ) @ ( groups5301882518646026715o_assn @ G @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.remove
% 4.69/5.04 thf(fact_7366_prod_Oremove,axiom,
% 4.69/5.04 ! [A: set_int,X: int,G: int > assn] :
% 4.69/5.04 ( ( finite_finite_int @ A )
% 4.69/5.04 => ( ( member_int @ X @ A )
% 4.69/5.04 => ( ( groups7882442080178216443t_assn @ G @ A )
% 4.69/5.04 = ( times_times_assn @ ( G @ X ) @ ( groups7882442080178216443t_assn @ G @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.remove
% 4.69/5.04 thf(fact_7367_prod_Oremove,axiom,
% 4.69/5.04 ! [A: set_nat,X: nat,G: nat > assn] :
% 4.69/5.04 ( ( finite_finite_nat @ A )
% 4.69/5.04 => ( ( member_nat @ X @ A )
% 4.69/5.04 => ( ( groups6906906614972039071t_assn @ G @ A )
% 4.69/5.04 = ( times_times_assn @ ( G @ X ) @ ( groups6906906614972039071t_assn @ G @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.remove
% 4.69/5.04 thf(fact_7368_prod_Oremove,axiom,
% 4.69/5.04 ! [A: set_Code_integer,X: code_integer,G: code_integer > rat] :
% 4.69/5.04 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.04 => ( ( member_Code_integer @ X @ A )
% 4.69/5.04 => ( ( groups2555765274223993564er_rat @ G @ A )
% 4.69/5.04 = ( times_times_rat @ ( G @ X ) @ ( groups2555765274223993564er_rat @ G @ ( minus_2355218937544613996nteger @ A @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.remove
% 4.69/5.04 thf(fact_7369_prod_Oremove,axiom,
% 4.69/5.04 ! [A: set_Product_unit,X: product_unit,G: product_unit > rat] :
% 4.69/5.04 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.04 => ( ( member_Product_unit @ X @ A )
% 4.69/5.04 => ( ( groups8984663225794451456it_rat @ G @ A )
% 4.69/5.04 = ( times_times_rat @ ( G @ X ) @ ( groups8984663225794451456it_rat @ G @ ( minus_6452836326544984404t_unit @ A @ ( insert_Product_unit @ X @ bot_bo3957492148770167129t_unit ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.remove
% 4.69/5.04 thf(fact_7370_prod_Oremove,axiom,
% 4.69/5.04 ! [A: set_o,X: $o,G: $o > rat] :
% 4.69/5.04 ( ( finite_finite_o @ A )
% 4.69/5.04 => ( ( member_o @ X @ A )
% 4.69/5.04 => ( ( groups2869687844427037835_o_rat @ G @ A )
% 4.69/5.04 = ( times_times_rat @ ( G @ X ) @ ( groups2869687844427037835_o_rat @ G @ ( minus_minus_set_o @ A @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.remove
% 4.69/5.04 thf(fact_7371_prod_Oremove,axiom,
% 4.69/5.04 ! [A: set_int,X: int,G: int > rat] :
% 4.69/5.04 ( ( finite_finite_int @ A )
% 4.69/5.04 => ( ( member_int @ X @ A )
% 4.69/5.04 => ( ( groups1072433553688619179nt_rat @ G @ A )
% 4.69/5.04 = ( times_times_rat @ ( G @ X ) @ ( groups1072433553688619179nt_rat @ G @ ( minus_minus_set_int @ A @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.remove
% 4.69/5.04 thf(fact_7372_prod_Oremove,axiom,
% 4.69/5.04 ! [A: set_nat,X: nat,G: nat > rat] :
% 4.69/5.04 ( ( finite_finite_nat @ A )
% 4.69/5.04 => ( ( member_nat @ X @ A )
% 4.69/5.04 => ( ( groups73079841787564623at_rat @ G @ A )
% 4.69/5.04 = ( times_times_rat @ ( G @ X ) @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.remove
% 4.69/5.04 thf(fact_7373_prod_Ounion__inter__neutral,axiom,
% 4.69/5.04 ! [A: set_Code_integer,B4: set_Code_integer,G: code_integer > code_integer] :
% 4.69/5.04 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.04 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.04 => ( ! [X3: code_integer] :
% 4.69/5.04 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ A @ B4 ) )
% 4.69/5.04 => ( ( G @ X3 )
% 4.69/5.04 = one_one_Code_integer ) )
% 4.69/5.04 => ( ( groups3674199335183972705nteger @ G @ ( sup_su848401254843788991nteger @ A @ B4 ) )
% 4.69/5.04 = ( times_3573771949741848930nteger @ ( groups3674199335183972705nteger @ G @ A ) @ ( groups3674199335183972705nteger @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_inter_neutral
% 4.69/5.04 thf(fact_7374_prod_Ounion__inter__neutral,axiom,
% 4.69/5.04 ! [A: set_Code_integer,B4: set_Code_integer,G: code_integer > code_natural] :
% 4.69/5.04 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.04 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.04 => ( ! [X3: code_integer] :
% 4.69/5.04 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ A @ B4 ) )
% 4.69/5.04 => ( ( G @ X3 )
% 4.69/5.04 = one_one_Code_natural ) )
% 4.69/5.04 => ( ( groups2497794486940690220atural @ G @ ( sup_su848401254843788991nteger @ A @ B4 ) )
% 4.69/5.04 = ( times_2397367101498566445atural @ ( groups2497794486940690220atural @ G @ A ) @ ( groups2497794486940690220atural @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_inter_neutral
% 4.69/5.04 thf(fact_7375_prod_Ounion__inter__neutral,axiom,
% 4.69/5.04 ! [A: set_nat,B4: set_nat,G: nat > code_integer] :
% 4.69/5.04 ( ( finite_finite_nat @ A )
% 4.69/5.04 => ( ( finite_finite_nat @ B4 )
% 4.69/5.04 => ( ! [X3: nat] :
% 4.69/5.04 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A @ B4 ) )
% 4.69/5.04 => ( ( G @ X3 )
% 4.69/5.04 = one_one_Code_integer ) )
% 4.69/5.04 => ( ( groups3455450783089532116nteger @ G @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/5.04 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ A ) @ ( groups3455450783089532116nteger @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_inter_neutral
% 4.69/5.04 thf(fact_7376_prod_Ounion__inter__neutral,axiom,
% 4.69/5.04 ! [A: set_nat,B4: set_nat,G: nat > code_natural] :
% 4.69/5.04 ( ( finite_finite_nat @ A )
% 4.69/5.04 => ( ( finite_finite_nat @ B4 )
% 4.69/5.04 => ( ! [X3: nat] :
% 4.69/5.04 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A @ B4 ) )
% 4.69/5.04 => ( ( G @ X3 )
% 4.69/5.04 = one_one_Code_natural ) )
% 4.69/5.04 => ( ( groups2279045934846249631atural @ G @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/5.04 = ( times_2397367101498566445atural @ ( groups2279045934846249631atural @ G @ A ) @ ( groups2279045934846249631atural @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_inter_neutral
% 4.69/5.04 thf(fact_7377_prod_Ounion__inter__neutral,axiom,
% 4.69/5.04 ! [A: set_Code_integer,B4: set_Code_integer,G: code_integer > assn] :
% 4.69/5.04 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.04 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.04 => ( ! [X3: code_integer] :
% 4.69/5.04 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ A @ B4 ) )
% 4.69/5.04 => ( ( G @ X3 )
% 4.69/5.04 = one_one_assn ) )
% 4.69/5.04 => ( ( groups1304777262505850412r_assn @ G @ ( sup_su848401254843788991nteger @ A @ B4 ) )
% 4.69/5.04 = ( times_times_assn @ ( groups1304777262505850412r_assn @ G @ A ) @ ( groups1304777262505850412r_assn @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_inter_neutral
% 4.69/5.04 thf(fact_7378_prod_Ounion__inter__neutral,axiom,
% 4.69/5.04 ! [A: set_nat,B4: set_nat,G: nat > assn] :
% 4.69/5.04 ( ( finite_finite_nat @ A )
% 4.69/5.04 => ( ( finite_finite_nat @ B4 )
% 4.69/5.04 => ( ! [X3: nat] :
% 4.69/5.04 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A @ B4 ) )
% 4.69/5.04 => ( ( G @ X3 )
% 4.69/5.04 = one_one_assn ) )
% 4.69/5.04 => ( ( groups6906906614972039071t_assn @ G @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/5.04 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ A ) @ ( groups6906906614972039071t_assn @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_inter_neutral
% 4.69/5.04 thf(fact_7379_prod_Ounion__inter__neutral,axiom,
% 4.69/5.04 ! [A: set_Code_integer,B4: set_Code_integer,G: code_integer > rat] :
% 4.69/5.04 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.04 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.04 => ( ! [X3: code_integer] :
% 4.69/5.04 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ A @ B4 ) )
% 4.69/5.04 => ( ( G @ X3 )
% 4.69/5.04 = one_one_rat ) )
% 4.69/5.04 => ( ( groups2555765274223993564er_rat @ G @ ( sup_su848401254843788991nteger @ A @ B4 ) )
% 4.69/5.04 = ( times_times_rat @ ( groups2555765274223993564er_rat @ G @ A ) @ ( groups2555765274223993564er_rat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_inter_neutral
% 4.69/5.04 thf(fact_7380_prod_Ounion__inter__neutral,axiom,
% 4.69/5.04 ! [A: set_nat,B4: set_nat,G: nat > rat] :
% 4.69/5.04 ( ( finite_finite_nat @ A )
% 4.69/5.04 => ( ( finite_finite_nat @ B4 )
% 4.69/5.04 => ( ! [X3: nat] :
% 4.69/5.04 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A @ B4 ) )
% 4.69/5.04 => ( ( G @ X3 )
% 4.69/5.04 = one_one_rat ) )
% 4.69/5.04 => ( ( groups73079841787564623at_rat @ G @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/5.04 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ A ) @ ( groups73079841787564623at_rat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_inter_neutral
% 4.69/5.04 thf(fact_7381_prod_Ounion__inter__neutral,axiom,
% 4.69/5.04 ! [A: set_Code_integer,B4: set_Code_integer,G: code_integer > nat] :
% 4.69/5.04 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.04 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.04 => ( ! [X3: code_integer] :
% 4.69/5.04 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ A @ B4 ) )
% 4.69/5.04 => ( ( G @ X3 )
% 4.69/5.04 = one_one_nat ) )
% 4.69/5.04 => ( ( groups3190895334310489300er_nat @ G @ ( sup_su848401254843788991nteger @ A @ B4 ) )
% 4.69/5.04 = ( times_times_nat @ ( groups3190895334310489300er_nat @ G @ A ) @ ( groups3190895334310489300er_nat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_inter_neutral
% 4.69/5.04 thf(fact_7382_prod_Ounion__inter__neutral,axiom,
% 4.69/5.04 ! [A: set_Code_integer,B4: set_Code_integer,G: code_integer > int] :
% 4.69/5.04 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.04 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.04 => ( ! [X3: code_integer] :
% 4.69/5.04 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ A @ B4 ) )
% 4.69/5.04 => ( ( G @ X3 )
% 4.69/5.04 = one_one_int ) )
% 4.69/5.04 => ( ( groups3188404863801439024er_int @ G @ ( sup_su848401254843788991nteger @ A @ B4 ) )
% 4.69/5.04 = ( times_times_int @ ( groups3188404863801439024er_int @ G @ A ) @ ( groups3188404863801439024er_int @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_inter_neutral
% 4.69/5.04 thf(fact_7383_prod_Ounion__disjoint,axiom,
% 4.69/5.04 ! [A: set_Code_integer,B4: set_Code_integer,G: code_integer > assn] :
% 4.69/5.04 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.04 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.04 => ( ( ( inf_in1364745209274528805nteger @ A @ B4 )
% 4.69/5.04 = bot_bo3990330152332043303nteger )
% 4.69/5.04 => ( ( groups1304777262505850412r_assn @ G @ ( sup_su848401254843788991nteger @ A @ B4 ) )
% 4.69/5.04 = ( times_times_assn @ ( groups1304777262505850412r_assn @ G @ A ) @ ( groups1304777262505850412r_assn @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_disjoint
% 4.69/5.04 thf(fact_7384_prod_Ounion__disjoint,axiom,
% 4.69/5.04 ! [A: set_Product_unit,B4: set_Product_unit,G: product_unit > assn] :
% 4.69/5.04 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.04 => ( ( finite4290736615968046902t_unit @ B4 )
% 4.69/5.04 => ( ( ( inf_in4660618365625256667t_unit @ A @ B4 )
% 4.69/5.04 = bot_bo3957492148770167129t_unit )
% 4.69/5.04 => ( ( groups5360233303959380816t_assn @ G @ ( sup_su793286257634532545t_unit @ A @ B4 ) )
% 4.69/5.04 = ( times_times_assn @ ( groups5360233303959380816t_assn @ G @ A ) @ ( groups5360233303959380816t_assn @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_disjoint
% 4.69/5.04 thf(fact_7385_prod_Ounion__disjoint,axiom,
% 4.69/5.04 ! [A: set_o,B4: set_o,G: $o > assn] :
% 4.69/5.04 ( ( finite_finite_o @ A )
% 4.69/5.04 => ( ( finite_finite_o @ B4 )
% 4.69/5.04 => ( ( ( inf_inf_set_o @ A @ B4 )
% 4.69/5.04 = bot_bot_set_o )
% 4.69/5.04 => ( ( groups5301882518646026715o_assn @ G @ ( sup_sup_set_o @ A @ B4 ) )
% 4.69/5.04 = ( times_times_assn @ ( groups5301882518646026715o_assn @ G @ A ) @ ( groups5301882518646026715o_assn @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_disjoint
% 4.69/5.04 thf(fact_7386_prod_Ounion__disjoint,axiom,
% 4.69/5.04 ! [A: set_nat,B4: set_nat,G: nat > assn] :
% 4.69/5.04 ( ( finite_finite_nat @ A )
% 4.69/5.04 => ( ( finite_finite_nat @ B4 )
% 4.69/5.04 => ( ( ( inf_inf_set_nat @ A @ B4 )
% 4.69/5.04 = bot_bot_set_nat )
% 4.69/5.04 => ( ( groups6906906614972039071t_assn @ G @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/5.04 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ A ) @ ( groups6906906614972039071t_assn @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_disjoint
% 4.69/5.04 thf(fact_7387_prod_Ounion__disjoint,axiom,
% 4.69/5.04 ! [A: set_int,B4: set_int,G: int > assn] :
% 4.69/5.04 ( ( finite_finite_int @ A )
% 4.69/5.04 => ( ( finite_finite_int @ B4 )
% 4.69/5.04 => ( ( ( inf_inf_set_int @ A @ B4 )
% 4.69/5.04 = bot_bot_set_int )
% 4.69/5.04 => ( ( groups7882442080178216443t_assn @ G @ ( sup_sup_set_int @ A @ B4 ) )
% 4.69/5.04 = ( times_times_assn @ ( groups7882442080178216443t_assn @ G @ A ) @ ( groups7882442080178216443t_assn @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_disjoint
% 4.69/5.04 thf(fact_7388_prod_Ounion__disjoint,axiom,
% 4.69/5.04 ! [A: set_Code_integer,B4: set_Code_integer,G: code_integer > rat] :
% 4.69/5.04 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.04 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.04 => ( ( ( inf_in1364745209274528805nteger @ A @ B4 )
% 4.69/5.04 = bot_bo3990330152332043303nteger )
% 4.69/5.04 => ( ( groups2555765274223993564er_rat @ G @ ( sup_su848401254843788991nteger @ A @ B4 ) )
% 4.69/5.04 = ( times_times_rat @ ( groups2555765274223993564er_rat @ G @ A ) @ ( groups2555765274223993564er_rat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_disjoint
% 4.69/5.04 thf(fact_7389_prod_Ounion__disjoint,axiom,
% 4.69/5.04 ! [A: set_Product_unit,B4: set_Product_unit,G: product_unit > rat] :
% 4.69/5.04 ( ( finite4290736615968046902t_unit @ A )
% 4.69/5.04 => ( ( finite4290736615968046902t_unit @ B4 )
% 4.69/5.04 => ( ( ( inf_in4660618365625256667t_unit @ A @ B4 )
% 4.69/5.04 = bot_bo3957492148770167129t_unit )
% 4.69/5.04 => ( ( groups8984663225794451456it_rat @ G @ ( sup_su793286257634532545t_unit @ A @ B4 ) )
% 4.69/5.04 = ( times_times_rat @ ( groups8984663225794451456it_rat @ G @ A ) @ ( groups8984663225794451456it_rat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_disjoint
% 4.69/5.04 thf(fact_7390_prod_Ounion__disjoint,axiom,
% 4.69/5.04 ! [A: set_o,B4: set_o,G: $o > rat] :
% 4.69/5.04 ( ( finite_finite_o @ A )
% 4.69/5.04 => ( ( finite_finite_o @ B4 )
% 4.69/5.04 => ( ( ( inf_inf_set_o @ A @ B4 )
% 4.69/5.04 = bot_bot_set_o )
% 4.69/5.04 => ( ( groups2869687844427037835_o_rat @ G @ ( sup_sup_set_o @ A @ B4 ) )
% 4.69/5.04 = ( times_times_rat @ ( groups2869687844427037835_o_rat @ G @ A ) @ ( groups2869687844427037835_o_rat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_disjoint
% 4.69/5.04 thf(fact_7391_prod_Ounion__disjoint,axiom,
% 4.69/5.04 ! [A: set_nat,B4: set_nat,G: nat > rat] :
% 4.69/5.04 ( ( finite_finite_nat @ A )
% 4.69/5.04 => ( ( finite_finite_nat @ B4 )
% 4.69/5.04 => ( ( ( inf_inf_set_nat @ A @ B4 )
% 4.69/5.04 = bot_bot_set_nat )
% 4.69/5.04 => ( ( groups73079841787564623at_rat @ G @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/5.04 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ A ) @ ( groups73079841787564623at_rat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_disjoint
% 4.69/5.04 thf(fact_7392_prod_Ounion__disjoint,axiom,
% 4.69/5.04 ! [A: set_int,B4: set_int,G: int > rat] :
% 4.69/5.04 ( ( finite_finite_int @ A )
% 4.69/5.04 => ( ( finite_finite_int @ B4 )
% 4.69/5.04 => ( ( ( inf_inf_set_int @ A @ B4 )
% 4.69/5.04 = bot_bot_set_int )
% 4.69/5.04 => ( ( groups1072433553688619179nt_rat @ G @ ( sup_sup_set_int @ A @ B4 ) )
% 4.69/5.04 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G @ A ) @ ( groups1072433553688619179nt_rat @ G @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_disjoint
% 4.69/5.04 thf(fact_7393_prod_Ounion__diff2,axiom,
% 4.69/5.04 ! [A: set_Code_integer,B4: set_Code_integer,G: code_integer > assn] :
% 4.69/5.04 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.04 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.04 => ( ( groups1304777262505850412r_assn @ G @ ( sup_su848401254843788991nteger @ A @ B4 ) )
% 4.69/5.04 = ( times_times_assn @ ( times_times_assn @ ( groups1304777262505850412r_assn @ G @ ( minus_2355218937544613996nteger @ A @ B4 ) ) @ ( groups1304777262505850412r_assn @ G @ ( minus_2355218937544613996nteger @ B4 @ A ) ) ) @ ( groups1304777262505850412r_assn @ G @ ( inf_in1364745209274528805nteger @ A @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_diff2
% 4.69/5.04 thf(fact_7394_prod_Ounion__diff2,axiom,
% 4.69/5.04 ! [A: set_nat,B4: set_nat,G: nat > assn] :
% 4.69/5.04 ( ( finite_finite_nat @ A )
% 4.69/5.04 => ( ( finite_finite_nat @ B4 )
% 4.69/5.04 => ( ( groups6906906614972039071t_assn @ G @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/5.04 = ( times_times_assn @ ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( minus_minus_set_nat @ A @ B4 ) ) @ ( groups6906906614972039071t_assn @ G @ ( minus_minus_set_nat @ B4 @ A ) ) ) @ ( groups6906906614972039071t_assn @ G @ ( inf_inf_set_nat @ A @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_diff2
% 4.69/5.04 thf(fact_7395_prod_Ounion__diff2,axiom,
% 4.69/5.04 ! [A: set_Code_integer,B4: set_Code_integer,G: code_integer > rat] :
% 4.69/5.04 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.04 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.04 => ( ( groups2555765274223993564er_rat @ G @ ( sup_su848401254843788991nteger @ A @ B4 ) )
% 4.69/5.04 = ( times_times_rat @ ( times_times_rat @ ( groups2555765274223993564er_rat @ G @ ( minus_2355218937544613996nteger @ A @ B4 ) ) @ ( groups2555765274223993564er_rat @ G @ ( minus_2355218937544613996nteger @ B4 @ A ) ) ) @ ( groups2555765274223993564er_rat @ G @ ( inf_in1364745209274528805nteger @ A @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_diff2
% 4.69/5.04 thf(fact_7396_prod_Ounion__diff2,axiom,
% 4.69/5.04 ! [A: set_nat,B4: set_nat,G: nat > rat] :
% 4.69/5.04 ( ( finite_finite_nat @ A )
% 4.69/5.04 => ( ( finite_finite_nat @ B4 )
% 4.69/5.04 => ( ( groups73079841787564623at_rat @ G @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/5.04 = ( times_times_rat @ ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A @ B4 ) ) @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ B4 @ A ) ) ) @ ( groups73079841787564623at_rat @ G @ ( inf_inf_set_nat @ A @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_diff2
% 4.69/5.04 thf(fact_7397_prod_Ounion__diff2,axiom,
% 4.69/5.04 ! [A: set_Code_integer,B4: set_Code_integer,G: code_integer > nat] :
% 4.69/5.04 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.04 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.04 => ( ( groups3190895334310489300er_nat @ G @ ( sup_su848401254843788991nteger @ A @ B4 ) )
% 4.69/5.04 = ( times_times_nat @ ( times_times_nat @ ( groups3190895334310489300er_nat @ G @ ( minus_2355218937544613996nteger @ A @ B4 ) ) @ ( groups3190895334310489300er_nat @ G @ ( minus_2355218937544613996nteger @ B4 @ A ) ) ) @ ( groups3190895334310489300er_nat @ G @ ( inf_in1364745209274528805nteger @ A @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_diff2
% 4.69/5.04 thf(fact_7398_prod_Ounion__diff2,axiom,
% 4.69/5.04 ! [A: set_Code_integer,B4: set_Code_integer,G: code_integer > int] :
% 4.69/5.04 ( ( finite6017078050557962740nteger @ A )
% 4.69/5.04 => ( ( finite6017078050557962740nteger @ B4 )
% 4.69/5.04 => ( ( groups3188404863801439024er_int @ G @ ( sup_su848401254843788991nteger @ A @ B4 ) )
% 4.69/5.04 = ( times_times_int @ ( times_times_int @ ( groups3188404863801439024er_int @ G @ ( minus_2355218937544613996nteger @ A @ B4 ) ) @ ( groups3188404863801439024er_int @ G @ ( minus_2355218937544613996nteger @ B4 @ A ) ) ) @ ( groups3188404863801439024er_int @ G @ ( inf_in1364745209274528805nteger @ A @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_diff2
% 4.69/5.04 thf(fact_7399_prod_Ounion__diff2,axiom,
% 4.69/5.04 ! [A: set_nat,B4: set_nat,G: nat > int] :
% 4.69/5.04 ( ( finite_finite_nat @ A )
% 4.69/5.04 => ( ( finite_finite_nat @ B4 )
% 4.69/5.04 => ( ( groups705719431365010083at_int @ G @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/5.04 = ( times_times_int @ ( times_times_int @ ( groups705719431365010083at_int @ G @ ( minus_minus_set_nat @ A @ B4 ) ) @ ( groups705719431365010083at_int @ G @ ( minus_minus_set_nat @ B4 @ A ) ) ) @ ( groups705719431365010083at_int @ G @ ( inf_inf_set_nat @ A @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_diff2
% 4.69/5.04 thf(fact_7400_prod_Ounion__diff2,axiom,
% 4.69/5.04 ! [A: set_nat,B4: set_nat,G: nat > nat] :
% 4.69/5.04 ( ( finite_finite_nat @ A )
% 4.69/5.04 => ( ( finite_finite_nat @ B4 )
% 4.69/5.04 => ( ( groups708209901874060359at_nat @ G @ ( sup_sup_set_nat @ A @ B4 ) )
% 4.69/5.04 = ( times_times_nat @ ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( minus_minus_set_nat @ A @ B4 ) ) @ ( groups708209901874060359at_nat @ G @ ( minus_minus_set_nat @ B4 @ A ) ) ) @ ( groups708209901874060359at_nat @ G @ ( inf_inf_set_nat @ A @ B4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod.union_diff2
% 4.69/5.04 thf(fact_7401_Suc__times__gbinomial,axiom,
% 4.69/5.04 ! [K3: nat,A2: rat] :
% 4.69/5.04 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K3 ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A2 @ one_one_rat ) @ ( suc @ K3 ) ) )
% 4.69/5.04 = ( times_times_rat @ ( plus_plus_rat @ A2 @ one_one_rat ) @ ( gbinomial_rat @ A2 @ K3 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % Suc_times_gbinomial
% 4.69/5.04 thf(fact_7402_gbinomial__absorption,axiom,
% 4.69/5.04 ! [K3: nat,A2: rat] :
% 4.69/5.04 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K3 ) ) @ ( gbinomial_rat @ A2 @ ( suc @ K3 ) ) )
% 4.69/5.04 = ( times_times_rat @ A2 @ ( gbinomial_rat @ ( minus_minus_rat @ A2 @ one_one_rat ) @ K3 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % gbinomial_absorption
% 4.69/5.04 thf(fact_7403_gbinomial__trinomial__revision,axiom,
% 4.69/5.04 ! [K3: nat,M4: nat,A2: rat] :
% 4.69/5.04 ( ( ord_less_eq_nat @ K3 @ M4 )
% 4.69/5.04 => ( ( times_times_rat @ ( gbinomial_rat @ A2 @ M4 ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M4 ) @ K3 ) )
% 4.69/5.04 = ( times_times_rat @ ( gbinomial_rat @ A2 @ K3 ) @ ( gbinomial_rat @ ( minus_minus_rat @ A2 @ ( semiri681578069525770553at_rat @ K3 ) ) @ ( minus_minus_nat @ M4 @ K3 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % gbinomial_trinomial_revision
% 4.69/5.04 thf(fact_7404_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 4.69/5.04 ! [K3: nat,N2: nat] :
% 4.69/5.04 ( ( ord_less_eq_nat @ K3 @ N2 )
% 4.69/5.04 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N2 @ K3 ) )
% 4.69/5.04 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N2 @ K3 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % neg_one_power_add_eq_neg_one_power_diff
% 4.69/5.04 thf(fact_7405_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 4.69/5.04 ! [K3: nat,N2: nat] :
% 4.69/5.04 ( ( ord_less_eq_nat @ K3 @ N2 )
% 4.69/5.04 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N2 @ K3 ) )
% 4.69/5.04 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N2 @ K3 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % neg_one_power_add_eq_neg_one_power_diff
% 4.69/5.04 thf(fact_7406_ex__less__of__nat__mult,axiom,
% 4.69/5.04 ! [X: rat,Y: rat] :
% 4.69/5.04 ( ( ord_less_rat @ zero_zero_rat @ X )
% 4.69/5.04 => ? [N3: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % ex_less_of_nat_mult
% 4.69/5.04 thf(fact_7407_gbinomial__absorption_H,axiom,
% 4.69/5.04 ! [K3: nat,A2: rat] :
% 4.69/5.04 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 4.69/5.04 => ( ( gbinomial_rat @ A2 @ K3 )
% 4.69/5.04 = ( times_times_rat @ ( divide_divide_rat @ A2 @ ( semiri681578069525770553at_rat @ K3 ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A2 @ one_one_rat ) @ ( minus_minus_nat @ K3 @ one_one_nat ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % gbinomial_absorption'
% 4.69/5.04 thf(fact_7408_pochhammer__minus,axiom,
% 4.69/5.04 ! [B: rat,K3: nat] :
% 4.69/5.04 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K3 )
% 4.69/5.04 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K3 ) ) @ one_one_rat ) @ K3 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % pochhammer_minus
% 4.69/5.04 thf(fact_7409_pochhammer__minus,axiom,
% 4.69/5.04 ! [B: int,K3: nat] :
% 4.69/5.04 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K3 )
% 4.69/5.04 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K3 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K3 ) ) @ one_one_int ) @ K3 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % pochhammer_minus
% 4.69/5.04 thf(fact_7410_pochhammer__minus,axiom,
% 4.69/5.04 ! [B: code_integer,K3: nat] :
% 4.69/5.04 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K3 )
% 4.69/5.04 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K3 ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K3 ) ) @ one_one_Code_integer ) @ K3 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % pochhammer_minus
% 4.69/5.04 thf(fact_7411_pochhammer__minus_H,axiom,
% 4.69/5.04 ! [B: rat,K3: nat] :
% 4.69/5.04 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K3 ) ) @ one_one_rat ) @ K3 )
% 4.69/5.04 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K3 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % pochhammer_minus'
% 4.69/5.04 thf(fact_7412_pochhammer__minus_H,axiom,
% 4.69/5.04 ! [B: int,K3: nat] :
% 4.69/5.04 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K3 ) ) @ one_one_int ) @ K3 )
% 4.69/5.04 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K3 ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K3 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % pochhammer_minus'
% 4.69/5.04 thf(fact_7413_pochhammer__minus_H,axiom,
% 4.69/5.04 ! [B: code_integer,K3: nat] :
% 4.69/5.04 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K3 ) ) @ one_one_Code_integer ) @ K3 )
% 4.69/5.04 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K3 ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K3 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % pochhammer_minus'
% 4.69/5.04 thf(fact_7414_zmult__zless__mono2__lemma,axiom,
% 4.69/5.04 ! [I2: int,J: int,K3: nat] :
% 4.69/5.04 ( ( ord_less_int @ I2 @ J )
% 4.69/5.04 => ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 4.69/5.04 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K3 ) @ I2 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K3 ) @ J ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % zmult_zless_mono2_lemma
% 4.69/5.04 thf(fact_7415_nat__mult__div__cancel__disj,axiom,
% 4.69/5.04 ! [K3: nat,M4: nat,N2: nat] :
% 4.69/5.04 ( ( ( K3 = zero_zero_nat )
% 4.69/5.04 => ( ( divide_divide_nat @ ( times_times_nat @ K3 @ M4 ) @ ( times_times_nat @ K3 @ N2 ) )
% 4.69/5.04 = zero_zero_nat ) )
% 4.69/5.04 & ( ( K3 != zero_zero_nat )
% 4.69/5.04 => ( ( divide_divide_nat @ ( times_times_nat @ K3 @ M4 ) @ ( times_times_nat @ K3 @ N2 ) )
% 4.69/5.04 = ( divide_divide_nat @ M4 @ N2 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % nat_mult_div_cancel_disj
% 4.69/5.04 thf(fact_7416_pos__zmult__eq__1__iff__lemma,axiom,
% 4.69/5.04 ! [M4: int,N2: int] :
% 4.69/5.04 ( ( ( times_times_int @ M4 @ N2 )
% 4.69/5.04 = one_one_int )
% 4.69/5.04 => ( ( M4 = one_one_int )
% 4.69/5.04 | ( M4
% 4.69/5.04 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % pos_zmult_eq_1_iff_lemma
% 4.69/5.04 thf(fact_7417_zmult__eq__1__iff,axiom,
% 4.69/5.04 ! [M4: int,N2: int] :
% 4.69/5.04 ( ( ( times_times_int @ M4 @ N2 )
% 4.69/5.04 = one_one_int )
% 4.69/5.04 = ( ( ( M4 = one_one_int )
% 4.69/5.04 & ( N2 = one_one_int ) )
% 4.69/5.04 | ( ( M4
% 4.69/5.04 = ( uminus_uminus_int @ one_one_int ) )
% 4.69/5.04 & ( N2
% 4.69/5.04 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % zmult_eq_1_iff
% 4.69/5.04 thf(fact_7418_zdvd__mono,axiom,
% 4.69/5.04 ! [K3: int,M4: int,T4: int] :
% 4.69/5.04 ( ( K3 != zero_zero_int )
% 4.69/5.04 => ( ( dvd_dvd_int @ M4 @ T4 )
% 4.69/5.04 = ( dvd_dvd_int @ ( times_times_int @ K3 @ M4 ) @ ( times_times_int @ K3 @ T4 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % zdvd_mono
% 4.69/5.04 thf(fact_7419_zdvd__mult__cancel,axiom,
% 4.69/5.04 ! [K3: int,M4: int,N2: int] :
% 4.69/5.04 ( ( dvd_dvd_int @ ( times_times_int @ K3 @ M4 ) @ ( times_times_int @ K3 @ N2 ) )
% 4.69/5.04 => ( ( K3 != zero_zero_int )
% 4.69/5.04 => ( dvd_dvd_int @ M4 @ N2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % zdvd_mult_cancel
% 4.69/5.04 thf(fact_7420_zdvd__reduce,axiom,
% 4.69/5.04 ! [K3: int,N2: int,M4: int] :
% 4.69/5.04 ( ( dvd_dvd_int @ K3 @ ( plus_plus_int @ N2 @ ( times_times_int @ K3 @ M4 ) ) )
% 4.69/5.04 = ( dvd_dvd_int @ K3 @ N2 ) ) ).
% 4.69/5.04
% 4.69/5.04 % zdvd_reduce
% 4.69/5.04 thf(fact_7421_zdvd__period,axiom,
% 4.69/5.04 ! [A2: int,D2: int,X: int,T4: int,C: int] :
% 4.69/5.04 ( ( dvd_dvd_int @ A2 @ D2 )
% 4.69/5.04 => ( ( dvd_dvd_int @ A2 @ ( plus_plus_int @ X @ T4 ) )
% 4.69/5.04 = ( dvd_dvd_int @ A2 @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C @ D2 ) ) @ T4 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % zdvd_period
% 4.69/5.04 thf(fact_7422_unique__quotient__lemma__neg,axiom,
% 4.69/5.04 ! [B: int,Q5: int,R6: int,Q4: int,R2: int] :
% 4.69/5.04 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R6 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R2 ) )
% 4.69/5.04 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 4.69/5.04 => ( ( ord_less_int @ B @ R2 )
% 4.69/5.04 => ( ( ord_less_int @ B @ R6 )
% 4.69/5.04 => ( ord_less_eq_int @ Q4 @ Q5 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % unique_quotient_lemma_neg
% 4.69/5.04 thf(fact_7423_unique__quotient__lemma,axiom,
% 4.69/5.04 ! [B: int,Q5: int,R6: int,Q4: int,R2: int] :
% 4.69/5.04 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R6 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R2 ) )
% 4.69/5.04 => ( ( ord_less_eq_int @ zero_zero_int @ R6 )
% 4.69/5.04 => ( ( ord_less_int @ R6 @ B )
% 4.69/5.04 => ( ( ord_less_int @ R2 @ B )
% 4.69/5.04 => ( ord_less_eq_int @ Q5 @ Q4 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % unique_quotient_lemma
% 4.69/5.04 thf(fact_7424_zdiv__mono2__neg__lemma,axiom,
% 4.69/5.04 ! [B: int,Q4: int,R2: int,B3: int,Q5: int,R6: int] :
% 4.69/5.04 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R2 )
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ B3 @ Q5 ) @ R6 ) )
% 4.69/5.04 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B3 @ Q5 ) @ R6 ) @ zero_zero_int )
% 4.69/5.04 => ( ( ord_less_int @ R2 @ B )
% 4.69/5.04 => ( ( ord_less_eq_int @ zero_zero_int @ R6 )
% 4.69/5.04 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 4.69/5.04 => ( ( ord_less_eq_int @ B3 @ B )
% 4.69/5.04 => ( ord_less_eq_int @ Q5 @ Q4 ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % zdiv_mono2_neg_lemma
% 4.69/5.04 thf(fact_7425_zdiv__mono2__lemma,axiom,
% 4.69/5.04 ! [B: int,Q4: int,R2: int,B3: int,Q5: int,R6: int] :
% 4.69/5.04 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R2 )
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ B3 @ Q5 ) @ R6 ) )
% 4.69/5.04 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B3 @ Q5 ) @ R6 ) )
% 4.69/5.04 => ( ( ord_less_int @ R6 @ B3 )
% 4.69/5.04 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 4.69/5.04 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 4.69/5.04 => ( ( ord_less_eq_int @ B3 @ B )
% 4.69/5.04 => ( ord_less_eq_int @ Q4 @ Q5 ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % zdiv_mono2_lemma
% 4.69/5.04 thf(fact_7426_int__div__pos__eq,axiom,
% 4.69/5.04 ! [A2: int,B: int,Q4: int,R2: int] :
% 4.69/5.04 ( ( A2
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R2 ) )
% 4.69/5.04 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 4.69/5.04 => ( ( ord_less_int @ R2 @ B )
% 4.69/5.04 => ( ( divide_divide_int @ A2 @ B )
% 4.69/5.04 = Q4 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % int_div_pos_eq
% 4.69/5.04 thf(fact_7427_int__div__neg__eq,axiom,
% 4.69/5.04 ! [A2: int,B: int,Q4: int,R2: int] :
% 4.69/5.04 ( ( A2
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R2 ) )
% 4.69/5.04 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 4.69/5.04 => ( ( ord_less_int @ B @ R2 )
% 4.69/5.04 => ( ( divide_divide_int @ A2 @ B )
% 4.69/5.04 = Q4 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % int_div_neg_eq
% 4.69/5.04 thf(fact_7428_q__pos__lemma,axiom,
% 4.69/5.04 ! [B3: int,Q5: int,R6: int] :
% 4.69/5.04 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B3 @ Q5 ) @ R6 ) )
% 4.69/5.04 => ( ( ord_less_int @ R6 @ B3 )
% 4.69/5.04 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 4.69/5.04 => ( ord_less_eq_int @ zero_zero_int @ Q5 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % q_pos_lemma
% 4.69/5.04 thf(fact_7429_split__zdiv,axiom,
% 4.69/5.04 ! [P: int > $o,N2: int,K3: int] :
% 4.69/5.04 ( ( P @ ( divide_divide_int @ N2 @ K3 ) )
% 4.69/5.04 = ( ( ( K3 = zero_zero_int )
% 4.69/5.04 => ( P @ zero_zero_int ) )
% 4.69/5.04 & ( ( ord_less_int @ zero_zero_int @ K3 )
% 4.69/5.04 => ! [I4: int,J3: int] :
% 4.69/5.04 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 4.69/5.04 & ( ord_less_int @ J3 @ K3 )
% 4.69/5.04 & ( N2
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ K3 @ I4 ) @ J3 ) ) )
% 4.69/5.04 => ( P @ I4 ) ) )
% 4.69/5.04 & ( ( ord_less_int @ K3 @ zero_zero_int )
% 4.69/5.04 => ! [I4: int,J3: int] :
% 4.69/5.04 ( ( ( ord_less_int @ K3 @ J3 )
% 4.69/5.04 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 4.69/5.04 & ( N2
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ K3 @ I4 ) @ J3 ) ) )
% 4.69/5.04 => ( P @ I4 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % split_zdiv
% 4.69/5.04 thf(fact_7430_incr__mult__lemma,axiom,
% 4.69/5.04 ! [D2: int,P: int > $o,K3: int] :
% 4.69/5.04 ( ( ord_less_int @ zero_zero_int @ D2 )
% 4.69/5.04 => ( ! [X3: int] :
% 4.69/5.04 ( ( P @ X3 )
% 4.69/5.04 => ( P @ ( plus_plus_int @ X3 @ D2 ) ) )
% 4.69/5.04 => ( ( ord_less_eq_int @ zero_zero_int @ K3 )
% 4.69/5.04 => ! [X6: int] :
% 4.69/5.04 ( ( P @ X6 )
% 4.69/5.04 => ( P @ ( plus_plus_int @ X6 @ ( times_times_int @ K3 @ D2 ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % incr_mult_lemma
% 4.69/5.04 thf(fact_7431_pos__zmult__eq__1__iff,axiom,
% 4.69/5.04 ! [M4: int,N2: int] :
% 4.69/5.04 ( ( ord_less_int @ zero_zero_int @ M4 )
% 4.69/5.04 => ( ( ( times_times_int @ M4 @ N2 )
% 4.69/5.04 = one_one_int )
% 4.69/5.04 = ( ( M4 = one_one_int )
% 4.69/5.04 & ( N2 = one_one_int ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % pos_zmult_eq_1_iff
% 4.69/5.04 thf(fact_7432_zmult__zless__mono2,axiom,
% 4.69/5.04 ! [I2: int,J: int,K3: int] :
% 4.69/5.04 ( ( ord_less_int @ I2 @ J )
% 4.69/5.04 => ( ( ord_less_int @ zero_zero_int @ K3 )
% 4.69/5.04 => ( ord_less_int @ ( times_times_int @ K3 @ I2 ) @ ( times_times_int @ K3 @ J ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % zmult_zless_mono2
% 4.69/5.04 thf(fact_7433_minusinfinity,axiom,
% 4.69/5.04 ! [D2: int,P1: int > $o,P: int > $o] :
% 4.69/5.04 ( ( ord_less_int @ zero_zero_int @ D2 )
% 4.69/5.04 => ( ! [X3: int,K: int] :
% 4.69/5.04 ( ( P1 @ X3 )
% 4.69/5.04 = ( P1 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D2 ) ) ) )
% 4.69/5.04 => ( ? [Z6: int] :
% 4.69/5.04 ! [X3: int] :
% 4.69/5.04 ( ( ord_less_int @ X3 @ Z6 )
% 4.69/5.04 => ( ( P @ X3 )
% 4.69/5.04 = ( P1 @ X3 ) ) )
% 4.69/5.04 => ( ? [X_12: int] : ( P1 @ X_12 )
% 4.69/5.04 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % minusinfinity
% 4.69/5.04 thf(fact_7434_plusinfinity,axiom,
% 4.69/5.04 ! [D2: int,P7: int > $o,P: int > $o] :
% 4.69/5.04 ( ( ord_less_int @ zero_zero_int @ D2 )
% 4.69/5.04 => ( ! [X3: int,K: int] :
% 4.69/5.04 ( ( P7 @ X3 )
% 4.69/5.04 = ( P7 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D2 ) ) ) )
% 4.69/5.04 => ( ? [Z6: int] :
% 4.69/5.04 ! [X3: int] :
% 4.69/5.04 ( ( ord_less_int @ Z6 @ X3 )
% 4.69/5.04 => ( ( P @ X3 )
% 4.69/5.04 = ( P7 @ X3 ) ) )
% 4.69/5.04 => ( ? [X_12: int] : ( P7 @ X_12 )
% 4.69/5.04 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % plusinfinity
% 4.69/5.04 thf(fact_7435_decr__mult__lemma,axiom,
% 4.69/5.04 ! [D2: int,P: int > $o,K3: int] :
% 4.69/5.04 ( ( ord_less_int @ zero_zero_int @ D2 )
% 4.69/5.04 => ( ! [X3: int] :
% 4.69/5.04 ( ( P @ X3 )
% 4.69/5.04 => ( P @ ( minus_minus_int @ X3 @ D2 ) ) )
% 4.69/5.04 => ( ( ord_less_eq_int @ zero_zero_int @ K3 )
% 4.69/5.04 => ! [X6: int] :
% 4.69/5.04 ( ( P @ X6 )
% 4.69/5.04 => ( P @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D2 ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % decr_mult_lemma
% 4.69/5.04 thf(fact_7436_times__int__code_I2_J,axiom,
% 4.69/5.04 ! [L: int] :
% 4.69/5.04 ( ( times_times_int @ zero_zero_int @ L )
% 4.69/5.04 = zero_zero_int ) ).
% 4.69/5.04
% 4.69/5.04 % times_int_code(2)
% 4.69/5.04 thf(fact_7437_times__int__code_I1_J,axiom,
% 4.69/5.04 ! [K3: int] :
% 4.69/5.04 ( ( times_times_int @ K3 @ zero_zero_int )
% 4.69/5.04 = zero_zero_int ) ).
% 4.69/5.04
% 4.69/5.04 % times_int_code(1)
% 4.69/5.04 thf(fact_7438_int__distrib_I1_J,axiom,
% 4.69/5.04 ! [Z1: int,Z22: int,W: int] :
% 4.69/5.04 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W )
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % int_distrib(1)
% 4.69/5.04 thf(fact_7439_int__distrib_I2_J,axiom,
% 4.69/5.04 ! [W: int,Z1: int,Z22: int] :
% 4.69/5.04 ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z22 ) )
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % int_distrib(2)
% 4.69/5.04 thf(fact_7440_int__distrib_I4_J,axiom,
% 4.69/5.04 ! [W: int,Z1: int,Z22: int] :
% 4.69/5.04 ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z22 ) )
% 4.69/5.04 = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % int_distrib(4)
% 4.69/5.04 thf(fact_7441_int__distrib_I3_J,axiom,
% 4.69/5.04 ! [Z1: int,Z22: int,W: int] :
% 4.69/5.04 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W )
% 4.69/5.04 = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % int_distrib(3)
% 4.69/5.04 thf(fact_7442_nat__mult__div__cancel1,axiom,
% 4.69/5.04 ! [K3: nat,M4: nat,N2: nat] :
% 4.69/5.04 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 4.69/5.04 => ( ( divide_divide_nat @ ( times_times_nat @ K3 @ M4 ) @ ( times_times_nat @ K3 @ N2 ) )
% 4.69/5.04 = ( divide_divide_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % nat_mult_div_cancel1
% 4.69/5.04 thf(fact_7443_div__mult__self__is__m,axiom,
% 4.69/5.04 ! [N2: nat,M4: nat] :
% 4.69/5.04 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.04 => ( ( divide_divide_nat @ ( times_times_nat @ M4 @ N2 ) @ N2 )
% 4.69/5.04 = M4 ) ) ).
% 4.69/5.04
% 4.69/5.04 % div_mult_self_is_m
% 4.69/5.04 thf(fact_7444_div__mult__self1__is__m,axiom,
% 4.69/5.04 ! [N2: nat,M4: nat] :
% 4.69/5.04 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.04 => ( ( divide_divide_nat @ ( times_times_nat @ N2 @ M4 ) @ N2 )
% 4.69/5.04 = M4 ) ) ).
% 4.69/5.04
% 4.69/5.04 % div_mult_self1_is_m
% 4.69/5.04 thf(fact_7445_div__mult2__eq,axiom,
% 4.69/5.04 ! [M4: nat,N2: nat,Q4: nat] :
% 4.69/5.04 ( ( divide_divide_nat @ M4 @ ( times_times_nat @ N2 @ Q4 ) )
% 4.69/5.04 = ( divide_divide_nat @ ( divide_divide_nat @ M4 @ N2 ) @ Q4 ) ) ).
% 4.69/5.04
% 4.69/5.04 % div_mult2_eq
% 4.69/5.04 thf(fact_7446_zdiv__zmult2__eq,axiom,
% 4.69/5.04 ! [C: int,A2: int,B: int] :
% 4.69/5.04 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.69/5.04 => ( ( divide_divide_int @ A2 @ ( times_times_int @ B @ C ) )
% 4.69/5.04 = ( divide_divide_int @ ( divide_divide_int @ A2 @ B ) @ C ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % zdiv_zmult2_eq
% 4.69/5.04 thf(fact_7447_less__mult__imp__div__less,axiom,
% 4.69/5.04 ! [M4: nat,I2: nat,N2: nat] :
% 4.69/5.04 ( ( ord_less_nat @ M4 @ ( times_times_nat @ I2 @ N2 ) )
% 4.69/5.04 => ( ord_less_nat @ ( divide_divide_nat @ M4 @ N2 ) @ I2 ) ) ).
% 4.69/5.04
% 4.69/5.04 % less_mult_imp_div_less
% 4.69/5.04 thf(fact_7448_div__times__less__eq__dividend,axiom,
% 4.69/5.04 ! [M4: nat,N2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M4 @ N2 ) @ N2 ) @ M4 ) ).
% 4.69/5.04
% 4.69/5.04 % div_times_less_eq_dividend
% 4.69/5.04 thf(fact_7449_times__div__less__eq__dividend,axiom,
% 4.69/5.04 ! [N2: nat,M4: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M4 @ N2 ) ) @ M4 ) ).
% 4.69/5.04
% 4.69/5.04 % times_div_less_eq_dividend
% 4.69/5.04 thf(fact_7450_div__less__iff__less__mult,axiom,
% 4.69/5.04 ! [Q4: nat,M4: nat,N2: nat] :
% 4.69/5.04 ( ( ord_less_nat @ zero_zero_nat @ Q4 )
% 4.69/5.04 => ( ( ord_less_nat @ ( divide_divide_nat @ M4 @ Q4 ) @ N2 )
% 4.69/5.04 = ( ord_less_nat @ M4 @ ( times_times_nat @ N2 @ Q4 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % div_less_iff_less_mult
% 4.69/5.04 thf(fact_7451_less__eq__div__iff__mult__less__eq,axiom,
% 4.69/5.04 ! [Q4: nat,M4: nat,N2: nat] :
% 4.69/5.04 ( ( ord_less_nat @ zero_zero_nat @ Q4 )
% 4.69/5.04 => ( ( ord_less_eq_nat @ M4 @ ( divide_divide_nat @ N2 @ Q4 ) )
% 4.69/5.04 = ( ord_less_eq_nat @ ( times_times_nat @ M4 @ Q4 ) @ N2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % less_eq_div_iff_mult_less_eq
% 4.69/5.04 thf(fact_7452_div__nat__eqI,axiom,
% 4.69/5.04 ! [N2: nat,Q4: nat,M4: nat] :
% 4.69/5.04 ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q4 ) @ M4 )
% 4.69/5.04 => ( ( ord_less_nat @ M4 @ ( times_times_nat @ N2 @ ( suc @ Q4 ) ) )
% 4.69/5.04 => ( ( divide_divide_nat @ M4 @ N2 )
% 4.69/5.04 = Q4 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % div_nat_eqI
% 4.69/5.04 thf(fact_7453_dividend__less__times__div,axiom,
% 4.69/5.04 ! [N2: nat,M4: nat] :
% 4.69/5.04 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.04 => ( ord_less_nat @ M4 @ ( plus_plus_nat @ N2 @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M4 @ N2 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % dividend_less_times_div
% 4.69/5.04 thf(fact_7454_dividend__less__div__times,axiom,
% 4.69/5.04 ! [N2: nat,M4: nat] :
% 4.69/5.04 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.04 => ( ord_less_nat @ M4 @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( divide_divide_nat @ M4 @ N2 ) @ N2 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % dividend_less_div_times
% 4.69/5.04 thf(fact_7455_split__div,axiom,
% 4.69/5.04 ! [P: nat > $o,M4: nat,N2: nat] :
% 4.69/5.04 ( ( P @ ( divide_divide_nat @ M4 @ N2 ) )
% 4.69/5.04 = ( ( ( N2 = zero_zero_nat )
% 4.69/5.04 => ( P @ zero_zero_nat ) )
% 4.69/5.04 & ( ( N2 != zero_zero_nat )
% 4.69/5.04 => ! [I4: nat,J3: nat] :
% 4.69/5.04 ( ( ord_less_nat @ J3 @ N2 )
% 4.69/5.04 => ( ( M4
% 4.69/5.04 = ( plus_plus_nat @ ( times_times_nat @ N2 @ I4 ) @ J3 ) )
% 4.69/5.04 => ( P @ I4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % split_div
% 4.69/5.04 thf(fact_7456_split__div_H,axiom,
% 4.69/5.04 ! [P: nat > $o,M4: nat,N2: nat] :
% 4.69/5.04 ( ( P @ ( divide_divide_nat @ M4 @ N2 ) )
% 4.69/5.04 = ( ( ( N2 = zero_zero_nat )
% 4.69/5.04 & ( P @ zero_zero_nat ) )
% 4.69/5.04 | ? [Q6: nat] :
% 4.69/5.04 ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q6 ) @ M4 )
% 4.69/5.04 & ( ord_less_nat @ M4 @ ( times_times_nat @ N2 @ ( suc @ Q6 ) ) )
% 4.69/5.04 & ( P @ Q6 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % split_div'
% 4.69/5.04 thf(fact_7457_int__ops_I7_J,axiom,
% 4.69/5.04 ! [A2: nat,B: nat] :
% 4.69/5.04 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A2 @ B ) )
% 4.69/5.04 = ( times_times_int @ ( semiri1314217659103216013at_int @ A2 ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % int_ops(7)
% 4.69/5.04 thf(fact_7458_eucl__rel__int__iff,axiom,
% 4.69/5.04 ! [K3: int,L: int,Q4: int,R2: int] :
% 4.69/5.04 ( ( eucl_rel_int @ K3 @ L @ ( product_Pair_int_int @ Q4 @ R2 ) )
% 4.69/5.04 = ( ( K3
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ L @ Q4 ) @ R2 ) )
% 4.69/5.04 & ( ( ord_less_int @ zero_zero_int @ L )
% 4.69/5.04 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 4.69/5.04 & ( ord_less_int @ R2 @ L ) ) )
% 4.69/5.04 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 4.69/5.04 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 4.69/5.04 => ( ( ord_less_int @ L @ R2 )
% 4.69/5.04 & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 4.69/5.04 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 4.69/5.04 => ( Q4 = zero_zero_int ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % eucl_rel_int_iff
% 4.69/5.04 thf(fact_7459_eucl__rel__int__dividesI,axiom,
% 4.69/5.04 ! [L: int,K3: int,Q4: int] :
% 4.69/5.04 ( ( L != zero_zero_int )
% 4.69/5.04 => ( ( K3
% 4.69/5.04 = ( times_times_int @ Q4 @ L ) )
% 4.69/5.04 => ( eucl_rel_int @ K3 @ L @ ( product_Pair_int_int @ Q4 @ zero_zero_int ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % eucl_rel_int_dividesI
% 4.69/5.04 thf(fact_7460_split__pos__lemma,axiom,
% 4.69/5.04 ! [K3: int,P: int > int > $o,N2: int] :
% 4.69/5.04 ( ( ord_less_int @ zero_zero_int @ K3 )
% 4.69/5.04 => ( ( P @ ( divide_divide_int @ N2 @ K3 ) @ ( modulo_modulo_int @ N2 @ K3 ) )
% 4.69/5.04 = ( ! [I4: int,J3: int] :
% 4.69/5.04 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 4.69/5.04 & ( ord_less_int @ J3 @ K3 )
% 4.69/5.04 & ( N2
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ K3 @ I4 ) @ J3 ) ) )
% 4.69/5.04 => ( P @ I4 @ J3 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % split_pos_lemma
% 4.69/5.04 thf(fact_7461_split__neg__lemma,axiom,
% 4.69/5.04 ! [K3: int,P: int > int > $o,N2: int] :
% 4.69/5.04 ( ( ord_less_int @ K3 @ zero_zero_int )
% 4.69/5.04 => ( ( P @ ( divide_divide_int @ N2 @ K3 ) @ ( modulo_modulo_int @ N2 @ K3 ) )
% 4.69/5.04 = ( ! [I4: int,J3: int] :
% 4.69/5.04 ( ( ( ord_less_int @ K3 @ J3 )
% 4.69/5.04 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 4.69/5.04 & ( N2
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ K3 @ I4 ) @ J3 ) ) )
% 4.69/5.04 => ( P @ I4 @ J3 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % split_neg_lemma
% 4.69/5.04 thf(fact_7462_decr__lemma,axiom,
% 4.69/5.04 ! [D2: int,X: int,Z: int] :
% 4.69/5.04 ( ( ord_less_int @ zero_zero_int @ D2 )
% 4.69/5.04 => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D2 ) ) @ Z ) ) ).
% 4.69/5.04
% 4.69/5.04 % decr_lemma
% 4.69/5.04 thf(fact_7463_incr__lemma,axiom,
% 4.69/5.04 ! [D2: int,Z: int,X: int] :
% 4.69/5.04 ( ( ord_less_int @ zero_zero_int @ D2 )
% 4.69/5.04 => ( ord_less_int @ Z @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D2 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % incr_lemma
% 4.69/5.04 thf(fact_7464_zmod__eq__0__iff,axiom,
% 4.69/5.04 ! [M4: int,D2: int] :
% 4.69/5.04 ( ( ( modulo_modulo_int @ M4 @ D2 )
% 4.69/5.04 = zero_zero_int )
% 4.69/5.04 = ( ? [Q6: int] :
% 4.69/5.04 ( M4
% 4.69/5.04 = ( times_times_int @ D2 @ Q6 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % zmod_eq_0_iff
% 4.69/5.04 thf(fact_7465_zmod__eq__0D,axiom,
% 4.69/5.04 ! [M4: int,D2: int] :
% 4.69/5.04 ( ( ( modulo_modulo_int @ M4 @ D2 )
% 4.69/5.04 = zero_zero_int )
% 4.69/5.04 => ? [Q7: int] :
% 4.69/5.04 ( M4
% 4.69/5.04 = ( times_times_int @ D2 @ Q7 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % zmod_eq_0D
% 4.69/5.04 thf(fact_7466_abs__zmult__eq__1,axiom,
% 4.69/5.04 ! [M4: int,N2: int] :
% 4.69/5.04 ( ( ( abs_abs_int @ ( times_times_int @ M4 @ N2 ) )
% 4.69/5.04 = one_one_int )
% 4.69/5.04 => ( ( abs_abs_int @ M4 )
% 4.69/5.04 = one_one_int ) ) ).
% 4.69/5.04
% 4.69/5.04 % abs_zmult_eq_1
% 4.69/5.04 thf(fact_7467_div__mod__decomp__int,axiom,
% 4.69/5.04 ! [A: int,N2: int] :
% 4.69/5.04 ( A
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ N2 ) @ N2 ) @ ( modulo_modulo_int @ A @ N2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % div_mod_decomp_int
% 4.69/5.04 thf(fact_7468_zdvd__mult__cancel1,axiom,
% 4.69/5.04 ! [M4: int,N2: int] :
% 4.69/5.04 ( ( M4 != zero_zero_int )
% 4.69/5.04 => ( ( dvd_dvd_int @ ( times_times_int @ M4 @ N2 ) @ M4 )
% 4.69/5.04 = ( ( abs_abs_int @ N2 )
% 4.69/5.04 = one_one_int ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % zdvd_mult_cancel1
% 4.69/5.04 thf(fact_7469_split__zmod,axiom,
% 4.69/5.04 ! [P: int > $o,N2: int,K3: int] :
% 4.69/5.04 ( ( P @ ( modulo_modulo_int @ N2 @ K3 ) )
% 4.69/5.04 = ( ( ( K3 = zero_zero_int )
% 4.69/5.04 => ( P @ N2 ) )
% 4.69/5.04 & ( ( ord_less_int @ zero_zero_int @ K3 )
% 4.69/5.04 => ! [I4: int,J3: int] :
% 4.69/5.04 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 4.69/5.04 & ( ord_less_int @ J3 @ K3 )
% 4.69/5.04 & ( N2
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ K3 @ I4 ) @ J3 ) ) )
% 4.69/5.04 => ( P @ J3 ) ) )
% 4.69/5.04 & ( ( ord_less_int @ K3 @ zero_zero_int )
% 4.69/5.04 => ! [I4: int,J3: int] :
% 4.69/5.04 ( ( ( ord_less_int @ K3 @ J3 )
% 4.69/5.04 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 4.69/5.04 & ( N2
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ K3 @ I4 ) @ J3 ) ) )
% 4.69/5.04 => ( P @ J3 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % split_zmod
% 4.69/5.04 thf(fact_7470_int__mod__neg__eq,axiom,
% 4.69/5.04 ! [A2: int,B: int,Q4: int,R2: int] :
% 4.69/5.04 ( ( A2
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R2 ) )
% 4.69/5.04 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 4.69/5.04 => ( ( ord_less_int @ B @ R2 )
% 4.69/5.04 => ( ( modulo_modulo_int @ A2 @ B )
% 4.69/5.04 = R2 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % int_mod_neg_eq
% 4.69/5.04 thf(fact_7471_int__mod__pos__eq,axiom,
% 4.69/5.04 ! [A2: int,B: int,Q4: int,R2: int] :
% 4.69/5.04 ( ( A2
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R2 ) )
% 4.69/5.04 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 4.69/5.04 => ( ( ord_less_int @ R2 @ B )
% 4.69/5.04 => ( ( modulo_modulo_int @ A2 @ B )
% 4.69/5.04 = R2 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % int_mod_pos_eq
% 4.69/5.04 thf(fact_7472_zmod__zmult2__eq,axiom,
% 4.69/5.04 ! [C: int,A2: int,B: int] :
% 4.69/5.04 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.69/5.04 => ( ( modulo_modulo_int @ A2 @ ( times_times_int @ B @ C ) )
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A2 @ B ) @ C ) ) @ ( modulo_modulo_int @ A2 @ B ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % zmod_zmult2_eq
% 4.69/5.04 thf(fact_7473_eucl__rel__int_Osimps,axiom,
% 4.69/5.04 ( eucl_rel_int
% 4.69/5.04 = ( ^ [A13: int,A24: int,A32: product_prod_int_int] :
% 4.69/5.04 ( ? [K5: int] :
% 4.69/5.04 ( ( A13 = K5 )
% 4.69/5.04 & ( A24 = zero_zero_int )
% 4.69/5.04 & ( A32
% 4.69/5.04 = ( product_Pair_int_int @ zero_zero_int @ K5 ) ) )
% 4.69/5.04 | ? [L2: int,K5: int,Q6: int] :
% 4.69/5.04 ( ( A13 = K5 )
% 4.69/5.04 & ( A24 = L2 )
% 4.69/5.04 & ( A32
% 4.69/5.04 = ( product_Pair_int_int @ Q6 @ zero_zero_int ) )
% 4.69/5.04 & ( L2 != zero_zero_int )
% 4.69/5.04 & ( K5
% 4.69/5.04 = ( times_times_int @ Q6 @ L2 ) ) )
% 4.69/5.04 | ? [R4: int,L2: int,K5: int,Q6: int] :
% 4.69/5.04 ( ( A13 = K5 )
% 4.69/5.04 & ( A24 = L2 )
% 4.69/5.04 & ( A32
% 4.69/5.04 = ( product_Pair_int_int @ Q6 @ R4 ) )
% 4.69/5.04 & ( ( sgn_sgn_int @ R4 )
% 4.69/5.04 = ( sgn_sgn_int @ L2 ) )
% 4.69/5.04 & ( ord_less_int @ ( abs_abs_int @ R4 ) @ ( abs_abs_int @ L2 ) )
% 4.69/5.04 & ( K5
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ Q6 @ L2 ) @ R4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % eucl_rel_int.simps
% 4.69/5.04 thf(fact_7474_Suc__mod__mult__self4,axiom,
% 4.69/5.04 ! [N2: nat,K3: nat,M4: nat] :
% 4.69/5.04 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N2 @ K3 ) @ M4 ) ) @ N2 )
% 4.69/5.04 = ( modulo_modulo_nat @ ( suc @ M4 ) @ N2 ) ) ).
% 4.69/5.04
% 4.69/5.04 % Suc_mod_mult_self4
% 4.69/5.04 thf(fact_7475_Suc__mod__mult__self3,axiom,
% 4.69/5.04 ! [K3: nat,N2: nat,M4: nat] :
% 4.69/5.04 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K3 @ N2 ) @ M4 ) ) @ N2 )
% 4.69/5.04 = ( modulo_modulo_nat @ ( suc @ M4 ) @ N2 ) ) ).
% 4.69/5.04
% 4.69/5.04 % Suc_mod_mult_self3
% 4.69/5.04 thf(fact_7476_Suc__mod__mult__self2,axiom,
% 4.69/5.04 ! [M4: nat,N2: nat,K3: nat] :
% 4.69/5.04 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M4 @ ( times_times_nat @ N2 @ K3 ) ) ) @ N2 )
% 4.69/5.04 = ( modulo_modulo_nat @ ( suc @ M4 ) @ N2 ) ) ).
% 4.69/5.04
% 4.69/5.04 % Suc_mod_mult_self2
% 4.69/5.04 thf(fact_7477_Suc__mod__mult__self1,axiom,
% 4.69/5.04 ! [M4: nat,K3: nat,N2: nat] :
% 4.69/5.04 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M4 @ ( times_times_nat @ K3 @ N2 ) ) ) @ N2 )
% 4.69/5.04 = ( modulo_modulo_nat @ ( suc @ M4 ) @ N2 ) ) ).
% 4.69/5.04
% 4.69/5.04 % Suc_mod_mult_self1
% 4.69/5.04 thf(fact_7478_Suc__times__numeral__mod__eq,axiom,
% 4.69/5.04 ! [K3: num,N2: nat] :
% 4.69/5.04 ( ( ( numeral_numeral_nat @ K3 )
% 4.69/5.04 != one_one_nat )
% 4.69/5.04 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K3 ) @ N2 ) ) @ ( numeral_numeral_nat @ K3 ) )
% 4.69/5.04 = one_one_nat ) ) ).
% 4.69/5.04
% 4.69/5.04 % Suc_times_numeral_mod_eq
% 4.69/5.04 thf(fact_7479_dvd__mult__sgn__iff,axiom,
% 4.69/5.04 ! [L: int,K3: int,R2: int] :
% 4.69/5.04 ( ( dvd_dvd_int @ L @ ( times_times_int @ K3 @ ( sgn_sgn_int @ R2 ) ) )
% 4.69/5.04 = ( ( dvd_dvd_int @ L @ K3 )
% 4.69/5.04 | ( R2 = zero_zero_int ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % dvd_mult_sgn_iff
% 4.69/5.04 thf(fact_7480_dvd__sgn__mult__iff,axiom,
% 4.69/5.04 ! [L: int,R2: int,K3: int] :
% 4.69/5.04 ( ( dvd_dvd_int @ L @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ K3 ) )
% 4.69/5.04 = ( ( dvd_dvd_int @ L @ K3 )
% 4.69/5.04 | ( R2 = zero_zero_int ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % dvd_sgn_mult_iff
% 4.69/5.04 thf(fact_7481_mult__sgn__dvd__iff,axiom,
% 4.69/5.04 ! [L: int,R2: int,K3: int] :
% 4.69/5.04 ( ( dvd_dvd_int @ ( times_times_int @ L @ ( sgn_sgn_int @ R2 ) ) @ K3 )
% 4.69/5.04 = ( ( dvd_dvd_int @ L @ K3 )
% 4.69/5.04 & ( ( R2 = zero_zero_int )
% 4.69/5.04 => ( K3 = zero_zero_int ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % mult_sgn_dvd_iff
% 4.69/5.04 thf(fact_7482_sgn__mult__dvd__iff,axiom,
% 4.69/5.04 ! [R2: int,L: int,K3: int] :
% 4.69/5.04 ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ L ) @ K3 )
% 4.69/5.04 = ( ( dvd_dvd_int @ L @ K3 )
% 4.69/5.04 & ( ( R2 = zero_zero_int )
% 4.69/5.04 => ( K3 = zero_zero_int ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sgn_mult_dvd_iff
% 4.69/5.04 thf(fact_7483_int__sgnE,axiom,
% 4.69/5.04 ! [K3: int] :
% 4.69/5.04 ~ ! [N3: nat,L3: int] :
% 4.69/5.04 ( K3
% 4.69/5.04 != ( times_times_int @ ( sgn_sgn_int @ L3 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % int_sgnE
% 4.69/5.04 thf(fact_7484_mod__eq__0D,axiom,
% 4.69/5.04 ! [M4: nat,D2: nat] :
% 4.69/5.04 ( ( ( modulo_modulo_nat @ M4 @ D2 )
% 4.69/5.04 = zero_zero_nat )
% 4.69/5.04 => ? [Q7: nat] :
% 4.69/5.04 ( M4
% 4.69/5.04 = ( times_times_nat @ D2 @ Q7 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % mod_eq_0D
% 4.69/5.04 thf(fact_7485_nat__mod__eq__iff,axiom,
% 4.69/5.04 ! [X: nat,N2: nat,Y: nat] :
% 4.69/5.04 ( ( ( modulo_modulo_nat @ X @ N2 )
% 4.69/5.04 = ( modulo_modulo_nat @ Y @ N2 ) )
% 4.69/5.04 = ( ? [Q1: nat,Q22: nat] :
% 4.69/5.04 ( ( plus_plus_nat @ X @ ( times_times_nat @ N2 @ Q1 ) )
% 4.69/5.04 = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q22 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % nat_mod_eq_iff
% 4.69/5.04 thf(fact_7486_nat__mod__eq__lemma,axiom,
% 4.69/5.04 ! [X: nat,N2: nat,Y: nat] :
% 4.69/5.04 ( ( ( modulo_modulo_nat @ X @ N2 )
% 4.69/5.04 = ( modulo_modulo_nat @ Y @ N2 ) )
% 4.69/5.04 => ( ( ord_less_eq_nat @ Y @ X )
% 4.69/5.04 => ? [Q7: nat] :
% 4.69/5.04 ( X
% 4.69/5.04 = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q7 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % nat_mod_eq_lemma
% 4.69/5.04 thf(fact_7487_mod__eq__nat2E,axiom,
% 4.69/5.04 ! [M4: nat,Q4: nat,N2: nat] :
% 4.69/5.04 ( ( ( modulo_modulo_nat @ M4 @ Q4 )
% 4.69/5.04 = ( modulo_modulo_nat @ N2 @ Q4 ) )
% 4.69/5.04 => ( ( ord_less_eq_nat @ M4 @ N2 )
% 4.69/5.04 => ~ ! [S8: nat] :
% 4.69/5.04 ( N2
% 4.69/5.04 != ( plus_plus_nat @ M4 @ ( times_times_nat @ Q4 @ S8 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % mod_eq_nat2E
% 4.69/5.04 thf(fact_7488_mod__eq__nat1E,axiom,
% 4.69/5.04 ! [M4: nat,Q4: nat,N2: nat] :
% 4.69/5.04 ( ( ( modulo_modulo_nat @ M4 @ Q4 )
% 4.69/5.04 = ( modulo_modulo_nat @ N2 @ Q4 ) )
% 4.69/5.04 => ( ( ord_less_eq_nat @ N2 @ M4 )
% 4.69/5.04 => ~ ! [S8: nat] :
% 4.69/5.04 ( M4
% 4.69/5.04 != ( plus_plus_nat @ N2 @ ( times_times_nat @ Q4 @ S8 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % mod_eq_nat1E
% 4.69/5.04 thf(fact_7489_div__mod__decomp,axiom,
% 4.69/5.04 ! [A: nat,N2: nat] :
% 4.69/5.04 ( A
% 4.69/5.04 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ N2 ) @ N2 ) @ ( modulo_modulo_nat @ A @ N2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % div_mod_decomp
% 4.69/5.04 thf(fact_7490_mod__mult2__eq,axiom,
% 4.69/5.04 ! [M4: nat,N2: nat,Q4: nat] :
% 4.69/5.04 ( ( modulo_modulo_nat @ M4 @ ( times_times_nat @ N2 @ Q4 ) )
% 4.69/5.04 = ( plus_plus_nat @ ( times_times_nat @ N2 @ ( modulo_modulo_nat @ ( divide_divide_nat @ M4 @ N2 ) @ Q4 ) ) @ ( modulo_modulo_nat @ M4 @ N2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % mod_mult2_eq
% 4.69/5.04 thf(fact_7491_modulo__nat__def,axiom,
% 4.69/5.04 ( modulo_modulo_nat
% 4.69/5.04 = ( ^ [M3: nat,N4: nat] : ( minus_minus_nat @ M3 @ ( times_times_nat @ ( divide_divide_nat @ M3 @ N4 ) @ N4 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % modulo_nat_def
% 4.69/5.04 thf(fact_7492_div__sgn__abs__cancel,axiom,
% 4.69/5.04 ! [V: int,K3: int,L: int] :
% 4.69/5.04 ( ( V != zero_zero_int )
% 4.69/5.04 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ K3 ) ) @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ L ) ) )
% 4.69/5.04 = ( divide_divide_int @ ( abs_abs_int @ K3 ) @ ( abs_abs_int @ L ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % div_sgn_abs_cancel
% 4.69/5.04 thf(fact_7493_div__dvd__sgn__abs,axiom,
% 4.69/5.04 ! [L: int,K3: int] :
% 4.69/5.04 ( ( dvd_dvd_int @ L @ K3 )
% 4.69/5.04 => ( ( divide_divide_int @ K3 @ L )
% 4.69/5.04 = ( times_times_int @ ( times_times_int @ ( sgn_sgn_int @ K3 ) @ ( sgn_sgn_int @ L ) ) @ ( divide_divide_int @ ( abs_abs_int @ K3 ) @ ( abs_abs_int @ L ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % div_dvd_sgn_abs
% 4.69/5.04 thf(fact_7494_split__mod,axiom,
% 4.69/5.04 ! [P: nat > $o,M4: nat,N2: nat] :
% 4.69/5.04 ( ( P @ ( modulo_modulo_nat @ M4 @ N2 ) )
% 4.69/5.04 = ( ( ( N2 = zero_zero_nat )
% 4.69/5.04 => ( P @ M4 ) )
% 4.69/5.04 & ( ( N2 != zero_zero_nat )
% 4.69/5.04 => ! [I4: nat,J3: nat] :
% 4.69/5.04 ( ( ord_less_nat @ J3 @ N2 )
% 4.69/5.04 => ( ( M4
% 4.69/5.04 = ( plus_plus_nat @ ( times_times_nat @ N2 @ I4 ) @ J3 ) )
% 4.69/5.04 => ( P @ J3 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % split_mod
% 4.69/5.04 thf(fact_7495_Suc__times__mod__eq,axiom,
% 4.69/5.04 ! [M4: nat,N2: nat] :
% 4.69/5.04 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M4 )
% 4.69/5.04 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M4 @ N2 ) ) @ M4 )
% 4.69/5.04 = one_one_nat ) ) ).
% 4.69/5.04
% 4.69/5.04 % Suc_times_mod_eq
% 4.69/5.04 thf(fact_7496_eucl__rel__int__remainderI,axiom,
% 4.69/5.04 ! [R2: int,L: int,K3: int,Q4: int] :
% 4.69/5.04 ( ( ( sgn_sgn_int @ R2 )
% 4.69/5.04 = ( sgn_sgn_int @ L ) )
% 4.69/5.04 => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L ) )
% 4.69/5.04 => ( ( K3
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ Q4 @ L ) @ R2 ) )
% 4.69/5.04 => ( eucl_rel_int @ K3 @ L @ ( product_Pair_int_int @ Q4 @ R2 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % eucl_rel_int_remainderI
% 4.69/5.04 thf(fact_7497_eucl__rel__int_Ocases,axiom,
% 4.69/5.04 ! [A1: int,A22: int,A33: product_prod_int_int] :
% 4.69/5.04 ( ( eucl_rel_int @ A1 @ A22 @ A33 )
% 4.69/5.04 => ( ( ( A22 = zero_zero_int )
% 4.69/5.04 => ( A33
% 4.69/5.04 != ( product_Pair_int_int @ zero_zero_int @ A1 ) ) )
% 4.69/5.04 => ( ! [Q7: int] :
% 4.69/5.04 ( ( A33
% 4.69/5.04 = ( product_Pair_int_int @ Q7 @ zero_zero_int ) )
% 4.69/5.04 => ( ( A22 != zero_zero_int )
% 4.69/5.04 => ( A1
% 4.69/5.04 != ( times_times_int @ Q7 @ A22 ) ) ) )
% 4.69/5.04 => ~ ! [R7: int,Q7: int] :
% 4.69/5.04 ( ( A33
% 4.69/5.04 = ( product_Pair_int_int @ Q7 @ R7 ) )
% 4.69/5.04 => ( ( ( sgn_sgn_int @ R7 )
% 4.69/5.04 = ( sgn_sgn_int @ A22 ) )
% 4.69/5.04 => ( ( ord_less_int @ ( abs_abs_int @ R7 ) @ ( abs_abs_int @ A22 ) )
% 4.69/5.04 => ( A1
% 4.69/5.04 != ( plus_plus_int @ ( times_times_int @ Q7 @ A22 ) @ R7 ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % eucl_rel_int.cases
% 4.69/5.04 thf(fact_7498_bezw_Oelims,axiom,
% 4.69/5.04 ! [X: nat,Xa: nat,Y: product_prod_int_int] :
% 4.69/5.04 ( ( ( bezw @ X @ Xa )
% 4.69/5.04 = Y )
% 4.69/5.04 => ( ( ( Xa = zero_zero_nat )
% 4.69/5.04 => ( Y
% 4.69/5.04 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 4.69/5.04 & ( ( Xa != zero_zero_nat )
% 4.69/5.04 => ( Y
% 4.69/5.04 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa ) ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % bezw.elims
% 4.69/5.04 thf(fact_7499_bezw_Osimps,axiom,
% 4.69/5.04 ( bezw
% 4.69/5.04 = ( ^ [X2: nat,Y3: nat] : ( if_Pro3027730157355071871nt_int @ ( Y3 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X2 @ Y3 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X2 @ Y3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X2 @ Y3 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Y3 ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % bezw.simps
% 4.69/5.04 thf(fact_7500_bezw__non__0,axiom,
% 4.69/5.04 ! [Y: nat,X: nat] :
% 4.69/5.04 ( ( ord_less_nat @ zero_zero_nat @ Y )
% 4.69/5.04 => ( ( bezw @ X @ Y )
% 4.69/5.04 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % bezw_non_0
% 4.69/5.04 thf(fact_7501_divide__int__unfold,axiom,
% 4.69/5.04 ! [L: int,K3: int,N2: nat,M4: nat] :
% 4.69/5.04 ( ( ( ( ( sgn_sgn_int @ L )
% 4.69/5.04 = zero_zero_int )
% 4.69/5.04 | ( ( sgn_sgn_int @ K3 )
% 4.69/5.04 = zero_zero_int )
% 4.69/5.04 | ( N2 = zero_zero_nat ) )
% 4.69/5.04 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K3 ) @ ( semiri1314217659103216013at_int @ M4 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 4.69/5.04 = zero_zero_int ) )
% 4.69/5.04 & ( ~ ( ( ( sgn_sgn_int @ L )
% 4.69/5.04 = zero_zero_int )
% 4.69/5.04 | ( ( sgn_sgn_int @ K3 )
% 4.69/5.04 = zero_zero_int )
% 4.69/5.04 | ( N2 = zero_zero_nat ) )
% 4.69/5.04 => ( ( ( ( sgn_sgn_int @ K3 )
% 4.69/5.04 = ( sgn_sgn_int @ L ) )
% 4.69/5.04 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K3 ) @ ( semiri1314217659103216013at_int @ M4 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 4.69/5.04 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M4 @ N2 ) ) ) )
% 4.69/5.04 & ( ( ( sgn_sgn_int @ K3 )
% 4.69/5.04 != ( sgn_sgn_int @ L ) )
% 4.69/5.04 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K3 ) @ ( semiri1314217659103216013at_int @ M4 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 4.69/5.04 = ( uminus_uminus_int
% 4.69/5.04 @ ( semiri1314217659103216013at_int
% 4.69/5.04 @ ( plus_plus_nat @ ( divide_divide_nat @ M4 @ N2 )
% 4.69/5.04 @ ( zero_n2687167440665602831ol_nat
% 4.69/5.04 @ ~ ( dvd_dvd_nat @ N2 @ M4 ) ) ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % divide_int_unfold
% 4.69/5.04 thf(fact_7502_modulo__int__unfold,axiom,
% 4.69/5.04 ! [L: int,K3: int,N2: nat,M4: nat] :
% 4.69/5.04 ( ( ( ( ( sgn_sgn_int @ L )
% 4.69/5.04 = zero_zero_int )
% 4.69/5.04 | ( ( sgn_sgn_int @ K3 )
% 4.69/5.04 = zero_zero_int )
% 4.69/5.04 | ( N2 = zero_zero_nat ) )
% 4.69/5.04 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K3 ) @ ( semiri1314217659103216013at_int @ M4 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 4.69/5.04 = ( times_times_int @ ( sgn_sgn_int @ K3 ) @ ( semiri1314217659103216013at_int @ M4 ) ) ) )
% 4.69/5.04 & ( ~ ( ( ( sgn_sgn_int @ L )
% 4.69/5.04 = zero_zero_int )
% 4.69/5.04 | ( ( sgn_sgn_int @ K3 )
% 4.69/5.04 = zero_zero_int )
% 4.69/5.04 | ( N2 = zero_zero_nat ) )
% 4.69/5.04 => ( ( ( ( sgn_sgn_int @ K3 )
% 4.69/5.04 = ( sgn_sgn_int @ L ) )
% 4.69/5.04 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K3 ) @ ( semiri1314217659103216013at_int @ M4 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 4.69/5.04 = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M4 @ N2 ) ) ) ) )
% 4.69/5.04 & ( ( ( sgn_sgn_int @ K3 )
% 4.69/5.04 != ( sgn_sgn_int @ L ) )
% 4.69/5.04 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K3 ) @ ( semiri1314217659103216013at_int @ M4 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 4.69/5.04 = ( times_times_int @ ( sgn_sgn_int @ L )
% 4.69/5.04 @ ( minus_minus_int
% 4.69/5.04 @ ( semiri1314217659103216013at_int
% 4.69/5.04 @ ( times_times_nat @ N2
% 4.69/5.04 @ ( zero_n2687167440665602831ol_nat
% 4.69/5.04 @ ~ ( dvd_dvd_nat @ N2 @ M4 ) ) ) )
% 4.69/5.04 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M4 @ N2 ) ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % modulo_int_unfold
% 4.69/5.04 thf(fact_7503_bezw_Opelims,axiom,
% 4.69/5.04 ! [X: nat,Xa: nat,Y: product_prod_int_int] :
% 4.69/5.04 ( ( ( bezw @ X @ Xa )
% 4.69/5.04 = Y )
% 4.69/5.04 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 4.69/5.04 => ~ ( ( ( ( Xa = zero_zero_nat )
% 4.69/5.04 => ( Y
% 4.69/5.04 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 4.69/5.04 & ( ( Xa != zero_zero_nat )
% 4.69/5.04 => ( Y
% 4.69/5.04 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa ) ) ) ) ) ) ) )
% 4.69/5.04 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % bezw.pelims
% 4.69/5.04 thf(fact_7504_semiring__norm_I12_J,axiom,
% 4.69/5.04 ! [N2: num] :
% 4.69/5.04 ( ( times_times_num @ one @ N2 )
% 4.69/5.04 = N2 ) ).
% 4.69/5.04
% 4.69/5.04 % semiring_norm(12)
% 4.69/5.04 thf(fact_7505_semiring__norm_I11_J,axiom,
% 4.69/5.04 ! [M4: num] :
% 4.69/5.04 ( ( times_times_num @ M4 @ one )
% 4.69/5.04 = M4 ) ).
% 4.69/5.04
% 4.69/5.04 % semiring_norm(11)
% 4.69/5.04 thf(fact_7506_neg__eucl__rel__int__mult__2,axiom,
% 4.69/5.04 ! [B: int,A2: int,Q4: int,R2: int] :
% 4.69/5.04 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 4.69/5.04 => ( ( eucl_rel_int @ ( plus_plus_int @ A2 @ one_one_int ) @ B @ ( product_Pair_int_int @ Q4 @ R2 ) )
% 4.69/5.04 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q4 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) @ one_one_int ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % neg_eucl_rel_int_mult_2
% 4.69/5.04 thf(fact_7507_semiring__norm_I13_J,axiom,
% 4.69/5.04 ! [M4: num,N2: num] :
% 4.69/5.04 ( ( times_times_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) )
% 4.69/5.04 = ( bit0 @ ( bit0 @ ( times_times_num @ M4 @ N2 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % semiring_norm(13)
% 4.69/5.04 thf(fact_7508_num__double,axiom,
% 4.69/5.04 ! [N2: num] :
% 4.69/5.04 ( ( times_times_num @ ( bit0 @ one ) @ N2 )
% 4.69/5.04 = ( bit0 @ N2 ) ) ).
% 4.69/5.04
% 4.69/5.04 % num_double
% 4.69/5.04 thf(fact_7509_zmod__numeral__Bit0,axiom,
% 4.69/5.04 ! [V: num,W: num] :
% 4.69/5.04 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 4.69/5.04 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % zmod_numeral_Bit0
% 4.69/5.04 thf(fact_7510_odd__two__times__div__two__nat,axiom,
% 4.69/5.04 ! [N2: nat] :
% 4.69/5.04 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 4.69/5.04 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.69/5.04 = ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % odd_two_times_div_two_nat
% 4.69/5.04 thf(fact_7511_Suc__double__not__eq__double,axiom,
% 4.69/5.04 ! [M4: nat,N2: nat] :
% 4.69/5.04 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 4.69/5.04 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 4.69/5.04
% 4.69/5.04 % Suc_double_not_eq_double
% 4.69/5.04 thf(fact_7512_double__not__eq__Suc__double,axiom,
% 4.69/5.04 ! [M4: nat,N2: nat] :
% 4.69/5.04 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 )
% 4.69/5.04 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % double_not_eq_Suc_double
% 4.69/5.04 thf(fact_7513_nat__bit__induct,axiom,
% 4.69/5.04 ! [P: nat > $o,N2: nat] :
% 4.69/5.04 ( ( P @ zero_zero_nat )
% 4.69/5.04 => ( ! [N3: nat] :
% 4.69/5.04 ( ( P @ N3 )
% 4.69/5.04 => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 4.69/5.04 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 4.69/5.04 => ( ! [N3: nat] :
% 4.69/5.04 ( ( P @ N3 )
% 4.69/5.04 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 4.69/5.04 => ( P @ N2 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % nat_bit_induct
% 4.69/5.04 thf(fact_7514_int__bit__induct,axiom,
% 4.69/5.04 ! [P: int > $o,K3: int] :
% 4.69/5.04 ( ( P @ zero_zero_int )
% 4.69/5.04 => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 4.69/5.04 => ( ! [K: int] :
% 4.69/5.04 ( ( P @ K )
% 4.69/5.04 => ( ( K != zero_zero_int )
% 4.69/5.04 => ( P @ ( times_times_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 4.69/5.04 => ( ! [K: int] :
% 4.69/5.04 ( ( P @ K )
% 4.69/5.04 => ( ( K
% 4.69/5.04 != ( uminus_uminus_int @ one_one_int ) )
% 4.69/5.04 => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 4.69/5.04 => ( P @ K3 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % int_bit_induct
% 4.69/5.04 thf(fact_7515_pos__zdiv__mult__2,axiom,
% 4.69/5.04 ! [A2: int,B: int] :
% 4.69/5.04 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 4.69/5.04 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) )
% 4.69/5.04 = ( divide_divide_int @ B @ A2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % pos_zdiv_mult_2
% 4.69/5.04 thf(fact_7516_neg__zdiv__mult__2,axiom,
% 4.69/5.04 ! [A2: int,B: int] :
% 4.69/5.04 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 4.69/5.04 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) )
% 4.69/5.04 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % neg_zdiv_mult_2
% 4.69/5.04 thf(fact_7517_pos__zmod__mult__2,axiom,
% 4.69/5.04 ! [A2: int,B: int] :
% 4.69/5.04 ( ( ord_less_eq_int @ zero_zero_int @ A2 )
% 4.69/5.04 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) )
% 4.69/5.04 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A2 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % pos_zmod_mult_2
% 4.69/5.04 thf(fact_7518_neg__zmod__mult__2,axiom,
% 4.69/5.04 ! [A2: int,B: int] :
% 4.69/5.04 ( ( ord_less_eq_int @ A2 @ zero_zero_int )
% 4.69/5.04 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) )
% 4.69/5.04 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ B @ one_one_int ) @ A2 ) ) @ one_one_int ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % neg_zmod_mult_2
% 4.69/5.04 thf(fact_7519_pos__eucl__rel__int__mult__2,axiom,
% 4.69/5.04 ! [B: int,A2: int,Q4: int,R2: int] :
% 4.69/5.04 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.69/5.04 => ( ( eucl_rel_int @ A2 @ B @ ( product_Pair_int_int @ Q4 @ R2 ) )
% 4.69/5.04 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q4 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % pos_eucl_rel_int_mult_2
% 4.69/5.04 thf(fact_7520_signed__take__bit__Suc__bit0,axiom,
% 4.69/5.04 ! [N2: nat,K3: num] :
% 4.69/5.04 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ K3 ) ) )
% 4.69/5.04 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( numeral_numeral_int @ K3 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % signed_take_bit_Suc_bit0
% 4.69/5.04 thf(fact_7521_signed__take__bit__Suc__minus__bit0,axiom,
% 4.69/5.04 ! [N2: nat,K3: num] :
% 4.69/5.04 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K3 ) ) ) )
% 4.69/5.04 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K3 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % signed_take_bit_Suc_minus_bit0
% 4.69/5.04 thf(fact_7522_signed__take__bit__mult,axiom,
% 4.69/5.04 ! [N2: nat,K3: int,L: int] :
% 4.69/5.04 ( ( bit_ri631733984087533419it_int @ N2 @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ K3 ) @ ( bit_ri631733984087533419it_int @ N2 @ L ) ) )
% 4.69/5.04 = ( bit_ri631733984087533419it_int @ N2 @ ( times_times_int @ K3 @ L ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % signed_take_bit_mult
% 4.69/5.04 thf(fact_7523_and__int_Oelims,axiom,
% 4.69/5.04 ! [X: int,Xa: int,Y: int] :
% 4.69/5.04 ( ( ( bit_se725231765392027082nd_int @ X @ Xa )
% 4.69/5.04 = Y )
% 4.69/5.04 => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 4.69/5.04 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 4.69/5.04 => ( Y
% 4.69/5.04 = ( uminus_uminus_int
% 4.69/5.04 @ ( zero_n2684676970156552555ol_int
% 4.69/5.04 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 4.69/5.04 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 4.69/5.04 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 4.69/5.04 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 4.69/5.04 => ( Y
% 4.69/5.04 = ( plus_plus_int
% 4.69/5.04 @ ( zero_n2684676970156552555ol_int
% 4.69/5.04 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 4.69/5.04 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 4.69/5.04 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % and_int.elims
% 4.69/5.04 thf(fact_7524_and__int_Osimps,axiom,
% 4.69/5.04 ( bit_se725231765392027082nd_int
% 4.69/5.04 = ( ^ [K5: int,L2: int] :
% 4.69/5.04 ( if_int
% 4.69/5.04 @ ( ( member_int @ K5 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 4.69/5.04 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 4.69/5.04 @ ( uminus_uminus_int
% 4.69/5.04 @ ( zero_n2684676970156552555ol_int
% 4.69/5.04 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K5 )
% 4.69/5.04 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 4.69/5.04 @ ( plus_plus_int
% 4.69/5.04 @ ( zero_n2684676970156552555ol_int
% 4.69/5.04 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K5 )
% 4.69/5.04 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 4.69/5.04 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % and_int.simps
% 4.69/5.04 thf(fact_7525_signed__take__bit__Suc__minus__bit1,axiom,
% 4.69/5.04 ! [N2: nat,K3: num] :
% 4.69/5.04 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K3 ) ) ) )
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K3 ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 4.69/5.04
% 4.69/5.04 % signed_take_bit_Suc_minus_bit1
% 4.69/5.04 thf(fact_7526_concat__bit__Suc,axiom,
% 4.69/5.04 ! [N2: nat,K3: int,L: int] :
% 4.69/5.04 ( ( bit_concat_bit @ ( suc @ N2 ) @ K3 @ L )
% 4.69/5.04 = ( plus_plus_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N2 @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % concat_bit_Suc
% 4.69/5.04 thf(fact_7527_semiring__norm_I14_J,axiom,
% 4.69/5.04 ! [M4: num,N2: num] :
% 4.69/5.04 ( ( times_times_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) )
% 4.69/5.04 = ( bit0 @ ( times_times_num @ M4 @ ( bit1 @ N2 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % semiring_norm(14)
% 4.69/5.04 thf(fact_7528_semiring__norm_I15_J,axiom,
% 4.69/5.04 ! [M4: num,N2: num] :
% 4.69/5.04 ( ( times_times_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) )
% 4.69/5.04 = ( bit0 @ ( times_times_num @ ( bit1 @ M4 ) @ N2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % semiring_norm(15)
% 4.69/5.04 thf(fact_7529_semiring__norm_I16_J,axiom,
% 4.69/5.04 ! [M4: num,N2: num] :
% 4.69/5.04 ( ( times_times_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) )
% 4.69/5.04 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M4 @ N2 ) @ ( bit0 @ ( times_times_num @ M4 @ N2 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % semiring_norm(16)
% 4.69/5.04 thf(fact_7530_zmod__numeral__Bit1,axiom,
% 4.69/5.04 ! [V: num,W: num] :
% 4.69/5.04 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) @ one_one_int ) ) ).
% 4.69/5.04
% 4.69/5.04 % zmod_numeral_Bit1
% 4.69/5.04 thf(fact_7531_signed__take__bit__Suc__bit1,axiom,
% 4.69/5.04 ! [N2: nat,K3: num] :
% 4.69/5.04 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K3 ) ) )
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( numeral_numeral_int @ K3 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 4.69/5.04
% 4.69/5.04 % signed_take_bit_Suc_bit1
% 4.69/5.04 thf(fact_7532_take__bit__mult,axiom,
% 4.69/5.04 ! [N2: nat,K3: int,L: int] :
% 4.69/5.04 ( ( bit_se2923211474154528505it_int @ N2 @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ K3 ) @ ( bit_se2923211474154528505it_int @ N2 @ L ) ) )
% 4.69/5.04 = ( bit_se2923211474154528505it_int @ N2 @ ( times_times_int @ K3 @ L ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % take_bit_mult
% 4.69/5.04 thf(fact_7533_take__bit__Suc__minus__bit0,axiom,
% 4.69/5.04 ! [N2: nat,K3: num] :
% 4.69/5.04 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K3 ) ) ) )
% 4.69/5.04 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K3 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % take_bit_Suc_minus_bit0
% 4.69/5.04 thf(fact_7534_and__int__rec,axiom,
% 4.69/5.04 ( bit_se725231765392027082nd_int
% 4.69/5.04 = ( ^ [K5: int,L2: int] :
% 4.69/5.04 ( plus_plus_int
% 4.69/5.04 @ ( zero_n2684676970156552555ol_int
% 4.69/5.04 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K5 )
% 4.69/5.04 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 4.69/5.04 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % and_int_rec
% 4.69/5.04 thf(fact_7535_and__int__unfold,axiom,
% 4.69/5.04 ( bit_se725231765392027082nd_int
% 4.69/5.04 = ( ^ [K5: int,L2: int] :
% 4.69/5.04 ( if_int
% 4.69/5.04 @ ( ( K5 = zero_zero_int )
% 4.69/5.04 | ( L2 = zero_zero_int ) )
% 4.69/5.04 @ zero_zero_int
% 4.69/5.04 @ ( if_int
% 4.69/5.04 @ ( K5
% 4.69/5.04 = ( uminus_uminus_int @ one_one_int ) )
% 4.69/5.04 @ L2
% 4.69/5.04 @ ( if_int
% 4.69/5.04 @ ( L2
% 4.69/5.04 = ( uminus_uminus_int @ one_one_int ) )
% 4.69/5.04 @ K5
% 4.69/5.04 @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % and_int_unfold
% 4.69/5.04 thf(fact_7536_signed__take__bit__numeral__minus__bit1,axiom,
% 4.69/5.04 ! [L: num,K3: num] :
% 4.69/5.04 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K3 ) ) ) )
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K3 ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 4.69/5.04
% 4.69/5.04 % signed_take_bit_numeral_minus_bit1
% 4.69/5.04 thf(fact_7537_signed__take__bit__numeral__bit1,axiom,
% 4.69/5.04 ! [L: num,K3: num] :
% 4.69/5.04 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K3 ) ) )
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K3 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 4.69/5.04
% 4.69/5.04 % signed_take_bit_numeral_bit1
% 4.69/5.04 thf(fact_7538_and__int_Opsimps,axiom,
% 4.69/5.04 ! [K3: int,L: int] :
% 4.69/5.04 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K3 @ L ) )
% 4.69/5.04 => ( ( ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 4.69/5.04 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 4.69/5.04 => ( ( bit_se725231765392027082nd_int @ K3 @ L )
% 4.69/5.04 = ( uminus_uminus_int
% 4.69/5.04 @ ( zero_n2684676970156552555ol_int
% 4.69/5.04 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 4.69/5.04 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 4.69/5.04 & ( ~ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 4.69/5.04 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 4.69/5.04 => ( ( bit_se725231765392027082nd_int @ K3 @ L )
% 4.69/5.04 = ( plus_plus_int
% 4.69/5.04 @ ( zero_n2684676970156552555ol_int
% 4.69/5.04 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 4.69/5.04 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 4.69/5.04 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % and_int.psimps
% 4.69/5.04 thf(fact_7539_and__int_Opelims,axiom,
% 4.69/5.04 ! [X: int,Xa: int,Y: int] :
% 4.69/5.04 ( ( ( bit_se725231765392027082nd_int @ X @ Xa )
% 4.69/5.04 = Y )
% 4.69/5.04 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa ) )
% 4.69/5.04 => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 4.69/5.04 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 4.69/5.04 => ( Y
% 4.69/5.04 = ( uminus_uminus_int
% 4.69/5.04 @ ( zero_n2684676970156552555ol_int
% 4.69/5.04 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 4.69/5.04 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 4.69/5.04 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 4.69/5.04 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 4.69/5.04 => ( Y
% 4.69/5.04 = ( plus_plus_int
% 4.69/5.04 @ ( zero_n2684676970156552555ol_int
% 4.69/5.04 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 4.69/5.04 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 4.69/5.04 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 4.69/5.04 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % and_int.pelims
% 4.69/5.04 thf(fact_7540_signed__take__bit__numeral__bit0,axiom,
% 4.69/5.04 ! [L: num,K3: num] :
% 4.69/5.04 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K3 ) ) )
% 4.69/5.04 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K3 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % signed_take_bit_numeral_bit0
% 4.69/5.04 thf(fact_7541_signed__take__bit__numeral__minus__bit0,axiom,
% 4.69/5.04 ! [L: num,K3: num] :
% 4.69/5.04 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K3 ) ) ) )
% 4.69/5.04 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K3 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % signed_take_bit_numeral_minus_bit0
% 4.69/5.04 thf(fact_7542_take__bit__numeral__minus__bit0,axiom,
% 4.69/5.04 ! [L: num,K3: num] :
% 4.69/5.04 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K3 ) ) ) )
% 4.69/5.04 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K3 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % take_bit_numeral_minus_bit0
% 4.69/5.04 thf(fact_7543_and__nat__unfold,axiom,
% 4.69/5.04 ( bit_se727722235901077358nd_nat
% 4.69/5.04 = ( ^ [M3: nat,N4: nat] :
% 4.69/5.04 ( if_nat
% 4.69/5.04 @ ( ( M3 = zero_zero_nat )
% 4.69/5.04 | ( N4 = zero_zero_nat ) )
% 4.69/5.04 @ zero_zero_nat
% 4.69/5.04 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % and_nat_unfold
% 4.69/5.04 thf(fact_7544_and__nat__rec,axiom,
% 4.69/5.04 ( bit_se727722235901077358nd_nat
% 4.69/5.04 = ( ^ [M3: nat,N4: nat] :
% 4.69/5.04 ( plus_plus_nat
% 4.69/5.04 @ ( zero_n2687167440665602831ol_nat
% 4.69/5.04 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 4.69/5.04 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 4.69/5.04 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % and_nat_rec
% 4.69/5.04 thf(fact_7545_and__int_Opinduct,axiom,
% 4.69/5.04 ! [A0: int,A1: int,P: int > int > $o] :
% 4.69/5.04 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 4.69/5.04 => ( ! [K: int,L3: int] :
% 4.69/5.04 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L3 ) )
% 4.69/5.04 => ( ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 4.69/5.04 & ( member_int @ L3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 4.69/5.04 => ( P @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 4.69/5.04 => ( P @ K @ L3 ) ) )
% 4.69/5.04 => ( P @ A0 @ A1 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % and_int.pinduct
% 4.69/5.04 thf(fact_7546_take__bit__numeral__minus__bit1,axiom,
% 4.69/5.04 ! [L: num,K3: num] :
% 4.69/5.04 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K3 ) ) ) )
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K3 ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 4.69/5.04
% 4.69/5.04 % take_bit_numeral_minus_bit1
% 4.69/5.04 thf(fact_7547_take__bit__Suc__minus__bit1,axiom,
% 4.69/5.04 ! [N2: nat,K3: num] :
% 4.69/5.04 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K3 ) ) ) )
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K3 ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 4.69/5.04
% 4.69/5.04 % take_bit_Suc_minus_bit1
% 4.69/5.04 thf(fact_7548_binomial__code,axiom,
% 4.69/5.04 ( binomial
% 4.69/5.04 = ( ^ [N4: nat,K5: nat] : ( if_nat @ ( ord_less_nat @ N4 @ K5 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K5 ) ) @ ( binomial @ N4 @ ( minus_minus_nat @ N4 @ K5 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N4 @ K5 ) @ one_one_nat ) @ N4 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K5 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % binomial_code
% 4.69/5.04 thf(fact_7549_modulo__int__def,axiom,
% 4.69/5.04 ( modulo_modulo_int
% 4.69/5.04 = ( ^ [K5: int,L2: int] :
% 4.69/5.04 ( if_int @ ( L2 = zero_zero_int ) @ K5
% 4.69/5.04 @ ( if_int
% 4.69/5.04 @ ( ( sgn_sgn_int @ K5 )
% 4.69/5.04 = ( sgn_sgn_int @ L2 ) )
% 4.69/5.04 @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K5 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) )
% 4.69/5.04 @ ( times_times_int @ ( sgn_sgn_int @ L2 )
% 4.69/5.04 @ ( minus_minus_int
% 4.69/5.04 @ ( times_times_int @ ( abs_abs_int @ L2 )
% 4.69/5.04 @ ( zero_n2684676970156552555ol_int
% 4.69/5.04 @ ~ ( dvd_dvd_int @ L2 @ K5 ) ) )
% 4.69/5.04 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K5 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % modulo_int_def
% 4.69/5.04 thf(fact_7550_or__int__unfold,axiom,
% 4.69/5.04 ( bit_se1409905431419307370or_int
% 4.69/5.04 = ( ^ [K5: int,L2: int] :
% 4.69/5.04 ( if_int
% 4.69/5.04 @ ( ( K5
% 4.69/5.04 = ( uminus_uminus_int @ one_one_int ) )
% 4.69/5.04 | ( L2
% 4.69/5.04 = ( uminus_uminus_int @ one_one_int ) ) )
% 4.69/5.04 @ ( uminus_uminus_int @ one_one_int )
% 4.69/5.04 @ ( if_int @ ( K5 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K5 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % or_int_unfold
% 4.69/5.04 thf(fact_7551_Suc__times__binomial__eq,axiom,
% 4.69/5.04 ! [N2: nat,K3: nat] :
% 4.69/5.04 ( ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K3 ) )
% 4.69/5.04 = ( times_times_nat @ ( binomial @ ( suc @ N2 ) @ ( suc @ K3 ) ) @ ( suc @ K3 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % Suc_times_binomial_eq
% 4.69/5.04 thf(fact_7552_Suc__times__binomial,axiom,
% 4.69/5.04 ! [K3: nat,N2: nat] :
% 4.69/5.04 ( ( times_times_nat @ ( suc @ K3 ) @ ( binomial @ ( suc @ N2 ) @ ( suc @ K3 ) ) )
% 4.69/5.04 = ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K3 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % Suc_times_binomial
% 4.69/5.04 thf(fact_7553_choose__mult__lemma,axiom,
% 4.69/5.04 ! [M4: nat,R2: nat,K3: nat] :
% 4.69/5.04 ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M4 @ R2 ) @ K3 ) @ ( plus_plus_nat @ M4 @ K3 ) ) @ ( binomial @ ( plus_plus_nat @ M4 @ K3 ) @ K3 ) )
% 4.69/5.04 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M4 @ R2 ) @ K3 ) @ K3 ) @ ( binomial @ ( plus_plus_nat @ M4 @ R2 ) @ M4 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % choose_mult_lemma
% 4.69/5.04 thf(fact_7554_Suc__times__binomial__add,axiom,
% 4.69/5.04 ! [A2: nat,B: nat] :
% 4.69/5.04 ( ( times_times_nat @ ( suc @ A2 ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A2 @ B ) ) @ ( suc @ A2 ) ) )
% 4.69/5.04 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A2 @ B ) ) @ A2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % Suc_times_binomial_add
% 4.69/5.04 thf(fact_7555_binomial__fact__lemma,axiom,
% 4.69/5.04 ! [K3: nat,N2: nat] :
% 4.69/5.04 ( ( ord_less_eq_nat @ K3 @ N2 )
% 4.69/5.04 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K3 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K3 ) ) ) @ ( binomial @ N2 @ K3 ) )
% 4.69/5.04 = ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % binomial_fact_lemma
% 4.69/5.04 thf(fact_7556_choose__mult,axiom,
% 4.69/5.04 ! [K3: nat,M4: nat,N2: nat] :
% 4.69/5.04 ( ( ord_less_eq_nat @ K3 @ M4 )
% 4.69/5.04 => ( ( ord_less_eq_nat @ M4 @ N2 )
% 4.69/5.04 => ( ( times_times_nat @ ( binomial @ N2 @ M4 ) @ ( binomial @ M4 @ K3 ) )
% 4.69/5.04 = ( times_times_nat @ ( binomial @ N2 @ K3 ) @ ( binomial @ ( minus_minus_nat @ N2 @ K3 ) @ ( minus_minus_nat @ M4 @ K3 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % choose_mult
% 4.69/5.04 thf(fact_7557_binomial__absorb__comp,axiom,
% 4.69/5.04 ! [N2: nat,K3: nat] :
% 4.69/5.04 ( ( times_times_nat @ ( minus_minus_nat @ N2 @ K3 ) @ ( binomial @ N2 @ K3 ) )
% 4.69/5.04 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K3 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % binomial_absorb_comp
% 4.69/5.04 thf(fact_7558_binomial__Suc__Suc__eq__times,axiom,
% 4.69/5.04 ! [N2: nat,K3: nat] :
% 4.69/5.04 ( ( binomial @ ( suc @ N2 ) @ ( suc @ K3 ) )
% 4.69/5.04 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K3 ) ) @ ( suc @ K3 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % binomial_Suc_Suc_eq_times
% 4.69/5.04 thf(fact_7559_nat__abs__mult__distrib,axiom,
% 4.69/5.04 ! [W: int,Z: int] :
% 4.69/5.04 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 4.69/5.04 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % nat_abs_mult_distrib
% 4.69/5.04 thf(fact_7560_mult__inc,axiom,
% 4.69/5.04 ! [X: num,Y: num] :
% 4.69/5.04 ( ( times_times_num @ X @ ( inc @ Y ) )
% 4.69/5.04 = ( plus_plus_num @ ( times_times_num @ X @ Y ) @ X ) ) ).
% 4.69/5.04
% 4.69/5.04 % mult_inc
% 4.69/5.04 thf(fact_7561_binomial__absorption,axiom,
% 4.69/5.04 ! [K3: nat,N2: nat] :
% 4.69/5.04 ( ( times_times_nat @ ( suc @ K3 ) @ ( binomial @ N2 @ ( suc @ K3 ) ) )
% 4.69/5.04 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K3 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % binomial_absorption
% 4.69/5.04 thf(fact_7562_nat__mult__distrib,axiom,
% 4.69/5.04 ! [Z: int,Z7: int] :
% 4.69/5.04 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 4.69/5.04 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 4.69/5.04 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % nat_mult_distrib
% 4.69/5.04 thf(fact_7563_binomial__altdef__nat,axiom,
% 4.69/5.04 ! [K3: nat,N2: nat] :
% 4.69/5.04 ( ( ord_less_eq_nat @ K3 @ N2 )
% 4.69/5.04 => ( ( binomial @ N2 @ K3 )
% 4.69/5.04 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K3 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K3 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % binomial_altdef_nat
% 4.69/5.04 thf(fact_7564_times__binomial__minus1__eq,axiom,
% 4.69/5.04 ! [K3: nat,N2: nat] :
% 4.69/5.04 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 4.69/5.04 => ( ( times_times_nat @ K3 @ ( binomial @ N2 @ K3 ) )
% 4.69/5.04 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K3 @ one_one_nat ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % times_binomial_minus1_eq
% 4.69/5.04 thf(fact_7565_nat__mult__distrib__neg,axiom,
% 4.69/5.04 ! [Z: int,Z7: int] :
% 4.69/5.04 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 4.69/5.04 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 4.69/5.04 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z7 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % nat_mult_distrib_neg
% 4.69/5.04 thf(fact_7566_choose__two,axiom,
% 4.69/5.04 ! [N2: nat] :
% 4.69/5.04 ( ( binomial @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.69/5.04 = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % choose_two
% 4.69/5.04 thf(fact_7567_or__int__rec,axiom,
% 4.69/5.04 ( bit_se1409905431419307370or_int
% 4.69/5.04 = ( ^ [K5: int,L2: int] :
% 4.69/5.04 ( plus_plus_int
% 4.69/5.04 @ ( zero_n2684676970156552555ol_int
% 4.69/5.04 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K5 )
% 4.69/5.04 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 4.69/5.04 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % or_int_rec
% 4.69/5.04 thf(fact_7568_signed__take__bit__eq__take__bit__minus,axiom,
% 4.69/5.04 ( bit_ri631733984087533419it_int
% 4.69/5.04 = ( ^ [N4: nat,K5: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ K5 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K5 @ N4 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % signed_take_bit_eq_take_bit_minus
% 4.69/5.04 thf(fact_7569_or__nat__unfold,axiom,
% 4.69/5.04 ( bit_se1412395901928357646or_nat
% 4.69/5.04 = ( ^ [M3: nat,N4: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N4 @ ( if_nat @ ( N4 = zero_zero_nat ) @ M3 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % or_nat_unfold
% 4.69/5.04 thf(fact_7570_push__bit__int__def,axiom,
% 4.69/5.04 ( bit_se545348938243370406it_int
% 4.69/5.04 = ( ^ [N4: nat,K5: int] : ( times_times_int @ K5 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % push_bit_int_def
% 4.69/5.04 thf(fact_7571_push__bit__nat__def,axiom,
% 4.69/5.04 ( bit_se547839408752420682it_nat
% 4.69/5.04 = ( ^ [N4: nat,M3: nat] : ( times_times_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % push_bit_nat_def
% 4.69/5.04 thf(fact_7572_set__bit__eq,axiom,
% 4.69/5.04 ( bit_se7879613467334960850it_int
% 4.69/5.04 = ( ^ [N4: nat,K5: int] :
% 4.69/5.04 ( plus_plus_int @ K5
% 4.69/5.04 @ ( times_times_int
% 4.69/5.04 @ ( zero_n2684676970156552555ol_int
% 4.69/5.04 @ ~ ( bit_se1146084159140164899it_int @ K5 @ N4 ) )
% 4.69/5.04 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % set_bit_eq
% 4.69/5.04 thf(fact_7573_unset__bit__eq,axiom,
% 4.69/5.04 ( bit_se4203085406695923979it_int
% 4.69/5.04 = ( ^ [N4: nat,K5: int] : ( minus_minus_int @ K5 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K5 @ N4 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % unset_bit_eq
% 4.69/5.04 thf(fact_7574_or__nat__rec,axiom,
% 4.69/5.04 ( bit_se1412395901928357646or_nat
% 4.69/5.04 = ( ^ [M3: nat,N4: nat] :
% 4.69/5.04 ( plus_plus_nat
% 4.69/5.04 @ ( zero_n2687167440665602831ol_nat
% 4.69/5.04 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 4.69/5.04 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 4.69/5.04 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % or_nat_rec
% 4.69/5.04 thf(fact_7575_xor__nat__unfold,axiom,
% 4.69/5.04 ( bit_se6528837805403552850or_nat
% 4.69/5.04 = ( ^ [M3: nat,N4: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N4 @ ( if_nat @ ( N4 = zero_zero_nat ) @ M3 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % xor_nat_unfold
% 4.69/5.04 thf(fact_7576_take__bit__Suc__from__most,axiom,
% 4.69/5.04 ! [N2: nat,K3: int] :
% 4.69/5.04 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ K3 )
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N2 ) ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K3 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % take_bit_Suc_from_most
% 4.69/5.04 thf(fact_7577_xor__int__rec,axiom,
% 4.69/5.04 ( bit_se6526347334894502574or_int
% 4.69/5.04 = ( ^ [K5: int,L2: int] :
% 4.69/5.04 ( plus_plus_int
% 4.69/5.04 @ ( zero_n2684676970156552555ol_int
% 4.69/5.04 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K5 ) )
% 4.69/5.04 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 4.69/5.04 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % xor_int_rec
% 4.69/5.04 thf(fact_7578_xor__nat__rec,axiom,
% 4.69/5.04 ( bit_se6528837805403552850or_nat
% 4.69/5.04 = ( ^ [M3: nat,N4: nat] :
% 4.69/5.04 ( plus_plus_nat
% 4.69/5.04 @ ( zero_n2687167440665602831ol_nat
% 4.69/5.04 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 4.69/5.04 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) )
% 4.69/5.04 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % xor_nat_rec
% 4.69/5.04 thf(fact_7579_xor__int__unfold,axiom,
% 4.69/5.04 ( bit_se6526347334894502574or_int
% 4.69/5.04 = ( ^ [K5: int,L2: int] :
% 4.69/5.04 ( if_int
% 4.69/5.04 @ ( K5
% 4.69/5.04 = ( uminus_uminus_int @ one_one_int ) )
% 4.69/5.04 @ ( bit_ri7919022796975470100ot_int @ L2 )
% 4.69/5.04 @ ( if_int
% 4.69/5.04 @ ( L2
% 4.69/5.04 = ( uminus_uminus_int @ one_one_int ) )
% 4.69/5.04 @ ( bit_ri7919022796975470100ot_int @ K5 )
% 4.69/5.04 @ ( if_int @ ( K5 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K5 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % xor_int_unfold
% 4.69/5.04 thf(fact_7580_not__int__rec,axiom,
% 4.69/5.04 ( bit_ri7919022796975470100ot_int
% 4.69/5.04 = ( ^ [K5: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K5 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % not_int_rec
% 4.69/5.04 thf(fact_7581_or__not__numerals_I8_J,axiom,
% 4.69/5.04 ! [M4: num,N2: num] :
% 4.69/5.04 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M4 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 4.69/5.04 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M4 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % or_not_numerals(8)
% 4.69/5.04 thf(fact_7582_or__not__numerals_I9_J,axiom,
% 4.69/5.04 ! [M4: num,N2: num] :
% 4.69/5.04 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M4 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 4.69/5.04 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M4 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % or_not_numerals(9)
% 4.69/5.04 thf(fact_7583_and__not__numerals_I8_J,axiom,
% 4.69/5.04 ! [M4: num,N2: num] :
% 4.69/5.04 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M4 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 4.69/5.04 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M4 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % and_not_numerals(8)
% 4.69/5.04 thf(fact_7584_bool__assn__proper_I4_J,axiom,
% 4.69/5.04 ! [P: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o] :
% 4.69/5.04 ( ( proper @ P )
% 4.69/5.04 => ( ( proper @ Q2 )
% 4.69/5.04 => ( proper
% 4.69/5.04 @ ^ [H4: produc3658429121746597890et_nat] :
% 4.69/5.04 ( ( P @ H4 )
% 4.69/5.04 & ( Q2 @ H4 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % bool_assn_proper(4)
% 4.69/5.04 thf(fact_7585_bool__assn__proper_I3_J,axiom,
% 4.69/5.04 ! [P: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o] :
% 4.69/5.04 ( ( proper @ P )
% 4.69/5.04 => ( ( proper @ Q2 )
% 4.69/5.04 => ( proper
% 4.69/5.04 @ ^ [H4: produc3658429121746597890et_nat] :
% 4.69/5.04 ( ( P @ H4 )
% 4.69/5.04 | ( Q2 @ H4 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % bool_assn_proper(3)
% 4.69/5.04 thf(fact_7586_bool__assn__proper_I2_J,axiom,
% 4.69/5.04 ( proper
% 4.69/5.04 @ ^ [Uu: produc3658429121746597890et_nat] : $false ) ).
% 4.69/5.04
% 4.69/5.04 % bool_assn_proper(2)
% 4.69/5.04 thf(fact_7587_bool__assn__proper_I5_J,axiom,
% 4.69/5.04 ! [P: produc3658429121746597890et_nat > $o] :
% 4.69/5.04 ( ( proper @ P )
% 4.69/5.04 => ( proper
% 4.69/5.04 @ ^ [H4: produc3658429121746597890et_nat] :
% 4.69/5.04 ( ( in_range @ H4 )
% 4.69/5.04 & ~ ( P @ H4 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % bool_assn_proper(5)
% 4.69/5.04 thf(fact_7588_bot__assn__def,axiom,
% 4.69/5.04 ( bot_bot_assn
% 4.69/5.04 = ( abs_assn
% 4.69/5.04 @ ^ [Uu: produc3658429121746597890et_nat] : $false ) ) ).
% 4.69/5.04
% 4.69/5.04 % bot_assn_def
% 4.69/5.04 thf(fact_7589_sup__assn__def,axiom,
% 4.69/5.04 ( sup_sup_assn
% 4.69/5.04 = ( ^ [P2: assn,Q: assn] :
% 4.69/5.04 ( abs_assn
% 4.69/5.04 @ ^ [H4: produc3658429121746597890et_nat] :
% 4.69/5.04 ( ( rep_assn @ P2 @ H4 )
% 4.69/5.04 | ( rep_assn @ Q @ H4 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sup_assn_def
% 4.69/5.04 thf(fact_7590_inf__assn__def,axiom,
% 4.69/5.04 ( inf_inf_assn
% 4.69/5.04 = ( ^ [P2: assn,Q: assn] :
% 4.69/5.04 ( abs_assn
% 4.69/5.04 @ ^ [H4: produc3658429121746597890et_nat] :
% 4.69/5.04 ( ( rep_assn @ P2 @ H4 )
% 4.69/5.04 & ( rep_assn @ Q @ H4 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % inf_assn_def
% 4.69/5.04 thf(fact_7591_nat__times__as__int,axiom,
% 4.69/5.04 ( times_times_nat
% 4.69/5.04 = ( ^ [A6: nat,B6: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A6 ) @ ( semiri1314217659103216013at_int @ B6 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % nat_times_as_int
% 4.69/5.04 thf(fact_7592_divide__nat__def,axiom,
% 4.69/5.04 ( divide_divide_nat
% 4.69/5.04 = ( ^ [M3: nat,N4: nat] :
% 4.69/5.04 ( if_nat @ ( N4 = zero_zero_nat ) @ zero_zero_nat
% 4.69/5.04 @ ( lattic8265883725875713057ax_nat
% 4.69/5.04 @ ( collect_nat
% 4.69/5.04 @ ^ [K5: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K5 @ N4 ) @ M3 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % divide_nat_def
% 4.69/5.04 thf(fact_7593_uminus__assn__def,axiom,
% 4.69/5.04 ( uminus_uminus_assn
% 4.69/5.04 = ( ^ [P2: assn] :
% 4.69/5.04 ( abs_assn
% 4.69/5.04 @ ^ [H4: produc3658429121746597890et_nat] :
% 4.69/5.04 ( ( in_range @ H4 )
% 4.69/5.04 & ~ ( rep_assn @ P2 @ H4 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % uminus_assn_def
% 4.69/5.04 thf(fact_7594_Gcd__eq__Max,axiom,
% 4.69/5.04 ! [M: set_nat] :
% 4.69/5.04 ( ( finite_finite_nat @ M )
% 4.69/5.04 => ( ( M != bot_bot_set_nat )
% 4.69/5.04 => ( ~ ( member_nat @ zero_zero_nat @ M )
% 4.69/5.04 => ( ( gcd_Gcd_nat @ M )
% 4.69/5.04 = ( lattic8265883725875713057ax_nat
% 4.69/5.04 @ ( comple7806235888213564991et_nat
% 4.69/5.04 @ ( image_nat_set_nat
% 4.69/5.04 @ ^ [M3: nat] :
% 4.69/5.04 ( collect_nat
% 4.69/5.04 @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M3 ) )
% 4.69/5.04 @ M ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % Gcd_eq_Max
% 4.69/5.04 thf(fact_7595_and__not__numerals_I5_J,axiom,
% 4.69/5.04 ! [M4: num,N2: num] :
% 4.69/5.04 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M4 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 4.69/5.04 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M4 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % and_not_numerals(5)
% 4.69/5.04 thf(fact_7596_and__not__numerals_I6_J,axiom,
% 4.69/5.04 ! [M4: num,N2: num] :
% 4.69/5.04 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M4 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 4.69/5.04 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M4 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % and_not_numerals(6)
% 4.69/5.04 thf(fact_7597_and__not__numerals_I9_J,axiom,
% 4.69/5.04 ! [M4: num,N2: num] :
% 4.69/5.04 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M4 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 4.69/5.04 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M4 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % and_not_numerals(9)
% 4.69/5.04 thf(fact_7598_or__not__numerals_I6_J,axiom,
% 4.69/5.04 ! [M4: num,N2: num] :
% 4.69/5.04 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M4 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 4.69/5.04 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M4 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % or_not_numerals(6)
% 4.69/5.04 thf(fact_7599_or__not__numerals_I5_J,axiom,
% 4.69/5.04 ! [M4: num,N2: num] :
% 4.69/5.04 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M4 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 4.69/5.04 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M4 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % or_not_numerals(5)
% 4.69/5.04 thf(fact_7600_atMost__0,axiom,
% 4.69/5.04 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 4.69/5.04 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 4.69/5.04
% 4.69/5.04 % atMost_0
% 4.69/5.04 thf(fact_7601_atLeast1__atMost__eq__remove0,axiom,
% 4.69/5.04 ! [N2: nat] :
% 4.69/5.04 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 4.69/5.04 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % atLeast1_atMost_eq_remove0
% 4.69/5.04 thf(fact_7602_vandermonde,axiom,
% 4.69/5.04 ! [M4: nat,N2: nat,R2: nat] :
% 4.69/5.04 ( ( groups3542108847815614940at_nat
% 4.69/5.04 @ ^ [K5: nat] : ( times_times_nat @ ( binomial @ M4 @ K5 ) @ ( binomial @ N2 @ ( minus_minus_nat @ R2 @ K5 ) ) )
% 4.69/5.04 @ ( set_ord_atMost_nat @ R2 ) )
% 4.69/5.04 = ( binomial @ ( plus_plus_nat @ M4 @ N2 ) @ R2 ) ) ).
% 4.69/5.04
% 4.69/5.04 % vandermonde
% 4.69/5.04 thf(fact_7603_fact__eq__fact__times,axiom,
% 4.69/5.04 ! [N2: nat,M4: nat] :
% 4.69/5.04 ( ( ord_less_eq_nat @ N2 @ M4 )
% 4.69/5.04 => ( ( semiri1408675320244567234ct_nat @ M4 )
% 4.69/5.04 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N2 )
% 4.69/5.04 @ ( groups708209901874060359at_nat
% 4.69/5.04 @ ^ [X2: nat] : X2
% 4.69/5.04 @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M4 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % fact_eq_fact_times
% 4.69/5.04 thf(fact_7604_binomial,axiom,
% 4.69/5.04 ! [A2: nat,B: nat,N2: nat] :
% 4.69/5.04 ( ( power_power_nat @ ( plus_plus_nat @ A2 @ B ) @ N2 )
% 4.69/5.04 = ( groups3542108847815614940at_nat
% 4.69/5.04 @ ^ [K5: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K5 ) ) @ ( power_power_nat @ A2 @ K5 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K5 ) ) )
% 4.69/5.04 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % binomial
% 4.69/5.04 thf(fact_7605_choose__square__sum,axiom,
% 4.69/5.04 ! [N2: nat] :
% 4.69/5.04 ( ( groups3542108847815614940at_nat
% 4.69/5.04 @ ^ [K5: nat] : ( power_power_nat @ ( binomial @ N2 @ K5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.69/5.04 @ ( set_ord_atMost_nat @ N2 ) )
% 4.69/5.04 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ).
% 4.69/5.04
% 4.69/5.04 % choose_square_sum
% 4.69/5.04 thf(fact_7606_gauss__sum__nat,axiom,
% 4.69/5.04 ! [N2: nat] :
% 4.69/5.04 ( ( groups3542108847815614940at_nat
% 4.69/5.04 @ ^ [X2: nat] : X2
% 4.69/5.04 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 4.69/5.04 = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % gauss_sum_nat
% 4.69/5.04 thf(fact_7607_binomial__r__part__sum,axiom,
% 4.69/5.04 ! [M4: nat] :
% 4.69/5.04 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M4 ) )
% 4.69/5.04 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % binomial_r_part_sum
% 4.69/5.04 thf(fact_7608_choose__linear__sum,axiom,
% 4.69/5.04 ! [N2: nat] :
% 4.69/5.04 ( ( groups3542108847815614940at_nat
% 4.69/5.04 @ ^ [I4: nat] : ( times_times_nat @ I4 @ ( binomial @ N2 @ I4 ) )
% 4.69/5.04 @ ( set_ord_atMost_nat @ N2 ) )
% 4.69/5.04 = ( times_times_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % choose_linear_sum
% 4.69/5.04 thf(fact_7609_arith__series__nat,axiom,
% 4.69/5.04 ! [A2: nat,D2: nat,N2: nat] :
% 4.69/5.04 ( ( groups3542108847815614940at_nat
% 4.69/5.04 @ ^ [I4: nat] : ( plus_plus_nat @ A2 @ ( times_times_nat @ I4 @ D2 ) )
% 4.69/5.04 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 4.69/5.04 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A2 ) @ ( times_times_nat @ N2 @ D2 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % arith_series_nat
% 4.69/5.04 thf(fact_7610_Sum__Icc__nat,axiom,
% 4.69/5.04 ! [M4: nat,N2: nat] :
% 4.69/5.04 ( ( groups3542108847815614940at_nat
% 4.69/5.04 @ ^ [X2: nat] : X2
% 4.69/5.04 @ ( set_or1269000886237332187st_nat @ M4 @ N2 ) )
% 4.69/5.04 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( plus_plus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M4 @ ( minus_minus_nat @ M4 @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % Sum_Icc_nat
% 4.69/5.04 thf(fact_7611_periodic__finite__ex,axiom,
% 4.69/5.04 ! [D2: int,P: int > $o] :
% 4.69/5.04 ( ( ord_less_int @ zero_zero_int @ D2 )
% 4.69/5.04 => ( ! [X3: int,K: int] :
% 4.69/5.04 ( ( P @ X3 )
% 4.69/5.04 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D2 ) ) ) )
% 4.69/5.04 => ( ( ? [X7: int] : ( P @ X7 ) )
% 4.69/5.04 = ( ? [X2: int] :
% 4.69/5.04 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D2 ) )
% 4.69/5.04 & ( P @ X2 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % periodic_finite_ex
% 4.69/5.04 thf(fact_7612_simp__from__to,axiom,
% 4.69/5.04 ( set_or1266510415728281911st_int
% 4.69/5.04 = ( ^ [I4: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I4 ) @ bot_bot_set_int @ ( insert_int @ I4 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % simp_from_to
% 4.69/5.04 thf(fact_7613_cpmi,axiom,
% 4.69/5.04 ! [D3: int,P: int > $o,P7: int > $o,B4: set_int] :
% 4.69/5.04 ( ( ord_less_int @ zero_zero_int @ D3 )
% 4.69/5.04 => ( ? [Z6: int] :
% 4.69/5.04 ! [X3: int] :
% 4.69/5.04 ( ( ord_less_int @ X3 @ Z6 )
% 4.69/5.04 => ( ( P @ X3 )
% 4.69/5.04 = ( P7 @ X3 ) ) )
% 4.69/5.04 => ( ! [X3: int] :
% 4.69/5.04 ( ! [Xa2: int] :
% 4.69/5.04 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 4.69/5.04 => ! [Xb2: int] :
% 4.69/5.04 ( ( member_int @ Xb2 @ B4 )
% 4.69/5.04 => ( X3
% 4.69/5.04 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 4.69/5.04 => ( ( P @ X3 )
% 4.69/5.04 => ( P @ ( minus_minus_int @ X3 @ D3 ) ) ) )
% 4.69/5.04 => ( ! [X3: int,K: int] :
% 4.69/5.04 ( ( P7 @ X3 )
% 4.69/5.04 = ( P7 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 4.69/5.04 => ( ( ? [X7: int] : ( P @ X7 ) )
% 4.69/5.04 = ( ? [X2: int] :
% 4.69/5.04 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 4.69/5.04 & ( P7 @ X2 ) )
% 4.69/5.04 | ? [X2: int] :
% 4.69/5.04 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 4.69/5.04 & ? [Y3: int] :
% 4.69/5.04 ( ( member_int @ Y3 @ B4 )
% 4.69/5.04 & ( P @ ( plus_plus_int @ Y3 @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % cpmi
% 4.69/5.04 thf(fact_7614_cppi,axiom,
% 4.69/5.04 ! [D3: int,P: int > $o,P7: int > $o,A: set_int] :
% 4.69/5.04 ( ( ord_less_int @ zero_zero_int @ D3 )
% 4.69/5.04 => ( ? [Z6: int] :
% 4.69/5.04 ! [X3: int] :
% 4.69/5.04 ( ( ord_less_int @ Z6 @ X3 )
% 4.69/5.04 => ( ( P @ X3 )
% 4.69/5.04 = ( P7 @ X3 ) ) )
% 4.69/5.04 => ( ! [X3: int] :
% 4.69/5.04 ( ! [Xa2: int] :
% 4.69/5.04 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 4.69/5.04 => ! [Xb2: int] :
% 4.69/5.04 ( ( member_int @ Xb2 @ A )
% 4.69/5.04 => ( X3
% 4.69/5.04 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 4.69/5.04 => ( ( P @ X3 )
% 4.69/5.04 => ( P @ ( plus_plus_int @ X3 @ D3 ) ) ) )
% 4.69/5.04 => ( ! [X3: int,K: int] :
% 4.69/5.04 ( ( P7 @ X3 )
% 4.69/5.04 = ( P7 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 4.69/5.04 => ( ( ? [X7: int] : ( P @ X7 ) )
% 4.69/5.04 = ( ? [X2: int] :
% 4.69/5.04 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 4.69/5.04 & ( P7 @ X2 ) )
% 4.69/5.04 | ? [X2: int] :
% 4.69/5.04 ( ( member_int @ X2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 4.69/5.04 & ? [Y3: int] :
% 4.69/5.04 ( ( member_int @ Y3 @ A )
% 4.69/5.04 & ( P @ ( minus_minus_int @ Y3 @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % cppi
% 4.69/5.04 thf(fact_7615_divmod__step__nat__def,axiom,
% 4.69/5.04 ( unique5026877609467782581ep_nat
% 4.69/5.04 = ( ^ [L2: num] :
% 4.69/5.04 ( produc2626176000494625587at_nat
% 4.69/5.04 @ ^ [Q6: nat,R4: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R4 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q6 ) @ one_one_nat ) @ ( minus_minus_nat @ R4 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q6 ) @ R4 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % divmod_step_nat_def
% 4.69/5.04 thf(fact_7616_divmod__step__int__def,axiom,
% 4.69/5.04 ( unique5024387138958732305ep_int
% 4.69/5.04 = ( ^ [L2: num] :
% 4.69/5.04 ( produc4245557441103728435nt_int
% 4.69/5.04 @ ^ [Q6: int,R4: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R4 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q6 ) @ one_one_int ) @ ( minus_minus_int @ R4 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q6 ) @ R4 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % divmod_step_int_def
% 4.69/5.04 thf(fact_7617_Sum__Icc__int,axiom,
% 4.69/5.04 ! [M4: int,N2: int] :
% 4.69/5.04 ( ( ord_less_eq_int @ M4 @ N2 )
% 4.69/5.04 => ( ( groups4538972089207619220nt_int
% 4.69/5.04 @ ^ [X2: int] : X2
% 4.69/5.04 @ ( set_or1266510415728281911st_int @ M4 @ N2 ) )
% 4.69/5.04 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N2 @ ( plus_plus_int @ N2 @ one_one_int ) ) @ ( times_times_int @ M4 @ ( minus_minus_int @ M4 @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % Sum_Icc_int
% 4.69/5.04 thf(fact_7618_Sum__Ico__nat,axiom,
% 4.69/5.04 ! [M4: nat,N2: nat] :
% 4.69/5.04 ( ( groups3542108847815614940at_nat
% 4.69/5.04 @ ^ [X2: nat] : X2
% 4.69/5.04 @ ( set_or4665077453230672383an_nat @ M4 @ N2 ) )
% 4.69/5.04 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M4 @ ( minus_minus_nat @ M4 @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % Sum_Ico_nat
% 4.69/5.04 thf(fact_7619_atLeastLessThan__singleton,axiom,
% 4.69/5.04 ! [M4: nat] :
% 4.69/5.04 ( ( set_or4665077453230672383an_nat @ M4 @ ( suc @ M4 ) )
% 4.69/5.04 = ( insert_nat @ M4 @ bot_bot_set_nat ) ) ).
% 4.69/5.04
% 4.69/5.04 % atLeastLessThan_singleton
% 4.69/5.04 thf(fact_7620_atLeastLessThan0,axiom,
% 4.69/5.04 ! [M4: nat] :
% 4.69/5.04 ( ( set_or4665077453230672383an_nat @ M4 @ zero_zero_nat )
% 4.69/5.04 = bot_bot_set_nat ) ).
% 4.69/5.04
% 4.69/5.04 % atLeastLessThan0
% 4.69/5.04 thf(fact_7621_atLeastLessThanSuc,axiom,
% 4.69/5.04 ! [M4: nat,N2: nat] :
% 4.69/5.04 ( ( ( ord_less_eq_nat @ M4 @ N2 )
% 4.69/5.04 => ( ( set_or4665077453230672383an_nat @ M4 @ ( suc @ N2 ) )
% 4.69/5.04 = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ M4 @ N2 ) ) ) )
% 4.69/5.04 & ( ~ ( ord_less_eq_nat @ M4 @ N2 )
% 4.69/5.04 => ( ( set_or4665077453230672383an_nat @ M4 @ ( suc @ N2 ) )
% 4.69/5.04 = bot_bot_set_nat ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % atLeastLessThanSuc
% 4.69/5.04 thf(fact_7622_atLeastLessThan__nat__numeral,axiom,
% 4.69/5.04 ! [M4: nat,K3: num] :
% 4.69/5.04 ( ( ( ord_less_eq_nat @ M4 @ ( pred_numeral @ K3 ) )
% 4.69/5.04 => ( ( set_or4665077453230672383an_nat @ M4 @ ( numeral_numeral_nat @ K3 ) )
% 4.69/5.04 = ( insert_nat @ ( pred_numeral @ K3 ) @ ( set_or4665077453230672383an_nat @ M4 @ ( pred_numeral @ K3 ) ) ) ) )
% 4.69/5.04 & ( ~ ( ord_less_eq_nat @ M4 @ ( pred_numeral @ K3 ) )
% 4.69/5.04 => ( ( set_or4665077453230672383an_nat @ M4 @ ( numeral_numeral_nat @ K3 ) )
% 4.69/5.04 = bot_bot_set_nat ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % atLeastLessThan_nat_numeral
% 4.69/5.04 thf(fact_7623_image__minus__const__atLeastLessThan__nat,axiom,
% 4.69/5.04 ! [C: nat,Y: nat,X: nat] :
% 4.69/5.04 ( ( ( ord_less_nat @ C @ Y )
% 4.69/5.04 => ( ( image_nat_nat2
% 4.69/5.04 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 4.69/5.04 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 4.69/5.04 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 4.69/5.04 & ( ~ ( ord_less_nat @ C @ Y )
% 4.69/5.04 => ( ( ( ord_less_nat @ X @ Y )
% 4.69/5.04 => ( ( image_nat_nat2
% 4.69/5.04 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 4.69/5.04 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 4.69/5.04 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 4.69/5.04 & ( ~ ( ord_less_nat @ X @ Y )
% 4.69/5.04 => ( ( image_nat_nat2
% 4.69/5.04 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 4.69/5.04 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 4.69/5.04 = bot_bot_set_nat ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % image_minus_const_atLeastLessThan_nat
% 4.69/5.04 thf(fact_7624_divmod__step__integer__def,axiom,
% 4.69/5.04 ( unique4921790084139445826nteger
% 4.69/5.04 = ( ^ [L2: num] :
% 4.69/5.04 ( produc6916734918728496179nteger
% 4.69/5.04 @ ^ [Q6: code_integer,R4: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R4 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q6 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R4 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q6 ) @ R4 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % divmod_step_integer_def
% 4.69/5.04 thf(fact_7625_triangle__def,axiom,
% 4.69/5.04 ( nat_triangle
% 4.69/5.04 = ( ^ [N4: nat] : ( divide_divide_nat @ ( times_times_nat @ N4 @ ( suc @ N4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % triangle_def
% 4.69/5.04 thf(fact_7626_image__add__integer__atLeastLessThan,axiom,
% 4.69/5.04 ! [L: code_integer,U: code_integer] :
% 4.69/5.04 ( ( image_4470545334726330049nteger
% 4.69/5.04 @ ^ [X2: code_integer] : ( plus_p5714425477246183910nteger @ X2 @ L )
% 4.69/5.04 @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ U @ L ) ) )
% 4.69/5.04 = ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 4.69/5.04
% 4.69/5.04 % image_add_integer_atLeastLessThan
% 4.69/5.04 thf(fact_7627_atLeastLessThanPlusOne__atLeastAtMost__integer,axiom,
% 4.69/5.04 ! [L: code_integer,U: code_integer] :
% 4.69/5.04 ( ( set_or8404916559141939852nteger @ L @ ( plus_p5714425477246183910nteger @ U @ one_one_Code_integer ) )
% 4.69/5.04 = ( set_or189985376899183464nteger @ L @ U ) ) ).
% 4.69/5.04
% 4.69/5.04 % atLeastLessThanPlusOne_atLeastAtMost_integer
% 4.69/5.04 thf(fact_7628_times__integer__code_I2_J,axiom,
% 4.69/5.04 ! [L: code_integer] :
% 4.69/5.04 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L )
% 4.69/5.04 = zero_z3403309356797280102nteger ) ).
% 4.69/5.04
% 4.69/5.04 % times_integer_code(2)
% 4.69/5.04 thf(fact_7629_times__integer__code_I1_J,axiom,
% 4.69/5.04 ! [K3: code_integer] :
% 4.69/5.04 ( ( times_3573771949741848930nteger @ K3 @ zero_z3403309356797280102nteger )
% 4.69/5.04 = zero_z3403309356797280102nteger ) ).
% 4.69/5.04
% 4.69/5.04 % times_integer_code(1)
% 4.69/5.04 thf(fact_7630_integer__of__int__code,axiom,
% 4.69/5.04 ( code_integer_of_int
% 4.69/5.04 = ( ^ [K5: int] :
% 4.69/5.04 ( if_Code_integer @ ( ord_less_int @ K5 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K5 ) ) )
% 4.69/5.04 @ ( if_Code_integer @ ( K5 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 4.69/5.04 @ ( if_Code_integer
% 4.69/5.04 @ ( ( modulo_modulo_int @ K5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.69/5.04 = zero_zero_int )
% 4.69/5.04 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 4.69/5.04 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % integer_of_int_code
% 4.69/5.04 thf(fact_7631_finite__atLeastLessThan__integer,axiom,
% 4.69/5.04 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 4.69/5.04
% 4.69/5.04 % finite_atLeastLessThan_integer
% 4.69/5.04 thf(fact_7632_finite__atLeastAtMost__integer,axiom,
% 4.69/5.04 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or189985376899183464nteger @ L @ U ) ) ).
% 4.69/5.04
% 4.69/5.04 % finite_atLeastAtMost_integer
% 4.69/5.04 thf(fact_7633_finite__atLeastZeroLessThan__integer,axiom,
% 4.69/5.04 ! [U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ U ) ) ).
% 4.69/5.04
% 4.69/5.04 % finite_atLeastZeroLessThan_integer
% 4.69/5.04 thf(fact_7634_times__integer_Orsp,axiom,
% 4.69/5.04 ( bNF_re711492959462206631nt_int
% 4.69/5.04 @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 4.69/5.04 @ ( bNF_re4712519889275205905nt_int
% 4.69/5.04 @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 4.69/5.04 @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 4.69/5.04 @ times_times_int
% 4.69/5.04 @ times_times_int ) ).
% 4.69/5.04
% 4.69/5.04 % times_integer.rsp
% 4.69/5.04 thf(fact_7635_times__natural_Orsp,axiom,
% 4.69/5.04 ( bNF_re1345281282404953727at_nat
% 4.69/5.04 @ ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 )
% 4.69/5.04 @ ( bNF_re5653821019739307937at_nat
% 4.69/5.04 @ ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 )
% 4.69/5.04 @ ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 ) )
% 4.69/5.04 @ times_times_nat
% 4.69/5.04 @ times_times_nat ) ).
% 4.69/5.04
% 4.69/5.04 % times_natural.rsp
% 4.69/5.04 thf(fact_7636_times__integer_Oabs__eq,axiom,
% 4.69/5.04 ! [Xa: int,X: int] :
% 4.69/5.04 ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 4.69/5.04 = ( code_integer_of_int @ ( times_times_int @ Xa @ X ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % times_integer.abs_eq
% 4.69/5.04 thf(fact_7637_divmod__integer__eq__cases,axiom,
% 4.69/5.04 ( code_divmod_integer
% 4.69/5.04 = ( ^ [K5: code_integer,L2: code_integer] :
% 4.69/5.04 ( if_Pro6119634080678213985nteger @ ( K5 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 4.69/5.04 @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K5 )
% 4.69/5.04 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L2
% 4.69/5.04 @ ( if_Pro6119634080678213985nteger
% 4.69/5.04 @ ( ( sgn_sgn_Code_integer @ K5 )
% 4.69/5.04 = ( sgn_sgn_Code_integer @ L2 ) )
% 4.69/5.04 @ ( code_divmod_abs @ K5 @ L2 )
% 4.69/5.04 @ ( produc6916734918728496179nteger
% 4.69/5.04 @ ^ [R4: code_integer,S7: code_integer] : ( if_Pro6119634080678213985nteger @ ( S7 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R4 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L2 ) @ S7 ) ) )
% 4.69/5.04 @ ( code_divmod_abs @ K5 @ L2 ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % divmod_integer_eq_cases
% 4.69/5.04 thf(fact_7638_plus__rat_Otransfer,axiom,
% 4.69/5.04 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 4.69/5.04 @ ^ [X2: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Y3 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y3 ) ) )
% 4.69/5.04 @ plus_plus_rat ) ).
% 4.69/5.04
% 4.69/5.04 % plus_rat.transfer
% 4.69/5.04 thf(fact_7639_times__rat_Otransfer,axiom,
% 4.69/5.04 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 4.69/5.04 @ ^ [X2: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_fst_int_int @ Y3 ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y3 ) ) )
% 4.69/5.04 @ times_times_rat ) ).
% 4.69/5.04
% 4.69/5.04 % times_rat.transfer
% 4.69/5.04 thf(fact_7640_int__of__integer__code,axiom,
% 4.69/5.04 ( code_int_of_integer
% 4.69/5.04 = ( ^ [K5: code_integer] :
% 4.69/5.04 ( if_int @ ( ord_le6747313008572928689nteger @ K5 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K5 ) ) )
% 4.69/5.04 @ ( if_int @ ( K5 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 4.69/5.04 @ ( produc1553301316500091796er_int
% 4.69/5.04 @ ^ [L2: code_integer,J3: code_integer] : ( if_int @ ( J3 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ one_one_int ) )
% 4.69/5.04 @ ( code_divmod_integer @ K5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % int_of_integer_code
% 4.69/5.04 thf(fact_7641_positive_Otransfer,axiom,
% 4.69/5.04 ( bNF_re1494630372529172596at_o_o @ pcr_rat
% 4.69/5.04 @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 4.69/5.04 @ ^ [X2: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) )
% 4.69/5.04 @ positive ) ).
% 4.69/5.04
% 4.69/5.04 % positive.transfer
% 4.69/5.04 thf(fact_7642_times__int_Otransfer,axiom,
% 4.69/5.04 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 4.69/5.04 @ ( produc27273713700761075at_nat
% 4.69/5.04 @ ^ [X2: nat,Y3: nat] :
% 4.69/5.04 ( produc2626176000494625587at_nat
% 4.69/5.04 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U3 ) @ ( times_times_nat @ Y3 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y3 @ U3 ) ) ) ) )
% 4.69/5.04 @ times_times_int ) ).
% 4.69/5.04
% 4.69/5.04 % times_int.transfer
% 4.69/5.04 thf(fact_7643_times__int_Oabs__eq,axiom,
% 4.69/5.04 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 4.69/5.04 ( ( times_times_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 4.69/5.04 = ( abs_Integ
% 4.69/5.04 @ ( produc27273713700761075at_nat
% 4.69/5.04 @ ^ [X2: nat,Y3: nat] :
% 4.69/5.04 ( produc2626176000494625587at_nat
% 4.69/5.04 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U3 ) @ ( times_times_nat @ Y3 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y3 @ U3 ) ) ) )
% 4.69/5.04 @ Xa
% 4.69/5.04 @ X ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % times_int.abs_eq
% 4.69/5.04 thf(fact_7644_times__integer_Orep__eq,axiom,
% 4.69/5.04 ! [X: code_integer,Xa: code_integer] :
% 4.69/5.04 ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X @ Xa ) )
% 4.69/5.04 = ( times_times_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % times_integer.rep_eq
% 4.69/5.04 thf(fact_7645_positive__mult,axiom,
% 4.69/5.04 ! [X: rat,Y: rat] :
% 4.69/5.04 ( ( positive @ X )
% 4.69/5.04 => ( ( positive @ Y )
% 4.69/5.04 => ( positive @ ( times_times_rat @ X @ Y ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % positive_mult
% 4.69/5.04 thf(fact_7646_int__of__integer__less__iff,axiom,
% 4.69/5.04 ! [X: code_integer,Y: code_integer] :
% 4.69/5.04 ( ( ord_less_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Y ) )
% 4.69/5.04 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ).
% 4.69/5.04
% 4.69/5.04 % int_of_integer_less_iff
% 4.69/5.04 thf(fact_7647_type__definition__integer,axiom,
% 4.69/5.04 type_d8366093980585677751er_int @ code_int_of_integer @ code_integer_of_int @ top_top_set_int ).
% 4.69/5.04
% 4.69/5.04 % type_definition_integer
% 4.69/5.04 thf(fact_7648_positive_Orep__eq,axiom,
% 4.69/5.04 ( positive
% 4.69/5.04 = ( ^ [X2: rat] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ ( rep_Rat @ X2 ) ) @ ( product_snd_int_int @ ( rep_Rat @ X2 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % positive.rep_eq
% 4.69/5.04 thf(fact_7649_nat__of__integer__less__iff,axiom,
% 4.69/5.04 ! [X: code_integer,Y: code_integer] :
% 4.69/5.04 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 4.69/5.04 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 4.69/5.04 => ( ( ord_less_nat @ ( code_nat_of_integer @ X ) @ ( code_nat_of_integer @ Y ) )
% 4.69/5.04 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % nat_of_integer_less_iff
% 4.69/5.04 thf(fact_7650_times__int_Orsp,axiom,
% 4.69/5.04 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 4.69/5.04 @ ( produc27273713700761075at_nat
% 4.69/5.04 @ ^ [X2: nat,Y3: nat] :
% 4.69/5.04 ( produc2626176000494625587at_nat
% 4.69/5.04 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U3 ) @ ( times_times_nat @ Y3 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y3 @ U3 ) ) ) ) )
% 4.69/5.04 @ ( produc27273713700761075at_nat
% 4.69/5.04 @ ^ [X2: nat,Y3: nat] :
% 4.69/5.04 ( produc2626176000494625587at_nat
% 4.69/5.04 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U3 ) @ ( times_times_nat @ Y3 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y3 @ U3 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % times_int.rsp
% 4.69/5.04 thf(fact_7651_atLeast1__lessThan__eq__remove0,axiom,
% 4.69/5.04 ! [N2: nat] :
% 4.69/5.04 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 4.69/5.04 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % atLeast1_lessThan_eq_remove0
% 4.69/5.04 thf(fact_7652_min__Suc__gt_I1_J,axiom,
% 4.69/5.04 ! [A2: nat,B: nat] :
% 4.69/5.04 ( ( ord_less_nat @ A2 @ B )
% 4.69/5.04 => ( ( ord_min_nat @ ( suc @ A2 ) @ B )
% 4.69/5.04 = ( suc @ A2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % min_Suc_gt(1)
% 4.69/5.04 thf(fact_7653_min__Suc__gt_I2_J,axiom,
% 4.69/5.04 ! [A2: nat,B: nat] :
% 4.69/5.04 ( ( ord_less_nat @ A2 @ B )
% 4.69/5.04 => ( ( ord_min_nat @ B @ ( suc @ A2 ) )
% 4.69/5.04 = ( suc @ A2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % min_Suc_gt(2)
% 4.69/5.04 thf(fact_7654_lessThan__0,axiom,
% 4.69/5.04 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 4.69/5.04 = bot_bot_set_nat ) ).
% 4.69/5.04
% 4.69/5.04 % lessThan_0
% 4.69/5.04 thf(fact_7655_nat__mult__min__right,axiom,
% 4.69/5.04 ! [M4: nat,N2: nat,Q4: nat] :
% 4.69/5.04 ( ( times_times_nat @ M4 @ ( ord_min_nat @ N2 @ Q4 ) )
% 4.69/5.04 = ( ord_min_nat @ ( times_times_nat @ M4 @ N2 ) @ ( times_times_nat @ M4 @ Q4 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % nat_mult_min_right
% 4.69/5.04 thf(fact_7656_nat__mult__min__left,axiom,
% 4.69/5.04 ! [M4: nat,N2: nat,Q4: nat] :
% 4.69/5.04 ( ( times_times_nat @ ( ord_min_nat @ M4 @ N2 ) @ Q4 )
% 4.69/5.04 = ( ord_min_nat @ ( times_times_nat @ M4 @ Q4 ) @ ( times_times_nat @ N2 @ Q4 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % nat_mult_min_left
% 4.69/5.04 thf(fact_7657_lessThan__empty__iff,axiom,
% 4.69/5.04 ! [N2: nat] :
% 4.69/5.04 ( ( ( set_ord_lessThan_nat @ N2 )
% 4.69/5.04 = bot_bot_set_nat )
% 4.69/5.04 = ( N2 = zero_zero_nat ) ) ).
% 4.69/5.04
% 4.69/5.04 % lessThan_empty_iff
% 4.69/5.04 thf(fact_7658_image__atLeastZeroLessThan__integer,axiom,
% 4.69/5.04 ! [U: code_integer] :
% 4.69/5.04 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 4.69/5.04 => ( ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ U )
% 4.69/5.04 = ( image_1215581382706833972nteger @ semiri4939895301339042750nteger @ ( set_ord_lessThan_nat @ ( code_nat_of_integer @ U ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % image_atLeastZeroLessThan_integer
% 4.69/5.04 thf(fact_7659_bezw__aux,axiom,
% 4.69/5.04 ! [X: nat,Y: nat] :
% 4.69/5.04 ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X @ Y ) )
% 4.69/5.04 = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % bezw_aux
% 4.69/5.04 thf(fact_7660_INT__greaterThan__UNIV,axiom,
% 4.69/5.04 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 4.69/5.04 = bot_bot_set_nat ) ).
% 4.69/5.04
% 4.69/5.04 % INT_greaterThan_UNIV
% 4.69/5.04 thf(fact_7661_gcd__mult__distrib__nat,axiom,
% 4.69/5.04 ! [K3: nat,M4: nat,N2: nat] :
% 4.69/5.04 ( ( times_times_nat @ K3 @ ( gcd_gcd_nat @ M4 @ N2 ) )
% 4.69/5.04 = ( gcd_gcd_nat @ ( times_times_nat @ K3 @ M4 ) @ ( times_times_nat @ K3 @ N2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % gcd_mult_distrib_nat
% 4.69/5.04 thf(fact_7662_Gcd__in,axiom,
% 4.69/5.04 ! [A: set_nat] :
% 4.69/5.04 ( ! [A4: nat,B2: nat] :
% 4.69/5.04 ( ( member_nat @ A4 @ A )
% 4.69/5.04 => ( ( member_nat @ B2 @ A )
% 4.69/5.04 => ( member_nat @ ( gcd_gcd_nat @ A4 @ B2 ) @ A ) ) )
% 4.69/5.04 => ( ( A != bot_bot_set_nat )
% 4.69/5.04 => ( member_nat @ ( gcd_Gcd_nat @ A ) @ A ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % Gcd_in
% 4.69/5.04 thf(fact_7663_bezout__nat,axiom,
% 4.69/5.04 ! [A2: nat,B: nat] :
% 4.69/5.04 ( ( A2 != zero_zero_nat )
% 4.69/5.04 => ? [X3: nat,Y2: nat] :
% 4.69/5.04 ( ( times_times_nat @ A2 @ X3 )
% 4.69/5.04 = ( plus_plus_nat @ ( times_times_nat @ B @ Y2 ) @ ( gcd_gcd_nat @ A2 @ B ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % bezout_nat
% 4.69/5.04 thf(fact_7664_bezout__gcd__nat_H,axiom,
% 4.69/5.04 ! [B: nat,A2: nat] :
% 4.69/5.04 ? [X3: nat,Y2: nat] :
% 4.69/5.04 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y2 ) @ ( times_times_nat @ A2 @ X3 ) )
% 4.69/5.04 & ( ( minus_minus_nat @ ( times_times_nat @ A2 @ X3 ) @ ( times_times_nat @ B @ Y2 ) )
% 4.69/5.04 = ( gcd_gcd_nat @ A2 @ B ) ) )
% 4.69/5.04 | ( ( ord_less_eq_nat @ ( times_times_nat @ A2 @ Y2 ) @ ( times_times_nat @ B @ X3 ) )
% 4.69/5.04 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A2 @ Y2 ) )
% 4.69/5.04 = ( gcd_gcd_nat @ A2 @ B ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % bezout_gcd_nat'
% 4.69/5.04 thf(fact_7665_greaterThan__Suc,axiom,
% 4.69/5.04 ! [K3: nat] :
% 4.69/5.04 ( ( set_or1210151606488870762an_nat @ ( suc @ K3 ) )
% 4.69/5.04 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K3 ) @ ( insert_nat @ ( suc @ K3 ) @ bot_bot_set_nat ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % greaterThan_Suc
% 4.69/5.04 thf(fact_7666_plus__rat_Orsp,axiom,
% 4.69/5.04 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 4.69/5.04 @ ^ [X2: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Y3 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y3 ) ) )
% 4.69/5.04 @ ^ [X2: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Y3 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y3 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % plus_rat.rsp
% 4.69/5.04 thf(fact_7667_positive_Orsp,axiom,
% 4.69/5.04 ( bNF_re8699439704749558557nt_o_o @ ratrel
% 4.69/5.04 @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 4.69/5.04 @ ^ [X2: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) )
% 4.69/5.04 @ ^ [X2: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % positive.rsp
% 4.69/5.04 thf(fact_7668_ratrel__iff,axiom,
% 4.69/5.04 ( ratrel
% 4.69/5.04 = ( ^ [X2: product_prod_int_int,Y3: product_prod_int_int] :
% 4.69/5.04 ( ( ( product_snd_int_int @ X2 )
% 4.69/5.04 != zero_zero_int )
% 4.69/5.04 & ( ( product_snd_int_int @ Y3 )
% 4.69/5.04 != zero_zero_int )
% 4.69/5.04 & ( ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Y3 ) )
% 4.69/5.04 = ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X2 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % ratrel_iff
% 4.69/5.04 thf(fact_7669_bezout__int,axiom,
% 4.69/5.04 ! [X: int,Y: int] :
% 4.69/5.04 ? [U4: int,V3: int] :
% 4.69/5.04 ( ( plus_plus_int @ ( times_times_int @ U4 @ X ) @ ( times_times_int @ V3 @ Y ) )
% 4.69/5.04 = ( gcd_gcd_int @ X @ Y ) ) ).
% 4.69/5.04
% 4.69/5.04 % bezout_int
% 4.69/5.04 thf(fact_7670_gcd__mult__distrib__int,axiom,
% 4.69/5.04 ! [K3: int,M4: int,N2: int] :
% 4.69/5.04 ( ( times_times_int @ ( abs_abs_int @ K3 ) @ ( gcd_gcd_int @ M4 @ N2 ) )
% 4.69/5.04 = ( gcd_gcd_int @ ( times_times_int @ K3 @ M4 ) @ ( times_times_int @ K3 @ N2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % gcd_mult_distrib_int
% 4.69/5.04 thf(fact_7671_ratrel__def,axiom,
% 4.69/5.04 ( ratrel
% 4.69/5.04 = ( ^ [X2: product_prod_int_int,Y3: product_prod_int_int] :
% 4.69/5.04 ( ( ( product_snd_int_int @ X2 )
% 4.69/5.04 != zero_zero_int )
% 4.69/5.04 & ( ( product_snd_int_int @ Y3 )
% 4.69/5.04 != zero_zero_int )
% 4.69/5.04 & ( ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Y3 ) )
% 4.69/5.04 = ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X2 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % ratrel_def
% 4.69/5.04 thf(fact_7672_times__rat_Orsp,axiom,
% 4.69/5.04 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 4.69/5.04 @ ^ [X2: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_fst_int_int @ Y3 ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y3 ) ) )
% 4.69/5.04 @ ^ [X2: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_fst_int_int @ Y3 ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y3 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % times_rat.rsp
% 4.69/5.04 thf(fact_7673_plus__rat_Oabs__eq,axiom,
% 4.69/5.04 ! [Xa: product_prod_int_int,X: product_prod_int_int] :
% 4.69/5.04 ( ( ratrel @ Xa @ Xa )
% 4.69/5.04 => ( ( ratrel @ X @ X )
% 4.69/5.04 => ( ( plus_plus_rat @ ( abs_Rat @ Xa ) @ ( abs_Rat @ X ) )
% 4.69/5.04 = ( abs_Rat @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ Xa ) @ ( product_snd_int_int @ X ) ) @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % plus_rat.abs_eq
% 4.69/5.04 thf(fact_7674_positive_Oabs__eq,axiom,
% 4.69/5.04 ! [X: product_prod_int_int] :
% 4.69/5.04 ( ( ratrel @ X @ X )
% 4.69/5.04 => ( ( positive @ ( abs_Rat @ X ) )
% 4.69/5.04 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % positive.abs_eq
% 4.69/5.04 thf(fact_7675_times__rat_Oabs__eq,axiom,
% 4.69/5.04 ! [Xa: product_prod_int_int,X: product_prod_int_int] :
% 4.69/5.04 ( ( ratrel @ Xa @ Xa )
% 4.69/5.04 => ( ( ratrel @ X @ X )
% 4.69/5.04 => ( ( times_times_rat @ ( abs_Rat @ Xa ) @ ( abs_Rat @ X ) )
% 4.69/5.04 = ( abs_Rat @ ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ Xa ) @ ( product_fst_int_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % times_rat.abs_eq
% 4.69/5.04 thf(fact_7676_finite__greaterThanLessThan__integer,axiom,
% 4.69/5.04 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 4.69/5.04
% 4.69/5.04 % finite_greaterThanLessThan_integer
% 4.69/5.04 thf(fact_7677_atLeastPlusOneLessThan__greaterThanLessThan__integer,axiom,
% 4.69/5.04 ! [L: code_integer,U: code_integer] :
% 4.69/5.04 ( ( set_or8404916559141939852nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 4.69/5.04 = ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 4.69/5.04
% 4.69/5.04 % atLeastPlusOneLessThan_greaterThanLessThan_integer
% 4.69/5.04 thf(fact_7678_positive__def,axiom,
% 4.69/5.04 ( positive
% 4.69/5.04 = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 4.69/5.04 @ ^ [X2: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % positive_def
% 4.69/5.04 thf(fact_7679_finite__greaterThanAtMost__integer,axiom,
% 4.69/5.04 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 4.69/5.04
% 4.69/5.04 % finite_greaterThanAtMost_integer
% 4.69/5.04 thf(fact_7680_atLeastPlusOneAtMost__greaterThanAtMost__integer,axiom,
% 4.69/5.04 ! [L: code_integer,U: code_integer] :
% 4.69/5.04 ( ( set_or189985376899183464nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 4.69/5.04 = ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 4.69/5.04
% 4.69/5.04 % atLeastPlusOneAtMost_greaterThanAtMost_integer
% 4.69/5.04 thf(fact_7681_atLeast__Suc,axiom,
% 4.69/5.04 ! [K3: nat] :
% 4.69/5.04 ( ( set_ord_atLeast_nat @ ( suc @ K3 ) )
% 4.69/5.04 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K3 ) @ ( insert_nat @ K3 @ bot_bot_set_nat ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % atLeast_Suc
% 4.69/5.04 thf(fact_7682_eventually__sequentially__Suc,axiom,
% 4.69/5.04 ! [P: nat > $o] :
% 4.69/5.04 ( ( eventually_nat
% 4.69/5.04 @ ^ [I4: nat] : ( P @ ( suc @ I4 ) )
% 4.69/5.04 @ at_top_nat )
% 4.69/5.04 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 4.69/5.04
% 4.69/5.04 % eventually_sequentially_Suc
% 4.69/5.04 thf(fact_7683_eventually__sequentially__seg,axiom,
% 4.69/5.04 ! [P: nat > $o,K3: nat] :
% 4.69/5.04 ( ( eventually_nat
% 4.69/5.04 @ ^ [N4: nat] : ( P @ ( plus_plus_nat @ N4 @ K3 ) )
% 4.69/5.04 @ at_top_nat )
% 4.69/5.04 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 4.69/5.04
% 4.69/5.04 % eventually_sequentially_seg
% 4.69/5.04 thf(fact_7684_filterlim__Suc,axiom,
% 4.69/5.04 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 4.69/5.04
% 4.69/5.04 % filterlim_Suc
% 4.69/5.04 thf(fact_7685_eventually__sequentiallyI,axiom,
% 4.69/5.04 ! [C: nat,P: nat > $o] :
% 4.69/5.04 ( ! [X3: nat] :
% 4.69/5.04 ( ( ord_less_eq_nat @ C @ X3 )
% 4.69/5.04 => ( P @ X3 ) )
% 4.69/5.04 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 4.69/5.04
% 4.69/5.04 % eventually_sequentiallyI
% 4.69/5.04 thf(fact_7686_eventually__sequentially,axiom,
% 4.69/5.04 ! [P: nat > $o] :
% 4.69/5.04 ( ( eventually_nat @ P @ at_top_nat )
% 4.69/5.04 = ( ? [N7: nat] :
% 4.69/5.04 ! [N4: nat] :
% 4.69/5.04 ( ( ord_less_eq_nat @ N7 @ N4 )
% 4.69/5.04 => ( P @ N4 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % eventually_sequentially
% 4.69/5.04 thf(fact_7687_le__sequentially,axiom,
% 4.69/5.04 ! [F2: filter_nat] :
% 4.69/5.04 ( ( ord_le2510731241096832064er_nat @ F2 @ at_top_nat )
% 4.69/5.04 = ( ! [N7: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N7 ) @ F2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % le_sequentially
% 4.69/5.04 thf(fact_7688_filterlim__atMost__at__top,axiom,
% 4.69/5.04 filter3212408913953519116et_nat @ set_ord_atMost_nat @ ( finite3254316476582989077op_nat @ top_top_set_nat ) @ at_top_nat ).
% 4.69/5.04
% 4.69/5.04 % filterlim_atMost_at_top
% 4.69/5.04 thf(fact_7689_filterlim__lessThan__at__top,axiom,
% 4.69/5.04 filter3212408913953519116et_nat @ set_ord_lessThan_nat @ ( finite3254316476582989077op_nat @ top_top_set_nat ) @ at_top_nat ).
% 4.69/5.04
% 4.69/5.04 % filterlim_lessThan_at_top
% 4.69/5.04 thf(fact_7690_trivial__limit__sequentially,axiom,
% 4.69/5.04 at_top_nat != bot_bot_filter_nat ).
% 4.69/5.04
% 4.69/5.04 % trivial_limit_sequentially
% 4.69/5.04 thf(fact_7691_eventually__False__sequentially,axiom,
% 4.69/5.04 ~ ( eventually_nat
% 4.69/5.04 @ ^ [N4: nat] : $false
% 4.69/5.04 @ at_top_nat ) ).
% 4.69/5.04
% 4.69/5.04 % eventually_False_sequentially
% 4.69/5.04 thf(fact_7692_plus__rat__def,axiom,
% 4.69/5.04 ( plus_plus_rat
% 4.69/5.04 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 4.69/5.04 @ ^ [X2: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Y3 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y3 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % plus_rat_def
% 4.69/5.04 thf(fact_7693_eventually__prod__sequentially,axiom,
% 4.69/5.04 ! [P: product_prod_nat_nat > $o] :
% 4.69/5.04 ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 4.69/5.04 = ( ? [N7: nat] :
% 4.69/5.04 ! [M3: nat] :
% 4.69/5.04 ( ( ord_less_eq_nat @ N7 @ M3 )
% 4.69/5.04 => ! [N4: nat] :
% 4.69/5.04 ( ( ord_less_eq_nat @ N7 @ N4 )
% 4.69/5.04 => ( P @ ( product_Pair_nat_nat @ N4 @ M3 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % eventually_prod_sequentially
% 4.69/5.04 thf(fact_7694_times__rat__def,axiom,
% 4.69/5.04 ( times_times_rat
% 4.69/5.04 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 4.69/5.04 @ ^ [X2: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_fst_int_int @ Y3 ) ) @ ( times_times_int @ ( product_snd_int_int @ X2 ) @ ( product_snd_int_int @ Y3 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % times_rat_def
% 4.69/5.04 thf(fact_7695_add__rat,axiom,
% 4.69/5.04 ! [B: int,D2: int,A2: int,C: int] :
% 4.69/5.04 ( ( B != zero_zero_int )
% 4.69/5.04 => ( ( D2 != zero_zero_int )
% 4.69/5.04 => ( ( plus_plus_rat @ ( fract @ A2 @ B ) @ ( fract @ C @ D2 ) )
% 4.69/5.04 = ( fract @ ( plus_plus_int @ ( times_times_int @ A2 @ D2 ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % add_rat
% 4.69/5.04 thf(fact_7696_divide__rat,axiom,
% 4.69/5.04 ! [A2: int,B: int,C: int,D2: int] :
% 4.69/5.04 ( ( divide_divide_rat @ ( fract @ A2 @ B ) @ ( fract @ C @ D2 ) )
% 4.69/5.04 = ( fract @ ( times_times_int @ A2 @ D2 ) @ ( times_times_int @ B @ C ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % divide_rat
% 4.69/5.04 thf(fact_7697_sgn__rat,axiom,
% 4.69/5.04 ! [A2: int,B: int] :
% 4.69/5.04 ( ( sgn_sgn_rat @ ( fract @ A2 @ B ) )
% 4.69/5.04 = ( ring_1_of_int_rat @ ( times_times_int @ ( sgn_sgn_int @ A2 ) @ ( sgn_sgn_int @ B ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sgn_rat
% 4.69/5.04 thf(fact_7698_mult__rat,axiom,
% 4.69/5.04 ! [A2: int,B: int,C: int,D2: int] :
% 4.69/5.04 ( ( times_times_rat @ ( fract @ A2 @ B ) @ ( fract @ C @ D2 ) )
% 4.69/5.04 = ( fract @ ( times_times_int @ A2 @ C ) @ ( times_times_int @ B @ D2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % mult_rat
% 4.69/5.04 thf(fact_7699_le__rat,axiom,
% 4.69/5.04 ! [B: int,D2: int,A2: int,C: int] :
% 4.69/5.04 ( ( B != zero_zero_int )
% 4.69/5.04 => ( ( D2 != zero_zero_int )
% 4.69/5.04 => ( ( ord_less_eq_rat @ ( fract @ A2 @ B ) @ ( fract @ C @ D2 ) )
% 4.69/5.04 = ( ord_less_eq_int @ ( times_times_int @ ( times_times_int @ A2 @ D2 ) @ ( times_times_int @ B @ D2 ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % le_rat
% 4.69/5.04 thf(fact_7700_less__rat,axiom,
% 4.69/5.04 ! [B: int,D2: int,A2: int,C: int] :
% 4.69/5.04 ( ( B != zero_zero_int )
% 4.69/5.04 => ( ( D2 != zero_zero_int )
% 4.69/5.04 => ( ( ord_less_rat @ ( fract @ A2 @ B ) @ ( fract @ C @ D2 ) )
% 4.69/5.04 = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A2 @ D2 ) @ ( times_times_int @ B @ D2 ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % less_rat
% 4.69/5.04 thf(fact_7701_diff__rat,axiom,
% 4.69/5.04 ! [B: int,D2: int,A2: int,C: int] :
% 4.69/5.04 ( ( B != zero_zero_int )
% 4.69/5.04 => ( ( D2 != zero_zero_int )
% 4.69/5.04 => ( ( minus_minus_rat @ ( fract @ A2 @ B ) @ ( fract @ C @ D2 ) )
% 4.69/5.04 = ( fract @ ( minus_minus_int @ ( times_times_int @ A2 @ D2 ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % diff_rat
% 4.69/5.04 thf(fact_7702_eq__rat_I1_J,axiom,
% 4.69/5.04 ! [B: int,D2: int,A2: int,C: int] :
% 4.69/5.04 ( ( B != zero_zero_int )
% 4.69/5.04 => ( ( D2 != zero_zero_int )
% 4.69/5.04 => ( ( ( fract @ A2 @ B )
% 4.69/5.04 = ( fract @ C @ D2 ) )
% 4.69/5.04 = ( ( times_times_int @ A2 @ D2 )
% 4.69/5.04 = ( times_times_int @ C @ B ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % eq_rat(1)
% 4.69/5.04 thf(fact_7703_mult__rat__cancel,axiom,
% 4.69/5.04 ! [C: int,A2: int,B: int] :
% 4.69/5.04 ( ( C != zero_zero_int )
% 4.69/5.04 => ( ( fract @ ( times_times_int @ C @ A2 ) @ ( times_times_int @ C @ B ) )
% 4.69/5.04 = ( fract @ A2 @ B ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % mult_rat_cancel
% 4.69/5.04 thf(fact_7704_mono__times__nat,axiom,
% 4.69/5.04 ! [N2: nat] :
% 4.69/5.04 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.69/5.04 => ( order_mono_nat_nat @ ( times_times_nat @ N2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % mono_times_nat
% 4.69/5.04 thf(fact_7705_positive__rat,axiom,
% 4.69/5.04 ! [A2: int,B: int] :
% 4.69/5.04 ( ( positive @ ( fract @ A2 @ B ) )
% 4.69/5.04 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A2 @ B ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % positive_rat
% 4.69/5.04 thf(fact_7706_set__encode__empty,axiom,
% 4.69/5.04 ( ( nat_set_encode @ bot_bot_set_nat )
% 4.69/5.04 = zero_zero_nat ) ).
% 4.69/5.04
% 4.69/5.04 % set_encode_empty
% 4.69/5.04 thf(fact_7707_normalize__crossproduct,axiom,
% 4.69/5.04 ! [Q4: int,S2: int,P3: int,R2: int] :
% 4.69/5.04 ( ( Q4 != zero_zero_int )
% 4.69/5.04 => ( ( S2 != zero_zero_int )
% 4.69/5.04 => ( ( ( normalize @ ( product_Pair_int_int @ P3 @ Q4 ) )
% 4.69/5.04 = ( normalize @ ( product_Pair_int_int @ R2 @ S2 ) ) )
% 4.69/5.04 => ( ( times_times_int @ P3 @ S2 )
% 4.69/5.04 = ( times_times_int @ R2 @ Q4 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % normalize_crossproduct
% 4.69/5.04 thf(fact_7708_rat__minus__code,axiom,
% 4.69/5.04 ! [P3: rat,Q4: rat] :
% 4.69/5.04 ( ( quotient_of @ ( minus_minus_rat @ P3 @ Q4 ) )
% 4.69/5.04 = ( produc4245557441103728435nt_int
% 4.69/5.04 @ ^ [A6: int,C4: int] :
% 4.69/5.04 ( produc4245557441103728435nt_int
% 4.69/5.04 @ ^ [B6: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A6 @ D4 ) @ ( times_times_int @ B6 @ C4 ) ) @ ( times_times_int @ C4 @ D4 ) ) )
% 4.69/5.04 @ ( quotient_of @ Q4 ) )
% 4.69/5.04 @ ( quotient_of @ P3 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % rat_minus_code
% 4.69/5.04 thf(fact_7709_rat__plus__code,axiom,
% 4.69/5.04 ! [P3: rat,Q4: rat] :
% 4.69/5.04 ( ( quotient_of @ ( plus_plus_rat @ P3 @ Q4 ) )
% 4.69/5.04 = ( produc4245557441103728435nt_int
% 4.69/5.04 @ ^ [A6: int,C4: int] :
% 4.69/5.04 ( produc4245557441103728435nt_int
% 4.69/5.04 @ ^ [B6: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A6 @ D4 ) @ ( times_times_int @ B6 @ C4 ) ) @ ( times_times_int @ C4 @ D4 ) ) )
% 4.69/5.04 @ ( quotient_of @ Q4 ) )
% 4.69/5.04 @ ( quotient_of @ P3 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % rat_plus_code
% 4.69/5.04 thf(fact_7710_rat__times__code,axiom,
% 4.69/5.04 ! [P3: rat,Q4: rat] :
% 4.69/5.04 ( ( quotient_of @ ( times_times_rat @ P3 @ Q4 ) )
% 4.69/5.04 = ( produc4245557441103728435nt_int
% 4.69/5.04 @ ^ [A6: int,C4: int] :
% 4.69/5.04 ( produc4245557441103728435nt_int
% 4.69/5.04 @ ^ [B6: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A6 @ B6 ) @ ( times_times_int @ C4 @ D4 ) ) )
% 4.69/5.04 @ ( quotient_of @ Q4 ) )
% 4.69/5.04 @ ( quotient_of @ P3 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % rat_times_code
% 4.69/5.04 thf(fact_7711_rat__less__code,axiom,
% 4.69/5.04 ( ord_less_rat
% 4.69/5.04 = ( ^ [P5: rat,Q6: rat] :
% 4.69/5.04 ( produc4947309494688390418_int_o
% 4.69/5.04 @ ^ [A6: int,C4: int] :
% 4.69/5.04 ( produc4947309494688390418_int_o
% 4.69/5.04 @ ^ [B6: int,D4: int] : ( ord_less_int @ ( times_times_int @ A6 @ D4 ) @ ( times_times_int @ C4 @ B6 ) )
% 4.69/5.04 @ ( quotient_of @ Q6 ) )
% 4.69/5.04 @ ( quotient_of @ P5 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % rat_less_code
% 4.69/5.04 thf(fact_7712_rat__less__eq__code,axiom,
% 4.69/5.04 ( ord_less_eq_rat
% 4.69/5.04 = ( ^ [P5: rat,Q6: rat] :
% 4.69/5.04 ( produc4947309494688390418_int_o
% 4.69/5.04 @ ^ [A6: int,C4: int] :
% 4.69/5.04 ( produc4947309494688390418_int_o
% 4.69/5.04 @ ^ [B6: int,D4: int] : ( ord_less_eq_int @ ( times_times_int @ A6 @ D4 ) @ ( times_times_int @ C4 @ B6 ) )
% 4.69/5.04 @ ( quotient_of @ Q6 ) )
% 4.69/5.04 @ ( quotient_of @ P5 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % rat_less_eq_code
% 4.69/5.04 thf(fact_7713_rat__divide__code,axiom,
% 4.69/5.04 ! [P3: rat,Q4: rat] :
% 4.69/5.04 ( ( quotient_of @ ( divide_divide_rat @ P3 @ Q4 ) )
% 4.69/5.04 = ( produc4245557441103728435nt_int
% 4.69/5.04 @ ^ [A6: int,C4: int] :
% 4.69/5.04 ( produc4245557441103728435nt_int
% 4.69/5.04 @ ^ [B6: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A6 @ D4 ) @ ( times_times_int @ C4 @ B6 ) ) )
% 4.69/5.04 @ ( quotient_of @ Q4 ) )
% 4.69/5.04 @ ( quotient_of @ P3 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % rat_divide_code
% 4.69/5.04 thf(fact_7714_rat__inverse__code,axiom,
% 4.69/5.04 ! [P3: rat] :
% 4.69/5.04 ( ( quotient_of @ ( inverse_inverse_rat @ P3 ) )
% 4.69/5.04 = ( produc4245557441103728435nt_int
% 4.69/5.04 @ ^ [A6: int,B6: int] : ( if_Pro3027730157355071871nt_int @ ( A6 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A6 ) @ B6 ) @ ( abs_abs_int @ A6 ) ) )
% 4.69/5.04 @ ( quotient_of @ P3 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % rat_inverse_code
% 4.69/5.04 thf(fact_7715_divide__rat__def,axiom,
% 4.69/5.04 ( divide_divide_rat
% 4.69/5.04 = ( ^ [Q6: rat,R4: rat] : ( times_times_rat @ Q6 @ ( inverse_inverse_rat @ R4 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % divide_rat_def
% 4.69/5.04 thf(fact_7716_sub__BitM__One__eq,axiom,
% 4.69/5.04 ! [N2: num] :
% 4.69/5.04 ( ( neg_numeral_sub_int @ ( bitM @ N2 ) @ one )
% 4.69/5.04 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N2 @ one ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sub_BitM_One_eq
% 4.69/5.04 thf(fact_7717_set__decode__zero,axiom,
% 4.69/5.04 ( ( nat_set_decode @ zero_zero_nat )
% 4.69/5.04 = bot_bot_set_nat ) ).
% 4.69/5.04
% 4.69/5.04 % set_decode_zero
% 4.69/5.04 thf(fact_7718_cofinite__eq__sequentially,axiom,
% 4.69/5.04 cofinite_nat = at_top_nat ).
% 4.69/5.04
% 4.69/5.04 % cofinite_eq_sequentially
% 4.69/5.04 thf(fact_7719_INFM__nat__inductI,axiom,
% 4.69/5.04 ! [P: nat > $o,Q2: nat > $o] :
% 4.69/5.04 ( ( P @ zero_zero_nat )
% 4.69/5.04 => ( ! [I3: nat] :
% 4.69/5.04 ( ( P @ I3 )
% 4.69/5.04 => ? [J4: nat] :
% 4.69/5.04 ( ( ord_less_nat @ I3 @ J4 )
% 4.69/5.04 & ( P @ J4 )
% 4.69/5.04 & ( Q2 @ J4 ) ) )
% 4.69/5.04 => ( frequently_nat @ Q2 @ cofinite_nat ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % INFM_nat_inductI
% 4.69/5.04 thf(fact_7720_lcm__altdef__int,axiom,
% 4.69/5.04 ( gcd_lcm_int
% 4.69/5.04 = ( ^ [A6: int,B6: int] : ( divide_divide_int @ ( times_times_int @ ( abs_abs_int @ A6 ) @ ( abs_abs_int @ B6 ) ) @ ( gcd_gcd_int @ A6 @ B6 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % lcm_altdef_int
% 4.69/5.04 thf(fact_7721_times__num__def,axiom,
% 4.69/5.04 ( times_times_num
% 4.69/5.04 = ( ^ [M3: num,N4: num] : ( num_of_nat @ ( times_times_nat @ ( nat_of_num @ M3 ) @ ( nat_of_num @ N4 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % times_num_def
% 4.69/5.04 thf(fact_7722_nat__of__num__mult,axiom,
% 4.69/5.04 ! [X: num,Y: num] :
% 4.69/5.04 ( ( nat_of_num @ ( times_times_num @ X @ Y ) )
% 4.69/5.04 = ( times_times_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ Y ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % nat_of_num_mult
% 4.69/5.04 thf(fact_7723_prod__gcd__lcm__int,axiom,
% 4.69/5.04 ! [M4: int,N2: int] :
% 4.69/5.04 ( ( times_times_int @ ( abs_abs_int @ M4 ) @ ( abs_abs_int @ N2 ) )
% 4.69/5.04 = ( times_times_int @ ( gcd_gcd_int @ M4 @ N2 ) @ ( gcd_lcm_int @ M4 @ N2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod_gcd_lcm_int
% 4.69/5.04 thf(fact_7724_prod__gcd__lcm__nat,axiom,
% 4.69/5.04 ( times_times_nat
% 4.69/5.04 = ( ^ [M3: nat,N4: nat] : ( times_times_nat @ ( gcd_gcd_nat @ M3 @ N4 ) @ ( gcd_lcm_nat @ M3 @ N4 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % prod_gcd_lcm_nat
% 4.69/5.04 thf(fact_7725_lcm__code__integer,axiom,
% 4.69/5.04 ( gcd_lcm_Code_integer
% 4.69/5.04 = ( ^ [A6: code_integer,B6: code_integer] : ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A6 ) @ ( abs_abs_Code_integer @ B6 ) ) @ ( gcd_gcd_Code_integer @ A6 @ B6 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % lcm_code_integer
% 4.69/5.04 thf(fact_7726_lcm__nat__def,axiom,
% 4.69/5.04 ( gcd_lcm_nat
% 4.69/5.04 = ( ^ [X2: nat,Y3: nat] : ( divide_divide_nat @ ( times_times_nat @ X2 @ Y3 ) @ ( gcd_gcd_nat @ X2 @ Y3 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % lcm_nat_def
% 4.69/5.04 thf(fact_7727_Lcm__eq__Max__nat,axiom,
% 4.69/5.04 ! [M: set_nat] :
% 4.69/5.04 ( ( finite_finite_nat @ M )
% 4.69/5.04 => ( ( M != bot_bot_set_nat )
% 4.69/5.04 => ( ~ ( member_nat @ zero_zero_nat @ M )
% 4.69/5.04 => ( ! [M2: nat,N3: nat] :
% 4.69/5.04 ( ( member_nat @ M2 @ M )
% 4.69/5.04 => ( ( member_nat @ N3 @ M )
% 4.69/5.04 => ( member_nat @ ( gcd_lcm_nat @ M2 @ N3 ) @ M ) ) )
% 4.69/5.04 => ( ( gcd_Lcm_nat @ M )
% 4.69/5.04 = ( lattic8265883725875713057ax_nat @ M ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % Lcm_eq_Max_nat
% 4.69/5.04 thf(fact_7728_nat__of__num__sqr,axiom,
% 4.69/5.04 ! [X: num] :
% 4.69/5.04 ( ( nat_of_num @ ( sqr @ X ) )
% 4.69/5.04 = ( times_times_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ X ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % nat_of_num_sqr
% 4.69/5.04 thf(fact_7729_Lcm__nat__empty,axiom,
% 4.69/5.04 ( ( gcd_Lcm_nat @ bot_bot_set_nat )
% 4.69/5.04 = one_one_nat ) ).
% 4.69/5.04
% 4.69/5.04 % Lcm_nat_empty
% 4.69/5.04 thf(fact_7730_sqr__conv__mult,axiom,
% 4.69/5.04 ( sqr
% 4.69/5.04 = ( ^ [X2: num] : ( times_times_num @ X2 @ X2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sqr_conv_mult
% 4.69/5.04 thf(fact_7731_Lcm__in__lcm__closed__set__nat,axiom,
% 4.69/5.04 ! [M: set_nat] :
% 4.69/5.04 ( ( finite_finite_nat @ M )
% 4.69/5.04 => ( ( M != bot_bot_set_nat )
% 4.69/5.04 => ( ! [M2: nat,N3: nat] :
% 4.69/5.04 ( ( member_nat @ M2 @ M )
% 4.69/5.04 => ( ( member_nat @ N3 @ M )
% 4.69/5.04 => ( member_nat @ ( gcd_lcm_nat @ M2 @ N3 ) @ M ) ) )
% 4.69/5.04 => ( member_nat @ ( gcd_Lcm_nat @ M ) @ M ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % Lcm_in_lcm_closed_set_nat
% 4.69/5.04 thf(fact_7732_pow_Osimps_I3_J,axiom,
% 4.69/5.04 ! [X: num,Y: num] :
% 4.69/5.04 ( ( pow @ X @ ( bit1 @ Y ) )
% 4.69/5.04 = ( times_times_num @ ( sqr @ ( pow @ X @ Y ) ) @ X ) ) ).
% 4.69/5.04
% 4.69/5.04 % pow.simps(3)
% 4.69/5.04 thf(fact_7733_coprime__crossproduct__nat,axiom,
% 4.69/5.04 ! [A2: nat,D2: nat,B: nat,C: nat] :
% 4.69/5.04 ( ( algebr934650988132801477me_nat @ A2 @ D2 )
% 4.69/5.04 => ( ( algebr934650988132801477me_nat @ B @ C )
% 4.69/5.04 => ( ( ( times_times_nat @ A2 @ C )
% 4.69/5.04 = ( times_times_nat @ B @ D2 ) )
% 4.69/5.04 = ( ( A2 = B )
% 4.69/5.04 & ( C = D2 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % coprime_crossproduct_nat
% 4.69/5.04 thf(fact_7734_coprime__crossproduct__int,axiom,
% 4.69/5.04 ! [A2: int,D2: int,B: int,C: int] :
% 4.69/5.04 ( ( algebr932160517623751201me_int @ A2 @ D2 )
% 4.69/5.04 => ( ( algebr932160517623751201me_int @ B @ C )
% 4.69/5.04 => ( ( ( times_times_int @ ( abs_abs_int @ A2 ) @ ( abs_abs_int @ C ) )
% 4.69/5.04 = ( times_times_int @ ( abs_abs_int @ B ) @ ( abs_abs_int @ D2 ) ) )
% 4.69/5.04 = ( ( ( abs_abs_int @ A2 )
% 4.69/5.04 = ( abs_abs_int @ B ) )
% 4.69/5.04 & ( ( abs_abs_int @ C )
% 4.69/5.04 = ( abs_abs_int @ D2 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % coprime_crossproduct_int
% 4.69/5.04 thf(fact_7735_in__range_Oelims_I3_J,axiom,
% 4.69/5.04 ! [X: produc3658429121746597890et_nat] :
% 4.69/5.04 ( ~ ( in_range @ X )
% 4.69/5.04 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/5.04 ( ( X
% 4.69/5.04 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/5.04 => ! [X3: nat] :
% 4.69/5.04 ( ( member_nat @ X3 @ As2 )
% 4.69/5.04 => ( ord_less_nat @ X3 @ ( lim_Product_unit @ H ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % in_range.elims(3)
% 4.69/5.04 thf(fact_7736_in__range_Osimps,axiom,
% 4.69/5.04 ! [H2: heap_e7401611519738050253t_unit,As: set_nat] :
% 4.69/5.04 ( ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As ) )
% 4.69/5.04 = ( ! [X2: nat] :
% 4.69/5.04 ( ( member_nat @ X2 @ As )
% 4.69/5.04 => ( ord_less_nat @ X2 @ ( lim_Product_unit @ H2 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % in_range.simps
% 4.69/5.04 thf(fact_7737_in__range_Oelims_I1_J,axiom,
% 4.69/5.04 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 4.69/5.04 ( ( ( in_range @ X )
% 4.69/5.04 = Y )
% 4.69/5.04 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/5.04 ( ( X
% 4.69/5.04 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/5.04 => ( Y
% 4.69/5.04 = ( ~ ! [X2: nat] :
% 4.69/5.04 ( ( member_nat @ X2 @ As2 )
% 4.69/5.04 => ( ord_less_nat @ X2 @ ( lim_Product_unit @ H ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % in_range.elims(1)
% 4.69/5.04 thf(fact_7738_in__range_Oelims_I2_J,axiom,
% 4.69/5.04 ! [X: produc3658429121746597890et_nat] :
% 4.69/5.04 ( ( in_range @ X )
% 4.69/5.04 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/5.04 ( ( X
% 4.69/5.04 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/5.04 => ~ ! [X6: nat] :
% 4.69/5.04 ( ( member_nat @ X6 @ As2 )
% 4.69/5.04 => ( ord_less_nat @ X6 @ ( lim_Product_unit @ H ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % in_range.elims(2)
% 4.69/5.04 thf(fact_7739_UNIV__bool,axiom,
% 4.69/5.04 ( top_top_set_o
% 4.69/5.04 = ( insert_o @ $false @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % UNIV_bool
% 4.69/5.04 thf(fact_7740_Rep__unit__induct,axiom,
% 4.69/5.04 ! [Y: $o,P: $o > $o] :
% 4.69/5.04 ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 4.69/5.04 => ( ! [X3: product_unit] : ( P @ ( product_Rep_unit @ X3 ) )
% 4.69/5.04 => ( P @ Y ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % Rep_unit_induct
% 4.69/5.04 thf(fact_7741_Abs__unit__inject,axiom,
% 4.69/5.04 ! [X: $o,Y: $o] :
% 4.69/5.04 ( ( member_o @ X @ ( insert_o @ $true @ bot_bot_set_o ) )
% 4.69/5.04 => ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 4.69/5.04 => ( ( ( product_Abs_unit @ X )
% 4.69/5.04 = ( product_Abs_unit @ Y ) )
% 4.69/5.04 = ( X = Y ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % Abs_unit_inject
% 4.69/5.04 thf(fact_7742_Rep__unit__inject,axiom,
% 4.69/5.04 ! [X: product_unit,Y: product_unit] :
% 4.69/5.04 ( ( ( product_Rep_unit @ X )
% 4.69/5.04 = ( product_Rep_unit @ Y ) )
% 4.69/5.04 = ( X = Y ) ) ).
% 4.69/5.04
% 4.69/5.04 % Rep_unit_inject
% 4.69/5.04 thf(fact_7743_Rep__unit__inverse,axiom,
% 4.69/5.04 ! [X: product_unit] :
% 4.69/5.04 ( ( product_Abs_unit @ ( product_Rep_unit @ X ) )
% 4.69/5.04 = X ) ).
% 4.69/5.04
% 4.69/5.04 % Rep_unit_inverse
% 4.69/5.04 thf(fact_7744_Abs__unit__inverse,axiom,
% 4.69/5.04 ! [Y: $o] :
% 4.69/5.04 ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 4.69/5.04 => ( ( product_Rep_unit @ ( product_Abs_unit @ Y ) )
% 4.69/5.04 = Y ) ) ).
% 4.69/5.04
% 4.69/5.04 % Abs_unit_inverse
% 4.69/5.04 thf(fact_7745_type__definition__unit,axiom,
% 4.69/5.04 type_d6188575255521822967unit_o @ product_Rep_unit @ product_Abs_unit @ ( insert_o @ $true @ bot_bot_set_o ) ).
% 4.69/5.04
% 4.69/5.04 % type_definition_unit
% 4.69/5.04 thf(fact_7746_Rep__unit,axiom,
% 4.69/5.04 ! [X: product_unit] : ( member_o @ ( product_Rep_unit @ X ) @ ( insert_o @ $true @ bot_bot_set_o ) ) ).
% 4.69/5.04
% 4.69/5.04 % Rep_unit
% 4.69/5.04 thf(fact_7747_Abs__unit__cases,axiom,
% 4.69/5.04 ! [X: product_unit] :
% 4.69/5.04 ~ ! [Y2: $o] :
% 4.69/5.04 ( ( X
% 4.69/5.04 = ( product_Abs_unit @ Y2 ) )
% 4.69/5.04 => ~ ( member_o @ Y2 @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % Abs_unit_cases
% 4.69/5.04 thf(fact_7748_Rep__unit__cases,axiom,
% 4.69/5.04 ! [Y: $o] :
% 4.69/5.04 ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 4.69/5.04 => ~ ! [X3: product_unit] :
% 4.69/5.04 ( Y
% 4.69/5.04 = ( ~ ( product_Rep_unit @ X3 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % Rep_unit_cases
% 4.69/5.04 thf(fact_7749_Abs__unit__induct,axiom,
% 4.69/5.04 ! [P: product_unit > $o,X: product_unit] :
% 4.69/5.04 ( ! [Y2: $o] :
% 4.69/5.04 ( ( member_o @ Y2 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 4.69/5.04 => ( P @ ( product_Abs_unit @ Y2 ) ) )
% 4.69/5.04 => ( P @ X ) ) ).
% 4.69/5.04
% 4.69/5.04 % Abs_unit_induct
% 4.69/5.04 thf(fact_7750_integer__of__char__code,axiom,
% 4.69/5.04 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 4.69/5.04 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 4.69/5.04 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ B72 ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B62 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B52 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B42 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B32 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B22 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B1 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B0 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % integer_of_char_code
% 4.69/5.04 thf(fact_7751_sum__encode__def,axiom,
% 4.69/5.04 ( nat_sum_encode
% 4.69/5.04 = ( sum_ca6763686470577984908at_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.69/5.04 @ ^ [B6: nat] : ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B6 ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % sum_encode_def
% 4.69/5.04 thf(fact_7752_upt__0__eq__Nil__conv,axiom,
% 4.69/5.04 ! [J: nat] :
% 4.69/5.04 ( ( ( upt @ zero_zero_nat @ J )
% 4.69/5.04 = nil_nat )
% 4.69/5.04 = ( J = zero_zero_nat ) ) ).
% 4.69/5.04
% 4.69/5.04 % upt_0_eq_Nil_conv
% 4.69/5.04 thf(fact_7753_upt__merge,axiom,
% 4.69/5.04 ! [I2: nat,J: nat,K3: nat] :
% 4.69/5.04 ( ( ( ord_less_eq_nat @ I2 @ J )
% 4.69/5.04 & ( ord_less_eq_nat @ J @ K3 ) )
% 4.69/5.04 => ( ( append_nat @ ( upt @ I2 @ J ) @ ( upt @ J @ K3 ) )
% 4.69/5.04 = ( upt @ I2 @ K3 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % upt_merge
% 4.69/5.04 thf(fact_7754_map__add__upt_H,axiom,
% 4.69/5.04 ! [Ofs: nat,A2: nat,B: nat] :
% 4.69/5.04 ( ( map_nat_nat
% 4.69/5.04 @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ Ofs )
% 4.69/5.04 @ ( upt @ A2 @ B ) )
% 4.69/5.04 = ( upt @ ( plus_plus_nat @ A2 @ Ofs ) @ ( plus_plus_nat @ B @ Ofs ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % map_add_upt'
% 4.69/5.04 thf(fact_7755_upt__eq__append__conv,axiom,
% 4.69/5.04 ! [I2: nat,J: nat,Xs: list_nat,Ys: list_nat] :
% 4.69/5.04 ( ( ord_less_eq_nat @ I2 @ J )
% 4.69/5.04 => ( ( ( upt @ I2 @ J )
% 4.69/5.04 = ( append_nat @ Xs @ Ys ) )
% 4.69/5.04 = ( ? [K5: nat] :
% 4.69/5.04 ( ( ord_less_eq_nat @ I2 @ K5 )
% 4.69/5.04 & ( ord_less_eq_nat @ K5 @ J )
% 4.69/5.04 & ( ( upt @ I2 @ K5 )
% 4.69/5.04 = Xs )
% 4.69/5.04 & ( ( upt @ K5 @ J )
% 4.69/5.04 = Ys ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % upt_eq_append_conv
% 4.69/5.04 thf(fact_7756_upt__append,axiom,
% 4.69/5.04 ! [I2: nat,J: nat] :
% 4.69/5.04 ( ( ord_less_nat @ I2 @ J )
% 4.69/5.04 => ( ( append_nat @ ( upt @ zero_zero_nat @ I2 ) @ ( upt @ I2 @ J ) )
% 4.69/5.04 = ( upt @ zero_zero_nat @ J ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % upt_append
% 4.69/5.04 thf(fact_7757_butlast__upt,axiom,
% 4.69/5.04 ! [M4: nat,N2: nat] :
% 4.69/5.04 ( ( butlast_nat @ ( upt @ M4 @ N2 ) )
% 4.69/5.04 = ( upt @ M4 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % butlast_upt
% 4.69/5.04 thf(fact_7758_upt__eq__lel__conv,axiom,
% 4.69/5.04 ! [L: nat,H2: nat,Is1: list_nat,I2: nat,Is2: list_nat] :
% 4.69/5.04 ( ( ( upt @ L @ H2 )
% 4.69/5.04 = ( append_nat @ Is1 @ ( cons_nat @ I2 @ Is2 ) ) )
% 4.69/5.04 = ( ( Is1
% 4.69/5.04 = ( upt @ L @ I2 ) )
% 4.69/5.04 & ( Is2
% 4.69/5.04 = ( upt @ ( suc @ I2 ) @ H2 ) )
% 4.69/5.04 & ( ord_less_eq_nat @ L @ I2 )
% 4.69/5.04 & ( ord_less_nat @ I2 @ H2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % upt_eq_lel_conv
% 4.69/5.04 thf(fact_7759_upt__filter__extend,axiom,
% 4.69/5.04 ! [U: nat,U5: nat,P: nat > $o] :
% 4.69/5.04 ( ( ord_less_eq_nat @ U @ U5 )
% 4.69/5.04 => ( ! [I3: nat] :
% 4.69/5.04 ( ( ( ord_less_eq_nat @ U @ I3 )
% 4.69/5.04 & ( ord_less_nat @ I3 @ U5 ) )
% 4.69/5.04 => ~ ( P @ I3 ) )
% 4.69/5.04 => ( ( filter_nat2 @ P @ ( upt @ zero_zero_nat @ U ) )
% 4.69/5.04 = ( filter_nat2 @ P @ ( upt @ zero_zero_nat @ U5 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % upt_filter_extend
% 4.69/5.04 thf(fact_7760_in__range_Opelims_I3_J,axiom,
% 4.69/5.04 ! [X: produc3658429121746597890et_nat] :
% 4.69/5.04 ( ~ ( in_range @ X )
% 4.69/5.04 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ X )
% 4.69/5.04 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/5.04 ( ( X
% 4.69/5.04 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/5.04 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/5.04 => ! [X3: nat] :
% 4.69/5.04 ( ( member_nat @ X3 @ As2 )
% 4.69/5.04 => ( ord_less_nat @ X3 @ ( lim_Product_unit @ H ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % in_range.pelims(3)
% 4.69/5.04 thf(fact_7761_in__range_Opelims_I1_J,axiom,
% 4.69/5.04 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 4.69/5.04 ( ( ( in_range @ X )
% 4.69/5.04 = Y )
% 4.69/5.04 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ X )
% 4.69/5.04 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/5.04 ( ( X
% 4.69/5.04 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/5.04 => ( ( Y
% 4.69/5.04 = ( ! [X2: nat] :
% 4.69/5.04 ( ( member_nat @ X2 @ As2 )
% 4.69/5.04 => ( ord_less_nat @ X2 @ ( lim_Product_unit @ H ) ) ) ) )
% 4.69/5.04 => ~ ( accp_P5801069581201407417et_nat @ in_range_rel @ ( produc7507926704131184380et_nat @ H @ As2 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % in_range.pelims(1)
% 4.69/5.04 thf(fact_7762_in__range_Opelims_I2_J,axiom,
% 4.69/5.04 ! [X: produc3658429121746597890et_nat] :
% 4.69/5.04 ( ( in_range @ X )
% 4.69/5.04 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ X )
% 4.69/5.04 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/5.04 ( ( X
% 4.69/5.04 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/5.04 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/5.04 => ~ ! [X6: nat] :
% 4.69/5.04 ( ( member_nat @ X6 @ As2 )
% 4.69/5.04 => ( ord_less_nat @ X6 @ ( lim_Product_unit @ H ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % in_range.pelims(2)
% 4.69/5.04 thf(fact_7763_one__assn__raw_Opelims_I3_J,axiom,
% 4.69/5.04 ! [X: produc3658429121746597890et_nat] :
% 4.69/5.04 ( ~ ( one_assn_raw @ X )
% 4.69/5.04 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ X )
% 4.69/5.04 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/5.04 ( ( X
% 4.69/5.04 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/5.04 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/5.04 => ( As2 = bot_bot_set_nat ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % one_assn_raw.pelims(3)
% 4.69/5.04 thf(fact_7764_one__assn__raw_Opelims_I2_J,axiom,
% 4.69/5.04 ! [X: produc3658429121746597890et_nat] :
% 4.69/5.04 ( ( one_assn_raw @ X )
% 4.69/5.04 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ X )
% 4.69/5.04 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/5.04 ( ( X
% 4.69/5.04 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/5.04 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/5.04 => ( As2 != bot_bot_set_nat ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % one_assn_raw.pelims(2)
% 4.69/5.04 thf(fact_7765_one__assn__raw_Opelims_I1_J,axiom,
% 4.69/5.04 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 4.69/5.04 ( ( ( one_assn_raw @ X )
% 4.69/5.04 = Y )
% 4.69/5.04 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ X )
% 4.69/5.04 => ~ ! [H: heap_e7401611519738050253t_unit,As2: set_nat] :
% 4.69/5.04 ( ( X
% 4.69/5.04 = ( produc7507926704131184380et_nat @ H @ As2 ) )
% 4.69/5.04 => ( ( Y
% 4.69/5.04 = ( As2 = bot_bot_set_nat ) )
% 4.69/5.04 => ~ ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ ( produc7507926704131184380et_nat @ H @ As2 ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % one_assn_raw.pelims(1)
% 4.69/5.04 thf(fact_7766_times__int__def,axiom,
% 4.69/5.04 ( times_times_int
% 4.69/5.04 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 4.69/5.04 @ ( produc27273713700761075at_nat
% 4.69/5.04 @ ^ [X2: nat,Y3: nat] :
% 4.69/5.04 ( produc2626176000494625587at_nat
% 4.69/5.04 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X2 @ U3 ) @ ( times_times_nat @ Y3 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X2 @ V4 ) @ ( times_times_nat @ Y3 @ U3 ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % times_int_def
% 4.69/5.04 thf(fact_7767_next_Osimps,axiom,
% 4.69/5.04 ! [V: code_natural,W: code_natural] :
% 4.69/5.04 ( ( next @ ( produc3574140220909816553atural @ V @ W ) )
% 4.69/5.04 = ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( plus_p4538020629002901425atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ W @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ W @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ one_one_Code_natural ) ) @ one_one_Code_natural ) @ ( produc3574140220909816553atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ V @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ W @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ W @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % next.simps
% 4.69/5.04 thf(fact_7768_Random_Orange__def,axiom,
% 4.69/5.04 ( range
% 4.69/5.04 = ( ^ [K5: code_natural] :
% 4.69/5.04 ( produc5538323210962509403atural
% 4.69/5.04 @ ( iterat8892046348760725948atural @ ( log @ ( numera5444537566228673987atural @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ K5 )
% 4.69/5.04 @ ^ [L2: code_natural] :
% 4.69/5.04 ( produc5538323210962509403atural @ next
% 4.69/5.04 @ ^ [V4: code_natural] : ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ V4 @ ( times_2397367101498566445atural @ L2 @ ( numera5444537566228673987atural @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 4.69/5.04 @ one_one_Code_natural )
% 4.69/5.04 @ ^ [V4: code_natural] : ( produc6639722614265839536atural @ ( modulo8411746178871703098atural @ V4 @ K5 ) ) ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % Random.range_def
% 4.69/5.04 thf(fact_7769_bot__unit__def,axiom,
% 4.69/5.04 bot_bot_Product_unit = product_Unity ).
% 4.69/5.04
% 4.69/5.04 % bot_unit_def
% 4.69/5.04 thf(fact_7770_sup__unit__def,axiom,
% 4.69/5.04 ( sup_sup_Product_unit
% 4.69/5.04 = ( ^ [Uu2: product_unit,Uv: product_unit] : product_Unity ) ) ).
% 4.69/5.04
% 4.69/5.04 % sup_unit_def
% 4.69/5.04 thf(fact_7771_old_Ounit_Oexhaust,axiom,
% 4.69/5.04 ! [Y: product_unit] : ( Y = product_Unity ) ).
% 4.69/5.04
% 4.69/5.04 % old.unit.exhaust
% 4.69/5.04 thf(fact_7772_Inf__unit__def,axiom,
% 4.69/5.04 ( comple2584293577114468500t_unit
% 4.69/5.04 = ( ^ [Uu2: set_Product_unit] : product_Unity ) ) ).
% 4.69/5.04
% 4.69/5.04 % Inf_unit_def
% 4.69/5.04 thf(fact_7773_uminus__unit__def,axiom,
% 4.69/5.04 ( uminus2952777764628376836t_unit
% 4.69/5.04 = ( ^ [Uu2: product_unit] : product_Unity ) ) ).
% 4.69/5.04
% 4.69/5.04 % uminus_unit_def
% 4.69/5.04 thf(fact_7774_top__unit__def,axiom,
% 4.69/5.04 top_top_Product_unit = product_Unity ).
% 4.69/5.04
% 4.69/5.04 % top_unit_def
% 4.69/5.04 thf(fact_7775_Unity__def,axiom,
% 4.69/5.04 ( product_Unity
% 4.69/5.04 = ( product_Abs_unit @ $true ) ) ).
% 4.69/5.04
% 4.69/5.04 % Unity_def
% 4.69/5.04 thf(fact_7776_Sup__unit__def,axiom,
% 4.69/5.04 ( comple4687483117567863418t_unit
% 4.69/5.04 = ( ^ [Uu2: set_Product_unit] : product_Unity ) ) ).
% 4.69/5.04
% 4.69/5.04 % Sup_unit_def
% 4.69/5.04 thf(fact_7777_inf__unit__def,axiom,
% 4.69/5.04 ( inf_inf_Product_unit
% 4.69/5.04 = ( ^ [Uu2: product_unit,Uv: product_unit] : product_Unity ) ) ).
% 4.69/5.04
% 4.69/5.04 % inf_unit_def
% 4.69/5.04 thf(fact_7778_UNIV__unit,axiom,
% 4.69/5.04 ( top_to1996260823553986621t_unit
% 4.69/5.04 = ( insert_Product_unit @ product_Unity @ bot_bo3957492148770167129t_unit ) ) ).
% 4.69/5.04
% 4.69/5.04 % UNIV_unit
% 4.69/5.04 thf(fact_7779_default__unit__def,axiom,
% 4.69/5.04 defaul566961228789861419t_unit = product_Unity ).
% 4.69/5.04
% 4.69/5.04 % default_unit_def
% 4.69/5.04 thf(fact_7780_cone__def,axiom,
% 4.69/5.04 ( bNF_Cardinal_cone
% 4.69/5.04 = ( bNF_Ca7083678892733797993t_unit @ ( insert_Product_unit @ product_Unity @ bot_bo3957492148770167129t_unit ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % cone_def
% 4.69/5.04 thf(fact_7781_times__integer__code_I3_J,axiom,
% 4.69/5.04 ! [M4: num,N2: num] :
% 4.69/5.04 ( ( times_3573771949741848930nteger @ ( code_Pos @ M4 ) @ ( code_Pos @ N2 ) )
% 4.69/5.04 = ( code_Pos @ ( times_times_num @ M4 @ N2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % times_integer_code(3)
% 4.69/5.04 thf(fact_7782_times__integer__code_I6_J,axiom,
% 4.69/5.04 ! [M4: num,N2: num] :
% 4.69/5.04 ( ( times_3573771949741848930nteger @ ( code_Neg @ M4 ) @ ( code_Neg @ N2 ) )
% 4.69/5.04 = ( code_Pos @ ( times_times_num @ M4 @ N2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % times_integer_code(6)
% 4.69/5.04 thf(fact_7783_times__integer__code_I5_J,axiom,
% 4.69/5.04 ! [M4: num,N2: num] :
% 4.69/5.04 ( ( times_3573771949741848930nteger @ ( code_Neg @ M4 ) @ ( code_Pos @ N2 ) )
% 4.69/5.04 = ( code_Neg @ ( times_times_num @ M4 @ N2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % times_integer_code(5)
% 4.69/5.04 thf(fact_7784_times__integer__code_I4_J,axiom,
% 4.69/5.04 ! [M4: num,N2: num] :
% 4.69/5.04 ( ( times_3573771949741848930nteger @ ( code_Pos @ M4 ) @ ( code_Neg @ N2 ) )
% 4.69/5.04 = ( code_Neg @ ( times_times_num @ M4 @ N2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % times_integer_code(4)
% 4.69/5.04 thf(fact_7785_times__natural_Orep__eq,axiom,
% 4.69/5.04 ! [X: code_natural,Xa: code_natural] :
% 4.69/5.04 ( ( code_nat_of_natural @ ( times_2397367101498566445atural @ X @ Xa ) )
% 4.69/5.04 = ( times_times_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % times_natural.rep_eq
% 4.69/5.04 thf(fact_7786_times__int__code_I3_J,axiom,
% 4.69/5.04 ! [M4: num,N2: num] :
% 4.69/5.04 ( ( times_times_int @ ( pos @ M4 ) @ ( pos @ N2 ) )
% 4.69/5.04 = ( pos @ ( times_times_num @ M4 @ N2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % times_int_code(3)
% 4.69/5.04 thf(fact_7787_times__int__code_I4_J,axiom,
% 4.69/5.04 ! [M4: num,N2: num] :
% 4.69/5.04 ( ( times_times_int @ ( pos @ M4 ) @ ( neg @ N2 ) )
% 4.69/5.04 = ( neg @ ( times_times_num @ M4 @ N2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % times_int_code(4)
% 4.69/5.04 thf(fact_7788_times__int__code_I5_J,axiom,
% 4.69/5.04 ! [M4: num,N2: num] :
% 4.69/5.04 ( ( times_times_int @ ( neg @ M4 ) @ ( pos @ N2 ) )
% 4.69/5.04 = ( neg @ ( times_times_num @ M4 @ N2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % times_int_code(5)
% 4.69/5.04 thf(fact_7789_times__int__code_I6_J,axiom,
% 4.69/5.04 ! [M4: num,N2: num] :
% 4.69/5.04 ( ( times_times_int @ ( neg @ M4 ) @ ( neg @ N2 ) )
% 4.69/5.04 = ( pos @ ( times_times_num @ M4 @ N2 ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % times_int_code(6)
% 4.69/5.04 thf(fact_7790_times__natural_Otransfer,axiom,
% 4.69/5.04 bNF_re88643428490162567atural @ code_pcr_natural @ ( bNF_re3704215830270325841atural @ code_pcr_natural @ code_pcr_natural ) @ times_times_nat @ times_2397367101498566445atural ).
% 4.69/5.04
% 4.69/5.04 % times_natural.transfer
% 4.69/5.04 thf(fact_7791_times__natural_Oabs__eq,axiom,
% 4.69/5.04 ! [Xa: nat,X: nat] :
% 4.69/5.04 ( ( times_2397367101498566445atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 4.69/5.04 = ( code_natural_of_nat @ ( times_times_nat @ Xa @ X ) ) ) ).
% 4.69/5.04
% 4.69/5.04 % times_natural.abs_eq
% 4.69/5.04 thf(fact_7792_type__definition__natural,axiom,
% 4.69/5.04 type_d4410041424927559462al_nat @ code_nat_of_natural @ code_natural_of_nat @ top_top_set_nat ).
% 4.69/5.04
% 4.69/5.04 % type_definition_natural
% 4.69/5.04 thf(fact_7793_times__natural__def,axiom,
% 4.69/5.04 ( times_2397367101498566445atural
% 4.69/5.04 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ times_times_nat ) ) ).
% 4.69/5.04
% 4.69/5.04 % times_natural_def
% 4.69/5.04 thf(fact_7794_times__integer_Otransfer,axiom,
% 4.69/5.04 bNF_re398004352372739002nteger @ code_pcr_integer @ ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer ) @ times_times_int @ times_3573771949741848930nteger ).
% 4.69/5.04
% 4.69/5.04 % times_integer.transfer
% 4.69/5.04 thf(fact_7795_times__integer__def,axiom,
% 4.69/5.04 ( times_3573771949741848930nteger
% 4.69/5.04 = ( map_fu8272188784021352819nteger @ code_int_of_integer @ ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int ) @ times_times_int ) ) ).
% 4.69/5.04
% 4.69/5.04 % times_integer_def
% 4.69/5.04
% 4.69/5.04 % Helper facts (29)
% 4.69/5.04 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 4.69/5.04 ! [X: int,Y: int] :
% 4.69/5.04 ( ( if_int @ $false @ X @ Y )
% 4.69/5.04 = Y ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 4.69/5.04 ! [X: int,Y: int] :
% 4.69/5.04 ( ( if_int @ $true @ X @ Y )
% 4.69/5.04 = X ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 4.69/5.04 ! [X: nat,Y: nat] :
% 4.69/5.04 ( ( if_nat @ $false @ X @ Y )
% 4.69/5.04 = Y ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 4.69/5.04 ! [X: nat,Y: nat] :
% 4.69/5.04 ( ( if_nat @ $true @ X @ Y )
% 4.69/5.04 = X ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 4.69/5.04 ! [X: rat,Y: rat] :
% 4.69/5.04 ( ( if_rat @ $false @ X @ Y )
% 4.69/5.04 = Y ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 4.69/5.04 ! [X: rat,Y: rat] :
% 4.69/5.04 ( ( if_rat @ $true @ X @ Y )
% 4.69/5.04 = X ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_2_1_If_001t__Set__Oset_I_Eo_J_T,axiom,
% 4.69/5.04 ! [X: set_o,Y: set_o] :
% 4.69/5.04 ( ( if_set_o @ $false @ X @ Y )
% 4.69/5.04 = Y ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_1_1_If_001t__Set__Oset_I_Eo_J_T,axiom,
% 4.69/5.04 ! [X: set_o,Y: set_o] :
% 4.69/5.04 ( ( if_set_o @ $true @ X @ Y )
% 4.69/5.04 = X ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_2_1_If_001t__Assertions__Oassn_T,axiom,
% 4.69/5.04 ! [X: assn,Y: assn] :
% 4.69/5.04 ( ( if_assn @ $false @ X @ Y )
% 4.69/5.04 = Y ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_1_1_If_001t__Assertions__Oassn_T,axiom,
% 4.69/5.04 ! [X: assn,Y: assn] :
% 4.69/5.04 ( ( if_assn @ $true @ X @ Y )
% 4.69/5.04 = X ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 4.69/5.04 ! [X: code_integer,Y: code_integer] :
% 4.69/5.04 ( ( if_Code_integer @ $false @ X @ Y )
% 4.69/5.04 = Y ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 4.69/5.04 ! [X: code_integer,Y: code_integer] :
% 4.69/5.04 ( ( if_Code_integer @ $true @ X @ Y )
% 4.69/5.04 = X ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_2_1_If_001t__Code____Numeral__Onatural_T,axiom,
% 4.69/5.04 ! [X: code_natural,Y: code_natural] :
% 4.69/5.04 ( ( if_Code_natural @ $false @ X @ Y )
% 4.69/5.04 = Y ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_1_1_If_001t__Code____Numeral__Onatural_T,axiom,
% 4.69/5.04 ! [X: code_natural,Y: code_natural] :
% 4.69/5.04 ( ( if_Code_natural @ $true @ X @ Y )
% 4.69/5.04 = X ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 4.69/5.04 ! [X: set_int,Y: set_int] :
% 4.69/5.04 ( ( if_set_int @ $false @ X @ Y )
% 4.69/5.04 = Y ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 4.69/5.04 ! [X: set_int,Y: set_int] :
% 4.69/5.04 ( ( if_set_int @ $true @ X @ Y )
% 4.69/5.04 = X ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_2_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 4.69/5.04 ! [X: set_nat,Y: set_nat] :
% 4.69/5.04 ( ( if_set_nat @ $false @ X @ Y )
% 4.69/5.04 = Y ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_1_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 4.69/5.04 ! [X: set_nat,Y: set_nat] :
% 4.69/5.04 ( ( if_set_nat @ $true @ X @ Y )
% 4.69/5.04 = X ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_2_1_If_001t__Filter__Ofilter_It__Nat__Onat_J_T,axiom,
% 4.69/5.04 ! [X: filter_nat,Y: filter_nat] :
% 4.69/5.04 ( ( if_filter_nat @ $false @ X @ Y )
% 4.69/5.04 = Y ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_1_1_If_001t__Filter__Ofilter_It__Nat__Onat_J_T,axiom,
% 4.69/5.04 ! [X: filter_nat,Y: filter_nat] :
% 4.69/5.04 ( ( if_filter_nat @ $true @ X @ Y )
% 4.69/5.04 = X ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_2_1_If_001t__Set__Oset_It__Product____Type__Ounit_J_T,axiom,
% 4.69/5.04 ! [X: set_Product_unit,Y: set_Product_unit] :
% 4.69/5.04 ( ( if_set_Product_unit @ $false @ X @ Y )
% 4.69/5.04 = Y ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_1_1_If_001t__Set__Oset_It__Product____Type__Ounit_J_T,axiom,
% 4.69/5.04 ! [X: set_Product_unit,Y: set_Product_unit] :
% 4.69/5.04 ( ( if_set_Product_unit @ $true @ X @ Y )
% 4.69/5.04 = X ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 4.69/5.04 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 4.69/5.04 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 4.69/5.04 = Y ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 4.69/5.04 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 4.69/5.04 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 4.69/5.04 = X ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 4.69/5.04 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 4.69/5.04 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
% 4.69/5.04 = Y ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 4.69/5.04 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 4.69/5.04 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
% 4.69/5.04 = X ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 4.69/5.04 ! [P: $o] :
% 4.69/5.04 ( ( P = $true )
% 4.69/5.04 | ( P = $false ) ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 4.69/5.04 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 4.69/5.04 ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y )
% 4.69/5.04 = Y ) ).
% 4.69/5.04
% 4.69/5.04 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.61/5.90 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 5.61/5.90 ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y )
% 5.61/5.90 = X ) ).
% 5.61/5.90
% 5.61/5.90 % Conjectures (1)
% 5.61/5.90 thf(conj_0,conjecture,
% 5.61/5.90 ( ( rep_assn @ ( abs_assn @ one_assn_raw ) @ h )
% 5.61/5.90 = ( ( produc8586169260539613262et_nat @ h )
% 5.61/5.90 = bot_bot_set_nat ) ) ).
% 5.61/5.90
% 5.61/5.90 %------------------------------------------------------------------------------
% 5.61/5.90 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.TMbufHVJYq/cvc5---1.0.5_28539.p...
% 5.61/5.90 (declare-sort $$unsorted 0)
% 5.61/5.90 (declare-sort tptp.set_Pr3444600963470892981et_nat 0)
% 5.61/5.90 (declare-sort tptp.produc5657529347773406293et_nat 0)
% 5.61/5.90 (declare-sort tptp.set_Pr7928877670098842301et_nat 0)
% 5.61/5.90 (declare-sort tptp.produc6830853553727218525et_nat 0)
% 5.61/5.90 (declare-sort tptp.set_Pr7705059561495379578_nat_o 0)
% 5.61/5.90 (declare-sort tptp.set_Pr8536935166611901872et_nat 0)
% 5.61/5.90 (declare-sort tptp.set_Pr8807100098903490369et_nat 0)
% 5.61/5.90 (declare-sort tptp.set_Pr3721596426557623617et_nat 0)
% 5.61/5.90 (declare-sort tptp.produc4962441903510821572_nat_o 0)
% 5.61/5.90 (declare-sort tptp.produc2732055786443039994et_nat 0)
% 5.61/5.90 (declare-sort tptp.produc7389280635074931169et_nat 0)
% 5.61/5.90 (declare-sort tptp.produc4658369026151987169et_nat 0)
% 5.61/5.90 (declare-sort tptp.produc101387210554329899nteger 0)
% 5.61/5.90 (declare-sort tptp.produc7936767299998605306et_nat 0)
% 5.61/5.90 (declare-sort tptp.set_Pr3813038829465207111_nat_o 0)
% 5.61/5.90 (declare-sort tptp.set_se7663487083892625191_nat_o 0)
% 5.61/5.90 (declare-sort tptp.produc6666532470309664615_nat_o 0)
% 5.61/5.90 (declare-sort tptp.produc1049655590333717003et_nat 0)
% 5.61/5.90 (declare-sort tptp.set_Pr2161125870931222855_nat_o 0)
% 5.61/5.90 (declare-sort tptp.set_Pr4208978187861016310_nat_o 0)
% 5.61/5.90 (declare-sort tptp.set_Pr3286484037609594932et_nat 0)
% 5.61/5.90 (declare-sort tptp.produc4928098042776334183_nat_o 0)
% 5.61/5.90 (declare-sort tptp.set_Pr719794911490849221et_nat 0)
% 5.61/5.90 (declare-sort tptp.produc6907119039986491712_nat_o 0)
% 5.61/5.90 (declare-sort tptp.produc3925858234332021118et_nat 0)
% 5.61/5.90 (declare-sort tptp.produc8111630337999740517et_nat 0)
% 5.61/5.90 (declare-sort tptp.produc5966032636589952099nteger 0)
% 5.61/5.90 (declare-sort tptp.produc5697189838369619070et_nat 0)
% 5.61/5.90 (declare-sort tptp.set_Pr5623950326363488168_nat_o 0)
% 5.61/5.90 (declare-sort tptp.set_Pr4769669219625338370_o_nat 0)
% 5.61/5.90 (declare-sort tptp.produc6500295350249520386et_nat 0)
% 5.61/5.90 (declare-sort tptp.produc3776562785724475560_o_int 0)
% 5.61/5.90 (declare-sort tptp.produc723880050079548563nteger 0)
% 5.61/5.90 (declare-sort tptp.set_se1353816476878259085_nat_o 0)
% 5.61/5.90 (declare-sort tptp.set_Pr1776176089890104647t_unit 0)
% 5.61/5.90 (declare-sort tptp.produc8065447618272157327et_nat 0)
% 5.61/5.90 (declare-sort tptp.set_Pr6409761941060870310at_o_o 0)
% 5.61/5.90 (declare-sort tptp.set_Pr8693737435421807431at_nat 0)
% 5.61/5.90 (declare-sort tptp.set_Pr5557702248415638087at_int 0)
% 5.61/5.90 (declare-sort tptp.set_Pr5696620967126086215nt_nat 0)
% 5.61/5.90 (declare-sort tptp.set_Pr2560585780119916871nt_int 0)
% 5.61/5.90 (declare-sort tptp.produc6197004810343482825et_nat 0)
% 5.61/5.90 (declare-sort tptp.produc5835291356934675326atural 0)
% 5.61/5.90 (declare-sort tptp.set_Pr4532377907799695533_nat_o 0)
% 5.61/5.90 (declare-sort tptp.produc8126358835630522215t_unit 0)
% 5.61/5.90 (declare-sort tptp.produc859450856879609959at_nat 0)
% 5.61/5.90 (declare-sort tptp.produc6495656768158660455at_int 0)
% 5.61/5.90 (declare-sort tptp.produc4806409095325742951nt_nat 0)
% 5.61/5.90 (declare-sort tptp.produc1219242969750017639nt_int 0)
% 5.61/5.90 (declare-sort tptp.set_Pr7577011563204128103nteger 0)
% 5.61/5.90 (declare-sort tptp.set_Pr4071100604818519410t_unit 0)
% 5.61/5.90 (declare-sort tptp.set_Pr3948176798113811640et_nat 0)
% 5.61/5.90 (declare-sort tptp.set_Pr3980508049012409671t_unit 0)
% 5.61/5.90 (declare-sort tptp.produc1397831737260518551nteger 0)
% 5.61/5.90 (declare-sort tptp.produc2221115339011613079nteger 0)
% 5.61/5.90 (declare-sort tptp.produc4671145554997361783at_nat 0)
% 5.61/5.90 (declare-sort tptp.produc3574062574353363227at_nat 0)
% 5.61/5.90 (declare-sort tptp.produc6128020648511768019nt_int 0)
% 5.61/5.90 (declare-sort tptp.produc5030937667867769463nt_int 0)
% 5.61/5.90 (declare-sort tptp.produc6491284506569428743nteger 0)
% 5.61/5.90 (declare-sort tptp.produc7348995623955488188t_unit 0)
% 5.61/5.90 (declare-sort tptp.produc3658429121746597890et_nat 0)
% 5.61/5.90 (declare-sort tptp.set_se8994758365886191399t_unit 0)
% 5.61/5.90 (declare-sort tptp.produc1357844946079266663t_unit 0)
% 5.61/5.90 (declare-sort tptp.set_Pr5488025237498180813et_nat 0)
% 5.61/5.90 (declare-sort tptp.set_Pr2522554150109002629et_int 0)
% 5.61/5.90 (declare-sort tptp.set_Pr4811707699266497531nteger 0)
% 5.61/5.90 (declare-sort tptp.set_Pr4580871404036792859t_unit 0)
% 5.61/5.90 (declare-sort tptp.produc6653097349344004940it_nat 0)
% 5.61/5.90 (declare-sort tptp.produc2475246329834808232it_int 0)
% 5.61/5.90 (declare-sort tptp.set_Pr5094982260447487303t_unit 0)
% 5.61/5.90 (declare-sort tptp.set_se7855581050983116737at_nat 0)
% 5.61/5.90 (declare-sort tptp.set_se6260736226359567993nt_int 0)
% 5.61/5.90 (declare-sort tptp.set_Pr2406931829603198446nteger 0)
% 5.61/5.90 (declare-sort tptp.set_Pr8986988648414616686er_nat 0)
% 5.61/5.90 (declare-sort tptp.set_Pr6496905503482889930er_int 0)
% 5.61/5.90 (declare-sort tptp.produc7819656566062154093et_nat 0)
% 5.61/5.90 (declare-sort tptp.produc2115011035271226405et_int 0)
% 5.61/5.90 (declare-sort tptp.produc7822875418678951345atural 0)
% 5.61/5.90 (declare-sort tptp.produc8923325533196201883nteger 0)
% 5.61/5.90 (declare-sort tptp.set_Pr4577759397028426247_set_o 0)
% 5.61/5.90 (declare-sort tptp.set_Pr1763845938948868674it_nat 0)
% 5.61/5.90 (declare-sort tptp.set_Pr8497134830871917726it_int 0)
% 5.61/5.90 (declare-sort tptp.set_Pr4334478416066269672t_unit 0)
% 5.61/5.90 (declare-sort tptp.set_Pr5889264611543340172t_unit 0)
% 5.61/5.90 (declare-sort tptp.produc5496629617739085541t_unit 0)
% 5.61/5.90 (declare-sort tptp.set_Co726186806682698383nteger 0)
% 5.61/5.90 (declare-sort tptp.produc8459935480633519975t_unit 0)
% 5.61/5.90 (declare-sort tptp.set_Pr448751882837621926eger_o 0)
% 5.61/5.90 (declare-sort tptp.filter1242075044329608583at_nat 0)
% 5.61/5.90 (declare-sort tptp.set_Pr5464989305201766866unit_o 0)
% 5.61/5.90 (declare-sort tptp.set_Pr6671815714118170108t_unit 0)
% 5.61/5.90 (declare-sort tptp.set_he8644174446132254637t_unit 0)
% 5.61/5.90 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 5.61/5.90 (declare-sort tptp.set_Pr7995236796853374141at_int 0)
% 5.61/5.90 (declare-sort tptp.set_Pr3448869479623346877nt_nat 0)
% 5.61/5.90 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 5.61/5.90 (declare-sort tptp.produc2400336064389900727et_nat 0)
% 5.61/5.90 (declare-sort tptp.produc2591615631378489102nteger 0)
% 5.61/5.90 (declare-sort tptp.produc2771989624626745363et_nat 0)
% 5.61/5.90 (declare-sort tptp.produc6433947425880249742er_nat 0)
% 5.61/5.90 (declare-sort tptp.produc2256096406371053034er_int 0)
% 5.61/5.90 (declare-sort tptp.set_se491199571785101031od_o_o 0)
% 5.61/5.90 (declare-sort tptp.produc7369051934464679207_set_o 0)
% 5.61/5.90 (declare-sort tptp.produc600557818389255820it_nat 0)
% 5.61/5.90 (declare-sort tptp.produc5646078835734834920it_int 0)
% 5.61/5.90 (declare-sort tptp.produc526117512892780850t_unit 0)
% 5.61/5.90 (declare-sort tptp.produc6865911496949736918t_unit 0)
% 5.61/5.90 (declare-sort tptp.set_Pr3149072824959771635_nat_o 0)
% 5.61/5.90 (declare-sort tptp.set_Pr903927857289325719_int_o 0)
% 5.61/5.90 (declare-sort tptp.set_Pr2101469702781467981_o_nat 0)
% 5.61/5.90 (declare-sort tptp.set_Pr8834758594704517033_o_int 0)
% 5.61/5.90 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 5.61/5.90 (declare-sort tptp.set_set_set_nat 0)
% 5.61/5.90 (declare-sort tptp.set_set_Code_integer 0)
% 5.61/5.90 (declare-sort tptp.produc7485711547916492274unit_o 0)
% 5.61/5.90 (declare-sort tptp.produc3788275437394581276t_unit 0)
% 5.61/5.90 (declare-sort tptp.set_set_Product_unit 0)
% 5.61/5.90 (declare-sort tptp.heap_e7401611519738050253t_unit 0)
% 5.61/5.90 (declare-sort tptp.product_prod_nat_nat 0)
% 5.61/5.90 (declare-sort tptp.product_prod_nat_int 0)
% 5.61/5.90 (declare-sort tptp.product_prod_int_nat 0)
% 5.61/5.90 (declare-sort tptp.product_prod_int_int 0)
% 5.61/5.90 (declare-sort tptp.set_Product_unit_o 0)
% 5.61/5.90 (declare-sort tptp.set_Product_prod_o_o 0)
% 5.61/5.90 (declare-sort tptp.sum_sum_nat_nat 0)
% 5.61/5.90 (declare-sort tptp.set_filter_nat 0)
% 5.61/5.90 (declare-sort tptp.filter_set_nat 0)
% 5.61/5.90 (declare-sort tptp.product_prod_nat_o 0)
% 5.61/5.90 (declare-sort tptp.product_prod_int_o 0)
% 5.61/5.90 (declare-sort tptp.product_prod_o_nat 0)
% 5.61/5.90 (declare-sort tptp.product_prod_o_int 0)
% 5.61/5.90 (declare-sort tptp.set_set_nat 0)
% 5.61/5.90 (declare-sort tptp.set_set_int 0)
% 5.61/5.90 (declare-sort tptp.set_Code_natural 0)
% 5.61/5.90 (declare-sort tptp.set_Code_integer 0)
% 5.61/5.90 (declare-sort tptp.set_Product_unit 0)
% 5.61/5.90 (declare-sort tptp.set_nat_o 0)
% 5.61/5.90 (declare-sort tptp.set_int_o 0)
% 5.61/5.90 (declare-sort tptp.product_prod_o_o 0)
% 5.61/5.90 (declare-sort tptp.set_assn 0)
% 5.61/5.90 (declare-sort tptp.set_set_o 0)
% 5.61/5.90 (declare-sort tptp.filter_nat 0)
% 5.61/5.90 (declare-sort tptp.set_o_o 0)
% 5.61/5.90 (declare-sort tptp.list_nat 0)
% 5.61/5.90 (declare-sort tptp.set_rat 0)
% 5.61/5.90 (declare-sort tptp.set_nat 0)
% 5.61/5.90 (declare-sort tptp.set_int 0)
% 5.61/5.90 (declare-sort tptp.code_natural 0)
% 5.61/5.90 (declare-sort tptp.code_integer 0)
% 5.61/5.90 (declare-sort tptp.product_unit 0)
% 5.61/5.90 (declare-sort tptp.typerep 0)
% 5.61/5.90 (declare-sort tptp.assn 0)
% 5.61/5.90 (declare-sort tptp.set_o 0)
% 5.61/5.90 (declare-sort tptp.char 0)
% 5.61/5.90 (declare-sort tptp.rat 0)
% 5.61/5.90 (declare-sort tptp.num 0)
% 5.61/5.90 (declare-sort tptp.nat 0)
% 5.61/5.90 (declare-sort tptp.int 0)
% 5.61/5.90 (declare-fun tptp.abs_assn ((-> tptp.produc3658429121746597890et_nat Bool)) tptp.assn)
% 5.61/5.90 (declare-fun tptp.rep_assn (tptp.assn tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.in_range (tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.in_range_rel (tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.is_pure_assn (tptp.assn) Bool)
% 5.61/5.90 (declare-fun tptp.one_assn_raw (tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.one_assn_raw_rel (tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.proper ((-> tptp.produc3658429121746597890et_nat Bool)) Bool)
% 5.61/5.90 (declare-fun tptp.pure_assn (Bool) tptp.assn)
% 5.61/5.90 (declare-fun tptp.pure_a825153325127701367it_nat (Bool tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.pure_a6022498039421069578it_nat (tptp.produc6197004810343482825et_nat tptp.produc6197004810343482825et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.relH (tptp.set_nat tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit) Bool)
% 5.61/5.90 (declare-fun tptp.times_assn_raw ((-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.times_assn_raw_rel (tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.wand_assn (tptp.assn tptp.assn) tptp.assn)
% 5.61/5.90 (declare-fun tptp.wand_raw ((-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.wand_raw_rel (tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_Cardinal_cone () tptp.set_Pr5094982260447487303t_unit)
% 5.61/5.90 (declare-fun tptp.bNF_Ca7083678892733797993t_unit (tptp.set_Product_unit) tptp.set_Pr5094982260447487303t_unit)
% 5.61/5.90 (declare-fun tptp.bNF_fs3871268833404974121et_nat ((-> tptp.heap_e7401611519738050253t_unit tptp.set_nat Bool) (-> tptp.set_nat tptp.set_nat Bool) tptp.produc3658429121746597890et_nat) tptp.produc3658429121746597890et_nat)
% 5.61/5.90 (declare-fun tptp.bNF_fs8167890477030535480nt_int ((-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 5.61/5.90 (declare-fun tptp.bNF_pi3450177011487049898et_nat ((-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit Bool) (-> tptp.heap_e7401611519738050253t_unit tptp.set_nat Bool) tptp.heap_e7401611519738050253t_unit tptp.set_nat) tptp.heap_e7401611519738050253t_unit)
% 5.61/5.90 (declare-fun tptp.bNF_pi4042512755101277815et_nat ((-> tptp.heap_e7401611519738050253t_unit tptp.set_nat Bool) (-> tptp.set_nat tptp.set_nat Bool) tptp.heap_e7401611519738050253t_unit tptp.set_nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.bNF_pi8853482479757052266nt_int ((-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool) tptp.int tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.bNF_re398004352372739002nteger ((-> tptp.int tptp.code_integer Bool) (-> (-> tptp.int tptp.int) (-> tptp.code_integer tptp.code_integer) Bool) (-> tptp.int tptp.int tptp.int) (-> tptp.code_integer tptp.code_integer tptp.code_integer)) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_re3379532845092657523nteger ((-> tptp.int tptp.code_integer Bool) (-> tptp.int tptp.code_integer Bool) (-> tptp.int tptp.int) (-> tptp.code_integer tptp.code_integer)) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_re711492959462206631nt_int ((-> tptp.int tptp.int Bool) (-> (-> tptp.int tptp.int) (-> tptp.int tptp.int) Bool) (-> tptp.int tptp.int tptp.int) (-> tptp.int tptp.int tptp.int)) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_re4712519889275205905nt_int ((-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool) (-> tptp.int tptp.int) (-> tptp.int tptp.int)) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_re88643428490162567atural ((-> tptp.nat tptp.code_natural Bool) (-> (-> tptp.nat tptp.nat) (-> tptp.code_natural tptp.code_natural) Bool) (-> tptp.nat tptp.nat tptp.nat) (-> tptp.code_natural tptp.code_natural tptp.code_natural)) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_re3704215830270325841atural ((-> tptp.nat tptp.code_natural Bool) (-> tptp.nat tptp.code_natural Bool) (-> tptp.nat tptp.nat) (-> tptp.code_natural tptp.code_natural)) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_re1345281282404953727at_nat ((-> tptp.nat tptp.nat Bool) (-> (-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) Bool) (-> tptp.nat tptp.nat tptp.nat) (-> tptp.nat tptp.nat tptp.nat)) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_re5653821019739307937at_nat ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat)) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_re5228765855967844073nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> (-> tptp.product_prod_int_int tptp.product_prod_int_int) (-> tptp.product_prod_int_int tptp.product_prod_int_int) Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int) (-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_re8699439704749558557nt_o_o ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> Bool Bool Bool) (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool)) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_re7145576690424134365nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int) (-> tptp.product_prod_int_int tptp.product_prod_int_int)) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_re7627151682743391978at_rat ((-> tptp.product_prod_int_int tptp.rat Bool) (-> (-> tptp.product_prod_int_int tptp.product_prod_int_int) (-> tptp.rat tptp.rat) Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int) (-> tptp.rat tptp.rat tptp.rat)) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_re1494630372529172596at_o_o ((-> tptp.product_prod_int_int tptp.rat Bool) (-> Bool Bool Bool) (-> tptp.product_prod_int_int Bool) (-> tptp.rat Bool)) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_re8279943556446156061nt_rat ((-> tptp.product_prod_int_int tptp.rat Bool) (-> tptp.product_prod_int_int tptp.rat Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int) (-> tptp.rat tptp.rat)) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_re7408651293131936558nt_int ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.int tptp.int) Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.int tptp.int tptp.int)) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_re7400052026677387805at_int ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> tptp.product_prod_nat_nat tptp.int Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.int tptp.int)) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_re3099431351363272937at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_re2241393799969408733at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_sn4039337771197282234et_nat ((-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit Bool) (-> tptp.heap_e7401611519738050253t_unit tptp.set_nat Bool) tptp.produc3658429121746597890et_nat) tptp.produc3658429121746597890et_nat)
% 5.61/5.90 (declare-fun tptp.bNF_sn1062102010912252026nt_int ((-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 5.61/5.90 (declare-fun tptp.bNF_We1730399552001240015qr_int (tptp.set_Pr958786334691620121nt_int) tptp.set_Pr2560585780119916871nt_int)
% 5.61/5.90 (declare-fun tptp.bNF_We1732890022510290291qr_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr8693737435421807431at_nat)
% 5.61/5.90 (declare-fun tptp.bNF_We740377018556551609_nat_o (tptp.set_Pr2161125870931222855_nat_o) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_We6437023980930612612_rel_o (tptp.set_Product_prod_o_o) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_We3815749466139970368el_int (tptp.set_Pr958786334691620121nt_int) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_We3818239936649020644el_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_We2091578341578594809t_unit (tptp.set_Pr5094982260447487303t_unit) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_We5608535359669600131_nat_o (tptp.set_Pr2161125870931222855_nat_o tptp.set_Pr4532377907799695533_nat_o (-> tptp.produc3658429121746597890et_nat Bool)) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_We4647864369647134286inim_o (tptp.set_Product_prod_o_o tptp.set_o Bool) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_We6511469253196982518im_int (tptp.set_Pr958786334691620121nt_int tptp.set_int tptp.int) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_We6513959723706032794im_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_nat tptp.nat) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_We909621271159000003t_unit (tptp.set_Pr5094982260447487303t_unit tptp.set_Product_unit tptp.product_unit) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_We6400040844883348763_nat_o (tptp.set_Pr2161125870931222855_nat_o (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_We3104086342435940326max2_o (tptp.set_Product_prod_o_o Bool Bool) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_We2378448595015613790x2_int (tptp.set_Pr958786334691620121nt_int tptp.int tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.bNF_We2380939065524664066x2_nat (tptp.set_Pr1261947904930325089at_nat tptp.nat tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.bNF_We7204996500647184731t_unit (tptp.set_Pr5094982260447487303t_unit tptp.product_unit tptp.product_unit) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.bNF_We8236795211600914329_nat_o (tptp.set_Pr2161125870931222855_nat_o tptp.set_Pr4532377907799695533_nat_o tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_We537455116209922916inim_o (tptp.set_Product_prod_o_o tptp.set_o) Bool)
% 5.61/5.90 (declare-fun tptp.bNF_We3272633801743244640im_int (tptp.set_Pr958786334691620121nt_int tptp.set_int) tptp.int)
% 5.61/5.90 (declare-fun tptp.bNF_We3275124272252294916im_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.bNF_We7185707985517244377t_unit (tptp.set_Pr5094982260447487303t_unit tptp.set_Product_unit) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.basic_5567952622663070111et_nat ((-> tptp.heap_e7401611519738050253t_unit tptp.nat) (-> tptp.set_nat tptp.nat) tptp.produc3658429121746597890et_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.basic_1872990034501187214nt_int ((-> tptp.int tptp.nat) (-> tptp.int tptp.nat) tptp.product_prod_int_int) tptp.nat)
% 5.61/5.90 (declare-fun tptp.basic_3966130907827183364et_nat (tptp.produc2732055786443039994et_nat) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.90 (declare-fun tptp.basic_8654530971723826568et_nat (tptp.produc3925858234332021118et_nat) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.90 (declare-fun tptp.basic_7833836874476830220et_nat (tptp.produc3658429121746597890et_nat) tptp.set_he8644174446132254637t_unit)
% 5.61/5.90 (declare-fun tptp.basic_fsts_int_int (tptp.product_prod_int_int) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.basic_fsts_nat_nat (tptp.product_prod_nat_nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.basic_2768200282441914438et_nat (tptp.produc2732055786443039994et_nat) tptp.set_Pr3286484037609594932et_nat)
% 5.61/5.90 (declare-fun tptp.basic_8479756702517612234et_nat (tptp.produc3925858234332021118et_nat) tptp.set_Pr3948176798113811640et_nat)
% 5.61/5.90 (declare-fun tptp.basic_2698842327037663054et_nat (tptp.produc3658429121746597890et_nat) tptp.set_set_nat)
% 5.61/5.90 (declare-fun tptp.basic_snds_int_int (tptp.product_prod_int_int) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.basic_snds_nat_nat (tptp.product_prod_nat_nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.gbinom8545251970709558553nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.gbinom7368847122466276068atural (tptp.code_natural tptp.nat) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.gbinomial_int (tptp.int tptp.nat) tptp.int)
% 5.61/5.90 (declare-fun tptp.gbinomial_nat (tptp.nat tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.gbinomial_rat (tptp.rat tptp.nat) tptp.rat)
% 5.61/5.90 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 5.61/5.90 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 5.61/5.90 (declare-fun tptp.code_Neg (tptp.num) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.code_Pos (tptp.num) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 5.61/5.90 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 5.61/5.90 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 5.61/5.90 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 5.61/5.90 (declare-fun tptp.code_nat_of_natural (tptp.code_natural) tptp.nat)
% 5.61/5.90 (declare-fun tptp.code_natural_of_nat (tptp.nat) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.code_pcr_integer (tptp.int tptp.code_integer) Bool)
% 5.61/5.90 (declare-fun tptp.code_pcr_natural (tptp.nat tptp.code_natural) Bool)
% 5.61/5.90 (declare-fun tptp.comple4605987646318907561at_o_o (tptp.set_Pr6409761941060870310at_o_o (-> tptp.produc3658429121746597890et_nat Bool)) Bool)
% 5.61/5.90 (declare-fun tptp.complete_Inf_Inf_o_o (tptp.set_o_o Bool) Bool)
% 5.61/5.90 (declare-fun tptp.comple4393433247856107946_int_o (tptp.set_int_o tptp.int) Bool)
% 5.61/5.90 (declare-fun tptp.comple6214475593288795910_nat_o (tptp.set_nat_o tptp.nat) Bool)
% 5.61/5.90 (declare-fun tptp.comple90455603224345172_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.comple2092403528524206185unit_o (tptp.set_Product_unit_o tptp.product_unit) Bool)
% 5.61/5.90 (declare-fun tptp.complete_Inf_Inf_o (tptp.set_o) Bool)
% 5.61/5.90 (declare-fun tptp.comple6612786467464916249er_nat (tptp.set_filter_nat) tptp.filter_nat)
% 5.61/5.90 (declare-fun tptp.complete_Inf_Inf_int (tptp.set_int) tptp.int)
% 5.61/5.90 (declare-fun tptp.complete_Inf_Inf_nat (tptp.set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.comple2584293577114468500t_unit (tptp.set_Product_unit) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.comple79274577958421812_nat_o (tptp.set_se1353816476878259085_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.90 (declare-fun tptp.comple3063163877087187839_set_o (tptp.set_set_o) tptp.set_o)
% 5.61/5.90 (declare-fun tptp.comple3628384868704368283et_int (tptp.set_set_int) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.comple7806235888213564991et_nat (tptp.set_set_nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.comple1930127330929219688at_nat (tptp.set_se7855581050983116737at_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.90 (declare-fun tptp.comple7216939928495492468t_unit (tptp.set_set_Product_unit) tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.comple3590721164184202819at_o_o (tptp.set_Pr6409761941060870310at_o_o (-> tptp.produc3658429121746597890et_nat Bool)) Bool)
% 5.61/5.90 (declare-fun tptp.complete_Sup_Sup_o_o (tptp.set_o_o Bool) Bool)
% 5.61/5.90 (declare-fun tptp.comple6496622788309502864_int_o (tptp.set_int_o tptp.int) Bool)
% 5.61/5.90 (declare-fun tptp.comple8317665133742190828_nat_o (tptp.set_nat_o tptp.nat) Bool)
% 5.61/5.90 (declare-fun tptp.comple4225350640907012154_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.comple4773641153059738115unit_o (tptp.set_Product_unit_o tptp.product_unit) Bool)
% 5.61/5.90 (declare-fun tptp.complete_Sup_Sup_o (tptp.set_o) Bool)
% 5.61/5.90 (declare-fun tptp.comple2454491259644266675er_nat (tptp.set_filter_nat) tptp.filter_nat)
% 5.61/5.90 (declare-fun tptp.complete_Sup_Sup_int (tptp.set_int) tptp.int)
% 5.61/5.90 (declare-fun tptp.complete_Sup_Sup_nat (tptp.set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.comple4687483117567863418t_unit (tptp.set_Product_unit) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.comple3382087578465172250_nat_o (tptp.set_se1353816476878259085_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.90 (declare-fun tptp.comple90263536869209701_set_o (tptp.set_set_o) tptp.set_o)
% 5.61/5.90 (declare-fun tptp.comple739944243200306918nteger (tptp.set_set_Code_integer) tptp.set_Code_integer)
% 5.61/5.90 (declare-fun tptp.comple3221217463730067765et_int (tptp.set_set_int) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.comple7399068483239264473et_nat (tptp.set_set_nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.comple8164645552537203636_nat_o (tptp.set_se7663487083892625191_nat_o) tptp.set_Pr2161125870931222855_nat_o)
% 5.61/5.90 (declare-fun tptp.comple2567785453016644468od_o_o (tptp.set_se491199571785101031od_o_o) tptp.set_Product_prod_o_o)
% 5.61/5.90 (declare-fun tptp.comple5382143125604098054nt_int (tptp.set_se6260736226359567993nt_int) tptp.set_Pr958786334691620121nt_int)
% 5.61/5.90 (declare-fun tptp.comple5685304695842803022at_nat (tptp.set_se7855581050983116737at_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.90 (declare-fun tptp.comple2798140142350441396t_unit (tptp.set_se8994758365886191399t_unit) tptp.set_Pr5094982260447487303t_unit)
% 5.61/5.90 (declare-fun tptp.comple3349607820504768346t_unit (tptp.set_set_Product_unit) tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.condit4352657709669162033_nat_o (tptp.set_Pr4532377907799695533_nat_o) Bool)
% 5.61/5.90 (declare-fun tptp.condit5488710616941104124bove_o (tptp.set_o) Bool)
% 5.61/5.90 (declare-fun tptp.condit4029664723990530684er_nat (tptp.set_filter_nat) Bool)
% 5.61/5.90 (declare-fun tptp.condit2212336002400062152ve_int (tptp.set_int) Bool)
% 5.61/5.90 (declare-fun tptp.condit2214826472909112428ve_nat (tptp.set_nat) Bool)
% 5.61/5.90 (declare-fun tptp.condit2080475194861589617t_unit (tptp.set_Product_unit) Bool)
% 5.61/5.90 (declare-fun tptp.condit5477540289124974626et_nat (tptp.set_set_nat) Bool)
% 5.61/5.90 (declare-fun tptp.condit8399017556247434269_nat_o (tptp.set_Pr4532377907799695533_nat_o) Bool)
% 5.61/5.90 (declare-fun tptp.condit5413489452508810728elow_o (tptp.set_o) Bool)
% 5.61/5.90 (declare-fun tptp.condit3133331395780078992er_nat (tptp.set_filter_nat) Bool)
% 5.61/5.90 (declare-fun tptp.condit1735850657277959132ow_int (tptp.set_int) Bool)
% 5.61/5.90 (declare-fun tptp.condit1738341127787009408ow_nat (tptp.set_nat) Bool)
% 5.61/5.90 (declare-fun tptp.condit9161856309968323677t_unit (tptp.set_Product_unit) Bool)
% 5.61/5.90 (declare-fun tptp.condit68592940725977398et_nat (tptp.set_set_nat) Bool)
% 5.61/5.90 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 5.61/5.90 (declare-fun tptp.unique5706413561485394159nteger (tptp.produc8923325533196201883nteger) Bool)
% 5.61/5.90 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 5.61/5.90 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 5.61/5.90 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.61/5.90 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 5.61/5.90 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 5.61/5.90 (declare-fun tptp.equiv_6726761681920839555_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr2161125870931222855_nat_o) Bool)
% 5.61/5.90 (declare-fun tptp.equiv_equiv_o (tptp.set_o tptp.set_Product_prod_o_o) Bool)
% 5.61/5.90 (declare-fun tptp.equiv_equiv_int (tptp.set_int tptp.set_Pr958786334691620121nt_int) Bool)
% 5.61/5.90 (declare-fun tptp.equiv_equiv_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.61/5.90 (declare-fun tptp.equiv_4189356295871601603t_unit (tptp.set_Product_unit tptp.set_Pr5094982260447487303t_unit) Bool)
% 5.61/5.90 (declare-fun tptp.equiv_3235788788526563786_nat_o (tptp.set_Pr2161125870931222855_nat_o (-> tptp.produc3658429121746597890et_nat Bool)) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.90 (declare-fun tptp.equiv_proj_o_o (tptp.set_Product_prod_o_o Bool) tptp.set_o)
% 5.61/5.90 (declare-fun tptp.equiv_proj_int_int (tptp.set_Pr958786334691620121nt_int tptp.int) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.equiv_proj_nat_nat (tptp.set_Pr1261947904930325089at_nat tptp.nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.equiv_5763582929720877514t_unit (tptp.set_Pr5094982260447487303t_unit tptp.product_unit) tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.equiv_7899955228204526484_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr2161125870931222855_nat_o) tptp.set_se1353816476878259085_nat_o)
% 5.61/5.90 (declare-fun tptp.equiv_quotient_o (tptp.set_o tptp.set_Product_prod_o_o) tptp.set_set_o)
% 5.61/5.90 (declare-fun tptp.equiv_quotient_int (tptp.set_int tptp.set_Pr958786334691620121nt_int) tptp.set_set_int)
% 5.61/5.90 (declare-fun tptp.equiv_quotient_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_set_nat)
% 5.61/5.90 (declare-fun tptp.equiv_5172566880711946708t_unit (tptp.set_Product_unit tptp.set_Pr5094982260447487303t_unit) tptp.set_set_Product_unit)
% 5.61/5.90 (declare-fun tptp.comm_s8582702949713902594nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 5.61/5.90 (declare-fun tptp.comm_s4028243227959126397er_rat (tptp.rat tptp.nat) tptp.rat)
% 5.61/5.90 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 5.61/5.90 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 5.61/5.90 (declare-fun tptp.cofinite_nat () tptp.filter_nat)
% 5.61/5.90 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 5.61/5.90 (declare-fun tptp.eventu1038000079068216329at_nat ((-> tptp.product_prod_nat_nat Bool) tptp.filter1242075044329608583at_nat) Bool)
% 5.61/5.90 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 5.61/5.90 (declare-fun tptp.filter3212408913953519116et_nat ((-> tptp.nat tptp.set_nat) tptp.filter_set_nat tptp.filter_nat) Bool)
% 5.61/5.90 (declare-fun tptp.finite3254316476582989077op_nat (tptp.set_nat) tptp.filter_set_nat)
% 5.61/5.90 (declare-fun tptp.frequently_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 5.61/5.90 (declare-fun tptp.prod_filter_nat_nat (tptp.filter_nat tptp.filter_nat) tptp.filter1242075044329608583at_nat)
% 5.61/5.90 (declare-fun tptp.finite1363419556375932405_nat_o (tptp.set_Pr4532377907799695533_nat_o) tptp.nat)
% 5.61/5.90 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 5.61/5.90 (declare-fun tptp.finite4902975817058060853nteger (tptp.set_Code_integer) tptp.nat)
% 5.61/5.90 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 5.61/5.90 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.finite410649719033368117t_unit (tptp.set_Product_unit) tptp.nat)
% 5.61/5.90 (declare-fun tptp.finite4731484169140532437_nat_o (tptp.set_se1353816476878259085_nat_o) tptp.nat)
% 5.61/5.90 (declare-fun tptp.finite_card_set_o (tptp.set_set_o) tptp.nat)
% 5.61/5.90 (declare-fun tptp.finite1340570857867686763nteger (tptp.set_set_Code_integer) tptp.nat)
% 5.61/5.90 (declare-fun tptp.finite_card_set_int (tptp.set_set_int) tptp.nat)
% 5.61/5.90 (declare-fun tptp.finite_card_set_nat (tptp.set_set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.finite22775419188893461t_unit (tptp.set_set_Product_unit) tptp.nat)
% 5.61/5.90 (declare-fun tptp.finite3252695134891459830_nat_o (tptp.set_Pr4532377907799695533_nat_o) Bool)
% 5.61/5.90 (declare-fun tptp.finite_finite_o (tptp.set_o) Bool)
% 5.61/5.90 (declare-fun tptp.finite_finite_assn (tptp.set_assn) Bool)
% 5.61/5.90 (declare-fun tptp.finite6017078050557962740nteger (tptp.set_Code_integer) Bool)
% 5.61/5.90 (declare-fun tptp.finite2119507909894593271er_nat (tptp.set_filter_nat) Bool)
% 5.61/5.90 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 5.61/5.90 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 5.61/5.90 (declare-fun tptp.finite2154694888287295812nteger (tptp.set_Pr4811707699266497531nteger) Bool)
% 5.61/5.90 (declare-fun tptp.finite4996374594527322935er_nat (tptp.set_Pr8986988648414616686er_nat) Bool)
% 5.61/5.90 (declare-fun tptp.finite2998713641127702882nt_int (tptp.set_Pr958786334691620121nt_int) Bool)
% 5.61/5.90 (declare-fun tptp.finite1154042800025562295nteger (tptp.set_Pr2406931829603198446nteger) Bool)
% 5.61/5.90 (declare-fun tptp.finite6177210948735845034at_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.61/5.90 (declare-fun tptp.finite4290736615968046902t_unit (tptp.set_Product_unit) Bool)
% 5.61/5.90 (declare-fun tptp.finite_finite_rat (tptp.set_rat) Bool)
% 5.61/5.90 (declare-fun tptp.finite6069017635265841110_nat_o (tptp.set_se1353816476878259085_nat_o) Bool)
% 5.61/5.90 (declare-fun tptp.finite_finite_set_o (tptp.set_set_o) Bool)
% 5.61/5.90 (declare-fun tptp.finite6931041176100689706nteger (tptp.set_set_Code_integer) Bool)
% 5.61/5.90 (declare-fun tptp.finite6197958912794628473et_int (tptp.set_set_int) Bool)
% 5.61/5.90 (declare-fun tptp.finite1152437895449049373et_nat (tptp.set_set_nat) Bool)
% 5.61/5.90 (declare-fun tptp.finite1772178364199683094t_unit (tptp.set_set_Product_unit) Bool)
% 5.61/5.90 (declare-fun tptp.finite_fold_o_o ((-> Bool Bool Bool) Bool tptp.set_o) Bool)
% 5.61/5.90 (declare-fun tptp.finite_fold_o_set_o ((-> Bool tptp.set_o tptp.set_o) tptp.set_o tptp.set_o) tptp.set_o)
% 5.61/5.90 (declare-fun tptp.finite1440822074540989594n_assn ((-> tptp.assn tptp.assn tptp.assn) tptp.assn tptp.set_assn) tptp.assn)
% 5.61/5.90 (declare-fun tptp.finite6454954857057555716nteger ((-> tptp.code_integer tptp.code_integer tptp.code_integer) tptp.code_integer tptp.set_Code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.finite2281032298429728806t_unit ((-> tptp.code_integer tptp.product_unit tptp.product_unit) tptp.product_unit tptp.set_Code_integer) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.finite1928688952044918289_set_o ((-> tptp.code_integer tptp.set_o tptp.set_o) tptp.set_o tptp.set_Code_integer) tptp.set_o)
% 5.61/5.90 (declare-fun tptp.finite7486036041278456378nteger ((-> tptp.code_integer tptp.set_Code_integer tptp.set_Code_integer) tptp.set_Code_integer tptp.set_Code_integer) tptp.set_Code_integer)
% 5.61/5.90 (declare-fun tptp.finite6635835719294221449et_int ((-> tptp.code_integer tptp.set_int tptp.set_int) tptp.set_int tptp.set_Code_integer) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.finite1590314701948642349et_nat ((-> tptp.code_integer tptp.set_nat tptp.set_nat) tptp.set_nat tptp.set_Code_integer) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.finite3687622995246107910t_unit ((-> tptp.code_integer tptp.set_Product_unit tptp.set_Product_unit) tptp.set_Product_unit tptp.set_Code_integer) tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.finite_fold_int_int ((-> tptp.int tptp.int tptp.int) tptp.int tptp.set_int) tptp.int)
% 5.61/5.90 (declare-fun tptp.finite1723285575846220376et_int ((-> tptp.int tptp.set_int tptp.set_int) tptp.set_int tptp.set_int) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.finite_fold_nat_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.finite6602901031542678131t_unit ((-> tptp.nat tptp.product_unit tptp.product_unit) tptp.product_unit tptp.set_nat) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.finite3217087857726763998_set_o ((-> tptp.nat tptp.set_o tptp.set_o) tptp.set_o tptp.set_nat) tptp.set_o)
% 5.61/5.90 (declare-fun tptp.finite1351632015609375740et_int ((-> tptp.nat tptp.set_int tptp.set_int) tptp.set_int tptp.set_nat) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.finite5529483035118572448et_nat ((-> tptp.nat tptp.set_nat tptp.set_nat) tptp.set_nat tptp.set_nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.finite9145781422887121747t_unit ((-> tptp.nat tptp.set_Product_unit tptp.set_Product_unit) tptp.set_Product_unit tptp.set_nat) tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.finite8834431295148555784t_unit ((-> tptp.product_unit tptp.product_unit tptp.product_unit) tptp.product_unit tptp.set_Product_unit) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.finite2740360166580943592t_unit ((-> tptp.product_unit tptp.set_Product_unit tptp.set_Product_unit) tptp.set_Product_unit tptp.set_Product_unit) tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.finite8456856254070787592_nat_o ((-> tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr4532377907799695533_nat_o) tptp.set_Pr4532377907799695533_nat_o tptp.set_se1353816476878259085_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.90 (declare-fun tptp.finite4337638375924247368_set_o ((-> tptp.set_o tptp.set_o tptp.set_o) tptp.set_o tptp.set_set_o) tptp.set_o)
% 5.61/5.90 (declare-fun tptp.finite2508883933289561102et_int ((-> tptp.set_int tptp.set_int tptp.set_int) tptp.set_int tptp.set_set_int) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.finite677925301803182934et_nat ((-> tptp.set_nat tptp.set_nat tptp.set_nat) tptp.set_nat tptp.set_set_nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.finite4243028863286625800t_unit ((-> tptp.set_Product_unit tptp.set_Product_unit tptp.set_Product_unit) tptp.set_Product_unit tptp.set_set_Product_unit) tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.comp_C8797469213163452608nteger ((-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_integer tptp.code_integer tptp.code_integer) tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.61/5.90 (declare-fun tptp.comp_C5076291335850163704nteger ((-> (-> tptp.code_integer tptp.code_integer) tptp.code_integer) (-> tptp.code_integer tptp.code_integer tptp.code_integer) tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_P4885729792186999034nteger ((-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.set_Code_integer) (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.code_integer) tptp.set_Code_integer)
% 5.61/5.90 (declare-fun tptp.comp_P8262219321096090349nteger ((-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.set_nat) (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.code_integer) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.comp_s518380907012905326o_assn ((-> (-> tptp.set_o tptp.assn) tptp.set_set_o tptp.assn) (-> (-> Bool tptp.assn) tptp.set_o tptp.assn) (-> Bool tptp.assn) tptp.set_set_o) tptp.assn)
% 5.61/5.90 (declare-fun tptp.comp_s6084864194472624150_o_nat ((-> (-> tptp.set_o tptp.nat) tptp.set_set_o tptp.nat) (-> (-> Bool tptp.nat) tptp.set_o tptp.nat) (-> Bool tptp.nat) tptp.set_set_o) tptp.nat)
% 5.61/5.90 (declare-fun tptp.comp_s3531641609786562035r_assn ((-> (-> tptp.set_Code_integer tptp.assn) tptp.set_set_Code_integer tptp.assn) (-> (-> tptp.code_integer tptp.assn) tptp.set_Code_integer tptp.assn) (-> tptp.code_integer tptp.assn) tptp.set_set_Code_integer) tptp.assn)
% 5.61/5.90 (declare-fun tptp.comp_s8759123648413916139er_nat ((-> (-> tptp.set_Code_integer tptp.nat) tptp.set_set_Code_integer tptp.nat) (-> (-> tptp.code_integer tptp.nat) tptp.set_Code_integer tptp.nat) (-> tptp.code_integer tptp.nat) tptp.set_set_Code_integer) tptp.nat)
% 5.61/5.90 (declare-fun tptp.comp_s4595925057662634336t_assn ((-> (-> tptp.set_int tptp.assn) tptp.set_set_int tptp.assn) (-> (-> tptp.int tptp.assn) tptp.set_int tptp.assn) (-> tptp.int tptp.assn) tptp.set_set_int) tptp.assn)
% 5.61/5.90 (declare-fun tptp.comp_s9098231955081793132nt_int ((-> (-> tptp.set_int tptp.int) tptp.set_set_int tptp.int) (-> (-> tptp.int tptp.int) tptp.set_int tptp.int) (-> tptp.int tptp.int) tptp.set_set_int) tptp.int)
% 5.61/5.90 (declare-fun tptp.comp_s3237642481825588056nt_nat ((-> (-> tptp.set_int tptp.nat) tptp.set_set_int tptp.nat) (-> (-> tptp.int tptp.nat) tptp.set_int tptp.nat) (-> tptp.int tptp.nat) tptp.set_set_int) tptp.nat)
% 5.61/5.90 (declare-fun tptp.comp_s2451231738238893644t_assn ((-> (-> tptp.set_nat tptp.assn) tptp.set_set_nat tptp.assn) (-> (-> tptp.nat tptp.assn) tptp.set_nat tptp.assn) (-> tptp.nat tptp.assn) tptp.set_set_nat) tptp.assn)
% 5.61/5.90 (declare-fun tptp.comp_s5456809700045850692at_nat ((-> (-> tptp.set_nat tptp.nat) tptp.set_set_nat tptp.nat) (-> (-> tptp.nat tptp.nat) tptp.set_nat tptp.nat) (-> tptp.nat tptp.nat) tptp.set_set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.comp_s8247530669214396195t_assn ((-> (-> tptp.set_Product_unit tptp.assn) tptp.set_set_Product_unit tptp.assn) (-> (-> tptp.product_unit tptp.assn) tptp.set_Product_unit tptp.assn) (-> tptp.product_unit tptp.assn) tptp.set_set_Product_unit) tptp.assn)
% 5.61/5.90 (declare-fun tptp.comp_s8928436226432208331it_nat ((-> (-> tptp.set_Product_unit tptp.nat) tptp.set_set_Product_unit tptp.nat) (-> (-> tptp.product_unit tptp.nat) tptp.set_Product_unit tptp.nat) (-> tptp.product_unit tptp.nat) tptp.set_set_Product_unit) tptp.nat)
% 5.61/5.90 (declare-fun tptp.comp_o8922910837708301817nteger ((-> Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_integer Bool) tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.61/5.90 (declare-fun tptp.comp_o6961622296474427249t_unit ((-> Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.product_unit Bool) tptp.product_unit tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.61/5.90 (declare-fun tptp.comp_o1085144040659434033nteger ((-> Bool tptp.code_integer) (-> tptp.code_integer Bool) tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_o780160699970281785t_unit ((-> Bool tptp.code_integer) (-> tptp.product_unit Bool) tptp.product_unit) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_o2643362028263920430t_unit ((-> Bool tptp.code_natural) (-> tptp.product_unit Bool) tptp.product_unit) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.comp_o_int_int ((-> Bool tptp.int) (-> tptp.int Bool) tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.comp_o3916225744453444672unit_o ((-> Bool tptp.product_unit) (-> Bool Bool) Bool) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.comp_o6635994240230588853nteger ((-> Bool tptp.product_unit) (-> tptp.code_integer Bool) tptp.code_integer) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.comp_o7049022088938261380it_int ((-> Bool tptp.product_unit) (-> tptp.int Bool) tptp.int) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.comp_o7051512559447311656it_nat ((-> Bool tptp.product_unit) (-> tptp.nat Bool) tptp.nat) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.comp_o7724735231917782709t_unit ((-> Bool tptp.product_unit) (-> tptp.product_unit Bool) tptp.product_unit) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.comp_o6895741221744486154t_unit ((-> Bool tptp.set_o) (-> tptp.product_unit Bool) tptp.product_unit) tptp.set_o)
% 5.61/5.90 (declare-fun tptp.comp_o7929101295636871983nteger ((-> Bool tptp.set_Code_integer) (-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) Bool) (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) tptp.set_Code_integer)
% 5.61/5.90 (declare-fun tptp.comp_o4291842030903409511nteger ((-> Bool tptp.set_Code_integer) (-> tptp.code_integer Bool) tptp.code_integer) tptp.set_Code_integer)
% 5.61/5.90 (declare-fun tptp.comp_o1521574261646630388t_unit ((-> Bool tptp.set_int) (-> tptp.product_unit Bool) tptp.product_unit) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.comp_o1289984117834210338nteger ((-> Bool tptp.set_nat) (-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) Bool) (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.comp_o172754640513974618nteger ((-> Bool tptp.set_nat) (-> tptp.code_integer Bool) tptp.code_integer) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.comp_o9190160103024335696t_unit ((-> Bool tptp.set_nat) (-> tptp.product_unit Bool) tptp.product_unit) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.comp_o2086126948152544725t_unit ((-> Bool tptp.set_Product_unit) (-> tptp.product_unit Bool) tptp.product_unit) tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.comp_C2931745410781319416nteger ((-> tptp.code_integer tptp.code_integer tptp.code_integer) (-> tptp.code_integer tptp.code_integer) tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_C95226695241045696nteger ((-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> (-> tptp.code_integer tptp.code_integer) tptp.code_integer) (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.61/5.90 (declare-fun tptp.comp_C5733264393235242609eger_o ((-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> Bool tptp.code_integer) Bool tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.61/5.90 (declare-fun tptp.comp_C1593894019821074884nteger ((-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_integer tptp.code_integer) tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.61/5.90 (declare-fun tptp.comp_C834242911430131603er_int ((-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.int tptp.code_integer) tptp.int tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.61/5.90 (declare-fun tptp.comp_C836733381939181879er_nat ((-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.nat tptp.code_integer) tptp.nat tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.61/5.90 (declare-fun tptp.comp_C5854136495726678886t_unit ((-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.product_unit tptp.code_integer) tptp.product_unit tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.61/5.90 (declare-fun tptp.comp_C3026223900822616519nteger ((-> tptp.code_integer tptp.assn) (-> tptp.code_integer tptp.code_integer) tptp.code_integer) tptp.assn)
% 5.61/5.90 (declare-fun tptp.comp_C8462447471145125178sn_nat ((-> tptp.code_integer tptp.assn) (-> tptp.nat tptp.code_integer) tptp.nat) tptp.assn)
% 5.61/5.90 (declare-fun tptp.comp_C7449957260575251196nteger ((-> tptp.code_integer tptp.code_integer) (-> tptp.code_integer tptp.code_integer) tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_C6273552412331968711atural ((-> tptp.code_integer tptp.code_integer) (-> tptp.code_natural tptp.code_integer) tptp.code_natural) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_C6974050283906349679er_nat ((-> tptp.code_integer tptp.code_integer) (-> tptp.nat tptp.code_integer) tptp.nat) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_C1043215000170864188nteger ((-> tptp.code_integer tptp.code_integer) (-> tptp.produc8923325533196201883nteger tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_C2290379119555921966t_unit ((-> tptp.code_integer tptp.code_integer) (-> tptp.product_unit tptp.code_integer) tptp.product_unit) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_C1891057325546811591nteger ((-> tptp.code_integer tptp.code_natural) (-> tptp.code_integer tptp.code_integer) tptp.code_integer) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.comp_C714652477303529106atural ((-> tptp.code_integer tptp.code_natural) (-> tptp.code_natural tptp.code_integer) tptp.code_natural) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.comp_C4153580447849560611t_unit ((-> tptp.code_integer tptp.code_natural) (-> tptp.product_unit tptp.code_integer) tptp.product_unit) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.comp_C7610259292922237131nteger ((-> tptp.code_integer tptp.int) (-> tptp.code_integer tptp.code_integer) tptp.code_integer) tptp.int)
% 5.61/5.90 (declare-fun tptp.comp_C5048910307564104766nt_nat ((-> tptp.code_integer tptp.int) (-> tptp.nat tptp.code_integer) tptp.nat) tptp.int)
% 5.61/5.90 (declare-fun tptp.comp_C7238605732685392495nteger ((-> tptp.code_integer tptp.nat) (-> tptp.code_integer tptp.code_integer) tptp.code_integer) tptp.nat)
% 5.61/5.90 (declare-fun tptp.comp_C8146212659816229034nteger ((-> tptp.code_integer tptp.product_unit) (-> tptp.code_integer tptp.code_integer) tptp.code_integer) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.comp_C6969807811572946549atural ((-> tptp.code_integer tptp.product_unit) (-> tptp.code_natural tptp.code_integer) tptp.code_natural) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.comp_C2408090164605745152t_unit ((-> tptp.code_integer tptp.product_unit) (-> tptp.product_unit tptp.code_integer) tptp.product_unit) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.comp_C6344129587964912378nteger ((-> tptp.code_integer tptp.set_Code_integer) (-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.code_integer) (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) tptp.set_Code_integer)
% 5.61/5.90 (declare-fun tptp.comp_C8186931911283765298nteger ((-> tptp.code_integer tptp.set_Code_integer) (-> tptp.code_integer tptp.code_integer) tptp.code_integer) tptp.set_Code_integer)
% 5.61/5.90 (declare-fun tptp.comp_C3184339336801759213nteger ((-> tptp.code_integer tptp.set_nat) (-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.code_integer) (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.comp_C6537567860429791781nteger ((-> tptp.code_integer tptp.set_nat) (-> tptp.code_integer tptp.code_integer) tptp.code_integer) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.comp_C456341964420721295nteger ((-> tptp.code_natural tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_integer tptp.code_natural) tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.61/5.90 (declare-fun tptp.comp_i2874689474467862163nteger ((-> tptp.int tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_integer tptp.int) tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.61/5.90 (declare-fun tptp.comp_int_o_o ((-> tptp.int Bool) (-> Bool tptp.int) Bool) Bool)
% 5.61/5.90 (declare-fun tptp.comp_int_o_int ((-> tptp.int Bool) (-> tptp.int tptp.int) tptp.int) Bool)
% 5.61/5.90 (declare-fun tptp.comp_int_o_nat ((-> tptp.int Bool) (-> tptp.nat tptp.int) tptp.nat) Bool)
% 5.61/5.90 (declare-fun tptp.comp_i5286552343147518890eger_o ((-> tptp.int tptp.code_integer) (-> Bool tptp.int) Bool) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_i6014793192326455499nteger ((-> tptp.int tptp.code_integer) (-> tptp.code_integer tptp.int) tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_i1585864551200866970er_int ((-> tptp.int tptp.code_integer) (-> tptp.int tptp.int) tptp.int) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_i1588355021709917246er_nat ((-> tptp.int tptp.code_integer) (-> tptp.nat tptp.int) tptp.nat) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_i455893257298015894nteger ((-> tptp.int tptp.code_natural) (-> tptp.code_integer tptp.int) tptp.code_integer) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.comp_int_int_o ((-> tptp.int tptp.int) (-> Bool tptp.int) Bool) tptp.int)
% 5.61/5.90 (declare-fun tptp.comp_int_int_int ((-> tptp.int tptp.int) (-> tptp.int tptp.int) tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.comp_int_int_nat ((-> tptp.int tptp.int) (-> tptp.nat tptp.int) tptp.nat) tptp.int)
% 5.61/5.90 (declare-fun tptp.comp_i4330622015127193916nt_int ((-> tptp.int tptp.int) (-> tptp.product_prod_int_int tptp.int) tptp.product_prod_int_int) tptp.int)
% 5.61/5.90 (declare-fun tptp.comp_int_nat_o ((-> tptp.int tptp.nat) (-> Bool tptp.int) Bool) tptp.nat)
% 5.61/5.90 (declare-fun tptp.comp_int_nat_int ((-> tptp.int tptp.nat) (-> tptp.int tptp.int) tptp.int) tptp.nat)
% 5.61/5.90 (declare-fun tptp.comp_int_nat_nat ((-> tptp.int tptp.nat) (-> tptp.nat tptp.int) tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.comp_i8439899303502915483nteger ((-> tptp.int tptp.product_unit) (-> tptp.code_integer tptp.int) tptp.code_integer) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.comp_i5479505385629679622nteger ((-> tptp.int tptp.set_o) (-> tptp.code_integer tptp.int) tptp.code_integer) tptp.set_o)
% 5.61/5.90 (declare-fun tptp.comp_i1887841406321795152nteger ((-> tptp.int tptp.set_int) (-> tptp.code_integer tptp.int) tptp.code_integer) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.comp_i5103216804979976198nt_int ((-> tptp.int tptp.set_int) (-> tptp.product_prod_int_int tptp.int) tptp.product_prod_int_int) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.comp_i5102403792180996084nteger ((-> tptp.int tptp.set_nat) (-> tptp.code_integer tptp.int) tptp.code_integer) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.comp_i6200299785623974754nt_int ((-> tptp.int tptp.set_nat) (-> tptp.product_prod_int_int tptp.int) tptp.product_prod_int_int) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.comp_i3319814986458681467nteger ((-> tptp.int tptp.set_Product_unit) (-> tptp.code_integer tptp.int) tptp.code_integer) tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.comp_nat_nat_nat_nat ((-> tptp.nat tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.nat tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.comp_n2033352843805742135nteger ((-> tptp.nat tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_integer tptp.nat) tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.61/5.90 (declare-fun tptp.comp_n856947995562459650atural ((-> tptp.nat tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_natural tptp.nat) tptp.code_natural tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.61/5.90 (declare-fun tptp.comp_nat_assn_nat ((-> tptp.nat tptp.assn) (-> tptp.nat tptp.nat) tptp.nat) tptp.assn)
% 5.61/5.90 (declare-fun tptp.comp_n6876073255676942959nteger ((-> tptp.nat tptp.code_integer) (-> tptp.code_integer tptp.nat) tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_n5699668407433660474atural ((-> tptp.nat tptp.code_integer) (-> tptp.code_natural tptp.nat) tptp.code_natural) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_n3898172953802868194er_nat ((-> tptp.nat tptp.code_integer) (-> tptp.nat tptp.nat) tptp.nat) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_n2857367870785791611ural_o ((-> tptp.nat tptp.code_natural) (-> Bool tptp.nat) Bool) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.comp_n1317173320648503354nteger ((-> tptp.nat tptp.code_natural) (-> tptp.code_integer tptp.nat) tptp.code_integer) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.comp_n140768472405220869atural ((-> tptp.nat tptp.code_natural) (-> tptp.code_natural tptp.nat) tptp.code_natural) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.comp_n9160511493981425161al_int ((-> tptp.nat tptp.code_natural) (-> tptp.int tptp.nat) tptp.int) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.comp_n9163001964490475437al_nat ((-> tptp.nat tptp.code_natural) (-> tptp.nat tptp.nat) tptp.nat) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.comp_nat_int_nat ((-> tptp.nat tptp.int) (-> tptp.nat tptp.nat) tptp.nat) tptp.int)
% 5.61/5.90 (declare-fun tptp.comp_n8360577435903631554atural ((-> tptp.nat tptp.product_unit) (-> tptp.code_natural tptp.nat) tptp.code_natural) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.comp_n1572716621429000127atural ((-> tptp.nat tptp.set_int) (-> tptp.code_natural tptp.nat) tptp.code_natural) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.comp_n3623798160786426464nteger ((-> tptp.nat tptp.set_nat) (-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.nat) (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.comp_n5963683855531483544nteger ((-> tptp.nat tptp.set_nat) (-> tptp.code_integer tptp.nat) tptp.code_integer) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.comp_n4787279007288201059atural ((-> tptp.nat tptp.set_nat) (-> tptp.code_natural tptp.nat) tptp.code_natural) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.comp_P5544053077415136032nteger ((-> tptp.produc723880050079548563nteger tptp.produc101387210554329899nteger) (-> tptp.produc8923325533196201883nteger tptp.produc723880050079548563nteger) tptp.produc8923325533196201883nteger) tptp.produc101387210554329899nteger)
% 5.61/5.90 (declare-fun tptp.comp_P1414880308642389412nteger ((-> tptp.produc2221115339011613079nteger tptp.produc101387210554329899nteger) (-> tptp.produc8923325533196201883nteger tptp.produc2221115339011613079nteger) tptp.produc8923325533196201883nteger) tptp.produc101387210554329899nteger)
% 5.61/5.90 (declare-fun tptp.comp_P6312383820422015140nteger ((-> tptp.produc1397831737260518551nteger tptp.produc101387210554329899nteger) (-> tptp.produc8923325533196201883nteger tptp.produc1397831737260518551nteger) tptp.produc8923325533196201883nteger) tptp.produc101387210554329899nteger)
% 5.61/5.90 (declare-fun tptp.comp_P7111796090210262324nteger ((-> tptp.produc8923325533196201883nteger tptp.code_integer) (-> tptp.code_integer tptp.produc8923325533196201883nteger) tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_P3428181540658402820nteger ((-> tptp.produc8923325533196201883nteger tptp.code_integer) (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_P659088277599099894t_unit ((-> tptp.produc8923325533196201883nteger tptp.code_integer) (-> tptp.product_unit tptp.produc8923325533196201883nteger) tptp.product_unit) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_P234064951390806312nteger ((-> tptp.produc8923325533196201883nteger tptp.produc101387210554329899nteger) (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc101387210554329899nteger)
% 5.61/5.90 (declare-fun tptp.comp_P7101464685127059239nteger ((-> tptp.produc6433947425880249742er_nat tptp.code_integer) (-> tptp.code_integer tptp.produc6433947425880249742er_nat) tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_P7581484221039074243t_unit ((-> tptp.produc6433947425880249742er_nat tptp.code_integer) (-> tptp.product_unit tptp.produc6433947425880249742er_nat) tptp.product_unit) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_P5964733648194011802nteger ((-> tptp.produc6433947425880249742er_nat tptp.nat) (-> tptp.code_integer tptp.produc6433947425880249742er_nat) tptp.code_integer) tptp.nat)
% 5.61/5.90 (declare-fun tptp.comp_P6821003776282389008t_unit ((-> tptp.produc6433947425880249742er_nat tptp.nat) (-> tptp.product_unit tptp.produc6433947425880249742er_nat) tptp.product_unit) tptp.nat)
% 5.61/5.90 (declare-fun tptp.comp_P2930521774885306735et_nat ((-> tptp.produc3658429121746597890et_nat tptp.set_nat) (-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat) tptp.produc3658429121746597890et_nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.comp_P8606889026643445772nt_int ((-> tptp.produc3658429121746597890et_nat tptp.set_nat) (-> tptp.product_prod_int_int tptp.produc3658429121746597890et_nat) tptp.product_prod_int_int) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.comp_P8308861049717174982et_nat ((-> tptp.product_prod_int_int tptp.int) (-> tptp.produc3658429121746597890et_nat tptp.product_prod_int_int) tptp.produc3658429121746597890et_nat) tptp.int)
% 5.61/5.90 (declare-fun tptp.comp_P5356232565778667509nt_int ((-> tptp.product_prod_int_int tptp.int) (-> tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.int)
% 5.61/5.90 (declare-fun tptp.comp_P6796073005956588617t_unit ((-> tptp.product_prod_int_int tptp.int) (-> tptp.product_unit tptp.product_prod_int_int) tptp.product_unit) tptp.int)
% 5.61/5.90 (declare-fun tptp.comp_P7177471617286032590eger_o ((-> tptp.produc2591615631378489102nteger tptp.code_integer) (-> Bool tptp.produc2591615631378489102nteger) Bool) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_P6122662217367900327nteger ((-> tptp.produc2591615631378489102nteger tptp.code_integer) (-> tptp.code_integer tptp.produc2591615631378489102nteger) tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_P7320554561093743171t_unit ((-> tptp.produc2591615631378489102nteger tptp.code_integer) (-> tptp.product_unit tptp.produc2591615631378489102nteger) tptp.product_unit) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_P7179991235626930843_nat_o ((-> tptp.produc2591615631378489102nteger tptp.nat) (-> Bool tptp.produc2591615631378489102nteger) Bool) tptp.nat)
% 5.61/5.90 (declare-fun tptp.comp_P5725896914063526938nteger ((-> tptp.produc2591615631378489102nteger tptp.nat) (-> tptp.code_integer tptp.produc2591615631378489102nteger) tptp.code_integer) tptp.nat)
% 5.61/5.90 (declare-fun tptp.comp_P7621350044865347728t_unit ((-> tptp.produc2591615631378489102nteger tptp.nat) (-> tptp.product_unit tptp.produc2591615631378489102nteger) tptp.product_unit) tptp.nat)
% 5.61/5.90 (declare-fun tptp.comp_P4394204175247225320_nat_o ((-> tptp.product_prod_nat_nat tptp.nat) (-> Bool tptp.product_prod_nat_nat) Bool) tptp.nat)
% 5.61/5.90 (declare-fun tptp.comp_P2980510830910040157t_unit ((-> tptp.product_prod_nat_nat tptp.nat) (-> tptp.product_unit tptp.product_prod_nat_nat) tptp.product_unit) tptp.nat)
% 5.61/5.90 (declare-fun tptp.comp_P4511551582283981294nteger ((-> tptp.product_unit tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_integer tptp.product_unit) tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.61/5.90 (declare-fun tptp.comp_P4558236313141964142nteger ((-> tptp.product_unit tptp.product_unit tptp.product_unit) (-> tptp.code_integer tptp.product_unit) tptp.code_integer tptp.product_unit) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.comp_P6204500334276302049it_nat ((-> tptp.product_unit tptp.product_unit tptp.product_unit) (-> tptp.nat tptp.product_unit) tptp.nat tptp.product_unit) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.comp_P6790823133229852966nteger ((-> tptp.product_unit tptp.code_integer) (-> tptp.code_integer tptp.product_unit) tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.comp_P4635212033913086756nteger ((-> tptp.product_unit tptp.set_Code_integer) (-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.product_unit) (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) tptp.set_Code_integer)
% 5.61/5.90 (declare-fun tptp.comp_P4767411901762164316nteger ((-> tptp.product_unit tptp.set_Code_integer) (-> tptp.code_integer tptp.product_unit) tptp.code_integer) tptp.set_Code_integer)
% 5.61/5.90 (declare-fun tptp.comp_P6101996899264665623nteger ((-> tptp.product_unit tptp.set_nat) (-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.product_unit) (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.comp_P5878433733084393551nteger ((-> tptp.product_unit tptp.set_nat) (-> tptp.code_integer tptp.product_unit) tptp.code_integer) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.comp_s90868338361139993nteger ((-> tptp.set_o tptp.set_o tptp.set_o) (-> tptp.code_integer tptp.set_o) tptp.code_integer tptp.set_o) tptp.set_o)
% 5.61/5.90 (declare-fun tptp.comp_s4424444925706540684_o_nat ((-> tptp.set_o tptp.set_o tptp.set_o) (-> tptp.nat tptp.set_o) tptp.nat tptp.set_o) tptp.set_o)
% 5.61/5.90 (declare-fun tptp.comp_s956550612328592744nteger ((-> tptp.set_Code_integer tptp.set_Code_integer) (-> tptp.code_integer tptp.set_Code_integer) tptp.code_integer) tptp.set_Code_integer)
% 5.61/5.90 (declare-fun tptp.comp_s3634918272309710215nteger ((-> tptp.set_int tptp.set_int tptp.set_int) (-> tptp.code_integer tptp.set_int) tptp.code_integer tptp.set_int) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.comp_s6689493721604790522nt_nat ((-> tptp.set_int tptp.set_int tptp.set_int) (-> tptp.nat tptp.set_int) tptp.nat tptp.set_int) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.comp_s3169385134670675059nteger ((-> tptp.set_nat tptp.set_nat tptp.set_nat) (-> tptp.code_integer tptp.set_nat) tptp.code_integer tptp.set_nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.comp_s2351873599094224870at_nat ((-> tptp.set_nat tptp.set_nat tptp.set_nat) (-> tptp.nat tptp.set_nat) tptp.nat tptp.set_nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.comp_s1601710177542341017et_nat ((-> tptp.set_nat tptp.int) (-> tptp.produc3658429121746597890et_nat tptp.set_nat) tptp.produc3658429121746597890et_nat) tptp.int)
% 5.61/5.90 (declare-fun tptp.comp_s8292494440407567195nteger ((-> tptp.set_nat tptp.set_Code_integer) (-> tptp.code_integer tptp.set_nat) tptp.code_integer) tptp.set_Code_integer)
% 5.61/5.90 (declare-fun tptp.comp_s4605850120322998606nteger ((-> tptp.set_nat tptp.set_nat) (-> tptp.code_integer tptp.set_nat) tptp.code_integer) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.comp_s5696514601250091763et_nat ((-> tptp.set_nat tptp.set_nat) (-> tptp.produc3658429121746597890et_nat tptp.set_nat) tptp.produc3658429121746597890et_nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.comp_s3199726385246003790nteger ((-> tptp.set_Product_unit tptp.set_Product_unit tptp.set_Product_unit) (-> tptp.code_integer tptp.set_Product_unit) tptp.code_integer tptp.set_Product_unit) tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.comp_s6943286182646368705it_nat ((-> tptp.set_Product_unit tptp.set_Product_unit tptp.set_Product_unit) (-> tptp.nat tptp.set_Product_unit) tptp.nat tptp.set_Product_unit) tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.fun_upd_o_o ((-> Bool Bool) Bool Bool Bool) Bool)
% 5.61/5.90 (declare-fun tptp.fun_upd_o_int ((-> Bool tptp.int) Bool tptp.int Bool) tptp.int)
% 5.61/5.90 (declare-fun tptp.fun_upd_o_nat ((-> Bool tptp.nat) Bool tptp.nat Bool) tptp.nat)
% 5.61/5.90 (declare-fun tptp.fun_up846054379331416818t_unit ((-> Bool tptp.product_unit) Bool tptp.product_unit Bool) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.fun_upd_o_set_o ((-> Bool tptp.set_o) Bool tptp.set_o Bool) tptp.set_o)
% 5.61/5.90 (declare-fun tptp.fun_upd_o_set_int ((-> Bool tptp.set_int) Bool tptp.set_int Bool) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.fun_upd_o_set_nat ((-> Bool tptp.set_nat) Bool tptp.set_nat Bool) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.fun_up4718931970374059986t_unit ((-> Bool tptp.set_Product_unit) Bool tptp.set_Product_unit Bool) tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.fun_up8355007323143964473nteger ((-> tptp.code_integer tptp.code_integer) tptp.code_integer tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.fun_upd_int_nat ((-> tptp.int tptp.nat) tptp.int tptp.nat tptp.int) tptp.nat)
% 5.61/5.90 (declare-fun tptp.fun_upd_int_set_o ((-> tptp.int tptp.set_o) tptp.int tptp.set_o tptp.int) tptp.set_o)
% 5.61/5.90 (declare-fun tptp.fun_up5054257004045450754t_unit ((-> tptp.int tptp.set_Product_unit) tptp.int tptp.set_Product_unit tptp.int) tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.fun_up3904115110581602988nteger ((-> tptp.nat tptp.code_integer) tptp.nat tptp.code_integer tptp.nat) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.fun_upd_nat_nat ((-> tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.fun_upd_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.nat tptp.set_nat tptp.nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.fun_up5432024876597553480unit_o ((-> tptp.product_unit Bool) tptp.product_unit Bool tptp.product_unit) Bool)
% 5.61/5.90 (declare-fun tptp.fun_up6470560416331323516it_int ((-> tptp.product_unit tptp.int) tptp.product_unit tptp.int tptp.product_unit) tptp.int)
% 5.61/5.90 (declare-fun tptp.fun_up6473050886840373792it_nat ((-> tptp.product_unit tptp.nat) tptp.product_unit tptp.nat tptp.product_unit) tptp.nat)
% 5.61/5.90 (declare-fun tptp.fun_up6875000483049295805t_unit ((-> tptp.product_unit tptp.product_unit) tptp.product_unit tptp.product_unit tptp.product_unit) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.fun_up1762901246852280360_set_o ((-> tptp.product_unit tptp.set_o) tptp.product_unit tptp.set_o tptp.product_unit) tptp.set_o)
% 5.61/5.90 (declare-fun tptp.fun_up391983181201004082et_int ((-> tptp.product_unit tptp.set_int) tptp.product_unit tptp.set_int tptp.product_unit) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.fun_up4569834200710200790et_nat ((-> tptp.product_unit tptp.set_nat) tptp.product_unit tptp.set_nat tptp.product_unit) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.fun_up488859312337516701t_unit ((-> tptp.product_unit tptp.set_Product_unit) tptp.product_unit tptp.set_Product_unit tptp.product_unit) tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.id_o (Bool) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on5271586719803267564_o_nat ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.nat) tptp.set_Pr4532377907799695533_nat_o) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on_o_o ((-> Bool Bool) tptp.set_o) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on_o_int ((-> Bool tptp.int) tptp.set_o) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on_o_nat ((-> Bool tptp.nat) tptp.set_o) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on4268752236855399398t_unit ((-> Bool tptp.product_unit) tptp.set_o) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on1158064722259180589nteger ((-> tptp.code_integer tptp.code_integer) tptp.set_Code_integer) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on1981279154655846304er_nat ((-> tptp.code_integer tptp.nat) tptp.set_Code_integer) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on_int_int ((-> tptp.int tptp.int) tptp.set_int) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on_int_nat ((-> tptp.int tptp.nat) tptp.set_int) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on7779444506608719434_nat_o ((-> tptp.nat tptp.produc3658429121746597890et_nat Bool) tptp.set_nat) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on_nat_o ((-> tptp.nat Bool) tptp.set_nat) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on2245834603434889120nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on7061601236592826506t_unit ((-> tptp.nat tptp.product_unit) tptp.set_nat) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_nat) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on20428373856169009nteger ((-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.set_Pr4811707699266497531nteger) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on8854722734121536060unit_o ((-> tptp.product_unit Bool) tptp.set_Product_unit) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on8427948621271784584it_int ((-> tptp.product_unit tptp.int) tptp.set_Product_unit) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on8430439091780834860it_nat ((-> tptp.product_unit tptp.nat) tptp.set_Product_unit) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on8151373323710067377t_unit ((-> tptp.product_unit tptp.product_unit) tptp.set_Product_unit) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on_rat_rat ((-> tptp.rat tptp.rat) tptp.set_rat) Bool)
% 5.61/5.90 (declare-fun tptp.inj_on_set_nat_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) Bool)
% 5.61/5.90 (declare-fun tptp.map_fu8272188784021352819nteger ((-> tptp.code_integer tptp.int) (-> (-> tptp.int tptp.int) tptp.code_integer tptp.code_integer) (-> tptp.int tptp.int tptp.int) tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.map_fu2599414010547811884nteger ((-> tptp.code_integer tptp.int) (-> tptp.int tptp.code_integer) (-> tptp.int tptp.int) tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.map_fu6549440983881763648atural ((-> tptp.code_natural tptp.nat) (-> (-> tptp.nat tptp.nat) tptp.code_natural tptp.code_natural) (-> tptp.nat tptp.nat tptp.nat) tptp.code_natural tptp.code_natural) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.map_fu1239815594074539274atural ((-> tptp.code_natural tptp.nat) (-> tptp.nat tptp.code_natural) (-> tptp.nat tptp.nat) tptp.code_natural) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.map_fu4960017516451851995nt_int ((-> tptp.int tptp.product_prod_nat_nat) (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.int tptp.int) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.int tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.map_fu3667384564859982768at_int ((-> tptp.int tptp.product_prod_nat_nat) (-> tptp.product_prod_nat_nat tptp.int) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.map_fu4333342158222067775at_rat ((-> tptp.rat tptp.product_prod_int_int) (-> (-> tptp.product_prod_int_int tptp.product_prod_int_int) tptp.rat tptp.rat) (-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int) tptp.rat tptp.rat) tptp.rat)
% 5.61/5.90 (declare-fun tptp.map_fu898904425404107465nt_o_o ((-> tptp.rat tptp.product_prod_int_int) (-> Bool Bool) (-> tptp.product_prod_int_int Bool) tptp.rat) Bool)
% 5.61/5.90 (declare-fun tptp.map_fu5673905371560938248nt_rat ((-> tptp.rat tptp.product_prod_int_int) (-> tptp.product_prod_int_int tptp.rat) (-> tptp.product_prod_int_int tptp.product_prod_int_int) tptp.rat) tptp.rat)
% 5.61/5.90 (declare-fun tptp.gcd_Gcd_int (tptp.set_int) tptp.int)
% 5.61/5.90 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.gcd_Lcm_nat (tptp.set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 5.61/5.90 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 5.61/5.90 (declare-fun tptp.gcd_gcd_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.gcd_lcm_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.gcd_lcm_int (tptp.int tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.gcd_lcm_nat (tptp.nat tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.semiri4256215615220890538in_int (tptp.set_int) tptp.int)
% 5.61/5.90 (declare-fun tptp.semiri4258706085729940814in_nat (tptp.set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.minus_minus_assn (tptp.assn tptp.assn) tptp.assn)
% 5.61/5.90 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 5.61/5.90 (declare-fun tptp.minus_1801376950450012436_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr4532377907799695533_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.90 (declare-fun tptp.minus_minus_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 5.61/5.90 (declare-fun tptp.minus_minus_set_assn (tptp.set_assn tptp.set_assn) tptp.set_assn)
% 5.61/5.90 (declare-fun tptp.minus_2355218937544613996nteger (tptp.set_Code_integer tptp.set_Code_integer) tptp.set_Code_integer)
% 5.61/5.90 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.minus_9189903262233110958_nat_o (tptp.set_Pr2161125870931222855_nat_o tptp.set_Pr2161125870931222855_nat_o) tptp.set_Pr2161125870931222855_nat_o)
% 5.61/5.90 (declare-fun tptp.minus_7052513330764642158od_o_o (tptp.set_Product_prod_o_o tptp.set_Product_prod_o_o) tptp.set_Product_prod_o_o)
% 5.61/5.90 (declare-fun tptp.minus_1052850069191792384nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 5.61/5.90 (declare-fun tptp.minus_1356011639430497352at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.90 (declare-fun tptp.minus_6985556733573110190t_unit (tptp.set_Pr5094982260447487303t_unit tptp.set_Pr5094982260447487303t_unit) tptp.set_Pr5094982260447487303t_unit)
% 5.61/5.90 (declare-fun tptp.minus_6452836326544984404t_unit (tptp.set_Product_unit tptp.set_Product_unit) tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.minus_2163939370556025621et_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 5.61/5.90 (declare-fun tptp.one_one_assn () tptp.assn)
% 5.61/5.90 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.one_one_Code_natural () tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.one_one_int () tptp.int)
% 5.61/5.90 (declare-fun tptp.one_one_nat () tptp.nat)
% 5.61/5.90 (declare-fun tptp.one_one_rat () tptp.rat)
% 5.61/5.90 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.plus_p4538020629002901425atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 5.61/5.90 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 5.61/5.90 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 5.61/5.90 (declare-fun tptp.times_times_assn (tptp.assn tptp.assn) tptp.assn)
% 5.61/5.90 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.times_2397367101498566445atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 5.61/5.90 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 5.61/5.90 (declare-fun tptp.uminus_uminus_assn (tptp.assn) tptp.assn)
% 5.61/5.90 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.uminus2952777764628376836t_unit (tptp.product_unit) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 5.61/5.90 (declare-fun tptp.uminus5254974436814262692_nat_o (tptp.set_Pr4532377907799695533_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.90 (declare-fun tptp.uminus_uminus_set_o (tptp.set_o) tptp.set_o)
% 5.61/5.90 (declare-fun tptp.uminus1532241313380277803et_int (tptp.set_int) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.uminus5710092332889474511et_nat (tptp.set_nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.uminus5944136376168626660t_unit (tptp.set_Product_unit) tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.zero_z2226904508553997617atural () tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.zero_zero_int () tptp.int)
% 5.61/5.90 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 5.61/5.90 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 5.61/5.90 (declare-fun tptp.groups6742167275697360483_o_nat ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.nat) tptp.set_Pr4532377907799695533_nat_o) tptp.nat)
% 5.61/5.90 (declare-fun tptp.groups4406642042086082107nteger ((-> Bool tptp.code_integer) tptp.set_o) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.groups8505340233167759370_o_int ((-> Bool tptp.int) tptp.set_o) tptp.int)
% 5.61/5.90 (declare-fun tptp.groups8507830703676809646_o_nat ((-> Bool tptp.nat) tptp.set_o) tptp.nat)
% 5.61/5.90 (declare-fun tptp.groups7872700643590313910_o_rat ((-> Bool tptp.rat) tptp.set_o) tptp.rat)
% 5.61/5.90 (declare-fun tptp.groups879477027807139574nteger ((-> tptp.code_integer tptp.code_integer) tptp.set_Code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.groups7234854612051535045er_int ((-> tptp.code_integer tptp.int) tptp.set_Code_integer) tptp.int)
% 5.61/5.90 (declare-fun tptp.groups7237345082560585321er_nat ((-> tptp.code_integer tptp.nat) tptp.set_Code_integer) tptp.nat)
% 5.61/5.90 (declare-fun tptp.groups6602215022474089585er_rat ((-> tptp.code_integer tptp.rat) tptp.set_Code_integer) tptp.rat)
% 5.61/5.90 (declare-fun tptp.groups7873554091576472773nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 5.61/5.90 (declare-fun tptp.groups4541462559716669496nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 5.61/5.90 (declare-fun tptp.groups3906332499630173760nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 5.61/5.90 (declare-fun tptp.groups7501900531339628137nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.groups3539618377306564664at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 5.61/5.90 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.groups2906978787729119204at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 5.61/5.90 (declare-fun tptp.groups5393439102872367408nteger ((-> tptp.product_unit tptp.code_integer) tptp.set_Product_unit) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.groups8764306707065906943it_int ((-> tptp.product_unit tptp.int) tptp.set_Product_unit) tptp.int)
% 5.61/5.90 (declare-fun tptp.groups8766797177574957219it_nat ((-> tptp.product_unit tptp.nat) tptp.set_Product_unit) tptp.nat)
% 5.61/5.90 (declare-fun tptp.groups8131667117488461483it_rat ((-> tptp.product_unit tptp.rat) tptp.set_Product_unit) tptp.rat)
% 5.61/5.90 (declare-fun tptp.groups1256056575759317066nt_int ((-> tptp.set_int tptp.int) tptp.set_set_int) tptp.int)
% 5.61/5.90 (declare-fun tptp.groups8294997508430121362at_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.groups5301882518646026715o_assn ((-> Bool tptp.assn) tptp.set_o) tptp.assn)
% 5.61/5.90 (declare-fun tptp.groups7694694392188491536nteger ((-> Bool tptp.code_integer) tptp.set_o) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.groups6518289543945209051atural ((-> Bool tptp.code_natural) tptp.set_o) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.groups3502327434004483295_o_int ((-> Bool tptp.int) tptp.set_o) tptp.int)
% 5.61/5.90 (declare-fun tptp.groups3504817904513533571_o_nat ((-> Bool tptp.nat) tptp.set_o) tptp.nat)
% 5.61/5.90 (declare-fun tptp.groups2869687844427037835_o_rat ((-> Bool tptp.rat) tptp.set_o) tptp.rat)
% 5.61/5.90 (declare-fun tptp.groups1304777262505850412r_assn ((-> tptp.code_integer tptp.assn) tptp.set_Code_integer) tptp.assn)
% 5.61/5.90 (declare-fun tptp.groups3674199335183972705nteger ((-> tptp.code_integer tptp.code_integer) tptp.set_Code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.groups2497794486940690220atural ((-> tptp.code_integer tptp.code_natural) tptp.set_Code_integer) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.groups3188404863801439024er_int ((-> tptp.code_integer tptp.int) tptp.set_Code_integer) tptp.int)
% 5.61/5.90 (declare-fun tptp.groups3190895334310489300er_nat ((-> tptp.code_integer tptp.nat) tptp.set_Code_integer) tptp.nat)
% 5.61/5.90 (declare-fun tptp.groups2555765274223993564er_rat ((-> tptp.code_integer tptp.rat) tptp.set_Code_integer) tptp.rat)
% 5.61/5.90 (declare-fun tptp.groups7882442080178216443t_assn ((-> tptp.int tptp.assn) tptp.set_int) tptp.assn)
% 5.61/5.90 (declare-fun tptp.groups3827104343326376752nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.groups2650699495083094267atural ((-> tptp.int tptp.code_natural) tptp.set_int) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 5.61/5.90 (declare-fun tptp.groups1707563613775114915nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 5.61/5.90 (declare-fun tptp.groups1072433553688619179nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 5.61/5.90 (declare-fun tptp.groups6906906614972039071t_assn ((-> tptp.nat tptp.assn) tptp.set_nat) tptp.assn)
% 5.61/5.90 (declare-fun tptp.groups3455450783089532116nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.groups2279045934846249631atural ((-> tptp.nat tptp.code_natural) tptp.set_nat) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 5.61/5.90 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.groups73079841787564623at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 5.61/5.90 (declare-fun tptp.groups5360233303959380816t_assn ((-> tptp.product_unit tptp.assn) tptp.set_Product_unit) tptp.assn)
% 5.61/5.90 (declare-fun tptp.groups8185359811944078981nteger ((-> tptp.product_unit tptp.code_integer) tptp.set_Product_unit) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.groups7008954963700796496atural ((-> tptp.product_unit tptp.code_natural) tptp.set_Product_unit) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.groups393930778517121108it_int ((-> tptp.product_unit tptp.int) tptp.set_Product_unit) tptp.int)
% 5.61/5.90 (declare-fun tptp.groups396421249026171384it_nat ((-> tptp.product_unit tptp.nat) tptp.set_Product_unit) tptp.nat)
% 5.61/5.90 (declare-fun tptp.groups8984663225794451456it_rat ((-> tptp.product_unit tptp.rat) tptp.set_Product_unit) tptp.rat)
% 5.61/5.90 (declare-fun tptp.groups6963733262650904763o_assn ((-> tptp.set_o tptp.assn) tptp.set_set_o) tptp.assn)
% 5.61/5.90 (declare-fun tptp.groups4868773677410035043_o_nat ((-> tptp.set_o tptp.nat) tptp.set_set_o) tptp.nat)
% 5.61/5.90 (declare-fun tptp.groups4245288774754739042r_assn ((-> tptp.set_Code_integer tptp.assn) tptp.set_set_Code_integer) tptp.assn)
% 5.61/5.90 (declare-fun tptp.groups6044384099095135754er_nat ((-> tptp.set_Code_integer tptp.nat) tptp.set_set_Code_integer) tptp.nat)
% 5.61/5.90 (declare-fun tptp.groups5950967880310095793t_assn ((-> tptp.set_int tptp.assn) tptp.set_set_int) tptp.assn)
% 5.61/5.90 (declare-fun tptp.groups6432978864363996853nt_int ((-> tptp.set_int tptp.int) tptp.set_set_int) tptp.int)
% 5.61/5.90 (declare-fun tptp.groups6435469334873047129nt_nat ((-> tptp.set_int tptp.nat) tptp.set_set_int) tptp.nat)
% 5.61/5.90 (declare-fun tptp.groups1535173586962943829t_assn ((-> tptp.set_nat tptp.assn) tptp.set_set_nat) tptp.assn)
% 5.61/5.90 (declare-fun tptp.groups4248547760180025341at_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.groups2392624107559085104t_assn ((-> tptp.set_Product_unit tptp.assn) tptp.set_set_Product_unit) tptp.assn)
% 5.61/5.90 (declare-fun tptp.groups8454329047868613336it_nat ((-> tptp.set_Product_unit tptp.nat) tptp.set_set_Product_unit) tptp.nat)
% 5.61/5.90 (declare-fun tptp.defaul566961228789861419t_unit () tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.arrays_Product_unit (tptp.heap_e7401611519738050253t_unit tptp.typerep tptp.nat) tptp.list_nat)
% 5.61/5.90 (declare-fun tptp.lim_Product_unit (tptp.heap_e7401611519738050253t_unit) tptp.nat)
% 5.61/5.90 (declare-fun tptp.refs_Product_unit (tptp.heap_e7401611519738050253t_unit tptp.typerep tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.if_assn (Bool tptp.assn tptp.assn) tptp.assn)
% 5.61/5.90 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.if_Code_natural (Bool tptp.code_natural tptp.code_natural) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.if_filter_nat (Bool tptp.filter_nat tptp.filter_nat) tptp.filter_nat)
% 5.61/5.90 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.61/5.90 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 5.61/5.90 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 5.61/5.90 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 5.61/5.90 (declare-fun tptp.if_set_o (Bool tptp.set_o tptp.set_o) tptp.set_o)
% 5.61/5.90 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.if_set_nat (Bool tptp.set_nat tptp.set_nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.if_set_Product_unit (Bool tptp.set_Product_unit tptp.set_Product_unit) tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.infini8530281810654367211te_nat (tptp.set_nat tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.infini7930543730640340914t_unit (tptp.set_Product_unit tptp.nat) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 5.61/5.90 (declare-fun tptp.neg (tptp.num) tptp.int)
% 5.61/5.90 (declare-fun tptp.pos (tptp.num) tptp.int)
% 5.61/5.90 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 5.61/5.90 (declare-fun tptp.intrel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 5.61/5.90 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 5.61/5.90 (declare-fun tptp.pcr_int (tptp.product_prod_nat_nat tptp.int) Bool)
% 5.61/5.90 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 5.61/5.90 (declare-fun tptp.inf_in1318976480646536635_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.inf_inf_o (Bool Bool) Bool)
% 5.61/5.90 (declare-fun tptp.inf_inf_assn (tptp.assn tptp.assn) tptp.assn)
% 5.61/5.90 (declare-fun tptp.inf_inf_filter_nat (tptp.filter_nat tptp.filter_nat) tptp.filter_nat)
% 5.61/5.90 (declare-fun tptp.inf_inf_int (tptp.int tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.inf_inf_nat (tptp.nat tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.inf_inf_Product_unit (tptp.product_unit tptp.product_unit) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.inf_in1906310914598751387_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr4532377907799695533_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.90 (declare-fun tptp.inf_inf_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 5.61/5.90 (declare-fun tptp.inf_in1364745209274528805nteger (tptp.set_Code_integer tptp.set_Code_integer) tptp.set_Code_integer)
% 5.61/5.90 (declare-fun tptp.inf_in7395780696554941096er_nat (tptp.set_filter_nat tptp.set_filter_nat) tptp.set_filter_nat)
% 5.61/5.90 (declare-fun tptp.inf_inf_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.inf_inf_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.inf_in2269163501485487111nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 5.61/5.90 (declare-fun tptp.inf_in2572325071724192079at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.90 (declare-fun tptp.inf_in4660618365625256667t_unit (tptp.set_Product_unit tptp.set_Product_unit) tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.inf_inf_set_set_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 5.61/5.90 (declare-fun tptp.sup_su1942872429929737346at_o_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool) (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool) (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool)) Bool)
% 5.61/5.90 (declare-fun tptp.sup_sup_o_o_o ((-> Bool Bool Bool) (-> Bool Bool Bool) Bool Bool) Bool)
% 5.61/5.90 (declare-fun tptp.sup_sup_int_int_o ((-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool) tptp.int tptp.int) Bool)
% 5.61/5.90 (declare-fun tptp.sup_sup_nat_nat_o ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool) tptp.nat tptp.nat) Bool)
% 5.61/5.90 (declare-fun tptp.sup_su5453871518329203617_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.sup_su3411595859437804162unit_o ((-> tptp.product_unit tptp.product_unit Bool) (-> tptp.product_unit tptp.product_unit Bool) tptp.product_unit tptp.product_unit) Bool)
% 5.61/5.90 (declare-fun tptp.sup_sup_o (Bool Bool) Bool)
% 5.61/5.90 (declare-fun tptp.sup_sup_assn (tptp.assn tptp.assn) tptp.assn)
% 5.61/5.90 (declare-fun tptp.sup_sup_filter_nat (tptp.filter_nat tptp.filter_nat) tptp.filter_nat)
% 5.61/5.90 (declare-fun tptp.sup_sup_int (tptp.int tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.sup_sup_Product_unit (tptp.product_unit tptp.product_unit) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.sup_su5209123915105501825_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr4532377907799695533_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.90 (declare-fun tptp.sup_sup_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 5.61/5.90 (declare-fun tptp.sup_sup_set_assn (tptp.set_assn tptp.set_assn) tptp.set_assn)
% 5.61/5.90 (declare-fun tptp.sup_su848401254843788991nteger (tptp.set_Code_integer tptp.set_Code_integer) tptp.set_Code_integer)
% 5.61/5.90 (declare-fun tptp.sup_sup_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.sup_su8328026650783933211_nat_o (tptp.set_Pr2161125870931222855_nat_o tptp.set_Pr2161125870931222855_nat_o) tptp.set_Pr2161125870931222855_nat_o)
% 5.61/5.90 (declare-fun tptp.sup_su5769328420594410459od_o_o (tptp.set_Product_prod_o_o tptp.set_Product_prod_o_o) tptp.set_Product_prod_o_o)
% 5.61/5.90 (declare-fun tptp.sup_su6024340866399070445nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 5.61/5.90 (declare-fun tptp.sup_su6327502436637775413at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.90 (declare-fun tptp.sup_su6481247232241170203t_unit (tptp.set_Pr5094982260447487303t_unit tptp.set_Pr5094982260447487303t_unit) tptp.set_Pr5094982260447487303t_unit)
% 5.61/5.90 (declare-fun tptp.sup_su4863159966000489243_nat_o (tptp.set_Pr3813038829465207111_nat_o tptp.set_Pr3813038829465207111_nat_o) tptp.set_Pr3813038829465207111_nat_o)
% 5.61/5.90 (declare-fun tptp.sup_su7766833992073560027_set_o (tptp.set_Pr4577759397028426247_set_o tptp.set_Pr4577759397028426247_set_o) tptp.set_Pr4577759397028426247_set_o)
% 5.61/5.90 (declare-fun tptp.sup_su1286422330746572633et_int (tptp.set_Pr2522554150109002629et_int tptp.set_Pr2522554150109002629et_int) tptp.set_Pr2522554150109002629et_int)
% 5.61/5.90 (declare-fun tptp.sup_su4251893418135750817et_nat (tptp.set_Pr5488025237498180813et_nat tptp.set_Pr5488025237498180813et_nat) tptp.set_Pr5488025237498180813et_nat)
% 5.61/5.90 (declare-fun tptp.sup_su3573767163274163995t_unit (tptp.set_Pr3980508049012409671t_unit tptp.set_Pr3980508049012409671t_unit) tptp.set_Pr3980508049012409671t_unit)
% 5.61/5.90 (declare-fun tptp.sup_su793286257634532545t_unit (tptp.set_Product_unit tptp.set_Product_unit) tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.sup_sup_set_set_o (tptp.set_set_o tptp.set_set_o) tptp.set_set_o)
% 5.61/5.90 (declare-fun tptp.sup_sup_set_set_int (tptp.set_set_int tptp.set_set_int) tptp.set_set_int)
% 5.61/5.90 (declare-fun tptp.sup_sup_set_set_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 5.61/5.90 (declare-fun tptp.sup_su5975557051335651745t_unit (tptp.set_set_Product_unit tptp.set_set_Product_unit) tptp.set_set_Product_unit)
% 5.61/5.90 (declare-fun tptp.lattic1921953407002678535_Max_o (tptp.set_o) Bool)
% 5.61/5.90 (declare-fun tptp.lattic4901227151466704046nteger (tptp.set_Code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.lattic8263393255366662781ax_int (tptp.set_int) tptp.int)
% 5.61/5.90 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.lattic1210392890313158908t_unit (tptp.set_Product_unit) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.lattic7630753665789217321ax_rat (tptp.set_rat) tptp.rat)
% 5.61/5.90 (declare-fun tptp.lattic1973801136483472281_Min_o (tptp.set_o) Bool)
% 5.61/5.90 (declare-fun tptp.lattic1063845414844153500nteger (tptp.set_Code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.lattic8718645017227715691in_int (tptp.set_int) tptp.int)
% 5.61/5.90 (declare-fun tptp.lattic8721135487736765967in_nat (tptp.set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.lattic8554435388794137742t_unit (tptp.set_Product_unit) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.lattic8086005427650270231in_rat (tptp.set_rat) tptp.rat)
% 5.61/5.90 (declare-fun tptp.lattic7708394068118247271o_assn ((-> Bool tptp.assn) tptp.set_o) Bool)
% 5.61/5.90 (declare-fun tptp.lattic2775856028456453135_o_nat ((-> Bool tptp.nat) tptp.set_o) Bool)
% 5.61/5.90 (declare-fun tptp.lattic2140725968369957399_o_rat ((-> Bool tptp.rat) tptp.set_o) Bool)
% 5.61/5.90 (declare-fun tptp.lattic4682378690128378784r_assn ((-> tptp.code_integer tptp.assn) tptp.set_Code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.lattic6074936555552774728er_nat ((-> tptp.code_integer tptp.nat) tptp.set_Code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.lattic5439806495466278992er_rat ((-> tptp.code_integer tptp.rat) tptp.set_Code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.lattic3162799611691135855t_assn ((-> tptp.int tptp.assn) tptp.set_int) tptp.int)
% 5.61/5.90 (declare-fun tptp.lattic8446286672483414039nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.int)
% 5.61/5.90 (declare-fun tptp.lattic7811156612396918303nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.int)
% 5.61/5.90 (declare-fun tptp.lattic2187264146484958483t_assn ((-> tptp.nat tptp.assn) tptp.set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.lattic7446932960582359483at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.lattic6811802900495863747at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.lattic4376901495776413404t_assn ((-> tptp.product_unit tptp.assn) tptp.set_Product_unit) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.lattic1360832392136924548it_nat ((-> tptp.product_unit tptp.nat) tptp.set_Product_unit) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.lattic725702332050428812it_rat ((-> tptp.product_unit tptp.rat) tptp.set_Product_unit) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.lattic956194824204696298_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.lattic4107685809792843317_fin_o (tptp.set_o) Bool)
% 5.61/5.90 (declare-fun tptp.lattic47131356835913163n_assn (tptp.set_assn) tptp.assn)
% 5.61/5.90 (declare-fun tptp.lattic9128708996678779395er_nat (tptp.set_filter_nat) tptp.filter_nat)
% 5.61/5.90 (declare-fun tptp.lattic5235898064620869839in_int (tptp.set_int) tptp.int)
% 5.61/5.90 (declare-fun tptp.lattic5238388535129920115in_nat (tptp.set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.lattic1263872656861969706t_unit (tptp.set_Product_unit) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.lattic4603258475043424379in_rat (tptp.set_rat) tptp.rat)
% 5.61/5.90 (declare-fun tptp.lattic3014633134055518761et_nat (tptp.set_set_nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.lattic7320199455484906628_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.lattic1508158080041050831_fin_o (tptp.set_o) Bool)
% 5.61/5.90 (declare-fun tptp.lattic2150320897289308081n_assn (tptp.set_assn) tptp.assn)
% 5.61/5.90 (declare-fun tptp.lattic5930898082463196905er_nat (tptp.set_filter_nat) tptp.filter_nat)
% 5.61/5.90 (declare-fun tptp.lattic1091506334969745077in_int (tptp.set_int) tptp.int)
% 5.61/5.90 (declare-fun tptp.lattic1093996805478795353in_nat (tptp.set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.lattic5294303975357428420t_unit (tptp.set_Product_unit) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.lattic458866745392299617in_rat (tptp.set_rat) tptp.rat)
% 5.61/5.90 (declare-fun tptp.lattic3835124923745554447et_nat (tptp.set_set_nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 5.61/5.90 (declare-fun tptp.butlast_nat (tptp.list_nat) tptp.list_nat)
% 5.61/5.90 (declare-fun tptp.filter_nat2 ((-> tptp.nat Bool) tptp.list_nat) tptp.list_nat)
% 5.61/5.90 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 5.61/5.90 (declare-fun tptp.nil_nat () tptp.list_nat)
% 5.61/5.90 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 5.61/5.90 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 5.61/5.90 (declare-fun tptp.biject1468766312547416318et_nat (tptp.set_Pr8536935166611901872et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.biject2615096655818420098et_nat (tptp.set_Pr3286484037609594932et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.biject2219996528949639174et_nat (tptp.set_Pr3948176798113811640et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.bijective_int_int (tptp.set_Pr958786334691620121nt_int) Bool)
% 5.61/5.90 (declare-fun tptp.bijective_nat_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.61/5.90 (declare-fun tptp.fun_of384177504262425200et_nat (tptp.set_Pr8536935166611901872et_nat (-> tptp.produc3658429121746597890et_nat Bool)) tptp.produc3925858234332021118et_nat)
% 5.61/5.90 (declare-fun tptp.fun_of3673525222065131764et_nat (tptp.set_Pr3286484037609594932et_nat (-> tptp.produc3658429121746597890et_nat Bool)) tptp.produc3658429121746597890et_nat)
% 5.61/5.90 (declare-fun tptp.fun_of5878246503291251064et_nat (tptp.set_Pr3948176798113811640et_nat tptp.heap_e7401611519738050253t_unit) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.fun_of_rel_int_int (tptp.set_Pr958786334691620121nt_int tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.fun_of_rel_nat_nat (tptp.set_Pr1261947904930325089at_nat tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.inv_on_o_int ((-> Bool tptp.int) tptp.set_o tptp.int) Bool)
% 5.61/5.90 (declare-fun tptp.inv_on_o_nat ((-> Bool tptp.nat) tptp.set_o tptp.nat) Bool)
% 5.61/5.90 (declare-fun tptp.inv_on4869000451854154612nteger ((-> tptp.code_integer tptp.code_integer) tptp.set_Code_integer tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.inv_on_int_int ((-> tptp.int tptp.int) tptp.set_int tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.inv_on_int_nat ((-> tptp.int tptp.nat) tptp.set_int tptp.nat) tptp.int)
% 5.61/5.90 (declare-fun tptp.inv_on1369624593536199399nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat tptp.code_integer) tptp.nat)
% 5.61/5.90 (declare-fun tptp.inv_on_nat_int ((-> tptp.nat tptp.int) tptp.set_nat tptp.int) tptp.nat)
% 5.61/5.90 (declare-fun tptp.inv_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.inv_on_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_nat tptp.set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.inv_on7725125254116338689it_int ((-> tptp.product_unit tptp.int) tptp.set_Product_unit tptp.int) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.inv_on7727615724625388965it_nat ((-> tptp.product_unit tptp.nat) tptp.set_Product_unit tptp.nat) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.pairself_int_int ((-> tptp.int tptp.int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 5.61/5.90 (declare-fun tptp.pairself_int_nat ((-> tptp.int tptp.nat) tptp.product_prod_int_int) tptp.product_prod_nat_nat)
% 5.61/5.90 (declare-fun tptp.pairself_nat_int ((-> tptp.nat tptp.int) tptp.product_prod_nat_nat) tptp.product_prod_int_int)
% 5.61/5.90 (declare-fun tptp.pairself_nat_nat ((-> tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 5.61/5.90 (declare-fun tptp.pairself_rel_int_int (tptp.produc5030937667867769463nt_int tptp.produc5030937667867769463nt_int) Bool)
% 5.61/5.90 (declare-fun tptp.pairself_rel_int_nat (tptp.produc6128020648511768019nt_int tptp.produc6128020648511768019nt_int) Bool)
% 5.61/5.90 (declare-fun tptp.pairself_rel_nat_int (tptp.produc3574062574353363227at_nat tptp.produc3574062574353363227at_nat) Bool)
% 5.61/5.90 (declare-fun tptp.pairself_rel_nat_nat (tptp.produc4671145554997361783at_nat tptp.produc4671145554997361783at_nat) Bool)
% 5.61/5.90 (declare-fun tptp.rel_re3331361160397388719_nat_o (tptp.set_Pr2161125870931222855_nat_o tptp.set_Pr4532377907799695533_nat_o) tptp.set_Pr2161125870931222855_nat_o)
% 5.61/5.90 (declare-fun tptp.rel_restrict_o (tptp.set_Product_prod_o_o tptp.set_o) tptp.set_Product_prod_o_o)
% 5.61/5.90 (declare-fun tptp.rel_restrict_int (tptp.set_Pr958786334691620121nt_int tptp.set_int) tptp.set_Pr958786334691620121nt_int)
% 5.61/5.90 (declare-fun tptp.rel_restrict_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.90 (declare-fun tptp.rel_re9207996470947987439t_unit (tptp.set_Pr5094982260447487303t_unit tptp.set_Product_unit) tptp.set_Pr5094982260447487303t_unit)
% 5.61/5.90 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.semiri3763490453095760265atural (tptp.nat) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 5.61/5.90 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 5.61/5.90 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.nat_sum_encode (tptp.sum_sum_nat_nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 5.61/5.90 (declare-fun tptp.inc (tptp.num) tptp.num)
% 5.61/5.90 (declare-fun tptp.nat_of_num (tptp.num) tptp.nat)
% 5.61/5.90 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 5.61/5.90 (declare-fun tptp.neg_nu5831290666863070958nteger (tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.neg_nu5219082963157363817nc_rat (tptp.rat) tptp.rat)
% 5.61/5.90 (declare-fun tptp.neg_numeral_sub_int (tptp.num tptp.num) tptp.int)
% 5.61/5.90 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 5.61/5.90 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 5.61/5.90 (declare-fun tptp.one () tptp.num)
% 5.61/5.90 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 5.61/5.90 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.numera5444537566228673987atural (tptp.num) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 5.61/5.90 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 5.61/5.90 (declare-fun tptp.pow (tptp.num tptp.num) tptp.num)
% 5.61/5.90 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 5.61/5.90 (declare-fun tptp.sqr (tptp.num) tptp.num)
% 5.61/5.90 (declare-fun tptp.order_1145710701291701250_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr2161125870931222855_nat_o) Bool)
% 5.61/5.90 (declare-fun tptp.order_6238756238976269133r_on_o (tptp.set_o tptp.set_Product_prod_o_o) Bool)
% 5.61/5.90 (declare-fun tptp.order_4471489696718655927on_int (tptp.set_int tptp.set_Pr958786334691620121nt_int) Bool)
% 5.61/5.90 (declare-fun tptp.order_4473980167227706203on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.61/5.90 (declare-fun tptp.order_888282469287196226t_unit (tptp.set_Product_unit tptp.set_Pr5094982260447487303t_unit) Bool)
% 5.61/5.90 (declare-fun tptp.order_3690095022144090562_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr2161125870931222855_nat_o) Bool)
% 5.61/5.90 (declare-fun tptp.order_8538205470752950541r_on_o (tptp.set_o tptp.set_Product_prod_o_o) Bool)
% 5.61/5.90 (declare-fun tptp.order_5248785102713058295on_int (tptp.set_int tptp.set_Pr958786334691620121nt_int) Bool)
% 5.61/5.90 (declare-fun tptp.order_5251275573222108571on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.61/5.90 (declare-fun tptp.order_2505591618835473410t_unit (tptp.set_Product_unit tptp.set_Pr5094982260447487303t_unit) Bool)
% 5.61/5.90 (declare-fun tptp.order_174704566861754596_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr2161125870931222855_nat_o) Bool)
% 5.61/5.90 (declare-fun tptp.order_preorder_on_o (tptp.set_o tptp.set_Product_prod_o_o) Bool)
% 5.61/5.90 (declare-fun tptp.order_4859164337913492053on_int (tptp.set_int tptp.set_Pr958786334691620121nt_int) Bool)
% 5.61/5.90 (declare-fun tptp.order_4861654808422542329on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.61/5.90 (declare-fun tptp.order_7534304569044981540t_unit (tptp.set_Product_unit tptp.set_Pr5094982260447487303t_unit) Bool)
% 5.61/5.90 (declare-fun tptp.order_7262550146012401043_nat_o (tptp.set_Pr2161125870931222855_nat_o (-> tptp.produc3658429121746597890et_nat Bool)) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.90 (declare-fun tptp.order_underS_o (tptp.set_Product_prod_o_o Bool) tptp.set_o)
% 5.61/5.90 (declare-fun tptp.order_underS_int (tptp.set_Pr958786334691620121nt_int tptp.int) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.order_underS_nat (tptp.set_Pr1261947904930325089at_nat tptp.nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.order_5809128134054296019t_unit (tptp.set_Pr5094982260447487303t_unit tptp.product_unit) tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.order_2885205318754725938_nat_o (tptp.set_Pr2161125870931222855_nat_o (-> tptp.produc3658429121746597890et_nat Bool)) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.90 (declare-fun tptp.order_under_o (tptp.set_Product_prod_o_o Bool) tptp.set_o)
% 5.61/5.90 (declare-fun tptp.order_under_int (tptp.set_Pr958786334691620121nt_int tptp.int) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.order_under_nat (tptp.set_Pr1261947904930325089at_nat tptp.nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.order_6949322460238004850t_unit (tptp.set_Pr5094982260447487303t_unit tptp.product_unit) tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.order_2118566763991480939_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr2161125870931222855_nat_o) Bool)
% 5.61/5.90 (declare-fun tptp.order_2615775362358406454r_on_o (tptp.set_o tptp.set_Product_prod_o_o) Bool)
% 5.61/5.90 (declare-fun tptp.order_2886507596567047182on_int (tptp.set_int tptp.set_Pr958786334691620121nt_int) Bool)
% 5.61/5.90 (declare-fun tptp.order_2888998067076097458on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.61/5.90 (declare-fun tptp.order_3164716736300062379t_unit (tptp.set_Product_unit tptp.set_Pr5094982260447487303t_unit) Bool)
% 5.61/5.90 (declare-fun tptp.bot_bo7963750851167320836at_o_o ((-> tptp.produc3658429121746597890et_nat Bool)) Bool)
% 5.61/5.90 (declare-fun tptp.bot_bot_o_o (Bool) Bool)
% 5.61/5.90 (declare-fun tptp.bot_bot_int_o (tptp.int) Bool)
% 5.61/5.90 (declare-fun tptp.bot_bot_nat_o (tptp.nat) Bool)
% 5.61/5.90 (declare-fun tptp.bot_bo6993851861578111033_nat_o (tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.bot_bo4642748612307482820unit_o (tptp.product_unit) Bool)
% 5.61/5.90 (declare-fun tptp.bot_bot_o () Bool)
% 5.61/5.90 (declare-fun tptp.bot_bot_assn () tptp.assn)
% 5.61/5.90 (declare-fun tptp.bot_bot_filter_nat () tptp.filter_nat)
% 5.61/5.90 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 5.61/5.90 (declare-fun tptp.bot_bot_Product_unit () tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.bot_bo7824918357723582233_nat_o () tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.90 (declare-fun tptp.bot_bot_set_o () tptp.set_o)
% 5.61/5.90 (declare-fun tptp.bot_bot_set_assn () tptp.set_assn)
% 5.61/5.90 (declare-fun tptp.bot_bo3990330152332043303nteger () tptp.set_Code_integer)
% 5.61/5.90 (declare-fun tptp.bot_bo498966703094740906er_nat () tptp.set_filter_nat)
% 5.61/5.90 (declare-fun tptp.bot_bo3686245532977126937t_unit () tptp.set_he8644174446132254637t_unit)
% 5.61/5.90 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 5.61/5.90 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.bot_bo3657187498359500723_nat_o () tptp.set_Pr2161125870931222855_nat_o)
% 5.61/5.90 (declare-fun tptp.bot_bo1481135142794719944et_nat () tptp.set_Pr3286484037609594932et_nat)
% 5.61/5.90 (declare-fun tptp.bot_bo7073875226086086771od_o_o () tptp.set_Product_prod_o_o)
% 5.61/5.90 (declare-fun tptp.bot_bo3771712512152092492et_nat () tptp.set_Pr3948176798113811640et_nat)
% 5.61/5.90 (declare-fun tptp.bot_bo1796632182523588997nt_int () tptp.set_Pr958786334691620121nt_int)
% 5.61/5.90 (declare-fun tptp.bot_bo2099793752762293965at_nat () tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.90 (declare-fun tptp.bot_bo1654022762305692595t_unit () tptp.set_Pr5094982260447487303t_unit)
% 5.61/5.90 (declare-fun tptp.bot_bo7535334947429593011_nat_o () tptp.set_Pr3813038829465207111_nat_o)
% 5.61/5.90 (declare-fun tptp.bot_bo8143257439550059635_set_o () tptp.set_Pr4577759397028426247_set_o)
% 5.61/5.90 (declare-fun tptp.bot_bo1987282549146081265et_int () tptp.set_Pr2522554150109002629et_int)
% 5.61/5.90 (declare-fun tptp.bot_bo4952753636535259449et_nat () tptp.set_Pr5488025237498180813et_nat)
% 5.61/5.90 (declare-fun tptp.bot_bo5113747506523071411t_unit () tptp.set_Pr3980508049012409671t_unit)
% 5.61/5.90 (declare-fun tptp.bot_bo3957492148770167129t_unit () tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.bot_bot_set_rat () tptp.set_rat)
% 5.61/5.90 (declare-fun tptp.bot_bo3736544561982865913_nat_o () tptp.set_se1353816476878259085_nat_o)
% 5.61/5.90 (declare-fun tptp.bot_bot_set_set_o () tptp.set_set_o)
% 5.61/5.90 (declare-fun tptp.bot_bo9204850693367297629nteger () tptp.set_set_Code_integer)
% 5.61/5.90 (declare-fun tptp.bot_bot_set_set_int () tptp.set_set_int)
% 5.61/5.90 (declare-fun tptp.bot_bot_set_set_nat () tptp.set_set_nat)
% 5.61/5.90 (declare-fun tptp.bot_bo6284674557190688313t_unit () tptp.set_set_Product_unit)
% 5.61/5.90 (declare-fun tptp.ord_le8176553561544679545_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool)) Bool)
% 5.61/5.90 (declare-fun tptp.ord_less_o (Bool Bool) Bool)
% 5.61/5.90 (declare-fun tptp.ord_less_assn (tptp.assn tptp.assn) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le5570908160329646204atural (tptp.code_natural tptp.code_natural) Bool)
% 5.61/5.90 (declare-fun tptp.ord_less_filter_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 5.61/5.90 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 5.61/5.90 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le361264281704409273t_unit (tptp.product_unit tptp.product_unit) Bool)
% 5.61/5.90 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le2453136405763929_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr4532377907799695533_nat_o) Bool)
% 5.61/5.90 (declare-fun tptp.ord_less_set_o (tptp.set_o tptp.set_o) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le1307284697595431911nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 5.61/5.90 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 5.61/5.90 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le8056459307392131481t_unit (tptp.set_Product_unit tptp.set_Product_unit) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le729326519192465773_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool)) Bool)
% 5.61/5.90 (declare-fun tptp.ord_less_eq_o (Bool Bool) Bool)
% 5.61/5.90 (declare-fun tptp.ord_less_eq_assn (tptp.assn tptp.assn) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le1926595141338095240atural (tptp.code_natural tptp.code_natural) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 5.61/5.90 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 5.61/5.90 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le3221252021190050221t_unit (tptp.product_unit tptp.product_unit) Bool)
% 5.61/5.90 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le2965882846123202637_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr4532377907799695533_nat_o) Bool)
% 5.61/5.90 (declare-fun tptp.ord_less_eq_set_o (tptp.set_o tptp.set_o) Bool)
% 5.61/5.90 (declare-fun tptp.ord_less_eq_set_assn (tptp.set_assn tptp.set_assn) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le7084787975880047091nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le2426478655948331894er_nat (tptp.set_filter_nat tptp.set_filter_nat) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le4903435234951335757t_unit (tptp.set_he8644174446132254637t_unit tptp.set_he8644174446132254637t_unit) Bool)
% 5.61/5.90 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 5.61/5.90 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le6659818918159358183_nat_o (tptp.set_Pr2161125870931222855_nat_o tptp.set_Pr2161125870931222855_nat_o) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le4460016228128491106_o_nat (tptp.set_Pr4769669219625338370_o_nat tptp.set_Pr4769669219625338370_o_nat) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le4763372923235995152et_nat (tptp.set_Pr8536935166611901872et_nat tptp.set_Pr8536935166611901872et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le5966269811547037844et_nat (tptp.set_Pr3286484037609594932et_nat tptp.set_Pr3286484037609594932et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le192195778054999463od_o_o (tptp.set_Product_prod_o_o tptp.set_Product_prod_o_o) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le6472378536984071597_o_nat (tptp.set_Pr2101469702781467981_o_nat tptp.set_Pr2101469702781467981_o_nat) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le8090042543978450200et_nat (tptp.set_Pr3948176798113811640et_nat tptp.set_Pr3948176798113811640et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le2843351958646193337nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le5333435103577920093nt_nat (tptp.set_Pr3448869479623346877nt_nat tptp.set_Pr3448869479623346877nt_nat) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le3146513528884898305at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le8121013740822022818it_nat (tptp.set_Pr1763845938948868674it_nat tptp.set_Pr1763845938948868674it_nat) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le930853871177014503t_unit (tptp.set_Pr5094982260447487303t_unit tptp.set_Pr5094982260447487303t_unit) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le8001614231985977575_nat_o (tptp.set_Pr3813038829465207111_nat_o tptp.set_Pr3813038829465207111_nat_o) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le2885120122233735591_set_o (tptp.set_Pr4577759397028426247_set_o tptp.set_Pr4577759397028426247_set_o) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le1436784781161120549et_int (tptp.set_Pr2522554150109002629et_int tptp.set_Pr2522554150109002629et_int) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le4402255868550298733et_nat (tptp.set_Pr5488025237498180813et_nat tptp.set_Pr5488025237498180813et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le8072594200992201959t_unit (tptp.set_Pr3980508049012409671t_unit tptp.set_Pr3980508049012409671t_unit) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le3507040750410214029t_unit (tptp.set_Product_unit tptp.set_Product_unit) Bool)
% 5.61/5.90 (declare-fun tptp.ord_less_eq_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le1914454125413604393nteger (tptp.set_set_Code_integer tptp.set_set_Code_integer) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 5.61/5.90 (declare-fun tptp.ord_le9131159989063066194et_nat (tptp.set_set_set_nat tptp.set_set_set_nat) Bool)
% 5.61/5.90 (declare-fun tptp.ord_max_o (Bool Bool) Bool)
% 5.61/5.90 (declare-fun tptp.ord_max_assn (tptp.assn tptp.assn) tptp.assn)
% 5.61/5.90 (declare-fun tptp.ord_max_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.61/5.90 (declare-fun tptp.ord_max_Code_natural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 5.61/5.90 (declare-fun tptp.ord_max_filter_nat (tptp.filter_nat tptp.filter_nat) tptp.filter_nat)
% 5.61/5.90 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 5.61/5.90 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.ord_max_Product_unit (tptp.product_unit tptp.product_unit) tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.ord_max_rat (tptp.rat tptp.rat) tptp.rat)
% 5.61/5.90 (declare-fun tptp.ord_ma8206644353667601538_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr4532377907799695533_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.90 (declare-fun tptp.ord_max_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 5.61/5.90 (declare-fun tptp.ord_max_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 5.61/5.90 (declare-fun tptp.ord_max_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.ord_ma508538259134630082t_unit (tptp.set_Product_unit tptp.set_Product_unit) tptp.set_Product_unit)
% 5.61/5.90 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 5.61/5.90 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 5.61/5.90 (declare-fun tptp.ordering_top_assn ((-> tptp.assn tptp.assn Bool) (-> tptp.assn tptp.assn Bool) tptp.assn) Bool)
% 5.61/5.90 (declare-fun tptp.orderi2807725203697798511er_nat ((-> tptp.filter_nat tptp.filter_nat Bool) (-> tptp.filter_nat tptp.filter_nat Bool) tptp.filter_nat) Bool)
% 5.61/5.90 (declare-fun tptp.ordering_top_set_o ((-> tptp.set_o tptp.set_o Bool) (-> tptp.set_o tptp.set_o Bool) tptp.set_o) Bool)
% 5.61/5.90 (declare-fun tptp.ordering_top_set_int ((-> tptp.set_int tptp.set_int Bool) (-> tptp.set_int tptp.set_int Bool) tptp.set_int) Bool)
% 5.61/5.90 (declare-fun tptp.ordering_top_set_nat ((-> tptp.set_nat tptp.set_nat Bool) (-> tptp.set_nat tptp.set_nat Bool) tptp.set_nat) Bool)
% 5.61/5.90 (declare-fun tptp.orderi2935705153647960990t_unit ((-> tptp.set_Product_unit tptp.set_Product_unit Bool) (-> tptp.set_Product_unit tptp.set_Product_unit Bool) tptp.set_Product_unit) Bool)
% 5.61/5.90 (declare-fun tptp.top_to2462227307520033056at_o_o ((-> tptp.produc3658429121746597890et_nat Bool)) Bool)
% 5.61/5.90 (declare-fun tptp.top_top_o_o (Bool) Bool)
% 5.61/5.90 (declare-fun tptp.top_top_int_o (tptp.int) Bool)
% 5.61/5.90 (declare-fun tptp.top_top_nat_o (tptp.nat) Bool)
% 5.61/5.90 (declare-fun tptp.top_to5213382387105117981_nat_o (tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.90 (declare-fun tptp.top_to2465898995584390880unit_o (tptp.product_unit) Bool)
% 5.61/5.90 (declare-fun tptp.top_top_o () Bool)
% 5.61/5.90 (declare-fun tptp.top_top_assn () tptp.assn)
% 5.61/5.90 (declare-fun tptp.top_top_filter_nat () tptp.filter_nat)
% 5.61/5.90 (declare-fun tptp.top_top_Product_unit () tptp.product_unit)
% 5.61/5.90 (declare-fun tptp.top_to3804862627464599871nteger () tptp.set_Co726186806682698383nteger)
% 5.61/5.90 (declare-fun tptp.top_to4869887016220417533_nat_o () tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.90 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 5.61/5.90 (declare-fun tptp.top_top_set_assn () tptp.set_assn)
% 5.61/5.90 (declare-fun tptp.top_to4645266643341252675nteger () tptp.set_Code_integer)
% 5.61/5.90 (declare-fun tptp.top_to9103716463852441742atural () tptp.set_Code_natural)
% 5.61/5.90 (declare-fun tptp.top_top_set_int () tptp.set_int)
% 5.61/5.90 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 5.61/5.90 (declare-fun tptp.top_to2658285827425157974eger_o () tptp.set_Pr448751882837621926eger_o)
% 5.61/5.90 (declare-fun tptp.top_to2363841527343591755nteger () tptp.set_Pr4811707699266497531nteger)
% 5.61/5.90 (declare-fun tptp.top_to6270328743839206426er_int () tptp.set_Pr6496905503482889930er_int)
% 5.61/5.90 (declare-fun tptp.top_to8760411888770933182er_nat () tptp.set_Pr8986988648414616686er_nat)
% 5.61/5.90 (declare-fun tptp.top_to3244471725241573579t_unit () tptp.set_Pr4580871404036792859t_unit)
% 5.61/5.90 (declare-fun tptp.top_to2524957550908328808et_nat () tptp.set_Pr3948176798113811640et_nat)
% 5.61/5.91 (declare-fun tptp.top_to4366644338036079209nt_int () tptp.set_Pr958786334691620121nt_int)
% 5.61/5.91 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.top_top_set_rat () tptp.set_rat)
% 5.61/5.91 (declare-fun tptp.top_to8515903933492314333_nat_o () tptp.set_se1353816476878259085_nat_o)
% 5.61/5.91 (declare-fun tptp.top_top_set_set_o () tptp.set_set_o)
% 5.61/5.91 (declare-fun tptp.top_top_set_set_int () tptp.set_set_int)
% 5.61/5.91 (declare-fun tptp.top_top_set_set_nat () tptp.set_set_nat)
% 5.61/5.91 (declare-fun tptp.top_to1767297665138865437t_unit () tptp.set_set_Product_unit)
% 5.61/5.91 (declare-fun tptp.power_power_assn (tptp.assn tptp.nat) tptp.assn)
% 5.61/5.91 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 5.61/5.91 (declare-fun tptp.power_7079662738309270450atural (tptp.code_natural tptp.nat) tptp.code_natural)
% 5.61/5.91 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 5.61/5.91 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 5.61/5.91 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 5.61/5.91 (declare-fun tptp.produc1721739103881910569nt_int ((-> tptp.int tptp.int) tptp.product_prod_int_int) tptp.produc5030937667867769463nt_int)
% 5.61/5.91 (declare-fun tptp.produc2818822084525909125nt_int ((-> tptp.int tptp.nat) tptp.product_prod_int_int) tptp.produc6128020648511768019nt_int)
% 5.61/5.91 (declare-fun tptp.produc3140199747736941517at_nat ((-> tptp.nat tptp.int) tptp.product_prod_nat_nat) tptp.produc3574062574353363227at_nat)
% 5.61/5.91 (declare-fun tptp.produc4237282728380940073at_nat ((-> tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.produc4671145554997361783at_nat)
% 5.61/5.91 (declare-fun tptp.produc7368190662567826135_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool)) tptp.produc4928098042776334183_nat_o)
% 5.61/5.91 (declare-fun tptp.produc2245416461498447860et_nat ((-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat) tptp.produc2732055786443039994et_nat)
% 5.61/5.91 (declare-fun tptp.produc5001842942810119800et_nat ((-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) tptp.produc3925858234332021118et_nat)
% 5.61/5.91 (declare-fun tptp.product_Pair_o_o (Bool Bool) tptp.product_prod_o_o)
% 5.61/5.91 (declare-fun tptp.product_Pair_o_int (Bool tptp.int) tptp.product_prod_o_int)
% 5.61/5.91 (declare-fun tptp.product_Pair_o_nat (Bool tptp.nat) tptp.product_prod_o_nat)
% 5.61/5.91 (declare-fun tptp.produc3762353314782720579et_nat (Bool tptp.produc3658429121746597890et_nat) tptp.produc6197004810343482825et_nat)
% 5.61/5.91 (declare-fun tptp.produc3901946521647900940t_unit (Bool tptp.product_unit) tptp.produc3788275437394581276t_unit)
% 5.61/5.91 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 5.61/5.91 (declare-fun tptp.produc3574140220909816553atural (tptp.code_natural tptp.code_natural) tptp.produc7822875418678951345atural)
% 5.61/5.91 (declare-fun tptp.produc6639722614265839536atural (tptp.code_natural tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 5.61/5.91 (declare-fun tptp.produc8256076736985659095t_unit (tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit) tptp.produc8126358835630522215t_unit)
% 5.61/5.91 (declare-fun tptp.produc7507926704131184380et_nat (tptp.heap_e7401611519738050253t_unit tptp.set_nat) tptp.produc3658429121746597890et_nat)
% 5.61/5.91 (declare-fun tptp.product_Pair_int_o (tptp.int Bool) tptp.product_prod_int_o)
% 5.61/5.91 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 5.61/5.91 (declare-fun tptp.product_Pair_int_nat (tptp.int tptp.nat) tptp.product_prod_int_nat)
% 5.61/5.91 (declare-fun tptp.produc550872421827702152t_unit (tptp.int tptp.product_unit) tptp.produc6865911496949736918t_unit)
% 5.61/5.91 (declare-fun tptp.product_Pair_nat_o (tptp.nat Bool) tptp.product_prod_nat_o)
% 5.61/5.91 (declare-fun tptp.product_Pair_nat_int (tptp.nat tptp.int) tptp.product_prod_nat_int)
% 5.61/5.91 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 5.61/5.91 (declare-fun tptp.produc3434450474625521892t_unit (tptp.nat tptp.product_unit) tptp.produc526117512892780850t_unit)
% 5.61/5.91 (declare-fun tptp.produc1940133919992309389et_nat (tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat) tptp.produc5657529347773406293et_nat)
% 5.61/5.91 (declare-fun tptp.produc3674526432113299062_nat_o (tptp.produc3925858234332021118et_nat (-> tptp.produc3658429121746597890et_nat Bool)) tptp.produc4962441903510821572_nat_o)
% 5.61/5.91 (declare-fun tptp.produc8599840265553166229et_nat (tptp.produc3925858234332021118et_nat tptp.produc3925858234332021118et_nat) tptp.produc6830853553727218525et_nat)
% 5.61/5.91 (declare-fun tptp.produc5530789758353788441et_nat (tptp.produc3925858234332021118et_nat tptp.produc3658429121746597890et_nat) tptp.produc4658369026151987169et_nat)
% 5.61/5.91 (declare-fun tptp.produc2829238748666232050_nat_o (tptp.produc3658429121746597890et_nat (-> tptp.produc3658429121746597890et_nat Bool)) tptp.produc6907119039986491712_nat_o)
% 5.61/5.91 (declare-fun tptp.produc3909112513931304473et_nat (tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat) tptp.produc7389280635074931169et_nat)
% 5.61/5.91 (declare-fun tptp.produc8199053930788261021et_nat (tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat) tptp.produc8111630337999740517et_nat)
% 5.61/5.91 (declare-fun tptp.produc3646306378393792727nt_int (tptp.product_prod_int_int tptp.product_prod_int_int) tptp.produc1219242969750017639nt_int)
% 5.61/5.91 (declare-fun tptp.produc8921240378546987991nt_nat (tptp.product_prod_int_nat tptp.product_prod_int_nat) tptp.produc4806409095325742951nt_nat)
% 5.61/5.91 (declare-fun tptp.produc886916002739626967at_int (tptp.product_prod_nat_int tptp.product_prod_nat_int) tptp.produc6495656768158660455at_int)
% 5.61/5.91 (declare-fun tptp.produc6161850002892822231at_nat (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.produc859450856879609959at_nat)
% 5.61/5.91 (declare-fun tptp.produc8487917018914037602unit_o (tptp.product_unit Bool) tptp.produc7485711547916492274unit_o)
% 5.61/5.91 (declare-fun tptp.produc4800797859304479970it_int (tptp.product_unit tptp.int) tptp.produc5646078835734834920it_int)
% 5.61/5.91 (declare-fun tptp.produc4803288329813530246it_nat (tptp.product_unit tptp.nat) tptp.produc600557818389255820it_nat)
% 5.61/5.91 (declare-fun tptp.produc5692694829384537815t_unit (tptp.product_unit tptp.product_unit) tptp.produc8459935480633519975t_unit)
% 5.61/5.91 (declare-fun tptp.produc5149316574908490455_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr4532377907799695533_nat_o) tptp.produc6666532470309664615_nat_o)
% 5.61/5.91 (declare-fun tptp.produc5838405689764958487_set_o (tptp.set_o tptp.set_o) tptp.produc7369051934464679207_set_o)
% 5.61/5.91 (declare-fun tptp.produc7443773368509356479nteger (tptp.set_Code_integer tptp.set_Code_integer) tptp.produc6491284506569428743nteger)
% 5.61/5.91 (declare-fun tptp.produc6363374080413544029et_int (tptp.set_int tptp.set_int) tptp.produc2115011035271226405et_int)
% 5.61/5.91 (declare-fun tptp.produc2471974422597015918t_unit (tptp.set_nat tptp.heap_e7401611519738050253t_unit) tptp.produc7348995623955488188t_unit)
% 5.61/5.91 (declare-fun tptp.produc4532415448927165861et_nat (tptp.set_nat tptp.set_nat) tptp.produc7819656566062154093et_nat)
% 5.61/5.91 (declare-fun tptp.produc7269801343787132631t_unit (tptp.set_Product_unit tptp.set_Product_unit) tptp.produc1357844946079266663t_unit)
% 5.61/5.91 (declare-fun tptp.produc3142209312014666069_o_nat (tptp.set_Pr4532377907799695533_nat_o (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.set_nat)) tptp.set_Pr4769669219625338370_o_nat)
% 5.61/5.91 (declare-fun tptp.produc7016705354093686019et_nat (tptp.set_Pr4532377907799695533_nat_o (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.set_Pr3286484037609594932et_nat)) tptp.set_Pr8536935166611901872et_nat)
% 5.61/5.91 (declare-fun tptp.produc8052021730408606599et_nat (tptp.set_Pr4532377907799695533_nat_o (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.set_Pr3948176798113811640et_nat)) tptp.set_Pr3286484037609594932et_nat)
% 5.61/5.91 (declare-fun tptp.product_Sigma_o_o (tptp.set_o (-> Bool tptp.set_o)) tptp.set_Product_prod_o_o)
% 5.61/5.91 (declare-fun tptp.product_Sigma_o_int (tptp.set_o (-> Bool tptp.set_int)) tptp.set_Pr8834758594704517033_o_int)
% 5.61/5.91 (declare-fun tptp.product_Sigma_o_nat (tptp.set_o (-> Bool tptp.set_nat)) tptp.set_Pr2101469702781467981_o_nat)
% 5.61/5.91 (declare-fun tptp.produc411009820408249917t_unit (tptp.set_o (-> Bool tptp.set_Product_unit)) tptp.set_Pr6671815714118170108t_unit)
% 5.61/5.91 (declare-fun tptp.produc5260988393495149579et_nat (tptp.set_he8644174446132254637t_unit (-> tptp.heap_e7401611519738050253t_unit tptp.set_set_nat)) tptp.set_Pr3948176798113811640et_nat)
% 5.61/5.91 (declare-fun tptp.product_Sigma_int_o (tptp.set_int (-> tptp.int tptp.set_o)) tptp.set_Pr903927857289325719_int_o)
% 5.61/5.91 (declare-fun tptp.produc1453890548195736866nt_int (tptp.set_int (-> tptp.int tptp.set_int)) tptp.set_Pr958786334691620121nt_int)
% 5.61/5.91 (declare-fun tptp.produc1456381018704787142nt_nat (tptp.set_int (-> tptp.int tptp.set_nat)) tptp.set_Pr3448869479623346877nt_nat)
% 5.61/5.91 (declare-fun tptp.produc2622961094310184599t_unit (tptp.set_int (-> tptp.int tptp.set_Product_unit)) tptp.set_Pr5889264611543340172t_unit)
% 5.61/5.91 (declare-fun tptp.produc5650067098820117939_nat_o (tptp.set_nat (-> tptp.nat tptp.set_Pr4532377907799695533_nat_o)) tptp.set_Pr5623950326363488168_nat_o)
% 5.61/5.91 (declare-fun tptp.product_Sigma_nat_o (tptp.set_nat (-> tptp.nat tptp.set_o)) tptp.set_Pr3149072824959771635_nat_o)
% 5.61/5.91 (declare-fun tptp.produc454536836294682310at_int (tptp.set_nat (-> tptp.nat tptp.set_int)) tptp.set_Pr7995236796853374141at_int)
% 5.61/5.91 (declare-fun tptp.produc457027306803732586at_nat (tptp.set_nat (-> tptp.nat tptp.set_nat)) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.91 (declare-fun tptp.produc5506539147108004339t_unit (tptp.set_nat (-> tptp.nat tptp.set_Product_unit)) tptp.set_Pr4334478416066269672t_unit)
% 5.61/5.91 (declare-fun tptp.produc4996980317674386579unit_o (tptp.set_Product_unit (-> tptp.product_unit tptp.set_o)) tptp.set_Pr5464989305201766866unit_o)
% 5.61/5.91 (declare-fun tptp.produc6875377002296012693it_nat (tptp.set_Product_unit (-> tptp.product_unit tptp.set_nat)) tptp.set_Pr1763845938948868674it_nat)
% 5.61/5.91 (declare-fun tptp.produc6121607364029222536t_unit (tptp.set_Product_unit (-> tptp.product_unit tptp.set_Product_unit)) tptp.set_Pr5094982260447487303t_unit)
% 5.61/5.91 (declare-fun tptp.product_Unity () tptp.product_unit)
% 5.61/5.91 (declare-fun tptp.produc1442628905706551930et_nat ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool) tptp.produc2732055786443039994et_nat) tptp.produc2732055786443039994et_nat)
% 5.61/5.91 (declare-fun tptp.produc3198230245617193214et_nat ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat) tptp.produc3925858234332021118et_nat)
% 5.61/5.91 (declare-fun tptp.produc3195571438000033749nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.61/5.91 (declare-fun tptp.produc4273547285574235514et_nat ((-> tptp.heap_e7401611519738050253t_unit tptp.produc3658429121746597890et_nat Bool) tptp.produc7936767299998605306et_nat) tptp.produc2732055786443039994et_nat)
% 5.61/5.91 (declare-fun tptp.produc6095824665904122878et_nat ((-> tptp.heap_e7401611519738050253t_unit tptp.produc3658429121746597890et_nat Bool) tptp.produc5697189838369619070et_nat) tptp.produc3925858234332021118et_nat)
% 5.61/5.91 (declare-fun tptp.produc962520821680634754et_nat ((-> tptp.heap_e7401611519738050253t_unit tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) tptp.produc6500295350249520386et_nat)
% 5.61/5.91 (declare-fun tptp.produc4172003873565521026et_nat ((-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit) tptp.produc3658429121746597890et_nat) tptp.produc3658429121746597890et_nat)
% 5.61/5.91 (declare-fun tptp.produc7422730317258219nt_int ((-> tptp.heap_e7401611519738050253t_unit tptp.int) tptp.produc2475246329834808232it_int) tptp.product_prod_int_int)
% 5.61/5.91 (declare-fun tptp.produc3346058198459025221et_nat ((-> tptp.heap_e7401611519738050253t_unit tptp.int) tptp.produc3658429121746597890et_nat) tptp.produc2771989624626745363et_nat)
% 5.61/5.91 (declare-fun tptp.produc8233931525780029747at_nat ((-> tptp.heap_e7401611519738050253t_unit tptp.nat) tptp.produc6653097349344004940it_nat) tptp.product_prod_nat_nat)
% 5.61/5.91 (declare-fun tptp.produc2974404638222180585et_nat ((-> tptp.heap_e7401611519738050253t_unit tptp.nat) tptp.produc3658429121746597890et_nat) tptp.produc2400336064389900727et_nat)
% 5.61/5.91 (declare-fun tptp.produc1933289243015553937_o_int ((-> tptp.int tptp.produc3658429121746597890et_nat Bool) tptp.product_prod_int_int) tptp.produc3776562785724475560_o_int)
% 5.61/5.91 (declare-fun tptp.produc3602029435013415139et_nat ((-> tptp.int tptp.produc3658429121746597890et_nat Bool) tptp.produc1049655590333717003et_nat) tptp.produc2732055786443039994et_nat)
% 5.61/5.91 (declare-fun tptp.produc5259063908904861543et_nat ((-> tptp.int tptp.produc3658429121746597890et_nat Bool) tptp.produc8065447618272157327et_nat) tptp.produc3925858234332021118et_nat)
% 5.61/5.91 (declare-fun tptp.produc1158806734383251089it_int ((-> tptp.int tptp.heap_e7401611519738050253t_unit) tptp.product_prod_int_int) tptp.produc2475246329834808232it_int)
% 5.61/5.91 (declare-fun tptp.produc7086134074927288299et_nat ((-> tptp.int tptp.heap_e7401611519738050253t_unit) tptp.produc2771989624626745363et_nat) tptp.produc3658429121746597890et_nat)
% 5.61/5.91 (declare-fun tptp.produc2355237562570658114nt_int ((-> tptp.int tptp.int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 5.61/5.91 (declare-fun tptp.produc1355883850669603558at_int ((-> tptp.int tptp.nat) tptp.product_prod_int_int) tptp.product_prod_nat_int)
% 5.61/5.91 (declare-fun tptp.produc1358374321178653834at_nat ((-> tptp.int tptp.nat) tptp.product_prod_int_nat) tptp.product_prod_nat_nat)
% 5.61/5.91 (declare-fun tptp.produc986720760941809198at_nat ((-> tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 5.61/5.91 (declare-fun tptp.produc9020447175693601247nteger ((-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc5966032636589952099nteger)
% 5.61/5.91 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.61/5.91 (declare-fun tptp.produc4463282112584876420nt_int ((-> tptp.int tptp.int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 5.61/5.91 (declare-fun tptp.produc3463928400683821864at_int ((-> tptp.int tptp.nat) tptp.product_prod_int_int) tptp.product_prod_int_nat)
% 5.61/5.91 (declare-fun tptp.produc3466418871192872140at_nat ((-> tptp.int tptp.nat) tptp.product_prod_nat_int) tptp.product_prod_nat_nat)
% 5.61/5.91 (declare-fun tptp.produc1783401272518604195_nat_o ((-> tptp.int tptp.produc3925858234332021118et_nat) tptp.produc3776562785724475560_o_int) tptp.produc2732055786443039994et_nat)
% 5.61/5.91 (declare-fun tptp.produc2878475440847162070at_int ((-> tptp.int tptp.produc3925858234332021118et_nat) tptp.product_prod_int_int) tptp.produc1049655590333717003et_nat)
% 5.61/5.91 (declare-fun tptp.produc3447581998352395295_nat_o ((-> tptp.int tptp.produc3658429121746597890et_nat) tptp.produc3776562785724475560_o_int) tptp.produc3925858234332021118et_nat)
% 5.61/5.91 (declare-fun tptp.produc9121118195053341018at_int ((-> tptp.int tptp.produc3658429121746597890et_nat) tptp.product_prod_int_int) tptp.produc8065447618272157327et_nat)
% 5.61/5.91 (declare-fun tptp.produc2122153897363312795t_unit ((-> tptp.int tptp.set_nat) tptp.produc2475246329834808232it_int) tptp.produc3658429121746597890et_nat)
% 5.61/5.91 (declare-fun tptp.produc1253519502038700766at_int ((-> tptp.int tptp.set_nat) tptp.product_prod_int_int) tptp.produc2771989624626745363et_nat)
% 5.61/5.91 (declare-fun tptp.produc3094765310956027504at_nat ((-> tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 5.61/5.91 (declare-fun tptp.produc969530845752564945_nat_o ((-> tptp.produc3925858234332021118et_nat tptp.produc3925858234332021118et_nat) tptp.produc2732055786443039994et_nat) tptp.produc2732055786443039994et_nat)
% 5.61/5.91 (declare-fun tptp.produc1515462096303866701_nat_o ((-> tptp.produc3925858234332021118et_nat tptp.produc3658429121746597890et_nat) tptp.produc2732055786443039994et_nat) tptp.produc3925858234332021118et_nat)
% 5.61/5.91 (declare-fun tptp.produc7714581247149323085_nat_o ((-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat) tptp.produc3925858234332021118et_nat) tptp.produc2732055786443039994et_nat)
% 5.61/5.91 (declare-fun tptp.produc8750854537940449737_nat_o ((-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat) tptp.produc3925858234332021118et_nat) tptp.produc3925858234332021118et_nat)
% 5.61/5.91 (declare-fun tptp.produc7345612820240450715t_unit ((-> tptp.set_nat tptp.int) tptp.produc3658429121746597890et_nat) tptp.produc2475246329834808232it_int)
% 5.61/5.91 (declare-fun tptp.produc2744032961877892830nt_int ((-> tptp.set_nat tptp.int) tptp.produc2771989624626745363et_nat) tptp.product_prod_int_int)
% 5.61/5.91 (declare-fun tptp.produc8442695800884449271t_unit ((-> tptp.set_nat tptp.nat) tptp.produc3658429121746597890et_nat) tptp.produc6653097349344004940it_nat)
% 5.61/5.91 (declare-fun tptp.produc1747169720485888550at_nat ((-> tptp.set_nat tptp.nat) tptp.produc2400336064389900727et_nat) tptp.product_prod_nat_nat)
% 5.61/5.91 (declare-fun tptp.produc3009152965630989513_nat_o ((-> tptp.set_nat tptp.produc3925858234332021118et_nat) tptp.produc6500295350249520386et_nat) tptp.produc2732055786443039994et_nat)
% 5.61/5.91 (declare-fun tptp.produc7176435795764513225t_unit ((-> tptp.set_nat tptp.produc3925858234332021118et_nat) tptp.produc3658429121746597890et_nat) tptp.produc7936767299998605306et_nat)
% 5.61/5.91 (declare-fun tptp.produc1718959742329256773_nat_o ((-> tptp.set_nat tptp.produc3658429121746597890et_nat) tptp.produc6500295350249520386et_nat) tptp.produc3925858234332021118et_nat)
% 5.61/5.91 (declare-fun tptp.produc7441988914112407621t_unit ((-> tptp.set_nat tptp.produc3658429121746597890et_nat) tptp.produc3658429121746597890et_nat) tptp.produc5697189838369619070et_nat)
% 5.61/5.91 (declare-fun tptp.produc3286488329990770625t_unit ((-> tptp.set_nat tptp.set_nat) tptp.produc3658429121746597890et_nat) tptp.produc3658429121746597890et_nat)
% 5.61/5.91 (declare-fun tptp.produc5101573711933517782_nat_o ((-> tptp.produc2732055786443039994et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat) Bool)
% 5.61/5.91 (declare-fun tptp.produc6216949301066131538_nat_o ((-> tptp.produc3925858234332021118et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.91 (declare-fun tptp.produc1807123492089482958_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) tptp.heap_e7401611519738050253t_unit tptp.set_nat) Bool)
% 5.61/5.91 (declare-fun tptp.produc175634133007206835_int_o ((-> tptp.product_prod_int_int Bool) tptp.int tptp.int) Bool)
% 5.61/5.91 (declare-fun tptp.produc1310100445399344235_nat_o ((-> tptp.product_prod_nat_nat Bool) tptp.nat tptp.nat) Bool)
% 5.61/5.91 (declare-fun tptp.produc4724772261320961782nteger ((-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc723880050079548563nteger) tptp.produc101387210554329899nteger)
% 5.61/5.91 (declare-fun tptp.produc6158254626097298938nteger ((-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc2221115339011613079nteger) tptp.produc101387210554329899nteger)
% 5.61/5.91 (declare-fun tptp.produc2784369760062397435at_nat ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.nat) (-> tptp.produc3658429121746597890et_nat tptp.nat) tptp.produc3925858234332021118et_nat) tptp.product_prod_nat_nat)
% 5.61/5.91 (declare-fun tptp.produc7818937854452556646nteger ((-> tptp.code_integer tptp.code_integer tptp.code_integer) (-> tptp.code_integer tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc723880050079548563nteger)
% 5.61/5.91 (declare-fun tptp.produc3789967387199524714nteger ((-> tptp.code_integer tptp.code_integer tptp.code_integer) (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc2221115339011613079nteger)
% 5.61/5.91 (declare-fun tptp.produc3090791198996863994nteger ((-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc1397831737260518551nteger) tptp.produc101387210554329899nteger)
% 5.61/5.91 (declare-fun tptp.produc5081366107664765182nteger ((-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc101387210554329899nteger)
% 5.61/5.91 (declare-fun tptp.produc1084426483498010290er_o_o ((-> tptp.code_integer tptp.code_integer) (-> Bool Bool) tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 5.61/5.91 (declare-fun tptp.produc7547902865030867346_o_int ((-> tptp.code_integer tptp.code_integer) (-> Bool tptp.int) tptp.produc6271795597528267376eger_o) tptp.produc2256096406371053034er_int)
% 5.61/5.91 (declare-fun tptp.produc7550393335539917622_o_nat ((-> tptp.code_integer tptp.code_integer) (-> Bool tptp.nat) tptp.produc6271795597528267376eger_o) tptp.produc6433947425880249742er_nat)
% 5.61/5.91 (declare-fun tptp.produc3530376873132787239t_unit ((-> tptp.code_integer tptp.code_integer) (-> Bool tptp.product_unit) tptp.produc6271795597528267376eger_o) tptp.produc5496629617739085541t_unit)
% 5.61/5.91 (declare-fun tptp.produc6023007152014423402nteger ((-> tptp.code_integer tptp.code_integer) (-> tptp.code_integer tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc1397831737260518551nteger)
% 5.61/5.91 (declare-fun tptp.produc1802105962441033582nteger ((-> tptp.code_integer tptp.code_integer) (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.61/5.91 (declare-fun tptp.produc1622059938646302433nteger ((-> tptp.code_integer tptp.code_integer) (-> tptp.nat tptp.code_integer) tptp.produc6433947425880249742er_nat) tptp.produc8923325533196201883nteger)
% 5.61/5.91 (declare-fun tptp.produc8116347370398923901unit_o ((-> tptp.code_integer tptp.code_integer) (-> tptp.product_unit Bool) tptp.produc5496629617739085541t_unit) tptp.produc6271795597528267376eger_o)
% 5.61/5.91 (declare-fun tptp.produc4019910415967566983it_int ((-> tptp.code_integer tptp.code_integer) (-> tptp.product_unit tptp.int) tptp.produc5496629617739085541t_unit) tptp.produc2256096406371053034er_int)
% 5.61/5.91 (declare-fun tptp.produc4022400886476617259it_nat ((-> tptp.code_integer tptp.code_integer) (-> tptp.product_unit tptp.nat) tptp.produc5496629617739085541t_unit) tptp.produc6433947425880249742er_nat)
% 5.61/5.91 (declare-fun tptp.produc3346700480963112818t_unit ((-> tptp.code_integer tptp.code_integer) (-> tptp.product_unit tptp.product_unit) tptp.produc5496629617739085541t_unit) tptp.produc5496629617739085541t_unit)
% 5.61/5.91 (declare-fun tptp.produc8234977478398262212et_nat ((-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit) (-> tptp.set_nat tptp.set_nat) tptp.produc3658429121746597890et_nat) tptp.produc3658429121746597890et_nat)
% 5.61/5.91 (declare-fun tptp.produc5973434381925408567at_int ((-> tptp.heap_e7401611519738050253t_unit tptp.int) (-> tptp.set_nat tptp.int) tptp.produc3658429121746597890et_nat) tptp.product_prod_int_int)
% 5.61/5.91 (declare-fun tptp.produc8285742784527409791at_nat ((-> tptp.heap_e7401611519738050253t_unit tptp.nat) (-> tptp.set_nat tptp.nat) tptp.produc3658429121746597890et_nat) tptp.product_prod_nat_nat)
% 5.61/5.91 (declare-fun tptp.produc3152090231653401565et_nat ((-> tptp.int tptp.heap_e7401611519738050253t_unit) (-> tptp.int tptp.set_nat) tptp.product_prod_int_int) tptp.produc3658429121746597890et_nat)
% 5.61/5.91 (declare-fun tptp.produc6036585564866528938nt_int ((-> tptp.int tptp.int) (-> tptp.int tptp.int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 5.61/5.91 (declare-fun tptp.produc5667422475138734578nt_nat ((-> tptp.int tptp.nat) (-> tptp.int tptp.nat) tptp.product_prod_int_int) tptp.product_prod_nat_nat)
% 5.61/5.91 (declare-fun tptp.produc79747477514316377et_nat ((-> tptp.nat tptp.produc3658429121746597890et_nat Bool) (-> tptp.nat tptp.produc3658429121746597890et_nat) tptp.product_prod_nat_nat) tptp.produc3925858234332021118et_nat)
% 5.61/5.91 (declare-fun tptp.produc2064153442785501et_nat ((-> tptp.nat tptp.heap_e7401611519738050253t_unit) (-> tptp.nat tptp.set_nat) tptp.product_prod_nat_nat) tptp.produc3658429121746597890et_nat)
% 5.61/5.91 (declare-fun tptp.produc7347049785058425330at_int ((-> tptp.nat tptp.int) (-> tptp.nat tptp.int) tptp.product_prod_nat_nat) tptp.product_prod_int_int)
% 5.61/5.91 (declare-fun tptp.produc6977886695330630970at_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 5.61/5.91 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 5.61/5.91 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 5.61/5.91 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 5.61/5.91 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 5.61/5.91 (declare-fun tptp.produc27273713700761075at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 5.61/5.91 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 5.61/5.91 (declare-fun tptp.produc180342877477747464et_nat (tptp.produc2732055786443039994et_nat tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.91 (declare-fun tptp.produc995936583742144908et_nat (tptp.produc3925858234332021118et_nat tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.91 (declare-fun tptp.produc8508995932063986495nteger (tptp.produc8923325533196201883nteger) tptp.code_integer)
% 5.61/5.91 (declare-fun tptp.produc8632663045010267826er_nat (tptp.produc6433947425880249742er_nat) tptp.code_integer)
% 5.61/5.91 (declare-fun tptp.produc1824681642469235216et_nat (tptp.produc3658429121746597890et_nat) tptp.heap_e7401611519738050253t_unit)
% 5.61/5.91 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 5.61/5.91 (declare-fun tptp.produc8897218493789310642nteger (tptp.produc2591615631378489102nteger) tptp.nat)
% 5.61/5.91 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 5.61/5.91 (declare-fun tptp.produc1609452848092598666_nat_o (tptp.produc4962441903510821572_nat_o) tptp.produc3925858234332021118et_nat)
% 5.61/5.91 (declare-fun tptp.produc8046704426453032966_nat_o (tptp.produc6907119039986491712_nat_o) tptp.produc3658429121746597890et_nat)
% 5.61/5.91 (declare-fun tptp.produc6012101397789842562t_unit (tptp.produc7348995623955488188t_unit) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.produc5374455773327741254et_nat (tptp.produc2732055786443039994et_nat) tptp.produc3925858234332021118et_nat)
% 5.61/5.91 (declare-fun tptp.produc4011572625026189258et_nat (tptp.produc3925858234332021118et_nat) tptp.produc3658429121746597890et_nat)
% 5.61/5.91 (declare-fun tptp.produc6174133586879617921nteger (tptp.produc8923325533196201883nteger) tptp.code_integer)
% 5.61/5.91 (declare-fun tptp.produc1517335558169710324er_nat (tptp.produc6433947425880249742er_nat) tptp.nat)
% 5.61/5.91 (declare-fun tptp.produc8586169260539613262et_nat (tptp.produc3658429121746597890et_nat) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 5.61/5.91 (declare-fun tptp.produc1781891006948753140nteger (tptp.produc2591615631378489102nteger) tptp.code_integer)
% 5.61/5.91 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 5.61/5.91 (declare-fun tptp.produc6803565743942592456_nat_o (tptp.produc4962441903510821572_nat_o tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.91 (declare-fun tptp.produc1838968430882301508_nat_o (tptp.produc6907119039986491712_nat_o tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.91 (declare-fun tptp.produc3550216979005444800t_unit (tptp.produc7348995623955488188t_unit) tptp.heap_e7401611519738050253t_unit)
% 5.61/5.91 (declare-fun tptp.produc1151471490888544852et_nat (tptp.produc2732055786443039994et_nat) tptp.produc4962441903510821572_nat_o)
% 5.61/5.91 (declare-fun tptp.produc3251101204053596376et_nat (tptp.produc3925858234332021118et_nat) tptp.produc6907119039986491712_nat_o)
% 5.61/5.91 (declare-fun tptp.produc6300697153377358172et_nat (tptp.produc3658429121746597890et_nat) tptp.produc7348995623955488188t_unit)
% 5.61/5.91 (declare-fun tptp.product_swap_int_int (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 5.61/5.91 (declare-fun tptp.product_swap_nat_nat (tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 5.61/5.91 (declare-fun tptp.produc2580581461503396054_nat_o (tptp.produc4962441903510821572_nat_o) tptp.produc2732055786443039994et_nat)
% 5.61/5.91 (declare-fun tptp.produc1078497009909708626_nat_o (tptp.produc6907119039986491712_nat_o) tptp.produc3925858234332021118et_nat)
% 5.61/5.91 (declare-fun tptp.produc1264744871843189710t_unit (tptp.produc7348995623955488188t_unit) tptp.produc3658429121746597890et_nat)
% 5.61/5.91 (declare-fun tptp.produc5538323210962509403atural ((-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 5.61/5.91 (declare-fun tptp.product_Abs_unit (Bool) tptp.product_unit)
% 5.61/5.91 (declare-fun tptp.product_Rep_unit (tptp.product_unit) Bool)
% 5.61/5.91 (declare-fun tptp.iterat8892046348760725948atural (tptp.code_natural (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) tptp.code_natural tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 5.61/5.91 (declare-fun tptp.log (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 5.61/5.91 (declare-fun tptp.minus_shift (tptp.code_natural tptp.code_natural tptp.code_natural) tptp.code_natural)
% 5.61/5.91 (declare-fun tptp.next (tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 5.61/5.91 (declare-fun tptp.range (tptp.code_natural tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 5.61/5.91 (declare-fun tptp.abs_Rat (tptp.product_prod_int_int) tptp.rat)
% 5.61/5.91 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 5.61/5.91 (declare-fun tptp.rep_Rat (tptp.rat) tptp.product_prod_int_int)
% 5.61/5.91 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 5.61/5.91 (declare-fun tptp.pcr_rat (tptp.product_prod_int_int tptp.rat) Bool)
% 5.61/5.91 (declare-fun tptp.positive (tptp.rat) Bool)
% 5.61/5.91 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 5.61/5.91 (declare-fun tptp.ratrel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 5.61/5.91 (declare-fun tptp.domain4881241903163524940_nat_o (tptp.set_Pr2161125870931222855_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.91 (declare-fun tptp.domain3618434998481624895et_nat (tptp.set_Pr8536935166611901872et_nat) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.91 (declare-fun tptp.domain2358961613337345475et_nat (tptp.set_Pr3286484037609594932et_nat) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.91 (declare-fun tptp.domain_o_o (tptp.set_Product_prod_o_o) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.domain2007548326387822151et_nat (tptp.set_Pr3948176798113811640et_nat) tptp.set_he8644174446132254637t_unit)
% 5.61/5.91 (declare-fun tptp.domain_int_int (tptp.set_Pr958786334691620121nt_int) tptp.set_int)
% 5.61/5.91 (declare-fun tptp.domain_nat_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.domain4292024440186670924t_unit (tptp.set_Pr5094982260447487303t_unit) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.field_81821745747897882_nat_o (tptp.set_Pr2161125870931222855_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.91 (declare-fun tptp.field_o (tptp.set_Product_prod_o_o) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.field_Code_integer (tptp.set_Pr4811707699266497531nteger) tptp.set_Code_integer)
% 5.61/5.91 (declare-fun tptp.field_int (tptp.set_Pr958786334691620121nt_int) tptp.set_int)
% 5.61/5.91 (declare-fun tptp.field_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.field_Product_unit (tptp.set_Pr5094982260447487303t_unit) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.id_Pro6775173067513470761_nat_o () tptp.set_Pr2161125870931222855_nat_o)
% 5.61/5.91 (declare-fun tptp.id_o2 () tptp.set_Product_prod_o_o)
% 5.61/5.91 (declare-fun tptp.id_int () tptp.set_Pr958786334691620121nt_int)
% 5.61/5.91 (declare-fun tptp.id_nat () tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.91 (declare-fun tptp.id_Product_unit () tptp.set_Pr5094982260447487303t_unit)
% 5.61/5.91 (declare-fun tptp.id_on_7438695062414216554_nat_o (tptp.set_Pr4532377907799695533_nat_o) tptp.set_Pr2161125870931222855_nat_o)
% 5.61/5.91 (declare-fun tptp.id_on_o (tptp.set_o) tptp.set_Product_prod_o_o)
% 5.61/5.91 (declare-fun tptp.id_on_int (tptp.set_int) tptp.set_Pr958786334691620121nt_int)
% 5.61/5.91 (declare-fun tptp.id_on_nat (tptp.set_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.91 (declare-fun tptp.id_on_Product_unit (tptp.set_Product_unit) tptp.set_Pr5094982260447487303t_unit)
% 5.61/5.91 (declare-fun tptp.image_2232984160439939859_nat_o (tptp.set_Pr2161125870931222855_nat_o tptp.set_Pr4532377907799695533_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.91 (declare-fun tptp.image_7240710759097644216et_nat (tptp.set_Pr8536935166611901872et_nat tptp.set_Pr4532377907799695533_nat_o) tptp.set_Pr3286484037609594932et_nat)
% 5.61/5.91 (declare-fun tptp.image_1814916760386648892et_nat (tptp.set_Pr3286484037609594932et_nat tptp.set_Pr4532377907799695533_nat_o) tptp.set_Pr3948176798113811640et_nat)
% 5.61/5.91 (declare-fun tptp.image_o_o (tptp.set_Product_prod_o_o tptp.set_o) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.image_o_int (tptp.set_Pr8834758594704517033_o_int tptp.set_o) tptp.set_int)
% 5.61/5.91 (declare-fun tptp.image_o_nat (tptp.set_Pr2101469702781467981_o_nat tptp.set_o) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.image_o_Product_unit (tptp.set_Pr6671815714118170108t_unit tptp.set_o) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.image_4147621952751189391nteger (tptp.set_Pr4811707699266497531nteger tptp.set_Code_integer) tptp.set_Code_integer)
% 5.61/5.91 (declare-fun tptp.image_3942343239045813184et_nat (tptp.set_Pr3948176798113811640et_nat tptp.set_he8644174446132254637t_unit) tptp.set_set_nat)
% 5.61/5.91 (declare-fun tptp.image_int_o (tptp.set_Pr903927857289325719_int_o tptp.set_int) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.image_int_int (tptp.set_Pr958786334691620121nt_int tptp.set_int) tptp.set_int)
% 5.61/5.91 (declare-fun tptp.image_int_nat (tptp.set_Pr3448869479623346877nt_nat tptp.set_int) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.image_1405326909533657676t_unit (tptp.set_Pr5889264611543340172t_unit tptp.set_int) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.image_nat_o (tptp.set_Pr3149072824959771635_nat_o tptp.set_nat) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.image_nat_int (tptp.set_Pr7995236796853374141at_int tptp.set_nat) tptp.set_int)
% 5.61/5.91 (declare-fun tptp.image_nat_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_nat) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.image_4288904962331477416t_unit (tptp.set_Pr4334478416066269672t_unit tptp.set_nat) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.image_Product_unit_o (tptp.set_Pr5464989305201766866unit_o tptp.set_Product_unit) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.image_5655252347010435494it_int (tptp.set_Pr8497134830871917726it_int tptp.set_Product_unit) tptp.set_int)
% 5.61/5.91 (declare-fun tptp.image_5657742817519485770it_nat (tptp.set_Pr1763845938948868674it_nat tptp.set_Product_unit) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.image_8431784415008483091t_unit (tptp.set_Pr5094982260447487303t_unit tptp.set_Product_unit) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.range_5289318983786108341_nat_o (tptp.set_Pr2161125870931222855_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.91 (declare-fun tptp.range_7260058354244137878et_nat (tptp.set_Pr8536935166611901872et_nat) tptp.set_Pr3286484037609594932et_nat)
% 5.61/5.91 (declare-fun tptp.range_3398330936903821850et_nat (tptp.set_Pr3286484037609594932et_nat) tptp.set_Pr3948176798113811640et_nat)
% 5.61/5.91 (declare-fun tptp.range_o_o (tptp.set_Product_prod_o_o) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.range_1907724884897625393nteger (tptp.set_Pr4811707699266497531nteger) tptp.set_Code_integer)
% 5.61/5.91 (declare-fun tptp.range_9132311542094983838et_nat (tptp.set_Pr3948176798113811640et_nat) tptp.set_set_nat)
% 5.61/5.91 (declare-fun tptp.range_int_int (tptp.set_Pr958786334691620121nt_int) tptp.set_int)
% 5.61/5.91 (declare-fun tptp.range_nat_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.range_6617724647562260917t_unit (tptp.set_Pr5094982260447487303t_unit) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.antisy9190549550370998639_nat_o (tptp.set_Pr2161125870931222855_nat_o) Bool)
% 5.61/5.91 (declare-fun tptp.antisym_o (tptp.set_Product_prod_o_o) Bool)
% 5.61/5.91 (declare-fun tptp.antisym_int (tptp.set_Pr958786334691620121nt_int) Bool)
% 5.61/5.91 (declare-fun tptp.antisym_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.61/5.91 (declare-fun tptp.antisym_Product_unit (tptp.set_Pr5094982260447487303t_unit) Bool)
% 5.61/5.91 (declare-fun tptp.conver2764731894203590139_nat_o (tptp.set_Pr2161125870931222855_nat_o) tptp.set_Pr2161125870931222855_nat_o)
% 5.61/5.91 (declare-fun tptp.conver3577387295554834384et_nat (tptp.set_Pr8536935166611901872et_nat) tptp.set_Pr7705059561495379578_nat_o)
% 5.61/5.91 (declare-fun tptp.conver4003969491454187092et_nat (tptp.set_Pr3286484037609594932et_nat) tptp.set_Pr4208978187861016310_nat_o)
% 5.61/5.91 (declare-fun tptp.converse_o_o (tptp.set_Product_prod_o_o) tptp.set_Product_prod_o_o)
% 5.61/5.91 (declare-fun tptp.conver7272282955447398104et_nat (tptp.set_Pr3948176798113811640et_nat) tptp.set_Pr4071100604818519410t_unit)
% 5.61/5.91 (declare-fun tptp.converse_int_int (tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 5.61/5.91 (declare-fun tptp.converse_nat_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.91 (declare-fun tptp.conver5006497266169685586_nat_o (tptp.set_Pr7705059561495379578_nat_o) tptp.set_Pr8536935166611901872et_nat)
% 5.61/5.91 (declare-fun tptp.conver1831365297310299342_nat_o (tptp.set_Pr4208978187861016310_nat_o) tptp.set_Pr3286484037609594932et_nat)
% 5.61/5.91 (declare-fun tptp.conver2495244158383847931t_unit (tptp.set_Pr5094982260447487303t_unit) tptp.set_Pr5094982260447487303t_unit)
% 5.61/5.91 (declare-fun tptp.conver2236330673913229642t_unit (tptp.set_Pr4071100604818519410t_unit) tptp.set_Pr3948176798113811640et_nat)
% 5.61/5.91 (declare-fun tptp.inv_image_o_o (tptp.set_Product_prod_o_o (-> Bool Bool)) tptp.set_Product_prod_o_o)
% 5.61/5.91 (declare-fun tptp.inv_image_o_nat (tptp.set_Product_prod_o_o (-> tptp.nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.91 (declare-fun tptp.inv_im4602722609573551687t_unit (tptp.set_Product_prod_o_o (-> tptp.product_unit Bool)) tptp.set_Pr5094982260447487303t_unit)
% 5.61/5.91 (declare-fun tptp.inv_image_int_o (tptp.set_Pr958786334691620121nt_int (-> Bool tptp.int)) tptp.set_Product_prod_o_o)
% 5.61/5.91 (declare-fun tptp.inv_image_int_int (tptp.set_Pr958786334691620121nt_int (-> tptp.int tptp.int)) tptp.set_Pr958786334691620121nt_int)
% 5.61/5.91 (declare-fun tptp.inv_image_int_nat (tptp.set_Pr958786334691620121nt_int (-> tptp.nat tptp.int)) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.91 (declare-fun tptp.inv_im4740476784543923469t_unit (tptp.set_Pr958786334691620121nt_int (-> tptp.product_unit tptp.int)) tptp.set_Pr5094982260447487303t_unit)
% 5.61/5.91 (declare-fun tptp.inv_image_nat_o (tptp.set_Pr1261947904930325089at_nat (-> Bool tptp.nat)) tptp.set_Product_prod_o_o)
% 5.61/5.91 (declare-fun tptp.inv_image_nat_int (tptp.set_Pr1261947904930325089at_nat (-> tptp.int tptp.nat)) tptp.set_Pr958786334691620121nt_int)
% 5.61/5.91 (declare-fun tptp.inv_image_nat_nat (tptp.set_Pr1261947904930325089at_nat (-> tptp.nat tptp.nat)) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.91 (declare-fun tptp.inv_im7624054837341743209t_unit (tptp.set_Pr1261947904930325089at_nat (-> tptp.product_unit tptp.nat)) tptp.set_Pr5094982260447487303t_unit)
% 5.61/5.91 (declare-fun tptp.inv_im9188693106839688349unit_o (tptp.set_Pr5094982260447487303t_unit (-> Bool tptp.product_unit)) tptp.set_Product_prod_o_o)
% 5.61/5.91 (declare-fun tptp.inv_im8992892692529751563it_nat (tptp.set_Pr5094982260447487303t_unit (-> tptp.nat tptp.product_unit)) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.91 (declare-fun tptp.inv_im8770536620514187154t_unit (tptp.set_Pr5094982260447487303t_unit (-> tptp.product_unit tptp.product_unit)) tptp.set_Pr5094982260447487303t_unit)
% 5.61/5.91 (declare-fun tptp.refl_o1075864025857821388_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr2161125870931222855_nat_o) Bool)
% 5.61/5.91 (declare-fun tptp.refl_on_o (tptp.set_o tptp.set_Product_prod_o_o) Bool)
% 5.61/5.91 (declare-fun tptp.refl_on_int (tptp.set_int tptp.set_Pr958786334691620121nt_int) Bool)
% 5.61/5.91 (declare-fun tptp.refl_on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.61/5.91 (declare-fun tptp.refl_on_Product_unit (tptp.set_Product_unit tptp.set_Pr5094982260447487303t_unit) Bool)
% 5.61/5.91 (declare-fun tptp.relcom6251035627269349452_nat_o (tptp.set_Pr2161125870931222855_nat_o tptp.set_Pr2161125870931222855_nat_o) tptp.set_Pr2161125870931222855_nat_o)
% 5.61/5.91 (declare-fun tptp.relcom2608444778321954367et_nat (tptp.set_Pr2161125870931222855_nat_o tptp.set_Pr8536935166611901872et_nat) tptp.set_Pr8536935166611901872et_nat)
% 5.61/5.91 (declare-fun tptp.relcom6619595054755144899et_nat (tptp.set_Pr2161125870931222855_nat_o tptp.set_Pr3286484037609594932et_nat) tptp.set_Pr3286484037609594932et_nat)
% 5.61/5.91 (declare-fun tptp.relcom8303140135939483018et_nat (tptp.set_Pr8536935166611901872et_nat tptp.set_Pr7928877670098842301et_nat) tptp.set_Pr8536935166611901872et_nat)
% 5.61/5.91 (declare-fun tptp.relcom430014394250001422et_nat (tptp.set_Pr8536935166611901872et_nat tptp.set_Pr3721596426557623617et_nat) tptp.set_Pr3286484037609594932et_nat)
% 5.61/5.91 (declare-fun tptp.relcom8031709186682293262et_nat (tptp.set_Pr3286484037609594932et_nat tptp.set_Pr8807100098903490369et_nat) tptp.set_Pr8536935166611901872et_nat)
% 5.61/5.91 (declare-fun tptp.relcom5975814107203797650et_nat (tptp.set_Pr3286484037609594932et_nat tptp.set_Pr719794911490849221et_nat) tptp.set_Pr3286484037609594932et_nat)
% 5.61/5.91 (declare-fun tptp.relcomp_o_o_o (tptp.set_Product_prod_o_o tptp.set_Product_prod_o_o) tptp.set_Product_prod_o_o)
% 5.61/5.91 (declare-fun tptp.relcom4930750947919833671et_nat (tptp.set_Pr1776176089890104647t_unit tptp.set_Pr3948176798113811640et_nat) tptp.set_Pr3948176798113811640et_nat)
% 5.61/5.91 (declare-fun tptp.relcom8881708762719574682et_nat (tptp.set_Pr3948176798113811640et_nat tptp.set_Pr5488025237498180813et_nat) tptp.set_Pr3948176798113811640et_nat)
% 5.61/5.91 (declare-fun tptp.relcomp_int_int_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 5.61/5.91 (declare-fun tptp.relcomp_nat_nat_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.91 (declare-fun tptp.relcom848357998638694028t_unit (tptp.set_Pr5094982260447487303t_unit tptp.set_Pr5094982260447487303t_unit) tptp.set_Pr5094982260447487303t_unit)
% 5.61/5.91 (declare-fun tptp.relcom7236094467932586796_nat_o (tptp.set_Pr3813038829465207111_nat_o tptp.set_Pr3813038829465207111_nat_o) tptp.set_Pr3813038829465207111_nat_o)
% 5.61/5.91 (declare-fun tptp.relcom7534720040753365047_set_o (tptp.set_Pr4577759397028426247_set_o tptp.set_Pr4577759397028426247_set_o) tptp.set_Pr4577759397028426247_set_o)
% 5.61/5.91 (declare-fun tptp.relcom4034950705519254697et_int (tptp.set_Pr2522554150109002629et_int tptp.set_Pr2522554150109002629et_int) tptp.set_Pr2522554150109002629et_int)
% 5.61/5.91 (declare-fun tptp.relcom236561585145426837et_nat (tptp.set_Pr5488025237498180813et_nat tptp.set_Pr5488025237498180813et_nat) tptp.set_Pr5488025237498180813et_nat)
% 5.61/5.91 (declare-fun tptp.relcom7108816970757792620t_unit (tptp.set_Pr3980508049012409671t_unit tptp.set_Pr3980508049012409671t_unit) tptp.set_Pr3980508049012409671t_unit)
% 5.61/5.91 (declare-fun tptp.single261872189793494280et_nat (tptp.set_Pr8536935166611901872et_nat) Bool)
% 5.61/5.91 (declare-fun tptp.single7715245794981374860et_nat (tptp.set_Pr3286484037609594932et_nat) Bool)
% 5.61/5.91 (declare-fun tptp.single6620584844202787856et_nat (tptp.set_Pr3948176798113811640et_nat) Bool)
% 5.61/5.91 (declare-fun tptp.single6503947681363884253nt_int (tptp.set_Pr958786334691620121nt_int) Bool)
% 5.61/5.91 (declare-fun tptp.single5507084439971879973at_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.61/5.91 (declare-fun tptp.total_7429123086324524369_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr2161125870931222855_nat_o) Bool)
% 5.61/5.91 (declare-fun tptp.total_on_o (tptp.set_o tptp.set_Product_prod_o_o) Bool)
% 5.61/5.91 (declare-fun tptp.total_on_int (tptp.set_int tptp.set_Pr958786334691620121nt_int) Bool)
% 5.61/5.91 (declare-fun tptp.total_on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.61/5.91 (declare-fun tptp.total_5665700600833547665t_unit (tptp.set_Product_unit tptp.set_Pr5094982260447487303t_unit) Bool)
% 5.61/5.91 (declare-fun tptp.trans_int (tptp.set_Pr958786334691620121nt_int) Bool)
% 5.61/5.91 (declare-fun tptp.trans_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.61/5.91 (declare-fun tptp.algebr932160517623751201me_int (tptp.int tptp.int) Bool)
% 5.61/5.91 (declare-fun tptp.algebr934650988132801477me_nat (tptp.nat tptp.nat) Bool)
% 5.61/5.91 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 5.61/5.91 (declare-fun tptp.divide5121882707175180666atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 5.61/5.91 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 5.61/5.91 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 5.61/5.91 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 5.61/5.91 (declare-fun tptp.dvd_dvd_assn (tptp.assn tptp.assn) Bool)
% 5.61/5.91 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 5.61/5.91 (declare-fun tptp.dvd_dvd_Code_natural (tptp.code_natural tptp.code_natural) Bool)
% 5.61/5.91 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 5.61/5.91 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 5.61/5.91 (declare-fun tptp.dvd_dvd_rat (tptp.rat tptp.rat) Bool)
% 5.61/5.91 (declare-fun tptp.modulo8411746178871703098atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 5.61/5.91 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 5.61/5.91 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 5.61/5.91 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 5.61/5.91 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 5.61/5.91 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 5.61/5.91 (declare-fun tptp.collec939566748876313656_nat_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.91 (declare-fun tptp.collect_o ((-> Bool Bool)) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 5.61/5.91 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.collect_Product_unit ((-> tptp.product_unit Bool)) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.pow_Pr7829143134171777386_nat_o (tptp.set_Pr4532377907799695533_nat_o) tptp.set_se1353816476878259085_nat_o)
% 5.61/5.91 (declare-fun tptp.pow_o (tptp.set_o) tptp.set_set_o)
% 5.61/5.91 (declare-fun tptp.pow_Code_integer (tptp.set_Code_integer) tptp.set_set_Code_integer)
% 5.61/5.91 (declare-fun tptp.pow_int (tptp.set_int) tptp.set_set_int)
% 5.61/5.91 (declare-fun tptp.pow_nat (tptp.set_nat) tptp.set_set_nat)
% 5.61/5.91 (declare-fun tptp.pow_Product_unit (tptp.set_Product_unit) tptp.set_set_Product_unit)
% 5.61/5.91 (declare-fun tptp.pow_set_nat (tptp.set_set_nat) tptp.set_set_set_nat)
% 5.61/5.91 (declare-fun tptp.disjnt7869448817988085652_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr4532377907799695533_nat_o) Bool)
% 5.61/5.91 (declare-fun tptp.disjnt_o (tptp.set_o tptp.set_o) Bool)
% 5.61/5.91 (declare-fun tptp.disjnt_int (tptp.set_int tptp.set_int) Bool)
% 5.61/5.91 (declare-fun tptp.disjnt_nat (tptp.set_nat tptp.set_nat) Bool)
% 5.61/5.91 (declare-fun tptp.disjnt4476176636800211563_nat_o (tptp.set_Pr5623950326363488168_nat_o tptp.set_Pr5623950326363488168_nat_o) Bool)
% 5.61/5.91 (declare-fun tptp.disjnt5652777605541633334_nat_o (tptp.set_Pr3149072824959771635_nat_o tptp.set_Pr3149072824959771635_nat_o) Bool)
% 5.61/5.91 (declare-fun tptp.disjnt7759068009871657124at_int (tptp.set_Pr7995236796853374141at_int tptp.set_Pr7995236796853374141at_int) Bool)
% 5.61/5.91 (declare-fun tptp.disjnt2713546992526078024at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.61/5.91 (declare-fun tptp.disjnt595863415355979947t_unit (tptp.set_Pr4334478416066269672t_unit tptp.set_Pr4334478416066269672t_unit) Bool)
% 5.61/5.91 (declare-fun tptp.disjnt_Product_unit (tptp.set_Product_unit tptp.set_Product_unit) Bool)
% 5.61/5.91 (declare-fun tptp.image_8639947063239330806_nat_o ((-> (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool) tptp.set_Pr4532377907799695533_nat_o) tptp.set_Pr6409761941060870310at_o_o) tptp.set_se1353816476878259085_nat_o)
% 5.61/5.91 (declare-fun tptp.image_o_o_set_o ((-> (-> Bool Bool) tptp.set_o) tptp.set_o_o) tptp.set_set_o)
% 5.61/5.91 (declare-fun tptp.image_int_o_set_int ((-> (-> tptp.int Bool) tptp.set_int) tptp.set_int_o) tptp.set_set_int)
% 5.61/5.91 (declare-fun tptp.image_nat_o_set_nat ((-> (-> tptp.nat Bool) tptp.set_nat) tptp.set_nat_o) tptp.set_set_nat)
% 5.61/5.91 (declare-fun tptp.image_3399141053782081349_nat_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool) tptp.set_Pr4532377907799695533_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.91 (declare-fun tptp.image_6451031022632655280o_assn ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.assn) tptp.set_Pr4532377907799695533_nat_o) tptp.set_assn)
% 5.61/5.91 (declare-fun tptp.image_2174381888560928856_o_nat ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.nat) tptp.set_Pr4532377907799695533_nat_o) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.image_8451000719036923781t_unit ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.product_unit) tptp.set_Pr4532377907799695533_nat_o) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.image_8657708916238040603nteger ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.set_Code_integer) tptp.set_Pr4532377907799695533_nat_o) tptp.set_set_Code_integer)
% 5.61/5.91 (declare-fun tptp.image_6888641473154130958et_nat ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.set_nat) tptp.set_Pr4532377907799695533_nat_o) tptp.set_set_nat)
% 5.61/5.91 (declare-fun tptp.image_5138372075374782070t_unit ((-> (-> tptp.product_unit Bool) tptp.set_Product_unit) tptp.set_Product_unit_o) tptp.set_set_Product_unit)
% 5.61/5.91 (declare-fun tptp.image_o_o2 ((-> Bool Bool) tptp.set_o) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.image_o_Code_integer ((-> Bool tptp.code_integer) tptp.set_o) tptp.set_Code_integer)
% 5.61/5.91 (declare-fun tptp.image_o_filter_nat ((-> Bool tptp.filter_nat) tptp.set_o) tptp.set_filter_nat)
% 5.61/5.91 (declare-fun tptp.image_o_int2 ((-> Bool tptp.int) tptp.set_o) tptp.set_int)
% 5.61/5.91 (declare-fun tptp.image_o_nat2 ((-> Bool tptp.nat) tptp.set_o) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.image_8407096251609565691nteger ((-> Bool tptp.produc2591615631378489102nteger) tptp.set_o) tptp.set_Pr2406931829603198446nteger)
% 5.61/5.91 (declare-fun tptp.image_3855930084881510382at_nat ((-> Bool tptp.product_prod_nat_nat) tptp.set_o) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.91 (declare-fun tptp.image_o_Product_unit2 ((-> Bool tptp.product_unit) tptp.set_o) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.image_o_set_o ((-> Bool tptp.set_o) tptp.set_o) tptp.set_set_o)
% 5.61/5.91 (declare-fun tptp.image_6491638074533506790nteger ((-> Bool tptp.set_Code_integer) tptp.set_o) tptp.set_set_Code_integer)
% 5.61/5.91 (declare-fun tptp.image_o_set_int ((-> Bool tptp.set_int) tptp.set_o) tptp.set_set_int)
% 5.61/5.91 (declare-fun tptp.image_o_set_nat ((-> Bool tptp.set_nat) tptp.set_o) tptp.set_set_nat)
% 5.61/5.91 (declare-fun tptp.image_663195431845683034t_unit ((-> Bool tptp.set_Product_unit) tptp.set_o) tptp.set_set_Product_unit)
% 5.61/5.91 (declare-fun tptp.image_5465535159827709278_nat_o ((-> tptp.assn tptp.produc3658429121746597890et_nat Bool) tptp.set_assn) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.91 (declare-fun tptp.image_assn_assn ((-> tptp.assn tptp.assn) tptp.set_assn) tptp.set_assn)
% 5.61/5.91 (declare-fun tptp.image_2177946750938214461nteger ((-> tptp.code_integer tptp.code_integer tptp.code_integer) tptp.set_Code_integer) tptp.set_Co726186806682698383nteger)
% 5.61/5.91 (declare-fun tptp.image_Code_integer_o ((-> tptp.code_integer Bool) tptp.set_Code_integer) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.image_4470545334726330049nteger ((-> tptp.code_integer tptp.code_integer) tptp.set_Code_integer) tptp.set_Code_integer)
% 5.61/5.91 (declare-fun tptp.image_948535463418740880er_int ((-> tptp.code_integer tptp.int) tptp.set_Code_integer) tptp.set_int)
% 5.61/5.91 (declare-fun tptp.image_951025933927791156er_nat ((-> tptp.code_integer tptp.nat) tptp.set_Code_integer) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.image_8049062792287394871nteger ((-> tptp.code_integer tptp.produc8923325533196201883nteger) tptp.set_Code_integer) tptp.set_Pr4811707699266497531nteger)
% 5.61/5.91 (declare-fun tptp.image_7250923904792228394er_nat ((-> tptp.code_integer tptp.produc6433947425880249742er_nat) tptp.set_Code_integer) tptp.set_Pr8986988648414616686er_nat)
% 5.61/5.91 (declare-fun tptp.image_3408592110290467754nteger ((-> tptp.code_integer tptp.produc2591615631378489102nteger) tptp.set_Code_integer) tptp.set_Pr2406931829603198446nteger)
% 5.61/5.91 (declare-fun tptp.image_7182656606676592809t_unit ((-> tptp.code_integer tptp.product_unit) tptp.set_Code_integer) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.image_1867029960091478804_set_o ((-> tptp.code_integer tptp.set_o) tptp.set_Code_integer) tptp.set_set_o)
% 5.61/5.91 (declare-fun tptp.image_4651426196962995782et_int ((-> tptp.code_integer tptp.set_int) tptp.set_Code_integer) tptp.set_set_int)
% 5.61/5.91 (declare-fun tptp.image_8829277216472192490et_nat ((-> tptp.code_integer tptp.set_nat) tptp.set_Code_integer) tptp.set_set_nat)
% 5.61/5.91 (declare-fun tptp.image_5870443399019143561t_unit ((-> tptp.code_integer tptp.set_Product_unit) tptp.set_Code_integer) tptp.set_set_Product_unit)
% 5.61/5.91 (declare-fun tptp.image_6215854944615398399al_nat ((-> tptp.code_natural tptp.nat) tptp.set_Code_natural) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.image_int_o2 ((-> tptp.int Bool) tptp.set_int) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.image_1587234942943678608nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.set_Code_integer)
% 5.61/5.91 (declare-fun tptp.image_int_filter_nat ((-> tptp.int tptp.filter_nat) tptp.set_int) tptp.set_filter_nat)
% 5.61/5.91 (declare-fun tptp.image_int_int2 ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 5.61/5.91 (declare-fun tptp.image_int_nat2 ((-> tptp.int tptp.nat) tptp.set_int) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.image_5846526143423701914t_unit ((-> tptp.int tptp.product_unit) tptp.set_int) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.image_int_set_o ((-> tptp.int tptp.set_o) tptp.set_int) tptp.set_set_o)
% 5.61/5.91 (declare-fun tptp.image_75573793354812870nteger ((-> tptp.int tptp.set_Code_integer) tptp.set_int) tptp.set_set_Code_integer)
% 5.61/5.91 (declare-fun tptp.image_int_set_nat ((-> tptp.int tptp.set_nat) tptp.set_int) tptp.set_set_nat)
% 5.61/5.91 (declare-fun tptp.image_8658272795163236474t_unit ((-> tptp.int tptp.set_Product_unit) tptp.set_int) tptp.set_set_Product_unit)
% 5.61/5.91 (declare-fun tptp.image_4682239675366380726_nat_o ((-> tptp.nat tptp.produc3658429121746597890et_nat Bool) tptp.set_nat) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.91 (declare-fun tptp.image_nat_o2 ((-> tptp.nat Bool) tptp.set_nat) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.image_1215581382706833972nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.set_Code_integer)
% 5.61/5.91 (declare-fun tptp.image_39176534463551487atural ((-> tptp.nat tptp.code_natural) tptp.set_nat) tptp.set_Code_natural)
% 5.61/5.91 (declare-fun tptp.image_nat_filter_nat ((-> tptp.nat tptp.filter_nat) tptp.set_nat) tptp.set_filter_nat)
% 5.61/5.91 (declare-fun tptp.image_nat_int2 ((-> tptp.nat tptp.int) tptp.set_nat) tptp.set_int)
% 5.61/5.91 (declare-fun tptp.image_nat_nat2 ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.image_8730104196221521654t_unit ((-> tptp.nat tptp.product_unit) tptp.set_nat) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.image_nat_set_o ((-> tptp.nat tptp.set_o) tptp.set_nat) tptp.set_set_o)
% 5.61/5.91 (declare-fun tptp.image_2385391725447763818nteger ((-> tptp.nat tptp.set_Code_integer) tptp.set_nat) tptp.set_set_Code_integer)
% 5.61/5.91 (declare-fun tptp.image_nat_set_int ((-> tptp.nat tptp.set_int) tptp.set_nat) tptp.set_set_int)
% 5.61/5.91 (declare-fun tptp.image_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_nat) tptp.set_set_nat)
% 5.61/5.91 (declare-fun tptp.image_7178329752028323786at_nat ((-> tptp.nat tptp.set_Pr1261947904930325089at_nat) tptp.set_nat) tptp.set_se7855581050983116737at_nat)
% 5.61/5.91 (declare-fun tptp.image_4824033694279209942t_unit ((-> tptp.nat tptp.set_Product_unit) tptp.set_nat) tptp.set_set_Product_unit)
% 5.61/5.91 (declare-fun tptp.image_2517677226577294348_nat_o ((-> tptp.produc2732055786443039994et_nat tptp.produc3658429121746597890et_nat Bool) tptp.set_Pr8536935166611901872et_nat) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.91 (declare-fun tptp.image_4557310310409863807et_nat ((-> tptp.produc2732055786443039994et_nat tptp.produc3925858234332021118et_nat) tptp.set_Pr8536935166611901872et_nat) tptp.set_Pr3286484037609594932et_nat)
% 5.61/5.91 (declare-fun tptp.image_4071802983491761093_nat_o ((-> tptp.produc2732055786443039994et_nat tptp.produc4962441903510821572_nat_o) tptp.set_Pr8536935166611901872et_nat) tptp.set_Pr7705059561495379578_nat_o)
% 5.61/5.91 (declare-fun tptp.image_6802380912191114376_nat_o ((-> tptp.produc3925858234332021118et_nat tptp.produc3658429121746597890et_nat Bool) tptp.set_Pr3286484037609594932et_nat) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.91 (declare-fun tptp.image_4390311411407041927et_nat ((-> tptp.produc3925858234332021118et_nat tptp.produc3658429121746597890et_nat) tptp.set_Pr3286484037609594932et_nat) tptp.set_Pr3948176798113811640et_nat)
% 5.61/5.91 (declare-fun tptp.image_7073998564157519676at_nat ((-> tptp.produc3925858234332021118et_nat tptp.product_prod_nat_nat) tptp.set_Pr3286484037609594932et_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.91 (declare-fun tptp.image_6229134628169569989_nat_o ((-> tptp.produc3925858234332021118et_nat tptp.produc6907119039986491712_nat_o) tptp.set_Pr3286484037609594932et_nat) tptp.set_Pr4208978187861016310_nat_o)
% 5.61/5.91 (declare-fun tptp.image_227735840630799463eger_o ((-> tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.set_Pr448751882837621926eger_o) tptp.set_Pr448751882837621926eger_o)
% 5.61/5.91 (declare-fun tptp.image_6298138160576288691er_int ((-> tptp.produc6271795597528267376eger_o tptp.produc2256096406371053034er_int) tptp.set_Pr448751882837621926eger_o) tptp.set_Pr6496905503482889930er_int)
% 5.61/5.91 (declare-fun tptp.image_1252617143230709591er_nat ((-> tptp.produc6271795597528267376eger_o tptp.produc6433947425880249742er_nat) tptp.set_Pr448751882837621926eger_o) tptp.set_Pr8986988648414616686er_nat)
% 5.61/5.91 (declare-fun tptp.image_2425804817718344284t_unit ((-> tptp.produc6271795597528267376eger_o tptp.produc5496629617739085541t_unit) tptp.set_Pr448751882837621926eger_o) tptp.set_Pr4580871404036792859t_unit)
% 5.61/5.91 (declare-fun tptp.image_7082141833288935621nteger ((-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.set_Pr4811707699266497531nteger) tptp.set_Pr4811707699266497531nteger)
% 5.61/5.91 (declare-fun tptp.image_4921214744877245202nteger ((-> tptp.produc6433947425880249742er_nat tptp.produc8923325533196201883nteger) tptp.set_Pr8986988648414616686er_nat) tptp.set_Pr4811707699266497531nteger)
% 5.61/5.91 (declare-fun tptp.image_7060974388358999388eger_o ((-> tptp.produc5496629617739085541t_unit tptp.produc6271795597528267376eger_o) tptp.set_Pr4580871404036792859t_unit) tptp.set_Pr448751882837621926eger_o)
% 5.61/5.91 (declare-fun tptp.image_4058522669889801726er_int ((-> tptp.produc5496629617739085541t_unit tptp.produc2256096406371053034er_int) tptp.set_Pr4580871404036792859t_unit) tptp.set_Pr6496905503482889930er_int)
% 5.61/5.91 (declare-fun tptp.image_8236373689398998434er_nat ((-> tptp.produc5496629617739085541t_unit tptp.produc6433947425880249742er_nat) tptp.set_Pr4580871404036792859t_unit) tptp.set_Pr8986988648414616686er_nat)
% 5.61/5.91 (declare-fun tptp.image_3456600171786721233t_unit ((-> tptp.produc5496629617739085541t_unit tptp.produc5496629617739085541t_unit) tptp.set_Pr4580871404036792859t_unit) tptp.set_Pr4580871404036792859t_unit)
% 5.61/5.91 (declare-fun tptp.image_6824039242672219652t_unit ((-> tptp.produc3658429121746597890et_nat tptp.heap_e7401611519738050253t_unit) tptp.set_Pr3948176798113811640et_nat) tptp.set_he8644174446132254637t_unit)
% 5.61/5.91 (declare-fun tptp.image_7426123528223433739et_nat ((-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat) tptp.set_Pr3948176798113811640et_nat) tptp.set_Pr3948176798113811640et_nat)
% 5.61/5.91 (declare-fun tptp.image_4579277974391593584nt_int ((-> tptp.produc3658429121746597890et_nat tptp.product_prod_int_int) tptp.set_Pr3948176798113811640et_nat) tptp.set_Pr958786334691620121nt_int)
% 5.61/5.91 (declare-fun tptp.image_7757775281999735736at_nat ((-> tptp.produc3658429121746597890et_nat tptp.product_prod_nat_nat) tptp.set_Pr3948176798113811640et_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.91 (declare-fun tptp.image_1893317993577548229t_unit ((-> tptp.produc3658429121746597890et_nat tptp.produc7348995623955488188t_unit) tptp.set_Pr3948176798113811640et_nat) tptp.set_Pr4071100604818519410t_unit)
% 5.61/5.91 (declare-fun tptp.image_6088997261112373647et_nat ((-> tptp.produc3658429121746597890et_nat tptp.set_nat) tptp.set_Pr3948176798113811640et_nat) tptp.set_set_nat)
% 5.61/5.91 (declare-fun tptp.image_5042161079198086560nt_int ((-> tptp.product_prod_int_int tptp.int) tptp.set_Pr958786334691620121nt_int) tptp.set_int)
% 5.61/5.91 (declare-fun tptp.image_2127501072796355446et_nat ((-> tptp.product_prod_int_int tptp.produc3658429121746597890et_nat) tptp.set_Pr958786334691620121nt_int) tptp.set_Pr3948176798113811640et_nat)
% 5.61/5.91 (declare-fun tptp.image_2653370878348428101nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int) tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 5.61/5.91 (declare-fun tptp.image_5831868185956570253at_nat ((-> tptp.product_prod_int_int tptp.product_prod_nat_nat) tptp.set_Pr958786334691620121nt_int) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.91 (declare-fun tptp.image_2486076414777270412at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.image_5744643625575355962et_nat ((-> tptp.product_prod_nat_nat tptp.produc3925858234332021118et_nat) tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr3286484037609594932et_nat)
% 5.61/5.91 (declare-fun tptp.image_9068448769188195518et_nat ((-> tptp.product_prod_nat_nat tptp.produc3658429121746597890et_nat) tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr3948176798113811640et_nat)
% 5.61/5.91 (declare-fun tptp.image_1990417195239315453nt_int ((-> tptp.product_prod_nat_nat tptp.product_prod_int_int) tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr958786334691620121nt_int)
% 5.61/5.91 (declare-fun tptp.image_5168914502847457605at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.91 (declare-fun tptp.image_7255662321850427333et_nat ((-> tptp.produc4962441903510821572_nat_o tptp.produc2732055786443039994et_nat) tptp.set_Pr7705059561495379578_nat_o) tptp.set_Pr8536935166611901872et_nat)
% 5.61/5.91 (declare-fun tptp.image_4501728140019976901et_nat ((-> tptp.produc6907119039986491712_nat_o tptp.produc3925858234332021118et_nat) tptp.set_Pr4208978187861016310_nat_o) tptp.set_Pr3286484037609594932et_nat)
% 5.61/5.91 (declare-fun tptp.image_5838825082199883205et_nat ((-> tptp.produc7348995623955488188t_unit tptp.produc3658429121746597890et_nat) tptp.set_Pr4071100604818519410t_unit) tptp.set_Pr3948176798113811640et_nat)
% 5.61/5.91 (declare-fun tptp.image_Product_unit_o2 ((-> tptp.product_unit Bool) tptp.set_Product_unit) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.image_3815118110082124069nteger ((-> tptp.product_unit tptp.code_integer) tptp.set_Product_unit) tptp.set_Code_integer)
% 5.61/5.91 (declare-fun tptp.image_1853478764106424488er_nat ((-> tptp.product_unit tptp.filter_nat) tptp.set_Product_unit) tptp.set_filter_nat)
% 5.61/5.91 (declare-fun tptp.image_873079544045703924it_int ((-> tptp.product_unit tptp.int) tptp.set_Product_unit) tptp.set_int)
% 5.61/5.91 (declare-fun tptp.image_875570014554754200it_nat ((-> tptp.product_unit tptp.nat) tptp.set_Product_unit) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.image_8089323762101378259nteger ((-> tptp.product_unit tptp.produc8923325533196201883nteger) tptp.set_Product_unit) tptp.set_Pr4811707699266497531nteger)
% 5.61/5.91 (declare-fun tptp.image_8789315437038609094er_nat ((-> tptp.product_unit tptp.produc6433947425880249742er_nat) tptp.set_Product_unit) tptp.set_Pr8986988648414616686er_nat)
% 5.61/5.91 (declare-fun tptp.image_4103462098156874993nt_int ((-> tptp.product_unit tptp.product_prod_int_int) tptp.set_Product_unit) tptp.set_Pr958786334691620121nt_int)
% 5.61/5.91 (declare-fun tptp.image_4946983642536848454nteger ((-> tptp.product_unit tptp.produc2591615631378489102nteger) tptp.set_Product_unit) tptp.set_Pr2406931829603198446nteger)
% 5.61/5.91 (declare-fun tptp.image_7281959405765017145at_nat ((-> tptp.product_unit tptp.product_prod_nat_nat) tptp.set_Product_unit) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.91 (declare-fun tptp.image_405062704495631173t_unit ((-> tptp.product_unit tptp.product_unit) tptp.set_Product_unit) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.image_6930536745178679216_set_o ((-> tptp.product_unit tptp.set_o) tptp.set_Product_unit) tptp.set_set_o)
% 5.61/5.91 (declare-fun tptp.image_4571654851662262875nteger ((-> tptp.product_unit tptp.set_Code_integer) tptp.set_Product_unit) tptp.set_set_Code_integer)
% 5.61/5.91 (declare-fun tptp.image_3995998972318789802et_int ((-> tptp.product_unit tptp.set_int) tptp.set_Product_unit) tptp.set_set_int)
% 5.61/5.91 (declare-fun tptp.image_8173849991827986510et_nat ((-> tptp.product_unit tptp.set_nat) tptp.set_Product_unit) tptp.set_set_nat)
% 5.61/5.91 (declare-fun tptp.image_7778121751606633509t_unit ((-> tptp.product_unit tptp.set_Product_unit) tptp.set_Product_unit) tptp.set_set_Product_unit)
% 5.61/5.91 (declare-fun tptp.image_rat_rat ((-> tptp.rat tptp.rat) tptp.set_rat) tptp.set_rat)
% 5.61/5.91 (declare-fun tptp.image_8925030434418351941_nat_o ((-> tptp.set_Pr4532377907799695533_nat_o tptp.set_Pr4532377907799695533_nat_o) tptp.set_se1353816476878259085_nat_o) tptp.set_se1353816476878259085_nat_o)
% 5.61/5.91 (declare-fun tptp.image_set_o_set_o ((-> tptp.set_o tptp.set_o) tptp.set_set_o) tptp.set_set_o)
% 5.61/5.91 (declare-fun tptp.image_6270750266955655469nteger ((-> tptp.set_Code_integer tptp.set_Code_integer) tptp.set_set_Code_integer) tptp.set_set_Code_integer)
% 5.61/5.91 (declare-fun tptp.image_524474410958335435et_int ((-> tptp.set_int tptp.set_int) tptp.set_set_int) tptp.set_set_int)
% 5.61/5.91 (declare-fun tptp.image_set_nat_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.image_6916300684244607776nteger ((-> tptp.set_nat tptp.set_Code_integer) tptp.set_set_nat) tptp.set_set_Code_integer)
% 5.61/5.91 (declare-fun tptp.image_7916887816326733075et_nat ((-> tptp.set_nat tptp.set_nat) tptp.set_set_nat) tptp.set_set_nat)
% 5.61/5.91 (declare-fun tptp.image_6725021117256019401et_nat ((-> tptp.set_nat tptp.set_set_nat) tptp.set_set_nat) tptp.set_set_set_nat)
% 5.61/5.91 (declare-fun tptp.image_4019945301284682565t_unit ((-> tptp.set_Product_unit tptp.set_Product_unit) tptp.set_set_Product_unit) tptp.set_set_Product_unit)
% 5.61/5.91 (declare-fun tptp.insert5175938949040314269_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) tptp.set_Pr4532377907799695533_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.91 (declare-fun tptp.insert_o (Bool tptp.set_o) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.insert_assn (tptp.assn tptp.set_assn) tptp.set_assn)
% 5.61/5.91 (declare-fun tptp.insert_Code_integer (tptp.code_integer tptp.set_Code_integer) tptp.set_Code_integer)
% 5.61/5.91 (declare-fun tptp.insert8563697753282147485t_unit (tptp.heap_e7401611519738050253t_unit tptp.set_he8644174446132254637t_unit) tptp.set_he8644174446132254637t_unit)
% 5.61/5.91 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 5.61/5.91 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.insert5309882203591314743_nat_o (tptp.produc4928098042776334183_nat_o tptp.set_Pr2161125870931222855_nat_o) tptp.set_Pr2161125870931222855_nat_o)
% 5.61/5.91 (declare-fun tptp.insert8297122186708525866et_nat (tptp.produc2732055786443039994et_nat tptp.set_Pr8536935166611901872et_nat) tptp.set_Pr8536935166611901872et_nat)
% 5.61/5.91 (declare-fun tptp.insert3111075074545270702et_nat (tptp.produc3925858234332021118et_nat tptp.set_Pr3286484037609594932et_nat) tptp.set_Pr3286484037609594932et_nat)
% 5.61/5.91 (declare-fun tptp.insert6201435330877294327od_o_o (tptp.product_prod_o_o tptp.set_Product_prod_o_o) tptp.set_Product_prod_o_o)
% 5.61/5.91 (declare-fun tptp.insert1271470778893645362et_nat (tptp.produc3658429121746597890et_nat tptp.set_Pr3948176798113811640et_nat) tptp.set_Pr3948176798113811640et_nat)
% 5.61/5.91 (declare-fun tptp.insert5033312907999012233nt_int (tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 5.61/5.91 (declare-fun tptp.insert8211810215607154385at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.91 (declare-fun tptp.insert4616891024742550839t_unit (tptp.produc8459935480633519975t_unit tptp.set_Pr5094982260447487303t_unit) tptp.set_Pr5094982260447487303t_unit)
% 5.61/5.91 (declare-fun tptp.insert3244108804717745463_nat_o (tptp.produc6666532470309664615_nat_o tptp.set_Pr3813038829465207111_nat_o) tptp.set_Pr3813038829465207111_nat_o)
% 5.61/5.91 (declare-fun tptp.insert1494450971503307511_set_o (tptp.produc7369051934464679207_set_o tptp.set_Pr4577759397028426247_set_o) tptp.set_Pr4577759397028426247_set_o)
% 5.61/5.91 (declare-fun tptp.insert7328952640415156725et_int (tptp.produc2115011035271226405et_int tptp.set_Pr2522554150109002629et_int) tptp.set_Pr2522554150109002629et_int)
% 5.61/5.91 (declare-fun tptp.insert3810226134351308605et_nat (tptp.produc7819656566062154093et_nat tptp.set_Pr5488025237498180813et_nat) tptp.set_Pr5488025237498180813et_nat)
% 5.61/5.91 (declare-fun tptp.insert6793119152790066487t_unit (tptp.produc1357844946079266663t_unit tptp.set_Pr3980508049012409671t_unit) tptp.set_Pr3980508049012409671t_unit)
% 5.61/5.91 (declare-fun tptp.insert_Product_unit (tptp.product_unit tptp.set_Product_unit) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.insert_rat (tptp.rat tptp.set_rat) tptp.set_rat)
% 5.61/5.91 (declare-fun tptp.insert2507855216428400253_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_se1353816476878259085_nat_o) tptp.set_se1353816476878259085_nat_o)
% 5.61/5.91 (declare-fun tptp.insert_set_o (tptp.set_o tptp.set_set_o) tptp.set_set_o)
% 5.61/5.91 (declare-fun tptp.insert_set_int (tptp.set_int tptp.set_set_int) tptp.set_set_int)
% 5.61/5.91 (declare-fun tptp.insert_set_nat (tptp.set_nat tptp.set_set_nat) tptp.set_set_nat)
% 5.61/5.91 (declare-fun tptp.insert8986028188087627965t_unit (tptp.set_Product_unit tptp.set_set_Product_unit) tptp.set_set_Product_unit)
% 5.61/5.91 (declare-fun tptp.is_emp6650082560925436063_nat_o (tptp.set_Pr4532377907799695533_nat_o) Bool)
% 5.61/5.91 (declare-fun tptp.is_empty_o (tptp.set_o) Bool)
% 5.61/5.91 (declare-fun tptp.is_empty_int (tptp.set_int) Bool)
% 5.61/5.91 (declare-fun tptp.is_empty_nat (tptp.set_nat) Bool)
% 5.61/5.91 (declare-fun tptp.is_emp5529367068699929823t_unit (tptp.set_Product_unit) Bool)
% 5.61/5.91 (declare-fun tptp.is_sin5180296473474724033_nat_o (tptp.set_Pr4532377907799695533_nat_o) Bool)
% 5.61/5.91 (declare-fun tptp.is_singleton_o (tptp.set_o) Bool)
% 5.61/5.91 (declare-fun tptp.is_singleton_int (tptp.set_int) Bool)
% 5.61/5.91 (declare-fun tptp.is_singleton_nat (tptp.set_nat) Bool)
% 5.61/5.91 (declare-fun tptp.is_sin2160648248035936513t_unit (tptp.set_Product_unit) Bool)
% 5.61/5.91 (declare-fun tptp.pairwi2432143822833250616_nat_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool) tptp.set_Pr4532377907799695533_nat_o) Bool)
% 5.61/5.91 (declare-fun tptp.pairwise_o ((-> Bool Bool Bool) tptp.set_o) Bool)
% 5.61/5.91 (declare-fun tptp.pairwi4741737654671186738nteger ((-> tptp.code_integer tptp.code_integer Bool) tptp.set_Code_integer) Bool)
% 5.61/5.91 (declare-fun tptp.pairwise_int ((-> tptp.int tptp.int Bool) tptp.set_int) Bool)
% 5.61/5.91 (declare-fun tptp.pairwise_nat ((-> tptp.nat tptp.nat Bool) tptp.set_nat) Bool)
% 5.61/5.91 (declare-fun tptp.pairwi7919127943033184120t_unit ((-> tptp.product_unit tptp.product_unit Bool) tptp.set_Product_unit) Bool)
% 5.61/5.91 (declare-fun tptp.pairwise_set_nat ((-> tptp.set_nat tptp.set_nat Bool) tptp.set_set_nat) Bool)
% 5.61/5.91 (declare-fun tptp.remove4651630035290841522_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) tptp.set_Pr4532377907799695533_nat_o) tptp.set_Pr4532377907799695533_nat_o)
% 5.61/5.91 (declare-fun tptp.remove_o (Bool tptp.set_o) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.remove_int (tptp.int tptp.set_int) tptp.set_int)
% 5.61/5.91 (declare-fun tptp.remove_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.remove_Product_unit (tptp.product_unit tptp.set_Product_unit) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.the_el5959152443890766018_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.91 (declare-fun tptp.the_elem_o (tptp.set_o) Bool)
% 5.61/5.91 (declare-fun tptp.the_el4656377885804969768nteger (tptp.set_Code_integer) tptp.code_integer)
% 5.61/5.91 (declare-fun tptp.the_elem_int (tptp.set_int) tptp.int)
% 5.61/5.91 (declare-fun tptp.the_elem_nat (tptp.set_nat) tptp.nat)
% 5.61/5.91 (declare-fun tptp.the_el608902216710161154t_unit (tptp.set_Product_unit) tptp.product_unit)
% 5.61/5.91 (declare-fun tptp.the_elem_set_nat (tptp.set_set_nat) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.vimage_o_o ((-> Bool Bool) tptp.set_o) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.vimage_o_int ((-> Bool tptp.int) tptp.set_int) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.vimage_o_nat ((-> Bool tptp.nat) tptp.set_nat) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.vimage8945963521958007626od_o_o ((-> Bool tptp.product_prod_o_o) tptp.set_Product_prod_o_o) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.vimage4304346610107161470_int_o ((-> Bool tptp.product_prod_int_o) tptp.set_Pr903927857289325719_int_o) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.vimage6125388955539849434_nat_o ((-> Bool tptp.product_prod_nat_o) tptp.set_Pr3149072824959771635_nat_o) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.vimage9156843197228287893unit_o ((-> Bool tptp.produc7485711547916492274unit_o) tptp.set_Pr5464989305201766866unit_o) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.vimage4222377557387472176t_unit ((-> Bool tptp.product_unit) tptp.set_Product_unit) tptp.set_o)
% 5.61/5.91 (declare-fun tptp.vimage3005800680117336574eger_o ((-> tptp.code_integer Bool) tptp.set_o) tptp.set_Code_integer)
% 5.61/5.91 (declare-fun tptp.vimage1318793397690208119nteger ((-> tptp.code_integer tptp.code_integer) tptp.set_Code_integer) tptp.set_Code_integer)
% 5.61/5.91 (declare-fun tptp.vimage5837348839036363078er_int ((-> tptp.code_integer tptp.int) tptp.set_int) tptp.set_Code_integer)
% 5.61/5.91 (declare-fun tptp.vimage5839839309545413354er_nat ((-> tptp.code_integer tptp.nat) tptp.set_nat) tptp.set_Code_integer)
% 5.61/5.91 (declare-fun tptp.vimage5651688891684837235t_unit ((-> tptp.code_integer tptp.product_unit) tptp.set_Product_unit) tptp.set_Code_integer)
% 5.61/5.91 (declare-fun tptp.vimage_int_o ((-> tptp.int Bool) tptp.set_o) tptp.set_int)
% 5.61/5.91 (declare-fun tptp.vimage_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 5.61/5.91 (declare-fun tptp.vimage_int_nat ((-> tptp.int tptp.nat) tptp.set_nat) tptp.set_int)
% 5.61/5.91 (declare-fun tptp.vimage7872673496510460816nt_int ((-> tptp.int tptp.product_prod_int_int) tptp.set_Pr958786334691620121nt_int) tptp.set_int)
% 5.61/5.91 (declare-fun tptp.vimage2000912565490760292t_unit ((-> tptp.int tptp.product_unit) tptp.set_Product_unit) tptp.set_int)
% 5.61/5.91 (declare-fun tptp.vimage8201027140005291904_nat_o ((-> tptp.nat tptp.produc3658429121746597890et_nat Bool) tptp.set_Pr4532377907799695533_nat_o) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.vimage_nat_o ((-> tptp.nat Bool) tptp.set_o) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.vimage6104394758324456170nteger ((-> tptp.nat tptp.code_integer) tptp.set_Code_integer) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.vimage_nat_int ((-> tptp.nat tptp.int) tptp.set_int) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.vimage_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.vimage5656379182745576100_o_nat ((-> tptp.nat tptp.product_prod_o_nat) tptp.set_Pr2101469702781467981_o_nat) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.vimage9012682431555523728nt_nat ((-> tptp.nat tptp.product_prod_int_nat) tptp.set_Pr3448869479623346877nt_nat) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.vimage8013328719654469172at_nat ((-> tptp.nat tptp.product_prod_nat_nat) tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.vimage4884490618288580032t_unit ((-> tptp.nat tptp.product_unit) tptp.set_Product_unit) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.vimage_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_set_nat) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.vimage7160910655466636085et_nat ((-> tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat) tptp.set_Pr8536935166611901872et_nat) tptp.set_Pr3286484037609594932et_nat)
% 5.61/5.91 (declare-fun tptp.vimage1990136491886319165et_nat ((-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat) tptp.set_Pr3286484037609594932et_nat) tptp.set_Pr3948176798113811640et_nat)
% 5.61/5.91 (declare-fun tptp.vimage8808348054653608838unit_o ((-> tptp.product_unit Bool) tptp.set_o) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.vimage6250838002967538110it_int ((-> tptp.product_unit tptp.int) tptp.set_int) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.vimage6253328473476588386it_nat ((-> tptp.product_unit tptp.nat) tptp.set_nat) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.vimage508909887551888138t_unit ((-> tptp.product_unit tptp.produc3788275437394581276t_unit) tptp.set_Pr6671815714118170108t_unit) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.vimage4422279681566046568t_unit ((-> tptp.product_unit tptp.produc6865911496949736918t_unit) tptp.set_Pr5889264611543340172t_unit) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.vimage7305857734363866308t_unit ((-> tptp.product_unit tptp.produc526117512892780850t_unit) tptp.set_Pr4334478416066269672t_unit) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.vimage8114940889160087125t_unit ((-> tptp.product_unit tptp.produc8459935480633519975t_unit) tptp.set_Pr5094982260447487303t_unit) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.vimage7995052115951654139t_unit ((-> tptp.product_unit tptp.product_unit) tptp.set_Product_unit) tptp.set_Product_unit)
% 5.61/5.91 (declare-fun tptp.vimage5412618565253405765et_nat ((-> tptp.set_nat tptp.produc3658429121746597890et_nat) tptp.set_Pr3948176798113811640et_nat) tptp.set_set_nat)
% 5.61/5.91 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 5.61/5.91 (declare-fun tptp.set_or189985376899183464nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 5.61/5.91 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 5.61/5.91 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.set_or8404916559141939852nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 5.61/5.91 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.set_or2715278749043346189nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 5.61/5.91 (declare-fun tptp.set_or4266950643985792945nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 5.61/5.91 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 5.61/5.91 (declare-fun tptp.char2 (Bool Bool Bool Bool Bool Bool Bool Bool) tptp.char)
% 5.61/5.91 (declare-fun tptp.integer_of_char (tptp.char) tptp.code_integer)
% 5.61/5.91 (declare-fun tptp.sum_ca6763686470577984908at_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.sum_sum_nat_nat) tptp.nat)
% 5.61/5.91 (declare-fun tptp.syntax7398250324933576852n_assn (tptp.assn tptp.assn) Bool)
% 5.61/5.91 (declare-fun tptp.syntax5678989248478167196nt_int (tptp.int tptp.int) Bool)
% 5.61/5.91 (declare-fun tptp.syntax4682126007086162916at_nat (tptp.nat tptp.nat) Bool)
% 5.61/5.91 (declare-fun tptp.syntax3730441303064801268at_rat (tptp.rat tptp.rat) Bool)
% 5.61/5.91 (declare-fun tptp.transi3136567867383547549ic_int (tptp.set_Pr958786334691620121nt_int) Bool)
% 5.61/5.91 (declare-fun tptp.transi3139058337892597825ic_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.61/5.91 (declare-fun tptp.transi712980445759334096_nat_o (tptp.set_Pr2161125870931222855_nat_o) tptp.set_Pr2161125870931222855_nat_o)
% 5.61/5.91 (declare-fun tptp.transitive_rtrancl_o (tptp.set_Product_prod_o_o) tptp.set_Product_prod_o_o)
% 5.61/5.91 (declare-fun tptp.transi3984306202085910426nteger (tptp.set_Pr4811707699266497531nteger) tptp.set_Pr4811707699266497531nteger)
% 5.61/5.91 (declare-fun tptp.transi2902850859426252137cl_int (tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 5.61/5.91 (declare-fun tptp.transi2905341329935302413cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.91 (declare-fun tptp.transi344104063936286263et_nat (tptp.set_Pr3444600963470892981et_nat) tptp.set_Pr3444600963470892981et_nat)
% 5.61/5.91 (declare-fun tptp.transi2414916928880341691et_nat (tptp.set_Pr7928877670098842301et_nat) tptp.set_Pr7928877670098842301et_nat)
% 5.61/5.91 (declare-fun tptp.transi6919426408697524543et_nat (tptp.set_Pr719794911490849221et_nat) tptp.set_Pr719794911490849221et_nat)
% 5.61/5.91 (declare-fun tptp.transi5430920176653612092nt_int (tptp.set_Pr2560585780119916871nt_int) tptp.set_Pr2560585780119916871nt_int)
% 5.61/5.91 (declare-fun tptp.transi8609417484261754244at_nat (tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr8693737435421807431at_nat)
% 5.61/5.91 (declare-fun tptp.transi6481887417741755664t_unit (tptp.set_Pr5094982260447487303t_unit) tptp.set_Pr5094982260447487303t_unit)
% 5.61/5.91 (declare-fun tptp.transi4009562729418357614_nat_o (tptp.set_Pr2161125870931222855_nat_o) tptp.set_Pr2161125870931222855_nat_o)
% 5.61/5.91 (declare-fun tptp.transitive_trancl_o (tptp.set_Product_prod_o_o) tptp.set_Product_prod_o_o)
% 5.61/5.91 (declare-fun tptp.transi6261509568448316235cl_int (tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 5.61/5.91 (declare-fun tptp.transi6264000038957366511cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.91 (declare-fun tptp.transi5221092739591632921et_nat (tptp.set_Pr3444600963470892981et_nat) tptp.set_Pr3444600963470892981et_nat)
% 5.61/5.91 (declare-fun tptp.transi3145040225084697757et_nat (tptp.set_Pr7928877670098842301et_nat) tptp.set_Pr7928877670098842301et_nat)
% 5.61/5.91 (declare-fun tptp.transi4137310414928362273et_nat (tptp.set_Pr719794911490849221et_nat) tptp.set_Pr719794911490849221et_nat)
% 5.61/5.91 (declare-fun tptp.transi6288783178788033498nt_int (tptp.set_Pr2560585780119916871nt_int) tptp.set_Pr2560585780119916871nt_int)
% 5.61/5.91 (declare-fun tptp.transi243908449541399842at_nat (tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr8693737435421807431at_nat)
% 5.61/5.91 (declare-fun tptp.transi430408012122777006t_unit (tptp.set_Pr5094982260447487303t_unit) tptp.set_Pr5094982260447487303t_unit)
% 5.61/5.91 (declare-fun tptp.type_d5515310227294319076nteger ((-> (-> tptp.code_integer tptp.code_integer) tptp.code_integer) (-> tptp.code_integer tptp.code_integer tptp.code_integer) tptp.set_Code_integer) Bool)
% 5.61/5.91 (declare-fun tptp.type_d5661033022651575429eger_o ((-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) Bool) (-> Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.set_o) Bool)
% 5.61/5.91 (declare-fun tptp.type_d6544512618915850416nteger ((-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.code_integer) (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.set_Code_integer) Bool)
% 5.61/5.91 (declare-fun tptp.type_d6278479724763174947er_nat ((-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.nat) (-> tptp.nat tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.set_nat) Bool)
% 5.61/5.91 (declare-fun tptp.type_d6996789741066924922t_unit ((-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.product_unit) (-> tptp.product_unit tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.set_Product_unit) Bool)
% 5.61/5.91 (declare-fun tptp.type_d3909072315231072503_nat_o ((-> tptp.assn tptp.produc3658429121746597890et_nat Bool) (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.assn) tptp.set_Pr4532377907799695533_nat_o) Bool)
% 5.61/5.91 (declare-fun tptp.type_d669523880323286244nteger ((-> tptp.code_integer tptp.code_integer tptp.code_integer) (-> (-> tptp.code_integer tptp.code_integer) tptp.code_integer) tptp.set_Co726186806682698383nteger) Bool)
% 5.61/5.91 (declare-fun tptp.type_d6812736842639505741eger_o ((-> tptp.code_integer Bool) (-> Bool tptp.code_integer) tptp.set_o) Bool)
% 5.61/5.91 (declare-fun tptp.type_d4796611474492816872nteger ((-> tptp.code_integer tptp.code_integer) (-> tptp.code_integer tptp.code_integer) tptp.set_Code_integer) Bool)
% 5.61/5.91 (declare-fun tptp.type_d8366093980585677751er_int ((-> tptp.code_integer tptp.int) (-> tptp.int tptp.code_integer) tptp.set_int) Bool)
% 5.61/5.91 (declare-fun tptp.type_d8368584451094728027er_nat ((-> tptp.code_integer tptp.nat) (-> tptp.nat tptp.code_integer) tptp.set_nat) Bool)
% 5.61/5.91 (declare-fun tptp.type_d9006111508436661314t_unit ((-> tptp.code_integer tptp.product_unit) (-> tptp.product_unit tptp.code_integer) tptp.set_Product_unit) Bool)
% 5.61/5.91 (declare-fun tptp.type_d4410041424927559462al_nat ((-> tptp.code_natural tptp.nat) (-> tptp.nat tptp.code_natural) tptp.set_nat) Bool)
% 5.61/5.91 (declare-fun tptp.type_d8633139899873770843nteger ((-> tptp.nat tptp.code_integer) (-> tptp.code_integer tptp.nat) tptp.set_Code_integer) Bool)
% 5.61/5.91 (declare-fun tptp.type_d6250493948777748686at_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 5.61/5.91 (declare-fun tptp.type_d3768499744764857476et_nat ((-> tptp.nat tptp.set_nat) (-> tptp.set_nat tptp.nat) tptp.set_set_nat) Bool)
% 5.61/5.91 (declare-fun tptp.type_d6188575255521822967unit_o ((-> tptp.product_unit Bool) (-> Bool tptp.product_unit) tptp.set_o) Bool)
% 5.61/5.91 (declare-fun tptp.type_d202864840109488260at_nat ((-> tptp.set_nat tptp.nat) (-> tptp.nat tptp.set_nat) tptp.set_nat) Bool)
% 5.61/5.91 (declare-fun tptp.accp_P4507279754199951662nt_int ((-> tptp.produc5030937667867769463nt_int tptp.produc5030937667867769463nt_int Bool) tptp.produc5030937667867769463nt_int) Bool)
% 5.61/5.91 (declare-fun tptp.accp_P5604362734843950218nt_int ((-> tptp.produc6128020648511768019nt_int tptp.produc6128020648511768019nt_int Bool) tptp.produc6128020648511768019nt_int) Bool)
% 5.61/5.91 (declare-fun tptp.accp_P3050404660685545426at_nat ((-> tptp.produc3574062574353363227at_nat tptp.produc3574062574353363227at_nat Bool) tptp.produc3574062574353363227at_nat) Bool)
% 5.61/5.91 (declare-fun tptp.accp_P4147487641329543982at_nat ((-> tptp.produc4671145554997361783at_nat tptp.produc4671145554997361783at_nat Bool) tptp.produc4671145554997361783at_nat) Bool)
% 5.61/5.91 (declare-fun tptp.accp_P1862375125659990705et_nat ((-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool) tptp.produc2732055786443039994et_nat) Bool)
% 5.61/5.91 (declare-fun tptp.accp_P8458817951426537472et_nat ((-> tptp.produc6197004810343482825et_nat tptp.produc6197004810343482825et_nat Bool) tptp.produc6197004810343482825et_nat) Bool)
% 5.61/5.91 (declare-fun tptp.accp_P5801069581201407417et_nat ((-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 5.61/5.91 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 5.61/5.91 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 5.61/5.91 (declare-fun tptp.lex_pr4722427456421979612et_nat (tptp.set_Pr2161125870931222855_nat_o tptp.set_Pr7928877670098842301et_nat) tptp.set_Pr3444600963470892981et_nat)
% 5.61/5.91 (declare-fun tptp.lex_pr5340572901959109728et_nat (tptp.set_Pr2161125870931222855_nat_o tptp.set_Pr719794911490849221et_nat) tptp.set_Pr7928877670098842301et_nat)
% 5.61/5.91 (declare-fun tptp.lex_pr538634069021852900et_nat (tptp.set_Pr1776176089890104647t_unit tptp.set_Pr5488025237498180813et_nat) tptp.set_Pr719794911490849221et_nat)
% 5.61/5.91 (declare-fun tptp.lex_prod_int_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) tptp.set_Pr2560585780119916871nt_int)
% 5.61/5.91 (declare-fun tptp.lex_prod_int_nat (tptp.set_Pr958786334691620121nt_int tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr5696620967126086215nt_nat)
% 5.61/5.91 (declare-fun tptp.lex_prod_nat_int (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr958786334691620121nt_int) tptp.set_Pr5557702248415638087at_int)
% 5.61/5.91 (declare-fun tptp.lex_prod_nat_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr8693737435421807431at_nat)
% 5.61/5.91 (declare-fun tptp.max_ex5265246208886859912_nat_o (tptp.set_Pr2161125870931222855_nat_o) tptp.set_Pr3813038829465207111_nat_o)
% 5.61/5.91 (declare-fun tptp.max_ext_o (tptp.set_Product_prod_o_o) tptp.set_Pr4577759397028426247_set_o)
% 5.61/5.91 (declare-fun tptp.max_ext_Code_integer (tptp.set_Pr4811707699266497531nteger) tptp.set_Pr7577011563204128103nteger)
% 5.61/5.91 (declare-fun tptp.max_ext_int (tptp.set_Pr958786334691620121nt_int) tptp.set_Pr2522554150109002629et_int)
% 5.61/5.91 (declare-fun tptp.max_ext_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr5488025237498180813et_nat)
% 5.61/5.91 (declare-fun tptp.max_ext_Product_unit (tptp.set_Pr5094982260447487303t_unit) tptp.set_Pr3980508049012409671t_unit)
% 5.61/5.91 (declare-fun tptp.measure_int ((-> tptp.int tptp.nat)) tptp.set_Pr958786334691620121nt_int)
% 5.61/5.91 (declare-fun tptp.measure_nat ((-> tptp.nat tptp.nat)) tptp.set_Pr1261947904930325089at_nat)
% 5.61/5.91 (declare-fun tptp.min_ex3730736537596016502_nat_o (tptp.set_Pr2161125870931222855_nat_o) tptp.set_Pr3813038829465207111_nat_o)
% 5.61/5.91 (declare-fun tptp.min_ext_o (tptp.set_Product_prod_o_o) tptp.set_Pr4577759397028426247_set_o)
% 5.61/5.91 (declare-fun tptp.min_ext_int (tptp.set_Pr958786334691620121nt_int) tptp.set_Pr2522554150109002629et_int)
% 5.61/5.91 (declare-fun tptp.min_ext_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr5488025237498180813et_nat)
% 5.61/5.91 (declare-fun tptp.min_ext_Product_unit (tptp.set_Pr5094982260447487303t_unit) tptp.set_Pr3980508049012409671t_unit)
% 5.61/5.91 (declare-fun tptp.wf_Pro8787509627421085110_nat_o (tptp.set_Pr2161125870931222855_nat_o) Bool)
% 5.61/5.91 (declare-fun tptp.wf_o (tptp.set_Product_prod_o_o) Bool)
% 5.61/5.91 (declare-fun tptp.wf_int (tptp.set_Pr958786334691620121nt_int) Bool)
% 5.61/5.91 (declare-fun tptp.wf_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.61/5.91 (declare-fun tptp.wf_Product_unit (tptp.set_Pr5094982260447487303t_unit) Bool)
% 5.61/5.91 (declare-fun tptp.chains_int (tptp.set_Pr958786334691620121nt_int) tptp.set_set_int)
% 5.61/5.91 (declare-fun tptp.chains_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_set_nat)
% 5.61/5.91 (declare-fun tptp.chains_nat2 (tptp.set_set_nat) tptp.set_set_set_nat)
% 5.61/5.91 (declare-fun tptp.pred_c177362287423414904_nat_o (tptp.set_Pr4532377907799695533_nat_o (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool) tptp.set_Pr4532377907799695533_nat_o) Bool)
% 5.61/5.91 (declare-fun tptp.pred_chain_o (tptp.set_o (-> Bool Bool Bool) tptp.set_o) Bool)
% 5.61/5.91 (declare-fun tptp.pred_chain_int (tptp.set_int (-> tptp.int tptp.int Bool) tptp.set_int) Bool)
% 5.61/5.91 (declare-fun tptp.pred_chain_nat (tptp.set_nat (-> tptp.nat tptp.nat Bool) tptp.set_nat) Bool)
% 5.61/5.91 (declare-fun tptp.pred_c6915491785556283576t_unit (tptp.set_Product_unit (-> tptp.product_unit tptp.product_unit Bool) tptp.set_Product_unit) Bool)
% 5.61/5.91 (declare-fun tptp.pred_c5891848916688490280nteger (tptp.set_set_Code_integer (-> tptp.set_Code_integer tptp.set_Code_integer Bool) tptp.set_set_Code_integer) Bool)
% 5.61/5.91 (declare-fun tptp.pred_chain_set_nat (tptp.set_set_nat (-> tptp.set_nat tptp.set_nat Bool) tptp.set_set_nat) Bool)
% 5.61/5.91 (declare-fun tptp.member6576561426505652726_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) tptp.set_Pr4532377907799695533_nat_o) Bool)
% 5.61/5.91 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 5.61/5.91 (declare-fun tptp.member_assn (tptp.assn tptp.set_assn) Bool)
% 5.61/5.91 (declare-fun tptp.member_Code_integer (tptp.code_integer tptp.set_Code_integer) Bool)
% 5.61/5.91 (declare-fun tptp.member_filter_nat (tptp.filter_nat tptp.set_filter_nat) Bool)
% 5.61/5.91 (declare-fun tptp.member242389114213480694t_unit (tptp.heap_e7401611519738050253t_unit tptp.set_he8644174446132254637t_unit) Bool)
% 5.61/5.91 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 5.61/5.91 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 5.61/5.91 (declare-fun tptp.member8781333585448626064_nat_o (tptp.produc4928098042776334183_nat_o tptp.set_Pr2161125870931222855_nat_o) Bool)
% 5.61/5.91 (declare-fun tptp.member6124377750444531601et_nat (tptp.produc2732055786443039994et_nat tptp.set_Pr8536935166611901872et_nat) Bool)
% 5.61/5.91 (declare-fun tptp.member1996754912294343701et_nat (tptp.produc3925858234332021118et_nat tptp.set_Pr3286484037609594932et_nat) Bool)
% 5.61/5.91 (declare-fun tptp.member7466972457876170832od_o_o (tptp.product_prod_o_o tptp.set_Product_prod_o_o) Bool)
% 5.61/5.91 (declare-fun tptp.member7847949116333733898_o_int (tptp.product_prod_o_int tptp.set_Pr8834758594704517033_o_int) Bool)
% 5.61/5.91 (declare-fun tptp.member2802428098988154798_o_nat (tptp.product_prod_o_nat tptp.set_Pr2101469702781467981_o_nat) Bool)
% 5.61/5.91 (declare-fun tptp.member9215336023991391429t_unit (tptp.produc3788275437394581276t_unit tptp.set_Pr6671815714118170108t_unit) Bool)
% 5.61/5.91 (declare-fun tptp.member157494554546826820nteger (tptp.produc8923325533196201883nteger tptp.set_Pr4811707699266497531nteger) Bool)
% 5.61/5.91 (declare-fun tptp.member5046970461208427408t_unit (tptp.produc8126358835630522215t_unit tptp.set_Pr1776176089890104647t_unit) Bool)
% 5.61/5.91 (declare-fun tptp.member6260224972018164377et_nat (tptp.produc3658429121746597890et_nat tptp.set_Pr3948176798113811640et_nat) Bool)
% 5.61/5.91 (declare-fun tptp.member4489920277610959864_int_o (tptp.product_prod_int_o tptp.set_Pr903927857289325719_int_o) Bool)
% 5.61/5.91 (declare-fun tptp.member5262025264175285858nt_int (tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int) Bool)
% 5.61/5.91 (declare-fun tptp.member216504246829706758nt_nat (tptp.product_prod_int_nat tptp.set_Pr3448869479623346877nt_nat) Bool)
% 5.61/5.91 (declare-fun tptp.member6688357403439981677t_unit (tptp.produc6865911496949736918t_unit tptp.set_Pr5889264611543340172t_unit) Bool)
% 5.61/5.91 (declare-fun tptp.member6310962623043647828_nat_o (tptp.product_prod_nat_o tptp.set_Pr3149072824959771635_nat_o) Bool)
% 5.61/5.91 (declare-fun tptp.member4262671552274231302at_int (tptp.product_prod_nat_int tptp.set_Pr7995236796853374141at_int) Bool)
% 5.61/5.91 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 5.61/5.91 (declare-fun tptp.member348563419383025609t_unit (tptp.produc526117512892780850t_unit tptp.set_Pr4334478416066269672t_unit) Bool)
% 5.61/5.91 (declare-fun tptp.member6341495586645257982et_nat (tptp.produc5657529347773406293et_nat tptp.set_Pr3444600963470892981et_nat) Bool)
% 5.61/5.91 (declare-fun tptp.member8354763867512313179_nat_o (tptp.produc4962441903510821572_nat_o tptp.set_Pr7705059561495379578_nat_o) Bool)
% 5.61/5.91 (declare-fun tptp.member4763271486408492550et_nat (tptp.produc6830853553727218525et_nat tptp.set_Pr7928877670098842301et_nat) Bool)
% 5.61/5.91 (declare-fun tptp.member6613709072892554et_nat (tptp.produc4658369026151987169et_nat tptp.set_Pr3721596426557623617et_nat) Bool)
% 5.61/5.91 (declare-fun tptp.member4978015717948814295_nat_o (tptp.produc6907119039986491712_nat_o tptp.set_Pr4208978187861016310_nat_o) Bool)
% 5.61/5.91 (declare-fun tptp.member2737525317995836554et_nat (tptp.produc7389280635074931169et_nat tptp.set_Pr8807100098903490369et_nat) Bool)
% 5.61/5.91 (declare-fun tptp.member6099555550032318734et_nat (tptp.produc8111630337999740517et_nat tptp.set_Pr719794911490849221et_nat) Bool)
% 5.61/5.91 (declare-fun tptp.member8566619992076573584nt_int (tptp.produc1219242969750017639nt_int tptp.set_Pr2560585780119916871nt_int) Bool)
% 5.61/5.91 (declare-fun tptp.member2930414080797523088nt_nat (tptp.produc4806409095325742951nt_nat tptp.set_Pr5696620967126086215nt_nat) Bool)
% 5.61/5.91 (declare-fun tptp.member4619661753630440592at_int (tptp.produc6495656768158660455at_int tptp.set_Pr5557702248415638087at_int) Bool)
% 5.61/5.91 (declare-fun tptp.member8206827879206165904at_nat (tptp.produc859450856879609959at_nat tptp.set_Pr8693737435421807431at_nat) Bool)
% 5.61/5.91 (declare-fun tptp.member3689400097658526619unit_o (tptp.produc7485711547916492274unit_o tptp.set_Pr5464989305201766866unit_o) Bool)
% 5.61/5.91 (declare-fun tptp.member5468524742225079679it_int (tptp.produc5646078835734834920it_int tptp.set_Pr8497134830871917726it_int) Bool)
% 5.61/5.91 (declare-fun tptp.member423003724879500579it_nat (tptp.produc600557818389255820it_nat tptp.set_Pr1763845938948868674it_nat) Bool)
% 5.61/5.91 (declare-fun tptp.member7821138191923116944t_unit (tptp.produc8459935480633519975t_unit tptp.set_Pr5094982260447487303t_unit) Bool)
% 5.61/5.91 (declare-fun tptp.member6623172407746373520_nat_o (tptp.produc6666532470309664615_nat_o tptp.set_Pr3813038829465207111_nat_o) Bool)
% 5.61/5.91 (declare-fun tptp.member9116954335612470352_set_o (tptp.produc7369051934464679207_set_o tptp.set_Pr4577759397028426247_set_o) Bool)
% 5.61/5.91 (declare-fun tptp.member4307123515891402160nteger (tptp.produc6491284506569428743nteger tptp.set_Pr7577011563204128103nteger) Bool)
% 5.61/5.91 (declare-fun tptp.member2572552093476627150et_int (tptp.produc2115011035271226405et_int tptp.set_Pr2522554150109002629et_int) Bool)
% 5.61/5.91 (declare-fun tptp.member727419437372278867t_unit (tptp.produc7348995623955488188t_unit tptp.set_Pr4071100604818519410t_unit) Bool)
% 5.61/5.91 (declare-fun tptp.member8277197624267554838et_nat (tptp.produc7819656566062154093et_nat tptp.set_Pr5488025237498180813et_nat) Bool)
% 5.61/5.91 (declare-fun tptp.member4189953012975926160t_unit (tptp.produc1357844946079266663t_unit tptp.set_Pr3980508049012409671t_unit) Bool)
% 5.61/5.91 (declare-fun tptp.member_Product_unit (tptp.product_unit tptp.set_Product_unit) Bool)
% 5.61/5.91 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 5.61/5.91 (declare-fun tptp.member1452989533377600726_nat_o (tptp.set_Pr4532377907799695533_nat_o tptp.set_se1353816476878259085_nat_o) Bool)
% 5.61/5.91 (declare-fun tptp.member_set_o (tptp.set_o tptp.set_set_o) Bool)
% 5.61/5.91 (declare-fun tptp.member1834298987299537450nteger (tptp.set_Code_integer tptp.set_set_Code_integer) Bool)
% 5.61/5.91 (declare-fun tptp.member_set_int (tptp.set_int tptp.set_set_int) Bool)
% 5.61/5.91 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 5.61/5.91 (declare-fun tptp.member5475208728337331568_nat_o (tptp.set_Pr2161125870931222855_nat_o tptp.set_se7663487083892625191_nat_o) Bool)
% 5.61/5.91 (declare-fun tptp.member3157015407008874800od_o_o (tptp.set_Product_prod_o_o tptp.set_se491199571785101031od_o_o) Bool)
% 5.61/5.91 (declare-fun tptp.member2340774599025711042nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_se6260736226359567993nt_int) Bool)
% 5.61/5.91 (declare-fun tptp.member2643936169264416010at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_se7855581050983116737at_nat) Bool)
% 5.61/5.91 (declare-fun tptp.member1248447801810324848t_unit (tptp.set_Pr5094982260447487303t_unit tptp.set_se8994758365886191399t_unit) Bool)
% 5.61/5.91 (declare-fun tptp.member5877623283571906838t_unit (tptp.set_Product_unit tptp.set_set_Product_unit) Bool)
% 5.61/5.91 (declare-fun tptp.member_set_set_nat (tptp.set_set_nat tptp.set_set_set_nat) Bool)
% 5.61/5.91 (declare-fun tptp.h () tptp.produc3658429121746597890et_nat)
% 5.61/5.91 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (= (@ tptp.rep_assn X) (@ tptp.rep_assn Y)) (= X Y))))
% 5.61/5.91 (assert (forall ((X tptp.assn)) (= (@ tptp.abs_assn (@ tptp.rep_assn X)) X)))
% 5.61/5.91 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Pr tptp.assn)) (=> (forall ((H tptp.produc3658429121746597890et_nat)) (= (@ P H) (@ (@ tptp.rep_assn Pr) H))) (= Pr (@ tptp.abs_assn P)))))
% 5.61/5.91 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Pr tptp.assn)) (=> (forall ((H tptp.produc3658429121746597890et_nat)) (= (@ P H) (@ (@ tptp.rep_assn Pr) H))) (= (@ tptp.abs_assn P) Pr))))
% 5.61/5.91 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member6576561426505652726_nat_o C) tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.91 (assert (forall ((C tptp.product_unit)) (not (@ (@ tptp.member_Product_unit C) tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.91 (assert (forall ((C Bool)) (not (@ (@ tptp.member_o C) tptp.bot_bot_set_o))))
% 5.61/5.91 (assert (forall ((C tptp.nat)) (not (@ (@ tptp.member_nat C) tptp.bot_bot_set_nat))))
% 5.61/5.91 (assert (forall ((C tptp.int)) (not (@ (@ tptp.member_int C) tptp.bot_bot_set_int))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (= (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member6576561426505652726_nat_o X2) A))) (= A tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit)) (= (forall ((X2 tptp.product_unit)) (not (@ (@ tptp.member_Product_unit X2) A))) (= A tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.91 (assert (forall ((A tptp.set_o)) (= (forall ((X2 Bool)) (not (@ (@ tptp.member_o X2) A))) (= A tptp.bot_bot_set_o))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat)) (= (forall ((X2 tptp.nat)) (not (@ (@ tptp.member_nat X2) A))) (= A tptp.bot_bot_set_nat))))
% 5.61/5.91 (assert (forall ((A tptp.set_int)) (= (forall ((X2 tptp.int)) (not (@ (@ tptp.member_int X2) A))) (= A tptp.bot_bot_set_int))))
% 5.61/5.91 (assert (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (= (= (@ tptp.collec939566748876313656_nat_o P) tptp.bot_bo7824918357723582233_nat_o) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ P X2))))))
% 5.61/5.91 (assert (forall ((P (-> tptp.product_unit Bool))) (= (= (@ tptp.collect_Product_unit P) tptp.bot_bo3957492148770167129t_unit) (forall ((X2 tptp.product_unit)) (not (@ P X2))))))
% 5.61/5.91 (assert (forall ((P (-> Bool Bool))) (= (= (@ tptp.collect_o P) tptp.bot_bot_set_o) (forall ((X2 Bool)) (not (@ P X2))))))
% 5.61/5.91 (assert (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (forall ((X2 tptp.nat)) (not (@ P X2))))))
% 5.61/5.91 (assert (forall ((P (-> tptp.int Bool))) (= (= (@ tptp.collect_int P) tptp.bot_bot_set_int) (forall ((X2 tptp.int)) (not (@ P X2))))))
% 5.61/5.91 (assert (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (= (= tptp.bot_bo7824918357723582233_nat_o (@ tptp.collec939566748876313656_nat_o P)) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ P X2))))))
% 5.61/5.91 (assert (forall ((P (-> tptp.product_unit Bool))) (= (= tptp.bot_bo3957492148770167129t_unit (@ tptp.collect_Product_unit P)) (forall ((X2 tptp.product_unit)) (not (@ P X2))))))
% 5.61/5.91 (assert (forall ((P (-> Bool Bool))) (= (= tptp.bot_bot_set_o (@ tptp.collect_o P)) (forall ((X2 Bool)) (not (@ P X2))))))
% 5.61/5.91 (assert (forall ((P (-> tptp.nat Bool))) (= (= tptp.bot_bot_set_nat (@ tptp.collect_nat P)) (forall ((X2 tptp.nat)) (not (@ P X2))))))
% 5.61/5.91 (assert (forall ((P (-> tptp.int Bool))) (= (= tptp.bot_bot_set_int (@ tptp.collect_int P)) (forall ((X2 tptp.int)) (not (@ P X2))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member6576561426505652726_nat_o A2) tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit)) (not (@ (@ tptp.member_Product_unit A2) tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.91 (assert (forall ((A2 Bool)) (not (@ (@ tptp.member_o A2) tptp.bot_bot_set_o))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat)) (not (@ (@ tptp.member_nat A2) tptp.bot_bot_set_nat))))
% 5.61/5.91 (assert (forall ((A2 tptp.int)) (not (@ (@ tptp.member_int A2) tptp.bot_bot_set_int))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit) (A2 tptp.product_unit)) (=> (= A tptp.bot_bo3957492148770167129t_unit) (not (@ (@ tptp.member_Product_unit A2) A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_o) (A2 Bool)) (=> (= A tptp.bot_bot_set_o) (not (@ (@ tptp.member_o A2) A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (A2 tptp.nat)) (=> (= A tptp.bot_bot_set_nat) (not (@ (@ tptp.member_nat A2) A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_int) (A2 tptp.int)) (=> (= A tptp.bot_bot_set_int) (not (@ (@ tptp.member_int A2) A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (= A tptp.bot_bo7824918357723582233_nat_o) (not (@ (@ tptp.member6576561426505652726_nat_o A2) A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit)) (=> (forall ((Y2 tptp.product_unit)) (not (@ (@ tptp.member_Product_unit Y2) A))) (= A tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.91 (assert (forall ((A tptp.set_o)) (=> (forall ((Y2 Bool)) (not (@ (@ tptp.member_o Y2) A))) (= A tptp.bot_bot_set_o))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat)) (=> (forall ((Y2 tptp.nat)) (not (@ (@ tptp.member_nat Y2) A))) (= A tptp.bot_bot_set_nat))))
% 5.61/5.91 (assert (forall ((A tptp.set_int)) (=> (forall ((Y2 tptp.int)) (not (@ (@ tptp.member_int Y2) A))) (= A tptp.bot_bot_set_int))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (forall ((Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member6576561426505652726_nat_o Y2) A))) (= A tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit)) (= (exists ((X2 tptp.product_unit)) (@ (@ tptp.member_Product_unit X2) A)) (not (= A tptp.bot_bo3957492148770167129t_unit)))))
% 5.61/5.91 (assert (forall ((A tptp.set_o)) (= (exists ((X2 Bool)) (@ (@ tptp.member_o X2) A)) (not (= A tptp.bot_bot_set_o)))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat)) (= (exists ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A)) (not (= A tptp.bot_bot_set_nat)))))
% 5.61/5.91 (assert (forall ((A tptp.set_int)) (= (exists ((X2 tptp.int)) (@ (@ tptp.member_int X2) A)) (not (= A tptp.bot_bot_set_int)))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (= (exists ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o X2) A)) (not (= A tptp.bot_bo7824918357723582233_nat_o)))))
% 5.61/5.91 (assert (forall ((S tptp.set_Product_unit)) (=> (not (= S tptp.bot_bo3957492148770167129t_unit)) (not (forall ((X3 tptp.product_unit)) (not (@ (@ tptp.member_Product_unit X3) S)))))))
% 5.61/5.91 (assert (forall ((S tptp.set_o)) (=> (not (= S tptp.bot_bot_set_o)) (not (forall ((X3 Bool)) (not (@ (@ tptp.member_o X3) S)))))))
% 5.61/5.91 (assert (forall ((S tptp.set_nat)) (=> (not (= S tptp.bot_bot_set_nat)) (not (forall ((X3 tptp.nat)) (not (@ (@ tptp.member_nat X3) S)))))))
% 5.61/5.91 (assert (forall ((S tptp.set_int)) (=> (not (= S tptp.bot_bot_set_int)) (not (forall ((X3 tptp.int)) (not (@ (@ tptp.member_int X3) S)))))))
% 5.61/5.91 (assert (forall ((S tptp.set_Pr4532377907799695533_nat_o)) (=> (not (= S tptp.bot_bo7824918357723582233_nat_o)) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member6576561426505652726_nat_o X3) S)))))))
% 5.61/5.91 (assert (forall ((X tptp.product_unit) (S tptp.set_Product_unit)) (=> (@ (@ tptp.member_Product_unit X) S) (not (= S tptp.bot_bo3957492148770167129t_unit)))))
% 5.61/5.91 (assert (forall ((X Bool) (S tptp.set_o)) (=> (@ (@ tptp.member_o X) S) (not (= S tptp.bot_bot_set_o)))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (S tptp.set_nat)) (=> (@ (@ tptp.member_nat X) S) (not (= S tptp.bot_bot_set_nat)))))
% 5.61/5.91 (assert (forall ((X tptp.int) (S tptp.set_int)) (=> (@ (@ tptp.member_int X) S) (not (= S tptp.bot_bot_set_int)))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (S tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o X) S) (not (= S tptp.bot_bo7824918357723582233_nat_o)))))
% 5.61/5.91 (assert (= tptp.bot_bo3957492148770167129t_unit (@ tptp.collect_Product_unit tptp.bot_bo4642748612307482820unit_o)))
% 5.61/5.91 (assert (= tptp.bot_bot_set_o (@ tptp.collect_o tptp.bot_bot_o_o)))
% 5.61/5.91 (assert (= tptp.bot_bot_set_nat (@ tptp.collect_nat tptp.bot_bot_nat_o)))
% 5.61/5.91 (assert (= tptp.bot_bot_set_int (@ tptp.collect_int tptp.bot_bot_int_o)))
% 5.61/5.91 (assert (= tptp.bot_bo7824918357723582233_nat_o (@ tptp.collec939566748876313656_nat_o tptp.bot_bo7963750851167320836at_o_o)))
% 5.61/5.91 (assert (forall ((H2 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn tptp.bot_bot_assn) H2))))
% 5.61/5.91 (assert (= tptp.is_emp5529367068699929823t_unit (lambda ((A3 tptp.set_Product_unit)) (= A3 tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.91 (assert (= tptp.is_empty_o (lambda ((A3 tptp.set_o)) (= A3 tptp.bot_bot_set_o))))
% 5.61/5.91 (assert (= tptp.is_empty_nat (lambda ((A3 tptp.set_nat)) (= A3 tptp.bot_bot_set_nat))))
% 5.61/5.91 (assert (= tptp.is_empty_int (lambda ((A3 tptp.set_int)) (= A3 tptp.bot_bot_set_int))))
% 5.61/5.91 (assert (= tptp.is_emp6650082560925436063_nat_o (lambda ((A3 tptp.set_Pr4532377907799695533_nat_o)) (= A3 tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.91 (assert (forall ((P (-> tptp.product_unit Bool))) (= (= (@ tptp.collect_Product_unit P) tptp.bot_bo3957492148770167129t_unit) (= P tptp.bot_bo4642748612307482820unit_o))))
% 5.61/5.91 (assert (forall ((P (-> Bool Bool))) (= (= (@ tptp.collect_o P) tptp.bot_bot_set_o) (= P tptp.bot_bot_o_o))))
% 5.61/5.91 (assert (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (= P tptp.bot_bot_nat_o))))
% 5.61/5.91 (assert (forall ((P (-> tptp.int Bool))) (= (= (@ tptp.collect_int P) tptp.bot_bot_set_int) (= P tptp.bot_bot_int_o))))
% 5.61/5.91 (assert (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (= (= (@ tptp.collec939566748876313656_nat_o P) tptp.bot_bo7824918357723582233_nat_o) (= P tptp.bot_bo7963750851167320836at_o_o))))
% 5.61/5.91 (assert (= tptp.bot_bo4642748612307482820unit_o (lambda ((X2 tptp.product_unit)) (@ (@ tptp.member_Product_unit X2) tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.91 (assert (= tptp.bot_bot_o_o (lambda ((X2 Bool)) (@ (@ tptp.member_o X2) tptp.bot_bot_set_o))))
% 5.61/5.91 (assert (= tptp.bot_bot_nat_o (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) tptp.bot_bot_set_nat))))
% 5.61/5.91 (assert (= tptp.bot_bot_int_o (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) tptp.bot_bot_set_int))))
% 5.61/5.91 (assert (= tptp.bot_bo7963750851167320836at_o_o (lambda ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o X2) tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.91 (assert (= tptp.wand_assn (lambda ((P2 tptp.assn) (Q tptp.assn)) (@ tptp.abs_assn (@ (@ tptp.wand_raw (@ tptp.rep_assn P2)) (@ tptp.rep_assn Q))))))
% 5.61/5.91 (assert (= tptp.one_one_assn (@ tptp.abs_assn tptp.one_assn_raw)))
% 5.61/5.91 (assert (forall ((Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) (@ tptp.collec939566748876313656_nat_o tptp.proper)) (= (@ tptp.rep_assn (@ tptp.abs_assn Y)) Y))))
% 5.61/5.91 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (= (@ tptp.one_assn_raw (@ (@ tptp.produc7507926704131184380et_nat H2) As)) (= As tptp.bot_bot_set_nat))))
% 5.61/5.91 (assert (forall ((X tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ tptp.one_assn_raw X) Y) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H) As2)) (= Y (not (= As2 tptp.bot_bot_set_nat)))))))))
% 5.61/5.91 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (@ tptp.one_assn_raw X) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H) As2)) (not (= As2 tptp.bot_bot_set_nat))))))))
% 5.61/5.91 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (@ tptp.one_assn_raw X)) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H) As2)) (= As2 tptp.bot_bot_set_nat)))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit)) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((X3 tptp.product_unit) (Y2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) A) (=> (@ (@ tptp.member_Product_unit Y2) A) (= X3 Y2)))) (@ tptp.is_sin2160648248035936513t_unit A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_o)) (=> (not (= A tptp.bot_bot_set_o)) (=> (forall ((X3 Bool) (Y2 Bool)) (=> (@ (@ tptp.member_o X3) A) (=> (@ (@ tptp.member_o Y2) A) (= X3 Y2)))) (@ tptp.is_singleton_o A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat)) (=> (not (= A tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (=> (@ (@ tptp.member_nat Y2) A) (= X3 Y2)))) (@ tptp.is_singleton_nat A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_int)) (=> (not (= A tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (=> (@ (@ tptp.member_int Y2) A) (= X3 Y2)))) (@ tptp.is_singleton_int A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) A) (=> (@ (@ tptp.member6576561426505652726_nat_o Y2) A) (= X3 Y2)))) (@ tptp.is_sin5180296473474724033_nat_o A)))))
% 5.61/5.91 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Q2 (-> tptp.produc3658429121746597890et_nat Bool))) (@ tptp.proper (@ (@ tptp.wand_raw P) Q2))))
% 5.61/5.91 (assert (@ tptp.proper tptp.one_assn_raw))
% 5.61/5.91 (assert (not (= tptp.bot_bot_assn tptp.one_one_assn)))
% 5.61/5.91 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat) (S tptp.set_Pr3948176798113811640et_nat) (P (-> tptp.heap_e7401611519738050253t_unit tptp.set_nat Bool))) (let ((_let_1 (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) B)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B)) (exists ((A4 tptp.heap_e7401611519738050253t_unit) (B2 tptp.set_nat)) (and (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A4) B2)) S) (@ (@ P A4) B2))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (S tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.nat tptp.nat Bool))) (let ((_let_1 (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B)) (exists ((A4 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A4) B2)) S) (@ (@ P A4) B2))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (S tptp.set_Pr958786334691620121nt_int) (P (-> tptp.int tptp.int Bool))) (let ((_let_1 (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B)) (exists ((A4 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A4) B2)) S) (@ (@ P A4) B2))))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (S tptp.set_Pr3286484037609594932et_nat) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) B)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B)) (exists ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3658429121746597890et_nat)) (and (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A4) B2)) S) (@ (@ P A4) B2))))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (S tptp.set_Pr8536935166611901872et_nat) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool))) (let ((_let_1 (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) B)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A2) B)) (exists ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3925858234332021118et_nat)) (and (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A4) B2)) S) (@ (@ P A4) B2))))))))
% 5.61/5.91 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (not (= X (@ (@ tptp.produc7507926704131184380et_nat H) As2)))))))
% 5.61/5.91 (assert (forall ((X tptp.product_prod_nat_nat) (A2 tptp.nat) (B tptp.nat) (P (-> tptp.nat Bool))) (=> (= X (@ (@ tptp.product_Pair_nat_nat A2) B)) (=> (@ P (@ tptp.product_snd_nat_nat X)) (@ P B)))))
% 5.61/5.91 (assert (forall ((X tptp.produc3925858234332021118et_nat) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (P (-> tptp.produc3658429121746597890et_nat Bool))) (=> (= X (@ (@ tptp.produc5001842942810119800et_nat A2) B)) (=> (@ P (@ tptp.produc4011572625026189258et_nat X)) (@ P B)))))
% 5.61/5.91 (assert (forall ((X tptp.produc2732055786443039994et_nat) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (P (-> tptp.produc3925858234332021118et_nat Bool))) (=> (= X (@ (@ tptp.produc2245416461498447860et_nat A2) B)) (=> (@ P (@ tptp.produc5374455773327741254et_nat X)) (@ P B)))))
% 5.61/5.91 (assert (forall ((X tptp.produc3658429121746597890et_nat) (A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat A2) B)) (=> (@ P (@ tptp.produc8586169260539613262et_nat X)) (@ P B)))))
% 5.61/5.91 (assert (forall ((X tptp.product_prod_int_int) (A2 tptp.int) (B tptp.int) (P (-> tptp.int Bool))) (=> (= X (@ (@ tptp.product_Pair_int_int A2) B)) (=> (@ P (@ tptp.product_snd_int_int X)) (@ P B)))))
% 5.61/5.91 (assert (forall ((X tptp.assn)) (@ (@ tptp.member6576561426505652726_nat_o (@ tptp.rep_assn X)) (@ tptp.collec939566748876313656_nat_o tptp.proper))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (= (@ (@ tptp.member6576561426505652726_nat_o A2) (@ tptp.collec939566748876313656_nat_o P)) (@ P A2))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A2) (@ tptp.collect_nat P)) (@ P A2))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A2) (@ tptp.collect_int P)) (@ P A2))))
% 5.61/5.91 (assert (forall ((A2 Bool) (P (-> Bool Bool))) (= (@ (@ tptp.member_o A2) (@ tptp.collect_o P)) (@ P A2))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (P (-> tptp.product_unit Bool))) (= (@ (@ tptp.member_Product_unit A2) (@ tptp.collect_Product_unit P)) (@ P A2))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (= (@ tptp.collec939566748876313656_nat_o (lambda ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o X2) A))) A)))
% 5.61/5.91 (assert (forall ((A tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) A))) A)))
% 5.61/5.91 (assert (forall ((A tptp.set_int)) (= (@ tptp.collect_int (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) A))) A)))
% 5.61/5.91 (assert (forall ((A tptp.set_o)) (= (@ tptp.collect_o (lambda ((X2 Bool)) (@ (@ tptp.member_o X2) A))) A)))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit)) (= (@ tptp.collect_Product_unit (lambda ((X2 tptp.product_unit)) (@ (@ tptp.member_Product_unit X2) A))) A)))
% 5.61/5.91 (assert (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (Q2 (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (= (@ P X3) (@ Q2 X3))) (= (@ tptp.collec939566748876313656_nat_o P) (@ tptp.collec939566748876313656_nat_o Q2)))))
% 5.61/5.91 (assert (forall ((P (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (= (@ P X3) (@ Q2 X3))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q2)))))
% 5.61/5.91 (assert (forall ((P (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (= (@ P X3) (@ Q2 X3))) (= (@ tptp.collect_int P) (@ tptp.collect_int Q2)))))
% 5.61/5.91 (assert (forall ((P (-> Bool Bool)) (Q2 (-> Bool Bool))) (=> (forall ((X3 Bool)) (= (@ P X3) (@ Q2 X3))) (= (@ tptp.collect_o P) (@ tptp.collect_o Q2)))))
% 5.61/5.91 (assert (forall ((P (-> tptp.product_unit Bool)) (Q2 (-> tptp.product_unit Bool))) (=> (forall ((X3 tptp.product_unit)) (= (@ P X3) (@ Q2 X3))) (= (@ tptp.collect_Product_unit P) (@ tptp.collect_Product_unit Q2)))))
% 5.61/5.91 (assert (forall ((Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) (@ tptp.collec939566748876313656_nat_o tptp.proper)) (not (forall ((X3 tptp.assn)) (not (= Y (@ tptp.rep_assn X3))))))))
% 5.61/5.91 (assert (forall ((Y (-> tptp.produc3658429121746597890et_nat Bool)) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) (@ tptp.collec939566748876313656_nat_o tptp.proper)) (=> (forall ((X3 tptp.assn)) (@ P (@ tptp.rep_assn X3))) (@ P Y)))))
% 5.61/5.91 (assert (forall ((X tptp.assn)) (not (forall ((Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (= X (@ tptp.abs_assn Y2)) (not (@ (@ tptp.member6576561426505652726_nat_o Y2) (@ tptp.collec939566748876313656_nat_o tptp.proper))))))))
% 5.61/5.91 (assert (forall ((P (-> tptp.assn Bool)) (X tptp.assn)) (=> (forall ((Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y2) (@ tptp.collec939566748876313656_nat_o tptp.proper)) (@ P (@ tptp.abs_assn Y2)))) (@ P X))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.collec939566748876313656_nat_o tptp.proper))) (=> (@ (@ tptp.member6576561426505652726_nat_o X) _let_1) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) _let_1) (= (= (@ tptp.abs_assn X) (@ tptp.abs_assn Y)) (= X Y)))))))
% 5.61/5.91 (assert (forall ((P tptp.assn) (H2 tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.rep_assn P))) (= (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat)) (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H3) tptp.bot_bot_set_nat))))))
% 5.61/5.91 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat) (A5 tptp.heap_e7401611519738050253t_unit) (B3 tptp.set_nat)) (= (= (@ (@ tptp.produc7507926704131184380et_nat A2) B) (@ (@ tptp.produc7507926704131184380et_nat A5) B3)) (and (= A2 A5) (= B B3)))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (A5 tptp.nat) (B3 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat A2) B) (@ (@ tptp.product_Pair_nat_nat A5) B3)) (and (= A2 A5) (= B B3)))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (A5 tptp.int) (B3 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int A2) B) (@ (@ tptp.product_Pair_int_int A5) B3)) (and (= A2 A5) (= B B3)))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (A5 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 tptp.produc3658429121746597890et_nat)) (= (= (@ (@ tptp.produc5001842942810119800et_nat A2) B) (@ (@ tptp.produc5001842942810119800et_nat A5) B3)) (and (= A2 A5) (= B B3)))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (A5 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 tptp.produc3925858234332021118et_nat)) (= (= (@ (@ tptp.produc2245416461498447860et_nat A2) B) (@ (@ tptp.produc2245416461498447860et_nat A5) B3)) (and (= A2 A5) (= B B3)))))
% 5.61/5.91 (assert (forall ((X1 tptp.heap_e7401611519738050253t_unit) (X22 tptp.set_nat) (Y1 tptp.heap_e7401611519738050253t_unit) (Y22 tptp.set_nat)) (= (= (@ (@ tptp.produc7507926704131184380et_nat X1) X22) (@ (@ tptp.produc7507926704131184380et_nat Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 5.61/5.91 (assert (forall ((X1 tptp.nat) (X22 tptp.nat) (Y1 tptp.nat) (Y22 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat X1) X22) (@ (@ tptp.product_Pair_nat_nat Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 5.61/5.91 (assert (forall ((X1 tptp.int) (X22 tptp.int) (Y1 tptp.int) (Y22 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int X1) X22) (@ (@ tptp.product_Pair_int_int Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 5.61/5.91 (assert (forall ((X1 (-> tptp.produc3658429121746597890et_nat Bool)) (X22 tptp.produc3658429121746597890et_nat) (Y1 (-> tptp.produc3658429121746597890et_nat Bool)) (Y22 tptp.produc3658429121746597890et_nat)) (= (= (@ (@ tptp.produc5001842942810119800et_nat X1) X22) (@ (@ tptp.produc5001842942810119800et_nat Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 5.61/5.91 (assert (forall ((X1 (-> tptp.produc3658429121746597890et_nat Bool)) (X22 tptp.produc3925858234332021118et_nat) (Y1 (-> tptp.produc3658429121746597890et_nat Bool)) (Y22 tptp.produc3925858234332021118et_nat)) (= (= (@ (@ tptp.produc2245416461498447860et_nat X1) X22) (@ (@ tptp.produc2245416461498447860et_nat Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 5.61/5.91 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.nat) (Z tptp.nat)) (=> (= X (@ (@ tptp.product_Pair_nat_nat Y) Z)) (= (@ tptp.product_snd_nat_nat X) Z))))
% 5.61/5.91 (assert (forall ((X tptp.produc3925858234332021118et_nat) (Y (-> tptp.produc3658429121746597890et_nat Bool)) (Z tptp.produc3658429121746597890et_nat)) (=> (= X (@ (@ tptp.produc5001842942810119800et_nat Y) Z)) (= (@ tptp.produc4011572625026189258et_nat X) Z))))
% 5.61/5.91 (assert (forall ((X tptp.produc2732055786443039994et_nat) (Y (-> tptp.produc3658429121746597890et_nat Bool)) (Z tptp.produc3925858234332021118et_nat)) (=> (= X (@ (@ tptp.produc2245416461498447860et_nat Y) Z)) (= (@ tptp.produc5374455773327741254et_nat X) Z))))
% 5.61/5.91 (assert (forall ((X tptp.produc3658429121746597890et_nat) (Y tptp.heap_e7401611519738050253t_unit) (Z tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat Y) Z)) (= (@ tptp.produc8586169260539613262et_nat X) Z))))
% 5.61/5.91 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.int) (Z tptp.int)) (=> (= X (@ (@ tptp.product_Pair_int_int Y) Z)) (= (@ tptp.product_snd_int_int X) Z))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (Y tptp.nat) (A2 tptp.nat)) (=> (= (@ tptp.product_snd_nat_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) A2) (= Y A2))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3658429121746597890et_nat) (A2 tptp.produc3658429121746597890et_nat)) (=> (= (@ tptp.produc4011572625026189258et_nat (@ (@ tptp.produc5001842942810119800et_nat X) Y)) A2) (= Y A2))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3925858234332021118et_nat) (A2 tptp.produc3925858234332021118et_nat)) (=> (= (@ tptp.produc5374455773327741254et_nat (@ (@ tptp.produc2245416461498447860et_nat X) Y)) A2) (= Y A2))))
% 5.61/5.91 (assert (forall ((X tptp.heap_e7401611519738050253t_unit) (Y tptp.set_nat) (A2 tptp.set_nat)) (=> (= (@ tptp.produc8586169260539613262et_nat (@ (@ tptp.produc7507926704131184380et_nat X) Y)) A2) (= Y A2))))
% 5.61/5.91 (assert (forall ((X tptp.int) (Y tptp.int) (A2 tptp.int)) (=> (= (@ tptp.product_snd_int_int (@ (@ tptp.product_Pair_int_int X) Y)) A2) (= Y A2))))
% 5.61/5.91 (assert (forall ((X1 tptp.nat) (X22 tptp.nat)) (= (@ tptp.product_snd_nat_nat (@ (@ tptp.product_Pair_nat_nat X1) X22)) X22)))
% 5.61/5.91 (assert (forall ((X1 (-> tptp.produc3658429121746597890et_nat Bool)) (X22 tptp.produc3658429121746597890et_nat)) (= (@ tptp.produc4011572625026189258et_nat (@ (@ tptp.produc5001842942810119800et_nat X1) X22)) X22)))
% 5.61/5.91 (assert (forall ((X1 (-> tptp.produc3658429121746597890et_nat Bool)) (X22 tptp.produc3925858234332021118et_nat)) (= (@ tptp.produc5374455773327741254et_nat (@ (@ tptp.produc2245416461498447860et_nat X1) X22)) X22)))
% 5.61/5.91 (assert (forall ((X1 tptp.heap_e7401611519738050253t_unit) (X22 tptp.set_nat)) (= (@ tptp.produc8586169260539613262et_nat (@ (@ tptp.produc7507926704131184380et_nat X1) X22)) X22)))
% 5.61/5.91 (assert (forall ((X1 tptp.int) (X22 tptp.int)) (= (@ tptp.product_snd_int_int (@ (@ tptp.product_Pair_int_int X1) X22)) X22)))
% 5.61/5.91 (assert (forall ((B tptp.nat) (P3 tptp.product_prod_nat_nat)) (= (= B (@ tptp.product_snd_nat_nat P3)) (exists ((A6 tptp.nat)) (= P3 (@ (@ tptp.product_Pair_nat_nat A6) B))))))
% 5.61/5.91 (assert (forall ((B tptp.produc3658429121746597890et_nat) (P3 tptp.produc3925858234332021118et_nat)) (= (= B (@ tptp.produc4011572625026189258et_nat P3)) (exists ((A6 (-> tptp.produc3658429121746597890et_nat Bool))) (= P3 (@ (@ tptp.produc5001842942810119800et_nat A6) B))))))
% 5.61/5.91 (assert (forall ((B tptp.produc3925858234332021118et_nat) (P3 tptp.produc2732055786443039994et_nat)) (= (= B (@ tptp.produc5374455773327741254et_nat P3)) (exists ((A6 (-> tptp.produc3658429121746597890et_nat Bool))) (= P3 (@ (@ tptp.produc2245416461498447860et_nat A6) B))))))
% 5.61/5.91 (assert (forall ((B tptp.set_nat) (P3 tptp.produc3658429121746597890et_nat)) (= (= B (@ tptp.produc8586169260539613262et_nat P3)) (exists ((A6 tptp.heap_e7401611519738050253t_unit)) (= P3 (@ (@ tptp.produc7507926704131184380et_nat A6) B))))))
% 5.61/5.91 (assert (forall ((B tptp.int) (P3 tptp.product_prod_int_int)) (= (= B (@ tptp.product_snd_int_int P3)) (exists ((A6 tptp.int)) (= P3 (@ (@ tptp.product_Pair_int_int A6) B))))))
% 5.61/5.91 (assert (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat)) (=> (not (@ (@ tptp.pure_a825153325127701367it_nat X) Xa)) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= Xa (@ (@ tptp.produc7507926704131184380et_nat H) As2)) (and (= As2 tptp.bot_bot_set_nat) X)))))))
% 5.61/5.91 (assert (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.pure_a825153325127701367it_nat X) Xa) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= Xa (@ (@ tptp.produc7507926704131184380et_nat H) As2)) (not (and (= As2 tptp.bot_bot_set_nat) X))))))))
% 5.61/5.91 (assert (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ tptp.pure_a825153325127701367it_nat X) Xa) Y) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= Xa (@ (@ tptp.produc7507926704131184380et_nat H) As2)) (= Y (not (and (= As2 tptp.bot_bot_set_nat) X)))))))))
% 5.61/5.91 (assert (forall ((B Bool) (H2 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (= (@ (@ tptp.pure_a825153325127701367it_nat B) (@ (@ tptp.produc7507926704131184380et_nat H2) As)) (and (= As tptp.bot_bot_set_nat) B))))
% 5.61/5.91 (assert (forall ((B Bool)) (@ tptp.proper (@ tptp.pure_a825153325127701367it_nat B))))
% 5.61/5.91 (assert (forall ((X tptp.produc2732055786443039994et_nat)) (not (forall ((P4 (-> tptp.produc3658429121746597890et_nat Bool)) (Q3 (-> tptp.produc3658429121746597890et_nat Bool)) (H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (not (= X (@ (@ tptp.produc2245416461498447860et_nat P4) (@ (@ tptp.produc5001842942810119800et_nat Q3) (@ (@ tptp.produc7507926704131184380et_nat H) As2)))))))))
% 5.61/5.91 (assert (forall ((X tptp.produc6197004810343482825et_nat)) (not (forall ((B2 Bool) (H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (not (= X (@ (@ tptp.produc3762353314782720579et_nat B2) (@ (@ tptp.produc7507926704131184380et_nat H) As2))))))))
% 5.61/5.91 (assert (forall ((Y tptp.produc3658429121746597890et_nat)) (not (forall ((A4 tptp.heap_e7401611519738050253t_unit) (B2 tptp.set_nat)) (not (= Y (@ (@ tptp.produc7507926704131184380et_nat A4) B2)))))))
% 5.61/5.91 (assert (forall ((Y tptp.product_prod_nat_nat)) (not (forall ((A4 tptp.nat) (B2 tptp.nat)) (not (= Y (@ (@ tptp.product_Pair_nat_nat A4) B2)))))))
% 5.61/5.91 (assert (forall ((Y tptp.product_prod_int_int)) (not (forall ((A4 tptp.int) (B2 tptp.int)) (not (= Y (@ (@ tptp.product_Pair_int_int A4) B2)))))))
% 5.61/5.91 (assert (forall ((Y tptp.produc3925858234332021118et_nat)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3658429121746597890et_nat)) (not (= Y (@ (@ tptp.produc5001842942810119800et_nat A4) B2)))))))
% 5.61/5.91 (assert (forall ((Y tptp.produc2732055786443039994et_nat)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3925858234332021118et_nat)) (not (= Y (@ (@ tptp.produc2245416461498447860et_nat A4) B2)))))))
% 5.61/5.91 (assert (forall ((P3 tptp.produc3658429121746597890et_nat)) (exists ((X3 tptp.heap_e7401611519738050253t_unit) (Y2 tptp.set_nat)) (= P3 (@ (@ tptp.produc7507926704131184380et_nat X3) Y2)))))
% 5.61/5.91 (assert (forall ((P3 tptp.product_prod_nat_nat)) (exists ((X3 tptp.nat) (Y2 tptp.nat)) (= P3 (@ (@ tptp.product_Pair_nat_nat X3) Y2)))))
% 5.61/5.91 (assert (forall ((P3 tptp.product_prod_int_int)) (exists ((X3 tptp.int) (Y2 tptp.int)) (= P3 (@ (@ tptp.product_Pair_int_int X3) Y2)))))
% 5.61/5.91 (assert (forall ((P3 tptp.produc3925858234332021118et_nat)) (exists ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3658429121746597890et_nat)) (= P3 (@ (@ tptp.produc5001842942810119800et_nat X3) Y2)))))
% 5.61/5.91 (assert (forall ((P3 tptp.produc2732055786443039994et_nat)) (exists ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3925858234332021118et_nat)) (= P3 (@ (@ tptp.produc2245416461498447860et_nat X3) Y2)))))
% 5.61/5.91 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (P3 tptp.produc3658429121746597890et_nat)) (=> (forall ((A4 tptp.heap_e7401611519738050253t_unit) (B2 tptp.set_nat)) (@ P (@ (@ tptp.produc7507926704131184380et_nat A4) B2))) (@ P P3))))
% 5.61/5.91 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (P3 tptp.product_prod_nat_nat)) (=> (forall ((A4 tptp.nat) (B2 tptp.nat)) (@ P (@ (@ tptp.product_Pair_nat_nat A4) B2))) (@ P P3))))
% 5.61/5.91 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (P3 tptp.product_prod_int_int)) (=> (forall ((A4 tptp.int) (B2 tptp.int)) (@ P (@ (@ tptp.product_Pair_int_int A4) B2))) (@ P P3))))
% 5.61/5.91 (assert (forall ((P (-> tptp.produc3925858234332021118et_nat Bool)) (P3 tptp.produc3925858234332021118et_nat)) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3658429121746597890et_nat)) (@ P (@ (@ tptp.produc5001842942810119800et_nat A4) B2))) (@ P P3))))
% 5.61/5.91 (assert (forall ((P (-> tptp.produc2732055786443039994et_nat Bool)) (P3 tptp.produc2732055786443039994et_nat)) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3925858234332021118et_nat)) (@ P (@ (@ tptp.produc2245416461498447860et_nat A4) B2))) (@ P P3))))
% 5.61/5.91 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat) (A5 tptp.heap_e7401611519738050253t_unit) (B3 tptp.set_nat)) (=> (= (@ (@ tptp.produc7507926704131184380et_nat A2) B) (@ (@ tptp.produc7507926704131184380et_nat A5) B3)) (not (=> (= A2 A5) (not (= B B3)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (A5 tptp.nat) (B3 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A2) B) (@ (@ tptp.product_Pair_nat_nat A5) B3)) (not (=> (= A2 A5) (not (= B B3)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (A5 tptp.int) (B3 tptp.int)) (=> (= (@ (@ tptp.product_Pair_int_int A2) B) (@ (@ tptp.product_Pair_int_int A5) B3)) (not (=> (= A2 A5) (not (= B B3)))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (A5 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 tptp.produc3658429121746597890et_nat)) (=> (= (@ (@ tptp.produc5001842942810119800et_nat A2) B) (@ (@ tptp.produc5001842942810119800et_nat A5) B3)) (not (=> (= A2 A5) (not (= B B3)))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (A5 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 tptp.produc3925858234332021118et_nat)) (=> (= (@ (@ tptp.produc2245416461498447860et_nat A2) B) (@ (@ tptp.produc2245416461498447860et_nat A5) B3)) (not (=> (= A2 A5) (not (= B B3)))))))
% 5.61/5.91 (assert (forall ((Y tptp.produc3925858234332021118et_nat)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.heap_e7401611519738050253t_unit) (C2 tptp.set_nat)) (not (= Y (@ (@ tptp.produc5001842942810119800et_nat A4) (@ (@ tptp.produc7507926704131184380et_nat B2) C2))))))))
% 5.61/5.91 (assert (forall ((Y tptp.produc2732055786443039994et_nat)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 (-> tptp.produc3658429121746597890et_nat Bool)) (C2 tptp.produc3658429121746597890et_nat)) (not (= Y (@ (@ tptp.produc2245416461498447860et_nat A4) (@ (@ tptp.produc5001842942810119800et_nat B2) C2))))))))
% 5.61/5.91 (assert (forall ((Y tptp.produc2732055786443039994et_nat)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 (-> tptp.produc3658429121746597890et_nat Bool)) (C2 tptp.heap_e7401611519738050253t_unit) (D tptp.set_nat)) (not (= Y (@ (@ tptp.produc2245416461498447860et_nat A4) (@ (@ tptp.produc5001842942810119800et_nat B2) (@ (@ tptp.produc7507926704131184380et_nat C2) D)))))))))
% 5.61/5.91 (assert (forall ((P (-> tptp.produc3925858234332021118et_nat Bool)) (X tptp.produc3925858234332021118et_nat)) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.heap_e7401611519738050253t_unit) (C2 tptp.set_nat)) (@ P (@ (@ tptp.produc5001842942810119800et_nat A4) (@ (@ tptp.produc7507926704131184380et_nat B2) C2)))) (@ P X))))
% 5.61/5.91 (assert (forall ((P (-> tptp.produc2732055786443039994et_nat Bool)) (X tptp.produc2732055786443039994et_nat)) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 (-> tptp.produc3658429121746597890et_nat Bool)) (C2 tptp.produc3658429121746597890et_nat)) (@ P (@ (@ tptp.produc2245416461498447860et_nat A4) (@ (@ tptp.produc5001842942810119800et_nat B2) C2)))) (@ P X))))
% 5.61/5.91 (assert (forall ((P (-> tptp.produc2732055786443039994et_nat Bool)) (X tptp.produc2732055786443039994et_nat)) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 (-> tptp.produc3658429121746597890et_nat Bool)) (C2 tptp.heap_e7401611519738050253t_unit) (D tptp.set_nat)) (@ P (@ (@ tptp.produc2245416461498447860et_nat A4) (@ (@ tptp.produc5001842942810119800et_nat B2) (@ (@ tptp.produc7507926704131184380et_nat C2) D))))) (@ P X))))
% 5.61/5.91 (assert (forall ((X tptp.assn)) (= (= tptp.one_one_assn X) (= X tptp.one_one_assn))))
% 5.61/5.91 (assert (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))))
% 5.61/5.91 (assert (forall ((X tptp.int)) (= (= tptp.one_one_int X) (= X tptp.one_one_int))))
% 5.61/5.91 (assert (forall ((X tptp.code_integer)) (= (= tptp.one_one_Code_integer X) (= X tptp.one_one_Code_integer))))
% 5.61/5.91 (assert (forall ((X tptp.code_natural)) (= (= tptp.one_one_Code_natural X) (= X tptp.one_one_Code_natural))))
% 5.61/5.91 (assert (@ (@ (@ tptp.type_d3909072315231072503_nat_o tptp.rep_assn) tptp.abs_assn) (@ tptp.collec939566748876313656_nat_o tptp.proper)))
% 5.61/5.91 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Q2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.proper P) (=> (@ tptp.proper Q2) (@ tptp.proper (@ (@ tptp.times_assn_raw P) Q2))))))
% 5.61/5.91 (assert (@ tptp.is_pure_assn tptp.one_one_assn))
% 5.61/5.91 (assert (= tptp.biject2219996528949639174et_nat (lambda ((R tptp.set_Pr3948176798113811640et_nat)) (and (forall ((X2 tptp.heap_e7401611519738050253t_unit) (Y3 tptp.set_nat) (Z2 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat X2))) (=> (and (@ (@ tptp.member6260224972018164377et_nat (@ _let_1 Y3)) R) (@ (@ tptp.member6260224972018164377et_nat (@ _let_1 Z2)) R)) (= Y3 Z2)))) (forall ((X2 tptp.heap_e7401611519738050253t_unit) (Y3 tptp.heap_e7401611519738050253t_unit) (Z2 tptp.set_nat)) (=> (and (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat X2) Z2)) R) (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat Y3) Z2)) R)) (= X2 Y3)))))))
% 5.61/5.91 (assert (= tptp.bijective_nat_nat (lambda ((R tptp.set_Pr1261947904930325089at_nat)) (and (forall ((X2 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X2))) (=> (and (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 Y3)) R) (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 Z2)) R)) (= Y3 Z2)))) (forall ((X2 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (=> (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Z2)) R) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y3) Z2)) R)) (= X2 Y3)))))))
% 5.61/5.91 (assert (= tptp.bijective_int_int (lambda ((R tptp.set_Pr958786334691620121nt_int)) (and (forall ((X2 tptp.int) (Y3 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int X2))) (=> (and (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 Y3)) R) (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 Z2)) R)) (= Y3 Z2)))) (forall ((X2 tptp.int) (Y3 tptp.int) (Z2 tptp.int)) (=> (and (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X2) Z2)) R) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y3) Z2)) R)) (= X2 Y3)))))))
% 5.61/5.91 (assert (= tptp.biject2615096655818420098et_nat (lambda ((R tptp.set_Pr3286484037609594932et_nat)) (and (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool)) (Y3 tptp.produc3658429121746597890et_nat) (Z2 tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.produc5001842942810119800et_nat X2))) (=> (and (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 Y3)) R) (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 Z2)) R)) (= Y3 Z2)))) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool)) (Y3 (-> tptp.produc3658429121746597890et_nat Bool)) (Z2 tptp.produc3658429121746597890et_nat)) (=> (and (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X2) Z2)) R) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat Y3) Z2)) R)) (= X2 Y3)))))))
% 5.61/5.91 (assert (= tptp.biject1468766312547416318et_nat (lambda ((R tptp.set_Pr8536935166611901872et_nat)) (and (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool)) (Y3 tptp.produc3925858234332021118et_nat) (Z2 tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ tptp.produc2245416461498447860et_nat X2))) (=> (and (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 Y3)) R) (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 Z2)) R)) (= Y3 Z2)))) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool)) (Y3 (-> tptp.produc3658429121746597890et_nat Bool)) (Z2 tptp.produc3925858234332021118et_nat)) (=> (and (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X2) Z2)) R) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat Y3) Z2)) R)) (= X2 Y3)))))))
% 5.61/5.91 (assert (forall ((R2 tptp.heap_e7401611519738050253t_unit) (S2 tptp.set_nat) (R3 tptp.set_Pr3948176798113811640et_nat) (S3 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat R2))) (=> (@ (@ tptp.member6260224972018164377et_nat (@ _let_1 S2)) R3) (=> (= S3 S2) (@ (@ tptp.member6260224972018164377et_nat (@ _let_1 S3)) R3))))))
% 5.61/5.91 (assert (forall ((R2 tptp.nat) (S2 tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat) (S3 tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat R2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 S2)) R3) (=> (= S3 S2) (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 S3)) R3))))))
% 5.61/5.91 (assert (forall ((R2 tptp.int) (S2 tptp.int) (R3 tptp.set_Pr958786334691620121nt_int) (S3 tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int R2))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 S2)) R3) (=> (= S3 S2) (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 S3)) R3))))))
% 5.61/5.91 (assert (forall ((R2 (-> tptp.produc3658429121746597890et_nat Bool)) (S2 tptp.produc3658429121746597890et_nat) (R3 tptp.set_Pr3286484037609594932et_nat) (S3 tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.produc5001842942810119800et_nat R2))) (=> (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 S2)) R3) (=> (= S3 S2) (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 S3)) R3))))))
% 5.61/5.91 (assert (forall ((R2 (-> tptp.produc3658429121746597890et_nat Bool)) (S2 tptp.produc3925858234332021118et_nat) (R3 tptp.set_Pr8536935166611901872et_nat) (S3 tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ tptp.produc2245416461498447860et_nat R2))) (=> (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 S2)) R3) (=> (= S3 S2) (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 S3)) R3))))))
% 5.61/5.91 (assert (forall ((X tptp.product_unit)) (@ tptp.is_sin2160648248035936513t_unit (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.91 (assert (forall ((X Bool)) (@ tptp.is_singleton_o (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))))
% 5.61/5.91 (assert (forall ((X tptp.nat)) (@ tptp.is_singleton_nat (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))
% 5.61/5.91 (assert (forall ((X tptp.int)) (@ tptp.is_singleton_int (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool))) (@ tptp.is_sin5180296473474724033_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.91 (assert (forall ((F (-> tptp.produc3658429121746597890et_nat Bool)) (A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat)) (=> (@ F (@ (@ tptp.produc7507926704131184380et_nat A2) B)) (@ (@ (@ tptp.produc1807123492089482958_nat_o F) A2) B))))
% 5.61/5.91 (assert (forall ((F (-> tptp.product_prod_nat_nat Bool)) (A2 tptp.nat) (B tptp.nat)) (=> (@ F (@ (@ tptp.product_Pair_nat_nat A2) B)) (@ (@ (@ tptp.produc1310100445399344235_nat_o F) A2) B))))
% 5.61/5.91 (assert (forall ((F (-> tptp.product_prod_int_int Bool)) (A2 tptp.int) (B tptp.int)) (=> (@ F (@ (@ tptp.product_Pair_int_int A2) B)) (@ (@ (@ tptp.produc175634133007206835_int_o F) A2) B))))
% 5.61/5.91 (assert (forall ((F (-> tptp.produc3925858234332021118et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat)) (=> (@ F (@ (@ tptp.produc5001842942810119800et_nat A2) B)) (@ (@ (@ tptp.produc6216949301066131538_nat_o F) A2) B))))
% 5.61/5.91 (assert (forall ((F (-> tptp.produc2732055786443039994et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat)) (=> (@ F (@ (@ tptp.produc2245416461498447860et_nat A2) B)) (@ (@ (@ tptp.produc5101573711933517782_nat_o F) A2) B))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.set_Pr4532377907799695533_nat_o) (B (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o A2))) (=> (=> (not (@ _let_1 B4)) (= A2 B)) (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o B) B4))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B4 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (=> (not (@ _let_1 B4)) (= A2 B)) (@ _let_1 (@ (@ tptp.insert_nat B) B4))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B4 tptp.set_int) (B tptp.int)) (let ((_let_1 (@ tptp.member_int A2))) (=> (=> (not (@ _let_1 B4)) (= A2 B)) (@ _let_1 (@ (@ tptp.insert_int B) B4))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (B4 tptp.set_o) (B Bool)) (let ((_let_1 (@ tptp.member_o A2))) (=> (=> (not (@ _let_1 B4)) (= A2 B)) (@ _let_1 (@ (@ tptp.insert_o B) B4))))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (B4 tptp.set_Product_unit) (B tptp.product_unit)) (let ((_let_1 (@ tptp.member_Product_unit A2))) (=> (=> (not (@ _let_1 B4)) (= A2 B)) (@ _let_1 (@ (@ tptp.insert_Product_unit B) B4))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o A2))) (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o B) A)) (or (= A2 B) (@ _let_1 A))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A2))) (= (@ _let_1 (@ (@ tptp.insert_nat B) A)) (or (= A2 B) (@ _let_1 A))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.member_int A2))) (= (@ _let_1 (@ (@ tptp.insert_int B) A)) (or (= A2 B) (@ _let_1 A))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (B Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.member_o A2))) (= (@ _let_1 (@ (@ tptp.insert_o B) A)) (or (= A2 B) (@ _let_1 A))))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (B tptp.product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member_Product_unit A2))) (= (@ _let_1 (@ (@ tptp.insert_Product_unit B) A)) (or (= A2 B) (@ _let_1 A))))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ _let_1 A))) (= (@ _let_1 _let_2) _let_2)))))
% 5.61/5.91 (assert (forall ((X tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ _let_1 A))) (= (@ _let_1 _let_2) _let_2)))))
% 5.61/5.91 (assert (forall ((X Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X))) (let ((_let_2 (@ _let_1 A))) (= (@ _let_1 _let_2) _let_2)))))
% 5.61/5.91 (assert (forall ((X tptp.product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit X))) (let ((_let_2 (@ _let_1 A))) (= (@ _let_1 _let_2) _let_2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit)) (@ (@ tptp.member_Product_unit A2) (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.91 (assert (forall ((A2 Bool)) (@ (@ tptp.member_o A2) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.member_nat A2) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))))
% 5.61/5.91 (assert (forall ((A2 tptp.int)) (@ (@ tptp.member_int A2) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o A2) (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o A2))) (=> (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o B) A)) (=> (not (= A2 B)) (@ _let_1 A))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (@ _let_1 (@ (@ tptp.insert_nat B) A)) (=> (not (= A2 B)) (@ _let_1 A))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.member_int A2))) (=> (@ _let_1 (@ (@ tptp.insert_int B) A)) (=> (not (= A2 B)) (@ _let_1 A))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (B Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.member_o A2))) (=> (@ _let_1 (@ (@ tptp.insert_o B) A)) (=> (= A2 (not B)) (@ _let_1 A))))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (B tptp.product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member_Product_unit A2))) (=> (@ _let_1 (@ (@ tptp.insert_Product_unit B) A)) (=> (not (= A2 B)) (@ _let_1 A))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.set_Pr4532377907799695533_nat_o)) (@ (@ tptp.member6576561426505652726_nat_o A2) (@ (@ tptp.insert5175938949040314269_nat_o A2) B4))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B4 tptp.set_nat)) (@ (@ tptp.member_nat A2) (@ (@ tptp.insert_nat A2) B4))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B4 tptp.set_int)) (@ (@ tptp.member_int A2) (@ (@ tptp.insert_int A2) B4))))
% 5.61/5.91 (assert (forall ((A2 Bool) (B4 tptp.set_o)) (@ (@ tptp.member_o A2) (@ (@ tptp.insert_o A2) B4))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (B4 tptp.set_Product_unit)) (@ (@ tptp.member_Product_unit A2) (@ (@ tptp.insert_Product_unit A2) B4))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.set_Pr4532377907799695533_nat_o) (B (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o A2))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o B) B4))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B4 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert_nat B) B4))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B4 tptp.set_int) (B tptp.int)) (let ((_let_1 (@ tptp.member_int A2))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert_int B) B4))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (B4 tptp.set_o) (B Bool)) (let ((_let_1 (@ tptp.member_o A2))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert_o B) B4))))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (B4 tptp.set_Product_unit) (B tptp.product_unit)) (let ((_let_1 (@ tptp.member_Product_unit A2))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert_Product_unit B) B4))))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o X) A) (not (forall ((B5 tptp.set_Pr4532377907799695533_nat_o)) (=> (= A (@ (@ tptp.insert5175938949040314269_nat_o X) B5)) (@ (@ tptp.member6576561426505652726_nat_o X) B5)))))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat X) A) (not (forall ((B5 tptp.set_nat)) (=> (= A (@ (@ tptp.insert_nat X) B5)) (@ (@ tptp.member_nat X) B5)))))))
% 5.61/5.91 (assert (forall ((X tptp.int) (A tptp.set_int)) (=> (@ (@ tptp.member_int X) A) (not (forall ((B5 tptp.set_int)) (=> (= A (@ (@ tptp.insert_int X) B5)) (@ (@ tptp.member_int X) B5)))))))
% 5.61/5.91 (assert (forall ((X Bool) (A tptp.set_o)) (=> (@ (@ tptp.member_o X) A) (not (forall ((B5 tptp.set_o)) (=> (= A (@ (@ tptp.insert_o X) B5)) (@ (@ tptp.member_o X) B5)))))))
% 5.61/5.91 (assert (forall ((X tptp.product_unit) (A tptp.set_Product_unit)) (=> (@ (@ tptp.member_Product_unit X) A) (not (forall ((B5 tptp.set_Product_unit)) (=> (= A (@ (@ tptp.insert_Product_unit X) B5)) (@ (@ tptp.member_Product_unit X) B5)))))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.insert5175938949040314269_nat_o X))) (let ((_let_2 (@ tptp.member6576561426505652726_nat_o X))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B4)) (= (= (@ _let_1 A) (@ _let_1 B4)) (= A B4))))))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.member_nat X))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B4)) (= (= (@ _let_1 A) (@ _let_1 B4)) (= A B4))))))))
% 5.61/5.91 (assert (forall ((X tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.member_int X))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B4)) (= (= (@ _let_1 A) (@ _let_1 B4)) (= A B4))))))))
% 5.61/5.91 (assert (forall ((X Bool) (A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X))) (let ((_let_2 (@ tptp.member_o X))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B4)) (= (= (@ _let_1 A) (@ _let_1 B4)) (= A B4))))))))
% 5.61/5.91 (assert (forall ((X tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit X))) (let ((_let_2 (@ tptp.member_Product_unit X))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B4)) (= (= (@ _let_1 A) (@ _let_1 B4)) (= A B4))))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) A) (= (@ (@ tptp.insert5175938949040314269_nat_o A2) A) A))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat A2) A) (= (@ (@ tptp.insert_nat A2) A) A))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (A tptp.set_int)) (=> (@ (@ tptp.member_int A2) A) (= (@ (@ tptp.insert_int A2) A) A))))
% 5.61/5.91 (assert (forall ((A2 Bool) (A tptp.set_o)) (=> (@ (@ tptp.member_o A2) A) (= (@ (@ tptp.insert_o A2) A) A))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (A tptp.set_Product_unit)) (=> (@ (@ tptp.member_Product_unit A2) A) (= (@ (@ tptp.insert_Product_unit A2) A) A))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (= A2 B))) (=> (not (@ (@ tptp.member6576561426505652726_nat_o A2) A)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o B) B4)) (= (= (@ (@ tptp.insert5175938949040314269_nat_o A2) A) (@ (@ tptp.insert5175938949040314269_nat_o B) B4)) (and (=> _let_1 (= A B4)) (=> (not _let_1) (exists ((C3 tptp.set_Pr4532377907799695533_nat_o)) (and (= A (@ (@ tptp.insert5175938949040314269_nat_o B) C3)) (not (@ (@ tptp.member6576561426505652726_nat_o B) C3)) (= B4 (@ (@ tptp.insert5175938949040314269_nat_o A2) C3)) (not (@ (@ tptp.member6576561426505652726_nat_o A2) C3))))))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (= A2 B))) (=> (not (@ (@ tptp.member_nat A2) A)) (=> (not (@ (@ tptp.member_nat B) B4)) (= (= (@ (@ tptp.insert_nat A2) A) (@ (@ tptp.insert_nat B) B4)) (and (=> _let_1 (= A B4)) (=> (not _let_1) (exists ((C3 tptp.set_nat)) (and (= A (@ (@ tptp.insert_nat B) C3)) (not (@ (@ tptp.member_nat B) C3)) (= B4 (@ (@ tptp.insert_nat A2) C3)) (not (@ (@ tptp.member_nat A2) C3))))))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B tptp.int) (B4 tptp.set_int)) (let ((_let_1 (= A2 B))) (=> (not (@ (@ tptp.member_int A2) A)) (=> (not (@ (@ tptp.member_int B) B4)) (= (= (@ (@ tptp.insert_int A2) A) (@ (@ tptp.insert_int B) B4)) (and (=> _let_1 (= A B4)) (=> (not _let_1) (exists ((C3 tptp.set_int)) (and (= A (@ (@ tptp.insert_int B) C3)) (not (@ (@ tptp.member_int B) C3)) (= B4 (@ (@ tptp.insert_int A2) C3)) (not (@ (@ tptp.member_int A2) C3))))))))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (A tptp.set_o) (B Bool) (B4 tptp.set_o)) (=> (not (@ (@ tptp.member_o A2) A)) (=> (not (@ (@ tptp.member_o B) B4)) (= (= (@ (@ tptp.insert_o A2) A) (@ (@ tptp.insert_o B) B4)) (and (=> (= A2 B) (= A B4)) (=> (= A2 (not B)) (exists ((C3 tptp.set_o)) (and (= A (@ (@ tptp.insert_o B) C3)) (not (@ (@ tptp.member_o B) C3)) (= B4 (@ (@ tptp.insert_o A2) C3)) (not (@ (@ tptp.member_o A2) C3)))))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (A tptp.set_Product_unit) (B tptp.product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (= A2 B))) (=> (not (@ (@ tptp.member_Product_unit A2) A)) (=> (not (@ (@ tptp.member_Product_unit B) B4)) (= (= (@ (@ tptp.insert_Product_unit A2) A) (@ (@ tptp.insert_Product_unit B) B4)) (and (=> _let_1 (= A B4)) (=> (not _let_1) (exists ((C3 tptp.set_Product_unit)) (and (= A (@ (@ tptp.insert_Product_unit B) C3)) (not (@ (@ tptp.member_Product_unit B) C3)) (= B4 (@ (@ tptp.insert_Product_unit A2) C3)) (not (@ (@ tptp.member_Product_unit A2) C3))))))))))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.insert_nat Y))) (= (@ _let_1 (@ _let_2 A)) (@ _let_2 (@ _let_1 A)))))))
% 5.61/5.91 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.insert_int Y))) (= (@ _let_1 (@ _let_2 A)) (@ _let_2 (@ _let_1 A)))))))
% 5.61/5.91 (assert (forall ((X Bool) (Y Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X))) (let ((_let_2 (@ tptp.insert_o Y))) (= (@ _let_1 (@ _let_2 A)) (@ _let_2 (@ _let_1 A)))))))
% 5.61/5.91 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit X))) (let ((_let_2 (@ tptp.insert_Product_unit Y))) (= (@ _let_1 (@ _let_2 A)) (@ _let_2 (@ _let_1 A)))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) A) (exists ((B5 tptp.set_Pr4532377907799695533_nat_o)) (and (= A (@ (@ tptp.insert5175938949040314269_nat_o A2) B5)) (not (@ (@ tptp.member6576561426505652726_nat_o A2) B5)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat A2) A) (exists ((B5 tptp.set_nat)) (and (= A (@ (@ tptp.insert_nat A2) B5)) (not (@ (@ tptp.member_nat A2) B5)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (A tptp.set_int)) (=> (@ (@ tptp.member_int A2) A) (exists ((B5 tptp.set_int)) (and (= A (@ (@ tptp.insert_int A2) B5)) (not (@ (@ tptp.member_int A2) B5)))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (A tptp.set_o)) (=> (@ (@ tptp.member_o A2) A) (exists ((B5 tptp.set_o)) (and (= A (@ (@ tptp.insert_o A2) B5)) (not (@ (@ tptp.member_o A2) B5)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (A tptp.set_Product_unit)) (=> (@ (@ tptp.member_Product_unit A2) A) (exists ((B5 tptp.set_Product_unit)) (and (= A (@ (@ tptp.insert_Product_unit A2) B5)) (not (@ (@ tptp.member_Product_unit A2) B5)))))))
% 5.61/5.91 (assert (forall ((B tptp.product_unit) (A2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit B) (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit)) (= B A2))))
% 5.61/5.91 (assert (forall ((B Bool) (A2 Bool)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o)) (= B A2))))
% 5.61/5.91 (assert (forall ((B tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat)) (= B A2))))
% 5.61/5.91 (assert (forall ((B tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.member_int B) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int)) (= B A2))))
% 5.61/5.91 (assert (forall ((B (-> tptp.produc3658429121746597890et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o B) (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o)) (= B A2))))
% 5.61/5.91 (assert (forall ((B tptp.product_unit) (A2 tptp.product_unit)) (= (@ (@ tptp.member_Product_unit B) (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit)) (= B A2))))
% 5.61/5.91 (assert (forall ((B Bool) (A2 Bool)) (= (@ (@ tptp.member_o B) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o)) (= B A2))))
% 5.61/5.91 (assert (forall ((B tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.member_nat B) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat)) (= B A2))))
% 5.61/5.91 (assert (forall ((B tptp.int) (A2 tptp.int)) (= (@ (@ tptp.member_int B) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int)) (= B A2))))
% 5.61/5.91 (assert (forall ((B (-> tptp.produc3658429121746597890et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (= (@ (@ tptp.member6576561426505652726_nat_o B) (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o)) (= B A2))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (B tptp.product_unit) (C tptp.product_unit) (D2 tptp.product_unit)) (= (= (@ (@ tptp.insert_Product_unit A2) (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit)) (@ (@ tptp.insert_Product_unit C) (@ (@ tptp.insert_Product_unit D2) tptp.bot_bo3957492148770167129t_unit))) (or (and (= A2 C) (= B D2)) (and (= A2 D2) (= B C))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (B Bool) (C Bool) (D2 Bool)) (= (= (@ (@ tptp.insert_o A2) (@ (@ tptp.insert_o B) tptp.bot_bot_set_o)) (@ (@ tptp.insert_o C) (@ (@ tptp.insert_o D2) tptp.bot_bot_set_o))) (or (and (= A2 C) (= B D2)) (and (= A2 D2) (= B C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (= (= (@ (@ tptp.insert_nat A2) (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat)) (@ (@ tptp.insert_nat C) (@ (@ tptp.insert_nat D2) tptp.bot_bot_set_nat))) (or (and (= A2 C) (= B D2)) (and (= A2 D2) (= B C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.insert_int A2) (@ (@ tptp.insert_int B) tptp.bot_bot_set_int)) (@ (@ tptp.insert_int C) (@ (@ tptp.insert_int D2) tptp.bot_bot_set_int))) (or (and (= A2 C) (= B D2)) (and (= A2 D2) (= B C))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool)) (C (-> tptp.produc3658429121746597890et_nat Bool)) (D2 (-> tptp.produc3658429121746597890et_nat Bool))) (= (= (@ (@ tptp.insert5175938949040314269_nat_o A2) (@ (@ tptp.insert5175938949040314269_nat_o B) tptp.bot_bo7824918357723582233_nat_o)) (@ (@ tptp.insert5175938949040314269_nat_o C) (@ (@ tptp.insert5175938949040314269_nat_o D2) tptp.bot_bo7824918357723582233_nat_o))) (or (and (= A2 C) (= B D2)) (and (= A2 D2) (= B C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (A tptp.set_Product_unit)) (not (= (@ (@ tptp.insert_Product_unit A2) A) tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.91 (assert (forall ((A2 Bool) (A tptp.set_o)) (not (= (@ (@ tptp.insert_o A2) A) tptp.bot_bot_set_o))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (A tptp.set_nat)) (not (= (@ (@ tptp.insert_nat A2) A) tptp.bot_bot_set_nat))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (A tptp.set_int)) (not (= (@ (@ tptp.insert_int A2) A) tptp.bot_bot_set_int))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (not (= (@ (@ tptp.insert5175938949040314269_nat_o A2) A) tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (B tptp.product_unit)) (=> (= (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit) (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit)) (= A2 B))))
% 5.61/5.91 (assert (forall ((A2 Bool) (B Bool)) (=> (= (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o) (@ (@ tptp.insert_o B) tptp.bot_bot_set_o)) (= A2 B))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat) (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat)) (= A2 B))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int) (@ (@ tptp.insert_int B) tptp.bot_bot_set_int)) (= A2 B))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool))) (=> (= (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o) (@ (@ tptp.insert5175938949040314269_nat_o B) tptp.bot_bo7824918357723582233_nat_o)) (= A2 B))))
% 5.61/5.91 (assert (forall ((F (-> tptp.produc3658429121746597890et_nat Bool)) (A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat)) (=> (@ (@ (@ tptp.produc1807123492089482958_nat_o F) A2) B) (@ F (@ (@ tptp.produc7507926704131184380et_nat A2) B)))))
% 5.61/5.91 (assert (forall ((F (-> tptp.product_prod_nat_nat Bool)) (A2 tptp.nat) (B tptp.nat)) (=> (@ (@ (@ tptp.produc1310100445399344235_nat_o F) A2) B) (@ F (@ (@ tptp.product_Pair_nat_nat A2) B)))))
% 5.61/5.91 (assert (forall ((F (-> tptp.product_prod_int_int Bool)) (A2 tptp.int) (B tptp.int)) (=> (@ (@ (@ tptp.produc175634133007206835_int_o F) A2) B) (@ F (@ (@ tptp.product_Pair_int_int A2) B)))))
% 5.61/5.91 (assert (forall ((F (-> tptp.produc3925858234332021118et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat)) (=> (@ (@ (@ tptp.produc6216949301066131538_nat_o F) A2) B) (@ F (@ (@ tptp.produc5001842942810119800et_nat A2) B)))))
% 5.61/5.91 (assert (forall ((F (-> tptp.produc2732055786443039994et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat)) (=> (@ (@ (@ tptp.produc5101573711933517782_nat_o F) A2) B) (@ F (@ (@ tptp.produc2245416461498447860et_nat A2) B)))))
% 5.61/5.91 (assert (forall ((F (-> tptp.produc3658429121746597890et_nat Bool)) (A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat)) (=> (@ (@ (@ tptp.produc1807123492089482958_nat_o F) A2) B) (@ F (@ (@ tptp.produc7507926704131184380et_nat A2) B)))))
% 5.61/5.91 (assert (forall ((F (-> tptp.product_prod_nat_nat Bool)) (A2 tptp.nat) (B tptp.nat)) (=> (@ (@ (@ tptp.produc1310100445399344235_nat_o F) A2) B) (@ F (@ (@ tptp.product_Pair_nat_nat A2) B)))))
% 5.61/5.91 (assert (forall ((F (-> tptp.product_prod_int_int Bool)) (A2 tptp.int) (B tptp.int)) (=> (@ (@ (@ tptp.produc175634133007206835_int_o F) A2) B) (@ F (@ (@ tptp.product_Pair_int_int A2) B)))))
% 5.61/5.91 (assert (forall ((F (-> tptp.produc3925858234332021118et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat)) (=> (@ (@ (@ tptp.produc6216949301066131538_nat_o F) A2) B) (@ F (@ (@ tptp.produc5001842942810119800et_nat A2) B)))))
% 5.61/5.91 (assert (forall ((F (-> tptp.produc2732055786443039994et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat)) (=> (@ (@ (@ tptp.produc5101573711933517782_nat_o F) A2) B) (@ F (@ (@ tptp.produc2245416461498447860et_nat A2) B)))))
% 5.61/5.91 (assert (= tptp.is_sin2160648248035936513t_unit (lambda ((A3 tptp.set_Product_unit)) (exists ((X2 tptp.product_unit)) (= A3 (@ (@ tptp.insert_Product_unit X2) tptp.bot_bo3957492148770167129t_unit))))))
% 5.61/5.91 (assert (= tptp.is_singleton_o (lambda ((A3 tptp.set_o)) (exists ((X2 Bool)) (= A3 (@ (@ tptp.insert_o X2) tptp.bot_bot_set_o))))))
% 5.61/5.91 (assert (= tptp.is_singleton_nat (lambda ((A3 tptp.set_nat)) (exists ((X2 tptp.nat)) (= A3 (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))))))
% 5.61/5.91 (assert (= tptp.is_singleton_int (lambda ((A3 tptp.set_int)) (exists ((X2 tptp.int)) (= A3 (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))))
% 5.61/5.91 (assert (= tptp.is_sin5180296473474724033_nat_o (lambda ((A3 tptp.set_Pr4532377907799695533_nat_o)) (exists ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (= A3 (@ (@ tptp.insert5175938949040314269_nat_o X2) tptp.bot_bo7824918357723582233_nat_o))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit)) (=> (@ tptp.is_sin2160648248035936513t_unit A) (not (forall ((X3 tptp.product_unit)) (not (= A (@ (@ tptp.insert_Product_unit X3) tptp.bot_bo3957492148770167129t_unit))))))))
% 5.61/5.91 (assert (forall ((A tptp.set_o)) (=> (@ tptp.is_singleton_o A) (not (forall ((X3 Bool)) (not (= A (@ (@ tptp.insert_o X3) tptp.bot_bot_set_o))))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat)) (=> (@ tptp.is_singleton_nat A) (not (forall ((X3 tptp.nat)) (not (= A (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat))))))))
% 5.61/5.91 (assert (forall ((A tptp.set_int)) (=> (@ tptp.is_singleton_int A) (not (forall ((X3 tptp.int)) (not (= A (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int))))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.is_sin5180296473474724033_nat_o A) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (not (= A (@ (@ tptp.insert5175938949040314269_nat_o X3) tptp.bot_bo7824918357723582233_nat_o))))))))
% 5.61/5.91 (assert (@ tptp.is_pure_assn tptp.bot_bot_assn))
% 5.61/5.91 (assert (= tptp.is_sin2160648248035936513t_unit (lambda ((A3 tptp.set_Product_unit)) (= A3 (@ (@ tptp.insert_Product_unit (@ tptp.the_el608902216710161154t_unit A3)) tptp.bot_bo3957492148770167129t_unit)))))
% 5.61/5.91 (assert (= tptp.is_singleton_o (lambda ((A3 tptp.set_o)) (= A3 (@ (@ tptp.insert_o (@ tptp.the_elem_o A3)) tptp.bot_bot_set_o)))))
% 5.61/5.91 (assert (= tptp.is_singleton_nat (lambda ((A3 tptp.set_nat)) (= A3 (@ (@ tptp.insert_nat (@ tptp.the_elem_nat A3)) tptp.bot_bot_set_nat)))))
% 5.61/5.91 (assert (= tptp.is_singleton_int (lambda ((A3 tptp.set_int)) (= A3 (@ (@ tptp.insert_int (@ tptp.the_elem_int A3)) tptp.bot_bot_set_int)))))
% 5.61/5.91 (assert (= tptp.is_sin5180296473474724033_nat_o (lambda ((A3 tptp.set_Pr4532377907799695533_nat_o)) (= A3 (@ (@ tptp.insert5175938949040314269_nat_o (@ tptp.the_el5959152443890766018_nat_o A3)) tptp.bot_bo7824918357723582233_nat_o)))))
% 5.61/5.91 (assert (forall ((X tptp.product_unit)) (= (@ tptp.the_el608902216710161154t_unit (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)) X)))
% 5.61/5.91 (assert (forall ((X Bool)) (= (@ tptp.the_elem_o (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)) X)))
% 5.61/5.91 (assert (forall ((X tptp.nat)) (= (@ tptp.the_elem_nat (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)) X)))
% 5.61/5.91 (assert (forall ((X tptp.int)) (= (@ tptp.the_elem_int (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)) X)))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool))) (= (@ tptp.the_el5959152443890766018_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)) X)))
% 5.61/5.91 (assert (= tptp.pure_assn (lambda ((B6 Bool)) (@ tptp.abs_assn (@ tptp.pure_a825153325127701367it_nat B6)))))
% 5.61/5.91 (assert (= tptp.times_times_assn (lambda ((P2 tptp.assn) (Q tptp.assn)) (@ tptp.abs_assn (@ (@ tptp.times_assn_raw (@ tptp.rep_assn P2)) (@ tptp.rep_assn Q))))))
% 5.61/5.91 (assert (= tptp.type_d3909072315231072503_nat_o (lambda ((Rep (-> tptp.assn tptp.produc3658429121746597890et_nat Bool)) (Abs (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.assn)) (A3 tptp.set_Pr4532377907799695533_nat_o)) (and (forall ((X2 tptp.assn)) (@ (@ tptp.member6576561426505652726_nat_o (@ Rep X2)) A3)) (forall ((X2 tptp.assn)) (= (@ Abs (@ Rep X2)) X2)) (forall ((Y3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y3) A3) (= (@ Rep (@ Abs Y3)) Y3)))))))
% 5.61/5.91 (assert (= tptp.type_d8366093980585677751er_int (lambda ((Rep (-> tptp.code_integer tptp.int)) (Abs (-> tptp.int tptp.code_integer)) (A3 tptp.set_int)) (and (forall ((X2 tptp.code_integer)) (@ (@ tptp.member_int (@ Rep X2)) A3)) (forall ((X2 tptp.code_integer)) (= (@ Abs (@ Rep X2)) X2)) (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) A3) (= (@ Rep (@ Abs Y3)) Y3)))))))
% 5.61/5.91 (assert (= tptp.type_d6188575255521822967unit_o (lambda ((Rep (-> tptp.product_unit Bool)) (Abs (-> Bool tptp.product_unit)) (A3 tptp.set_o)) (and (forall ((X2 tptp.product_unit)) (@ (@ tptp.member_o (@ Rep X2)) A3)) (forall ((X2 tptp.product_unit)) (= (@ Abs (@ Rep X2)) X2)) (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) A3) (= (@ Rep (@ Abs Y3)) Y3)))))))
% 5.61/5.91 (assert (= tptp.type_d4410041424927559462al_nat (lambda ((Rep (-> tptp.code_natural tptp.nat)) (Abs (-> tptp.nat tptp.code_natural)) (A3 tptp.set_nat)) (and (forall ((X2 tptp.code_natural)) (@ (@ tptp.member_nat (@ Rep X2)) A3)) (forall ((X2 tptp.code_natural)) (= (@ Abs (@ Rep X2)) X2)) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) A3) (= (@ Rep (@ Abs Y3)) Y3)))))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.assn tptp.produc3658429121746597890et_nat Bool)) (Abs2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.assn)) (A tptp.set_Pr4532377907799695533_nat_o) (X tptp.assn)) (=> (@ (@ (@ tptp.type_d3909072315231072503_nat_o Rep2) Abs2) A) (= (@ Abs2 (@ Rep2 X)) X))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (A tptp.set_int) (X tptp.code_integer)) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) A) (= (@ Abs2 (@ Rep2 X)) X))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.product_unit Bool)) (Abs2 (-> Bool tptp.product_unit)) (A tptp.set_o) (X tptp.product_unit)) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep2) Abs2) A) (= (@ Abs2 (@ Rep2 X)) X))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.code_natural tptp.nat)) (Abs2 (-> tptp.nat tptp.code_natural)) (A tptp.set_nat) (X tptp.code_natural)) (=> (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep2) Abs2) A) (= (@ Abs2 (@ Rep2 X)) X))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.assn tptp.produc3658429121746597890et_nat Bool)) (Abs2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.assn)) (A tptp.set_Pr4532377907799695533_nat_o) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ (@ tptp.type_d3909072315231072503_nat_o Rep2) Abs2) A) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) A) (= (@ Rep2 (@ Abs2 Y)) Y)))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (A tptp.set_int) (Y tptp.int)) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) A) (=> (@ (@ tptp.member_int Y) A) (= (@ Rep2 (@ Abs2 Y)) Y)))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.product_unit Bool)) (Abs2 (-> Bool tptp.product_unit)) (A tptp.set_o) (Y Bool)) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep2) Abs2) A) (=> (@ (@ tptp.member_o Y) A) (= (@ Rep2 (@ Abs2 Y)) Y)))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.code_natural tptp.nat)) (Abs2 (-> tptp.nat tptp.code_natural)) (A tptp.set_nat) (Y tptp.nat)) (=> (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep2) Abs2) A) (=> (@ (@ tptp.member_nat Y) A) (= (@ Rep2 (@ Abs2 Y)) Y)))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.assn tptp.produc3658429121746597890et_nat Bool)) (Abs2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.assn)) (A tptp.set_Pr4532377907799695533_nat_o) (X tptp.assn) (Y tptp.assn)) (=> (@ (@ (@ tptp.type_d3909072315231072503_nat_o Rep2) Abs2) A) (= (= (@ Rep2 X) (@ Rep2 Y)) (= X Y)))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (A tptp.set_int) (X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) A) (= (= (@ Rep2 X) (@ Rep2 Y)) (= X Y)))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.product_unit Bool)) (Abs2 (-> Bool tptp.product_unit)) (A tptp.set_o) (X tptp.product_unit) (Y tptp.product_unit)) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep2) Abs2) A) (= (= (@ Rep2 X) (@ Rep2 Y)) (= X Y)))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.code_natural tptp.nat)) (Abs2 (-> tptp.nat tptp.code_natural)) (A tptp.set_nat) (X tptp.code_natural) (Y tptp.code_natural)) (=> (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep2) Abs2) A) (= (= (@ Rep2 X) (@ Rep2 Y)) (= X Y)))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.assn tptp.produc3658429121746597890et_nat Bool)) (Abs2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.assn)) (A tptp.set_Pr4532377907799695533_nat_o) (Y (-> tptp.produc3658429121746597890et_nat Bool)) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (@ (@ (@ tptp.type_d3909072315231072503_nat_o Rep2) Abs2) A) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) A) (=> (forall ((X3 tptp.assn)) (@ P (@ Rep2 X3))) (@ P Y))))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (A tptp.set_int) (Y tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) A) (=> (@ (@ tptp.member_int Y) A) (=> (forall ((X3 tptp.code_integer)) (@ P (@ Rep2 X3))) (@ P Y))))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.product_unit Bool)) (Abs2 (-> Bool tptp.product_unit)) (A tptp.set_o) (Y Bool) (P (-> Bool Bool))) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep2) Abs2) A) (=> (@ (@ tptp.member_o Y) A) (=> (forall ((X3 tptp.product_unit)) (@ P (@ Rep2 X3))) (@ P Y))))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.code_natural tptp.nat)) (Abs2 (-> tptp.nat tptp.code_natural)) (A tptp.set_nat) (Y tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep2) Abs2) A) (=> (@ (@ tptp.member_nat Y) A) (=> (forall ((X3 tptp.code_natural)) (@ P (@ Rep2 X3))) (@ P Y))))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.assn tptp.produc3658429121746597890et_nat Bool)) (Abs2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.assn)) (A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ (@ tptp.type_d3909072315231072503_nat_o Rep2) Abs2) A) (=> (@ (@ tptp.member6576561426505652726_nat_o X) A) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) A) (= (= (@ Abs2 X) (@ Abs2 Y)) (= X Y)))))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (A tptp.set_int) (X tptp.int) (Y tptp.int)) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) A) (=> (@ (@ tptp.member_int X) A) (=> (@ (@ tptp.member_int Y) A) (= (= (@ Abs2 X) (@ Abs2 Y)) (= X Y)))))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.product_unit Bool)) (Abs2 (-> Bool tptp.product_unit)) (A tptp.set_o) (X Bool) (Y Bool)) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep2) Abs2) A) (=> (@ (@ tptp.member_o X) A) (=> (@ (@ tptp.member_o Y) A) (= (= (@ Abs2 X) (@ Abs2 Y)) (= X Y)))))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.code_natural tptp.nat)) (Abs2 (-> tptp.nat tptp.code_natural)) (A tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep2) Abs2) A) (=> (@ (@ tptp.member_nat X) A) (=> (@ (@ tptp.member_nat Y) A) (= (= (@ Abs2 X) (@ Abs2 Y)) (= X Y)))))))
% 5.61/5.91 (assert (forall ((P Bool) (Q2 Bool)) (= (= (@ tptp.pure_assn P) (@ tptp.pure_assn Q2)) (= P Q2))))
% 5.61/5.91 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A2) tptp.one_one_Code_integer) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural A2) tptp.one_one_Code_natural) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.times_times_assn A2) tptp.one_one_assn) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat A2) tptp.one_one_rat) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat A2) tptp.one_one_nat) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int A2) tptp.one_one_int) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.one_one_Code_integer) A2) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural tptp.one_one_Code_natural) A2) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) A2) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A2) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A2) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A2) A2)))
% 5.61/5.91 (assert (forall ((A2 Bool) (B Bool)) (= (@ (@ tptp.times_times_assn (@ tptp.pure_assn A2)) (@ tptp.pure_assn B)) (@ tptp.pure_assn (and A2 B)))))
% 5.61/5.91 (assert (forall ((P tptp.assn)) (= (@ (@ tptp.times_times_assn P) tptp.bot_bot_assn) tptp.bot_bot_assn)))
% 5.61/5.91 (assert (forall ((P tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.bot_bot_assn) P) tptp.bot_bot_assn)))
% 5.61/5.91 (assert (= (@ tptp.pure_assn false) tptp.bot_bot_assn))
% 5.61/5.91 (assert (forall ((P Bool)) (= (= (@ tptp.pure_assn P) tptp.bot_bot_assn) (not P))))
% 5.61/5.91 (assert (forall ((A2 tptp.assn) (B tptp.assn)) (=> (@ tptp.is_pure_assn A2) (=> (@ tptp.is_pure_assn B) (@ tptp.is_pure_assn (@ (@ tptp.times_times_assn A2) B))))))
% 5.61/5.91 (assert (forall ((P Bool)) (@ tptp.is_pure_assn (@ tptp.pure_assn P))))
% 5.61/5.91 (assert (= (@ tptp.pure_assn true) tptp.one_one_assn))
% 5.61/5.91 (assert (forall ((P Bool)) (= (= (@ tptp.pure_assn P) tptp.one_one_assn) P)))
% 5.61/5.91 (assert (= tptp.times_times_assn (lambda ((P2 tptp.assn) (Q tptp.assn)) (@ (@ tptp.times_times_assn Q) P2))))
% 5.61/5.91 (assert (forall ((P tptp.assn) (Q2 tptp.assn) (R3 tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn P))) (= (@ (@ tptp.times_times_assn (@ _let_1 Q2)) R3) (@ _let_1 (@ (@ tptp.times_times_assn Q2) R3))))))
% 5.61/5.91 (assert (forall ((B tptp.assn) (A2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn B))) (let ((_let_2 (@ tptp.times_times_assn A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.61/5.91 (assert (forall ((B tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.61/5.91 (assert (forall ((B tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.61/5.91 (assert (forall ((B tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.61/5.91 (assert (= tptp.times_times_assn (lambda ((A6 tptp.assn) (B6 tptp.assn)) (@ (@ tptp.times_times_assn B6) A6))))
% 5.61/5.91 (assert (= tptp.times_times_rat (lambda ((A6 tptp.rat) (B6 tptp.rat)) (@ (@ tptp.times_times_rat B6) A6))))
% 5.61/5.91 (assert (= tptp.times_times_nat (lambda ((A6 tptp.nat) (B6 tptp.nat)) (@ (@ tptp.times_times_nat B6) A6))))
% 5.61/5.91 (assert (= tptp.times_times_int (lambda ((A6 tptp.int) (B6 tptp.int)) (@ (@ tptp.times_times_int B6) A6))))
% 5.61/5.91 (assert (forall ((A2 tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A2))) (= (@ (@ tptp.times_times_assn (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_assn B) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.one_one_Code_integer) A2) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural tptp.one_one_Code_natural) A2) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) A2) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A2) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A2) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A2) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A2) tptp.one_one_Code_integer) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural A2) tptp.one_one_Code_natural) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.times_times_assn A2) tptp.one_one_assn) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat A2) tptp.one_one_rat) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat A2) tptp.one_one_nat) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int A2) tptp.one_one_int) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.assn) (B tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn A2) B)) H2) (not (=> (exists ((X_1 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.rep_assn A2) X_1)) (forall ((H_2 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn B) H_2))))))))
% 5.61/5.91 (assert (forall ((A tptp.assn) (B4 tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn A) B4)) H2) (exists ((H1 tptp.produc3658429121746597890et_nat) (H22 tptp.produc3658429121746597890et_nat)) (and (@ (@ tptp.rep_assn A) H1) (@ (@ tptp.rep_assn B4) H22))))))
% 5.61/5.91 (assert (forall ((P tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) P) P)))
% 5.61/5.91 (assert (forall ((A2 tptp.assn)) (=> (@ tptp.is_pure_assn A2) (not (forall ((P4 Bool)) (not (= A2 (@ tptp.pure_assn P4))))))))
% 5.61/5.91 (assert (= tptp.is_pure_assn (lambda ((A6 tptp.assn)) (exists ((P2 Bool)) (= A6 (@ tptp.pure_assn P2))))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.assn tptp.produc3658429121746597890et_nat Bool)) (Abs2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.assn)) (A tptp.set_Pr4532377907799695533_nat_o) (X tptp.assn)) (=> (@ (@ (@ tptp.type_d3909072315231072503_nat_o Rep2) Abs2) A) (@ (@ tptp.member6576561426505652726_nat_o (@ Rep2 X)) A))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (A tptp.set_int) (X tptp.code_integer)) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) A) (@ (@ tptp.member_int (@ Rep2 X)) A))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.product_unit Bool)) (Abs2 (-> Bool tptp.product_unit)) (A tptp.set_o) (X tptp.product_unit)) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep2) Abs2) A) (@ (@ tptp.member_o (@ Rep2 X)) A))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.code_natural tptp.nat)) (Abs2 (-> tptp.nat tptp.code_natural)) (A tptp.set_nat) (X tptp.code_natural)) (=> (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep2) Abs2) A) (@ (@ tptp.member_nat (@ Rep2 X)) A))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.assn tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (Abs2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.assn))) (=> (forall ((X3 tptp.assn)) (@ (@ tptp.member6576561426505652726_nat_o (@ Rep2 X3)) A)) (=> (forall ((X3 tptp.assn)) (= (@ Abs2 (@ Rep2 X3)) X3)) (=> (forall ((Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y2) A) (= (@ Rep2 (@ Abs2 Y2)) Y2))) (@ (@ (@ tptp.type_d3909072315231072503_nat_o Rep2) Abs2) A))))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (A tptp.set_int) (Abs2 (-> tptp.int tptp.code_integer))) (=> (forall ((X3 tptp.code_integer)) (@ (@ tptp.member_int (@ Rep2 X3)) A)) (=> (forall ((X3 tptp.code_integer)) (= (@ Abs2 (@ Rep2 X3)) X3)) (=> (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) A) (= (@ Rep2 (@ Abs2 Y2)) Y2))) (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) A))))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.product_unit Bool)) (A tptp.set_o) (Abs2 (-> Bool tptp.product_unit))) (=> (forall ((X3 tptp.product_unit)) (@ (@ tptp.member_o (@ Rep2 X3)) A)) (=> (forall ((X3 tptp.product_unit)) (= (@ Abs2 (@ Rep2 X3)) X3)) (=> (forall ((Y2 Bool)) (=> (@ (@ tptp.member_o Y2) A) (= (@ Rep2 (@ Abs2 Y2)) Y2))) (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep2) Abs2) A))))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.code_natural tptp.nat)) (A tptp.set_nat) (Abs2 (-> tptp.nat tptp.code_natural))) (=> (forall ((X3 tptp.code_natural)) (@ (@ tptp.member_nat (@ Rep2 X3)) A)) (=> (forall ((X3 tptp.code_natural)) (= (@ Abs2 (@ Rep2 X3)) X3)) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) A) (= (@ Rep2 (@ Abs2 Y2)) Y2))) (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep2) Abs2) A))))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.assn tptp.produc3658429121746597890et_nat Bool)) (Abs2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.assn)) (A tptp.set_Pr4532377907799695533_nat_o) (X tptp.assn)) (=> (@ (@ (@ tptp.type_d3909072315231072503_nat_o Rep2) Abs2) A) (not (forall ((Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (= X (@ Abs2 Y2)) (not (@ (@ tptp.member6576561426505652726_nat_o Y2) A))))))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (A tptp.set_int) (X tptp.code_integer)) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) A) (not (forall ((Y2 tptp.int)) (=> (= X (@ Abs2 Y2)) (not (@ (@ tptp.member_int Y2) A))))))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.product_unit Bool)) (Abs2 (-> Bool tptp.product_unit)) (A tptp.set_o) (X tptp.product_unit)) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep2) Abs2) A) (not (forall ((Y2 Bool)) (=> (= X (@ Abs2 Y2)) (not (@ (@ tptp.member_o Y2) A))))))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.code_natural tptp.nat)) (Abs2 (-> tptp.nat tptp.code_natural)) (A tptp.set_nat) (X tptp.code_natural)) (=> (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep2) Abs2) A) (not (forall ((Y2 tptp.nat)) (=> (= X (@ Abs2 Y2)) (not (@ (@ tptp.member_nat Y2) A))))))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.assn tptp.produc3658429121746597890et_nat Bool)) (Abs2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.assn)) (A tptp.set_Pr4532377907799695533_nat_o) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ (@ tptp.type_d3909072315231072503_nat_o Rep2) Abs2) A) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) A) (not (forall ((X3 tptp.assn)) (not (= Y (@ Rep2 X3)))))))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (A tptp.set_int) (Y tptp.int)) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) A) (=> (@ (@ tptp.member_int Y) A) (not (forall ((X3 tptp.code_integer)) (not (= Y (@ Rep2 X3)))))))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.product_unit Bool)) (Abs2 (-> Bool tptp.product_unit)) (A tptp.set_o) (Y Bool)) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep2) Abs2) A) (=> (@ (@ tptp.member_o Y) A) (not (forall ((X3 tptp.product_unit)) (= Y (not (@ Rep2 X3)))))))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.code_natural tptp.nat)) (Abs2 (-> tptp.nat tptp.code_natural)) (A tptp.set_nat) (Y tptp.nat)) (=> (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep2) Abs2) A) (=> (@ (@ tptp.member_nat Y) A) (not (forall ((X3 tptp.code_natural)) (not (= Y (@ Rep2 X3)))))))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.assn tptp.produc3658429121746597890et_nat Bool)) (Abs2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.assn)) (A tptp.set_Pr4532377907799695533_nat_o) (P (-> tptp.assn Bool)) (X tptp.assn)) (=> (@ (@ (@ tptp.type_d3909072315231072503_nat_o Rep2) Abs2) A) (=> (forall ((Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y2) A) (@ P (@ Abs2 Y2)))) (@ P X)))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (A tptp.set_int) (P (-> tptp.code_integer Bool)) (X tptp.code_integer)) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) A) (=> (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) A) (@ P (@ Abs2 Y2)))) (@ P X)))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.product_unit Bool)) (Abs2 (-> Bool tptp.product_unit)) (A tptp.set_o) (P (-> tptp.product_unit Bool)) (X tptp.product_unit)) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep2) Abs2) A) (=> (forall ((Y2 Bool)) (=> (@ (@ tptp.member_o Y2) A) (@ P (@ Abs2 Y2)))) (@ P X)))))
% 5.61/5.91 (assert (forall ((Rep2 (-> tptp.code_natural tptp.nat)) (Abs2 (-> tptp.nat tptp.code_natural)) (A tptp.set_nat) (P (-> tptp.code_natural Bool)) (X tptp.code_natural)) (=> (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep2) Abs2) A) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) A) (@ P (@ Abs2 Y2)))) (@ P X)))))
% 5.61/5.91 (assert (forall ((X tptp.product_unit)) (@ (@ tptp.total_5665700600833547665t_unit (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)) (@ (@ tptp.insert4616891024742550839t_unit (@ (@ tptp.produc5692694829384537815t_unit X) X)) tptp.bot_bo1654022762305692595t_unit))))
% 5.61/5.91 (assert (forall ((X Bool)) (@ (@ tptp.total_on_o (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)) (@ (@ tptp.insert6201435330877294327od_o_o (@ (@ tptp.product_Pair_o_o X) X)) tptp.bot_bo7073875226086086771od_o_o))))
% 5.61/5.91 (assert (forall ((X tptp.nat)) (@ (@ tptp.total_on_nat (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)) (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.product_Pair_nat_nat X) X)) tptp.bot_bo2099793752762293965at_nat))))
% 5.61/5.91 (assert (forall ((X tptp.int)) (@ (@ tptp.total_on_int (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)) (@ (@ tptp.insert5033312907999012233nt_int (@ (@ tptp.product_Pair_int_int X) X)) tptp.bot_bo1796632182523588997nt_int))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.total_7429123086324524369_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)) (@ (@ tptp.insert5309882203591314743_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X) X)) tptp.bot_bo3657187498359500723_nat_o))))
% 5.61/5.91 (assert (forall ((X tptp.product_unit)) (@ (@ tptp.refl_on_Product_unit (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)) (@ (@ tptp.insert4616891024742550839t_unit (@ (@ tptp.produc5692694829384537815t_unit X) X)) tptp.bot_bo1654022762305692595t_unit))))
% 5.61/5.91 (assert (forall ((X Bool)) (@ (@ tptp.refl_on_o (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)) (@ (@ tptp.insert6201435330877294327od_o_o (@ (@ tptp.product_Pair_o_o X) X)) tptp.bot_bo7073875226086086771od_o_o))))
% 5.61/5.91 (assert (forall ((X tptp.nat)) (@ (@ tptp.refl_on_nat (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)) (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.product_Pair_nat_nat X) X)) tptp.bot_bo2099793752762293965at_nat))))
% 5.61/5.91 (assert (forall ((X tptp.int)) (@ (@ tptp.refl_on_int (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)) (@ (@ tptp.insert5033312907999012233nt_int (@ (@ tptp.product_Pair_int_int X) X)) tptp.bot_bo1796632182523588997nt_int))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.refl_o1075864025857821388_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)) (@ (@ tptp.insert5309882203591314743_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X) X)) tptp.bot_bo3657187498359500723_nat_o))))
% 5.61/5.91 (assert (= (@ tptp.id_on_Product_unit tptp.bot_bo3957492148770167129t_unit) tptp.bot_bo1654022762305692595t_unit))
% 5.61/5.91 (assert (= (@ tptp.id_on_o tptp.bot_bot_set_o) tptp.bot_bo7073875226086086771od_o_o))
% 5.61/5.91 (assert (= (@ tptp.id_on_nat tptp.bot_bot_set_nat) tptp.bot_bo2099793752762293965at_nat))
% 5.61/5.91 (assert (= (@ tptp.id_on_int tptp.bot_bot_set_int) tptp.bot_bo1796632182523588997nt_int))
% 5.61/5.91 (assert (= (@ tptp.id_on_7438695062414216554_nat_o tptp.bot_bo7824918357723582233_nat_o) tptp.bot_bo3657187498359500723_nat_o))
% 5.61/5.91 (assert (forall ((X tptp.product_unit)) (@ (@ tptp.order_888282469287196226t_unit (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)) (@ (@ tptp.insert4616891024742550839t_unit (@ (@ tptp.produc5692694829384537815t_unit X) X)) tptp.bot_bo1654022762305692595t_unit))))
% 5.61/5.91 (assert (forall ((X Bool)) (@ (@ tptp.order_6238756238976269133r_on_o (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)) (@ (@ tptp.insert6201435330877294327od_o_o (@ (@ tptp.product_Pair_o_o X) X)) tptp.bot_bo7073875226086086771od_o_o))))
% 5.61/5.91 (assert (forall ((X tptp.nat)) (@ (@ tptp.order_4473980167227706203on_nat (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)) (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.product_Pair_nat_nat X) X)) tptp.bot_bo2099793752762293965at_nat))))
% 5.61/5.91 (assert (forall ((X tptp.int)) (@ (@ tptp.order_4471489696718655927on_int (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)) (@ (@ tptp.insert5033312907999012233nt_int (@ (@ tptp.product_Pair_int_int X) X)) tptp.bot_bo1796632182523588997nt_int))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.order_1145710701291701250_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)) (@ (@ tptp.insert5309882203591314743_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X) X)) tptp.bot_bo3657187498359500723_nat_o))))
% 5.61/5.91 (assert (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ tptp.pure_a825153325127701367it_nat X) Xa) Y) (=> (@ (@ tptp.accp_P8458817951426537472et_nat tptp.pure_a6022498039421069578it_nat) (@ (@ tptp.produc3762353314782720579et_nat X) Xa)) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As2))) (=> (= Xa _let_1) (=> (= Y (and (= As2 tptp.bot_bot_set_nat) X)) (not (@ (@ tptp.accp_P8458817951426537472et_nat tptp.pure_a6022498039421069578it_nat) (@ (@ tptp.produc3762353314782720579et_nat X) _let_1))))))))))))
% 5.61/5.91 (assert (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.pure_a825153325127701367it_nat X) Xa) (=> (@ (@ tptp.accp_P8458817951426537472et_nat tptp.pure_a6022498039421069578it_nat) (@ (@ tptp.produc3762353314782720579et_nat X) Xa)) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As2))) (=> (= Xa _let_1) (=> (@ (@ tptp.accp_P8458817951426537472et_nat tptp.pure_a6022498039421069578it_nat) (@ (@ tptp.produc3762353314782720579et_nat X) _let_1)) (not (and (= As2 tptp.bot_bot_set_nat) X)))))))))))
% 5.61/5.91 (assert (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat)) (=> (not (@ (@ tptp.pure_a825153325127701367it_nat X) Xa)) (=> (@ (@ tptp.accp_P8458817951426537472et_nat tptp.pure_a6022498039421069578it_nat) (@ (@ tptp.produc3762353314782720579et_nat X) Xa)) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As2))) (=> (= Xa _let_1) (=> (@ (@ tptp.accp_P8458817951426537472et_nat tptp.pure_a6022498039421069578it_nat) (@ (@ tptp.produc3762353314782720579et_nat X) _let_1)) (and (= As2 tptp.bot_bot_set_nat) X))))))))))
% 5.61/5.91 (assert (forall ((B tptp.nat) (R2 tptp.set_Pr1763845938948868674it_nat) (A2 tptp.product_unit)) (= (@ (@ tptp.member_nat B) (@ (@ tptp.image_5657742817519485770it_nat R2) (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit))) (@ (@ tptp.member423003724879500579it_nat (@ (@ tptp.produc4803288329813530246it_nat A2) B)) R2))))
% 5.61/5.91 (assert (forall ((B tptp.int) (R2 tptp.set_Pr8497134830871917726it_int) (A2 tptp.product_unit)) (= (@ (@ tptp.member_int B) (@ (@ tptp.image_5655252347010435494it_int R2) (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit))) (@ (@ tptp.member5468524742225079679it_int (@ (@ tptp.produc4800797859304479970it_int A2) B)) R2))))
% 5.61/5.91 (assert (forall ((B Bool) (R2 tptp.set_Pr5464989305201766866unit_o) (A2 tptp.product_unit)) (= (@ (@ tptp.member_o B) (@ (@ tptp.image_Product_unit_o R2) (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit))) (@ (@ tptp.member3689400097658526619unit_o (@ (@ tptp.produc8487917018914037602unit_o A2) B)) R2))))
% 5.61/5.91 (assert (forall ((B tptp.product_unit) (R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit)) (= (@ (@ tptp.member_Product_unit B) (@ (@ tptp.image_8431784415008483091t_unit R2) (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit))) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit A2) B)) R2))))
% 5.61/5.91 (assert (forall ((B tptp.nat) (R2 tptp.set_Pr2101469702781467981_o_nat) (A2 Bool)) (= (@ (@ tptp.member_nat B) (@ (@ tptp.image_o_nat R2) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))) (@ (@ tptp.member2802428098988154798_o_nat (@ (@ tptp.product_Pair_o_nat A2) B)) R2))))
% 5.61/5.91 (assert (forall ((B tptp.int) (R2 tptp.set_Pr8834758594704517033_o_int) (A2 Bool)) (= (@ (@ tptp.member_int B) (@ (@ tptp.image_o_int R2) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))) (@ (@ tptp.member7847949116333733898_o_int (@ (@ tptp.product_Pair_o_int A2) B)) R2))))
% 5.61/5.91 (assert (forall ((B Bool) (R2 tptp.set_Product_prod_o_o) (A2 Bool)) (= (@ (@ tptp.member_o B) (@ (@ tptp.image_o_o R2) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) B)) R2))))
% 5.61/5.91 (assert (forall ((B tptp.product_unit) (R2 tptp.set_Pr6671815714118170108t_unit) (A2 Bool)) (= (@ (@ tptp.member_Product_unit B) (@ (@ tptp.image_o_Product_unit R2) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))) (@ (@ tptp.member9215336023991391429t_unit (@ (@ tptp.produc3901946521647900940t_unit A2) B)) R2))))
% 5.61/5.91 (assert (forall ((B tptp.int) (R2 tptp.set_Pr7995236796853374141at_int) (A2 tptp.nat)) (= (@ (@ tptp.member_int B) (@ (@ tptp.image_nat_int R2) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))) (@ (@ tptp.member4262671552274231302at_int (@ (@ tptp.product_Pair_nat_int A2) B)) R2))))
% 5.61/5.91 (assert (forall ((B Bool) (R2 tptp.set_Pr3149072824959771635_nat_o) (A2 tptp.nat)) (= (@ (@ tptp.member_o B) (@ (@ tptp.image_nat_o R2) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))) (@ (@ tptp.member6310962623043647828_nat_o (@ (@ tptp.product_Pair_nat_o A2) B)) R2))))
% 5.61/5.91 (assert (forall ((A2 tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A2))) (= (@ (@ tptp.times_times_assn (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_assn B) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A2))) (= (@ (@ tptp.times_times_assn (@ _let_1 B)) C) (@ (@ tptp.times_times_assn (@ _let_1 C)) B)))))
% 5.61/5.91 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C) (@ (@ tptp.times_times_rat (@ _let_1 C)) B)))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ (@ tptp.times_times_nat (@ _let_1 C)) B)))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ (@ tptp.times_times_int (@ _let_1 C)) B)))))
% 5.61/5.91 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit)) (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H2) tptp.bot_bot_set_nat))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.int) (R2 tptp.set_Pr7995236796853374141at_int) (A tptp.set_nat)) (=> (@ (@ tptp.member4262671552274231302at_int (@ (@ tptp.product_Pair_nat_int A2) B)) R2) (=> (@ (@ tptp.member_nat A2) A) (@ (@ tptp.member_int B) (@ (@ tptp.image_nat_int R2) A))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B Bool) (R2 tptp.set_Pr3149072824959771635_nat_o) (A tptp.set_nat)) (=> (@ (@ tptp.member6310962623043647828_nat_o (@ (@ tptp.product_Pair_nat_o A2) B)) R2) (=> (@ (@ tptp.member_nat A2) A) (@ (@ tptp.member_o B) (@ (@ tptp.image_nat_o R2) A))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.product_unit) (R2 tptp.set_Pr4334478416066269672t_unit) (A tptp.set_nat)) (=> (@ (@ tptp.member348563419383025609t_unit (@ (@ tptp.produc3434450474625521892t_unit A2) B)) R2) (=> (@ (@ tptp.member_nat A2) A) (@ (@ tptp.member_Product_unit B) (@ (@ tptp.image_4288904962331477416t_unit R2) A))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.nat) (R2 tptp.set_Pr3448869479623346877nt_nat) (A tptp.set_int)) (=> (@ (@ tptp.member216504246829706758nt_nat (@ (@ tptp.product_Pair_int_nat A2) B)) R2) (=> (@ (@ tptp.member_int A2) A) (@ (@ tptp.member_nat B) (@ (@ tptp.image_int_nat R2) A))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B Bool) (R2 tptp.set_Pr903927857289325719_int_o) (A tptp.set_int)) (=> (@ (@ tptp.member4489920277610959864_int_o (@ (@ tptp.product_Pair_int_o A2) B)) R2) (=> (@ (@ tptp.member_int A2) A) (@ (@ tptp.member_o B) (@ (@ tptp.image_int_o R2) A))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.product_unit) (R2 tptp.set_Pr5889264611543340172t_unit) (A tptp.set_int)) (=> (@ (@ tptp.member6688357403439981677t_unit (@ (@ tptp.produc550872421827702152t_unit A2) B)) R2) (=> (@ (@ tptp.member_int A2) A) (@ (@ tptp.member_Product_unit B) (@ (@ tptp.image_1405326909533657676t_unit R2) A))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (B tptp.nat) (R2 tptp.set_Pr2101469702781467981_o_nat) (A tptp.set_o)) (=> (@ (@ tptp.member2802428098988154798_o_nat (@ (@ tptp.product_Pair_o_nat A2) B)) R2) (=> (@ (@ tptp.member_o A2) A) (@ (@ tptp.member_nat B) (@ (@ tptp.image_o_nat R2) A))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (B tptp.int) (R2 tptp.set_Pr8834758594704517033_o_int) (A tptp.set_o)) (=> (@ (@ tptp.member7847949116333733898_o_int (@ (@ tptp.product_Pair_o_int A2) B)) R2) (=> (@ (@ tptp.member_o A2) A) (@ (@ tptp.member_int B) (@ (@ tptp.image_o_int R2) A))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (B Bool) (R2 tptp.set_Product_prod_o_o) (A tptp.set_o)) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) B)) R2) (=> (@ (@ tptp.member_o A2) A) (@ (@ tptp.member_o B) (@ (@ tptp.image_o_o R2) A))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (B tptp.product_unit) (R2 tptp.set_Pr6671815714118170108t_unit) (A tptp.set_o)) (=> (@ (@ tptp.member9215336023991391429t_unit (@ (@ tptp.produc3901946521647900940t_unit A2) B)) R2) (=> (@ (@ tptp.member_o A2) A) (@ (@ tptp.member_Product_unit B) (@ (@ tptp.image_o_Product_unit R2) A))))))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr5094982260447487303t_unit)) (= (@ (@ tptp.image_8431784415008483091t_unit R3) tptp.bot_bo3957492148770167129t_unit) tptp.bot_bo3957492148770167129t_unit)))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr5464989305201766866unit_o)) (= (@ (@ tptp.image_Product_unit_o R3) tptp.bot_bo3957492148770167129t_unit) tptp.bot_bot_set_o)))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr1763845938948868674it_nat)) (= (@ (@ tptp.image_5657742817519485770it_nat R3) tptp.bot_bo3957492148770167129t_unit) tptp.bot_bot_set_nat)))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr8497134830871917726it_int)) (= (@ (@ tptp.image_5655252347010435494it_int R3) tptp.bot_bo3957492148770167129t_unit) tptp.bot_bot_set_int)))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr6671815714118170108t_unit)) (= (@ (@ tptp.image_o_Product_unit R3) tptp.bot_bot_set_o) tptp.bot_bo3957492148770167129t_unit)))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Product_prod_o_o)) (= (@ (@ tptp.image_o_o R3) tptp.bot_bot_set_o) tptp.bot_bot_set_o)))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr2101469702781467981_o_nat)) (= (@ (@ tptp.image_o_nat R3) tptp.bot_bot_set_o) tptp.bot_bot_set_nat)))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr8834758594704517033_o_int)) (= (@ (@ tptp.image_o_int R3) tptp.bot_bot_set_o) tptp.bot_bot_set_int)))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr4334478416066269672t_unit)) (= (@ (@ tptp.image_4288904962331477416t_unit R3) tptp.bot_bot_set_nat) tptp.bot_bo3957492148770167129t_unit)))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr3149072824959771635_nat_o)) (= (@ (@ tptp.image_nat_o R3) tptp.bot_bot_set_nat) tptp.bot_bot_set_o)))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) A) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) A2)) (@ tptp.id_on_7438695062414216554_nat_o A)))))
% 5.61/5.91 (assert (forall ((A2 Bool) (A tptp.set_o)) (=> (@ (@ tptp.member_o A2) A) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) A2)) (@ tptp.id_on_o A)))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (A tptp.set_Product_unit)) (=> (@ (@ tptp.member_Product_unit A2) A) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit A2) A2)) (@ tptp.id_on_Product_unit A)))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat A2) A) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) A2)) (@ tptp.id_on_nat A)))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (A tptp.set_int)) (=> (@ (@ tptp.member_int A2) A) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) A2)) (@ tptp.id_on_int A)))))
% 5.61/5.91 (assert (@ tptp.proper tptp.in_range))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.refl_o1075864025857821388_nat_o A) R2) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) B)) R2) (and (@ (@ tptp.member6576561426505652726_nat_o A2) A) (@ (@ tptp.member6576561426505652726_nat_o B) A))))))
% 5.61/5.91 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o) (A2 Bool) (B Bool)) (=> (@ (@ tptp.refl_on_o A) R2) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) B)) R2) (and (@ (@ tptp.member_o A2) A) (@ (@ tptp.member_o B) A))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit) (B tptp.product_unit)) (=> (@ (@ tptp.refl_on_Product_unit A) R2) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit A2) B)) R2) (and (@ (@ tptp.member_Product_unit A2) A) (@ (@ tptp.member_Product_unit B) A))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.refl_on_nat A) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R2) (and (@ (@ tptp.member_nat A2) A) (@ (@ tptp.member_nat B) A))))))
% 5.61/5.91 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.refl_on_int A) R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R2) (and (@ (@ tptp.member_int A2) A) (@ (@ tptp.member_int B) A))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B tptp.int) (R2 tptp.set_Pr7995236796853374141at_int)) (=> (@ (@ tptp.member_nat A2) A) (=> (@ (@ tptp.member4262671552274231302at_int (@ (@ tptp.product_Pair_nat_int A2) B)) R2) (@ (@ tptp.member_int B) (@ (@ tptp.image_nat_int R2) A))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B Bool) (R2 tptp.set_Pr3149072824959771635_nat_o)) (=> (@ (@ tptp.member_nat A2) A) (=> (@ (@ tptp.member6310962623043647828_nat_o (@ (@ tptp.product_Pair_nat_o A2) B)) R2) (@ (@ tptp.member_o B) (@ (@ tptp.image_nat_o R2) A))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B tptp.product_unit) (R2 tptp.set_Pr4334478416066269672t_unit)) (=> (@ (@ tptp.member_nat A2) A) (=> (@ (@ tptp.member348563419383025609t_unit (@ (@ tptp.produc3434450474625521892t_unit A2) B)) R2) (@ (@ tptp.member_Product_unit B) (@ (@ tptp.image_4288904962331477416t_unit R2) A))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B tptp.nat) (R2 tptp.set_Pr3448869479623346877nt_nat)) (=> (@ (@ tptp.member_int A2) A) (=> (@ (@ tptp.member216504246829706758nt_nat (@ (@ tptp.product_Pair_int_nat A2) B)) R2) (@ (@ tptp.member_nat B) (@ (@ tptp.image_int_nat R2) A))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B Bool) (R2 tptp.set_Pr903927857289325719_int_o)) (=> (@ (@ tptp.member_int A2) A) (=> (@ (@ tptp.member4489920277610959864_int_o (@ (@ tptp.product_Pair_int_o A2) B)) R2) (@ (@ tptp.member_o B) (@ (@ tptp.image_int_o R2) A))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B tptp.product_unit) (R2 tptp.set_Pr5889264611543340172t_unit)) (=> (@ (@ tptp.member_int A2) A) (=> (@ (@ tptp.member6688357403439981677t_unit (@ (@ tptp.produc550872421827702152t_unit A2) B)) R2) (@ (@ tptp.member_Product_unit B) (@ (@ tptp.image_1405326909533657676t_unit R2) A))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (A tptp.set_o) (B tptp.nat) (R2 tptp.set_Pr2101469702781467981_o_nat)) (=> (@ (@ tptp.member_o A2) A) (=> (@ (@ tptp.member2802428098988154798_o_nat (@ (@ tptp.product_Pair_o_nat A2) B)) R2) (@ (@ tptp.member_nat B) (@ (@ tptp.image_o_nat R2) A))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (A tptp.set_o) (B tptp.int) (R2 tptp.set_Pr8834758594704517033_o_int)) (=> (@ (@ tptp.member_o A2) A) (=> (@ (@ tptp.member7847949116333733898_o_int (@ (@ tptp.product_Pair_o_int A2) B)) R2) (@ (@ tptp.member_int B) (@ (@ tptp.image_o_int R2) A))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (A tptp.set_o) (B Bool) (R2 tptp.set_Product_prod_o_o)) (=> (@ (@ tptp.member_o A2) A) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) B)) R2) (@ (@ tptp.member_o B) (@ (@ tptp.image_o_o R2) A))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (A tptp.set_o) (B tptp.product_unit) (R2 tptp.set_Pr6671815714118170108t_unit)) (=> (@ (@ tptp.member_o A2) A) (=> (@ (@ tptp.member9215336023991391429t_unit (@ (@ tptp.produc3901946521647900940t_unit A2) B)) R2) (@ (@ tptp.member_Product_unit B) (@ (@ tptp.image_o_Product_unit R2) A))))))
% 5.61/5.91 (assert (forall ((B tptp.set_nat) (R2 tptp.set_Pr3948176798113811640et_nat) (A tptp.set_he8644174446132254637t_unit)) (= (@ (@ tptp.member_set_nat B) (@ (@ tptp.image_3942343239045813184et_nat R2) A)) (exists ((X2 tptp.heap_e7401611519738050253t_unit)) (and (@ (@ tptp.member242389114213480694t_unit X2) A) (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat X2) B)) R2))))))
% 5.61/5.91 (assert (forall ((B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_nat)) (= (@ (@ tptp.member_nat B) (@ (@ tptp.image_nat_nat R2) A)) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) B)) R2))))))
% 5.61/5.91 (assert (forall ((B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (A tptp.set_int)) (= (@ (@ tptp.member_int B) (@ (@ tptp.image_int_int R2) A)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X2) B)) R2))))))
% 5.61/5.91 (assert (forall ((B tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr3286484037609594932et_nat) (A tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.member6260224972018164377et_nat B) (@ (@ tptp.image_1814916760386648892et_nat R2) A)) (exists ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (and (@ (@ tptp.member6576561426505652726_nat_o X2) A) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X2) B)) R2))))))
% 5.61/5.91 (assert (forall ((B tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr8536935166611901872et_nat) (A tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.member1996754912294343701et_nat B) (@ (@ tptp.image_7240710759097644216et_nat R2) A)) (exists ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (and (@ (@ tptp.member6576561426505652726_nat_o X2) A) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X2) B)) R2))))))
% 5.61/5.91 (assert (forall ((B tptp.nat) (R2 tptp.set_Pr3448869479623346877nt_nat) (A tptp.set_int)) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.image_int_nat R2) A)) (not (forall ((X3 tptp.int)) (=> (@ (@ tptp.member216504246829706758nt_nat (@ (@ tptp.product_Pair_int_nat X3) B)) R2) (not (@ (@ tptp.member_int X3) A))))))))
% 5.61/5.91 (assert (forall ((B tptp.nat) (R2 tptp.set_Pr2101469702781467981_o_nat) (A tptp.set_o)) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.image_o_nat R2) A)) (not (forall ((X3 Bool)) (=> (@ (@ tptp.member2802428098988154798_o_nat (@ (@ tptp.product_Pair_o_nat X3) B)) R2) (not (@ (@ tptp.member_o X3) A))))))))
% 5.61/5.91 (assert (forall ((B tptp.nat) (R2 tptp.set_Pr1763845938948868674it_nat) (A tptp.set_Product_unit)) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.image_5657742817519485770it_nat R2) A)) (not (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member423003724879500579it_nat (@ (@ tptp.produc4803288329813530246it_nat X3) B)) R2) (not (@ (@ tptp.member_Product_unit X3) A))))))))
% 5.61/5.91 (assert (forall ((B tptp.int) (R2 tptp.set_Pr7995236796853374141at_int) (A tptp.set_nat)) (=> (@ (@ tptp.member_int B) (@ (@ tptp.image_nat_int R2) A)) (not (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member4262671552274231302at_int (@ (@ tptp.product_Pair_nat_int X3) B)) R2) (not (@ (@ tptp.member_nat X3) A))))))))
% 5.61/5.91 (assert (forall ((B tptp.int) (R2 tptp.set_Pr8834758594704517033_o_int) (A tptp.set_o)) (=> (@ (@ tptp.member_int B) (@ (@ tptp.image_o_int R2) A)) (not (forall ((X3 Bool)) (=> (@ (@ tptp.member7847949116333733898_o_int (@ (@ tptp.product_Pair_o_int X3) B)) R2) (not (@ (@ tptp.member_o X3) A))))))))
% 5.61/5.91 (assert (forall ((B tptp.int) (R2 tptp.set_Pr8497134830871917726it_int) (A tptp.set_Product_unit)) (=> (@ (@ tptp.member_int B) (@ (@ tptp.image_5655252347010435494it_int R2) A)) (not (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member5468524742225079679it_int (@ (@ tptp.produc4800797859304479970it_int X3) B)) R2) (not (@ (@ tptp.member_Product_unit X3) A))))))))
% 5.61/5.91 (assert (forall ((B Bool) (R2 tptp.set_Pr3149072824959771635_nat_o) (A tptp.set_nat)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.image_nat_o R2) A)) (not (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member6310962623043647828_nat_o (@ (@ tptp.product_Pair_nat_o X3) B)) R2) (not (@ (@ tptp.member_nat X3) A))))))))
% 5.61/5.91 (assert (forall ((B Bool) (R2 tptp.set_Pr903927857289325719_int_o) (A tptp.set_int)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.image_int_o R2) A)) (not (forall ((X3 tptp.int)) (=> (@ (@ tptp.member4489920277610959864_int_o (@ (@ tptp.product_Pair_int_o X3) B)) R2) (not (@ (@ tptp.member_int X3) A))))))))
% 5.61/5.91 (assert (forall ((B Bool) (R2 tptp.set_Product_prod_o_o) (A tptp.set_o)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.image_o_o R2) A)) (not (forall ((X3 Bool)) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X3) B)) R2) (not (@ (@ tptp.member_o X3) A))))))))
% 5.61/5.91 (assert (forall ((B Bool) (R2 tptp.set_Pr5464989305201766866unit_o) (A tptp.set_Product_unit)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.image_Product_unit_o R2) A)) (not (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member3689400097658526619unit_o (@ (@ tptp.produc8487917018914037602unit_o X3) B)) R2) (not (@ (@ tptp.member_Product_unit X3) A))))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.refl_o1075864025857821388_nat_o A) R2) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X) Y)) R2) (@ (@ tptp.member6576561426505652726_nat_o Y) A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o) (X Bool) (Y Bool)) (=> (@ (@ tptp.refl_on_o A) R2) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X) Y)) R2) (@ (@ tptp.member_o Y) A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit) (X tptp.product_unit) (Y tptp.product_unit)) (=> (@ (@ tptp.refl_on_Product_unit A) R2) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit X) Y)) R2) (@ (@ tptp.member_Product_unit Y) A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.refl_on_nat A) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R2) (@ (@ tptp.member_nat Y) A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.refl_on_int A) R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R2) (@ (@ tptp.member_int Y) A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.refl_o1075864025857821388_nat_o A) R2) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X) Y)) R2) (@ (@ tptp.member6576561426505652726_nat_o X) A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o) (X Bool) (Y Bool)) (=> (@ (@ tptp.refl_on_o A) R2) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X) Y)) R2) (@ (@ tptp.member_o X) A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit) (X tptp.product_unit) (Y tptp.product_unit)) (=> (@ (@ tptp.refl_on_Product_unit A) R2) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit X) Y)) R2) (@ (@ tptp.member_Product_unit X) A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.refl_on_nat A) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R2) (@ (@ tptp.member_nat X) A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.refl_on_int A) R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R2) (@ (@ tptp.member_int X) A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.refl_o1075864025857821388_nat_o A) R2) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) A) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) A2)) R2)))))
% 5.61/5.91 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o) (A2 Bool)) (=> (@ (@ tptp.refl_on_o A) R2) (=> (@ (@ tptp.member_o A2) A) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) A2)) R2)))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit)) (=> (@ (@ tptp.refl_on_Product_unit A) R2) (=> (@ (@ tptp.member_Product_unit A2) A) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit A2) A2)) R2)))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat)) (=> (@ (@ tptp.refl_on_nat A) R2) (=> (@ (@ tptp.member_nat A2) A) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) A2)) R2)))))
% 5.61/5.91 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int)) (=> (@ (@ tptp.refl_on_int A) R2) (=> (@ (@ tptp.member_int A2) A) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) A2)) R2)))))
% 5.61/5.91 (assert (= tptp.total_on_nat (lambda ((A3 tptp.set_nat) (R4 tptp.set_Pr1261947904930325089at_nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A3) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) A3) (=> (not (= X2 Y3)) (or (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y3)) R4) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y3) X2)) R4))))))))))
% 5.61/5.91 (assert (= tptp.total_on_int (lambda ((A3 tptp.set_int) (R4 tptp.set_Pr958786334691620121nt_int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A3) (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) A3) (=> (not (= X2 Y3)) (or (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X2) Y3)) R4) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y3) X2)) R4))))))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) A) (=> (@ (@ tptp.member6576561426505652726_nat_o Y2) A) (=> (not (= X3 Y2)) (or (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X3) Y2)) R2) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o Y2) X3)) R2)))))) (@ (@ tptp.total_7429123086324524369_nat_o A) R2))))
% 5.61/5.91 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o)) (=> (forall ((X3 Bool) (Y2 Bool)) (=> (@ (@ tptp.member_o X3) A) (=> (@ (@ tptp.member_o Y2) A) (=> (not (= X3 Y2)) (or (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X3) Y2)) R2) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o Y2) X3)) R2)))))) (@ (@ tptp.total_on_o A) R2))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit)) (=> (forall ((X3 tptp.product_unit) (Y2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) A) (=> (@ (@ tptp.member_Product_unit Y2) A) (=> (not (= X3 Y2)) (or (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit X3) Y2)) R2) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit Y2) X3)) R2)))))) (@ (@ tptp.total_5665700600833547665t_unit A) R2))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (=> (@ (@ tptp.member_nat Y2) A) (=> (not (= X3 Y2)) (or (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)) R2) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) X3)) R2)))))) (@ (@ tptp.total_on_nat A) R2))))
% 5.61/5.91 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (=> (@ (@ tptp.member_int Y2) A) (=> (not (= X3 Y2)) (or (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y2)) R2) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y2) X3)) R2)))))) (@ (@ tptp.total_on_int A) R2))))
% 5.61/5.91 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit)) (@ (@ tptp.total_5665700600833547665t_unit tptp.bot_bo3957492148770167129t_unit) R2)))
% 5.61/5.91 (assert (forall ((R2 tptp.set_Product_prod_o_o)) (@ (@ tptp.total_on_o tptp.bot_bot_set_o) R2)))
% 5.61/5.91 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.total_on_nat tptp.bot_bot_set_nat) R2)))
% 5.61/5.91 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.total_on_int tptp.bot_bot_set_int) R2)))
% 5.61/5.91 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o)) (@ (@ tptp.total_7429123086324524369_nat_o tptp.bot_bo7824918357723582233_nat_o) R2)))
% 5.61/5.91 (assert (forall ((P tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H2) (@ tptp.in_range H2))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X) Y)) (@ tptp.id_on_7438695062414216554_nat_o A)) (and (= X Y) (@ (@ tptp.member6576561426505652726_nat_o X) A)))))
% 5.61/5.91 (assert (forall ((X Bool) (Y Bool) (A tptp.set_o)) (= (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X) Y)) (@ tptp.id_on_o A)) (and (= X Y) (@ (@ tptp.member_o X) A)))))
% 5.61/5.91 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (A tptp.set_Product_unit)) (= (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit X) Y)) (@ tptp.id_on_Product_unit A)) (and (= X Y) (@ (@ tptp.member_Product_unit X) A)))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.set_nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.id_on_nat A)) (and (= X Y) (@ (@ tptp.member_nat X) A)))))
% 5.61/5.91 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.set_int)) (= (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ tptp.id_on_int A)) (and (= X Y) (@ (@ tptp.member_int X) A)))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (=> (= A2 B) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) A) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) B)) (@ tptp.id_on_7438695062414216554_nat_o A))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (B Bool) (A tptp.set_o)) (=> (= A2 B) (=> (@ (@ tptp.member_o A2) A) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) B)) (@ tptp.id_on_o A))))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (B tptp.product_unit) (A tptp.set_Product_unit)) (=> (= A2 B) (=> (@ (@ tptp.member_Product_unit A2) A) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit A2) B)) (@ tptp.id_on_Product_unit A))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (A tptp.set_nat)) (=> (= A2 B) (=> (@ (@ tptp.member_nat A2) A) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) (@ tptp.id_on_nat A))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (A tptp.set_int)) (=> (= A2 B) (=> (@ (@ tptp.member_int A2) A) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) (@ tptp.id_on_int A))))))
% 5.61/5.91 (assert (forall ((C tptp.produc4928098042776334183_nat_o) (A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member8781333585448626064_nat_o C) (@ tptp.id_on_7438695062414216554_nat_o A)) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) A) (not (= C (@ (@ tptp.produc7368190662567826135_nat_o X3) X3)))))))))
% 5.61/5.91 (assert (forall ((C tptp.product_prod_o_o) (A tptp.set_o)) (=> (@ (@ tptp.member7466972457876170832od_o_o C) (@ tptp.id_on_o A)) (not (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (not (= C (@ (@ tptp.product_Pair_o_o X3) X3)))))))))
% 5.61/5.91 (assert (forall ((C tptp.produc8459935480633519975t_unit) (A tptp.set_Product_unit)) (=> (@ (@ tptp.member7821138191923116944t_unit C) (@ tptp.id_on_Product_unit A)) (not (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) A) (not (= C (@ (@ tptp.produc5692694829384537815t_unit X3) X3)))))))))
% 5.61/5.91 (assert (forall ((C tptp.product_prod_nat_nat) (A tptp.set_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat C) (@ tptp.id_on_nat A)) (not (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (not (= C (@ (@ tptp.product_Pair_nat_nat X3) X3)))))))))
% 5.61/5.91 (assert (forall ((C tptp.product_prod_int_int) (A tptp.set_int)) (=> (@ (@ tptp.member5262025264175285858nt_int C) (@ tptp.id_on_int A)) (not (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (not (= C (@ (@ tptp.product_Pair_int_int X3) X3)))))))))
% 5.61/5.91 (assert (@ (@ tptp.order_888282469287196226t_unit tptp.bot_bo3957492148770167129t_unit) tptp.bot_bo1654022762305692595t_unit))
% 5.61/5.91 (assert (@ (@ tptp.order_6238756238976269133r_on_o tptp.bot_bot_set_o) tptp.bot_bo7073875226086086771od_o_o))
% 5.61/5.91 (assert (@ (@ tptp.order_4473980167227706203on_nat tptp.bot_bot_set_nat) tptp.bot_bo2099793752762293965at_nat))
% 5.61/5.91 (assert (@ (@ tptp.order_4471489696718655927on_int tptp.bot_bot_set_int) tptp.bot_bo1796632182523588997nt_int))
% 5.61/5.91 (assert (@ (@ tptp.order_1145710701291701250_nat_o tptp.bot_bo7824918357723582233_nat_o) tptp.bot_bo3657187498359500723_nat_o))
% 5.61/5.91 (assert (@ (@ tptp.refl_on_Product_unit tptp.bot_bo3957492148770167129t_unit) tptp.bot_bo1654022762305692595t_unit))
% 5.61/5.91 (assert (@ (@ tptp.refl_on_o tptp.bot_bot_set_o) tptp.bot_bo7073875226086086771od_o_o))
% 5.61/5.91 (assert (@ (@ tptp.refl_on_nat tptp.bot_bot_set_nat) tptp.bot_bo2099793752762293965at_nat))
% 5.61/5.91 (assert (@ (@ tptp.refl_on_int tptp.bot_bot_set_int) tptp.bot_bo1796632182523588997nt_int))
% 5.61/5.91 (assert (@ (@ tptp.refl_o1075864025857821388_nat_o tptp.bot_bo7824918357723582233_nat_o) tptp.bot_bo3657187498359500723_nat_o))
% 5.61/5.91 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (H2 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As))) (=> (@ tptp.proper P) (=> (@ P _let_1) (@ tptp.in_range _let_1))))))
% 5.61/5.91 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (As tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H3) As))) (=> (@ tptp.proper P) (=> (@ (@ (@ tptp.relH As) H2) H3) (=> (@ tptp.in_range _let_1) (= (@ P (@ (@ tptp.produc7507926704131184380et_nat H2) As)) (@ P _let_1))))))))
% 5.61/5.91 (assert (= tptp.proper (lambda ((P2 (-> tptp.produc3658429121746597890et_nat Bool))) (forall ((H4 tptp.heap_e7401611519738050253t_unit) (H5 tptp.heap_e7401611519738050253t_unit) (As3 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H5) As3))) (let ((_let_2 (@ (@ tptp.produc7507926704131184380et_nat H4) As3))) (let ((_let_3 (@ P2 _let_2))) (and (=> _let_3 (@ tptp.in_range _let_2)) (=> (and _let_3 (@ (@ (@ tptp.relH As3) H4) H5) (@ tptp.in_range _let_1)) (@ P2 _let_1))))))))))
% 5.61/5.91 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (H2 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat) (H3 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H3) As))) (=> (@ tptp.proper P) (=> (@ P (@ (@ tptp.produc7507926704131184380et_nat H2) As)) (=> (@ (@ (@ tptp.relH As) H2) H3) (=> (@ tptp.in_range _let_1) (@ P _let_1))))))))
% 5.61/5.91 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool))) (=> (forall ((As2 tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As2))) (=> (@ P _let_1) (@ tptp.in_range _let_1)))) (=> (forall ((As2 tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit) (H6 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H6) As2))) (=> (@ P (@ (@ tptp.produc7507926704131184380et_nat H) As2)) (=> (@ (@ (@ tptp.relH As2) H) H6) (=> (@ tptp.in_range _let_1) (@ P _let_1)))))) (@ tptp.proper P)))))
% 5.61/5.91 (assert (forall ((U tptp.heap_e7401611519738050253t_unit) (E tptp.set_Pr3948176798113811640et_nat)) (= (@ (@ tptp.vimage5412618565253405765et_nat (@ tptp.produc7507926704131184380et_nat U)) E) (@ (@ tptp.image_3942343239045813184et_nat E) (@ (@ tptp.insert8563697753282147485t_unit U) tptp.bot_bo3686245532977126937t_unit)))))
% 5.61/5.91 (assert (forall ((U tptp.nat) (E tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.vimage8013328719654469172at_nat (@ tptp.product_Pair_nat_nat U)) E) (@ (@ tptp.image_nat_nat E) (@ (@ tptp.insert_nat U) tptp.bot_bot_set_nat)))))
% 5.61/5.91 (assert (forall ((U tptp.int) (E tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.vimage7872673496510460816nt_int (@ tptp.product_Pair_int_int U)) E) (@ (@ tptp.image_int_int E) (@ (@ tptp.insert_int U) tptp.bot_bot_set_int)))))
% 5.61/5.91 (assert (forall ((U (-> tptp.produc3658429121746597890et_nat Bool)) (E tptp.set_Pr3286484037609594932et_nat)) (= (@ (@ tptp.vimage1990136491886319165et_nat (@ tptp.produc5001842942810119800et_nat U)) E) (@ (@ tptp.image_1814916760386648892et_nat E) (@ (@ tptp.insert5175938949040314269_nat_o U) tptp.bot_bo7824918357723582233_nat_o)))))
% 5.61/5.91 (assert (forall ((U (-> tptp.produc3658429121746597890et_nat Bool)) (E tptp.set_Pr8536935166611901872et_nat)) (= (@ (@ tptp.vimage7160910655466636085et_nat (@ tptp.produc2245416461498447860et_nat U)) E) (@ (@ tptp.image_7240710759097644216et_nat E) (@ (@ tptp.insert5175938949040314269_nat_o U) tptp.bot_bo7824918357723582233_nat_o)))))
% 5.61/5.91 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat) (R2 tptp.set_Pr3948176798113811640et_nat)) (= (@ tptp.range_9132311542094983838et_nat (@ (@ tptp.insert1271470778893645362et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) B)) R2)) (@ (@ tptp.insert_set_nat B) (@ tptp.range_9132311542094983838et_nat R2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.range_nat_nat (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R2)) (@ (@ tptp.insert_nat B) (@ tptp.range_nat_nat R2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ tptp.range_int_int (@ (@ tptp.insert5033312907999012233nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R2)) (@ (@ tptp.insert_int B) (@ tptp.range_int_int R2)))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr3286484037609594932et_nat)) (= (@ tptp.range_3398330936903821850et_nat (@ (@ tptp.insert3111075074545270702et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) B)) R2)) (@ (@ tptp.insert1271470778893645362et_nat B) (@ tptp.range_3398330936903821850et_nat R2)))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr8536935166611901872et_nat)) (= (@ tptp.range_7260058354244137878et_nat (@ (@ tptp.insert8297122186708525866et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) B)) R2)) (@ (@ tptp.insert3111075074545270702et_nat B) (@ tptp.range_7260058354244137878et_nat R2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat) (R2 tptp.set_Pr3948176798113811640et_nat)) (= (@ tptp.domain2007548326387822151et_nat (@ (@ tptp.insert1271470778893645362et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) B)) R2)) (@ (@ tptp.insert8563697753282147485t_unit A2) (@ tptp.domain2007548326387822151et_nat R2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.domain_nat_nat (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R2)) (@ (@ tptp.insert_nat A2) (@ tptp.domain_nat_nat R2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ tptp.domain_int_int (@ (@ tptp.insert5033312907999012233nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R2)) (@ (@ tptp.insert_int A2) (@ tptp.domain_int_int R2)))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr3286484037609594932et_nat)) (= (@ tptp.domain2358961613337345475et_nat (@ (@ tptp.insert3111075074545270702et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) B)) R2)) (@ (@ tptp.insert5175938949040314269_nat_o A2) (@ tptp.domain2358961613337345475et_nat R2)))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr8536935166611901872et_nat)) (= (@ tptp.domain3618434998481624895et_nat (@ (@ tptp.insert8297122186708525866et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) B)) R2)) (@ (@ tptp.insert5175938949040314269_nat_o A2) (@ tptp.domain3618434998481624895et_nat R2)))))
% 5.61/5.91 (assert (@ (@ tptp.order_7534304569044981540t_unit tptp.bot_bo3957492148770167129t_unit) tptp.bot_bo1654022762305692595t_unit))
% 5.61/5.91 (assert (@ (@ tptp.order_preorder_on_o tptp.bot_bot_set_o) tptp.bot_bo7073875226086086771od_o_o))
% 5.61/5.91 (assert (@ (@ tptp.order_4861654808422542329on_nat tptp.bot_bot_set_nat) tptp.bot_bo2099793752762293965at_nat))
% 5.61/5.91 (assert (@ (@ tptp.order_4859164337913492053on_int tptp.bot_bot_set_int) tptp.bot_bo1796632182523588997nt_int))
% 5.61/5.91 (assert (@ (@ tptp.order_174704566861754596_nat_o tptp.bot_bo7824918357723582233_nat_o) tptp.bot_bo3657187498359500723_nat_o))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) tptp.bot_bo2099793752762293965at_nat))) (= (@ tptp.transi6264000038957366511cl_nat _let_1) _let_1))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.insert5033312907999012233nt_int (@ (@ tptp.product_Pair_int_int A2) B)) tptp.bot_bo1796632182523588997nt_int))) (= (@ tptp.transi6261509568448316235cl_int _let_1) _let_1))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat)) (@ tptp.trans_nat (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.product_Pair_nat_nat A2) A2)) tptp.bot_bo2099793752762293965at_nat))))
% 5.61/5.91 (assert (forall ((A2 tptp.int)) (@ tptp.trans_int (@ (@ tptp.insert5033312907999012233nt_int (@ (@ tptp.product_Pair_int_int A2) A2)) tptp.bot_bo1796632182523588997nt_int))))
% 5.61/5.91 (assert (forall ((X tptp.assn) (Y tptp.assn) (A2 tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.syntax7398250324933576852n_assn (@ (@ tptp.times_times_assn X) Y)) A2) (= (@ (@ tptp.times_times_assn A2) B) (@ (@ tptp.times_times_assn B) A2)))))
% 5.61/5.91 (assert (forall ((X tptp.rat) (Y tptp.rat) (A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.syntax3730441303064801268at_rat (@ (@ tptp.times_times_rat X) Y)) A2) (= (@ (@ tptp.times_times_rat A2) B) (@ (@ tptp.times_times_rat B) A2)))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (Y tptp.nat) (A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.syntax4682126007086162916at_nat (@ (@ tptp.times_times_nat X) Y)) A2) (= (@ (@ tptp.times_times_nat A2) B) (@ (@ tptp.times_times_nat B) A2)))))
% 5.61/5.91 (assert (forall ((X tptp.int) (Y tptp.int) (A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.syntax5678989248478167196nt_int (@ (@ tptp.times_times_int X) Y)) A2) (= (@ (@ tptp.times_times_int A2) B) (@ (@ tptp.times_times_int B) A2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B4 tptp.set_nat)) (= (@ (@ tptp.member_nat A2) (@ (@ tptp.vimage_nat_nat F) B4)) (@ (@ tptp.member_nat (@ F A2)) B4))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.int)) (B4 tptp.set_int)) (= (@ (@ tptp.member_nat A2) (@ (@ tptp.vimage_nat_int F) B4)) (@ (@ tptp.member_int (@ F A2)) B4))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat Bool)) (B4 tptp.set_o)) (= (@ (@ tptp.member_nat A2) (@ (@ tptp.vimage_nat_o F) B4)) (@ (@ tptp.member_o (@ F A2)) B4))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.product_unit)) (B4 tptp.set_Product_unit)) (= (@ (@ tptp.member_nat A2) (@ (@ tptp.vimage4884490618288580032t_unit F) B4)) (@ (@ tptp.member_Product_unit (@ F A2)) B4))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (F (-> tptp.int tptp.nat)) (B4 tptp.set_nat)) (= (@ (@ tptp.member_int A2) (@ (@ tptp.vimage_int_nat F) B4)) (@ (@ tptp.member_nat (@ F A2)) B4))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (F (-> tptp.int tptp.int)) (B4 tptp.set_int)) (= (@ (@ tptp.member_int A2) (@ (@ tptp.vimage_int_int F) B4)) (@ (@ tptp.member_int (@ F A2)) B4))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (F (-> tptp.int Bool)) (B4 tptp.set_o)) (= (@ (@ tptp.member_int A2) (@ (@ tptp.vimage_int_o F) B4)) (@ (@ tptp.member_o (@ F A2)) B4))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (F (-> tptp.int tptp.product_unit)) (B4 tptp.set_Product_unit)) (= (@ (@ tptp.member_int A2) (@ (@ tptp.vimage2000912565490760292t_unit F) B4)) (@ (@ tptp.member_Product_unit (@ F A2)) B4))))
% 5.61/5.91 (assert (forall ((A2 Bool) (F (-> Bool tptp.nat)) (B4 tptp.set_nat)) (= (@ (@ tptp.member_o A2) (@ (@ tptp.vimage_o_nat F) B4)) (@ (@ tptp.member_nat (@ F A2)) B4))))
% 5.61/5.91 (assert (forall ((A2 Bool) (F (-> Bool tptp.int)) (B4 tptp.set_int)) (= (@ (@ tptp.member_o A2) (@ (@ tptp.vimage_o_int F) B4)) (@ (@ tptp.member_int (@ F A2)) B4))))
% 5.61/5.91 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.nat) (B tptp.nat) (B4 tptp.set_nat)) (=> (= (@ F A2) B) (=> (@ (@ tptp.member_nat B) B4) (@ (@ tptp.member_nat A2) (@ (@ tptp.vimage_nat_nat F) B4))))))
% 5.61/5.91 (assert (forall ((F (-> tptp.int tptp.nat)) (A2 tptp.int) (B tptp.nat) (B4 tptp.set_nat)) (=> (= (@ F A2) B) (=> (@ (@ tptp.member_nat B) B4) (@ (@ tptp.member_int A2) (@ (@ tptp.vimage_int_nat F) B4))))))
% 5.61/5.91 (assert (forall ((F (-> Bool tptp.nat)) (A2 Bool) (B tptp.nat) (B4 tptp.set_nat)) (=> (= (@ F A2) B) (=> (@ (@ tptp.member_nat B) B4) (@ (@ tptp.member_o A2) (@ (@ tptp.vimage_o_nat F) B4))))))
% 5.61/5.91 (assert (forall ((F (-> tptp.product_unit tptp.nat)) (A2 tptp.product_unit) (B tptp.nat) (B4 tptp.set_nat)) (=> (= (@ F A2) B) (=> (@ (@ tptp.member_nat B) B4) (@ (@ tptp.member_Product_unit A2) (@ (@ tptp.vimage6253328473476588386it_nat F) B4))))))
% 5.61/5.91 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.nat) (B tptp.int) (B4 tptp.set_int)) (=> (= (@ F A2) B) (=> (@ (@ tptp.member_int B) B4) (@ (@ tptp.member_nat A2) (@ (@ tptp.vimage_nat_int F) B4))))))
% 5.61/5.91 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.int) (B tptp.int) (B4 tptp.set_int)) (=> (= (@ F A2) B) (=> (@ (@ tptp.member_int B) B4) (@ (@ tptp.member_int A2) (@ (@ tptp.vimage_int_int F) B4))))))
% 5.61/5.91 (assert (forall ((F (-> Bool tptp.int)) (A2 Bool) (B tptp.int) (B4 tptp.set_int)) (=> (= (@ F A2) B) (=> (@ (@ tptp.member_int B) B4) (@ (@ tptp.member_o A2) (@ (@ tptp.vimage_o_int F) B4))))))
% 5.61/5.91 (assert (forall ((F (-> tptp.product_unit tptp.int)) (A2 tptp.product_unit) (B tptp.int) (B4 tptp.set_int)) (=> (= (@ F A2) B) (=> (@ (@ tptp.member_int B) B4) (@ (@ tptp.member_Product_unit A2) (@ (@ tptp.vimage6250838002967538110it_int F) B4))))))
% 5.61/5.91 (assert (forall ((F (-> tptp.nat Bool)) (A2 tptp.nat) (B Bool) (B4 tptp.set_o)) (=> (= (@ F A2) B) (=> (@ (@ tptp.member_o B) B4) (@ (@ tptp.member_nat A2) (@ (@ tptp.vimage_nat_o F) B4))))))
% 5.61/5.91 (assert (forall ((F (-> tptp.int Bool)) (A2 tptp.int) (B Bool) (B4 tptp.set_o)) (=> (= (@ F A2) B) (=> (@ (@ tptp.member_o B) B4) (@ (@ tptp.member_int A2) (@ (@ tptp.vimage_int_o F) B4))))))
% 5.61/5.91 (assert (forall ((F (-> tptp.product_unit tptp.product_unit))) (= (@ (@ tptp.vimage7995052115951654139t_unit F) tptp.bot_bo3957492148770167129t_unit) tptp.bot_bo3957492148770167129t_unit)))
% 5.61/5.91 (assert (forall ((F (-> Bool tptp.product_unit))) (= (@ (@ tptp.vimage4222377557387472176t_unit F) tptp.bot_bo3957492148770167129t_unit) tptp.bot_bot_set_o)))
% 5.61/5.91 (assert (forall ((F (-> tptp.nat tptp.product_unit))) (= (@ (@ tptp.vimage4884490618288580032t_unit F) tptp.bot_bo3957492148770167129t_unit) tptp.bot_bot_set_nat)))
% 5.61/5.91 (assert (forall ((F (-> tptp.int tptp.product_unit))) (= (@ (@ tptp.vimage2000912565490760292t_unit F) tptp.bot_bo3957492148770167129t_unit) tptp.bot_bot_set_int)))
% 5.61/5.91 (assert (forall ((F (-> tptp.product_unit Bool))) (= (@ (@ tptp.vimage8808348054653608838unit_o F) tptp.bot_bot_set_o) tptp.bot_bo3957492148770167129t_unit)))
% 5.61/5.91 (assert (forall ((F (-> Bool Bool))) (= (@ (@ tptp.vimage_o_o F) tptp.bot_bot_set_o) tptp.bot_bot_set_o)))
% 5.61/5.91 (assert (forall ((F (-> tptp.nat Bool))) (= (@ (@ tptp.vimage_nat_o F) tptp.bot_bot_set_o) tptp.bot_bot_set_nat)))
% 5.61/5.91 (assert (forall ((F (-> tptp.int Bool))) (= (@ (@ tptp.vimage_int_o F) tptp.bot_bot_set_o) tptp.bot_bot_set_int)))
% 5.61/5.91 (assert (forall ((F (-> tptp.product_unit tptp.nat))) (= (@ (@ tptp.vimage6253328473476588386it_nat F) tptp.bot_bot_set_nat) tptp.bot_bo3957492148770167129t_unit)))
% 5.61/5.91 (assert (forall ((F (-> Bool tptp.nat))) (= (@ (@ tptp.vimage_o_nat F) tptp.bot_bot_set_nat) tptp.bot_bot_set_o)))
% 5.61/5.91 (assert (forall ((As tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.relH As))) (=> (@ (@ _let_1 H2) H3) (@ (@ _let_1 H3) H2)))))
% 5.61/5.91 (assert (forall ((As tptp.set_nat) (H12 tptp.heap_e7401611519738050253t_unit) (H23 tptp.heap_e7401611519738050253t_unit) (H32 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.relH As))) (let ((_let_2 (@ _let_1 H12))) (=> (@ _let_2 H23) (=> (@ (@ _let_1 H23) H32) (@ _let_2 H32)))))))
% 5.61/5.91 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.nat)) (Q2 (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (= (@ P (@ F X3)) (@ Q2 X3))) (= (@ (@ tptp.vimage_nat_nat F) (@ tptp.collect_nat P)) (@ tptp.collect_nat Q2)))))
% 5.61/5.91 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.int tptp.nat)) (Q2 (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (= (@ P (@ F X3)) (@ Q2 X3))) (= (@ (@ tptp.vimage_int_nat F) (@ tptp.collect_nat P)) (@ tptp.collect_int Q2)))))
% 5.61/5.91 (assert (forall ((P (-> tptp.nat Bool)) (F (-> Bool tptp.nat)) (Q2 (-> Bool Bool))) (=> (forall ((X3 Bool)) (= (@ P (@ F X3)) (@ Q2 X3))) (= (@ (@ tptp.vimage_o_nat F) (@ tptp.collect_nat P)) (@ tptp.collect_o Q2)))))
% 5.61/5.91 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.product_unit tptp.nat)) (Q2 (-> tptp.product_unit Bool))) (=> (forall ((X3 tptp.product_unit)) (= (@ P (@ F X3)) (@ Q2 X3))) (= (@ (@ tptp.vimage6253328473476588386it_nat F) (@ tptp.collect_nat P)) (@ tptp.collect_Product_unit Q2)))))
% 5.61/5.91 (assert (forall ((P (-> tptp.int Bool)) (F (-> tptp.nat tptp.int)) (Q2 (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (= (@ P (@ F X3)) (@ Q2 X3))) (= (@ (@ tptp.vimage_nat_int F) (@ tptp.collect_int P)) (@ tptp.collect_nat Q2)))))
% 5.61/5.91 (assert (forall ((P (-> tptp.int Bool)) (F (-> tptp.int tptp.int)) (Q2 (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (= (@ P (@ F X3)) (@ Q2 X3))) (= (@ (@ tptp.vimage_int_int F) (@ tptp.collect_int P)) (@ tptp.collect_int Q2)))))
% 5.61/5.91 (assert (forall ((P (-> tptp.int Bool)) (F (-> Bool tptp.int)) (Q2 (-> Bool Bool))) (=> (forall ((X3 Bool)) (= (@ P (@ F X3)) (@ Q2 X3))) (= (@ (@ tptp.vimage_o_int F) (@ tptp.collect_int P)) (@ tptp.collect_o Q2)))))
% 5.61/5.91 (assert (forall ((P (-> tptp.int Bool)) (F (-> tptp.product_unit tptp.int)) (Q2 (-> tptp.product_unit Bool))) (=> (forall ((X3 tptp.product_unit)) (= (@ P (@ F X3)) (@ Q2 X3))) (= (@ (@ tptp.vimage6250838002967538110it_int F) (@ tptp.collect_int P)) (@ tptp.collect_Product_unit Q2)))))
% 5.61/5.91 (assert (forall ((P (-> Bool Bool)) (F (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (= (@ P (@ F X3)) (@ Q2 X3))) (= (@ (@ tptp.vimage_nat_o F) (@ tptp.collect_o P)) (@ tptp.collect_nat Q2)))))
% 5.61/5.91 (assert (forall ((P (-> Bool Bool)) (F (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (= (@ P (@ F X3)) (@ Q2 X3))) (= (@ (@ tptp.vimage_int_o F) (@ tptp.collect_o P)) (@ tptp.collect_int Q2)))))
% 5.61/5.91 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat (@ F A2)) A) (@ (@ tptp.member_nat A2) (@ (@ tptp.vimage_nat_nat F) A)))))
% 5.61/5.91 (assert (forall ((F (-> tptp.int tptp.nat)) (A2 tptp.int) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat (@ F A2)) A) (@ (@ tptp.member_int A2) (@ (@ tptp.vimage_int_nat F) A)))))
% 5.61/5.91 (assert (forall ((F (-> Bool tptp.nat)) (A2 Bool) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat (@ F A2)) A) (@ (@ tptp.member_o A2) (@ (@ tptp.vimage_o_nat F) A)))))
% 5.61/5.91 (assert (forall ((F (-> tptp.product_unit tptp.nat)) (A2 tptp.product_unit) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat (@ F A2)) A) (@ (@ tptp.member_Product_unit A2) (@ (@ tptp.vimage6253328473476588386it_nat F) A)))))
% 5.61/5.91 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.nat) (A tptp.set_int)) (=> (@ (@ tptp.member_int (@ F A2)) A) (@ (@ tptp.member_nat A2) (@ (@ tptp.vimage_nat_int F) A)))))
% 5.61/5.91 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.int) (A tptp.set_int)) (=> (@ (@ tptp.member_int (@ F A2)) A) (@ (@ tptp.member_int A2) (@ (@ tptp.vimage_int_int F) A)))))
% 5.61/5.91 (assert (forall ((F (-> Bool tptp.int)) (A2 Bool) (A tptp.set_int)) (=> (@ (@ tptp.member_int (@ F A2)) A) (@ (@ tptp.member_o A2) (@ (@ tptp.vimage_o_int F) A)))))
% 5.61/5.91 (assert (forall ((F (-> tptp.product_unit tptp.int)) (A2 tptp.product_unit) (A tptp.set_int)) (=> (@ (@ tptp.member_int (@ F A2)) A) (@ (@ tptp.member_Product_unit A2) (@ (@ tptp.vimage6250838002967538110it_int F) A)))))
% 5.61/5.91 (assert (forall ((F (-> tptp.nat Bool)) (A2 tptp.nat) (A tptp.set_o)) (=> (@ (@ tptp.member_o (@ F A2)) A) (@ (@ tptp.member_nat A2) (@ (@ tptp.vimage_nat_o F) A)))))
% 5.61/5.91 (assert (forall ((F (-> tptp.int Bool)) (A2 tptp.int) (A tptp.set_o)) (=> (@ (@ tptp.member_o (@ F A2)) A) (@ (@ tptp.member_int A2) (@ (@ tptp.vimage_int_o F) A)))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B4 tptp.set_nat)) (=> (@ (@ tptp.member_nat A2) (@ (@ tptp.vimage_nat_nat F) B4)) (@ (@ tptp.member_nat (@ F A2)) B4))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.int)) (B4 tptp.set_int)) (=> (@ (@ tptp.member_nat A2) (@ (@ tptp.vimage_nat_int F) B4)) (@ (@ tptp.member_int (@ F A2)) B4))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat Bool)) (B4 tptp.set_o)) (=> (@ (@ tptp.member_nat A2) (@ (@ tptp.vimage_nat_o F) B4)) (@ (@ tptp.member_o (@ F A2)) B4))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.product_unit)) (B4 tptp.set_Product_unit)) (=> (@ (@ tptp.member_nat A2) (@ (@ tptp.vimage4884490618288580032t_unit F) B4)) (@ (@ tptp.member_Product_unit (@ F A2)) B4))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (F (-> tptp.int tptp.nat)) (B4 tptp.set_nat)) (=> (@ (@ tptp.member_int A2) (@ (@ tptp.vimage_int_nat F) B4)) (@ (@ tptp.member_nat (@ F A2)) B4))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (F (-> tptp.int tptp.int)) (B4 tptp.set_int)) (=> (@ (@ tptp.member_int A2) (@ (@ tptp.vimage_int_int F) B4)) (@ (@ tptp.member_int (@ F A2)) B4))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (F (-> tptp.int Bool)) (B4 tptp.set_o)) (=> (@ (@ tptp.member_int A2) (@ (@ tptp.vimage_int_o F) B4)) (@ (@ tptp.member_o (@ F A2)) B4))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (F (-> tptp.int tptp.product_unit)) (B4 tptp.set_Product_unit)) (=> (@ (@ tptp.member_int A2) (@ (@ tptp.vimage2000912565490760292t_unit F) B4)) (@ (@ tptp.member_Product_unit (@ F A2)) B4))))
% 5.61/5.91 (assert (forall ((A2 Bool) (F (-> Bool tptp.nat)) (B4 tptp.set_nat)) (=> (@ (@ tptp.member_o A2) (@ (@ tptp.vimage_o_nat F) B4)) (@ (@ tptp.member_nat (@ F A2)) B4))))
% 5.61/5.91 (assert (forall ((A2 Bool) (F (-> Bool tptp.int)) (B4 tptp.set_int)) (=> (@ (@ tptp.member_o A2) (@ (@ tptp.vimage_o_int F) B4)) (@ (@ tptp.member_int (@ F A2)) B4))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat A2) (@ (@ tptp.vimage_nat_nat F) A)) (@ (@ tptp.member_nat (@ F A2)) A))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.int)) (A tptp.set_int)) (=> (@ (@ tptp.member_nat A2) (@ (@ tptp.vimage_nat_int F) A)) (@ (@ tptp.member_int (@ F A2)) A))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat Bool)) (A tptp.set_o)) (=> (@ (@ tptp.member_nat A2) (@ (@ tptp.vimage_nat_o F) A)) (@ (@ tptp.member_o (@ F A2)) A))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.product_unit)) (A tptp.set_Product_unit)) (=> (@ (@ tptp.member_nat A2) (@ (@ tptp.vimage4884490618288580032t_unit F) A)) (@ (@ tptp.member_Product_unit (@ F A2)) A))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (F (-> tptp.int tptp.nat)) (A tptp.set_nat)) (=> (@ (@ tptp.member_int A2) (@ (@ tptp.vimage_int_nat F) A)) (@ (@ tptp.member_nat (@ F A2)) A))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (F (-> tptp.int tptp.int)) (A tptp.set_int)) (=> (@ (@ tptp.member_int A2) (@ (@ tptp.vimage_int_int F) A)) (@ (@ tptp.member_int (@ F A2)) A))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (F (-> tptp.int Bool)) (A tptp.set_o)) (=> (@ (@ tptp.member_int A2) (@ (@ tptp.vimage_int_o F) A)) (@ (@ tptp.member_o (@ F A2)) A))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (F (-> tptp.int tptp.product_unit)) (A tptp.set_Product_unit)) (=> (@ (@ tptp.member_int A2) (@ (@ tptp.vimage2000912565490760292t_unit F) A)) (@ (@ tptp.member_Product_unit (@ F A2)) A))))
% 5.61/5.91 (assert (forall ((A2 Bool) (F (-> Bool tptp.nat)) (A tptp.set_nat)) (=> (@ (@ tptp.member_o A2) (@ (@ tptp.vimage_o_nat F) A)) (@ (@ tptp.member_nat (@ F A2)) A))))
% 5.61/5.91 (assert (forall ((A2 Bool) (F (-> Bool tptp.int)) (A tptp.set_int)) (=> (@ (@ tptp.member_o A2) (@ (@ tptp.vimage_o_int F) A)) (@ (@ tptp.member_int (@ F A2)) A))))
% 5.61/5.91 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X))) (=> (@ tptp.trans_nat R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 Y)) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y) Z)) R2) (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 Z)) R2)))))))
% 5.61/5.91 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int X))) (=> (@ tptp.trans_int R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 Y)) R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y) Z)) R2) (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 Z)) R2)))))))
% 5.61/5.91 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X))) (=> (@ tptp.trans_nat R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 Y)) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y) Z)) R2) (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 Z)) R2)))))))
% 5.61/5.91 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int X))) (=> (@ tptp.trans_int R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 Y)) R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y) Z)) R2) (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 Z)) R2)))))))
% 5.61/5.91 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X3))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 Y2)) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Z3)) R2) (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 Z3)) R2))))) (@ tptp.trans_nat R2))))
% 5.61/5.91 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int)) (=> (forall ((X3 tptp.int) (Y2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int X3))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 Y2)) R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y2) Z3)) R2) (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 Z3)) R2))))) (@ tptp.trans_int R2))))
% 5.61/5.91 (assert (= tptp.trans_nat (lambda ((R4 tptp.set_Pr1261947904930325089at_nat)) (forall ((X2 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 Y3)) R4) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y3) Z2)) R4) (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 Z2)) R4))))))))
% 5.61/5.91 (assert (= tptp.trans_int (lambda ((R4 tptp.set_Pr958786334691620121nt_int)) (forall ((X2 tptp.int) (Y3 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int X2))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 Y3)) R4) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y3) Z2)) R4) (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 Z2)) R4))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (R2 tptp.set_Pr3948176798113811640et_nat)) (=> (@ (@ tptp.member242389114213480694t_unit A2) (@ tptp.domain2007548326387822151et_nat R2)) (not (forall ((B2 tptp.set_nat)) (not (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) B2)) R2)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member_nat A2) (@ tptp.domain_nat_nat R2)) (not (forall ((B2 tptp.nat)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B2)) R2)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member_int A2) (@ tptp.domain_int_int R2)) (not (forall ((B2 tptp.int)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B2)) R2)))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr3286484037609594932et_nat)) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) (@ tptp.domain2358961613337345475et_nat R2)) (not (forall ((B2 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) B2)) R2)))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr8536935166611901872et_nat)) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) (@ tptp.domain3618434998481624895et_nat R2)) (not (forall ((B2 tptp.produc3925858234332021118et_nat)) (not (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) B2)) R2)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (R2 tptp.set_Pr3948176798113811640et_nat)) (= (@ (@ tptp.member242389114213480694t_unit A2) (@ tptp.domain2007548326387822151et_nat R2)) (exists ((A6 tptp.heap_e7401611519738050253t_unit) (B6 tptp.set_nat)) (and (= A2 A6) (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A6) B6)) R2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member_nat A2) (@ tptp.domain_nat_nat R2)) (exists ((A6 tptp.nat) (B6 tptp.nat)) (and (= A2 A6) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A6) B6)) R2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member_int A2) (@ tptp.domain_int_int R2)) (exists ((A6 tptp.int) (B6 tptp.int)) (and (= A2 A6) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A6) B6)) R2))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr3286484037609594932et_nat)) (= (@ (@ tptp.member6576561426505652726_nat_o A2) (@ tptp.domain2358961613337345475et_nat R2)) (exists ((A6 (-> tptp.produc3658429121746597890et_nat Bool)) (B6 tptp.produc3658429121746597890et_nat)) (and (= A2 A6) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A6) B6)) R2))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr8536935166611901872et_nat)) (= (@ (@ tptp.member6576561426505652726_nat_o A2) (@ tptp.domain3618434998481624895et_nat R2)) (exists ((A6 (-> tptp.produc3658429121746597890et_nat Bool)) (B6 tptp.produc3925858234332021118et_nat)) (and (= A2 A6) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A6) B6)) R2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat) (R2 tptp.set_Pr3948176798113811640et_nat)) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) B)) R2) (@ (@ tptp.member242389114213480694t_unit A2) (@ tptp.domain2007548326387822151et_nat R2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R2) (@ (@ tptp.member_nat A2) (@ tptp.domain_nat_nat R2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R2) (@ (@ tptp.member_int A2) (@ tptp.domain_int_int R2)))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr3286484037609594932et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) B)) R2) (@ (@ tptp.member6576561426505652726_nat_o A2) (@ tptp.domain2358961613337345475et_nat R2)))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr8536935166611901872et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) B)) R2) (@ (@ tptp.member6576561426505652726_nat_o A2) (@ tptp.domain3618434998481624895et_nat R2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (R2 tptp.set_Pr3948176798113811640et_nat)) (=> (@ (@ tptp.member242389114213480694t_unit A2) (@ tptp.domain2007548326387822151et_nat R2)) (not (forall ((B2 tptp.set_nat)) (not (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) B2)) R2)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member_nat A2) (@ tptp.domain_nat_nat R2)) (not (forall ((B2 tptp.nat)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B2)) R2)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member_int A2) (@ tptp.domain_int_int R2)) (not (forall ((B2 tptp.int)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B2)) R2)))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr3286484037609594932et_nat)) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) (@ tptp.domain2358961613337345475et_nat R2)) (not (forall ((B2 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) B2)) R2)))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr8536935166611901872et_nat)) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) (@ tptp.domain3618434998481624895et_nat R2)) (not (forall ((B2 tptp.produc3925858234332021118et_nat)) (not (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) B2)) R2)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (R2 tptp.set_Pr3948176798113811640et_nat)) (= (@ (@ tptp.member242389114213480694t_unit A2) (@ tptp.domain2007548326387822151et_nat R2)) (exists ((Y3 tptp.set_nat)) (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) Y3)) R2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member_nat A2) (@ tptp.domain_nat_nat R2)) (exists ((Y3 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) Y3)) R2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member_int A2) (@ tptp.domain_int_int R2)) (exists ((Y3 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) Y3)) R2)))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr3286484037609594932et_nat)) (= (@ (@ tptp.member6576561426505652726_nat_o A2) (@ tptp.domain2358961613337345475et_nat R2)) (exists ((Y3 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) Y3)) R2)))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr8536935166611901872et_nat)) (= (@ (@ tptp.member6576561426505652726_nat_o A2) (@ tptp.domain3618434998481624895et_nat R2)) (exists ((Y3 tptp.produc3925858234332021118et_nat)) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) Y3)) R2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_nat) (R2 tptp.set_Pr3948176798113811640et_nat)) (=> (@ (@ tptp.member_set_nat A2) (@ tptp.range_9132311542094983838et_nat R2)) (not (forall ((A4 tptp.heap_e7401611519738050253t_unit)) (not (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A4) A2)) R2)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member_nat A2) (@ tptp.range_nat_nat R2)) (not (forall ((A4 tptp.nat)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A4) A2)) R2)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member_int A2) (@ tptp.range_int_int R2)) (not (forall ((A4 tptp.int)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A4) A2)) R2)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr3286484037609594932et_nat)) (=> (@ (@ tptp.member6260224972018164377et_nat A2) (@ tptp.range_3398330936903821850et_nat R2)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A4) A2)) R2)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr8536935166611901872et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat A2) (@ tptp.range_7260058354244137878et_nat R2)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A4) A2)) R2)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_nat) (R2 tptp.set_Pr3948176798113811640et_nat)) (= (@ (@ tptp.member_set_nat A2) (@ tptp.range_9132311542094983838et_nat R2)) (exists ((A6 tptp.heap_e7401611519738050253t_unit) (B6 tptp.set_nat)) (and (= A2 B6) (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A6) B6)) R2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member_nat A2) (@ tptp.range_nat_nat R2)) (exists ((A6 tptp.nat) (B6 tptp.nat)) (and (= A2 B6) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A6) B6)) R2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member_int A2) (@ tptp.range_int_int R2)) (exists ((A6 tptp.int) (B6 tptp.int)) (and (= A2 B6) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A6) B6)) R2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr3286484037609594932et_nat)) (= (@ (@ tptp.member6260224972018164377et_nat A2) (@ tptp.range_3398330936903821850et_nat R2)) (exists ((A6 (-> tptp.produc3658429121746597890et_nat Bool)) (B6 tptp.produc3658429121746597890et_nat)) (and (= A2 B6) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A6) B6)) R2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr8536935166611901872et_nat)) (= (@ (@ tptp.member1996754912294343701et_nat A2) (@ tptp.range_7260058354244137878et_nat R2)) (exists ((A6 (-> tptp.produc3658429121746597890et_nat Bool)) (B6 tptp.produc3925858234332021118et_nat)) (and (= A2 B6) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A6) B6)) R2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat) (R2 tptp.set_Pr3948176798113811640et_nat)) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) B)) R2) (@ (@ tptp.member_set_nat B) (@ tptp.range_9132311542094983838et_nat R2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R2) (@ (@ tptp.member_nat B) (@ tptp.range_nat_nat R2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R2) (@ (@ tptp.member_int B) (@ tptp.range_int_int R2)))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr3286484037609594932et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) B)) R2) (@ (@ tptp.member6260224972018164377et_nat B) (@ tptp.range_3398330936903821850et_nat R2)))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr8536935166611901872et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) B)) R2) (@ (@ tptp.member1996754912294343701et_nat B) (@ tptp.range_7260058354244137878et_nat R2)))))
% 5.61/5.91 (assert (forall ((B tptp.set_nat) (R2 tptp.set_Pr3948176798113811640et_nat)) (=> (@ (@ tptp.member_set_nat B) (@ tptp.range_9132311542094983838et_nat R2)) (not (forall ((A4 tptp.heap_e7401611519738050253t_unit)) (not (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A4) B)) R2)))))))
% 5.61/5.91 (assert (forall ((B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member_nat B) (@ tptp.range_nat_nat R2)) (not (forall ((A4 tptp.nat)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A4) B)) R2)))))))
% 5.61/5.91 (assert (forall ((B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member_int B) (@ tptp.range_int_int R2)) (not (forall ((A4 tptp.int)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A4) B)) R2)))))))
% 5.61/5.91 (assert (forall ((B tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr3286484037609594932et_nat)) (=> (@ (@ tptp.member6260224972018164377et_nat B) (@ tptp.range_3398330936903821850et_nat R2)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A4) B)) R2)))))))
% 5.61/5.91 (assert (forall ((B tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr8536935166611901872et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat B) (@ tptp.range_7260058354244137878et_nat R2)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A4) B)) R2)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_nat) (R2 tptp.set_Pr3948176798113811640et_nat)) (= (@ (@ tptp.member_set_nat A2) (@ tptp.range_9132311542094983838et_nat R2)) (exists ((Y3 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat Y3) A2)) R2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member_nat A2) (@ tptp.range_nat_nat R2)) (exists ((Y3 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y3) A2)) R2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member_int A2) (@ tptp.range_int_int R2)) (exists ((Y3 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y3) A2)) R2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr3286484037609594932et_nat)) (= (@ (@ tptp.member6260224972018164377et_nat A2) (@ tptp.range_3398330936903821850et_nat R2)) (exists ((Y3 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat Y3) A2)) R2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr8536935166611901872et_nat)) (= (@ (@ tptp.member1996754912294343701et_nat A2) (@ tptp.range_7260058354244137878et_nat R2)) (exists ((Y3 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat Y3) A2)) R2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.product_unit)) (B tptp.product_unit)) (= (@ (@ tptp.member_nat A2) (@ (@ tptp.vimage4884490618288580032t_unit F) (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit))) (= (@ F A2) B))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (F (-> tptp.int tptp.product_unit)) (B tptp.product_unit)) (= (@ (@ tptp.member_int A2) (@ (@ tptp.vimage2000912565490760292t_unit F) (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit))) (= (@ F A2) B))))
% 5.61/5.91 (assert (forall ((A2 Bool) (F (-> Bool tptp.product_unit)) (B tptp.product_unit)) (= (@ (@ tptp.member_o A2) (@ (@ tptp.vimage4222377557387472176t_unit F) (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit))) (= (@ F A2) B))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (F (-> tptp.product_unit tptp.product_unit)) (B tptp.product_unit)) (= (@ (@ tptp.member_Product_unit A2) (@ (@ tptp.vimage7995052115951654139t_unit F) (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit))) (= (@ F A2) B))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat Bool)) (B Bool)) (= (@ (@ tptp.member_nat A2) (@ (@ tptp.vimage_nat_o F) (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (= (@ F A2) B))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (F (-> tptp.int Bool)) (B Bool)) (= (@ (@ tptp.member_int A2) (@ (@ tptp.vimage_int_o F) (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (= (@ F A2) B))))
% 5.61/5.91 (assert (forall ((A2 Bool) (F (-> Bool Bool)) (B Bool)) (= (@ (@ tptp.member_o A2) (@ (@ tptp.vimage_o_o F) (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (= (@ F A2) B))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (F (-> tptp.product_unit Bool)) (B Bool)) (= (@ (@ tptp.member_Product_unit A2) (@ (@ tptp.vimage8808348054653608838unit_o F) (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (= (@ F A2) B))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat)) (= (@ (@ tptp.member_nat A2) (@ (@ tptp.vimage_nat_nat F) (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (= (@ F A2) B))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (F (-> tptp.int tptp.nat)) (B tptp.nat)) (= (@ (@ tptp.member_int A2) (@ (@ tptp.vimage_int_nat F) (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (= (@ F A2) B))))
% 5.61/5.91 (assert (forall ((As tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ (@ tptp.relH As) H2) H3) (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H3) As)))))
% 5.61/5.91 (assert (forall ((As tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ (@ tptp.relH As) H2) H3) (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H2) As)))))
% 5.61/5.91 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H2) As)) (@ (@ (@ tptp.relH As) H2) H2))))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr5094982260447487303t_unit) (V tptp.product_unit)) (let ((_let_1 (@ (@ tptp.insert_Product_unit V) tptp.bot_bo3957492148770167129t_unit))) (=> (= (@ (@ tptp.image_8431784415008483091t_unit R3) _let_1) tptp.bot_bo3957492148770167129t_unit) (= (@ (@ tptp.image_8431784415008483091t_unit (@ tptp.transi430408012122777006t_unit R3)) _let_1) tptp.bot_bo3957492148770167129t_unit)))))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Product_prod_o_o) (V Bool)) (let ((_let_1 (@ (@ tptp.insert_o V) tptp.bot_bot_set_o))) (=> (= (@ (@ tptp.image_o_o R3) _let_1) tptp.bot_bot_set_o) (= (@ (@ tptp.image_o_o (@ tptp.transitive_trancl_o R3)) _let_1) tptp.bot_bot_set_o)))))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (V tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat V) tptp.bot_bot_set_nat))) (=> (= (@ (@ tptp.image_nat_nat R3) _let_1) tptp.bot_bot_set_nat) (= (@ (@ tptp.image_nat_nat (@ tptp.transi6264000038957366511cl_nat R3)) _let_1) tptp.bot_bot_set_nat)))))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int) (V tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int V) tptp.bot_bot_set_int))) (=> (= (@ (@ tptp.image_int_int R3) _let_1) tptp.bot_bot_set_int) (= (@ (@ tptp.image_int_int (@ tptp.transi6261509568448316235cl_int R3)) _let_1) tptp.bot_bot_set_int)))))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr2161125870931222855_nat_o) (V (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ tptp.insert5175938949040314269_nat_o V) tptp.bot_bo7824918357723582233_nat_o))) (=> (= (@ (@ tptp.image_2232984160439939859_nat_o R3) _let_1) tptp.bot_bo7824918357723582233_nat_o) (= (@ (@ tptp.image_2232984160439939859_nat_o (@ tptp.transi4009562729418357614_nat_o R3)) _let_1) tptp.bot_bo7824918357723582233_nat_o)))))
% 5.61/5.91 (assert (forall ((As tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit) (P tptp.assn)) (let ((_let_1 (@ tptp.rep_assn P))) (=> (@ (@ (@ tptp.relH As) H2) H3) (= (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As)) (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H3) As)))))))
% 5.61/5.91 (assert (forall ((X tptp.heap_e7401611519738050253t_unit) (R3 tptp.set_Pr3948176798113811640et_nat)) (=> (@ (@ tptp.member242389114213480694t_unit X) (@ tptp.domain2007548326387822151et_nat R3)) (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat X) (@ (@ tptp.fun_of5878246503291251064et_nat R3) X))) R3))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.domain_nat_nat R3)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) (@ (@ tptp.fun_of_rel_nat_nat R3) X))) R3))))
% 5.61/5.91 (assert (forall ((X tptp.int) (R3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member_int X) (@ tptp.domain_int_int R3)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) (@ (@ tptp.fun_of_rel_int_int R3) X))) R3))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (R3 tptp.set_Pr3286484037609594932et_nat)) (=> (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.domain2358961613337345475et_nat R3)) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X) (@ (@ tptp.fun_of3673525222065131764et_nat R3) X))) R3))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (R3 tptp.set_Pr8536935166611901872et_nat)) (=> (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.domain3618434998481624895et_nat R3)) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.fun_of384177504262425200et_nat R3) X))) R3))))
% 5.61/5.91 (assert (forall ((A1 tptp.nat) (A22 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A1) A22)))) (=> (@ _let_1 (@ tptp.transi6264000038957366511cl_nat R2)) (=> (not (@ _let_1 R2)) (not (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A1) B2)) (@ tptp.transi6264000038957366511cl_nat R2)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B2) A22)) R2))))))))))
% 5.61/5.91 (assert (forall ((A1 tptp.int) (A22 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A1) A22)))) (=> (@ _let_1 (@ tptp.transi6261509568448316235cl_int R2)) (=> (not (@ _let_1 R2)) (not (forall ((B2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A1) B2)) (@ tptp.transi6261509568448316235cl_int R2)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B2) A22)) R2))))))))))
% 5.61/5.91 (assert (forall ((A1 tptp.nat) (A22 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A1) A22)) (@ tptp.transi6264000038957366511cl_nat R2)) (or (exists ((A6 tptp.nat) (B6 tptp.nat)) (and (= A1 A6) (= A22 B6) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A6) B6)) R2))) (exists ((A6 tptp.nat) (B6 tptp.nat) (C4 tptp.nat)) (and (= A1 A6) (= A22 C4) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A6) B6)) (@ tptp.transi6264000038957366511cl_nat R2)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B6) C4)) R2)))))))
% 5.61/5.91 (assert (forall ((A1 tptp.int) (A22 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A1) A22)) (@ tptp.transi6261509568448316235cl_int R2)) (or (exists ((A6 tptp.int) (B6 tptp.int)) (and (= A1 A6) (= A22 B6) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A6) B6)) R2))) (exists ((A6 tptp.int) (B6 tptp.int) (C4 tptp.int)) (and (= A1 A6) (= A22 C4) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A6) B6)) (@ tptp.transi6261509568448316235cl_int R2)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B6) C4)) R2)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)))) (=> (@ _let_1 R2) (@ _let_1 (@ tptp.transi6264000038957366511cl_nat R2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)))) (=> (@ _let_1 R2) (@ _let_1 (@ tptp.transi6261509568448316235cl_int R2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)))) (=> (@ _let_1 (@ tptp.transi6264000038957366511cl_nat R2)) (=> (not (@ _let_1 R2)) (not (forall ((C2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) C2)) (@ tptp.transi6264000038957366511cl_nat R2)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat C2) B)) R2))))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)))) (=> (@ _let_1 (@ tptp.transi6261509568448316235cl_int R2)) (=> (not (@ _let_1 R2)) (not (forall ((C2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) C2)) (@ tptp.transi6261509568448316235cl_int R2)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int C2) B)) R2))))))))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (Y tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.transi6264000038957366511cl_nat R2))) (let ((_let_2 (@ tptp.product_Pair_nat_nat X))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 Y)) _let_1) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y) Z)) _let_1) (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 Z)) _let_1)))))))
% 5.61/5.91 (assert (forall ((X tptp.int) (Y tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (Z tptp.int)) (let ((_let_1 (@ tptp.transi6261509568448316235cl_int R2))) (let ((_let_2 (@ tptp.product_Pair_int_int X))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 Y)) _let_1) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y) Z)) _let_1) (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 Z)) _let_1)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) (@ tptp.transi6264000038957366511cl_nat R2)) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) Y2)) R2) (@ P Y2))) (=> (forall ((Y2 tptp.nat) (Z3 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) Y2)) (@ tptp.transi6264000038957366511cl_nat R2)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Z3)) R2) (=> (@ P Y2) (@ P Z3))))) (@ P B))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) (@ tptp.transi6261509568448316235cl_int R2)) (=> (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) Y2)) R2) (@ P Y2))) (=> (forall ((Y2 tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) Y2)) (@ tptp.transi6261509568448316235cl_int R2)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y2) Z3)) R2) (=> (@ P Y2) (@ P Z3))))) (@ P B))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 B)) R3) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) C)) R3) (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 C)) (@ tptp.transi6264000038957366511cl_nat R3)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (R3 tptp.set_Pr958786334691620121nt_int) (C tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int A2))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 B)) R3) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) C)) R3) (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 C)) (@ tptp.transi6261509568448316235cl_int R3)))))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (Z tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Z)))) (=> (@ _let_1 (@ tptp.transi6264000038957366511cl_nat R2)) (=> (not (@ _let_1 R2)) (not (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y2)) R2) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Z)) (@ tptp.transi6264000038957366511cl_nat R2)))))))))))
% 5.61/5.91 (assert (forall ((X tptp.int) (Z tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Z)))) (=> (@ _let_1 (@ tptp.transi6261509568448316235cl_int R2)) (=> (not (@ _let_1 R2)) (not (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y2)) R2) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y2) Z)) (@ tptp.transi6261509568448316235cl_int R2)))))))))))
% 5.61/5.91 (assert (forall ((Ax tptp.heap_e7401611519738050253t_unit) (Ay tptp.set_nat) (Bx tptp.heap_e7401611519738050253t_unit) (By tptp.set_nat) (R2 tptp.set_Pr719794911490849221et_nat) (P (-> tptp.heap_e7401611519738050253t_unit tptp.set_nat Bool))) (=> (@ (@ tptp.member6099555550032318734et_nat (@ (@ tptp.produc8199053930788261021et_nat (@ (@ tptp.produc7507926704131184380et_nat Ax) Ay)) (@ (@ tptp.produc7507926704131184380et_nat Bx) By))) (@ tptp.transi4137310414928362273et_nat R2)) (=> (forall ((A4 tptp.heap_e7401611519738050253t_unit) (B2 tptp.set_nat)) (=> (@ (@ tptp.member6099555550032318734et_nat (@ (@ tptp.produc8199053930788261021et_nat (@ (@ tptp.produc7507926704131184380et_nat Ax) Ay)) (@ (@ tptp.produc7507926704131184380et_nat A4) B2))) R2) (@ (@ P A4) B2))) (=> (forall ((A4 tptp.heap_e7401611519738050253t_unit) (B2 tptp.set_nat) (Aa tptp.heap_e7401611519738050253t_unit) (Ba tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat A4) B2))) (=> (@ (@ tptp.member6099555550032318734et_nat (@ (@ tptp.produc8199053930788261021et_nat (@ (@ tptp.produc7507926704131184380et_nat Ax) Ay)) _let_1)) (@ tptp.transi4137310414928362273et_nat R2)) (=> (@ (@ tptp.member6099555550032318734et_nat (@ (@ tptp.produc8199053930788261021et_nat _let_1) (@ (@ tptp.produc7507926704131184380et_nat Aa) Ba))) R2) (=> (@ (@ P A4) B2) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 5.61/5.91 (assert (forall ((Ax tptp.nat) (Ay tptp.nat) (Bx tptp.nat) (By tptp.nat) (R2 tptp.set_Pr8693737435421807431at_nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat Ax) Ay)) (@ (@ tptp.product_Pair_nat_nat Bx) By))) (@ tptp.transi243908449541399842at_nat R2)) (=> (forall ((A4 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat Ax) Ay)) (@ (@ tptp.product_Pair_nat_nat A4) B2))) R2) (@ (@ P A4) B2))) (=> (forall ((A4 tptp.nat) (B2 tptp.nat) (Aa tptp.nat) (Ba tptp.nat)) (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat A4) B2))) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat Ax) Ay)) _let_1)) (@ tptp.transi243908449541399842at_nat R2)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat _let_1) (@ (@ tptp.product_Pair_nat_nat Aa) Ba))) R2) (=> (@ (@ P A4) B2) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 5.61/5.91 (assert (forall ((Ax tptp.int) (Ay tptp.int) (Bx tptp.int) (By tptp.int) (R2 tptp.set_Pr2560585780119916871nt_int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.member8566619992076573584nt_int (@ (@ tptp.produc3646306378393792727nt_int (@ (@ tptp.product_Pair_int_int Ax) Ay)) (@ (@ tptp.product_Pair_int_int Bx) By))) (@ tptp.transi6288783178788033498nt_int R2)) (=> (forall ((A4 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.member8566619992076573584nt_int (@ (@ tptp.produc3646306378393792727nt_int (@ (@ tptp.product_Pair_int_int Ax) Ay)) (@ (@ tptp.product_Pair_int_int A4) B2))) R2) (@ (@ P A4) B2))) (=> (forall ((A4 tptp.int) (B2 tptp.int) (Aa tptp.int) (Ba tptp.int)) (let ((_let_1 (@ (@ tptp.product_Pair_int_int A4) B2))) (=> (@ (@ tptp.member8566619992076573584nt_int (@ (@ tptp.produc3646306378393792727nt_int (@ (@ tptp.product_Pair_int_int Ax) Ay)) _let_1)) (@ tptp.transi6288783178788033498nt_int R2)) (=> (@ (@ tptp.member8566619992076573584nt_int (@ (@ tptp.produc3646306378393792727nt_int _let_1) (@ (@ tptp.product_Pair_int_int Aa) Ba))) R2) (=> (@ (@ P A4) B2) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 5.61/5.91 (assert (forall ((Ax (-> tptp.produc3658429121746597890et_nat Bool)) (Ay tptp.produc3658429121746597890et_nat) (Bx (-> tptp.produc3658429121746597890et_nat Bool)) (By tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr7928877670098842301et_nat) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat (@ (@ tptp.produc5001842942810119800et_nat Ax) Ay)) (@ (@ tptp.produc5001842942810119800et_nat Bx) By))) (@ tptp.transi3145040225084697757et_nat R2)) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat (@ (@ tptp.produc5001842942810119800et_nat Ax) Ay)) (@ (@ tptp.produc5001842942810119800et_nat A4) B2))) R2) (@ (@ P A4) B2))) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3658429121746597890et_nat) (Aa (-> tptp.produc3658429121746597890et_nat Bool)) (Ba tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ (@ tptp.produc5001842942810119800et_nat A4) B2))) (=> (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat (@ (@ tptp.produc5001842942810119800et_nat Ax) Ay)) _let_1)) (@ tptp.transi3145040225084697757et_nat R2)) (=> (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat _let_1) (@ (@ tptp.produc5001842942810119800et_nat Aa) Ba))) R2) (=> (@ (@ P A4) B2) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 5.61/5.91 (assert (forall ((Ax (-> tptp.produc3658429121746597890et_nat Bool)) (Ay tptp.produc3925858234332021118et_nat) (Bx (-> tptp.produc3658429121746597890et_nat Bool)) (By tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr3444600963470892981et_nat) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool))) (=> (@ (@ tptp.member6341495586645257982et_nat (@ (@ tptp.produc1940133919992309389et_nat (@ (@ tptp.produc2245416461498447860et_nat Ax) Ay)) (@ (@ tptp.produc2245416461498447860et_nat Bx) By))) (@ tptp.transi5221092739591632921et_nat R2)) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3925858234332021118et_nat)) (=> (@ (@ tptp.member6341495586645257982et_nat (@ (@ tptp.produc1940133919992309389et_nat (@ (@ tptp.produc2245416461498447860et_nat Ax) Ay)) (@ (@ tptp.produc2245416461498447860et_nat A4) B2))) R2) (@ (@ P A4) B2))) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3925858234332021118et_nat) (Aa (-> tptp.produc3658429121746597890et_nat Bool)) (Ba tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ (@ tptp.produc2245416461498447860et_nat A4) B2))) (=> (@ (@ tptp.member6341495586645257982et_nat (@ (@ tptp.produc1940133919992309389et_nat (@ (@ tptp.produc2245416461498447860et_nat Ax) Ay)) _let_1)) (@ tptp.transi5221092739591632921et_nat R2)) (=> (@ (@ tptp.member6341495586645257982et_nat (@ (@ tptp.produc1940133919992309389et_nat _let_1) (@ (@ tptp.produc2245416461498447860et_nat Aa) Ba))) R2) (=> (@ (@ P A4) B2) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) (@ tptp.transi6264000038957366511cl_nat R2)) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) B)) R2) (@ P Y2))) (=> (forall ((Y2 tptp.nat) (Z3 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Z3)) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Z3) B)) (@ tptp.transi6264000038957366511cl_nat R2)) (=> (@ P Z3) (@ P Y2))))) (@ P A2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) (@ tptp.transi6261509568448316235cl_int R2)) (=> (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y2) B)) R2) (@ P Y2))) (=> (forall ((Y2 tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y2) Z3)) R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Z3) B)) (@ tptp.transi6261509568448316235cl_int R2)) (=> (@ P Z3) (@ P Y2))))) (@ P A2))))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (Y tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.transi6264000038957366511cl_nat R2)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)) R2) (@ (@ P X3) Y2))) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ P X3))) (let ((_let_2 (@ tptp.transi6264000038957366511cl_nat R2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)) _let_2) (=> (@ _let_1 Y2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Z3)) _let_2) (=> (@ (@ P Y2) Z3) (@ _let_1 Z3)))))))) (@ (@ P X) Y))))))
% 5.61/5.91 (assert (forall ((X tptp.int) (Y tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ tptp.transi6261509568448316235cl_int R2)) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y2)) R2) (@ (@ P X3) Y2))) (=> (forall ((X3 tptp.int) (Y2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ P X3))) (let ((_let_2 (@ tptp.transi6261509568448316235cl_int R2))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y2)) _let_2) (=> (@ _let_1 Y2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y2) Z3)) _let_2) (=> (@ (@ P Y2) Z3) (@ _let_1 Z3)))))))) (@ (@ P X) Y))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.transi6264000038957366511cl_nat R2))) (let ((_let_2 (@ tptp.product_Pair_nat_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 B)) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) C)) _let_1) (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 C)) _let_1)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (C tptp.int)) (let ((_let_1 (@ tptp.transi6261509568448316235cl_int R2))) (let ((_let_2 (@ tptp.product_Pair_int_int A2))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 B)) R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) C)) _let_1) (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 C)) _let_1)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.transi6264000038957366511cl_nat R2))) (let ((_let_2 (@ tptp.product_Pair_nat_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 B)) _let_1) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) C)) R2) (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 C)) _let_1)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (C tptp.int)) (let ((_let_1 (@ tptp.transi6261509568448316235cl_int R2))) (let ((_let_2 (@ tptp.product_Pair_int_int A2))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 B)) _let_1) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) C)) R2) (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 C)) _let_1)))))))
% 5.61/5.91 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (X tptp.nat) (Y tptp.nat)) (=> (forall ((X3 tptp.nat)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) X3)) (@ tptp.transi6264000038957366511cl_nat R2)))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R2) (not (= X Y))))))
% 5.61/5.91 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (X tptp.int) (Y tptp.int)) (=> (forall ((X3 tptp.int)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) X3)) (@ tptp.transi6261509568448316235cl_int R2)))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R2) (not (= X Y))))))
% 5.61/5.91 (assert (forall ((U tptp.product_unit) (V tptp.product_unit) (E tptp.set_Pr5094982260447487303t_unit)) (let ((_let_1 (@ tptp.image_8431784415008483091t_unit (@ tptp.transi430408012122777006t_unit E)))) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit U) V)) E) (@ (@ tptp.ord_le3507040750410214029t_unit (@ _let_1 (@ (@ tptp.insert_Product_unit V) tptp.bot_bo3957492148770167129t_unit))) (@ _let_1 (@ (@ tptp.insert_Product_unit U) tptp.bot_bo3957492148770167129t_unit)))))))
% 5.61/5.91 (assert (forall ((U Bool) (V Bool) (E tptp.set_Product_prod_o_o)) (let ((_let_1 (@ tptp.image_o_o (@ tptp.transitive_trancl_o E)))) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o U) V)) E) (@ (@ tptp.ord_less_eq_set_o (@ _let_1 (@ (@ tptp.insert_o V) tptp.bot_bot_set_o))) (@ _let_1 (@ (@ tptp.insert_o U) tptp.bot_bot_set_o)))))))
% 5.61/5.91 (assert (forall ((U tptp.int) (V tptp.int) (E tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.image_int_int (@ tptp.transi6261509568448316235cl_int E)))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int U) V)) E) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 (@ (@ tptp.insert_int V) tptp.bot_bot_set_int))) (@ _let_1 (@ (@ tptp.insert_int U) tptp.bot_bot_set_int)))))))
% 5.61/5.91 (assert (forall ((U (-> tptp.produc3658429121746597890et_nat Bool)) (V (-> tptp.produc3658429121746597890et_nat Bool)) (E tptp.set_Pr2161125870931222855_nat_o)) (let ((_let_1 (@ tptp.image_2232984160439939859_nat_o (@ tptp.transi4009562729418357614_nat_o E)))) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o U) V)) E) (@ (@ tptp.ord_le2965882846123202637_nat_o (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o V) tptp.bot_bo7824918357723582233_nat_o))) (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o U) tptp.bot_bo7824918357723582233_nat_o)))))))
% 5.61/5.91 (assert (forall ((U tptp.nat) (V tptp.nat) (E tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.image_nat_nat (@ tptp.transi6264000038957366511cl_nat E)))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat U) V)) E) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 (@ (@ tptp.insert_nat V) tptp.bot_bot_set_nat))) (@ _let_1 (@ (@ tptp.insert_nat U) tptp.bot_bot_set_nat)))))))
% 5.61/5.91 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat) (Q2 tptp.assn) (R3 tptp.assn)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As))) (=> (@ tptp.in_range _let_1) (=> (forall ((H6 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H6))) (=> (= (@ (@ tptp.inf_inf_set_nat As) As4) tptp.bot_bot_set_nat) (=> (@ (@ (@ tptp.relH As) H2) H6) (=> (@ tptp.in_range (@ _let_1 As)) (=> (@ (@ tptp.rep_assn Q2) (@ _let_1 As4)) (@ (@ tptp.rep_assn R3) (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As4))))))))) (@ (@ tptp.rep_assn (@ (@ tptp.wand_assn Q2) R3)) _let_1))))))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (V2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat (@ tptp.transi6264000038957366511cl_nat R3)) V2)) (@ tptp.range_nat_nat R3))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (A tptp.set_nat) (F (-> tptp.nat tptp.set_Product_unit))) (let ((_let_1 (@ (@ tptp.vimage7305857734363866308t_unit (@ tptp.produc3434450474625521892t_unit X)) (@ (@ tptp.produc5506539147108004339t_unit A) F)))) (let ((_let_2 (@ (@ tptp.member_nat X) A))) (and (=> _let_2 (= _let_1 (@ F X))) (=> (not _let_2) (= _let_1 tptp.bot_bo3957492148770167129t_unit)))))))
% 5.61/5.91 (assert (forall ((X tptp.int) (A tptp.set_int) (F (-> tptp.int tptp.set_Product_unit))) (let ((_let_1 (@ (@ tptp.vimage4422279681566046568t_unit (@ tptp.produc550872421827702152t_unit X)) (@ (@ tptp.produc2622961094310184599t_unit A) F)))) (let ((_let_2 (@ (@ tptp.member_int X) A))) (and (=> _let_2 (= _let_1 (@ F X))) (=> (not _let_2) (= _let_1 tptp.bot_bo3957492148770167129t_unit)))))))
% 5.61/5.91 (assert (forall ((X Bool) (A tptp.set_o) (F (-> Bool tptp.set_Product_unit))) (let ((_let_1 (@ (@ tptp.vimage508909887551888138t_unit (@ tptp.produc3901946521647900940t_unit X)) (@ (@ tptp.produc411009820408249917t_unit A) F)))) (let ((_let_2 (@ (@ tptp.member_o X) A))) (and (=> _let_2 (= _let_1 (@ F X))) (=> (not _let_2) (= _let_1 tptp.bot_bo3957492148770167129t_unit)))))))
% 5.61/5.91 (assert (forall ((X tptp.product_unit) (A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.set_Product_unit))) (let ((_let_1 (@ (@ tptp.vimage8114940889160087125t_unit (@ tptp.produc5692694829384537815t_unit X)) (@ (@ tptp.produc6121607364029222536t_unit A) F)))) (let ((_let_2 (@ (@ tptp.member_Product_unit X) A))) (and (=> _let_2 (= _let_1 (@ F X))) (=> (not _let_2) (= _let_1 tptp.bot_bo3957492148770167129t_unit)))))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (A tptp.set_nat) (F (-> tptp.nat tptp.set_o))) (let ((_let_1 (@ (@ tptp.vimage6125388955539849434_nat_o (@ tptp.product_Pair_nat_o X)) (@ (@ tptp.product_Sigma_nat_o A) F)))) (let ((_let_2 (@ (@ tptp.member_nat X) A))) (and (=> _let_2 (= _let_1 (@ F X))) (=> (not _let_2) (= _let_1 tptp.bot_bot_set_o)))))))
% 5.61/5.91 (assert (forall ((X tptp.int) (A tptp.set_int) (F (-> tptp.int tptp.set_o))) (let ((_let_1 (@ (@ tptp.vimage4304346610107161470_int_o (@ tptp.product_Pair_int_o X)) (@ (@ tptp.product_Sigma_int_o A) F)))) (let ((_let_2 (@ (@ tptp.member_int X) A))) (and (=> _let_2 (= _let_1 (@ F X))) (=> (not _let_2) (= _let_1 tptp.bot_bot_set_o)))))))
% 5.61/5.91 (assert (forall ((X Bool) (A tptp.set_o) (F (-> Bool tptp.set_o))) (let ((_let_1 (@ (@ tptp.vimage8945963521958007626od_o_o (@ tptp.product_Pair_o_o X)) (@ (@ tptp.product_Sigma_o_o A) F)))) (let ((_let_2 (@ (@ tptp.member_o X) A))) (and (=> _let_2 (= _let_1 (@ F X))) (=> (not _let_2) (= _let_1 tptp.bot_bot_set_o)))))))
% 5.61/5.91 (assert (forall ((X tptp.product_unit) (A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.set_o))) (let ((_let_1 (@ (@ tptp.vimage9156843197228287893unit_o (@ tptp.produc8487917018914037602unit_o X)) (@ (@ tptp.produc4996980317674386579unit_o A) F)))) (let ((_let_2 (@ (@ tptp.member_Product_unit X) A))) (and (=> _let_2 (= _let_1 (@ F X))) (=> (not _let_2) (= _let_1 tptp.bot_bot_set_o)))))))
% 5.61/5.91 (assert (forall ((X tptp.int) (A tptp.set_int) (F (-> tptp.int tptp.set_nat))) (let ((_let_1 (@ (@ tptp.vimage9012682431555523728nt_nat (@ tptp.product_Pair_int_nat X)) (@ (@ tptp.produc1456381018704787142nt_nat A) F)))) (let ((_let_2 (@ (@ tptp.member_int X) A))) (and (=> _let_2 (= _let_1 (@ F X))) (=> (not _let_2) (= _let_1 tptp.bot_bot_set_nat)))))))
% 5.61/5.91 (assert (forall ((X Bool) (A tptp.set_o) (F (-> Bool tptp.set_nat))) (let ((_let_1 (@ (@ tptp.vimage5656379182745576100_o_nat (@ tptp.product_Pair_o_nat X)) (@ (@ tptp.product_Sigma_o_nat A) F)))) (let ((_let_2 (@ (@ tptp.member_o X) A))) (and (=> _let_2 (= _let_1 (@ F X))) (=> (not _let_2) (= _let_1 tptp.bot_bot_set_nat)))))))
% 5.61/5.91 (assert (= tptp.relH (lambda ((As3 tptp.set_nat) (H4 tptp.heap_e7401611519738050253t_unit) (H5 tptp.heap_e7401611519738050253t_unit)) (and (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H4) As3)) (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H5) As3)) (forall ((T tptp.typerep) (X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) As3) (and (= (@ (@ (@ tptp.refs_Product_unit H4) T) X2) (@ (@ (@ tptp.refs_Product_unit H5) T) X2)) (= (@ (@ (@ tptp.arrays_Product_unit H4) T) X2) (@ (@ (@ tptp.arrays_Product_unit H5) T) X2)))))))))
% 5.61/5.91 (assert (forall ((F (-> tptp.nat tptp.product_unit)) (A2 tptp.product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.vimage4884490618288580032t_unit F))) (let ((_let_2 (@ tptp.insert_Product_unit A2))) (= (@ _let_1 (@ _let_2 B4)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 (@ _let_2 tptp.bot_bo3957492148770167129t_unit))) (@ _let_1 B4)))))))
% 5.61/5.91 (assert (forall ((F (-> tptp.nat Bool)) (A2 Bool) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.vimage_nat_o F))) (let ((_let_2 (@ tptp.insert_o A2))) (= (@ _let_1 (@ _let_2 B4)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 (@ _let_2 tptp.bot_bot_set_o))) (@ _let_1 B4)))))))
% 5.61/5.91 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat F))) (let ((_let_2 (@ tptp.insert_nat A2))) (= (@ _let_1 (@ _let_2 B4)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 (@ _let_2 tptp.bot_bot_set_nat))) (@ _let_1 B4)))))))
% 5.61/5.91 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.vimage_nat_int F))) (let ((_let_2 (@ tptp.insert_int A2))) (= (@ _let_1 (@ _let_2 B4)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 (@ _let_2 tptp.bot_bot_set_int))) (@ _let_1 B4)))))))
% 5.61/5.91 (assert (forall ((F (-> tptp.nat tptp.produc3658429121746597890et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.vimage8201027140005291904_nat_o F))) (let ((_let_2 (@ tptp.insert5175938949040314269_nat_o A2))) (= (@ _let_1 (@ _let_2 B4)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 (@ _let_2 tptp.bot_bo7824918357723582233_nat_o))) (@ _let_1 B4)))))))
% 5.61/5.91 (assert (forall ((U tptp.nat) (W tptp.nat) (V1 tptp.nat) (V22 tptp.nat) (E tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.transi2905341329935302413cl_nat E))) (let ((_let_2 (@ tptp.product_Pair_nat_nat U))) (let ((_let_3 (@ tptp.member8440522571783428010at_nat (@ _let_2 W)))) (=> (@ _let_3 (@ tptp.transi6264000038957366511cl_nat (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.product_Pair_nat_nat V1) V22)) E))) (=> (not (@ _let_3 (@ tptp.transi6264000038957366511cl_nat E))) (not (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 V1)) _let_1) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat V22) W)) _let_1)))))))))))
% 5.61/5.91 (assert (forall ((U tptp.int) (W tptp.int) (V1 tptp.int) (V22 tptp.int) (E tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.transi2902850859426252137cl_int E))) (let ((_let_2 (@ tptp.product_Pair_int_int U))) (let ((_let_3 (@ tptp.member5262025264175285858nt_int (@ _let_2 W)))) (=> (@ _let_3 (@ tptp.transi6261509568448316235cl_int (@ (@ tptp.insert5033312907999012233nt_int (@ (@ tptp.product_Pair_int_int V1) V22)) E))) (=> (not (@ _let_3 (@ tptp.transi6261509568448316235cl_int E))) (not (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 V1)) _let_1) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int V22) W)) _let_1)))))))))))
% 5.61/5.91 (assert (@ (@ tptp.order_2505591618835473410t_unit tptp.bot_bo3957492148770167129t_unit) tptp.bot_bo1654022762305692595t_unit))
% 5.61/5.91 (assert (@ (@ tptp.order_8538205470752950541r_on_o tptp.bot_bot_set_o) tptp.bot_bo7073875226086086771od_o_o))
% 5.61/5.91 (assert (@ (@ tptp.order_5251275573222108571on_nat tptp.bot_bot_set_nat) tptp.bot_bo2099793752762293965at_nat))
% 5.61/5.91 (assert (@ (@ tptp.order_5248785102713058295on_int tptp.bot_bot_set_int) tptp.bot_bo1796632182523588997nt_int))
% 5.61/5.91 (assert (@ (@ tptp.order_3690095022144090562_nat_o tptp.bot_bo7824918357723582233_nat_o) tptp.bot_bo3657187498359500723_nat_o))
% 5.61/5.91 (assert (forall ((X tptp.heap_e7401611519738050253t_unit) (Y tptp.set_nat)) (= (@ tptp.basic_2698842327037663054et_nat (@ (@ tptp.produc7507926704131184380et_nat X) Y)) (@ (@ tptp.insert_set_nat Y) tptp.bot_bot_set_set_nat))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3658429121746597890et_nat)) (= (@ tptp.basic_8479756702517612234et_nat (@ (@ tptp.produc5001842942810119800et_nat X) Y)) (@ (@ tptp.insert1271470778893645362et_nat Y) tptp.bot_bo3771712512152092492et_nat))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3925858234332021118et_nat)) (= (@ tptp.basic_2768200282441914438et_nat (@ (@ tptp.produc2245416461498447860et_nat X) Y)) (@ (@ tptp.insert3111075074545270702et_nat Y) tptp.bot_bo1481135142794719944et_nat))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.basic_snds_nat_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ tptp.insert_nat Y) tptp.bot_bot_set_nat))))
% 5.61/5.91 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ tptp.basic_snds_int_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ (@ tptp.insert_int Y) tptp.bot_bot_set_int))))
% 5.61/5.91 (assert (forall ((A2 tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat A2) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A2) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat A2) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A2) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.int)) (@ (@ tptp.ord_less_eq_int A2) A2)))
% 5.61/5.91 (assert (forall ((X tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat X) X)))
% 5.61/5.91 (assert (forall ((X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) X)))
% 5.61/5.91 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) X)))
% 5.61/5.91 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) X)))
% 5.61/5.91 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) X)))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A) (= A B4)))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X3))) (=> (@ _let_1 A) (@ _let_1 B4)))) (@ (@ tptp.ord_le2965882846123202637_nat_o A) B4))))
% 5.61/5.91 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 A) (@ _let_1 B4)))) (@ (@ tptp.ord_less_eq_set_int A) B4))))
% 5.61/5.91 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (=> (forall ((X3 Bool)) (let ((_let_1 (@ tptp.member_o X3))) (=> (@ _let_1 A) (@ _let_1 B4)))) (@ (@ tptp.ord_less_eq_set_o A) B4))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (=> (forall ((X3 tptp.product_unit)) (let ((_let_1 (@ tptp.member_Product_unit X3))) (=> (@ _let_1 A) (@ _let_1 B4)))) (@ (@ tptp.ord_le3507040750410214029t_unit A) B4))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 A) (@ _let_1 B4)))) (@ (@ tptp.ord_less_eq_set_nat A) B4))))
% 5.61/5.91 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (= (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o A) B4)) (and (@ _let_1 A) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((C tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_int A) B4)) (and (@ _let_1 A) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((C Bool) (A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_o A) B4)) (and (@ _let_1 A) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((C tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member_Product_unit C))) (= (@ _let_1 (@ (@ tptp.inf_in4660618365625256667t_unit A) B4)) (and (@ _let_1 A) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)) (and (@ _let_1 A) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 A) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o A) B4)))))))
% 5.61/5.91 (assert (forall ((C tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.inf_inf_set_int A) B4)))))))
% 5.61/5.91 (assert (forall ((C Bool) (A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 A) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.inf_inf_set_o A) B4)))))))
% 5.61/5.91 (assert (forall ((C tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member_Product_unit C))) (=> (@ _let_1 A) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.inf_in4660618365625256667t_unit A) B4)))))))
% 5.61/5.91 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)))))))
% 5.61/5.91 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (= (@ _let_1 (@ (@ tptp.sup_su5209123915105501825_nat_o A) B4)) (or (@ _let_1 A) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((C tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B4)) (or (@ _let_1 A) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((C Bool) (A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_o A) B4)) (or (@ _let_1 A) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((C tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member_Product_unit C))) (= (@ _let_1 (@ (@ tptp.sup_su793286257634532545t_unit A) B4)) (or (@ _let_1 A) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (or (@ _let_1 A) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.set_Pr4532377907799695533_nat_o) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (=> (not (@ _let_1 B4)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_su5209123915105501825_nat_o A) B4))))))
% 5.61/5.91 (assert (forall ((C tptp.int) (B4 tptp.set_int) (A tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (=> (not (@ _let_1 B4)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B4))))))
% 5.61/5.91 (assert (forall ((C Bool) (B4 tptp.set_o) (A tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (=> (not (@ _let_1 B4)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_sup_set_o A) B4))))))
% 5.61/5.91 (assert (forall ((C tptp.product_unit) (B4 tptp.set_Product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member_Product_unit C))) (=> (=> (not (@ _let_1 B4)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_su793286257634532545t_unit A) B4))))))
% 5.61/5.91 (assert (forall ((C tptp.nat) (B4 tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (=> (not (@ _let_1 B4)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit)) (@ (@ tptp.ord_le3507040750410214029t_unit tptp.bot_bo3957492148770167129t_unit) A)))
% 5.61/5.91 (assert (forall ((A tptp.set_o)) (@ (@ tptp.ord_less_eq_set_o tptp.bot_bot_set_o) A)))
% 5.61/5.91 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A)))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (@ (@ tptp.ord_le2965882846123202637_nat_o tptp.bot_bo7824918357723582233_nat_o) A)))
% 5.61/5.91 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit)) (= (@ (@ tptp.ord_le3507040750410214029t_unit A) tptp.bot_bo3957492148770167129t_unit) (= A tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.91 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o A) tptp.bot_bot_set_o) (= A tptp.bot_bot_set_o))))
% 5.61/5.91 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.ord_le2965882846123202637_nat_o A) tptp.bot_bo7824918357723582233_nat_o) (= A tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.ord_le2965882846123202637_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) A)) B4) (and (@ (@ tptp.member6576561426505652726_nat_o X) B4) (@ (@ tptp.ord_le2965882846123202637_nat_o A) B4)))))
% 5.61/5.91 (assert (forall ((X tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int X) A)) B4) (and (@ (@ tptp.member_int X) B4) (@ (@ tptp.ord_less_eq_set_int A) B4)))))
% 5.61/5.91 (assert (forall ((X Bool) (A tptp.set_o) (B4 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.insert_o X) A)) B4) (and (@ (@ tptp.member_o X) B4) (@ (@ tptp.ord_less_eq_set_o A) B4)))))
% 5.61/5.91 (assert (forall ((X tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (= (@ (@ tptp.ord_le3507040750410214029t_unit (@ (@ tptp.insert_Product_unit X) A)) B4) (and (@ (@ tptp.member_Product_unit X) B4) (@ (@ tptp.ord_le3507040750410214029t_unit A) B4)))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X) A)) B4) (and (@ (@ tptp.member_nat X) B4) (@ (@ tptp.ord_less_eq_set_nat A) B4)))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B tptp.int) (B4 (-> tptp.nat tptp.set_int))) (=> (@ (@ tptp.member_nat A2) A) (=> (@ (@ tptp.member_int B) (@ B4 A2)) (@ (@ tptp.member4262671552274231302at_int (@ (@ tptp.product_Pair_nat_int A2) B)) (@ (@ tptp.produc454536836294682310at_int A) B4))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B Bool) (B4 (-> tptp.nat tptp.set_o))) (=> (@ (@ tptp.member_nat A2) A) (=> (@ (@ tptp.member_o B) (@ B4 A2)) (@ (@ tptp.member6310962623043647828_nat_o (@ (@ tptp.product_Pair_nat_o A2) B)) (@ (@ tptp.product_Sigma_nat_o A) B4))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B tptp.product_unit) (B4 (-> tptp.nat tptp.set_Product_unit))) (=> (@ (@ tptp.member_nat A2) A) (=> (@ (@ tptp.member_Product_unit B) (@ B4 A2)) (@ (@ tptp.member348563419383025609t_unit (@ (@ tptp.produc3434450474625521892t_unit A2) B)) (@ (@ tptp.produc5506539147108004339t_unit A) B4))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B tptp.nat) (B4 (-> tptp.int tptp.set_nat))) (=> (@ (@ tptp.member_int A2) A) (=> (@ (@ tptp.member_nat B) (@ B4 A2)) (@ (@ tptp.member216504246829706758nt_nat (@ (@ tptp.product_Pair_int_nat A2) B)) (@ (@ tptp.produc1456381018704787142nt_nat A) B4))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B Bool) (B4 (-> tptp.int tptp.set_o))) (=> (@ (@ tptp.member_int A2) A) (=> (@ (@ tptp.member_o B) (@ B4 A2)) (@ (@ tptp.member4489920277610959864_int_o (@ (@ tptp.product_Pair_int_o A2) B)) (@ (@ tptp.product_Sigma_int_o A) B4))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B tptp.product_unit) (B4 (-> tptp.int tptp.set_Product_unit))) (=> (@ (@ tptp.member_int A2) A) (=> (@ (@ tptp.member_Product_unit B) (@ B4 A2)) (@ (@ tptp.member6688357403439981677t_unit (@ (@ tptp.produc550872421827702152t_unit A2) B)) (@ (@ tptp.produc2622961094310184599t_unit A) B4))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (A tptp.set_o) (B tptp.nat) (B4 (-> Bool tptp.set_nat))) (=> (@ (@ tptp.member_o A2) A) (=> (@ (@ tptp.member_nat B) (@ B4 A2)) (@ (@ tptp.member2802428098988154798_o_nat (@ (@ tptp.product_Pair_o_nat A2) B)) (@ (@ tptp.product_Sigma_o_nat A) B4))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (A tptp.set_o) (B tptp.int) (B4 (-> Bool tptp.set_int))) (=> (@ (@ tptp.member_o A2) A) (=> (@ (@ tptp.member_int B) (@ B4 A2)) (@ (@ tptp.member7847949116333733898_o_int (@ (@ tptp.product_Pair_o_int A2) B)) (@ (@ tptp.product_Sigma_o_int A) B4))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (A tptp.set_o) (B Bool) (B4 (-> Bool tptp.set_o))) (=> (@ (@ tptp.member_o A2) A) (=> (@ (@ tptp.member_o B) (@ B4 A2)) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) B)) (@ (@ tptp.product_Sigma_o_o A) B4))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (A tptp.set_o) (B tptp.product_unit) (B4 (-> Bool tptp.set_Product_unit))) (=> (@ (@ tptp.member_o A2) A) (=> (@ (@ tptp.member_Product_unit B) (@ B4 A2)) (@ (@ tptp.member9215336023991391429t_unit (@ (@ tptp.produc3901946521647900940t_unit A2) B)) (@ (@ tptp.produc411009820408249917t_unit A) B4))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.int) (A tptp.set_nat) (B4 (-> tptp.nat tptp.set_int))) (= (@ (@ tptp.member4262671552274231302at_int (@ (@ tptp.product_Pair_nat_int A2) B)) (@ (@ tptp.produc454536836294682310at_int A) B4)) (and (@ (@ tptp.member_nat A2) A) (@ (@ tptp.member_int B) (@ B4 A2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B Bool) (A tptp.set_nat) (B4 (-> tptp.nat tptp.set_o))) (= (@ (@ tptp.member6310962623043647828_nat_o (@ (@ tptp.product_Pair_nat_o A2) B)) (@ (@ tptp.product_Sigma_nat_o A) B4)) (and (@ (@ tptp.member_nat A2) A) (@ (@ tptp.member_o B) (@ B4 A2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.product_unit) (A tptp.set_nat) (B4 (-> tptp.nat tptp.set_Product_unit))) (= (@ (@ tptp.member348563419383025609t_unit (@ (@ tptp.produc3434450474625521892t_unit A2) B)) (@ (@ tptp.produc5506539147108004339t_unit A) B4)) (and (@ (@ tptp.member_nat A2) A) (@ (@ tptp.member_Product_unit B) (@ B4 A2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.nat) (A tptp.set_int) (B4 (-> tptp.int tptp.set_nat))) (= (@ (@ tptp.member216504246829706758nt_nat (@ (@ tptp.product_Pair_int_nat A2) B)) (@ (@ tptp.produc1456381018704787142nt_nat A) B4)) (and (@ (@ tptp.member_int A2) A) (@ (@ tptp.member_nat B) (@ B4 A2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B Bool) (A tptp.set_int) (B4 (-> tptp.int tptp.set_o))) (= (@ (@ tptp.member4489920277610959864_int_o (@ (@ tptp.product_Pair_int_o A2) B)) (@ (@ tptp.product_Sigma_int_o A) B4)) (and (@ (@ tptp.member_int A2) A) (@ (@ tptp.member_o B) (@ B4 A2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.product_unit) (A tptp.set_int) (B4 (-> tptp.int tptp.set_Product_unit))) (= (@ (@ tptp.member6688357403439981677t_unit (@ (@ tptp.produc550872421827702152t_unit A2) B)) (@ (@ tptp.produc2622961094310184599t_unit A) B4)) (and (@ (@ tptp.member_int A2) A) (@ (@ tptp.member_Product_unit B) (@ B4 A2))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (B tptp.nat) (A tptp.set_o) (B4 (-> Bool tptp.set_nat))) (= (@ (@ tptp.member2802428098988154798_o_nat (@ (@ tptp.product_Pair_o_nat A2) B)) (@ (@ tptp.product_Sigma_o_nat A) B4)) (and (@ (@ tptp.member_o A2) A) (@ (@ tptp.member_nat B) (@ B4 A2))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (B tptp.int) (A tptp.set_o) (B4 (-> Bool tptp.set_int))) (= (@ (@ tptp.member7847949116333733898_o_int (@ (@ tptp.product_Pair_o_int A2) B)) (@ (@ tptp.product_Sigma_o_int A) B4)) (and (@ (@ tptp.member_o A2) A) (@ (@ tptp.member_int B) (@ B4 A2))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (B Bool) (A tptp.set_o) (B4 (-> Bool tptp.set_o))) (= (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) B)) (@ (@ tptp.product_Sigma_o_o A) B4)) (and (@ (@ tptp.member_o A2) A) (@ (@ tptp.member_o B) (@ B4 A2))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (B tptp.product_unit) (A tptp.set_o) (B4 (-> Bool tptp.set_Product_unit))) (= (@ (@ tptp.member9215336023991391429t_unit (@ (@ tptp.produc3901946521647900940t_unit A2) B)) (@ (@ tptp.produc411009820408249917t_unit A) B4)) (and (@ (@ tptp.member_o A2) A) (@ (@ tptp.member_Product_unit B) (@ B4 A2))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (= (= (@ (@ tptp.sup_su793286257634532545t_unit A) B4) tptp.bot_bo3957492148770167129t_unit) (and (= A tptp.bot_bo3957492148770167129t_unit) (= B4 tptp.bot_bo3957492148770167129t_unit)))))
% 5.61/5.91 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (= (= (@ (@ tptp.sup_sup_set_o A) B4) tptp.bot_bot_set_o) (and (= A tptp.bot_bot_set_o) (= B4 tptp.bot_bot_set_o)))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (= (@ (@ tptp.sup_sup_set_nat A) B4) tptp.bot_bot_set_nat) (and (= A tptp.bot_bot_set_nat) (= B4 tptp.bot_bot_set_nat)))))
% 5.61/5.91 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (= (= (@ (@ tptp.sup_sup_set_int A) B4) tptp.bot_bot_set_int) (and (= A tptp.bot_bot_set_int) (= B4 tptp.bot_bot_set_int)))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (= (= (@ (@ tptp.sup_su5209123915105501825_nat_o A) B4) tptp.bot_bo7824918357723582233_nat_o) (and (= A tptp.bot_bo7824918357723582233_nat_o) (= B4 tptp.bot_bo7824918357723582233_nat_o)))))
% 5.61/5.91 (assert (forall ((C5 tptp.set_nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C5))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)) (and (@ _let_1 A) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.inf_in1906310914598751387_nat_o A))) (let ((_let_2 (@ tptp.insert5175938949040314269_nat_o A2))) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) A) (= (@ _let_1 (@ _let_2 B4)) (@ _let_2 (@ _let_1 B4))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A))) (let ((_let_2 (@ tptp.insert_int A2))) (=> (@ (@ tptp.member_int A2) A) (= (@ _let_1 (@ _let_2 B4)) (@ _let_2 (@ _let_1 B4))))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o A))) (let ((_let_2 (@ tptp.insert_o A2))) (=> (@ (@ tptp.member_o A2) A) (= (@ _let_1 (@ _let_2 B4)) (@ _let_2 (@ _let_1 B4))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.inf_in4660618365625256667t_unit A))) (let ((_let_2 (@ tptp.insert_Product_unit A2))) (=> (@ (@ tptp.member_Product_unit A2) A) (= (@ _let_1 (@ _let_2 B4)) (@ _let_2 (@ _let_1 B4))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (let ((_let_2 (@ tptp.insert_nat A2))) (=> (@ (@ tptp.member_nat A2) A) (= (@ _let_1 (@ _let_2 B4)) (@ _let_2 (@ _let_1 B4))))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.inf_in1906310914598751387_nat_o A))) (=> (not (@ (@ tptp.member6576561426505652726_nat_o A2) A)) (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o A2) B4)) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A))) (=> (not (@ (@ tptp.member_int A2) A)) (= (@ _let_1 (@ (@ tptp.insert_int A2) B4)) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o A))) (=> (not (@ (@ tptp.member_o A2) A)) (= (@ _let_1 (@ (@ tptp.insert_o A2) B4)) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.inf_in4660618365625256667t_unit A))) (=> (not (@ (@ tptp.member_Product_unit A2) A)) (= (@ _let_1 (@ (@ tptp.insert_Product_unit A2) B4)) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (=> (not (@ (@ tptp.member_nat A2) A)) (= (@ _let_1 (@ (@ tptp.insert_nat A2) B4)) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A2))) (= (@ (@ tptp.inf_inf_set_int (@ _let_1 A)) (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.inf_inf_set_int A) B4))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A2))) (= (@ (@ tptp.inf_inf_set_o (@ _let_1 A)) (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.inf_inf_set_o A) B4))))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit A2))) (= (@ (@ tptp.inf_in4660618365625256667t_unit (@ _let_1 A)) (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.inf_in4660618365625256667t_unit A) B4))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 A)) (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (C5 tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.insert5175938949040314269_nat_o A2))) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) C5) (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ _let_1 B4)) C5) (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o B4) C5)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (C5 tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A2))) (=> (@ (@ tptp.member_int A2) C5) (= (@ (@ tptp.inf_inf_set_int (@ _let_1 B4)) C5) (@ _let_1 (@ (@ tptp.inf_inf_set_int B4) C5)))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (C5 tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A2))) (=> (@ (@ tptp.member_o A2) C5) (= (@ (@ tptp.inf_inf_set_o (@ _let_1 B4)) C5) (@ _let_1 (@ (@ tptp.inf_inf_set_o B4) C5)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (C5 tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit A2))) (=> (@ (@ tptp.member_Product_unit A2) C5) (= (@ (@ tptp.inf_in4660618365625256667t_unit (@ _let_1 B4)) C5) (@ _let_1 (@ (@ tptp.inf_in4660618365625256667t_unit B4) C5)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (C5 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (=> (@ (@ tptp.member_nat A2) C5) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 B4)) C5) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B4) C5)))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (C5 tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o A2) C5)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ (@ tptp.insert5175938949040314269_nat_o A2) B4)) C5) (@ (@ tptp.inf_in1906310914598751387_nat_o B4) C5)))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (C5 tptp.set_int) (B4 tptp.set_int)) (=> (not (@ (@ tptp.member_int A2) C5)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.insert_int A2) B4)) C5) (@ (@ tptp.inf_inf_set_int B4) C5)))))
% 5.61/5.91 (assert (forall ((A2 Bool) (C5 tptp.set_o) (B4 tptp.set_o)) (=> (not (@ (@ tptp.member_o A2) C5)) (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.insert_o A2) B4)) C5) (@ (@ tptp.inf_inf_set_o B4) C5)))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (C5 tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (=> (not (@ (@ tptp.member_Product_unit A2) C5)) (= (@ (@ tptp.inf_in4660618365625256667t_unit (@ (@ tptp.insert_Product_unit A2) B4)) C5) (@ (@ tptp.inf_in4660618365625256667t_unit B4) C5)))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (C5 tptp.set_nat) (B4 tptp.set_nat)) (=> (not (@ (@ tptp.member_nat A2) C5)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.insert_nat A2) B4)) C5) (@ (@ tptp.inf_inf_set_nat B4) C5)))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A) B4)) C5) (and (@ (@ tptp.ord_less_eq_set_nat A) C5) (@ (@ tptp.ord_less_eq_set_nat B4) C5)))))
% 5.61/5.91 (assert (forall ((A tptp.set_int) (A2 tptp.int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.sup_sup_set_int A))) (let ((_let_2 (@ tptp.insert_int A2))) (= (@ _let_1 (@ _let_2 B4)) (@ _let_2 (@ _let_1 B4)))))))
% 5.61/5.91 (assert (forall ((A tptp.set_o) (A2 Bool) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.sup_sup_set_o A))) (let ((_let_2 (@ tptp.insert_o A2))) (= (@ _let_1 (@ _let_2 B4)) (@ _let_2 (@ _let_1 B4)))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit) (A2 tptp.product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.sup_su793286257634532545t_unit A))) (let ((_let_2 (@ tptp.insert_Product_unit A2))) (= (@ _let_1 (@ _let_2 B4)) (@ _let_2 (@ _let_1 B4)))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (A2 tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A))) (let ((_let_2 (@ tptp.insert_nat A2))) (= (@ _let_1 (@ _let_2 B4)) (@ _let_2 (@ _let_1 B4)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B4 tptp.set_int) (C5 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A2))) (= (@ (@ tptp.sup_sup_set_int (@ _let_1 B4)) C5) (@ _let_1 (@ (@ tptp.sup_sup_set_int B4) C5))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (B4 tptp.set_o) (C5 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A2))) (= (@ (@ tptp.sup_sup_set_o (@ _let_1 B4)) C5) (@ _let_1 (@ (@ tptp.sup_sup_set_o B4) C5))))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (B4 tptp.set_Product_unit) (C5 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit A2))) (= (@ (@ tptp.sup_su793286257634532545t_unit (@ _let_1 B4)) C5) (@ _let_1 (@ (@ tptp.sup_su793286257634532545t_unit B4) C5))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B4)) C5) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B4) C5))))))
% 5.61/5.91 (assert (forall ((S tptp.set_nat) (T2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat S) T2)) S) S)))
% 5.61/5.91 (assert (forall ((S tptp.set_nat) (T2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat S) T2)) T2) T2)))
% 5.61/5.91 (assert (forall ((S tptp.set_nat) (T2 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat S) (@ (@ tptp.sup_sup_set_nat S) T2)) S)))
% 5.61/5.91 (assert (forall ((T2 tptp.set_nat) (S tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat T2) (@ (@ tptp.sup_sup_set_nat S) T2)) T2)))
% 5.61/5.91 (assert (forall ((S tptp.set_nat) (T2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat S) T2)) S) S)))
% 5.61/5.91 (assert (forall ((S tptp.set_nat) (T2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat S) T2)) T2) T2)))
% 5.61/5.91 (assert (forall ((S tptp.set_nat) (T2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat S) (@ (@ tptp.inf_inf_set_nat S) T2)) S)))
% 5.61/5.91 (assert (forall ((T2 tptp.set_nat) (S tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat T2) (@ (@ tptp.inf_inf_set_nat S) T2)) T2)))
% 5.61/5.91 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat F))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat F))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((As tptp.set_nat) (As5 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit)) (= (@ (@ (@ tptp.relH (@ (@ tptp.sup_sup_set_nat As) As5)) H2) H3) (and (@ (@ (@ tptp.relH As) H2) H3) (@ (@ (@ tptp.relH As5) H2) H3)))))
% 5.61/5.91 (assert (forall ((B tptp.product_unit) (A2 tptp.product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit))) (= (= _let_1 (@ (@ tptp.insert_Product_unit A2) A)) (and (= A2 B) (@ (@ tptp.ord_le3507040750410214029t_unit A) _let_1))))))
% 5.61/5.91 (assert (forall ((B Bool) (A2 Bool) (A tptp.set_o)) (let ((_let_1 (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (= (= _let_1 (@ (@ tptp.insert_o A2) A)) (and (= A2 B) (@ (@ tptp.ord_less_eq_set_o A) _let_1))))))
% 5.61/5.91 (assert (forall ((B tptp.int) (A2 tptp.int) (A tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (= (= _let_1 (@ (@ tptp.insert_int A2) A)) (and (= A2 B) (@ (@ tptp.ord_less_eq_set_int A) _let_1))))))
% 5.61/5.91 (assert (forall ((B (-> tptp.produc3658429121746597890et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ (@ tptp.insert5175938949040314269_nat_o B) tptp.bot_bo7824918357723582233_nat_o))) (= (= _let_1 (@ (@ tptp.insert5175938949040314269_nat_o A2) A)) (and (= A2 B) (@ (@ tptp.ord_le2965882846123202637_nat_o A) _let_1))))))
% 5.61/5.91 (assert (forall ((B tptp.nat) (A2 tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (= (= _let_1 (@ (@ tptp.insert_nat A2) A)) (and (= A2 B) (@ (@ tptp.ord_less_eq_set_nat A) _let_1))))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (A tptp.set_Product_unit) (B tptp.product_unit)) (let ((_let_1 (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit))) (= (= (@ (@ tptp.insert_Product_unit A2) A) _let_1) (and (= A2 B) (@ (@ tptp.ord_le3507040750410214029t_unit A) _let_1))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (A tptp.set_o) (B Bool)) (let ((_let_1 (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (= (= (@ (@ tptp.insert_o A2) A) _let_1) (and (= A2 B) (@ (@ tptp.ord_less_eq_set_o A) _let_1))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (= (= (@ (@ tptp.insert_int A2) A) _let_1) (and (= A2 B) (@ (@ tptp.ord_less_eq_set_int A) _let_1))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ tptp.insert5175938949040314269_nat_o B) tptp.bot_bo7824918357723582233_nat_o))) (= (= (@ (@ tptp.insert5175938949040314269_nat_o A2) A) _let_1) (and (= A2 B) (@ (@ tptp.ord_le2965882846123202637_nat_o A) _let_1))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (= (= (@ (@ tptp.insert_nat A2) A) _let_1) (and (= A2 B) (@ (@ tptp.ord_less_eq_set_nat A) _let_1))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit) (B tptp.product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.inf_in4660618365625256667t_unit A))) (= (= tptp.bot_bo3957492148770167129t_unit (@ _let_1 (@ (@ tptp.insert_Product_unit B) B4))) (and (not (@ (@ tptp.member_Product_unit B) A)) (= tptp.bot_bo3957492148770167129t_unit (@ _let_1 B4)))))))
% 5.61/5.91 (assert (forall ((A tptp.set_o) (B Bool) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o A))) (= (= tptp.bot_bot_set_o (@ _let_1 (@ (@ tptp.insert_o B) B4))) (and (not (@ (@ tptp.member_o B) A)) (= tptp.bot_bot_set_o (@ _let_1 B4)))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (= (= tptp.bot_bot_set_nat (@ _let_1 (@ (@ tptp.insert_nat B) B4))) (and (not (@ (@ tptp.member_nat B) A)) (= tptp.bot_bot_set_nat (@ _let_1 B4)))))))
% 5.61/5.91 (assert (forall ((A tptp.set_int) (B tptp.int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A))) (= (= tptp.bot_bot_set_int (@ _let_1 (@ (@ tptp.insert_int B) B4))) (and (not (@ (@ tptp.member_int B) A)) (= tptp.bot_bot_set_int (@ _let_1 B4)))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.inf_in1906310914598751387_nat_o A))) (= (= tptp.bot_bo7824918357723582233_nat_o (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o B) B4))) (and (not (@ (@ tptp.member6576561426505652726_nat_o B) A)) (= tptp.bot_bo7824918357723582233_nat_o (@ _let_1 B4)))))))
% 5.61/5.91 (assert (forall ((B4 tptp.set_Product_unit) (A2 tptp.product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ tptp.inf_in4660618365625256667t_unit B4))) (= (= (@ _let_1 (@ (@ tptp.insert_Product_unit A2) A)) tptp.bot_bo3957492148770167129t_unit) (and (not (@ (@ tptp.member_Product_unit A2) B4)) (= (@ _let_1 A) tptp.bot_bo3957492148770167129t_unit))))))
% 5.61/5.91 (assert (forall ((B4 tptp.set_o) (A2 Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o B4))) (= (= (@ _let_1 (@ (@ tptp.insert_o A2) A)) tptp.bot_bot_set_o) (and (not (@ (@ tptp.member_o A2) B4)) (= (@ _let_1 A) tptp.bot_bot_set_o))))))
% 5.61/5.91 (assert (forall ((B4 tptp.set_nat) (A2 tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat B4))) (= (= (@ _let_1 (@ (@ tptp.insert_nat A2) A)) tptp.bot_bot_set_nat) (and (not (@ (@ tptp.member_nat A2) B4)) (= (@ _let_1 A) tptp.bot_bot_set_nat))))))
% 5.61/5.91 (assert (forall ((B4 tptp.set_int) (A2 tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int B4))) (= (= (@ _let_1 (@ (@ tptp.insert_int A2) A)) tptp.bot_bot_set_int) (and (not (@ (@ tptp.member_int A2) B4)) (= (@ _let_1 A) tptp.bot_bot_set_int))))))
% 5.61/5.91 (assert (forall ((B4 tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.inf_in1906310914598751387_nat_o B4))) (= (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o A2) A)) tptp.bot_bo7824918357723582233_nat_o) (and (not (@ (@ tptp.member6576561426505652726_nat_o A2) B4)) (= (@ _let_1 A) tptp.bot_bo7824918357723582233_nat_o))))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (= (= tptp.bot_bo3957492148770167129t_unit (@ (@ tptp.inf_in4660618365625256667t_unit (@ (@ tptp.insert_Product_unit A2) A)) B4)) (and (not (@ (@ tptp.member_Product_unit A2) B4)) (= tptp.bot_bo3957492148770167129t_unit (@ (@ tptp.inf_in4660618365625256667t_unit A) B4))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (A tptp.set_o) (B4 tptp.set_o)) (= (= tptp.bot_bot_set_o (@ (@ tptp.inf_inf_set_o (@ (@ tptp.insert_o A2) A)) B4)) (and (not (@ (@ tptp.member_o A2) B4)) (= tptp.bot_bot_set_o (@ (@ tptp.inf_inf_set_o A) B4))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.insert_nat A2) A)) B4)) (and (not (@ (@ tptp.member_nat A2) B4)) (= tptp.bot_bot_set_nat (@ (@ tptp.inf_inf_set_nat A) B4))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.inf_inf_set_int (@ (@ tptp.insert_int A2) A)) B4)) (and (not (@ (@ tptp.member_int A2) B4)) (= tptp.bot_bot_set_int (@ (@ tptp.inf_inf_set_int A) B4))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (= (= tptp.bot_bo7824918357723582233_nat_o (@ (@ tptp.inf_in1906310914598751387_nat_o (@ (@ tptp.insert5175938949040314269_nat_o A2) A)) B4)) (and (not (@ (@ tptp.member6576561426505652726_nat_o A2) B4)) (= tptp.bot_bo7824918357723582233_nat_o (@ (@ tptp.inf_in1906310914598751387_nat_o A) B4))))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (= (= (@ (@ tptp.inf_in4660618365625256667t_unit (@ (@ tptp.insert_Product_unit A2) A)) B4) tptp.bot_bo3957492148770167129t_unit) (and (not (@ (@ tptp.member_Product_unit A2) B4)) (= (@ (@ tptp.inf_in4660618365625256667t_unit A) B4) tptp.bot_bo3957492148770167129t_unit)))))
% 5.61/5.91 (assert (forall ((A2 Bool) (A tptp.set_o) (B4 tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.insert_o A2) A)) B4) tptp.bot_bot_set_o) (and (not (@ (@ tptp.member_o A2) B4)) (= (@ (@ tptp.inf_inf_set_o A) B4) tptp.bot_bot_set_o)))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.insert_nat A2) A)) B4) tptp.bot_bot_set_nat) (and (not (@ (@ tptp.member_nat A2) B4)) (= (@ (@ tptp.inf_inf_set_nat A) B4) tptp.bot_bot_set_nat)))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.insert_int A2) A)) B4) tptp.bot_bot_set_int) (and (not (@ (@ tptp.member_int A2) B4)) (= (@ (@ tptp.inf_inf_set_int A) B4) tptp.bot_bot_set_int)))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (= (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ (@ tptp.insert5175938949040314269_nat_o A2) A)) B4) tptp.bot_bo7824918357723582233_nat_o) (and (not (@ (@ tptp.member6576561426505652726_nat_o A2) B4)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o A) B4) tptp.bot_bo7824918357723582233_nat_o)))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.image_nat_nat (@ tptp.id_on_nat A)) B4) (@ (@ tptp.inf_inf_set_nat A) B4))))
% 5.61/5.91 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat) (As5 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H2))) (= (@ tptp.in_range (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As5))) (and (@ tptp.in_range (@ _let_1 As)) (@ tptp.in_range (@ _let_1 As5)))))))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (R5 tptp.set_Pr1261947904930325089at_nat) (X4 tptp.set_nat) (X5 tptp.set_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat R3) R5) (=> (@ (@ tptp.ord_less_eq_set_nat X4) X5) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat (@ tptp.transi2905341329935302413cl_nat R3)) X4)) (@ (@ tptp.image_nat_nat (@ tptp.transi2905341329935302413cl_nat R5)) X5))))))
% 5.61/5.91 (assert (forall ((Y tptp.filter_nat) (X tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) X) (= (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (= X Y)))))
% 5.61/5.91 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.ord_less_eq_set_nat X) Y) (= X Y)))))
% 5.61/5.91 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.ord_less_eq_rat X) Y) (= X Y)))))
% 5.61/5.91 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 5.61/5.91 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))))
% 5.61/5.91 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 5.61/5.91 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 5.61/5.91 (assert (forall ((A2 tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_rat (@ F A2)) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_int (@ F A2)) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_rat (@ F A2)) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_int (@ F A2)) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (F (-> tptp.int tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_int A2) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_rat (@ F A2)) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (F (-> tptp.int tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A2) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (F (-> tptp.int tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_int (@ F A2)) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.filter_nat) (B tptp.filter_nat) (F (-> tptp.filter_nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.filter_nat) (Y2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X3) Y2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_rat (@ F A2)) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_rat A2) (@ F C)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F C)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_int A2) (@ F C)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_rat A2) (@ F C)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F C)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (F (-> tptp.nat tptp.int)) (B tptp.nat) (C tptp.nat)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_int A2) (@ F C)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_rat A2) (@ F C)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (F (-> tptp.int tptp.nat)) (B tptp.int) (C tptp.int)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F C)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (F (-> tptp.int tptp.int)) (B tptp.int) (C tptp.int)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_int A2) (@ F C)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.rat) (F (-> tptp.filter_nat tptp.rat)) (B tptp.filter_nat) (C tptp.filter_nat)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B) C) (=> (forall ((X3 tptp.filter_nat) (Y2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X3) Y2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_rat A2) (@ F C)))))))
% 5.61/5.91 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 5.61/5.91 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_int Y) X))))
% 5.61/5.91 (assert (forall ((S tptp.set_Pr4532377907799695533_nat_o) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (= (@ (@ tptp.ord_le2965882846123202637_nat_o S) (@ tptp.collec939566748876313656_nat_o P)) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X2) S) (@ P X2))))))
% 5.61/5.91 (assert (forall ((S tptp.set_int) (P (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_set_int S) (@ tptp.collect_int P)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) S) (@ P X2))))))
% 5.61/5.91 (assert (forall ((S tptp.set_o) (P (-> Bool Bool))) (= (@ (@ tptp.ord_less_eq_set_o S) (@ tptp.collect_o P)) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) S) (@ P X2))))))
% 5.61/5.91 (assert (forall ((S tptp.set_Product_unit) (P (-> tptp.product_unit Bool))) (= (@ (@ tptp.ord_le3507040750410214029t_unit S) (@ tptp.collect_Product_unit P)) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) S) (@ P X2))))))
% 5.61/5.91 (assert (forall ((S tptp.set_nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_set_nat S) (@ tptp.collect_nat P)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) S) (@ P X2))))))
% 5.61/5.91 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (= X Y) (@ (@ tptp.ord_le2510731241096832064er_nat X) Y))))
% 5.61/5.91 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 5.61/5.91 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 5.61/5.91 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (= X Y) (@ (@ tptp.ord_less_eq_int X) Y))))
% 5.61/5.91 (assert (forall ((A2 tptp.filter_nat) (B tptp.filter_nat) (C tptp.filter_nat) (D2 tptp.filter_nat)) (=> (= A2 B) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B) C) (=> (= C D2) (@ (@ tptp.ord_le2510731241096832064er_nat A2) D2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat) (D2 tptp.set_nat)) (=> (= A2 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C) (=> (= C D2) (@ (@ tptp.ord_less_eq_set_nat A2) D2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= A2 B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (= C D2) (@ (@ tptp.ord_less_eq_rat A2) D2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (= A2 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (= C D2) (@ (@ tptp.ord_less_eq_nat A2) D2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= A2 B) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (= C D2) (@ (@ tptp.ord_less_eq_int A2) D2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_rat (@ F A2)) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_int (@ F A2)) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_rat (@ F A2)) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_int (@ F A2)) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (F (-> tptp.int tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_int A2) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_rat (@ F A2)) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (F (-> tptp.int tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A2) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (F (-> tptp.int tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_int (@ F A2)) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.filter_nat) (B tptp.filter_nat) (F (-> tptp.filter_nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.filter_nat) (Y2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X3) Y2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_eq_rat (@ F A2)) C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (F (-> tptp.int tptp.nat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (F (-> tptp.nat tptp.int)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (F (-> tptp.int tptp.int)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.filter_nat) (F (-> tptp.rat tptp.filter_nat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_le2510731241096832064er_nat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.61/5.91 (assert (= (lambda ((Y4 tptp.filter_nat) (Z4 tptp.filter_nat)) (= Y4 Z4)) (lambda ((A6 tptp.filter_nat) (B6 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat A6) B6) (@ (@ tptp.ord_le2510731241096832064er_nat B6) A6)))))
% 5.61/5.91 (assert (= (lambda ((Y4 tptp.set_nat) (Z4 tptp.set_nat)) (= Y4 Z4)) (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A6) B6) (@ (@ tptp.ord_less_eq_set_nat B6) A6)))))
% 5.61/5.91 (assert (= (lambda ((Y4 tptp.rat) (Z4 tptp.rat)) (= Y4 Z4)) (lambda ((A6 tptp.rat) (B6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A6) B6) (@ (@ tptp.ord_less_eq_rat B6) A6)))))
% 5.61/5.91 (assert (= (lambda ((Y4 tptp.nat) (Z4 tptp.nat)) (= Y4 Z4)) (lambda ((A6 tptp.nat) (B6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A6) B6) (@ (@ tptp.ord_less_eq_nat B6) A6)))))
% 5.61/5.91 (assert (= (lambda ((Y4 tptp.int) (Z4 tptp.int)) (= Y4 Z4)) (lambda ((A6 tptp.int) (B6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A6) B6) (@ (@ tptp.ord_less_eq_int B6) A6)))))
% 5.61/5.91 (assert (forall ((S tptp.set_nat) (S4 tptp.set_nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat B4))) (let ((_let_2 (@ tptp.inf_inf_set_nat A))) (=> (@ (@ tptp.ord_less_eq_set_nat S) S4) (=> (= (@ _let_2 S4) (@ _let_1 S4)) (= (@ _let_2 S) (@ _let_1 S))))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (let ((_let_2 (@ tptp.inf_inf_set_nat B4))) (= (@ _let_1 (@ _let_2 C5)) (@ _let_2 (@ _let_1 C5)))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (Q2 (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A) B4) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) A) (=> (@ P X3) (@ Q2 X3)))) (@ (@ tptp.ord_le2965882846123202637_nat_o (@ (@ tptp.inf_in1906310914598751387_nat_o A) (@ tptp.collec939566748876313656_nat_o P))) (@ (@ tptp.inf_in1906310914598751387_nat_o B4) (@ tptp.collec939566748876313656_nat_o Q2)))))))
% 5.61/5.91 (assert (forall ((A tptp.set_int) (B4 tptp.set_int) (P (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_set_int A) B4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (=> (@ P X3) (@ Q2 X3)))) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A) (@ tptp.collect_int P))) (@ (@ tptp.inf_inf_set_int B4) (@ tptp.collect_int Q2)))))))
% 5.61/5.91 (assert (forall ((A tptp.set_o) (B4 tptp.set_o) (P (-> Bool Bool)) (Q2 (-> Bool Bool))) (=> (@ (@ tptp.ord_less_eq_set_o A) B4) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (=> (@ P X3) (@ Q2 X3)))) (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.inf_inf_set_o A) (@ tptp.collect_o P))) (@ (@ tptp.inf_inf_set_o B4) (@ tptp.collect_o Q2)))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit) (P (-> tptp.product_unit Bool)) (Q2 (-> tptp.product_unit Bool))) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) B4) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) A) (=> (@ P X3) (@ Q2 X3)))) (@ (@ tptp.ord_le3507040750410214029t_unit (@ (@ tptp.inf_in4660618365625256667t_unit A) (@ tptp.collect_Product_unit P))) (@ (@ tptp.inf_in4660618365625256667t_unit B4) (@ tptp.collect_Product_unit Q2)))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (P (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (=> (@ P X3) (@ Q2 X3)))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) (@ tptp.collect_nat P))) (@ (@ tptp.inf_inf_set_nat B4) (@ tptp.collect_nat Q2)))))))
% 5.61/5.91 (assert (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (Q2 (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (= (@ (@ tptp.ord_le2965882846123202637_nat_o (@ tptp.collec939566748876313656_nat_o P)) (@ tptp.collec939566748876313656_nat_o Q2)) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ P X2) (@ Q2 X2))))))
% 5.61/5.91 (assert (forall ((P (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q2)) (forall ((X2 tptp.int)) (=> (@ P X2) (@ Q2 X2))))))
% 5.61/5.91 (assert (forall ((P (-> Bool Bool)) (Q2 (-> Bool Bool))) (= (@ (@ tptp.ord_less_eq_set_o (@ tptp.collect_o P)) (@ tptp.collect_o Q2)) (forall ((X2 Bool)) (=> (@ P X2) (@ Q2 X2))))))
% 5.61/5.91 (assert (forall ((P (-> tptp.product_unit Bool)) (Q2 (-> tptp.product_unit Bool))) (= (@ (@ tptp.ord_le3507040750410214029t_unit (@ tptp.collect_Product_unit P)) (@ tptp.collect_Product_unit Q2)) (forall ((X2 tptp.product_unit)) (=> (@ P X2) (@ Q2 X2))))))
% 5.61/5.91 (assert (forall ((P (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q2)) (forall ((X2 tptp.nat)) (=> (@ P X2) (@ Q2 X2))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A))) (let ((_let_2 (@ tptp.sup_sup_set_nat B4))) (= (@ _let_1 (@ _let_2 C5)) (@ _let_2 (@ _let_1 C5)))))))
% 5.61/5.91 (assert (forall ((B4 tptp.set_nat) (C5 tptp.set_nat) (A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat B4) C5)) A) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat B4) A)) (@ (@ tptp.sup_sup_set_nat C5) A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (= (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B4)) C5) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B4) C5))) (@ (@ tptp.ord_less_eq_set_nat C5) A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (let ((_let_2 (@ _let_1 B4))) (= (@ _let_1 _let_2) _let_2)))))
% 5.61/5.91 (assert (forall ((B4 tptp.set_nat) (C5 tptp.set_nat) (A tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat B4) C5)) A) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat B4) A)) (@ (@ tptp.inf_inf_set_nat C5) A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A))) (let ((_let_2 (@ _let_1 B4))) (= (@ _let_1 _let_2) _let_2)))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B4) C5)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 B4)) (@ _let_1 C5))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat B4) C5)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 B4)) (@ _let_1 C5))))))
% 5.61/5.91 (assert (= (lambda ((Y4 tptp.set_nat) (Z4 tptp.set_nat)) (= Y4 Z4)) (lambda ((A3 tptp.set_nat) (B7 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A3) B7) (@ (@ tptp.ord_less_eq_set_nat B7) A3)))))
% 5.61/5.91 (assert (forall ((A2 tptp.filter_nat) (B tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B) A2) (= A2 B)))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (@ (@ tptp.ord_less_eq_set_nat B) A2) (= A2 B)))))
% 5.61/5.91 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (@ (@ tptp.ord_less_eq_rat B) A2) (= A2 B)))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (@ (@ tptp.ord_less_eq_nat B) A2) (= A2 B)))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B) (=> (@ (@ tptp.ord_less_eq_int B) A2) (= A2 B)))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) C5) (@ _let_1 C5))))))
% 5.61/5.91 (assert (= tptp.ord_less_eq_set_nat (lambda ((A3 tptp.set_nat) (B7 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A3) B7) B7))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat A) B4)) (@ (@ tptp.inf_inf_set_nat B4) C5))) (@ (@ tptp.inf_inf_set_nat C5) A)) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.sup_sup_set_nat B4) C5))) (@ (@ tptp.sup_sup_set_nat C5) A)))))
% 5.61/5.91 (assert (forall ((C5 tptp.set_nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C5))) (=> (@ _let_1 A) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)))))))
% 5.61/5.91 (assert (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (Q2 (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ P X3) (@ Q2 X3))) (@ (@ tptp.ord_le2965882846123202637_nat_o (@ tptp.collec939566748876313656_nat_o P)) (@ tptp.collec939566748876313656_nat_o Q2)))))
% 5.61/5.91 (assert (forall ((P (-> tptp.int Bool)) (Q2 (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ Q2 X3))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q2)))))
% 5.61/5.91 (assert (forall ((P (-> Bool Bool)) (Q2 (-> Bool Bool))) (=> (forall ((X3 Bool)) (=> (@ P X3) (@ Q2 X3))) (@ (@ tptp.ord_less_eq_set_o (@ tptp.collect_o P)) (@ tptp.collect_o Q2)))))
% 5.61/5.91 (assert (forall ((P (-> tptp.product_unit Bool)) (Q2 (-> tptp.product_unit Bool))) (=> (forall ((X3 tptp.product_unit)) (=> (@ P X3) (@ Q2 X3))) (@ (@ tptp.ord_le3507040750410214029t_unit (@ tptp.collect_Product_unit P)) (@ tptp.collect_Product_unit Q2)))))
% 5.61/5.91 (assert (forall ((P (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (=> (@ P X3) (@ Q2 X3))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q2)))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)))
% 5.61/5.91 (assert (= tptp.inf_inf_set_nat (lambda ((A3 tptp.set_nat) (B7 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat B7) A3))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (= (@ (@ tptp.inf_inf_set_nat A) B4) A))))
% 5.61/5.91 (assert (forall ((B4 tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A) (= (@ (@ tptp.inf_inf_set_nat A) B4) B4))))
% 5.61/5.91 (assert (= tptp.ord_le2965882846123202637_nat_o (lambda ((A3 tptp.set_Pr4532377907799695533_nat_o) (B7 tptp.set_Pr4532377907799695533_nat_o)) (forall ((T (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o T))) (=> (@ _let_1 A3) (@ _let_1 B7)))))))
% 5.61/5.91 (assert (= tptp.ord_less_eq_set_int (lambda ((A3 tptp.set_int) (B7 tptp.set_int)) (forall ((T tptp.int)) (let ((_let_1 (@ tptp.member_int T))) (=> (@ _let_1 A3) (@ _let_1 B7)))))))
% 5.61/5.91 (assert (= tptp.ord_less_eq_set_o (lambda ((A3 tptp.set_o) (B7 tptp.set_o)) (forall ((T Bool)) (let ((_let_1 (@ tptp.member_o T))) (=> (@ _let_1 A3) (@ _let_1 B7)))))))
% 5.61/5.91 (assert (= tptp.ord_le3507040750410214029t_unit (lambda ((A3 tptp.set_Product_unit) (B7 tptp.set_Product_unit)) (forall ((T tptp.product_unit)) (let ((_let_1 (@ tptp.member_Product_unit T))) (=> (@ _let_1 A3) (@ _let_1 B7)))))))
% 5.61/5.91 (assert (= tptp.ord_less_eq_set_nat (lambda ((A3 tptp.set_nat) (B7 tptp.set_nat)) (forall ((T tptp.nat)) (let ((_let_1 (@ tptp.member_nat T))) (=> (@ _let_1 A3) (@ _let_1 B7)))))))
% 5.61/5.91 (assert (forall ((C5 tptp.set_nat) (A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat C5) (@ (@ tptp.sup_sup_set_nat A) B4)) (not (forall ((A7 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A7) A) (forall ((B8 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B8) B4) (not (= C5 (@ (@ tptp.sup_sup_set_nat A7) B8)))))))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (= A B4) (@ (@ tptp.ord_less_eq_set_nat B4) A))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (= A B4) (@ (@ tptp.ord_less_eq_set_nat A) B4))))
% 5.61/5.91 (assert (= tptp.sup_sup_set_nat (lambda ((A3 tptp.set_nat) (B7 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat B7) A3))))
% 5.61/5.91 (assert (forall ((B4 tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A) (= (@ (@ tptp.sup_sup_set_nat A) B4) A))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (= (@ (@ tptp.sup_sup_set_nat A) B4) B4))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B4)) B4)))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B4)) A)))
% 5.61/5.91 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A) A) A)))
% 5.61/5.91 (assert (= tptp.ord_le2965882846123202637_nat_o (lambda ((A3 tptp.set_Pr4532377907799695533_nat_o) (B7 tptp.set_Pr4532377907799695533_nat_o)) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X2))) (=> (@ _let_1 A3) (@ _let_1 B7)))))))
% 5.61/5.91 (assert (= tptp.ord_less_eq_set_int (lambda ((A3 tptp.set_int) (B7 tptp.set_int)) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 A3) (@ _let_1 B7)))))))
% 5.61/5.91 (assert (= tptp.ord_less_eq_set_o (lambda ((A3 tptp.set_o) (B7 tptp.set_o)) (forall ((X2 Bool)) (let ((_let_1 (@ tptp.member_o X2))) (=> (@ _let_1 A3) (@ _let_1 B7)))))))
% 5.61/5.91 (assert (= tptp.ord_le3507040750410214029t_unit (lambda ((A3 tptp.set_Product_unit) (B7 tptp.set_Product_unit)) (forall ((X2 tptp.product_unit)) (let ((_let_1 (@ tptp.member_Product_unit X2))) (=> (@ _let_1 A3) (@ _let_1 B7)))))))
% 5.61/5.91 (assert (= tptp.ord_less_eq_set_nat (lambda ((A3 tptp.set_nat) (B7 tptp.set_nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 A3) (@ _let_1 B7)))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (= A B4) (not (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (not (@ (@ tptp.ord_less_eq_set_nat B4) A)))))))
% 5.61/5.91 (assert (forall ((B4 tptp.set_nat) (A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B4) (@ (@ tptp.sup_sup_set_nat A) B4))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) (@ (@ tptp.sup_sup_set_nat A) B4))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A) A) A)))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 B4)) C5) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B4) C5))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (C5 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C5) (=> (@ (@ tptp.ord_less_eq_set_nat B4) C5) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A) B4)) C5)))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B4)) C5) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B4) C5))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (C5 tptp.set_nat) (B4 tptp.set_nat) (D3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C5) (=> (@ (@ tptp.ord_less_eq_set_nat B4) D3) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B4)) (@ (@ tptp.inf_inf_set_nat C5) D3))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o) (C (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A) B4) (=> (@ _let_1 A) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((A tptp.set_int) (B4 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_eq_set_int A) B4) (=> (@ _let_1 A) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((A tptp.set_o) (B4 tptp.set_o) (C Bool)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ (@ tptp.ord_less_eq_set_o A) B4) (=> (@ _let_1 A) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit) (C tptp.product_unit)) (let ((_let_1 (@ tptp.member_Product_unit C))) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) B4) (=> (@ _let_1 A) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (=> (@ _let_1 A) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X))) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A) B4) (=> (@ _let_1 A) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((A tptp.set_int) (B4 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ (@ tptp.ord_less_eq_set_int A) B4) (=> (@ _let_1 A) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((A tptp.set_o) (B4 tptp.set_o) (X Bool)) (let ((_let_1 (@ tptp.member_o X))) (=> (@ (@ tptp.ord_less_eq_set_o A) B4) (=> (@ _let_1 A) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit) (X tptp.product_unit)) (let ((_let_1 (@ tptp.member_Product_unit X))) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) B4) (=> (@ _let_1 A) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (=> (@ _let_1 A) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (P (-> tptp.nat Bool))) (= (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.sup_sup_set_nat A) B4)) (@ P X2))) (and (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ P X2))) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) B4) (@ P X2)))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (C5 tptp.set_nat) (B4 tptp.set_nat) (D3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C5) (=> (@ (@ tptp.ord_less_eq_set_nat B4) D3) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.sup_sup_set_nat C5) D3))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (P (-> tptp.nat Bool))) (= (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) (@ (@ tptp.sup_sup_set_nat A) B4)) (@ P X2))) (or (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A) (@ P X2))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) B4) (@ P X2)))))))
% 5.61/5.91 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o A) B4)) (@ _let_1 B4)))))
% 5.61/5.91 (assert (forall ((C tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A) B4)) (@ _let_1 B4)))))
% 5.61/5.91 (assert (forall ((C Bool) (A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_o A) B4)) (@ _let_1 B4)))))
% 5.61/5.91 (assert (forall ((C tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member_Product_unit C))) (=> (@ _let_1 (@ (@ tptp.inf_in4660618365625256667t_unit A) B4)) (@ _let_1 B4)))))
% 5.61/5.91 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)) (@ _let_1 B4)))))
% 5.61/5.91 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o A) B4)) (@ _let_1 A)))))
% 5.61/5.91 (assert (forall ((C tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A) B4)) (@ _let_1 A)))))
% 5.61/5.91 (assert (forall ((C Bool) (A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_o A) B4)) (@ _let_1 A)))))
% 5.61/5.91 (assert (forall ((C tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member_Product_unit C))) (=> (@ _let_1 (@ (@ tptp.inf_in4660618365625256667t_unit A) B4)) (@ _let_1 A)))))
% 5.61/5.91 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)) (@ _let_1 A)))))
% 5.61/5.91 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.set_Pr4532377907799695533_nat_o) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.sup_su5209123915105501825_nat_o A) B4))))))
% 5.61/5.91 (assert (forall ((C tptp.int) (B4 tptp.set_int) (A tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B4))))))
% 5.61/5.91 (assert (forall ((C Bool) (B4 tptp.set_o) (A tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.sup_sup_set_o A) B4))))))
% 5.61/5.91 (assert (forall ((C tptp.product_unit) (B4 tptp.set_Product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member_Product_unit C))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.sup_su793286257634532545t_unit A) B4))))))
% 5.61/5.91 (assert (forall ((C tptp.nat) (B4 tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4))))))
% 5.61/5.91 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su5209123915105501825_nat_o A) B4))))))
% 5.61/5.91 (assert (forall ((C tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B4))))))
% 5.61/5.91 (assert (forall ((C Bool) (A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_o A) B4))))))
% 5.61/5.91 (assert (forall ((C tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member_Product_unit C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su793286257634532545t_unit A) B4))))))
% 5.61/5.91 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4))))))
% 5.61/5.91 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o A) B4)) (not (=> (@ _let_1 A) (not (@ _let_1 B4))))))))
% 5.61/5.91 (assert (forall ((C tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A) B4)) (not (=> (@ _let_1 A) (not (@ _let_1 B4))))))))
% 5.61/5.91 (assert (forall ((C Bool) (A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_o A) B4)) (not (=> (@ _let_1 A) (not (@ _let_1 B4))))))))
% 5.61/5.91 (assert (forall ((C tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member_Product_unit C))) (=> (@ _let_1 (@ (@ tptp.inf_in4660618365625256667t_unit A) B4)) (not (=> (@ _let_1 A) (not (@ _let_1 B4))))))))
% 5.61/5.91 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)) (not (=> (@ _let_1 A) (not (@ _let_1 B4))))))))
% 5.61/5.91 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.sup_su5209123915105501825_nat_o A) B4)) (=> (not (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((C tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B4)) (=> (not (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((C Bool) (A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_o A) B4)) (=> (not (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((C tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member_Product_unit C))) (=> (@ _let_1 (@ (@ tptp.sup_su793286257634532545t_unit A) B4)) (=> (not (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (=> (not (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((B tptp.filter_nat) (A2 tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat C))) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))))
% 5.61/5.91 (assert (forall ((B tptp.set_nat) (A2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))))
% 5.61/5.91 (assert (forall ((B tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))))
% 5.61/5.91 (assert (forall ((B tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))))
% 5.61/5.91 (assert (forall ((B tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))))
% 5.61/5.91 (assert (forall ((B tptp.filter_nat) (A2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B) A2) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B) (= A2 B)))))
% 5.61/5.91 (assert (forall ((B tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) A2) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (= A2 B)))))
% 5.61/5.91 (assert (forall ((B tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A2) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (= A2 B)))))
% 5.61/5.91 (assert (forall ((B tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A2) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (= A2 B)))))
% 5.61/5.91 (assert (forall ((B tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A2) (=> (@ (@ tptp.ord_less_eq_int A2) B) (= A2 B)))))
% 5.61/5.91 (assert (= (lambda ((Y4 tptp.filter_nat) (Z4 tptp.filter_nat)) (= Y4 Z4)) (lambda ((A6 tptp.filter_nat) (B6 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat B6) A6) (@ (@ tptp.ord_le2510731241096832064er_nat A6) B6)))))
% 5.61/5.91 (assert (= (lambda ((Y4 tptp.set_nat) (Z4 tptp.set_nat)) (= Y4 Z4)) (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B6) A6) (@ (@ tptp.ord_less_eq_set_nat A6) B6)))))
% 5.61/5.91 (assert (= (lambda ((Y4 tptp.rat) (Z4 tptp.rat)) (= Y4 Z4)) (lambda ((A6 tptp.rat) (B6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B6) A6) (@ (@ tptp.ord_less_eq_rat A6) B6)))))
% 5.61/5.91 (assert (= (lambda ((Y4 tptp.nat) (Z4 tptp.nat)) (= Y4 Z4)) (lambda ((A6 tptp.nat) (B6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B6) A6) (@ (@ tptp.ord_less_eq_nat A6) B6)))))
% 5.61/5.91 (assert (= (lambda ((Y4 tptp.int) (Z4 tptp.int)) (= Y4 Z4)) (lambda ((A6 tptp.int) (B6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B6) A6) (@ (@ tptp.ord_less_eq_int A6) B6)))))
% 5.61/5.91 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A2 tptp.rat) (B tptp.rat)) (=> (forall ((A4 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A4) B2) (@ (@ P A4) B2))) (=> (forall ((A4 tptp.rat) (B2 tptp.rat)) (=> (@ (@ P B2) A4) (@ (@ P A4) B2))) (@ (@ P A2) B)))))
% 5.61/5.91 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A4) B2) (@ (@ P A4) B2))) (=> (forall ((A4 tptp.nat) (B2 tptp.nat)) (=> (@ (@ P B2) A4) (@ (@ P A4) B2))) (@ (@ P A2) B)))))
% 5.61/5.91 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A2 tptp.int) (B tptp.int)) (=> (forall ((A4 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A4) B2) (@ (@ P A4) B2))) (=> (forall ((A4 tptp.int) (B2 tptp.int)) (=> (@ (@ P B2) A4) (@ (@ P A4) B2))) (@ (@ P A2) B)))))
% 5.61/5.91 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat) (Z tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) Z) (@ _let_1 Z))))))
% 5.61/5.91 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) Z) (@ _let_1 Z))))))
% 5.61/5.91 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z) (@ _let_1 Z))))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 5.61/5.91 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))))
% 5.61/5.91 (assert (forall ((A2 tptp.filter_nat) (B tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B) C) (@ _let_1 C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C) (@ _let_1 C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ _let_1 C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ _let_1 C))))))
% 5.61/5.91 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) X) (= X Y)))))
% 5.61/5.91 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= X Y)))))
% 5.61/5.91 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= X Y)))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= X Y)))))
% 5.61/5.91 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= X Y)))))
% 5.61/5.91 (assert (forall ((A2 tptp.filter_nat) (B tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_le2510731241096832064er_nat A2))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.61/5.91 (assert (forall ((A2 tptp.filter_nat) (B tptp.filter_nat) (C tptp.filter_nat)) (=> (= A2 B) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B) C) (@ (@ tptp.ord_le2510731241096832064er_nat A2) C)))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (=> (= A2 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C) (@ (@ tptp.ord_less_eq_set_nat A2) C)))))
% 5.61/5.91 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A2 B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_eq_rat A2) C)))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A2 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat A2) C)))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (=> (= A2 B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ (@ tptp.ord_less_eq_int A2) C)))))
% 5.61/5.91 (assert (= (lambda ((Y4 tptp.filter_nat) (Z4 tptp.filter_nat)) (= Y4 Z4)) (lambda ((X2 tptp.filter_nat) (Y3 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat X2) Y3) (@ (@ tptp.ord_le2510731241096832064er_nat Y3) X2)))))
% 5.61/5.91 (assert (= (lambda ((Y4 tptp.set_nat) (Z4 tptp.set_nat)) (= Y4 Z4)) (lambda ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X2) Y3) (@ (@ tptp.ord_less_eq_set_nat Y3) X2)))))
% 5.61/5.91 (assert (= (lambda ((Y4 tptp.rat) (Z4 tptp.rat)) (= Y4 Z4)) (lambda ((X2 tptp.rat) (Y3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X2) Y3) (@ (@ tptp.ord_less_eq_rat Y3) X2)))))
% 5.61/5.91 (assert (= (lambda ((Y4 tptp.nat) (Z4 tptp.nat)) (= Y4 Z4)) (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y3) (@ (@ tptp.ord_less_eq_nat Y3) X2)))))
% 5.61/5.91 (assert (= (lambda ((Y4 tptp.int) (Z4 tptp.int)) (= Y4 Z4)) (lambda ((X2 tptp.int) (Y3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y3) (@ (@ tptp.ord_less_eq_int Y3) X2)))))
% 5.61/5.91 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_rat Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_rat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 5.61/5.91 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_int Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_int Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat A2) B)) (and (@ (@ tptp.ord_less_eq_rat B) A2) (not (= B A2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat A2) B)) (and (@ (@ tptp.ord_less_eq_nat B) A2) (not (= B A2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int A2) B)) (and (@ (@ tptp.ord_less_eq_int B) A2) (not (= B A2))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (C5 tptp.set_Pr4532377907799695533_nat_o) (B4 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.set_nat)) (D3 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.set_nat))) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A) C5) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) A) (@ (@ tptp.ord_less_eq_set_nat (@ B4 X3)) (@ D3 X3)))) (@ (@ tptp.ord_le4460016228128491106_o_nat (@ (@ tptp.produc3142209312014666069_o_nat A) B4)) (@ (@ tptp.produc3142209312014666069_o_nat C5) D3))))))
% 5.61/5.91 (assert (forall ((A tptp.set_int) (C5 tptp.set_int) (B4 (-> tptp.int tptp.set_nat)) (D3 (-> tptp.int tptp.set_nat))) (=> (@ (@ tptp.ord_less_eq_set_int A) C5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (@ (@ tptp.ord_less_eq_set_nat (@ B4 X3)) (@ D3 X3)))) (@ (@ tptp.ord_le5333435103577920093nt_nat (@ (@ tptp.produc1456381018704787142nt_nat A) B4)) (@ (@ tptp.produc1456381018704787142nt_nat C5) D3))))))
% 5.61/5.91 (assert (forall ((A tptp.set_o) (C5 tptp.set_o) (B4 (-> Bool tptp.set_nat)) (D3 (-> Bool tptp.set_nat))) (=> (@ (@ tptp.ord_less_eq_set_o A) C5) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (@ (@ tptp.ord_less_eq_set_nat (@ B4 X3)) (@ D3 X3)))) (@ (@ tptp.ord_le6472378536984071597_o_nat (@ (@ tptp.product_Sigma_o_nat A) B4)) (@ (@ tptp.product_Sigma_o_nat C5) D3))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit) (C5 tptp.set_Product_unit) (B4 (-> tptp.product_unit tptp.set_nat)) (D3 (-> tptp.product_unit tptp.set_nat))) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) C5) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) A) (@ (@ tptp.ord_less_eq_set_nat (@ B4 X3)) (@ D3 X3)))) (@ (@ tptp.ord_le8121013740822022818it_nat (@ (@ tptp.produc6875377002296012693it_nat A) B4)) (@ (@ tptp.produc6875377002296012693it_nat C5) D3))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (C5 tptp.set_nat) (B4 (-> tptp.nat tptp.set_nat)) (D3 (-> tptp.nat tptp.set_nat))) (=> (@ (@ tptp.ord_less_eq_set_nat A) C5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (@ (@ tptp.ord_less_eq_set_nat (@ B4 X3)) (@ D3 X3)))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.produc457027306803732586at_nat A) B4)) (@ (@ tptp.produc457027306803732586at_nat C5) D3))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (P tptp.set_Pr1261947904930325089at_nat) (Q2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)))) (=> (@ _let_1 (@ tptp.transi2905341329935302413cl_nat (@ (@ tptp.sup_su6327502436637775413at_nat P) Q2))) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) B)) (@ tptp.transi2905341329935302413cl_nat P)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) X3)) Q2) (= Y2 X3)))) (@ _let_1 (@ tptp.transi2905341329935302413cl_nat P)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (P tptp.set_Pr958786334691620121nt_int) (Q2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)))) (=> (@ _let_1 (@ tptp.transi2902850859426252137cl_int (@ (@ tptp.sup_su6024340866399070445nt_int P) Q2))) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) B)) (@ tptp.transi2902850859426252137cl_int P)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y2) X3)) Q2) (= Y2 X3)))) (@ _let_1 (@ tptp.transi2902850859426252137cl_int P)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (P tptp.set_Pr1261947904930325089at_nat) (Q2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)))) (=> (@ _let_1 (@ tptp.transi2905341329935302413cl_nat (@ (@ tptp.sup_su6327502436637775413at_nat P) Q2))) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) X3)) (@ tptp.transi2905341329935302413cl_nat P)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)) Q2) (= X3 Y2)))) (@ _let_1 (@ tptp.transi2905341329935302413cl_nat P)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (P tptp.set_Pr958786334691620121nt_int) (Q2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)))) (=> (@ _let_1 (@ tptp.transi2902850859426252137cl_int (@ (@ tptp.sup_su6024340866399070445nt_int P) Q2))) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) X3)) (@ tptp.transi2902850859426252137cl_int P)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y2)) Q2) (= X3 Y2)))) (@ _let_1 (@ tptp.transi2902850859426252137cl_int P)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_Product_unit) (A5 tptp.set_Product_unit) (B tptp.set_Product_unit) (B3 tptp.set_Product_unit)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A2) A5) (=> (@ (@ tptp.ord_le3507040750410214029t_unit B) B3) (=> (= (@ (@ tptp.inf_in4660618365625256667t_unit A5) B3) tptp.bot_bo3957492148770167129t_unit) (= (@ (@ tptp.inf_in4660618365625256667t_unit A2) B) tptp.bot_bo3957492148770167129t_unit))))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_o) (A5 tptp.set_o) (B tptp.set_o) (B3 tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A2) A5) (=> (@ (@ tptp.ord_less_eq_set_o B) B3) (=> (= (@ (@ tptp.inf_inf_set_o A5) B3) tptp.bot_bot_set_o) (= (@ (@ tptp.inf_inf_set_o A2) B) tptp.bot_bot_set_o))))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_int) (A5 tptp.set_int) (B tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) A5) (=> (@ (@ tptp.ord_less_eq_set_int B) B3) (=> (= (@ (@ tptp.inf_inf_set_int A5) B3) tptp.bot_bot_set_int) (= (@ (@ tptp.inf_inf_set_int A2) B) tptp.bot_bot_set_int))))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_Pr4532377907799695533_nat_o) (A5 tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o) (B3 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A2) A5) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o B) B3) (=> (= (@ (@ tptp.inf_in1906310914598751387_nat_o A5) B3) tptp.bot_bo7824918357723582233_nat_o) (= (@ (@ tptp.inf_in1906310914598751387_nat_o A2) B) tptp.bot_bo7824918357723582233_nat_o))))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_nat) (A5 tptp.set_nat) (B tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) A5) (=> (@ (@ tptp.ord_less_eq_set_nat B) B3) (=> (= (@ (@ tptp.inf_inf_set_nat A5) B3) tptp.bot_bot_set_nat) (= (@ (@ tptp.inf_inf_set_nat A2) B) tptp.bot_bot_set_nat))))))
% 5.61/5.91 (assert (forall ((E tptp.set_Pr1261947904930325089at_nat) (V2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.image_nat_nat (@ tptp.transi2905341329935302413cl_nat E)) V2))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat E) _let_1)) _let_1))))
% 5.61/5.91 (assert (forall ((I tptp.set_nat) (INV tptp.set_nat) (E tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat I) INV) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat E) INV)) INV) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat (@ tptp.transi2905341329935302413cl_nat E)) I)) INV)))))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_nat R3))) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4))) (@ (@ tptp.inf_inf_set_nat (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((R6 tptp.set_Pr1261947904930325089at_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (A8 tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat R6) R2) (=> (@ (@ tptp.ord_less_eq_set_nat A8) A) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat R6) A8)) (@ (@ tptp.image_nat_nat R2) A))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.refl_on_nat A) R2) (=> (@ (@ tptp.refl_on_nat B4) S2) (@ (@ tptp.refl_on_nat (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.sup_su6327502436637775413at_nat R2) S2))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.refl_on_nat A) R2) (=> (@ (@ tptp.refl_on_nat B4) S2) (@ (@ tptp.refl_on_nat (@ (@ tptp.inf_inf_set_nat A) B4)) (@ (@ tptp.inf_in2572325071724192079at_nat R2) S2))))))
% 5.61/5.91 (assert (forall ((V tptp.nat) (W tptp.nat) (E tptp.set_Pr1261947904930325089at_nat) (U2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat V) W)))) (=> (@ _let_1 (@ tptp.transi6264000038957366511cl_nat (@ (@ tptp.sup_su6327502436637775413at_nat E) U2))) (=> (not (@ _let_1 (@ tptp.transi6264000038957366511cl_nat E))) (exists ((X3 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.transi2905341329935302413cl_nat (@ (@ tptp.sup_su6327502436637775413at_nat E) U2)))) (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat V) X3)) _let_1) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)) U2) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) W)) _let_1)))))))))
% 5.61/5.91 (assert (forall ((V tptp.int) (W tptp.int) (E tptp.set_Pr958786334691620121nt_int) (U2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int V) W)))) (=> (@ _let_1 (@ tptp.transi6261509568448316235cl_int (@ (@ tptp.sup_su6024340866399070445nt_int E) U2))) (=> (not (@ _let_1 (@ tptp.transi6261509568448316235cl_int E))) (exists ((X3 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.transi2902850859426252137cl_int (@ (@ tptp.sup_su6024340866399070445nt_int E) U2)))) (and (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int V) X3)) _let_1) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y2)) U2) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y2) W)) _let_1)))))))))
% 5.61/5.91 (assert (forall ((C tptp.product_prod_nat_int) (A tptp.set_nat) (B4 (-> tptp.nat tptp.set_int))) (=> (@ (@ tptp.member4262671552274231302at_int C) (@ (@ tptp.produc454536836294682310at_int A) B4)) (not (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) (@ B4 X3)) (not (= C (@ (@ tptp.product_Pair_nat_int X3) Y2)))))))))))
% 5.61/5.91 (assert (forall ((C tptp.product_prod_nat_o) (A tptp.set_nat) (B4 (-> tptp.nat tptp.set_o))) (=> (@ (@ tptp.member6310962623043647828_nat_o C) (@ (@ tptp.product_Sigma_nat_o A) B4)) (not (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (forall ((Y2 Bool)) (=> (@ (@ tptp.member_o Y2) (@ B4 X3)) (not (= C (@ (@ tptp.product_Pair_nat_o X3) Y2)))))))))))
% 5.61/5.91 (assert (forall ((C tptp.produc526117512892780850t_unit) (A tptp.set_nat) (B4 (-> tptp.nat tptp.set_Product_unit))) (=> (@ (@ tptp.member348563419383025609t_unit C) (@ (@ tptp.produc5506539147108004339t_unit A) B4)) (not (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (forall ((Y2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit Y2) (@ B4 X3)) (not (= C (@ (@ tptp.produc3434450474625521892t_unit X3) Y2)))))))))))
% 5.61/5.91 (assert (forall ((C tptp.product_prod_int_nat) (A tptp.set_int) (B4 (-> tptp.int tptp.set_nat))) (=> (@ (@ tptp.member216504246829706758nt_nat C) (@ (@ tptp.produc1456381018704787142nt_nat A) B4)) (not (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) (@ B4 X3)) (not (= C (@ (@ tptp.product_Pair_int_nat X3) Y2)))))))))))
% 5.61/5.91 (assert (forall ((C tptp.product_prod_int_o) (A tptp.set_int) (B4 (-> tptp.int tptp.set_o))) (=> (@ (@ tptp.member4489920277610959864_int_o C) (@ (@ tptp.product_Sigma_int_o A) B4)) (not (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (forall ((Y2 Bool)) (=> (@ (@ tptp.member_o Y2) (@ B4 X3)) (not (= C (@ (@ tptp.product_Pair_int_o X3) Y2)))))))))))
% 5.61/5.91 (assert (forall ((C tptp.produc6865911496949736918t_unit) (A tptp.set_int) (B4 (-> tptp.int tptp.set_Product_unit))) (=> (@ (@ tptp.member6688357403439981677t_unit C) (@ (@ tptp.produc2622961094310184599t_unit A) B4)) (not (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (forall ((Y2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit Y2) (@ B4 X3)) (not (= C (@ (@ tptp.produc550872421827702152t_unit X3) Y2)))))))))))
% 5.61/5.91 (assert (forall ((C tptp.product_prod_o_nat) (A tptp.set_o) (B4 (-> Bool tptp.set_nat))) (=> (@ (@ tptp.member2802428098988154798_o_nat C) (@ (@ tptp.product_Sigma_o_nat A) B4)) (not (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) (@ B4 X3)) (not (= C (@ (@ tptp.product_Pair_o_nat X3) Y2)))))))))))
% 5.61/5.91 (assert (forall ((C tptp.product_prod_o_int) (A tptp.set_o) (B4 (-> Bool tptp.set_int))) (=> (@ (@ tptp.member7847949116333733898_o_int C) (@ (@ tptp.product_Sigma_o_int A) B4)) (not (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) (@ B4 X3)) (not (= C (@ (@ tptp.product_Pair_o_int X3) Y2)))))))))))
% 5.61/5.91 (assert (forall ((C tptp.product_prod_o_o) (A tptp.set_o) (B4 (-> Bool tptp.set_o))) (=> (@ (@ tptp.member7466972457876170832od_o_o C) (@ (@ tptp.product_Sigma_o_o A) B4)) (not (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (forall ((Y2 Bool)) (=> (@ (@ tptp.member_o Y2) (@ B4 X3)) (not (= C (@ (@ tptp.product_Pair_o_o X3) Y2)))))))))))
% 5.61/5.91 (assert (forall ((C tptp.produc3788275437394581276t_unit) (A tptp.set_o) (B4 (-> Bool tptp.set_Product_unit))) (=> (@ (@ tptp.member9215336023991391429t_unit C) (@ (@ tptp.produc411009820408249917t_unit A) B4)) (not (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (forall ((Y2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit Y2) (@ B4 X3)) (not (= C (@ (@ tptp.produc3901946521647900940t_unit X3) Y2)))))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat) (A tptp.set_he8644174446132254637t_unit) (B4 (-> tptp.heap_e7401611519738050253t_unit tptp.set_set_nat))) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) B)) (@ (@ tptp.produc5260988393495149579et_nat A) B4)) (@ (@ tptp.member242389114213480694t_unit A2) A))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (A tptp.set_nat) (B4 (-> tptp.nat tptp.set_nat))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) (@ (@ tptp.produc457027306803732586at_nat A) B4)) (@ (@ tptp.member_nat A2) A))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (A tptp.set_int) (B4 (-> tptp.int tptp.set_int))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) (@ (@ tptp.produc1453890548195736866nt_int A) B4)) (@ (@ tptp.member_int A2) A))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (A tptp.set_Pr4532377907799695533_nat_o) (B4 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.set_Pr3948176798113811640et_nat))) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) B)) (@ (@ tptp.produc8052021730408606599et_nat A) B4)) (@ (@ tptp.member6576561426505652726_nat_o A2) A))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (A tptp.set_Pr4532377907799695533_nat_o) (B4 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.set_Pr3286484037609594932et_nat))) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) B)) (@ (@ tptp.produc7016705354093686019et_nat A) B4)) (@ (@ tptp.member6576561426505652726_nat_o A2) A))))
% 5.61/5.91 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat) (A tptp.set_he8644174446132254637t_unit) (B4 (-> tptp.heap_e7401611519738050253t_unit tptp.set_set_nat))) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) B)) (@ (@ tptp.produc5260988393495149579et_nat A) B4)) (@ (@ tptp.member_set_nat B) (@ B4 A2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (A tptp.set_nat) (B4 (-> tptp.nat tptp.set_nat))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) (@ (@ tptp.produc457027306803732586at_nat A) B4)) (@ (@ tptp.member_nat B) (@ B4 A2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (A tptp.set_int) (B4 (-> tptp.int tptp.set_int))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) (@ (@ tptp.produc1453890548195736866nt_int A) B4)) (@ (@ tptp.member_int B) (@ B4 A2)))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (A tptp.set_Pr4532377907799695533_nat_o) (B4 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.set_Pr3948176798113811640et_nat))) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) B)) (@ (@ tptp.produc8052021730408606599et_nat A) B4)) (@ (@ tptp.member6260224972018164377et_nat B) (@ B4 A2)))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (A tptp.set_Pr4532377907799695533_nat_o) (B4 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.set_Pr3286484037609594932et_nat))) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) B)) (@ (@ tptp.produc7016705354093686019et_nat A) B4)) (@ (@ tptp.member1996754912294343701et_nat B) (@ B4 A2)))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.int) (A tptp.set_nat) (B4 (-> tptp.nat tptp.set_int))) (=> (@ (@ tptp.member4262671552274231302at_int (@ (@ tptp.product_Pair_nat_int A2) B)) (@ (@ tptp.produc454536836294682310at_int A) B4)) (not (=> (@ (@ tptp.member_nat A2) A) (not (@ (@ tptp.member_int B) (@ B4 A2))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B Bool) (A tptp.set_nat) (B4 (-> tptp.nat tptp.set_o))) (=> (@ (@ tptp.member6310962623043647828_nat_o (@ (@ tptp.product_Pair_nat_o A2) B)) (@ (@ tptp.product_Sigma_nat_o A) B4)) (not (=> (@ (@ tptp.member_nat A2) A) (not (@ (@ tptp.member_o B) (@ B4 A2))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.product_unit) (A tptp.set_nat) (B4 (-> tptp.nat tptp.set_Product_unit))) (=> (@ (@ tptp.member348563419383025609t_unit (@ (@ tptp.produc3434450474625521892t_unit A2) B)) (@ (@ tptp.produc5506539147108004339t_unit A) B4)) (not (=> (@ (@ tptp.member_nat A2) A) (not (@ (@ tptp.member_Product_unit B) (@ B4 A2))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.nat) (A tptp.set_int) (B4 (-> tptp.int tptp.set_nat))) (=> (@ (@ tptp.member216504246829706758nt_nat (@ (@ tptp.product_Pair_int_nat A2) B)) (@ (@ tptp.produc1456381018704787142nt_nat A) B4)) (not (=> (@ (@ tptp.member_int A2) A) (not (@ (@ tptp.member_nat B) (@ B4 A2))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B Bool) (A tptp.set_int) (B4 (-> tptp.int tptp.set_o))) (=> (@ (@ tptp.member4489920277610959864_int_o (@ (@ tptp.product_Pair_int_o A2) B)) (@ (@ tptp.product_Sigma_int_o A) B4)) (not (=> (@ (@ tptp.member_int A2) A) (not (@ (@ tptp.member_o B) (@ B4 A2))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.product_unit) (A tptp.set_int) (B4 (-> tptp.int tptp.set_Product_unit))) (=> (@ (@ tptp.member6688357403439981677t_unit (@ (@ tptp.produc550872421827702152t_unit A2) B)) (@ (@ tptp.produc2622961094310184599t_unit A) B4)) (not (=> (@ (@ tptp.member_int A2) A) (not (@ (@ tptp.member_Product_unit B) (@ B4 A2))))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (B tptp.nat) (A tptp.set_o) (B4 (-> Bool tptp.set_nat))) (=> (@ (@ tptp.member2802428098988154798_o_nat (@ (@ tptp.product_Pair_o_nat A2) B)) (@ (@ tptp.product_Sigma_o_nat A) B4)) (not (=> (@ (@ tptp.member_o A2) A) (not (@ (@ tptp.member_nat B) (@ B4 A2))))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (B tptp.int) (A tptp.set_o) (B4 (-> Bool tptp.set_int))) (=> (@ (@ tptp.member7847949116333733898_o_int (@ (@ tptp.product_Pair_o_int A2) B)) (@ (@ tptp.product_Sigma_o_int A) B4)) (not (=> (@ (@ tptp.member_o A2) A) (not (@ (@ tptp.member_int B) (@ B4 A2))))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (B Bool) (A tptp.set_o) (B4 (-> Bool tptp.set_o))) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) B)) (@ (@ tptp.product_Sigma_o_o A) B4)) (not (=> (@ (@ tptp.member_o A2) A) (not (@ (@ tptp.member_o B) (@ B4 A2))))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (B tptp.product_unit) (A tptp.set_o) (B4 (-> Bool tptp.set_Product_unit))) (=> (@ (@ tptp.member9215336023991391429t_unit (@ (@ tptp.produc3901946521647900940t_unit A2) B)) (@ (@ tptp.produc411009820408249917t_unit A) B4)) (not (=> (@ (@ tptp.member_o A2) A) (not (@ (@ tptp.member_Product_unit B) (@ B4 A2))))))))
% 5.61/5.91 (assert (forall ((E tptp.set_Pr1261947904930325089at_nat) (Vi tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.image_nat_nat (@ tptp.transi6264000038957366511cl_nat E)) Vi)) Vi) (@ (@ tptp.image_nat_nat (@ tptp.transi2905341329935302413cl_nat E)) Vi))))
% 5.61/5.91 (assert (forall ((U tptp.nat) (V tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat U) V)) (@ tptp.transi2905341329935302413cl_nat R3)) (=> (not (= U V)) (not (forall ((Vh tptp.nat)) (=> (not (= U Vh)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat U) Vh)) R3) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Vh) V)) (@ tptp.transi2905341329935302413cl_nat R3)))))))))))
% 5.61/5.91 (assert (forall ((U tptp.int) (V tptp.int) (R3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int U) V)) (@ tptp.transi2902850859426252137cl_int R3)) (=> (not (= U V)) (not (forall ((Vh tptp.int)) (=> (not (= U Vh)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int U) Vh)) R3) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Vh) V)) (@ tptp.transi2902850859426252137cl_int R3)))))))))))
% 5.61/5.91 (assert (forall ((A1 tptp.nat) (A22 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A1) A22)) (@ tptp.transi2905341329935302413cl_nat R2)) (=> (not (= A22 A1)) (not (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A1) B2)) (@ tptp.transi2905341329935302413cl_nat R2)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B2) A22)) R2)))))))))
% 5.61/5.91 (assert (forall ((A1 tptp.int) (A22 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A1) A22)) (@ tptp.transi2902850859426252137cl_int R2)) (=> (not (= A22 A1)) (not (forall ((B2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A1) B2)) (@ tptp.transi2902850859426252137cl_int R2)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B2) A22)) R2)))))))))
% 5.61/5.91 (assert (forall ((A1 tptp.nat) (A22 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A1) A22)) (@ tptp.transi2905341329935302413cl_nat R2)) (or (exists ((A6 tptp.nat)) (and (= A1 A6) (= A22 A6))) (exists ((A6 tptp.nat) (B6 tptp.nat) (C4 tptp.nat)) (and (= A1 A6) (= A22 C4) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A6) B6)) (@ tptp.transi2905341329935302413cl_nat R2)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B6) C4)) R2)))))))
% 5.61/5.91 (assert (forall ((A1 tptp.int) (A22 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A1) A22)) (@ tptp.transi2902850859426252137cl_int R2)) (or (exists ((A6 tptp.int)) (and (= A1 A6) (= A22 A6))) (exists ((A6 tptp.int) (B6 tptp.int) (C4 tptp.int)) (and (= A1 A6) (= A22 C4) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A6) B6)) (@ tptp.transi2902850859426252137cl_int R2)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B6) C4)) R2)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) A2)) (@ tptp.transi2905341329935302413cl_nat R2))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) A2)) (@ tptp.transi2902850859426252137cl_int R2))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.transi2905341329935302413cl_nat R2))) (let ((_let_2 (@ tptp.product_Pair_nat_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 B)) _let_1) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) C)) R2) (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 C)) _let_1)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (C tptp.int)) (let ((_let_1 (@ tptp.transi2902850859426252137cl_int R2))) (let ((_let_2 (@ tptp.product_Pair_int_int A2))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 B)) _let_1) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) C)) R2) (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 C)) _let_1)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) (@ tptp.transi2905341329935302413cl_nat R2)) (=> (not (= A2 B)) (not (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) Y2)) (@ tptp.transi2905341329935302413cl_nat R2)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) B)) R2)))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) (@ tptp.transi2902850859426252137cl_int R2)) (=> (not (= A2 B)) (not (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) Y2)) (@ tptp.transi2902850859426252137cl_int R2)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y2) B)) R2)))))))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (Y tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.transi2905341329935302413cl_nat R2))) (let ((_let_2 (@ tptp.product_Pair_nat_nat X))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 Y)) _let_1) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y) Z)) _let_1) (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 Z)) _let_1)))))))
% 5.61/5.91 (assert (forall ((X tptp.int) (Y tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (Z tptp.int)) (let ((_let_1 (@ tptp.transi2902850859426252137cl_int R2))) (let ((_let_2 (@ tptp.product_Pair_int_int X))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 Y)) _let_1) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y) Z)) _let_1) (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 Z)) _let_1)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) (@ tptp.transi2905341329935302413cl_nat R2)) (=> (@ P A2) (=> (forall ((Y2 tptp.nat) (Z3 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) Y2)) (@ tptp.transi2905341329935302413cl_nat R2)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Z3)) R2) (=> (@ P Y2) (@ P Z3))))) (@ P B))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) (@ tptp.transi2902850859426252137cl_int R2)) (=> (@ P A2) (=> (forall ((Y2 tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) Y2)) (@ tptp.transi2902850859426252137cl_int R2)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y2) Z3)) R2) (=> (@ P Y2) (@ P Z3))))) (@ P B))))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (Z tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Z)) (@ tptp.transi2905341329935302413cl_nat R2)) (=> (not (= X Z)) (not (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y2)) R2) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Z)) (@ tptp.transi2905341329935302413cl_nat R2))))))))))
% 5.61/5.91 (assert (forall ((X tptp.int) (Z tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Z)) (@ tptp.transi2902850859426252137cl_int R2)) (=> (not (= X Z)) (not (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y2)) R2) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y2) Z)) (@ tptp.transi2902850859426252137cl_int R2))))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) (@ tptp.transi2905341329935302413cl_nat R2)) (=> (@ P B) (=> (forall ((Y2 tptp.nat) (Z3 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Z3)) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Z3) B)) (@ tptp.transi2905341329935302413cl_nat R2)) (=> (@ P Z3) (@ P Y2))))) (@ P A2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) (@ tptp.transi2902850859426252137cl_int R2)) (=> (@ P B) (=> (forall ((Y2 tptp.int) (Z3 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y2) Z3)) R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Z3) B)) (@ tptp.transi2902850859426252137cl_int R2)) (=> (@ P Z3) (@ P Y2))))) (@ P A2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.transi2905341329935302413cl_nat R2))) (let ((_let_2 (@ tptp.product_Pair_nat_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 B)) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) C)) _let_1) (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 C)) _let_1)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (C tptp.int)) (let ((_let_1 (@ tptp.transi2902850859426252137cl_int R2))) (let ((_let_2 (@ tptp.product_Pair_int_int A2))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 B)) R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) C)) _let_1) (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 C)) _let_1)))))))
% 5.61/5.91 (assert (forall ((Ax tptp.heap_e7401611519738050253t_unit) (Ay tptp.set_nat) (Bx tptp.heap_e7401611519738050253t_unit) (By tptp.set_nat) (R2 tptp.set_Pr719794911490849221et_nat) (P (-> tptp.heap_e7401611519738050253t_unit tptp.set_nat Bool))) (=> (@ (@ tptp.member6099555550032318734et_nat (@ (@ tptp.produc8199053930788261021et_nat (@ (@ tptp.produc7507926704131184380et_nat Ax) Ay)) (@ (@ tptp.produc7507926704131184380et_nat Bx) By))) (@ tptp.transi6919426408697524543et_nat R2)) (=> (@ (@ P Ax) Ay) (=> (forall ((A4 tptp.heap_e7401611519738050253t_unit) (B2 tptp.set_nat) (Aa tptp.heap_e7401611519738050253t_unit) (Ba tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat A4) B2))) (=> (@ (@ tptp.member6099555550032318734et_nat (@ (@ tptp.produc8199053930788261021et_nat (@ (@ tptp.produc7507926704131184380et_nat Ax) Ay)) _let_1)) (@ tptp.transi6919426408697524543et_nat R2)) (=> (@ (@ tptp.member6099555550032318734et_nat (@ (@ tptp.produc8199053930788261021et_nat _let_1) (@ (@ tptp.produc7507926704131184380et_nat Aa) Ba))) R2) (=> (@ (@ P A4) B2) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 5.61/5.91 (assert (forall ((Ax tptp.nat) (Ay tptp.nat) (Bx tptp.nat) (By tptp.nat) (R2 tptp.set_Pr8693737435421807431at_nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat Ax) Ay)) (@ (@ tptp.product_Pair_nat_nat Bx) By))) (@ tptp.transi8609417484261754244at_nat R2)) (=> (@ (@ P Ax) Ay) (=> (forall ((A4 tptp.nat) (B2 tptp.nat) (Aa tptp.nat) (Ba tptp.nat)) (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat A4) B2))) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat Ax) Ay)) _let_1)) (@ tptp.transi8609417484261754244at_nat R2)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat _let_1) (@ (@ tptp.product_Pair_nat_nat Aa) Ba))) R2) (=> (@ (@ P A4) B2) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 5.61/5.91 (assert (forall ((Ax tptp.int) (Ay tptp.int) (Bx tptp.int) (By tptp.int) (R2 tptp.set_Pr2560585780119916871nt_int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.member8566619992076573584nt_int (@ (@ tptp.produc3646306378393792727nt_int (@ (@ tptp.product_Pair_int_int Ax) Ay)) (@ (@ tptp.product_Pair_int_int Bx) By))) (@ tptp.transi5430920176653612092nt_int R2)) (=> (@ (@ P Ax) Ay) (=> (forall ((A4 tptp.int) (B2 tptp.int) (Aa tptp.int) (Ba tptp.int)) (let ((_let_1 (@ (@ tptp.product_Pair_int_int A4) B2))) (=> (@ (@ tptp.member8566619992076573584nt_int (@ (@ tptp.produc3646306378393792727nt_int (@ (@ tptp.product_Pair_int_int Ax) Ay)) _let_1)) (@ tptp.transi5430920176653612092nt_int R2)) (=> (@ (@ tptp.member8566619992076573584nt_int (@ (@ tptp.produc3646306378393792727nt_int _let_1) (@ (@ tptp.product_Pair_int_int Aa) Ba))) R2) (=> (@ (@ P A4) B2) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 5.61/5.91 (assert (forall ((Ax (-> tptp.produc3658429121746597890et_nat Bool)) (Ay tptp.produc3658429121746597890et_nat) (Bx (-> tptp.produc3658429121746597890et_nat Bool)) (By tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr7928877670098842301et_nat) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat (@ (@ tptp.produc5001842942810119800et_nat Ax) Ay)) (@ (@ tptp.produc5001842942810119800et_nat Bx) By))) (@ tptp.transi2414916928880341691et_nat R2)) (=> (@ (@ P Ax) Ay) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3658429121746597890et_nat) (Aa (-> tptp.produc3658429121746597890et_nat Bool)) (Ba tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ (@ tptp.produc5001842942810119800et_nat A4) B2))) (=> (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat (@ (@ tptp.produc5001842942810119800et_nat Ax) Ay)) _let_1)) (@ tptp.transi2414916928880341691et_nat R2)) (=> (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat _let_1) (@ (@ tptp.produc5001842942810119800et_nat Aa) Ba))) R2) (=> (@ (@ P A4) B2) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 5.61/5.91 (assert (forall ((Ax (-> tptp.produc3658429121746597890et_nat Bool)) (Ay tptp.produc3925858234332021118et_nat) (Bx (-> tptp.produc3658429121746597890et_nat Bool)) (By tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr3444600963470892981et_nat) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool))) (=> (@ (@ tptp.member6341495586645257982et_nat (@ (@ tptp.produc1940133919992309389et_nat (@ (@ tptp.produc2245416461498447860et_nat Ax) Ay)) (@ (@ tptp.produc2245416461498447860et_nat Bx) By))) (@ tptp.transi344104063936286263et_nat R2)) (=> (@ (@ P Ax) Ay) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3925858234332021118et_nat) (Aa (-> tptp.produc3658429121746597890et_nat Bool)) (Ba tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ (@ tptp.produc2245416461498447860et_nat A4) B2))) (=> (@ (@ tptp.member6341495586645257982et_nat (@ (@ tptp.produc1940133919992309389et_nat (@ (@ tptp.produc2245416461498447860et_nat Ax) Ay)) _let_1)) (@ tptp.transi344104063936286263et_nat R2)) (=> (@ (@ tptp.member6341495586645257982et_nat (@ (@ tptp.produc1940133919992309389et_nat _let_1) (@ (@ tptp.produc2245416461498447860et_nat Aa) Ba))) R2) (=> (@ (@ P A4) B2) (@ (@ P Aa) Ba)))))) (@ (@ P Bx) By))))))
% 5.61/5.91 (assert (forall ((Xa tptp.heap_e7401611519738050253t_unit) (Xb tptp.set_nat) (Za tptp.heap_e7401611519738050253t_unit) (Zb tptp.set_nat) (R2 tptp.set_Pr719794911490849221et_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat Za) Zb))) (let ((_let_2 (@ (@ tptp.produc7507926704131184380et_nat Xa) Xb))) (=> (@ (@ tptp.member6099555550032318734et_nat (@ (@ tptp.produc8199053930788261021et_nat _let_2) _let_1)) (@ tptp.transi6919426408697524543et_nat R2)) (=> (not (= _let_2 _let_1)) (not (forall ((A4 tptp.heap_e7401611519738050253t_unit) (B2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat A4) B2))) (=> (@ (@ tptp.member6099555550032318734et_nat (@ (@ tptp.produc8199053930788261021et_nat (@ (@ tptp.produc7507926704131184380et_nat Xa) Xb)) _let_1)) R2) (not (@ (@ tptp.member6099555550032318734et_nat (@ (@ tptp.produc8199053930788261021et_nat _let_1) (@ (@ tptp.produc7507926704131184380et_nat Za) Zb))) (@ tptp.transi6919426408697524543et_nat R2)))))))))))))
% 5.61/5.91 (assert (forall ((Xa tptp.nat) (Xb tptp.nat) (Za tptp.nat) (Zb tptp.nat) (R2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat Za) Zb))) (let ((_let_2 (@ (@ tptp.product_Pair_nat_nat Xa) Xb))) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat _let_2) _let_1)) (@ tptp.transi8609417484261754244at_nat R2)) (=> (not (= _let_2 _let_1)) (not (forall ((A4 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat A4) B2))) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat Xa) Xb)) _let_1)) R2) (not (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat _let_1) (@ (@ tptp.product_Pair_nat_nat Za) Zb))) (@ tptp.transi8609417484261754244at_nat R2)))))))))))))
% 5.61/5.91 (assert (forall ((Xa tptp.int) (Xb tptp.int) (Za tptp.int) (Zb tptp.int) (R2 tptp.set_Pr2560585780119916871nt_int)) (let ((_let_1 (@ (@ tptp.product_Pair_int_int Za) Zb))) (let ((_let_2 (@ (@ tptp.product_Pair_int_int Xa) Xb))) (=> (@ (@ tptp.member8566619992076573584nt_int (@ (@ tptp.produc3646306378393792727nt_int _let_2) _let_1)) (@ tptp.transi5430920176653612092nt_int R2)) (=> (not (= _let_2 _let_1)) (not (forall ((A4 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ (@ tptp.product_Pair_int_int A4) B2))) (=> (@ (@ tptp.member8566619992076573584nt_int (@ (@ tptp.produc3646306378393792727nt_int (@ (@ tptp.product_Pair_int_int Xa) Xb)) _let_1)) R2) (not (@ (@ tptp.member8566619992076573584nt_int (@ (@ tptp.produc3646306378393792727nt_int _let_1) (@ (@ tptp.product_Pair_int_int Za) Zb))) (@ tptp.transi5430920176653612092nt_int R2)))))))))))))
% 5.61/5.91 (assert (forall ((Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat) (Za (-> tptp.produc3658429121746597890et_nat Bool)) (Zb tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr7928877670098842301et_nat)) (let ((_let_1 (@ (@ tptp.produc5001842942810119800et_nat Za) Zb))) (let ((_let_2 (@ (@ tptp.produc5001842942810119800et_nat Xa) Xb))) (=> (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat _let_2) _let_1)) (@ tptp.transi2414916928880341691et_nat R2)) (=> (not (= _let_2 _let_1)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ (@ tptp.produc5001842942810119800et_nat A4) B2))) (=> (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat (@ (@ tptp.produc5001842942810119800et_nat Xa) Xb)) _let_1)) R2) (not (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat _let_1) (@ (@ tptp.produc5001842942810119800et_nat Za) Zb))) (@ tptp.transi2414916928880341691et_nat R2)))))))))))))
% 5.61/5.91 (assert (forall ((Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3925858234332021118et_nat) (Za (-> tptp.produc3658429121746597890et_nat Bool)) (Zb tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr3444600963470892981et_nat)) (let ((_let_1 (@ (@ tptp.produc2245416461498447860et_nat Za) Zb))) (let ((_let_2 (@ (@ tptp.produc2245416461498447860et_nat Xa) Xb))) (=> (@ (@ tptp.member6341495586645257982et_nat (@ (@ tptp.produc1940133919992309389et_nat _let_2) _let_1)) (@ tptp.transi344104063936286263et_nat R2)) (=> (not (= _let_2 _let_1)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ (@ tptp.produc2245416461498447860et_nat A4) B2))) (=> (@ (@ tptp.member6341495586645257982et_nat (@ (@ tptp.produc1940133919992309389et_nat (@ (@ tptp.produc2245416461498447860et_nat Xa) Xb)) _let_1)) R2) (not (@ (@ tptp.member6341495586645257982et_nat (@ (@ tptp.produc1940133919992309389et_nat _let_1) (@ (@ tptp.produc2245416461498447860et_nat Za) Zb))) (@ tptp.transi344104063936286263et_nat R2)))))))))))))
% 5.61/5.91 (assert (forall ((Ax tptp.heap_e7401611519738050253t_unit) (Ay tptp.set_nat) (Bx tptp.heap_e7401611519738050253t_unit) (By tptp.set_nat) (R2 tptp.set_Pr719794911490849221et_nat) (P (-> tptp.heap_e7401611519738050253t_unit tptp.set_nat Bool))) (=> (@ (@ tptp.member6099555550032318734et_nat (@ (@ tptp.produc8199053930788261021et_nat (@ (@ tptp.produc7507926704131184380et_nat Ax) Ay)) (@ (@ tptp.produc7507926704131184380et_nat Bx) By))) (@ tptp.transi6919426408697524543et_nat R2)) (=> (@ (@ P Bx) By) (=> (forall ((A4 tptp.heap_e7401611519738050253t_unit) (B2 tptp.set_nat) (Aa tptp.heap_e7401611519738050253t_unit) (Ba tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat Aa) Ba))) (=> (@ (@ tptp.member6099555550032318734et_nat (@ (@ tptp.produc8199053930788261021et_nat (@ (@ tptp.produc7507926704131184380et_nat A4) B2)) _let_1)) R2) (=> (@ (@ tptp.member6099555550032318734et_nat (@ (@ tptp.produc8199053930788261021et_nat _let_1) (@ (@ tptp.produc7507926704131184380et_nat Bx) By))) (@ tptp.transi6919426408697524543et_nat R2)) (=> (@ (@ P Aa) Ba) (@ (@ P A4) B2)))))) (@ (@ P Ax) Ay))))))
% 5.61/5.91 (assert (forall ((Ax tptp.nat) (Ay tptp.nat) (Bx tptp.nat) (By tptp.nat) (R2 tptp.set_Pr8693737435421807431at_nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat Ax) Ay)) (@ (@ tptp.product_Pair_nat_nat Bx) By))) (@ tptp.transi8609417484261754244at_nat R2)) (=> (@ (@ P Bx) By) (=> (forall ((A4 tptp.nat) (B2 tptp.nat) (Aa tptp.nat) (Ba tptp.nat)) (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat Aa) Ba))) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A4) B2)) _let_1)) R2) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat _let_1) (@ (@ tptp.product_Pair_nat_nat Bx) By))) (@ tptp.transi8609417484261754244at_nat R2)) (=> (@ (@ P Aa) Ba) (@ (@ P A4) B2)))))) (@ (@ P Ax) Ay))))))
% 5.61/5.91 (assert (forall ((Ax tptp.int) (Ay tptp.int) (Bx tptp.int) (By tptp.int) (R2 tptp.set_Pr2560585780119916871nt_int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.member8566619992076573584nt_int (@ (@ tptp.produc3646306378393792727nt_int (@ (@ tptp.product_Pair_int_int Ax) Ay)) (@ (@ tptp.product_Pair_int_int Bx) By))) (@ tptp.transi5430920176653612092nt_int R2)) (=> (@ (@ P Bx) By) (=> (forall ((A4 tptp.int) (B2 tptp.int) (Aa tptp.int) (Ba tptp.int)) (let ((_let_1 (@ (@ tptp.product_Pair_int_int Aa) Ba))) (=> (@ (@ tptp.member8566619992076573584nt_int (@ (@ tptp.produc3646306378393792727nt_int (@ (@ tptp.product_Pair_int_int A4) B2)) _let_1)) R2) (=> (@ (@ tptp.member8566619992076573584nt_int (@ (@ tptp.produc3646306378393792727nt_int _let_1) (@ (@ tptp.product_Pair_int_int Bx) By))) (@ tptp.transi5430920176653612092nt_int R2)) (=> (@ (@ P Aa) Ba) (@ (@ P A4) B2)))))) (@ (@ P Ax) Ay))))))
% 5.61/5.91 (assert (forall ((Ax (-> tptp.produc3658429121746597890et_nat Bool)) (Ay tptp.produc3658429121746597890et_nat) (Bx (-> tptp.produc3658429121746597890et_nat Bool)) (By tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr7928877670098842301et_nat) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat (@ (@ tptp.produc5001842942810119800et_nat Ax) Ay)) (@ (@ tptp.produc5001842942810119800et_nat Bx) By))) (@ tptp.transi2414916928880341691et_nat R2)) (=> (@ (@ P Bx) By) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3658429121746597890et_nat) (Aa (-> tptp.produc3658429121746597890et_nat Bool)) (Ba tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ (@ tptp.produc5001842942810119800et_nat Aa) Ba))) (=> (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat (@ (@ tptp.produc5001842942810119800et_nat A4) B2)) _let_1)) R2) (=> (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat _let_1) (@ (@ tptp.produc5001842942810119800et_nat Bx) By))) (@ tptp.transi2414916928880341691et_nat R2)) (=> (@ (@ P Aa) Ba) (@ (@ P A4) B2)))))) (@ (@ P Ax) Ay))))))
% 5.61/5.91 (assert (forall ((Ax (-> tptp.produc3658429121746597890et_nat Bool)) (Ay tptp.produc3925858234332021118et_nat) (Bx (-> tptp.produc3658429121746597890et_nat Bool)) (By tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr3444600963470892981et_nat) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool))) (=> (@ (@ tptp.member6341495586645257982et_nat (@ (@ tptp.produc1940133919992309389et_nat (@ (@ tptp.produc2245416461498447860et_nat Ax) Ay)) (@ (@ tptp.produc2245416461498447860et_nat Bx) By))) (@ tptp.transi344104063936286263et_nat R2)) (=> (@ (@ P Bx) By) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3925858234332021118et_nat) (Aa (-> tptp.produc3658429121746597890et_nat Bool)) (Ba tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ (@ tptp.produc2245416461498447860et_nat Aa) Ba))) (=> (@ (@ tptp.member6341495586645257982et_nat (@ (@ tptp.produc1940133919992309389et_nat (@ (@ tptp.produc2245416461498447860et_nat A4) B2)) _let_1)) R2) (=> (@ (@ tptp.member6341495586645257982et_nat (@ (@ tptp.produc1940133919992309389et_nat _let_1) (@ (@ tptp.produc2245416461498447860et_nat Bx) By))) (@ tptp.transi344104063936286263et_nat R2)) (=> (@ (@ P Aa) Ba) (@ (@ P A4) B2)))))) (@ (@ P Ax) Ay))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit)) (= (@ (@ tptp.sup_su793286257634532545t_unit A) tptp.bot_bo3957492148770167129t_unit) A)))
% 5.61/5.91 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o A) tptp.bot_bot_set_o) A)))
% 5.61/5.91 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A) tptp.bot_bot_set_nat) A)))
% 5.61/5.91 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A) tptp.bot_bot_set_int) A)))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.sup_su5209123915105501825_nat_o A) tptp.bot_bo7824918357723582233_nat_o) A)))
% 5.61/5.91 (assert (forall ((B4 tptp.set_Product_unit)) (= (@ (@ tptp.sup_su793286257634532545t_unit tptp.bot_bo3957492148770167129t_unit) B4) B4)))
% 5.61/5.91 (assert (forall ((B4 tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o tptp.bot_bot_set_o) B4) B4)))
% 5.61/5.91 (assert (forall ((B4 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.bot_bot_set_nat) B4) B4)))
% 5.61/5.91 (assert (forall ((B4 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int tptp.bot_bot_set_int) B4) B4)))
% 5.61/5.91 (assert (forall ((B4 tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.sup_su5209123915105501825_nat_o tptp.bot_bo7824918357723582233_nat_o) B4) B4)))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (= (= (@ (@ tptp.inf_in4660618365625256667t_unit A) B4) tptp.bot_bo3957492148770167129t_unit) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) A) (forall ((Y3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit Y3) B4) (not (= X2 Y3)))))))))
% 5.61/5.91 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o A) B4) tptp.bot_bot_set_o) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A) (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) B4) (= X2 (not Y3)))))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A) B4) tptp.bot_bot_set_nat) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) B4) (not (= X2 Y3)))))))))
% 5.61/5.91 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int A) B4) tptp.bot_bot_set_int) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A) (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) B4) (not (= X2 Y3)))))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (= (= (@ (@ tptp.inf_in1906310914598751387_nat_o A) B4) tptp.bot_bo7824918357723582233_nat_o) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X2) A) (forall ((Y3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y3) B4) (not (= X2 Y3)))))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit A) tptp.bot_bo3957492148770167129t_unit) tptp.bot_bo3957492148770167129t_unit)))
% 5.61/5.91 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o A) tptp.bot_bot_set_o) tptp.bot_bot_set_o)))
% 5.61/5.91 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)))
% 5.61/5.91 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A) tptp.bot_bot_set_int) tptp.bot_bot_set_int)))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o A) tptp.bot_bo7824918357723582233_nat_o) tptp.bot_bo7824918357723582233_nat_o)))
% 5.61/5.91 (assert (forall ((B4 tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit tptp.bot_bo3957492148770167129t_unit) B4) tptp.bot_bo3957492148770167129t_unit)))
% 5.61/5.91 (assert (forall ((B4 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o tptp.bot_bot_set_o) B4) tptp.bot_bot_set_o)))
% 5.61/5.91 (assert (forall ((B4 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.bot_bot_set_nat) B4) tptp.bot_bot_set_nat)))
% 5.61/5.91 (assert (forall ((B4 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int tptp.bot_bot_set_int) B4) tptp.bot_bot_set_int)))
% 5.61/5.91 (assert (forall ((B4 tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o tptp.bot_bo7824918357723582233_nat_o) B4) tptp.bot_bo7824918357723582233_nat_o)))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (= (= (@ (@ tptp.inf_in4660618365625256667t_unit A) B4) tptp.bot_bo3957492148770167129t_unit) (forall ((X2 tptp.product_unit)) (let ((_let_1 (@ tptp.member_Product_unit X2))) (=> (@ _let_1 A) (not (@ _let_1 B4))))))))
% 5.61/5.91 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o A) B4) tptp.bot_bot_set_o) (forall ((X2 Bool)) (let ((_let_1 (@ tptp.member_o X2))) (=> (@ _let_1 A) (not (@ _let_1 B4))))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A) B4) tptp.bot_bot_set_nat) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ _let_1 A) (not (@ _let_1 B4))))))))
% 5.61/5.91 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int A) B4) tptp.bot_bot_set_int) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ _let_1 A) (not (@ _let_1 B4))))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (= (= (@ (@ tptp.inf_in1906310914598751387_nat_o A) B4) tptp.bot_bo7824918357723582233_nat_o) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X2))) (=> (@ _let_1 A) (not (@ _let_1 B4))))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (=> (forall ((X3 tptp.product_unit)) (let ((_let_1 (@ tptp.member_Product_unit X3))) (=> (@ _let_1 A) (not (@ _let_1 B4))))) (= (@ (@ tptp.inf_in4660618365625256667t_unit A) B4) tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.91 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (=> (forall ((X3 Bool)) (let ((_let_1 (@ tptp.member_o X3))) (=> (@ _let_1 A) (not (@ _let_1 B4))))) (= (@ (@ tptp.inf_inf_set_o A) B4) tptp.bot_bot_set_o))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 A) (not (@ _let_1 B4))))) (= (@ (@ tptp.inf_inf_set_nat A) B4) tptp.bot_bot_set_nat))))
% 5.61/5.91 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 A) (not (@ _let_1 B4))))) (= (@ (@ tptp.inf_inf_set_int A) B4) tptp.bot_bot_set_int))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X3))) (=> (@ _let_1 A) (not (@ _let_1 B4))))) (= (@ (@ tptp.inf_in1906310914598751387_nat_o A) B4) tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_Product_unit) (B tptp.set_Product_unit)) (=> (forall ((X3 tptp.product_unit)) (let ((_let_1 (@ tptp.member_Product_unit X3))) (=> (@ _let_1 A2) (not (@ _let_1 B))))) (= (@ (@ tptp.inf_in4660618365625256667t_unit A2) B) tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_o) (B tptp.set_o)) (=> (forall ((X3 Bool)) (let ((_let_1 (@ tptp.member_o X3))) (=> (@ _let_1 A2) (not (@ _let_1 B))))) (= (@ (@ tptp.inf_inf_set_o A2) B) tptp.bot_bot_set_o))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 A2) (not (@ _let_1 B))))) (= (@ (@ tptp.inf_inf_set_nat A2) B) tptp.bot_bot_set_nat))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_int) (B tptp.set_int)) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 A2) (not (@ _let_1 B))))) (= (@ (@ tptp.inf_inf_set_int A2) B) tptp.bot_bot_set_int))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X3))) (=> (@ _let_1 A2) (not (@ _let_1 B))))) (= (@ (@ tptp.inf_in1906310914598751387_nat_o A2) B) tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.inf_in1906310914598751387_nat_o A))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ tptp.insert5175938949040314269_nat_o A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B4)))) (let ((_let_5 (@ (@ tptp.member6576561426505652726_nat_o A2) A))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ tptp.insert_int A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B4)))) (let ((_let_5 (@ (@ tptp.member_int A2) A))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.inf_inf_set_o A))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ tptp.insert_o A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B4)))) (let ((_let_5 (@ (@ tptp.member_o A2) A))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.inf_in4660618365625256667t_unit A))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ tptp.insert_Product_unit A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B4)))) (let ((_let_5 (@ (@ tptp.member_Product_unit A2) A))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ tptp.insert_nat A2))) (let ((_let_4 (@ _let_1 (@ _let_3 B4)))) (let ((_let_5 (@ (@ tptp.member_nat A2) A))) (and (=> _let_5 (= _let_4 (@ _let_3 _let_2))) (=> (not _let_5) (= _let_4 _let_2))))))))))
% 5.61/5.91 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (C5 tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o B4) C5))) (let ((_let_2 (@ tptp.insert5175938949040314269_nat_o A2))) (let ((_let_3 (@ (@ tptp.inf_in1906310914598751387_nat_o (@ _let_2 B4)) C5))) (let ((_let_4 (@ (@ tptp.member6576561426505652726_nat_o A2) C5))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (C5 tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ (@ tptp.inf_inf_set_int B4) C5))) (let ((_let_2 (@ tptp.insert_int A2))) (let ((_let_3 (@ (@ tptp.inf_inf_set_int (@ _let_2 B4)) C5))) (let ((_let_4 (@ (@ tptp.member_int A2) C5))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 5.61/5.91 (assert (forall ((A2 Bool) (C5 tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ (@ tptp.inf_inf_set_o B4) C5))) (let ((_let_2 (@ tptp.insert_o A2))) (let ((_let_3 (@ (@ tptp.inf_inf_set_o (@ _let_2 B4)) C5))) (let ((_let_4 (@ (@ tptp.member_o A2) C5))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (C5 tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ (@ tptp.inf_in4660618365625256667t_unit B4) C5))) (let ((_let_2 (@ tptp.insert_Product_unit A2))) (let ((_let_3 (@ (@ tptp.inf_in4660618365625256667t_unit (@ _let_2 B4)) C5))) (let ((_let_4 (@ (@ tptp.member_Product_unit A2) C5))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (C5 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat B4) C5))) (let ((_let_2 (@ tptp.insert_nat A2))) (let ((_let_3 (@ (@ tptp.inf_inf_set_nat (@ _let_2 B4)) C5))) (let ((_let_4 (@ (@ tptp.member_nat A2) C5))) (and (=> _let_4 (= _let_3 (@ _let_2 _let_1))) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 5.61/5.91 (assert (forall ((R2 tptp.set_Pr3948176798113811640et_nat) (S2 tptp.set_Pr3948176798113811640et_nat)) (=> (forall ((X3 tptp.heap_e7401611519738050253t_unit) (Y2 tptp.set_nat)) (let ((_let_1 (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat X3) Y2)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le8090042543978450200et_nat R2) S2))))
% 5.61/5.91 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le3146513528884898305at_nat R2) S2))))
% 5.61/5.91 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (S2 tptp.set_Pr958786334691620121nt_int)) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y2)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le2843351958646193337nt_int R2) S2))))
% 5.61/5.91 (assert (forall ((R2 tptp.set_Pr3286484037609594932et_nat) (S2 tptp.set_Pr3286484037609594932et_nat)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X3) Y2)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le5966269811547037844et_nat R2) S2))))
% 5.61/5.91 (assert (forall ((R2 tptp.set_Pr8536935166611901872et_nat) (S2 tptp.set_Pr8536935166611901872et_nat)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X3) Y2)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le4763372923235995152et_nat R2) S2))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_Product_unit)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A2) tptp.bot_bo3957492148770167129t_unit) (= A2 tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A2) tptp.bot_bot_set_o) (= A2 tptp.bot_bot_set_o))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int) (= A2 tptp.bot_bot_set_int))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A2) tptp.bot_bo7824918357723582233_nat_o) (= A2 tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.91 (assert (forall ((A2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) tptp.bot_bot_filter_nat) (= A2 tptp.bot_bot_filter_nat))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat) (= A2 tptp.bot_bot_set_nat))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.bot_bot_nat) (= A2 tptp.bot_bot_nat))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_Product_unit)) (= (@ (@ tptp.ord_le3507040750410214029t_unit A2) tptp.bot_bo3957492148770167129t_unit) (= A2 tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o A2) tptp.bot_bot_set_o) (= A2 tptp.bot_bot_set_o))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int) (= A2 tptp.bot_bot_set_int))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.ord_le2965882846123202637_nat_o A2) tptp.bot_bo7824918357723582233_nat_o) (= A2 tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.91 (assert (forall ((A2 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat A2) tptp.bot_bot_filter_nat) (= A2 tptp.bot_bot_filter_nat))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat) (= A2 tptp.bot_bot_set_nat))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A2) tptp.bot_bot_nat) (= A2 tptp.bot_bot_nat))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_Product_unit)) (@ (@ tptp.ord_le3507040750410214029t_unit tptp.bot_bo3957492148770167129t_unit) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.set_o)) (@ (@ tptp.ord_less_eq_set_o tptp.bot_bot_set_o) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.set_Pr4532377907799695533_nat_o)) (@ (@ tptp.ord_le2965882846123202637_nat_o tptp.bot_bo7824918357723582233_nat_o) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat tptp.bot_bot_filter_nat) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A2)))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit)) (=> (forall ((X3 tptp.product_unit)) (not (@ (@ tptp.member_Product_unit X3) A))) (@ (@ tptp.ord_le3507040750410214029t_unit A) tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.91 (assert (forall ((A tptp.set_o)) (=> (forall ((X3 Bool)) (not (@ (@ tptp.member_o X3) A))) (@ (@ tptp.ord_less_eq_set_o A) tptp.bot_bot_set_o))))
% 5.61/5.91 (assert (forall ((A tptp.set_int)) (=> (forall ((X3 tptp.int)) (not (@ (@ tptp.member_int X3) A))) (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member6576561426505652726_nat_o X3) A))) (@ (@ tptp.ord_le2965882846123202637_nat_o A) tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (not (@ (@ tptp.member_nat X3) A))) (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (X4 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o X) A) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o X4) A) (@ (@ tptp.ord_le2965882846123202637_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) X4)) A)))))
% 5.61/5.91 (assert (forall ((X tptp.int) (A tptp.set_int) (X4 tptp.set_int)) (=> (@ (@ tptp.member_int X) A) (=> (@ (@ tptp.ord_less_eq_set_int X4) A) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int X) X4)) A)))))
% 5.61/5.91 (assert (forall ((X Bool) (A tptp.set_o) (X4 tptp.set_o)) (=> (@ (@ tptp.member_o X) A) (=> (@ (@ tptp.ord_less_eq_set_o X4) A) (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.insert_o X) X4)) A)))))
% 5.61/5.91 (assert (forall ((X tptp.product_unit) (A tptp.set_Product_unit) (X4 tptp.set_Product_unit)) (=> (@ (@ tptp.member_Product_unit X) A) (=> (@ (@ tptp.ord_le3507040750410214029t_unit X4) A) (@ (@ tptp.ord_le3507040750410214029t_unit (@ (@ tptp.insert_Product_unit X) X4)) A)))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (A tptp.set_nat) (X4 tptp.set_nat)) (=> (@ (@ tptp.member_nat X) A) (=> (@ (@ tptp.ord_less_eq_set_nat X4) A) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X) X4)) A)))))
% 5.61/5.91 (assert (forall ((A tptp.set_int) (B4 tptp.set_int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert_int B) B4))))))
% 5.61/5.91 (assert (forall ((A tptp.set_o) (B4 tptp.set_o) (B Bool)) (let ((_let_1 (@ tptp.ord_less_eq_set_o A))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert_o B) B4))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit) (B tptp.product_unit)) (let ((_let_1 (@ tptp.ord_le3507040750410214029t_unit A))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert_Product_unit B) B4))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert_nat B) B4))))))
% 5.61/5.91 (assert (forall ((B4 tptp.set_int) (A2 tptp.int)) (@ (@ tptp.ord_less_eq_set_int B4) (@ (@ tptp.insert_int A2) B4))))
% 5.61/5.91 (assert (forall ((B4 tptp.set_o) (A2 Bool)) (@ (@ tptp.ord_less_eq_set_o B4) (@ (@ tptp.insert_o A2) B4))))
% 5.61/5.91 (assert (forall ((B4 tptp.set_Product_unit) (A2 tptp.product_unit)) (@ (@ tptp.ord_le3507040750410214029t_unit B4) (@ (@ tptp.insert_Product_unit A2) B4))))
% 5.61/5.91 (assert (forall ((B4 tptp.set_nat) (A2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat B4) (@ (@ tptp.insert_nat A2) B4))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.ord_le2965882846123202637_nat_o A))) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) A)) (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o X) B4)) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((X tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (not (@ (@ tptp.member_int X) A)) (= (@ _let_1 (@ (@ tptp.insert_int X) B4)) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((X Bool) (A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.ord_less_eq_set_o A))) (=> (not (@ (@ tptp.member_o X) A)) (= (@ _let_1 (@ (@ tptp.insert_o X) B4)) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((X tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.ord_le3507040750410214029t_unit A))) (=> (not (@ (@ tptp.member_Product_unit X) A)) (= (@ _let_1 (@ (@ tptp.insert_Product_unit X) B4)) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (not (@ (@ tptp.member_nat X) A)) (= (@ _let_1 (@ (@ tptp.insert_nat X) B4)) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((C5 tptp.set_int) (D3 tptp.set_int) (A2 tptp.int)) (let ((_let_1 (@ tptp.insert_int A2))) (=> (@ (@ tptp.ord_less_eq_set_int C5) D3) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 C5)) (@ _let_1 D3))))))
% 5.61/5.91 (assert (forall ((C5 tptp.set_o) (D3 tptp.set_o) (A2 Bool)) (let ((_let_1 (@ tptp.insert_o A2))) (=> (@ (@ tptp.ord_less_eq_set_o C5) D3) (@ (@ tptp.ord_less_eq_set_o (@ _let_1 C5)) (@ _let_1 D3))))))
% 5.61/5.91 (assert (forall ((C5 tptp.set_Product_unit) (D3 tptp.set_Product_unit) (A2 tptp.product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit A2))) (=> (@ (@ tptp.ord_le3507040750410214029t_unit C5) D3) (@ (@ tptp.ord_le3507040750410214029t_unit (@ _let_1 C5)) (@ _let_1 D3))))))
% 5.61/5.91 (assert (forall ((C5 tptp.set_nat) (D3 tptp.set_nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (=> (@ (@ tptp.ord_less_eq_set_nat C5) D3) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 C5)) (@ _let_1 D3))))))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_nat R3))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.ord_less_eq_set_nat A) (@ (@ tptp.vimage8201027140005291904_nat_o F) B4)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.member6576561426505652726_nat_o (@ F X2)) B4))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat)) (B4 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) (@ (@ tptp.vimage_nat_nat F) B4)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.member_nat (@ F X2)) B4))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.int)) (B4 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_nat A) (@ (@ tptp.vimage_nat_int F) B4)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.member_int (@ F X2)) B4))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat Bool)) (B4 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_nat A) (@ (@ tptp.vimage_nat_o F) B4)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.member_o (@ F X2)) B4))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.product_unit)) (B4 tptp.set_Product_unit)) (= (@ (@ tptp.ord_less_eq_set_nat A) (@ (@ tptp.vimage4884490618288580032t_unit F) B4)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.member_Product_unit (@ F X2)) B4))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.vimage_nat_nat F))) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.91 (assert (forall ((Bs tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ (@ (@ tptp.relH Bs) H2) H3) (=> (@ (@ tptp.ord_less_eq_set_nat As) Bs) (@ (@ (@ tptp.relH As) H2) H3)))))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr5094982260447487303t_unit) (X tptp.product_unit) (S tptp.set_Product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit X))) (let ((_let_2 (@ tptp.image_8431784415008483091t_unit (@ tptp.transi6481887417741755664t_unit R3)))) (= (@ _let_2 (@ _let_1 S)) (@ _let_1 (@ _let_2 (@ (@ tptp.sup_su793286257634532545t_unit S) (@ (@ tptp.image_8431784415008483091t_unit R3) (@ _let_1 tptp.bot_bo3957492148770167129t_unit))))))))))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Product_prod_o_o) (X Bool) (S tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X))) (let ((_let_2 (@ tptp.image_o_o (@ tptp.transitive_rtrancl_o R3)))) (= (@ _let_2 (@ _let_1 S)) (@ _let_1 (@ _let_2 (@ (@ tptp.sup_sup_set_o S) (@ (@ tptp.image_o_o R3) (@ _let_1 tptp.bot_bot_set_o))))))))))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (X tptp.nat) (S tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.image_nat_nat (@ tptp.transi2905341329935302413cl_nat R3)))) (= (@ _let_2 (@ _let_1 S)) (@ _let_1 (@ _let_2 (@ (@ tptp.sup_sup_set_nat S) (@ (@ tptp.image_nat_nat R3) (@ _let_1 tptp.bot_bot_set_nat))))))))))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int) (X tptp.int) (S tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.image_int_int (@ tptp.transi2902850859426252137cl_int R3)))) (= (@ _let_2 (@ _let_1 S)) (@ _let_1 (@ _let_2 (@ (@ tptp.sup_sup_set_int S) (@ (@ tptp.image_int_int R3) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr2161125870931222855_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (S tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.insert5175938949040314269_nat_o X))) (let ((_let_2 (@ tptp.image_2232984160439939859_nat_o (@ tptp.transi712980445759334096_nat_o R3)))) (= (@ _let_2 (@ _let_1 S)) (@ _let_1 (@ _let_2 (@ (@ tptp.sup_su5209123915105501825_nat_o S) (@ (@ tptp.image_2232984160439939859_nat_o R3) (@ _let_1 tptp.bot_bo7824918357723582233_nat_o))))))))))
% 5.61/5.91 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (B tptp.nat)) (=> (@ tptp.antisym_nat R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) A2)) R2) (= A2 B))))))
% 5.61/5.91 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (B tptp.int)) (=> (@ tptp.antisym_int R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) A2)) R2) (= A2 B))))))
% 5.61/5.91 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) X3)) R2) (= X3 Y2)))) (@ tptp.antisym_nat R2))))
% 5.61/5.91 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int)) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y2)) R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y2) X3)) R2) (= X3 Y2)))) (@ tptp.antisym_int R2))))
% 5.61/5.91 (assert (= tptp.antisym_nat (lambda ((R4 tptp.set_Pr1261947904930325089at_nat)) (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y3)) R4) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y3) X2)) R4) (= X2 Y3)))))))
% 5.61/5.91 (assert (= tptp.antisym_int (lambda ((R4 tptp.set_Pr958786334691620121nt_int)) (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X2) Y3)) R4) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y3) X2)) R4) (= X2 Y3)))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (=> (@ tptp.trans_nat A) (=> (@ (@ tptp.refl_on_nat B4) A) (=> (@ (@ tptp.ord_less_eq_set_nat C5) B4) (= (@ (@ tptp.image_nat_nat (@ tptp.transi2905341329935302413cl_nat A)) C5) (@ (@ tptp.image_nat_nat A) C5)))))))
% 5.61/5.91 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Q2 (-> tptp.produc3658429121746597890et_nat Bool)) (H2 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (= (@ (@ (@ tptp.times_assn_raw P) Q2) (@ (@ tptp.produc7507926704131184380et_nat H2) As)) (exists ((As1 tptp.set_nat) (As22 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H2))) (and (= As (@ (@ tptp.sup_sup_set_nat As1) As22)) (= (@ (@ tptp.inf_inf_set_nat As1) As22) tptp.bot_bot_set_nat) (@ P (@ _let_1 As1)) (@ Q2 (@ _let_1 As22))))))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ (@ tptp.times_assn_raw X) Xa) Xb) Y) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= Xb (@ (@ tptp.produc7507926704131184380et_nat H) As2)) (= Y (not (exists ((As1 tptp.set_nat) (As22 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H))) (and (= As2 (@ (@ tptp.sup_sup_set_nat As1) As22)) (= (@ (@ tptp.inf_inf_set_nat As1) As22) tptp.bot_bot_set_nat) (@ X (@ _let_1 As1)) (@ Xa (@ _let_1 As22)))))))))))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (@ (@ (@ tptp.times_assn_raw X) Xa) Xb) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= Xb (@ (@ tptp.produc7507926704131184380et_nat H) As2)) (not (exists ((As12 tptp.set_nat) (As23 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H))) (and (= As2 (@ (@ tptp.sup_sup_set_nat As12) As23)) (= (@ (@ tptp.inf_inf_set_nat As12) As23) tptp.bot_bot_set_nat) (@ X (@ _let_1 As12)) (@ Xa (@ _let_1 As23))))))))))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (not (@ (@ (@ tptp.times_assn_raw X) Xa) Xb)) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= Xb (@ (@ tptp.produc7507926704131184380et_nat H) As2)) (exists ((As13 tptp.set_nat) (As24 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H))) (and (= As2 (@ (@ tptp.sup_sup_set_nat As13) As24)) (= (@ (@ tptp.inf_inf_set_nat As13) As24) tptp.bot_bot_set_nat) (@ X (@ _let_1 As13)) (@ Xa (@ _let_1 As24)))))))))))
% 5.61/5.91 (assert (forall ((U tptp.product_unit) (V tptp.product_unit) (E tptp.set_Pr5094982260447487303t_unit)) (let ((_let_1 (@ tptp.image_8431784415008483091t_unit (@ tptp.transi6481887417741755664t_unit E)))) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit U) V)) E) (@ (@ tptp.ord_le3507040750410214029t_unit (@ _let_1 (@ (@ tptp.insert_Product_unit V) tptp.bot_bo3957492148770167129t_unit))) (@ _let_1 (@ (@ tptp.insert_Product_unit U) tptp.bot_bo3957492148770167129t_unit)))))))
% 5.61/5.91 (assert (forall ((U Bool) (V Bool) (E tptp.set_Product_prod_o_o)) (let ((_let_1 (@ tptp.image_o_o (@ tptp.transitive_rtrancl_o E)))) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o U) V)) E) (@ (@ tptp.ord_less_eq_set_o (@ _let_1 (@ (@ tptp.insert_o V) tptp.bot_bot_set_o))) (@ _let_1 (@ (@ tptp.insert_o U) tptp.bot_bot_set_o)))))))
% 5.61/5.91 (assert (forall ((U tptp.int) (V tptp.int) (E tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.image_int_int (@ tptp.transi2902850859426252137cl_int E)))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int U) V)) E) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 (@ (@ tptp.insert_int V) tptp.bot_bot_set_int))) (@ _let_1 (@ (@ tptp.insert_int U) tptp.bot_bot_set_int)))))))
% 5.61/5.91 (assert (forall ((U (-> tptp.produc3658429121746597890et_nat Bool)) (V (-> tptp.produc3658429121746597890et_nat Bool)) (E tptp.set_Pr2161125870931222855_nat_o)) (let ((_let_1 (@ tptp.image_2232984160439939859_nat_o (@ tptp.transi712980445759334096_nat_o E)))) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o U) V)) E) (@ (@ tptp.ord_le2965882846123202637_nat_o (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o V) tptp.bot_bo7824918357723582233_nat_o))) (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o U) tptp.bot_bo7824918357723582233_nat_o)))))))
% 5.61/5.91 (assert (forall ((U tptp.nat) (V tptp.nat) (E tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.image_nat_nat (@ tptp.transi2905341329935302413cl_nat E)))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat U) V)) E) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 (@ (@ tptp.insert_nat V) tptp.bot_bot_set_nat))) (@ _let_1 (@ (@ tptp.insert_nat U) tptp.bot_bot_set_nat)))))))
% 5.61/5.91 (assert (forall ((Q4 (-> tptp.produc3658429121746597890et_nat Bool)) (R3 tptp.set_Pr2161125870931222855_nat_o) (Q0 tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.transi712980445759334096_nat_o R3))) (let ((_let_2 (@ (@ tptp.image_2232984160439939859_nat_o _let_1) Q0))) (=> (@ (@ tptp.member6576561426505652726_nat_o Q4) _let_2) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o Q4) X)) _let_1) (@ (@ tptp.member6576561426505652726_nat_o X) _let_2)))))))
% 5.61/5.91 (assert (forall ((Q4 Bool) (R3 tptp.set_Product_prod_o_o) (Q0 tptp.set_o) (X Bool)) (let ((_let_1 (@ tptp.transitive_rtrancl_o R3))) (let ((_let_2 (@ (@ tptp.image_o_o _let_1) Q0))) (=> (@ (@ tptp.member_o Q4) _let_2) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o Q4) X)) _let_1) (@ (@ tptp.member_o X) _let_2)))))))
% 5.61/5.91 (assert (forall ((Q4 tptp.product_unit) (R3 tptp.set_Pr5094982260447487303t_unit) (Q0 tptp.set_Product_unit) (X tptp.product_unit)) (let ((_let_1 (@ tptp.transi6481887417741755664t_unit R3))) (let ((_let_2 (@ (@ tptp.image_8431784415008483091t_unit _let_1) Q0))) (=> (@ (@ tptp.member_Product_unit Q4) _let_2) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit Q4) X)) _let_1) (@ (@ tptp.member_Product_unit X) _let_2)))))))
% 5.61/5.91 (assert (forall ((Q4 tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat) (Q0 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.transi2905341329935302413cl_nat R3))) (let ((_let_2 (@ (@ tptp.image_nat_nat _let_1) Q0))) (=> (@ (@ tptp.member_nat Q4) _let_2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Q4) X)) _let_1) (@ (@ tptp.member_nat X) _let_2)))))))
% 5.61/5.91 (assert (forall ((Q4 tptp.int) (R3 tptp.set_Pr958786334691620121nt_int) (Q0 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.transi2902850859426252137cl_int R3))) (let ((_let_2 (@ (@ tptp.image_int_int _let_1) Q0))) (=> (@ (@ tptp.member_int Q4) _let_2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Q4) X)) _let_1) (@ (@ tptp.member_int X) _let_2)))))))
% 5.61/5.91 (assert (forall ((Q4 (-> tptp.produc3658429121746597890et_nat Bool)) (R3 tptp.set_Pr2161125870931222855_nat_o) (Q0 tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ tptp.image_2232984160439939859_nat_o (@ tptp.transi712980445759334096_nat_o R3)) Q0))) (=> (@ (@ tptp.member6576561426505652726_nat_o Q4) _let_1) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o Q4) X)) R3) (@ (@ tptp.member6576561426505652726_nat_o X) _let_1))))))
% 5.61/5.91 (assert (forall ((Q4 Bool) (R3 tptp.set_Product_prod_o_o) (Q0 tptp.set_o) (X Bool)) (let ((_let_1 (@ (@ tptp.image_o_o (@ tptp.transitive_rtrancl_o R3)) Q0))) (=> (@ (@ tptp.member_o Q4) _let_1) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o Q4) X)) R3) (@ (@ tptp.member_o X) _let_1))))))
% 5.61/5.91 (assert (forall ((Q4 tptp.product_unit) (R3 tptp.set_Pr5094982260447487303t_unit) (Q0 tptp.set_Product_unit) (X tptp.product_unit)) (let ((_let_1 (@ (@ tptp.image_8431784415008483091t_unit (@ tptp.transi6481887417741755664t_unit R3)) Q0))) (=> (@ (@ tptp.member_Product_unit Q4) _let_1) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit Q4) X)) R3) (@ (@ tptp.member_Product_unit X) _let_1))))))
% 5.61/5.91 (assert (forall ((Q4 tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat) (Q0 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.image_nat_nat (@ tptp.transi2905341329935302413cl_nat R3)) Q0))) (=> (@ (@ tptp.member_nat Q4) _let_1) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Q4) X)) R3) (@ (@ tptp.member_nat X) _let_1))))))
% 5.61/5.91 (assert (forall ((Q4 tptp.int) (R3 tptp.set_Pr958786334691620121nt_int) (Q0 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.image_int_int (@ tptp.transi2902850859426252137cl_int R3)) Q0))) (=> (@ (@ tptp.member_int Q4) _let_1) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Q4) X)) R3) (@ (@ tptp.member_int X) _let_1))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.transi6264000038957366511cl_nat R2))) (let ((_let_2 (@ tptp.product_Pair_nat_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 B)) _let_1) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) C)) (@ tptp.transi2905341329935302413cl_nat R2)) (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 C)) _let_1)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (C tptp.int)) (let ((_let_1 (@ tptp.transi6261509568448316235cl_int R2))) (let ((_let_2 (@ tptp.product_Pair_int_int A2))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 B)) _let_1) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) C)) (@ tptp.transi2902850859426252137cl_int R2)) (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 C)) _let_1)))))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (Y tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.transi6264000038957366511cl_nat R2))) (let ((_let_2 (@ tptp.product_Pair_nat_nat X))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 Y)) (@ tptp.transi2905341329935302413cl_nat R2)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y) Z)) _let_1) (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 Z)) _let_1)))))))
% 5.61/5.91 (assert (forall ((X tptp.int) (Y tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (Z tptp.int)) (let ((_let_1 (@ tptp.transi6261509568448316235cl_int R2))) (let ((_let_2 (@ tptp.product_Pair_int_int X))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 Y)) (@ tptp.transi2902850859426252137cl_int R2)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y) Z)) _let_1) (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 Z)) _let_1)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 B)) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) C)) (@ tptp.transi2905341329935302413cl_nat R2)) (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 C)) (@ tptp.transi6264000038957366511cl_nat R2)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (C tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int A2))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 B)) R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) C)) (@ tptp.transi2902850859426252137cl_int R2)) (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 C)) (@ tptp.transi6261509568448316235cl_int R2)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 B)) (@ tptp.transi2905341329935302413cl_nat R2)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) C)) R2) (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 C)) (@ tptp.transi6264000038957366511cl_nat R2)))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (C tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int A2))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 B)) (@ tptp.transi2902850859426252137cl_int R2)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) C)) R2) (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 C)) (@ tptp.transi6261509568448316235cl_int R2)))))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (Y tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)))) (let ((_let_2 (= X Y))) (= (@ _let_1 (@ tptp.transi2905341329935302413cl_nat R3)) (or _let_2 (and (not _let_2) (@ _let_1 (@ tptp.transi6264000038957366511cl_nat R3)))))))))
% 5.61/5.91 (assert (forall ((X tptp.int) (Y tptp.int) (R3 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)))) (let ((_let_2 (= X Y))) (= (@ _let_1 (@ tptp.transi2902850859426252137cl_int R3)) (or _let_2 (and (not _let_2) (@ _let_1 (@ tptp.transi6261509568448316235cl_int R3)))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)))) (=> (@ _let_1 (@ tptp.transi6264000038957366511cl_nat R2)) (@ _let_1 (@ tptp.transi2905341329935302413cl_nat R2))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)))) (=> (@ _let_1 (@ tptp.transi6261509568448316235cl_int R2)) (@ _let_1 (@ tptp.transi2902850859426252137cl_int R2))))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (Y tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.transi6264000038957366511cl_nat R3)) (exists ((Z3 tptp.nat)) (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Z3)) (@ tptp.transi2905341329935302413cl_nat R3)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Z3) Y)) R3))))))
% 5.61/5.91 (assert (forall ((X tptp.int) (Y tptp.int) (R3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ tptp.transi6261509568448316235cl_int R3)) (exists ((Z3 tptp.int)) (and (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Z3)) (@ tptp.transi2902850859426252137cl_int R3)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Z3) Y)) R3))))))
% 5.61/5.91 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)))) (let ((_let_2 (= A2 B))) (=> (@ _let_1 (@ tptp.transi2905341329935302413cl_nat R3)) (or _let_2 (and (not _let_2) (@ _let_1 (@ tptp.transi6264000038957366511cl_nat R3)))))))))
% 5.61/5.91 (assert (forall ((A2 tptp.int) (B tptp.int) (R3 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)))) (let ((_let_2 (= A2 B))) (=> (@ _let_1 (@ tptp.transi2902850859426252137cl_int R3)) (or _let_2 (and (not _let_2) (@ _let_1 (@ tptp.transi6261509568448316235cl_int R3)))))))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (Y tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.transi6264000038957366511cl_nat R3)) (exists ((Z3 tptp.nat)) (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Z3)) R3) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Z3) Y)) (@ tptp.transi2905341329935302413cl_nat R3)))))))
% 5.61/5.91 (assert (forall ((X tptp.int) (Y tptp.int) (R3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ tptp.transi6261509568448316235cl_int R3)) (exists ((Z3 tptp.int)) (and (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Z3)) R3) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Z3) Y)) (@ tptp.transi2902850859426252137cl_int R3)))))))
% 5.61/5.91 (assert (= tptp.insert_Product_unit (lambda ((A6 tptp.product_unit) (__flatten_var_0 tptp.set_Product_unit)) (@ (@ tptp.sup_su793286257634532545t_unit (@ (@ tptp.insert_Product_unit A6) tptp.bot_bo3957492148770167129t_unit)) __flatten_var_0))))
% 5.61/5.91 (assert (= tptp.insert_o (lambda ((A6 Bool) (__flatten_var_0 tptp.set_o)) (@ (@ tptp.sup_sup_set_o (@ (@ tptp.insert_o A6) tptp.bot_bot_set_o)) __flatten_var_0))))
% 5.61/5.91 (assert (= tptp.insert_nat (lambda ((A6 tptp.nat) (__flatten_var_0 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.insert_nat A6) tptp.bot_bot_set_nat)) __flatten_var_0))))
% 5.61/5.91 (assert (= tptp.insert_int (lambda ((A6 tptp.int) (__flatten_var_0 tptp.set_int)) (@ (@ tptp.sup_sup_set_int (@ (@ tptp.insert_int A6) tptp.bot_bot_set_int)) __flatten_var_0))))
% 5.61/5.91 (assert (= tptp.insert5175938949040314269_nat_o (lambda ((A6 (-> tptp.produc3658429121746597890et_nat Bool)) (__flatten_var_0 tptp.set_Pr4532377907799695533_nat_o)) (@ (@ tptp.sup_su5209123915105501825_nat_o (@ (@ tptp.insert5175938949040314269_nat_o A6) tptp.bot_bo7824918357723582233_nat_o)) __flatten_var_0))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit) (X tptp.product_unit)) (let ((_let_1 (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit))) (let ((_let_2 (= B4 _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ tptp.sup_su793286257634532545t_unit A) B4) _let_1) (or (and (= A tptp.bot_bo3957492148770167129t_unit) _let_2) (and _let_3 (= B4 tptp.bot_bo3957492148770167129t_unit)) (and _let_3 _let_2))))))))
% 5.61/5.91 (assert (forall ((A tptp.set_o) (B4 tptp.set_o) (X Bool)) (let ((_let_1 (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))) (let ((_let_2 (= B4 _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ tptp.sup_sup_set_o A) B4) _let_1) (or (and (= A tptp.bot_bot_set_o) _let_2) (and _let_3 (= B4 tptp.bot_bot_set_o)) (and _let_3 _let_2))))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (let ((_let_2 (= B4 _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ tptp.sup_sup_set_nat A) B4) _let_1) (or (and (= A tptp.bot_bot_set_nat) _let_2) (and _let_3 (= B4 tptp.bot_bot_set_nat)) (and _let_3 _let_2))))))))
% 5.61/5.91 (assert (forall ((A tptp.set_int) (B4 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (let ((_let_2 (= B4 _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ tptp.sup_sup_set_int A) B4) _let_1) (or (and (= A tptp.bot_bot_set_int) _let_2) (and _let_3 (= B4 tptp.bot_bot_set_int)) (and _let_3 _let_2))))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o))) (let ((_let_2 (= B4 _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ tptp.sup_su5209123915105501825_nat_o A) B4) _let_1) (or (and (= A tptp.bot_bo7824918357723582233_nat_o) _let_2) (and _let_3 (= B4 tptp.bot_bo7824918357723582233_nat_o)) (and _let_3 _let_2))))))))
% 5.61/5.91 (assert (forall ((X tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit))) (let ((_let_2 (= B4 _let_1))) (let ((_let_3 (= A _let_1))) (= (= _let_1 (@ (@ tptp.sup_su793286257634532545t_unit A) B4)) (or (and (= A tptp.bot_bo3957492148770167129t_unit) _let_2) (and _let_3 (= B4 tptp.bot_bo3957492148770167129t_unit)) (and _let_3 _let_2))))))))
% 5.61/5.91 (assert (forall ((X Bool) (A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))) (let ((_let_2 (= B4 _let_1))) (let ((_let_3 (= A _let_1))) (= (= _let_1 (@ (@ tptp.sup_sup_set_o A) B4)) (or (and (= A tptp.bot_bot_set_o) _let_2) (and _let_3 (= B4 tptp.bot_bot_set_o)) (and _let_3 _let_2))))))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (let ((_let_2 (= B4 _let_1))) (let ((_let_3 (= A _let_1))) (= (= _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (or (and (= A tptp.bot_bot_set_nat) _let_2) (and _let_3 (= B4 tptp.bot_bot_set_nat)) (and _let_3 _let_2))))))))
% 5.61/5.91 (assert (forall ((X tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (let ((_let_2 (= B4 _let_1))) (let ((_let_3 (= A _let_1))) (= (= _let_1 (@ (@ tptp.sup_sup_set_int A) B4)) (or (and (= A tptp.bot_bot_set_int) _let_2) (and _let_3 (= B4 tptp.bot_bot_set_int)) (and _let_3 _let_2))))))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o))) (let ((_let_2 (= B4 _let_1))) (let ((_let_3 (= A _let_1))) (= (= _let_1 (@ (@ tptp.sup_su5209123915105501825_nat_o A) B4)) (or (and (= A tptp.bot_bo7824918357723582233_nat_o) _let_2) (and _let_3 (= B4 tptp.bot_bo7824918357723582233_nat_o)) (and _let_3 _let_2))))))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (R3 tptp.set_Pr2161125870931222855_nat_o) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) (@ tptp.domain4881241903163524940_nat_o R3))) (= (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X) Y)) (@ tptp.transi712980445759334096_nat_o R3)) (= X Y)))))
% 5.61/5.91 (assert (forall ((X Bool) (R3 tptp.set_Product_prod_o_o) (Y Bool)) (=> (not (@ (@ tptp.member_o X) (@ tptp.domain_o_o R3))) (= (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X) Y)) (@ tptp.transitive_rtrancl_o R3)) (= X Y)))))
% 5.61/5.91 (assert (forall ((X tptp.product_unit) (R3 tptp.set_Pr5094982260447487303t_unit) (Y tptp.product_unit)) (=> (not (@ (@ tptp.member_Product_unit X) (@ tptp.domain4292024440186670924t_unit R3))) (= (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit X) Y)) (@ tptp.transi6481887417741755664t_unit R3)) (= X Y)))))
% 5.61/5.91 (assert (forall ((X tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat) (Y tptp.nat)) (=> (not (@ (@ tptp.member_nat X) (@ tptp.domain_nat_nat R3))) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.transi2905341329935302413cl_nat R3)) (= X Y)))))
% 5.61/5.91 (assert (forall ((X tptp.int) (R3 tptp.set_Pr958786334691620121nt_int) (Y tptp.int)) (=> (not (@ (@ tptp.member_int X) (@ tptp.domain_int_int R3))) (= (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ tptp.transi2902850859426252137cl_int R3)) (= X Y)))))
% 5.61/5.91 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (let ((_let_1 (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit))) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) _let_1) (or (= A tptp.bot_bo3957492148770167129t_unit) (= A _let_1))))))
% 5.61/5.91 (assert (forall ((A tptp.set_o) (X Bool)) (let ((_let_1 (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))) (=> (@ (@ tptp.ord_less_eq_set_o A) _let_1) (or (= A tptp.bot_bot_set_o) (= A _let_1))))))
% 5.61/5.91 (assert (forall ((A tptp.set_int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (=> (@ (@ tptp.ord_less_eq_set_int A) _let_1) (or (= A tptp.bot_bot_set_int) (= A _let_1))))))
% 5.61/5.91 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o))) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A) _let_1) (or (= A tptp.bot_bo7824918357723582233_nat_o) (= A _let_1))))))
% 5.61/5.91 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (=> (@ (@ tptp.ord_less_eq_set_nat A) _let_1) (or (= A tptp.bot_bot_set_nat) (= A _let_1))))))
% 5.61/5.91 (assert (forall ((X4 tptp.set_Product_unit) (A2 tptp.product_unit)) (let ((_let_1 (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit))) (= (@ (@ tptp.ord_le3507040750410214029t_unit X4) _let_1) (or (= X4 tptp.bot_bo3957492148770167129t_unit) (= X4 _let_1))))))
% 5.61/5.91 (assert (forall ((X4 tptp.set_o) (A2 Bool)) (let ((_let_1 (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))) (= (@ (@ tptp.ord_less_eq_set_o X4) _let_1) (or (= X4 tptp.bot_bot_set_o) (= X4 _let_1))))))
% 5.61/5.91 (assert (forall ((X4 tptp.set_int) (A2 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))) (= (@ (@ tptp.ord_less_eq_set_int X4) _let_1) (or (= X4 tptp.bot_bot_set_int) (= X4 _let_1))))))
% 5.61/5.91 (assert (forall ((X4 tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o))) (= (@ (@ tptp.ord_le2965882846123202637_nat_o X4) _let_1) (or (= X4 tptp.bot_bo7824918357723582233_nat_o) (= X4 _let_1))))))
% 5.61/5.91 (assert (forall ((X4 tptp.set_nat) (A2 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))) (= (@ (@ tptp.ord_less_eq_set_nat X4) _let_1) (or (= X4 tptp.bot_bot_set_nat) (= X4 _let_1))))))
% 5.61/5.91 (assert (forall ((A tptp.assn) (B4 tptp.assn) (H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn A) B4)) H2) (exists ((Hr tptp.heap_e7401611519738050253t_unit) (As1 tptp.set_nat) (As22 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat Hr))) (and (= H2 (@ _let_1 (@ (@ tptp.sup_sup_set_nat As1) As22))) (= (@ (@ tptp.inf_inf_set_nat As1) As22) tptp.bot_bot_set_nat) (@ (@ tptp.rep_assn A) (@ _let_1 As1)) (@ (@ tptp.rep_assn B4) (@ _let_1 As22))))))))
% 5.61/5.91 (assert (forall ((P tptp.assn) (H2 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat) (Q2 tptp.assn) (As5 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H2))) (=> (@ (@ tptp.rep_assn P) (@ _let_1 As)) (=> (@ (@ tptp.rep_assn Q2) (@ _let_1 As5)) (=> (= (@ (@ tptp.inf_inf_set_nat As) As5) tptp.bot_bot_set_nat) (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P) Q2)) (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As5)))))))))
% 5.61/5.91 (assert (forall ((As tptp.set_nat) (As5 tptp.set_nat) (H2 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H2))) (=> (@ (@ tptp.ord_less_eq_set_nat As) As5) (=> (@ tptp.in_range (@ _let_1 As5)) (@ tptp.in_range (@ _let_1 As)))))))
% 5.61/5.91 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Q2 (-> tptp.produc3658429121746597890et_nat Bool)) (H2 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H2) As))) (= (@ (@ (@ tptp.wand_raw P) Q2) _let_1) (and (@ tptp.in_range _let_1) (forall ((H5 tptp.heap_e7401611519738050253t_unit) (As6 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H5))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As) As6) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As) H2) H5) (@ tptp.in_range (@ _let_1 As)) (@ P (@ _let_1 As6))) (@ Q2 (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As6)))))))))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ (@ tptp.wand_raw X) Xa) Xb) Y) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As2))) (=> (= Xb _let_1) (= Y (not (and (@ tptp.in_range _let_1) (forall ((H5 tptp.heap_e7401611519738050253t_unit) (As6 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H5))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As2) As6) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As2) H) H5) (@ tptp.in_range (@ _let_1 As2)) (@ X (@ _let_1 As6))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As6))))))))))))))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (@ (@ (@ tptp.wand_raw X) Xa) Xb) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As2))) (=> (= Xb _let_1) (not (and (@ tptp.in_range _let_1) (forall ((H7 tptp.heap_e7401611519738050253t_unit) (As7 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H7))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As2) As7) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As2) H) H7) (@ tptp.in_range (@ _let_1 As2)) (@ X (@ _let_1 As7))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As7)))))))))))))))
% 5.61/5.91 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (not (@ (@ (@ tptp.wand_raw X) Xa) Xb)) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As2))) (=> (= Xb _let_1) (and (@ tptp.in_range _let_1) (forall ((H6 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H6))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As2) As4) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As2) H) H6) (@ tptp.in_range (@ _let_1 As2)) (@ X (@ _let_1 As4))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As4))))))))))))))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr5094982260447487303t_unit) (V tptp.product_unit)) (let ((_let_1 (@ (@ tptp.insert_Product_unit V) tptp.bot_bo3957492148770167129t_unit))) (=> (= (@ (@ tptp.image_8431784415008483091t_unit R3) _let_1) tptp.bot_bo3957492148770167129t_unit) (= (@ (@ tptp.image_8431784415008483091t_unit (@ tptp.transi6481887417741755664t_unit R3)) _let_1) _let_1)))))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Product_prod_o_o) (V Bool)) (let ((_let_1 (@ (@ tptp.insert_o V) tptp.bot_bot_set_o))) (=> (= (@ (@ tptp.image_o_o R3) _let_1) tptp.bot_bot_set_o) (= (@ (@ tptp.image_o_o (@ tptp.transitive_rtrancl_o R3)) _let_1) _let_1)))))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (V tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat V) tptp.bot_bot_set_nat))) (=> (= (@ (@ tptp.image_nat_nat R3) _let_1) tptp.bot_bot_set_nat) (= (@ (@ tptp.image_nat_nat (@ tptp.transi2905341329935302413cl_nat R3)) _let_1) _let_1)))))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int) (V tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int V) tptp.bot_bot_set_int))) (=> (= (@ (@ tptp.image_int_int R3) _let_1) tptp.bot_bot_set_int) (= (@ (@ tptp.image_int_int (@ tptp.transi2902850859426252137cl_int R3)) _let_1) _let_1)))))
% 5.61/5.91 (assert (forall ((R3 tptp.set_Pr2161125870931222855_nat_o) (V (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ tptp.insert5175938949040314269_nat_o V) tptp.bot_bo7824918357723582233_nat_o))) (=> (= (@ (@ tptp.image_2232984160439939859_nat_o R3) _let_1) tptp.bot_bo7824918357723582233_nat_o) (= (@ (@ tptp.image_2232984160439939859_nat_o (@ tptp.transi712980445759334096_nat_o R3)) _let_1) _let_1)))))
% 5.61/5.91 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.sup_sup_assn A2) tptp.bot_bot_assn) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit)) (= (@ (@ tptp.sup_sup_Product_unit A2) tptp.bot_bot_Product_unit) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.set_Product_unit)) (= (@ (@ tptp.sup_su793286257634532545t_unit A2) tptp.bot_bo3957492148770167129t_unit) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o A2) tptp.bot_bot_set_o) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A2) tptp.bot_bot_set_nat) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A2) tptp.bot_bot_set_int) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.sup_su5209123915105501825_nat_o A2) tptp.bot_bo7824918357723582233_nat_o) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.assn) (B tptp.assn)) (= (= tptp.bot_bot_assn (@ (@ tptp.sup_sup_assn A2) B)) (and (= A2 tptp.bot_bot_assn) (= B tptp.bot_bot_assn)))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (B tptp.product_unit)) (= (= tptp.bot_bot_Product_unit (@ (@ tptp.sup_sup_Product_unit A2) B)) (and (= A2 tptp.bot_bot_Product_unit) (= B tptp.bot_bot_Product_unit)))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_Product_unit) (B tptp.set_Product_unit)) (= (= tptp.bot_bo3957492148770167129t_unit (@ (@ tptp.sup_su793286257634532545t_unit A2) B)) (and (= A2 tptp.bot_bo3957492148770167129t_unit) (= B tptp.bot_bo3957492148770167129t_unit)))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_o) (B tptp.set_o)) (= (= tptp.bot_bot_set_o (@ (@ tptp.sup_sup_set_o A2) B)) (and (= A2 tptp.bot_bot_set_o) (= B tptp.bot_bot_set_o)))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.sup_sup_set_nat A2) B)) (and (= A2 tptp.bot_bot_set_nat) (= B tptp.bot_bot_set_nat)))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_int) (B tptp.set_int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.sup_sup_set_int A2) B)) (and (= A2 tptp.bot_bot_set_int) (= B tptp.bot_bot_set_int)))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (= (= tptp.bot_bo7824918357723582233_nat_o (@ (@ tptp.sup_su5209123915105501825_nat_o A2) B)) (and (= A2 tptp.bot_bo7824918357723582233_nat_o) (= B tptp.bot_bo7824918357723582233_nat_o)))))
% 5.61/5.91 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.sup_sup_assn tptp.bot_bot_assn) A2) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit)) (= (@ (@ tptp.sup_sup_Product_unit tptp.bot_bot_Product_unit) A2) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.set_Product_unit)) (= (@ (@ tptp.sup_su793286257634532545t_unit tptp.bot_bo3957492148770167129t_unit) A2) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o tptp.bot_bot_set_o) A2) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.bot_bot_set_nat) A2) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int tptp.bot_bot_set_int) A2) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.sup_su5209123915105501825_nat_o tptp.bot_bo7824918357723582233_nat_o) A2) A2)))
% 5.61/5.91 (assert (forall ((A2 tptp.assn) (B tptp.assn)) (= (= (@ (@ tptp.sup_sup_assn A2) B) tptp.bot_bot_assn) (and (= A2 tptp.bot_bot_assn) (= B tptp.bot_bot_assn)))))
% 5.61/5.91 (assert (forall ((A2 tptp.product_unit) (B tptp.product_unit)) (= (= (@ (@ tptp.sup_sup_Product_unit A2) B) tptp.bot_bot_Product_unit) (and (= A2 tptp.bot_bot_Product_unit) (= B tptp.bot_bot_Product_unit)))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_Product_unit) (B tptp.set_Product_unit)) (= (= (@ (@ tptp.sup_su793286257634532545t_unit A2) B) tptp.bot_bo3957492148770167129t_unit) (and (= A2 tptp.bot_bo3957492148770167129t_unit) (= B tptp.bot_bo3957492148770167129t_unit)))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_o) (B tptp.set_o)) (= (= (@ (@ tptp.sup_sup_set_o A2) B) tptp.bot_bot_set_o) (and (= A2 tptp.bot_bot_set_o) (= B tptp.bot_bot_set_o)))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.sup_sup_set_nat A2) B) tptp.bot_bot_set_nat) (and (= A2 tptp.bot_bot_set_nat) (= B tptp.bot_bot_set_nat)))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.sup_sup_set_int A2) B) tptp.bot_bot_set_int) (and (= A2 tptp.bot_bot_set_int) (= B tptp.bot_bot_set_int)))))
% 5.61/5.91 (assert (forall ((A2 tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (= (= (@ (@ tptp.sup_su5209123915105501825_nat_o A2) B) tptp.bot_bo7824918357723582233_nat_o) (and (= A2 tptp.bot_bo7824918357723582233_nat_o) (= B tptp.bot_bo7824918357723582233_nat_o)))))
% 5.61/5.91 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (= (@ (@ tptp.sup_sup_assn X) Y) tptp.bot_bot_assn) (and (= X tptp.bot_bot_assn) (= Y tptp.bot_bot_assn)))))
% 5.61/5.91 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (= (@ (@ tptp.sup_sup_Product_unit X) Y) tptp.bot_bot_Product_unit) (and (= X tptp.bot_bot_Product_unit) (= Y tptp.bot_bot_Product_unit)))))
% 5.61/5.91 (assert (forall ((X tptp.set_Product_unit) (Y tptp.set_Product_unit)) (= (= (@ (@ tptp.sup_su793286257634532545t_unit X) Y) tptp.bot_bo3957492148770167129t_unit) (and (= X tptp.bot_bo3957492148770167129t_unit) (= Y tptp.bot_bo3957492148770167129t_unit)))))
% 5.61/5.91 (assert (forall ((X tptp.set_o) (Y tptp.set_o)) (= (= (@ (@ tptp.sup_sup_set_o X) Y) tptp.bot_bot_set_o) (and (= X tptp.bot_bot_set_o) (= Y tptp.bot_bot_set_o)))))
% 5.61/5.91 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.sup_sup_set_nat X) Y) tptp.bot_bot_set_nat) (and (= X tptp.bot_bot_set_nat) (= Y tptp.bot_bot_set_nat)))))
% 5.61/5.91 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.sup_sup_set_int X) Y) tptp.bot_bot_set_int) (and (= X tptp.bot_bot_set_int) (= Y tptp.bot_bot_set_int)))))
% 5.61/5.91 (assert (forall ((X tptp.set_Pr4532377907799695533_nat_o) (Y tptp.set_Pr4532377907799695533_nat_o)) (= (= (@ (@ tptp.sup_su5209123915105501825_nat_o X) Y) tptp.bot_bo7824918357723582233_nat_o) (and (= X tptp.bot_bo7824918357723582233_nat_o) (= Y tptp.bot_bo7824918357723582233_nat_o)))))
% 5.61/5.91 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (= tptp.bot_bot_assn (@ (@ tptp.sup_sup_assn X) Y)) (and (= X tptp.bot_bot_assn) (= Y tptp.bot_bot_assn)))))
% 5.61/5.91 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (= tptp.bot_bot_Product_unit (@ (@ tptp.sup_sup_Product_unit X) Y)) (and (= X tptp.bot_bot_Product_unit) (= Y tptp.bot_bot_Product_unit)))))
% 5.61/5.91 (assert (forall ((X tptp.set_Product_unit) (Y tptp.set_Product_unit)) (= (= tptp.bot_bo3957492148770167129t_unit (@ (@ tptp.sup_su793286257634532545t_unit X) Y)) (and (= X tptp.bot_bo3957492148770167129t_unit) (= Y tptp.bot_bo3957492148770167129t_unit)))))
% 5.61/5.91 (assert (forall ((X tptp.set_o) (Y tptp.set_o)) (= (= tptp.bot_bot_set_o (@ (@ tptp.sup_sup_set_o X) Y)) (and (= X tptp.bot_bot_set_o) (= Y tptp.bot_bot_set_o)))))
% 5.61/5.91 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.sup_sup_set_nat X) Y)) (and (= X tptp.bot_bot_set_nat) (= Y tptp.bot_bot_set_nat)))))
% 5.61/5.91 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.sup_sup_set_int X) Y)) (and (= X tptp.bot_bot_set_int) (= Y tptp.bot_bot_set_int)))))
% 5.61/5.91 (assert (forall ((X tptp.set_Pr4532377907799695533_nat_o) (Y tptp.set_Pr4532377907799695533_nat_o)) (= (= tptp.bot_bo7824918357723582233_nat_o (@ (@ tptp.sup_su5209123915105501825_nat_o X) Y)) (and (= X tptp.bot_bo7824918357723582233_nat_o) (= Y tptp.bot_bo7824918357723582233_nat_o)))))
% 5.61/5.91 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) tptp.bot_bot_assn) X)))
% 5.61/5.91 (assert (forall ((X tptp.product_unit)) (= (@ (@ tptp.sup_sup_Product_unit X) tptp.bot_bot_Product_unit) X)))
% 5.61/5.91 (assert (forall ((X tptp.set_Product_unit)) (= (@ (@ tptp.sup_su793286257634532545t_unit X) tptp.bot_bo3957492148770167129t_unit) X)))
% 5.61/5.91 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o X) tptp.bot_bot_set_o) X)))
% 5.61/5.91 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) tptp.bot_bot_set_nat) X)))
% 5.61/5.91 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int X) tptp.bot_bot_set_int) X)))
% 5.61/5.91 (assert (forall ((X tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.sup_su5209123915105501825_nat_o X) tptp.bot_bo7824918357723582233_nat_o) X)))
% 5.61/5.91 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn tptp.bot_bot_assn) X) X)))
% 5.61/5.91 (assert (forall ((X tptp.product_unit)) (= (@ (@ tptp.sup_sup_Product_unit tptp.bot_bot_Product_unit) X) X)))
% 5.61/5.91 (assert (forall ((X tptp.set_Product_unit)) (= (@ (@ tptp.sup_su793286257634532545t_unit tptp.bot_bo3957492148770167129t_unit) X) X)))
% 5.61/5.91 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o tptp.bot_bot_set_o) X) X)))
% 5.61/5.92 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.bot_bot_set_nat) X) X)))
% 5.61/5.92 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int tptp.bot_bot_set_int) X) X)))
% 5.61/5.92 (assert (forall ((X tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.sup_su5209123915105501825_nat_o tptp.bot_bo7824918357723582233_nat_o) X) X)))
% 5.61/5.92 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) tptp.bot_bot_assn) tptp.bot_bot_assn)))
% 5.61/5.92 (assert (forall ((X tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit X) tptp.bot_bot_Product_unit) tptp.bot_bot_Product_unit)))
% 5.61/5.92 (assert (forall ((X tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit X) tptp.bot_bo3957492148770167129t_unit) tptp.bot_bo3957492148770167129t_unit)))
% 5.61/5.92 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o X) tptp.bot_bot_set_o) tptp.bot_bot_set_o)))
% 5.61/5.92 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)))
% 5.61/5.92 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X) tptp.bot_bot_set_int) tptp.bot_bot_set_int)))
% 5.61/5.92 (assert (forall ((X tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o X) tptp.bot_bo7824918357723582233_nat_o) tptp.bot_bo7824918357723582233_nat_o)))
% 5.61/5.92 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn tptp.bot_bot_assn) X) tptp.bot_bot_assn)))
% 5.61/5.92 (assert (forall ((X tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit tptp.bot_bot_Product_unit) X) tptp.bot_bot_Product_unit)))
% 5.61/5.92 (assert (forall ((X tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit tptp.bot_bo3957492148770167129t_unit) X) tptp.bot_bo3957492148770167129t_unit)))
% 5.61/5.92 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o tptp.bot_bot_set_o) X) tptp.bot_bot_set_o)))
% 5.61/5.92 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.bot_bot_set_nat) X) tptp.bot_bot_set_nat)))
% 5.61/5.92 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int tptp.bot_bot_set_int) X) tptp.bot_bot_set_int)))
% 5.61/5.92 (assert (forall ((X tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o tptp.bot_bo7824918357723582233_nat_o) X) tptp.bot_bo7824918357723582233_nat_o)))
% 5.61/5.92 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) tptp.bot_bot_assn) tptp.bot_bot_assn)))
% 5.61/5.92 (assert (forall ((X tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit X) tptp.bot_bot_Product_unit) tptp.bot_bot_Product_unit)))
% 5.61/5.92 (assert (forall ((X tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit X) tptp.bot_bo3957492148770167129t_unit) tptp.bot_bo3957492148770167129t_unit)))
% 5.61/5.92 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o X) tptp.bot_bot_set_o) tptp.bot_bot_set_o)))
% 5.61/5.92 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)))
% 5.61/5.92 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X) tptp.bot_bot_set_int) tptp.bot_bot_set_int)))
% 5.61/5.92 (assert (forall ((X tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o X) tptp.bot_bo7824918357723582233_nat_o) tptp.bot_bo7824918357723582233_nat_o)))
% 5.61/5.92 (assert (forall ((A2 Bool) (B Bool)) (= (@ (@ tptp.sup_sup_assn (@ tptp.pure_assn A2)) (@ tptp.pure_assn B)) (@ tptp.pure_assn (or A2 B)))))
% 5.61/5.92 (assert (forall ((A2 Bool) (B Bool)) (= (@ (@ tptp.inf_inf_assn (@ tptp.pure_assn A2)) (@ tptp.pure_assn B)) (@ tptp.pure_assn (and A2 B)))))
% 5.61/5.92 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn tptp.bot_bot_assn) X) tptp.bot_bot_assn)))
% 5.61/5.92 (assert (forall ((X tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit tptp.bot_bot_Product_unit) X) tptp.bot_bot_Product_unit)))
% 5.61/5.92 (assert (forall ((X tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit tptp.bot_bo3957492148770167129t_unit) X) tptp.bot_bo3957492148770167129t_unit)))
% 5.61/5.92 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o tptp.bot_bot_set_o) X) tptp.bot_bot_set_o)))
% 5.61/5.92 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.bot_bot_set_nat) X) tptp.bot_bot_set_nat)))
% 5.61/5.92 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int tptp.bot_bot_set_int) X) tptp.bot_bot_set_int)))
% 5.61/5.92 (assert (forall ((X tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o tptp.bot_bo7824918357723582233_nat_o) X) tptp.bot_bo7824918357723582233_nat_o)))
% 5.61/5.92 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) tptp.bot_bot_assn) X)))
% 5.61/5.92 (assert (forall ((X tptp.product_unit)) (= (@ (@ tptp.sup_sup_Product_unit X) tptp.bot_bot_Product_unit) X)))
% 5.61/5.92 (assert (forall ((X tptp.set_Product_unit)) (= (@ (@ tptp.sup_su793286257634532545t_unit X) tptp.bot_bo3957492148770167129t_unit) X)))
% 5.61/5.92 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o X) tptp.bot_bot_set_o) X)))
% 5.61/5.92 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) tptp.bot_bot_set_nat) X)))
% 5.61/5.92 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int X) tptp.bot_bot_set_int) X)))
% 5.61/5.92 (assert (forall ((X tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.sup_su5209123915105501825_nat_o X) tptp.bot_bo7824918357723582233_nat_o) X)))
% 5.61/5.92 (assert (= tptp.basic_2698842327037663054et_nat (lambda ((P5 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.insert_set_nat (@ tptp.produc8586169260539613262et_nat P5)) tptp.bot_bot_set_set_nat))))
% 5.61/5.92 (assert (= tptp.basic_snds_int_int (lambda ((P5 tptp.product_prod_int_int)) (@ (@ tptp.insert_int (@ tptp.product_snd_int_int P5)) tptp.bot_bot_set_int))))
% 5.61/5.92 (assert (forall ((A2 tptp.set_nat) (P3 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.member_set_nat A2) (@ tptp.basic_2698842327037663054et_nat P3)) (= A2 (@ tptp.produc8586169260539613262et_nat P3)))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (P3 tptp.product_prod_int_int)) (=> (@ (@ tptp.member_int A2) (@ tptp.basic_snds_int_int P3)) (= A2 (@ tptp.product_snd_int_int P3)))))
% 5.61/5.92 (assert (forall ((A2 tptp.set_nat) (P3 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.member_set_nat A2) (@ tptp.basic_2698842327037663054et_nat P3)) (= A2 (@ tptp.produc8586169260539613262et_nat P3)))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (P3 tptp.product_prod_int_int)) (= (@ (@ tptp.member_int A2) (@ tptp.basic_snds_int_int P3)) (= A2 (@ tptp.product_snd_int_int P3)))))
% 5.61/5.92 (assert (forall ((P3 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.member_set_nat (@ tptp.produc8586169260539613262et_nat P3)) (@ tptp.basic_2698842327037663054et_nat P3))))
% 5.61/5.92 (assert (forall ((P3 tptp.product_prod_int_int)) (@ (@ tptp.member_int (@ tptp.product_snd_int_int P3)) (@ tptp.basic_snds_int_int P3))))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ (@ tptp.wand_raw X) Xa) Xb) Y) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) Xb))) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As2))) (=> (= Xb _let_1) (=> (= Y (and (@ tptp.in_range _let_1) (forall ((H5 tptp.heap_e7401611519738050253t_unit) (As6 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H5))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As2) As6) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As2) H) H5) (@ tptp.in_range (@ _let_1 As2)) (@ X (@ _let_1 As6))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As6)))))))) (not (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1)))))))))))))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (@ (@ (@ tptp.wand_raw X) Xa) Xb) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) Xb))) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As2))) (=> (= Xb _let_1) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1))) (not (and (@ tptp.in_range _let_1) (forall ((H7 tptp.heap_e7401611519738050253t_unit) (As7 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H7))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As2) As7) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As2) H) H7) (@ tptp.in_range (@ _let_1 As2)) (@ X (@ _let_1 As7))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As7)))))))))))))))))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (not (@ (@ (@ tptp.wand_raw X) Xa) Xb)) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) Xb))) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As2))) (=> (= Xb _let_1) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1))) (and (@ tptp.in_range _let_1) (forall ((H6 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H6))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As2) As4) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As2) H) H6) (@ tptp.in_range (@ _let_1 As2)) (@ X (@ _let_1 As4))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As2) As4))))))))))))))))
% 5.61/5.92 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 5.61/5.92 (assert (@ (@ tptp.ord_le1926595141338095240atural tptp.one_one_Code_natural) tptp.one_one_Code_natural))
% 5.61/5.92 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 5.61/5.92 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 5.61/5.92 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 5.61/5.92 (assert (= tptp.ord_less_eq_assn (lambda ((A6 tptp.assn) (B6 tptp.assn)) (= A6 (@ (@ tptp.inf_inf_assn A6) B6)))))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (not (@ (@ (@ tptp.times_assn_raw X) Xa) Xb)) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) Xb))) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As2))) (=> (= Xb _let_1) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1))) (exists ((As13 tptp.set_nat) (As24 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H))) (and (= As2 (@ (@ tptp.sup_sup_set_nat As13) As24)) (= (@ (@ tptp.inf_inf_set_nat As13) As24) tptp.bot_bot_set_nat) (@ X (@ _let_1 As13)) (@ Xa (@ _let_1 As24))))))))))))))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (@ (@ (@ tptp.times_assn_raw X) Xa) Xb) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) Xb))) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As2))) (=> (= Xb _let_1) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1))) (not (exists ((As12 tptp.set_nat) (As23 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H))) (and (= As2 (@ (@ tptp.sup_sup_set_nat As12) As23)) (= (@ (@ tptp.inf_inf_set_nat As12) As23) tptp.bot_bot_set_nat) (@ X (@ _let_1 As12)) (@ Xa (@ _let_1 As23)))))))))))))))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ (@ tptp.times_assn_raw X) Xa) Xb) Y) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) Xb))) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As2))) (=> (= Xb _let_1) (=> (= Y (exists ((As1 tptp.set_nat) (As22 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H))) (and (= As2 (@ (@ tptp.sup_sup_set_nat As1) As22)) (= (@ (@ tptp.inf_inf_set_nat As1) As22) tptp.bot_bot_set_nat) (@ X (@ _let_1 As1)) (@ Xa (@ _let_1 As22)))))) (not (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1)))))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (@ tptp.image_8431784415008483091t_unit R2))) (let ((_let_2 (@ tptp.field_Product_unit R2))) (=> (@ (@ tptp.order_7534304569044981540t_unit _let_2) R2) (=> (@ (@ tptp.member_Product_unit A2) _let_2) (=> (@ (@ tptp.member_Product_unit B) _let_2) (= (@ (@ tptp.ord_le3507040750410214029t_unit (@ _let_1 (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit))) (@ _let_1 (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit))) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit B) A2)) R2)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (A2 Bool) (B Bool)) (let ((_let_1 (@ tptp.image_o_o R2))) (let ((_let_2 (@ tptp.field_o R2))) (=> (@ (@ tptp.order_preorder_on_o _let_2) R2) (=> (@ (@ tptp.member_o A2) _let_2) (=> (@ (@ tptp.member_o B) _let_2) (= (@ (@ tptp.ord_less_eq_set_o (@ _let_1 (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))) (@ _let_1 (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o B) A2)) R2)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.image_int_int R2))) (let ((_let_2 (@ tptp.field_int R2))) (=> (@ (@ tptp.order_4859164337913492053on_int _let_2) R2) (=> (@ (@ tptp.member_int A2) _let_2) (=> (@ (@ tptp.member_int B) _let_2) (= (@ (@ tptp.ord_less_eq_set_int (@ _let_1 (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))) (@ _let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) A2)) R2)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.image_2232984160439939859_nat_o R2))) (let ((_let_2 (@ tptp.field_81821745747897882_nat_o R2))) (=> (@ (@ tptp.order_174704566861754596_nat_o _let_2) R2) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) _let_2) (=> (@ (@ tptp.member6576561426505652726_nat_o B) _let_2) (= (@ (@ tptp.ord_le2965882846123202637_nat_o (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o))) (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o B) tptp.bot_bo7824918357723582233_nat_o))) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o B) A2)) R2)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.image_nat_nat R2))) (let ((_let_2 (@ tptp.field_nat R2))) (=> (@ (@ tptp.order_4861654808422542329on_nat _let_2) R2) (=> (@ (@ tptp.member_nat A2) _let_2) (=> (@ (@ tptp.member_nat B) _let_2) (= (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))) (@ _let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) A2)) R2)))))))))
% 5.61/5.92 (assert (forall ((A2 tptp.product_unit) (B tptp.product_unit) (R2 tptp.set_Pr5094982260447487303t_unit)) (= (@ tptp.field_Product_unit (@ (@ tptp.insert4616891024742550839t_unit (@ (@ tptp.produc5692694829384537815t_unit A2) B)) R2)) (@ (@ tptp.sup_su793286257634532545t_unit (@ (@ tptp.insert_Product_unit A2) (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit))) (@ tptp.field_Product_unit R2)))))
% 5.61/5.92 (assert (forall ((A2 Bool) (B Bool) (R2 tptp.set_Product_prod_o_o)) (= (@ tptp.field_o (@ (@ tptp.insert6201435330877294327od_o_o (@ (@ tptp.product_Pair_o_o A2) B)) R2)) (@ (@ tptp.sup_sup_set_o (@ (@ tptp.insert_o A2) (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (@ tptp.field_o R2)))))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.field_nat (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R2)) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.insert_nat A2) (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (@ tptp.field_nat R2)))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ tptp.field_int (@ (@ tptp.insert5033312907999012233nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R2)) (@ (@ tptp.sup_sup_set_int (@ (@ tptp.insert_int A2) (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (@ tptp.field_int R2)))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr2161125870931222855_nat_o)) (= (@ tptp.field_81821745747897882_nat_o (@ (@ tptp.insert5309882203591314743_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) B)) R2)) (@ (@ tptp.sup_su5209123915105501825_nat_o (@ (@ tptp.insert5175938949040314269_nat_o A2) (@ (@ tptp.insert5175938949040314269_nat_o B) tptp.bot_bo7824918357723582233_nat_o))) (@ tptp.field_81821745747897882_nat_o R2)))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr5094982260447487303t_unit)) (=> (= (@ (@ tptp.inf_in4660618365625256667t_unit (@ tptp.domain4292024440186670924t_unit R3)) (@ tptp.range_6617724647562260917t_unit R3)) tptp.bot_bo3957492148770167129t_unit) (= (@ (@ tptp.relcom848357998638694028t_unit R3) R3) tptp.bot_bo1654022762305692595t_unit))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Product_prod_o_o)) (=> (= (@ (@ tptp.inf_inf_set_o (@ tptp.domain_o_o R3)) (@ tptp.range_o_o R3)) tptp.bot_bot_set_o) (= (@ (@ tptp.relcomp_o_o_o R3) R3) tptp.bot_bo7073875226086086771od_o_o))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat)) (=> (= (@ (@ tptp.inf_inf_set_nat (@ tptp.domain_nat_nat R3)) (@ tptp.range_nat_nat R3)) tptp.bot_bot_set_nat) (= (@ (@ tptp.relcomp_nat_nat_nat R3) R3) tptp.bot_bo2099793752762293965at_nat))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int)) (=> (= (@ (@ tptp.inf_inf_set_int (@ tptp.domain_int_int R3)) (@ tptp.range_int_int R3)) tptp.bot_bot_set_int) (= (@ (@ tptp.relcomp_int_int_int R3) R3) tptp.bot_bo1796632182523588997nt_int))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr2161125870931222855_nat_o)) (=> (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ tptp.domain4881241903163524940_nat_o R3)) (@ tptp.range_5289318983786108341_nat_o R3)) tptp.bot_bo7824918357723582233_nat_o) (= (@ (@ tptp.relcom6251035627269349452_nat_o R3) R3) tptp.bot_bo3657187498359500723_nat_o))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit) (X tptp.product_unit) (Y tptp.product_unit)) (let ((_let_1 (@ tptp.equiv_5763582929720877514t_unit R2))) (=> (@ (@ tptp.equiv_4189356295871601603t_unit A) R2) (=> (@ (@ tptp.ord_le3507040750410214029t_unit (@ (@ tptp.insert_Product_unit X) (@ (@ tptp.insert_Product_unit Y) tptp.bot_bo3957492148770167129t_unit))) A) (= (= (@ _let_1 X) (@ _let_1 Y)) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit X) Y)) R2)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o) (X Bool) (Y Bool)) (let ((_let_1 (@ tptp.equiv_proj_o_o R2))) (=> (@ (@ tptp.equiv_equiv_o A) R2) (=> (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.insert_o X) (@ (@ tptp.insert_o Y) tptp.bot_bot_set_o))) A) (= (= (@ _let_1 X) (@ _let_1 Y)) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X) Y)) R2)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.equiv_proj_int_int R2))) (=> (@ (@ tptp.equiv_equiv_int A) R2) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int X) (@ (@ tptp.insert_int Y) tptp.bot_bot_set_int))) A) (= (= (@ _let_1 X) (@ _let_1 Y)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R2)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.equiv_3235788788526563786_nat_o R2))) (=> (@ (@ tptp.equiv_6726761681920839555_nat_o A) R2) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) (@ (@ tptp.insert5175938949040314269_nat_o Y) tptp.bot_bo7824918357723582233_nat_o))) A) (= (= (@ _let_1 X) (@ _let_1 Y)) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X) Y)) R2)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.equiv_proj_nat_nat R2))) (=> (@ (@ tptp.equiv_equiv_nat A) R2) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X) (@ (@ tptp.insert_nat Y) tptp.bot_bot_set_nat))) A) (= (= (@ _let_1 X) (@ _let_1 Y)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R2)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (@ tptp.image_8431784415008483091t_unit R2))) (let ((_let_2 (@ tptp.field_Product_unit R2))) (=> (@ (@ tptp.refl_on_Product_unit _let_2) R2) (=> (@ tptp.antisym_Product_unit R2) (=> (@ (@ tptp.member_Product_unit A2) _let_2) (=> (@ (@ tptp.member_Product_unit B) _let_2) (= (= (@ _let_1 (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit)) (@ _let_1 (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit))) (= A2 B))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (A2 Bool) (B Bool)) (let ((_let_1 (@ tptp.image_o_o R2))) (let ((_let_2 (@ tptp.field_o R2))) (=> (@ (@ tptp.refl_on_o _let_2) R2) (=> (@ tptp.antisym_o R2) (=> (@ (@ tptp.member_o A2) _let_2) (=> (@ (@ tptp.member_o B) _let_2) (= (= (@ _let_1 (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o)) (@ _let_1 (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (= A2 B))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.image_nat_nat R2))) (let ((_let_2 (@ tptp.field_nat R2))) (=> (@ (@ tptp.refl_on_nat _let_2) R2) (=> (@ tptp.antisym_nat R2) (=> (@ (@ tptp.member_nat A2) _let_2) (=> (@ (@ tptp.member_nat B) _let_2) (= (= (@ _let_1 (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat)) (@ _let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (= A2 B))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.image_int_int R2))) (let ((_let_2 (@ tptp.field_int R2))) (=> (@ (@ tptp.refl_on_int _let_2) R2) (=> (@ tptp.antisym_int R2) (=> (@ (@ tptp.member_int A2) _let_2) (=> (@ (@ tptp.member_int B) _let_2) (= (= (@ _let_1 (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int)) (@ _let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (= A2 B))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.image_2232984160439939859_nat_o R2))) (let ((_let_2 (@ tptp.field_81821745747897882_nat_o R2))) (=> (@ (@ tptp.refl_o1075864025857821388_nat_o _let_2) R2) (=> (@ tptp.antisy9190549550370998639_nat_o R2) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) _let_2) (=> (@ (@ tptp.member6576561426505652726_nat_o B) _let_2) (= (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o)) (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o B) tptp.bot_bo7824918357723582233_nat_o))) (= A2 B))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit) (X tptp.product_unit) (A2 tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (@ tptp.image_8431784415008483091t_unit R2))) (=> (@ (@ tptp.equiv_4189356295871601603t_unit A) R2) (=> (@ (@ tptp.member_Product_unit X) (@ (@ tptp.inf_in4660618365625256667t_unit (@ _let_1 (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit))) (@ _let_1 (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit)))) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit A2) B)) R2))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o) (X Bool) (A2 Bool) (B Bool)) (let ((_let_1 (@ tptp.image_o_o R2))) (=> (@ (@ tptp.equiv_equiv_o A) R2) (=> (@ (@ tptp.member_o X) (@ (@ tptp.inf_inf_set_o (@ _let_1 (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))) (@ _let_1 (@ (@ tptp.insert_o B) tptp.bot_bot_set_o)))) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) B)) R2))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (X tptp.nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.image_nat_nat R2))) (=> (@ (@ tptp.equiv_equiv_nat A) R2) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.inf_inf_set_nat (@ _let_1 (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))) (@ _let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat)))) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R2))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int) (X tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.image_int_int R2))) (=> (@ (@ tptp.equiv_equiv_int A) R2) (=> (@ (@ tptp.member_int X) (@ (@ tptp.inf_inf_set_int (@ _let_1 (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))) (@ _let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int)))) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R2))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.image_2232984160439939859_nat_o R2))) (=> (@ (@ tptp.equiv_6726761681920839555_nat_o A) R2) (=> (@ (@ tptp.member6576561426505652726_nat_o X) (@ (@ tptp.inf_in1906310914598751387_nat_o (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o))) (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o B) tptp.bot_bo7824918357723582233_nat_o)))) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) B)) R2))))))
% 5.61/5.92 (assert (forall ((E tptp.set_Pr4811707699266497531nteger) (V0 tptp.code_integer) (V tptp.code_integer)) (let ((_let_1 (@ tptp.transi3984306202085910426nteger E))) (let ((_let_2 (@ tptp.image_4147621952751189391nteger _let_1))) (=> (@ tptp.finite6017078050557962740nteger (@ _let_2 (@ (@ tptp.insert_Code_integer V0) tptp.bot_bo3990330152332043303nteger))) (=> (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger V0) V)) _let_1) (@ tptp.finite6017078050557962740nteger (@ _let_2 (@ (@ tptp.insert_Code_integer V) tptp.bot_bo3990330152332043303nteger)))))))))
% 5.61/5.92 (assert (forall ((E tptp.set_Pr5094982260447487303t_unit) (V0 tptp.product_unit) (V tptp.product_unit)) (let ((_let_1 (@ tptp.transi6481887417741755664t_unit E))) (let ((_let_2 (@ tptp.image_8431784415008483091t_unit _let_1))) (=> (@ tptp.finite4290736615968046902t_unit (@ _let_2 (@ (@ tptp.insert_Product_unit V0) tptp.bot_bo3957492148770167129t_unit))) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit V0) V)) _let_1) (@ tptp.finite4290736615968046902t_unit (@ _let_2 (@ (@ tptp.insert_Product_unit V) tptp.bot_bo3957492148770167129t_unit)))))))))
% 5.61/5.92 (assert (forall ((E tptp.set_Product_prod_o_o) (V0 Bool) (V Bool)) (let ((_let_1 (@ tptp.transitive_rtrancl_o E))) (let ((_let_2 (@ tptp.image_o_o _let_1))) (=> (@ tptp.finite_finite_o (@ _let_2 (@ (@ tptp.insert_o V0) tptp.bot_bot_set_o))) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o V0) V)) _let_1) (@ tptp.finite_finite_o (@ _let_2 (@ (@ tptp.insert_o V) tptp.bot_bot_set_o)))))))))
% 5.61/5.92 (assert (forall ((E tptp.set_Pr1261947904930325089at_nat) (V0 tptp.nat) (V tptp.nat)) (let ((_let_1 (@ tptp.transi2905341329935302413cl_nat E))) (let ((_let_2 (@ tptp.image_nat_nat _let_1))) (=> (@ tptp.finite_finite_nat (@ _let_2 (@ (@ tptp.insert_nat V0) tptp.bot_bot_set_nat))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat V0) V)) _let_1) (@ tptp.finite_finite_nat (@ _let_2 (@ (@ tptp.insert_nat V) tptp.bot_bot_set_nat)))))))))
% 5.61/5.92 (assert (forall ((E tptp.set_Pr958786334691620121nt_int) (V0 tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.transi2902850859426252137cl_int E))) (let ((_let_2 (@ tptp.image_int_int _let_1))) (=> (@ tptp.finite_finite_int (@ _let_2 (@ (@ tptp.insert_int V0) tptp.bot_bot_set_int))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int V0) V)) _let_1) (@ tptp.finite_finite_int (@ _let_2 (@ (@ tptp.insert_int V) tptp.bot_bot_set_int)))))))))
% 5.61/5.92 (assert (forall ((E tptp.set_Pr2161125870931222855_nat_o) (V0 (-> tptp.produc3658429121746597890et_nat Bool)) (V (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.transi712980445759334096_nat_o E))) (let ((_let_2 (@ tptp.image_2232984160439939859_nat_o _let_1))) (=> (@ tptp.finite3252695134891459830_nat_o (@ _let_2 (@ (@ tptp.insert5175938949040314269_nat_o V0) tptp.bot_bo7824918357723582233_nat_o))) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o V0) V)) _let_1) (@ tptp.finite3252695134891459830_nat_o (@ _let_2 (@ (@ tptp.insert5175938949040314269_nat_o V) tptp.bot_bo7824918357723582233_nat_o)))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.finite_finite_nat (@ tptp.field_nat R3)) (@ tptp.finite6177210948735845034at_nat R3))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr4811707699266497531nteger)) (= (@ tptp.finite6017078050557962740nteger (@ tptp.field_Code_integer R3)) (@ tptp.finite2154694888287295812nteger R3))))
% 5.61/5.92 (assert (= (@ tptp.field_Product_unit tptp.bot_bo1654022762305692595t_unit) tptp.bot_bo3957492148770167129t_unit))
% 5.61/5.92 (assert (= (@ tptp.field_o tptp.bot_bo7073875226086086771od_o_o) tptp.bot_bot_set_o))
% 5.61/5.92 (assert (= (@ tptp.field_nat tptp.bot_bo2099793752762293965at_nat) tptp.bot_bot_set_nat))
% 5.61/5.92 (assert (= (@ tptp.field_int tptp.bot_bo1796632182523588997nt_int) tptp.bot_bot_set_int))
% 5.61/5.92 (assert (= (@ tptp.field_81821745747897882_nat_o tptp.bot_bo3657187498359500723_nat_o) tptp.bot_bo7824918357723582233_nat_o))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.field_nat (@ (@ tptp.sup_su6327502436637775413at_nat R2) S2)) (@ (@ tptp.sup_sup_set_nat (@ tptp.field_nat R2)) (@ tptp.field_nat S2)))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat R2) (@ tptp.finite_finite_nat (@ tptp.field_nat R2)))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr4811707699266497531nteger)) (=> (@ tptp.finite2154694888287295812nteger R2) (@ tptp.finite6017078050557962740nteger (@ tptp.field_Code_integer R2)))))
% 5.61/5.92 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (C tptp.set_nat) (R2 tptp.set_Pr1776176089890104647t_unit) (S2 tptp.set_Pr3948176798113811640et_nat)) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) C)) (@ (@ tptp.relcom4930750947919833671et_nat R2) S2)) (not (forall ((B2 tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ tptp.member5046970461208427408t_unit (@ (@ tptp.produc8256076736985659095t_unit A2) B2)) R2) (not (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat B2) C)) S2))))))))
% 5.61/5.92 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (C tptp.set_nat) (R2 tptp.set_Pr3948176798113811640et_nat) (S2 tptp.set_Pr5488025237498180813et_nat)) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) C)) (@ (@ tptp.relcom8881708762719574682et_nat R2) S2)) (not (forall ((B2 tptp.set_nat)) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) B2)) R2) (not (@ (@ tptp.member8277197624267554838et_nat (@ (@ tptp.produc4532415448927165861et_nat B2) C)) S2))))))))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (C tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) C)) (@ (@ tptp.relcomp_nat_nat_nat R2) S2)) (not (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B2)) R2) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B2) C)) S2))))))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (C tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (S2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) C)) (@ (@ tptp.relcomp_int_int_int R2) S2)) (not (forall ((B2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B2)) R2) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B2) C)) S2))))))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (C tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr2161125870931222855_nat_o) (S2 tptp.set_Pr3286484037609594932et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) C)) (@ (@ tptp.relcom6619595054755144899et_nat R2) S2)) (not (forall ((B2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) B2)) R2) (not (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat B2) C)) S2))))))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (C tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr3286484037609594932et_nat) (S2 tptp.set_Pr719794911490849221et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) C)) (@ (@ tptp.relcom5975814107203797650et_nat R2) S2)) (not (forall ((B2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) B2)) R2) (not (@ (@ tptp.member6099555550032318734et_nat (@ (@ tptp.produc8199053930788261021et_nat B2) C)) S2))))))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (C tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr8536935166611901872et_nat) (S2 tptp.set_Pr3721596426557623617et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) C)) (@ (@ tptp.relcom430014394250001422et_nat R2) S2)) (not (forall ((B2 tptp.produc3925858234332021118et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) B2)) R2) (not (@ (@ tptp.member6613709072892554et_nat (@ (@ tptp.produc5530789758353788441et_nat B2) C)) S2))))))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (C tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr2161125870931222855_nat_o) (S2 tptp.set_Pr8536935166611901872et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) C)) (@ (@ tptp.relcom2608444778321954367et_nat R2) S2)) (not (forall ((B2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) B2)) R2) (not (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat B2) C)) S2))))))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (C tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr3286484037609594932et_nat) (S2 tptp.set_Pr8807100098903490369et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) C)) (@ (@ tptp.relcom8031709186682293262et_nat R2) S2)) (not (forall ((B2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) B2)) R2) (not (@ (@ tptp.member2737525317995836554et_nat (@ (@ tptp.produc3909112513931304473et_nat B2) C)) S2))))))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (C tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr8536935166611901872et_nat) (S2 tptp.set_Pr7928877670098842301et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) C)) (@ (@ tptp.relcom8303140135939483018et_nat R2) S2)) (not (forall ((B2 tptp.produc3925858234332021118et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) B2)) R2) (not (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat B2) C)) S2))))))))
% 5.61/5.92 (assert (forall ((Xz tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr1776176089890104647t_unit) (S2 tptp.set_Pr3948176798113811640et_nat)) (=> (@ (@ tptp.member6260224972018164377et_nat Xz) (@ (@ tptp.relcom4930750947919833671et_nat R2) S2)) (not (forall ((X3 tptp.heap_e7401611519738050253t_unit) (Y2 tptp.heap_e7401611519738050253t_unit) (Z3 tptp.set_nat)) (=> (= Xz (@ (@ tptp.produc7507926704131184380et_nat X3) Z3)) (=> (@ (@ tptp.member5046970461208427408t_unit (@ (@ tptp.produc8256076736985659095t_unit X3) Y2)) R2) (not (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat Y2) Z3)) S2)))))))))
% 5.61/5.92 (assert (forall ((Xz tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr3948176798113811640et_nat) (S2 tptp.set_Pr5488025237498180813et_nat)) (=> (@ (@ tptp.member6260224972018164377et_nat Xz) (@ (@ tptp.relcom8881708762719574682et_nat R2) S2)) (not (forall ((X3 tptp.heap_e7401611519738050253t_unit) (Y2 tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat X3))) (=> (= Xz (@ _let_1 Z3)) (=> (@ (@ tptp.member6260224972018164377et_nat (@ _let_1 Y2)) R2) (not (@ (@ tptp.member8277197624267554838et_nat (@ (@ tptp.produc4532415448927165861et_nat Y2) Z3)) S2))))))))))
% 5.61/5.92 (assert (forall ((Xz tptp.product_prod_nat_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Xz) (@ (@ tptp.relcomp_nat_nat_nat R2) S2)) (not (forall ((X3 tptp.nat) (Y2 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X3))) (=> (= Xz (@ _let_1 Z3)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 Y2)) R2) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Z3)) S2))))))))))
% 5.61/5.92 (assert (forall ((Xz tptp.product_prod_int_int) (R2 tptp.set_Pr958786334691620121nt_int) (S2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int Xz) (@ (@ tptp.relcomp_int_int_int R2) S2)) (not (forall ((X3 tptp.int) (Y2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int X3))) (=> (= Xz (@ _let_1 Z3)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 Y2)) R2) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y2) Z3)) S2))))))))))
% 5.61/5.92 (assert (forall ((Xz tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr2161125870931222855_nat_o) (S2 tptp.set_Pr3286484037609594932et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat Xz) (@ (@ tptp.relcom6619595054755144899et_nat R2) S2)) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 (-> tptp.produc3658429121746597890et_nat Bool)) (Z3 tptp.produc3658429121746597890et_nat)) (=> (= Xz (@ (@ tptp.produc5001842942810119800et_nat X3) Z3)) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X3) Y2)) R2) (not (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat Y2) Z3)) S2)))))))))
% 5.61/5.92 (assert (forall ((Xz tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr3286484037609594932et_nat) (S2 tptp.set_Pr719794911490849221et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat Xz) (@ (@ tptp.relcom5975814107203797650et_nat R2) S2)) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3658429121746597890et_nat) (Z3 tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.produc5001842942810119800et_nat X3))) (=> (= Xz (@ _let_1 Z3)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 Y2)) R2) (not (@ (@ tptp.member6099555550032318734et_nat (@ (@ tptp.produc8199053930788261021et_nat Y2) Z3)) S2))))))))))
% 5.61/5.92 (assert (forall ((Xz tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr8536935166611901872et_nat) (S2 tptp.set_Pr3721596426557623617et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat Xz) (@ (@ tptp.relcom430014394250001422et_nat R2) S2)) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3925858234332021118et_nat) (Z3 tptp.produc3658429121746597890et_nat)) (=> (= Xz (@ (@ tptp.produc5001842942810119800et_nat X3) Z3)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X3) Y2)) R2) (not (@ (@ tptp.member6613709072892554et_nat (@ (@ tptp.produc5530789758353788441et_nat Y2) Z3)) S2)))))))))
% 5.61/5.92 (assert (forall ((Xz tptp.produc2732055786443039994et_nat) (R2 tptp.set_Pr2161125870931222855_nat_o) (S2 tptp.set_Pr8536935166611901872et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat Xz) (@ (@ tptp.relcom2608444778321954367et_nat R2) S2)) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 (-> tptp.produc3658429121746597890et_nat Bool)) (Z3 tptp.produc3925858234332021118et_nat)) (=> (= Xz (@ (@ tptp.produc2245416461498447860et_nat X3) Z3)) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X3) Y2)) R2) (not (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat Y2) Z3)) S2)))))))))
% 5.61/5.92 (assert (forall ((Xz tptp.produc2732055786443039994et_nat) (R2 tptp.set_Pr3286484037609594932et_nat) (S2 tptp.set_Pr8807100098903490369et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat Xz) (@ (@ tptp.relcom8031709186682293262et_nat R2) S2)) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3658429121746597890et_nat) (Z3 tptp.produc3925858234332021118et_nat)) (=> (= Xz (@ (@ tptp.produc2245416461498447860et_nat X3) Z3)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X3) Y2)) R2) (not (@ (@ tptp.member2737525317995836554et_nat (@ (@ tptp.produc3909112513931304473et_nat Y2) Z3)) S2)))))))))
% 5.61/5.92 (assert (forall ((Xz tptp.produc2732055786443039994et_nat) (R2 tptp.set_Pr8536935166611901872et_nat) (S2 tptp.set_Pr7928877670098842301et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat Xz) (@ (@ tptp.relcom8303140135939483018et_nat R2) S2)) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3925858234332021118et_nat) (Z3 tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ tptp.produc2245416461498447860et_nat X3))) (=> (= Xz (@ _let_1 Z3)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 Y2)) R2) (not (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat Y2) Z3)) S2))))))))))
% 5.61/5.92 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B tptp.heap_e7401611519738050253t_unit) (R2 tptp.set_Pr1776176089890104647t_unit) (C tptp.set_nat) (S2 tptp.set_Pr3948176798113811640et_nat)) (=> (@ (@ tptp.member5046970461208427408t_unit (@ (@ tptp.produc8256076736985659095t_unit A2) B)) R2) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat B) C)) S2) (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) C)) (@ (@ tptp.relcom4930750947919833671et_nat R2) S2))))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr2161125870931222855_nat_o) (C tptp.produc3658429121746597890et_nat) (S2 tptp.set_Pr3286484037609594932et_nat)) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) B)) R2) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat B) C)) S2) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) C)) (@ (@ tptp.relcom6619595054755144899et_nat R2) S2))))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr2161125870931222855_nat_o) (C tptp.produc3925858234332021118et_nat) (S2 tptp.set_Pr8536935166611901872et_nat)) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) B)) R2) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat B) C)) S2) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) C)) (@ (@ tptp.relcom2608444778321954367et_nat R2) S2))))))
% 5.61/5.92 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat) (R2 tptp.set_Pr3948176798113811640et_nat) (C tptp.set_nat) (S2 tptp.set_Pr5488025237498180813et_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat A2))) (=> (@ (@ tptp.member6260224972018164377et_nat (@ _let_1 B)) R2) (=> (@ (@ tptp.member8277197624267554838et_nat (@ (@ tptp.produc4532415448927165861et_nat B) C)) S2) (@ (@ tptp.member6260224972018164377et_nat (@ _let_1 C)) (@ (@ tptp.relcom8881708762719574682et_nat R2) S2)))))))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (C tptp.nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat A2))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 B)) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) C)) S2) (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 C)) (@ (@ tptp.relcomp_nat_nat_nat R2) S2)))))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (C tptp.int) (S2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.product_Pair_int_int A2))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 B)) R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) C)) S2) (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 C)) (@ (@ tptp.relcomp_int_int_int R2) S2)))))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr3286484037609594932et_nat) (C tptp.produc3658429121746597890et_nat) (S2 tptp.set_Pr719794911490849221et_nat)) (let ((_let_1 (@ tptp.produc5001842942810119800et_nat A2))) (=> (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 B)) R2) (=> (@ (@ tptp.member6099555550032318734et_nat (@ (@ tptp.produc8199053930788261021et_nat B) C)) S2) (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 C)) (@ (@ tptp.relcom5975814107203797650et_nat R2) S2)))))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr3286484037609594932et_nat) (C tptp.produc3925858234332021118et_nat) (S2 tptp.set_Pr8807100098903490369et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) B)) R2) (=> (@ (@ tptp.member2737525317995836554et_nat (@ (@ tptp.produc3909112513931304473et_nat B) C)) S2) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) C)) (@ (@ tptp.relcom8031709186682293262et_nat R2) S2))))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr8536935166611901872et_nat) (C tptp.produc3658429121746597890et_nat) (S2 tptp.set_Pr3721596426557623617et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) B)) R2) (=> (@ (@ tptp.member6613709072892554et_nat (@ (@ tptp.produc5530789758353788441et_nat B) C)) S2) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) C)) (@ (@ tptp.relcom430014394250001422et_nat R2) S2))))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr8536935166611901872et_nat) (C tptp.produc3925858234332021118et_nat) (S2 tptp.set_Pr7928877670098842301et_nat)) (let ((_let_1 (@ tptp.produc2245416461498447860et_nat A2))) (=> (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 B)) R2) (=> (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat B) C)) S2) (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 C)) (@ (@ tptp.relcom8303140135939483018et_nat R2) S2)))))))
% 5.61/5.92 (assert (forall ((A1 tptp.heap_e7401611519738050253t_unit) (A22 tptp.set_nat) (R2 tptp.set_Pr1776176089890104647t_unit) (S2 tptp.set_Pr3948176798113811640et_nat)) (= (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A1) A22)) (@ (@ tptp.relcom4930750947919833671et_nat R2) S2)) (exists ((A6 tptp.heap_e7401611519738050253t_unit) (B6 tptp.heap_e7401611519738050253t_unit) (C4 tptp.set_nat)) (and (= A1 A6) (= A22 C4) (@ (@ tptp.member5046970461208427408t_unit (@ (@ tptp.produc8256076736985659095t_unit A6) B6)) R2) (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat B6) C4)) S2))))))
% 5.61/5.92 (assert (forall ((A1 tptp.heap_e7401611519738050253t_unit) (A22 tptp.set_nat) (R2 tptp.set_Pr3948176798113811640et_nat) (S2 tptp.set_Pr5488025237498180813et_nat)) (= (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A1) A22)) (@ (@ tptp.relcom8881708762719574682et_nat R2) S2)) (exists ((A6 tptp.heap_e7401611519738050253t_unit) (B6 tptp.set_nat) (C4 tptp.set_nat)) (and (= A1 A6) (= A22 C4) (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A6) B6)) R2) (@ (@ tptp.member8277197624267554838et_nat (@ (@ tptp.produc4532415448927165861et_nat B6) C4)) S2))))))
% 5.61/5.92 (assert (forall ((A1 tptp.nat) (A22 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A1) A22)) (@ (@ tptp.relcomp_nat_nat_nat R2) S2)) (exists ((A6 tptp.nat) (B6 tptp.nat) (C4 tptp.nat)) (and (= A1 A6) (= A22 C4) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A6) B6)) R2) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B6) C4)) S2))))))
% 5.61/5.92 (assert (forall ((A1 tptp.int) (A22 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (S2 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A1) A22)) (@ (@ tptp.relcomp_int_int_int R2) S2)) (exists ((A6 tptp.int) (B6 tptp.int) (C4 tptp.int)) (and (= A1 A6) (= A22 C4) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A6) B6)) R2) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B6) C4)) S2))))))
% 5.61/5.92 (assert (forall ((A1 (-> tptp.produc3658429121746597890et_nat Bool)) (A22 tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr2161125870931222855_nat_o) (S2 tptp.set_Pr3286484037609594932et_nat)) (= (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A1) A22)) (@ (@ tptp.relcom6619595054755144899et_nat R2) S2)) (exists ((A6 (-> tptp.produc3658429121746597890et_nat Bool)) (B6 (-> tptp.produc3658429121746597890et_nat Bool)) (C4 tptp.produc3658429121746597890et_nat)) (and (= A1 A6) (= A22 C4) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A6) B6)) R2) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat B6) C4)) S2))))))
% 5.61/5.92 (assert (forall ((A1 (-> tptp.produc3658429121746597890et_nat Bool)) (A22 tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr3286484037609594932et_nat) (S2 tptp.set_Pr719794911490849221et_nat)) (= (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A1) A22)) (@ (@ tptp.relcom5975814107203797650et_nat R2) S2)) (exists ((A6 (-> tptp.produc3658429121746597890et_nat Bool)) (B6 tptp.produc3658429121746597890et_nat) (C4 tptp.produc3658429121746597890et_nat)) (and (= A1 A6) (= A22 C4) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A6) B6)) R2) (@ (@ tptp.member6099555550032318734et_nat (@ (@ tptp.produc8199053930788261021et_nat B6) C4)) S2))))))
% 5.61/5.92 (assert (forall ((A1 (-> tptp.produc3658429121746597890et_nat Bool)) (A22 tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr8536935166611901872et_nat) (S2 tptp.set_Pr3721596426557623617et_nat)) (= (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A1) A22)) (@ (@ tptp.relcom430014394250001422et_nat R2) S2)) (exists ((A6 (-> tptp.produc3658429121746597890et_nat Bool)) (B6 tptp.produc3925858234332021118et_nat) (C4 tptp.produc3658429121746597890et_nat)) (and (= A1 A6) (= A22 C4) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A6) B6)) R2) (@ (@ tptp.member6613709072892554et_nat (@ (@ tptp.produc5530789758353788441et_nat B6) C4)) S2))))))
% 5.61/5.92 (assert (forall ((A1 (-> tptp.produc3658429121746597890et_nat Bool)) (A22 tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr2161125870931222855_nat_o) (S2 tptp.set_Pr8536935166611901872et_nat)) (= (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A1) A22)) (@ (@ tptp.relcom2608444778321954367et_nat R2) S2)) (exists ((A6 (-> tptp.produc3658429121746597890et_nat Bool)) (B6 (-> tptp.produc3658429121746597890et_nat Bool)) (C4 tptp.produc3925858234332021118et_nat)) (and (= A1 A6) (= A22 C4) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A6) B6)) R2) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat B6) C4)) S2))))))
% 5.61/5.92 (assert (forall ((A1 (-> tptp.produc3658429121746597890et_nat Bool)) (A22 tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr3286484037609594932et_nat) (S2 tptp.set_Pr8807100098903490369et_nat)) (= (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A1) A22)) (@ (@ tptp.relcom8031709186682293262et_nat R2) S2)) (exists ((A6 (-> tptp.produc3658429121746597890et_nat Bool)) (B6 tptp.produc3658429121746597890et_nat) (C4 tptp.produc3925858234332021118et_nat)) (and (= A1 A6) (= A22 C4) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A6) B6)) R2) (@ (@ tptp.member2737525317995836554et_nat (@ (@ tptp.produc3909112513931304473et_nat B6) C4)) S2))))))
% 5.61/5.92 (assert (forall ((A1 (-> tptp.produc3658429121746597890et_nat Bool)) (A22 tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr8536935166611901872et_nat) (S2 tptp.set_Pr7928877670098842301et_nat)) (= (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A1) A22)) (@ (@ tptp.relcom8303140135939483018et_nat R2) S2)) (exists ((A6 (-> tptp.produc3658429121746597890et_nat Bool)) (B6 tptp.produc3925858234332021118et_nat) (C4 tptp.produc3925858234332021118et_nat)) (and (= A1 A6) (= A22 C4) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A6) B6)) R2) (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat B6) C4)) S2))))))
% 5.61/5.92 (assert (forall ((A1 tptp.heap_e7401611519738050253t_unit) (A22 tptp.set_nat) (R2 tptp.set_Pr1776176089890104647t_unit) (S2 tptp.set_Pr3948176798113811640et_nat)) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A1) A22)) (@ (@ tptp.relcom4930750947919833671et_nat R2) S2)) (not (forall ((B2 tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ tptp.member5046970461208427408t_unit (@ (@ tptp.produc8256076736985659095t_unit A1) B2)) R2) (not (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat B2) A22)) S2))))))))
% 5.61/5.92 (assert (forall ((A1 tptp.heap_e7401611519738050253t_unit) (A22 tptp.set_nat) (R2 tptp.set_Pr3948176798113811640et_nat) (S2 tptp.set_Pr5488025237498180813et_nat)) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A1) A22)) (@ (@ tptp.relcom8881708762719574682et_nat R2) S2)) (not (forall ((B2 tptp.set_nat)) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A1) B2)) R2) (not (@ (@ tptp.member8277197624267554838et_nat (@ (@ tptp.produc4532415448927165861et_nat B2) A22)) S2))))))))
% 5.61/5.92 (assert (forall ((A1 tptp.nat) (A22 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A1) A22)) (@ (@ tptp.relcomp_nat_nat_nat R2) S2)) (not (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A1) B2)) R2) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B2) A22)) S2))))))))
% 5.61/5.92 (assert (forall ((A1 tptp.int) (A22 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (S2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A1) A22)) (@ (@ tptp.relcomp_int_int_int R2) S2)) (not (forall ((B2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A1) B2)) R2) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B2) A22)) S2))))))))
% 5.61/5.92 (assert (forall ((A1 (-> tptp.produc3658429121746597890et_nat Bool)) (A22 tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr2161125870931222855_nat_o) (S2 tptp.set_Pr3286484037609594932et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A1) A22)) (@ (@ tptp.relcom6619595054755144899et_nat R2) S2)) (not (forall ((B2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A1) B2)) R2) (not (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat B2) A22)) S2))))))))
% 5.61/5.92 (assert (forall ((A1 (-> tptp.produc3658429121746597890et_nat Bool)) (A22 tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr3286484037609594932et_nat) (S2 tptp.set_Pr719794911490849221et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A1) A22)) (@ (@ tptp.relcom5975814107203797650et_nat R2) S2)) (not (forall ((B2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A1) B2)) R2) (not (@ (@ tptp.member6099555550032318734et_nat (@ (@ tptp.produc8199053930788261021et_nat B2) A22)) S2))))))))
% 5.61/5.92 (assert (forall ((A1 (-> tptp.produc3658429121746597890et_nat Bool)) (A22 tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr8536935166611901872et_nat) (S2 tptp.set_Pr3721596426557623617et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A1) A22)) (@ (@ tptp.relcom430014394250001422et_nat R2) S2)) (not (forall ((B2 tptp.produc3925858234332021118et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A1) B2)) R2) (not (@ (@ tptp.member6613709072892554et_nat (@ (@ tptp.produc5530789758353788441et_nat B2) A22)) S2))))))))
% 5.61/5.92 (assert (forall ((A1 (-> tptp.produc3658429121746597890et_nat Bool)) (A22 tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr2161125870931222855_nat_o) (S2 tptp.set_Pr8536935166611901872et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A1) A22)) (@ (@ tptp.relcom2608444778321954367et_nat R2) S2)) (not (forall ((B2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A1) B2)) R2) (not (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat B2) A22)) S2))))))))
% 5.61/5.92 (assert (forall ((A1 (-> tptp.produc3658429121746597890et_nat Bool)) (A22 tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr3286484037609594932et_nat) (S2 tptp.set_Pr8807100098903490369et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A1) A22)) (@ (@ tptp.relcom8031709186682293262et_nat R2) S2)) (not (forall ((B2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A1) B2)) R2) (not (@ (@ tptp.member2737525317995836554et_nat (@ (@ tptp.produc3909112513931304473et_nat B2) A22)) S2))))))))
% 5.61/5.92 (assert (forall ((A1 (-> tptp.produc3658429121746597890et_nat Bool)) (A22 tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr8536935166611901872et_nat) (S2 tptp.set_Pr7928877670098842301et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A1) A22)) (@ (@ tptp.relcom8303140135939483018et_nat R2) S2)) (not (forall ((B2 tptp.produc3925858234332021118et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A1) B2)) R2) (not (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat B2) A22)) S2))))))))
% 5.61/5.92 (assert (forall ((I2 (-> tptp.produc3658429121746597890et_nat Bool)) (J (-> tptp.produc3658429121746597890et_nat Bool)) (R3 tptp.set_Pr2161125870931222855_nat_o)) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o I2) J)) R3) (@ (@ tptp.member6576561426505652726_nat_o J) (@ tptp.field_81821745747897882_nat_o R3)))))
% 5.61/5.92 (assert (forall ((I2 Bool) (J Bool) (R3 tptp.set_Product_prod_o_o)) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o I2) J)) R3) (@ (@ tptp.member_o J) (@ tptp.field_o R3)))))
% 5.61/5.92 (assert (forall ((I2 tptp.product_unit) (J tptp.product_unit) (R3 tptp.set_Pr5094982260447487303t_unit)) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit I2) J)) R3) (@ (@ tptp.member_Product_unit J) (@ tptp.field_Product_unit R3)))))
% 5.61/5.92 (assert (forall ((I2 tptp.nat) (J tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat I2) J)) R3) (@ (@ tptp.member_nat J) (@ tptp.field_nat R3)))))
% 5.61/5.92 (assert (forall ((I2 tptp.int) (J tptp.int) (R3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I2) J)) R3) (@ (@ tptp.member_int J) (@ tptp.field_int R3)))))
% 5.61/5.92 (assert (forall ((I2 (-> tptp.produc3658429121746597890et_nat Bool)) (J (-> tptp.produc3658429121746597890et_nat Bool)) (R3 tptp.set_Pr2161125870931222855_nat_o)) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o I2) J)) R3) (@ (@ tptp.member6576561426505652726_nat_o I2) (@ tptp.field_81821745747897882_nat_o R3)))))
% 5.61/5.92 (assert (forall ((I2 Bool) (J Bool) (R3 tptp.set_Product_prod_o_o)) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o I2) J)) R3) (@ (@ tptp.member_o I2) (@ tptp.field_o R3)))))
% 5.61/5.92 (assert (forall ((I2 tptp.product_unit) (J tptp.product_unit) (R3 tptp.set_Pr5094982260447487303t_unit)) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit I2) J)) R3) (@ (@ tptp.member_Product_unit I2) (@ tptp.field_Product_unit R3)))))
% 5.61/5.92 (assert (forall ((I2 tptp.nat) (J tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat I2) J)) R3) (@ (@ tptp.member_nat I2) (@ tptp.field_nat R3)))))
% 5.61/5.92 (assert (forall ((I2 tptp.int) (J tptp.int) (R3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I2) J)) R3) (@ (@ tptp.member_int I2) (@ tptp.field_int R3)))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat R2) S2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.field_nat R2)) (@ tptp.field_nat S2)))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit)) (let ((_let_1 (@ tptp.member_Product_unit A2))) (=> (@ (@ tptp.equiv_4189356295871601603t_unit A) R2) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.image_8431784415008483091t_unit R2) (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o) (A2 Bool)) (let ((_let_1 (@ tptp.member_o A2))) (=> (@ (@ tptp.equiv_equiv_o A) R2) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.image_o_o R2) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat A2))) (=> (@ (@ tptp.equiv_equiv_nat A) R2) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.image_nat_nat R2) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int)) (let ((_let_1 (@ tptp.member_int A2))) (=> (@ (@ tptp.equiv_equiv_int A) R2) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.image_int_int R2) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o A2))) (=> (@ (@ tptp.equiv_6726761681920839555_nat_o A) R2) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.image_2232984160439939859_nat_o R2) (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o))))))))
% 5.61/5.92 (assert (= tptp.field_nat (lambda ((R4 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.sup_sup_set_nat (@ tptp.domain_nat_nat R4)) (@ tptp.range_nat_nat R4)))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit) (X tptp.product_unit) (Y tptp.product_unit)) (let ((_let_1 (@ tptp.image_8431784415008483091t_unit R2))) (=> (@ (@ tptp.equiv_4189356295871601603t_unit A) R2) (= (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit X) Y)) R2) (and (= (@ _let_1 (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)) (@ _let_1 (@ (@ tptp.insert_Product_unit Y) tptp.bot_bo3957492148770167129t_unit))) (@ (@ tptp.member_Product_unit X) A) (@ (@ tptp.member_Product_unit Y) A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o) (X Bool) (Y Bool)) (let ((_let_1 (@ tptp.image_o_o R2))) (=> (@ (@ tptp.equiv_equiv_o A) R2) (= (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X) Y)) R2) (and (= (@ _let_1 (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)) (@ _let_1 (@ (@ tptp.insert_o Y) tptp.bot_bot_set_o))) (@ (@ tptp.member_o X) A) (@ (@ tptp.member_o Y) A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.image_nat_nat R2))) (=> (@ (@ tptp.equiv_equiv_nat A) R2) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R2) (and (= (@ _let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)) (@ _let_1 (@ (@ tptp.insert_nat Y) tptp.bot_bot_set_nat))) (@ (@ tptp.member_nat X) A) (@ (@ tptp.member_nat Y) A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.image_int_int R2))) (=> (@ (@ tptp.equiv_equiv_int A) R2) (= (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R2) (and (= (@ _let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)) (@ _let_1 (@ (@ tptp.insert_int Y) tptp.bot_bot_set_int))) (@ (@ tptp.member_int X) A) (@ (@ tptp.member_int Y) A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.image_2232984160439939859_nat_o R2))) (=> (@ (@ tptp.equiv_6726761681920839555_nat_o A) R2) (= (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X) Y)) R2) (and (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)) (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o Y) tptp.bot_bo7824918357723582233_nat_o))) (@ (@ tptp.member6576561426505652726_nat_o X) A) (@ (@ tptp.member6576561426505652726_nat_o Y) A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit) (X tptp.product_unit) (Y tptp.product_unit)) (let ((_let_1 (@ tptp.image_8431784415008483091t_unit R2))) (=> (@ (@ tptp.equiv_4189356295871601603t_unit A) R2) (=> (@ (@ tptp.member_Product_unit X) A) (=> (@ (@ tptp.member_Product_unit Y) A) (= (= (@ _let_1 (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)) (@ _let_1 (@ (@ tptp.insert_Product_unit Y) tptp.bot_bo3957492148770167129t_unit))) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit X) Y)) R2))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o) (X Bool) (Y Bool)) (let ((_let_1 (@ tptp.image_o_o R2))) (=> (@ (@ tptp.equiv_equiv_o A) R2) (=> (@ (@ tptp.member_o X) A) (=> (@ (@ tptp.member_o Y) A) (= (= (@ _let_1 (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)) (@ _let_1 (@ (@ tptp.insert_o Y) tptp.bot_bot_set_o))) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X) Y)) R2))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.image_nat_nat R2))) (=> (@ (@ tptp.equiv_equiv_nat A) R2) (=> (@ (@ tptp.member_nat X) A) (=> (@ (@ tptp.member_nat Y) A) (= (= (@ _let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)) (@ _let_1 (@ (@ tptp.insert_nat Y) tptp.bot_bot_set_nat))) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R2))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.image_int_int R2))) (=> (@ (@ tptp.equiv_equiv_int A) R2) (=> (@ (@ tptp.member_int X) A) (=> (@ (@ tptp.member_int Y) A) (= (= (@ _let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)) (@ _let_1 (@ (@ tptp.insert_int Y) tptp.bot_bot_set_int))) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R2))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.image_2232984160439939859_nat_o R2))) (=> (@ (@ tptp.equiv_6726761681920839555_nat_o A) R2) (=> (@ (@ tptp.member6576561426505652726_nat_o X) A) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) A) (= (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)) (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o Y) tptp.bot_bo7824918357723582233_nat_o))) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X) Y)) R2))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (@ tptp.image_8431784415008483091t_unit R2))) (=> (@ (@ tptp.equiv_4189356295871601603t_unit A) R2) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit A2) B)) R2) (= (@ _let_1 (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit)) (@ _let_1 (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o) (A2 Bool) (B Bool)) (let ((_let_1 (@ tptp.image_o_o R2))) (=> (@ (@ tptp.equiv_equiv_o A) R2) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) B)) R2) (= (@ _let_1 (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o)) (@ _let_1 (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.image_nat_nat R2))) (=> (@ (@ tptp.equiv_equiv_nat A) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R2) (= (@ _let_1 (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat)) (@ _let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.image_int_int R2))) (=> (@ (@ tptp.equiv_equiv_int A) R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R2) (= (@ _let_1 (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int)) (@ _let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.image_2232984160439939859_nat_o R2))) (=> (@ (@ tptp.equiv_6726761681920839555_nat_o A) R2) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) B)) R2) (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o)) (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o B) tptp.bot_bo7824918357723582233_nat_o))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit) (B tptp.product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ tptp.image_8431784415008483091t_unit R2))) (=> (= (@ _let_1 (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit)) (@ _let_1 (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit))) (=> (@ (@ tptp.equiv_4189356295871601603t_unit A) R2) (=> (@ (@ tptp.member_Product_unit B) A) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit A2) B)) R2)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (A2 Bool) (B Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.image_o_o R2))) (=> (= (@ _let_1 (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o)) (@ _let_1 (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (=> (@ (@ tptp.equiv_equiv_o A) R2) (=> (@ (@ tptp.member_o B) A) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) B)) R2)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (B tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_nat R2))) (=> (= (@ _let_1 (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat)) (@ _let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (=> (@ (@ tptp.equiv_equiv_nat A) R2) (=> (@ (@ tptp.member_nat B) A) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R2)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (B tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.image_int_int R2))) (=> (= (@ _let_1 (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int)) (@ _let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (=> (@ (@ tptp.equiv_equiv_int A) R2) (=> (@ (@ tptp.member_int B) A) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R2)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.image_2232984160439939859_nat_o R2))) (=> (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o)) (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o B) tptp.bot_bo7824918357723582233_nat_o))) (=> (@ (@ tptp.equiv_6726761681920839555_nat_o A) R2) (=> (@ (@ tptp.member6576561426505652726_nat_o B) A) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) B)) R2)))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (V2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat (@ tptp.transi2905341329935302413cl_nat R3)) V2)) (@ (@ tptp.sup_sup_set_nat (@ tptp.field_nat R3)) V2))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr5094982260447487303t_unit) (S tptp.set_Pr5094982260447487303t_unit) (A tptp.set_Product_unit) (A2 tptp.product_unit)) (let ((_let_1 (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit))) (let ((_let_2 (@ tptp.image_8431784415008483091t_unit S))) (let ((_let_3 (@ tptp.equiv_4189356295871601603t_unit A))) (=> (@ (@ tptp.ord_le930853871177014503t_unit R3) S) (=> (@ _let_3 R3) (=> (@ _let_3 S) (= (@ _let_2 (@ (@ tptp.image_8431784415008483091t_unit R3) _let_1)) (@ _let_2 _let_1))))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Product_prod_o_o) (S tptp.set_Product_prod_o_o) (A tptp.set_o) (A2 Bool)) (let ((_let_1 (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))) (let ((_let_2 (@ tptp.image_o_o S))) (let ((_let_3 (@ tptp.equiv_equiv_o A))) (=> (@ (@ tptp.ord_le192195778054999463od_o_o R3) S) (=> (@ _let_3 R3) (=> (@ _let_3 S) (= (@ _let_2 (@ (@ tptp.image_o_o R3) _let_1)) (@ _let_2 _let_1))))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat) (A tptp.set_nat) (A2 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))) (let ((_let_2 (@ tptp.image_nat_nat S))) (let ((_let_3 (@ tptp.equiv_equiv_nat A))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat R3) S) (=> (@ _let_3 R3) (=> (@ _let_3 S) (= (@ _let_2 (@ (@ tptp.image_nat_nat R3) _let_1)) (@ _let_2 _let_1))))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int) (S tptp.set_Pr958786334691620121nt_int) (A tptp.set_int) (A2 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))) (let ((_let_2 (@ tptp.image_int_int S))) (let ((_let_3 (@ tptp.equiv_equiv_int A))) (=> (@ (@ tptp.ord_le2843351958646193337nt_int R3) S) (=> (@ _let_3 R3) (=> (@ _let_3 S) (= (@ _let_2 (@ (@ tptp.image_int_int R3) _let_1)) (@ _let_2 _let_1))))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr2161125870931222855_nat_o) (S tptp.set_Pr2161125870931222855_nat_o) (A tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o))) (let ((_let_2 (@ tptp.image_2232984160439939859_nat_o S))) (let ((_let_3 (@ tptp.equiv_6726761681920839555_nat_o A))) (=> (@ (@ tptp.ord_le6659818918159358183_nat_o R3) S) (=> (@ _let_3 R3) (=> (@ _let_3 S) (= (@ _let_2 (@ (@ tptp.image_2232984160439939859_nat_o R3) _let_1)) (@ _let_2 _let_1))))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr5094982260447487303t_unit) (S tptp.set_Pr5094982260447487303t_unit) (A tptp.set_Product_unit) (A2 tptp.product_unit)) (let ((_let_1 (@ (@ tptp.image_8431784415008483091t_unit S) (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit)))) (let ((_let_2 (@ tptp.equiv_4189356295871601603t_unit A))) (=> (@ (@ tptp.ord_le930853871177014503t_unit R3) S) (=> (@ _let_2 R3) (=> (@ _let_2 S) (= (@ (@ tptp.image_8431784415008483091t_unit R3) _let_1) _let_1))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Product_prod_o_o) (S tptp.set_Product_prod_o_o) (A tptp.set_o) (A2 Bool)) (let ((_let_1 (@ (@ tptp.image_o_o S) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o)))) (let ((_let_2 (@ tptp.equiv_equiv_o A))) (=> (@ (@ tptp.ord_le192195778054999463od_o_o R3) S) (=> (@ _let_2 R3) (=> (@ _let_2 S) (= (@ (@ tptp.image_o_o R3) _let_1) _let_1))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat) (A tptp.set_nat) (A2 tptp.nat)) (let ((_let_1 (@ (@ tptp.image_nat_nat S) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat)))) (let ((_let_2 (@ tptp.equiv_equiv_nat A))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat R3) S) (=> (@ _let_2 R3) (=> (@ _let_2 S) (= (@ (@ tptp.image_nat_nat R3) _let_1) _let_1))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int) (S tptp.set_Pr958786334691620121nt_int) (A tptp.set_int) (A2 tptp.int)) (let ((_let_1 (@ (@ tptp.image_int_int S) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int)))) (let ((_let_2 (@ tptp.equiv_equiv_int A))) (=> (@ (@ tptp.ord_le2843351958646193337nt_int R3) S) (=> (@ _let_2 R3) (=> (@ _let_2 S) (= (@ (@ tptp.image_int_int R3) _let_1) _let_1))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr2161125870931222855_nat_o) (S tptp.set_Pr2161125870931222855_nat_o) (A tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ tptp.image_2232984160439939859_nat_o S) (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o)))) (let ((_let_2 (@ tptp.equiv_6726761681920839555_nat_o A))) (=> (@ (@ tptp.ord_le6659818918159358183_nat_o R3) S) (=> (@ _let_2 R3) (=> (@ _let_2 S) (= (@ (@ tptp.image_2232984160439939859_nat_o R3) _let_1) _let_1))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (@ tptp.image_8431784415008483091t_unit R2))) (let ((_let_2 (@ tptp.field_Product_unit R2))) (=> (@ (@ tptp.order_2505591618835473410t_unit _let_2) R2) (=> (@ (@ tptp.member_Product_unit A2) _let_2) (=> (@ (@ tptp.member_Product_unit B) _let_2) (= (= (@ _let_1 (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit)) (@ _let_1 (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit))) (= A2 B)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (A2 Bool) (B Bool)) (let ((_let_1 (@ tptp.image_o_o R2))) (let ((_let_2 (@ tptp.field_o R2))) (=> (@ (@ tptp.order_8538205470752950541r_on_o _let_2) R2) (=> (@ (@ tptp.member_o A2) _let_2) (=> (@ (@ tptp.member_o B) _let_2) (= (= (@ _let_1 (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o)) (@ _let_1 (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (= A2 B)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.image_nat_nat R2))) (let ((_let_2 (@ tptp.field_nat R2))) (=> (@ (@ tptp.order_5251275573222108571on_nat _let_2) R2) (=> (@ (@ tptp.member_nat A2) _let_2) (=> (@ (@ tptp.member_nat B) _let_2) (= (= (@ _let_1 (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat)) (@ _let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (= A2 B)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.image_int_int R2))) (let ((_let_2 (@ tptp.field_int R2))) (=> (@ (@ tptp.order_5248785102713058295on_int _let_2) R2) (=> (@ (@ tptp.member_int A2) _let_2) (=> (@ (@ tptp.member_int B) _let_2) (= (= (@ _let_1 (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int)) (@ _let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (= A2 B)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.image_2232984160439939859_nat_o R2))) (let ((_let_2 (@ tptp.field_81821745747897882_nat_o R2))) (=> (@ (@ tptp.order_3690095022144090562_nat_o _let_2) R2) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) _let_2) (=> (@ (@ tptp.member6576561426505652726_nat_o B) _let_2) (= (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o)) (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o B) tptp.bot_bo7824918357723582233_nat_o))) (= A2 B)))))))))
% 5.61/5.92 (assert (forall ((Q2 tptp.set_Code_integer) (I tptp.set_Code_integer) (E tptp.set_Pr4811707699266497531nteger)) (=> (@ tptp.finite6017078050557962740nteger Q2) (=> (@ (@ tptp.ord_le7084787975880047091nteger I) Q2) (=> (@ (@ tptp.ord_le7084787975880047091nteger (@ tptp.range_1907724884897625393nteger E)) Q2) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.image_4147621952751189391nteger (@ tptp.transi3984306202085910426nteger E)) I)))))))
% 5.61/5.92 (assert (forall ((Q2 tptp.set_nat) (I tptp.set_nat) (E tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite_finite_nat Q2) (=> (@ (@ tptp.ord_less_eq_set_nat I) Q2) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.range_nat_nat E)) Q2) (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_nat (@ tptp.transi2905341329935302413cl_nat E)) I)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.image_int_int R2))) (let ((_let_2 (@ tptp.field_int R2))) (=> (@ (@ tptp.order_4859164337913492053on_int _let_2) R2) (=> (@ (@ tptp.ord_less_eq_set_int A) _let_2) (=> (@ (@ tptp.ord_less_eq_set_int B4) _let_2) (= (@ (@ tptp.ord_less_eq_set_int (@ _let_1 A)) (@ _let_1 B4)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A) (exists ((Y3 tptp.int)) (and (@ (@ tptp.member_int Y3) B4) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y3) X2)) R2)))))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_nat R2))) (let ((_let_2 (@ tptp.field_nat R2))) (=> (@ (@ tptp.order_4861654808422542329on_nat _let_2) R2) (=> (@ (@ tptp.ord_less_eq_set_nat A) _let_2) (=> (@ (@ tptp.ord_less_eq_set_nat B4) _let_2) (= (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 A)) (@ _let_1 B4)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (exists ((Y3 tptp.nat)) (and (@ (@ tptp.member_nat Y3) B4) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y3) X2)) R2)))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (@ tptp.image_8431784415008483091t_unit R2))) (=> (@ (@ tptp.equiv_4189356295871601603t_unit A) R2) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit A2) B)) R2) (@ (@ tptp.ord_le3507040750410214029t_unit (@ _let_1 (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit))) (@ _let_1 (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o) (A2 Bool) (B Bool)) (let ((_let_1 (@ tptp.image_o_o R2))) (=> (@ (@ tptp.equiv_equiv_o A) R2) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) B)) R2) (@ (@ tptp.ord_less_eq_set_o (@ _let_1 (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))) (@ _let_1 (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.image_int_int R2))) (=> (@ (@ tptp.equiv_equiv_int A) R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R2) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))) (@ _let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.image_2232984160439939859_nat_o R2))) (=> (@ (@ tptp.equiv_6726761681920839555_nat_o A) R2) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) B)) R2) (@ (@ tptp.ord_le2965882846123202637_nat_o (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o))) (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o B) tptp.bot_bo7824918357723582233_nat_o))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.image_nat_nat R2))) (=> (@ (@ tptp.equiv_equiv_nat A) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R2) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))) (@ _let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit) (B tptp.product_unit) (A2 tptp.product_unit)) (let ((_let_1 (@ tptp.image_8431784415008483091t_unit R2))) (=> (@ (@ tptp.equiv_4189356295871601603t_unit A) R2) (=> (@ (@ tptp.ord_le3507040750410214029t_unit (@ _let_1 (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit))) (@ _let_1 (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit))) (=> (@ (@ tptp.member_Product_unit B) A) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit A2) B)) R2)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o) (B Bool) (A2 Bool)) (let ((_let_1 (@ tptp.image_o_o R2))) (=> (@ (@ tptp.equiv_equiv_o A) R2) (=> (@ (@ tptp.ord_less_eq_set_o (@ _let_1 (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (@ _let_1 (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))) (=> (@ (@ tptp.member_o B) A) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) B)) R2)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int) (B tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.image_int_int R2))) (=> (@ (@ tptp.equiv_equiv_int A) R2) (=> (@ (@ tptp.ord_less_eq_set_int (@ _let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (@ _let_1 (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))) (=> (@ (@ tptp.member_int B) A) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R2)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o) (B (-> tptp.produc3658429121746597890et_nat Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.image_2232984160439939859_nat_o R2))) (=> (@ (@ tptp.equiv_6726761681920839555_nat_o A) R2) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o B) tptp.bot_bo7824918357723582233_nat_o))) (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o))) (=> (@ (@ tptp.member6576561426505652726_nat_o B) A) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) B)) R2)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (B tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.image_nat_nat R2))) (=> (@ (@ tptp.equiv_equiv_nat A) R2) (=> (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (@ _let_1 (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))) (=> (@ (@ tptp.member_nat B) A) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R2)))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger F2) (=> (forall ((Y2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Y2) F2) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.inf_in1364745209274528805nteger (@ (@ tptp.vimage1318793397690208119nteger H2) (@ (@ tptp.insert_Code_integer Y2) tptp.bot_bo3990330152332043303nteger))) A)))) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.inf_in1364745209274528805nteger (@ (@ tptp.vimage1318793397690208119nteger H2) F2)) A))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_Code_integer) (H2 (-> tptp.nat tptp.code_integer)) (A tptp.set_nat)) (=> (@ tptp.finite6017078050557962740nteger F2) (=> (forall ((Y2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Y2) F2) (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.vimage6104394758324456170nteger H2) (@ (@ tptp.insert_Code_integer Y2) tptp.bot_bo3990330152332043303nteger))) A)))) (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.vimage6104394758324456170nteger H2) F2)) A))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_Product_unit) (H2 (-> tptp.code_integer tptp.product_unit)) (A tptp.set_Code_integer)) (=> (@ tptp.finite4290736615968046902t_unit F2) (=> (forall ((Y2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit Y2) F2) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.inf_in1364745209274528805nteger (@ (@ tptp.vimage5651688891684837235t_unit H2) (@ (@ tptp.insert_Product_unit Y2) tptp.bot_bo3957492148770167129t_unit))) A)))) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.inf_in1364745209274528805nteger (@ (@ tptp.vimage5651688891684837235t_unit H2) F2)) A))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_Product_unit) (H2 (-> tptp.nat tptp.product_unit)) (A tptp.set_nat)) (=> (@ tptp.finite4290736615968046902t_unit F2) (=> (forall ((Y2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit Y2) F2) (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.vimage4884490618288580032t_unit H2) (@ (@ tptp.insert_Product_unit Y2) tptp.bot_bo3957492148770167129t_unit))) A)))) (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.vimage4884490618288580032t_unit H2) F2)) A))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_o) (H2 (-> tptp.code_integer Bool)) (A tptp.set_Code_integer)) (=> (@ tptp.finite_finite_o F2) (=> (forall ((Y2 Bool)) (=> (@ (@ tptp.member_o Y2) F2) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.inf_in1364745209274528805nteger (@ (@ tptp.vimage3005800680117336574eger_o H2) (@ (@ tptp.insert_o Y2) tptp.bot_bot_set_o))) A)))) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.inf_in1364745209274528805nteger (@ (@ tptp.vimage3005800680117336574eger_o H2) F2)) A))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_o) (H2 (-> tptp.nat Bool)) (A tptp.set_nat)) (=> (@ tptp.finite_finite_o F2) (=> (forall ((Y2 Bool)) (=> (@ (@ tptp.member_o Y2) F2) (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.vimage_nat_o H2) (@ (@ tptp.insert_o Y2) tptp.bot_bot_set_o))) A)))) (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.vimage_nat_o H2) F2)) A))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_nat) (H2 (-> tptp.code_integer tptp.nat)) (A tptp.set_Code_integer)) (=> (@ tptp.finite_finite_nat F2) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) F2) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.inf_in1364745209274528805nteger (@ (@ tptp.vimage5839839309545413354er_nat H2) (@ (@ tptp.insert_nat Y2) tptp.bot_bot_set_nat))) A)))) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.inf_in1364745209274528805nteger (@ (@ tptp.vimage5839839309545413354er_nat H2) F2)) A))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_nat) (H2 (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (=> (@ tptp.finite_finite_nat F2) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) F2) (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.vimage_nat_nat H2) (@ (@ tptp.insert_nat Y2) tptp.bot_bot_set_nat))) A)))) (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.vimage_nat_nat H2) F2)) A))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_int) (H2 (-> tptp.code_integer tptp.int)) (A tptp.set_Code_integer)) (=> (@ tptp.finite_finite_int F2) (=> (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) F2) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.inf_in1364745209274528805nteger (@ (@ tptp.vimage5837348839036363078er_int H2) (@ (@ tptp.insert_int Y2) tptp.bot_bot_set_int))) A)))) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.inf_in1364745209274528805nteger (@ (@ tptp.vimage5837348839036363078er_int H2) F2)) A))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_int) (H2 (-> tptp.nat tptp.int)) (A tptp.set_nat)) (=> (@ tptp.finite_finite_int F2) (=> (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) F2) (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.vimage_nat_int H2) (@ (@ tptp.insert_int Y2) tptp.bot_bot_set_int))) A)))) (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.vimage_nat_int H2) F2)) A))))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (A tptp.set_int)) (= (@ tptp.finite_finite_int (@ (@ tptp.insert_int A2) A)) (@ tptp.finite_finite_int A))))
% 5.61/5.92 (assert (forall ((A2 Bool) (A tptp.set_o)) (= (@ tptp.finite_finite_o (@ (@ tptp.insert_o A2) A)) (@ tptp.finite_finite_o A))))
% 5.61/5.92 (assert (forall ((A2 tptp.product_unit) (A tptp.set_Product_unit)) (= (@ tptp.finite4290736615968046902t_unit (@ (@ tptp.insert_Product_unit A2) A)) (@ tptp.finite4290736615968046902t_unit A))))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (A tptp.set_nat)) (= (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A2) A)) (@ tptp.finite_finite_nat A))))
% 5.61/5.92 (assert (forall ((A2 tptp.code_integer) (A tptp.set_Code_integer)) (= (@ tptp.finite6017078050557962740nteger (@ (@ tptp.insert_Code_integer A2) A)) (@ tptp.finite6017078050557962740nteger A))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_Code_integer) (A tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger F2) (=> (@ (@ tptp.ord_le7084787975880047091nteger F2) A) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (forall ((A4 tptp.code_integer) (F3 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.member_Code_integer A4))) (=> (@ tptp.finite6017078050557962740nteger F3) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_le7084787975880047091nteger F3) A) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_Code_integer A4) F3))))))))) (@ P F2)))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_Product_unit) (A tptp.set_Product_unit) (P (-> tptp.set_Product_unit Bool))) (=> (@ tptp.finite4290736615968046902t_unit F2) (=> (@ (@ tptp.ord_le3507040750410214029t_unit F2) A) (=> (@ P tptp.bot_bo3957492148770167129t_unit) (=> (forall ((A4 tptp.product_unit) (F3 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member_Product_unit A4))) (=> (@ tptp.finite4290736615968046902t_unit F3) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_le3507040750410214029t_unit F3) A) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_Product_unit A4) F3))))))))) (@ P F2)))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_o) (A tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o F2) (=> (@ (@ tptp.ord_less_eq_set_o F2) A) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((A4 Bool) (F3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o A4))) (=> (@ tptp.finite_finite_o F3) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_set_o F3) A) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_o A4) F3))))))))) (@ P F2)))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_int) (A tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F2) (=> (@ (@ tptp.ord_less_eq_set_int F2) A) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A4 tptp.int) (F3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A4))) (=> (@ tptp.finite_finite_int F3) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_set_int F3) A) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_int A4) F3))))))))) (@ P F2)))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_Pr4532377907799695533_nat_o) (A tptp.set_Pr4532377907799695533_nat_o) (P (-> tptp.set_Pr4532377907799695533_nat_o Bool))) (=> (@ tptp.finite3252695134891459830_nat_o F2) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o F2) A) (=> (@ P tptp.bot_bo7824918357723582233_nat_o) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (F3 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o A4))) (=> (@ tptp.finite3252695134891459830_nat_o F3) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o F3) A) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert5175938949040314269_nat_o A4) F3))))))))) (@ P F2)))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_nat) (A tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F2) (=> (@ (@ tptp.ord_less_eq_set_nat F2) A) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A4 tptp.nat) (F3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A4))) (=> (@ tptp.finite_finite_nat F3) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_set_nat F3) A) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_nat A4) F3))))))))) (@ P F2)))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_Code_integer) (A tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger F2) (=> (@ (@ tptp.ord_le7084787975880047091nteger F2) A) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (forall ((A4 tptp.code_integer) (F3 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.member_Code_integer A4))) (=> (@ tptp.finite6017078050557962740nteger F3) (=> (@ _let_1 A) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_Code_integer A4) F3)))))))) (@ P F2)))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_Product_unit) (A tptp.set_Product_unit) (P (-> tptp.set_Product_unit Bool))) (=> (@ tptp.finite4290736615968046902t_unit F2) (=> (@ (@ tptp.ord_le3507040750410214029t_unit F2) A) (=> (@ P tptp.bot_bo3957492148770167129t_unit) (=> (forall ((A4 tptp.product_unit) (F3 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member_Product_unit A4))) (=> (@ tptp.finite4290736615968046902t_unit F3) (=> (@ _let_1 A) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_Product_unit A4) F3)))))))) (@ P F2)))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_o) (A tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o F2) (=> (@ (@ tptp.ord_less_eq_set_o F2) A) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((A4 Bool) (F3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o A4))) (=> (@ tptp.finite_finite_o F3) (=> (@ _let_1 A) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_o A4) F3)))))))) (@ P F2)))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_int) (A tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F2) (=> (@ (@ tptp.ord_less_eq_set_int F2) A) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A4 tptp.int) (F3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A4))) (=> (@ tptp.finite_finite_int F3) (=> (@ _let_1 A) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_int A4) F3)))))))) (@ P F2)))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_Pr4532377907799695533_nat_o) (A tptp.set_Pr4532377907799695533_nat_o) (P (-> tptp.set_Pr4532377907799695533_nat_o Bool))) (=> (@ tptp.finite3252695134891459830_nat_o F2) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o F2) A) (=> (@ P tptp.bot_bo7824918357723582233_nat_o) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (F3 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o A4))) (=> (@ tptp.finite3252695134891459830_nat_o F3) (=> (@ _let_1 A) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert5175938949040314269_nat_o A4) F3)))))))) (@ P F2)))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_nat) (A tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F2) (=> (@ (@ tptp.ord_less_eq_set_nat F2) A) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A4 tptp.nat) (F3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A4))) (=> (@ tptp.finite_finite_nat F3) (=> (@ _let_1 A) (=> (not (@ _let_1 F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_nat A4) F3)))))))) (@ P F2)))))))
% 5.61/5.92 (assert (forall ((S tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool)) (F (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (forall ((X3 tptp.code_integer) (S5 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger S5) (=> (forall ((Y5 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Y5) S5) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X3)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_Code_integer X3) S5)))))) (@ P S))))))
% 5.61/5.92 (assert (forall ((S tptp.set_Product_unit) (P (-> tptp.set_Product_unit Bool)) (F (-> tptp.product_unit tptp.rat))) (=> (@ tptp.finite4290736615968046902t_unit S) (=> (@ P tptp.bot_bo3957492148770167129t_unit) (=> (forall ((X3 tptp.product_unit) (S5 tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit S5) (=> (forall ((Y5 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit Y5) S5) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X3)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_Product_unit X3) S5)))))) (@ P S))))))
% 5.61/5.92 (assert (forall ((S tptp.set_o) (P (-> tptp.set_o Bool)) (F (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o S) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((X3 Bool) (S5 tptp.set_o)) (=> (@ tptp.finite_finite_o S5) (=> (forall ((Y5 Bool)) (=> (@ (@ tptp.member_o Y5) S5) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X3)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_o X3) S5)))))) (@ P S))))))
% 5.61/5.92 (assert (forall ((S tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X3 tptp.nat) (S5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S5) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) S5) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X3)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_nat X3) S5)))))) (@ P S))))))
% 5.61/5.92 (assert (forall ((S tptp.set_int) (P (-> tptp.set_int Bool)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X3 tptp.int) (S5 tptp.set_int)) (=> (@ tptp.finite_finite_int S5) (=> (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member_int Y5) S5) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X3)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_int X3) S5)))))) (@ P S))))))
% 5.61/5.92 (assert (forall ((S tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool)) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (forall ((X3 tptp.code_integer) (S5 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger S5) (=> (forall ((Y5 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Y5) S5) (@ (@ tptp.ord_less_eq_nat (@ F Y5)) (@ F X3)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_Code_integer X3) S5)))))) (@ P S))))))
% 5.61/5.92 (assert (forall ((S tptp.set_Product_unit) (P (-> tptp.set_Product_unit Bool)) (F (-> tptp.product_unit tptp.nat))) (=> (@ tptp.finite4290736615968046902t_unit S) (=> (@ P tptp.bot_bo3957492148770167129t_unit) (=> (forall ((X3 tptp.product_unit) (S5 tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit S5) (=> (forall ((Y5 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit Y5) S5) (@ (@ tptp.ord_less_eq_nat (@ F Y5)) (@ F X3)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_Product_unit X3) S5)))))) (@ P S))))))
% 5.61/5.92 (assert (forall ((S tptp.set_o) (P (-> tptp.set_o Bool)) (F (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o S) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((X3 Bool) (S5 tptp.set_o)) (=> (@ tptp.finite_finite_o S5) (=> (forall ((Y5 Bool)) (=> (@ (@ tptp.member_o Y5) S5) (@ (@ tptp.ord_less_eq_nat (@ F Y5)) (@ F X3)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_o X3) S5)))))) (@ P S))))))
% 5.61/5.92 (assert (forall ((S tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X3 tptp.nat) (S5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S5) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) S5) (@ (@ tptp.ord_less_eq_nat (@ F Y5)) (@ F X3)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_nat X3) S5)))))) (@ P S))))))
% 5.61/5.92 (assert (forall ((S tptp.set_int) (P (-> tptp.set_int Bool)) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int S) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X3 tptp.int) (S5 tptp.set_int)) (=> (@ tptp.finite_finite_int S5) (=> (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member_int Y5) S5) (@ (@ tptp.ord_less_eq_nat (@ F Y5)) (@ F X3)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_int X3) S5)))))) (@ P S))))))
% 5.61/5.92 (assert (forall ((P (-> tptp.set_Code_integer Bool)) (A tptp.set_Code_integer)) (=> (forall ((A9 tptp.set_Code_integer)) (=> (not (@ tptp.finite6017078050557962740nteger A9)) (@ P A9))) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (forall ((X3 tptp.code_integer) (F3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger F3) (=> (not (@ (@ tptp.member_Code_integer X3) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_Code_integer X3) F3)))))) (@ P A))))))
% 5.61/5.92 (assert (forall ((P (-> tptp.set_Product_unit Bool)) (A tptp.set_Product_unit)) (=> (forall ((A9 tptp.set_Product_unit)) (=> (not (@ tptp.finite4290736615968046902t_unit A9)) (@ P A9))) (=> (@ P tptp.bot_bo3957492148770167129t_unit) (=> (forall ((X3 tptp.product_unit) (F3 tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit F3) (=> (not (@ (@ tptp.member_Product_unit X3) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_Product_unit X3) F3)))))) (@ P A))))))
% 5.61/5.92 (assert (forall ((P (-> tptp.set_o Bool)) (A tptp.set_o)) (=> (forall ((A9 tptp.set_o)) (=> (not (@ tptp.finite_finite_o A9)) (@ P A9))) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((X3 Bool) (F3 tptp.set_o)) (=> (@ tptp.finite_finite_o F3) (=> (not (@ (@ tptp.member_o X3) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_o X3) F3)))))) (@ P A))))))
% 5.61/5.92 (assert (forall ((P (-> tptp.set_nat Bool)) (A tptp.set_nat)) (=> (forall ((A9 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A9)) (@ P A9))) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X3 tptp.nat) (F3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F3) (=> (not (@ (@ tptp.member_nat X3) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_nat X3) F3)))))) (@ P A))))))
% 5.61/5.92 (assert (forall ((P (-> tptp.set_int Bool)) (A tptp.set_int)) (=> (forall ((A9 tptp.set_int)) (=> (not (@ tptp.finite_finite_int A9)) (@ P A9))) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X3 tptp.int) (F3 tptp.set_int)) (=> (@ tptp.finite_finite_int F3) (=> (not (@ (@ tptp.member_int X3) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_int X3) F3)))))) (@ P A))))))
% 5.61/5.92 (assert (forall ((P (-> tptp.set_Pr4532377907799695533_nat_o Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (=> (forall ((A9 tptp.set_Pr4532377907799695533_nat_o)) (=> (not (@ tptp.finite3252695134891459830_nat_o A9)) (@ P A9))) (=> (@ P tptp.bot_bo7824918357723582233_nat_o) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (F3 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o F3) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X3) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert5175938949040314269_nat_o X3) F3)))))) (@ P A))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger F2) (=> (not (= F2 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X3 tptp.code_integer)) (@ P (@ (@ tptp.insert_Code_integer X3) tptp.bot_bo3990330152332043303nteger))) (=> (forall ((X3 tptp.code_integer) (F3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger F3) (=> (not (= F3 tptp.bot_bo3990330152332043303nteger)) (=> (not (@ (@ tptp.member_Code_integer X3) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_Code_integer X3) F3))))))) (@ P F2)))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_Product_unit) (P (-> tptp.set_Product_unit Bool))) (=> (@ tptp.finite4290736615968046902t_unit F2) (=> (not (= F2 tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((X3 tptp.product_unit)) (@ P (@ (@ tptp.insert_Product_unit X3) tptp.bot_bo3957492148770167129t_unit))) (=> (forall ((X3 tptp.product_unit) (F3 tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit F3) (=> (not (= F3 tptp.bot_bo3957492148770167129t_unit)) (=> (not (@ (@ tptp.member_Product_unit X3) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_Product_unit X3) F3))))))) (@ P F2)))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o F2) (=> (not (= F2 tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (@ P (@ (@ tptp.insert_o X3) tptp.bot_bot_set_o))) (=> (forall ((X3 Bool) (F3 tptp.set_o)) (=> (@ tptp.finite_finite_o F3) (=> (not (= F3 tptp.bot_bot_set_o)) (=> (not (@ (@ tptp.member_o X3) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_o X3) F3))))))) (@ P F2)))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F2) (=> (not (= F2 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (@ P (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat))) (=> (forall ((X3 tptp.nat) (F3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F3) (=> (not (= F3 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat X3) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_nat X3) F3))))))) (@ P F2)))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F2) (=> (not (= F2 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (@ P (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int))) (=> (forall ((X3 tptp.int) (F3 tptp.set_int)) (=> (@ tptp.finite_finite_int F3) (=> (not (= F3 tptp.bot_bot_set_int)) (=> (not (@ (@ tptp.member_int X3) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_int X3) F3))))))) (@ P F2)))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_Pr4532377907799695533_nat_o) (P (-> tptp.set_Pr4532377907799695533_nat_o Bool))) (=> (@ tptp.finite3252695134891459830_nat_o F2) (=> (not (= F2 tptp.bot_bo7824918357723582233_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (@ P (@ (@ tptp.insert5175938949040314269_nat_o X3) tptp.bot_bo7824918357723582233_nat_o))) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (F3 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o F3) (=> (not (= F3 tptp.bot_bo7824918357723582233_nat_o)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X3) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert5175938949040314269_nat_o X3) F3))))))) (@ P F2)))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger F2) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (forall ((X3 tptp.code_integer) (F3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger F3) (=> (not (@ (@ tptp.member_Code_integer X3) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_Code_integer X3) F3)))))) (@ P F2))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_Product_unit) (P (-> tptp.set_Product_unit Bool))) (=> (@ tptp.finite4290736615968046902t_unit F2) (=> (@ P tptp.bot_bo3957492148770167129t_unit) (=> (forall ((X3 tptp.product_unit) (F3 tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit F3) (=> (not (@ (@ tptp.member_Product_unit X3) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_Product_unit X3) F3)))))) (@ P F2))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o F2) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((X3 Bool) (F3 tptp.set_o)) (=> (@ tptp.finite_finite_o F3) (=> (not (@ (@ tptp.member_o X3) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_o X3) F3)))))) (@ P F2))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat F2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X3 tptp.nat) (F3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F3) (=> (not (@ (@ tptp.member_nat X3) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_nat X3) F3)))))) (@ P F2))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int F2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X3 tptp.int) (F3 tptp.set_int)) (=> (@ tptp.finite_finite_int F3) (=> (not (@ (@ tptp.member_int X3) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert_int X3) F3)))))) (@ P F2))))))
% 5.61/5.92 (assert (forall ((F2 tptp.set_Pr4532377907799695533_nat_o) (P (-> tptp.set_Pr4532377907799695533_nat_o Bool))) (=> (@ tptp.finite3252695134891459830_nat_o F2) (=> (@ P tptp.bot_bo7824918357723582233_nat_o) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (F3 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o F3) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X3) F3)) (=> (@ P F3) (@ P (@ (@ tptp.insert5175938949040314269_nat_o X3) F3)))))) (@ P F2))))))
% 5.61/5.92 (assert (= tptp.finite6017078050557962740nteger (lambda ((A6 tptp.set_Code_integer)) (or (= A6 tptp.bot_bo3990330152332043303nteger) (exists ((A3 tptp.set_Code_integer) (B6 tptp.code_integer)) (and (= A6 (@ (@ tptp.insert_Code_integer B6) A3)) (@ tptp.finite6017078050557962740nteger A3)))))))
% 5.61/5.92 (assert (= tptp.finite4290736615968046902t_unit (lambda ((A6 tptp.set_Product_unit)) (or (= A6 tptp.bot_bo3957492148770167129t_unit) (exists ((A3 tptp.set_Product_unit) (B6 tptp.product_unit)) (and (= A6 (@ (@ tptp.insert_Product_unit B6) A3)) (@ tptp.finite4290736615968046902t_unit A3)))))))
% 5.61/5.92 (assert (= tptp.finite_finite_o (lambda ((A6 tptp.set_o)) (or (= A6 tptp.bot_bot_set_o) (exists ((A3 tptp.set_o) (B6 Bool)) (and (= A6 (@ (@ tptp.insert_o B6) A3)) (@ tptp.finite_finite_o A3)))))))
% 5.61/5.92 (assert (= tptp.finite_finite_nat (lambda ((A6 tptp.set_nat)) (or (= A6 tptp.bot_bot_set_nat) (exists ((A3 tptp.set_nat) (B6 tptp.nat)) (and (= A6 (@ (@ tptp.insert_nat B6) A3)) (@ tptp.finite_finite_nat A3)))))))
% 5.61/5.92 (assert (= tptp.finite_finite_int (lambda ((A6 tptp.set_int)) (or (= A6 tptp.bot_bot_set_int) (exists ((A3 tptp.set_int) (B6 tptp.int)) (and (= A6 (@ (@ tptp.insert_int B6) A3)) (@ tptp.finite_finite_int A3)))))))
% 5.61/5.92 (assert (= tptp.finite3252695134891459830_nat_o (lambda ((A6 tptp.set_Pr4532377907799695533_nat_o)) (or (= A6 tptp.bot_bo7824918357723582233_nat_o) (exists ((A3 tptp.set_Pr4532377907799695533_nat_o) (B6 (-> tptp.produc3658429121746597890et_nat Bool))) (and (= A6 (@ (@ tptp.insert5175938949040314269_nat_o B6) A3)) (@ tptp.finite3252695134891459830_nat_o A3)))))))
% 5.61/5.92 (assert (forall ((S tptp.set_Code_integer)) (=> (not (@ tptp.finite6017078050557962740nteger S)) (not (= S tptp.bot_bo3990330152332043303nteger)))))
% 5.61/5.92 (assert (forall ((S tptp.set_Product_unit)) (=> (not (@ tptp.finite4290736615968046902t_unit S)) (not (= S tptp.bot_bo3957492148770167129t_unit)))))
% 5.61/5.92 (assert (forall ((S tptp.set_o)) (=> (not (@ tptp.finite_finite_o S)) (not (= S tptp.bot_bot_set_o)))))
% 5.61/5.92 (assert (forall ((S tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S)) (not (= S tptp.bot_bot_set_nat)))))
% 5.61/5.92 (assert (forall ((S tptp.set_int)) (=> (not (@ tptp.finite_finite_int S)) (not (= S tptp.bot_bot_set_int)))))
% 5.61/5.92 (assert (forall ((S tptp.set_Pr4532377907799695533_nat_o)) (=> (not (@ tptp.finite3252695134891459830_nat_o S)) (not (= S tptp.bot_bo7824918357723582233_nat_o)))))
% 5.61/5.92 (assert (@ tptp.finite6017078050557962740nteger tptp.bot_bo3990330152332043303nteger))
% 5.61/5.92 (assert (@ tptp.finite4290736615968046902t_unit tptp.bot_bo3957492148770167129t_unit))
% 5.61/5.92 (assert (@ tptp.finite_finite_o tptp.bot_bot_set_o))
% 5.61/5.92 (assert (@ tptp.finite_finite_nat tptp.bot_bot_set_nat))
% 5.61/5.92 (assert (@ tptp.finite_finite_int tptp.bot_bot_set_int))
% 5.61/5.92 (assert (@ tptp.finite3252695134891459830_nat_o tptp.bot_bo7824918357723582233_nat_o))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (A2 tptp.int)) (=> (@ tptp.finite_finite_int A) (@ tptp.finite_finite_int (@ (@ tptp.insert_int A2) A)))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (A2 Bool)) (=> (@ tptp.finite_finite_o A) (@ tptp.finite_finite_o (@ (@ tptp.insert_o A2) A)))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (A2 tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (@ tptp.finite4290736615968046902t_unit (@ (@ tptp.insert_Product_unit A2) A)))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (A2 tptp.nat)) (=> (@ tptp.finite_finite_nat A) (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A2) A)))))
% 5.61/5.92 (assert (forall ((A tptp.set_Code_integer) (A2 tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.insert_Code_integer A2) A)))))
% 5.61/5.92 (assert (forall ((A tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A) (forall ((Xa2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Xa2) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger Xa2) X3) (= X3 Xa2))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (exists ((X3 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X3) A) (forall ((Xa2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit Xa2) A) (=> (@ (@ tptp.ord_le3221252021190050221t_unit Xa2) X3) (= X3 Xa2))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (exists ((X3 Bool)) (and (@ (@ tptp.member_o X3) A) (forall ((Xa2 Bool)) (=> (@ (@ tptp.member_o Xa2) A) (=> (@ (@ tptp.ord_less_eq_o Xa2) X3) (= X3 Xa2))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (exists ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (and (@ (@ tptp.member6576561426505652726_nat_o X3) A) (forall ((Xa2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Xa2) A) (=> (@ (@ tptp.ord_le729326519192465773_nat_o Xa2) X3) (= X3 Xa2))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_filter_nat)) (=> (@ tptp.finite2119507909894593271er_nat A) (=> (not (= A tptp.bot_bo498966703094740906er_nat)) (exists ((X3 tptp.filter_nat)) (and (@ (@ tptp.member_filter_nat X3) A) (forall ((Xa2 tptp.filter_nat)) (=> (@ (@ tptp.member_filter_nat Xa2) A) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Xa2) X3) (= X3 Xa2))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (not (= A tptp.bot_bot_set_set_nat)) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A) (forall ((Xa2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa2) A) (=> (@ (@ tptp.ord_less_eq_set_nat Xa2) X3) (= X3 Xa2))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A) (forall ((Xa2 tptp.rat)) (=> (@ (@ tptp.member_rat Xa2) A) (=> (@ (@ tptp.ord_less_eq_rat Xa2) X3) (= X3 Xa2))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (forall ((Xa2 tptp.nat)) (=> (@ (@ tptp.member_nat Xa2) A) (=> (@ (@ tptp.ord_less_eq_nat Xa2) X3) (= X3 Xa2))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A) (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) A) (=> (@ (@ tptp.ord_less_eq_int Xa2) X3) (= X3 Xa2))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A) (forall ((Xa2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Xa2) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger X3) Xa2) (= X3 Xa2))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (exists ((X3 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X3) A) (forall ((Xa2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit Xa2) A) (=> (@ (@ tptp.ord_le3221252021190050221t_unit X3) Xa2) (= X3 Xa2))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (exists ((X3 Bool)) (and (@ (@ tptp.member_o X3) A) (forall ((Xa2 Bool)) (=> (@ (@ tptp.member_o Xa2) A) (=> (@ (@ tptp.ord_less_eq_o X3) Xa2) (= X3 Xa2))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (exists ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (and (@ (@ tptp.member6576561426505652726_nat_o X3) A) (forall ((Xa2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Xa2) A) (=> (@ (@ tptp.ord_le729326519192465773_nat_o X3) Xa2) (= X3 Xa2))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_filter_nat)) (=> (@ tptp.finite2119507909894593271er_nat A) (=> (not (= A tptp.bot_bo498966703094740906er_nat)) (exists ((X3 tptp.filter_nat)) (and (@ (@ tptp.member_filter_nat X3) A) (forall ((Xa2 tptp.filter_nat)) (=> (@ (@ tptp.member_filter_nat Xa2) A) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X3) Xa2) (= X3 Xa2))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (not (= A tptp.bot_bot_set_set_nat)) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A) (forall ((Xa2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa2) A) (=> (@ (@ tptp.ord_less_eq_set_nat X3) Xa2) (= X3 Xa2))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A) (forall ((Xa2 tptp.rat)) (=> (@ (@ tptp.member_rat Xa2) A) (=> (@ (@ tptp.ord_less_eq_rat X3) Xa2) (= X3 Xa2))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (forall ((Xa2 tptp.nat)) (=> (@ (@ tptp.member_nat Xa2) A) (=> (@ (@ tptp.ord_less_eq_nat X3) Xa2) (= X3 Xa2))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A) (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) A) (=> (@ (@ tptp.ord_less_eq_int X3) Xa2) (= X3 Xa2))))))))))
% 5.61/5.92 (assert (forall ((A2 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A2) (=> (not (= A2 tptp.bot_bo3990330152332043303nteger)) (not (forall ((A9 tptp.set_Code_integer)) (=> (exists ((A4 tptp.code_integer)) (= A2 (@ (@ tptp.insert_Code_integer A4) A9))) (not (@ tptp.finite6017078050557962740nteger A9)))))))))
% 5.61/5.92 (assert (forall ((A2 tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A2) (=> (not (= A2 tptp.bot_bo3957492148770167129t_unit)) (not (forall ((A9 tptp.set_Product_unit)) (=> (exists ((A4 tptp.product_unit)) (= A2 (@ (@ tptp.insert_Product_unit A4) A9))) (not (@ tptp.finite4290736615968046902t_unit A9)))))))))
% 5.61/5.92 (assert (forall ((A2 tptp.set_o)) (=> (@ tptp.finite_finite_o A2) (=> (not (= A2 tptp.bot_bot_set_o)) (not (forall ((A9 tptp.set_o)) (=> (exists ((A4 Bool)) (= A2 (@ (@ tptp.insert_o A4) A9))) (not (@ tptp.finite_finite_o A9)))))))))
% 5.61/5.92 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (not (forall ((A9 tptp.set_nat)) (=> (exists ((A4 tptp.nat)) (= A2 (@ (@ tptp.insert_nat A4) A9))) (not (@ tptp.finite_finite_nat A9)))))))))
% 5.61/5.92 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (not (forall ((A9 tptp.set_int)) (=> (exists ((A4 tptp.int)) (= A2 (@ (@ tptp.insert_int A4) A9))) (not (@ tptp.finite_finite_int A9)))))))))
% 5.61/5.92 (assert (forall ((A2 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o A2) (=> (not (= A2 tptp.bot_bo7824918357723582233_nat_o)) (not (forall ((A9 tptp.set_Pr4532377907799695533_nat_o)) (=> (exists ((A4 (-> tptp.produc3658429121746597890et_nat Bool))) (= A2 (@ (@ tptp.insert5175938949040314269_nat_o A4) A9))) (not (@ tptp.finite3252695134891459830_nat_o A9)))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr5094982260447487303t_unit) (S tptp.set_Pr5094982260447487303t_unit)) (let ((_let_1 (@ tptp.min_ext_Product_unit R3))) (=> (@ (@ tptp.ord_le930853871177014503t_unit (@ (@ tptp.relcom848357998638694028t_unit R3) S)) R3) (@ (@ tptp.ord_le8072594200992201959t_unit (@ (@ tptp.relcom7108816970757792620t_unit _let_1) (@ (@ tptp.sup_su3573767163274163995t_unit (@ tptp.min_ext_Product_unit S)) (@ (@ tptp.insert6793119152790066487t_unit (@ (@ tptp.produc7269801343787132631t_unit tptp.bot_bo3957492148770167129t_unit) tptp.bot_bo3957492148770167129t_unit)) tptp.bot_bo5113747506523071411t_unit)))) _let_1)))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Product_prod_o_o) (S tptp.set_Product_prod_o_o)) (let ((_let_1 (@ tptp.min_ext_o R3))) (=> (@ (@ tptp.ord_le192195778054999463od_o_o (@ (@ tptp.relcomp_o_o_o R3) S)) R3) (@ (@ tptp.ord_le2885120122233735591_set_o (@ (@ tptp.relcom7534720040753365047_set_o _let_1) (@ (@ tptp.sup_su7766833992073560027_set_o (@ tptp.min_ext_o S)) (@ (@ tptp.insert1494450971503307511_set_o (@ (@ tptp.produc5838405689764958487_set_o tptp.bot_bot_set_o) tptp.bot_bot_set_o)) tptp.bot_bo8143257439550059635_set_o)))) _let_1)))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.min_ext_nat R3))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.relcomp_nat_nat_nat R3) S)) R3) (@ (@ tptp.ord_le4402255868550298733et_nat (@ (@ tptp.relcom236561585145426837et_nat _let_1) (@ (@ tptp.sup_su4251893418135750817et_nat (@ tptp.min_ext_nat S)) (@ (@ tptp.insert3810226134351308605et_nat (@ (@ tptp.produc4532415448927165861et_nat tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)) tptp.bot_bo4952753636535259449et_nat)))) _let_1)))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int) (S tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.min_ext_int R3))) (=> (@ (@ tptp.ord_le2843351958646193337nt_int (@ (@ tptp.relcomp_int_int_int R3) S)) R3) (@ (@ tptp.ord_le1436784781161120549et_int (@ (@ tptp.relcom4034950705519254697et_int _let_1) (@ (@ tptp.sup_su1286422330746572633et_int (@ tptp.min_ext_int S)) (@ (@ tptp.insert7328952640415156725et_int (@ (@ tptp.produc6363374080413544029et_int tptp.bot_bot_set_int) tptp.bot_bot_set_int)) tptp.bot_bo1987282549146081265et_int)))) _let_1)))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr2161125870931222855_nat_o) (S tptp.set_Pr2161125870931222855_nat_o)) (let ((_let_1 (@ tptp.min_ex3730736537596016502_nat_o R3))) (=> (@ (@ tptp.ord_le6659818918159358183_nat_o (@ (@ tptp.relcom6251035627269349452_nat_o R3) S)) R3) (@ (@ tptp.ord_le8001614231985977575_nat_o (@ (@ tptp.relcom7236094467932586796_nat_o _let_1) (@ (@ tptp.sup_su4863159966000489243_nat_o (@ tptp.min_ex3730736537596016502_nat_o S)) (@ (@ tptp.insert3244108804717745463_nat_o (@ (@ tptp.produc5149316574908490455_nat_o tptp.bot_bo7824918357723582233_nat_o) tptp.bot_bo7824918357723582233_nat_o)) tptp.bot_bo7535334947429593011_nat_o)))) _let_1)))))
% 5.61/5.92 (assert (forall ((S tptp.set_Code_integer) (Y tptp.code_integer) (F (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (not (= S tptp.bot_bo3990330152332043303nteger)) (=> (@ (@ tptp.member_Code_integer Y) S) (@ (@ tptp.ord_less_eq_rat (@ F (@ (@ tptp.lattic5439806495466278992er_rat F) S))) (@ F Y)))))))
% 5.61/5.92 (assert (forall ((S tptp.set_Product_unit) (Y tptp.product_unit) (F (-> tptp.product_unit tptp.rat))) (=> (@ tptp.finite4290736615968046902t_unit S) (=> (not (= S tptp.bot_bo3957492148770167129t_unit)) (=> (@ (@ tptp.member_Product_unit Y) S) (@ (@ tptp.ord_less_eq_rat (@ F (@ (@ tptp.lattic725702332050428812it_rat F) S))) (@ F Y)))))))
% 5.61/5.92 (assert (forall ((S tptp.set_o) (Y Bool) (F (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o S) (=> (not (= S tptp.bot_bot_set_o)) (=> (@ (@ tptp.member_o Y) S) (@ (@ tptp.ord_less_eq_rat (@ F (@ (@ tptp.lattic2140725968369957399_o_rat F) S))) (@ F Y)))))))
% 5.61/5.92 (assert (forall ((S tptp.set_nat) (Y tptp.nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S) (=> (not (= S tptp.bot_bot_set_nat)) (=> (@ (@ tptp.member_nat Y) S) (@ (@ tptp.ord_less_eq_rat (@ F (@ (@ tptp.lattic6811802900495863747at_rat F) S))) (@ F Y)))))))
% 5.61/5.92 (assert (forall ((S tptp.set_int) (Y tptp.int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S) (=> (not (= S tptp.bot_bot_set_int)) (=> (@ (@ tptp.member_int Y) S) (@ (@ tptp.ord_less_eq_rat (@ F (@ (@ tptp.lattic7811156612396918303nt_rat F) S))) (@ F Y)))))))
% 5.61/5.92 (assert (forall ((S tptp.set_Code_integer) (Y tptp.code_integer) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (not (= S tptp.bot_bo3990330152332043303nteger)) (=> (@ (@ tptp.member_Code_integer Y) S) (@ (@ tptp.ord_less_eq_nat (@ F (@ (@ tptp.lattic6074936555552774728er_nat F) S))) (@ F Y)))))))
% 5.61/5.92 (assert (forall ((S tptp.set_Product_unit) (Y tptp.product_unit) (F (-> tptp.product_unit tptp.nat))) (=> (@ tptp.finite4290736615968046902t_unit S) (=> (not (= S tptp.bot_bo3957492148770167129t_unit)) (=> (@ (@ tptp.member_Product_unit Y) S) (@ (@ tptp.ord_less_eq_nat (@ F (@ (@ tptp.lattic1360832392136924548it_nat F) S))) (@ F Y)))))))
% 5.61/5.92 (assert (forall ((S tptp.set_o) (Y Bool) (F (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o S) (=> (not (= S tptp.bot_bot_set_o)) (=> (@ (@ tptp.member_o Y) S) (@ (@ tptp.ord_less_eq_nat (@ F (@ (@ tptp.lattic2775856028456453135_o_nat F) S))) (@ F Y)))))))
% 5.61/5.92 (assert (forall ((S tptp.set_nat) (Y tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S) (=> (not (= S tptp.bot_bot_set_nat)) (=> (@ (@ tptp.member_nat Y) S) (@ (@ tptp.ord_less_eq_nat (@ F (@ (@ tptp.lattic7446932960582359483at_nat F) S))) (@ F Y)))))))
% 5.61/5.92 (assert (forall ((S tptp.set_int) (Y tptp.int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int S) (=> (not (= S tptp.bot_bot_set_int)) (=> (@ (@ tptp.member_int Y) S) (@ (@ tptp.ord_less_eq_nat (@ F (@ (@ tptp.lattic8446286672483414039nt_nat F) S))) (@ F Y)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.total_on_nat (@ tptp.field_nat R2)) R2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat R2) tptp.id_nat) (or (= R2 tptp.bot_bo2099793752762293965at_nat) (exists ((A4 tptp.nat)) (= R2 (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.product_Pair_nat_nat A4) A4)) tptp.bot_bo2099793752762293965at_nat))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.total_on_int (@ tptp.field_int R2)) R2) (=> (@ (@ tptp.ord_le2843351958646193337nt_int R2) tptp.id_int) (or (= R2 tptp.bot_bo1796632182523588997nt_int) (exists ((A4 tptp.int)) (= R2 (@ (@ tptp.insert5033312907999012233nt_int (@ (@ tptp.product_Pair_int_int A4) A4)) tptp.bot_bo1796632182523588997nt_int))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Code_integer) (R3 (-> tptp.code_integer tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (forall ((X3 tptp.code_integer)) (not (@ (@ R3 X3) X3))) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer) (Z3 tptp.code_integer)) (let ((_let_1 (@ R3 X3))) (=> (@ _let_1 Y2) (=> (@ (@ R3 Y2) Z3) (@ _let_1 Z3))))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A) (exists ((Y5 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Y5) A) (@ (@ R3 X3) Y5))))) (= A tptp.bot_bo3990330152332043303nteger)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (R3 (-> tptp.product_unit tptp.product_unit Bool))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (forall ((X3 tptp.product_unit)) (not (@ (@ R3 X3) X3))) (=> (forall ((X3 tptp.product_unit) (Y2 tptp.product_unit) (Z3 tptp.product_unit)) (let ((_let_1 (@ R3 X3))) (=> (@ _let_1 Y2) (=> (@ (@ R3 Y2) Z3) (@ _let_1 Z3))))) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) A) (exists ((Y5 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit Y5) A) (@ (@ R3 X3) Y5))))) (= A tptp.bot_bo3957492148770167129t_unit)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (R3 (-> Bool Bool Bool))) (=> (@ tptp.finite_finite_o A) (=> (forall ((X3 Bool)) (not (@ (@ R3 X3) X3))) (=> (forall ((X3 Bool) (Y2 Bool) (Z3 Bool)) (let ((_let_1 (@ R3 X3))) (=> (@ _let_1 Y2) (=> (@ (@ R3 Y2) Z3) (@ _let_1 Z3))))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (exists ((Y5 Bool)) (and (@ (@ tptp.member_o Y5) A) (@ (@ R3 X3) Y5))))) (= A tptp.bot_bot_set_o)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (R3 (-> tptp.nat tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A) (=> (forall ((X3 tptp.nat)) (not (@ (@ R3 X3) X3))) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ R3 X3))) (=> (@ _let_1 Y2) (=> (@ (@ R3 Y2) Z3) (@ _let_1 Z3))))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (exists ((Y5 tptp.nat)) (and (@ (@ tptp.member_nat Y5) A) (@ (@ R3 X3) Y5))))) (= A tptp.bot_bot_set_nat)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (R3 (-> tptp.int tptp.int Bool))) (=> (@ tptp.finite_finite_int A) (=> (forall ((X3 tptp.int)) (not (@ (@ R3 X3) X3))) (=> (forall ((X3 tptp.int) (Y2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ R3 X3))) (=> (@ _let_1 Y2) (=> (@ (@ R3 Y2) Z3) (@ _let_1 Z3))))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (exists ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) A) (@ (@ R3 X3) Y5))))) (= A tptp.bot_bot_set_int)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R3 (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ R3 X3) X3))) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 (-> tptp.produc3658429121746597890et_nat Bool)) (Z3 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ R3 X3))) (=> (@ _let_1 Y2) (=> (@ (@ R3 Y2) Z3) (@ _let_1 Z3))))) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) A) (exists ((Y5 (-> tptp.produc3658429121746597890et_nat Bool))) (and (@ (@ tptp.member6576561426505652726_nat_o Y5) A) (@ (@ R3 X3) Y5))))) (= A tptp.bot_bo7824918357723582233_nat_o)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (@ tptp.image_8431784415008483091t_unit R2))) (=> (@ (@ tptp.equiv_4189356295871601603t_unit A) R2) (= (@ (@ tptp.disjnt_Product_unit (@ _let_1 (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit))) (@ _let_1 (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit))) (not (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit A2) B)) R2)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o) (A2 Bool) (B Bool)) (let ((_let_1 (@ tptp.image_o_o R2))) (=> (@ (@ tptp.equiv_equiv_o A) R2) (= (@ (@ tptp.disjnt_o (@ _let_1 (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))) (@ _let_1 (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (not (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) B)) R2)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.image_nat_nat R2))) (=> (@ (@ tptp.equiv_equiv_nat A) R2) (= (@ (@ tptp.disjnt_nat (@ _let_1 (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))) (@ _let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R2)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.image_int_int R2))) (=> (@ (@ tptp.equiv_equiv_int A) R2) (= (@ (@ tptp.disjnt_int (@ _let_1 (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))) (@ _let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R2)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.image_2232984160439939859_nat_o R2))) (=> (@ (@ tptp.equiv_6726761681920839555_nat_o A) R2) (= (@ (@ tptp.disjnt7869448817988085652_nat_o (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o))) (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o B) tptp.bot_bo7824918357723582233_nat_o))) (not (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) B)) R2)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat) (X tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (not (= A tptp.bot_bot_set_set_nat)) (= (@ tptp.lattic3835124923745554447et_nat (@ (@ tptp.insert_set_nat X) A)) (@ (@ tptp.sup_sup_set_nat X) (@ tptp.lattic3835124923745554447et_nat A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_assn) (X tptp.assn)) (=> (@ tptp.finite_finite_assn A) (=> (not (= A tptp.bot_bot_set_assn)) (= (@ tptp.lattic2150320897289308081n_assn (@ (@ tptp.insert_assn X) A)) (@ (@ tptp.sup_sup_assn X) (@ tptp.lattic2150320897289308081n_assn A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (@ tptp.lattic5294303975357428420t_unit (@ (@ tptp.insert_Product_unit X) A)) (@ (@ tptp.sup_sup_Product_unit X) (@ tptp.lattic5294303975357428420t_unit A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (= (@ tptp.lattic1508158080041050831_fin_o (@ (@ tptp.insert_o X) A)) (@ (@ tptp.sup_sup_o X) (@ tptp.lattic1508158080041050831_fin_o A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (= (@ tptp.lattic1093996805478795353in_nat (@ (@ tptp.insert_nat X) A)) (@ (@ tptp.sup_sup_nat X) (@ tptp.lattic1093996805478795353in_nat A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (= (@ tptp.lattic1091506334969745077in_int (@ (@ tptp.insert_int X) A)) (@ (@ tptp.sup_sup_int X) (@ tptp.lattic1091506334969745077in_int A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (= (@ tptp.lattic7320199455484906628_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) A)) (@ (@ tptp.sup_su5453871518329203617_nat_o X) (@ tptp.lattic7320199455484906628_nat_o A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat) (X tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (not (= A tptp.bot_bot_set_set_nat)) (= (@ tptp.lattic3014633134055518761et_nat (@ (@ tptp.insert_set_nat X) A)) (@ (@ tptp.inf_inf_set_nat X) (@ tptp.lattic3014633134055518761et_nat A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_assn) (X tptp.assn)) (=> (@ tptp.finite_finite_assn A) (=> (not (= A tptp.bot_bot_set_assn)) (= (@ tptp.lattic47131356835913163n_assn (@ (@ tptp.insert_assn X) A)) (@ (@ tptp.inf_inf_assn X) (@ tptp.lattic47131356835913163n_assn A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (@ tptp.lattic1263872656861969706t_unit (@ (@ tptp.insert_Product_unit X) A)) (@ (@ tptp.inf_inf_Product_unit X) (@ tptp.lattic1263872656861969706t_unit A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (= (@ tptp.lattic4107685809792843317_fin_o (@ (@ tptp.insert_o X) A)) (@ (@ tptp.inf_inf_o X) (@ tptp.lattic4107685809792843317_fin_o A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (= (@ tptp.lattic5238388535129920115in_nat (@ (@ tptp.insert_nat X) A)) (@ (@ tptp.inf_inf_nat X) (@ tptp.lattic5238388535129920115in_nat A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (= (@ tptp.lattic5235898064620869839in_int (@ (@ tptp.insert_int X) A)) (@ (@ tptp.inf_inf_int X) (@ tptp.lattic5235898064620869839in_int A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (= (@ tptp.lattic956194824204696298_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) A)) (@ (@ tptp.inf_in1318976480646536635_nat_o X) (@ tptp.lattic956194824204696298_nat_o A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit) (X4 tptp.set_Product_unit) (X tptp.product_unit) (Y tptp.product_unit)) (=> (@ (@ tptp.equiv_4189356295871601603t_unit A) R2) (=> (@ (@ tptp.member5877623283571906838t_unit X4) (@ (@ tptp.equiv_5172566880711946708t_unit A) R2)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit (@ (@ tptp.insert_Product_unit X) (@ (@ tptp.insert_Product_unit Y) tptp.bot_bo3957492148770167129t_unit))) X4) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit X) Y)) R2))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o) (X4 tptp.set_o) (X Bool) (Y Bool)) (=> (@ (@ tptp.equiv_equiv_o A) R2) (=> (@ (@ tptp.member_set_o X4) (@ (@ tptp.equiv_quotient_o A) R2)) (=> (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.insert_o X) (@ (@ tptp.insert_o Y) tptp.bot_bot_set_o))) X4) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X) Y)) R2))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int) (X4 tptp.set_int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.equiv_equiv_int A) R2) (=> (@ (@ tptp.member_set_int X4) (@ (@ tptp.equiv_quotient_int A) R2)) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int X) (@ (@ tptp.insert_int Y) tptp.bot_bot_set_int))) X4) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R2))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o) (X4 tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.equiv_6726761681920839555_nat_o A) R2) (=> (@ (@ tptp.member1452989533377600726_nat_o X4) (@ (@ tptp.equiv_7899955228204526484_nat_o A) R2)) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) (@ (@ tptp.insert5175938949040314269_nat_o Y) tptp.bot_bo7824918357723582233_nat_o))) X4) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X) Y)) R2))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (X4 tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.equiv_equiv_nat A) R2) (=> (@ (@ tptp.member_set_nat X4) (@ (@ tptp.equiv_quotient_nat A) R2)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X) (@ (@ tptp.insert_nat Y) tptp.bot_bot_set_nat))) X4) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R2))))))
% 5.61/5.92 (assert (forall ((X tptp.heap_e7401611519738050253t_unit) (Y tptp.set_nat)) (= (@ tptp.basic_7833836874476830220et_nat (@ (@ tptp.produc7507926704131184380et_nat X) Y)) (@ (@ tptp.insert8563697753282147485t_unit X) tptp.bot_bo3686245532977126937t_unit))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.basic_fsts_nat_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))
% 5.61/5.92 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ tptp.basic_fsts_int_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3658429121746597890et_nat)) (= (@ tptp.basic_8654530971723826568et_nat (@ (@ tptp.produc5001842942810119800et_nat X) Y)) (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3925858234332021118et_nat)) (= (@ tptp.basic_3966130907827183364et_nat (@ (@ tptp.produc2245416461498447860et_nat X) Y)) (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool)) (E tptp.set_Pr2161125870931222855_nat_o) (R3 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X) Y)))) (=> (@ _let_1 (@ tptp.transi4009562729418357614_nat_o E)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) R3)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o Y) R3)) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o (@ (@ tptp.image_2232984160439939859_nat_o E) R3)) R3) (@ _let_1 (@ tptp.transi4009562729418357614_nat_o (@ (@ tptp.rel_re3331361160397388719_nat_o E) R3))))))))))
% 5.61/5.92 (assert (forall ((X Bool) (Y Bool) (E tptp.set_Product_prod_o_o) (R3 tptp.set_o)) (let ((_let_1 (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X) Y)))) (=> (@ _let_1 (@ tptp.transitive_trancl_o E)) (=> (not (@ (@ tptp.member_o X) R3)) (=> (not (@ (@ tptp.member_o Y) R3)) (=> (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.image_o_o E) R3)) R3) (@ _let_1 (@ tptp.transitive_trancl_o (@ (@ tptp.rel_restrict_o E) R3))))))))))
% 5.61/5.92 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (E tptp.set_Pr5094982260447487303t_unit) (R3 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit X) Y)))) (=> (@ _let_1 (@ tptp.transi430408012122777006t_unit E)) (=> (not (@ (@ tptp.member_Product_unit X) R3)) (=> (not (@ (@ tptp.member_Product_unit Y) R3)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit (@ (@ tptp.image_8431784415008483091t_unit E) R3)) R3) (@ _let_1 (@ tptp.transi430408012122777006t_unit (@ (@ tptp.rel_re9207996470947987439t_unit E) R3))))))))))
% 5.61/5.92 (assert (forall ((X tptp.int) (Y tptp.int) (E tptp.set_Pr958786334691620121nt_int) (R3 tptp.set_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)))) (=> (@ _let_1 (@ tptp.transi6261509568448316235cl_int E)) (=> (not (@ (@ tptp.member_int X) R3)) (=> (not (@ (@ tptp.member_int Y) R3)) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int E) R3)) R3) (@ _let_1 (@ tptp.transi6261509568448316235cl_int (@ (@ tptp.rel_restrict_int E) R3))))))))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (Y tptp.nat) (E tptp.set_Pr1261947904930325089at_nat) (R3 tptp.set_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)))) (=> (@ _let_1 (@ tptp.transi6264000038957366511cl_nat E)) (=> (not (@ (@ tptp.member_nat X) R3)) (=> (not (@ (@ tptp.member_nat Y) R3)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat E) R3)) R3) (@ _let_1 (@ tptp.transi6264000038957366511cl_nat (@ (@ tptp.rel_restrict_nat E) R3))))))))))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) tptp.id_nat) (= A2 B))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) tptp.id_int) (= A2 B))))
% 5.61/5.92 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) A2)) tptp.id_nat)))
% 5.61/5.92 (assert (forall ((A2 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) A2)) tptp.id_int)))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit)) (= (@ (@ tptp.equiv_5172566880711946708t_unit tptp.bot_bo3957492148770167129t_unit) R2) tptp.bot_bo6284674557190688313t_unit)))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o)) (= (@ (@ tptp.equiv_quotient_o tptp.bot_bot_set_o) R2) tptp.bot_bot_set_set_o)))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.equiv_quotient_nat tptp.bot_bot_set_nat) R2) tptp.bot_bot_set_set_nat)))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.equiv_quotient_int tptp.bot_bot_set_int) R2) tptp.bot_bot_set_set_int)))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o)) (= (@ (@ tptp.equiv_7899955228204526484_nat_o tptp.bot_bo7824918357723582233_nat_o) R2) tptp.bot_bo3736544561982865913_nat_o)))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit)) (= (= (@ (@ tptp.equiv_5172566880711946708t_unit A) R2) tptp.bot_bo6284674557190688313t_unit) (= A tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o)) (= (= (@ (@ tptp.equiv_quotient_o A) R2) tptp.bot_bot_set_set_o) (= A tptp.bot_bot_set_o))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.equiv_quotient_nat A) R2) tptp.bot_bot_set_set_nat) (= A tptp.bot_bot_set_nat))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (= (@ (@ tptp.equiv_quotient_int A) R2) tptp.bot_bot_set_set_int) (= A tptp.bot_bot_set_int))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o)) (= (= (@ (@ tptp.equiv_7899955228204526484_nat_o A) R2) tptp.bot_bo3736544561982865913_nat_o) (= A tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit)) (= (= tptp.bot_bo6284674557190688313t_unit (@ (@ tptp.equiv_5172566880711946708t_unit A) R2)) (= A tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o)) (= (= tptp.bot_bot_set_set_o (@ (@ tptp.equiv_quotient_o A) R2)) (= A tptp.bot_bot_set_o))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (= tptp.bot_bot_set_set_nat (@ (@ tptp.equiv_quotient_nat A) R2)) (= A tptp.bot_bot_set_nat))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (= tptp.bot_bot_set_set_int (@ (@ tptp.equiv_quotient_int A) R2)) (= A tptp.bot_bot_set_int))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o)) (= (= tptp.bot_bo3736544561982865913_nat_o (@ (@ tptp.equiv_7899955228204526484_nat_o A) R2)) (= A tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.92 (assert (forall ((S tptp.set_Product_unit)) (= (@ (@ tptp.disjnt_Product_unit S) S) (= S tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.92 (assert (forall ((S tptp.set_o)) (= (@ (@ tptp.disjnt_o S) S) (= S tptp.bot_bot_set_o))))
% 5.61/5.92 (assert (forall ((S tptp.set_nat)) (= (@ (@ tptp.disjnt_nat S) S) (= S tptp.bot_bot_set_nat))))
% 5.61/5.92 (assert (forall ((S tptp.set_int)) (= (@ (@ tptp.disjnt_int S) S) (= S tptp.bot_bot_set_int))))
% 5.61/5.92 (assert (forall ((S tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.disjnt7869448817988085652_nat_o S) S) (= S tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (X4 tptp.set_Pr4532377907799695533_nat_o) (Y6 tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.disjnt7869448817988085652_nat_o (@ (@ tptp.insert5175938949040314269_nat_o A2) X4)) Y6) (and (not (@ (@ tptp.member6576561426505652726_nat_o A2) Y6)) (@ (@ tptp.disjnt7869448817988085652_nat_o X4) Y6)))))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (X4 tptp.set_nat) (Y6 tptp.set_nat)) (= (@ (@ tptp.disjnt_nat (@ (@ tptp.insert_nat A2) X4)) Y6) (and (not (@ (@ tptp.member_nat A2) Y6)) (@ (@ tptp.disjnt_nat X4) Y6)))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (X4 tptp.set_int) (Y6 tptp.set_int)) (= (@ (@ tptp.disjnt_int (@ (@ tptp.insert_int A2) X4)) Y6) (and (not (@ (@ tptp.member_int A2) Y6)) (@ (@ tptp.disjnt_int X4) Y6)))))
% 5.61/5.92 (assert (forall ((A2 Bool) (X4 tptp.set_o) (Y6 tptp.set_o)) (= (@ (@ tptp.disjnt_o (@ (@ tptp.insert_o A2) X4)) Y6) (and (not (@ (@ tptp.member_o A2) Y6)) (@ (@ tptp.disjnt_o X4) Y6)))))
% 5.61/5.92 (assert (forall ((A2 tptp.product_unit) (X4 tptp.set_Product_unit) (Y6 tptp.set_Product_unit)) (= (@ (@ tptp.disjnt_Product_unit (@ (@ tptp.insert_Product_unit A2) X4)) Y6) (and (not (@ (@ tptp.member_Product_unit A2) Y6)) (@ (@ tptp.disjnt_Product_unit X4) Y6)))))
% 5.61/5.92 (assert (forall ((Y6 tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (X4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.disjnt7869448817988085652_nat_o Y6))) (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o A2) X4)) (and (not (@ (@ tptp.member6576561426505652726_nat_o A2) Y6)) (@ _let_1 X4))))))
% 5.61/5.92 (assert (forall ((Y6 tptp.set_nat) (A2 tptp.nat) (X4 tptp.set_nat)) (let ((_let_1 (@ tptp.disjnt_nat Y6))) (= (@ _let_1 (@ (@ tptp.insert_nat A2) X4)) (and (not (@ (@ tptp.member_nat A2) Y6)) (@ _let_1 X4))))))
% 5.61/5.92 (assert (forall ((Y6 tptp.set_int) (A2 tptp.int) (X4 tptp.set_int)) (let ((_let_1 (@ tptp.disjnt_int Y6))) (= (@ _let_1 (@ (@ tptp.insert_int A2) X4)) (and (not (@ (@ tptp.member_int A2) Y6)) (@ _let_1 X4))))))
% 5.61/5.92 (assert (forall ((Y6 tptp.set_o) (A2 Bool) (X4 tptp.set_o)) (let ((_let_1 (@ tptp.disjnt_o Y6))) (= (@ _let_1 (@ (@ tptp.insert_o A2) X4)) (and (not (@ (@ tptp.member_o A2) Y6)) (@ _let_1 X4))))))
% 5.61/5.92 (assert (forall ((Y6 tptp.set_Product_unit) (A2 tptp.product_unit) (X4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.disjnt_Product_unit Y6))) (= (@ _let_1 (@ (@ tptp.insert_Product_unit A2) X4)) (and (not (@ (@ tptp.member_Product_unit A2) Y6)) (@ _let_1 X4))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr5094982260447487303t_unit)) (= (@ (@ tptp.rel_re9207996470947987439t_unit R3) tptp.bot_bo3957492148770167129t_unit) R3)))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Product_prod_o_o)) (= (@ (@ tptp.rel_restrict_o R3) tptp.bot_bot_set_o) R3)))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.rel_restrict_nat R3) tptp.bot_bot_set_nat) R3)))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.rel_restrict_int R3) tptp.bot_bot_set_int) R3)))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr2161125870931222855_nat_o)) (= (@ (@ tptp.rel_re3331361160397388719_nat_o R3) tptp.bot_bo7824918357723582233_nat_o) R3)))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (= (@ (@ tptp.disjnt_nat (@ (@ tptp.sup_sup_set_nat A) B4)) C5) (and (@ (@ tptp.disjnt_nat A) C5) (@ (@ tptp.disjnt_nat B4) C5)))))
% 5.61/5.92 (assert (forall ((C5 tptp.set_nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.disjnt_nat C5))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (and (@ _let_1 A) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((X tptp.product_unit)) (= (@ tptp.lattic5294303975357428420t_unit (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)) X)))
% 5.61/5.92 (assert (forall ((X Bool)) (= (@ tptp.lattic1508158080041050831_fin_o (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)) X)))
% 5.61/5.92 (assert (forall ((X tptp.nat)) (= (@ tptp.lattic1093996805478795353in_nat (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)) X)))
% 5.61/5.92 (assert (forall ((X tptp.int)) (= (@ tptp.lattic1091506334969745077in_int (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)) X)))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool))) (= (@ tptp.lattic7320199455484906628_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)) X)))
% 5.61/5.92 (assert (forall ((X tptp.product_unit)) (= (@ tptp.lattic1263872656861969706t_unit (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)) X)))
% 5.61/5.92 (assert (forall ((X Bool)) (= (@ tptp.lattic4107685809792843317_fin_o (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)) X)))
% 5.61/5.92 (assert (forall ((X tptp.nat)) (= (@ tptp.lattic5238388535129920115in_nat (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)) X)))
% 5.61/5.92 (assert (forall ((X tptp.int)) (= (@ tptp.lattic5235898064620869839in_int (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)) X)))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool))) (= (@ tptp.lattic956194824204696298_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)) X)))
% 5.61/5.92 (assert (= tptp.disjnt7869448817988085652_nat_o (lambda ((A3 tptp.set_Pr4532377907799695533_nat_o) (B7 tptp.set_Pr4532377907799695533_nat_o)) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X2))) (not (and (@ _let_1 A3) (@ _let_1 B7))))))))
% 5.61/5.92 (assert (= tptp.disjnt_nat (lambda ((A3 tptp.set_nat) (B7 tptp.set_nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (not (and (@ _let_1 A3) (@ _let_1 B7))))))))
% 5.61/5.92 (assert (= tptp.disjnt_int (lambda ((A3 tptp.set_int) (B7 tptp.set_int)) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (not (and (@ _let_1 A3) (@ _let_1 B7))))))))
% 5.61/5.92 (assert (= tptp.disjnt_o (lambda ((A3 tptp.set_o) (B7 tptp.set_o)) (forall ((X2 Bool)) (let ((_let_1 (@ tptp.member_o X2))) (not (and (@ _let_1 A3) (@ _let_1 B7))))))))
% 5.61/5.92 (assert (= tptp.disjnt_Product_unit (lambda ((A3 tptp.set_Product_unit) (B7 tptp.set_Product_unit)) (forall ((X2 tptp.product_unit)) (let ((_let_1 (@ tptp.member_Product_unit X2))) (not (and (@ _let_1 A3) (@ _let_1 B7))))))))
% 5.61/5.92 (assert (forall ((P3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat P3) tptp.id_nat) (not (forall ((X3 tptp.nat)) (not (= P3 (@ (@ tptp.product_Pair_nat_nat X3) X3))))))))
% 5.61/5.92 (assert (forall ((P3 tptp.product_prod_int_int)) (=> (@ (@ tptp.member5262025264175285858nt_int P3) tptp.id_int) (not (forall ((X3 tptp.int)) (not (= P3 (@ (@ tptp.product_Pair_int_int X3) X3))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit)) (@ (@ tptp.disjnt_Product_unit tptp.bot_bo3957492148770167129t_unit) A)))
% 5.61/5.92 (assert (forall ((A tptp.set_o)) (@ (@ tptp.disjnt_o tptp.bot_bot_set_o) A)))
% 5.61/5.92 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.disjnt_nat tptp.bot_bot_set_nat) A)))
% 5.61/5.92 (assert (forall ((A tptp.set_int)) (@ (@ tptp.disjnt_int tptp.bot_bot_set_int) A)))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (@ (@ tptp.disjnt7869448817988085652_nat_o tptp.bot_bo7824918357723582233_nat_o) A)))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit)) (@ (@ tptp.disjnt_Product_unit A) tptp.bot_bo3957492148770167129t_unit)))
% 5.61/5.92 (assert (forall ((A tptp.set_o)) (@ (@ tptp.disjnt_o A) tptp.bot_bot_set_o)))
% 5.61/5.92 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.disjnt_nat A) tptp.bot_bot_set_nat)))
% 5.61/5.92 (assert (forall ((A tptp.set_int)) (@ (@ tptp.disjnt_int A) tptp.bot_bot_set_int)))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (@ (@ tptp.disjnt7869448817988085652_nat_o A) tptp.bot_bo7824918357723582233_nat_o)))
% 5.61/5.92 (assert (forall ((X4 tptp.set_nat) (Y6 tptp.set_nat) (Z5 tptp.set_nat)) (=> (@ (@ tptp.disjnt_nat X4) Y6) (=> (@ (@ tptp.ord_less_eq_set_nat Z5) X4) (@ (@ tptp.disjnt_nat Z5) Y6)))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_nat) (Y6 tptp.set_nat) (Z5 tptp.set_nat)) (let ((_let_1 (@ tptp.disjnt_nat X4))) (=> (@ _let_1 Y6) (=> (@ (@ tptp.ord_less_eq_set_nat Z5) Y6) (@ _let_1 Z5))))))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (N tptp.set_Pr4532377907799695533_nat_o) (M tptp.set_Pr4532377907799695533_nat_o)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) N)) (=> (@ (@ tptp.disjnt7869448817988085652_nat_o M) N) (@ (@ tptp.disjnt7869448817988085652_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) M)) N)))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (N tptp.set_nat) (M tptp.set_nat)) (=> (not (@ (@ tptp.member_nat X) N)) (=> (@ (@ tptp.disjnt_nat M) N) (@ (@ tptp.disjnt_nat (@ (@ tptp.insert_nat X) M)) N)))))
% 5.61/5.92 (assert (forall ((X tptp.int) (N tptp.set_int) (M tptp.set_int)) (=> (not (@ (@ tptp.member_int X) N)) (=> (@ (@ tptp.disjnt_int M) N) (@ (@ tptp.disjnt_int (@ (@ tptp.insert_int X) M)) N)))))
% 5.61/5.92 (assert (forall ((X Bool) (N tptp.set_o) (M tptp.set_o)) (=> (not (@ (@ tptp.member_o X) N)) (=> (@ (@ tptp.disjnt_o M) N) (@ (@ tptp.disjnt_o (@ (@ tptp.insert_o X) M)) N)))))
% 5.61/5.92 (assert (forall ((X tptp.product_unit) (N tptp.set_Product_unit) (M tptp.set_Product_unit)) (=> (not (@ (@ tptp.member_Product_unit X) N)) (=> (@ (@ tptp.disjnt_Product_unit M) N) (@ (@ tptp.disjnt_Product_unit (@ (@ tptp.insert_Product_unit X) M)) N)))))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr2161125870931222855_nat_o) (R3 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X) Y)) (@ (@ tptp.rel_re3331361160397388719_nat_o A) R3)) (not (@ (@ tptp.member6576561426505652726_nat_o Y) R3)))))
% 5.61/5.92 (assert (forall ((X Bool) (Y Bool) (A tptp.set_Product_prod_o_o) (R3 tptp.set_o)) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X) Y)) (@ (@ tptp.rel_restrict_o A) R3)) (not (@ (@ tptp.member_o Y) R3)))))
% 5.61/5.92 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (A tptp.set_Pr5094982260447487303t_unit) (R3 tptp.set_Product_unit)) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit X) Y)) (@ (@ tptp.rel_re9207996470947987439t_unit A) R3)) (not (@ (@ tptp.member_Product_unit Y) R3)))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.set_Pr1261947904930325089at_nat) (R3 tptp.set_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ tptp.rel_restrict_nat A) R3)) (not (@ (@ tptp.member_nat Y) R3)))))
% 5.61/5.92 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.set_Pr958786334691620121nt_int) (R3 tptp.set_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ (@ tptp.rel_restrict_int A) R3)) (not (@ (@ tptp.member_int Y) R3)))))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr2161125870931222855_nat_o) (R3 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X) Y)) (@ (@ tptp.rel_re3331361160397388719_nat_o A) R3)) (not (@ (@ tptp.member6576561426505652726_nat_o X) R3)))))
% 5.61/5.92 (assert (forall ((X Bool) (Y Bool) (A tptp.set_Product_prod_o_o) (R3 tptp.set_o)) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X) Y)) (@ (@ tptp.rel_restrict_o A) R3)) (not (@ (@ tptp.member_o X) R3)))))
% 5.61/5.92 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (A tptp.set_Pr5094982260447487303t_unit) (R3 tptp.set_Product_unit)) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit X) Y)) (@ (@ tptp.rel_re9207996470947987439t_unit A) R3)) (not (@ (@ tptp.member_Product_unit X) R3)))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.set_Pr1261947904930325089at_nat) (R3 tptp.set_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ tptp.rel_restrict_nat A) R3)) (not (@ (@ tptp.member_nat X) R3)))))
% 5.61/5.92 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.set_Pr958786334691620121nt_int) (R3 tptp.set_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ (@ tptp.rel_restrict_int A) R3)) (not (@ (@ tptp.member_int X) R3)))))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (R3 tptp.set_Pr4532377907799695533_nat_o) (Y (-> tptp.produc3658429121746597890et_nat Bool)) (E tptp.set_Pr2161125870931222855_nat_o)) (let ((_let_1 (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X) Y)))) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) R3)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o Y) R3)) (=> (@ _let_1 E) (@ _let_1 (@ (@ tptp.rel_re3331361160397388719_nat_o E) R3))))))))
% 5.61/5.92 (assert (forall ((X Bool) (R3 tptp.set_o) (Y Bool) (E tptp.set_Product_prod_o_o)) (let ((_let_1 (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X) Y)))) (=> (not (@ (@ tptp.member_o X) R3)) (=> (not (@ (@ tptp.member_o Y) R3)) (=> (@ _let_1 E) (@ _let_1 (@ (@ tptp.rel_restrict_o E) R3))))))))
% 5.61/5.92 (assert (forall ((X tptp.product_unit) (R3 tptp.set_Product_unit) (Y tptp.product_unit) (E tptp.set_Pr5094982260447487303t_unit)) (let ((_let_1 (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit X) Y)))) (=> (not (@ (@ tptp.member_Product_unit X) R3)) (=> (not (@ (@ tptp.member_Product_unit Y) R3)) (=> (@ _let_1 E) (@ _let_1 (@ (@ tptp.rel_re9207996470947987439t_unit E) R3))))))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (R3 tptp.set_nat) (Y tptp.nat) (E tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)))) (=> (not (@ (@ tptp.member_nat X) R3)) (=> (not (@ (@ tptp.member_nat Y) R3)) (=> (@ _let_1 E) (@ _let_1 (@ (@ tptp.rel_restrict_nat E) R3))))))))
% 5.61/5.92 (assert (forall ((X tptp.int) (R3 tptp.set_int) (Y tptp.int) (E tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)))) (=> (not (@ (@ tptp.member_int X) R3)) (=> (not (@ (@ tptp.member_int Y) R3)) (=> (@ _let_1 E) (@ _let_1 (@ (@ tptp.rel_restrict_int E) R3))))))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (Y tptp.nat) (E tptp.set_Pr1261947904930325089at_nat) (R3 tptp.set_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)))) (=> (@ _let_1 (@ (@ tptp.rel_restrict_nat E) R3)) (@ _let_1 E)))))
% 5.61/5.92 (assert (forall ((X tptp.int) (Y tptp.int) (E tptp.set_Pr958786334691620121nt_int) (R3 tptp.set_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)))) (=> (@ _let_1 (@ (@ tptp.rel_restrict_int E) R3)) (@ _let_1 E)))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.rel_restrict_nat R3))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.rel_restrict_nat (@ _let_1 A)) B4)))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.lattic1263872656861969706t_unit A)) (@ tptp.lattic5294303975357428420t_unit A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_eq_o (@ tptp.lattic4107685809792843317_fin_o A)) (@ tptp.lattic1508158080041050831_fin_o A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (@ (@ tptp.ord_le729326519192465773_nat_o (@ tptp.lattic956194824204696298_nat_o A)) (@ tptp.lattic7320199455484906628_nat_o A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_filter_nat)) (=> (@ tptp.finite2119507909894593271er_nat A) (=> (not (= A tptp.bot_bo498966703094740906er_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ tptp.lattic9128708996678779395er_nat A)) (@ tptp.lattic5930898082463196905er_nat A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (not (= A tptp.bot_bot_set_set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.lattic3014633134055518761et_nat A)) (@ tptp.lattic3835124923745554447et_nat A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.lattic4603258475043424379in_rat A)) (@ tptp.lattic458866745392299617in_rat A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.lattic5238388535129920115in_nat A)) (@ tptp.lattic1093996805478795353in_nat A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_eq_int (@ tptp.lattic5235898064620869839in_int A)) (@ tptp.lattic1091506334969745077in_int A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (C5 (-> tptp.nat tptp.set_Product_unit)) (B4 tptp.set_nat)) (= (@ (@ tptp.disjnt595863415355979947t_unit (@ (@ tptp.produc5506539147108004339t_unit A) C5)) (@ (@ tptp.produc5506539147108004339t_unit B4) C5)) (or (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.inf_inf_set_nat A) B4)) (= (@ C5 X2) tptp.bot_bo3957492148770167129t_unit))) (@ (@ tptp.disjnt_nat A) B4)))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (C5 (-> tptp.nat tptp.set_o)) (B4 tptp.set_nat)) (= (@ (@ tptp.disjnt5652777605541633334_nat_o (@ (@ tptp.product_Sigma_nat_o A) C5)) (@ (@ tptp.product_Sigma_nat_o B4) C5)) (or (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.inf_inf_set_nat A) B4)) (= (@ C5 X2) tptp.bot_bot_set_o))) (@ (@ tptp.disjnt_nat A) B4)))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (C5 (-> tptp.nat tptp.set_nat)) (B4 tptp.set_nat)) (= (@ (@ tptp.disjnt2713546992526078024at_nat (@ (@ tptp.produc457027306803732586at_nat A) C5)) (@ (@ tptp.produc457027306803732586at_nat B4) C5)) (or (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.inf_inf_set_nat A) B4)) (= (@ C5 X2) tptp.bot_bot_set_nat))) (@ (@ tptp.disjnt_nat A) B4)))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (C5 (-> tptp.nat tptp.set_int)) (B4 tptp.set_nat)) (= (@ (@ tptp.disjnt7759068009871657124at_int (@ (@ tptp.produc454536836294682310at_int A) C5)) (@ (@ tptp.produc454536836294682310at_int B4) C5)) (or (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.inf_inf_set_nat A) B4)) (= (@ C5 X2) tptp.bot_bot_set_int))) (@ (@ tptp.disjnt_nat A) B4)))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (C5 (-> tptp.nat tptp.set_Pr4532377907799695533_nat_o)) (B4 tptp.set_nat)) (= (@ (@ tptp.disjnt4476176636800211563_nat_o (@ (@ tptp.produc5650067098820117939_nat_o A) C5)) (@ (@ tptp.produc5650067098820117939_nat_o B4) C5)) (or (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) (@ (@ tptp.inf_inf_set_nat A) B4)) (= (@ C5 X2) tptp.bot_bo7824918357723582233_nat_o))) (@ (@ tptp.disjnt_nat A) B4)))))
% 5.61/5.92 (assert (= tptp.disjnt_Product_unit (lambda ((A3 tptp.set_Product_unit) (B7 tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit A3) B7) tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.92 (assert (= tptp.disjnt_o (lambda ((A3 tptp.set_o) (B7 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o A3) B7) tptp.bot_bot_set_o))))
% 5.61/5.92 (assert (= tptp.disjnt_nat (lambda ((A3 tptp.set_nat) (B7 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A3) B7) tptp.bot_bot_set_nat))))
% 5.61/5.92 (assert (= tptp.disjnt_int (lambda ((A3 tptp.set_int) (B7 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A3) B7) tptp.bot_bot_set_int))))
% 5.61/5.92 (assert (= tptp.disjnt7869448817988085652_nat_o (lambda ((A3 tptp.set_Pr4532377907799695533_nat_o) (B7 tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o A3) B7) tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o) (X4 tptp.set_Pr4532377907799695533_nat_o) (Y6 tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ tptp.equiv_7899955228204526484_nat_o A) R2))) (=> (@ (@ tptp.equiv_6726761681920839555_nat_o A) R2) (=> (@ (@ tptp.member1452989533377600726_nat_o X4) _let_1) (=> (@ (@ tptp.member1452989533377600726_nat_o Y6) _let_1) (=> (@ (@ tptp.member6576561426505652726_nat_o X) X4) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) Y6) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X) Y)) R2) (= X4 Y6))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o) (X4 tptp.set_o) (Y6 tptp.set_o) (X Bool) (Y Bool)) (let ((_let_1 (@ (@ tptp.equiv_quotient_o A) R2))) (=> (@ (@ tptp.equiv_equiv_o A) R2) (=> (@ (@ tptp.member_set_o X4) _let_1) (=> (@ (@ tptp.member_set_o Y6) _let_1) (=> (@ (@ tptp.member_o X) X4) (=> (@ (@ tptp.member_o Y) Y6) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X) Y)) R2) (= X4 Y6))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit) (X4 tptp.set_Product_unit) (Y6 tptp.set_Product_unit) (X tptp.product_unit) (Y tptp.product_unit)) (let ((_let_1 (@ (@ tptp.equiv_5172566880711946708t_unit A) R2))) (=> (@ (@ tptp.equiv_4189356295871601603t_unit A) R2) (=> (@ (@ tptp.member5877623283571906838t_unit X4) _let_1) (=> (@ (@ tptp.member5877623283571906838t_unit Y6) _let_1) (=> (@ (@ tptp.member_Product_unit X) X4) (=> (@ (@ tptp.member_Product_unit Y) Y6) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit X) Y)) R2) (= X4 Y6))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (X4 tptp.set_nat) (Y6 tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.equiv_quotient_nat A) R2))) (=> (@ (@ tptp.equiv_equiv_nat A) R2) (=> (@ (@ tptp.member_set_nat X4) _let_1) (=> (@ (@ tptp.member_set_nat Y6) _let_1) (=> (@ (@ tptp.member_nat X) X4) (=> (@ (@ tptp.member_nat Y) Y6) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R2) (= X4 Y6))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int) (X4 tptp.set_int) (Y6 tptp.set_int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.equiv_quotient_int A) R2))) (=> (@ (@ tptp.equiv_equiv_int A) R2) (=> (@ (@ tptp.member_set_int X4) _let_1) (=> (@ (@ tptp.member_set_int Y6) _let_1) (=> (@ (@ tptp.member_int X) X4) (=> (@ (@ tptp.member_int Y) Y6) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R2) (= X4 Y6))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o) (X4 tptp.set_Pr4532377907799695533_nat_o) (Y6 tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ tptp.equiv_7899955228204526484_nat_o A) R2))) (=> (@ (@ tptp.equiv_6726761681920839555_nat_o A) R2) (=> (@ (@ tptp.member1452989533377600726_nat_o X4) _let_1) (=> (@ (@ tptp.member1452989533377600726_nat_o Y6) _let_1) (=> (@ (@ tptp.member6576561426505652726_nat_o X) X4) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) Y6) (= (= X4 Y6) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X) Y)) R2))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o) (X4 tptp.set_o) (Y6 tptp.set_o) (X Bool) (Y Bool)) (let ((_let_1 (@ (@ tptp.equiv_quotient_o A) R2))) (=> (@ (@ tptp.equiv_equiv_o A) R2) (=> (@ (@ tptp.member_set_o X4) _let_1) (=> (@ (@ tptp.member_set_o Y6) _let_1) (=> (@ (@ tptp.member_o X) X4) (=> (@ (@ tptp.member_o Y) Y6) (= (= X4 Y6) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X) Y)) R2))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit) (X4 tptp.set_Product_unit) (Y6 tptp.set_Product_unit) (X tptp.product_unit) (Y tptp.product_unit)) (let ((_let_1 (@ (@ tptp.equiv_5172566880711946708t_unit A) R2))) (=> (@ (@ tptp.equiv_4189356295871601603t_unit A) R2) (=> (@ (@ tptp.member5877623283571906838t_unit X4) _let_1) (=> (@ (@ tptp.member5877623283571906838t_unit Y6) _let_1) (=> (@ (@ tptp.member_Product_unit X) X4) (=> (@ (@ tptp.member_Product_unit Y) Y6) (= (= X4 Y6) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit X) Y)) R2))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (X4 tptp.set_nat) (Y6 tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.equiv_quotient_nat A) R2))) (=> (@ (@ tptp.equiv_equiv_nat A) R2) (=> (@ (@ tptp.member_set_nat X4) _let_1) (=> (@ (@ tptp.member_set_nat Y6) _let_1) (=> (@ (@ tptp.member_nat X) X4) (=> (@ (@ tptp.member_nat Y) Y6) (= (= X4 Y6) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R2))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int) (X4 tptp.set_int) (Y6 tptp.set_int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.equiv_quotient_int A) R2))) (=> (@ (@ tptp.equiv_equiv_int A) R2) (=> (@ (@ tptp.member_set_int X4) _let_1) (=> (@ (@ tptp.member_set_int Y6) _let_1) (=> (@ (@ tptp.member_int X) X4) (=> (@ (@ tptp.member_int Y) Y6) (= (= X4 Y6) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R2))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o) (X4 tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.equiv_6726761681920839555_nat_o A) R2) (=> (@ (@ tptp.member1452989533377600726_nat_o X4) (@ (@ tptp.equiv_7899955228204526484_nat_o A) R2)) (=> (@ (@ tptp.member6576561426505652726_nat_o X) X4) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X) Y)) R2) (@ (@ tptp.member6576561426505652726_nat_o Y) X4)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o) (X4 tptp.set_o) (X Bool) (Y Bool)) (=> (@ (@ tptp.equiv_equiv_o A) R2) (=> (@ (@ tptp.member_set_o X4) (@ (@ tptp.equiv_quotient_o A) R2)) (=> (@ (@ tptp.member_o X) X4) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X) Y)) R2) (@ (@ tptp.member_o Y) X4)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit) (X4 tptp.set_Product_unit) (X tptp.product_unit) (Y tptp.product_unit)) (=> (@ (@ tptp.equiv_4189356295871601603t_unit A) R2) (=> (@ (@ tptp.member5877623283571906838t_unit X4) (@ (@ tptp.equiv_5172566880711946708t_unit A) R2)) (=> (@ (@ tptp.member_Product_unit X) X4) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit X) Y)) R2) (@ (@ tptp.member_Product_unit Y) X4)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (X4 tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.equiv_equiv_nat A) R2) (=> (@ (@ tptp.member_set_nat X4) (@ (@ tptp.equiv_quotient_nat A) R2)) (=> (@ (@ tptp.member_nat X) X4) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R2) (@ (@ tptp.member_nat Y) X4)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int) (X4 tptp.set_int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.equiv_equiv_int A) R2) (=> (@ (@ tptp.member_set_int X4) (@ (@ tptp.equiv_quotient_int A) R2)) (=> (@ (@ tptp.member_int X) X4) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R2) (@ (@ tptp.member_int Y) X4)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit) (X4 tptp.set_Product_unit)) (=> (@ (@ tptp.equiv_4189356295871601603t_unit A) R2) (=> (@ (@ tptp.member5877623283571906838t_unit X4) (@ (@ tptp.equiv_5172566880711946708t_unit A) R2)) (not (= X4 tptp.bot_bo3957492148770167129t_unit))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o) (X4 tptp.set_o)) (=> (@ (@ tptp.equiv_equiv_o A) R2) (=> (@ (@ tptp.member_set_o X4) (@ (@ tptp.equiv_quotient_o A) R2)) (not (= X4 tptp.bot_bot_set_o))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (X4 tptp.set_nat)) (=> (@ (@ tptp.equiv_equiv_nat A) R2) (=> (@ (@ tptp.member_set_nat X4) (@ (@ tptp.equiv_quotient_nat A) R2)) (not (= X4 tptp.bot_bot_set_nat))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int) (X4 tptp.set_int)) (=> (@ (@ tptp.equiv_equiv_int A) R2) (=> (@ (@ tptp.member_set_int X4) (@ (@ tptp.equiv_quotient_int A) R2)) (not (= X4 tptp.bot_bot_set_int))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o) (X4 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.equiv_6726761681920839555_nat_o A) R2) (=> (@ (@ tptp.member1452989533377600726_nat_o X4) (@ (@ tptp.equiv_7899955228204526484_nat_o A) R2)) (not (= X4 tptp.bot_bo7824918357723582233_nat_o))))))
% 5.61/5.92 (assert (forall ((V (-> tptp.produc3658429121746597890et_nat Bool)) (W (-> tptp.produc3658429121746597890et_nat Bool)) (E tptp.set_Pr2161125870931222855_nat_o) (R3 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o V) W)) (@ tptp.transi4009562729418357614_nat_o (@ (@ tptp.rel_re3331361160397388719_nat_o E) R3))) (not (@ (@ tptp.member6576561426505652726_nat_o W) R3)))))
% 5.61/5.92 (assert (forall ((V Bool) (W Bool) (E tptp.set_Product_prod_o_o) (R3 tptp.set_o)) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o V) W)) (@ tptp.transitive_trancl_o (@ (@ tptp.rel_restrict_o E) R3))) (not (@ (@ tptp.member_o W) R3)))))
% 5.61/5.92 (assert (forall ((V tptp.product_unit) (W tptp.product_unit) (E tptp.set_Pr5094982260447487303t_unit) (R3 tptp.set_Product_unit)) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit V) W)) (@ tptp.transi430408012122777006t_unit (@ (@ tptp.rel_re9207996470947987439t_unit E) R3))) (not (@ (@ tptp.member_Product_unit W) R3)))))
% 5.61/5.92 (assert (forall ((V tptp.nat) (W tptp.nat) (E tptp.set_Pr1261947904930325089at_nat) (R3 tptp.set_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat V) W)) (@ tptp.transi6264000038957366511cl_nat (@ (@ tptp.rel_restrict_nat E) R3))) (not (@ (@ tptp.member_nat W) R3)))))
% 5.61/5.92 (assert (forall ((V tptp.int) (W tptp.int) (E tptp.set_Pr958786334691620121nt_int) (R3 tptp.set_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int V) W)) (@ tptp.transi6261509568448316235cl_int (@ (@ tptp.rel_restrict_int E) R3))) (not (@ (@ tptp.member_int W) R3)))))
% 5.61/5.92 (assert (forall ((V (-> tptp.produc3658429121746597890et_nat Bool)) (W (-> tptp.produc3658429121746597890et_nat Bool)) (E tptp.set_Pr2161125870931222855_nat_o) (R3 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o V) W)) (@ tptp.transi4009562729418357614_nat_o (@ (@ tptp.rel_re3331361160397388719_nat_o E) R3))) (not (@ (@ tptp.member6576561426505652726_nat_o V) R3)))))
% 5.61/5.92 (assert (forall ((V Bool) (W Bool) (E tptp.set_Product_prod_o_o) (R3 tptp.set_o)) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o V) W)) (@ tptp.transitive_trancl_o (@ (@ tptp.rel_restrict_o E) R3))) (not (@ (@ tptp.member_o V) R3)))))
% 5.61/5.92 (assert (forall ((V tptp.product_unit) (W tptp.product_unit) (E tptp.set_Pr5094982260447487303t_unit) (R3 tptp.set_Product_unit)) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit V) W)) (@ tptp.transi430408012122777006t_unit (@ (@ tptp.rel_re9207996470947987439t_unit E) R3))) (not (@ (@ tptp.member_Product_unit V) R3)))))
% 5.61/5.92 (assert (forall ((V tptp.nat) (W tptp.nat) (E tptp.set_Pr1261947904930325089at_nat) (R3 tptp.set_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat V) W)) (@ tptp.transi6264000038957366511cl_nat (@ (@ tptp.rel_restrict_nat E) R3))) (not (@ (@ tptp.member_nat V) R3)))))
% 5.61/5.92 (assert (forall ((V tptp.int) (W tptp.int) (E tptp.set_Pr958786334691620121nt_int) (R3 tptp.set_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int V) W)) (@ tptp.transi6261509568448316235cl_int (@ (@ tptp.rel_restrict_int E) R3))) (not (@ (@ tptp.member_int V) R3)))))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (B tptp.nat) (A tptp.set_Pr1261947904930325089at_nat) (R3 tptp.set_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)))) (=> (@ _let_1 (@ tptp.transi6264000038957366511cl_nat (@ (@ tptp.rel_restrict_nat A) R3))) (@ _let_1 (@ (@ tptp.rel_restrict_nat (@ tptp.transi6264000038957366511cl_nat A)) R3))))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (B tptp.int) (A tptp.set_Pr958786334691620121nt_int) (R3 tptp.set_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)))) (=> (@ _let_1 (@ tptp.transi6261509568448316235cl_int (@ (@ tptp.rel_restrict_int A) R3))) (@ _let_1 (@ (@ tptp.rel_restrict_int (@ tptp.transi6261509568448316235cl_int A)) R3))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_nat) (S tptp.set_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.rel_restrict_nat A))) (=> (@ (@ tptp.ord_less_eq_set_nat R3) S) (@ (@ tptp.ord_le3146513528884898305at_nat (@ _let_1 S)) (@ _let_1 R3))))))
% 5.61/5.92 (assert (forall ((X tptp.product_unit) (R2 tptp.set_Pr5094982260447487303t_unit)) (let ((_let_1 (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit))) (= (@ (@ tptp.equiv_5172566880711946708t_unit _let_1) R2) (@ (@ tptp.insert8986028188087627965t_unit (@ (@ tptp.image_8431784415008483091t_unit R2) _let_1)) tptp.bot_bo6284674557190688313t_unit)))))
% 5.61/5.92 (assert (forall ((X Bool) (R2 tptp.set_Product_prod_o_o)) (let ((_let_1 (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))) (= (@ (@ tptp.equiv_quotient_o _let_1) R2) (@ (@ tptp.insert_set_o (@ (@ tptp.image_o_o R2) _let_1)) tptp.bot_bot_set_set_o)))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (= (@ (@ tptp.equiv_quotient_nat _let_1) R2) (@ (@ tptp.insert_set_nat (@ (@ tptp.image_nat_nat R2) _let_1)) tptp.bot_bot_set_set_nat)))))
% 5.61/5.92 (assert (forall ((X tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (= (@ (@ tptp.equiv_quotient_int _let_1) R2) (@ (@ tptp.insert_set_int (@ (@ tptp.image_int_int R2) _let_1)) tptp.bot_bot_set_set_int)))))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr2161125870931222855_nat_o)) (let ((_let_1 (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o))) (= (@ (@ tptp.equiv_7899955228204526484_nat_o _let_1) R2) (@ (@ tptp.insert2507855216428400253_nat_o (@ (@ tptp.image_2232984160439939859_nat_o R2) _let_1)) tptp.bot_bo3736544561982865913_nat_o)))))
% 5.61/5.92 (assert (forall ((X tptp.product_unit) (A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit)) (=> (@ (@ tptp.member_Product_unit X) A) (@ (@ tptp.member5877623283571906838t_unit (@ (@ tptp.image_8431784415008483091t_unit R2) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit))) (@ (@ tptp.equiv_5172566880711946708t_unit A) R2)))))
% 5.61/5.92 (assert (forall ((X Bool) (A tptp.set_o) (R2 tptp.set_Product_prod_o_o)) (=> (@ (@ tptp.member_o X) A) (@ (@ tptp.member_set_o (@ (@ tptp.image_o_o R2) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))) (@ (@ tptp.equiv_quotient_o A) R2)))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member_nat X) A) (@ (@ tptp.member_set_nat (@ (@ tptp.image_nat_nat R2) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (@ (@ tptp.equiv_quotient_nat A) R2)))))
% 5.61/5.92 (assert (forall ((X tptp.int) (A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member_int X) A) (@ (@ tptp.member_set_int (@ (@ tptp.image_int_int R2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (@ (@ tptp.equiv_quotient_int A) R2)))))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o X) A) (@ (@ tptp.member1452989533377600726_nat_o (@ (@ tptp.image_2232984160439939859_nat_o R2) (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o))) (@ (@ tptp.equiv_7899955228204526484_nat_o A) R2)))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_Product_unit) (A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit)) (=> (@ (@ tptp.member5877623283571906838t_unit X4) (@ (@ tptp.equiv_5172566880711946708t_unit A) R2)) (not (forall ((X3 tptp.product_unit)) (=> (= X4 (@ (@ tptp.image_8431784415008483091t_unit R2) (@ (@ tptp.insert_Product_unit X3) tptp.bot_bo3957492148770167129t_unit))) (not (@ (@ tptp.member_Product_unit X3) A))))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_o) (A tptp.set_o) (R2 tptp.set_Product_prod_o_o)) (=> (@ (@ tptp.member_set_o X4) (@ (@ tptp.equiv_quotient_o A) R2)) (not (forall ((X3 Bool)) (=> (= X4 (@ (@ tptp.image_o_o R2) (@ (@ tptp.insert_o X3) tptp.bot_bot_set_o))) (not (@ (@ tptp.member_o X3) A))))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_nat) (A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member_set_nat X4) (@ (@ tptp.equiv_quotient_nat A) R2)) (not (forall ((X3 tptp.nat)) (=> (= X4 (@ (@ tptp.image_nat_nat R2) (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat))) (not (@ (@ tptp.member_nat X3) A))))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_int) (A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member_set_int X4) (@ (@ tptp.equiv_quotient_int A) R2)) (not (forall ((X3 tptp.int)) (=> (= X4 (@ (@ tptp.image_int_int R2) (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int))) (not (@ (@ tptp.member_int X3) A))))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_Pr4532377907799695533_nat_o) (A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o)) (=> (@ (@ tptp.member1452989533377600726_nat_o X4) (@ (@ tptp.equiv_7899955228204526484_nat_o A) R2)) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (= X4 (@ (@ tptp.image_2232984160439939859_nat_o R2) (@ (@ tptp.insert5175938949040314269_nat_o X3) tptp.bot_bo7824918357723582233_nat_o))) (not (@ (@ tptp.member6576561426505652726_nat_o X3) A))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ (@ tptp.ord_le3221252021190050221t_unit X) (@ tptp.lattic1263872656861969706t_unit A)) (forall ((A10 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A10) A) (@ (@ tptp.ord_le3221252021190050221t_unit X) A10))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ (@ tptp.ord_less_eq_o X) (@ tptp.lattic4107685809792843317_fin_o A)) (forall ((A10 Bool)) (=> (@ (@ tptp.member_o A10) A) (@ (@ tptp.ord_less_eq_o X) A10))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (=> (@ (@ tptp.ord_le729326519192465773_nat_o X) (@ tptp.lattic956194824204696298_nat_o A)) (forall ((A10 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o A10) A) (@ (@ tptp.ord_le729326519192465773_nat_o X) A10))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_filter_nat) (X tptp.filter_nat)) (=> (@ tptp.finite2119507909894593271er_nat A) (=> (not (= A tptp.bot_bo498966703094740906er_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X) (@ tptp.lattic9128708996678779395er_nat A)) (forall ((A10 tptp.filter_nat)) (=> (@ (@ tptp.member_filter_nat A10) A) (@ (@ tptp.ord_le2510731241096832064er_nat X) A10))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat) (X tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (not (= A tptp.bot_bot_set_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) (@ tptp.lattic3014633134055518761et_nat A)) (forall ((A10 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat A10) A) (@ (@ tptp.ord_less_eq_set_nat X) A10))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_rat) (X tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (=> (@ (@ tptp.ord_less_eq_rat X) (@ tptp.lattic4603258475043424379in_rat A)) (forall ((A10 tptp.rat)) (=> (@ (@ tptp.member_rat A10) A) (@ (@ tptp.ord_less_eq_rat X) A10))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_nat X) (@ tptp.lattic5238388535129920115in_nat A)) (forall ((A10 tptp.nat)) (=> (@ (@ tptp.member_nat A10) A) (@ (@ tptp.ord_less_eq_nat X) A10))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_int X) (@ tptp.lattic5235898064620869839in_int A)) (forall ((A10 tptp.int)) (=> (@ (@ tptp.member_int A10) A) (@ (@ tptp.ord_less_eq_int X) A10))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) A) (@ (@ tptp.ord_le3221252021190050221t_unit X) A4))) (@ (@ tptp.ord_le3221252021190050221t_unit X) (@ tptp.lattic1263872656861969706t_unit A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) A) (@ (@ tptp.ord_less_eq_o X) A4))) (@ (@ tptp.ord_less_eq_o X) (@ tptp.lattic4107685809792843317_fin_o A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o A4) A) (@ (@ tptp.ord_le729326519192465773_nat_o X) A4))) (@ (@ tptp.ord_le729326519192465773_nat_o X) (@ tptp.lattic956194824204696298_nat_o A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_filter_nat) (X tptp.filter_nat)) (=> (@ tptp.finite2119507909894593271er_nat A) (=> (not (= A tptp.bot_bo498966703094740906er_nat)) (=> (forall ((A4 tptp.filter_nat)) (=> (@ (@ tptp.member_filter_nat A4) A) (@ (@ tptp.ord_le2510731241096832064er_nat X) A4))) (@ (@ tptp.ord_le2510731241096832064er_nat X) (@ tptp.lattic9128708996678779395er_nat A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat) (X tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (not (= A tptp.bot_bot_set_set_nat)) (=> (forall ((A4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat A4) A) (@ (@ tptp.ord_less_eq_set_nat X) A4))) (@ (@ tptp.ord_less_eq_set_nat X) (@ tptp.lattic3014633134055518761et_nat A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_rat) (X tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (=> (forall ((A4 tptp.rat)) (=> (@ (@ tptp.member_rat A4) A) (@ (@ tptp.ord_less_eq_rat X) A4))) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.lattic4603258475043424379in_rat A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A) (@ (@ tptp.ord_less_eq_nat X) A4))) (@ (@ tptp.ord_less_eq_nat X) (@ tptp.lattic5238388535129920115in_nat A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A) (@ (@ tptp.ord_less_eq_int X) A4))) (@ (@ tptp.ord_less_eq_int X) (@ tptp.lattic5235898064620869839in_int A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.lattic5294303975357428420t_unit A)) X) (forall ((A10 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A10) A) (@ (@ tptp.ord_le3221252021190050221t_unit A10) X))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ (@ tptp.ord_less_eq_o (@ tptp.lattic1508158080041050831_fin_o A)) X) (forall ((A10 Bool)) (=> (@ (@ tptp.member_o A10) A) (@ (@ tptp.ord_less_eq_o A10) X))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (=> (@ (@ tptp.ord_le729326519192465773_nat_o (@ tptp.lattic7320199455484906628_nat_o A)) X) (forall ((A10 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o A10) A) (@ (@ tptp.ord_le729326519192465773_nat_o A10) X))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_filter_nat) (X tptp.filter_nat)) (=> (@ tptp.finite2119507909894593271er_nat A) (=> (not (= A tptp.bot_bo498966703094740906er_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat (@ tptp.lattic5930898082463196905er_nat A)) X) (forall ((A10 tptp.filter_nat)) (=> (@ (@ tptp.member_filter_nat A10) A) (@ (@ tptp.ord_le2510731241096832064er_nat A10) X))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat) (X tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (not (= A tptp.bot_bot_set_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.lattic3835124923745554447et_nat A)) X) (forall ((A10 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat A10) A) (@ (@ tptp.ord_less_eq_set_nat A10) X))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_rat) (X tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.lattic458866745392299617in_rat A)) X) (forall ((A10 tptp.rat)) (=> (@ (@ tptp.member_rat A10) A) (@ (@ tptp.ord_less_eq_rat A10) X))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.lattic1093996805478795353in_nat A)) X) (forall ((A10 tptp.nat)) (=> (@ (@ tptp.member_nat A10) A) (@ (@ tptp.ord_less_eq_nat A10) X))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.lattic1091506334969745077in_int A)) X) (forall ((A10 tptp.int)) (=> (@ (@ tptp.member_int A10) A) (@ (@ tptp.ord_less_eq_int A10) X))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) A) (@ (@ tptp.ord_le3221252021190050221t_unit A4) X))) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.lattic5294303975357428420t_unit A)) X))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) A) (@ (@ tptp.ord_less_eq_o A4) X))) (@ (@ tptp.ord_less_eq_o (@ tptp.lattic1508158080041050831_fin_o A)) X))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o A4) A) (@ (@ tptp.ord_le729326519192465773_nat_o A4) X))) (@ (@ tptp.ord_le729326519192465773_nat_o (@ tptp.lattic7320199455484906628_nat_o A)) X))))))
% 5.61/5.92 (assert (forall ((A tptp.set_filter_nat) (X tptp.filter_nat)) (=> (@ tptp.finite2119507909894593271er_nat A) (=> (not (= A tptp.bot_bo498966703094740906er_nat)) (=> (forall ((A4 tptp.filter_nat)) (=> (@ (@ tptp.member_filter_nat A4) A) (@ (@ tptp.ord_le2510731241096832064er_nat A4) X))) (@ (@ tptp.ord_le2510731241096832064er_nat (@ tptp.lattic5930898082463196905er_nat A)) X))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat) (X tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (not (= A tptp.bot_bot_set_set_nat)) (=> (forall ((A4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat A4) A) (@ (@ tptp.ord_less_eq_set_nat A4) X))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.lattic3835124923745554447et_nat A)) X))))))
% 5.61/5.92 (assert (forall ((A tptp.set_rat) (X tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (=> (forall ((A4 tptp.rat)) (=> (@ (@ tptp.member_rat A4) A) (@ (@ tptp.ord_less_eq_rat A4) X))) (@ (@ tptp.ord_less_eq_rat (@ tptp.lattic458866745392299617in_rat A)) X))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A) (@ (@ tptp.ord_less_eq_nat A4) X))) (@ (@ tptp.ord_less_eq_nat (@ tptp.lattic1093996805478795353in_nat A)) X))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A) (@ (@ tptp.ord_less_eq_int A4) X))) (@ (@ tptp.ord_less_eq_int (@ tptp.lattic1091506334969745077in_int A)) X))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (@ (@ tptp.ord_le3221252021190050221t_unit X) (@ tptp.lattic1263872656861969706t_unit A)) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) A) (@ (@ tptp.ord_le3221252021190050221t_unit X) X2))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (= (@ (@ tptp.ord_less_eq_o X) (@ tptp.lattic4107685809792843317_fin_o A)) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A) (@ (@ tptp.ord_less_eq_o X) X2))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (= (@ (@ tptp.ord_le729326519192465773_nat_o X) (@ tptp.lattic956194824204696298_nat_o A)) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X2) A) (@ (@ tptp.ord_le729326519192465773_nat_o X) X2))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_filter_nat) (X tptp.filter_nat)) (=> (@ tptp.finite2119507909894593271er_nat A) (=> (not (= A tptp.bot_bo498966703094740906er_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat X) (@ tptp.lattic9128708996678779395er_nat A)) (forall ((X2 tptp.filter_nat)) (=> (@ (@ tptp.member_filter_nat X2) A) (@ (@ tptp.ord_le2510731241096832064er_nat X) X2))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat) (X tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (not (= A tptp.bot_bot_set_set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat X) (@ tptp.lattic3014633134055518761et_nat A)) (forall ((X2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X2) A) (@ (@ tptp.ord_less_eq_set_nat X) X2))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_rat) (X tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (= (@ (@ tptp.ord_less_eq_rat X) (@ tptp.lattic4603258475043424379in_rat A)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.member_rat X2) A) (@ (@ tptp.ord_less_eq_rat X) X2))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (= (@ (@ tptp.ord_less_eq_nat X) (@ tptp.lattic5238388535129920115in_nat A)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.ord_less_eq_nat X) X2))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (= (@ (@ tptp.ord_less_eq_int X) (@ tptp.lattic5235898064620869839in_int A)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A) (@ (@ tptp.ord_less_eq_int X) X2))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.lattic5294303975357428420t_unit A)) X) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) A) (@ (@ tptp.ord_le3221252021190050221t_unit X2) X))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (= (@ (@ tptp.ord_less_eq_o (@ tptp.lattic1508158080041050831_fin_o A)) X) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A) (@ (@ tptp.ord_less_eq_o X2) X))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (= (@ (@ tptp.ord_le729326519192465773_nat_o (@ tptp.lattic7320199455484906628_nat_o A)) X) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X2) A) (@ (@ tptp.ord_le729326519192465773_nat_o X2) X))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_filter_nat) (X tptp.filter_nat)) (=> (@ tptp.finite2119507909894593271er_nat A) (=> (not (= A tptp.bot_bo498966703094740906er_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat (@ tptp.lattic5930898082463196905er_nat A)) X) (forall ((X2 tptp.filter_nat)) (=> (@ (@ tptp.member_filter_nat X2) A) (@ (@ tptp.ord_le2510731241096832064er_nat X2) X))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat) (X tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (not (= A tptp.bot_bot_set_set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.lattic3835124923745554447et_nat A)) X) (forall ((X2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X2) A) (@ (@ tptp.ord_less_eq_set_nat X2) X))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_rat) (X tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.lattic458866745392299617in_rat A)) X) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.member_rat X2) A) (@ (@ tptp.ord_less_eq_rat X2) X))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.lattic1093996805478795353in_nat A)) X) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.ord_less_eq_nat X2) X))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.lattic1091506334969745077in_int A)) X) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A) (@ (@ tptp.ord_less_eq_int X2) X))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit) (X4 tptp.set_Product_unit) (Y6 tptp.set_Product_unit)) (let ((_let_1 (@ (@ tptp.equiv_5172566880711946708t_unit A) R2))) (=> (@ (@ tptp.equiv_4189356295871601603t_unit A) R2) (=> (@ (@ tptp.member5877623283571906838t_unit X4) _let_1) (=> (@ (@ tptp.member5877623283571906838t_unit Y6) _let_1) (or (= X4 Y6) (= (@ (@ tptp.inf_in4660618365625256667t_unit X4) Y6) tptp.bot_bo3957492148770167129t_unit))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o) (X4 tptp.set_o) (Y6 tptp.set_o)) (let ((_let_1 (@ (@ tptp.equiv_quotient_o A) R2))) (=> (@ (@ tptp.equiv_equiv_o A) R2) (=> (@ (@ tptp.member_set_o X4) _let_1) (=> (@ (@ tptp.member_set_o Y6) _let_1) (or (= X4 Y6) (= (@ (@ tptp.inf_inf_set_o X4) Y6) tptp.bot_bot_set_o))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (X4 tptp.set_nat) (Y6 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.equiv_quotient_nat A) R2))) (=> (@ (@ tptp.equiv_equiv_nat A) R2) (=> (@ (@ tptp.member_set_nat X4) _let_1) (=> (@ (@ tptp.member_set_nat Y6) _let_1) (or (= X4 Y6) (= (@ (@ tptp.inf_inf_set_nat X4) Y6) tptp.bot_bot_set_nat))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int) (X4 tptp.set_int) (Y6 tptp.set_int)) (let ((_let_1 (@ (@ tptp.equiv_quotient_int A) R2))) (=> (@ (@ tptp.equiv_equiv_int A) R2) (=> (@ (@ tptp.member_set_int X4) _let_1) (=> (@ (@ tptp.member_set_int Y6) _let_1) (or (= X4 Y6) (= (@ (@ tptp.inf_inf_set_int X4) Y6) tptp.bot_bot_set_int))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o) (X4 tptp.set_Pr4532377907799695533_nat_o) (Y6 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ (@ tptp.equiv_7899955228204526484_nat_o A) R2))) (=> (@ (@ tptp.equiv_6726761681920839555_nat_o A) R2) (=> (@ (@ tptp.member1452989533377600726_nat_o X4) _let_1) (=> (@ (@ tptp.member1452989533377600726_nat_o Y6) _let_1) (or (= X4 Y6) (= (@ (@ tptp.inf_in1906310914598751387_nat_o X4) Y6) tptp.bot_bo7824918357723582233_nat_o))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (R3 tptp.set_Pr5094982260447487303t_unit)) (=> (= (@ (@ tptp.inf_in4660618365625256667t_unit A) (@ tptp.field_Product_unit R3)) tptp.bot_bo3957492148770167129t_unit) (= (@ (@ tptp.rel_re9207996470947987439t_unit R3) A) R3))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (R3 tptp.set_Product_prod_o_o)) (=> (= (@ (@ tptp.inf_inf_set_o A) (@ tptp.field_o R3)) tptp.bot_bot_set_o) (= (@ (@ tptp.rel_restrict_o R3) A) R3))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (=> (= (@ (@ tptp.inf_inf_set_nat A) (@ tptp.field_nat R3)) tptp.bot_bot_set_nat) (= (@ (@ tptp.rel_restrict_nat R3) A) R3))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (R3 tptp.set_Pr958786334691620121nt_int)) (=> (= (@ (@ tptp.inf_inf_set_int A) (@ tptp.field_int R3)) tptp.bot_bot_set_int) (= (@ (@ tptp.rel_restrict_int R3) A) R3))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R3 tptp.set_Pr2161125870931222855_nat_o)) (=> (= (@ (@ tptp.inf_in1906310914598751387_nat_o A) (@ tptp.field_81821745747897882_nat_o R3)) tptp.bot_bo7824918357723582233_nat_o) (= (@ (@ tptp.rel_re3331361160397388719_nat_o R3) A) R3))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit) (X tptp.product_unit) (Y tptp.product_unit)) (=> (@ (@ tptp.equiv_4189356295871601603t_unit A) R2) (=> (@ (@ tptp.member_Product_unit X) A) (=> (@ (@ tptp.member_Product_unit Y) A) (= (= (@ (@ tptp.equiv_5172566880711946708t_unit (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)) R2) (@ (@ tptp.equiv_5172566880711946708t_unit (@ (@ tptp.insert_Product_unit Y) tptp.bot_bo3957492148770167129t_unit)) R2)) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit X) Y)) R2)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o) (X Bool) (Y Bool)) (=> (@ (@ tptp.equiv_equiv_o A) R2) (=> (@ (@ tptp.member_o X) A) (=> (@ (@ tptp.member_o Y) A) (= (= (@ (@ tptp.equiv_quotient_o (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)) R2) (@ (@ tptp.equiv_quotient_o (@ (@ tptp.insert_o Y) tptp.bot_bot_set_o)) R2)) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X) Y)) R2)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.equiv_equiv_nat A) R2) (=> (@ (@ tptp.member_nat X) A) (=> (@ (@ tptp.member_nat Y) A) (= (= (@ (@ tptp.equiv_quotient_nat (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)) R2) (@ (@ tptp.equiv_quotient_nat (@ (@ tptp.insert_nat Y) tptp.bot_bot_set_nat)) R2)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R2)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.equiv_equiv_int A) R2) (=> (@ (@ tptp.member_int X) A) (=> (@ (@ tptp.member_int Y) A) (= (= (@ (@ tptp.equiv_quotient_int (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)) R2) (@ (@ tptp.equiv_quotient_int (@ (@ tptp.insert_int Y) tptp.bot_bot_set_int)) R2)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R2)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.equiv_6726761681920839555_nat_o A) R2) (=> (@ (@ tptp.member6576561426505652726_nat_o X) A) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) A) (= (= (@ (@ tptp.equiv_7899955228204526484_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)) R2) (@ (@ tptp.equiv_7899955228204526484_nat_o (@ (@ tptp.insert5175938949040314269_nat_o Y) tptp.bot_bo7824918357723582233_nat_o)) R2)) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X) Y)) R2)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) B4) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.finite4290736615968046902t_unit B4) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.lattic1263872656861969706t_unit B4)) (@ tptp.lattic1263872656861969706t_unit A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A) B4) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.finite_finite_o B4) (@ (@ tptp.ord_less_eq_o (@ tptp.lattic4107685809792843317_fin_o B4)) (@ tptp.lattic4107685809792843317_fin_o A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A) B4) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o B4) (@ (@ tptp.ord_le729326519192465773_nat_o (@ tptp.lattic956194824204696298_nat_o B4)) (@ tptp.lattic956194824204696298_nat_o A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_filter_nat) (B4 tptp.set_filter_nat)) (=> (@ (@ tptp.ord_le2426478655948331894er_nat A) B4) (=> (not (= A tptp.bot_bo498966703094740906er_nat)) (=> (@ tptp.finite2119507909894593271er_nat B4) (@ (@ tptp.ord_le2510731241096832064er_nat (@ tptp.lattic9128708996678779395er_nat B4)) (@ tptp.lattic9128708996678779395er_nat A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat) (B4 tptp.set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A) B4) (=> (not (= A tptp.bot_bot_set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B4) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.lattic3014633134055518761et_nat B4)) (@ tptp.lattic3014633134055518761et_nat A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_rat) (B4 tptp.set_rat)) (=> (@ (@ tptp.ord_less_eq_set_rat A) B4) (=> (not (= A tptp.bot_bot_set_rat)) (=> (@ tptp.finite_finite_rat B4) (@ (@ tptp.ord_less_eq_rat (@ tptp.lattic4603258475043424379in_rat B4)) (@ tptp.lattic4603258475043424379in_rat A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B4) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.finite_finite_int B4) (@ (@ tptp.ord_less_eq_int (@ tptp.lattic5235898064620869839in_int B4)) (@ tptp.lattic5235898064620869839in_int A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.finite_finite_nat B4) (@ (@ tptp.ord_less_eq_nat (@ tptp.lattic5238388535129920115in_nat B4)) (@ tptp.lattic5238388535129920115in_nat A)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) B4) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.finite4290736615968046902t_unit B4) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.lattic5294303975357428420t_unit A)) (@ tptp.lattic5294303975357428420t_unit B4)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A) B4) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.finite_finite_o B4) (@ (@ tptp.ord_less_eq_o (@ tptp.lattic1508158080041050831_fin_o A)) (@ tptp.lattic1508158080041050831_fin_o B4)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A) B4) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o B4) (@ (@ tptp.ord_le729326519192465773_nat_o (@ tptp.lattic7320199455484906628_nat_o A)) (@ tptp.lattic7320199455484906628_nat_o B4)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_filter_nat) (B4 tptp.set_filter_nat)) (=> (@ (@ tptp.ord_le2426478655948331894er_nat A) B4) (=> (not (= A tptp.bot_bo498966703094740906er_nat)) (=> (@ tptp.finite2119507909894593271er_nat B4) (@ (@ tptp.ord_le2510731241096832064er_nat (@ tptp.lattic5930898082463196905er_nat A)) (@ tptp.lattic5930898082463196905er_nat B4)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat) (B4 tptp.set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A) B4) (=> (not (= A tptp.bot_bot_set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B4) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.lattic3835124923745554447et_nat A)) (@ tptp.lattic3835124923745554447et_nat B4)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_rat) (B4 tptp.set_rat)) (=> (@ (@ tptp.ord_less_eq_set_rat A) B4) (=> (not (= A tptp.bot_bot_set_rat)) (=> (@ tptp.finite_finite_rat B4) (@ (@ tptp.ord_less_eq_rat (@ tptp.lattic458866745392299617in_rat A)) (@ tptp.lattic458866745392299617in_rat B4)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B4) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.finite_finite_int B4) (@ (@ tptp.ord_less_eq_int (@ tptp.lattic1091506334969745077in_int A)) (@ tptp.lattic1091506334969745077in_int B4)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.finite_finite_nat B4) (@ (@ tptp.ord_less_eq_nat (@ tptp.lattic1093996805478795353in_nat A)) (@ tptp.lattic1093996805478795353in_nat B4)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat) (B4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.lattic3014633134055518761et_nat A))) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (not (= B4 tptp.bot_bot_set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat B4) A) (= (@ (@ tptp.inf_inf_set_nat (@ tptp.lattic3014633134055518761et_nat B4)) _let_1) _let_1)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_assn) (B4 tptp.set_assn)) (let ((_let_1 (@ tptp.lattic47131356835913163n_assn A))) (=> (@ tptp.finite_finite_assn A) (=> (not (= B4 tptp.bot_bot_set_assn)) (=> (@ (@ tptp.ord_less_eq_set_assn B4) A) (= (@ (@ tptp.inf_inf_assn (@ tptp.lattic47131356835913163n_assn B4)) _let_1) _let_1)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.lattic1263872656861969706t_unit A))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= B4 tptp.bot_bo3957492148770167129t_unit)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit B4) A) (= (@ (@ tptp.inf_inf_Product_unit (@ tptp.lattic1263872656861969706t_unit B4)) _let_1) _let_1)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.lattic4107685809792843317_fin_o A))) (=> (@ tptp.finite_finite_o A) (=> (not (= B4 tptp.bot_bot_set_o)) (=> (@ (@ tptp.ord_less_eq_set_o B4) A) (= (@ (@ tptp.inf_inf_o (@ tptp.lattic4107685809792843317_fin_o B4)) _let_1) _let_1)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.lattic5235898064620869839in_int A))) (=> (@ tptp.finite_finite_int A) (=> (not (= B4 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B4) A) (= (@ (@ tptp.inf_inf_int (@ tptp.lattic5235898064620869839in_int B4)) _let_1) _let_1)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.lattic956194824204696298_nat_o A))) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (= B4 tptp.bot_bo7824918357723582233_nat_o)) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o B4) A) (= (@ (@ tptp.inf_in1318976480646536635_nat_o (@ tptp.lattic956194824204696298_nat_o B4)) _let_1) _let_1)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.lattic5238388535129920115in_nat A))) (=> (@ tptp.finite_finite_nat A) (=> (not (= B4 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A) (= (@ (@ tptp.inf_inf_nat (@ tptp.lattic5238388535129920115in_nat B4)) _let_1) _let_1)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat) (B4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.lattic3835124923745554447et_nat A))) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (not (= B4 tptp.bot_bot_set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat B4) A) (= (@ (@ tptp.sup_sup_set_nat (@ tptp.lattic3835124923745554447et_nat B4)) _let_1) _let_1)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_assn) (B4 tptp.set_assn)) (let ((_let_1 (@ tptp.lattic2150320897289308081n_assn A))) (=> (@ tptp.finite_finite_assn A) (=> (not (= B4 tptp.bot_bot_set_assn)) (=> (@ (@ tptp.ord_less_eq_set_assn B4) A) (= (@ (@ tptp.sup_sup_assn (@ tptp.lattic2150320897289308081n_assn B4)) _let_1) _let_1)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.lattic5294303975357428420t_unit A))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= B4 tptp.bot_bo3957492148770167129t_unit)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit B4) A) (= (@ (@ tptp.sup_sup_Product_unit (@ tptp.lattic5294303975357428420t_unit B4)) _let_1) _let_1)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.lattic1508158080041050831_fin_o A))) (=> (@ tptp.finite_finite_o A) (=> (not (= B4 tptp.bot_bot_set_o)) (=> (@ (@ tptp.ord_less_eq_set_o B4) A) (= (@ (@ tptp.sup_sup_o (@ tptp.lattic1508158080041050831_fin_o B4)) _let_1) _let_1)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.lattic1091506334969745077in_int A))) (=> (@ tptp.finite_finite_int A) (=> (not (= B4 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B4) A) (= (@ (@ tptp.sup_sup_int (@ tptp.lattic1091506334969745077in_int B4)) _let_1) _let_1)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.lattic7320199455484906628_nat_o A))) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (= B4 tptp.bot_bo7824918357723582233_nat_o)) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o B4) A) (= (@ (@ tptp.sup_su5453871518329203617_nat_o (@ tptp.lattic7320199455484906628_nat_o B4)) _let_1) _let_1)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.lattic1093996805478795353in_nat A))) (=> (@ tptp.finite_finite_nat A) (=> (not (= B4 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A) (= (@ (@ tptp.sup_sup_nat (@ tptp.lattic1093996805478795353in_nat B4)) _let_1) _let_1)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (not (= A tptp.bot_bot_set_set_nat)) (=> (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat)) (@ (@ tptp.member_set_nat (@ (@ tptp.inf_inf_set_nat X3) Y2)) (@ (@ tptp.insert_set_nat X3) (@ (@ tptp.insert_set_nat Y2) tptp.bot_bot_set_set_nat)))) (@ (@ tptp.member_set_nat (@ tptp.lattic3014633134055518761et_nat A)) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_assn)) (=> (@ tptp.finite_finite_assn A) (=> (not (= A tptp.bot_bot_set_assn)) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (@ (@ tptp.member_assn (@ (@ tptp.inf_inf_assn X3) Y2)) (@ (@ tptp.insert_assn X3) (@ (@ tptp.insert_assn Y2) tptp.bot_bot_set_assn)))) (@ (@ tptp.member_assn (@ tptp.lattic47131356835913163n_assn A)) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((X3 tptp.product_unit) (Y2 tptp.product_unit)) (@ (@ tptp.member_Product_unit (@ (@ tptp.inf_inf_Product_unit X3) Y2)) (@ (@ tptp.insert_Product_unit X3) (@ (@ tptp.insert_Product_unit Y2) tptp.bot_bo3957492148770167129t_unit)))) (@ (@ tptp.member_Product_unit (@ tptp.lattic1263872656861969706t_unit A)) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (=> (forall ((X3 Bool) (Y2 Bool)) (@ (@ tptp.member_o (@ (@ tptp.inf_inf_o X3) Y2)) (@ (@ tptp.insert_o X3) (@ (@ tptp.insert_o Y2) tptp.bot_bot_set_o)))) (@ (@ tptp.member_o (@ tptp.lattic4107685809792843317_fin_o A)) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.member_nat (@ (@ tptp.inf_inf_nat X3) Y2)) (@ (@ tptp.insert_nat X3) (@ (@ tptp.insert_nat Y2) tptp.bot_bot_set_nat)))) (@ (@ tptp.member_nat (@ tptp.lattic5238388535129920115in_nat A)) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (@ (@ tptp.member_int (@ (@ tptp.inf_inf_int X3) Y2)) (@ (@ tptp.insert_int X3) (@ (@ tptp.insert_int Y2) tptp.bot_bot_set_int)))) (@ (@ tptp.member_int (@ tptp.lattic5235898064620869839in_int A)) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o (@ (@ tptp.inf_in1318976480646536635_nat_o X3) Y2)) (@ (@ tptp.insert5175938949040314269_nat_o X3) (@ (@ tptp.insert5175938949040314269_nat_o Y2) tptp.bot_bo7824918357723582233_nat_o)))) (@ (@ tptp.member6576561426505652726_nat_o (@ tptp.lattic956194824204696298_nat_o A)) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat) (X tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (not (@ (@ tptp.member_set_nat X) A)) (=> (not (= A tptp.bot_bot_set_set_nat)) (= (@ tptp.lattic3014633134055518761et_nat (@ (@ tptp.insert_set_nat X) A)) (@ (@ tptp.inf_inf_set_nat X) (@ tptp.lattic3014633134055518761et_nat A))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_assn) (X tptp.assn)) (=> (@ tptp.finite_finite_assn A) (=> (not (@ (@ tptp.member_assn X) A)) (=> (not (= A tptp.bot_bot_set_assn)) (= (@ tptp.lattic47131356835913163n_assn (@ (@ tptp.insert_assn X) A)) (@ (@ tptp.inf_inf_assn X) (@ tptp.lattic47131356835913163n_assn A))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (@ (@ tptp.member_Product_unit X) A)) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (@ tptp.lattic1263872656861969706t_unit (@ (@ tptp.insert_Product_unit X) A)) (@ (@ tptp.inf_inf_Product_unit X) (@ tptp.lattic1263872656861969706t_unit A))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (@ (@ tptp.member_o X) A)) (=> (not (= A tptp.bot_bot_set_o)) (= (@ tptp.lattic4107685809792843317_fin_o (@ (@ tptp.insert_o X) A)) (@ (@ tptp.inf_inf_o X) (@ tptp.lattic4107685809792843317_fin_o A))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (@ (@ tptp.member_nat X) A)) (=> (not (= A tptp.bot_bot_set_nat)) (= (@ tptp.lattic5238388535129920115in_nat (@ (@ tptp.insert_nat X) A)) (@ (@ tptp.inf_inf_nat X) (@ tptp.lattic5238388535129920115in_nat A))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (@ (@ tptp.member_int X) A)) (=> (not (= A tptp.bot_bot_set_int)) (= (@ tptp.lattic5235898064620869839in_int (@ (@ tptp.insert_int X) A)) (@ (@ tptp.inf_inf_int X) (@ tptp.lattic5235898064620869839in_int A))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) A)) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (= (@ tptp.lattic956194824204696298_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) A)) (@ (@ tptp.inf_in1318976480646536635_nat_o X) (@ tptp.lattic956194824204696298_nat_o A))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (not (= A tptp.bot_bot_set_set_nat)) (=> (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat)) (@ (@ tptp.member_set_nat (@ (@ tptp.sup_sup_set_nat X3) Y2)) (@ (@ tptp.insert_set_nat X3) (@ (@ tptp.insert_set_nat Y2) tptp.bot_bot_set_set_nat)))) (@ (@ tptp.member_set_nat (@ tptp.lattic3835124923745554447et_nat A)) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_assn)) (=> (@ tptp.finite_finite_assn A) (=> (not (= A tptp.bot_bot_set_assn)) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (@ (@ tptp.member_assn (@ (@ tptp.sup_sup_assn X3) Y2)) (@ (@ tptp.insert_assn X3) (@ (@ tptp.insert_assn Y2) tptp.bot_bot_set_assn)))) (@ (@ tptp.member_assn (@ tptp.lattic2150320897289308081n_assn A)) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((X3 tptp.product_unit) (Y2 tptp.product_unit)) (@ (@ tptp.member_Product_unit (@ (@ tptp.sup_sup_Product_unit X3) Y2)) (@ (@ tptp.insert_Product_unit X3) (@ (@ tptp.insert_Product_unit Y2) tptp.bot_bo3957492148770167129t_unit)))) (@ (@ tptp.member_Product_unit (@ tptp.lattic5294303975357428420t_unit A)) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (=> (forall ((X3 Bool) (Y2 Bool)) (@ (@ tptp.member_o (@ (@ tptp.sup_sup_o X3) Y2)) (@ (@ tptp.insert_o X3) (@ (@ tptp.insert_o Y2) tptp.bot_bot_set_o)))) (@ (@ tptp.member_o (@ tptp.lattic1508158080041050831_fin_o A)) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.member_nat (@ (@ tptp.sup_sup_nat X3) Y2)) (@ (@ tptp.insert_nat X3) (@ (@ tptp.insert_nat Y2) tptp.bot_bot_set_nat)))) (@ (@ tptp.member_nat (@ tptp.lattic1093996805478795353in_nat A)) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (@ (@ tptp.member_int (@ (@ tptp.sup_sup_int X3) Y2)) (@ (@ tptp.insert_int X3) (@ (@ tptp.insert_int Y2) tptp.bot_bot_set_int)))) (@ (@ tptp.member_int (@ tptp.lattic1091506334969745077in_int A)) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o (@ (@ tptp.sup_su5453871518329203617_nat_o X3) Y2)) (@ (@ tptp.insert5175938949040314269_nat_o X3) (@ (@ tptp.insert5175938949040314269_nat_o Y2) tptp.bot_bo7824918357723582233_nat_o)))) (@ (@ tptp.member6576561426505652726_nat_o (@ tptp.lattic7320199455484906628_nat_o A)) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat) (X tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (not (@ (@ tptp.member_set_nat X) A)) (=> (not (= A tptp.bot_bot_set_set_nat)) (= (@ tptp.lattic3835124923745554447et_nat (@ (@ tptp.insert_set_nat X) A)) (@ (@ tptp.sup_sup_set_nat X) (@ tptp.lattic3835124923745554447et_nat A))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_assn) (X tptp.assn)) (=> (@ tptp.finite_finite_assn A) (=> (not (@ (@ tptp.member_assn X) A)) (=> (not (= A tptp.bot_bot_set_assn)) (= (@ tptp.lattic2150320897289308081n_assn (@ (@ tptp.insert_assn X) A)) (@ (@ tptp.sup_sup_assn X) (@ tptp.lattic2150320897289308081n_assn A))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (@ (@ tptp.member_Product_unit X) A)) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (@ tptp.lattic5294303975357428420t_unit (@ (@ tptp.insert_Product_unit X) A)) (@ (@ tptp.sup_sup_Product_unit X) (@ tptp.lattic5294303975357428420t_unit A))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (@ (@ tptp.member_o X) A)) (=> (not (= A tptp.bot_bot_set_o)) (= (@ tptp.lattic1508158080041050831_fin_o (@ (@ tptp.insert_o X) A)) (@ (@ tptp.sup_sup_o X) (@ tptp.lattic1508158080041050831_fin_o A))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (@ (@ tptp.member_nat X) A)) (=> (not (= A tptp.bot_bot_set_nat)) (= (@ tptp.lattic1093996805478795353in_nat (@ (@ tptp.insert_nat X) A)) (@ (@ tptp.sup_sup_nat X) (@ tptp.lattic1093996805478795353in_nat A))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (@ (@ tptp.member_int X) A)) (=> (not (= A tptp.bot_bot_set_int)) (= (@ tptp.lattic1091506334969745077in_int (@ (@ tptp.insert_int X) A)) (@ (@ tptp.sup_sup_int X) (@ tptp.lattic1091506334969745077in_int A))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) A)) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (= (@ tptp.lattic7320199455484906628_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) A)) (@ (@ tptp.sup_su5453871518329203617_nat_o X) (@ tptp.lattic7320199455484906628_nat_o A))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat) (B4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (not (= A tptp.bot_bot_set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B4) (=> (not (= B4 tptp.bot_bot_set_set_nat)) (= (@ tptp.lattic3014633134055518761et_nat (@ (@ tptp.sup_sup_set_set_nat A) B4)) (@ (@ tptp.inf_inf_set_nat (@ tptp.lattic3014633134055518761et_nat A)) (@ tptp.lattic3014633134055518761et_nat B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_assn) (B4 tptp.set_assn)) (=> (@ tptp.finite_finite_assn A) (=> (not (= A tptp.bot_bot_set_assn)) (=> (@ tptp.finite_finite_assn B4) (=> (not (= B4 tptp.bot_bot_set_assn)) (= (@ tptp.lattic47131356835913163n_assn (@ (@ tptp.sup_sup_set_assn A) B4)) (@ (@ tptp.inf_inf_assn (@ tptp.lattic47131356835913163n_assn A)) (@ tptp.lattic47131356835913163n_assn B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.finite4290736615968046902t_unit B4) (=> (not (= B4 tptp.bot_bo3957492148770167129t_unit)) (= (@ tptp.lattic1263872656861969706t_unit (@ (@ tptp.sup_su793286257634532545t_unit A) B4)) (@ (@ tptp.inf_inf_Product_unit (@ tptp.lattic1263872656861969706t_unit A)) (@ tptp.lattic1263872656861969706t_unit B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.finite_finite_o B4) (=> (not (= B4 tptp.bot_bot_set_o)) (= (@ tptp.lattic4107685809792843317_fin_o (@ (@ tptp.sup_sup_set_o A) B4)) (@ (@ tptp.inf_inf_o (@ tptp.lattic4107685809792843317_fin_o A)) (@ tptp.lattic4107685809792843317_fin_o B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.finite_finite_nat B4) (=> (not (= B4 tptp.bot_bot_set_nat)) (= (@ tptp.lattic5238388535129920115in_nat (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.inf_inf_nat (@ tptp.lattic5238388535129920115in_nat A)) (@ tptp.lattic5238388535129920115in_nat B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.finite_finite_int B4) (=> (not (= B4 tptp.bot_bot_set_int)) (= (@ tptp.lattic5235898064620869839in_int (@ (@ tptp.sup_sup_set_int A) B4)) (@ (@ tptp.inf_inf_int (@ tptp.lattic5235898064620869839in_int A)) (@ tptp.lattic5235898064620869839in_int B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o B4) (=> (not (= B4 tptp.bot_bo7824918357723582233_nat_o)) (= (@ tptp.lattic956194824204696298_nat_o (@ (@ tptp.sup_su5209123915105501825_nat_o A) B4)) (@ (@ tptp.inf_in1318976480646536635_nat_o (@ tptp.lattic956194824204696298_nat_o A)) (@ tptp.lattic956194824204696298_nat_o B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat) (B4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (not (= A tptp.bot_bot_set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B4) (=> (not (= B4 tptp.bot_bot_set_set_nat)) (= (@ tptp.lattic3835124923745554447et_nat (@ (@ tptp.sup_sup_set_set_nat A) B4)) (@ (@ tptp.sup_sup_set_nat (@ tptp.lattic3835124923745554447et_nat A)) (@ tptp.lattic3835124923745554447et_nat B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_assn) (B4 tptp.set_assn)) (=> (@ tptp.finite_finite_assn A) (=> (not (= A tptp.bot_bot_set_assn)) (=> (@ tptp.finite_finite_assn B4) (=> (not (= B4 tptp.bot_bot_set_assn)) (= (@ tptp.lattic2150320897289308081n_assn (@ (@ tptp.sup_sup_set_assn A) B4)) (@ (@ tptp.sup_sup_assn (@ tptp.lattic2150320897289308081n_assn A)) (@ tptp.lattic2150320897289308081n_assn B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.finite4290736615968046902t_unit B4) (=> (not (= B4 tptp.bot_bo3957492148770167129t_unit)) (= (@ tptp.lattic5294303975357428420t_unit (@ (@ tptp.sup_su793286257634532545t_unit A) B4)) (@ (@ tptp.sup_sup_Product_unit (@ tptp.lattic5294303975357428420t_unit A)) (@ tptp.lattic5294303975357428420t_unit B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.finite_finite_o B4) (=> (not (= B4 tptp.bot_bot_set_o)) (= (@ tptp.lattic1508158080041050831_fin_o (@ (@ tptp.sup_sup_set_o A) B4)) (@ (@ tptp.sup_sup_o (@ tptp.lattic1508158080041050831_fin_o A)) (@ tptp.lattic1508158080041050831_fin_o B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.finite_finite_nat B4) (=> (not (= B4 tptp.bot_bot_set_nat)) (= (@ tptp.lattic1093996805478795353in_nat (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.sup_sup_nat (@ tptp.lattic1093996805478795353in_nat A)) (@ tptp.lattic1093996805478795353in_nat B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.finite_finite_int B4) (=> (not (= B4 tptp.bot_bot_set_int)) (= (@ tptp.lattic1091506334969745077in_int (@ (@ tptp.sup_sup_set_int A) B4)) (@ (@ tptp.sup_sup_int (@ tptp.lattic1091506334969745077in_int A)) (@ tptp.lattic1091506334969745077in_int B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o B4) (=> (not (= B4 tptp.bot_bo7824918357723582233_nat_o)) (= (@ tptp.lattic7320199455484906628_nat_o (@ (@ tptp.sup_su5209123915105501825_nat_o A) B4)) (@ (@ tptp.sup_su5453871518329203617_nat_o (@ tptp.lattic7320199455484906628_nat_o A)) (@ tptp.lattic7320199455484906628_nat_o B4)))))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_nat) (A tptp.set_Pr1261947904930325089at_nat) (C5 tptp.set_nat)) (=> (@ (@ tptp.refl_on_nat B4) A) (=> (@ (@ tptp.ord_less_eq_set_nat C5) B4) (= (@ (@ tptp.image_nat_nat (@ (@ tptp.sup_su6327502436637775413at_nat A) tptp.id_nat)) C5) (@ (@ tptp.image_nat_nat A) C5))))))
% 5.61/5.92 (assert (forall ((U (-> tptp.produc3658429121746597890et_nat Bool)) (V (-> tptp.produc3658429121746597890et_nat Bool)) (E tptp.set_Pr2161125870931222855_nat_o) (R3 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o U) V)))) (=> (@ _let_1 (@ tptp.transi712980445759334096_nat_o E)) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o (@ (@ tptp.image_2232984160439939859_nat_o E) R3)) R3) (=> (not (@ (@ tptp.member6576561426505652726_nat_o V) R3)) (not (=> (not (@ (@ tptp.member6576561426505652726_nat_o U) R3)) (not (@ _let_1 (@ tptp.transi712980445759334096_nat_o (@ (@ tptp.rel_re3331361160397388719_nat_o E) R3))))))))))))
% 5.61/5.92 (assert (forall ((U Bool) (V Bool) (E tptp.set_Product_prod_o_o) (R3 tptp.set_o)) (let ((_let_1 (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o U) V)))) (=> (@ _let_1 (@ tptp.transitive_rtrancl_o E)) (=> (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.image_o_o E) R3)) R3) (=> (not (@ (@ tptp.member_o V) R3)) (not (=> (not (@ (@ tptp.member_o U) R3)) (not (@ _let_1 (@ tptp.transitive_rtrancl_o (@ (@ tptp.rel_restrict_o E) R3))))))))))))
% 5.61/5.92 (assert (forall ((U tptp.product_unit) (V tptp.product_unit) (E tptp.set_Pr5094982260447487303t_unit) (R3 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit U) V)))) (=> (@ _let_1 (@ tptp.transi6481887417741755664t_unit E)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit (@ (@ tptp.image_8431784415008483091t_unit E) R3)) R3) (=> (not (@ (@ tptp.member_Product_unit V) R3)) (not (=> (not (@ (@ tptp.member_Product_unit U) R3)) (not (@ _let_1 (@ tptp.transi6481887417741755664t_unit (@ (@ tptp.rel_re9207996470947987439t_unit E) R3))))))))))))
% 5.61/5.92 (assert (forall ((U tptp.int) (V tptp.int) (E tptp.set_Pr958786334691620121nt_int) (R3 tptp.set_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int U) V)))) (=> (@ _let_1 (@ tptp.transi2902850859426252137cl_int E)) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int E) R3)) R3) (=> (not (@ (@ tptp.member_int V) R3)) (not (=> (not (@ (@ tptp.member_int U) R3)) (not (@ _let_1 (@ tptp.transi2902850859426252137cl_int (@ (@ tptp.rel_restrict_int E) R3))))))))))))
% 5.61/5.92 (assert (forall ((U tptp.nat) (V tptp.nat) (E tptp.set_Pr1261947904930325089at_nat) (R3 tptp.set_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat U) V)))) (=> (@ _let_1 (@ tptp.transi2905341329935302413cl_nat E)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat E) R3)) R3) (=> (not (@ (@ tptp.member_nat V) R3)) (not (=> (not (@ (@ tptp.member_nat U) R3)) (not (@ _let_1 (@ tptp.transi2905341329935302413cl_nat (@ (@ tptp.rel_restrict_nat E) R3))))))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr5094982260447487303t_unit) (S tptp.set_Pr5094982260447487303t_unit)) (let ((_let_1 (@ tptp.max_ext_Product_unit R3))) (=> (@ (@ tptp.ord_le930853871177014503t_unit (@ (@ tptp.relcom848357998638694028t_unit R3) S)) R3) (@ (@ tptp.ord_le8072594200992201959t_unit (@ (@ tptp.relcom7108816970757792620t_unit _let_1) (@ (@ tptp.sup_su3573767163274163995t_unit (@ tptp.max_ext_Product_unit S)) (@ (@ tptp.insert6793119152790066487t_unit (@ (@ tptp.produc7269801343787132631t_unit tptp.bot_bo3957492148770167129t_unit) tptp.bot_bo3957492148770167129t_unit)) tptp.bot_bo5113747506523071411t_unit)))) _let_1)))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Product_prod_o_o) (S tptp.set_Product_prod_o_o)) (let ((_let_1 (@ tptp.max_ext_o R3))) (=> (@ (@ tptp.ord_le192195778054999463od_o_o (@ (@ tptp.relcomp_o_o_o R3) S)) R3) (@ (@ tptp.ord_le2885120122233735591_set_o (@ (@ tptp.relcom7534720040753365047_set_o _let_1) (@ (@ tptp.sup_su7766833992073560027_set_o (@ tptp.max_ext_o S)) (@ (@ tptp.insert1494450971503307511_set_o (@ (@ tptp.produc5838405689764958487_set_o tptp.bot_bot_set_o) tptp.bot_bot_set_o)) tptp.bot_bo8143257439550059635_set_o)))) _let_1)))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.max_ext_nat R3))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.relcomp_nat_nat_nat R3) S)) R3) (@ (@ tptp.ord_le4402255868550298733et_nat (@ (@ tptp.relcom236561585145426837et_nat _let_1) (@ (@ tptp.sup_su4251893418135750817et_nat (@ tptp.max_ext_nat S)) (@ (@ tptp.insert3810226134351308605et_nat (@ (@ tptp.produc4532415448927165861et_nat tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)) tptp.bot_bo4952753636535259449et_nat)))) _let_1)))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int) (S tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.max_ext_int R3))) (=> (@ (@ tptp.ord_le2843351958646193337nt_int (@ (@ tptp.relcomp_int_int_int R3) S)) R3) (@ (@ tptp.ord_le1436784781161120549et_int (@ (@ tptp.relcom4034950705519254697et_int _let_1) (@ (@ tptp.sup_su1286422330746572633et_int (@ tptp.max_ext_int S)) (@ (@ tptp.insert7328952640415156725et_int (@ (@ tptp.produc6363374080413544029et_int tptp.bot_bot_set_int) tptp.bot_bot_set_int)) tptp.bot_bo1987282549146081265et_int)))) _let_1)))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr2161125870931222855_nat_o) (S tptp.set_Pr2161125870931222855_nat_o)) (let ((_let_1 (@ tptp.max_ex5265246208886859912_nat_o R3))) (=> (@ (@ tptp.ord_le6659818918159358183_nat_o (@ (@ tptp.relcom6251035627269349452_nat_o R3) S)) R3) (@ (@ tptp.ord_le8001614231985977575_nat_o (@ (@ tptp.relcom7236094467932586796_nat_o _let_1) (@ (@ tptp.sup_su4863159966000489243_nat_o (@ tptp.max_ex5265246208886859912_nat_o S)) (@ (@ tptp.insert3244108804717745463_nat_o (@ (@ tptp.produc5149316574908490455_nat_o tptp.bot_bo7824918357723582233_nat_o) tptp.bot_bo7824918357723582233_nat_o)) tptp.bot_bo7535334947429593011_nat_o)))) _let_1)))))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) tptp.id_nat) (= A2 B))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) tptp.id_int) (= A2 B))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat) (X tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_2163939370556025621et_nat A) (@ (@ tptp.insert_set_nat X) tptp.bot_bot_set_set_nat)))) (let ((_let_2 (@ tptp.lattic3835124923745554447et_nat A))) (let ((_let_3 (= _let_1 tptp.bot_bot_set_set_nat))) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (@ (@ tptp.member_set_nat X) A) (and (=> _let_3 (= _let_2 X)) (=> (not _let_3) (= _let_2 (@ (@ tptp.sup_sup_set_nat X) (@ tptp.lattic3835124923745554447et_nat _let_1))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_assn) (X tptp.assn)) (let ((_let_1 (@ (@ tptp.minus_minus_set_assn A) (@ (@ tptp.insert_assn X) tptp.bot_bot_set_assn)))) (let ((_let_2 (@ tptp.lattic2150320897289308081n_assn A))) (let ((_let_3 (= _let_1 tptp.bot_bot_set_assn))) (=> (@ tptp.finite_finite_assn A) (=> (@ (@ tptp.member_assn X) A) (and (=> _let_3 (= _let_2 X)) (=> (not _let_3) (= _let_2 (@ (@ tptp.sup_sup_assn X) (@ tptp.lattic2150320897289308081n_assn _let_1))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (let ((_let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)))) (let ((_let_2 (@ tptp.lattic5294303975357428420t_unit A))) (let ((_let_3 (= _let_1 tptp.bot_bo3957492148770167129t_unit))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ (@ tptp.member_Product_unit X) A) (and (=> _let_3 (= _let_2 X)) (=> (not _let_3) (= _let_2 (@ (@ tptp.sup_sup_Product_unit X) (@ tptp.lattic5294303975357428420t_unit _let_1))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (X Bool)) (let ((_let_1 (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)))) (let ((_let_2 (= _let_1 tptp.bot_bot_set_o))) (=> (@ tptp.finite_finite_o A) (=> (@ (@ tptp.member_o X) A) (= (@ tptp.lattic1508158080041050831_fin_o A) (and (=> _let_2 X) (=> (not _let_2) (@ (@ tptp.sup_sup_o X) (@ tptp.lattic1508158080041050831_fin_o _let_1)))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))) (let ((_let_2 (@ tptp.lattic1091506334969745077in_int A))) (let ((_let_3 (= _let_1 tptp.bot_bot_set_int))) (=> (@ tptp.finite_finite_int A) (=> (@ (@ tptp.member_int X) A) (and (=> _let_3 (= _let_2 X)) (=> (not _let_3) (= _let_2 (@ (@ tptp.sup_sup_int X) (@ tptp.lattic1091506334969745077in_int _let_1))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)))) (let ((_let_2 (@ tptp.lattic7320199455484906628_nat_o A))) (let ((_let_3 (= _let_1 tptp.bot_bo7824918357723582233_nat_o))) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (@ (@ tptp.member6576561426505652726_nat_o X) A) (and (=> _let_3 (= _let_2 X)) (=> (not _let_3) (= _let_2 (@ (@ tptp.sup_su5453871518329203617_nat_o X) (@ tptp.lattic7320199455484906628_nat_o _let_1))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))) (let ((_let_2 (@ tptp.lattic1093996805478795353in_nat A))) (let ((_let_3 (= _let_1 tptp.bot_bot_set_nat))) (=> (@ tptp.finite_finite_nat A) (=> (@ (@ tptp.member_nat X) A) (and (=> _let_3 (= _let_2 X)) (=> (not _let_3) (= _let_2 (@ (@ tptp.sup_sup_nat X) (@ tptp.lattic1093996805478795353in_nat _let_1))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat) (X tptp.set_nat)) (let ((_let_1 (@ tptp.insert_set_nat X))) (let ((_let_2 (@ (@ tptp.minus_2163939370556025621et_nat A) (@ _let_1 tptp.bot_bot_set_set_nat)))) (let ((_let_3 (@ tptp.lattic3835124923745554447et_nat (@ _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bot_set_set_nat))) (=> (@ tptp.finite1152437895449049373et_nat A) (and (=> _let_4 (= _let_3 X)) (=> (not _let_4) (= _let_3 (@ (@ tptp.sup_sup_set_nat X) (@ tptp.lattic3835124923745554447et_nat _let_2))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_assn) (X tptp.assn)) (let ((_let_1 (@ tptp.insert_assn X))) (let ((_let_2 (@ (@ tptp.minus_minus_set_assn A) (@ _let_1 tptp.bot_bot_set_assn)))) (let ((_let_3 (@ tptp.lattic2150320897289308081n_assn (@ _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bot_set_assn))) (=> (@ tptp.finite_finite_assn A) (and (=> _let_4 (= _let_3 X)) (=> (not _let_4) (= _let_3 (@ (@ tptp.sup_sup_assn X) (@ tptp.lattic2150320897289308081n_assn _let_2))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit X))) (let ((_let_2 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ _let_1 tptp.bot_bo3957492148770167129t_unit)))) (let ((_let_3 (@ tptp.lattic5294303975357428420t_unit (@ _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bo3957492148770167129t_unit))) (=> (@ tptp.finite4290736615968046902t_unit A) (and (=> _let_4 (= _let_3 X)) (=> (not _let_4) (= _let_3 (@ (@ tptp.sup_sup_Product_unit X) (@ tptp.lattic5294303975357428420t_unit _let_2))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (X Bool)) (let ((_let_1 (@ tptp.insert_o X))) (let ((_let_2 (@ (@ tptp.minus_minus_set_o A) (@ _let_1 tptp.bot_bot_set_o)))) (let ((_let_3 (= _let_2 tptp.bot_bot_set_o))) (=> (@ tptp.finite_finite_o A) (= (@ tptp.lattic1508158080041050831_fin_o (@ _let_1 A)) (and (=> _let_3 X) (=> (not _let_3) (@ (@ tptp.sup_sup_o X) (@ tptp.lattic1508158080041050831_fin_o _let_2)))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ (@ tptp.minus_minus_set_int A) (@ _let_1 tptp.bot_bot_set_int)))) (let ((_let_3 (@ tptp.lattic1091506334969745077in_int (@ _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bot_set_int))) (=> (@ tptp.finite_finite_int A) (and (=> _let_4 (= _let_3 X)) (=> (not _let_4) (= _let_3 (@ (@ tptp.sup_sup_int X) (@ tptp.lattic1091506334969745077in_int _let_2))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.insert5175938949040314269_nat_o X))) (let ((_let_2 (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ _let_1 tptp.bot_bo7824918357723582233_nat_o)))) (let ((_let_3 (@ tptp.lattic7320199455484906628_nat_o (@ _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bo7824918357723582233_nat_o))) (=> (@ tptp.finite3252695134891459830_nat_o A) (and (=> _let_4 (= _let_3 X)) (=> (not _let_4) (= _let_3 (@ (@ tptp.sup_su5453871518329203617_nat_o X) (@ tptp.lattic7320199455484906628_nat_o _let_2))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ (@ tptp.minus_minus_set_nat A) (@ _let_1 tptp.bot_bot_set_nat)))) (let ((_let_3 (@ tptp.lattic1093996805478795353in_nat (@ _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bot_set_nat))) (=> (@ tptp.finite_finite_nat A) (and (=> _let_4 (= _let_3 X)) (=> (not _let_4) (= _let_3 (@ (@ tptp.sup_sup_nat X) (@ tptp.lattic1093996805478795353in_nat _let_2))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat) (X tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_2163939370556025621et_nat A) (@ (@ tptp.insert_set_nat X) tptp.bot_bot_set_set_nat)))) (let ((_let_2 (@ tptp.lattic3014633134055518761et_nat A))) (let ((_let_3 (= _let_1 tptp.bot_bot_set_set_nat))) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (@ (@ tptp.member_set_nat X) A) (and (=> _let_3 (= _let_2 X)) (=> (not _let_3) (= _let_2 (@ (@ tptp.inf_inf_set_nat X) (@ tptp.lattic3014633134055518761et_nat _let_1))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_assn) (X tptp.assn)) (let ((_let_1 (@ (@ tptp.minus_minus_set_assn A) (@ (@ tptp.insert_assn X) tptp.bot_bot_set_assn)))) (let ((_let_2 (@ tptp.lattic47131356835913163n_assn A))) (let ((_let_3 (= _let_1 tptp.bot_bot_set_assn))) (=> (@ tptp.finite_finite_assn A) (=> (@ (@ tptp.member_assn X) A) (and (=> _let_3 (= _let_2 X)) (=> (not _let_3) (= _let_2 (@ (@ tptp.inf_inf_assn X) (@ tptp.lattic47131356835913163n_assn _let_1))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (let ((_let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)))) (let ((_let_2 (@ tptp.lattic1263872656861969706t_unit A))) (let ((_let_3 (= _let_1 tptp.bot_bo3957492148770167129t_unit))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ (@ tptp.member_Product_unit X) A) (and (=> _let_3 (= _let_2 X)) (=> (not _let_3) (= _let_2 (@ (@ tptp.inf_inf_Product_unit X) (@ tptp.lattic1263872656861969706t_unit _let_1))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (X Bool)) (let ((_let_1 (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)))) (let ((_let_2 (= _let_1 tptp.bot_bot_set_o))) (=> (@ tptp.finite_finite_o A) (=> (@ (@ tptp.member_o X) A) (= (@ tptp.lattic4107685809792843317_fin_o A) (and (=> _let_2 X) (=> (not _let_2) (@ (@ tptp.inf_inf_o X) (@ tptp.lattic4107685809792843317_fin_o _let_1)))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))) (let ((_let_2 (@ tptp.lattic5235898064620869839in_int A))) (let ((_let_3 (= _let_1 tptp.bot_bot_set_int))) (=> (@ tptp.finite_finite_int A) (=> (@ (@ tptp.member_int X) A) (and (=> _let_3 (= _let_2 X)) (=> (not _let_3) (= _let_2 (@ (@ tptp.inf_inf_int X) (@ tptp.lattic5235898064620869839in_int _let_1))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)))) (let ((_let_2 (@ tptp.lattic956194824204696298_nat_o A))) (let ((_let_3 (= _let_1 tptp.bot_bo7824918357723582233_nat_o))) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (@ (@ tptp.member6576561426505652726_nat_o X) A) (and (=> _let_3 (= _let_2 X)) (=> (not _let_3) (= _let_2 (@ (@ tptp.inf_in1318976480646536635_nat_o X) (@ tptp.lattic956194824204696298_nat_o _let_1))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))) (let ((_let_2 (@ tptp.lattic5238388535129920115in_nat A))) (let ((_let_3 (= _let_1 tptp.bot_bot_set_nat))) (=> (@ tptp.finite_finite_nat A) (=> (@ (@ tptp.member_nat X) A) (and (=> _let_3 (= _let_2 X)) (=> (not _let_3) (= _let_2 (@ (@ tptp.inf_inf_nat X) (@ tptp.lattic5238388535129920115in_nat _let_1))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat) (X tptp.set_nat)) (let ((_let_1 (@ tptp.insert_set_nat X))) (let ((_let_2 (@ (@ tptp.minus_2163939370556025621et_nat A) (@ _let_1 tptp.bot_bot_set_set_nat)))) (let ((_let_3 (@ tptp.lattic3014633134055518761et_nat (@ _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bot_set_set_nat))) (=> (@ tptp.finite1152437895449049373et_nat A) (and (=> _let_4 (= _let_3 X)) (=> (not _let_4) (= _let_3 (@ (@ tptp.inf_inf_set_nat X) (@ tptp.lattic3014633134055518761et_nat _let_2))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_assn) (X tptp.assn)) (let ((_let_1 (@ tptp.insert_assn X))) (let ((_let_2 (@ (@ tptp.minus_minus_set_assn A) (@ _let_1 tptp.bot_bot_set_assn)))) (let ((_let_3 (@ tptp.lattic47131356835913163n_assn (@ _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bot_set_assn))) (=> (@ tptp.finite_finite_assn A) (and (=> _let_4 (= _let_3 X)) (=> (not _let_4) (= _let_3 (@ (@ tptp.inf_inf_assn X) (@ tptp.lattic47131356835913163n_assn _let_2))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit X))) (let ((_let_2 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ _let_1 tptp.bot_bo3957492148770167129t_unit)))) (let ((_let_3 (@ tptp.lattic1263872656861969706t_unit (@ _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bo3957492148770167129t_unit))) (=> (@ tptp.finite4290736615968046902t_unit A) (and (=> _let_4 (= _let_3 X)) (=> (not _let_4) (= _let_3 (@ (@ tptp.inf_inf_Product_unit X) (@ tptp.lattic1263872656861969706t_unit _let_2))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (X Bool)) (let ((_let_1 (@ tptp.insert_o X))) (let ((_let_2 (@ (@ tptp.minus_minus_set_o A) (@ _let_1 tptp.bot_bot_set_o)))) (let ((_let_3 (= _let_2 tptp.bot_bot_set_o))) (=> (@ tptp.finite_finite_o A) (= (@ tptp.lattic4107685809792843317_fin_o (@ _let_1 A)) (and (=> _let_3 X) (=> (not _let_3) (@ (@ tptp.inf_inf_o X) (@ tptp.lattic4107685809792843317_fin_o _let_2)))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ (@ tptp.minus_minus_set_int A) (@ _let_1 tptp.bot_bot_set_int)))) (let ((_let_3 (@ tptp.lattic5235898064620869839in_int (@ _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bot_set_int))) (=> (@ tptp.finite_finite_int A) (and (=> _let_4 (= _let_3 X)) (=> (not _let_4) (= _let_3 (@ (@ tptp.inf_inf_int X) (@ tptp.lattic5235898064620869839in_int _let_2))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.insert5175938949040314269_nat_o X))) (let ((_let_2 (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ _let_1 tptp.bot_bo7824918357723582233_nat_o)))) (let ((_let_3 (@ tptp.lattic956194824204696298_nat_o (@ _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bo7824918357723582233_nat_o))) (=> (@ tptp.finite3252695134891459830_nat_o A) (and (=> _let_4 (= _let_3 X)) (=> (not _let_4) (= _let_3 (@ (@ tptp.inf_in1318976480646536635_nat_o X) (@ tptp.lattic956194824204696298_nat_o _let_2))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ (@ tptp.minus_minus_set_nat A) (@ _let_1 tptp.bot_bot_set_nat)))) (let ((_let_3 (@ tptp.lattic5238388535129920115in_nat (@ _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bot_set_nat))) (=> (@ tptp.finite_finite_nat A) (and (=> _let_4 (= _let_3 X)) (=> (not _let_4) (= _let_3 (@ (@ tptp.inf_inf_nat X) (@ tptp.lattic5238388535129920115in_nat _let_2))))))))))))
% 5.61/5.92 (assert (forall ((Y tptp.nat) (X tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.transi3139058337892597825ic_nat (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.product_Pair_nat_nat Y) X)) R2)) (and (@ tptp.transi3139058337892597825ic_nat R2) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.transi2905341329935302413cl_nat R2)))))))
% 5.61/5.92 (assert (forall ((Y tptp.int) (X tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ tptp.transi3136567867383547549ic_int (@ (@ tptp.insert5033312907999012233nt_int (@ (@ tptp.product_Pair_int_int Y) X)) R2)) (and (@ tptp.transi3136567867383547549ic_int R2) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ tptp.transi2902850859426252137cl_int R2)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (X tptp.nat)) (=> (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.converse_nat_nat R2)) (@ tptp.transi2905341329935302413cl_nat R2)) tptp.bot_bo2099793752762293965at_nat) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) X)) (@ tptp.transi6264000038957366511cl_nat R2))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (X tptp.int)) (=> (= (@ (@ tptp.inf_in2269163501485487111nt_int (@ tptp.converse_int_int R2)) (@ tptp.transi2902850859426252137cl_int R2)) tptp.bot_bo1796632182523588997nt_int) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) X)) (@ tptp.transi6261509568448316235cl_int R2))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger (@ (@ tptp.image_4470545334726330049nteger F) A)) (=> (not (@ tptp.finite6017078050557962740nteger A)) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.image_4470545334726330049nteger F) A)) (not (@ tptp.finite6017078050557962740nteger (@ (@ tptp.inf_in1364745209274528805nteger (@ (@ tptp.vimage1318793397690208119nteger F) (@ (@ tptp.insert_Code_integer X3) tptp.bot_bo3990330152332043303nteger))) A)))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.set_nat)) (=> (@ tptp.finite6017078050557962740nteger (@ (@ tptp.image_1215581382706833972nteger F) A)) (=> (not (@ tptp.finite_finite_nat A)) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.image_1215581382706833972nteger F) A)) (not (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.vimage6104394758324456170nteger F) (@ (@ tptp.insert_Code_integer X3) tptp.bot_bo3990330152332043303nteger))) A)))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.product_unit)) (A tptp.set_Code_integer)) (=> (@ tptp.finite4290736615968046902t_unit (@ (@ tptp.image_7182656606676592809t_unit F) A)) (=> (not (@ tptp.finite6017078050557962740nteger A)) (exists ((X3 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X3) (@ (@ tptp.image_7182656606676592809t_unit F) A)) (not (@ tptp.finite6017078050557962740nteger (@ (@ tptp.inf_in1364745209274528805nteger (@ (@ tptp.vimage5651688891684837235t_unit F) (@ (@ tptp.insert_Product_unit X3) tptp.bot_bo3957492148770167129t_unit))) A)))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.product_unit)) (A tptp.set_nat)) (=> (@ tptp.finite4290736615968046902t_unit (@ (@ tptp.image_8730104196221521654t_unit F) A)) (=> (not (@ tptp.finite_finite_nat A)) (exists ((X3 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X3) (@ (@ tptp.image_8730104196221521654t_unit F) A)) (not (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.vimage4884490618288580032t_unit F) (@ (@ tptp.insert_Product_unit X3) tptp.bot_bo3957492148770167129t_unit))) A)))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer Bool)) (A tptp.set_Code_integer)) (=> (@ tptp.finite_finite_o (@ (@ tptp.image_Code_integer_o F) A)) (=> (not (@ tptp.finite6017078050557962740nteger A)) (exists ((X3 Bool)) (and (@ (@ tptp.member_o X3) (@ (@ tptp.image_Code_integer_o F) A)) (not (@ tptp.finite6017078050557962740nteger (@ (@ tptp.inf_in1364745209274528805nteger (@ (@ tptp.vimage3005800680117336574eger_o F) (@ (@ tptp.insert_o X3) tptp.bot_bot_set_o))) A)))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat Bool)) (A tptp.set_nat)) (=> (@ tptp.finite_finite_o (@ (@ tptp.image_nat_o2 F) A)) (=> (not (@ tptp.finite_finite_nat A)) (exists ((X3 Bool)) (and (@ (@ tptp.member_o X3) (@ (@ tptp.image_nat_o2 F) A)) (not (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.vimage_nat_o F) (@ (@ tptp.insert_o X3) tptp.bot_bot_set_o))) A)))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.nat)) (A tptp.set_Code_integer)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_951025933927791156er_nat F) A)) (=> (not (@ tptp.finite6017078050557962740nteger A)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) (@ (@ tptp.image_951025933927791156er_nat F) A)) (not (@ tptp.finite6017078050557962740nteger (@ (@ tptp.inf_in1364745209274528805nteger (@ (@ tptp.vimage5839839309545413354er_nat F) (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat))) A)))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_nat2 F) A)) (=> (not (@ tptp.finite_finite_nat A)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) (@ (@ tptp.image_nat_nat2 F) A)) (not (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.vimage_nat_nat F) (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat))) A)))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.int)) (A tptp.set_Code_integer)) (=> (@ tptp.finite_finite_int (@ (@ tptp.image_948535463418740880er_int F) A)) (=> (not (@ tptp.finite6017078050557962740nteger A)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.image_948535463418740880er_int F) A)) (not (@ tptp.finite6017078050557962740nteger (@ (@ tptp.inf_in1364745209274528805nteger (@ (@ tptp.vimage5837348839036363078er_int F) (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int))) A)))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.set_nat)) (=> (@ tptp.finite_finite_int (@ (@ tptp.image_nat_int2 F) A)) (=> (not (@ tptp.finite_finite_nat A)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.image_nat_int2 F) A)) (not (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.vimage_nat_int F) (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int))) A)))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger (@ (@ tptp.image_4470545334726330049nteger F) A)) (=> (not (@ tptp.finite6017078050557962740nteger A)) (not (forall ((Y2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Y2) (@ (@ tptp.image_4470545334726330049nteger F) A)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.inf_in1364745209274528805nteger (@ (@ tptp.vimage1318793397690208119nteger F) (@ (@ tptp.insert_Code_integer Y2) tptp.bot_bo3990330152332043303nteger))) A)))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.set_nat)) (=> (@ tptp.finite6017078050557962740nteger (@ (@ tptp.image_1215581382706833972nteger F) A)) (=> (not (@ tptp.finite_finite_nat A)) (not (forall ((Y2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Y2) (@ (@ tptp.image_1215581382706833972nteger F) A)) (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.vimage6104394758324456170nteger F) (@ (@ tptp.insert_Code_integer Y2) tptp.bot_bo3990330152332043303nteger))) A)))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.product_unit)) (A tptp.set_Code_integer)) (=> (@ tptp.finite4290736615968046902t_unit (@ (@ tptp.image_7182656606676592809t_unit F) A)) (=> (not (@ tptp.finite6017078050557962740nteger A)) (not (forall ((Y2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit Y2) (@ (@ tptp.image_7182656606676592809t_unit F) A)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.inf_in1364745209274528805nteger (@ (@ tptp.vimage5651688891684837235t_unit F) (@ (@ tptp.insert_Product_unit Y2) tptp.bot_bo3957492148770167129t_unit))) A)))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.product_unit)) (A tptp.set_nat)) (=> (@ tptp.finite4290736615968046902t_unit (@ (@ tptp.image_8730104196221521654t_unit F) A)) (=> (not (@ tptp.finite_finite_nat A)) (not (forall ((Y2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit Y2) (@ (@ tptp.image_8730104196221521654t_unit F) A)) (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.vimage4884490618288580032t_unit F) (@ (@ tptp.insert_Product_unit Y2) tptp.bot_bo3957492148770167129t_unit))) A)))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer Bool)) (A tptp.set_Code_integer)) (=> (@ tptp.finite_finite_o (@ (@ tptp.image_Code_integer_o F) A)) (=> (not (@ tptp.finite6017078050557962740nteger A)) (not (forall ((Y2 Bool)) (=> (@ (@ tptp.member_o Y2) (@ (@ tptp.image_Code_integer_o F) A)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.inf_in1364745209274528805nteger (@ (@ tptp.vimage3005800680117336574eger_o F) (@ (@ tptp.insert_o Y2) tptp.bot_bot_set_o))) A)))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat Bool)) (A tptp.set_nat)) (=> (@ tptp.finite_finite_o (@ (@ tptp.image_nat_o2 F) A)) (=> (not (@ tptp.finite_finite_nat A)) (not (forall ((Y2 Bool)) (=> (@ (@ tptp.member_o Y2) (@ (@ tptp.image_nat_o2 F) A)) (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.vimage_nat_o F) (@ (@ tptp.insert_o Y2) tptp.bot_bot_set_o))) A)))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.nat)) (A tptp.set_Code_integer)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_951025933927791156er_nat F) A)) (=> (not (@ tptp.finite6017078050557962740nteger A)) (not (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) (@ (@ tptp.image_951025933927791156er_nat F) A)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.inf_in1364745209274528805nteger (@ (@ tptp.vimage5839839309545413354er_nat F) (@ (@ tptp.insert_nat Y2) tptp.bot_bot_set_nat))) A)))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_nat2 F) A)) (=> (not (@ tptp.finite_finite_nat A)) (not (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) (@ (@ tptp.image_nat_nat2 F) A)) (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.vimage_nat_nat F) (@ (@ tptp.insert_nat Y2) tptp.bot_bot_set_nat))) A)))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.int)) (A tptp.set_Code_integer)) (=> (@ tptp.finite_finite_int (@ (@ tptp.image_948535463418740880er_int F) A)) (=> (not (@ tptp.finite6017078050557962740nteger A)) (not (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) (@ (@ tptp.image_948535463418740880er_int F) A)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.inf_in1364745209274528805nteger (@ (@ tptp.vimage5837348839036363078er_int F) (@ (@ tptp.insert_int Y2) tptp.bot_bot_set_int))) A)))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.set_nat)) (=> (@ tptp.finite_finite_int (@ (@ tptp.image_nat_int2 F) A)) (=> (not (@ tptp.finite_finite_nat A)) (not (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) (@ (@ tptp.image_nat_int2 F) A)) (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.vimage_nat_int F) (@ (@ tptp.insert_int Y2) tptp.bot_bot_set_int))) A)))))))))
% 5.61/5.92 (assert (forall ((B tptp.code_integer) (F (-> tptp.code_integer tptp.code_integer)) (X tptp.code_integer) (A tptp.set_Code_integer)) (=> (= B (@ F X)) (=> (@ (@ tptp.member_Code_integer X) A) (@ (@ tptp.member_Code_integer B) (@ (@ tptp.image_4470545334726330049nteger F) A))))))
% 5.61/5.92 (assert (forall ((B tptp.code_integer) (F (-> tptp.nat tptp.code_integer)) (X tptp.nat) (A tptp.set_nat)) (=> (= B (@ F X)) (=> (@ (@ tptp.member_nat X) A) (@ (@ tptp.member_Code_integer B) (@ (@ tptp.image_1215581382706833972nteger F) A))))))
% 5.61/5.92 (assert (forall ((B tptp.nat) (F (-> tptp.nat tptp.nat)) (X tptp.nat) (A tptp.set_nat)) (=> (= B (@ F X)) (=> (@ (@ tptp.member_nat X) A) (@ (@ tptp.member_nat B) (@ (@ tptp.image_nat_nat2 F) A))))))
% 5.61/5.92 (assert (forall ((B tptp.int) (F (-> tptp.nat tptp.int)) (X tptp.nat) (A tptp.set_nat)) (=> (= B (@ F X)) (=> (@ (@ tptp.member_nat X) A) (@ (@ tptp.member_int B) (@ (@ tptp.image_nat_int2 F) A))))))
% 5.61/5.92 (assert (forall ((B Bool) (F (-> tptp.nat Bool)) (X tptp.nat) (A tptp.set_nat)) (=> (= B (@ F X)) (=> (@ (@ tptp.member_nat X) A) (@ (@ tptp.member_o B) (@ (@ tptp.image_nat_o2 F) A))))))
% 5.61/5.92 (assert (forall ((B tptp.product_unit) (F (-> tptp.nat tptp.product_unit)) (X tptp.nat) (A tptp.set_nat)) (=> (= B (@ F X)) (=> (@ (@ tptp.member_nat X) A) (@ (@ tptp.member_Product_unit B) (@ (@ tptp.image_8730104196221521654t_unit F) A))))))
% 5.61/5.92 (assert (forall ((B tptp.nat) (F (-> tptp.int tptp.nat)) (X tptp.int) (A tptp.set_int)) (=> (= B (@ F X)) (=> (@ (@ tptp.member_int X) A) (@ (@ tptp.member_nat B) (@ (@ tptp.image_int_nat2 F) A))))))
% 5.61/5.92 (assert (forall ((B tptp.int) (F (-> tptp.int tptp.int)) (X tptp.int) (A tptp.set_int)) (=> (= B (@ F X)) (=> (@ (@ tptp.member_int X) A) (@ (@ tptp.member_int B) (@ (@ tptp.image_int_int2 F) A))))))
% 5.61/5.92 (assert (forall ((B Bool) (F (-> tptp.int Bool)) (X tptp.int) (A tptp.set_int)) (=> (= B (@ F X)) (=> (@ (@ tptp.member_int X) A) (@ (@ tptp.member_o B) (@ (@ tptp.image_int_o2 F) A))))))
% 5.61/5.92 (assert (forall ((B tptp.product_unit) (F (-> tptp.int tptp.product_unit)) (X tptp.int) (A tptp.set_int)) (=> (= B (@ F X)) (=> (@ (@ tptp.member_int X) A) (@ (@ tptp.member_Product_unit B) (@ (@ tptp.image_5846526143423701914t_unit F) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A) B4))) (= (@ (@ tptp.minus_minus_set_nat _let_1) B4) _let_1))))
% 5.61/5.92 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (= (@ _let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) B4)) (and (@ _let_1 A) (not (@ _let_1 B4)))))))
% 5.61/5.92 (assert (forall ((C tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B4)) (and (@ _let_1 A) (not (@ _let_1 B4)))))))
% 5.61/5.92 (assert (forall ((C Bool) (A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_o A) B4)) (and (@ _let_1 A) (not (@ _let_1 B4)))))))
% 5.61/5.92 (assert (forall ((C tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member_Product_unit C))) (= (@ _let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) B4)) (and (@ _let_1 A) (not (@ _let_1 B4)))))))
% 5.61/5.92 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4)) (and (@ _let_1 A) (not (@ _let_1 B4)))))))
% 5.61/5.92 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 A) (=> (not (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) B4)))))))
% 5.61/5.92 (assert (forall ((C tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A) (=> (not (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B4)))))))
% 5.61/5.92 (assert (forall ((C Bool) (A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 A) (=> (not (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.minus_minus_set_o A) B4)))))))
% 5.61/5.92 (assert (forall ((C tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member_Product_unit C))) (=> (@ _let_1 A) (=> (not (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) B4)))))))
% 5.61/5.92 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A) (=> (not (@ _let_1 B4)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4)))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer)) (= (= (@ (@ tptp.image_4470545334726330049nteger F) A) tptp.bot_bo3990330152332043303nteger) (= A tptp.bot_bo3990330152332043303nteger))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.set_nat)) (= (= (@ (@ tptp.image_1215581382706833972nteger F) A) tptp.bot_bo3990330152332043303nteger) (= A tptp.bot_bot_set_nat))))
% 5.61/5.92 (assert (forall ((F (-> tptp.product_unit tptp.product_unit)) (A tptp.set_Product_unit)) (= (= (@ (@ tptp.image_405062704495631173t_unit F) A) tptp.bot_bo3957492148770167129t_unit) (= A tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.92 (assert (forall ((F (-> Bool tptp.product_unit)) (A tptp.set_o)) (= (= (@ (@ tptp.image_o_Product_unit2 F) A) tptp.bot_bo3957492148770167129t_unit) (= A tptp.bot_bot_set_o))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.product_unit)) (A tptp.set_nat)) (= (= (@ (@ tptp.image_8730104196221521654t_unit F) A) tptp.bot_bo3957492148770167129t_unit) (= A tptp.bot_bot_set_nat))))
% 5.61/5.92 (assert (forall ((F (-> tptp.int tptp.product_unit)) (A tptp.set_int)) (= (= (@ (@ tptp.image_5846526143423701914t_unit F) A) tptp.bot_bo3957492148770167129t_unit) (= A tptp.bot_bot_set_int))))
% 5.61/5.92 (assert (forall ((F (-> tptp.product_unit Bool)) (A tptp.set_Product_unit)) (= (= (@ (@ tptp.image_Product_unit_o2 F) A) tptp.bot_bot_set_o) (= A tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.92 (assert (forall ((F (-> Bool Bool)) (A tptp.set_o)) (= (= (@ (@ tptp.image_o_o2 F) A) tptp.bot_bot_set_o) (= A tptp.bot_bot_set_o))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat Bool)) (A tptp.set_nat)) (= (= (@ (@ tptp.image_nat_o2 F) A) tptp.bot_bot_set_o) (= A tptp.bot_bot_set_nat))))
% 5.61/5.92 (assert (forall ((F (-> tptp.int Bool)) (A tptp.set_int)) (= (= (@ (@ tptp.image_int_o2 F) A) tptp.bot_bot_set_o) (= A tptp.bot_bot_set_int))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer)) (= (= tptp.bot_bo3990330152332043303nteger (@ (@ tptp.image_4470545334726330049nteger F) A)) (= A tptp.bot_bo3990330152332043303nteger))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.set_nat)) (= (= tptp.bot_bo3990330152332043303nteger (@ (@ tptp.image_1215581382706833972nteger F) A)) (= A tptp.bot_bot_set_nat))))
% 5.61/5.92 (assert (forall ((F (-> tptp.product_unit tptp.product_unit)) (A tptp.set_Product_unit)) (= (= tptp.bot_bo3957492148770167129t_unit (@ (@ tptp.image_405062704495631173t_unit F) A)) (= A tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.92 (assert (forall ((F (-> Bool tptp.product_unit)) (A tptp.set_o)) (= (= tptp.bot_bo3957492148770167129t_unit (@ (@ tptp.image_o_Product_unit2 F) A)) (= A tptp.bot_bot_set_o))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.product_unit)) (A tptp.set_nat)) (= (= tptp.bot_bo3957492148770167129t_unit (@ (@ tptp.image_8730104196221521654t_unit F) A)) (= A tptp.bot_bot_set_nat))))
% 5.61/5.92 (assert (forall ((F (-> tptp.int tptp.product_unit)) (A tptp.set_int)) (= (= tptp.bot_bo3957492148770167129t_unit (@ (@ tptp.image_5846526143423701914t_unit F) A)) (= A tptp.bot_bot_set_int))))
% 5.61/5.92 (assert (forall ((F (-> tptp.product_unit Bool)) (A tptp.set_Product_unit)) (= (= tptp.bot_bot_set_o (@ (@ tptp.image_Product_unit_o2 F) A)) (= A tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.92 (assert (forall ((F (-> Bool Bool)) (A tptp.set_o)) (= (= tptp.bot_bot_set_o (@ (@ tptp.image_o_o2 F) A)) (= A tptp.bot_bot_set_o))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat Bool)) (A tptp.set_nat)) (= (= tptp.bot_bot_set_o (@ (@ tptp.image_nat_o2 F) A)) (= A tptp.bot_bot_set_nat))))
% 5.61/5.92 (assert (forall ((F (-> tptp.int Bool)) (A tptp.set_int)) (= (= tptp.bot_bot_set_o (@ (@ tptp.image_int_o2 F) A)) (= A tptp.bot_bot_set_int))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.code_integer))) (= (@ (@ tptp.image_4470545334726330049nteger F) tptp.bot_bo3990330152332043303nteger) tptp.bot_bo3990330152332043303nteger)))
% 5.61/5.92 (assert (forall ((F (-> tptp.product_unit tptp.product_unit))) (= (@ (@ tptp.image_405062704495631173t_unit F) tptp.bot_bo3957492148770167129t_unit) tptp.bot_bo3957492148770167129t_unit)))
% 5.61/5.92 (assert (forall ((F (-> tptp.product_unit Bool))) (= (@ (@ tptp.image_Product_unit_o2 F) tptp.bot_bo3957492148770167129t_unit) tptp.bot_bot_set_o)))
% 5.61/5.92 (assert (forall ((F (-> tptp.product_unit tptp.nat))) (= (@ (@ tptp.image_875570014554754200it_nat F) tptp.bot_bo3957492148770167129t_unit) tptp.bot_bot_set_nat)))
% 5.61/5.92 (assert (forall ((F (-> tptp.product_unit tptp.int))) (= (@ (@ tptp.image_873079544045703924it_int F) tptp.bot_bo3957492148770167129t_unit) tptp.bot_bot_set_int)))
% 5.61/5.92 (assert (forall ((F (-> Bool tptp.product_unit))) (= (@ (@ tptp.image_o_Product_unit2 F) tptp.bot_bot_set_o) tptp.bot_bo3957492148770167129t_unit)))
% 5.61/5.92 (assert (forall ((F (-> Bool Bool))) (= (@ (@ tptp.image_o_o2 F) tptp.bot_bot_set_o) tptp.bot_bot_set_o)))
% 5.61/5.92 (assert (forall ((F (-> Bool tptp.nat))) (= (@ (@ tptp.image_o_nat2 F) tptp.bot_bot_set_o) tptp.bot_bot_set_nat)))
% 5.61/5.92 (assert (forall ((F (-> Bool tptp.int))) (= (@ (@ tptp.image_o_int2 F) tptp.bot_bot_set_o) tptp.bot_bot_set_int)))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.code_integer))) (= (@ (@ tptp.image_1215581382706833972nteger F) tptp.bot_bot_set_nat) tptp.bot_bo3990330152332043303nteger)))
% 5.61/5.92 (assert (forall ((X tptp.code_integer) (A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ (@ tptp.image_4470545334726330049nteger F) A))) (=> (@ (@ tptp.member_Code_integer X) A) (= (@ (@ tptp.insert_Code_integer (@ F X)) _let_1) _let_1)))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (A tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ (@ tptp.image_1215581382706833972nteger F) A))) (=> (@ (@ tptp.member_nat X) A) (= (@ (@ tptp.insert_Code_integer (@ F X)) _let_1) _let_1)))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (A tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.image_nat_nat2 F) A))) (=> (@ (@ tptp.member_nat X) A) (= (@ (@ tptp.insert_nat (@ F X)) _let_1) _let_1)))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (A tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.image_nat_int2 F) A))) (=> (@ (@ tptp.member_nat X) A) (= (@ (@ tptp.insert_int (@ F X)) _let_1) _let_1)))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (A tptp.set_nat) (F (-> tptp.nat Bool))) (let ((_let_1 (@ (@ tptp.image_nat_o2 F) A))) (=> (@ (@ tptp.member_nat X) A) (= (@ (@ tptp.insert_o (@ F X)) _let_1) _let_1)))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (A tptp.set_nat) (F (-> tptp.nat tptp.product_unit))) (let ((_let_1 (@ (@ tptp.image_8730104196221521654t_unit F) A))) (=> (@ (@ tptp.member_nat X) A) (= (@ (@ tptp.insert_Product_unit (@ F X)) _let_1) _let_1)))))
% 5.61/5.92 (assert (forall ((X tptp.int) (A tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.image_int_nat2 F) A))) (=> (@ (@ tptp.member_int X) A) (= (@ (@ tptp.insert_nat (@ F X)) _let_1) _let_1)))))
% 5.61/5.92 (assert (forall ((X tptp.int) (A tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ (@ tptp.image_int_int2 F) A))) (=> (@ (@ tptp.member_int X) A) (= (@ (@ tptp.insert_int (@ F X)) _let_1) _let_1)))))
% 5.61/5.92 (assert (forall ((X tptp.int) (A tptp.set_int) (F (-> tptp.int Bool))) (let ((_let_1 (@ (@ tptp.image_int_o2 F) A))) (=> (@ (@ tptp.member_int X) A) (= (@ (@ tptp.insert_o (@ F X)) _let_1) _let_1)))))
% 5.61/5.92 (assert (forall ((X tptp.int) (A tptp.set_int) (F (-> tptp.int tptp.product_unit))) (let ((_let_1 (@ (@ tptp.image_5846526143423701914t_unit F) A))) (=> (@ (@ tptp.member_int X) A) (= (@ (@ tptp.insert_Product_unit (@ F X)) _let_1) _let_1)))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A2 tptp.code_integer) (B4 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.image_4470545334726330049nteger F))) (= (@ _let_1 (@ (@ tptp.insert_Code_integer A2) B4)) (@ (@ tptp.insert_Code_integer (@ F A2)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A2 tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_1215581382706833972nteger F))) (= (@ _let_1 (@ (@ tptp.insert_nat A2) B4)) (@ (@ tptp.insert_Code_integer (@ F A2)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_nat2 F))) (= (@ _let_1 (@ (@ tptp.insert_nat A2) B4)) (@ (@ tptp.insert_nat (@ F A2)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_int2 F))) (= (@ _let_1 (@ (@ tptp.insert_nat A2) B4)) (@ (@ tptp.insert_int (@ F A2)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat Bool)) (A2 tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_o2 F))) (= (@ _let_1 (@ (@ tptp.insert_nat A2) B4)) (@ (@ tptp.insert_o (@ F A2)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.product_unit)) (A2 tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_8730104196221521654t_unit F))) (= (@ _let_1 (@ (@ tptp.insert_nat A2) B4)) (@ (@ tptp.insert_Product_unit (@ F A2)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.int tptp.nat)) (A2 tptp.int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.image_int_nat2 F))) (= (@ _let_1 (@ (@ tptp.insert_int A2) B4)) (@ (@ tptp.insert_nat (@ F A2)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.image_int_int2 F))) (= (@ _let_1 (@ (@ tptp.insert_int A2) B4)) (@ (@ tptp.insert_int (@ F A2)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.int Bool)) (A2 tptp.int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.image_int_o2 F))) (= (@ _let_1 (@ (@ tptp.insert_int A2) B4)) (@ (@ tptp.insert_o (@ F A2)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.int tptp.product_unit)) (A2 tptp.int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.image_5846526143423701914t_unit F))) (= (@ _let_1 (@ (@ tptp.insert_int A2) B4)) (@ (@ tptp.insert_Product_unit (@ F A2)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (B tptp.nat) (S tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) S) (@ (@ tptp.member_nat B) (@ (@ tptp.image_2486076414777270412at_nat tptp.product_snd_nat_nat) S)))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (S tptp.set_Pr3286484037609594932et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) B)) S) (@ (@ tptp.member6260224972018164377et_nat B) (@ (@ tptp.image_4390311411407041927et_nat tptp.produc4011572625026189258et_nat) S)))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (S tptp.set_Pr8536935166611901872et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) B)) S) (@ (@ tptp.member1996754912294343701et_nat B) (@ (@ tptp.image_4557310310409863807et_nat tptp.produc5374455773327741254et_nat) S)))))
% 5.61/5.92 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat) (S tptp.set_Pr3948176798113811640et_nat)) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) B)) S) (@ (@ tptp.member_set_nat B) (@ (@ tptp.image_6088997261112373647et_nat tptp.produc8586169260539613262et_nat) S)))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (B tptp.int) (S tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) S) (@ (@ tptp.member_int B) (@ (@ tptp.image_5042161079198086560nt_int tptp.product_snd_int_int) S)))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit)) (= (@ (@ tptp.minus_6452836326544984404t_unit A) A) tptp.bot_bo3957492148770167129t_unit)))
% 5.61/5.92 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.minus_minus_set_o A) A) tptp.bot_bot_set_o)))
% 5.61/5.92 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A) A) tptp.bot_bot_set_int)))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.minus_1801376950450012436_nat_o A) A) tptp.bot_bo7824918357723582233_nat_o)))
% 5.61/5.92 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A) A) tptp.bot_bot_set_nat)))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit)) (= (@ (@ tptp.minus_6452836326544984404t_unit tptp.bot_bo3957492148770167129t_unit) A) tptp.bot_bo3957492148770167129t_unit)))
% 5.61/5.92 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.minus_minus_set_o tptp.bot_bot_set_o) A) tptp.bot_bot_set_o)))
% 5.61/5.92 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int tptp.bot_bot_set_int) A) tptp.bot_bot_set_int)))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.minus_1801376950450012436_nat_o tptp.bot_bo7824918357723582233_nat_o) A) tptp.bot_bo7824918357723582233_nat_o)))
% 5.61/5.92 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat tptp.bot_bot_set_nat) A) tptp.bot_bot_set_nat)))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit)) (= (@ (@ tptp.minus_6452836326544984404t_unit A) tptp.bot_bo3957492148770167129t_unit) A)))
% 5.61/5.92 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.minus_minus_set_o A) tptp.bot_bot_set_o) A)))
% 5.61/5.92 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A) tptp.bot_bot_set_int) A)))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.minus_1801376950450012436_nat_o A) tptp.bot_bo7824918357723582233_nat_o) A)))
% 5.61/5.92 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A) tptp.bot_bot_set_nat) A)))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.set_Pr4532377907799695533_nat_o) (A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o X) B4) (= (@ (@ tptp.minus_1801376950450012436_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) A)) B4) (@ (@ tptp.minus_1801376950450012436_nat_o A) B4)))))
% 5.61/5.92 (assert (forall ((X tptp.int) (B4 tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.member_int X) B4) (= (@ (@ tptp.minus_minus_set_int (@ (@ tptp.insert_int X) A)) B4) (@ (@ tptp.minus_minus_set_int A) B4)))))
% 5.61/5.92 (assert (forall ((X Bool) (B4 tptp.set_o) (A tptp.set_o)) (=> (@ (@ tptp.member_o X) B4) (= (@ (@ tptp.minus_minus_set_o (@ (@ tptp.insert_o X) A)) B4) (@ (@ tptp.minus_minus_set_o A) B4)))))
% 5.61/5.92 (assert (forall ((X tptp.product_unit) (B4 tptp.set_Product_unit) (A tptp.set_Product_unit)) (=> (@ (@ tptp.member_Product_unit X) B4) (= (@ (@ tptp.minus_6452836326544984404t_unit (@ (@ tptp.insert_Product_unit X) A)) B4) (@ (@ tptp.minus_6452836326544984404t_unit A) B4)))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (B4 tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat X) B4) (= (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.insert_nat X) A)) B4) (@ (@ tptp.minus_minus_set_nat A) B4)))))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.minus_1801376950450012436_nat_o A))) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) A)) (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o X) B4)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((X tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int A))) (=> (not (@ (@ tptp.member_int X) A)) (= (@ _let_1 (@ (@ tptp.insert_int X) B4)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((X Bool) (A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.minus_minus_set_o A))) (=> (not (@ (@ tptp.member_o X) A)) (= (@ _let_1 (@ (@ tptp.insert_o X) B4)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((X tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.minus_6452836326544984404t_unit A))) (=> (not (@ (@ tptp.member_Product_unit X) A)) (= (@ _let_1 (@ (@ tptp.insert_Product_unit X) B4)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A))) (=> (not (@ (@ tptp.member_nat X) A)) (= (@ _let_1 (@ (@ tptp.insert_nat X) B4)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_nat) (A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.minus_minus_set_nat B4) A)) A) (@ (@ tptp.sup_sup_set_nat B4) A))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat B4) A)) (@ _let_1 B4)))))
% 5.61/5.92 (assert (forall ((A2 tptp.set_nat) (B tptp.heap_e7401611519738050253t_unit) (R2 tptp.set_Pr3948176798113811640et_nat)) (= (@ (@ tptp.member727419437372278867t_unit (@ (@ tptp.produc2471974422597015918t_unit A2) B)) (@ tptp.conver7272282955447398104et_nat R2)) (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat B) A2)) R2))))
% 5.61/5.92 (assert (forall ((A2 tptp.produc3658429121746597890et_nat) (B (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr3286484037609594932et_nat)) (= (@ (@ tptp.member4978015717948814295_nat_o (@ (@ tptp.produc2829238748666232050_nat_o A2) B)) (@ tptp.conver4003969491454187092et_nat R2)) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat B) A2)) R2))))
% 5.61/5.92 (assert (forall ((A2 tptp.produc3925858234332021118et_nat) (B (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr8536935166611901872et_nat)) (= (@ (@ tptp.member8354763867512313179_nat_o (@ (@ tptp.produc3674526432113299062_nat_o A2) B)) (@ tptp.conver3577387295554834384et_nat R2)) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat B) A2)) R2))))
% 5.61/5.92 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat) (R2 tptp.set_Pr4071100604818519410t_unit)) (= (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) B)) (@ tptp.conver2236330673913229642t_unit R2)) (@ (@ tptp.member727419437372278867t_unit (@ (@ tptp.produc2471974422597015918t_unit B) A2)) R2))))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) (@ tptp.converse_nat_nat R2)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) A2)) R2))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) (@ tptp.converse_int_int R2)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) A2)) R2))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr4208978187861016310_nat_o)) (= (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) B)) (@ tptp.conver1831365297310299342_nat_o R2)) (@ (@ tptp.member4978015717948814295_nat_o (@ (@ tptp.produc2829238748666232050_nat_o B) A2)) R2))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr7705059561495379578_nat_o)) (= (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) B)) (@ tptp.conver5006497266169685586_nat_o R2)) (@ (@ tptp.member8354763867512313179_nat_o (@ (@ tptp.produc3674526432113299062_nat_o B) A2)) R2))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (= (= (@ (@ tptp.minus_6452836326544984404t_unit A) B4) tptp.bot_bo3957492148770167129t_unit) (@ (@ tptp.ord_le3507040750410214029t_unit A) B4))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (= (= (@ (@ tptp.minus_minus_set_o A) B4) tptp.bot_bot_set_o) (@ (@ tptp.ord_less_eq_set_o A) B4))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A) B4) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A) B4))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (= (= (@ (@ tptp.minus_1801376950450012436_nat_o A) B4) tptp.bot_bo7824918357723582233_nat_o) (@ (@ tptp.ord_le2965882846123202637_nat_o A) B4))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A) B4) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A) B4))))
% 5.61/5.92 (assert (forall ((A2 tptp.product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit A2))) (= (@ _let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ _let_1 tptp.bot_bo3957492148770167129t_unit))) (@ _let_1 A)))))
% 5.61/5.92 (assert (forall ((A2 Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_o A) (@ _let_1 tptp.bot_bot_set_o))) (@ _let_1 A)))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ _let_1 tptp.bot_bot_set_int))) (@ _let_1 A)))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.insert5175938949040314269_nat_o A2))) (= (@ _let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ _let_1 tptp.bot_bo7824918357723582233_nat_o))) (@ _let_1 A)))))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) (@ _let_1 tptp.bot_bot_set_nat))) (@ _let_1 A)))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (A2 tptp.int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int A))) (= (@ tptp.finite_finite_int (@ _let_1 (@ (@ tptp.insert_int A2) B4))) (@ tptp.finite_finite_int (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (A2 Bool) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.minus_minus_set_o A))) (= (@ tptp.finite_finite_o (@ _let_1 (@ (@ tptp.insert_o A2) B4))) (@ tptp.finite_finite_o (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (A2 tptp.product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.minus_6452836326544984404t_unit A))) (= (@ tptp.finite4290736615968046902t_unit (@ _let_1 (@ (@ tptp.insert_Product_unit A2) B4))) (@ tptp.finite4290736615968046902t_unit (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Code_integer) (A2 tptp.code_integer) (B4 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.minus_2355218937544613996nteger A))) (= (@ tptp.finite6017078050557962740nteger (@ _let_1 (@ (@ tptp.insert_Code_integer A2) B4))) (@ tptp.finite6017078050557962740nteger (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (A2 tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A))) (= (@ tptp.finite_finite_nat (@ _let_1 (@ (@ tptp.insert_nat A2) B4))) (@ tptp.finite_finite_nat (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit A) (@ (@ tptp.minus_6452836326544984404t_unit B4) A)) tptp.bot_bo3957492148770167129t_unit)))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o A) (@ (@ tptp.minus_minus_set_o B4) A)) tptp.bot_bot_set_o)))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A) (@ (@ tptp.minus_minus_set_int B4) A)) tptp.bot_bot_set_int)))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o A) (@ (@ tptp.minus_1801376950450012436_nat_o B4) A)) tptp.bot_bo7824918357723582233_nat_o)))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A) (@ (@ tptp.minus_minus_set_nat B4) A)) tptp.bot_bot_set_nat)))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer) (B4 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.image_4470545334726330049nteger F))) (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.minus_2355218937544613996nteger (@ _let_1 A)) (@ _let_1 B4))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_set_nat F))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.minus_2163939370556025621et_nat (@ _let_1 A)) (@ _let_1 B4))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_1215581382706833972nteger F))) (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.minus_2355218937544613996nteger (@ _let_1 A)) (@ _let_1 B4))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_nat2 F))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat (@ _let_1 A)) (@ _let_1 B4))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4))))))
% 5.61/5.92 (assert (forall ((X tptp.code_integer) (A tptp.set_Code_integer) (B tptp.code_integer) (F (-> tptp.code_integer tptp.code_integer))) (=> (@ (@ tptp.member_Code_integer X) A) (=> (= B (@ F X)) (@ (@ tptp.member_Code_integer B) (@ (@ tptp.image_4470545334726330049nteger F) A))))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (A tptp.set_nat) (B tptp.code_integer) (F (-> tptp.nat tptp.code_integer))) (=> (@ (@ tptp.member_nat X) A) (=> (= B (@ F X)) (@ (@ tptp.member_Code_integer B) (@ (@ tptp.image_1215581382706833972nteger F) A))))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (A tptp.set_nat) (B tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.member_nat X) A) (=> (= B (@ F X)) (@ (@ tptp.member_nat B) (@ (@ tptp.image_nat_nat2 F) A))))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (A tptp.set_nat) (B tptp.int) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.member_nat X) A) (=> (= B (@ F X)) (@ (@ tptp.member_int B) (@ (@ tptp.image_nat_int2 F) A))))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (A tptp.set_nat) (B Bool) (F (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X) A) (=> (= B (@ F X)) (@ (@ tptp.member_o B) (@ (@ tptp.image_nat_o2 F) A))))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (A tptp.set_nat) (B tptp.product_unit) (F (-> tptp.nat tptp.product_unit))) (=> (@ (@ tptp.member_nat X) A) (=> (= B (@ F X)) (@ (@ tptp.member_Product_unit B) (@ (@ tptp.image_8730104196221521654t_unit F) A))))))
% 5.61/5.92 (assert (forall ((X tptp.int) (A tptp.set_int) (B tptp.nat) (F (-> tptp.int tptp.nat))) (=> (@ (@ tptp.member_int X) A) (=> (= B (@ F X)) (@ (@ tptp.member_nat B) (@ (@ tptp.image_int_nat2 F) A))))))
% 5.61/5.92 (assert (forall ((X tptp.int) (A tptp.set_int) (B tptp.int) (F (-> tptp.int tptp.int))) (=> (@ (@ tptp.member_int X) A) (=> (= B (@ F X)) (@ (@ tptp.member_int B) (@ (@ tptp.image_int_int2 F) A))))))
% 5.61/5.92 (assert (forall ((X tptp.int) (A tptp.set_int) (B Bool) (F (-> tptp.int Bool))) (=> (@ (@ tptp.member_int X) A) (=> (= B (@ F X)) (@ (@ tptp.member_o B) (@ (@ tptp.image_int_o2 F) A))))))
% 5.61/5.92 (assert (forall ((X tptp.int) (A tptp.set_int) (B tptp.product_unit) (F (-> tptp.int tptp.product_unit))) (=> (@ (@ tptp.member_int X) A) (=> (= B (@ F X)) (@ (@ tptp.member_Product_unit B) (@ (@ tptp.image_5846526143423701914t_unit F) A))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) (@ (@ tptp.image_nat_set_nat F) A)) (@ P X3))) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A) (@ P (@ F X6)))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (P (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.image_nat_nat2 F) A)) (@ P X3))) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A) (@ P (@ F X6)))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer) (P (-> tptp.code_integer Bool))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.image_4470545334726330049nteger F) A)) (@ P X3))) (forall ((X6 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X6) A) (@ P (@ F X6)))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.set_nat) (P (-> tptp.code_integer Bool))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.image_1215581382706833972nteger F) A)) (@ P X3))) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A) (@ P (@ F X6)))))))
% 5.61/5.92 (assert (forall ((M tptp.set_Code_integer) (N tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer))) (=> (= M N) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) N) (= (@ F X3) (@ G X3)))) (= (@ (@ tptp.image_4470545334726330049nteger F) M) (@ (@ tptp.image_4470545334726330049nteger G) N))))))
% 5.61/5.92 (assert (forall ((M tptp.set_nat) (N tptp.set_nat) (F (-> tptp.nat tptp.set_nat)) (G (-> tptp.nat tptp.set_nat))) (=> (= M N) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N) (= (@ F X3) (@ G X3)))) (= (@ (@ tptp.image_nat_set_nat F) M) (@ (@ tptp.image_nat_set_nat G) N))))))
% 5.61/5.92 (assert (forall ((M tptp.set_nat) (N tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (= M N) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N) (= (@ F X3) (@ G X3)))) (= (@ (@ tptp.image_nat_nat2 F) M) (@ (@ tptp.image_nat_nat2 G) N))))))
% 5.61/5.92 (assert (forall ((M tptp.set_nat) (N tptp.set_nat) (F (-> tptp.nat tptp.code_integer)) (G (-> tptp.nat tptp.code_integer))) (=> (= M N) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N) (= (@ F X3) (@ G X3)))) (= (@ (@ tptp.image_1215581382706833972nteger F) M) (@ (@ tptp.image_1215581382706833972nteger G) N))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (exists ((X6 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X6) (@ (@ tptp.image_nat_set_nat F) A)) (@ P X6))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (@ P (@ F X3)))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (P (-> tptp.nat Bool))) (=> (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) (@ (@ tptp.image_nat_nat2 F) A)) (@ P X6))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (@ P (@ F X3)))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer) (P (-> tptp.code_integer Bool))) (=> (exists ((X6 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X6) (@ (@ tptp.image_4470545334726330049nteger F) A)) (@ P X6))) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A) (@ P (@ F X3)))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.set_nat) (P (-> tptp.code_integer Bool))) (=> (exists ((X6 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X6) (@ (@ tptp.image_1215581382706833972nteger F) A)) (@ P X6))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A) (@ P (@ F X3)))))))
% 5.61/5.92 (assert (forall ((Z tptp.set_nat) (F (-> tptp.nat tptp.set_nat)) (A tptp.set_nat)) (= (@ (@ tptp.member_set_nat Z) (@ (@ tptp.image_nat_set_nat F) A)) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A) (= Z (@ F X2)))))))
% 5.61/5.92 (assert (forall ((Z tptp.code_integer) (F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer)) (= (@ (@ tptp.member_Code_integer Z) (@ (@ tptp.image_4470545334726330049nteger F) A)) (exists ((X2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X2) A) (= Z (@ F X2)))))))
% 5.61/5.92 (assert (forall ((Z tptp.code_integer) (F (-> tptp.nat tptp.code_integer)) (A tptp.set_nat)) (= (@ (@ tptp.member_Code_integer Z) (@ (@ tptp.image_1215581382706833972nteger F) A)) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A) (= Z (@ F X2)))))))
% 5.61/5.92 (assert (forall ((Z tptp.nat) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (= (@ (@ tptp.member_nat Z) (@ (@ tptp.image_nat_nat2 F) A)) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A) (= Z (@ F X2)))))))
% 5.61/5.92 (assert (forall ((X tptp.code_integer) (A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer))) (=> (@ (@ tptp.member_Code_integer X) A) (@ (@ tptp.member_Code_integer (@ F X)) (@ (@ tptp.image_4470545334726330049nteger F) A)))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (A tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (=> (@ (@ tptp.member_nat X) A) (@ (@ tptp.member_Code_integer (@ F X)) (@ (@ tptp.image_1215581382706833972nteger F) A)))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (A tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.member_nat X) A) (@ (@ tptp.member_nat (@ F X)) (@ (@ tptp.image_nat_nat2 F) A)))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (A tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.member_nat X) A) (@ (@ tptp.member_int (@ F X)) (@ (@ tptp.image_nat_int2 F) A)))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (A tptp.set_nat) (F (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X) A) (@ (@ tptp.member_o (@ F X)) (@ (@ tptp.image_nat_o2 F) A)))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (A tptp.set_nat) (F (-> tptp.nat tptp.product_unit))) (=> (@ (@ tptp.member_nat X) A) (@ (@ tptp.member_Product_unit (@ F X)) (@ (@ tptp.image_8730104196221521654t_unit F) A)))))
% 5.61/5.92 (assert (forall ((X tptp.int) (A tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ (@ tptp.member_int X) A) (@ (@ tptp.member_nat (@ F X)) (@ (@ tptp.image_int_nat2 F) A)))))
% 5.61/5.92 (assert (forall ((X tptp.int) (A tptp.set_int) (F (-> tptp.int tptp.int))) (=> (@ (@ tptp.member_int X) A) (@ (@ tptp.member_int (@ F X)) (@ (@ tptp.image_int_int2 F) A)))))
% 5.61/5.92 (assert (forall ((X tptp.int) (A tptp.set_int) (F (-> tptp.int Bool))) (=> (@ (@ tptp.member_int X) A) (@ (@ tptp.member_o (@ F X)) (@ (@ tptp.image_int_o2 F) A)))))
% 5.61/5.92 (assert (forall ((X tptp.int) (A tptp.set_int) (F (-> tptp.int tptp.product_unit))) (=> (@ (@ tptp.member_int X) A) (@ (@ tptp.member_Product_unit (@ F X)) (@ (@ tptp.image_5846526143423701914t_unit F) A)))))
% 5.61/5.92 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) B4)) (not (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((C tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B4)) (not (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((C Bool) (A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_o A) B4)) (not (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((C tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member_Product_unit C))) (=> (@ _let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) B4)) (not (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4)) (not (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) B4)) (@ _let_1 A)))))
% 5.61/5.92 (assert (forall ((C tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B4)) (@ _let_1 A)))))
% 5.61/5.92 (assert (forall ((C Bool) (A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_o A) B4)) (@ _let_1 A)))))
% 5.61/5.92 (assert (forall ((C tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member_Product_unit C))) (=> (@ _let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) B4)) (@ _let_1 A)))))
% 5.61/5.92 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4)) (@ _let_1 A)))))
% 5.61/5.92 (assert (forall ((C (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ _let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) B4)) (not (=> (@ _let_1 A) (@ _let_1 B4)))))))
% 5.61/5.92 (assert (forall ((C tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A) B4)) (not (=> (@ _let_1 A) (@ _let_1 B4)))))))
% 5.61/5.92 (assert (forall ((C Bool) (A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_o A) B4)) (not (=> (@ _let_1 A) (@ _let_1 B4)))))))
% 5.61/5.92 (assert (forall ((C tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member_Product_unit C))) (=> (@ _let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) B4)) (not (=> (@ _let_1 A) (@ _let_1 B4)))))))
% 5.61/5.92 (assert (forall ((C tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4)) (not (=> (@ _let_1 A) (@ _let_1 B4)))))))
% 5.61/5.92 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C)))))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C)))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 C)) B) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C)))))
% 5.61/5.92 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A2) B) (@ (@ tptp.minus_minus_rat C) D2)) (= (= A2 B) (= C D2)))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A2) B) (@ (@ tptp.minus_minus_int C) D2)) (= (= A2 B) (= C D2)))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_set_Product_unit) (X tptp.product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit X))) (=> (forall ((C6 tptp.set_Product_unit)) (=> (@ (@ tptp.member5877623283571906838t_unit C6) B4) (not (@ (@ tptp.member_Product_unit X) C6)))) (= (@ (@ tptp.member5877623283571906838t_unit A) (@ (@ tptp.image_4019945301284682565t_unit _let_1) B4)) (and (@ (@ tptp.member_Product_unit X) A) (@ (@ tptp.member5877623283571906838t_unit (@ (@ tptp.minus_6452836326544984404t_unit A) (@ _let_1 tptp.bot_bo3957492148770167129t_unit))) B4)))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_set_o) (X Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X))) (=> (forall ((C6 tptp.set_o)) (=> (@ (@ tptp.member_set_o C6) B4) (not (@ (@ tptp.member_o X) C6)))) (= (@ (@ tptp.member_set_o A) (@ (@ tptp.image_set_o_set_o _let_1) B4)) (and (@ (@ tptp.member_o X) A) (@ (@ tptp.member_set_o (@ (@ tptp.minus_minus_set_o A) (@ _let_1 tptp.bot_bot_set_o))) B4)))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_set_int) (X tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (=> (forall ((C6 tptp.set_int)) (=> (@ (@ tptp.member_set_int C6) B4) (not (@ (@ tptp.member_int X) C6)))) (= (@ (@ tptp.member_set_int A) (@ (@ tptp.image_524474410958335435et_int _let_1) B4)) (and (@ (@ tptp.member_int X) A) (@ (@ tptp.member_set_int (@ (@ tptp.minus_minus_set_int A) (@ _let_1 tptp.bot_bot_set_int))) B4)))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_se1353816476878259085_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.insert5175938949040314269_nat_o X))) (=> (forall ((C6 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member1452989533377600726_nat_o C6) B4) (not (@ (@ tptp.member6576561426505652726_nat_o X) C6)))) (= (@ (@ tptp.member1452989533377600726_nat_o A) (@ (@ tptp.image_8925030434418351941_nat_o _let_1) B4)) (and (@ (@ tptp.member6576561426505652726_nat_o X) A) (@ (@ tptp.member1452989533377600726_nat_o (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ _let_1 tptp.bot_bo7824918357723582233_nat_o))) B4)))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_set_nat) (X tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (=> (forall ((C6 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat C6) B4) (not (@ (@ tptp.member_nat X) C6)))) (= (@ (@ tptp.member_set_nat A) (@ (@ tptp.image_7916887816326733075et_nat _let_1) B4)) (and (@ (@ tptp.member_nat X) A) (@ (@ tptp.member_set_nat (@ (@ tptp.minus_minus_set_nat A) (@ _let_1 tptp.bot_bot_set_nat))) B4)))))))
% 5.61/5.92 (assert (forall ((A1 tptp.set_nat) (A22 tptp.heap_e7401611519738050253t_unit) (R2 tptp.set_Pr3948176798113811640et_nat)) (=> (@ (@ tptp.member727419437372278867t_unit (@ (@ tptp.produc2471974422597015918t_unit A1) A22)) (@ tptp.conver7272282955447398104et_nat R2)) (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A22) A1)) R2))))
% 5.61/5.92 (assert (forall ((A1 tptp.produc3658429121746597890et_nat) (A22 (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr3286484037609594932et_nat)) (=> (@ (@ tptp.member4978015717948814295_nat_o (@ (@ tptp.produc2829238748666232050_nat_o A1) A22)) (@ tptp.conver4003969491454187092et_nat R2)) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A22) A1)) R2))))
% 5.61/5.92 (assert (forall ((A1 tptp.produc3925858234332021118et_nat) (A22 (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr8536935166611901872et_nat)) (=> (@ (@ tptp.member8354763867512313179_nat_o (@ (@ tptp.produc3674526432113299062_nat_o A1) A22)) (@ tptp.conver3577387295554834384et_nat R2)) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A22) A1)) R2))))
% 5.61/5.92 (assert (forall ((A1 tptp.heap_e7401611519738050253t_unit) (A22 tptp.set_nat) (R2 tptp.set_Pr4071100604818519410t_unit)) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A1) A22)) (@ tptp.conver2236330673913229642t_unit R2)) (@ (@ tptp.member727419437372278867t_unit (@ (@ tptp.produc2471974422597015918t_unit A22) A1)) R2))))
% 5.61/5.92 (assert (forall ((A1 tptp.nat) (A22 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A1) A22)) (@ tptp.converse_nat_nat R2)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A22) A1)) R2))))
% 5.61/5.92 (assert (forall ((A1 tptp.int) (A22 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A1) A22)) (@ tptp.converse_int_int R2)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A22) A1)) R2))))
% 5.61/5.92 (assert (forall ((A1 (-> tptp.produc3658429121746597890et_nat Bool)) (A22 tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr4208978187861016310_nat_o)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A1) A22)) (@ tptp.conver1831365297310299342_nat_o R2)) (@ (@ tptp.member4978015717948814295_nat_o (@ (@ tptp.produc2829238748666232050_nat_o A22) A1)) R2))))
% 5.61/5.92 (assert (forall ((A1 (-> tptp.produc3658429121746597890et_nat Bool)) (A22 tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr7705059561495379578_nat_o)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A1) A22)) (@ tptp.conver5006497266169685586_nat_o R2)) (@ (@ tptp.member8354763867512313179_nat_o (@ (@ tptp.produc3674526432113299062_nat_o A22) A1)) R2))))
% 5.61/5.92 (assert (forall ((A1 tptp.set_nat) (A22 tptp.heap_e7401611519738050253t_unit) (R2 tptp.set_Pr3948176798113811640et_nat)) (= (@ (@ tptp.member727419437372278867t_unit (@ (@ tptp.produc2471974422597015918t_unit A1) A22)) (@ tptp.conver7272282955447398104et_nat R2)) (exists ((A6 tptp.heap_e7401611519738050253t_unit) (B6 tptp.set_nat)) (and (= A1 B6) (= A22 A6) (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A6) B6)) R2))))))
% 5.61/5.92 (assert (forall ((A1 tptp.produc3658429121746597890et_nat) (A22 (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr3286484037609594932et_nat)) (= (@ (@ tptp.member4978015717948814295_nat_o (@ (@ tptp.produc2829238748666232050_nat_o A1) A22)) (@ tptp.conver4003969491454187092et_nat R2)) (exists ((A6 (-> tptp.produc3658429121746597890et_nat Bool)) (B6 tptp.produc3658429121746597890et_nat)) (and (= A1 B6) (= A22 A6) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A6) B6)) R2))))))
% 5.61/5.92 (assert (forall ((A1 tptp.produc3925858234332021118et_nat) (A22 (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr8536935166611901872et_nat)) (= (@ (@ tptp.member8354763867512313179_nat_o (@ (@ tptp.produc3674526432113299062_nat_o A1) A22)) (@ tptp.conver3577387295554834384et_nat R2)) (exists ((A6 (-> tptp.produc3658429121746597890et_nat Bool)) (B6 tptp.produc3925858234332021118et_nat)) (and (= A1 B6) (= A22 A6) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A6) B6)) R2))))))
% 5.61/5.92 (assert (forall ((A1 tptp.heap_e7401611519738050253t_unit) (A22 tptp.set_nat) (R2 tptp.set_Pr4071100604818519410t_unit)) (= (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A1) A22)) (@ tptp.conver2236330673913229642t_unit R2)) (exists ((A6 tptp.set_nat) (B6 tptp.heap_e7401611519738050253t_unit)) (and (= A1 B6) (= A22 A6) (@ (@ tptp.member727419437372278867t_unit (@ (@ tptp.produc2471974422597015918t_unit A6) B6)) R2))))))
% 5.61/5.92 (assert (forall ((A1 tptp.nat) (A22 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A1) A22)) (@ tptp.converse_nat_nat R2)) (exists ((A6 tptp.nat) (B6 tptp.nat)) (and (= A1 B6) (= A22 A6) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A6) B6)) R2))))))
% 5.61/5.92 (assert (forall ((A1 tptp.int) (A22 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A1) A22)) (@ tptp.converse_int_int R2)) (exists ((A6 tptp.int) (B6 tptp.int)) (and (= A1 B6) (= A22 A6) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A6) B6)) R2))))))
% 5.61/5.92 (assert (forall ((A1 (-> tptp.produc3658429121746597890et_nat Bool)) (A22 tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr4208978187861016310_nat_o)) (= (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A1) A22)) (@ tptp.conver1831365297310299342_nat_o R2)) (exists ((A6 tptp.produc3658429121746597890et_nat) (B6 (-> tptp.produc3658429121746597890et_nat Bool))) (and (= A1 B6) (= A22 A6) (@ (@ tptp.member4978015717948814295_nat_o (@ (@ tptp.produc2829238748666232050_nat_o A6) B6)) R2))))))
% 5.61/5.92 (assert (forall ((A1 (-> tptp.produc3658429121746597890et_nat Bool)) (A22 tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr7705059561495379578_nat_o)) (= (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A1) A22)) (@ tptp.conver5006497266169685586_nat_o R2)) (exists ((A6 tptp.produc3925858234332021118et_nat) (B6 (-> tptp.produc3658429121746597890et_nat Bool))) (and (= A1 B6) (= A22 A6) (@ (@ tptp.member8354763867512313179_nat_o (@ (@ tptp.produc3674526432113299062_nat_o A6) B6)) R2))))))
% 5.61/5.92 (assert (forall ((A2 tptp.set_nat) (B tptp.heap_e7401611519738050253t_unit) (R2 tptp.set_Pr3948176798113811640et_nat)) (=> (@ (@ tptp.member727419437372278867t_unit (@ (@ tptp.produc2471974422597015918t_unit A2) B)) (@ tptp.conver7272282955447398104et_nat R2)) (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat B) A2)) R2))))
% 5.61/5.92 (assert (forall ((A2 tptp.produc3658429121746597890et_nat) (B (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr3286484037609594932et_nat)) (=> (@ (@ tptp.member4978015717948814295_nat_o (@ (@ tptp.produc2829238748666232050_nat_o A2) B)) (@ tptp.conver4003969491454187092et_nat R2)) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat B) A2)) R2))))
% 5.61/5.92 (assert (forall ((A2 tptp.produc3925858234332021118et_nat) (B (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr8536935166611901872et_nat)) (=> (@ (@ tptp.member8354763867512313179_nat_o (@ (@ tptp.produc3674526432113299062_nat_o A2) B)) (@ tptp.conver3577387295554834384et_nat R2)) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat B) A2)) R2))))
% 5.61/5.92 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat) (R2 tptp.set_Pr4071100604818519410t_unit)) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) B)) (@ tptp.conver2236330673913229642t_unit R2)) (@ (@ tptp.member727419437372278867t_unit (@ (@ tptp.produc2471974422597015918t_unit B) A2)) R2))))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) (@ tptp.converse_nat_nat R2)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) A2)) R2))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) (@ tptp.converse_int_int R2)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) A2)) R2))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr4208978187861016310_nat_o)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) B)) (@ tptp.conver1831365297310299342_nat_o R2)) (@ (@ tptp.member4978015717948814295_nat_o (@ (@ tptp.produc2829238748666232050_nat_o B) A2)) R2))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr7705059561495379578_nat_o)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) B)) (@ tptp.conver5006497266169685586_nat_o R2)) (@ (@ tptp.member8354763867512313179_nat_o (@ (@ tptp.produc3674526432113299062_nat_o B) A2)) R2))))
% 5.61/5.92 (assert (forall ((Yx tptp.produc7348995623955488188t_unit) (R2 tptp.set_Pr3948176798113811640et_nat)) (=> (@ (@ tptp.member727419437372278867t_unit Yx) (@ tptp.conver7272282955447398104et_nat R2)) (not (forall ((X3 tptp.heap_e7401611519738050253t_unit) (Y2 tptp.set_nat)) (=> (= Yx (@ (@ tptp.produc2471974422597015918t_unit Y2) X3)) (not (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat X3) Y2)) R2))))))))
% 5.61/5.92 (assert (forall ((Yx tptp.produc6907119039986491712_nat_o) (R2 tptp.set_Pr3286484037609594932et_nat)) (=> (@ (@ tptp.member4978015717948814295_nat_o Yx) (@ tptp.conver4003969491454187092et_nat R2)) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3658429121746597890et_nat)) (=> (= Yx (@ (@ tptp.produc2829238748666232050_nat_o Y2) X3)) (not (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X3) Y2)) R2))))))))
% 5.61/5.92 (assert (forall ((Yx tptp.produc4962441903510821572_nat_o) (R2 tptp.set_Pr8536935166611901872et_nat)) (=> (@ (@ tptp.member8354763867512313179_nat_o Yx) (@ tptp.conver3577387295554834384et_nat R2)) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3925858234332021118et_nat)) (=> (= Yx (@ (@ tptp.produc3674526432113299062_nat_o Y2) X3)) (not (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X3) Y2)) R2))))))))
% 5.61/5.92 (assert (forall ((Yx tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr4071100604818519410t_unit)) (=> (@ (@ tptp.member6260224972018164377et_nat Yx) (@ tptp.conver2236330673913229642t_unit R2)) (not (forall ((X3 tptp.set_nat) (Y2 tptp.heap_e7401611519738050253t_unit)) (=> (= Yx (@ (@ tptp.produc7507926704131184380et_nat Y2) X3)) (not (@ (@ tptp.member727419437372278867t_unit (@ (@ tptp.produc2471974422597015918t_unit X3) Y2)) R2))))))))
% 5.61/5.92 (assert (forall ((Yx tptp.product_prod_nat_nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Yx) (@ tptp.converse_nat_nat R2)) (not (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (= Yx (@ (@ tptp.product_Pair_nat_nat Y2) X3)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)) R2))))))))
% 5.61/5.92 (assert (forall ((Yx tptp.product_prod_int_int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int Yx) (@ tptp.converse_int_int R2)) (not (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (= Yx (@ (@ tptp.product_Pair_int_int Y2) X3)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y2)) R2))))))))
% 5.61/5.92 (assert (forall ((Yx tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr4208978187861016310_nat_o)) (=> (@ (@ tptp.member1996754912294343701et_nat Yx) (@ tptp.conver1831365297310299342_nat_o R2)) (not (forall ((X3 tptp.produc3658429121746597890et_nat) (Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (= Yx (@ (@ tptp.produc5001842942810119800et_nat Y2) X3)) (not (@ (@ tptp.member4978015717948814295_nat_o (@ (@ tptp.produc2829238748666232050_nat_o X3) Y2)) R2))))))))
% 5.61/5.92 (assert (forall ((Yx tptp.produc2732055786443039994et_nat) (R2 tptp.set_Pr7705059561495379578_nat_o)) (=> (@ (@ tptp.member6124377750444531601et_nat Yx) (@ tptp.conver5006497266169685586_nat_o R2)) (not (forall ((X3 tptp.produc3925858234332021118et_nat) (Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (= Yx (@ (@ tptp.produc2245416461498447860et_nat Y2) X3)) (not (@ (@ tptp.member8354763867512313179_nat_o (@ (@ tptp.produc3674526432113299062_nat_o X3) Y2)) R2))))))))
% 5.61/5.92 (assert (forall ((A2 tptp.set_nat) (B tptp.heap_e7401611519738050253t_unit) (R2 tptp.set_Pr4071100604818519410t_unit)) (=> (@ (@ tptp.member727419437372278867t_unit (@ (@ tptp.produc2471974422597015918t_unit A2) B)) R2) (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat B) A2)) (@ tptp.conver2236330673913229642t_unit R2)))))
% 5.61/5.92 (assert (forall ((A2 tptp.produc3658429121746597890et_nat) (B (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr4208978187861016310_nat_o)) (=> (@ (@ tptp.member4978015717948814295_nat_o (@ (@ tptp.produc2829238748666232050_nat_o A2) B)) R2) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat B) A2)) (@ tptp.conver1831365297310299342_nat_o R2)))))
% 5.61/5.92 (assert (forall ((A2 tptp.produc3925858234332021118et_nat) (B (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr7705059561495379578_nat_o)) (=> (@ (@ tptp.member8354763867512313179_nat_o (@ (@ tptp.produc3674526432113299062_nat_o A2) B)) R2) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat B) A2)) (@ tptp.conver5006497266169685586_nat_o R2)))))
% 5.61/5.92 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat) (R2 tptp.set_Pr3948176798113811640et_nat)) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) B)) R2) (@ (@ tptp.member727419437372278867t_unit (@ (@ tptp.produc2471974422597015918t_unit B) A2)) (@ tptp.conver7272282955447398104et_nat R2)))))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R2) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) A2)) (@ tptp.converse_nat_nat R2)))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (B tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R2) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) A2)) (@ tptp.converse_int_int R2)))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr3286484037609594932et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) B)) R2) (@ (@ tptp.member4978015717948814295_nat_o (@ (@ tptp.produc2829238748666232050_nat_o B) A2)) (@ tptp.conver4003969491454187092et_nat R2)))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr8536935166611901872et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) B)) R2) (@ (@ tptp.member8354763867512313179_nat_o (@ (@ tptp.produc3674526432113299062_nat_o B) A2)) (@ tptp.conver3577387295554834384et_nat R2)))))
% 5.61/5.92 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A2) B) (@ (@ tptp.minus_minus_rat C) D2)) (= (@ (@ tptp.ord_less_eq_rat A2) B) (@ (@ tptp.ord_less_eq_rat C) D2)))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A2) B) (@ (@ tptp.minus_minus_int C) D2)) (= (@ (@ tptp.ord_less_eq_int A2) B) (@ (@ tptp.ord_less_eq_int C) D2)))))
% 5.61/5.92 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A2) C)) (@ (@ tptp.minus_minus_rat B) C)))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A2) C)) (@ (@ tptp.minus_minus_int B) C)))))
% 5.61/5.92 (assert (forall ((B tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A2) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B))))))
% 5.61/5.92 (assert (forall ((B tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A2) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B))))))
% 5.61/5.92 (assert (forall ((A2 tptp.rat) (B tptp.rat) (D2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (@ (@ tptp.ord_less_eq_rat D2) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A2) C)) (@ (@ tptp.minus_minus_rat B) D2))))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (B tptp.int) (D2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B) (=> (@ (@ tptp.ord_less_eq_int D2) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A2) C)) (@ (@ tptp.minus_minus_int B) D2))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger B4) (@ (@ tptp.image_4470545334726330049nteger F) A)) (exists ((AA tptp.set_Code_integer)) (and (@ (@ tptp.ord_le7084787975880047091nteger AA) A) (= B4 (@ (@ tptp.image_4470545334726330049nteger F) AA)))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_set_nat) (F (-> tptp.nat tptp.set_nat)) (A tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat B4) (@ (@ tptp.image_nat_set_nat F) A)) (exists ((AA tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat AA) A) (= B4 (@ (@ tptp.image_nat_set_nat F) AA)))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_Code_integer) (F (-> tptp.nat tptp.code_integer)) (A tptp.set_nat)) (= (@ (@ tptp.ord_le7084787975880047091nteger B4) (@ (@ tptp.image_1215581382706833972nteger F) A)) (exists ((AA tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat AA) A) (= B4 (@ (@ tptp.image_1215581382706833972nteger F) AA)))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat B4) (@ (@ tptp.image_nat_nat2 F) A)) (exists ((AA tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat AA) A) (= B4 (@ (@ tptp.image_nat_nat2 F) AA)))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A tptp.set_nat) (B4 tptp.set_set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.image_nat_set_nat F) A)) B4) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.member_set_nat (@ F X2)) B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer) (B4 tptp.set_Code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.image_4470545334726330049nteger F) A)) B4) (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X2) A) (@ (@ tptp.member_Code_integer (@ F X2)) B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.set_nat) (B4 tptp.set_Code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.image_1215581382706833972nteger F) A)) B4) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.member_Code_integer (@ F X2)) B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat2 F) A)) B4) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.member_nat (@ F X2)) B4))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le7084787975880047091nteger B4) (@ (@ tptp.image_4470545334726330049nteger F) A)) (not (forall ((C6 tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le7084787975880047091nteger C6) A) (not (= B4 (@ (@ tptp.image_4470545334726330049nteger F) C6)))))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_set_nat) (F (-> tptp.nat tptp.set_nat)) (A tptp.set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat B4) (@ (@ tptp.image_nat_set_nat F) A)) (not (forall ((C6 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat C6) A) (not (= B4 (@ (@ tptp.image_nat_set_nat F) C6)))))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_Code_integer) (F (-> tptp.nat tptp.code_integer)) (A tptp.set_nat)) (=> (@ (@ tptp.ord_le7084787975880047091nteger B4) (@ (@ tptp.image_1215581382706833972nteger F) A)) (not (forall ((C6 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat C6) A) (not (= B4 (@ (@ tptp.image_1215581382706833972nteger F) C6)))))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B4) (@ (@ tptp.image_nat_nat2 F) A)) (not (forall ((C6 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat C6) A) (not (= B4 (@ (@ tptp.image_nat_nat2 F) C6)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer)) (B4 tptp.set_Code_integer)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A) (@ (@ tptp.member_Code_integer (@ F X3)) B4))) (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.image_4470545334726330049nteger F) A)) B4))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.code_integer)) (B4 tptp.set_Code_integer)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (@ (@ tptp.member_Code_integer (@ F X3)) B4))) (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.image_1215581382706833972nteger F) A)) B4))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.int)) (B4 tptp.set_int)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (@ (@ tptp.member_int (@ F X3)) B4))) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_nat_int2 F) A)) B4))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat Bool)) (B4 tptp.set_o)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (@ (@ tptp.member_o (@ F X3)) B4))) (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.image_nat_o2 F) A)) B4))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.product_unit)) (B4 tptp.set_Product_unit)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (@ (@ tptp.member_Product_unit (@ F X3)) B4))) (@ (@ tptp.ord_le3507040750410214029t_unit (@ (@ tptp.image_8730104196221521654t_unit F) A)) B4))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.int)) (B4 tptp.set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (@ (@ tptp.member_int (@ F X3)) B4))) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int2 F) A)) B4))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (F (-> tptp.int Bool)) (B4 tptp.set_o)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (@ (@ tptp.member_o (@ F X3)) B4))) (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.image_int_o2 F) A)) B4))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.product_unit)) (B4 tptp.set_Product_unit)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (@ (@ tptp.member_Product_unit (@ F X3)) B4))) (@ (@ tptp.ord_le3507040750410214029t_unit (@ (@ tptp.image_5846526143423701914t_unit F) A)) B4))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.int)) (B4 tptp.set_int)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (@ (@ tptp.member_int (@ F X3)) B4))) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_o_int2 F) A)) B4))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (F (-> Bool Bool)) (B4 tptp.set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (@ (@ tptp.member_o (@ F X3)) B4))) (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.image_o_o2 F) A)) B4))))
% 5.61/5.92 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.image_4470545334726330049nteger F))) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) B4) (@ (@ tptp.ord_le7084787975880047091nteger (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (F (-> tptp.nat tptp.set_nat))) (let ((_let_1 (@ tptp.image_nat_set_nat F))) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (@ (@ tptp.ord_le6893508408891458716et_nat (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.image_1215581382706833972nteger F))) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (@ (@ tptp.ord_le7084787975880047091nteger (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.image_nat_nat2 F))) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer) (B4 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.image_4470545334726330049nteger F))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A) B4)) (@ (@ tptp.sup_su848401254843788991nteger (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_set_nat F))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.sup_sup_set_set_nat (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_1215581382706833972nteger F))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.sup_su848401254843788991nteger (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_nat2 F))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) C5) (= (@ (@ tptp.minus_minus_set_nat B4) (@ (@ tptp.minus_minus_set_nat C5) A)) A)))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A) B4)) A)))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (C5 tptp.set_nat) (D3 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C5) (=> (@ (@ tptp.ord_less_eq_set_nat D3) B4) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A) B4)) (@ (@ tptp.minus_minus_set_nat C5) D3))))))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.set_Pr4532377907799695533_nat_o) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) B4))) (let ((_let_2 (@ tptp.insert5175938949040314269_nat_o X))) (let ((_let_3 (@ (@ tptp.minus_1801376950450012436_nat_o (@ _let_2 A)) B4))) (let ((_let_4 (@ (@ tptp.member6576561426505652726_nat_o X) B4))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 5.61/5.92 (assert (forall ((X tptp.int) (B4 tptp.set_int) (A tptp.set_int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A) B4))) (let ((_let_2 (@ tptp.insert_int X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_int (@ _let_2 A)) B4))) (let ((_let_4 (@ (@ tptp.member_int X) B4))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 5.61/5.92 (assert (forall ((X Bool) (B4 tptp.set_o) (A tptp.set_o)) (let ((_let_1 (@ (@ tptp.minus_minus_set_o A) B4))) (let ((_let_2 (@ tptp.insert_o X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_o (@ _let_2 A)) B4))) (let ((_let_4 (@ (@ tptp.member_o X) B4))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 5.61/5.92 (assert (forall ((X tptp.product_unit) (B4 tptp.set_Product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) B4))) (let ((_let_2 (@ tptp.insert_Product_unit X))) (let ((_let_3 (@ (@ tptp.minus_6452836326544984404t_unit (@ _let_2 A)) B4))) (let ((_let_4 (@ (@ tptp.member_Product_unit X) B4))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (B4 tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A) B4))) (let ((_let_2 (@ tptp.insert_nat X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_nat (@ _let_2 A)) B4))) (let ((_let_4 (@ (@ tptp.member_nat X) B4))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.minus_minus_set_nat A) B4)) C5) (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.inf_inf_set_nat A) C5)) (@ (@ tptp.inf_inf_set_nat B4) C5)))))
% 5.61/5.92 (assert (forall ((C5 tptp.set_nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat C5))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4)) (@ (@ tptp.minus_minus_set_nat (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A))) (= (@ _let_1 (@ _let_1 B4)) (@ (@ tptp.inf_inf_set_nat A) B4)))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (C5 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat (@ (@ tptp.inf_inf_set_nat A) C5)))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B4) C5)) (@ _let_1 B4)))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 B4)) C5) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B4) C5))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A))) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 B4)) C5) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B4) C5))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.sup_sup_set_nat A) B4)) C5) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.minus_minus_set_nat A) C5)) (@ (@ tptp.minus_minus_set_nat B4) C5)))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat F))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4)) (@ (@ tptp.minus_minus_set_nat (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((Y tptp.nat) (X tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y) X)) (@ tptp.transi2905341329935302413cl_nat R2)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.transi2905341329935302413cl_nat (@ tptp.converse_nat_nat R2))))))
% 5.61/5.92 (assert (forall ((Y tptp.int) (X tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y) X)) (@ tptp.transi2902850859426252137cl_int R2)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ tptp.transi2902850859426252137cl_int (@ tptp.converse_int_int R2))))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (Y tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.transi2905341329935302413cl_nat (@ tptp.converse_nat_nat R2))) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y) X)) (@ tptp.transi2905341329935302413cl_nat R2)))))
% 5.61/5.92 (assert (forall ((X tptp.int) (Y tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ tptp.transi2902850859426252137cl_int (@ tptp.converse_int_int R2))) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y) X)) (@ tptp.transi2902850859426252137cl_int R2)))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (Y tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)))) (=> (@ _let_1 (@ tptp.converse_nat_nat (@ tptp.transi6264000038957366511cl_nat R2))) (@ _let_1 (@ tptp.transi6264000038957366511cl_nat (@ tptp.converse_nat_nat R2)))))))
% 5.61/5.92 (assert (forall ((X tptp.int) (Y tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)))) (=> (@ _let_1 (@ tptp.converse_int_int (@ tptp.transi6261509568448316235cl_int R2))) (@ _let_1 (@ tptp.transi6261509568448316235cl_int (@ tptp.converse_int_int R2)))))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (Y tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)))) (=> (@ _let_1 (@ tptp.transi6264000038957366511cl_nat (@ tptp.converse_nat_nat R2))) (@ _let_1 (@ tptp.converse_nat_nat (@ tptp.transi6264000038957366511cl_nat R2)))))))
% 5.61/5.92 (assert (forall ((X tptp.int) (Y tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)))) (=> (@ _let_1 (@ tptp.transi6261509568448316235cl_int (@ tptp.converse_int_int R2))) (@ _let_1 (@ tptp.converse_int_int (@ tptp.transi6261509568448316235cl_int R2)))))))
% 5.61/5.92 (assert (forall ((X tptp.set_Product_unit) (Y tptp.set_Product_unit)) (= (= (@ (@ tptp.minus_6452836326544984404t_unit X) Y) tptp.bot_bo3957492148770167129t_unit) (@ (@ tptp.ord_le3507040750410214029t_unit X) Y))))
% 5.61/5.92 (assert (forall ((X tptp.set_o) (Y tptp.set_o)) (= (= (@ (@ tptp.minus_minus_set_o X) Y) tptp.bot_bot_set_o) (@ (@ tptp.ord_less_eq_set_o X) Y))))
% 5.61/5.92 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X) Y) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 5.61/5.92 (assert (forall ((X tptp.set_Pr4532377907799695533_nat_o) (Y tptp.set_Pr4532377907799695533_nat_o)) (= (= (@ (@ tptp.minus_1801376950450012436_nat_o X) Y) tptp.bot_bo7824918357723582233_nat_o) (@ (@ tptp.ord_le2965882846123202637_nat_o X) Y))))
% 5.61/5.92 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (= (@ (@ tptp.minus_minus_assn X) Y) tptp.bot_bot_assn) (@ (@ tptp.ord_less_eq_assn X) Y))))
% 5.61/5.92 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X) Y) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 5.61/5.92 (assert (forall ((Y tptp.nat) (S tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member_nat Y) (@ (@ tptp.image_2486076414777270412at_nat tptp.product_snd_nat_nat) S)) (not (forall ((X3 tptp.nat)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y)) S)))))))
% 5.61/5.92 (assert (forall ((Y tptp.produc3658429121746597890et_nat) (S tptp.set_Pr3286484037609594932et_nat)) (=> (@ (@ tptp.member6260224972018164377et_nat Y) (@ (@ tptp.image_4390311411407041927et_nat tptp.produc4011572625026189258et_nat) S)) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X3) Y)) S)))))))
% 5.61/5.92 (assert (forall ((Y tptp.produc3925858234332021118et_nat) (S tptp.set_Pr8536935166611901872et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat Y) (@ (@ tptp.image_4557310310409863807et_nat tptp.produc5374455773327741254et_nat) S)) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X3) Y)) S)))))))
% 5.61/5.92 (assert (forall ((Y tptp.set_nat) (S tptp.set_Pr3948176798113811640et_nat)) (=> (@ (@ tptp.member_set_nat Y) (@ (@ tptp.image_6088997261112373647et_nat tptp.produc8586169260539613262et_nat) S)) (not (forall ((X3 tptp.heap_e7401611519738050253t_unit)) (not (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat X3) Y)) S)))))))
% 5.61/5.92 (assert (forall ((Y tptp.int) (S tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member_int Y) (@ (@ tptp.image_5042161079198086560nt_int tptp.product_snd_int_int) S)) (not (forall ((X3 tptp.int)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y)) S)))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer) (B4 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.image_4470545334726330049nteger F))) (@ (@ tptp.ord_le7084787975880047091nteger (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A) B4))) (@ (@ tptp.inf_in1364745209274528805nteger (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_set_nat F))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4))) (@ (@ tptp.inf_inf_set_set_nat (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_1215581382706833972nteger F))) (@ (@ tptp.ord_le7084787975880047091nteger (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4))) (@ (@ tptp.inf_in1364745209274528805nteger (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_nat2 F))) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4))) (@ (@ tptp.inf_inf_set_nat (@ _let_1 A)) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) B4) (= (@ (@ tptp.minus_6452836326544984404t_unit A) B4) tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A) B4) (= (@ (@ tptp.minus_minus_set_o A) B4) tptp.bot_bot_set_o))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B4) (= (@ (@ tptp.minus_minus_set_int A) B4) tptp.bot_bot_set_int))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A) B4) (= (@ (@ tptp.minus_1801376950450012436_nat_o A) B4) tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (= (@ (@ tptp.minus_minus_set_nat A) B4) tptp.bot_bot_set_nat))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer) (B4 tptp.set_Code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.image_4470545334726330049nteger F) A)) B4) (@ (@ tptp.ord_le7084787975880047091nteger A) (@ (@ tptp.vimage1318793397690208119nteger F) B4)))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A tptp.set_nat) (B4 tptp.set_set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.image_nat_set_nat F) A)) B4) (@ (@ tptp.ord_less_eq_set_nat A) (@ (@ tptp.vimage_nat_set_nat F) B4)))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.set_nat) (B4 tptp.set_Code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.image_1215581382706833972nteger F) A)) B4) (@ (@ tptp.ord_less_eq_set_nat A) (@ (@ tptp.vimage6104394758324456170nteger F) B4)))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat2 F) A)) B4) (@ (@ tptp.ord_less_eq_set_nat A) (@ (@ tptp.vimage_nat_nat F) B4)))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A tptp.set_set_nat)) (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.image_nat_set_nat F) (@ (@ tptp.vimage_nat_set_nat F) A))) A)))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer)) (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.image_4470545334726330049nteger F) (@ (@ tptp.vimage1318793397690208119nteger F) A))) A)))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.set_Code_integer)) (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.image_1215581382706833972nteger F) (@ (@ tptp.vimage6104394758324456170nteger F) A))) A)))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat2 F) (@ (@ tptp.vimage_nat_nat F) A))) A)))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (A2 tptp.product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit A2))) (let ((_let_2 (@ tptp.minus_6452836326544984404t_unit A))) (= (@ _let_2 (@ _let_1 B4)) (@ (@ tptp.minus_6452836326544984404t_unit (@ _let_2 B4)) (@ _let_1 tptp.bot_bo3957492148770167129t_unit)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (A2 Bool) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A2))) (let ((_let_2 (@ tptp.minus_minus_set_o A))) (= (@ _let_2 (@ _let_1 B4)) (@ (@ tptp.minus_minus_set_o (@ _let_2 B4)) (@ _let_1 tptp.bot_bot_set_o)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (A2 tptp.int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A2))) (let ((_let_2 (@ tptp.minus_minus_set_int A))) (= (@ _let_2 (@ _let_1 B4)) (@ (@ tptp.minus_minus_set_int (@ _let_2 B4)) (@ _let_1 tptp.bot_bot_set_int)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.insert5175938949040314269_nat_o A2))) (let ((_let_2 (@ tptp.minus_1801376950450012436_nat_o A))) (= (@ _let_2 (@ _let_1 B4)) (@ (@ tptp.minus_1801376950450012436_nat_o (@ _let_2 B4)) (@ _let_1 tptp.bot_bo7824918357723582233_nat_o)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (A2 tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (let ((_let_2 (@ tptp.minus_minus_set_nat A))) (= (@ _let_2 (@ _let_1 B4)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 B4)) (@ _let_1 tptp.bot_bot_set_nat)))))))
% 5.61/5.92 (assert (forall ((A2 tptp.product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit A2))) (=> (@ (@ tptp.member_Product_unit A2) A) (= (@ _let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ _let_1 tptp.bot_bo3957492148770167129t_unit))) A)))))
% 5.61/5.92 (assert (forall ((A2 Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A2))) (=> (@ (@ tptp.member_o A2) A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_o A) (@ _let_1 tptp.bot_bot_set_o))) A)))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A2))) (=> (@ (@ tptp.member_int A2) A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ _let_1 tptp.bot_bot_set_int))) A)))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.insert5175938949040314269_nat_o A2))) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) A) (= (@ _let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ _let_1 tptp.bot_bo7824918357723582233_nat_o))) A)))))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (=> (@ (@ tptp.member_nat A2) A) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) (@ _let_1 tptp.bot_bot_set_nat))) A)))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (A2 tptp.product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit A2))) (let ((_let_2 (@ tptp.minus_6452836326544984404t_unit A))) (= (@ _let_2 (@ _let_1 B4)) (@ (@ tptp.minus_6452836326544984404t_unit (@ _let_2 (@ _let_1 tptp.bot_bo3957492148770167129t_unit))) B4))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (A2 Bool) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A2))) (let ((_let_2 (@ tptp.minus_minus_set_o A))) (= (@ _let_2 (@ _let_1 B4)) (@ (@ tptp.minus_minus_set_o (@ _let_2 (@ _let_1 tptp.bot_bot_set_o))) B4))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (A2 tptp.int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A2))) (let ((_let_2 (@ tptp.minus_minus_set_int A))) (= (@ _let_2 (@ _let_1 B4)) (@ (@ tptp.minus_minus_set_int (@ _let_2 (@ _let_1 tptp.bot_bot_set_int))) B4))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.insert5175938949040314269_nat_o A2))) (let ((_let_2 (@ tptp.minus_1801376950450012436_nat_o A))) (= (@ _let_2 (@ _let_1 B4)) (@ (@ tptp.minus_1801376950450012436_nat_o (@ _let_2 (@ _let_1 tptp.bot_bo7824918357723582233_nat_o))) B4))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (A2 tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A2))) (let ((_let_2 (@ tptp.minus_minus_set_nat A))) (= (@ _let_2 (@ _let_1 B4)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 (@ _let_1 tptp.bot_bot_set_nat))) B4))))))
% 5.61/5.92 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ (@ tptp.insert_Product_unit Y) tptp.bot_bo3957492148770167129t_unit))) (let ((_let_2 (@ tptp.insert_Product_unit X))) (=> (not (= X Y)) (= (@ (@ tptp.minus_6452836326544984404t_unit (@ _let_2 A)) _let_1) (@ _let_2 (@ (@ tptp.minus_6452836326544984404t_unit A) _let_1))))))))
% 5.61/5.92 (assert (forall ((X Bool) (Y Bool) (A tptp.set_o)) (let ((_let_1 (@ (@ tptp.insert_o Y) tptp.bot_bot_set_o))) (let ((_let_2 (@ tptp.insert_o X))) (=> (not (= X Y)) (= (@ (@ tptp.minus_minus_set_o (@ _let_2 A)) _let_1) (@ _let_2 (@ (@ tptp.minus_minus_set_o A) _let_1))))))))
% 5.61/5.92 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int Y) tptp.bot_bot_set_int))) (let ((_let_2 (@ tptp.insert_int X))) (=> (not (= X Y)) (= (@ (@ tptp.minus_minus_set_int (@ _let_2 A)) _let_1) (@ _let_2 (@ (@ tptp.minus_minus_set_int A) _let_1))))))))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ (@ tptp.insert5175938949040314269_nat_o Y) tptp.bot_bo7824918357723582233_nat_o))) (let ((_let_2 (@ tptp.insert5175938949040314269_nat_o X))) (=> (not (= X Y)) (= (@ (@ tptp.minus_1801376950450012436_nat_o (@ _let_2 A)) _let_1) (@ _let_2 (@ (@ tptp.minus_1801376950450012436_nat_o A) _let_1))))))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat Y) tptp.bot_bot_set_nat))) (let ((_let_2 (@ tptp.insert_nat X))) (=> (not (= X Y)) (= (@ (@ tptp.minus_minus_set_nat (@ _let_2 A)) _let_1) (@ _let_2 (@ (@ tptp.minus_minus_set_nat A) _let_1))))))))
% 5.61/5.92 (assert (forall ((X tptp.product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit X))) (=> (not (@ (@ tptp.member_Product_unit X) A)) (= (@ (@ tptp.minus_6452836326544984404t_unit (@ _let_1 A)) (@ _let_1 tptp.bot_bo3957492148770167129t_unit)) A)))))
% 5.61/5.92 (assert (forall ((X Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X))) (=> (not (@ (@ tptp.member_o X) A)) (= (@ (@ tptp.minus_minus_set_o (@ _let_1 A)) (@ _let_1 tptp.bot_bot_set_o)) A)))))
% 5.61/5.92 (assert (forall ((X tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (=> (not (@ (@ tptp.member_int X) A)) (= (@ (@ tptp.minus_minus_set_int (@ _let_1 A)) (@ _let_1 tptp.bot_bot_set_int)) A)))))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.insert5175938949040314269_nat_o X))) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) A)) (= (@ (@ tptp.minus_1801376950450012436_nat_o (@ _let_1 A)) (@ _let_1 tptp.bot_bo7824918357723582233_nat_o)) A)))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (=> (not (@ (@ tptp.member_nat X) A)) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 A)) (@ _let_1 tptp.bot_bot_set_nat)) A)))))
% 5.61/5.92 (assert (forall ((X tptp.product_unit) (X4 tptp.set_Product_unit)) (=> (not (@ (@ tptp.member_Product_unit X) X4)) (= (@ (@ tptp.minus_6452836326544984404t_unit X4) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)) X4))))
% 5.61/5.92 (assert (forall ((X Bool) (X4 tptp.set_o)) (=> (not (@ (@ tptp.member_o X) X4)) (= (@ (@ tptp.minus_minus_set_o X4) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)) X4))))
% 5.61/5.92 (assert (forall ((X tptp.int) (X4 tptp.set_int)) (=> (not (@ (@ tptp.member_int X) X4)) (= (@ (@ tptp.minus_minus_set_int X4) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)) X4))))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (X4 tptp.set_Pr4532377907799695533_nat_o)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) X4)) (= (@ (@ tptp.minus_1801376950450012436_nat_o X4) (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)) X4))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (X4 tptp.set_nat)) (=> (not (@ (@ tptp.member_nat X) X4)) (= (@ (@ tptp.minus_minus_set_nat X4) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)) X4))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (C5 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.minus_1801376950450012436_nat_o B4))) (let ((_let_2 (@ tptp.ord_le2965882846123202637_nat_o A))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o X) C5))) (and (@ _let_2 (@ _let_1 C5)) (not (@ (@ tptp.member6576561426505652726_nat_o X) A))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (B4 tptp.set_int) (X tptp.int) (C5 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int B4))) (let ((_let_2 (@ tptp.ord_less_eq_set_int A))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_int X) C5))) (and (@ _let_2 (@ _let_1 C5)) (not (@ (@ tptp.member_int X) A))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (B4 tptp.set_o) (X Bool) (C5 tptp.set_o)) (let ((_let_1 (@ tptp.minus_minus_set_o B4))) (let ((_let_2 (@ tptp.ord_less_eq_set_o A))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_o X) C5))) (and (@ _let_2 (@ _let_1 C5)) (not (@ (@ tptp.member_o X) A))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit) (X tptp.product_unit) (C5 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.minus_6452836326544984404t_unit B4))) (let ((_let_2 (@ tptp.ord_le3507040750410214029t_unit A))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_Product_unit X) C5))) (and (@ _let_2 (@ _let_1 C5)) (not (@ (@ tptp.member_Product_unit X) A))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (X tptp.nat) (C5 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat B4))) (let ((_let_2 (@ tptp.ord_less_eq_set_nat A))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_nat X) C5))) (and (@ _let_2 (@ _let_1 C5)) (not (@ (@ tptp.member_nat X) A))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (=> (= (@ (@ tptp.inf_in4660618365625256667t_unit A) B4) tptp.bot_bo3957492148770167129t_unit) (= (@ (@ tptp.minus_6452836326544984404t_unit A) B4) A))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (=> (= (@ (@ tptp.inf_inf_set_o A) B4) tptp.bot_bot_set_o) (= (@ (@ tptp.minus_minus_set_o A) B4) A))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (=> (= (@ (@ tptp.inf_inf_set_int A) B4) tptp.bot_bot_set_int) (= (@ (@ tptp.minus_minus_set_int A) B4) A))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (=> (= (@ (@ tptp.inf_in1906310914598751387_nat_o A) B4) tptp.bot_bo7824918357723582233_nat_o) (= (@ (@ tptp.minus_1801376950450012436_nat_o A) B4) A))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (= (@ (@ tptp.inf_inf_set_nat A) B4) tptp.bot_bot_set_nat) (= (@ (@ tptp.minus_minus_set_nat A) B4) A))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit (@ (@ tptp.inf_in4660618365625256667t_unit A) B4)) (@ (@ tptp.minus_6452836326544984404t_unit A) B4)) tptp.bot_bo3957492148770167129t_unit)))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.inf_inf_set_o A) B4)) (@ (@ tptp.minus_minus_set_o A) B4)) tptp.bot_bot_set_o)))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.inf_inf_set_int A) B4)) (@ (@ tptp.minus_minus_set_int A) B4)) tptp.bot_bot_set_int)))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ (@ tptp.inf_in1906310914598751387_nat_o A) B4)) (@ (@ tptp.minus_1801376950450012436_nat_o A) B4)) tptp.bot_bo7824918357723582233_nat_o)))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.inf_inf_set_nat A) B4)) (@ (@ tptp.minus_minus_set_nat A) B4)) tptp.bot_bot_set_nat)))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (= (= (@ (@ tptp.minus_6452836326544984404t_unit A) B4) A) (= (@ (@ tptp.inf_in4660618365625256667t_unit A) B4) tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (= (= (@ (@ tptp.minus_minus_set_o A) B4) A) (= (@ (@ tptp.inf_inf_set_o A) B4) tptp.bot_bot_set_o))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A) B4) A) (= (@ (@ tptp.inf_inf_set_int A) B4) tptp.bot_bot_set_int))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (= (= (@ (@ tptp.minus_1801376950450012436_nat_o A) B4) A) (= (@ (@ tptp.inf_in1906310914598751387_nat_o A) B4) tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A) B4) A) (= (@ (@ tptp.inf_inf_set_nat A) B4) tptp.bot_bot_set_nat))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (= (not (= (@ (@ tptp.minus_6452836326544984404t_unit A) B4) A)) (not (= (@ (@ tptp.inf_in4660618365625256667t_unit A) B4) tptp.bot_bo3957492148770167129t_unit)))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (= (not (= (@ (@ tptp.minus_minus_set_o A) B4) A)) (not (= (@ (@ tptp.inf_inf_set_o A) B4) tptp.bot_bot_set_o)))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (= (not (= (@ (@ tptp.minus_minus_set_int A) B4) A)) (not (= (@ (@ tptp.inf_inf_set_int A) B4) tptp.bot_bot_set_int)))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (= (not (= (@ (@ tptp.minus_1801376950450012436_nat_o A) B4) A)) (not (= (@ (@ tptp.inf_in1906310914598751387_nat_o A) B4) tptp.bot_bo7824918357723582233_nat_o)))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (not (= (@ (@ tptp.minus_minus_set_nat A) B4) A)) (not (= (@ (@ tptp.inf_inf_set_nat A) B4) tptp.bot_bot_set_nat)))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A) B4)) C5) (@ (@ tptp.ord_less_eq_set_nat A) (@ (@ tptp.sup_sup_set_nat B4) C5)))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (= (@ (@ tptp.sup_sup_set_nat A) (@ (@ tptp.minus_minus_set_nat B4) A)) B4))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.minus_minus_set_nat A) B4)) (@ (@ tptp.inf_inf_set_nat A) B4)) A)))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat A) B4)) (@ (@ tptp.minus_minus_set_nat A) B4)) A)))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B4) C5)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 B4)) (@ _let_1 C5))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat B4) C5)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 B4)) (@ _let_1 C5))))))
% 5.61/5.92 (assert (= tptp.range_9132311542094983838et_nat (@ tptp.image_6088997261112373647et_nat tptp.produc8586169260539613262et_nat)))
% 5.61/5.92 (assert (= tptp.range_int_int (@ tptp.image_5042161079198086560nt_int tptp.product_snd_int_int)))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr3948176798113811640et_nat)) (= (@ (@ tptp.image_6088997261112373647et_nat tptp.produc8586169260539613262et_nat) R3) (@ tptp.range_9132311542094983838et_nat R3))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.image_5042161079198086560nt_int tptp.product_snd_int_int) R3) (@ tptp.range_int_int R3))))
% 5.61/5.92 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer)) (X tptp.code_integer)) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (=> (forall ((Y2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Y2) A) (= (@ F Y2) (@ F X)))) (= (@ tptp.the_el4656377885804969768nteger (@ (@ tptp.image_4470545334726330049nteger F) A)) (@ F X))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.set_nat)) (X tptp.nat)) (=> (not (= A tptp.bot_bot_set_nat)) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) A) (= (@ F Y2) (@ F X)))) (= (@ tptp.the_elem_set_nat (@ (@ tptp.image_nat_set_nat F) A)) (@ F X))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat)) (X tptp.nat)) (=> (not (= A tptp.bot_bot_set_nat)) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) A) (= (@ F Y2) (@ F X)))) (= (@ tptp.the_elem_nat (@ (@ tptp.image_nat_nat2 F) A)) (@ F X))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.code_integer)) (X tptp.nat)) (=> (not (= A tptp.bot_bot_set_nat)) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) A) (= (@ F Y2) (@ F X)))) (= (@ tptp.the_el4656377885804969768nteger (@ (@ tptp.image_1215581382706833972nteger F) A)) (@ F X))))))
% 5.61/5.92 (assert (forall ((G tptp.set_Pr1261947904930325089at_nat)) (=> (not (@ tptp.transi3139058337892597825ic_nat G)) (not (forall ((X3 tptp.nat)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) X3)) (@ tptp.transi6264000038957366511cl_nat G))))))))
% 5.61/5.92 (assert (forall ((G tptp.set_Pr958786334691620121nt_int)) (=> (not (@ tptp.transi3136567867383547549ic_int G)) (not (forall ((X3 tptp.int)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) X3)) (@ tptp.transi6261509568448316235cl_int G))))))))
% 5.61/5.92 (assert (= tptp.transi3139058337892597825ic_nat (lambda ((R4 tptp.set_Pr1261947904930325089at_nat)) (forall ((X2 tptp.nat)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) X2)) (@ tptp.transi6264000038957366511cl_nat R4)))))))
% 5.61/5.92 (assert (= tptp.transi3136567867383547549ic_int (lambda ((R4 tptp.set_Pr958786334691620121nt_int)) (forall ((X2 tptp.int)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X2) X2)) (@ tptp.transi6261509568448316235cl_int R4)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.nat)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) X3)) (@ tptp.transi6264000038957366511cl_nat R2)))) (@ tptp.transi3139058337892597825ic_nat R2))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int)) (=> (forall ((X3 tptp.int)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) X3)) (@ tptp.transi6261509568448316235cl_int R2)))) (@ tptp.transi3136567867383547549ic_int R2))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr3286484037609594932et_nat) (B4 tptp.set_Pr3948176798113811640et_nat) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.ord_le8090042543978450200et_nat (@ (@ tptp.image_4390311411407041927et_nat tptp.produc4011572625026189258et_nat) A)) B4) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X) Y)) A) (@ (@ tptp.member6260224972018164377et_nat Y) B4)))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr8536935166611901872et_nat) (B4 tptp.set_Pr3286484037609594932et_nat) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3925858234332021118et_nat)) (=> (@ (@ tptp.ord_le5966269811547037844et_nat (@ (@ tptp.image_4557310310409863807et_nat tptp.produc5374455773327741254et_nat) A)) B4) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X) Y)) A) (@ (@ tptp.member1996754912294343701et_nat Y) B4)))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr3948176798113811640et_nat) (B4 tptp.set_set_nat) (X tptp.heap_e7401611519738050253t_unit) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.image_6088997261112373647et_nat tptp.produc8586169260539613262et_nat) A)) B4) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat X) Y)) A) (@ (@ tptp.member_set_nat Y) B4)))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (B4 tptp.set_int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_5042161079198086560nt_int tptp.product_snd_int_int) A)) B4) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) A) (@ (@ tptp.member_int Y) B4)))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_2486076414777270412at_nat tptp.product_snd_nat_nat) A)) B4) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) A) (@ (@ tptp.member_nat Y) B4)))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_5042161079198086560nt_int tptp.product_snd_int_int) R3)) (@ tptp.field_int R3))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_2486076414777270412at_nat tptp.product_snd_nat_nat) R3)) (@ tptp.field_nat R3))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr3948176798113811640et_nat) (B4 tptp.set_he8644174446132254637t_unit)) (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.image_3942343239045813184et_nat A) B4)) (@ (@ tptp.image_6088997261112373647et_nat tptp.produc8586169260539613262et_nat) A))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (B4 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int A) B4)) (@ (@ tptp.image_5042161079198086560nt_int tptp.product_snd_int_int) A))))
% 5.61/5.92 (assert (forall ((S tptp.set_Code_integer) (A2 tptp.code_integer)) (=> (not (@ tptp.finite6017078050557962740nteger S)) (not (@ tptp.finite6017078050557962740nteger (@ (@ tptp.minus_2355218937544613996nteger S) (@ (@ tptp.insert_Code_integer A2) tptp.bot_bo3990330152332043303nteger)))))))
% 5.61/5.92 (assert (forall ((S tptp.set_Product_unit) (A2 tptp.product_unit)) (=> (not (@ tptp.finite4290736615968046902t_unit S)) (not (@ tptp.finite4290736615968046902t_unit (@ (@ tptp.minus_6452836326544984404t_unit S) (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit)))))))
% 5.61/5.92 (assert (forall ((S tptp.set_o) (A2 Bool)) (=> (not (@ tptp.finite_finite_o S)) (not (@ tptp.finite_finite_o (@ (@ tptp.minus_minus_set_o S) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o)))))))
% 5.61/5.92 (assert (forall ((S tptp.set_int) (A2 tptp.int)) (=> (not (@ tptp.finite_finite_int S)) (not (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int S) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int)))))))
% 5.61/5.92 (assert (forall ((S tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (not (@ tptp.finite3252695134891459830_nat_o S)) (not (@ tptp.finite3252695134891459830_nat_o (@ (@ tptp.minus_1801376950450012436_nat_o S) (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o)))))))
% 5.61/5.92 (assert (forall ((S tptp.set_nat) (A2 tptp.nat)) (=> (not (@ tptp.finite_finite_nat S)) (not (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat S) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat)))))))
% 5.61/5.92 (assert (forall ((X4 (-> tptp.set_Code_integer Bool)) (A tptp.set_Code_integer)) (=> (@ X4 A) (=> (forall ((A9 tptp.set_Code_integer)) (=> (@ X4 A9) (exists ((X6 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.minus_2355218937544613996nteger A9) (@ (@ tptp.insert_Code_integer X6) tptp.bot_bo3990330152332043303nteger)))) (and (@ (@ tptp.member_Code_integer X6) A9) (or (@ X4 _let_1) (not (@ tptp.finite6017078050557962740nteger _let_1)))))))) (not (@ tptp.finite6017078050557962740nteger A))))))
% 5.61/5.92 (assert (forall ((X4 (-> tptp.set_Product_unit Bool)) (A tptp.set_Product_unit)) (=> (@ X4 A) (=> (forall ((A9 tptp.set_Product_unit)) (=> (@ X4 A9) (exists ((X6 tptp.product_unit)) (let ((_let_1 (@ (@ tptp.minus_6452836326544984404t_unit A9) (@ (@ tptp.insert_Product_unit X6) tptp.bot_bo3957492148770167129t_unit)))) (and (@ (@ tptp.member_Product_unit X6) A9) (or (@ X4 _let_1) (not (@ tptp.finite4290736615968046902t_unit _let_1)))))))) (not (@ tptp.finite4290736615968046902t_unit A))))))
% 5.61/5.92 (assert (forall ((X4 (-> tptp.set_o Bool)) (A tptp.set_o)) (=> (@ X4 A) (=> (forall ((A9 tptp.set_o)) (=> (@ X4 A9) (exists ((X6 Bool)) (let ((_let_1 (@ (@ tptp.minus_minus_set_o A9) (@ (@ tptp.insert_o X6) tptp.bot_bot_set_o)))) (and (@ (@ tptp.member_o X6) A9) (or (@ X4 _let_1) (not (@ tptp.finite_finite_o _let_1)))))))) (not (@ tptp.finite_finite_o A))))))
% 5.61/5.92 (assert (forall ((X4 (-> tptp.set_int Bool)) (A tptp.set_int)) (=> (@ X4 A) (=> (forall ((A9 tptp.set_int)) (=> (@ X4 A9) (exists ((X6 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A9) (@ (@ tptp.insert_int X6) tptp.bot_bot_set_int)))) (and (@ (@ tptp.member_int X6) A9) (or (@ X4 _let_1) (not (@ tptp.finite_finite_int _let_1)))))))) (not (@ tptp.finite_finite_int A))))))
% 5.61/5.92 (assert (forall ((X4 (-> tptp.set_Pr4532377907799695533_nat_o Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ X4 A) (=> (forall ((A9 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ X4 A9) (exists ((X6 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A9) (@ (@ tptp.insert5175938949040314269_nat_o X6) tptp.bot_bo7824918357723582233_nat_o)))) (and (@ (@ tptp.member6576561426505652726_nat_o X6) A9) (or (@ X4 _let_1) (not (@ tptp.finite3252695134891459830_nat_o _let_1)))))))) (not (@ tptp.finite3252695134891459830_nat_o A))))))
% 5.61/5.92 (assert (forall ((X4 (-> tptp.set_nat Bool)) (A tptp.set_nat)) (=> (@ X4 A) (=> (forall ((A9 tptp.set_nat)) (=> (@ X4 A9) (exists ((X6 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A9) (@ (@ tptp.insert_nat X6) tptp.bot_bot_set_nat)))) (and (@ (@ tptp.member_nat X6) A9) (or (@ X4 _let_1) (not (@ tptp.finite_finite_nat _let_1)))))))) (not (@ tptp.finite_finite_nat A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ P A) (=> (forall ((A4 tptp.code_integer) (A9 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A9) (=> (@ (@ tptp.member_Code_integer A4) A9) (=> (@ P A9) (@ P (@ (@ tptp.minus_2355218937544613996nteger A9) (@ (@ tptp.insert_Code_integer A4) tptp.bot_bo3990330152332043303nteger))))))) (@ P tptp.bot_bo3990330152332043303nteger))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (P (-> tptp.set_Product_unit Bool))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ P A) (=> (forall ((A4 tptp.product_unit) (A9 tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A9) (=> (@ (@ tptp.member_Product_unit A4) A9) (=> (@ P A9) (@ P (@ (@ tptp.minus_6452836326544984404t_unit A9) (@ (@ tptp.insert_Product_unit A4) tptp.bot_bo3957492148770167129t_unit))))))) (@ P tptp.bot_bo3957492148770167129t_unit))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o A) (=> (@ P A) (=> (forall ((A4 Bool) (A9 tptp.set_o)) (=> (@ tptp.finite_finite_o A9) (=> (@ (@ tptp.member_o A4) A9) (=> (@ P A9) (@ P (@ (@ tptp.minus_minus_set_o A9) (@ (@ tptp.insert_o A4) tptp.bot_bot_set_o))))))) (@ P tptp.bot_bot_set_o))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A) (=> (@ P A) (=> (forall ((A4 tptp.int) (A9 tptp.set_int)) (=> (@ tptp.finite_finite_int A9) (=> (@ (@ tptp.member_int A4) A9) (=> (@ P A9) (@ P (@ (@ tptp.minus_minus_set_int A9) (@ (@ tptp.insert_int A4) tptp.bot_bot_set_int))))))) (@ P tptp.bot_bot_set_int))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (P (-> tptp.set_Pr4532377907799695533_nat_o Bool))) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (@ P A) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (A9 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o A9) (=> (@ (@ tptp.member6576561426505652726_nat_o A4) A9) (=> (@ P A9) (@ P (@ (@ tptp.minus_1801376950450012436_nat_o A9) (@ (@ tptp.insert5175938949040314269_nat_o A4) tptp.bot_bo7824918357723582233_nat_o))))))) (@ P tptp.bot_bo7824918357723582233_nat_o))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A) (=> (@ P A) (=> (forall ((A4 tptp.nat) (A9 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A9) (=> (@ (@ tptp.member_nat A4) A9) (=> (@ P A9) (@ P (@ (@ tptp.minus_minus_set_nat A9) (@ (@ tptp.insert_nat A4) tptp.bot_bot_set_nat))))))) (@ P tptp.bot_bot_set_nat))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.ord_le3507040750410214029t_unit A))) (let ((_let_2 (@ (@ tptp.member_Product_unit X) A))) (let ((_let_3 (@ tptp.insert_Product_unit X))) (= (@ _let_1 (@ _let_3 B4)) (and (=> _let_2 (@ (@ tptp.ord_le3507040750410214029t_unit (@ (@ tptp.minus_6452836326544984404t_unit A) (@ _let_3 tptp.bot_bo3957492148770167129t_unit))) B4)) (=> (not _let_2) (@ _let_1 B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (X Bool) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.ord_less_eq_set_o A))) (let ((_let_2 (@ (@ tptp.member_o X) A))) (let ((_let_3 (@ tptp.insert_o X))) (= (@ _let_1 (@ _let_3 B4)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.minus_minus_set_o A) (@ _let_3 tptp.bot_bot_set_o))) B4)) (=> (not _let_2) (@ _let_1 B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (X tptp.int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (let ((_let_2 (@ (@ tptp.member_int X) A))) (let ((_let_3 (@ tptp.insert_int X))) (= (@ _let_1 (@ _let_3 B4)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A) (@ _let_3 tptp.bot_bot_set_int))) B4)) (=> (not _let_2) (@ _let_1 B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.ord_le2965882846123202637_nat_o A))) (let ((_let_2 (@ (@ tptp.member6576561426505652726_nat_o X) A))) (let ((_let_3 (@ tptp.insert5175938949040314269_nat_o X))) (= (@ _let_1 (@ _let_3 B4)) (and (=> _let_2 (@ (@ tptp.ord_le2965882846123202637_nat_o (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ _let_3 tptp.bot_bo7824918357723582233_nat_o))) B4)) (=> (not _let_2) (@ _let_1 B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (X tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (let ((_let_2 (@ (@ tptp.member_nat X) A))) (let ((_let_3 (@ tptp.insert_nat X))) (= (@ _let_1 (@ _let_3 B4)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A) (@ _let_3 tptp.bot_bot_set_nat))) B4)) (=> (not _let_2) (@ _let_1 B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit X))) (=> (@ (@ tptp.ord_le3507040750410214029t_unit (@ (@ tptp.minus_6452836326544984404t_unit A) (@ _let_1 tptp.bot_bo3957492148770167129t_unit))) B4) (@ (@ tptp.ord_le3507040750410214029t_unit A) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (X Bool) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X))) (=> (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.minus_minus_set_o A) (@ _let_1 tptp.bot_bot_set_o))) B4) (@ (@ tptp.ord_less_eq_set_o A) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (X tptp.int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A) (@ _let_1 tptp.bot_bot_set_int))) B4) (@ (@ tptp.ord_less_eq_set_int A) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.insert5175938949040314269_nat_o X))) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ _let_1 tptp.bot_bo7824918357723582233_nat_o))) B4) (@ (@ tptp.ord_le2965882846123202637_nat_o A) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (X tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A) (@ _let_1 tptp.bot_bot_set_nat))) B4) (@ (@ tptp.ord_less_eq_set_nat A) (@ _let_1 B4))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.field_nat (@ (@ tptp.rel_restrict_nat R3) A))) (@ (@ tptp.minus_minus_set_nat (@ tptp.field_nat R3)) A))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.domain_nat_nat (@ (@ tptp.rel_restrict_nat R3) A))) (@ (@ tptp.minus_minus_set_nat (@ tptp.domain_nat_nat R3)) A))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.range_nat_nat (@ (@ tptp.rel_restrict_nat R3) A))) (@ (@ tptp.minus_minus_set_nat (@ tptp.range_nat_nat R3)) A))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.set_nat)) (=> (@ tptp.finite6017078050557962740nteger (@ (@ tptp.image_1215581382706833972nteger F) A)) (=> (not (@ tptp.finite_finite_nat A)) (not (forall ((Y2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Y2) (@ (@ tptp.image_1215581382706833972nteger F) A)) (@ tptp.finite_finite_nat (@ (@ tptp.vimage6104394758324456170nteger F) (@ (@ tptp.insert_Code_integer Y2) tptp.bot_bo3990330152332043303nteger))))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger (@ (@ tptp.image_4470545334726330049nteger F) A)) (=> (not (@ tptp.finite6017078050557962740nteger A)) (not (forall ((Y2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Y2) (@ (@ tptp.image_4470545334726330049nteger F) A)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.vimage1318793397690208119nteger F) (@ (@ tptp.insert_Code_integer Y2) tptp.bot_bo3990330152332043303nteger))))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.product_unit)) (A tptp.set_nat)) (=> (@ tptp.finite4290736615968046902t_unit (@ (@ tptp.image_8730104196221521654t_unit F) A)) (=> (not (@ tptp.finite_finite_nat A)) (not (forall ((Y2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit Y2) (@ (@ tptp.image_8730104196221521654t_unit F) A)) (@ tptp.finite_finite_nat (@ (@ tptp.vimage4884490618288580032t_unit F) (@ (@ tptp.insert_Product_unit Y2) tptp.bot_bo3957492148770167129t_unit))))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.product_unit)) (A tptp.set_Code_integer)) (=> (@ tptp.finite4290736615968046902t_unit (@ (@ tptp.image_7182656606676592809t_unit F) A)) (=> (not (@ tptp.finite6017078050557962740nteger A)) (not (forall ((Y2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit Y2) (@ (@ tptp.image_7182656606676592809t_unit F) A)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.vimage5651688891684837235t_unit F) (@ (@ tptp.insert_Product_unit Y2) tptp.bot_bo3957492148770167129t_unit))))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat Bool)) (A tptp.set_nat)) (=> (@ tptp.finite_finite_o (@ (@ tptp.image_nat_o2 F) A)) (=> (not (@ tptp.finite_finite_nat A)) (not (forall ((Y2 Bool)) (=> (@ (@ tptp.member_o Y2) (@ (@ tptp.image_nat_o2 F) A)) (@ tptp.finite_finite_nat (@ (@ tptp.vimage_nat_o F) (@ (@ tptp.insert_o Y2) tptp.bot_bot_set_o))))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer Bool)) (A tptp.set_Code_integer)) (=> (@ tptp.finite_finite_o (@ (@ tptp.image_Code_integer_o F) A)) (=> (not (@ tptp.finite6017078050557962740nteger A)) (not (forall ((Y2 Bool)) (=> (@ (@ tptp.member_o Y2) (@ (@ tptp.image_Code_integer_o F) A)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.vimage3005800680117336574eger_o F) (@ (@ tptp.insert_o Y2) tptp.bot_bot_set_o))))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_nat2 F) A)) (=> (not (@ tptp.finite_finite_nat A)) (not (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) (@ (@ tptp.image_nat_nat2 F) A)) (@ tptp.finite_finite_nat (@ (@ tptp.vimage_nat_nat F) (@ (@ tptp.insert_nat Y2) tptp.bot_bot_set_nat))))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.nat)) (A tptp.set_Code_integer)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_951025933927791156er_nat F) A)) (=> (not (@ tptp.finite6017078050557962740nteger A)) (not (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) (@ (@ tptp.image_951025933927791156er_nat F) A)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.vimage5839839309545413354er_nat F) (@ (@ tptp.insert_nat Y2) tptp.bot_bot_set_nat))))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.set_nat)) (=> (@ tptp.finite_finite_int (@ (@ tptp.image_nat_int2 F) A)) (=> (not (@ tptp.finite_finite_nat A)) (not (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) (@ (@ tptp.image_nat_int2 F) A)) (@ tptp.finite_finite_nat (@ (@ tptp.vimage_nat_int F) (@ (@ tptp.insert_int Y2) tptp.bot_bot_set_int))))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.int)) (A tptp.set_Code_integer)) (=> (@ tptp.finite_finite_int (@ (@ tptp.image_948535463418740880er_int F) A)) (=> (not (@ tptp.finite6017078050557962740nteger A)) (not (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) (@ (@ tptp.image_948535463418740880er_int F) A)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.vimage5837348839036363078er_int F) (@ (@ tptp.insert_int Y2) tptp.bot_bot_set_int))))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.set_nat)) (=> (@ tptp.finite6017078050557962740nteger (@ (@ tptp.image_1215581382706833972nteger F) A)) (=> (not (@ tptp.finite_finite_nat A)) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.image_1215581382706833972nteger F) A)) (not (@ tptp.finite_finite_nat (@ (@ tptp.vimage6104394758324456170nteger F) (@ (@ tptp.insert_Code_integer X3) tptp.bot_bo3990330152332043303nteger))))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger (@ (@ tptp.image_4470545334726330049nteger F) A)) (=> (not (@ tptp.finite6017078050557962740nteger A)) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.image_4470545334726330049nteger F) A)) (not (@ tptp.finite6017078050557962740nteger (@ (@ tptp.vimage1318793397690208119nteger F) (@ (@ tptp.insert_Code_integer X3) tptp.bot_bo3990330152332043303nteger))))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.product_unit)) (A tptp.set_nat)) (=> (@ tptp.finite4290736615968046902t_unit (@ (@ tptp.image_8730104196221521654t_unit F) A)) (=> (not (@ tptp.finite_finite_nat A)) (exists ((X3 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X3) (@ (@ tptp.image_8730104196221521654t_unit F) A)) (not (@ tptp.finite_finite_nat (@ (@ tptp.vimage4884490618288580032t_unit F) (@ (@ tptp.insert_Product_unit X3) tptp.bot_bo3957492148770167129t_unit))))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.product_unit)) (A tptp.set_Code_integer)) (=> (@ tptp.finite4290736615968046902t_unit (@ (@ tptp.image_7182656606676592809t_unit F) A)) (=> (not (@ tptp.finite6017078050557962740nteger A)) (exists ((X3 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X3) (@ (@ tptp.image_7182656606676592809t_unit F) A)) (not (@ tptp.finite6017078050557962740nteger (@ (@ tptp.vimage5651688891684837235t_unit F) (@ (@ tptp.insert_Product_unit X3) tptp.bot_bo3957492148770167129t_unit))))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat Bool)) (A tptp.set_nat)) (=> (@ tptp.finite_finite_o (@ (@ tptp.image_nat_o2 F) A)) (=> (not (@ tptp.finite_finite_nat A)) (exists ((X3 Bool)) (and (@ (@ tptp.member_o X3) (@ (@ tptp.image_nat_o2 F) A)) (not (@ tptp.finite_finite_nat (@ (@ tptp.vimage_nat_o F) (@ (@ tptp.insert_o X3) tptp.bot_bot_set_o))))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer Bool)) (A tptp.set_Code_integer)) (=> (@ tptp.finite_finite_o (@ (@ tptp.image_Code_integer_o F) A)) (=> (not (@ tptp.finite6017078050557962740nteger A)) (exists ((X3 Bool)) (and (@ (@ tptp.member_o X3) (@ (@ tptp.image_Code_integer_o F) A)) (not (@ tptp.finite6017078050557962740nteger (@ (@ tptp.vimage3005800680117336574eger_o F) (@ (@ tptp.insert_o X3) tptp.bot_bot_set_o))))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_nat2 F) A)) (=> (not (@ tptp.finite_finite_nat A)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) (@ (@ tptp.image_nat_nat2 F) A)) (not (@ tptp.finite_finite_nat (@ (@ tptp.vimage_nat_nat F) (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat))))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.nat)) (A tptp.set_Code_integer)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_951025933927791156er_nat F) A)) (=> (not (@ tptp.finite6017078050557962740nteger A)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) (@ (@ tptp.image_951025933927791156er_nat F) A)) (not (@ tptp.finite6017078050557962740nteger (@ (@ tptp.vimage5839839309545413354er_nat F) (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat))))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.set_nat)) (=> (@ tptp.finite_finite_int (@ (@ tptp.image_nat_int2 F) A)) (=> (not (@ tptp.finite_finite_nat A)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.image_nat_int2 F) A)) (not (@ tptp.finite_finite_nat (@ (@ tptp.vimage_nat_int F) (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int))))))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.int)) (A tptp.set_Code_integer)) (=> (@ tptp.finite_finite_int (@ (@ tptp.image_948535463418740880er_int F) A)) (=> (not (@ tptp.finite6017078050557962740nteger A)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.image_948535463418740880er_int F) A)) (not (@ tptp.finite6017078050557962740nteger (@ (@ tptp.vimage5837348839036363078er_int F) (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int))))))))))
% 5.61/5.92 (assert (forall ((G tptp.set_Pr1261947904930325089at_nat) (X tptp.nat) (Y tptp.nat)) (=> (@ tptp.transi3139058337892597825ic_nat G) (=> (not (@ tptp.transi3139058337892597825ic_nat (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) G))) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y) X)) (@ tptp.transi2905341329935302413cl_nat G))))))
% 5.61/5.92 (assert (forall ((G tptp.set_Pr958786334691620121nt_int) (X tptp.int) (Y tptp.int)) (=> (@ tptp.transi3136567867383547549ic_int G) (=> (not (@ tptp.transi3136567867383547549ic_int (@ (@ tptp.insert5033312907999012233nt_int (@ (@ tptp.product_Pair_int_int X) Y)) G))) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y) X)) (@ tptp.transi2902850859426252137cl_int G))))))
% 5.61/5.92 (assert (forall ((H2 (-> tptp.set_nat tptp.set_nat)) (N tptp.set_set_nat)) (=> (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat)) (= (@ H2 (@ (@ tptp.inf_inf_set_nat X3) Y2)) (@ (@ tptp.inf_inf_set_nat (@ H2 X3)) (@ H2 Y2)))) (=> (@ tptp.finite1152437895449049373et_nat N) (=> (not (= N tptp.bot_bot_set_set_nat)) (= (@ H2 (@ tptp.lattic3014633134055518761et_nat N)) (@ tptp.lattic3014633134055518761et_nat (@ (@ tptp.image_7916887816326733075et_nat H2) N))))))))
% 5.61/5.92 (assert (forall ((H2 (-> tptp.assn tptp.assn)) (N tptp.set_assn)) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (= (@ H2 (@ (@ tptp.inf_inf_assn X3) Y2)) (@ (@ tptp.inf_inf_assn (@ H2 X3)) (@ H2 Y2)))) (=> (@ tptp.finite_finite_assn N) (=> (not (= N tptp.bot_bot_set_assn)) (= (@ H2 (@ tptp.lattic47131356835913163n_assn N)) (@ tptp.lattic47131356835913163n_assn (@ (@ tptp.image_assn_assn H2) N))))))))
% 5.61/5.92 (assert (forall ((H2 (-> tptp.product_unit tptp.product_unit)) (N tptp.set_Product_unit)) (=> (forall ((X3 tptp.product_unit) (Y2 tptp.product_unit)) (= (@ H2 (@ (@ tptp.inf_inf_Product_unit X3) Y2)) (@ (@ tptp.inf_inf_Product_unit (@ H2 X3)) (@ H2 Y2)))) (=> (@ tptp.finite4290736615968046902t_unit N) (=> (not (= N tptp.bot_bo3957492148770167129t_unit)) (= (@ H2 (@ tptp.lattic1263872656861969706t_unit N)) (@ tptp.lattic1263872656861969706t_unit (@ (@ tptp.image_405062704495631173t_unit H2) N))))))))
% 5.61/5.92 (assert (forall ((H2 (-> Bool Bool)) (N tptp.set_o)) (=> (forall ((X3 Bool) (Y2 Bool)) (= (@ H2 (@ (@ tptp.inf_inf_o X3) Y2)) (@ (@ tptp.inf_inf_o (@ H2 X3)) (@ H2 Y2)))) (=> (@ tptp.finite_finite_o N) (=> (not (= N tptp.bot_bot_set_o)) (= (@ H2 (@ tptp.lattic4107685809792843317_fin_o N)) (@ tptp.lattic4107685809792843317_fin_o (@ (@ tptp.image_o_o2 H2) N))))))))
% 5.61/5.92 (assert (forall ((H2 (-> tptp.nat tptp.nat)) (N tptp.set_nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (= (@ H2 (@ (@ tptp.inf_inf_nat X3) Y2)) (@ (@ tptp.inf_inf_nat (@ H2 X3)) (@ H2 Y2)))) (=> (@ tptp.finite_finite_nat N) (=> (not (= N tptp.bot_bot_set_nat)) (= (@ H2 (@ tptp.lattic5238388535129920115in_nat N)) (@ tptp.lattic5238388535129920115in_nat (@ (@ tptp.image_nat_nat2 H2) N))))))))
% 5.61/5.92 (assert (forall ((H2 (-> tptp.int tptp.int)) (N tptp.set_int)) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (= (@ H2 (@ (@ tptp.inf_inf_int X3) Y2)) (@ (@ tptp.inf_inf_int (@ H2 X3)) (@ H2 Y2)))) (=> (@ tptp.finite_finite_int N) (=> (not (= N tptp.bot_bot_set_int)) (= (@ H2 (@ tptp.lattic5235898064620869839in_int N)) (@ tptp.lattic5235898064620869839in_int (@ (@ tptp.image_int_int2 H2) N))))))))
% 5.61/5.92 (assert (forall ((H2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool)) (N tptp.set_Pr4532377907799695533_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (= (@ H2 (@ (@ tptp.inf_in1318976480646536635_nat_o X3) Y2)) (@ (@ tptp.inf_in1318976480646536635_nat_o (@ H2 X3)) (@ H2 Y2)))) (=> (@ tptp.finite3252695134891459830_nat_o N) (=> (not (= N tptp.bot_bo7824918357723582233_nat_o)) (= (@ H2 (@ tptp.lattic956194824204696298_nat_o N)) (@ tptp.lattic956194824204696298_nat_o (@ (@ tptp.image_3399141053782081349_nat_o H2) N))))))))
% 5.61/5.92 (assert (forall ((H2 (-> tptp.set_nat tptp.set_nat)) (N tptp.set_set_nat)) (=> (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat)) (= (@ H2 (@ (@ tptp.sup_sup_set_nat X3) Y2)) (@ (@ tptp.sup_sup_set_nat (@ H2 X3)) (@ H2 Y2)))) (=> (@ tptp.finite1152437895449049373et_nat N) (=> (not (= N tptp.bot_bot_set_set_nat)) (= (@ H2 (@ tptp.lattic3835124923745554447et_nat N)) (@ tptp.lattic3835124923745554447et_nat (@ (@ tptp.image_7916887816326733075et_nat H2) N))))))))
% 5.61/5.92 (assert (forall ((H2 (-> tptp.assn tptp.assn)) (N tptp.set_assn)) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (= (@ H2 (@ (@ tptp.sup_sup_assn X3) Y2)) (@ (@ tptp.sup_sup_assn (@ H2 X3)) (@ H2 Y2)))) (=> (@ tptp.finite_finite_assn N) (=> (not (= N tptp.bot_bot_set_assn)) (= (@ H2 (@ tptp.lattic2150320897289308081n_assn N)) (@ tptp.lattic2150320897289308081n_assn (@ (@ tptp.image_assn_assn H2) N))))))))
% 5.61/5.92 (assert (forall ((H2 (-> tptp.product_unit tptp.product_unit)) (N tptp.set_Product_unit)) (=> (forall ((X3 tptp.product_unit) (Y2 tptp.product_unit)) (= (@ H2 (@ (@ tptp.sup_sup_Product_unit X3) Y2)) (@ (@ tptp.sup_sup_Product_unit (@ H2 X3)) (@ H2 Y2)))) (=> (@ tptp.finite4290736615968046902t_unit N) (=> (not (= N tptp.bot_bo3957492148770167129t_unit)) (= (@ H2 (@ tptp.lattic5294303975357428420t_unit N)) (@ tptp.lattic5294303975357428420t_unit (@ (@ tptp.image_405062704495631173t_unit H2) N))))))))
% 5.61/5.92 (assert (forall ((H2 (-> Bool Bool)) (N tptp.set_o)) (=> (forall ((X3 Bool) (Y2 Bool)) (= (@ H2 (@ (@ tptp.sup_sup_o X3) Y2)) (@ (@ tptp.sup_sup_o (@ H2 X3)) (@ H2 Y2)))) (=> (@ tptp.finite_finite_o N) (=> (not (= N tptp.bot_bot_set_o)) (= (@ H2 (@ tptp.lattic1508158080041050831_fin_o N)) (@ tptp.lattic1508158080041050831_fin_o (@ (@ tptp.image_o_o2 H2) N))))))))
% 5.61/5.92 (assert (forall ((H2 (-> tptp.nat tptp.nat)) (N tptp.set_nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (= (@ H2 (@ (@ tptp.sup_sup_nat X3) Y2)) (@ (@ tptp.sup_sup_nat (@ H2 X3)) (@ H2 Y2)))) (=> (@ tptp.finite_finite_nat N) (=> (not (= N tptp.bot_bot_set_nat)) (= (@ H2 (@ tptp.lattic1093996805478795353in_nat N)) (@ tptp.lattic1093996805478795353in_nat (@ (@ tptp.image_nat_nat2 H2) N))))))))
% 5.61/5.92 (assert (forall ((H2 (-> tptp.int tptp.int)) (N tptp.set_int)) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (= (@ H2 (@ (@ tptp.sup_sup_int X3) Y2)) (@ (@ tptp.sup_sup_int (@ H2 X3)) (@ H2 Y2)))) (=> (@ tptp.finite_finite_int N) (=> (not (= N tptp.bot_bot_set_int)) (= (@ H2 (@ tptp.lattic1091506334969745077in_int N)) (@ tptp.lattic1091506334969745077in_int (@ (@ tptp.image_int_int2 H2) N))))))))
% 5.61/5.92 (assert (forall ((H2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool)) (N tptp.set_Pr4532377907799695533_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (= (@ H2 (@ (@ tptp.sup_su5453871518329203617_nat_o X3) Y2)) (@ (@ tptp.sup_su5453871518329203617_nat_o (@ H2 X3)) (@ H2 Y2)))) (=> (@ tptp.finite3252695134891459830_nat_o N) (=> (not (= N tptp.bot_bo7824918357723582233_nat_o)) (= (@ H2 (@ tptp.lattic7320199455484906628_nat_o N)) (@ tptp.lattic7320199455484906628_nat_o (@ (@ tptp.image_3399141053782081349_nat_o H2) N))))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger B4) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (forall ((A9 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A9) (=> (not (= A9 tptp.bot_bo3990330152332043303nteger)) (=> (@ (@ tptp.ord_le7084787975880047091nteger A9) B4) (=> (forall ((X6 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X6) A9) (@ P (@ (@ tptp.minus_2355218937544613996nteger A9) (@ (@ tptp.insert_Code_integer X6) tptp.bot_bo3990330152332043303nteger))))) (@ P A9)))))) (@ P B4))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_Product_unit) (P (-> tptp.set_Product_unit Bool))) (=> (@ tptp.finite4290736615968046902t_unit B4) (=> (@ P tptp.bot_bo3957492148770167129t_unit) (=> (forall ((A9 tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A9) (=> (not (= A9 tptp.bot_bo3957492148770167129t_unit)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A9) B4) (=> (forall ((X6 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X6) A9) (@ P (@ (@ tptp.minus_6452836326544984404t_unit A9) (@ (@ tptp.insert_Product_unit X6) tptp.bot_bo3957492148770167129t_unit))))) (@ P A9)))))) (@ P B4))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o B4) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((A9 tptp.set_o)) (=> (@ tptp.finite_finite_o A9) (=> (not (= A9 tptp.bot_bot_set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A9) B4) (=> (forall ((X6 Bool)) (=> (@ (@ tptp.member_o X6) A9) (@ P (@ (@ tptp.minus_minus_set_o A9) (@ (@ tptp.insert_o X6) tptp.bot_bot_set_o))))) (@ P A9)))))) (@ P B4))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int B4) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A9 tptp.set_int)) (=> (@ tptp.finite_finite_int A9) (=> (not (= A9 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A9) B4) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A9) (@ P (@ (@ tptp.minus_minus_set_int A9) (@ (@ tptp.insert_int X6) tptp.bot_bot_set_int))))) (@ P A9)))))) (@ P B4))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_Pr4532377907799695533_nat_o) (P (-> tptp.set_Pr4532377907799695533_nat_o Bool))) (=> (@ tptp.finite3252695134891459830_nat_o B4) (=> (@ P tptp.bot_bo7824918357723582233_nat_o) (=> (forall ((A9 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o A9) (=> (not (= A9 tptp.bot_bo7824918357723582233_nat_o)) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A9) B4) (=> (forall ((X6 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X6) A9) (@ P (@ (@ tptp.minus_1801376950450012436_nat_o A9) (@ (@ tptp.insert5175938949040314269_nat_o X6) tptp.bot_bo7824918357723582233_nat_o))))) (@ P A9)))))) (@ P B4))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat B4) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A9 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A9) (=> (not (= A9 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A9) B4) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A9) (@ P (@ (@ tptp.minus_minus_set_nat A9) (@ (@ tptp.insert_nat X6) tptp.bot_bot_set_nat))))) (@ P A9)))))) (@ P B4))))))
% 5.61/5.92 (assert (forall ((P (-> tptp.set_Code_integer Bool)) (B4 tptp.set_Code_integer)) (let ((_let_1 (@ P B4))) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (=> (not (@ tptp.finite6017078050557962740nteger B4)) _let_1) (=> (forall ((A9 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A9) (=> (not (= A9 tptp.bot_bo3990330152332043303nteger)) (=> (@ (@ tptp.ord_le7084787975880047091nteger A9) B4) (=> (forall ((X6 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X6) A9) (@ P (@ (@ tptp.minus_2355218937544613996nteger A9) (@ (@ tptp.insert_Code_integer X6) tptp.bot_bo3990330152332043303nteger))))) (@ P A9)))))) _let_1))))))
% 5.61/5.92 (assert (forall ((P (-> tptp.set_Product_unit Bool)) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ P B4))) (=> (@ P tptp.bot_bo3957492148770167129t_unit) (=> (=> (not (@ tptp.finite4290736615968046902t_unit B4)) _let_1) (=> (forall ((A9 tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A9) (=> (not (= A9 tptp.bot_bo3957492148770167129t_unit)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A9) B4) (=> (forall ((X6 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X6) A9) (@ P (@ (@ tptp.minus_6452836326544984404t_unit A9) (@ (@ tptp.insert_Product_unit X6) tptp.bot_bo3957492148770167129t_unit))))) (@ P A9)))))) _let_1))))))
% 5.61/5.92 (assert (forall ((P (-> tptp.set_o Bool)) (B4 tptp.set_o)) (let ((_let_1 (@ P B4))) (=> (@ P tptp.bot_bot_set_o) (=> (=> (not (@ tptp.finite_finite_o B4)) _let_1) (=> (forall ((A9 tptp.set_o)) (=> (@ tptp.finite_finite_o A9) (=> (not (= A9 tptp.bot_bot_set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A9) B4) (=> (forall ((X6 Bool)) (=> (@ (@ tptp.member_o X6) A9) (@ P (@ (@ tptp.minus_minus_set_o A9) (@ (@ tptp.insert_o X6) tptp.bot_bot_set_o))))) (@ P A9)))))) _let_1))))))
% 5.61/5.92 (assert (forall ((P (-> tptp.set_int Bool)) (B4 tptp.set_int)) (let ((_let_1 (@ P B4))) (=> (@ P tptp.bot_bot_set_int) (=> (=> (not (@ tptp.finite_finite_int B4)) _let_1) (=> (forall ((A9 tptp.set_int)) (=> (@ tptp.finite_finite_int A9) (=> (not (= A9 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A9) B4) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A9) (@ P (@ (@ tptp.minus_minus_set_int A9) (@ (@ tptp.insert_int X6) tptp.bot_bot_set_int))))) (@ P A9)))))) _let_1))))))
% 5.61/5.92 (assert (forall ((P (-> tptp.set_Pr4532377907799695533_nat_o Bool)) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ P B4))) (=> (@ P tptp.bot_bo7824918357723582233_nat_o) (=> (=> (not (@ tptp.finite3252695134891459830_nat_o B4)) _let_1) (=> (forall ((A9 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o A9) (=> (not (= A9 tptp.bot_bo7824918357723582233_nat_o)) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A9) B4) (=> (forall ((X6 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X6) A9) (@ P (@ (@ tptp.minus_1801376950450012436_nat_o A9) (@ (@ tptp.insert5175938949040314269_nat_o X6) tptp.bot_bo7824918357723582233_nat_o))))) (@ P A9)))))) _let_1))))))
% 5.61/5.92 (assert (forall ((P (-> tptp.set_nat Bool)) (B4 tptp.set_nat)) (let ((_let_1 (@ P B4))) (=> (@ P tptp.bot_bot_set_nat) (=> (=> (not (@ tptp.finite_finite_nat B4)) _let_1) (=> (forall ((A9 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A9) (=> (not (= A9 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A9) B4) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A9) (@ P (@ (@ tptp.minus_minus_set_nat A9) (@ (@ tptp.insert_nat X6) tptp.bot_bot_set_nat))))) (@ P A9)))))) _let_1))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.field_81821745747897882_nat_o R2))) (=> (@ (@ tptp.order_1145710701291701250_nat_o _let_1) R2) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) _let_1) (=> (@ (@ tptp.member6576561426505652726_nat_o B) _let_1) (= (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) B)) R2) (not (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o B) A2)) (@ (@ tptp.minus_9189903262233110958_nat_o R2) tptp.id_Pro6775173067513470761_nat_o))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (A2 Bool) (B Bool)) (let ((_let_1 (@ tptp.field_o R2))) (=> (@ (@ tptp.order_6238756238976269133r_on_o _let_1) R2) (=> (@ (@ tptp.member_o A2) _let_1) (=> (@ (@ tptp.member_o B) _let_1) (= (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) B)) R2) (not (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o B) A2)) (@ (@ tptp.minus_7052513330764642158od_o_o R2) tptp.id_o2))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (@ tptp.field_Product_unit R2))) (=> (@ (@ tptp.order_888282469287196226t_unit _let_1) R2) (=> (@ (@ tptp.member_Product_unit A2) _let_1) (=> (@ (@ tptp.member_Product_unit B) _let_1) (= (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit A2) B)) R2) (not (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit B) A2)) (@ (@ tptp.minus_6985556733573110190t_unit R2) tptp.id_Product_unit))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.field_nat R2))) (=> (@ (@ tptp.order_4473980167227706203on_nat _let_1) R2) (=> (@ (@ tptp.member_nat A2) _let_1) (=> (@ (@ tptp.member_nat B) _let_1) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R2) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) A2)) (@ (@ tptp.minus_1356011639430497352at_nat R2) tptp.id_nat))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.field_int R2))) (=> (@ (@ tptp.order_4471489696718655927on_int _let_1) R2) (=> (@ (@ tptp.member_int A2) _let_1) (=> (@ (@ tptp.member_int B) _let_1) (= (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R2) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) A2)) (@ (@ tptp.minus_1052850069191792384nt_int R2) tptp.id_int))))))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_Code_integer) (Y6 tptp.set_Code_integer) (R3 tptp.set_Pr4811707699266497531nteger)) (=> (@ tptp.finite6017078050557962740nteger X4) (=> (@ tptp.finite6017078050557962740nteger Y6) (=> (not (= Y6 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) X4) (exists ((Xa2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa2) Y6) (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger X3) Xa2)) R3))))) (@ (@ tptp.member4307123515891402160nteger (@ (@ tptp.produc7443773368509356479nteger X4) Y6)) (@ tptp.max_ext_Code_integer R3))))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_Product_unit) (Y6 tptp.set_Product_unit) (R3 tptp.set_Pr5094982260447487303t_unit)) (=> (@ tptp.finite4290736615968046902t_unit X4) (=> (@ tptp.finite4290736615968046902t_unit Y6) (=> (not (= Y6 tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) X4) (exists ((Xa2 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit Xa2) Y6) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit X3) Xa2)) R3))))) (@ (@ tptp.member4189953012975926160t_unit (@ (@ tptp.produc7269801343787132631t_unit X4) Y6)) (@ tptp.max_ext_Product_unit R3))))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_o) (Y6 tptp.set_o) (R3 tptp.set_Product_prod_o_o)) (=> (@ tptp.finite_finite_o X4) (=> (@ tptp.finite_finite_o Y6) (=> (not (= Y6 tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) X4) (exists ((Xa2 Bool)) (and (@ (@ tptp.member_o Xa2) Y6) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X3) Xa2)) R3))))) (@ (@ tptp.member9116954335612470352_set_o (@ (@ tptp.produc5838405689764958487_set_o X4) Y6)) (@ tptp.max_ext_o R3))))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_nat) (Y6 tptp.set_nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite_finite_nat X4) (=> (@ tptp.finite_finite_nat Y6) (=> (not (= Y6 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) X4) (exists ((Xa2 tptp.nat)) (and (@ (@ tptp.member_nat Xa2) Y6) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Xa2)) R3))))) (@ (@ tptp.member8277197624267554838et_nat (@ (@ tptp.produc4532415448927165861et_nat X4) Y6)) (@ tptp.max_ext_nat R3))))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_int) (Y6 tptp.set_int) (R3 tptp.set_Pr958786334691620121nt_int)) (=> (@ tptp.finite_finite_int X4) (=> (@ tptp.finite_finite_int Y6) (=> (not (= Y6 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) X4) (exists ((Xa2 tptp.int)) (and (@ (@ tptp.member_int Xa2) Y6) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Xa2)) R3))))) (@ (@ tptp.member2572552093476627150et_int (@ (@ tptp.produc6363374080413544029et_int X4) Y6)) (@ tptp.max_ext_int R3))))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_Pr4532377907799695533_nat_o) (Y6 tptp.set_Pr4532377907799695533_nat_o) (R3 tptp.set_Pr2161125870931222855_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o X4) (=> (@ tptp.finite3252695134891459830_nat_o Y6) (=> (not (= Y6 tptp.bot_bo7824918357723582233_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) X4) (exists ((Xa2 (-> tptp.produc3658429121746597890et_nat Bool))) (and (@ (@ tptp.member6576561426505652726_nat_o Xa2) Y6) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X3) Xa2)) R3))))) (@ (@ tptp.member6623172407746373520_nat_o (@ (@ tptp.produc5149316574908490455_nat_o X4) Y6)) (@ tptp.max_ex5265246208886859912_nat_o R3))))))))
% 5.61/5.92 (assert (forall ((A1 tptp.set_Code_integer) (A22 tptp.set_Code_integer) (R3 tptp.set_Pr4811707699266497531nteger)) (= (@ (@ tptp.member4307123515891402160nteger (@ (@ tptp.produc7443773368509356479nteger A1) A22)) (@ tptp.max_ext_Code_integer R3)) (and (@ tptp.finite6017078050557962740nteger A1) (@ tptp.finite6017078050557962740nteger A22) (not (= A22 tptp.bot_bo3990330152332043303nteger)) (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X2) A1) (exists ((Y3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Y3) A22) (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger X2) Y3)) R3)))))))))
% 5.61/5.92 (assert (forall ((A1 tptp.set_Product_unit) (A22 tptp.set_Product_unit) (R3 tptp.set_Pr5094982260447487303t_unit)) (= (@ (@ tptp.member4189953012975926160t_unit (@ (@ tptp.produc7269801343787132631t_unit A1) A22)) (@ tptp.max_ext_Product_unit R3)) (and (@ tptp.finite4290736615968046902t_unit A1) (@ tptp.finite4290736615968046902t_unit A22) (not (= A22 tptp.bot_bo3957492148770167129t_unit)) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) A1) (exists ((Y3 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit Y3) A22) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit X2) Y3)) R3)))))))))
% 5.61/5.92 (assert (forall ((A1 tptp.set_o) (A22 tptp.set_o) (R3 tptp.set_Product_prod_o_o)) (= (@ (@ tptp.member9116954335612470352_set_o (@ (@ tptp.produc5838405689764958487_set_o A1) A22)) (@ tptp.max_ext_o R3)) (and (@ tptp.finite_finite_o A1) (@ tptp.finite_finite_o A22) (not (= A22 tptp.bot_bot_set_o)) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A1) (exists ((Y3 Bool)) (and (@ (@ tptp.member_o Y3) A22) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X2) Y3)) R3)))))))))
% 5.61/5.92 (assert (forall ((A1 tptp.set_nat) (A22 tptp.set_nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member8277197624267554838et_nat (@ (@ tptp.produc4532415448927165861et_nat A1) A22)) (@ tptp.max_ext_nat R3)) (and (@ tptp.finite_finite_nat A1) (@ tptp.finite_finite_nat A22) (not (= A22 tptp.bot_bot_set_nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A1) (exists ((Y3 tptp.nat)) (and (@ (@ tptp.member_nat Y3) A22) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y3)) R3)))))))))
% 5.61/5.92 (assert (forall ((A1 tptp.set_int) (A22 tptp.set_int) (R3 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member2572552093476627150et_int (@ (@ tptp.produc6363374080413544029et_int A1) A22)) (@ tptp.max_ext_int R3)) (and (@ tptp.finite_finite_int A1) (@ tptp.finite_finite_int A22) (not (= A22 tptp.bot_bot_set_int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A1) (exists ((Y3 tptp.int)) (and (@ (@ tptp.member_int Y3) A22) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X2) Y3)) R3)))))))))
% 5.61/5.92 (assert (forall ((A1 tptp.set_Pr4532377907799695533_nat_o) (A22 tptp.set_Pr4532377907799695533_nat_o) (R3 tptp.set_Pr2161125870931222855_nat_o)) (= (@ (@ tptp.member6623172407746373520_nat_o (@ (@ tptp.produc5149316574908490455_nat_o A1) A22)) (@ tptp.max_ex5265246208886859912_nat_o R3)) (and (@ tptp.finite3252695134891459830_nat_o A1) (@ tptp.finite3252695134891459830_nat_o A22) (not (= A22 tptp.bot_bo7824918357723582233_nat_o)) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X2) A1) (exists ((Y3 (-> tptp.produc3658429121746597890et_nat Bool))) (and (@ (@ tptp.member6576561426505652726_nat_o Y3) A22) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X2) Y3)) R3)))))))))
% 5.61/5.92 (assert (forall ((A1 tptp.set_Code_integer) (A22 tptp.set_Code_integer) (R3 tptp.set_Pr4811707699266497531nteger)) (=> (@ (@ tptp.member4307123515891402160nteger (@ (@ tptp.produc7443773368509356479nteger A1) A22)) (@ tptp.max_ext_Code_integer R3)) (not (=> (@ tptp.finite6017078050557962740nteger A1) (=> (@ tptp.finite6017078050557962740nteger A22) (=> (not (= A22 tptp.bot_bo3990330152332043303nteger)) (not (forall ((X6 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X6) A1) (exists ((Xa3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa3) A22) (@ (@ tptp.member157494554546826820nteger (@ (@ tptp.produc1086072967326762835nteger X6) Xa3)) R3)))))))))))))
% 5.61/5.92 (assert (forall ((A1 tptp.set_Product_unit) (A22 tptp.set_Product_unit) (R3 tptp.set_Pr5094982260447487303t_unit)) (=> (@ (@ tptp.member4189953012975926160t_unit (@ (@ tptp.produc7269801343787132631t_unit A1) A22)) (@ tptp.max_ext_Product_unit R3)) (not (=> (@ tptp.finite4290736615968046902t_unit A1) (=> (@ tptp.finite4290736615968046902t_unit A22) (=> (not (= A22 tptp.bot_bo3957492148770167129t_unit)) (not (forall ((X6 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X6) A1) (exists ((Xa3 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit Xa3) A22) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit X6) Xa3)) R3)))))))))))))
% 5.61/5.92 (assert (forall ((A1 tptp.set_o) (A22 tptp.set_o) (R3 tptp.set_Product_prod_o_o)) (=> (@ (@ tptp.member9116954335612470352_set_o (@ (@ tptp.produc5838405689764958487_set_o A1) A22)) (@ tptp.max_ext_o R3)) (not (=> (@ tptp.finite_finite_o A1) (=> (@ tptp.finite_finite_o A22) (=> (not (= A22 tptp.bot_bot_set_o)) (not (forall ((X6 Bool)) (=> (@ (@ tptp.member_o X6) A1) (exists ((Xa3 Bool)) (and (@ (@ tptp.member_o Xa3) A22) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X6) Xa3)) R3)))))))))))))
% 5.61/5.92 (assert (forall ((A1 tptp.set_nat) (A22 tptp.set_nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8277197624267554838et_nat (@ (@ tptp.produc4532415448927165861et_nat A1) A22)) (@ tptp.max_ext_nat R3)) (not (=> (@ tptp.finite_finite_nat A1) (=> (@ tptp.finite_finite_nat A22) (=> (not (= A22 tptp.bot_bot_set_nat)) (not (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A1) (exists ((Xa3 tptp.nat)) (and (@ (@ tptp.member_nat Xa3) A22) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X6) Xa3)) R3)))))))))))))
% 5.61/5.92 (assert (forall ((A1 tptp.set_int) (A22 tptp.set_int) (R3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member2572552093476627150et_int (@ (@ tptp.produc6363374080413544029et_int A1) A22)) (@ tptp.max_ext_int R3)) (not (=> (@ tptp.finite_finite_int A1) (=> (@ tptp.finite_finite_int A22) (=> (not (= A22 tptp.bot_bot_set_int)) (not (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A1) (exists ((Xa3 tptp.int)) (and (@ (@ tptp.member_int Xa3) A22) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X6) Xa3)) R3)))))))))))))
% 5.61/5.92 (assert (forall ((A1 tptp.set_Pr4532377907799695533_nat_o) (A22 tptp.set_Pr4532377907799695533_nat_o) (R3 tptp.set_Pr2161125870931222855_nat_o)) (=> (@ (@ tptp.member6623172407746373520_nat_o (@ (@ tptp.produc5149316574908490455_nat_o A1) A22)) (@ tptp.max_ex5265246208886859912_nat_o R3)) (not (=> (@ tptp.finite3252695134891459830_nat_o A1) (=> (@ tptp.finite3252695134891459830_nat_o A22) (=> (not (= A22 tptp.bot_bo7824918357723582233_nat_o)) (not (forall ((X6 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X6) A1) (exists ((Xa3 (-> tptp.produc3658429121746597890et_nat Bool))) (and (@ (@ tptp.member6576561426505652726_nat_o Xa3) A22) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X6) Xa3)) R3)))))))))))))
% 5.61/5.92 (assert (forall ((P (-> tptp.rat Bool)) (D3 tptp.rat) (Q2 (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D3))))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ Q2 X3) (@ Q2 (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D3))))) (forall ((X6 tptp.rat) (K2 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X6) (@ (@ tptp.times_times_rat K2) D3)))) (= (or (@ P X6) (@ Q2 X6)) (or (@ P _let_1) (@ Q2 _let_1)))))))))
% 5.61/5.92 (assert (forall ((P (-> tptp.int Bool)) (D3 tptp.int) (Q2 (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D3))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ Q2 X3) (@ Q2 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D3))))) (forall ((X6 tptp.int) (K2 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K2) D3)))) (= (or (@ P X6) (@ Q2 X6)) (or (@ P _let_1) (@ Q2 _let_1)))))))))
% 5.61/5.92 (assert (forall ((P (-> tptp.rat Bool)) (D3 tptp.rat) (Q2 (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D3))))) (=> (forall ((X3 tptp.rat) (K tptp.rat)) (= (@ Q2 X3) (@ Q2 (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K) D3))))) (forall ((X6 tptp.rat) (K2 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X6) (@ (@ tptp.times_times_rat K2) D3)))) (= (and (@ P X6) (@ Q2 X6)) (and (@ P _let_1) (@ Q2 _let_1)))))))))
% 5.61/5.92 (assert (forall ((P (-> tptp.int Bool)) (D3 tptp.int) (Q2 (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D3))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ Q2 X3) (@ Q2 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D3))))) (forall ((X6 tptp.int) (K2 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K2) D3)))) (= (and (@ P X6) (@ Q2 X6)) (and (@ P _let_1) (@ Q2 _let_1)))))))))
% 5.61/5.92 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A2) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B) C)))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A2) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B) C)))))
% 5.61/5.92 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 5.61/5.92 (assert (forall ((B tptp.rat) (C tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) C)) A2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat B) A2)) (@ (@ tptp.times_times_rat C) A2)))))
% 5.61/5.92 (assert (forall ((B tptp.nat) (C tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat B) C)) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat B) A2)) (@ (@ tptp.times_times_nat C) A2)))))
% 5.61/5.92 (assert (forall ((B tptp.int) (C tptp.int) (A2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) C)) A2) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int B) A2)) (@ (@ tptp.times_times_int C) A2)))))
% 5.61/5.92 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) C)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (B tptp.int) (A5 tptp.nat) (B3 tptp.int) (R2 tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member4619661753630440592at_int (@ (@ tptp.produc886916002739626967at_int (@ (@ tptp.product_Pair_nat_int A2) B)) (@ (@ tptp.product_Pair_nat_int A5) B3))) (@ (@ tptp.lex_prod_nat_int R2) S2)) (or (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) A5)) R2) (and (= A2 A5) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) B3)) S2))))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (B tptp.nat) (A5 tptp.int) (B3 tptp.nat) (R2 tptp.set_Pr958786334691620121nt_int) (S2 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member2930414080797523088nt_nat (@ (@ tptp.produc8921240378546987991nt_nat (@ (@ tptp.product_Pair_int_nat A2) B)) (@ (@ tptp.product_Pair_int_nat A5) B3))) (@ (@ tptp.lex_prod_int_nat R2) S2)) (or (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) A5)) R2) (and (= A2 A5) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) B3)) S2))))))
% 5.61/5.92 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat) (A5 tptp.heap_e7401611519738050253t_unit) (B3 tptp.set_nat) (R2 tptp.set_Pr1776176089890104647t_unit) (S2 tptp.set_Pr5488025237498180813et_nat)) (= (@ (@ tptp.member6099555550032318734et_nat (@ (@ tptp.produc8199053930788261021et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) B)) (@ (@ tptp.produc7507926704131184380et_nat A5) B3))) (@ (@ tptp.lex_pr538634069021852900et_nat R2) S2)) (or (@ (@ tptp.member5046970461208427408t_unit (@ (@ tptp.produc8256076736985659095t_unit A2) A5)) R2) (and (= A2 A5) (@ (@ tptp.member8277197624267554838et_nat (@ (@ tptp.produc4532415448927165861et_nat B) B3)) S2))))))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (B tptp.nat) (A5 tptp.nat) (B3 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat A2))) (= (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ _let_1 B)) (@ (@ tptp.product_Pair_nat_nat A5) B3))) (@ (@ tptp.lex_prod_nat_nat R2) S2)) (or (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 A5)) R2) (and (= A2 A5) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) B3)) S2)))))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (B tptp.int) (A5 tptp.int) (B3 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (S2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.product_Pair_int_int A2))) (= (@ (@ tptp.member8566619992076573584nt_int (@ (@ tptp.produc3646306378393792727nt_int (@ _let_1 B)) (@ (@ tptp.product_Pair_int_int A5) B3))) (@ (@ tptp.lex_prod_int_int R2) S2)) (or (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 A5)) R2) (and (= A2 A5) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) B3)) S2)))))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (A5 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 tptp.produc3658429121746597890et_nat) (R2 tptp.set_Pr2161125870931222855_nat_o) (S2 tptp.set_Pr719794911490849221et_nat)) (= (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) B)) (@ (@ tptp.produc5001842942810119800et_nat A5) B3))) (@ (@ tptp.lex_pr5340572901959109728et_nat R2) S2)) (or (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) A5)) R2) (and (= A2 A5) (@ (@ tptp.member6099555550032318734et_nat (@ (@ tptp.produc8199053930788261021et_nat B) B3)) S2))))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (A5 (-> tptp.produc3658429121746597890et_nat Bool)) (B3 tptp.produc3925858234332021118et_nat) (R2 tptp.set_Pr2161125870931222855_nat_o) (S2 tptp.set_Pr7928877670098842301et_nat)) (= (@ (@ tptp.member6341495586645257982et_nat (@ (@ tptp.produc1940133919992309389et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) B)) (@ (@ tptp.produc2245416461498447860et_nat A5) B3))) (@ (@ tptp.lex_pr4722427456421979612et_nat R2) S2)) (or (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) A5)) R2) (and (= A2 A5) (@ (@ tptp.member4763271486408492550et_nat (@ (@ tptp.produc8599840265553166229et_nat B) B3)) S2))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit)) (=> (@ (@ tptp.order_888282469287196226t_unit (@ tptp.field_Product_unit R2)) R2) (= (@ tptp.wf_Product_unit (@ (@ tptp.minus_6985556733573110190t_unit R2) tptp.id_Product_unit)) (forall ((A3 tptp.set_Product_unit)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A3) (@ tptp.field_Product_unit R2)) (=> (not (= A3 tptp.bot_bo3957492148770167129t_unit)) (exists ((X2 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X2) A3) (forall ((Y3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit Y3) A3) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit X2) Y3)) R2))))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o)) (=> (@ (@ tptp.order_6238756238976269133r_on_o (@ tptp.field_o R2)) R2) (= (@ tptp.wf_o (@ (@ tptp.minus_7052513330764642158od_o_o R2) tptp.id_o2)) (forall ((A3 tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A3) (@ tptp.field_o R2)) (=> (not (= A3 tptp.bot_bot_set_o)) (exists ((X2 Bool)) (and (@ (@ tptp.member_o X2) A3) (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) A3) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X2) Y3)) R2))))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.order_4471489696718655927on_int (@ tptp.field_int R2)) R2) (= (@ tptp.wf_int (@ (@ tptp.minus_1052850069191792384nt_int R2) tptp.id_int)) (forall ((A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) (@ tptp.field_int R2)) (=> (not (= A3 tptp.bot_bot_set_int)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A3) (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) A3) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X2) Y3)) R2))))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o)) (=> (@ (@ tptp.order_1145710701291701250_nat_o (@ tptp.field_81821745747897882_nat_o R2)) R2) (= (@ tptp.wf_Pro8787509627421085110_nat_o (@ (@ tptp.minus_9189903262233110958_nat_o R2) tptp.id_Pro6775173067513470761_nat_o)) (forall ((A3 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A3) (@ tptp.field_81821745747897882_nat_o R2)) (=> (not (= A3 tptp.bot_bo7824918357723582233_nat_o)) (exists ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (and (@ (@ tptp.member6576561426505652726_nat_o X2) A3) (forall ((Y3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y3) A3) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X2) Y3)) R2))))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.order_4473980167227706203on_nat (@ tptp.field_nat R2)) R2) (= (@ tptp.wf_nat (@ (@ tptp.minus_1356011639430497352at_nat R2) tptp.id_nat)) (forall ((A3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) (@ tptp.field_nat R2)) (=> (not (= A3 tptp.bot_bot_set_nat)) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A3) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) A3) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y3)) R2))))))))))))
% 5.61/5.92 (assert (= tptp.remove_Product_unit (lambda ((X2 tptp.product_unit) (A3 tptp.set_Product_unit)) (@ (@ tptp.minus_6452836326544984404t_unit A3) (@ (@ tptp.insert_Product_unit X2) tptp.bot_bo3957492148770167129t_unit)))))
% 5.61/5.92 (assert (= tptp.remove_o (lambda ((X2 Bool) (A3 tptp.set_o)) (@ (@ tptp.minus_minus_set_o A3) (@ (@ tptp.insert_o X2) tptp.bot_bot_set_o)))))
% 5.61/5.92 (assert (= tptp.remove_int (lambda ((X2 tptp.int) (A3 tptp.set_int)) (@ (@ tptp.minus_minus_set_int A3) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int)))))
% 5.61/5.92 (assert (= tptp.remove4651630035290841522_nat_o (lambda ((X2 (-> tptp.produc3658429121746597890et_nat Bool)) (A3 tptp.set_Pr4532377907799695533_nat_o)) (@ (@ tptp.minus_1801376950450012436_nat_o A3) (@ (@ tptp.insert5175938949040314269_nat_o X2) tptp.bot_bo7824918357723582233_nat_o)))))
% 5.61/5.92 (assert (= tptp.remove_nat (lambda ((X2 tptp.nat) (A3 tptp.set_nat)) (@ (@ tptp.minus_minus_set_nat A3) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit) (B tptp.product_unit) (Phi (-> tptp.product_unit tptp.product_unit Bool))) (let ((_let_1 (@ (@ Phi A2) B))) (let ((_let_2 (@ (@ tptp.minus_6985556733573110190t_unit R2) tptp.id_Product_unit))) (=> (@ tptp.bNF_We2091578341578594809t_unit R2) (=> (@ (@ tptp.ord_le3507040750410214029t_unit (@ (@ tptp.insert_Product_unit A2) (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit))) (@ tptp.field_Product_unit R2)) (=> (=> (or (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit A2) B)) _let_2) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit B) A2)) _let_2)) _let_1) (=> (=> (= A2 B) _let_1) _let_1))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (A2 Bool) (B Bool) (Phi (-> Bool Bool Bool))) (let ((_let_1 (@ (@ Phi A2) B))) (let ((_let_2 (@ (@ tptp.minus_7052513330764642158od_o_o R2) tptp.id_o2))) (=> (@ tptp.bNF_We6437023980930612612_rel_o R2) (=> (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.insert_o A2) (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (@ tptp.field_o R2)) (=> (=> (or (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) B)) _let_2) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o B) A2)) _let_2)) _let_1) (=> (=> (= A2 B) _let_1) _let_1))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (B tptp.int) (Phi (-> tptp.int tptp.int Bool))) (let ((_let_1 (@ (@ Phi A2) B))) (let ((_let_2 (@ (@ tptp.minus_1052850069191792384nt_int R2) tptp.id_int))) (=> (@ tptp.bNF_We3815749466139970368el_int R2) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int A2) (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (@ tptp.field_int R2)) (=> (=> (or (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) _let_2) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) A2)) _let_2)) _let_1) (=> (=> (= A2 B) _let_1) _let_1))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool)) (Phi (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (let ((_let_1 (@ (@ Phi A2) B))) (let ((_let_2 (@ (@ tptp.minus_9189903262233110958_nat_o R2) tptp.id_Pro6775173067513470761_nat_o))) (=> (@ tptp.bNF_We740377018556551609_nat_o R2) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o (@ (@ tptp.insert5175938949040314269_nat_o A2) (@ (@ tptp.insert5175938949040314269_nat_o B) tptp.bot_bo7824918357723582233_nat_o))) (@ tptp.field_81821745747897882_nat_o R2)) (=> (=> (or (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) B)) _let_2) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o B) A2)) _let_2)) _let_1) (=> (=> (= A2 B) _let_1) _let_1))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (B tptp.nat) (Phi (-> tptp.nat tptp.nat Bool))) (let ((_let_1 (@ (@ Phi A2) B))) (let ((_let_2 (@ (@ tptp.minus_1356011639430497352at_nat R2) tptp.id_nat))) (=> (@ tptp.bNF_We3818239936649020644el_nat R2) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat A2) (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (@ tptp.field_nat R2)) (=> (=> (or (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) _let_2) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) A2)) _let_2)) _let_1) (=> (=> (= A2 B) _let_1) _let_1))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr2161125870931222855_nat_o)) (=> (@ tptp.wf_Pro8787509627421085110_nat_o (@ tptp.conver2764731894203590139_nat_o R3)) (=> (not (= R3 tptp.bot_bo3657187498359500723_nat_o)) (not (forall ((M2 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member6576561426505652726_nat_o M2) (@ (@ tptp.minus_1801376950450012436_nat_o (@ tptp.range_5289318983786108341_nat_o R3)) (@ tptp.domain4881241903163524940_nat_o R3))))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int)) (=> (@ tptp.wf_int (@ tptp.converse_int_int R3)) (=> (not (= R3 tptp.bot_bo1796632182523588997nt_int)) (not (forall ((M2 tptp.int)) (not (@ (@ tptp.member_int M2) (@ (@ tptp.minus_minus_set_int (@ tptp.range_int_int R3)) (@ tptp.domain_int_int R3))))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Product_prod_o_o)) (=> (@ tptp.wf_o (@ tptp.converse_o_o R3)) (=> (not (= R3 tptp.bot_bo7073875226086086771od_o_o)) (not (forall ((M2 Bool)) (not (@ (@ tptp.member_o M2) (@ (@ tptp.minus_minus_set_o (@ tptp.range_o_o R3)) (@ tptp.domain_o_o R3))))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr5094982260447487303t_unit)) (=> (@ tptp.wf_Product_unit (@ tptp.conver2495244158383847931t_unit R3)) (=> (not (= R3 tptp.bot_bo1654022762305692595t_unit)) (not (forall ((M2 tptp.product_unit)) (not (@ (@ tptp.member_Product_unit M2) (@ (@ tptp.minus_6452836326544984404t_unit (@ tptp.range_6617724647562260917t_unit R3)) (@ tptp.domain4292024440186670924t_unit R3))))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.wf_nat (@ tptp.converse_nat_nat R3)) (=> (not (= R3 tptp.bot_bo2099793752762293965at_nat)) (not (forall ((M2 tptp.nat)) (not (@ (@ tptp.member_nat M2) (@ (@ tptp.minus_minus_set_nat (@ tptp.range_nat_nat R3)) (@ tptp.domain_nat_nat R3))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (S2 tptp.set_Pr5094982260447487303t_unit)) (=> (@ tptp.wf_Product_unit R2) (=> (@ tptp.wf_Product_unit S2) (=> (= (@ (@ tptp.inf_in4660618365625256667t_unit (@ tptp.domain4292024440186670924t_unit R2)) (@ tptp.range_6617724647562260917t_unit S2)) tptp.bot_bo3957492148770167129t_unit) (@ tptp.wf_Product_unit (@ (@ tptp.sup_su6481247232241170203t_unit R2) S2)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (S2 tptp.set_Product_prod_o_o)) (=> (@ tptp.wf_o R2) (=> (@ tptp.wf_o S2) (=> (= (@ (@ tptp.inf_inf_set_o (@ tptp.domain_o_o R2)) (@ tptp.range_o_o S2)) tptp.bot_bot_set_o) (@ tptp.wf_o (@ (@ tptp.sup_su5769328420594410459od_o_o R2) S2)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.wf_nat R2) (=> (@ tptp.wf_nat S2) (=> (= (@ (@ tptp.inf_inf_set_nat (@ tptp.domain_nat_nat R2)) (@ tptp.range_nat_nat S2)) tptp.bot_bot_set_nat) (@ tptp.wf_nat (@ (@ tptp.sup_su6327502436637775413at_nat R2) S2)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (S2 tptp.set_Pr958786334691620121nt_int)) (=> (@ tptp.wf_int R2) (=> (@ tptp.wf_int S2) (=> (= (@ (@ tptp.inf_inf_set_int (@ tptp.domain_int_int R2)) (@ tptp.range_int_int S2)) tptp.bot_bot_set_int) (@ tptp.wf_int (@ (@ tptp.sup_su6024340866399070445nt_int R2) S2)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (S2 tptp.set_Pr2161125870931222855_nat_o)) (=> (@ tptp.wf_Pro8787509627421085110_nat_o R2) (=> (@ tptp.wf_Pro8787509627421085110_nat_o S2) (=> (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ tptp.domain4881241903163524940_nat_o R2)) (@ tptp.range_5289318983786108341_nat_o S2)) tptp.bot_bo7824918357723582233_nat_o) (@ tptp.wf_Pro8787509627421085110_nat_o (@ (@ tptp.sup_su8328026650783933211_nat_o R2) S2)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit)) (let ((_let_1 (@ tptp.field_Product_unit R2))) (=> (@ (@ tptp.order_888282469287196226t_unit _let_1) R2) (= (@ (@ tptp.order_3164716736300062379t_unit _let_1) R2) (forall ((A3 tptp.set_Product_unit)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A3) (@ tptp.field_Product_unit R2)) (=> (not (= A3 tptp.bot_bo3957492148770167129t_unit)) (exists ((X2 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X2) A3) (forall ((Y3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit Y3) A3) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit X2) Y3)) R2)))))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o)) (let ((_let_1 (@ tptp.field_o R2))) (=> (@ (@ tptp.order_6238756238976269133r_on_o _let_1) R2) (= (@ (@ tptp.order_2615775362358406454r_on_o _let_1) R2) (forall ((A3 tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A3) (@ tptp.field_o R2)) (=> (not (= A3 tptp.bot_bot_set_o)) (exists ((X2 Bool)) (and (@ (@ tptp.member_o X2) A3) (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) A3) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o X2) Y3)) R2)))))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.field_int R2))) (=> (@ (@ tptp.order_4471489696718655927on_int _let_1) R2) (= (@ (@ tptp.order_2886507596567047182on_int _let_1) R2) (forall ((A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) (@ tptp.field_int R2)) (=> (not (= A3 tptp.bot_bot_set_int)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A3) (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) A3) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X2) Y3)) R2)))))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o)) (let ((_let_1 (@ tptp.field_81821745747897882_nat_o R2))) (=> (@ (@ tptp.order_1145710701291701250_nat_o _let_1) R2) (= (@ (@ tptp.order_2118566763991480939_nat_o _let_1) R2) (forall ((A3 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A3) (@ tptp.field_81821745747897882_nat_o R2)) (=> (not (= A3 tptp.bot_bo7824918357723582233_nat_o)) (exists ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (and (@ (@ tptp.member6576561426505652726_nat_o X2) A3) (forall ((Y3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y3) A3) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o X2) Y3)) R2)))))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.field_nat R2))) (=> (@ (@ tptp.order_4473980167227706203on_nat _let_1) R2) (= (@ (@ tptp.order_2888998067076097458on_nat _let_1) R2) (forall ((A3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) (@ tptp.field_nat R2)) (=> (not (= A3 tptp.bot_bot_set_nat)) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A3) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) A3) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y3)) R2)))))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.order_underS_int R2))) (=> (@ tptp.trans_int R2) (=> (@ tptp.antisym_int R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R2) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 A2)) (@ _let_1 B))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.order_underS_nat R2))) (=> (@ tptp.trans_nat R2) (=> (@ tptp.antisym_nat R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R2) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 A2)) (@ _let_1 B))))))))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X))) (= (@ _let_1 (@ (@ tptp.remove4651630035290841522_nat_o Y) A)) (and (@ _let_1 A) (not (= X Y)))))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X))) (= (@ _let_1 (@ (@ tptp.remove_nat Y) A)) (and (@ _let_1 A) (not (= X Y)))))))
% 5.61/5.92 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.member_int X))) (= (@ _let_1 (@ (@ tptp.remove_int Y) A)) (and (@ _let_1 A) (not (= X Y)))))))
% 5.61/5.92 (assert (forall ((X Bool) (Y Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.member_o X))) (= (@ _let_1 (@ (@ tptp.remove_o Y) A)) (and (@ _let_1 A) (not (= X Y)))))))
% 5.61/5.92 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member_Product_unit X))) (= (@ _let_1 (@ (@ tptp.remove_Product_unit Y) A)) (and (@ _let_1 A) (not (= X Y)))))))
% 5.61/5.92 (assert (forall ((Y tptp.nat) (X tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.wf_nat (@ (@ tptp.insert8211810215607154385at_nat (@ (@ tptp.product_Pair_nat_nat Y) X)) R2)) (and (@ tptp.wf_nat R2) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.transi2905341329935302413cl_nat R2)))))))
% 5.61/5.92 (assert (forall ((Y tptp.int) (X tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (= (@ tptp.wf_int (@ (@ tptp.insert5033312907999012233nt_int (@ (@ tptp.product_Pair_int_int Y) X)) R2)) (and (@ tptp.wf_int R2) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ tptp.transi2902850859426252137cl_int R2)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.nat Bool)) (A2 tptp.nat)) (=> (@ tptp.bNF_We3818239936649020644el_nat R2) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y5 tptp.nat)) (=> (and (not (= Y5 X3)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y5) X3)) R2)) (@ P Y5))) (@ P X3))) (@ P A2)))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (P (-> tptp.int Bool)) (A2 tptp.int)) (=> (@ tptp.bNF_We3815749466139970368el_int R2) (=> (forall ((X3 tptp.int)) (=> (forall ((Y5 tptp.int)) (=> (and (not (= Y5 X3)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y5) X3)) R2)) (@ P Y5))) (@ P X3))) (@ P A2)))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.nat Bool)) (A2 tptp.nat)) (=> (@ tptp.wf_nat R2) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y5) X3)) R2) (@ P Y5))) (@ P X3))) (@ P A2)))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (P (-> tptp.int Bool)) (A2 tptp.int)) (=> (@ tptp.wf_int R2) (=> (forall ((X3 tptp.int)) (=> (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y5) X3)) R2) (@ P Y5))) (@ P X3))) (@ P A2)))))
% 5.61/5.92 (assert (= tptp.wf_Pro8787509627421085110_nat_o (lambda ((R4 tptp.set_Pr2161125870931222855_nat_o)) (forall ((Q tptp.set_Pr4532377907799695533_nat_o)) (=> (exists ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o X2) Q)) (exists ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (and (@ (@ tptp.member6576561426505652726_nat_o X2) Q) (forall ((Y3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o Y3) X2)) R4) (not (@ (@ tptp.member6576561426505652726_nat_o Y3) Q)))))))))))
% 5.61/5.92 (assert (= tptp.wf_o (lambda ((R4 tptp.set_Product_prod_o_o)) (forall ((Q tptp.set_o)) (=> (exists ((X2 Bool)) (@ (@ tptp.member_o X2) Q)) (exists ((X2 Bool)) (and (@ (@ tptp.member_o X2) Q) (forall ((Y3 Bool)) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o Y3) X2)) R4) (not (@ (@ tptp.member_o Y3) Q)))))))))))
% 5.61/5.92 (assert (= tptp.wf_Product_unit (lambda ((R4 tptp.set_Pr5094982260447487303t_unit)) (forall ((Q tptp.set_Product_unit)) (=> (exists ((X2 tptp.product_unit)) (@ (@ tptp.member_Product_unit X2) Q)) (exists ((X2 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X2) Q) (forall ((Y3 tptp.product_unit)) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit Y3) X2)) R4) (not (@ (@ tptp.member_Product_unit Y3) Q)))))))))))
% 5.61/5.92 (assert (= tptp.wf_nat (lambda ((R4 tptp.set_Pr1261947904930325089at_nat)) (forall ((Q tptp.set_nat)) (=> (exists ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) Q)) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) Q) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y3) X2)) R4) (not (@ (@ tptp.member_nat Y3) Q)))))))))))
% 5.61/5.92 (assert (= tptp.wf_int (lambda ((R4 tptp.set_Pr958786334691620121nt_int)) (forall ((Q tptp.set_int)) (=> (exists ((X2 tptp.int)) (@ (@ tptp.member_int X2) Q)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) Q) (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y3) X2)) R4) (not (@ (@ tptp.member_int Y3) Q)))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat)) (=> (@ tptp.wf_nat R2) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) A2)) R2)))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int)) (=> (@ tptp.wf_int R2) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) A2)) R2)))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (X tptp.nat)) (=> (@ tptp.wf_nat R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) X)) R2) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) A2)) R2))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (X tptp.int)) (=> (@ tptp.wf_int R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) X)) R2) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) A2)) R2))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat)) (=> (@ tptp.wf_nat R2) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) A2)) R2)))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int)) (=> (@ tptp.wf_int R2) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) A2)) R2)))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.nat Bool)) (A2 tptp.nat)) (=> (@ tptp.wf_nat R2) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y5) X3)) R2) (@ P Y5))) (@ P X3))) (@ P A2)))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (P (-> tptp.int Bool)) (A2 tptp.int)) (=> (@ tptp.wf_int R2) (=> (forall ((X3 tptp.int)) (=> (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y5) X3)) R2) (@ P Y5))) (@ P X3))) (@ P A2)))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (X tptp.nat)) (=> (@ tptp.wf_nat R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) X)) R2) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) A2)) R2))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (X tptp.int)) (=> (@ tptp.wf_int R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) X)) R2) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) A2)) R2))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((P4 (-> tptp.nat Bool)) (X3 tptp.nat)) (=> (forall ((Xa2 tptp.nat)) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Xa2)) R2) (@ P4 Y2))) (@ P4 Xa2))) (@ P4 X3))) (@ tptp.wf_nat R2))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int)) (=> (forall ((P4 (-> tptp.int Bool)) (X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y2) Xa2)) R2) (@ P4 Y2))) (@ P4 Xa2))) (@ P4 X3))) (@ tptp.wf_int R2))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr2161125870931222855_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Q3 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) Q3) (exists ((Xa2 (-> tptp.produc3658429121746597890et_nat Bool))) (and (@ (@ tptp.member6576561426505652726_nat_o Xa2) Q3) (forall ((Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o Y2) Xa2)) R3) (not (@ (@ tptp.member6576561426505652726_nat_o Y2) Q3)))))))) (@ tptp.wf_Pro8787509627421085110_nat_o R3))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Product_prod_o_o)) (=> (forall ((X3 Bool) (Q3 tptp.set_o)) (=> (@ (@ tptp.member_o X3) Q3) (exists ((Xa2 Bool)) (and (@ (@ tptp.member_o Xa2) Q3) (forall ((Y2 Bool)) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o Y2) Xa2)) R3) (not (@ (@ tptp.member_o Y2) Q3)))))))) (@ tptp.wf_o R3))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr5094982260447487303t_unit)) (=> (forall ((X3 tptp.product_unit) (Q3 tptp.set_Product_unit)) (=> (@ (@ tptp.member_Product_unit X3) Q3) (exists ((Xa2 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit Xa2) Q3) (forall ((Y2 tptp.product_unit)) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit Y2) Xa2)) R3) (not (@ (@ tptp.member_Product_unit Y2) Q3)))))))) (@ tptp.wf_Product_unit R3))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.nat) (Q3 tptp.set_nat)) (=> (@ (@ tptp.member_nat X3) Q3) (exists ((Xa2 tptp.nat)) (and (@ (@ tptp.member_nat Xa2) Q3) (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y2) Xa2)) R3) (not (@ (@ tptp.member_nat Y2) Q3)))))))) (@ tptp.wf_nat R3))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int)) (=> (forall ((X3 tptp.int) (Q3 tptp.set_int)) (=> (@ (@ tptp.member_int X3) Q3) (exists ((Xa2 tptp.int)) (and (@ (@ tptp.member_int Xa2) Q3) (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y2) Xa2)) R3) (not (@ (@ tptp.member_int Y2) Q3)))))))) (@ tptp.wf_int R3))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr2161125870931222855_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Q2 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.wf_Pro8787509627421085110_nat_o R3) (=> (@ (@ tptp.member6576561426505652726_nat_o X) Q2) (not (forall ((Z3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Z3) Q2) (not (forall ((Y5 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o Y5) Z3)) R3) (not (@ (@ tptp.member6576561426505652726_nat_o Y5) Q2))))))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Product_prod_o_o) (X Bool) (Q2 tptp.set_o)) (=> (@ tptp.wf_o R3) (=> (@ (@ tptp.member_o X) Q2) (not (forall ((Z3 Bool)) (=> (@ (@ tptp.member_o Z3) Q2) (not (forall ((Y5 Bool)) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o Y5) Z3)) R3) (not (@ (@ tptp.member_o Y5) Q2))))))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr5094982260447487303t_unit) (X tptp.product_unit) (Q2 tptp.set_Product_unit)) (=> (@ tptp.wf_Product_unit R3) (=> (@ (@ tptp.member_Product_unit X) Q2) (not (forall ((Z3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit Z3) Q2) (not (forall ((Y5 tptp.product_unit)) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit Y5) Z3)) R3) (not (@ (@ tptp.member_Product_unit Y5) Q2))))))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (X tptp.nat) (Q2 tptp.set_nat)) (=> (@ tptp.wf_nat R3) (=> (@ (@ tptp.member_nat X) Q2) (not (forall ((Z3 tptp.nat)) (=> (@ (@ tptp.member_nat Z3) Q2) (not (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y5) Z3)) R3) (not (@ (@ tptp.member_nat Y5) Q2))))))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int) (X tptp.int) (Q2 tptp.set_int)) (=> (@ tptp.wf_int R3) (=> (@ (@ tptp.member_int X) Q2) (not (forall ((Z3 tptp.int)) (=> (@ (@ tptp.member_int Z3) Q2) (not (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y5) Z3)) R3) (not (@ (@ tptp.member_int Y5) Q2))))))))))))
% 5.61/5.92 (assert (= tptp.wf_nat (lambda ((R4 tptp.set_Pr1261947904930325089at_nat)) (forall ((P2 (-> tptp.nat Bool))) (=> (forall ((X2 tptp.nat)) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y3) X2)) R4) (@ P2 Y3))) (@ P2 X2))) (forall ((X7 tptp.nat)) (@ P2 X7)))))))
% 5.61/5.92 (assert (= tptp.wf_int (lambda ((R4 tptp.set_Pr958786334691620121nt_int)) (forall ((P2 (-> tptp.int Bool))) (=> (forall ((X2 tptp.int)) (=> (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y3) X2)) R4) (@ P2 Y3))) (@ P2 X2))) (forall ((X7 tptp.int)) (@ P2 X7)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (R2 tptp.set_Pr2161125870931222855_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.order_2118566763991480939_nat_o A) R2) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) B)) R2) (and (@ (@ tptp.member6576561426505652726_nat_o A2) A) (@ (@ tptp.member6576561426505652726_nat_o B) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (R2 tptp.set_Product_prod_o_o) (A2 Bool) (B Bool)) (=> (@ (@ tptp.order_2615775362358406454r_on_o A) R2) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) B)) R2) (and (@ (@ tptp.member_o A2) A) (@ (@ tptp.member_o B) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit) (B tptp.product_unit)) (=> (@ (@ tptp.order_3164716736300062379t_unit A) R2) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit A2) B)) R2) (and (@ (@ tptp.member_Product_unit A2) A) (@ (@ tptp.member_Product_unit B) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.order_2888998067076097458on_nat A) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R2) (and (@ (@ tptp.member_nat A2) A) (@ (@ tptp.member_nat B) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.order_2886507596567047182on_int A) R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R2) (and (@ (@ tptp.member_int A2) A) (@ (@ tptp.member_int B) A))))))
% 5.61/5.92 (assert (forall ((I2 (-> tptp.produc3658429121746597890et_nat Bool)) (R3 tptp.set_Pr2161125870931222855_nat_o) (J (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o I2) (@ (@ tptp.order_7262550146012401043_nat_o R3) J)) (and (not (= I2 J)) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o I2) J)) R3)))))
% 5.61/5.92 (assert (forall ((I2 Bool) (R3 tptp.set_Product_prod_o_o) (J Bool)) (=> (@ (@ tptp.member_o I2) (@ (@ tptp.order_underS_o R3) J)) (and (not (= I2 J)) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o I2) J)) R3)))))
% 5.61/5.92 (assert (forall ((I2 tptp.product_unit) (R3 tptp.set_Pr5094982260447487303t_unit) (J tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I2) (@ (@ tptp.order_5809128134054296019t_unit R3) J)) (and (not (= I2 J)) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit I2) J)) R3)))))
% 5.61/5.92 (assert (forall ((I2 tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat) (J tptp.nat)) (=> (@ (@ tptp.member_nat I2) (@ (@ tptp.order_underS_nat R3) J)) (and (not (= I2 J)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat I2) J)) R3)))))
% 5.61/5.92 (assert (forall ((I2 tptp.int) (R3 tptp.set_Pr958786334691620121nt_int) (J tptp.int)) (=> (@ (@ tptp.member_int I2) (@ (@ tptp.order_underS_int R3) J)) (and (not (= I2 J)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I2) J)) R3)))))
% 5.61/5.92 (assert (forall ((I2 (-> tptp.produc3658429121746597890et_nat Bool)) (J (-> tptp.produc3658429121746597890et_nat Bool)) (R3 tptp.set_Pr2161125870931222855_nat_o)) (=> (not (= I2 J)) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o I2) J)) R3) (@ (@ tptp.member6576561426505652726_nat_o I2) (@ (@ tptp.order_7262550146012401043_nat_o R3) J))))))
% 5.61/5.92 (assert (forall ((I2 Bool) (J Bool) (R3 tptp.set_Product_prod_o_o)) (=> (not (= I2 J)) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o I2) J)) R3) (@ (@ tptp.member_o I2) (@ (@ tptp.order_underS_o R3) J))))))
% 5.61/5.92 (assert (forall ((I2 tptp.product_unit) (J tptp.product_unit) (R3 tptp.set_Pr5094982260447487303t_unit)) (=> (not (= I2 J)) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit I2) J)) R3) (@ (@ tptp.member_Product_unit I2) (@ (@ tptp.order_5809128134054296019t_unit R3) J))))))
% 5.61/5.92 (assert (forall ((I2 tptp.nat) (J tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (=> (not (= I2 J)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat I2) J)) R3) (@ (@ tptp.member_nat I2) (@ (@ tptp.order_underS_nat R3) J))))))
% 5.61/5.92 (assert (forall ((I2 tptp.int) (J tptp.int) (R3 tptp.set_Pr958786334691620121nt_int)) (=> (not (= I2 J)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int I2) J)) R3) (@ (@ tptp.member_int I2) (@ (@ tptp.order_underS_int R3) J))))))
% 5.61/5.92 (assert (forall ((I2 (-> tptp.produc3658429121746597890et_nat Bool)) (R3 tptp.set_Pr2161125870931222855_nat_o) (J (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o I2))) (=> (@ _let_1 (@ (@ tptp.order_7262550146012401043_nat_o R3) J)) (@ _let_1 (@ tptp.field_81821745747897882_nat_o R3))))))
% 5.61/5.92 (assert (forall ((I2 tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat) (J tptp.nat)) (let ((_let_1 (@ tptp.member_nat I2))) (=> (@ _let_1 (@ (@ tptp.order_underS_nat R3) J)) (@ _let_1 (@ tptp.field_nat R3))))))
% 5.61/5.92 (assert (forall ((I2 tptp.int) (R3 tptp.set_Pr958786334691620121nt_int) (J tptp.int)) (let ((_let_1 (@ tptp.member_int I2))) (=> (@ _let_1 (@ (@ tptp.order_underS_int R3) J)) (@ _let_1 (@ tptp.field_int R3))))))
% 5.61/5.92 (assert (forall ((I2 Bool) (R3 tptp.set_Product_prod_o_o) (J Bool)) (let ((_let_1 (@ tptp.member_o I2))) (=> (@ _let_1 (@ (@ tptp.order_underS_o R3) J)) (@ _let_1 (@ tptp.field_o R3))))))
% 5.61/5.92 (assert (forall ((I2 tptp.product_unit) (R3 tptp.set_Pr5094982260447487303t_unit) (J tptp.product_unit)) (let ((_let_1 (@ tptp.member_Product_unit I2))) (=> (@ _let_1 (@ (@ tptp.order_5809128134054296019t_unit R3) J)) (@ _let_1 (@ tptp.field_Product_unit R3))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.bNF_We3818239936649020644el_nat R2) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) (@ tptp.field_nat R2)) (forall ((Xa2 tptp.nat)) (=> (@ (@ tptp.member_nat Xa2) (@ tptp.field_nat R2)) (or (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X6) Xa2)) R2) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) X6)) R2)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ tptp.bNF_We3815749466139970368el_int R2) (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) (@ tptp.field_int R2)) (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ tptp.field_int R2)) (or (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X6) Xa2)) R2) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Xa2) X6)) R2)))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr5094982260447487303t_unit) (Q2 tptp.set_Product_unit)) (=> (@ tptp.wf_Product_unit R3) (=> (not (= Q2 tptp.bot_bo3957492148770167129t_unit)) (not (forall ((Z3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit Z3) Q2) (not (forall ((Y5 tptp.product_unit)) (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit Y5) Z3)) R3) (not (@ (@ tptp.member_Product_unit Y5) Q2))))))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Product_prod_o_o) (Q2 tptp.set_o)) (=> (@ tptp.wf_o R3) (=> (not (= Q2 tptp.bot_bot_set_o)) (not (forall ((Z3 Bool)) (=> (@ (@ tptp.member_o Z3) Q2) (not (forall ((Y5 Bool)) (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o Y5) Z3)) R3) (not (@ (@ tptp.member_o Y5) Q2))))))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (Q2 tptp.set_nat)) (=> (@ tptp.wf_nat R3) (=> (not (= Q2 tptp.bot_bot_set_nat)) (not (forall ((Z3 tptp.nat)) (=> (@ (@ tptp.member_nat Z3) Q2) (not (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y5) Z3)) R3) (not (@ (@ tptp.member_nat Y5) Q2))))))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int) (Q2 tptp.set_int)) (=> (@ tptp.wf_int R3) (=> (not (= Q2 tptp.bot_bot_set_int)) (not (forall ((Z3 tptp.int)) (=> (@ (@ tptp.member_int Z3) Q2) (not (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y5) Z3)) R3) (not (@ (@ tptp.member_int Y5) Q2))))))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr2161125870931222855_nat_o) (Q2 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.wf_Pro8787509627421085110_nat_o R3) (=> (not (= Q2 tptp.bot_bo7824918357723582233_nat_o)) (not (forall ((Z3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Z3) Q2) (not (forall ((Y5 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o Y5) Z3)) R3) (not (@ (@ tptp.member6576561426505652726_nat_o Y5) Q2))))))))))))
% 5.61/5.92 (assert (@ (@ tptp.order_3164716736300062379t_unit tptp.bot_bo3957492148770167129t_unit) tptp.bot_bo1654022762305692595t_unit))
% 5.61/5.92 (assert (@ (@ tptp.order_2615775362358406454r_on_o tptp.bot_bot_set_o) tptp.bot_bo7073875226086086771od_o_o))
% 5.61/5.92 (assert (@ (@ tptp.order_2888998067076097458on_nat tptp.bot_bot_set_nat) tptp.bot_bo2099793752762293965at_nat))
% 5.61/5.92 (assert (@ (@ tptp.order_2886507596567047182on_int tptp.bot_bot_set_int) tptp.bot_bo1796632182523588997nt_int))
% 5.61/5.92 (assert (@ (@ tptp.order_2118566763991480939_nat_o tptp.bot_bo7824918357723582233_nat_o) tptp.bot_bo3657187498359500723_nat_o))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.bNF_We740377018556551609_nat_o R2) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (forall ((Y5 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (and (not (= Y5 X3)) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o Y5) X3)) R2)) (=> (@ (@ tptp.member6576561426505652726_nat_o Y5) (@ tptp.field_81821745747897882_nat_o R2)) (@ P Y5)))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) (@ tptp.field_81821745747897882_nat_o R2)) (@ P X3)))) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) (@ tptp.field_81821745747897882_nat_o R2)) (@ P A2))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (P (-> Bool Bool)) (A2 Bool)) (=> (@ tptp.bNF_We6437023980930612612_rel_o R2) (=> (forall ((X3 Bool)) (=> (forall ((Y5 Bool)) (=> (and (not (= Y5 X3)) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o Y5) X3)) R2)) (=> (@ (@ tptp.member_o Y5) (@ tptp.field_o R2)) (@ P Y5)))) (=> (@ (@ tptp.member_o X3) (@ tptp.field_o R2)) (@ P X3)))) (=> (@ (@ tptp.member_o A2) (@ tptp.field_o R2)) (@ P A2))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (P (-> tptp.product_unit Bool)) (A2 tptp.product_unit)) (=> (@ tptp.bNF_We2091578341578594809t_unit R2) (=> (forall ((X3 tptp.product_unit)) (=> (forall ((Y5 tptp.product_unit)) (=> (and (not (= Y5 X3)) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit Y5) X3)) R2)) (=> (@ (@ tptp.member_Product_unit Y5) (@ tptp.field_Product_unit R2)) (@ P Y5)))) (=> (@ (@ tptp.member_Product_unit X3) (@ tptp.field_Product_unit R2)) (@ P X3)))) (=> (@ (@ tptp.member_Product_unit A2) (@ tptp.field_Product_unit R2)) (@ P A2))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.nat Bool)) (A2 tptp.nat)) (=> (@ tptp.bNF_We3818239936649020644el_nat R2) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y5 tptp.nat)) (=> (and (not (= Y5 X3)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y5) X3)) R2)) (=> (@ (@ tptp.member_nat Y5) (@ tptp.field_nat R2)) (@ P Y5)))) (=> (@ (@ tptp.member_nat X3) (@ tptp.field_nat R2)) (@ P X3)))) (=> (@ (@ tptp.member_nat A2) (@ tptp.field_nat R2)) (@ P A2))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (P (-> tptp.int Bool)) (A2 tptp.int)) (=> (@ tptp.bNF_We3815749466139970368el_int R2) (=> (forall ((X3 tptp.int)) (=> (forall ((Y5 tptp.int)) (=> (and (not (= Y5 X3)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y5) X3)) R2)) (=> (@ (@ tptp.member_int Y5) (@ tptp.field_int R2)) (@ P Y5)))) (=> (@ (@ tptp.member_int X3) (@ tptp.field_int R2)) (@ P X3)))) (=> (@ (@ tptp.member_int A2) (@ tptp.field_int R2)) (@ P A2))))))
% 5.61/5.92 (assert (forall ((A2 tptp.product_unit) (R2 tptp.set_Pr5094982260447487303t_unit)) (=> (not (@ (@ tptp.member_Product_unit A2) (@ tptp.field_Product_unit R2))) (= (@ (@ tptp.order_5809128134054296019t_unit R2) A2) tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.92 (assert (forall ((A2 Bool) (R2 tptp.set_Product_prod_o_o)) (=> (not (@ (@ tptp.member_o A2) (@ tptp.field_o R2))) (= (@ (@ tptp.order_underS_o R2) A2) tptp.bot_bot_set_o))))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (not (@ (@ tptp.member_nat A2) (@ tptp.field_nat R2))) (= (@ (@ tptp.order_underS_nat R2) A2) tptp.bot_bot_set_nat))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (not (@ (@ tptp.member_int A2) (@ tptp.field_int R2))) (= (@ (@ tptp.order_underS_int R2) A2) tptp.bot_bot_set_int))))
% 5.61/5.92 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (R2 tptp.set_Pr2161125870931222855_nat_o)) (=> (not (@ (@ tptp.member6576561426505652726_nat_o A2) (@ tptp.field_81821745747897882_nat_o R2))) (= (@ (@ tptp.order_7262550146012401043_nat_o R2) A2) tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr5094982260447487303t_unit)) (=> (forall ((A9 tptp.set_Product_unit)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A9) (@ (@ tptp.image_8431784415008483091t_unit R3) A9)) (= A9 tptp.bot_bo3957492148770167129t_unit))) (@ tptp.wf_Product_unit R3))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Product_prod_o_o)) (=> (forall ((A9 tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A9) (@ (@ tptp.image_o_o R3) A9)) (= A9 tptp.bot_bot_set_o))) (@ tptp.wf_o R3))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int)) (=> (forall ((A9 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A9) (@ (@ tptp.image_int_int R3) A9)) (= A9 tptp.bot_bot_set_int))) (@ tptp.wf_int R3))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr2161125870931222855_nat_o)) (=> (forall ((A9 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A9) (@ (@ tptp.image_2232984160439939859_nat_o R3) A9)) (= A9 tptp.bot_bo7824918357723582233_nat_o))) (@ tptp.wf_Pro8787509627421085110_nat_o R3))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((A9 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A9) (@ (@ tptp.image_nat_nat R3) A9)) (= A9 tptp.bot_bot_set_nat))) (@ tptp.wf_nat R3))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr5094982260447487303t_unit) (A tptp.set_Product_unit)) (=> (@ tptp.wf_Product_unit R3) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) (@ (@ tptp.image_8431784415008483091t_unit R3) A)) (= A tptp.bot_bo3957492148770167129t_unit)))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Product_prod_o_o) (A tptp.set_o)) (=> (@ tptp.wf_o R3) (=> (@ (@ tptp.ord_less_eq_set_o A) (@ (@ tptp.image_o_o R3) A)) (= A tptp.bot_bot_set_o)))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int) (A tptp.set_int)) (=> (@ tptp.wf_int R3) (=> (@ (@ tptp.ord_less_eq_set_int A) (@ (@ tptp.image_int_int R3) A)) (= A tptp.bot_bot_set_int)))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr2161125870931222855_nat_o) (A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.wf_Pro8787509627421085110_nat_o R3) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A) (@ (@ tptp.image_2232984160439939859_nat_o R3) A)) (= A tptp.bot_bo7824918357723582233_nat_o)))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_nat)) (=> (@ tptp.wf_nat R3) (=> (@ (@ tptp.ord_less_eq_set_nat A) (@ (@ tptp.image_nat_nat R3) A)) (= A tptp.bot_bot_set_nat)))))
% 5.61/5.92 (assert (= tptp.wf_Product_unit (lambda ((R4 tptp.set_Pr5094982260447487303t_unit)) (forall ((A3 tptp.set_Product_unit)) (=> (and (@ (@ tptp.ord_le3507040750410214029t_unit A3) (@ tptp.field_Product_unit R4)) (not (= A3 tptp.bot_bo3957492148770167129t_unit))) (exists ((X2 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X2) A3) (forall ((Y3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit Y3) A3) (not (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit Y3) X2)) R4)))))))))))
% 5.61/5.92 (assert (= tptp.wf_o (lambda ((R4 tptp.set_Product_prod_o_o)) (forall ((A3 tptp.set_o)) (=> (and (@ (@ tptp.ord_less_eq_set_o A3) (@ tptp.field_o R4)) (not (= A3 tptp.bot_bot_set_o))) (exists ((X2 Bool)) (and (@ (@ tptp.member_o X2) A3) (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) A3) (not (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o Y3) X2)) R4)))))))))))
% 5.61/5.92 (assert (= tptp.wf_int (lambda ((R4 tptp.set_Pr958786334691620121nt_int)) (forall ((A3 tptp.set_int)) (=> (and (@ (@ tptp.ord_less_eq_set_int A3) (@ tptp.field_int R4)) (not (= A3 tptp.bot_bot_set_int))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A3) (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) A3) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y3) X2)) R4)))))))))))
% 5.61/5.92 (assert (= tptp.wf_Pro8787509627421085110_nat_o (lambda ((R4 tptp.set_Pr2161125870931222855_nat_o)) (forall ((A3 tptp.set_Pr4532377907799695533_nat_o)) (=> (and (@ (@ tptp.ord_le2965882846123202637_nat_o A3) (@ tptp.field_81821745747897882_nat_o R4)) (not (= A3 tptp.bot_bo7824918357723582233_nat_o))) (exists ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (and (@ (@ tptp.member6576561426505652726_nat_o X2) A3) (forall ((Y3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y3) A3) (not (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o Y3) X2)) R4)))))))))))
% 5.61/5.92 (assert (= tptp.wf_nat (lambda ((R4 tptp.set_Pr1261947904930325089at_nat)) (forall ((A3 tptp.set_nat)) (=> (and (@ (@ tptp.ord_less_eq_set_nat A3) (@ tptp.field_nat R4)) (not (= A3 tptp.bot_bot_set_nat))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A3) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) A3) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y3) X2)) R4)))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit) (B tptp.product_unit) (Phi (-> tptp.product_unit tptp.product_unit Bool))) (let ((_let_1 (@ (@ Phi A2) B))) (=> (@ tptp.bNF_We2091578341578594809t_unit R2) (=> (@ (@ tptp.ord_le3507040750410214029t_unit (@ (@ tptp.insert_Product_unit A2) (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit))) (@ tptp.field_Product_unit R2)) (=> (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit A2) B)) R2) _let_1) (=> (=> (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit B) A2)) R2) _let_1) _let_1)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (A2 Bool) (B Bool) (Phi (-> Bool Bool Bool))) (let ((_let_1 (@ (@ Phi A2) B))) (=> (@ tptp.bNF_We6437023980930612612_rel_o R2) (=> (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.insert_o A2) (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (@ tptp.field_o R2)) (=> (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) B)) R2) _let_1) (=> (=> (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o B) A2)) R2) _let_1) _let_1)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (B tptp.int) (Phi (-> tptp.int tptp.int Bool))) (let ((_let_1 (@ (@ Phi A2) B))) (=> (@ tptp.bNF_We3815749466139970368el_int R2) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int A2) (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (@ tptp.field_int R2)) (=> (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R2) _let_1) (=> (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) A2)) R2) _let_1) _let_1)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool)) (Phi (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (let ((_let_1 (@ (@ Phi A2) B))) (=> (@ tptp.bNF_We740377018556551609_nat_o R2) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o (@ (@ tptp.insert5175938949040314269_nat_o A2) (@ (@ tptp.insert5175938949040314269_nat_o B) tptp.bot_bo7824918357723582233_nat_o))) (@ tptp.field_81821745747897882_nat_o R2)) (=> (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) B)) R2) _let_1) (=> (=> (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o B) A2)) R2) _let_1) _let_1)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (B tptp.nat) (Phi (-> tptp.nat tptp.nat Bool))) (let ((_let_1 (@ (@ Phi A2) B))) (=> (@ tptp.bNF_We3818239936649020644el_nat R2) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat A2) (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (@ tptp.field_nat R2)) (=> (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R2) _let_1) (=> (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) A2)) R2) _let_1) _let_1)))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr5094982260447487303t_unit)) (=> (= (@ (@ tptp.inf_in4660618365625256667t_unit (@ tptp.domain4292024440186670924t_unit R3)) (@ tptp.range_6617724647562260917t_unit R3)) tptp.bot_bo3957492148770167129t_unit) (@ tptp.wf_Product_unit R3))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Product_prod_o_o)) (=> (= (@ (@ tptp.inf_inf_set_o (@ tptp.domain_o_o R3)) (@ tptp.range_o_o R3)) tptp.bot_bot_set_o) (@ tptp.wf_o R3))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat)) (=> (= (@ (@ tptp.inf_inf_set_nat (@ tptp.domain_nat_nat R3)) (@ tptp.range_nat_nat R3)) tptp.bot_bot_set_nat) (@ tptp.wf_nat R3))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int)) (=> (= (@ (@ tptp.inf_inf_set_int (@ tptp.domain_int_int R3)) (@ tptp.range_int_int R3)) tptp.bot_bot_set_int) (@ tptp.wf_int R3))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr2161125870931222855_nat_o)) (=> (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ tptp.domain4881241903163524940_nat_o R3)) (@ tptp.range_5289318983786108341_nat_o R3)) tptp.bot_bo7824918357723582233_nat_o) (@ tptp.wf_Pro8787509627421085110_nat_o R3))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr2161125870931222855_nat_o)) (=> (@ tptp.wf_Pro8787509627421085110_nat_o R3) (=> (not (= R3 tptp.bot_bo3657187498359500723_nat_o)) (not (forall ((M2 (-> tptp.produc3658429121746597890et_nat Bool))) (not (@ (@ tptp.member6576561426505652726_nat_o M2) (@ (@ tptp.minus_1801376950450012436_nat_o (@ tptp.domain4881241903163524940_nat_o R3)) (@ tptp.range_5289318983786108341_nat_o R3))))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int)) (=> (@ tptp.wf_int R3) (=> (not (= R3 tptp.bot_bo1796632182523588997nt_int)) (not (forall ((M2 tptp.int)) (not (@ (@ tptp.member_int M2) (@ (@ tptp.minus_minus_set_int (@ tptp.domain_int_int R3)) (@ tptp.range_int_int R3))))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Product_prod_o_o)) (=> (@ tptp.wf_o R3) (=> (not (= R3 tptp.bot_bo7073875226086086771od_o_o)) (not (forall ((M2 Bool)) (not (@ (@ tptp.member_o M2) (@ (@ tptp.minus_minus_set_o (@ tptp.domain_o_o R3)) (@ tptp.range_o_o R3))))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr5094982260447487303t_unit)) (=> (@ tptp.wf_Product_unit R3) (=> (not (= R3 tptp.bot_bo1654022762305692595t_unit)) (not (forall ((M2 tptp.product_unit)) (not (@ (@ tptp.member_Product_unit M2) (@ (@ tptp.minus_6452836326544984404t_unit (@ tptp.domain4292024440186670924t_unit R3)) (@ tptp.range_6617724647562260917t_unit R3))))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.wf_nat R3) (=> (not (= R3 tptp.bot_bo2099793752762293965at_nat)) (not (forall ((M2 tptp.nat)) (not (@ (@ tptp.member_nat M2) (@ (@ tptp.minus_minus_set_nat (@ tptp.domain_nat_nat R3)) (@ tptp.range_nat_nat R3))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.order_7262550146012401043_nat_o R2))) (let ((_let_2 (@ tptp.field_81821745747897882_nat_o R2))) (=> (@ (@ tptp.order_1145710701291701250_nat_o _let_2) R2) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) _let_2) (=> (@ (@ tptp.member6576561426505652726_nat_o B) _let_2) (= (@ (@ tptp.ord_le2965882846123202637_nat_o (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) B)) R2)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (A2 Bool) (B Bool)) (let ((_let_1 (@ tptp.order_underS_o R2))) (let ((_let_2 (@ tptp.field_o R2))) (=> (@ (@ tptp.order_6238756238976269133r_on_o _let_2) R2) (=> (@ (@ tptp.member_o A2) _let_2) (=> (@ (@ tptp.member_o B) _let_2) (= (@ (@ tptp.ord_less_eq_set_o (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) B)) R2)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (@ tptp.order_5809128134054296019t_unit R2))) (let ((_let_2 (@ tptp.field_Product_unit R2))) (=> (@ (@ tptp.order_888282469287196226t_unit _let_2) R2) (=> (@ (@ tptp.member_Product_unit A2) _let_2) (=> (@ (@ tptp.member_Product_unit B) _let_2) (= (@ (@ tptp.ord_le3507040750410214029t_unit (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit A2) B)) R2)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.order_underS_int R2))) (let ((_let_2 (@ tptp.field_int R2))) (=> (@ (@ tptp.order_4471489696718655927on_int _let_2) R2) (=> (@ (@ tptp.member_int A2) _let_2) (=> (@ (@ tptp.member_int B) _let_2) (= (@ (@ tptp.ord_less_eq_set_int (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R2)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.order_underS_nat R2))) (let ((_let_2 (@ tptp.field_nat R2))) (=> (@ (@ tptp.order_4473980167227706203on_nat _let_2) R2) (=> (@ (@ tptp.member_nat A2) _let_2) (=> (@ (@ tptp.member_nat B) _let_2) (= (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R2)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (B4 tptp.set_Product_unit)) (=> (@ tptp.bNF_We2091578341578594809t_unit R2) (=> (@ (@ tptp.ord_le3507040750410214029t_unit B4) (@ tptp.field_Product_unit R2)) (=> (not (= B4 tptp.bot_bo3957492148770167129t_unit)) (exists ((X_1 tptp.product_unit)) (@ (@ (@ tptp.bNF_We909621271159000003t_unit R2) B4) X_1)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (B4 tptp.set_o)) (=> (@ tptp.bNF_We6437023980930612612_rel_o R2) (=> (@ (@ tptp.ord_less_eq_set_o B4) (@ tptp.field_o R2)) (=> (not (= B4 tptp.bot_bot_set_o)) (exists ((X_1 Bool)) (@ (@ (@ tptp.bNF_We4647864369647134286inim_o R2) B4) X_1)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (B4 tptp.set_int)) (=> (@ tptp.bNF_We3815749466139970368el_int R2) (=> (@ (@ tptp.ord_less_eq_set_int B4) (@ tptp.field_int R2)) (=> (not (= B4 tptp.bot_bot_set_int)) (exists ((X_1 tptp.int)) (@ (@ (@ tptp.bNF_We6511469253196982518im_int R2) B4) X_1)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.bNF_We740377018556551609_nat_o R2) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o B4) (@ tptp.field_81821745747897882_nat_o R2)) (=> (not (= B4 tptp.bot_bo7824918357723582233_nat_o)) (exists ((X_1 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ (@ tptp.bNF_We5608535359669600131_nat_o R2) B4) X_1)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_nat)) (=> (@ tptp.bNF_We3818239936649020644el_nat R2) (=> (@ (@ tptp.ord_less_eq_set_nat B4) (@ tptp.field_nat R2)) (=> (not (= B4 tptp.bot_bot_set_nat)) (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.bNF_We6513959723706032794im_nat R2) B4) X_1)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit)) (let ((_let_1 (@ tptp.field_Product_unit R2))) (=> (@ (@ tptp.refl_on_Product_unit _let_1) R2) (=> (@ (@ tptp.member_Product_unit A2) _let_1) (= (@ (@ tptp.order_6949322460238004850t_unit R2) A2) (@ (@ tptp.sup_su793286257634532545t_unit (@ (@ tptp.order_5809128134054296019t_unit R2) A2)) (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (A2 Bool)) (let ((_let_1 (@ tptp.field_o R2))) (=> (@ (@ tptp.refl_on_o _let_1) R2) (=> (@ (@ tptp.member_o A2) _let_1) (= (@ (@ tptp.order_under_o R2) A2) (@ (@ tptp.sup_sup_set_o (@ (@ tptp.order_underS_o R2) A2)) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.field_nat R2))) (=> (@ (@ tptp.refl_on_nat _let_1) R2) (=> (@ (@ tptp.member_nat A2) _let_1) (= (@ (@ tptp.order_under_nat R2) A2) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.order_underS_nat R2) A2)) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int)) (let ((_let_1 (@ tptp.field_int R2))) (=> (@ (@ tptp.refl_on_int _let_1) R2) (=> (@ (@ tptp.member_int A2) _let_1) (= (@ (@ tptp.order_under_int R2) A2) (@ (@ tptp.sup_sup_set_int (@ (@ tptp.order_underS_int R2) A2)) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.field_81821745747897882_nat_o R2))) (=> (@ (@ tptp.refl_o1075864025857821388_nat_o _let_1) R2) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) _let_1) (= (@ (@ tptp.order_2885205318754725938_nat_o R2) A2) (@ (@ tptp.sup_su5209123915105501825_nat_o (@ (@ tptp.order_7262550146012401043_nat_o R2) A2)) (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.field_Product_unit R2))) (=> (@ tptp.bNF_We2091578341578594809t_unit R2) (=> (@ (@ tptp.ord_le3507040750410214029t_unit B4) _let_1) (=> (not (= B4 tptp.bot_bo3957492148770167129t_unit)) (@ (@ tptp.member_Product_unit (@ (@ tptp.bNF_We7185707985517244377t_unit R2) B4)) _let_1)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.field_o R2))) (=> (@ tptp.bNF_We6437023980930612612_rel_o R2) (=> (@ (@ tptp.ord_less_eq_set_o B4) _let_1) (=> (not (= B4 tptp.bot_bot_set_o)) (@ (@ tptp.member_o (@ (@ tptp.bNF_We537455116209922916inim_o R2) B4)) _let_1)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.field_int R2))) (=> (@ tptp.bNF_We3815749466139970368el_int R2) (=> (@ (@ tptp.ord_less_eq_set_int B4) _let_1) (=> (not (= B4 tptp.bot_bot_set_int)) (@ (@ tptp.member_int (@ (@ tptp.bNF_We3272633801743244640im_int R2) B4)) _let_1)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.field_81821745747897882_nat_o R2))) (=> (@ tptp.bNF_We740377018556551609_nat_o R2) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o B4) _let_1) (=> (not (= B4 tptp.bot_bo7824918357723582233_nat_o)) (@ (@ tptp.member6576561426505652726_nat_o (@ (@ tptp.bNF_We8236795211600914329_nat_o R2) B4)) _let_1)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.field_nat R2))) (=> (@ tptp.bNF_We3818239936649020644el_nat R2) (=> (@ (@ tptp.ord_less_eq_set_nat B4) _let_1) (=> (not (= B4 tptp.bot_bot_set_nat)) (@ (@ tptp.member_nat (@ (@ tptp.bNF_We3275124272252294916im_nat R2) B4)) _let_1)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (B4 tptp.set_Product_unit)) (=> (@ tptp.bNF_We2091578341578594809t_unit R2) (=> (@ (@ tptp.ord_le3507040750410214029t_unit B4) (@ tptp.field_Product_unit R2)) (=> (not (= B4 tptp.bot_bo3957492148770167129t_unit)) (@ (@ tptp.member_Product_unit (@ (@ tptp.bNF_We7185707985517244377t_unit R2) B4)) B4))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (B4 tptp.set_o)) (=> (@ tptp.bNF_We6437023980930612612_rel_o R2) (=> (@ (@ tptp.ord_less_eq_set_o B4) (@ tptp.field_o R2)) (=> (not (= B4 tptp.bot_bot_set_o)) (@ (@ tptp.member_o (@ (@ tptp.bNF_We537455116209922916inim_o R2) B4)) B4))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (B4 tptp.set_int)) (=> (@ tptp.bNF_We3815749466139970368el_int R2) (=> (@ (@ tptp.ord_less_eq_set_int B4) (@ tptp.field_int R2)) (=> (not (= B4 tptp.bot_bot_set_int)) (@ (@ tptp.member_int (@ (@ tptp.bNF_We3272633801743244640im_int R2) B4)) B4))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.bNF_We740377018556551609_nat_o R2) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o B4) (@ tptp.field_81821745747897882_nat_o R2)) (=> (not (= B4 tptp.bot_bo7824918357723582233_nat_o)) (@ (@ tptp.member6576561426505652726_nat_o (@ (@ tptp.bNF_We8236795211600914329_nat_o R2) B4)) B4))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_nat)) (=> (@ tptp.bNF_We3818239936649020644el_nat R2) (=> (@ (@ tptp.ord_less_eq_set_nat B4) (@ tptp.field_nat R2)) (=> (not (= B4 tptp.bot_bot_set_nat)) (@ (@ tptp.member_nat (@ (@ tptp.bNF_We3275124272252294916im_nat R2) B4)) B4))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.bNF_We740377018556551609_nat_o R2) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o B4) (@ tptp.field_81821745747897882_nat_o R2)) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) B4) (=> (forall ((B2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o B2) B4) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) B2)) R2))) (= A2 (@ (@ tptp.bNF_We8236795211600914329_nat_o R2) B4))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (B4 tptp.set_o) (A2 Bool)) (=> (@ tptp.bNF_We6437023980930612612_rel_o R2) (=> (@ (@ tptp.ord_less_eq_set_o B4) (@ tptp.field_o R2)) (=> (@ (@ tptp.member_o A2) B4) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) B4) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) B2)) R2))) (= A2 (@ (@ tptp.bNF_We537455116209922916inim_o R2) B4))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (B4 tptp.set_Product_unit) (A2 tptp.product_unit)) (=> (@ tptp.bNF_We2091578341578594809t_unit R2) (=> (@ (@ tptp.ord_le3507040750410214029t_unit B4) (@ tptp.field_Product_unit R2)) (=> (@ (@ tptp.member_Product_unit A2) B4) (=> (forall ((B2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit B2) B4) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit A2) B2)) R2))) (= A2 (@ (@ tptp.bNF_We7185707985517244377t_unit R2) B4))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (B4 tptp.set_int) (A2 tptp.int)) (=> (@ tptp.bNF_We3815749466139970368el_int R2) (=> (@ (@ tptp.ord_less_eq_set_int B4) (@ tptp.field_int R2)) (=> (@ (@ tptp.member_int A2) B4) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) B4) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B2)) R2))) (= A2 (@ (@ tptp.bNF_We3272633801743244640im_int R2) B4))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_nat) (A2 tptp.nat)) (=> (@ tptp.bNF_We3818239936649020644el_nat R2) (=> (@ (@ tptp.ord_less_eq_set_nat B4) (@ tptp.field_nat R2)) (=> (@ (@ tptp.member_nat A2) B4) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) B4) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B2)) R2))) (= A2 (@ (@ tptp.bNF_We3275124272252294916im_nat R2) B4))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o) (B (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.bNF_We740377018556551609_nat_o R2) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o B4) (@ tptp.field_81821745747897882_nat_o R2)) (=> (@ (@ tptp.member6576561426505652726_nat_o B) B4) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o (@ (@ tptp.bNF_We8236795211600914329_nat_o R2) B4)) B)) R2))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (B4 tptp.set_o) (B Bool)) (=> (@ tptp.bNF_We6437023980930612612_rel_o R2) (=> (@ (@ tptp.ord_less_eq_set_o B4) (@ tptp.field_o R2)) (=> (@ (@ tptp.member_o B) B4) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o (@ (@ tptp.bNF_We537455116209922916inim_o R2) B4)) B)) R2))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (B4 tptp.set_Product_unit) (B tptp.product_unit)) (=> (@ tptp.bNF_We2091578341578594809t_unit R2) (=> (@ (@ tptp.ord_le3507040750410214029t_unit B4) (@ tptp.field_Product_unit R2)) (=> (@ (@ tptp.member_Product_unit B) B4) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit (@ (@ tptp.bNF_We7185707985517244377t_unit R2) B4)) B)) R2))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (B4 tptp.set_int) (B tptp.int)) (=> (@ tptp.bNF_We3815749466139970368el_int R2) (=> (@ (@ tptp.ord_less_eq_set_int B4) (@ tptp.field_int R2)) (=> (@ (@ tptp.member_int B) B4) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int (@ (@ tptp.bNF_We3272633801743244640im_int R2) B4)) B)) R2))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_nat) (B tptp.nat)) (=> (@ tptp.bNF_We3818239936649020644el_nat R2) (=> (@ (@ tptp.ord_less_eq_set_nat B4) (@ tptp.field_nat R2)) (=> (@ (@ tptp.member_nat B) B4) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.bNF_We3275124272252294916im_nat R2) B4)) B)) R2))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (@ (@ (@ tptp.bNF_We7204996500647184731t_unit R2) A2) B))) (let ((_let_2 (@ tptp.field_Product_unit R2))) (=> (@ tptp.bNF_We2091578341578594809t_unit R2) (=> (@ (@ tptp.member_Product_unit A2) _let_2) (=> (@ (@ tptp.member_Product_unit B) _let_2) (and (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit A2) _let_1)) R2) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit B) _let_1)) R2) (@ (@ tptp.member_Product_unit _let_1) (@ (@ tptp.insert_Product_unit A2) (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit)))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (A2 Bool) (B Bool)) (let ((_let_1 (@ (@ (@ tptp.bNF_We3104086342435940326max2_o R2) A2) B))) (let ((_let_2 (@ tptp.field_o R2))) (=> (@ tptp.bNF_We6437023980930612612_rel_o R2) (=> (@ (@ tptp.member_o A2) _let_2) (=> (@ (@ tptp.member_o B) _let_2) (and (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) _let_1)) R2) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o B) _let_1)) R2) (@ (@ tptp.member_o _let_1) (@ (@ tptp.insert_o A2) (@ (@ tptp.insert_o B) tptp.bot_bot_set_o)))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ (@ tptp.bNF_We2380939065524664066x2_nat R2) A2) B))) (let ((_let_2 (@ tptp.field_nat R2))) (=> (@ tptp.bNF_We3818239936649020644el_nat R2) (=> (@ (@ tptp.member_nat A2) _let_2) (=> (@ (@ tptp.member_nat B) _let_2) (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) _let_1)) R2) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) _let_1)) R2) (@ (@ tptp.member_nat _let_1) (@ (@ tptp.insert_nat A2) (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat)))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ (@ tptp.bNF_We2378448595015613790x2_int R2) A2) B))) (let ((_let_2 (@ tptp.field_int R2))) (=> (@ tptp.bNF_We3815749466139970368el_int R2) (=> (@ (@ tptp.member_int A2) _let_2) (=> (@ (@ tptp.member_int B) _let_2) (and (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) _let_1)) R2) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) _let_1)) R2) (@ (@ tptp.member_int _let_1) (@ (@ tptp.insert_int A2) (@ (@ tptp.insert_int B) tptp.bot_bot_set_int)))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ (@ tptp.bNF_We6400040844883348763_nat_o R2) A2) B))) (let ((_let_2 (@ tptp.field_81821745747897882_nat_o R2))) (=> (@ tptp.bNF_We740377018556551609_nat_o R2) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) _let_2) (=> (@ (@ tptp.member6576561426505652726_nat_o B) _let_2) (and (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) _let_1)) R2) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o B) _let_1)) R2) (@ (@ tptp.member6576561426505652726_nat_o _let_1) (@ (@ tptp.insert5175938949040314269_nat_o A2) (@ (@ tptp.insert5175938949040314269_nat_o B) tptp.bot_bo7824918357723582233_nat_o)))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ (@ tptp.bNF_We2380939065524664066x2_nat R2) A2) B))) (let ((_let_2 (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R2))) (=> (@ tptp.bNF_We3818239936649020644el_nat R2) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 A2))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ (@ tptp.bNF_We2378448595015613790x2_int R2) A2) B))) (let ((_let_2 (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R2))) (=> (@ tptp.bNF_We3815749466139970368el_int R2) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 A2))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.order_under_int R2))) (=> (@ tptp.trans_int R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R2) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.order_under_nat R2))) (=> (@ tptp.trans_nat R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R2) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (B4 tptp.set_Product_unit)) (=> (@ tptp.bNF_We2091578341578594809t_unit R2) (=> (@ (@ tptp.ord_le3507040750410214029t_unit B4) (@ tptp.field_Product_unit R2)) (=> (not (= B4 tptp.bot_bo3957492148770167129t_unit)) (@ (@ (@ tptp.bNF_We909621271159000003t_unit R2) B4) (@ (@ tptp.bNF_We7185707985517244377t_unit R2) B4)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (B4 tptp.set_o)) (=> (@ tptp.bNF_We6437023980930612612_rel_o R2) (=> (@ (@ tptp.ord_less_eq_set_o B4) (@ tptp.field_o R2)) (=> (not (= B4 tptp.bot_bot_set_o)) (@ (@ (@ tptp.bNF_We4647864369647134286inim_o R2) B4) (@ (@ tptp.bNF_We537455116209922916inim_o R2) B4)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (B4 tptp.set_int)) (=> (@ tptp.bNF_We3815749466139970368el_int R2) (=> (@ (@ tptp.ord_less_eq_set_int B4) (@ tptp.field_int R2)) (=> (not (= B4 tptp.bot_bot_set_int)) (@ (@ (@ tptp.bNF_We6511469253196982518im_int R2) B4) (@ (@ tptp.bNF_We3272633801743244640im_int R2) B4)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.bNF_We740377018556551609_nat_o R2) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o B4) (@ tptp.field_81821745747897882_nat_o R2)) (=> (not (= B4 tptp.bot_bo7824918357723582233_nat_o)) (@ (@ (@ tptp.bNF_We5608535359669600131_nat_o R2) B4) (@ (@ tptp.bNF_We8236795211600914329_nat_o R2) B4)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_nat)) (=> (@ tptp.bNF_We3818239936649020644el_nat R2) (=> (@ (@ tptp.ord_less_eq_set_nat B4) (@ tptp.field_nat R2)) (=> (not (= B4 tptp.bot_bot_set_nat)) (@ (@ (@ tptp.bNF_We6513959723706032794im_nat R2) B4) (@ (@ tptp.bNF_We3275124272252294916im_nat R2) B4)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (A tptp.set_Pr4532377907799695533_nat_o) (B (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.bNF_We740377018556551609_nat_o R2) (= (@ (@ (@ tptp.bNF_We5608535359669600131_nat_o R2) A) B) (and (@ (@ tptp.member6576561426505652726_nat_o B) A) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X2) A) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o B) X2)) R2))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (A tptp.set_o) (B Bool)) (=> (@ tptp.bNF_We6437023980930612612_rel_o R2) (= (@ (@ (@ tptp.bNF_We4647864369647134286inim_o R2) A) B) (and (@ (@ tptp.member_o B) A) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o B) X2)) R2))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (A tptp.set_Product_unit) (B tptp.product_unit)) (=> (@ tptp.bNF_We2091578341578594809t_unit R2) (= (@ (@ (@ tptp.bNF_We909621271159000003t_unit R2) A) B) (and (@ (@ tptp.member_Product_unit B) A) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) A) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit B) X2)) R2))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_nat) (B tptp.nat)) (=> (@ tptp.bNF_We3818239936649020644el_nat R2) (= (@ (@ (@ tptp.bNF_We6513959723706032794im_nat R2) A) B) (and (@ (@ tptp.member_nat B) A) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) X2)) R2))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A tptp.set_int) (B tptp.int)) (=> (@ tptp.bNF_We3815749466139970368el_int R2) (= (@ (@ (@ tptp.bNF_We6511469253196982518im_int R2) A) B) (and (@ (@ tptp.member_int B) A) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) X2)) R2))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ (@ tptp.bNF_We6400040844883348763_nat_o R2) A2) B))) (let ((_let_2 (@ tptp.field_81821745747897882_nat_o R2))) (=> (@ tptp.bNF_We740377018556551609_nat_o R2) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) _let_2) (=> (@ (@ tptp.member6576561426505652726_nat_o B) _let_2) (and (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) _let_1)) R2) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o B) _let_1)) R2)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (A2 Bool) (B Bool)) (let ((_let_1 (@ (@ (@ tptp.bNF_We3104086342435940326max2_o R2) A2) B))) (let ((_let_2 (@ tptp.field_o R2))) (=> (@ tptp.bNF_We6437023980930612612_rel_o R2) (=> (@ (@ tptp.member_o A2) _let_2) (=> (@ (@ tptp.member_o B) _let_2) (and (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) _let_1)) R2) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o B) _let_1)) R2)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (@ (@ (@ tptp.bNF_We7204996500647184731t_unit R2) A2) B))) (let ((_let_2 (@ tptp.field_Product_unit R2))) (=> (@ tptp.bNF_We2091578341578594809t_unit R2) (=> (@ (@ tptp.member_Product_unit A2) _let_2) (=> (@ (@ tptp.member_Product_unit B) _let_2) (and (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit A2) _let_1)) R2) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit B) _let_1)) R2)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ (@ tptp.bNF_We2380939065524664066x2_nat R2) A2) B))) (let ((_let_2 (@ tptp.field_nat R2))) (=> (@ tptp.bNF_We3818239936649020644el_nat R2) (=> (@ (@ tptp.member_nat A2) _let_2) (=> (@ (@ tptp.member_nat B) _let_2) (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) _let_1)) R2) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) _let_1)) R2)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ (@ tptp.bNF_We2378448595015613790x2_int R2) A2) B))) (let ((_let_2 (@ tptp.field_int R2))) (=> (@ tptp.bNF_We3815749466139970368el_int R2) (=> (@ (@ tptp.member_int A2) _let_2) (=> (@ (@ tptp.member_int B) _let_2) (and (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) _let_1)) R2) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) _let_1)) R2)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.field_81821745747897882_nat_o R2))) (=> (@ tptp.bNF_We740377018556551609_nat_o R2) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) _let_1) (=> (@ (@ tptp.member6576561426505652726_nat_o B) _let_1) (= (= (@ (@ (@ tptp.bNF_We6400040844883348763_nat_o R2) A2) B) B) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o A2) B)) R2))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (A2 Bool) (B Bool)) (let ((_let_1 (@ tptp.field_o R2))) (=> (@ tptp.bNF_We6437023980930612612_rel_o R2) (=> (@ (@ tptp.member_o A2) _let_1) (=> (@ (@ tptp.member_o B) _let_1) (= (= (@ (@ (@ tptp.bNF_We3104086342435940326max2_o R2) A2) B) B) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o A2) B)) R2))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (@ tptp.field_Product_unit R2))) (=> (@ tptp.bNF_We2091578341578594809t_unit R2) (=> (@ (@ tptp.member_Product_unit A2) _let_1) (=> (@ (@ tptp.member_Product_unit B) _let_1) (= (= (@ (@ (@ tptp.bNF_We7204996500647184731t_unit R2) A2) B) B) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit A2) B)) R2))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.field_nat R2))) (=> (@ tptp.bNF_We3818239936649020644el_nat R2) (=> (@ (@ tptp.member_nat A2) _let_1) (=> (@ (@ tptp.member_nat B) _let_1) (= (= (@ (@ (@ tptp.bNF_We2380939065524664066x2_nat R2) A2) B) B) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R2))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.field_int R2))) (=> (@ tptp.bNF_We3815749466139970368el_int R2) (=> (@ (@ tptp.member_int A2) _let_1) (=> (@ (@ tptp.member_int B) _let_1) (= (= (@ (@ (@ tptp.bNF_We2378448595015613790x2_int R2) A2) B) B) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R2))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.field_81821745747897882_nat_o R2))) (=> (@ tptp.bNF_We740377018556551609_nat_o R2) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) _let_1) (=> (@ (@ tptp.member6576561426505652726_nat_o B) _let_1) (= (= (@ (@ (@ tptp.bNF_We6400040844883348763_nat_o R2) A2) B) A2) (@ (@ tptp.member8781333585448626064_nat_o (@ (@ tptp.produc7368190662567826135_nat_o B) A2)) R2))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (A2 Bool) (B Bool)) (let ((_let_1 (@ tptp.field_o R2))) (=> (@ tptp.bNF_We6437023980930612612_rel_o R2) (=> (@ (@ tptp.member_o A2) _let_1) (=> (@ (@ tptp.member_o B) _let_1) (= (= (@ (@ (@ tptp.bNF_We3104086342435940326max2_o R2) A2) B) A2) (@ (@ tptp.member7466972457876170832od_o_o (@ (@ tptp.product_Pair_o_o B) A2)) R2))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (@ tptp.field_Product_unit R2))) (=> (@ tptp.bNF_We2091578341578594809t_unit R2) (=> (@ (@ tptp.member_Product_unit A2) _let_1) (=> (@ (@ tptp.member_Product_unit B) _let_1) (= (= (@ (@ (@ tptp.bNF_We7204996500647184731t_unit R2) A2) B) A2) (@ (@ tptp.member7821138191923116944t_unit (@ (@ tptp.produc5692694829384537815t_unit B) A2)) R2))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.field_nat R2))) (=> (@ tptp.bNF_We3818239936649020644el_nat R2) (=> (@ (@ tptp.member_nat A2) _let_1) (=> (@ (@ tptp.member_nat B) _let_1) (= (= (@ (@ (@ tptp.bNF_We2380939065524664066x2_nat R2) A2) B) A2) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B) A2)) R2))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.field_int R2))) (=> (@ tptp.bNF_We3815749466139970368el_int R2) (=> (@ (@ tptp.member_int A2) _let_1) (=> (@ (@ tptp.member_int B) _let_1) (= (= (@ (@ (@ tptp.bNF_We2378448595015613790x2_int R2) A2) B) A2) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B) A2)) R2))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (@ tptp.field_Product_unit R2))) (=> (@ tptp.bNF_We2091578341578594809t_unit R2) (=> (@ (@ tptp.member_Product_unit A2) _let_1) (=> (@ (@ tptp.member_Product_unit B) _let_1) (@ (@ tptp.member_Product_unit (@ (@ (@ tptp.bNF_We7204996500647184731t_unit R2) A2) B)) (@ (@ tptp.insert_Product_unit A2) (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Product_prod_o_o) (A2 Bool) (B Bool)) (let ((_let_1 (@ tptp.field_o R2))) (=> (@ tptp.bNF_We6437023980930612612_rel_o R2) (=> (@ (@ tptp.member_o A2) _let_1) (=> (@ (@ tptp.member_o B) _let_1) (@ (@ tptp.member_o (@ (@ (@ tptp.bNF_We3104086342435940326max2_o R2) A2) B)) (@ (@ tptp.insert_o A2) (@ (@ tptp.insert_o B) tptp.bot_bot_set_o)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.field_nat R2))) (=> (@ tptp.bNF_We3818239936649020644el_nat R2) (=> (@ (@ tptp.member_nat A2) _let_1) (=> (@ (@ tptp.member_nat B) _let_1) (@ (@ tptp.member_nat (@ (@ (@ tptp.bNF_We2380939065524664066x2_nat R2) A2) B)) (@ (@ tptp.insert_nat A2) (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.field_int R2))) (=> (@ tptp.bNF_We3815749466139970368el_int R2) (=> (@ (@ tptp.member_int A2) _let_1) (=> (@ (@ tptp.member_int B) _let_1) (@ (@ tptp.member_int (@ (@ (@ tptp.bNF_We2378448595015613790x2_int R2) A2) B)) (@ (@ tptp.insert_int A2) (@ (@ tptp.insert_int B) tptp.bot_bot_set_int)))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.field_81821745747897882_nat_o R2))) (=> (@ tptp.bNF_We740377018556551609_nat_o R2) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) _let_1) (=> (@ (@ tptp.member6576561426505652726_nat_o B) _let_1) (@ (@ tptp.member6576561426505652726_nat_o (@ (@ (@ tptp.bNF_We6400040844883348763_nat_o R2) A2) B)) (@ (@ tptp.insert5175938949040314269_nat_o A2) (@ (@ tptp.insert5175938949040314269_nat_o B) tptp.bot_bo7824918357723582233_nat_o)))))))))
% 5.61/5.92 (assert (forall ((C tptp.set_set_nat) (S tptp.set_set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.chains_nat2 S))) (=> (@ (@ tptp.member_set_set_nat C) _let_1) (=> (@ (@ tptp.member_set_nat Z) S) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) C) (@ (@ tptp.ord_less_eq_set_nat X3) Z))) (@ (@ tptp.member_set_set_nat (@ (@ tptp.sup_sup_set_set_nat (@ (@ tptp.insert_set_nat Z) tptp.bot_bot_set_set_nat)) C)) _let_1)))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.order_5251275573222108571on_nat (@ tptp.field_nat R2)) R2) (=> (forall ((C6 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat C6) (@ tptp.chains_nat R2)) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) (@ tptp.field_nat R2)) (forall ((Xa3 tptp.nat)) (=> (@ (@ tptp.member_nat Xa3) C6) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Xa3) X6)) R2))))))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) (@ tptp.field_nat R2)) (forall ((Xa2 tptp.nat)) (=> (@ (@ tptp.member_nat Xa2) (@ tptp.field_nat R2)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Xa2)) R2) (= Xa2 X3))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.order_5248785102713058295on_int (@ tptp.field_int R2)) R2) (=> (forall ((C6 tptp.set_int)) (=> (@ (@ tptp.member_set_int C6) (@ tptp.chains_int R2)) (exists ((X6 tptp.int)) (and (@ (@ tptp.member_int X6) (@ tptp.field_int R2)) (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) C6) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Xa3) X6)) R2))))))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ tptp.field_int R2)) (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ tptp.field_int R2)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Xa2)) R2) (= Xa2 X3))))))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A1 tptp.nat) (A22 tptp.nat) (B1 tptp.nat) (B22 tptp.nat)) (let ((_let_1 (@ tptp.bNF_We2380939065524664066x2_nat R2))) (=> (@ (@ tptp.order_2888998067076097458on_nat (@ tptp.field_nat R2)) R2) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A1) A22)) (@ (@ tptp.product_Pair_nat_nat B1) B22))) (@ tptp.bNF_We1732890022510290291qr_nat R2)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_1 A1) A22)) (@ (@ _let_1 B1) B22))) R2))))))
% 5.61/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A1 tptp.int) (A22 tptp.int) (B1 tptp.int) (B22 tptp.int)) (let ((_let_1 (@ tptp.bNF_We2378448595015613790x2_int R2))) (=> (@ (@ tptp.order_2886507596567047182on_int (@ tptp.field_int R2)) R2) (=> (@ (@ tptp.member8566619992076573584nt_int (@ (@ tptp.produc3646306378393792727nt_int (@ (@ tptp.product_Pair_int_int A1) A22)) (@ (@ tptp.product_Pair_int_int B1) B22))) (@ tptp.bNF_We1730399552001240015qr_int R2)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int (@ (@ _let_1 A1) A22)) (@ (@ _let_1 B1) B22))) R2))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_se8994758365886191399t_unit)) (=> (forall ((X3 tptp.set_Pr5094982260447487303t_unit)) (=> (@ (@ tptp.member1248447801810324848t_unit X3) R3) (@ tptp.wf_Product_unit X3))) (=> (forall ((X3 tptp.set_Pr5094982260447487303t_unit)) (=> (@ (@ tptp.member1248447801810324848t_unit X3) R3) (forall ((Xa3 tptp.set_Pr5094982260447487303t_unit)) (=> (@ (@ tptp.member1248447801810324848t_unit Xa3) R3) (=> (not (= X3 Xa3)) (= (@ (@ tptp.inf_in4660618365625256667t_unit (@ tptp.domain4292024440186670924t_unit X3)) (@ tptp.range_6617724647562260917t_unit Xa3)) tptp.bot_bo3957492148770167129t_unit)))))) (@ tptp.wf_Product_unit (@ tptp.comple2798140142350441396t_unit R3))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_se491199571785101031od_o_o)) (=> (forall ((X3 tptp.set_Product_prod_o_o)) (=> (@ (@ tptp.member3157015407008874800od_o_o X3) R3) (@ tptp.wf_o X3))) (=> (forall ((X3 tptp.set_Product_prod_o_o)) (=> (@ (@ tptp.member3157015407008874800od_o_o X3) R3) (forall ((Xa3 tptp.set_Product_prod_o_o)) (=> (@ (@ tptp.member3157015407008874800od_o_o Xa3) R3) (=> (not (= X3 Xa3)) (= (@ (@ tptp.inf_inf_set_o (@ tptp.domain_o_o X3)) (@ tptp.range_o_o Xa3)) tptp.bot_bot_set_o)))))) (@ tptp.wf_o (@ tptp.comple2567785453016644468od_o_o R3))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_se7855581050983116737at_nat)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member2643936169264416010at_nat X3) R3) (@ tptp.wf_nat X3))) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member2643936169264416010at_nat X3) R3) (forall ((Xa3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member2643936169264416010at_nat Xa3) R3) (=> (not (= X3 Xa3)) (= (@ (@ tptp.inf_inf_set_nat (@ tptp.domain_nat_nat X3)) (@ tptp.range_nat_nat Xa3)) tptp.bot_bot_set_nat)))))) (@ tptp.wf_nat (@ tptp.comple5685304695842803022at_nat R3))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_se6260736226359567993nt_int)) (=> (forall ((X3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int X3) R3) (@ tptp.wf_int X3))) (=> (forall ((X3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int X3) R3) (forall ((Xa3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member2340774599025711042nt_int Xa3) R3) (=> (not (= X3 Xa3)) (= (@ (@ tptp.inf_inf_set_int (@ tptp.domain_int_int X3)) (@ tptp.range_int_int Xa3)) tptp.bot_bot_set_int)))))) (@ tptp.wf_int (@ tptp.comple5382143125604098054nt_int R3))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_se7663487083892625191_nat_o)) (=> (forall ((X3 tptp.set_Pr2161125870931222855_nat_o)) (=> (@ (@ tptp.member5475208728337331568_nat_o X3) R3) (@ tptp.wf_Pro8787509627421085110_nat_o X3))) (=> (forall ((X3 tptp.set_Pr2161125870931222855_nat_o)) (=> (@ (@ tptp.member5475208728337331568_nat_o X3) R3) (forall ((Xa3 tptp.set_Pr2161125870931222855_nat_o)) (=> (@ (@ tptp.member5475208728337331568_nat_o Xa3) R3) (=> (not (= X3 Xa3)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ tptp.domain4881241903163524940_nat_o X3)) (@ tptp.range_5289318983786108341_nat_o Xa3)) tptp.bot_bo7824918357723582233_nat_o)))))) (@ tptp.wf_Pro8787509627421085110_nat_o (@ tptp.comple8164645552537203636_nat_o R3))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_Product_unit) (Y6 tptp.set_Product_unit)) (= (= (@ tptp.pow_Product_unit X4) (@ (@ tptp.insert8986028188087627965t_unit Y6) tptp.bot_bo6284674557190688313t_unit)) (and (= X4 tptp.bot_bo3957492148770167129t_unit) (= Y6 tptp.bot_bo3957492148770167129t_unit)))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_o) (Y6 tptp.set_o)) (= (= (@ tptp.pow_o X4) (@ (@ tptp.insert_set_o Y6) tptp.bot_bot_set_set_o)) (and (= X4 tptp.bot_bot_set_o) (= Y6 tptp.bot_bot_set_o)))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_nat) (Y6 tptp.set_nat)) (= (= (@ tptp.pow_nat X4) (@ (@ tptp.insert_set_nat Y6) tptp.bot_bot_set_set_nat)) (and (= X4 tptp.bot_bot_set_nat) (= Y6 tptp.bot_bot_set_nat)))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_int) (Y6 tptp.set_int)) (= (= (@ tptp.pow_int X4) (@ (@ tptp.insert_set_int Y6) tptp.bot_bot_set_set_int)) (and (= X4 tptp.bot_bot_set_int) (= Y6 tptp.bot_bot_set_int)))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_Pr4532377907799695533_nat_o) (Y6 tptp.set_Pr4532377907799695533_nat_o)) (= (= (@ tptp.pow_Pr7829143134171777386_nat_o X4) (@ (@ tptp.insert2507855216428400253_nat_o Y6) tptp.bot_bo3736544561982865913_nat_o)) (and (= X4 tptp.bot_bo7824918357723582233_nat_o) (= Y6 tptp.bot_bo7824918357723582233_nat_o)))))
% 5.61/5.92 (assert (= (@ tptp.pow_Product_unit tptp.bot_bo3957492148770167129t_unit) (@ (@ tptp.insert8986028188087627965t_unit tptp.bot_bo3957492148770167129t_unit) tptp.bot_bo6284674557190688313t_unit)))
% 5.61/5.92 (assert (= (@ tptp.pow_o tptp.bot_bot_set_o) (@ (@ tptp.insert_set_o tptp.bot_bot_set_o) tptp.bot_bot_set_set_o)))
% 5.61/5.92 (assert (= (@ tptp.pow_nat tptp.bot_bot_set_nat) (@ (@ tptp.insert_set_nat tptp.bot_bot_set_nat) tptp.bot_bot_set_set_nat)))
% 5.61/5.92 (assert (= (@ tptp.pow_int tptp.bot_bot_set_int) (@ (@ tptp.insert_set_int tptp.bot_bot_set_int) tptp.bot_bot_set_set_int)))
% 5.61/5.92 (assert (= (@ tptp.pow_Pr7829143134171777386_nat_o tptp.bot_bo7824918357723582233_nat_o) (@ (@ tptp.insert2507855216428400253_nat_o tptp.bot_bo7824918357723582233_nat_o) tptp.bot_bo3736544561982865913_nat_o)))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (B tptp.nat) (E tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) (@ tptp.transi2905341329935302413cl_nat E)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat (@ F A2)) (@ F B))) (@ tptp.transi2905341329935302413cl_nat (@ (@ tptp.image_5168914502847457605at_nat (@ tptp.pairself_nat_nat F)) E))))))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (B tptp.nat) (E tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) (@ tptp.transi2905341329935302413cl_nat E)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int (@ F A2)) (@ F B))) (@ tptp.transi2902850859426252137cl_int (@ (@ tptp.image_1990417195239315453nt_int (@ tptp.pairself_nat_int F)) E))))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (B tptp.int) (E tptp.set_Pr958786334691620121nt_int) (F (-> tptp.int tptp.nat))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) (@ tptp.transi2902850859426252137cl_int E)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat (@ F A2)) (@ F B))) (@ tptp.transi2905341329935302413cl_nat (@ (@ tptp.image_5831868185956570253at_nat (@ tptp.pairself_int_nat F)) E))))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (B tptp.int) (E tptp.set_Pr958786334691620121nt_int) (F (-> tptp.int tptp.int))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) (@ tptp.transi2902850859426252137cl_int E)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int (@ F A2)) (@ F B))) (@ tptp.transi2902850859426252137cl_int (@ (@ tptp.image_2653370878348428101nt_int (@ tptp.pairself_int_int F)) E))))))
% 5.61/5.92 (assert (forall ((A11 tptp.set_set_nat) (F (-> tptp.set_nat tptp.set_nat))) (let ((_let_1 (@ tptp.pairwise_set_nat tptp.disjnt_nat))) (=> (@ _let_1 A11) (=> (forall ((X8 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X8) A11) (@ (@ tptp.ord_less_eq_set_nat (@ F X8)) X8))) (@ _let_1 (@ (@ tptp.image_7916887816326733075et_nat F) A11)))))))
% 5.61/5.92 (assert (forall ((X (-> tptp.nat tptp.nat)) (Xa tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (=> (= (@ (@ tptp.pairself_nat_nat X) Xa) Y) (=> (@ (@ tptp.accp_P4147487641329543982at_nat tptp.pairself_rel_nat_nat) (@ (@ tptp.produc4237282728380940073at_nat X) Xa)) (not (forall ((A4 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat A4) B2))) (=> (= Xa _let_1) (=> (= Y (@ (@ tptp.product_Pair_nat_nat (@ X A4)) (@ X B2))) (not (@ (@ tptp.accp_P4147487641329543982at_nat tptp.pairself_rel_nat_nat) (@ (@ tptp.produc4237282728380940073at_nat X) _let_1))))))))))))
% 5.61/5.92 (assert (forall ((X (-> tptp.nat tptp.int)) (Xa tptp.product_prod_nat_nat) (Y tptp.product_prod_int_int)) (=> (= (@ (@ tptp.pairself_nat_int X) Xa) Y) (=> (@ (@ tptp.accp_P3050404660685545426at_nat tptp.pairself_rel_nat_int) (@ (@ tptp.produc3140199747736941517at_nat X) Xa)) (not (forall ((A4 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat A4) B2))) (=> (= Xa _let_1) (=> (= Y (@ (@ tptp.product_Pair_int_int (@ X A4)) (@ X B2))) (not (@ (@ tptp.accp_P3050404660685545426at_nat tptp.pairself_rel_nat_int) (@ (@ tptp.produc3140199747736941517at_nat X) _let_1))))))))))))
% 5.61/5.92 (assert (forall ((X (-> tptp.int tptp.nat)) (Xa tptp.product_prod_int_int) (Y tptp.product_prod_nat_nat)) (=> (= (@ (@ tptp.pairself_int_nat X) Xa) Y) (=> (@ (@ tptp.accp_P5604362734843950218nt_int tptp.pairself_rel_int_nat) (@ (@ tptp.produc2818822084525909125nt_int X) Xa)) (not (forall ((A4 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ (@ tptp.product_Pair_int_int A4) B2))) (=> (= Xa _let_1) (=> (= Y (@ (@ tptp.product_Pair_nat_nat (@ X A4)) (@ X B2))) (not (@ (@ tptp.accp_P5604362734843950218nt_int tptp.pairself_rel_int_nat) (@ (@ tptp.produc2818822084525909125nt_int X) _let_1))))))))))))
% 5.61/5.92 (assert (forall ((X (-> tptp.int tptp.int)) (Xa tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (=> (= (@ (@ tptp.pairself_int_int X) Xa) Y) (=> (@ (@ tptp.accp_P4507279754199951662nt_int tptp.pairself_rel_int_int) (@ (@ tptp.produc1721739103881910569nt_int X) Xa)) (not (forall ((A4 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ (@ tptp.product_Pair_int_int A4) B2))) (=> (= Xa _let_1) (=> (= Y (@ (@ tptp.product_Pair_int_int (@ X A4)) (@ X B2))) (not (@ (@ tptp.accp_P4507279754199951662nt_int tptp.pairself_rel_int_int) (@ (@ tptp.produc1721739103881910569nt_int X) _let_1))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.member_set_nat A) (@ tptp.pow_nat B4)) (@ (@ tptp.ord_less_eq_set_nat A) B4))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (@ (@ tptp.member_set_nat A) (@ tptp.pow_nat B4)))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (@ tptp.pow_nat (@ (@ tptp.inf_inf_set_nat A) B4)) (@ (@ tptp.inf_inf_set_set_nat (@ tptp.pow_nat A)) (@ tptp.pow_nat B4)))))
% 5.61/5.92 (assert (forall ((S tptp.set_Pr4532377907799695533_nat_o) (R3 (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) S) (=> (@ (@ tptp.member6576561426505652726_nat_o Y2) S) (=> (not (= X3 Y2)) (@ (@ R3 X3) Y2))))) (@ (@ tptp.pairwi2432143822833250616_nat_o R3) S))))
% 5.61/5.92 (assert (forall ((S tptp.set_nat) (R3 (-> tptp.nat tptp.nat Bool))) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (=> (@ (@ tptp.member_nat Y2) S) (=> (not (= X3 Y2)) (@ (@ R3 X3) Y2))))) (@ (@ tptp.pairwise_nat R3) S))))
% 5.61/5.92 (assert (forall ((S tptp.set_int) (R3 (-> tptp.int tptp.int Bool))) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (=> (@ (@ tptp.member_int Y2) S) (=> (not (= X3 Y2)) (@ (@ R3 X3) Y2))))) (@ (@ tptp.pairwise_int R3) S))))
% 5.61/5.92 (assert (forall ((S tptp.set_o) (R3 (-> Bool Bool Bool))) (=> (forall ((X3 Bool) (Y2 Bool)) (=> (@ (@ tptp.member_o X3) S) (=> (@ (@ tptp.member_o Y2) S) (=> (not (= X3 Y2)) (@ (@ R3 X3) Y2))))) (@ (@ tptp.pairwise_o R3) S))))
% 5.61/5.92 (assert (forall ((S tptp.set_Product_unit) (R3 (-> tptp.product_unit tptp.product_unit Bool))) (=> (forall ((X3 tptp.product_unit) (Y2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) S) (=> (@ (@ tptp.member_Product_unit Y2) S) (=> (not (= X3 Y2)) (@ (@ R3 X3) Y2))))) (@ (@ tptp.pairwi7919127943033184120t_unit R3) S))))
% 5.61/5.92 (assert (forall ((R3 (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (S tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.pairwi2432143822833250616_nat_o R3) S) (=> (@ (@ tptp.member6576561426505652726_nat_o X) S) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) S) (=> (not (= X Y)) (@ (@ R3 X) Y)))))))
% 5.61/5.92 (assert (forall ((R3 (-> tptp.nat tptp.nat Bool)) (S tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.pairwise_nat R3) S) (=> (@ (@ tptp.member_nat X) S) (=> (@ (@ tptp.member_nat Y) S) (=> (not (= X Y)) (@ (@ R3 X) Y)))))))
% 5.61/5.92 (assert (forall ((R3 (-> tptp.int tptp.int Bool)) (S tptp.set_int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.pairwise_int R3) S) (=> (@ (@ tptp.member_int X) S) (=> (@ (@ tptp.member_int Y) S) (=> (not (= X Y)) (@ (@ R3 X) Y)))))))
% 5.61/5.92 (assert (forall ((R3 (-> Bool Bool Bool)) (S tptp.set_o) (X Bool) (Y Bool)) (=> (@ (@ tptp.pairwise_o R3) S) (=> (@ (@ tptp.member_o X) S) (=> (@ (@ tptp.member_o Y) S) (=> (not (= X Y)) (@ (@ R3 X) Y)))))))
% 5.61/5.92 (assert (forall ((R3 (-> tptp.product_unit tptp.product_unit Bool)) (S tptp.set_Product_unit) (X tptp.product_unit) (Y tptp.product_unit)) (=> (@ (@ tptp.pairwi7919127943033184120t_unit R3) S) (=> (@ (@ tptp.member_Product_unit X) S) (=> (@ (@ tptp.member_Product_unit Y) S) (=> (not (= X Y)) (@ (@ R3 X) Y)))))))
% 5.61/5.92 (assert (forall ((S tptp.set_nat) (A (-> tptp.nat tptp.set_nat)) (R2 (-> tptp.nat tptp.set_Pr1261947904930325089at_nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (@ (@ tptp.refl_on_nat (@ A X3)) (@ R2 X3)))) (@ (@ tptp.refl_on_nat (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat A) S))) (@ tptp.comple5685304695842803022at_nat (@ (@ tptp.image_7178329752028323786at_nat R2) S))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_Product_unit)) (@ (@ tptp.member5877623283571906838t_unit tptp.bot_bo3957492148770167129t_unit) (@ tptp.pow_Product_unit B4))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_o)) (@ (@ tptp.member_set_o tptp.bot_bot_set_o) (@ tptp.pow_o B4))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_nat)) (@ (@ tptp.member_set_nat tptp.bot_bot_set_nat) (@ tptp.pow_nat B4))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_int)) (@ (@ tptp.member_set_int tptp.bot_bot_set_int) (@ tptp.pow_int B4))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_Pr4532377907799695533_nat_o)) (@ (@ tptp.member1452989533377600726_nat_o tptp.bot_bo7824918357723582233_nat_o) (@ tptp.pow_Pr7829143134171777386_nat_o B4))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.pow_nat A)) (@ tptp.pow_nat B4)))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat A) (@ tptp.pow_nat B4)) (@ (@ tptp.ord_less_eq_set_nat A) B4))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.sup_sup_set_set_nat (@ tptp.pow_nat A)) (@ tptp.pow_nat B4))) (@ tptp.pow_nat (@ (@ tptp.sup_sup_set_nat A) B4)))))
% 5.61/5.92 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer)) (P (-> tptp.code_integer tptp.code_integer Bool))) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (let ((_let_1 (@ F Y2))) (let ((_let_2 (@ F X3))) (=> (@ (@ tptp.member_Code_integer X3) A) (=> (@ (@ tptp.member_Code_integer Y2) A) (=> (not (= X3 Y2)) (=> (not (= _let_2 _let_1)) (@ (@ P _let_2) _let_1)))))))) (@ (@ tptp.pairwi4741737654671186738nteger P) (@ (@ tptp.image_4470545334726330049nteger F) A)))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.set_nat)) (P (-> tptp.set_nat tptp.set_nat Bool))) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ F Y2))) (let ((_let_2 (@ F X3))) (=> (@ (@ tptp.member_nat X3) A) (=> (@ (@ tptp.member_nat Y2) A) (=> (not (= X3 Y2)) (=> (not (= _let_2 _let_1)) (@ (@ P _let_2) _let_1)))))))) (@ (@ tptp.pairwise_set_nat P) (@ (@ tptp.image_nat_set_nat F) A)))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat)) (P (-> tptp.nat tptp.nat Bool))) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ F Y2))) (let ((_let_2 (@ F X3))) (=> (@ (@ tptp.member_nat X3) A) (=> (@ (@ tptp.member_nat Y2) A) (=> (not (= X3 Y2)) (=> (not (= _let_2 _let_1)) (@ (@ P _let_2) _let_1)))))))) (@ (@ tptp.pairwise_nat P) (@ (@ tptp.image_nat_nat2 F) A)))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.code_integer)) (P (-> tptp.code_integer tptp.code_integer Bool))) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ F Y2))) (let ((_let_2 (@ F X3))) (=> (@ (@ tptp.member_nat X3) A) (=> (@ (@ tptp.member_nat Y2) A) (=> (not (= X3 Y2)) (=> (not (= _let_2 _let_1)) (@ (@ P _let_2) _let_1)))))))) (@ (@ tptp.pairwi4741737654671186738nteger P) (@ (@ tptp.image_1215581382706833972nteger F) A)))))
% 5.61/5.92 (assert (forall ((P (-> tptp.product_unit tptp.product_unit Bool))) (@ (@ tptp.pairwi7919127943033184120t_unit P) tptp.bot_bo3957492148770167129t_unit)))
% 5.61/5.92 (assert (forall ((P (-> Bool Bool Bool))) (@ (@ tptp.pairwise_o P) tptp.bot_bot_set_o)))
% 5.61/5.92 (assert (forall ((P (-> tptp.nat tptp.nat Bool))) (@ (@ tptp.pairwise_nat P) tptp.bot_bot_set_nat)))
% 5.61/5.92 (assert (forall ((P (-> tptp.int tptp.int Bool))) (@ (@ tptp.pairwise_int P) tptp.bot_bot_set_int)))
% 5.61/5.92 (assert (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (@ (@ tptp.pairwi2432143822833250616_nat_o P) tptp.bot_bo7824918357723582233_nat_o)))
% 5.61/5.92 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (S tptp.set_nat) (T2 tptp.set_nat)) (let ((_let_1 (@ tptp.pairwise_nat P))) (=> (@ _let_1 S) (=> (@ (@ tptp.ord_less_eq_set_nat T2) S) (@ _let_1 T2))))))
% 5.61/5.92 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.set_nat) (Q2 (-> tptp.nat tptp.nat Bool)) (B4 tptp.set_nat)) (=> (@ (@ tptp.pairwise_nat P) A) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ P X3) Y2) (@ (@ Q2 X3) Y2))) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A) (@ (@ tptp.pairwise_nat Q2) B4))))))
% 5.61/5.92 (assert (forall ((R2 (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (X (-> tptp.produc3658429121746597890et_nat Bool)) (S2 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.pairwi2432143822833250616_nat_o R2))) (= (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o X) S2)) (and (forall ((Y3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (and (@ (@ tptp.member6576561426505652726_nat_o Y3) S2) (not (= Y3 X))) (and (@ (@ R2 X) Y3) (@ (@ R2 Y3) X)))) (@ _let_1 S2))))))
% 5.61/5.92 (assert (forall ((R2 (-> tptp.nat tptp.nat Bool)) (X tptp.nat) (S2 tptp.set_nat)) (let ((_let_1 (@ tptp.pairwise_nat R2))) (= (@ _let_1 (@ (@ tptp.insert_nat X) S2)) (and (forall ((Y3 tptp.nat)) (=> (and (@ (@ tptp.member_nat Y3) S2) (not (= Y3 X))) (and (@ (@ R2 X) Y3) (@ (@ R2 Y3) X)))) (@ _let_1 S2))))))
% 5.61/5.92 (assert (forall ((R2 (-> tptp.int tptp.int Bool)) (X tptp.int) (S2 tptp.set_int)) (let ((_let_1 (@ tptp.pairwise_int R2))) (= (@ _let_1 (@ (@ tptp.insert_int X) S2)) (and (forall ((Y3 tptp.int)) (=> (and (@ (@ tptp.member_int Y3) S2) (not (= Y3 X))) (and (@ (@ R2 X) Y3) (@ (@ R2 Y3) X)))) (@ _let_1 S2))))))
% 5.61/5.92 (assert (forall ((R2 (-> Bool Bool Bool)) (X Bool) (S2 tptp.set_o)) (let ((_let_1 (@ tptp.pairwise_o R2))) (= (@ _let_1 (@ (@ tptp.insert_o X) S2)) (and (forall ((Y3 Bool)) (=> (and (@ (@ tptp.member_o Y3) S2) (not (= Y3 X))) (and (@ (@ R2 X) Y3) (@ (@ R2 Y3) X)))) (@ _let_1 S2))))))
% 5.61/5.92 (assert (forall ((R2 (-> tptp.product_unit tptp.product_unit Bool)) (X tptp.product_unit) (S2 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.pairwi7919127943033184120t_unit R2))) (= (@ _let_1 (@ (@ tptp.insert_Product_unit X) S2)) (and (forall ((Y3 tptp.product_unit)) (=> (and (@ (@ tptp.member_Product_unit Y3) S2) (not (= Y3 X))) (and (@ (@ R2 X) Y3) (@ (@ R2 Y3) X)))) (@ _let_1 S2))))))
% 5.61/5.92 (assert (forall ((B4 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.set_nat)) (A tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.finite_finite_nat (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_6888641473154130958et_nat B4) A))) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) A) (@ tptp.finite_finite_nat (@ B4 A2))))))
% 5.61/5.92 (assert (forall ((B4 (-> tptp.nat tptp.set_nat)) (A tptp.set_nat) (A2 tptp.nat)) (=> (@ tptp.finite_finite_nat (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat B4) A))) (=> (@ (@ tptp.member_nat A2) A) (@ tptp.finite_finite_nat (@ B4 A2))))))
% 5.61/5.92 (assert (forall ((B4 (-> tptp.int tptp.set_nat)) (A tptp.set_int) (A2 tptp.int)) (=> (@ tptp.finite_finite_nat (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_int_set_nat B4) A))) (=> (@ (@ tptp.member_int A2) A) (@ tptp.finite_finite_nat (@ B4 A2))))))
% 5.61/5.92 (assert (forall ((B4 (-> Bool tptp.set_nat)) (A tptp.set_o) (A2 Bool)) (=> (@ tptp.finite_finite_nat (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_o_set_nat B4) A))) (=> (@ (@ tptp.member_o A2) A) (@ tptp.finite_finite_nat (@ B4 A2))))))
% 5.61/5.92 (assert (forall ((B4 (-> tptp.product_unit tptp.set_nat)) (A tptp.set_Product_unit) (A2 tptp.product_unit)) (=> (@ tptp.finite_finite_nat (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_8173849991827986510et_nat B4) A))) (=> (@ (@ tptp.member_Product_unit A2) A) (@ tptp.finite_finite_nat (@ B4 A2))))))
% 5.61/5.92 (assert (forall ((B4 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.set_Code_integer)) (A tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.comple739944243200306918nteger (@ (@ tptp.image_8657708916238040603nteger B4) A))) (=> (@ (@ tptp.member6576561426505652726_nat_o A2) A) (@ tptp.finite6017078050557962740nteger (@ B4 A2))))))
% 5.61/5.92 (assert (forall ((B4 (-> tptp.nat tptp.set_Code_integer)) (A tptp.set_nat) (A2 tptp.nat)) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.comple739944243200306918nteger (@ (@ tptp.image_2385391725447763818nteger B4) A))) (=> (@ (@ tptp.member_nat A2) A) (@ tptp.finite6017078050557962740nteger (@ B4 A2))))))
% 5.61/5.92 (assert (forall ((B4 (-> tptp.int tptp.set_Code_integer)) (A tptp.set_int) (A2 tptp.int)) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.comple739944243200306918nteger (@ (@ tptp.image_75573793354812870nteger B4) A))) (=> (@ (@ tptp.member_int A2) A) (@ tptp.finite6017078050557962740nteger (@ B4 A2))))))
% 5.61/5.92 (assert (forall ((B4 (-> Bool tptp.set_Code_integer)) (A tptp.set_o) (A2 Bool)) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.comple739944243200306918nteger (@ (@ tptp.image_6491638074533506790nteger B4) A))) (=> (@ (@ tptp.member_o A2) A) (@ tptp.finite6017078050557962740nteger (@ B4 A2))))))
% 5.61/5.92 (assert (forall ((B4 (-> tptp.product_unit tptp.set_Code_integer)) (A tptp.set_Product_unit) (A2 tptp.product_unit)) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.comple739944243200306918nteger (@ (@ tptp.image_4571654851662262875nteger B4) A))) (=> (@ (@ tptp.member_Product_unit A2) A) (@ tptp.finite6017078050557962740nteger (@ B4 A2))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A tptp.set_nat) (B4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.image_nat_set_nat F))) (=> (= (@ _let_1 A) B4) (= (@ (@ tptp.image_6725021117256019401et_nat _let_1) (@ tptp.pow_nat A)) (@ tptp.pow_set_nat B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_nat2 F))) (=> (= (@ _let_1 A) B4) (= (@ (@ tptp.image_7916887816326733075et_nat _let_1) (@ tptp.pow_nat A)) (@ tptp.pow_nat B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer) (B4 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.image_4470545334726330049nteger F))) (=> (= (@ _let_1 A) B4) (= (@ (@ tptp.image_6270750266955655469nteger _let_1) (@ tptp.pow_Code_integer A)) (@ tptp.pow_Code_integer B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.set_nat) (B4 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.image_1215581382706833972nteger F))) (=> (= (@ _let_1 A) B4) (= (@ (@ tptp.image_6916300684244607776nteger _let_1) (@ tptp.pow_nat A)) (@ tptp.pow_Code_integer B4))))))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.pow_nat A))) (let ((_let_2 (@ tptp.insert_nat A2))) (= (@ tptp.pow_nat (@ _let_2 A)) (@ (@ tptp.sup_sup_set_set_nat _let_1) (@ (@ tptp.image_7916887816326733075et_nat _let_2) _let_1)))))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.pow_int A))) (let ((_let_2 (@ tptp.insert_int A2))) (= (@ tptp.pow_int (@ _let_2 A)) (@ (@ tptp.sup_sup_set_set_int _let_1) (@ (@ tptp.image_524474410958335435et_int _let_2) _let_1)))))))
% 5.61/5.92 (assert (forall ((A2 Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.pow_o A))) (let ((_let_2 (@ tptp.insert_o A2))) (= (@ tptp.pow_o (@ _let_2 A)) (@ (@ tptp.sup_sup_set_set_o _let_1) (@ (@ tptp.image_set_o_set_o _let_2) _let_1)))))))
% 5.61/5.92 (assert (forall ((A2 tptp.product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ tptp.pow_Product_unit A))) (let ((_let_2 (@ tptp.insert_Product_unit A2))) (= (@ tptp.pow_Product_unit (@ _let_2 A)) (@ (@ tptp.sup_su5975557051335651745t_unit _let_1) (@ (@ tptp.image_4019945301284682565t_unit _let_2) _let_1)))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.pairself_nat_nat F) (@ (@ tptp.product_Pair_nat_nat A2) B)) (@ (@ tptp.product_Pair_nat_nat (@ F A2)) (@ F B)))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.pairself_nat_int F) (@ (@ tptp.product_Pair_nat_nat A2) B)) (@ (@ tptp.product_Pair_int_int (@ F A2)) (@ F B)))))
% 5.61/5.92 (assert (forall ((F (-> tptp.int tptp.nat)) (A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.pairself_int_nat F) (@ (@ tptp.product_Pair_int_int A2) B)) (@ (@ tptp.product_Pair_nat_nat (@ F A2)) (@ F B)))))
% 5.61/5.92 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.pairself_int_int F) (@ (@ tptp.product_Pair_int_int A2) B)) (@ (@ tptp.product_Pair_int_int (@ F A2)) (@ F B)))))
% 5.61/5.92 (assert (forall ((X (-> tptp.nat tptp.nat)) (Xa tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (=> (= (@ (@ tptp.pairself_nat_nat X) Xa) Y) (not (forall ((A4 tptp.nat) (B2 tptp.nat)) (=> (= Xa (@ (@ tptp.product_Pair_nat_nat A4) B2)) (not (= Y (@ (@ tptp.product_Pair_nat_nat (@ X A4)) (@ X B2))))))))))
% 5.61/5.92 (assert (forall ((X (-> tptp.nat tptp.int)) (Xa tptp.product_prod_nat_nat) (Y tptp.product_prod_int_int)) (=> (= (@ (@ tptp.pairself_nat_int X) Xa) Y) (not (forall ((A4 tptp.nat) (B2 tptp.nat)) (=> (= Xa (@ (@ tptp.product_Pair_nat_nat A4) B2)) (not (= Y (@ (@ tptp.product_Pair_int_int (@ X A4)) (@ X B2))))))))))
% 5.61/5.92 (assert (forall ((X (-> tptp.int tptp.nat)) (Xa tptp.product_prod_int_int) (Y tptp.product_prod_nat_nat)) (=> (= (@ (@ tptp.pairself_int_nat X) Xa) Y) (not (forall ((A4 tptp.int) (B2 tptp.int)) (=> (= Xa (@ (@ tptp.product_Pair_int_int A4) B2)) (not (= Y (@ (@ tptp.product_Pair_nat_nat (@ X A4)) (@ X B2))))))))))
% 5.61/5.92 (assert (forall ((X (-> tptp.int tptp.int)) (Xa tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (=> (= (@ (@ tptp.pairself_int_int X) Xa) Y) (not (forall ((A4 tptp.int) (B2 tptp.int)) (=> (= Xa (@ (@ tptp.product_Pair_int_int A4) B2)) (not (= Y (@ (@ tptp.product_Pair_int_int (@ X A4)) (@ X B2))))))))))
% 5.61/5.92 (assert (forall ((P (-> tptp.product_unit tptp.product_unit Bool)) (A tptp.product_unit)) (@ (@ tptp.pairwi7919127943033184120t_unit P) (@ (@ tptp.insert_Product_unit A) tptp.bot_bo3957492148770167129t_unit))))
% 5.61/5.92 (assert (forall ((P (-> Bool Bool Bool)) (A Bool)) (@ (@ tptp.pairwise_o P) (@ (@ tptp.insert_o A) tptp.bot_bot_set_o))))
% 5.61/5.92 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat)) (@ (@ tptp.pairwise_nat P) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))
% 5.61/5.92 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int)) (@ (@ tptp.pairwise_int P) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))
% 5.61/5.92 (assert (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (A (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.pairwi2432143822833250616_nat_o P) (@ (@ tptp.insert5175938949040314269_nat_o A) tptp.bot_bo7824918357723582233_nat_o))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (not (= A tptp.bot_bot_set_set_nat)) (=> (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) A) (=> (@ (@ tptp.member_set_nat Y2) A) (@ (@ tptp.member_set_nat (@ (@ tptp.sup_sup_set_nat X3) Y2)) A)))) (@ (@ tptp.member_set_nat (@ tptp.comple7399068483239264473et_nat A)) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (=> (forall ((X3 Bool) (Y2 Bool)) (=> (@ (@ tptp.member_o X3) A) (=> (@ (@ tptp.member_o Y2) A) (@ (@ tptp.member_o (@ (@ tptp.sup_sup_o X3) Y2)) A)))) (@ (@ tptp.member_o (@ tptp.complete_Sup_Sup_o A)) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) A) (=> (@ (@ tptp.member6576561426505652726_nat_o Y2) A) (@ (@ tptp.member6576561426505652726_nat_o (@ (@ tptp.sup_su5453871518329203617_nat_o X3) Y2)) A)))) (@ (@ tptp.member6576561426505652726_nat_o (@ tptp.comple4225350640907012154_nat_o A)) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((X3 tptp.product_unit) (Y2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) A) (=> (@ (@ tptp.member_Product_unit Y2) A) (@ (@ tptp.member_Product_unit (@ (@ tptp.sup_sup_Product_unit X3) Y2)) A)))) (@ (@ tptp.member_Product_unit (@ tptp.comple4687483117567863418t_unit A)) A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (= (@ tptp.lattic1508158080041050831_fin_o A) (@ tptp.complete_Sup_Sup_o A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (= (@ tptp.lattic7320199455484906628_nat_o A) (@ tptp.comple4225350640907012154_nat_o A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (@ tptp.lattic5294303975357428420t_unit A) (@ tptp.comple4687483117567863418t_unit A))))))
% 5.61/5.92 (assert (forall ((X tptp.set_Product_unit) (F2 tptp.set_set_Product_unit)) (=> (not (@ (@ tptp.member5877623283571906838t_unit X) F2)) (=> (forall ((X3 tptp.set_Product_unit)) (=> (@ (@ tptp.member5877623283571906838t_unit X3) (@ (@ tptp.insert8986028188087627965t_unit X) F2)) (forall ((Xa3 tptp.set_Product_unit)) (=> (@ (@ tptp.member5877623283571906838t_unit Xa3) (@ (@ tptp.insert8986028188087627965t_unit X) F2)) (=> (not (= X3 Xa3)) (= (@ (@ tptp.inf_in4660618365625256667t_unit X3) Xa3) tptp.bot_bo3957492148770167129t_unit)))))) (= (@ (@ tptp.inf_in4660618365625256667t_unit X) (@ tptp.comple3349607820504768346t_unit F2)) tptp.bot_bo3957492148770167129t_unit)))))
% 5.61/5.92 (assert (forall ((X tptp.set_o) (F2 tptp.set_set_o)) (=> (not (@ (@ tptp.member_set_o X) F2)) (=> (forall ((X3 tptp.set_o)) (=> (@ (@ tptp.member_set_o X3) (@ (@ tptp.insert_set_o X) F2)) (forall ((Xa3 tptp.set_o)) (=> (@ (@ tptp.member_set_o Xa3) (@ (@ tptp.insert_set_o X) F2)) (=> (not (= X3 Xa3)) (= (@ (@ tptp.inf_inf_set_o X3) Xa3) tptp.bot_bot_set_o)))))) (= (@ (@ tptp.inf_inf_set_o X) (@ tptp.comple90263536869209701_set_o F2)) tptp.bot_bot_set_o)))))
% 5.61/5.92 (assert (forall ((X tptp.set_nat) (F2 tptp.set_set_nat)) (=> (not (@ (@ tptp.member_set_nat X) F2)) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) (@ (@ tptp.insert_set_nat X) F2)) (forall ((Xa3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa3) (@ (@ tptp.insert_set_nat X) F2)) (=> (not (= X3 Xa3)) (= (@ (@ tptp.inf_inf_set_nat X3) Xa3) tptp.bot_bot_set_nat)))))) (= (@ (@ tptp.inf_inf_set_nat X) (@ tptp.comple7399068483239264473et_nat F2)) tptp.bot_bot_set_nat)))))
% 5.61/5.92 (assert (forall ((X tptp.set_int) (F2 tptp.set_set_int)) (=> (not (@ (@ tptp.member_set_int X) F2)) (=> (forall ((X3 tptp.set_int)) (=> (@ (@ tptp.member_set_int X3) (@ (@ tptp.insert_set_int X) F2)) (forall ((Xa3 tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa3) (@ (@ tptp.insert_set_int X) F2)) (=> (not (= X3 Xa3)) (= (@ (@ tptp.inf_inf_set_int X3) Xa3) tptp.bot_bot_set_int)))))) (= (@ (@ tptp.inf_inf_set_int X) (@ tptp.comple3221217463730067765et_int F2)) tptp.bot_bot_set_int)))))
% 5.61/5.92 (assert (forall ((X tptp.set_Pr4532377907799695533_nat_o) (F2 tptp.set_se1353816476878259085_nat_o)) (=> (not (@ (@ tptp.member1452989533377600726_nat_o X) F2)) (=> (forall ((X3 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member1452989533377600726_nat_o X3) (@ (@ tptp.insert2507855216428400253_nat_o X) F2)) (forall ((Xa3 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member1452989533377600726_nat_o Xa3) (@ (@ tptp.insert2507855216428400253_nat_o X) F2)) (=> (not (= X3 Xa3)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o X3) Xa3) tptp.bot_bo7824918357723582233_nat_o)))))) (= (@ (@ tptp.inf_in1906310914598751387_nat_o X) (@ tptp.comple3382087578465172250_nat_o F2)) tptp.bot_bo7824918357723582233_nat_o)))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A tptp.set_nat) (B4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.image_nat_set_nat F))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat (@ _let_1 A)) B4) (@ (@ tptp.ord_le9131159989063066194et_nat (@ (@ tptp.image_6725021117256019401et_nat _let_1) (@ tptp.pow_nat A))) (@ tptp.pow_set_nat B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer) (B4 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.image_4470545334726330049nteger F))) (=> (@ (@ tptp.ord_le7084787975880047091nteger (@ _let_1 A)) B4) (@ (@ tptp.ord_le1914454125413604393nteger (@ (@ tptp.image_6270750266955655469nteger _let_1) (@ tptp.pow_Code_integer A))) (@ tptp.pow_Code_integer B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.set_nat) (B4 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.image_1215581382706833972nteger F))) (=> (@ (@ tptp.ord_le7084787975880047091nteger (@ _let_1 A)) B4) (@ (@ tptp.ord_le1914454125413604393nteger (@ (@ tptp.image_6916300684244607776nteger _let_1) (@ tptp.pow_nat A))) (@ tptp.pow_Code_integer B4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_nat2 F))) (=> (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 A)) B4) (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.image_7916887816326733075et_nat _let_1) (@ tptp.pow_nat A))) (@ tptp.pow_nat B4))))))
% 5.61/5.92 (assert (= tptp.pairwi7919127943033184120t_unit (lambda ((R (-> tptp.product_unit tptp.product_unit Bool)) (S6 tptp.set_Product_unit)) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) S6) (forall ((Y3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit Y3) (@ (@ tptp.minus_6452836326544984404t_unit S6) (@ (@ tptp.insert_Product_unit X2) tptp.bot_bo3957492148770167129t_unit))) (@ (@ R X2) Y3))))))))
% 5.61/5.92 (assert (= tptp.pairwise_o (lambda ((R (-> Bool Bool Bool)) (S6 tptp.set_o)) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) S6) (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) (@ (@ tptp.minus_minus_set_o S6) (@ (@ tptp.insert_o X2) tptp.bot_bot_set_o))) (@ (@ R X2) Y3))))))))
% 5.61/5.92 (assert (= tptp.pairwise_int (lambda ((R (-> tptp.int tptp.int Bool)) (S6 tptp.set_int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) S6) (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) (@ (@ tptp.minus_minus_set_int S6) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))) (@ (@ R X2) Y3))))))))
% 5.61/5.92 (assert (= tptp.pairwi2432143822833250616_nat_o (lambda ((R (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (S6 tptp.set_Pr4532377907799695533_nat_o)) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X2) S6) (forall ((Y3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o Y3) (@ (@ tptp.minus_1801376950450012436_nat_o S6) (@ (@ tptp.insert5175938949040314269_nat_o X2) tptp.bot_bo7824918357723582233_nat_o))) (@ (@ R X2) Y3))))))))
% 5.61/5.92 (assert (= tptp.pairwise_nat (lambda ((R (-> tptp.nat tptp.nat Bool)) (S6 tptp.set_nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) S6) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) (@ (@ tptp.minus_minus_set_nat S6) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))) (@ (@ R X2) Y3))))))))
% 5.61/5.92 (assert (forall ((A2 Bool) (A tptp.set_o)) (= (@ tptp.complete_Sup_Sup_o (@ (@ tptp.insert_o A2) A)) (@ (@ tptp.sup_sup_o A2) (@ tptp.complete_Sup_Sup_o A)))))
% 5.61/5.92 (assert (forall ((A2 tptp.set_nat) (A tptp.set_set_nat)) (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.insert_set_nat A2) A)) (@ (@ tptp.sup_sup_set_nat A2) (@ tptp.comple7399068483239264473et_nat A)))))
% 5.61/5.92 (assert (forall ((A2 tptp.product_unit) (A tptp.set_Product_unit)) (= (@ tptp.comple4687483117567863418t_unit (@ (@ tptp.insert_Product_unit A2) A)) (@ (@ tptp.sup_sup_Product_unit A2) (@ tptp.comple4687483117567863418t_unit A)))))
% 5.61/5.92 (assert (forall ((X Bool)) (= (@ tptp.complete_Sup_Sup_o (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)) X)))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool))) (= (@ tptp.comple4225350640907012154_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)) X)))
% 5.61/5.92 (assert (forall ((X tptp.product_unit)) (= (@ tptp.comple4687483117567863418t_unit (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)) X)))
% 5.61/5.92 (assert (forall ((X Bool)) (= (@ tptp.complete_Sup_Sup_o (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)) X)))
% 5.61/5.92 (assert (forall ((X tptp.int)) (= (@ tptp.complete_Sup_Sup_int (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)) X)))
% 5.61/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool))) (= (@ tptp.comple4225350640907012154_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)) X)))
% 5.61/5.92 (assert (forall ((X tptp.nat)) (= (@ tptp.complete_Sup_Sup_nat (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)) X)))
% 5.61/5.92 (assert (forall ((X tptp.product_unit)) (= (@ tptp.comple4687483117567863418t_unit (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)) X)))
% 5.61/5.92 (assert (= (@ tptp.comple3349607820504768346t_unit tptp.bot_bo6284674557190688313t_unit) tptp.bot_bo3957492148770167129t_unit))
% 5.61/5.92 (assert (= (@ tptp.comple90263536869209701_set_o tptp.bot_bot_set_set_o) tptp.bot_bot_set_o))
% 5.61/5.92 (assert (= (@ tptp.comple7399068483239264473et_nat tptp.bot_bot_set_set_nat) tptp.bot_bot_set_nat))
% 5.61/5.92 (assert (= (@ tptp.comple3221217463730067765et_int tptp.bot_bot_set_set_int) tptp.bot_bot_set_int))
% 5.61/5.92 (assert (= (@ tptp.comple3382087578465172250_nat_o tptp.bot_bo3736544561982865913_nat_o) tptp.bot_bo7824918357723582233_nat_o))
% 5.61/5.92 (assert (= (@ tptp.complete_Sup_Sup_o tptp.bot_bot_set_o) tptp.bot_bot_o))
% 5.61/5.92 (assert (= (@ tptp.comple4225350640907012154_nat_o tptp.bot_bo7824918357723582233_nat_o) tptp.bot_bo6993851861578111033_nat_o))
% 5.61/5.92 (assert (= (@ tptp.comple4687483117567863418t_unit tptp.bot_bo3957492148770167129t_unit) tptp.bot_bot_Product_unit))
% 5.61/5.92 (assert (forall ((A tptp.set_set_Product_unit)) (= (= (@ tptp.comple3349607820504768346t_unit A) tptp.bot_bo3957492148770167129t_unit) (forall ((X2 tptp.set_Product_unit)) (=> (@ (@ tptp.member5877623283571906838t_unit X2) A) (= X2 tptp.bot_bo3957492148770167129t_unit))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_o)) (= (= (@ tptp.comple90263536869209701_set_o A) tptp.bot_bot_set_o) (forall ((X2 tptp.set_o)) (=> (@ (@ tptp.member_set_o X2) A) (= X2 tptp.bot_bot_set_o))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat)) (= (= (@ tptp.comple7399068483239264473et_nat A) tptp.bot_bot_set_nat) (forall ((X2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X2) A) (= X2 tptp.bot_bot_set_nat))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_int)) (= (= (@ tptp.comple3221217463730067765et_int A) tptp.bot_bot_set_int) (forall ((X2 tptp.set_int)) (=> (@ (@ tptp.member_set_int X2) A) (= X2 tptp.bot_bot_set_int))))))
% 5.61/5.92 (assert (forall ((A tptp.set_se1353816476878259085_nat_o)) (= (= (@ tptp.comple3382087578465172250_nat_o A) tptp.bot_bo7824918357723582233_nat_o) (forall ((X2 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member1452989533377600726_nat_o X2) A) (= X2 tptp.bot_bo7824918357723582233_nat_o))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit)) (= (= (@ tptp.comple4687483117567863418t_unit A) tptp.bot_bot_Product_unit) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) A) (= X2 tptp.bot_bot_Product_unit))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_Product_unit)) (= (= tptp.bot_bo3957492148770167129t_unit (@ tptp.comple3349607820504768346t_unit A)) (forall ((X2 tptp.set_Product_unit)) (=> (@ (@ tptp.member5877623283571906838t_unit X2) A) (= X2 tptp.bot_bo3957492148770167129t_unit))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_o)) (= (= tptp.bot_bot_set_o (@ tptp.comple90263536869209701_set_o A)) (forall ((X2 tptp.set_o)) (=> (@ (@ tptp.member_set_o X2) A) (= X2 tptp.bot_bot_set_o))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat)) (= (= tptp.bot_bot_set_nat (@ tptp.comple7399068483239264473et_nat A)) (forall ((X2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X2) A) (= X2 tptp.bot_bot_set_nat))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_int)) (= (= tptp.bot_bot_set_int (@ tptp.comple3221217463730067765et_int A)) (forall ((X2 tptp.set_int)) (=> (@ (@ tptp.member_set_int X2) A) (= X2 tptp.bot_bot_set_int))))))
% 5.61/5.92 (assert (forall ((A tptp.set_se1353816476878259085_nat_o)) (= (= tptp.bot_bo7824918357723582233_nat_o (@ tptp.comple3382087578465172250_nat_o A)) (forall ((X2 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member1452989533377600726_nat_o X2) A) (= X2 tptp.bot_bo7824918357723582233_nat_o))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit)) (= (= tptp.bot_bot_Product_unit (@ tptp.comple4687483117567863418t_unit A)) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) A) (= X2 tptp.bot_bot_Product_unit))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_o)) (=> (@ tptp.finite_finite_o X4) (=> (not (= X4 tptp.bot_bot_set_o)) (= (@ tptp.complete_Sup_Sup_o X4) (@ tptp.lattic1508158080041050831_fin_o X4))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_int)) (=> (@ tptp.finite_finite_int X4) (=> (not (= X4 tptp.bot_bot_set_int)) (= (@ tptp.complete_Sup_Sup_int X4) (@ tptp.lattic1091506334969745077in_int X4))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o X4) (=> (not (= X4 tptp.bot_bo7824918357723582233_nat_o)) (= (@ tptp.comple4225350640907012154_nat_o X4) (@ tptp.lattic7320199455484906628_nat_o X4))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat X4) (=> (not (= X4 tptp.bot_bot_set_nat)) (= (@ tptp.complete_Sup_Sup_nat X4) (@ tptp.lattic1093996805478795353in_nat X4))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit X4) (=> (not (= X4 tptp.bot_bo3957492148770167129t_unit)) (= (@ tptp.comple4687483117567863418t_unit X4) (@ tptp.lattic5294303975357428420t_unit X4))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A2 tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_set_nat F))) (= (@ tptp.comple7399068483239264473et_nat (@ _let_1 (@ (@ tptp.insert_nat A2) B4))) (@ (@ tptp.sup_sup_set_nat (@ F A2)) (@ tptp.comple7399068483239264473et_nat (@ _let_1 B4)))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.int tptp.set_nat)) (A2 tptp.int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.image_int_set_nat F))) (= (@ tptp.comple7399068483239264473et_nat (@ _let_1 (@ (@ tptp.insert_int A2) B4))) (@ (@ tptp.sup_sup_set_nat (@ F A2)) (@ tptp.comple7399068483239264473et_nat (@ _let_1 B4)))))))
% 5.61/5.92 (assert (forall ((F (-> Bool tptp.set_nat)) (A2 Bool) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.image_o_set_nat F))) (= (@ tptp.comple7399068483239264473et_nat (@ _let_1 (@ (@ tptp.insert_o A2) B4))) (@ (@ tptp.sup_sup_set_nat (@ F A2)) (@ tptp.comple7399068483239264473et_nat (@ _let_1 B4)))))))
% 5.61/5.92 (assert (forall ((F (-> tptp.product_unit tptp.set_nat)) (A2 tptp.product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.image_8173849991827986510et_nat F))) (= (@ tptp.comple7399068483239264473et_nat (@ _let_1 (@ (@ tptp.insert_Product_unit A2) B4))) (@ (@ tptp.sup_sup_set_nat (@ F A2)) (@ tptp.comple7399068483239264473et_nat (@ _let_1 B4)))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (F (-> tptp.product_unit tptp.set_nat))) (= (@ (@ tptp.sup_sup_set_nat A) (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_8173849991827986510et_nat F) tptp.bot_bo3957492148770167129t_unit))) A)))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (F (-> Bool tptp.set_nat))) (= (@ (@ tptp.sup_sup_set_nat A) (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_o_set_nat F) tptp.bot_bot_set_o))) A)))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.set_nat))) (= (@ (@ tptp.sup_sup_set_nat A) (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat F) tptp.bot_bot_set_nat))) A)))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (F (-> tptp.int tptp.set_nat))) (= (@ (@ tptp.sup_sup_set_nat A) (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_int_set_nat F) tptp.bot_bot_set_int))) A)))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (F (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.set_nat))) (= (@ (@ tptp.sup_sup_set_nat A) (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_6888641473154130958et_nat F) tptp.bot_bo7824918357723582233_nat_o))) A)))
% 5.61/5.92 (assert (= tptp.comple3590721164184202819at_o_o (lambda ((S6 tptp.set_Pr6409761941060870310at_o_o) (X2 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o X2) (@ tptp.comple3382087578465172250_nat_o (@ (@ tptp.image_8639947063239330806_nat_o tptp.collec939566748876313656_nat_o) S6))))))
% 5.61/5.92 (assert (= tptp.comple8317665133742190828_nat_o (lambda ((S6 tptp.set_nat_o) (X2 tptp.nat)) (@ (@ tptp.member_nat X2) (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_o_set_nat tptp.collect_nat) S6))))))
% 5.61/5.92 (assert (= tptp.comple6496622788309502864_int_o (lambda ((S6 tptp.set_int_o) (X2 tptp.int)) (@ (@ tptp.member_int X2) (@ tptp.comple3221217463730067765et_int (@ (@ tptp.image_int_o_set_int tptp.collect_int) S6))))))
% 5.61/5.92 (assert (= tptp.complete_Sup_Sup_o_o (lambda ((S6 tptp.set_o_o) (X2 Bool)) (@ (@ tptp.member_o X2) (@ tptp.comple90263536869209701_set_o (@ (@ tptp.image_o_o_set_o tptp.collect_o) S6))))))
% 5.61/5.92 (assert (= tptp.comple4773641153059738115unit_o (lambda ((S6 tptp.set_Product_unit_o) (X2 tptp.product_unit)) (@ (@ tptp.member_Product_unit X2) (@ tptp.comple3349607820504768346t_unit (@ (@ tptp.image_5138372075374782070t_unit tptp.collect_Product_unit) S6))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_Product_unit)) (= (= tptp.bot_bo3957492148770167129t_unit (@ tptp.comple3349607820504768346t_unit A)) (forall ((X2 tptp.set_Product_unit)) (=> (@ (@ tptp.member5877623283571906838t_unit X2) A) (= X2 tptp.bot_bo3957492148770167129t_unit))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_o)) (= (= tptp.bot_bot_set_o (@ tptp.comple90263536869209701_set_o A)) (forall ((X2 tptp.set_o)) (=> (@ (@ tptp.member_set_o X2) A) (= X2 tptp.bot_bot_set_o))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat)) (= (= tptp.bot_bot_set_nat (@ tptp.comple7399068483239264473et_nat A)) (forall ((X2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X2) A) (= X2 tptp.bot_bot_set_nat))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_int)) (= (= tptp.bot_bot_set_int (@ tptp.comple3221217463730067765et_int A)) (forall ((X2 tptp.set_int)) (=> (@ (@ tptp.member_set_int X2) A) (= X2 tptp.bot_bot_set_int))))))
% 5.61/5.92 (assert (forall ((A tptp.set_se1353816476878259085_nat_o)) (= (= tptp.bot_bo7824918357723582233_nat_o (@ tptp.comple3382087578465172250_nat_o A)) (forall ((X2 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member1452989533377600726_nat_o X2) A) (= X2 tptp.bot_bo7824918357723582233_nat_o))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_Product_unit)) (= (= (@ tptp.comple3349607820504768346t_unit A) tptp.bot_bo3957492148770167129t_unit) (forall ((X2 tptp.set_Product_unit)) (=> (@ (@ tptp.member5877623283571906838t_unit X2) A) (= X2 tptp.bot_bo3957492148770167129t_unit))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_o)) (= (= (@ tptp.comple90263536869209701_set_o A) tptp.bot_bot_set_o) (forall ((X2 tptp.set_o)) (=> (@ (@ tptp.member_set_o X2) A) (= X2 tptp.bot_bot_set_o))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat)) (= (= (@ tptp.comple7399068483239264473et_nat A) tptp.bot_bot_set_nat) (forall ((X2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X2) A) (= X2 tptp.bot_bot_set_nat))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_int)) (= (= (@ tptp.comple3221217463730067765et_int A) tptp.bot_bot_set_int) (forall ((X2 tptp.set_int)) (=> (@ (@ tptp.member_set_int X2) A) (= X2 tptp.bot_bot_set_int))))))
% 5.61/5.92 (assert (forall ((A tptp.set_se1353816476878259085_nat_o)) (= (= (@ tptp.comple3382087578465172250_nat_o A) tptp.bot_bo7824918357723582233_nat_o) (forall ((X2 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member1452989533377600726_nat_o X2) A) (= X2 tptp.bot_bo7824918357723582233_nat_o))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (U Bool)) (=> (forall ((V3 Bool)) (=> (@ (@ tptp.member_o V3) A) (@ (@ tptp.ord_less_eq_o U) V3))) (=> (not (= A tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_eq_o U) (@ tptp.complete_Sup_Sup_o A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (U (-> tptp.produc3658429121746597890et_nat Bool))) (=> (forall ((V3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o V3) A) (@ (@ tptp.ord_le729326519192465773_nat_o U) V3))) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (@ (@ tptp.ord_le729326519192465773_nat_o U) (@ tptp.comple4225350640907012154_nat_o A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_filter_nat) (U tptp.filter_nat)) (=> (forall ((V3 tptp.filter_nat)) (=> (@ (@ tptp.member_filter_nat V3) A) (@ (@ tptp.ord_le2510731241096832064er_nat U) V3))) (=> (not (= A tptp.bot_bo498966703094740906er_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat U) (@ tptp.comple2454491259644266675er_nat A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat) (U tptp.set_nat)) (=> (forall ((V3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat V3) A) (@ (@ tptp.ord_less_eq_set_nat U) V3))) (=> (not (= A tptp.bot_bot_set_set_nat)) (@ (@ tptp.ord_less_eq_set_nat U) (@ tptp.comple7399068483239264473et_nat A))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (U tptp.product_unit)) (=> (forall ((V3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit V3) A) (@ (@ tptp.ord_le3221252021190050221t_unit U) V3))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (@ (@ tptp.ord_le3221252021190050221t_unit U) (@ tptp.comple4687483117567863418t_unit A))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_o) (Z Bool)) (=> (not (= X4 tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) X4) (@ (@ tptp.ord_less_eq_o X3) Z))) (@ (@ tptp.ord_less_eq_o (@ tptp.complete_Sup_Sup_o X4)) Z)))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_Pr4532377907799695533_nat_o) (Z (-> tptp.produc3658429121746597890et_nat Bool))) (=> (not (= X4 tptp.bot_bo7824918357723582233_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) X4) (@ (@ tptp.ord_le729326519192465773_nat_o X3) Z))) (@ (@ tptp.ord_le729326519192465773_nat_o (@ tptp.comple4225350640907012154_nat_o X4)) Z)))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_filter_nat) (Z tptp.filter_nat)) (=> (not (= X4 tptp.bot_bo498966703094740906er_nat)) (=> (forall ((X3 tptp.filter_nat)) (=> (@ (@ tptp.member_filter_nat X3) X4) (@ (@ tptp.ord_le2510731241096832064er_nat X3) Z))) (@ (@ tptp.ord_le2510731241096832064er_nat (@ tptp.comple2454491259644266675er_nat X4)) Z)))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_set_nat) (Z tptp.set_nat)) (=> (not (= X4 tptp.bot_bot_set_set_nat)) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) X4) (@ (@ tptp.ord_less_eq_set_nat X3) Z))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7399068483239264473et_nat X4)) Z)))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_int) (Z tptp.int)) (=> (not (= X4 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) X4) (@ (@ tptp.ord_less_eq_int X3) Z))) (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Sup_Sup_int X4)) Z)))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_nat) (Z tptp.nat)) (=> (not (= X4 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) X4) (@ (@ tptp.ord_less_eq_nat X3) Z))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Sup_Sup_nat X4)) Z)))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_Product_unit) (Z tptp.product_unit)) (=> (not (= X4 tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) X4) (@ (@ tptp.ord_le3221252021190050221t_unit X3) Z))) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.comple4687483117567863418t_unit X4)) Z)))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_o) (A2 Bool)) (=> (not (= X4 tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) X4) (@ (@ tptp.ord_less_eq_o X3) A2))) (=> (forall ((Y2 Bool)) (=> (forall ((X6 Bool)) (=> (@ (@ tptp.member_o X6) X4) (@ (@ tptp.ord_less_eq_o X6) Y2))) (@ (@ tptp.ord_less_eq_o A2) Y2))) (= (@ tptp.complete_Sup_Sup_o X4) A2))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (not (= X4 tptp.bot_bo7824918357723582233_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) X4) (@ (@ tptp.ord_le729326519192465773_nat_o X3) A2))) (=> (forall ((Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (forall ((X6 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X6) X4) (@ (@ tptp.ord_le729326519192465773_nat_o X6) Y2))) (@ (@ tptp.ord_le729326519192465773_nat_o A2) Y2))) (= (@ tptp.comple4225350640907012154_nat_o X4) A2))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_filter_nat) (A2 tptp.filter_nat)) (=> (not (= X4 tptp.bot_bo498966703094740906er_nat)) (=> (forall ((X3 tptp.filter_nat)) (=> (@ (@ tptp.member_filter_nat X3) X4) (@ (@ tptp.ord_le2510731241096832064er_nat X3) A2))) (=> (forall ((Y2 tptp.filter_nat)) (=> (forall ((X6 tptp.filter_nat)) (=> (@ (@ tptp.member_filter_nat X6) X4) (@ (@ tptp.ord_le2510731241096832064er_nat X6) Y2))) (@ (@ tptp.ord_le2510731241096832064er_nat A2) Y2))) (= (@ tptp.comple2454491259644266675er_nat X4) A2))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_set_nat) (A2 tptp.set_nat)) (=> (not (= X4 tptp.bot_bot_set_set_nat)) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) X4) (@ (@ tptp.ord_less_eq_set_nat X3) A2))) (=> (forall ((Y2 tptp.set_nat)) (=> (forall ((X6 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X6) X4) (@ (@ tptp.ord_less_eq_set_nat X6) Y2))) (@ (@ tptp.ord_less_eq_set_nat A2) Y2))) (= (@ tptp.comple7399068483239264473et_nat X4) A2))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_int) (A2 tptp.int)) (=> (not (= X4 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) X4) (@ (@ tptp.ord_less_eq_int X3) A2))) (=> (forall ((Y2 tptp.int)) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) X4) (@ (@ tptp.ord_less_eq_int X6) Y2))) (@ (@ tptp.ord_less_eq_int A2) Y2))) (= (@ tptp.complete_Sup_Sup_int X4) A2))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_nat) (A2 tptp.nat)) (=> (not (= X4 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) X4) (@ (@ tptp.ord_less_eq_nat X3) A2))) (=> (forall ((Y2 tptp.nat)) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) X4) (@ (@ tptp.ord_less_eq_nat X6) Y2))) (@ (@ tptp.ord_less_eq_nat A2) Y2))) (= (@ tptp.complete_Sup_Sup_nat X4) A2))))))
% 5.61/5.92 (assert (forall ((X4 tptp.set_Product_unit) (A2 tptp.product_unit)) (=> (not (= X4 tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) X4) (@ (@ tptp.ord_le3221252021190050221t_unit X3) A2))) (=> (forall ((Y2 tptp.product_unit)) (=> (forall ((X6 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X6) X4) (@ (@ tptp.ord_le3221252021190050221t_unit X6) Y2))) (@ (@ tptp.ord_le3221252021190050221t_unit A2) Y2))) (= (@ tptp.comple4687483117567863418t_unit X4) A2))))))
% 5.61/5.92 (assert (forall ((I tptp.set_nat) (F (-> tptp.nat tptp.set_nat)) (X tptp.set_nat)) (=> (not (= I tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I) (= (@ F I3) X))) (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat F) I)) X)))))
% 5.61/5.92 (assert (forall ((I tptp.set_Product_unit) (F (-> tptp.product_unit tptp.product_unit)) (X tptp.product_unit)) (=> (not (= I tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) I) (= (@ F I3) X))) (= (@ tptp.comple4687483117567863418t_unit (@ (@ tptp.image_405062704495631173t_unit F) I)) X)))))
% 5.61/5.92 (assert (forall ((I tptp.set_o) (F (-> Bool tptp.product_unit)) (X tptp.product_unit)) (=> (not (= I tptp.bot_bot_set_o)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I) (= (@ F I3) X))) (= (@ tptp.comple4687483117567863418t_unit (@ (@ tptp.image_o_Product_unit2 F) I)) X)))))
% 5.61/5.92 (assert (forall ((I tptp.set_nat) (F (-> tptp.nat tptp.product_unit)) (X tptp.product_unit)) (=> (not (= I tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I) (= (@ F I3) X))) (= (@ tptp.comple4687483117567863418t_unit (@ (@ tptp.image_8730104196221521654t_unit F) I)) X)))))
% 5.61/5.92 (assert (forall ((I tptp.set_int) (F (-> tptp.int tptp.product_unit)) (X tptp.product_unit)) (=> (not (= I tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I) (= (@ F I3) X))) (= (@ tptp.comple4687483117567863418t_unit (@ (@ tptp.image_5846526143423701914t_unit F) I)) X)))))
% 5.61/5.92 (assert (forall ((I tptp.set_Pr4532377907799695533_nat_o) (F (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.product_unit)) (X tptp.product_unit)) (=> (not (= I tptp.bot_bo7824918357723582233_nat_o)) (=> (forall ((I3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o I3) I) (= (@ F I3) X))) (= (@ tptp.comple4687483117567863418t_unit (@ (@ tptp.image_8451000719036923781t_unit F) I)) X)))))
% 5.61/5.92 (assert (forall ((C5 tptp.set_set_Product_unit) (A tptp.set_Product_unit)) (= (= (@ (@ tptp.inf_in4660618365625256667t_unit (@ tptp.comple3349607820504768346t_unit C5)) A) tptp.bot_bo3957492148770167129t_unit) (forall ((X2 tptp.set_Product_unit)) (=> (@ (@ tptp.member5877623283571906838t_unit X2) C5) (= (@ (@ tptp.inf_in4660618365625256667t_unit X2) A) tptp.bot_bo3957492148770167129t_unit))))))
% 5.61/5.92 (assert (forall ((C5 tptp.set_set_o) (A tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o (@ tptp.comple90263536869209701_set_o C5)) A) tptp.bot_bot_set_o) (forall ((X2 tptp.set_o)) (=> (@ (@ tptp.member_set_o X2) C5) (= (@ (@ tptp.inf_inf_set_o X2) A) tptp.bot_bot_set_o))))))
% 5.61/5.92 (assert (forall ((C5 tptp.set_set_nat) (A tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat (@ tptp.comple7399068483239264473et_nat C5)) A) tptp.bot_bot_set_nat) (forall ((X2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X2) C5) (= (@ (@ tptp.inf_inf_set_nat X2) A) tptp.bot_bot_set_nat))))))
% 5.61/5.92 (assert (forall ((C5 tptp.set_set_int) (A tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int (@ tptp.comple3221217463730067765et_int C5)) A) tptp.bot_bot_set_int) (forall ((X2 tptp.set_int)) (=> (@ (@ tptp.member_set_int X2) C5) (= (@ (@ tptp.inf_inf_set_int X2) A) tptp.bot_bot_set_int))))))
% 5.61/5.92 (assert (forall ((C5 tptp.set_se1353816476878259085_nat_o) (A tptp.set_Pr4532377907799695533_nat_o)) (= (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ tptp.comple3382087578465172250_nat_o C5)) A) tptp.bot_bo7824918357723582233_nat_o) (forall ((X2 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member1452989533377600726_nat_o X2) C5) (= (@ (@ tptp.inf_in1906310914598751387_nat_o X2) A) tptp.bot_bo7824918357723582233_nat_o))))))
% 5.61/5.92 (assert (= (@ tptp.comple3349607820504768346t_unit tptp.bot_bo6284674557190688313t_unit) tptp.bot_bo3957492148770167129t_unit))
% 5.61/5.92 (assert (= (@ tptp.comple90263536869209701_set_o tptp.bot_bot_set_set_o) tptp.bot_bot_set_o))
% 5.61/5.92 (assert (= (@ tptp.comple7399068483239264473et_nat tptp.bot_bot_set_set_nat) tptp.bot_bot_set_nat))
% 5.61/5.92 (assert (= (@ tptp.comple3221217463730067765et_int tptp.bot_bot_set_set_int) tptp.bot_bot_set_int))
% 5.61/5.92 (assert (= (@ tptp.comple3382087578465172250_nat_o tptp.bot_bo3736544561982865913_nat_o) tptp.bot_bo7824918357723582233_nat_o))
% 5.61/5.92 (assert (forall ((I tptp.set_Product_unit) (C tptp.product_unit) (F (-> tptp.product_unit tptp.product_unit))) (=> (not (= I tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) I) (@ (@ tptp.ord_le3221252021190050221t_unit C) (@ F I3)))) (= (= (@ tptp.comple4687483117567863418t_unit (@ (@ tptp.image_405062704495631173t_unit F) I)) C) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) I) (= (@ F X2) C))))))))
% 5.61/5.92 (assert (forall ((I tptp.set_o) (C tptp.product_unit) (F (-> Bool tptp.product_unit))) (=> (not (= I tptp.bot_bot_set_o)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I) (@ (@ tptp.ord_le3221252021190050221t_unit C) (@ F I3)))) (= (= (@ tptp.comple4687483117567863418t_unit (@ (@ tptp.image_o_Product_unit2 F) I)) C) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) I) (= (@ F X2) C))))))))
% 5.61/5.92 (assert (forall ((I tptp.set_nat) (C tptp.product_unit) (F (-> tptp.nat tptp.product_unit))) (=> (not (= I tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I) (@ (@ tptp.ord_le3221252021190050221t_unit C) (@ F I3)))) (= (= (@ tptp.comple4687483117567863418t_unit (@ (@ tptp.image_8730104196221521654t_unit F) I)) C) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) I) (= (@ F X2) C))))))))
% 5.61/5.92 (assert (forall ((I tptp.set_int) (C tptp.product_unit) (F (-> tptp.int tptp.product_unit))) (=> (not (= I tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I) (@ (@ tptp.ord_le3221252021190050221t_unit C) (@ F I3)))) (= (= (@ tptp.comple4687483117567863418t_unit (@ (@ tptp.image_5846526143423701914t_unit F) I)) C) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) I) (= (@ F X2) C))))))))
% 5.61/5.92 (assert (forall ((I tptp.set_Product_unit) (C tptp.filter_nat) (F (-> tptp.product_unit tptp.filter_nat))) (=> (not (= I tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) I) (@ (@ tptp.ord_le2510731241096832064er_nat C) (@ F I3)))) (= (= (@ tptp.comple2454491259644266675er_nat (@ (@ tptp.image_1853478764106424488er_nat F) I)) C) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) I) (= (@ F X2) C))))))))
% 5.61/5.92 (assert (forall ((I tptp.set_o) (C tptp.filter_nat) (F (-> Bool tptp.filter_nat))) (=> (not (= I tptp.bot_bot_set_o)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I) (@ (@ tptp.ord_le2510731241096832064er_nat C) (@ F I3)))) (= (= (@ tptp.comple2454491259644266675er_nat (@ (@ tptp.image_o_filter_nat F) I)) C) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) I) (= (@ F X2) C))))))))
% 5.61/5.92 (assert (forall ((I tptp.set_nat) (C tptp.filter_nat) (F (-> tptp.nat tptp.filter_nat))) (=> (not (= I tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I) (@ (@ tptp.ord_le2510731241096832064er_nat C) (@ F I3)))) (= (= (@ tptp.comple2454491259644266675er_nat (@ (@ tptp.image_nat_filter_nat F) I)) C) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) I) (= (@ F X2) C))))))))
% 5.61/5.92 (assert (forall ((I tptp.set_int) (C tptp.filter_nat) (F (-> tptp.int tptp.filter_nat))) (=> (not (= I tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I) (@ (@ tptp.ord_le2510731241096832064er_nat C) (@ F I3)))) (= (= (@ tptp.comple2454491259644266675er_nat (@ (@ tptp.image_int_filter_nat F) I)) C) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) I) (= (@ F X2) C))))))))
% 5.61/5.92 (assert (forall ((I tptp.set_Product_unit) (C tptp.set_nat) (F (-> tptp.product_unit tptp.set_nat))) (=> (not (= I tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) I) (@ (@ tptp.ord_less_eq_set_nat C) (@ F I3)))) (= (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_8173849991827986510et_nat F) I)) C) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) I) (= (@ F X2) C))))))))
% 5.61/5.92 (assert (forall ((I tptp.set_o) (C tptp.set_nat) (F (-> Bool tptp.set_nat))) (=> (not (= I tptp.bot_bot_set_o)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I) (@ (@ tptp.ord_less_eq_set_nat C) (@ F I3)))) (= (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_o_set_nat F) I)) C) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) I) (= (@ F X2) C))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.int)) (M tptp.int)) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) A) (@ (@ tptp.ord_less_eq_int (@ F X3)) M))) (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Sup_Sup_int (@ (@ tptp.image_873079544045703924it_int F) A))) M)))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.int)) (M tptp.int)) (=> (not (= A tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (@ (@ tptp.ord_less_eq_int (@ F X3)) M))) (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Sup_Sup_int (@ (@ tptp.image_o_int2 F) A))) M)))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.int)) (M tptp.int)) (=> (not (= A tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (@ (@ tptp.ord_less_eq_int (@ F X3)) M))) (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Sup_Sup_int (@ (@ tptp.image_nat_int2 F) A))) M)))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.int)) (M tptp.int)) (=> (not (= A tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (@ (@ tptp.ord_less_eq_int (@ F X3)) M))) (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Sup_Sup_int (@ (@ tptp.image_int_int2 F) A))) M)))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.nat)) (M tptp.nat)) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) A) (@ (@ tptp.ord_less_eq_nat (@ F X3)) M))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Sup_Sup_nat (@ (@ tptp.image_875570014554754200it_nat F) A))) M)))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.nat)) (M tptp.nat)) (=> (not (= A tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (@ (@ tptp.ord_less_eq_nat (@ F X3)) M))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Sup_Sup_nat (@ (@ tptp.image_o_nat2 F) A))) M)))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat)) (M tptp.nat)) (=> (not (= A tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (@ (@ tptp.ord_less_eq_nat (@ F X3)) M))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Sup_Sup_nat (@ (@ tptp.image_nat_nat2 F) A))) M)))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.nat)) (M tptp.nat)) (=> (not (= A tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (@ (@ tptp.ord_less_eq_nat (@ F X3)) M))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Sup_Sup_nat (@ (@ tptp.image_int_nat2 F) A))) M)))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.product_unit)) (M tptp.product_unit)) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) A) (@ (@ tptp.ord_le3221252021190050221t_unit (@ F X3)) M))) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.comple4687483117567863418t_unit (@ (@ tptp.image_405062704495631173t_unit F) A))) M)))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.product_unit)) (M tptp.product_unit)) (=> (not (= A tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (@ (@ tptp.ord_le3221252021190050221t_unit (@ F X3)) M))) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.comple4687483117567863418t_unit (@ (@ tptp.image_o_Product_unit2 F) A))) M)))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_set_Product_unit) (A2 tptp.set_Product_unit)) (= (= (@ (@ tptp.inf_in4660618365625256667t_unit (@ tptp.comple3349607820504768346t_unit B4)) A2) tptp.bot_bo3957492148770167129t_unit) (forall ((X2 tptp.set_Product_unit)) (=> (@ (@ tptp.member5877623283571906838t_unit X2) B4) (= (@ (@ tptp.inf_in4660618365625256667t_unit X2) A2) tptp.bot_bo3957492148770167129t_unit))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_set_o) (A2 tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o (@ tptp.comple90263536869209701_set_o B4)) A2) tptp.bot_bot_set_o) (forall ((X2 tptp.set_o)) (=> (@ (@ tptp.member_set_o X2) B4) (= (@ (@ tptp.inf_inf_set_o X2) A2) tptp.bot_bot_set_o))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_set_nat) (A2 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat (@ tptp.comple7399068483239264473et_nat B4)) A2) tptp.bot_bot_set_nat) (forall ((X2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X2) B4) (= (@ (@ tptp.inf_inf_set_nat X2) A2) tptp.bot_bot_set_nat))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_set_int) (A2 tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int (@ tptp.comple3221217463730067765et_int B4)) A2) tptp.bot_bot_set_int) (forall ((X2 tptp.set_int)) (=> (@ (@ tptp.member_set_int X2) B4) (= (@ (@ tptp.inf_inf_set_int X2) A2) tptp.bot_bot_set_int))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_se1353816476878259085_nat_o) (A2 tptp.set_Pr4532377907799695533_nat_o)) (= (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ tptp.comple3382087578465172250_nat_o B4)) A2) tptp.bot_bo7824918357723582233_nat_o) (forall ((X2 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member1452989533377600726_nat_o X2) B4) (= (@ (@ tptp.inf_in1906310914598751387_nat_o X2) A2) tptp.bot_bo7824918357723582233_nat_o))))))
% 5.61/5.92 (assert (forall ((B4 tptp.set_Product_unit) (A2 tptp.product_unit)) (= (= (@ (@ tptp.inf_inf_Product_unit (@ tptp.comple4687483117567863418t_unit B4)) A2) tptp.bot_bot_Product_unit) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) B4) (= (@ (@ tptp.inf_inf_Product_unit X2) A2) tptp.bot_bot_Product_unit))))))
% 5.61/5.92 (assert (forall ((A (-> tptp.product_unit tptp.set_Product_unit)) (I2 tptp.product_unit) (B4 tptp.set_Product_unit) (J2 tptp.set_Product_unit)) (= (@ tptp.comple3349607820504768346t_unit (@ (@ tptp.image_7778121751606633509t_unit (@ (@ (@ tptp.fun_up488859312337516701t_unit A) I2) B4)) J2)) (@ (@ tptp.sup_su793286257634532545t_unit (@ tptp.comple3349607820504768346t_unit (@ (@ tptp.image_7778121751606633509t_unit A) (@ (@ tptp.minus_6452836326544984404t_unit J2) (@ (@ tptp.insert_Product_unit I2) tptp.bot_bo3957492148770167129t_unit))))) (@ (@ (@ tptp.if_set_Product_unit (@ (@ tptp.member_Product_unit I2) J2)) B4) tptp.bot_bo3957492148770167129t_unit)))))
% 5.61/5.92 (assert (forall ((A (-> tptp.product_unit tptp.set_o)) (I2 tptp.product_unit) (B4 tptp.set_o) (J2 tptp.set_Product_unit)) (= (@ tptp.comple90263536869209701_set_o (@ (@ tptp.image_6930536745178679216_set_o (@ (@ (@ tptp.fun_up1762901246852280360_set_o A) I2) B4)) J2)) (@ (@ tptp.sup_sup_set_o (@ tptp.comple90263536869209701_set_o (@ (@ tptp.image_6930536745178679216_set_o A) (@ (@ tptp.minus_6452836326544984404t_unit J2) (@ (@ tptp.insert_Product_unit I2) tptp.bot_bo3957492148770167129t_unit))))) (@ (@ (@ tptp.if_set_o (@ (@ tptp.member_Product_unit I2) J2)) B4) tptp.bot_bot_set_o)))))
% 5.61/5.92 (assert (forall ((A (-> tptp.product_unit tptp.set_nat)) (I2 tptp.product_unit) (B4 tptp.set_nat) (J2 tptp.set_Product_unit)) (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_8173849991827986510et_nat (@ (@ (@ tptp.fun_up4569834200710200790et_nat A) I2) B4)) J2)) (@ (@ tptp.sup_sup_set_nat (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_8173849991827986510et_nat A) (@ (@ tptp.minus_6452836326544984404t_unit J2) (@ (@ tptp.insert_Product_unit I2) tptp.bot_bo3957492148770167129t_unit))))) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.member_Product_unit I2) J2)) B4) tptp.bot_bot_set_nat)))))
% 5.61/5.92 (assert (forall ((A (-> tptp.product_unit tptp.set_int)) (I2 tptp.product_unit) (B4 tptp.set_int) (J2 tptp.set_Product_unit)) (= (@ tptp.comple3221217463730067765et_int (@ (@ tptp.image_3995998972318789802et_int (@ (@ (@ tptp.fun_up391983181201004082et_int A) I2) B4)) J2)) (@ (@ tptp.sup_sup_set_int (@ tptp.comple3221217463730067765et_int (@ (@ tptp.image_3995998972318789802et_int A) (@ (@ tptp.minus_6452836326544984404t_unit J2) (@ (@ tptp.insert_Product_unit I2) tptp.bot_bo3957492148770167129t_unit))))) (@ (@ (@ tptp.if_set_int (@ (@ tptp.member_Product_unit I2) J2)) B4) tptp.bot_bot_set_int)))))
% 5.61/5.92 (assert (forall ((A (-> Bool tptp.set_Product_unit)) (I2 Bool) (B4 tptp.set_Product_unit) (J2 tptp.set_o)) (= (@ tptp.comple3349607820504768346t_unit (@ (@ tptp.image_663195431845683034t_unit (@ (@ (@ tptp.fun_up4718931970374059986t_unit A) I2) B4)) J2)) (@ (@ tptp.sup_su793286257634532545t_unit (@ tptp.comple3349607820504768346t_unit (@ (@ tptp.image_663195431845683034t_unit A) (@ (@ tptp.minus_minus_set_o J2) (@ (@ tptp.insert_o I2) tptp.bot_bot_set_o))))) (@ (@ (@ tptp.if_set_Product_unit (@ (@ tptp.member_o I2) J2)) B4) tptp.bot_bo3957492148770167129t_unit)))))
% 5.61/5.92 (assert (forall ((A (-> Bool tptp.set_o)) (I2 Bool) (B4 tptp.set_o) (J2 tptp.set_o)) (= (@ tptp.comple90263536869209701_set_o (@ (@ tptp.image_o_set_o (@ (@ (@ tptp.fun_upd_o_set_o A) I2) B4)) J2)) (@ (@ tptp.sup_sup_set_o (@ tptp.comple90263536869209701_set_o (@ (@ tptp.image_o_set_o A) (@ (@ tptp.minus_minus_set_o J2) (@ (@ tptp.insert_o I2) tptp.bot_bot_set_o))))) (@ (@ (@ tptp.if_set_o (@ (@ tptp.member_o I2) J2)) B4) tptp.bot_bot_set_o)))))
% 5.61/5.92 (assert (forall ((A (-> Bool tptp.set_nat)) (I2 Bool) (B4 tptp.set_nat) (J2 tptp.set_o)) (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_o_set_nat (@ (@ (@ tptp.fun_upd_o_set_nat A) I2) B4)) J2)) (@ (@ tptp.sup_sup_set_nat (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_o_set_nat A) (@ (@ tptp.minus_minus_set_o J2) (@ (@ tptp.insert_o I2) tptp.bot_bot_set_o))))) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.member_o I2) J2)) B4) tptp.bot_bot_set_nat)))))
% 5.61/5.92 (assert (forall ((A (-> Bool tptp.set_int)) (I2 Bool) (B4 tptp.set_int) (J2 tptp.set_o)) (= (@ tptp.comple3221217463730067765et_int (@ (@ tptp.image_o_set_int (@ (@ (@ tptp.fun_upd_o_set_int A) I2) B4)) J2)) (@ (@ tptp.sup_sup_set_int (@ tptp.comple3221217463730067765et_int (@ (@ tptp.image_o_set_int A) (@ (@ tptp.minus_minus_set_o J2) (@ (@ tptp.insert_o I2) tptp.bot_bot_set_o))))) (@ (@ (@ tptp.if_set_int (@ (@ tptp.member_o I2) J2)) B4) tptp.bot_bot_set_int)))))
% 5.61/5.92 (assert (forall ((A (-> tptp.int tptp.set_Product_unit)) (I2 tptp.int) (B4 tptp.set_Product_unit) (J2 tptp.set_int)) (= (@ tptp.comple3349607820504768346t_unit (@ (@ tptp.image_8658272795163236474t_unit (@ (@ (@ tptp.fun_up5054257004045450754t_unit A) I2) B4)) J2)) (@ (@ tptp.sup_su793286257634532545t_unit (@ tptp.comple3349607820504768346t_unit (@ (@ tptp.image_8658272795163236474t_unit A) (@ (@ tptp.minus_minus_set_int J2) (@ (@ tptp.insert_int I2) tptp.bot_bot_set_int))))) (@ (@ (@ tptp.if_set_Product_unit (@ (@ tptp.member_int I2) J2)) B4) tptp.bot_bo3957492148770167129t_unit)))))
% 5.61/5.92 (assert (forall ((A (-> tptp.int tptp.set_o)) (I2 tptp.int) (B4 tptp.set_o) (J2 tptp.set_int)) (= (@ tptp.comple90263536869209701_set_o (@ (@ tptp.image_int_set_o (@ (@ (@ tptp.fun_upd_int_set_o A) I2) B4)) J2)) (@ (@ tptp.sup_sup_set_o (@ tptp.comple90263536869209701_set_o (@ (@ tptp.image_int_set_o A) (@ (@ tptp.minus_minus_set_int J2) (@ (@ tptp.insert_int I2) tptp.bot_bot_set_int))))) (@ (@ (@ tptp.if_set_o (@ (@ tptp.member_int I2) J2)) B4) tptp.bot_bot_set_o)))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.nat)) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.image_875570014554754200it_nat F))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ _let_1 A))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit2214826472909112428ve_nat _let_3) (=> (not (= B4 tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit2214826472909112428ve_nat _let_2) (= (@ tptp.complete_Sup_Sup_nat (@ _let_1 (@ (@ tptp.sup_su793286257634532545t_unit A) B4))) (@ (@ tptp.sup_sup_nat (@ tptp.complete_Sup_Sup_nat _let_3)) (@ tptp.complete_Sup_Sup_nat _let_2))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.nat)) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.image_o_nat2 F))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit2214826472909112428ve_nat _let_3) (=> (not (= B4 tptp.bot_bot_set_o)) (=> (@ tptp.condit2214826472909112428ve_nat _let_2) (= (@ tptp.complete_Sup_Sup_nat (@ _let_1 (@ (@ tptp.sup_sup_set_o A) B4))) (@ (@ tptp.sup_sup_nat (@ tptp.complete_Sup_Sup_nat _let_3)) (@ tptp.complete_Sup_Sup_nat _let_2))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat)) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_nat2 F))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit2214826472909112428ve_nat _let_3) (=> (not (= B4 tptp.bot_bot_set_nat)) (=> (@ tptp.condit2214826472909112428ve_nat _let_2) (= (@ tptp.complete_Sup_Sup_nat (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4))) (@ (@ tptp.sup_sup_nat (@ tptp.complete_Sup_Sup_nat _let_3)) (@ tptp.complete_Sup_Sup_nat _let_2))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.nat)) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.image_int_nat2 F))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit2214826472909112428ve_nat _let_3) (=> (not (= B4 tptp.bot_bot_set_int)) (=> (@ tptp.condit2214826472909112428ve_nat _let_2) (= (@ tptp.complete_Sup_Sup_nat (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B4))) (@ (@ tptp.sup_sup_nat (@ tptp.complete_Sup_Sup_nat _let_3)) (@ tptp.complete_Sup_Sup_nat _let_2))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.product_unit)) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.image_405062704495631173t_unit F))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ _let_1 A))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit2080475194861589617t_unit _let_3) (=> (not (= B4 tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit2080475194861589617t_unit _let_2) (= (@ tptp.comple4687483117567863418t_unit (@ _let_1 (@ (@ tptp.sup_su793286257634532545t_unit A) B4))) (@ (@ tptp.sup_sup_Product_unit (@ tptp.comple4687483117567863418t_unit _let_3)) (@ tptp.comple4687483117567863418t_unit _let_2))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.product_unit)) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.image_o_Product_unit2 F))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit2080475194861589617t_unit _let_3) (=> (not (= B4 tptp.bot_bot_set_o)) (=> (@ tptp.condit2080475194861589617t_unit _let_2) (= (@ tptp.comple4687483117567863418t_unit (@ _let_1 (@ (@ tptp.sup_sup_set_o A) B4))) (@ (@ tptp.sup_sup_Product_unit (@ tptp.comple4687483117567863418t_unit _let_3)) (@ tptp.comple4687483117567863418t_unit _let_2))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.product_unit)) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_8730104196221521654t_unit F))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit2080475194861589617t_unit _let_3) (=> (not (= B4 tptp.bot_bot_set_nat)) (=> (@ tptp.condit2080475194861589617t_unit _let_2) (= (@ tptp.comple4687483117567863418t_unit (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4))) (@ (@ tptp.sup_sup_Product_unit (@ tptp.comple4687483117567863418t_unit _let_3)) (@ tptp.comple4687483117567863418t_unit _let_2))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.product_unit)) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.image_5846526143423701914t_unit F))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit2080475194861589617t_unit _let_3) (=> (not (= B4 tptp.bot_bot_set_int)) (=> (@ tptp.condit2080475194861589617t_unit _let_2) (= (@ tptp.comple4687483117567863418t_unit (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B4))) (@ (@ tptp.sup_sup_Product_unit (@ tptp.comple4687483117567863418t_unit _let_3)) (@ tptp.comple4687483117567863418t_unit _let_2))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.set_nat)) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.image_8173849991827986510et_nat F))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ _let_1 A))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit5477540289124974626et_nat _let_3) (=> (not (= B4 tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit5477540289124974626et_nat _let_2) (= (@ tptp.comple7399068483239264473et_nat (@ _let_1 (@ (@ tptp.sup_su793286257634532545t_unit A) B4))) (@ (@ tptp.sup_sup_set_nat (@ tptp.comple7399068483239264473et_nat _let_3)) (@ tptp.comple7399068483239264473et_nat _let_2))))))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.set_nat)) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.image_o_set_nat F))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit5477540289124974626et_nat _let_3) (=> (not (= B4 tptp.bot_bot_set_o)) (=> (@ tptp.condit5477540289124974626et_nat _let_2) (= (@ tptp.comple7399068483239264473et_nat (@ _let_1 (@ (@ tptp.sup_sup_set_o A) B4))) (@ (@ tptp.sup_sup_set_nat (@ tptp.comple7399068483239264473et_nat _let_3)) (@ tptp.comple7399068483239264473et_nat _let_2))))))))))))
% 5.61/5.92 (assert (forall ((Y tptp.set_nat) (X tptp.heap_e7401611519738050253t_unit) (A tptp.set_Pr3948176798113811640et_nat)) (= (@ (@ tptp.member727419437372278867t_unit (@ (@ tptp.produc2471974422597015918t_unit Y) X)) (@ (@ tptp.image_1893317993577548229t_unit tptp.produc6300697153377358172et_nat) A)) (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat X) Y)) A))))
% 5.61/5.92 (assert (forall ((Y tptp.produc3658429121746597890et_nat) (X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr3286484037609594932et_nat)) (= (@ (@ tptp.member4978015717948814295_nat_o (@ (@ tptp.produc2829238748666232050_nat_o Y) X)) (@ (@ tptp.image_6229134628169569989_nat_o tptp.produc3251101204053596376et_nat) A)) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X) Y)) A))))
% 5.61/5.92 (assert (forall ((Y tptp.produc3925858234332021118et_nat) (X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr8536935166611901872et_nat)) (= (@ (@ tptp.member8354763867512313179_nat_o (@ (@ tptp.produc3674526432113299062_nat_o Y) X)) (@ (@ tptp.image_4071802983491761093_nat_o tptp.produc1151471490888544852et_nat) A)) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X) Y)) A))))
% 5.61/5.92 (assert (forall ((Y tptp.heap_e7401611519738050253t_unit) (X tptp.set_nat) (A tptp.set_Pr4071100604818519410t_unit)) (= (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat Y) X)) (@ (@ tptp.image_5838825082199883205et_nat tptp.produc1264744871843189710t_unit) A)) (@ (@ tptp.member727419437372278867t_unit (@ (@ tptp.produc2471974422597015918t_unit X) Y)) A))))
% 5.61/5.92 (assert (forall ((Y tptp.nat) (X tptp.nat) (A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y) X)) (@ (@ tptp.image_5168914502847457605at_nat tptp.product_swap_nat_nat) A)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) A))))
% 5.61/5.92 (assert (forall ((Y tptp.int) (X tptp.int) (A tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y) X)) (@ (@ tptp.image_2653370878348428101nt_int tptp.product_swap_int_int) A)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) A))))
% 5.61/5.92 (assert (forall ((Y (-> tptp.produc3658429121746597890et_nat Bool)) (X tptp.produc3658429121746597890et_nat) (A tptp.set_Pr4208978187861016310_nat_o)) (= (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat Y) X)) (@ (@ tptp.image_4501728140019976901et_nat tptp.produc1078497009909708626_nat_o) A)) (@ (@ tptp.member4978015717948814295_nat_o (@ (@ tptp.produc2829238748666232050_nat_o X) Y)) A))))
% 5.61/5.92 (assert (forall ((Y (-> tptp.produc3658429121746597890et_nat Bool)) (X tptp.produc3925858234332021118et_nat) (A tptp.set_Pr7705059561495379578_nat_o)) (= (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat Y) X)) (@ (@ tptp.image_7255662321850427333et_nat tptp.produc2580581461503396054_nat_o) A)) (@ (@ tptp.member8354763867512313179_nat_o (@ (@ tptp.produc3674526432113299062_nat_o X) Y)) A))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.nat)) (A2 tptp.product_unit)) (let ((_let_1 (@ tptp.image_875570014554754200it_nat F))) (let ((_let_2 (@ _let_1 A))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit2214826472909112428ve_nat _let_2) (= (@ tptp.complete_Sup_Sup_nat (@ _let_1 (@ (@ tptp.insert_Product_unit A2) A))) (@ (@ tptp.sup_sup_nat (@ F A2)) (@ tptp.complete_Sup_Sup_nat _let_2)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.nat)) (A2 Bool)) (let ((_let_1 (@ tptp.image_o_nat2 F))) (let ((_let_2 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit2214826472909112428ve_nat _let_2) (= (@ tptp.complete_Sup_Sup_nat (@ _let_1 (@ (@ tptp.insert_o A2) A))) (@ (@ tptp.sup_sup_nat (@ F A2)) (@ tptp.complete_Sup_Sup_nat _let_2)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat)) (A2 tptp.nat)) (let ((_let_1 (@ tptp.image_nat_nat2 F))) (let ((_let_2 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit2214826472909112428ve_nat _let_2) (= (@ tptp.complete_Sup_Sup_nat (@ _let_1 (@ (@ tptp.insert_nat A2) A))) (@ (@ tptp.sup_sup_nat (@ F A2)) (@ tptp.complete_Sup_Sup_nat _let_2)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.nat)) (A2 tptp.int)) (let ((_let_1 (@ tptp.image_int_nat2 F))) (let ((_let_2 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit2214826472909112428ve_nat _let_2) (= (@ tptp.complete_Sup_Sup_nat (@ _let_1 (@ (@ tptp.insert_int A2) A))) (@ (@ tptp.sup_sup_nat (@ F A2)) (@ tptp.complete_Sup_Sup_nat _let_2)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.product_unit)) (A2 tptp.product_unit)) (let ((_let_1 (@ tptp.image_405062704495631173t_unit F))) (let ((_let_2 (@ _let_1 A))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit2080475194861589617t_unit _let_2) (= (@ tptp.comple4687483117567863418t_unit (@ _let_1 (@ (@ tptp.insert_Product_unit A2) A))) (@ (@ tptp.sup_sup_Product_unit (@ F A2)) (@ tptp.comple4687483117567863418t_unit _let_2)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.product_unit)) (A2 Bool)) (let ((_let_1 (@ tptp.image_o_Product_unit2 F))) (let ((_let_2 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit2080475194861589617t_unit _let_2) (= (@ tptp.comple4687483117567863418t_unit (@ _let_1 (@ (@ tptp.insert_o A2) A))) (@ (@ tptp.sup_sup_Product_unit (@ F A2)) (@ tptp.comple4687483117567863418t_unit _let_2)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.product_unit)) (A2 tptp.nat)) (let ((_let_1 (@ tptp.image_8730104196221521654t_unit F))) (let ((_let_2 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit2080475194861589617t_unit _let_2) (= (@ tptp.comple4687483117567863418t_unit (@ _let_1 (@ (@ tptp.insert_nat A2) A))) (@ (@ tptp.sup_sup_Product_unit (@ F A2)) (@ tptp.comple4687483117567863418t_unit _let_2)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.product_unit)) (A2 tptp.int)) (let ((_let_1 (@ tptp.image_5846526143423701914t_unit F))) (let ((_let_2 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit2080475194861589617t_unit _let_2) (= (@ tptp.comple4687483117567863418t_unit (@ _let_1 (@ (@ tptp.insert_int A2) A))) (@ (@ tptp.sup_sup_Product_unit (@ F A2)) (@ tptp.comple4687483117567863418t_unit _let_2)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.set_nat)) (A2 tptp.product_unit)) (let ((_let_1 (@ tptp.image_8173849991827986510et_nat F))) (let ((_let_2 (@ _let_1 A))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit5477540289124974626et_nat _let_2) (= (@ tptp.comple7399068483239264473et_nat (@ _let_1 (@ (@ tptp.insert_Product_unit A2) A))) (@ (@ tptp.sup_sup_set_nat (@ F A2)) (@ tptp.comple7399068483239264473et_nat _let_2)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.set_nat)) (A2 Bool)) (let ((_let_1 (@ tptp.image_o_set_nat F))) (let ((_let_2 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit5477540289124974626et_nat _let_2) (= (@ tptp.comple7399068483239264473et_nat (@ _let_1 (@ (@ tptp.insert_o A2) A))) (@ (@ tptp.sup_sup_set_nat (@ F A2)) (@ tptp.comple7399068483239264473et_nat _let_2)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ (@ tptp.inf_inf_set_o A) B4))) (=> (@ tptp.condit5488710616941104124bove_o A) (=> (@ tptp.condit5488710616941104124bove_o B4) (=> (not (= _let_1 tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_eq_o (@ tptp.complete_Sup_Sup_o _let_1)) (@ (@ tptp.sup_sup_o (@ tptp.complete_Sup_Sup_o A)) (@ tptp.complete_Sup_Sup_o B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o A) B4))) (=> (@ tptp.condit4352657709669162033_nat_o A) (=> (@ tptp.condit4352657709669162033_nat_o B4) (=> (not (= _let_1 tptp.bot_bo7824918357723582233_nat_o)) (@ (@ tptp.ord_le729326519192465773_nat_o (@ tptp.comple4225350640907012154_nat_o _let_1)) (@ (@ tptp.sup_su5453871518329203617_nat_o (@ tptp.comple4225350640907012154_nat_o A)) (@ tptp.comple4225350640907012154_nat_o B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_filter_nat) (B4 tptp.set_filter_nat)) (let ((_let_1 (@ (@ tptp.inf_in7395780696554941096er_nat A) B4))) (=> (@ tptp.condit4029664723990530684er_nat A) (=> (@ tptp.condit4029664723990530684er_nat B4) (=> (not (= _let_1 tptp.bot_bo498966703094740906er_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ tptp.comple2454491259644266675er_nat _let_1)) (@ (@ tptp.sup_sup_filter_nat (@ tptp.comple2454491259644266675er_nat A)) (@ tptp.comple2454491259644266675er_nat B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_set_nat) (B4 tptp.set_set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_set_nat A) B4))) (=> (@ tptp.condit5477540289124974626et_nat A) (=> (@ tptp.condit5477540289124974626et_nat B4) (=> (not (= _let_1 tptp.bot_bot_set_set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7399068483239264473et_nat _let_1)) (@ (@ tptp.sup_sup_set_nat (@ tptp.comple7399068483239264473et_nat A)) (@ tptp.comple7399068483239264473et_nat B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ (@ tptp.inf_inf_set_int A) B4))) (=> (@ tptp.condit2212336002400062152ve_int A) (=> (@ tptp.condit2212336002400062152ve_int B4) (=> (not (= _let_1 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Sup_Sup_int _let_1)) (@ (@ tptp.sup_sup_int (@ tptp.complete_Sup_Sup_int A)) (@ tptp.complete_Sup_Sup_int B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat A) B4))) (=> (@ tptp.condit2214826472909112428ve_nat A) (=> (@ tptp.condit2214826472909112428ve_nat B4) (=> (not (= _let_1 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Sup_Sup_nat _let_1)) (@ (@ tptp.sup_sup_nat (@ tptp.complete_Sup_Sup_nat A)) (@ tptp.complete_Sup_Sup_nat B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ (@ tptp.inf_in4660618365625256667t_unit A) B4))) (=> (@ tptp.condit2080475194861589617t_unit A) (=> (@ tptp.condit2080475194861589617t_unit B4) (=> (not (= _let_1 tptp.bot_bo3957492148770167129t_unit)) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.comple4687483117567863418t_unit _let_1)) (@ (@ tptp.sup_sup_Product_unit (@ tptp.comple4687483117567863418t_unit A)) (@ tptp.comple4687483117567863418t_unit B4)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (G (-> tptp.product_unit tptp.int)) (B4 tptp.set_Product_unit) (F (-> tptp.product_unit tptp.int))) (let ((_let_1 (@ (@ tptp.image_873079544045703924it_int G) B4))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit2212336002400062152ve_int _let_1) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) B4) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) A) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Sup_Sup_int (@ (@ tptp.image_873079544045703924it_int F) A))) (@ tptp.complete_Sup_Sup_int _let_1)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (G (-> Bool tptp.int)) (B4 tptp.set_o) (F (-> Bool tptp.int))) (let ((_let_1 (@ (@ tptp.image_o_int2 G) B4))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit2212336002400062152ve_int _let_1) (=> (@ (@ tptp.ord_less_eq_set_o A) B4) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Sup_Sup_int (@ (@ tptp.image_o_int2 F) A))) (@ tptp.complete_Sup_Sup_int _let_1)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.int)) (B4 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ (@ tptp.image_int_int2 G) B4))) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit2212336002400062152ve_int _let_1) (=> (@ (@ tptp.ord_less_eq_set_int A) B4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Sup_Sup_int (@ (@ tptp.image_int_int2 F) A))) (@ tptp.complete_Sup_Sup_int _let_1)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.int)) (B4 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.image_nat_int2 G) B4))) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit2212336002400062152ve_int _let_1) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Sup_Sup_int (@ (@ tptp.image_nat_int2 F) A))) (@ tptp.complete_Sup_Sup_int _let_1)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (G (-> tptp.product_unit tptp.nat)) (B4 tptp.set_Product_unit) (F (-> tptp.product_unit tptp.nat))) (let ((_let_1 (@ (@ tptp.image_875570014554754200it_nat G) B4))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit2214826472909112428ve_nat _let_1) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) B4) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) A) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Sup_Sup_nat (@ (@ tptp.image_875570014554754200it_nat F) A))) (@ tptp.complete_Sup_Sup_nat _let_1)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (G (-> Bool tptp.nat)) (B4 tptp.set_o) (F (-> Bool tptp.nat))) (let ((_let_1 (@ (@ tptp.image_o_nat2 G) B4))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit2214826472909112428ve_nat _let_1) (=> (@ (@ tptp.ord_less_eq_set_o A) B4) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Sup_Sup_nat (@ (@ tptp.image_o_nat2 F) A))) (@ tptp.complete_Sup_Sup_nat _let_1)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.nat)) (B4 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.image_int_nat2 G) B4))) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit2214826472909112428ve_nat _let_1) (=> (@ (@ tptp.ord_less_eq_set_int A) B4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Sup_Sup_nat (@ (@ tptp.image_int_nat2 F) A))) (@ tptp.complete_Sup_Sup_nat _let_1)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.nat)) (B4 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.image_nat_nat2 G) B4))) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit2214826472909112428ve_nat _let_1) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Sup_Sup_nat (@ (@ tptp.image_nat_nat2 F) A))) (@ tptp.complete_Sup_Sup_nat _let_1)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_Product_unit) (G (-> tptp.product_unit tptp.product_unit)) (B4 tptp.set_Product_unit) (F (-> tptp.product_unit tptp.product_unit))) (let ((_let_1 (@ (@ tptp.image_405062704495631173t_unit G) B4))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit2080475194861589617t_unit _let_1) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) B4) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) A) (@ (@ tptp.ord_le3221252021190050221t_unit (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.comple4687483117567863418t_unit (@ (@ tptp.image_405062704495631173t_unit F) A))) (@ tptp.comple4687483117567863418t_unit _let_1)))))))))
% 5.61/5.92 (assert (forall ((A tptp.set_o) (G (-> Bool tptp.product_unit)) (B4 tptp.set_o) (F (-> Bool tptp.product_unit))) (let ((_let_1 (@ (@ tptp.image_o_Product_unit2 G) B4))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit2080475194861589617t_unit _let_1) (=> (@ (@ tptp.ord_less_eq_set_o A) B4) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (@ (@ tptp.ord_le3221252021190050221t_unit (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.comple4687483117567863418t_unit (@ (@ tptp.image_o_Product_unit2 F) A))) (@ tptp.comple4687483117567863418t_unit _let_1)))))))))
% 5.61/5.92 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_nat R3))) (=> (@ tptp.single5507084439971879973at_nat (@ tptp.converse_nat_nat R3)) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 A)) (@ _let_1 B4)))))))
% 5.61/5.92 (assert (forall ((X tptp.code_integer) (A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer)) (N2 tptp.code_integer)) (=> (not (@ (@ tptp.member_Code_integer X) A)) (= (@ (@ tptp.image_4470545334726330049nteger (@ (@ (@ tptp.fun_up8355007323143964473nteger F) X) N2)) A) (@ (@ tptp.image_4470545334726330049nteger F) A)))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (A tptp.set_nat) (F (-> tptp.nat tptp.set_nat)) (N2 tptp.set_nat)) (=> (not (@ (@ tptp.member_nat X) A)) (= (@ (@ tptp.image_nat_set_nat (@ (@ (@ tptp.fun_upd_nat_set_nat F) X) N2)) A) (@ (@ tptp.image_nat_set_nat F) A)))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (A tptp.set_nat) (F (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (=> (not (@ (@ tptp.member_nat X) A)) (= (@ (@ tptp.image_nat_nat2 (@ (@ (@ tptp.fun_upd_nat_nat F) X) N2)) A) (@ (@ tptp.image_nat_nat2 F) A)))))
% 5.61/5.92 (assert (forall ((X tptp.nat) (A tptp.set_nat) (F (-> tptp.nat tptp.code_integer)) (N2 tptp.code_integer)) (=> (not (@ (@ tptp.member_nat X) A)) (= (@ (@ tptp.image_1215581382706833972nteger (@ (@ (@ tptp.fun_up3904115110581602988nteger F) X) N2)) A) (@ (@ tptp.image_1215581382706833972nteger F) A)))))
% 5.61/5.92 (assert (@ tptp.condit2080475194861589617t_unit tptp.bot_bo3957492148770167129t_unit))
% 5.61/5.92 (assert (@ tptp.condit5488710616941104124bove_o tptp.bot_bot_set_o))
% 5.61/5.92 (assert (@ tptp.condit2214826472909112428ve_nat tptp.bot_bot_set_nat))
% 5.61/5.92 (assert (@ tptp.condit2212336002400062152ve_int tptp.bot_bot_set_int))
% 5.61/5.92 (assert (@ tptp.condit4352657709669162033_nat_o tptp.bot_bo7824918357723582233_nat_o))
% 5.61/5.92 (assert (forall ((A2 tptp.nat) (A tptp.set_nat)) (= (@ tptp.condit2214826472909112428ve_nat (@ (@ tptp.insert_nat A2) A)) (@ tptp.condit2214826472909112428ve_nat A))))
% 5.61/5.92 (assert (forall ((A2 tptp.int) (A tptp.set_int)) (= (@ tptp.condit2212336002400062152ve_int (@ (@ tptp.insert_int A2) A)) (@ tptp.condit2212336002400062152ve_int A))))
% 5.61/5.92 (assert (forall ((A2 Bool) (A tptp.set_o)) (= (@ tptp.condit5488710616941104124bove_o (@ (@ tptp.insert_o A2) A)) (@ tptp.condit5488710616941104124bove_o A))))
% 5.65/5.92 (assert (forall ((A2 tptp.product_unit) (A tptp.set_Product_unit)) (= (@ tptp.condit2080475194861589617t_unit (@ (@ tptp.insert_Product_unit A2) A)) (@ tptp.condit2080475194861589617t_unit A))))
% 5.65/5.92 (assert (forall ((X tptp.set_nat) (Y tptp.heap_e7401611519738050253t_unit)) (= (@ tptp.produc1264744871843189710t_unit (@ (@ tptp.produc2471974422597015918t_unit X) Y)) (@ (@ tptp.produc7507926704131184380et_nat Y) X))))
% 5.65/5.92 (assert (forall ((X tptp.produc3658429121746597890et_nat) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (= (@ tptp.produc1078497009909708626_nat_o (@ (@ tptp.produc2829238748666232050_nat_o X) Y)) (@ (@ tptp.produc5001842942810119800et_nat Y) X))))
% 5.65/5.92 (assert (forall ((X tptp.produc3925858234332021118et_nat) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (= (@ tptp.produc2580581461503396054_nat_o (@ (@ tptp.produc3674526432113299062_nat_o X) Y)) (@ (@ tptp.produc2245416461498447860et_nat Y) X))))
% 5.65/5.92 (assert (forall ((X tptp.heap_e7401611519738050253t_unit) (Y tptp.set_nat)) (= (@ tptp.produc6300697153377358172et_nat (@ (@ tptp.produc7507926704131184380et_nat X) Y)) (@ (@ tptp.produc2471974422597015918t_unit Y) X))))
% 5.65/5.92 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.product_swap_nat_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ tptp.product_Pair_nat_nat Y) X))))
% 5.65/5.92 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ tptp.product_swap_int_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ (@ tptp.product_Pair_int_int Y) X))))
% 5.65/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3658429121746597890et_nat)) (= (@ tptp.produc3251101204053596376et_nat (@ (@ tptp.produc5001842942810119800et_nat X) Y)) (@ (@ tptp.produc2829238748666232050_nat_o Y) X))))
% 5.65/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3925858234332021118et_nat)) (= (@ tptp.produc1151471490888544852et_nat (@ (@ tptp.produc2245416461498447860et_nat X) Y)) (@ (@ tptp.produc3674526432113299062_nat_o Y) X))))
% 5.65/5.92 (assert (forall ((R2 tptp.set_Pr3948176798113811640et_nat) (X tptp.heap_e7401611519738050253t_unit) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat X))) (=> (@ tptp.single6620584844202787856et_nat R2) (=> (@ (@ tptp.member6260224972018164377et_nat (@ _let_1 Y)) R2) (=> (@ (@ tptp.member6260224972018164377et_nat (@ _let_1 Z)) R2) (= Y Z)))))))
% 5.65/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X))) (=> (@ tptp.single5507084439971879973at_nat R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 Y)) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 Z)) R2) (= Y Z)))))))
% 5.65/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int X))) (=> (@ tptp.single6503947681363884253nt_int R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 Y)) R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 Z)) R2) (= Y Z)))))))
% 5.65/5.92 (assert (forall ((R2 tptp.set_Pr3286484037609594932et_nat) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3658429121746597890et_nat) (Z tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.produc5001842942810119800et_nat X))) (=> (@ tptp.single7715245794981374860et_nat R2) (=> (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 Y)) R2) (=> (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 Z)) R2) (= Y Z)))))))
% 5.65/5.92 (assert (forall ((R2 tptp.set_Pr8536935166611901872et_nat) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3925858234332021118et_nat) (Z tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ tptp.produc2245416461498447860et_nat X))) (=> (@ tptp.single261872189793494280et_nat R2) (=> (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 Y)) R2) (=> (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 Z)) R2) (= Y Z)))))))
% 5.65/5.92 (assert (forall ((R2 tptp.set_Pr3948176798113811640et_nat)) (=> (forall ((X3 tptp.heap_e7401611519738050253t_unit) (Y2 tptp.set_nat) (Z3 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat X3))) (=> (@ (@ tptp.member6260224972018164377et_nat (@ _let_1 Y2)) R2) (=> (@ (@ tptp.member6260224972018164377et_nat (@ _let_1 Z3)) R2) (= Y2 Z3))))) (@ tptp.single6620584844202787856et_nat R2))))
% 5.65/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X3))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 Y2)) R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 Z3)) R2) (= Y2 Z3))))) (@ tptp.single5507084439971879973at_nat R2))))
% 5.65/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int)) (=> (forall ((X3 tptp.int) (Y2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int X3))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 Y2)) R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_1 Z3)) R2) (= Y2 Z3))))) (@ tptp.single6503947681363884253nt_int R2))))
% 5.65/5.92 (assert (forall ((R2 tptp.set_Pr3286484037609594932et_nat)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3658429121746597890et_nat) (Z3 tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.produc5001842942810119800et_nat X3))) (=> (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 Y2)) R2) (=> (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 Z3)) R2) (= Y2 Z3))))) (@ tptp.single7715245794981374860et_nat R2))))
% 5.65/5.92 (assert (forall ((R2 tptp.set_Pr8536935166611901872et_nat)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3925858234332021118et_nat) (Z3 tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ tptp.produc2245416461498447860et_nat X3))) (=> (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 Y2)) R2) (=> (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 Z3)) R2) (= Y2 Z3))))) (@ tptp.single261872189793494280et_nat R2))))
% 5.65/5.92 (assert (= tptp.single6620584844202787856et_nat (lambda ((R4 tptp.set_Pr3948176798113811640et_nat)) (forall ((X2 tptp.heap_e7401611519738050253t_unit) (Y3 tptp.set_nat)) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat X2) Y3)) R4) (forall ((Z2 tptp.set_nat)) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat X2) Z2)) R4) (= Y3 Z2))))))))
% 5.65/5.92 (assert (= tptp.single5507084439971879973at_nat (lambda ((R4 tptp.set_Pr1261947904930325089at_nat)) (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Y3)) R4) (forall ((Z2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X2) Z2)) R4) (= Y3 Z2))))))))
% 5.65/5.92 (assert (= tptp.single6503947681363884253nt_int (lambda ((R4 tptp.set_Pr958786334691620121nt_int)) (forall ((X2 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X2) Y3)) R4) (forall ((Z2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X2) Z2)) R4) (= Y3 Z2))))))))
% 5.65/5.92 (assert (= tptp.single7715245794981374860et_nat (lambda ((R4 tptp.set_Pr3286484037609594932et_nat)) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool)) (Y3 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X2) Y3)) R4) (forall ((Z2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X2) Z2)) R4) (= Y3 Z2))))))))
% 5.65/5.92 (assert (= tptp.single261872189793494280et_nat (lambda ((R4 tptp.set_Pr8536935166611901872et_nat)) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool)) (Y3 tptp.produc3925858234332021118et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X2) Y3)) R4) (forall ((Z2 tptp.produc3925858234332021118et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X2) Z2)) R4) (= Y3 Z2))))))))
% 5.65/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.transi2905341329935302413cl_nat R2))) (let ((_let_2 (@ tptp.product_Pair_nat_nat X))) (=> (@ tptp.single5507084439971879973at_nat R2) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 Y)) _let_1) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_2 Z)) _let_1) (or (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y) Z)) _let_1) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Z) Y)) _let_1)))))))))
% 5.65/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.transi2902850859426252137cl_int R2))) (let ((_let_2 (@ tptp.product_Pair_int_int X))) (=> (@ tptp.single6503947681363884253nt_int R2) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 Y)) _let_1) (=> (@ (@ tptp.member5262025264175285858nt_int (@ _let_2 Z)) _let_1) (or (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Y) Z)) _let_1) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int Z) Y)) _let_1)))))))))
% 5.65/5.92 (assert (forall ((S tptp.set_o) (A2 Bool)) (=> (not (= S tptp.bot_bot_set_o)) (=> (@ tptp.condit5488710616941104124bove_o S) (= (@ (@ tptp.ord_less_eq_o (@ tptp.complete_Sup_Sup_o S)) A2) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) S) (@ (@ tptp.ord_less_eq_o X2) A2))))))))
% 5.65/5.92 (assert (forall ((S tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (not (= S tptp.bot_bo7824918357723582233_nat_o)) (=> (@ tptp.condit4352657709669162033_nat_o S) (= (@ (@ tptp.ord_le729326519192465773_nat_o (@ tptp.comple4225350640907012154_nat_o S)) A2) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X2) S) (@ (@ tptp.ord_le729326519192465773_nat_o X2) A2))))))))
% 5.65/5.92 (assert (forall ((S tptp.set_filter_nat) (A2 tptp.filter_nat)) (=> (not (= S tptp.bot_bo498966703094740906er_nat)) (=> (@ tptp.condit4029664723990530684er_nat S) (= (@ (@ tptp.ord_le2510731241096832064er_nat (@ tptp.comple2454491259644266675er_nat S)) A2) (forall ((X2 tptp.filter_nat)) (=> (@ (@ tptp.member_filter_nat X2) S) (@ (@ tptp.ord_le2510731241096832064er_nat X2) A2))))))))
% 5.65/5.92 (assert (forall ((S tptp.set_set_nat) (A2 tptp.set_nat)) (=> (not (= S tptp.bot_bot_set_set_nat)) (=> (@ tptp.condit5477540289124974626et_nat S) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7399068483239264473et_nat S)) A2) (forall ((X2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X2) S) (@ (@ tptp.ord_less_eq_set_nat X2) A2))))))))
% 5.65/5.92 (assert (forall ((S tptp.set_int) (A2 tptp.int)) (=> (not (= S tptp.bot_bot_set_int)) (=> (@ tptp.condit2212336002400062152ve_int S) (= (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Sup_Sup_int S)) A2) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) S) (@ (@ tptp.ord_less_eq_int X2) A2))))))))
% 5.65/5.92 (assert (forall ((S tptp.set_nat) (A2 tptp.nat)) (=> (not (= S tptp.bot_bot_set_nat)) (=> (@ tptp.condit2214826472909112428ve_nat S) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Sup_Sup_nat S)) A2) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) S) (@ (@ tptp.ord_less_eq_nat X2) A2))))))))
% 5.65/5.92 (assert (forall ((S tptp.set_Product_unit) (A2 tptp.product_unit)) (=> (not (= S tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit2080475194861589617t_unit S) (= (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.comple4687483117567863418t_unit S)) A2) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) S) (@ (@ tptp.ord_le3221252021190050221t_unit X2) A2))))))))
% 5.65/5.92 (assert (forall ((B4 tptp.set_o) (A tptp.set_o)) (=> (not (= B4 tptp.bot_bot_set_o)) (=> (@ tptp.condit5488710616941104124bove_o A) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) B4) (exists ((X6 Bool)) (and (@ (@ tptp.member_o X6) A) (@ (@ tptp.ord_less_eq_o B2) X6))))) (@ (@ tptp.ord_less_eq_o (@ tptp.complete_Sup_Sup_o B4)) (@ tptp.complete_Sup_Sup_o A)))))))
% 5.65/5.92 (assert (forall ((B4 tptp.set_Pr4532377907799695533_nat_o) (A tptp.set_Pr4532377907799695533_nat_o)) (=> (not (= B4 tptp.bot_bo7824918357723582233_nat_o)) (=> (@ tptp.condit4352657709669162033_nat_o A) (=> (forall ((B2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o B2) B4) (exists ((X6 (-> tptp.produc3658429121746597890et_nat Bool))) (and (@ (@ tptp.member6576561426505652726_nat_o X6) A) (@ (@ tptp.ord_le729326519192465773_nat_o B2) X6))))) (@ (@ tptp.ord_le729326519192465773_nat_o (@ tptp.comple4225350640907012154_nat_o B4)) (@ tptp.comple4225350640907012154_nat_o A)))))))
% 5.65/5.92 (assert (forall ((B4 tptp.set_filter_nat) (A tptp.set_filter_nat)) (=> (not (= B4 tptp.bot_bo498966703094740906er_nat)) (=> (@ tptp.condit4029664723990530684er_nat A) (=> (forall ((B2 tptp.filter_nat)) (=> (@ (@ tptp.member_filter_nat B2) B4) (exists ((X6 tptp.filter_nat)) (and (@ (@ tptp.member_filter_nat X6) A) (@ (@ tptp.ord_le2510731241096832064er_nat B2) X6))))) (@ (@ tptp.ord_le2510731241096832064er_nat (@ tptp.comple2454491259644266675er_nat B4)) (@ tptp.comple2454491259644266675er_nat A)))))))
% 5.65/5.92 (assert (forall ((B4 tptp.set_set_nat) (A tptp.set_set_nat)) (=> (not (= B4 tptp.bot_bot_set_set_nat)) (=> (@ tptp.condit5477540289124974626et_nat A) (=> (forall ((B2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat B2) B4) (exists ((X6 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X6) A) (@ (@ tptp.ord_less_eq_set_nat B2) X6))))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7399068483239264473et_nat B4)) (@ tptp.comple7399068483239264473et_nat A)))))))
% 5.65/5.92 (assert (forall ((B4 tptp.set_int) (A tptp.set_int)) (=> (not (= B4 tptp.bot_bot_set_int)) (=> (@ tptp.condit2212336002400062152ve_int A) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) B4) (exists ((X6 tptp.int)) (and (@ (@ tptp.member_int X6) A) (@ (@ tptp.ord_less_eq_int B2) X6))))) (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Sup_Sup_int B4)) (@ tptp.complete_Sup_Sup_int A)))))))
% 5.65/5.92 (assert (forall ((B4 tptp.set_nat) (A tptp.set_nat)) (=> (not (= B4 tptp.bot_bot_set_nat)) (=> (@ tptp.condit2214826472909112428ve_nat A) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) B4) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) A) (@ (@ tptp.ord_less_eq_nat B2) X6))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Sup_Sup_nat B4)) (@ tptp.complete_Sup_Sup_nat A)))))))
% 5.65/5.92 (assert (forall ((B4 tptp.set_Product_unit) (A tptp.set_Product_unit)) (=> (not (= B4 tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit2080475194861589617t_unit A) (=> (forall ((B2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit B2) B4) (exists ((X6 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X6) A) (@ (@ tptp.ord_le3221252021190050221t_unit B2) X6))))) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.comple4687483117567863418t_unit B4)) (@ tptp.comple4687483117567863418t_unit A)))))))
% 5.65/5.92 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.int)) (U tptp.int)) (let ((_let_1 (@ (@ tptp.image_873079544045703924it_int F) A))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit2212336002400062152ve_int _let_1) (= (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Sup_Sup_int _let_1)) U) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) A) (@ (@ tptp.ord_less_eq_int (@ F X2)) U)))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.int)) (U tptp.int)) (let ((_let_1 (@ (@ tptp.image_o_int2 F) A))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit2212336002400062152ve_int _let_1) (= (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Sup_Sup_int _let_1)) U) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A) (@ (@ tptp.ord_less_eq_int (@ F X2)) U)))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.int)) (U tptp.int)) (let ((_let_1 (@ (@ tptp.image_nat_int2 F) A))) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit2212336002400062152ve_int _let_1) (= (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Sup_Sup_int _let_1)) U) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.ord_less_eq_int (@ F X2)) U)))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.int)) (U tptp.int)) (let ((_let_1 (@ (@ tptp.image_int_int2 F) A))) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit2212336002400062152ve_int _let_1) (= (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Sup_Sup_int _let_1)) U) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A) (@ (@ tptp.ord_less_eq_int (@ F X2)) U)))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.nat)) (U tptp.nat)) (let ((_let_1 (@ (@ tptp.image_875570014554754200it_nat F) A))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit2214826472909112428ve_nat _let_1) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Sup_Sup_nat _let_1)) U) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) A) (@ (@ tptp.ord_less_eq_nat (@ F X2)) U)))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.nat)) (U tptp.nat)) (let ((_let_1 (@ (@ tptp.image_o_nat2 F) A))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit2214826472909112428ve_nat _let_1) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Sup_Sup_nat _let_1)) U) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A) (@ (@ tptp.ord_less_eq_nat (@ F X2)) U)))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat)) (U tptp.nat)) (let ((_let_1 (@ (@ tptp.image_nat_nat2 F) A))) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit2214826472909112428ve_nat _let_1) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Sup_Sup_nat _let_1)) U) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.ord_less_eq_nat (@ F X2)) U)))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.nat)) (U tptp.nat)) (let ((_let_1 (@ (@ tptp.image_int_nat2 F) A))) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit2214826472909112428ve_nat _let_1) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Sup_Sup_nat _let_1)) U) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A) (@ (@ tptp.ord_less_eq_nat (@ F X2)) U)))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.product_unit)) (U tptp.product_unit)) (let ((_let_1 (@ (@ tptp.image_405062704495631173t_unit F) A))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit2080475194861589617t_unit _let_1) (= (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.comple4687483117567863418t_unit _let_1)) U) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) A) (@ (@ tptp.ord_le3221252021190050221t_unit (@ F X2)) U)))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.product_unit)) (U tptp.product_unit)) (let ((_let_1 (@ (@ tptp.image_o_Product_unit2 F) A))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit2080475194861589617t_unit _let_1) (= (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.comple4687483117567863418t_unit _let_1)) U) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A) (@ (@ tptp.ord_le3221252021190050221t_unit (@ F X2)) U)))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_Product_unit) (G (-> tptp.nat tptp.set_nat)) (B4 tptp.set_nat) (F (-> tptp.product_unit tptp.set_nat))) (let ((_let_1 (@ (@ tptp.image_nat_set_nat G) B4))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit5477540289124974626et_nat _let_1) (=> (forall ((N3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit N3) A) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) B4) (@ (@ tptp.ord_less_eq_set_nat (@ F N3)) (@ G X6)))))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_8173849991827986510et_nat F) A))) (@ tptp.comple7399068483239264473et_nat _let_1))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_o) (G (-> tptp.nat tptp.set_nat)) (B4 tptp.set_nat) (F (-> Bool tptp.set_nat))) (let ((_let_1 (@ (@ tptp.image_nat_set_nat G) B4))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit5477540289124974626et_nat _let_1) (=> (forall ((N3 Bool)) (=> (@ (@ tptp.member_o N3) A) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) B4) (@ (@ tptp.ord_less_eq_set_nat (@ F N3)) (@ G X6)))))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_o_set_nat F) A))) (@ tptp.comple7399068483239264473et_nat _let_1))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.set_nat)) (B4 tptp.set_nat) (F (-> tptp.nat tptp.set_nat))) (let ((_let_1 (@ (@ tptp.image_nat_set_nat G) B4))) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit5477540289124974626et_nat _let_1) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) A) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) B4) (@ (@ tptp.ord_less_eq_set_nat (@ F N3)) (@ G X6)))))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat F) A))) (@ tptp.comple7399068483239264473et_nat _let_1))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_int) (G (-> tptp.nat tptp.set_nat)) (B4 tptp.set_nat) (F (-> tptp.int tptp.set_nat))) (let ((_let_1 (@ (@ tptp.image_nat_set_nat G) B4))) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit5477540289124974626et_nat _let_1) (=> (forall ((N3 tptp.int)) (=> (@ (@ tptp.member_int N3) A) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) B4) (@ (@ tptp.ord_less_eq_set_nat (@ F N3)) (@ G X6)))))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_int_set_nat F) A))) (@ tptp.comple7399068483239264473et_nat _let_1))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (G (-> tptp.nat tptp.set_nat)) (B4 tptp.set_nat) (F (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.set_nat))) (let ((_let_1 (@ (@ tptp.image_nat_set_nat G) B4))) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (=> (@ tptp.condit5477540289124974626et_nat _let_1) (=> (forall ((N3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o N3) A) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) B4) (@ (@ tptp.ord_less_eq_set_nat (@ F N3)) (@ G X6)))))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_6888641473154130958et_nat F) A))) (@ tptp.comple7399068483239264473et_nat _let_1))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_Product_unit) (G (-> tptp.nat tptp.nat)) (B4 tptp.set_nat) (F (-> tptp.product_unit tptp.nat))) (let ((_let_1 (@ (@ tptp.image_nat_nat2 G) B4))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit2214826472909112428ve_nat _let_1) (=> (forall ((N3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit N3) A) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) B4) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G X6)))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Sup_Sup_nat (@ (@ tptp.image_875570014554754200it_nat F) A))) (@ tptp.complete_Sup_Sup_nat _let_1))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_o) (G (-> tptp.nat tptp.nat)) (B4 tptp.set_nat) (F (-> Bool tptp.nat))) (let ((_let_1 (@ (@ tptp.image_nat_nat2 G) B4))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit2214826472909112428ve_nat _let_1) (=> (forall ((N3 Bool)) (=> (@ (@ tptp.member_o N3) A) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) B4) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G X6)))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Sup_Sup_nat (@ (@ tptp.image_o_nat2 F) A))) (@ tptp.complete_Sup_Sup_nat _let_1))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.nat)) (B4 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.image_nat_nat2 G) B4))) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit2214826472909112428ve_nat _let_1) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) A) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) B4) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G X6)))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Sup_Sup_nat (@ (@ tptp.image_nat_nat2 F) A))) (@ tptp.complete_Sup_Sup_nat _let_1))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_int) (G (-> tptp.nat tptp.nat)) (B4 tptp.set_nat) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.image_nat_nat2 G) B4))) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit2214826472909112428ve_nat _let_1) (=> (forall ((N3 tptp.int)) (=> (@ (@ tptp.member_int N3) A) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) B4) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G X6)))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Sup_Sup_nat (@ (@ tptp.image_int_nat2 F) A))) (@ tptp.complete_Sup_Sup_nat _let_1))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (G (-> tptp.nat tptp.nat)) (B4 tptp.set_nat) (F (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.nat))) (let ((_let_1 (@ (@ tptp.image_nat_nat2 G) B4))) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (=> (@ tptp.condit2214826472909112428ve_nat _let_1) (=> (forall ((N3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o N3) A) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) B4) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G X6)))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Sup_Sup_nat (@ (@ tptp.image_2174381888560928856_o_nat F) A))) (@ tptp.complete_Sup_Sup_nat _let_1))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit5488710616941104124bove_o B4) (=> (@ (@ tptp.ord_less_eq_set_o A) B4) (@ (@ tptp.ord_less_eq_o (@ tptp.complete_Sup_Sup_o A)) (@ tptp.complete_Sup_Sup_o B4)))))))
% 5.65/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (=> (@ tptp.condit4352657709669162033_nat_o B4) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A) B4) (@ (@ tptp.ord_le729326519192465773_nat_o (@ tptp.comple4225350640907012154_nat_o A)) (@ tptp.comple4225350640907012154_nat_o B4)))))))
% 5.65/5.92 (assert (forall ((A tptp.set_filter_nat) (B4 tptp.set_filter_nat)) (=> (not (= A tptp.bot_bo498966703094740906er_nat)) (=> (@ tptp.condit4029664723990530684er_nat B4) (=> (@ (@ tptp.ord_le2426478655948331894er_nat A) B4) (@ (@ tptp.ord_le2510731241096832064er_nat (@ tptp.comple2454491259644266675er_nat A)) (@ tptp.comple2454491259644266675er_nat B4)))))))
% 5.65/5.92 (assert (forall ((A tptp.set_set_nat) (B4 tptp.set_set_nat)) (=> (not (= A tptp.bot_bot_set_set_nat)) (=> (@ tptp.condit5477540289124974626et_nat B4) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A) B4) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7399068483239264473et_nat A)) (@ tptp.comple7399068483239264473et_nat B4)))))))
% 5.65/5.92 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit2212336002400062152ve_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A) B4) (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Sup_Sup_int A)) (@ tptp.complete_Sup_Sup_int B4)))))))
% 5.65/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit2214826472909112428ve_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Sup_Sup_nat A)) (@ tptp.complete_Sup_Sup_nat B4)))))))
% 5.65/5.92 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit2080475194861589617t_unit B4) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) B4) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.comple4687483117567863418t_unit A)) (@ tptp.comple4687483117567863418t_unit B4)))))))
% 5.65/5.92 (assert (forall ((X4 tptp.set_set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.insert_set_nat A2) X4)))) (let ((_let_2 (= X4 tptp.bot_bot_set_set_nat))) (=> (@ tptp.condit5477540289124974626et_nat X4) (and (=> _let_2 (= _let_1 A2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.sup_sup_set_nat A2) (@ tptp.comple7399068483239264473et_nat X4))))))))))
% 5.65/5.92 (assert (forall ((X4 tptp.set_o) (A2 Bool)) (let ((_let_1 (= X4 tptp.bot_bot_set_o))) (=> (@ tptp.condit5488710616941104124bove_o X4) (= (@ tptp.complete_Sup_Sup_o (@ (@ tptp.insert_o A2) X4)) (and (=> _let_1 A2) (=> (not _let_1) (@ (@ tptp.sup_sup_o A2) (@ tptp.complete_Sup_Sup_o X4)))))))))
% 5.65/5.92 (assert (forall ((X4 tptp.set_int) (A2 tptp.int)) (let ((_let_1 (@ tptp.complete_Sup_Sup_int (@ (@ tptp.insert_int A2) X4)))) (let ((_let_2 (= X4 tptp.bot_bot_set_int))) (=> (@ tptp.condit2212336002400062152ve_int X4) (and (=> _let_2 (= _let_1 A2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.sup_sup_int A2) (@ tptp.complete_Sup_Sup_int X4))))))))))
% 5.65/5.92 (assert (forall ((X4 tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.comple4225350640907012154_nat_o (@ (@ tptp.insert5175938949040314269_nat_o A2) X4)))) (let ((_let_2 (= X4 tptp.bot_bo7824918357723582233_nat_o))) (=> (@ tptp.condit4352657709669162033_nat_o X4) (and (=> _let_2 (= _let_1 A2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.sup_su5453871518329203617_nat_o A2) (@ tptp.comple4225350640907012154_nat_o X4))))))))))
% 5.65/5.92 (assert (forall ((X4 tptp.set_nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.complete_Sup_Sup_nat (@ (@ tptp.insert_nat A2) X4)))) (let ((_let_2 (= X4 tptp.bot_bot_set_nat))) (=> (@ tptp.condit2214826472909112428ve_nat X4) (and (=> _let_2 (= _let_1 A2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.sup_sup_nat A2) (@ tptp.complete_Sup_Sup_nat X4))))))))))
% 5.65/5.92 (assert (forall ((X4 tptp.set_Product_unit) (A2 tptp.product_unit)) (let ((_let_1 (@ tptp.comple4687483117567863418t_unit (@ (@ tptp.insert_Product_unit A2) X4)))) (let ((_let_2 (= X4 tptp.bot_bo3957492148770167129t_unit))) (=> (@ tptp.condit2080475194861589617t_unit X4) (and (=> _let_2 (= _let_1 A2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.sup_sup_Product_unit A2) (@ tptp.comple4687483117567863418t_unit X4))))))))))
% 5.65/5.92 (assert (forall ((X4 tptp.set_set_nat) (A2 tptp.set_nat)) (=> (not (= X4 tptp.bot_bot_set_set_nat)) (=> (@ tptp.condit5477540289124974626et_nat X4) (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.insert_set_nat A2) X4)) (@ (@ tptp.sup_sup_set_nat A2) (@ tptp.comple7399068483239264473et_nat X4)))))))
% 5.65/5.92 (assert (forall ((X4 tptp.set_o) (A2 Bool)) (=> (not (= X4 tptp.bot_bot_set_o)) (=> (@ tptp.condit5488710616941104124bove_o X4) (= (@ tptp.complete_Sup_Sup_o (@ (@ tptp.insert_o A2) X4)) (@ (@ tptp.sup_sup_o A2) (@ tptp.complete_Sup_Sup_o X4)))))))
% 5.65/5.92 (assert (forall ((X4 tptp.set_int) (A2 tptp.int)) (=> (not (= X4 tptp.bot_bot_set_int)) (=> (@ tptp.condit2212336002400062152ve_int X4) (= (@ tptp.complete_Sup_Sup_int (@ (@ tptp.insert_int A2) X4)) (@ (@ tptp.sup_sup_int A2) (@ tptp.complete_Sup_Sup_int X4)))))))
% 5.65/5.92 (assert (forall ((X4 tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (not (= X4 tptp.bot_bo7824918357723582233_nat_o)) (=> (@ tptp.condit4352657709669162033_nat_o X4) (= (@ tptp.comple4225350640907012154_nat_o (@ (@ tptp.insert5175938949040314269_nat_o A2) X4)) (@ (@ tptp.sup_su5453871518329203617_nat_o A2) (@ tptp.comple4225350640907012154_nat_o X4)))))))
% 5.65/5.92 (assert (forall ((X4 tptp.set_nat) (A2 tptp.nat)) (=> (not (= X4 tptp.bot_bot_set_nat)) (=> (@ tptp.condit2214826472909112428ve_nat X4) (= (@ tptp.complete_Sup_Sup_nat (@ (@ tptp.insert_nat A2) X4)) (@ (@ tptp.sup_sup_nat A2) (@ tptp.complete_Sup_Sup_nat X4)))))))
% 5.65/5.92 (assert (forall ((X4 tptp.set_Product_unit) (A2 tptp.product_unit)) (=> (not (= X4 tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit2080475194861589617t_unit X4) (= (@ tptp.comple4687483117567863418t_unit (@ (@ tptp.insert_Product_unit A2) X4)) (@ (@ tptp.sup_sup_Product_unit A2) (@ tptp.comple4687483117567863418t_unit X4)))))))
% 5.65/5.92 (assert (forall ((A tptp.set_set_nat) (B4 tptp.set_set_nat)) (=> (not (= A tptp.bot_bot_set_set_nat)) (=> (@ tptp.condit5477540289124974626et_nat A) (=> (not (= B4 tptp.bot_bot_set_set_nat)) (=> (@ tptp.condit5477540289124974626et_nat B4) (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.sup_sup_set_set_nat A) B4)) (@ (@ tptp.sup_sup_set_nat (@ tptp.comple7399068483239264473et_nat A)) (@ tptp.comple7399068483239264473et_nat B4)))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit5488710616941104124bove_o A) (=> (not (= B4 tptp.bot_bot_set_o)) (=> (@ tptp.condit5488710616941104124bove_o B4) (= (@ tptp.complete_Sup_Sup_o (@ (@ tptp.sup_sup_set_o A) B4)) (@ (@ tptp.sup_sup_o (@ tptp.complete_Sup_Sup_o A)) (@ tptp.complete_Sup_Sup_o B4)))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit2212336002400062152ve_int A) (=> (not (= B4 tptp.bot_bot_set_int)) (=> (@ tptp.condit2212336002400062152ve_int B4) (= (@ tptp.complete_Sup_Sup_int (@ (@ tptp.sup_sup_set_int A) B4)) (@ (@ tptp.sup_sup_int (@ tptp.complete_Sup_Sup_int A)) (@ tptp.complete_Sup_Sup_int B4)))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (=> (@ tptp.condit4352657709669162033_nat_o A) (=> (not (= B4 tptp.bot_bo7824918357723582233_nat_o)) (=> (@ tptp.condit4352657709669162033_nat_o B4) (= (@ tptp.comple4225350640907012154_nat_o (@ (@ tptp.sup_su5209123915105501825_nat_o A) B4)) (@ (@ tptp.sup_su5453871518329203617_nat_o (@ tptp.comple4225350640907012154_nat_o A)) (@ tptp.comple4225350640907012154_nat_o B4)))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit2214826472909112428ve_nat A) (=> (not (= B4 tptp.bot_bot_set_nat)) (=> (@ tptp.condit2214826472909112428ve_nat B4) (= (@ tptp.complete_Sup_Sup_nat (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.sup_sup_nat (@ tptp.complete_Sup_Sup_nat A)) (@ tptp.complete_Sup_Sup_nat B4)))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit2080475194861589617t_unit A) (=> (not (= B4 tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit2080475194861589617t_unit B4) (= (@ tptp.comple4687483117567863418t_unit (@ (@ tptp.sup_su793286257634532545t_unit A) B4)) (@ (@ tptp.sup_sup_Product_unit (@ tptp.comple4687483117567863418t_unit A)) (@ tptp.comple4687483117567863418t_unit B4)))))))))
% 5.65/5.92 (assert (forall ((X tptp.code_integer) (A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer)) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.image_4470545334726330049nteger F))) (let ((_let_2 (@ (@ tptp.image_4470545334726330049nteger (@ (@ (@ tptp.fun_up8355007323143964473nteger F) X) Y)) A))) (let ((_let_3 (@ (@ tptp.member_Code_integer X) A))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_Code_integer Y) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer X) tptp.bot_bo3990330152332043303nteger)))))) (=> (not _let_3) (= _let_2 (@ _let_1 A)))))))))
% 5.65/5.92 (assert (forall ((X tptp.product_unit) (A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.nat)) (Y tptp.nat)) (let ((_let_1 (@ tptp.image_875570014554754200it_nat F))) (let ((_let_2 (@ (@ tptp.image_875570014554754200it_nat (@ (@ (@ tptp.fun_up6473050886840373792it_nat F) X) Y)) A))) (let ((_let_3 (@ (@ tptp.member_Product_unit X) A))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat Y) (@ _let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)))))) (=> (not _let_3) (= _let_2 (@ _let_1 A)))))))))
% 5.65/5.92 (assert (forall ((X tptp.product_unit) (A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.int)) (Y tptp.int)) (let ((_let_1 (@ tptp.image_873079544045703924it_int F))) (let ((_let_2 (@ (@ tptp.image_873079544045703924it_int (@ (@ (@ tptp.fun_up6470560416331323516it_int F) X) Y)) A))) (let ((_let_3 (@ (@ tptp.member_Product_unit X) A))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_int Y) (@ _let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)))))) (=> (not _let_3) (= _let_2 (@ _let_1 A)))))))))
% 5.65/5.92 (assert (forall ((X tptp.product_unit) (A tptp.set_Product_unit) (F (-> tptp.product_unit Bool)) (Y Bool)) (let ((_let_1 (@ tptp.image_Product_unit_o2 F))) (let ((_let_2 (@ (@ tptp.image_Product_unit_o2 (@ (@ (@ tptp.fun_up5432024876597553480unit_o F) X) Y)) A))) (let ((_let_3 (@ (@ tptp.member_Product_unit X) A))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_o Y) (@ _let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)))))) (=> (not _let_3) (= _let_2 (@ _let_1 A)))))))))
% 5.65/5.92 (assert (forall ((X tptp.product_unit) (A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.product_unit)) (Y tptp.product_unit)) (let ((_let_1 (@ tptp.image_405062704495631173t_unit F))) (let ((_let_2 (@ (@ tptp.image_405062704495631173t_unit (@ (@ (@ tptp.fun_up6875000483049295805t_unit F) X) Y)) A))) (let ((_let_3 (@ (@ tptp.member_Product_unit X) A))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_Product_unit Y) (@ _let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)))))) (=> (not _let_3) (= _let_2 (@ _let_1 A)))))))))
% 5.65/5.92 (assert (forall ((X Bool) (A tptp.set_o) (F (-> Bool tptp.nat)) (Y tptp.nat)) (let ((_let_1 (@ tptp.image_o_nat2 F))) (let ((_let_2 (@ (@ tptp.image_o_nat2 (@ (@ (@ tptp.fun_upd_o_nat F) X) Y)) A))) (let ((_let_3 (@ (@ tptp.member_o X) A))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat Y) (@ _let_1 (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)))))) (=> (not _let_3) (= _let_2 (@ _let_1 A)))))))))
% 5.65/5.92 (assert (forall ((X Bool) (A tptp.set_o) (F (-> Bool tptp.int)) (Y tptp.int)) (let ((_let_1 (@ tptp.image_o_int2 F))) (let ((_let_2 (@ (@ tptp.image_o_int2 (@ (@ (@ tptp.fun_upd_o_int F) X) Y)) A))) (let ((_let_3 (@ (@ tptp.member_o X) A))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_int Y) (@ _let_1 (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)))))) (=> (not _let_3) (= _let_2 (@ _let_1 A)))))))))
% 5.65/5.92 (assert (forall ((X Bool) (A tptp.set_o) (F (-> Bool Bool)) (Y Bool)) (let ((_let_1 (@ tptp.image_o_o2 F))) (let ((_let_2 (@ (@ tptp.image_o_o2 (@ (@ (@ tptp.fun_upd_o_o F) X) Y)) A))) (let ((_let_3 (@ (@ tptp.member_o X) A))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_o Y) (@ _let_1 (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)))))) (=> (not _let_3) (= _let_2 (@ _let_1 A)))))))))
% 5.65/5.92 (assert (forall ((X Bool) (A tptp.set_o) (F (-> Bool tptp.product_unit)) (Y tptp.product_unit)) (let ((_let_1 (@ tptp.image_o_Product_unit2 F))) (let ((_let_2 (@ (@ tptp.image_o_Product_unit2 (@ (@ (@ tptp.fun_up846054379331416818t_unit F) X) Y)) A))) (let ((_let_3 (@ (@ tptp.member_o X) A))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_Product_unit Y) (@ _let_1 (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)))))) (=> (not _let_3) (= _let_2 (@ _let_1 A)))))))))
% 5.65/5.92 (assert (forall ((X tptp.int) (A tptp.set_int) (F (-> tptp.int tptp.nat)) (Y tptp.nat)) (let ((_let_1 (@ tptp.image_int_nat2 F))) (let ((_let_2 (@ (@ tptp.image_int_nat2 (@ (@ (@ tptp.fun_upd_int_nat F) X) Y)) A))) (let ((_let_3 (@ (@ tptp.member_int X) A))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat Y) (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))))) (=> (not _let_3) (= _let_2 (@ _let_1 A)))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (= (@ tptp.lattic1091506334969745077in_int (@ (@ tptp.insert_int X) A)) (@ (@ (@ tptp.finite_fold_int_int tptp.sup_sup_int) X) A)))))
% 5.65/5.92 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (= (@ tptp.lattic1508158080041050831_fin_o (@ (@ tptp.insert_o X) A)) (@ (@ (@ tptp.finite_fold_o_o tptp.sup_sup_o) X) A)))))
% 5.65/5.92 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (= (@ tptp.lattic1093996805478795353in_nat (@ (@ tptp.insert_nat X) A)) (@ (@ (@ tptp.finite_fold_nat_nat tptp.sup_sup_nat) X) A)))))
% 5.65/5.92 (assert (forall ((A tptp.set_set_nat) (X tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (= (@ tptp.lattic3835124923745554447et_nat (@ (@ tptp.insert_set_nat X) A)) (@ (@ (@ tptp.finite677925301803182934et_nat tptp.sup_sup_set_nat) X) A)))))
% 5.65/5.92 (assert (forall ((A tptp.set_assn) (X tptp.assn)) (=> (@ tptp.finite_finite_assn A) (= (@ tptp.lattic2150320897289308081n_assn (@ (@ tptp.insert_assn X) A)) (@ (@ (@ tptp.finite1440822074540989594n_assn tptp.sup_sup_assn) X) A)))))
% 5.65/5.92 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (= (@ tptp.lattic5294303975357428420t_unit (@ (@ tptp.insert_Product_unit X) A)) (@ (@ (@ tptp.finite8834431295148555784t_unit tptp.sup_sup_Product_unit) X) A)))))
% 5.65/5.92 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (= (@ tptp.lattic5235898064620869839in_int (@ (@ tptp.insert_int X) A)) (@ (@ (@ tptp.finite_fold_int_int tptp.inf_inf_int) X) A)))))
% 5.65/5.92 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (= (@ tptp.lattic4107685809792843317_fin_o (@ (@ tptp.insert_o X) A)) (@ (@ (@ tptp.finite_fold_o_o tptp.inf_inf_o) X) A)))))
% 5.65/5.92 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (= (@ tptp.lattic5238388535129920115in_nat (@ (@ tptp.insert_nat X) A)) (@ (@ (@ tptp.finite_fold_nat_nat tptp.inf_inf_nat) X) A)))))
% 5.65/5.92 (assert (forall ((A tptp.set_set_nat) (X tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (= (@ tptp.lattic3014633134055518761et_nat (@ (@ tptp.insert_set_nat X) A)) (@ (@ (@ tptp.finite677925301803182934et_nat tptp.inf_inf_set_nat) X) A)))))
% 5.65/5.92 (assert (forall ((A tptp.set_assn) (X tptp.assn)) (=> (@ tptp.finite_finite_assn A) (= (@ tptp.lattic47131356835913163n_assn (@ (@ tptp.insert_assn X) A)) (@ (@ (@ tptp.finite1440822074540989594n_assn tptp.inf_inf_assn) X) A)))))
% 5.65/5.92 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (= (@ tptp.lattic1263872656861969706t_unit (@ (@ tptp.insert_Product_unit X) A)) (@ (@ (@ tptp.finite8834431295148555784t_unit tptp.inf_inf_Product_unit) X) A)))))
% 5.65/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (Ub (-> tptp.nat tptp.set_Code_integer)) (F (-> tptp.nat tptp.set_Code_integer))) (=> (forall ((A4 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ F B2))) (let ((_let_2 (@ Ub A4))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B2) A4)) R2) (and (@ tptp.finite6017078050557962740nteger _let_2) (@ (@ tptp.ord_le7084787975880047091nteger (@ Ub B2)) _let_2) (@ (@ tptp.ord_le7084787975880047091nteger _let_1) _let_2) (@ (@ tptp.ord_le1307284697595431911nteger (@ F A4)) _let_1)))))) (@ tptp.wf_nat R2))))
% 5.65/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (Ub (-> tptp.int tptp.set_Code_integer)) (F (-> tptp.int tptp.set_Code_integer))) (=> (forall ((A4 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ F B2))) (let ((_let_2 (@ Ub A4))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B2) A4)) R2) (and (@ tptp.finite6017078050557962740nteger _let_2) (@ (@ tptp.ord_le7084787975880047091nteger (@ Ub B2)) _let_2) (@ (@ tptp.ord_le7084787975880047091nteger _let_1) _let_2) (@ (@ tptp.ord_le1307284697595431911nteger (@ F A4)) _let_1)))))) (@ tptp.wf_int R2))))
% 5.65/5.92 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (Ub (-> tptp.nat tptp.set_nat)) (F (-> tptp.nat tptp.set_nat))) (=> (forall ((A4 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ F B2))) (let ((_let_2 (@ Ub A4))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B2) A4)) R2) (and (@ tptp.finite_finite_nat _let_2) (@ (@ tptp.ord_less_eq_set_nat (@ Ub B2)) _let_2) (@ (@ tptp.ord_less_eq_set_nat _let_1) _let_2) (@ (@ tptp.ord_less_set_nat (@ F A4)) _let_1)))))) (@ tptp.wf_nat R2))))
% 5.65/5.92 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (Ub (-> tptp.int tptp.set_nat)) (F (-> tptp.int tptp.set_nat))) (=> (forall ((A4 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ F B2))) (let ((_let_2 (@ Ub A4))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B2) A4)) R2) (and (@ tptp.finite_finite_nat _let_2) (@ (@ tptp.ord_less_eq_set_nat (@ Ub B2)) _let_2) (@ (@ tptp.ord_less_eq_set_nat _let_1) _let_2) (@ (@ tptp.ord_less_set_nat (@ F A4)) _let_1)))))) (@ tptp.wf_int R2))))
% 5.65/5.92 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.member_Product_unit X))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.insert_Product_unit X))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_le8056459307392131481t_unit A))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le8056459307392131481t_unit (@ (@ tptp.minus_6452836326544984404t_unit A) (@ _let_3 tptp.bot_bo3957492148770167129t_unit))) B4)) (=> (not _let_2) (@ (@ tptp.ord_le3507040750410214029t_unit A) B4)))))))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_o) (X Bool) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.member_o X))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.insert_o X))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_less_set_o A))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_o (@ (@ tptp.minus_minus_set_o A) (@ _let_3 tptp.bot_bot_set_o))) B4)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_o A) B4)))))))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_int) (X tptp.int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int X))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.insert_int X))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_less_set_int A))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A) (@ _let_3 tptp.bot_bot_set_int))) B4)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_int A) B4)))))))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o X))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.insert5175938949040314269_nat_o X))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_le2453136405763929_nat_o A))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le2453136405763929_nat_o (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ _let_3 tptp.bot_bo7824918357723582233_nat_o))) B4)) (=> (not _let_2) (@ (@ tptp.ord_le2965882846123202637_nat_o A) B4)))))))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_nat) (X tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.insert_nat X))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_less_set_nat A))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A) (@ _let_3 tptp.bot_bot_set_nat))) B4)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_nat A) B4)))))))))))))
% 5.65/5.92 (assert (forall ((S tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (forall ((T3 tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le1307284697595431911nteger T3) S) (=> (@ P T3) (exists ((X6 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X6) (@ (@ tptp.minus_2355218937544613996nteger S) T3)) (@ P (@ (@ tptp.insert_Code_integer X6) T3))))))) (@ P S))))))
% 5.65/5.92 (assert (forall ((S tptp.set_Product_unit) (P (-> tptp.set_Product_unit Bool))) (=> (@ tptp.finite4290736615968046902t_unit S) (=> (@ P tptp.bot_bo3957492148770167129t_unit) (=> (forall ((T3 tptp.set_Product_unit)) (=> (@ (@ tptp.ord_le8056459307392131481t_unit T3) S) (=> (@ P T3) (exists ((X6 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X6) (@ (@ tptp.minus_6452836326544984404t_unit S) T3)) (@ P (@ (@ tptp.insert_Product_unit X6) T3))))))) (@ P S))))))
% 5.65/5.92 (assert (forall ((S tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o S) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((T3 tptp.set_o)) (=> (@ (@ tptp.ord_less_set_o T3) S) (=> (@ P T3) (exists ((X6 Bool)) (and (@ (@ tptp.member_o X6) (@ (@ tptp.minus_minus_set_o S) T3)) (@ P (@ (@ tptp.insert_o X6) T3))))))) (@ P S))))))
% 5.65/5.92 (assert (forall ((S tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int S) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((T3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int T3) S) (=> (@ P T3) (exists ((X6 tptp.int)) (and (@ (@ tptp.member_int X6) (@ (@ tptp.minus_minus_set_int S) T3)) (@ P (@ (@ tptp.insert_int X6) T3))))))) (@ P S))))))
% 5.65/5.92 (assert (forall ((S tptp.set_Pr4532377907799695533_nat_o) (P (-> tptp.set_Pr4532377907799695533_nat_o Bool))) (=> (@ tptp.finite3252695134891459830_nat_o S) (=> (@ P tptp.bot_bo7824918357723582233_nat_o) (=> (forall ((T3 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.ord_le2453136405763929_nat_o T3) S) (=> (@ P T3) (exists ((X6 (-> tptp.produc3658429121746597890et_nat Bool))) (and (@ (@ tptp.member6576561426505652726_nat_o X6) (@ (@ tptp.minus_1801376950450012436_nat_o S) T3)) (@ P (@ (@ tptp.insert5175938949040314269_nat_o X6) T3))))))) (@ P S))))))
% 5.65/5.92 (assert (forall ((S tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat S) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((T3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat T3) S) (=> (@ P T3) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) (@ (@ tptp.minus_minus_set_nat S) T3)) (@ P (@ (@ tptp.insert_nat X6) T3))))))) (@ P S))))))
% 5.65/5.92 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) B4) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (=> (@ tptp.finite6017078050557962740nteger B4) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.lattic4901227151466704046nteger A)) (@ tptp.lattic4901227151466704046nteger B4)))))))
% 5.65/5.92 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) B4) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.finite4290736615968046902t_unit B4) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.lattic1210392890313158908t_unit A)) (@ tptp.lattic1210392890313158908t_unit B4)))))))
% 5.65/5.92 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A) B4) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.finite_finite_o B4) (@ (@ tptp.ord_less_eq_o (@ tptp.lattic1921953407002678535_Max_o A)) (@ tptp.lattic1921953407002678535_Max_o B4)))))))
% 5.65/5.92 (assert (forall ((A tptp.set_rat) (B4 tptp.set_rat)) (=> (@ (@ tptp.ord_less_eq_set_rat A) B4) (=> (not (= A tptp.bot_bot_set_rat)) (=> (@ tptp.finite_finite_rat B4) (@ (@ tptp.ord_less_eq_rat (@ tptp.lattic7630753665789217321ax_rat A)) (@ tptp.lattic7630753665789217321ax_rat B4)))))))
% 5.65/5.92 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B4) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.finite_finite_int B4) (@ (@ tptp.ord_less_eq_int (@ tptp.lattic8263393255366662781ax_int A)) (@ tptp.lattic8263393255366662781ax_int B4)))))))
% 5.65/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.finite_finite_nat B4) (@ (@ tptp.ord_less_eq_nat (@ tptp.lattic8265883725875713057ax_nat A)) (@ tptp.lattic8265883725875713057ax_nat B4)))))))
% 5.65/5.92 (assert (forall ((M tptp.set_Code_integer) (N tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le7084787975880047091nteger M) N) (=> (not (= M tptp.bot_bo3990330152332043303nteger)) (=> (@ tptp.finite6017078050557962740nteger N) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.lattic4901227151466704046nteger M)) (@ tptp.lattic4901227151466704046nteger N)))))))
% 5.65/5.92 (assert (forall ((M tptp.set_Product_unit) (N tptp.set_Product_unit)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit M) N) (=> (not (= M tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.finite4290736615968046902t_unit N) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.lattic1210392890313158908t_unit M)) (@ tptp.lattic1210392890313158908t_unit N)))))))
% 5.65/5.92 (assert (forall ((M tptp.set_o) (N tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o M) N) (=> (not (= M tptp.bot_bot_set_o)) (=> (@ tptp.finite_finite_o N) (@ (@ tptp.ord_less_eq_o (@ tptp.lattic1921953407002678535_Max_o M)) (@ tptp.lattic1921953407002678535_Max_o N)))))))
% 5.65/5.92 (assert (forall ((M tptp.set_rat) (N tptp.set_rat)) (=> (@ (@ tptp.ord_less_eq_set_rat M) N) (=> (not (= M tptp.bot_bot_set_rat)) (=> (@ tptp.finite_finite_rat N) (@ (@ tptp.ord_less_eq_rat (@ tptp.lattic7630753665789217321ax_rat M)) (@ tptp.lattic7630753665789217321ax_rat N)))))))
% 5.65/5.92 (assert (forall ((M tptp.set_int) (N tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int M) N) (=> (not (= M tptp.bot_bot_set_int)) (=> (@ tptp.finite_finite_int N) (@ (@ tptp.ord_less_eq_int (@ tptp.lattic8263393255366662781ax_int M)) (@ tptp.lattic8263393255366662781ax_int N)))))))
% 5.65/5.92 (assert (forall ((M tptp.set_nat) (N tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat M) N) (=> (not (= M tptp.bot_bot_set_nat)) (=> (@ tptp.finite_finite_nat N) (@ (@ tptp.ord_less_eq_nat (@ tptp.lattic8265883725875713057ax_nat M)) (@ tptp.lattic8265883725875713057ax_nat N)))))))
% 5.65/5.92 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer)) (let ((_let_1 (@ tptp.image_4470545334726330049nteger F))) (= (@ _let_1 (@ (@ tptp.vimage1318793397690208119nteger F) A)) (@ (@ tptp.inf_in1364745209274528805nteger A) (@ _let_1 tptp.top_to4645266643341252675nteger))))))
% 5.65/5.92 (assert (forall ((F (-> tptp.product_unit tptp.nat)) (A tptp.set_nat)) (let ((_let_1 (@ tptp.image_875570014554754200it_nat F))) (= (@ _let_1 (@ (@ tptp.vimage6253328473476588386it_nat F) A)) (@ (@ tptp.inf_inf_set_nat A) (@ _let_1 tptp.top_to1996260823553986621t_unit))))))
% 5.65/5.92 (assert (forall ((F (-> Bool tptp.nat)) (A tptp.set_nat)) (let ((_let_1 (@ tptp.image_o_nat2 F))) (= (@ _let_1 (@ (@ tptp.vimage_o_nat F) A)) (@ (@ tptp.inf_inf_set_nat A) (@ _let_1 tptp.top_top_set_o))))))
% 5.65/5.92 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A tptp.set_set_nat)) (let ((_let_1 (@ tptp.image_nat_set_nat F))) (= (@ _let_1 (@ (@ tptp.vimage_nat_set_nat F) A)) (@ (@ tptp.inf_inf_set_set_nat A) (@ _let_1 tptp.top_top_set_nat))))))
% 5.65/5.92 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.set_Code_integer)) (let ((_let_1 (@ tptp.image_1215581382706833972nteger F))) (= (@ _let_1 (@ (@ tptp.vimage6104394758324456170nteger F) A)) (@ (@ tptp.inf_in1364745209274528805nteger A) (@ _let_1 tptp.top_top_set_nat))))))
% 5.65/5.92 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_nat2 F))) (= (@ _let_1 (@ (@ tptp.vimage_nat_nat F) A)) (@ (@ tptp.inf_inf_set_nat A) (@ _let_1 tptp.top_top_set_nat))))))
% 5.65/5.92 (assert (forall ((F (-> tptp.int tptp.nat)) (A tptp.set_nat)) (let ((_let_1 (@ tptp.image_int_nat2 F))) (= (@ _let_1 (@ (@ tptp.vimage_int_nat F) A)) (@ (@ tptp.inf_inf_set_nat A) (@ _let_1 tptp.top_top_set_int))))))
% 5.65/5.92 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o X) tptp.top_to4869887016220417533_nat_o)))
% 5.65/5.92 (assert (forall ((X tptp.product_unit)) (@ (@ tptp.member_Product_unit X) tptp.top_to1996260823553986621t_unit)))
% 5.65/5.92 (assert (forall ((X Bool)) (@ (@ tptp.member_o X) tptp.top_top_set_o)))
% 5.65/5.92 (assert (forall ((X tptp.nat)) (@ (@ tptp.member_nat X) tptp.top_top_set_nat)))
% 5.65/5.92 (assert (forall ((X tptp.int)) (@ (@ tptp.member_int X) tptp.top_top_set_int)))
% 5.65/5.92 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (= (= (@ (@ tptp.inf_in4660618365625256667t_unit A) B4) tptp.top_to1996260823553986621t_unit) (and (= A tptp.top_to1996260823553986621t_unit) (= B4 tptp.top_to1996260823553986621t_unit)))))
% 5.65/5.92 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o A) B4) tptp.top_top_set_o) (and (= A tptp.top_top_set_o) (= B4 tptp.top_top_set_o)))))
% 5.65/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A) B4) tptp.top_top_set_nat) (and (= A tptp.top_top_set_nat) (= B4 tptp.top_top_set_nat)))))
% 5.65/5.92 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int A) B4) tptp.top_top_set_int) (and (= A tptp.top_top_set_int) (= B4 tptp.top_top_set_int)))))
% 5.65/5.92 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (=> (not (= A B4)) (@ (@ tptp.ord_less_set_nat A) B4)))))
% 5.65/5.92 (assert (forall ((F (-> tptp.product_unit tptp.product_unit))) (= (@ (@ tptp.vimage7995052115951654139t_unit F) tptp.top_to1996260823553986621t_unit) tptp.top_to1996260823553986621t_unit)))
% 5.65/5.92 (assert (forall ((F (-> Bool tptp.product_unit))) (= (@ (@ tptp.vimage4222377557387472176t_unit F) tptp.top_to1996260823553986621t_unit) tptp.top_top_set_o)))
% 5.65/5.92 (assert (forall ((F (-> tptp.nat tptp.product_unit))) (= (@ (@ tptp.vimage4884490618288580032t_unit F) tptp.top_to1996260823553986621t_unit) tptp.top_top_set_nat)))
% 5.65/5.92 (assert (forall ((F (-> tptp.int tptp.product_unit))) (= (@ (@ tptp.vimage2000912565490760292t_unit F) tptp.top_to1996260823553986621t_unit) tptp.top_top_set_int)))
% 5.65/5.92 (assert (forall ((F (-> tptp.product_unit Bool))) (= (@ (@ tptp.vimage8808348054653608838unit_o F) tptp.top_top_set_o) tptp.top_to1996260823553986621t_unit)))
% 5.65/5.92 (assert (forall ((F (-> Bool Bool))) (= (@ (@ tptp.vimage_o_o F) tptp.top_top_set_o) tptp.top_top_set_o)))
% 5.65/5.92 (assert (forall ((F (-> tptp.nat Bool))) (= (@ (@ tptp.vimage_nat_o F) tptp.top_top_set_o) tptp.top_top_set_nat)))
% 5.65/5.92 (assert (forall ((F (-> tptp.int Bool))) (= (@ (@ tptp.vimage_int_o F) tptp.top_top_set_o) tptp.top_top_set_int)))
% 5.65/5.92 (assert (forall ((F (-> tptp.product_unit tptp.nat))) (= (@ (@ tptp.vimage6253328473476588386it_nat F) tptp.top_top_set_nat) tptp.top_to1996260823553986621t_unit)))
% 5.65/5.92 (assert (forall ((F (-> Bool tptp.nat))) (= (@ (@ tptp.vimage_o_nat F) tptp.top_top_set_nat) tptp.top_top_set_o)))
% 5.65/5.92 (assert (= (@ tptp.pow_Product_unit tptp.top_to1996260823553986621t_unit) tptp.top_to1767297665138865437t_unit))
% 5.65/5.92 (assert (= (@ tptp.pow_o tptp.top_top_set_o) tptp.top_top_set_set_o))
% 5.65/5.92 (assert (= (@ tptp.pow_nat tptp.top_top_set_nat) tptp.top_top_set_set_nat))
% 5.65/5.92 (assert (= (@ tptp.pow_int tptp.top_top_set_int) tptp.top_top_set_set_int))
% 5.65/5.92 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.minus_1801376950450012436_nat_o A) tptp.top_to4869887016220417533_nat_o) tptp.bot_bo7824918357723582233_nat_o)))
% 5.65/5.92 (assert (forall ((A tptp.set_Product_unit)) (= (@ (@ tptp.minus_6452836326544984404t_unit A) tptp.top_to1996260823553986621t_unit) tptp.bot_bo3957492148770167129t_unit)))
% 5.65/5.92 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.minus_minus_set_o A) tptp.top_top_set_o) tptp.bot_bot_set_o)))
% 5.65/5.92 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A) tptp.top_top_set_int) tptp.bot_bot_set_int)))
% 5.65/5.92 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A) tptp.top_top_set_nat) tptp.bot_bot_set_nat)))
% 5.65/5.92 (assert (forall ((X tptp.product_unit)) (= (@ tptp.lattic1210392890313158908t_unit (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)) X)))
% 5.65/5.92 (assert (forall ((X Bool)) (= (@ tptp.lattic1921953407002678535_Max_o (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)) X)))
% 5.65/5.92 (assert (forall ((X tptp.int)) (= (@ tptp.lattic8263393255366662781ax_int (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)) X)))
% 5.65/5.92 (assert (forall ((X tptp.nat)) (= (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)) X)))
% 5.65/5.92 (assert (= (@ (@ tptp.image_6088997261112373647et_nat tptp.produc8586169260539613262et_nat) tptp.top_to2524957550908328808et_nat) tptp.top_top_set_set_nat))
% 5.65/5.92 (assert (= (@ (@ tptp.image_5042161079198086560nt_int tptp.product_snd_int_int) tptp.top_to4366644338036079209nt_int) tptp.top_top_set_int))
% 5.65/5.92 (assert (= (@ tptp.domain4292024440186670924t_unit tptp.id_Product_unit) tptp.top_to1996260823553986621t_unit))
% 5.65/5.92 (assert (= (@ tptp.domain_o_o tptp.id_o2) tptp.top_top_set_o))
% 5.65/5.92 (assert (= (@ tptp.domain_nat_nat tptp.id_nat) tptp.top_top_set_nat))
% 5.65/5.92 (assert (= (@ tptp.domain_int_int tptp.id_int) tptp.top_top_set_int))
% 5.65/5.92 (assert (= (@ tptp.range_6617724647562260917t_unit tptp.id_Product_unit) tptp.top_to1996260823553986621t_unit))
% 5.65/5.92 (assert (= (@ tptp.range_o_o tptp.id_o2) tptp.top_top_set_o))
% 5.65/5.92 (assert (= (@ tptp.range_nat_nat tptp.id_nat) tptp.top_top_set_nat))
% 5.65/5.92 (assert (= (@ tptp.range_int_int tptp.id_int) tptp.top_top_set_int))
% 5.65/5.92 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.lattic4901227151466704046nteger A)) X) (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X2) A) (@ (@ tptp.ord_le3102999989581377725nteger X2) X))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.lattic1210392890313158908t_unit A)) X) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) A) (@ (@ tptp.ord_le3221252021190050221t_unit X2) X))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (= (@ (@ tptp.ord_less_eq_o (@ tptp.lattic1921953407002678535_Max_o A)) X) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A) (@ (@ tptp.ord_less_eq_o X2) X))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_rat) (X tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.lattic7630753665789217321ax_rat A)) X) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.member_rat X2) A) (@ (@ tptp.ord_less_eq_rat X2) X))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.lattic8263393255366662781ax_int A)) X) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A) (@ (@ tptp.ord_less_eq_int X2) X))))))))
% 5.65/5.92 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.lattic8265883725875713057ax_nat A)) X) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.ord_less_eq_nat X2) X))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (@ (@ tptp.ord_le361264281704409273t_unit (@ tptp.lattic1210392890313158908t_unit A)) X) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) A) (@ (@ tptp.ord_le361264281704409273t_unit X2) X))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (= (@ (@ tptp.ord_less_o (@ tptp.lattic1921953407002678535_Max_o A)) X) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A) (@ (@ tptp.ord_less_o X2) X))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (= (@ (@ tptp.ord_less_int (@ tptp.lattic8263393255366662781ax_int A)) X) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A) (@ (@ tptp.ord_less_int X2) X))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.lattic4901227151466704046nteger A)) X) (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X2) A) (@ (@ tptp.ord_le6747313008572928689nteger X2) X))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_rat) (X tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.lattic7630753665789217321ax_rat A)) X) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.member_rat X2) A) (@ (@ tptp.ord_less_rat X2) X))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.lattic8265883725875713057ax_nat A)) X) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.ord_less_nat X2) X))))))))
% 5.65/5.93 (assert (forall ((X tptp.int)) (exists ((Y2 tptp.int)) (@ (@ tptp.ord_less_int Y2) X))))
% 5.65/5.93 (assert (forall ((X tptp.rat)) (exists ((Y2 tptp.rat)) (@ (@ tptp.ord_less_rat Y2) X))))
% 5.65/5.93 (assert (forall ((X tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X) X_1))))
% 5.65/5.93 (assert (forall ((X tptp.int)) (exists ((X_1 tptp.int)) (@ (@ tptp.ord_less_int X) X_1))))
% 5.65/5.93 (assert (forall ((X tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X) X_1))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (exists ((Z3 tptp.rat)) (and (@ (@ tptp.ord_less_rat X) Z3) (@ (@ tptp.ord_less_rat Z3) Y))))))
% 5.65/5.93 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (not (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= X Y)))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) B) (not (@ (@ tptp.ord_less_assn B) A2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (not (@ (@ tptp.ord_less_nat B) A2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B) (not (@ (@ tptp.ord_less_int B) A2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B) (not (@ (@ tptp.ord_le6747313008572928689nteger B) A2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B) (not (@ (@ tptp.ord_less_rat B) A2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn) (C tptp.assn)) (=> (= A2 B) (=> (@ (@ tptp.ord_less_assn B) C) (@ (@ tptp.ord_less_assn A2) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A2 B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A2) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (=> (= A2 B) (=> (@ (@ tptp.ord_less_int B) C) (@ (@ tptp.ord_less_int A2) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (= A2 B) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A2 B) (=> (@ (@ tptp.ord_less_rat B) C) (@ (@ tptp.ord_less_rat A2) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((P (-> tptp.nat Bool)) (A2 tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y5) X3) (@ P Y5))) (@ P X3))) (@ P A2))))
% 5.65/5.93 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 5.65/5.93 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y) X)) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))))
% 5.65/5.93 (assert (forall ((Y tptp.code_integer) (X tptp.code_integer)) (=> (not (@ (@ tptp.ord_le6747313008572928689nteger Y) X)) (= (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (= X Y)))))
% 5.65/5.93 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat Y) X)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_le6747313008572928689nteger Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 5.65/5.93 (assert (forall ((B tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) A2) (not (@ (@ tptp.ord_less_assn A2) B)))))
% 5.65/5.93 (assert (forall ((B tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A2) (not (@ (@ tptp.ord_less_nat A2) B)))))
% 5.65/5.93 (assert (forall ((B tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B) A2) (not (@ (@ tptp.ord_less_int A2) B)))))
% 5.65/5.93 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A2) (not (@ (@ tptp.ord_le6747313008572928689nteger A2) B)))))
% 5.65/5.93 (assert (forall ((B tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A2) (not (@ (@ tptp.ord_less_rat A2) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn)) (not (@ (@ tptp.ord_less_assn A2) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat)) (not (@ (@ tptp.ord_less_nat A2) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.int)) (not (@ (@ tptp.ord_less_int A2) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger A2) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat)) (not (@ (@ tptp.ord_less_rat A2) A2))))
% 5.65/5.93 (assert (= (lambda ((P6 (-> tptp.nat Bool))) (exists ((X9 tptp.nat)) (@ P6 X9))) (lambda ((P2 (-> tptp.nat Bool))) (exists ((N4 tptp.nat)) (and (@ P2 N4) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N4) (not (@ P2 M3)))))))))
% 5.65/5.93 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A4) B2) (@ (@ P A4) B2))) (=> (forall ((A4 tptp.nat)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.nat) (B2 tptp.nat)) (=> (@ (@ P B2) A4) (@ (@ P A4) B2))) (@ (@ P A2) B))))))
% 5.65/5.93 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A2 tptp.int) (B tptp.int)) (=> (forall ((A4 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A4) B2) (@ (@ P A4) B2))) (=> (forall ((A4 tptp.int)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.int) (B2 tptp.int)) (=> (@ (@ P B2) A4) (@ (@ P A4) B2))) (@ (@ P A2) B))))))
% 5.65/5.93 (assert (forall ((P (-> tptp.code_integer tptp.code_integer Bool)) (A2 tptp.code_integer) (B tptp.code_integer)) (=> (forall ((A4 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A4) B2) (@ (@ P A4) B2))) (=> (forall ((A4 tptp.code_integer)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.code_integer) (B2 tptp.code_integer)) (=> (@ (@ P B2) A4) (@ (@ P A4) B2))) (@ (@ P A2) B))))))
% 5.65/5.93 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A2 tptp.rat) (B tptp.rat)) (=> (forall ((A4 tptp.rat) (B2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A4) B2) (@ (@ P A4) B2))) (=> (forall ((A4 tptp.rat)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.rat) (B2 tptp.rat)) (=> (@ (@ P B2) A4) (@ (@ P A4) B2))) (@ (@ P A2) B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_assn B) C) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_int B) C) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) C) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_rat B) C) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_Product_unit)) (not (@ (@ tptp.ord_le8056459307392131481t_unit tptp.top_to1996260823553986621t_unit) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_o)) (not (@ (@ tptp.ord_less_set_o tptp.top_top_set_o) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat tptp.top_top_set_nat) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_int)) (not (@ (@ tptp.ord_less_set_int tptp.top_top_set_int) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn)) (not (@ (@ tptp.ord_less_assn tptp.top_top_assn) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_Product_unit)) (= (not (= A2 tptp.top_to1996260823553986621t_unit)) (@ (@ tptp.ord_le8056459307392131481t_unit A2) tptp.top_to1996260823553986621t_unit))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_o)) (= (not (= A2 tptp.top_top_set_o)) (@ (@ tptp.ord_less_set_o A2) tptp.top_top_set_o))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_nat)) (= (not (= A2 tptp.top_top_set_nat)) (@ (@ tptp.ord_less_set_nat A2) tptp.top_top_set_nat))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_int)) (= (not (= A2 tptp.top_top_set_int)) (@ (@ tptp.ord_less_set_int A2) tptp.top_top_set_int))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn)) (= (not (= A2 tptp.top_top_assn)) (@ (@ tptp.ord_less_assn A2) tptp.top_top_assn))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (or (@ (@ tptp.ord_less_nat Y) X) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (or (@ (@ tptp.ord_less_int Y) X) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (or (@ (@ tptp.ord_le6747313008572928689nteger Y) X) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (or (@ (@ tptp.ord_less_rat Y) X) (= X Y)))))
% 5.65/5.93 (assert (forall ((B tptp.assn) (A2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn C))) (=> (@ (@ tptp.ord_less_assn B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))))
% 5.65/5.93 (assert (forall ((B tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))))
% 5.65/5.93 (assert (forall ((B tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_int B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))))
% 5.65/5.93 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))))
% 5.65/5.93 (assert (forall ((B tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_rat B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) B) (not (= A2 B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (not (= A2 B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B) (not (= A2 B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B) (not (= A2 B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B) (not (= A2 B)))))
% 5.65/5.93 (assert (forall ((B tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) A2) (not (= A2 B)))))
% 5.65/5.93 (assert (forall ((B tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A2) (not (= A2 B)))))
% 5.65/5.93 (assert (forall ((B tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B) A2) (not (= A2 B)))))
% 5.65/5.93 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A2) (not (= A2 B)))))
% 5.65/5.93 (assert (forall ((B tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A2) (not (= A2 B)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o) (C (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.member6576561426505652726_nat_o C))) (=> (@ (@ tptp.ord_le2453136405763929_nat_o A) B4) (=> (@ _let_1 A) (@ _let_1 B4))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_set_nat A) B4) (=> (@ _let_1 A) (@ _let_1 B4))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (B4 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_set_int A) B4) (=> (@ _let_1 A) (@ _let_1 B4))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (B4 tptp.set_o) (C Bool)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ (@ tptp.ord_less_set_o A) B4) (=> (@ _let_1 A) (@ _let_1 B4))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit) (C tptp.product_unit)) (let ((_let_1 (@ tptp.member_Product_unit C))) (=> (@ (@ tptp.ord_le8056459307392131481t_unit A) B4) (=> (@ _let_1 A) (@ _let_1 B4))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o X3) A)) (= tptp.top_to4869887016220417533_nat_o A))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit)) (=> (forall ((X3 tptp.product_unit)) (@ (@ tptp.member_Product_unit X3) A)) (= tptp.top_to1996260823553986621t_unit A))))
% 5.65/5.93 (assert (forall ((A tptp.set_o)) (=> (forall ((X3 Bool)) (@ (@ tptp.member_o X3) A)) (= tptp.top_top_set_o A))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A)) (= tptp.top_top_set_nat A))))
% 5.65/5.93 (assert (forall ((A tptp.set_int)) (=> (forall ((X3 tptp.int)) (@ (@ tptp.member_int X3) A)) (= tptp.top_top_set_int A))))
% 5.65/5.93 (assert (exists ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o X3) tptp.top_to4869887016220417533_nat_o)))
% 5.65/5.93 (assert (exists ((X3 tptp.product_unit)) (@ (@ tptp.member_Product_unit X3) tptp.top_to1996260823553986621t_unit)))
% 5.65/5.93 (assert (exists ((X3 Bool)) (@ (@ tptp.member_o X3) tptp.top_top_set_o)))
% 5.65/5.93 (assert (exists ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) tptp.top_top_set_nat)))
% 5.65/5.93 (assert (exists ((X3 tptp.int)) (@ (@ tptp.member_int X3) tptp.top_top_set_int)))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (@ (@ tptp.ord_le6747313008572928689nteger Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (@ (@ tptp.ord_less_assn Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (not (@ (@ tptp.ord_le6747313008572928689nteger Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_int Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (not (= X Y)) (or (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (@ (@ tptp.ord_le6747313008572928689nteger Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_rat X) Y) (@ (@ tptp.ord_less_rat Y) X)))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) B) (not (@ (@ tptp.ord_less_assn B) A2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (not (@ (@ tptp.ord_less_nat B) A2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B) (not (@ (@ tptp.ord_less_int B) A2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B) (not (@ (@ tptp.ord_le6747313008572928689nteger B) A2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B) (not (@ (@ tptp.ord_less_rat B) A2)))))
% 5.65/5.93 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_assn Y) Z) (@ _let_1 Z))))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ _let_1 Z))))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ _let_1 Z))))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le6747313008572928689nteger Y) Z) (@ _let_1 Z))))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_rat Y) Z) (@ _let_1 Z))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (F (-> tptp.assn tptp.assn)) (B tptp.assn) (C tptp.assn)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_assn A2) (@ F C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (F (-> tptp.assn tptp.nat)) (B tptp.assn) (C tptp.assn)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat A2) (@ F C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (F (-> tptp.assn tptp.int)) (B tptp.assn) (C tptp.assn)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_int A2) (@ F C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (F (-> tptp.assn tptp.code_integer)) (B tptp.assn) (C tptp.assn)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ F C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (F (-> tptp.assn tptp.rat)) (B tptp.assn) (C tptp.assn)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_rat A2) (@ F C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (F (-> tptp.nat tptp.assn)) (B tptp.nat) (C tptp.nat)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_assn A2) (@ F C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat A2) (@ F C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (F (-> tptp.nat tptp.int)) (B tptp.nat) (C tptp.nat)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_int A2) (@ F C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (F (-> tptp.nat tptp.code_integer)) (B tptp.nat) (C tptp.nat)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ F C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_rat A2) (@ F C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_assn (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_assn A2) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_assn A2) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_int (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_assn A2) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_assn A2) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_rat (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_assn (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_int (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_rat (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((X tptp.assn)) (not (@ (@ tptp.ord_less_assn X) X))))
% 5.65/5.93 (assert (forall ((X tptp.nat)) (not (@ (@ tptp.ord_less_nat X) X))))
% 5.65/5.93 (assert (forall ((X tptp.int)) (not (@ (@ tptp.ord_less_int X) X))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger X) X))))
% 5.65/5.93 (assert (forall ((X tptp.rat)) (not (@ (@ tptp.ord_less_rat X) X))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (F (-> tptp.assn tptp.assn)) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (F (-> tptp.nat tptp.assn)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (F (-> tptp.int tptp.assn)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y2) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (F (-> tptp.code_integer tptp.assn)) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (F (-> tptp.rat tptp.assn)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y2) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (F (-> tptp.assn tptp.nat)) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (F (-> tptp.int tptp.nat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (F (-> tptp.code_integer tptp.nat)) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) B) (=> (@ (@ tptp.ord_less_assn (@ F B)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_assn (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_assn A2) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_assn A2) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_int (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_assn A2) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ F B)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_assn A2) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_rat (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (@ (@ tptp.ord_less_assn (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_assn (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_int (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_rat (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (@ (@ tptp.ord_less_assn Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (not (@ (@ tptp.ord_le6747313008572928689nteger Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.assn) (Y tptp.assn) (P Bool)) (=> (@ (@ tptp.ord_less_assn X) Y) (=> (@ (@ tptp.ord_less_assn Y) X) P))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) X) P))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X) Y) (=> (@ (@ tptp.ord_less_int Y) X) P))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (P Bool)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (=> (@ (@ tptp.ord_le6747313008572928689nteger Y) X) P))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat) (P Bool)) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (@ (@ tptp.ord_less_rat Y) X) P))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y) (@ (@ tptp.ord_less_nat Y) X))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y) (@ (@ tptp.ord_less_int Y) X))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (or (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (= X Y) (@ (@ tptp.ord_le6747313008572928689nteger Y) X))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y) (@ (@ tptp.ord_less_rat Y) X))))
% 5.65/5.93 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (not (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (= Y X)))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= Y X)))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= Y X)))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (not (= Y X)))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= Y X)))))
% 5.65/5.93 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (@ (@ tptp.ord_less_assn Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (not (@ (@ tptp.ord_le6747313008572928689nteger Y) X)))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (@ (@ tptp.ord_le361264281704409273t_unit X) (@ tptp.lattic1210392890313158908t_unit A)) (exists ((X2 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X2) A) (@ (@ tptp.ord_le361264281704409273t_unit X) X2))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (= (@ (@ tptp.ord_less_o X) (@ tptp.lattic1921953407002678535_Max_o A)) (exists ((X2 Bool)) (and (@ (@ tptp.member_o X2) A) (@ (@ tptp.ord_less_o X) X2))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (= (@ (@ tptp.ord_less_int X) (@ tptp.lattic8263393255366662781ax_int A)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A) (@ (@ tptp.ord_less_int X) X2))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (= (@ (@ tptp.ord_le6747313008572928689nteger X) (@ tptp.lattic4901227151466704046nteger A)) (exists ((X2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X2) A) (@ (@ tptp.ord_le6747313008572928689nteger X) X2))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_rat) (X tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (= (@ (@ tptp.ord_less_rat X) (@ tptp.lattic7630753665789217321ax_rat A)) (exists ((X2 tptp.rat)) (and (@ (@ tptp.member_rat X2) A) (@ (@ tptp.ord_less_rat X) X2))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (= (@ (@ tptp.ord_less_nat X) (@ tptp.lattic8265883725875713057ax_nat A)) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A) (@ (@ tptp.ord_less_nat X) X2))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn)) (@ (@ tptp.ord_less_eq_assn A2) tptp.top_top_assn)))
% 5.65/5.93 (assert (forall ((A2 tptp.set_Product_unit)) (@ (@ tptp.ord_le3507040750410214029t_unit A2) tptp.top_to1996260823553986621t_unit)))
% 5.65/5.93 (assert (forall ((A2 tptp.set_o)) (@ (@ tptp.ord_less_eq_set_o A2) tptp.top_top_set_o)))
% 5.65/5.93 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A2) tptp.top_top_set_int)))
% 5.65/5.93 (assert (forall ((A2 tptp.filter_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat A2) tptp.top_top_filter_nat)))
% 5.65/5.93 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A2) tptp.top_top_set_nat)))
% 5.65/5.93 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.ord_less_eq_assn tptp.top_top_assn) A2) (= A2 tptp.top_top_assn))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_Product_unit)) (= (@ (@ tptp.ord_le3507040750410214029t_unit tptp.top_to1996260823553986621t_unit) A2) (= A2 tptp.top_to1996260823553986621t_unit))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o tptp.top_top_set_o) A2) (= A2 tptp.top_top_set_o))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int tptp.top_top_set_int) A2) (= A2 tptp.top_top_set_int))))
% 5.65/5.93 (assert (forall ((A2 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat tptp.top_top_filter_nat) A2) (= A2 tptp.top_top_filter_nat))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat tptp.top_top_set_nat) A2) (= A2 tptp.top_top_set_nat))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn tptp.top_top_assn) A2) (= A2 tptp.top_top_assn))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_Product_unit)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit tptp.top_to1996260823553986621t_unit) A2) (= A2 tptp.top_to1996260823553986621t_unit))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o tptp.top_top_set_o) A2) (= A2 tptp.top_top_set_o))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int tptp.top_top_set_int) A2) (= A2 tptp.top_top_set_int))))
% 5.65/5.93 (assert (forall ((A2 tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat tptp.top_top_filter_nat) A2) (= A2 tptp.top_top_filter_nat))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat tptp.top_top_set_nat) A2) (= A2 tptp.top_top_set_nat))))
% 5.65/5.93 (assert (forall ((Y tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y) X) (not (@ (@ tptp.ord_less_assn X) Y)))))
% 5.65/5.93 (assert (forall ((Y tptp.code_integer) (X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) X) (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)))))
% 5.65/5.93 (assert (forall ((Y tptp.filter_nat) (X tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) X) (not (@ (@ tptp.ord_less_filter_nat X) Y)))))
% 5.65/5.93 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (not (@ (@ tptp.ord_less_set_nat X) Y)))))
% 5.65/5.93 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (not (@ (@ tptp.ord_less_rat X) Y)))))
% 5.65/5.93 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (not (@ (@ tptp.ord_less_nat X) Y)))))
% 5.65/5.93 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (not (@ (@ tptp.ord_less_int X) Y)))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (@ (@ tptp.ord_le3102999989581377725nteger Y) X))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn)) (= (not (@ (@ tptp.ord_less_assn A2) B)) (or (not (@ (@ tptp.ord_less_eq_assn A2) B)) (= A2 B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (not (@ (@ tptp.ord_le6747313008572928689nteger A2) B)) (or (not (@ (@ tptp.ord_le3102999989581377725nteger A2) B)) (= A2 B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.filter_nat) (B tptp.filter_nat)) (= (not (@ (@ tptp.ord_less_filter_nat A2) B)) (or (not (@ (@ tptp.ord_le2510731241096832064er_nat A2) B)) (= A2 B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (= (not (@ (@ tptp.ord_less_set_nat A2) B)) (or (not (@ (@ tptp.ord_less_eq_set_nat A2) B)) (= A2 B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (not (@ (@ tptp.ord_less_rat A2) B)) (or (not (@ (@ tptp.ord_less_eq_rat A2) B)) (= A2 B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (= (not (@ (@ tptp.ord_less_nat A2) B)) (or (not (@ (@ tptp.ord_less_eq_nat A2) B)) (= A2 B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (not (@ (@ tptp.ord_less_int A2) B)) (or (not (@ (@ tptp.ord_less_eq_int A2) B)) (= A2 B)))))
% 5.65/5.93 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (not (@ (@ tptp.ord_less_assn X) Y)) (= (@ (@ tptp.ord_less_eq_assn X) Y) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (= (@ (@ tptp.ord_le3102999989581377725nteger X) Y) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (not (@ (@ tptp.ord_less_filter_nat X) Y)) (= (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (not (@ (@ tptp.ord_less_set_nat X) Y)) (= (@ (@ tptp.ord_less_eq_set_nat X) Y) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (= (@ (@ tptp.ord_less_eq_rat X) Y) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (= (not (@ (@ tptp.ord_less_assn X) Y)) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) Y) (= (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (= (not (@ (@ tptp.ord_less_filter_nat X) Y)) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (not (@ (@ tptp.ord_less_set_nat X) Y)) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (not (@ (@ tptp.ord_less_rat X) Y)) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))))
% 5.65/5.93 (assert (forall ((Z tptp.rat) (Y tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X3) (@ (@ tptp.ord_less_eq_rat Y) X3))) (@ (@ tptp.ord_less_eq_rat Y) Z))))
% 5.65/5.93 (assert (forall ((Y tptp.rat) (Z tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y) (@ (@ tptp.ord_less_eq_rat X3) Z))) (@ (@ tptp.ord_less_eq_rat Y) Z))))
% 5.65/5.93 (assert (= tptp.ord_less_assn (lambda ((X2 tptp.assn) (Y3 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn X2) Y3) (not (@ (@ tptp.ord_less_eq_assn Y3) X2))))))
% 5.65/5.93 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((X2 tptp.code_integer) (Y3 tptp.code_integer)) (and (@ (@ tptp.ord_le3102999989581377725nteger X2) Y3) (not (@ (@ tptp.ord_le3102999989581377725nteger Y3) X2))))))
% 5.65/5.93 (assert (= tptp.ord_less_filter_nat (lambda ((X2 tptp.filter_nat) (Y3 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat X2) Y3) (not (@ (@ tptp.ord_le2510731241096832064er_nat Y3) X2))))))
% 5.65/5.93 (assert (= tptp.ord_less_set_nat (lambda ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X2) Y3) (not (@ (@ tptp.ord_less_eq_set_nat Y3) X2))))))
% 5.65/5.93 (assert (= tptp.ord_less_rat (lambda ((X2 tptp.rat) (Y3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X2) Y3) (not (@ (@ tptp.ord_less_eq_rat Y3) X2))))))
% 5.65/5.93 (assert (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y3) (not (@ (@ tptp.ord_less_eq_nat Y3) X2))))))
% 5.65/5.93 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Y3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y3) (not (@ (@ tptp.ord_less_eq_int Y3) X2))))))
% 5.65/5.93 (assert (forall ((Y tptp.code_integer) (X tptp.code_integer)) (=> (not (@ (@ tptp.ord_le3102999989581377725nteger Y) X)) (@ (@ tptp.ord_le6747313008572928689nteger X) Y))))
% 5.65/5.93 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat Y) X)) (@ (@ tptp.ord_less_rat X) Y))))
% 5.65/5.93 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X)) (@ (@ tptp.ord_less_nat X) Y))))
% 5.65/5.93 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y) X)) (@ (@ tptp.ord_less_int X) Y))))
% 5.65/5.93 (assert (= tptp.ord_less_eq_assn (lambda ((A6 tptp.assn) (B6 tptp.assn)) (or (@ (@ tptp.ord_less_assn A6) B6) (= A6 B6)))))
% 5.65/5.93 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((A6 tptp.code_integer) (B6 tptp.code_integer)) (or (@ (@ tptp.ord_le6747313008572928689nteger A6) B6) (= A6 B6)))))
% 5.65/5.93 (assert (= tptp.ord_le2510731241096832064er_nat (lambda ((A6 tptp.filter_nat) (B6 tptp.filter_nat)) (or (@ (@ tptp.ord_less_filter_nat A6) B6) (= A6 B6)))))
% 5.65/5.93 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A6) B6) (= A6 B6)))))
% 5.65/5.93 (assert (= tptp.ord_less_eq_rat (lambda ((A6 tptp.rat) (B6 tptp.rat)) (or (@ (@ tptp.ord_less_rat A6) B6) (= A6 B6)))))
% 5.65/5.93 (assert (= tptp.ord_less_eq_nat (lambda ((A6 tptp.nat) (B6 tptp.nat)) (or (@ (@ tptp.ord_less_nat A6) B6) (= A6 B6)))))
% 5.65/5.93 (assert (= tptp.ord_less_eq_int (lambda ((A6 tptp.int) (B6 tptp.int)) (or (@ (@ tptp.ord_less_int A6) B6) (= A6 B6)))))
% 5.65/5.93 (assert (= tptp.ord_less_assn (lambda ((A6 tptp.assn) (B6 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn A6) B6) (not (= A6 B6))))))
% 5.65/5.93 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((A6 tptp.code_integer) (B6 tptp.code_integer)) (and (@ (@ tptp.ord_le3102999989581377725nteger A6) B6) (not (= A6 B6))))))
% 5.65/5.93 (assert (= tptp.ord_less_filter_nat (lambda ((A6 tptp.filter_nat) (B6 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat A6) B6) (not (= A6 B6))))))
% 5.65/5.93 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A6) B6) (not (= A6 B6))))))
% 5.65/5.93 (assert (= tptp.ord_less_rat (lambda ((A6 tptp.rat) (B6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A6) B6) (not (= A6 B6))))))
% 5.65/5.93 (assert (= tptp.ord_less_nat (lambda ((A6 tptp.nat) (B6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A6) B6) (not (= A6 B6))))))
% 5.65/5.93 (assert (= tptp.ord_less_int (lambda ((A6 tptp.int) (B6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A6) B6) (not (= A6 B6))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) B) (=> (@ (@ tptp.ord_less_assn B) C) (@ (@ tptp.ord_less_assn A2) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.filter_nat) (B tptp.filter_nat) (C tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B) (=> (@ (@ tptp.ord_less_filter_nat B) C) (@ (@ tptp.ord_less_filter_nat A2) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (@ (@ tptp.ord_less_set_nat B) C) (@ (@ tptp.ord_less_set_nat A2) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (@ (@ tptp.ord_less_rat B) C) (@ (@ tptp.ord_less_rat A2) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A2) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B) (=> (@ (@ tptp.ord_less_int B) C) (@ (@ tptp.ord_less_int A2) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_assn B) C) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) C) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.filter_nat) (B tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_less_filter_nat A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B) C) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ _let_1 C))))))
% 5.65/5.93 (assert (= tptp.ord_less_assn (lambda ((A6 tptp.assn) (B6 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn A6) B6) (not (@ (@ tptp.ord_less_eq_assn B6) A6))))))
% 5.65/5.93 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((A6 tptp.code_integer) (B6 tptp.code_integer)) (and (@ (@ tptp.ord_le3102999989581377725nteger A6) B6) (not (@ (@ tptp.ord_le3102999989581377725nteger B6) A6))))))
% 5.65/5.93 (assert (= tptp.ord_less_filter_nat (lambda ((A6 tptp.filter_nat) (B6 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat A6) B6) (not (@ (@ tptp.ord_le2510731241096832064er_nat B6) A6))))))
% 5.65/5.93 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A6) B6) (not (@ (@ tptp.ord_less_eq_set_nat B6) A6))))))
% 5.65/5.93 (assert (= tptp.ord_less_rat (lambda ((A6 tptp.rat) (B6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A6) B6) (not (@ (@ tptp.ord_less_eq_rat B6) A6))))))
% 5.65/5.93 (assert (= tptp.ord_less_nat (lambda ((A6 tptp.nat) (B6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A6) B6) (not (@ (@ tptp.ord_less_eq_nat B6) A6))))))
% 5.65/5.93 (assert (= tptp.ord_less_int (lambda ((A6 tptp.int) (B6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A6) B6) (not (@ (@ tptp.ord_less_eq_int B6) A6))))))
% 5.65/5.93 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) W2) (=> (@ (@ tptp.ord_less_rat W2) X) (@ (@ tptp.ord_less_eq_rat Y) W2)))) (@ (@ tptp.ord_less_eq_rat Y) Z)))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) W2) (=> (@ (@ tptp.ord_less_rat W2) Y) (@ (@ tptp.ord_less_eq_rat W2) Z)))) (@ (@ tptp.ord_less_eq_rat Y) Z)))))
% 5.65/5.93 (assert (= tptp.ord_less_eq_assn (lambda ((B6 tptp.assn) (A6 tptp.assn)) (or (@ (@ tptp.ord_less_assn B6) A6) (= A6 B6)))))
% 5.65/5.93 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((B6 tptp.code_integer) (A6 tptp.code_integer)) (or (@ (@ tptp.ord_le6747313008572928689nteger B6) A6) (= A6 B6)))))
% 5.65/5.93 (assert (= tptp.ord_le2510731241096832064er_nat (lambda ((B6 tptp.filter_nat) (A6 tptp.filter_nat)) (or (@ (@ tptp.ord_less_filter_nat B6) A6) (= A6 B6)))))
% 5.65/5.93 (assert (= tptp.ord_less_eq_set_nat (lambda ((B6 tptp.set_nat) (A6 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat B6) A6) (= A6 B6)))))
% 5.65/5.93 (assert (= tptp.ord_less_eq_rat (lambda ((B6 tptp.rat) (A6 tptp.rat)) (or (@ (@ tptp.ord_less_rat B6) A6) (= A6 B6)))))
% 5.65/5.93 (assert (= tptp.ord_less_eq_nat (lambda ((B6 tptp.nat) (A6 tptp.nat)) (or (@ (@ tptp.ord_less_nat B6) A6) (= A6 B6)))))
% 5.65/5.93 (assert (= tptp.ord_less_eq_int (lambda ((B6 tptp.int) (A6 tptp.int)) (or (@ (@ tptp.ord_less_int B6) A6) (= A6 B6)))))
% 5.65/5.93 (assert (= tptp.ord_less_assn (lambda ((B6 tptp.assn) (A6 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn B6) A6) (not (= A6 B6))))))
% 5.65/5.93 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((B6 tptp.code_integer) (A6 tptp.code_integer)) (and (@ (@ tptp.ord_le3102999989581377725nteger B6) A6) (not (= A6 B6))))))
% 5.65/5.93 (assert (= tptp.ord_less_filter_nat (lambda ((B6 tptp.filter_nat) (A6 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat B6) A6) (not (= A6 B6))))))
% 5.65/5.93 (assert (= tptp.ord_less_set_nat (lambda ((B6 tptp.set_nat) (A6 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B6) A6) (not (= A6 B6))))))
% 5.65/5.93 (assert (= tptp.ord_less_rat (lambda ((B6 tptp.rat) (A6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B6) A6) (not (= A6 B6))))))
% 5.65/5.93 (assert (= tptp.ord_less_nat (lambda ((B6 tptp.nat) (A6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B6) A6) (not (= A6 B6))))))
% 5.65/5.93 (assert (= tptp.ord_less_int (lambda ((B6 tptp.int) (A6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B6) A6) (not (= A6 B6))))))
% 5.65/5.93 (assert (forall ((B tptp.assn) (A2 tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn C))) (=> (@ (@ tptp.ord_less_eq_assn B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))))
% 5.65/5.93 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))))
% 5.65/5.93 (assert (forall ((B tptp.filter_nat) (A2 tptp.filter_nat) (C tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_less_filter_nat C))) (=> (@ (@ tptp.ord_le2510731241096832064er_nat B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))))
% 5.65/5.93 (assert (forall ((B tptp.set_nat) (A2 tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))))
% 5.65/5.93 (assert (forall ((B tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))))
% 5.65/5.93 (assert (forall ((B tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))))
% 5.65/5.93 (assert (forall ((B tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))))
% 5.65/5.93 (assert (forall ((B tptp.assn) (A2 tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) A2) (=> (@ (@ tptp.ord_less_eq_assn C) B) (@ (@ tptp.ord_less_assn C) A2)))))
% 5.65/5.93 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) B) (@ (@ tptp.ord_le6747313008572928689nteger C) A2)))))
% 5.65/5.93 (assert (forall ((B tptp.filter_nat) (A2 tptp.filter_nat) (C tptp.filter_nat)) (=> (@ (@ tptp.ord_less_filter_nat B) A2) (=> (@ (@ tptp.ord_le2510731241096832064er_nat C) B) (@ (@ tptp.ord_less_filter_nat C) A2)))))
% 5.65/5.93 (assert (forall ((B tptp.set_nat) (A2 tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) A2) (=> (@ (@ tptp.ord_less_eq_set_nat C) B) (@ (@ tptp.ord_less_set_nat C) A2)))))
% 5.65/5.93 (assert (forall ((B tptp.rat) (A2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A2) (=> (@ (@ tptp.ord_less_eq_rat C) B) (@ (@ tptp.ord_less_rat C) A2)))))
% 5.65/5.93 (assert (forall ((B tptp.nat) (A2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A2) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_nat C) A2)))))
% 5.65/5.93 (assert (forall ((B tptp.int) (A2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B) A2) (=> (@ (@ tptp.ord_less_eq_int C) B) (@ (@ tptp.ord_less_int C) A2)))))
% 5.65/5.93 (assert (= tptp.ord_less_assn (lambda ((B6 tptp.assn) (A6 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn B6) A6) (not (@ (@ tptp.ord_less_eq_assn A6) B6))))))
% 5.65/5.93 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((B6 tptp.code_integer) (A6 tptp.code_integer)) (and (@ (@ tptp.ord_le3102999989581377725nteger B6) A6) (not (@ (@ tptp.ord_le3102999989581377725nteger A6) B6))))))
% 5.65/5.93 (assert (= tptp.ord_less_filter_nat (lambda ((B6 tptp.filter_nat) (A6 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat B6) A6) (not (@ (@ tptp.ord_le2510731241096832064er_nat A6) B6))))))
% 5.65/5.93 (assert (= tptp.ord_less_set_nat (lambda ((B6 tptp.set_nat) (A6 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B6) A6) (not (@ (@ tptp.ord_less_eq_set_nat A6) B6))))))
% 5.65/5.93 (assert (= tptp.ord_less_rat (lambda ((B6 tptp.rat) (A6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B6) A6) (not (@ (@ tptp.ord_less_eq_rat A6) B6))))))
% 5.65/5.93 (assert (= tptp.ord_less_nat (lambda ((B6 tptp.nat) (A6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B6) A6) (not (@ (@ tptp.ord_less_eq_nat A6) B6))))))
% 5.65/5.93 (assert (= tptp.ord_less_int (lambda ((B6 tptp.int) (A6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B6) A6) (not (@ (@ tptp.ord_less_eq_int A6) B6))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) B) (@ (@ tptp.ord_less_eq_assn A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B) (@ (@ tptp.ord_le3102999989581377725nteger A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.filter_nat) (B tptp.filter_nat)) (=> (@ (@ tptp.ord_less_filter_nat A2) B) (@ (@ tptp.ord_le2510731241096832064er_nat A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B) (@ (@ tptp.ord_less_eq_set_nat A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B) (@ (@ tptp.ord_less_eq_rat A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (@ (@ tptp.ord_less_eq_nat A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B) (@ (@ tptp.ord_less_eq_int A2) B))))
% 5.65/5.93 (assert (forall ((B tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) A2) (@ (@ tptp.ord_less_eq_assn B) A2))))
% 5.65/5.93 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A2) (@ (@ tptp.ord_le3102999989581377725nteger B) A2))))
% 5.65/5.93 (assert (forall ((B tptp.filter_nat) (A2 tptp.filter_nat)) (=> (@ (@ tptp.ord_less_filter_nat B) A2) (@ (@ tptp.ord_le2510731241096832064er_nat B) A2))))
% 5.65/5.93 (assert (forall ((B tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) A2) (@ (@ tptp.ord_less_eq_set_nat B) A2))))
% 5.65/5.93 (assert (forall ((B tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A2) (@ (@ tptp.ord_less_eq_rat B) A2))))
% 5.65/5.93 (assert (forall ((B tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A2) (@ (@ tptp.ord_less_eq_nat B) A2))))
% 5.65/5.93 (assert (forall ((B tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_int B) A2) (@ (@ tptp.ord_less_eq_int B) A2))))
% 5.65/5.93 (assert (= tptp.ord_less_eq_assn (lambda ((X2 tptp.assn) (Y3 tptp.assn)) (or (@ (@ tptp.ord_less_assn X2) Y3) (= X2 Y3)))))
% 5.65/5.93 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((X2 tptp.code_integer) (Y3 tptp.code_integer)) (or (@ (@ tptp.ord_le6747313008572928689nteger X2) Y3) (= X2 Y3)))))
% 5.65/5.93 (assert (= tptp.ord_le2510731241096832064er_nat (lambda ((X2 tptp.filter_nat) (Y3 tptp.filter_nat)) (or (@ (@ tptp.ord_less_filter_nat X2) Y3) (= X2 Y3)))))
% 5.65/5.93 (assert (= tptp.ord_less_eq_set_nat (lambda ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat X2) Y3) (= X2 Y3)))))
% 5.65/5.93 (assert (= tptp.ord_less_eq_rat (lambda ((X2 tptp.rat) (Y3 tptp.rat)) (or (@ (@ tptp.ord_less_rat X2) Y3) (= X2 Y3)))))
% 5.65/5.93 (assert (= tptp.ord_less_eq_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_nat X2) Y3) (= X2 Y3)))))
% 5.65/5.93 (assert (= tptp.ord_less_eq_int (lambda ((X2 tptp.int) (Y3 tptp.int)) (or (@ (@ tptp.ord_less_int X2) Y3) (= X2 Y3)))))
% 5.65/5.93 (assert (= tptp.ord_less_assn (lambda ((X2 tptp.assn) (Y3 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn X2) Y3) (not (= X2 Y3))))))
% 5.65/5.93 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((X2 tptp.code_integer) (Y3 tptp.code_integer)) (and (@ (@ tptp.ord_le3102999989581377725nteger X2) Y3) (not (= X2 Y3))))))
% 5.65/5.93 (assert (= tptp.ord_less_filter_nat (lambda ((X2 tptp.filter_nat) (Y3 tptp.filter_nat)) (and (@ (@ tptp.ord_le2510731241096832064er_nat X2) Y3) (not (= X2 Y3))))))
% 5.65/5.93 (assert (= tptp.ord_less_set_nat (lambda ((X2 tptp.set_nat) (Y3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X2) Y3) (not (= X2 Y3))))))
% 5.65/5.93 (assert (= tptp.ord_less_rat (lambda ((X2 tptp.rat) (Y3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X2) Y3) (not (= X2 Y3))))))
% 5.65/5.93 (assert (= tptp.ord_less_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X2) Y3) (not (= X2 Y3))))))
% 5.65/5.93 (assert (= tptp.ord_less_int (lambda ((X2 tptp.int) (Y3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X2) Y3) (not (= X2 Y3))))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (not (@ (@ tptp.ord_le3102999989581377725nteger X) Y)) (@ (@ tptp.ord_le6747313008572928689nteger Y) X))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_int Y) X))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (not (@ (@ tptp.ord_le6747313008572928689nteger X) Y)) (@ (@ tptp.ord_le3102999989581377725nteger Y) X))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 5.65/5.93 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (@ (@ tptp.ord_less_eq_assn X) Y))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (@ (@ tptp.ord_le3102999989581377725nteger X) Y))))
% 5.65/5.93 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (@ (@ tptp.ord_less_filter_nat X) Y) (@ (@ tptp.ord_le2510731241096832064er_nat X) Y))))
% 5.65/5.93 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat X) Y) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_eq_int X) Y))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) B) (=> (not (= A2 B)) (@ (@ tptp.ord_less_assn A2) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B) (=> (not (= A2 B)) (@ (@ tptp.ord_le6747313008572928689nteger A2) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.filter_nat) (B tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B) (=> (not (= A2 B)) (@ (@ tptp.ord_less_filter_nat A2) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (=> (not (= A2 B)) (@ (@ tptp.ord_less_set_nat A2) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (not (= A2 B)) (@ (@ tptp.ord_less_rat A2) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (not (= A2 B)) (@ (@ tptp.ord_less_nat A2) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B) (=> (not (= A2 B)) (@ (@ tptp.ord_less_int A2) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn)) (=> (not (= A2 B)) (=> (@ (@ tptp.ord_less_eq_assn A2) B) (@ (@ tptp.ord_less_assn A2) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (not (= A2 B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B) (@ (@ tptp.ord_le6747313008572928689nteger A2) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.filter_nat) (B tptp.filter_nat)) (=> (not (= A2 B)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat A2) B) (@ (@ tptp.ord_less_filter_nat A2) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_nat) (B tptp.set_nat)) (=> (not (= A2 B)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B) (@ (@ tptp.ord_less_set_nat A2) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (not (= A2 B)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (@ (@ tptp.ord_less_rat A2) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (not (= A2 B)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (@ (@ tptp.ord_less_nat A2) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (not (= A2 B)) (=> (@ (@ tptp.ord_less_eq_int A2) B) (@ (@ tptp.ord_less_int A2) B)))))
% 5.65/5.93 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (=> (@ (@ tptp.ord_less_assn Y) Z) (@ (@ tptp.ord_less_assn X) Z)))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) Y) (=> (@ (@ tptp.ord_le6747313008572928689nteger Y) Z) (@ (@ tptp.ord_le6747313008572928689nteger X) Z)))))
% 5.65/5.93 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat) (Z tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (=> (@ (@ tptp.ord_less_filter_nat Y) Z) (@ (@ tptp.ord_less_filter_nat X) Z)))))
% 5.65/5.93 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (=> (@ (@ tptp.ord_less_set_nat Y) Z) (@ (@ tptp.ord_less_set_nat X) Z)))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ tptp.ord_less_rat Y) Z) (@ (@ tptp.ord_less_rat X) Z)))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ (@ tptp.ord_less_nat X) Z)))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int X) Z)))))
% 5.65/5.93 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_assn Y) Z) (@ _let_1 Z))))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) Z) (@ _let_1 Z))))))
% 5.65/5.93 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat) (Z tptp.filter_nat)) (let ((_let_1 (@ tptp.ord_less_filter_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) Z) (@ _let_1 Z))))))
% 5.65/5.93 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) Z) (@ _let_1 Z))))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z) (@ _let_1 Z))))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (F (-> tptp.assn tptp.assn)) (B tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A2) (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_assn A2) (@ F C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (F (-> tptp.assn tptp.code_integer)) (B tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ F C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (F (-> tptp.nat tptp.assn)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_assn A2) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_assn A2) (@ F C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (F (-> tptp.nat tptp.code_integer)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ F C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (F (-> tptp.int tptp.assn)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_assn A2) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y2) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_assn A2) (@ F C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (F (-> tptp.int tptp.code_integer)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ F C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (F (-> tptp.code_integer tptp.assn)) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_eq_assn A2) (@ F B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_assn A2) (@ F C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (F (-> tptp.code_integer tptp.code_integer)) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ F B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ F C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (F (-> tptp.rat tptp.assn)) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_assn A2) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y2) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_assn A2) (@ F C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (F (-> tptp.rat tptp.code_integer)) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ F C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (@ (@ tptp.ord_less_assn (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_assn (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_rat (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_int (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (@ (@ tptp.ord_less_assn (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_assn (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_rat (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_int (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (F (-> tptp.rat tptp.assn)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (F (-> tptp.rat tptp.code_integer)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (F (-> tptp.nat tptp.assn)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_assn A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_assn (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (F (-> tptp.nat tptp.code_integer)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (F (-> tptp.nat tptp.int)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y2) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y2)))) (@ _let_1 (@ F C))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_assn A2) B) (=> (@ (@ tptp.ord_less_eq_assn (@ F B)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_assn (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_assn A2) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ F B)) C) (=> (forall ((X3 tptp.assn) (Y2 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (@ (@ tptp.ord_less_eq_assn (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_assn (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (F (-> tptp.int tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_int A2) B) (=> (@ (@ tptp.ord_less_eq_assn (@ F B)) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y2) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_assn (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (F (-> tptp.int tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_int A2) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ F B)) C) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (F (-> tptp.code_integer tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B) (=> (@ (@ tptp.ord_less_eq_assn (@ F B)) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_assn (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (F (-> tptp.code_integer tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ F B)) C) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_rat A2) B) (=> (@ (@ tptp.ord_less_eq_assn (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y2) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_less_assn (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.code_integer)) (C tptp.code_integer)) (=> (@ (@ tptp.ord_less_rat A2) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F X3)) (@ F Y2)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ F A2)) C))))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (or (@ (@ tptp.ord_le3102999989581377725nteger X) Y) (@ (@ tptp.ord_le6747313008572928689nteger Y) X))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_rat Y) X))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_nat Y) X))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_int Y) X))))
% 5.65/5.93 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (or (@ (@ tptp.ord_less_assn X) Y) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) Y) (or (@ (@ tptp.ord_le6747313008572928689nteger X) Y) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (or (@ (@ tptp.ord_less_filter_nat X) Y) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (or (@ (@ tptp.ord_less_set_nat X) Y) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y)))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (or (@ (@ tptp.ord_less_int X) Y) (= X Y)))))
% 5.65/5.93 (assert (not (@ (@ tptp.ord_le5570908160329646204atural tptp.one_one_Code_natural) tptp.one_one_Code_natural)))
% 5.65/5.93 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 5.65/5.93 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 5.65/5.93 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer)))
% 5.65/5.93 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (D2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B) (=> (@ (@ tptp.ord_less_int D2) C) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A2) C)) (@ (@ tptp.minus_minus_int B) D2))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger D2) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A2) C)) (@ (@ tptp.minus_8373710615458151222nteger B) D2))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (D2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B) (=> (@ (@ tptp.ord_less_rat D2) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A2) C)) (@ (@ tptp.minus_minus_rat B) D2))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A2) B) (@ (@ tptp.minus_minus_int C) D2)) (= (@ (@ tptp.ord_less_int A2) B) (@ (@ tptp.ord_less_int C) D2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (= (@ (@ tptp.minus_8373710615458151222nteger A2) B) (@ (@ tptp.minus_8373710615458151222nteger C) D2)) (= (@ (@ tptp.ord_le6747313008572928689nteger A2) B) (@ (@ tptp.ord_le6747313008572928689nteger C) D2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A2) B) (@ (@ tptp.minus_minus_rat C) D2)) (= (@ (@ tptp.ord_less_rat A2) B) (@ (@ tptp.ord_less_rat C) D2)))))
% 5.65/5.93 (assert (forall ((B tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_int B) A2) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B))))))
% 5.65/5.93 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A2) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B))))))
% 5.65/5.93 (assert (forall ((B tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_rat B) A2) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A2) C)) (@ (@ tptp.minus_minus_int B) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A2) C)) (@ (@ tptp.minus_8373710615458151222nteger B) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A2) C)) (@ (@ tptp.minus_minus_rat B) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_Product_unit)) (not (@ (@ tptp.ord_le8056459307392131481t_unit A2) tptp.bot_bo3957492148770167129t_unit))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_o)) (not (@ (@ tptp.ord_less_set_o A2) tptp.bot_bot_set_o))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A2) tptp.bot_bot_set_nat))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A2) tptp.bot_bot_set_int))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_Pr4532377907799695533_nat_o)) (not (@ (@ tptp.ord_le2453136405763929_nat_o A2) tptp.bot_bo7824918357723582233_nat_o))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn)) (not (@ (@ tptp.ord_less_assn A2) tptp.bot_bot_assn))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat)) (not (@ (@ tptp.ord_less_nat A2) tptp.bot_bot_nat))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_Product_unit)) (= (not (= A2 tptp.bot_bo3957492148770167129t_unit)) (@ (@ tptp.ord_le8056459307392131481t_unit tptp.bot_bo3957492148770167129t_unit) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_o)) (= (not (= A2 tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_set_o tptp.bot_bot_set_o) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_nat)) (= (not (= A2 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat tptp.bot_bot_set_nat) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_int)) (= (not (= A2 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int tptp.bot_bot_set_int) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_Pr4532377907799695533_nat_o)) (= (not (= A2 tptp.bot_bo7824918357723582233_nat_o)) (@ (@ tptp.ord_le2453136405763929_nat_o tptp.bot_bo7824918357723582233_nat_o) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn)) (= (not (= A2 tptp.bot_bot_assn)) (@ (@ tptp.ord_less_assn tptp.bot_bot_assn) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat)) (= (not (= A2 tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A2))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit)) (not (@ (@ tptp.ord_le8056459307392131481t_unit A) tptp.bot_bo3957492148770167129t_unit))))
% 5.65/5.93 (assert (forall ((A tptp.set_o)) (not (@ (@ tptp.ord_less_set_o A) tptp.bot_bot_set_o))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A) tptp.bot_bot_set_nat))))
% 5.65/5.93 (assert (forall ((A tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A) tptp.bot_bot_set_int))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (not (@ (@ tptp.ord_le2453136405763929_nat_o A) tptp.bot_bo7824918357723582233_nat_o))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B4) (not (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (@ (@ tptp.ord_less_eq_set_nat B4) A))))))
% 5.65/5.93 (assert (= tptp.ord_less_set_nat (lambda ((A3 tptp.set_nat) (B7 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A3) B7) (not (= A3 B7))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B4) (@ (@ tptp.ord_less_eq_set_nat A) B4))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A))) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) C5) (@ _let_1 C5))))))
% 5.65/5.93 (assert (= tptp.ord_less_set_nat (lambda ((A3 tptp.set_nat) (B7 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A3) B7) (not (@ (@ tptp.ord_less_eq_set_nat B7) A3))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (=> (@ (@ tptp.ord_less_set_nat B4) C5) (@ (@ tptp.ord_less_set_nat A) C5)))))
% 5.65/5.93 (assert (= tptp.ord_less_eq_set_nat (lambda ((A3 tptp.set_nat) (B7 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A3) B7) (= A3 B7)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (X tptp.code_integer)) (@ (@ tptp.member_Code_integer (@ F X)) (@ (@ tptp.image_4470545334726330049nteger F) tptp.top_to4645266643341252675nteger))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.nat)) (X tptp.product_unit)) (@ (@ tptp.member_nat (@ F X)) (@ (@ tptp.image_875570014554754200it_nat F) tptp.top_to1996260823553986621t_unit))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.int)) (X tptp.product_unit)) (@ (@ tptp.member_int (@ F X)) (@ (@ tptp.image_873079544045703924it_int F) tptp.top_to1996260823553986621t_unit))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit Bool)) (X tptp.product_unit)) (@ (@ tptp.member_o (@ F X)) (@ (@ tptp.image_Product_unit_o2 F) tptp.top_to1996260823553986621t_unit))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.product_unit)) (X tptp.product_unit)) (@ (@ tptp.member_Product_unit (@ F X)) (@ (@ tptp.image_405062704495631173t_unit F) tptp.top_to1996260823553986621t_unit))))
% 5.65/5.93 (assert (forall ((F (-> Bool tptp.nat)) (X Bool)) (@ (@ tptp.member_nat (@ F X)) (@ (@ tptp.image_o_nat2 F) tptp.top_top_set_o))))
% 5.65/5.93 (assert (forall ((F (-> Bool tptp.int)) (X Bool)) (@ (@ tptp.member_int (@ F X)) (@ (@ tptp.image_o_int2 F) tptp.top_top_set_o))))
% 5.65/5.93 (assert (forall ((F (-> Bool Bool)) (X Bool)) (@ (@ tptp.member_o (@ F X)) (@ (@ tptp.image_o_o2 F) tptp.top_top_set_o))))
% 5.65/5.93 (assert (forall ((F (-> Bool tptp.product_unit)) (X Bool)) (@ (@ tptp.member_Product_unit (@ F X)) (@ (@ tptp.image_o_Product_unit2 F) tptp.top_top_set_o))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (X tptp.nat)) (@ (@ tptp.member_Code_integer (@ F X)) (@ (@ tptp.image_1215581382706833972nteger F) tptp.top_top_set_nat))))
% 5.65/5.93 (assert (forall ((B tptp.code_integer) (F (-> tptp.code_integer tptp.code_integer)) (X tptp.code_integer)) (=> (= B (@ F X)) (@ (@ tptp.member_Code_integer B) (@ (@ tptp.image_4470545334726330049nteger F) tptp.top_to4645266643341252675nteger)))))
% 5.65/5.93 (assert (forall ((B tptp.nat) (F (-> tptp.product_unit tptp.nat)) (X tptp.product_unit)) (=> (= B (@ F X)) (@ (@ tptp.member_nat B) (@ (@ tptp.image_875570014554754200it_nat F) tptp.top_to1996260823553986621t_unit)))))
% 5.65/5.93 (assert (forall ((B tptp.int) (F (-> tptp.product_unit tptp.int)) (X tptp.product_unit)) (=> (= B (@ F X)) (@ (@ tptp.member_int B) (@ (@ tptp.image_873079544045703924it_int F) tptp.top_to1996260823553986621t_unit)))))
% 5.65/5.93 (assert (forall ((B Bool) (F (-> tptp.product_unit Bool)) (X tptp.product_unit)) (=> (= B (@ F X)) (@ (@ tptp.member_o B) (@ (@ tptp.image_Product_unit_o2 F) tptp.top_to1996260823553986621t_unit)))))
% 5.65/5.93 (assert (forall ((B tptp.product_unit) (F (-> tptp.product_unit tptp.product_unit)) (X tptp.product_unit)) (=> (= B (@ F X)) (@ (@ tptp.member_Product_unit B) (@ (@ tptp.image_405062704495631173t_unit F) tptp.top_to1996260823553986621t_unit)))))
% 5.65/5.93 (assert (forall ((B tptp.nat) (F (-> Bool tptp.nat)) (X Bool)) (=> (= B (@ F X)) (@ (@ tptp.member_nat B) (@ (@ tptp.image_o_nat2 F) tptp.top_top_set_o)))))
% 5.65/5.93 (assert (forall ((B tptp.int) (F (-> Bool tptp.int)) (X Bool)) (=> (= B (@ F X)) (@ (@ tptp.member_int B) (@ (@ tptp.image_o_int2 F) tptp.top_top_set_o)))))
% 5.65/5.93 (assert (forall ((B Bool) (F (-> Bool Bool)) (X Bool)) (=> (= B (@ F X)) (@ (@ tptp.member_o B) (@ (@ tptp.image_o_o2 F) tptp.top_top_set_o)))))
% 5.65/5.93 (assert (forall ((B tptp.product_unit) (F (-> Bool tptp.product_unit)) (X Bool)) (=> (= B (@ F X)) (@ (@ tptp.member_Product_unit B) (@ (@ tptp.image_o_Product_unit2 F) tptp.top_top_set_o)))))
% 5.65/5.93 (assert (forall ((B tptp.code_integer) (F (-> tptp.nat tptp.code_integer)) (X tptp.nat)) (=> (= B (@ F X)) (@ (@ tptp.member_Code_integer B) (@ (@ tptp.image_1215581382706833972nteger F) tptp.top_top_set_nat)))))
% 5.65/5.93 (assert (not (= tptp.bot_bo7824918357723582233_nat_o tptp.top_to4869887016220417533_nat_o)))
% 5.65/5.93 (assert (not (= tptp.bot_bo3957492148770167129t_unit tptp.top_to1996260823553986621t_unit)))
% 5.65/5.93 (assert (not (= tptp.bot_bot_set_o tptp.top_top_set_o)))
% 5.65/5.93 (assert (not (= tptp.bot_bot_set_nat tptp.top_top_set_nat)))
% 5.65/5.93 (assert (not (= tptp.bot_bot_set_int tptp.top_top_set_int)))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit)) (@ (@ tptp.ord_le3507040750410214029t_unit A) tptp.top_to1996260823553986621t_unit)))
% 5.65/5.93 (assert (forall ((A tptp.set_o)) (@ (@ tptp.ord_less_eq_set_o A) tptp.top_top_set_o)))
% 5.65/5.93 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) tptp.top_top_set_int)))
% 5.65/5.93 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) tptp.top_top_set_nat)))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.ord_le2453136405763929_nat_o A) B4) (exists ((B2 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o B2) (@ (@ tptp.minus_1801376950450012436_nat_o B4) A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A) B4) (exists ((B2 tptp.int)) (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int B4) A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (=> (@ (@ tptp.ord_less_set_o A) B4) (exists ((B2 Bool)) (@ (@ tptp.member_o B2) (@ (@ tptp.minus_minus_set_o B4) A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (=> (@ (@ tptp.ord_le8056459307392131481t_unit A) B4) (exists ((B2 tptp.product_unit)) (@ (@ tptp.member_Product_unit B2) (@ (@ tptp.minus_6452836326544984404t_unit B4) A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B4) (exists ((B2 tptp.nat)) (@ (@ tptp.member_nat B2) (@ (@ tptp.minus_minus_set_nat B4) A))))))
% 5.65/5.93 (assert (forall ((X tptp.product_unit)) (= (@ (@ tptp.insert_Product_unit X) tptp.top_to1996260823553986621t_unit) tptp.top_to1996260823553986621t_unit)))
% 5.65/5.93 (assert (forall ((X Bool)) (= (@ (@ tptp.insert_o X) tptp.top_top_set_o) tptp.top_top_set_o)))
% 5.65/5.93 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.insert_nat X) tptp.top_top_set_nat) tptp.top_top_set_nat)))
% 5.65/5.93 (assert (forall ((X tptp.int)) (= (@ (@ tptp.insert_int X) tptp.top_top_set_int) tptp.top_top_set_int)))
% 5.65/5.93 (assert (forall ((B4 tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit tptp.top_to1996260823553986621t_unit) B4) B4)))
% 5.65/5.93 (assert (forall ((B4 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o tptp.top_top_set_o) B4) B4)))
% 5.65/5.93 (assert (forall ((B4 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.top_top_set_nat) B4) B4)))
% 5.65/5.93 (assert (forall ((B4 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int tptp.top_top_set_int) B4) B4)))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit A) tptp.top_to1996260823553986621t_unit) A)))
% 5.65/5.93 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o A) tptp.top_top_set_o) A)))
% 5.65/5.93 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A) tptp.top_top_set_nat) A)))
% 5.65/5.93 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A) tptp.top_top_set_int) A)))
% 5.65/5.93 (assert (forall ((B4 tptp.set_Product_unit)) (= (@ (@ tptp.sup_su793286257634532545t_unit tptp.top_to1996260823553986621t_unit) B4) tptp.top_to1996260823553986621t_unit)))
% 5.65/5.93 (assert (forall ((B4 tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o tptp.top_top_set_o) B4) tptp.top_top_set_o)))
% 5.65/5.93 (assert (forall ((B4 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.top_top_set_nat) B4) tptp.top_top_set_nat)))
% 5.65/5.93 (assert (forall ((B4 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int tptp.top_top_set_int) B4) tptp.top_top_set_int)))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit)) (= (@ (@ tptp.sup_su793286257634532545t_unit A) tptp.top_to1996260823553986621t_unit) tptp.top_to1996260823553986621t_unit)))
% 5.65/5.93 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o A) tptp.top_top_set_o) tptp.top_top_set_o)))
% 5.65/5.93 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A) tptp.top_top_set_nat) tptp.top_top_set_nat)))
% 5.65/5.93 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A) tptp.top_top_set_int) tptp.top_top_set_int)))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.assn tptp.produc3658429121746597890et_nat Bool)) (Abs2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.assn)) (F2 (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (@ (@ (@ tptp.type_d3909072315231072503_nat_o Rep2) Abs2) tptp.top_to4869887016220417533_nat_o) (= (exists ((X7 (-> tptp.produc3658429121746597890et_nat Bool))) (@ F2 X7)) (exists ((B6 tptp.assn)) (@ F2 (@ Rep2 B6)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (F2 (-> tptp.int Bool))) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) tptp.top_top_set_int) (= (exists ((X7 tptp.int)) (@ F2 X7)) (exists ((B6 tptp.code_integer)) (@ F2 (@ Rep2 B6)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.product_unit Bool)) (Abs2 (-> Bool tptp.product_unit)) (F2 (-> Bool Bool))) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep2) Abs2) tptp.top_top_set_o) (= (exists ((X7 Bool)) (@ F2 X7)) (exists ((B6 tptp.product_unit)) (@ F2 (@ Rep2 B6)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_natural tptp.nat)) (Abs2 (-> tptp.nat tptp.code_natural)) (F2 (-> tptp.nat Bool))) (=> (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep2) Abs2) tptp.top_top_set_nat) (= (exists ((X7 tptp.nat)) (@ F2 X7)) (exists ((B6 tptp.code_natural)) (@ F2 (@ Rep2 B6)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.assn tptp.produc3658429121746597890et_nat Bool)) (Abs2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.assn)) (S2 tptp.assn)) (=> (@ (@ (@ tptp.type_d3909072315231072503_nat_o Rep2) Abs2) tptp.top_to4869887016220417533_nat_o) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (not (= S2 (@ Abs2 X3))))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (S2 tptp.code_integer)) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) tptp.top_top_set_int) (not (forall ((X3 tptp.int)) (not (= S2 (@ Abs2 X3))))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.product_unit Bool)) (Abs2 (-> Bool tptp.product_unit)) (S2 tptp.product_unit)) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep2) Abs2) tptp.top_top_set_o) (not (forall ((X3 Bool)) (not (= S2 (@ Abs2 X3))))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_natural tptp.nat)) (Abs2 (-> tptp.nat tptp.code_natural)) (S2 tptp.code_natural)) (=> (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep2) Abs2) tptp.top_top_set_nat) (not (forall ((X3 tptp.nat)) (not (= S2 (@ Abs2 X3))))))))
% 5.65/5.93 (assert (forall ((M4 tptp.code_natural) (N2 tptp.code_natural)) (let ((_let_1 (@ tptp.ord_le5570908160329646204atural tptp.one_one_Code_natural))) (=> (@ _let_1 M4) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_2397367101498566445atural M4) N2)))))))
% 5.65/5.93 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M4) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_nat M4) N2)))))))
% 5.65/5.93 (assert (forall ((M4 tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M4) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_int M4) N2)))))))
% 5.65/5.93 (assert (forall ((M4 tptp.code_integer) (N2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 M4) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger M4) N2)))))))
% 5.65/5.93 (assert (forall ((M4 tptp.rat) (N2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 M4) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_rat M4) N2)))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_Product_unit)) (=> (not (= X4 tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) X4) (exists ((Xa2 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit Xa2) X4) (@ (@ tptp.ord_le361264281704409273t_unit X3) Xa2))))) (not (@ tptp.finite4290736615968046902t_unit X4))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_o)) (=> (not (= X4 tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) X4) (exists ((Xa2 Bool)) (and (@ (@ tptp.member_o Xa2) X4) (@ (@ tptp.ord_less_o X3) Xa2))))) (not (@ tptp.finite_finite_o X4))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_nat)) (=> (not (= X4 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) X4) (exists ((Xa2 tptp.nat)) (and (@ (@ tptp.member_nat Xa2) X4) (@ (@ tptp.ord_less_nat X3) Xa2))))) (not (@ tptp.finite_finite_nat X4))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_int)) (=> (not (= X4 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) X4) (exists ((Xa2 tptp.int)) (and (@ (@ tptp.member_int Xa2) X4) (@ (@ tptp.ord_less_int X3) Xa2))))) (not (@ tptp.finite_finite_int X4))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_Code_integer)) (=> (not (= X4 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) X4) (exists ((Xa2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa2) X4) (@ (@ tptp.ord_le6747313008572928689nteger X3) Xa2))))) (not (@ tptp.finite6017078050557962740nteger X4))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_rat)) (=> (not (= X4 tptp.bot_bot_set_rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.member_rat X3) X4) (exists ((Xa2 tptp.rat)) (and (@ (@ tptp.member_rat Xa2) X4) (@ (@ tptp.ord_less_rat X3) Xa2))))) (not (@ tptp.finite_finite_rat X4))))))
% 5.65/5.93 (assert (forall ((S tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit S) (=> (not (= S tptp.bot_bo3957492148770167129t_unit)) (exists ((X3 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X3) S) (not (exists ((Xa2 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit Xa2) S) (@ (@ tptp.ord_le361264281704409273t_unit Xa2) X3))))))))))
% 5.65/5.93 (assert (forall ((S tptp.set_o)) (=> (@ tptp.finite_finite_o S) (=> (not (= S tptp.bot_bot_set_o)) (exists ((X3 Bool)) (and (@ (@ tptp.member_o X3) S) (not (exists ((Xa2 Bool)) (and (@ (@ tptp.member_o Xa2) S) (@ (@ tptp.ord_less_o Xa2) X3))))))))))
% 5.65/5.93 (assert (forall ((S tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o S) (=> (not (= S tptp.bot_bo7824918357723582233_nat_o)) (exists ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (and (@ (@ tptp.member6576561426505652726_nat_o X3) S) (not (exists ((Xa2 (-> tptp.produc3658429121746597890et_nat Bool))) (and (@ (@ tptp.member6576561426505652726_nat_o Xa2) S) (@ (@ tptp.ord_le8176553561544679545_nat_o Xa2) X3))))))))))
% 5.65/5.93 (assert (forall ((S tptp.set_assn)) (=> (@ tptp.finite_finite_assn S) (=> (not (= S tptp.bot_bot_set_assn)) (exists ((X3 tptp.assn)) (and (@ (@ tptp.member_assn X3) S) (not (exists ((Xa2 tptp.assn)) (and (@ (@ tptp.member_assn Xa2) S) (@ (@ tptp.ord_less_assn Xa2) X3))))))))))
% 5.65/5.93 (assert (forall ((S tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (=> (not (= S tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) S) (not (exists ((Xa2 tptp.nat)) (and (@ (@ tptp.member_nat Xa2) S) (@ (@ tptp.ord_less_nat Xa2) X3))))))))))
% 5.65/5.93 (assert (forall ((S tptp.set_int)) (=> (@ tptp.finite_finite_int S) (=> (not (= S tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) S) (not (exists ((Xa2 tptp.int)) (and (@ (@ tptp.member_int Xa2) S) (@ (@ tptp.ord_less_int Xa2) X3))))))))))
% 5.65/5.93 (assert (forall ((S tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger S) (=> (not (= S tptp.bot_bo3990330152332043303nteger)) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) S) (not (exists ((Xa2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa2) S) (@ (@ tptp.ord_le6747313008572928689nteger Xa2) X3))))))))))
% 5.65/5.93 (assert (forall ((S tptp.set_rat)) (=> (@ tptp.finite_finite_rat S) (=> (not (= S tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) S) (not (exists ((Xa2 tptp.rat)) (and (@ (@ tptp.member_rat Xa2) S) (@ (@ tptp.ord_less_rat Xa2) X3))))))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_int) (Z tptp.int)) (=> (not (= X4 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_int Z) (@ tptp.complete_Sup_Sup_int X4)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) X4) (@ (@ tptp.ord_less_int Z) X3)))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_nat) (Z tptp.nat)) (=> (not (= X4 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_nat Z) (@ tptp.complete_Sup_Sup_nat X4)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) X4) (@ (@ tptp.ord_less_nat Z) X3)))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_Product_unit) (Z tptp.product_unit)) (=> (not (= X4 tptp.bot_bo3957492148770167129t_unit)) (=> (@ (@ tptp.ord_le361264281704409273t_unit Z) (@ tptp.comple4687483117567863418t_unit X4)) (exists ((X3 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X3) X4) (@ (@ tptp.ord_le361264281704409273t_unit Z) X3)))))))
% 5.65/5.93 (assert (forall ((Y tptp.int) (X4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int Y) (@ tptp.complete_Sup_Sup_int X4)) (=> (not (= X4 tptp.bot_bot_set_int)) (not (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) X4) (not (@ (@ tptp.ord_less_int Y) X3)))))))))
% 5.65/5.93 (assert (forall ((Y tptp.nat) (X4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat Y) (@ tptp.complete_Sup_Sup_nat X4)) (=> (not (= X4 tptp.bot_bot_set_nat)) (not (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) X4) (not (@ (@ tptp.ord_less_nat Y) X3)))))))))
% 5.65/5.93 (assert (forall ((Y tptp.product_unit) (X4 tptp.set_Product_unit)) (=> (@ (@ tptp.ord_le361264281704409273t_unit Y) (@ tptp.comple4687483117567863418t_unit X4)) (=> (not (= X4 tptp.bot_bo3957492148770167129t_unit)) (not (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) X4) (not (@ (@ tptp.ord_le361264281704409273t_unit Y) X3)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (@ (@ tptp.member_Code_integer (@ tptp.lattic4901227151466704046nteger A)) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (@ (@ tptp.member_Product_unit (@ tptp.lattic1210392890313158908t_unit A)) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_o)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (@ (@ tptp.member_o (@ tptp.lattic1921953407002678535_Max_o A)) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.member_int (@ tptp.lattic8263393255366662781ax_int A)) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.member_nat (@ tptp.lattic8265883725875713057ax_nat A)) A)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (B4 tptp.set_Code_integer) (I2 tptp.code_integer)) (=> (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.image_4470545334726330049nteger F) tptp.top_to4645266643341252675nteger)) B4) (@ (@ tptp.member_Code_integer (@ F I2)) B4))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.int)) (B4 tptp.set_int) (I2 tptp.product_unit)) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_873079544045703924it_int F) tptp.top_to1996260823553986621t_unit)) B4) (@ (@ tptp.member_int (@ F I2)) B4))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit Bool)) (B4 tptp.set_o) (I2 tptp.product_unit)) (=> (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.image_Product_unit_o2 F) tptp.top_to1996260823553986621t_unit)) B4) (@ (@ tptp.member_o (@ F I2)) B4))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.product_unit)) (B4 tptp.set_Product_unit) (I2 tptp.product_unit)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit (@ (@ tptp.image_405062704495631173t_unit F) tptp.top_to1996260823553986621t_unit)) B4) (@ (@ tptp.member_Product_unit (@ F I2)) B4))))
% 5.65/5.93 (assert (forall ((F (-> Bool tptp.int)) (B4 tptp.set_int) (I2 Bool)) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_o_int2 F) tptp.top_top_set_o)) B4) (@ (@ tptp.member_int (@ F I2)) B4))))
% 5.65/5.93 (assert (forall ((F (-> Bool Bool)) (B4 tptp.set_o) (I2 Bool)) (=> (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.image_o_o2 F) tptp.top_top_set_o)) B4) (@ (@ tptp.member_o (@ F I2)) B4))))
% 5.65/5.93 (assert (forall ((F (-> Bool tptp.product_unit)) (B4 tptp.set_Product_unit) (I2 Bool)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit (@ (@ tptp.image_o_Product_unit2 F) tptp.top_top_set_o)) B4) (@ (@ tptp.member_Product_unit (@ F I2)) B4))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (B4 tptp.set_Code_integer) (I2 tptp.nat)) (=> (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.image_1215581382706833972nteger F) tptp.top_top_set_nat)) B4) (@ (@ tptp.member_Code_integer (@ F I2)) B4))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat tptp.int)) (B4 tptp.set_int) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_nat_int2 F) tptp.top_top_set_nat)) B4) (@ (@ tptp.member_int (@ F I2)) B4))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat Bool)) (B4 tptp.set_o) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.image_nat_o2 F) tptp.top_top_set_nat)) B4) (@ (@ tptp.member_o (@ F I2)) B4))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer)) (=> (= (@ (@ tptp.image_4470545334726330049nteger F) tptp.top_to4645266643341252675nteger) tptp.top_to4645266643341252675nteger) (= (= (@ (@ tptp.vimage1318793397690208119nteger F) A) tptp.bot_bo3990330152332043303nteger) (= A tptp.bot_bo3990330152332043303nteger)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.product_unit)) (A tptp.set_Product_unit)) (=> (= (@ (@ tptp.image_405062704495631173t_unit F) tptp.top_to1996260823553986621t_unit) tptp.top_to1996260823553986621t_unit) (= (= (@ (@ tptp.vimage7995052115951654139t_unit F) A) tptp.bot_bo3957492148770167129t_unit) (= A tptp.bot_bo3957492148770167129t_unit)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit Bool)) (A tptp.set_o)) (=> (= (@ (@ tptp.image_Product_unit_o2 F) tptp.top_to1996260823553986621t_unit) tptp.top_top_set_o) (= (= (@ (@ tptp.vimage8808348054653608838unit_o F) A) tptp.bot_bo3957492148770167129t_unit) (= A tptp.bot_bot_set_o)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.nat)) (A tptp.set_nat)) (=> (= (@ (@ tptp.image_875570014554754200it_nat F) tptp.top_to1996260823553986621t_unit) tptp.top_top_set_nat) (= (= (@ (@ tptp.vimage6253328473476588386it_nat F) A) tptp.bot_bo3957492148770167129t_unit) (= A tptp.bot_bot_set_nat)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.int)) (A tptp.set_int)) (=> (= (@ (@ tptp.image_873079544045703924it_int F) tptp.top_to1996260823553986621t_unit) tptp.top_top_set_int) (= (= (@ (@ tptp.vimage6250838002967538110it_int F) A) tptp.bot_bo3957492148770167129t_unit) (= A tptp.bot_bot_set_int)))))
% 5.65/5.93 (assert (forall ((F (-> Bool tptp.product_unit)) (A tptp.set_Product_unit)) (=> (= (@ (@ tptp.image_o_Product_unit2 F) tptp.top_top_set_o) tptp.top_to1996260823553986621t_unit) (= (= (@ (@ tptp.vimage4222377557387472176t_unit F) A) tptp.bot_bot_set_o) (= A tptp.bot_bo3957492148770167129t_unit)))))
% 5.65/5.93 (assert (forall ((F (-> Bool Bool)) (A tptp.set_o)) (=> (= (@ (@ tptp.image_o_o2 F) tptp.top_top_set_o) tptp.top_top_set_o) (= (= (@ (@ tptp.vimage_o_o F) A) tptp.bot_bot_set_o) (= A tptp.bot_bot_set_o)))))
% 5.65/5.93 (assert (forall ((F (-> Bool tptp.nat)) (A tptp.set_nat)) (=> (= (@ (@ tptp.image_o_nat2 F) tptp.top_top_set_o) tptp.top_top_set_nat) (= (= (@ (@ tptp.vimage_o_nat F) A) tptp.bot_bot_set_o) (= A tptp.bot_bot_set_nat)))))
% 5.65/5.93 (assert (forall ((F (-> Bool tptp.int)) (A tptp.set_int)) (=> (= (@ (@ tptp.image_o_int2 F) tptp.top_top_set_o) tptp.top_top_set_int) (= (= (@ (@ tptp.vimage_o_int F) A) tptp.bot_bot_set_o) (= A tptp.bot_bot_set_int)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.set_Code_integer)) (=> (= (@ (@ tptp.image_1215581382706833972nteger F) tptp.top_top_set_nat) tptp.top_to4645266643341252675nteger) (= (= (@ (@ tptp.vimage6104394758324456170nteger F) A) tptp.bot_bot_set_nat) (= A tptp.bot_bo3990330152332043303nteger)))))
% 5.65/5.93 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.nat tptp.assn))) (=> (forall ((A4 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A4) B2)) R2) (@ (@ tptp.ord_less_assn (@ F B2)) (@ F A4)))) (@ tptp.transi3139058337892597825ic_nat R2))))
% 5.65/5.93 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (F (-> tptp.int tptp.assn))) (=> (forall ((A4 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A4) B2)) R2) (@ (@ tptp.ord_less_assn (@ F B2)) (@ F A4)))) (@ tptp.transi3136567867383547549ic_int R2))))
% 5.65/5.93 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((A4 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A4) B2)) R2) (@ (@ tptp.ord_less_nat (@ F B2)) (@ F A4)))) (@ tptp.transi3139058337892597825ic_nat R2))))
% 5.65/5.93 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (F (-> tptp.int tptp.nat))) (=> (forall ((A4 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A4) B2)) R2) (@ (@ tptp.ord_less_nat (@ F B2)) (@ F A4)))) (@ tptp.transi3136567867383547549ic_int R2))))
% 5.65/5.93 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((A4 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A4) B2)) R2) (@ (@ tptp.ord_less_int (@ F B2)) (@ F A4)))) (@ tptp.transi3139058337892597825ic_nat R2))))
% 5.65/5.93 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (F (-> tptp.int tptp.int))) (=> (forall ((A4 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A4) B2)) R2) (@ (@ tptp.ord_less_int (@ F B2)) (@ F A4)))) (@ tptp.transi3136567867383547549ic_int R2))))
% 5.65/5.93 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.nat tptp.code_integer))) (=> (forall ((A4 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A4) B2)) R2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F B2)) (@ F A4)))) (@ tptp.transi3139058337892597825ic_nat R2))))
% 5.65/5.93 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (F (-> tptp.int tptp.code_integer))) (=> (forall ((A4 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A4) B2)) R2) (@ (@ tptp.ord_le6747313008572928689nteger (@ F B2)) (@ F A4)))) (@ tptp.transi3136567867383547549ic_int R2))))
% 5.65/5.93 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((A4 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A4) B2)) R2) (@ (@ tptp.ord_less_rat (@ F B2)) (@ F A4)))) (@ tptp.transi3139058337892597825ic_nat R2))))
% 5.65/5.93 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (F (-> tptp.int tptp.rat))) (=> (forall ((A4 tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A4) B2)) R2) (@ (@ tptp.ord_less_rat (@ F B2)) (@ F A4)))) (@ tptp.transi3136567867383547549ic_int R2))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.set_nat tptp.nat)) (Abs2 (-> tptp.nat tptp.set_nat)) (A tptp.set_nat)) (=> (@ (@ (@ tptp.type_d202864840109488260at_nat Rep2) Abs2) A) (= (@ (@ tptp.image_nat_set_nat Abs2) A) tptp.top_top_set_set_nat))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.code_integer)) (Abs2 (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer)) (=> (@ (@ (@ tptp.type_d4796611474492816872nteger Rep2) Abs2) A) (= (@ (@ tptp.image_4470545334726330049nteger Abs2) A) tptp.top_to4645266643341252675nteger))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.nat)) (Abs2 (-> tptp.nat tptp.code_integer)) (A tptp.set_nat)) (=> (@ (@ (@ tptp.type_d8368584451094728027er_nat Rep2) Abs2) A) (= (@ (@ tptp.image_1215581382706833972nteger Abs2) A) tptp.top_to4645266643341252675nteger))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.nat tptp.nat)) (Abs2 (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (=> (@ (@ (@ tptp.type_d6250493948777748686at_nat Rep2) Abs2) A) (= (@ (@ tptp.image_nat_nat2 Abs2) A) tptp.top_top_set_nat))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.assn tptp.produc3658429121746597890et_nat Bool)) (Abs2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.assn)) (A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ (@ tptp.type_d3909072315231072503_nat_o Rep2) Abs2) A) (= (@ (@ tptp.image_6451031022632655280o_assn Abs2) A) tptp.top_top_set_assn))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (A tptp.set_int)) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) A) (= (@ (@ tptp.image_1587234942943678608nteger Abs2) A) tptp.top_to4645266643341252675nteger))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.product_unit Bool)) (Abs2 (-> Bool tptp.product_unit)) (A tptp.set_o)) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep2) Abs2) A) (= (@ (@ tptp.image_o_Product_unit2 Abs2) A) tptp.top_to1996260823553986621t_unit))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_natural tptp.nat)) (Abs2 (-> tptp.nat tptp.code_natural)) (A tptp.set_nat)) (=> (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep2) Abs2) A) (= (@ (@ tptp.image_39176534463551487atural Abs2) A) tptp.top_to9103716463852441742atural))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.code_integer)) (Abs2 (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer)) (=> (@ (@ (@ tptp.type_d4796611474492816872nteger Rep2) Abs2) A) (= (@ (@ tptp.image_4470545334726330049nteger Rep2) tptp.top_to4645266643341252675nteger) A))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.nat tptp.set_nat)) (Abs2 (-> tptp.set_nat tptp.nat)) (A tptp.set_set_nat)) (=> (@ (@ (@ tptp.type_d3768499744764857476et_nat Rep2) Abs2) A) (= (@ (@ tptp.image_nat_set_nat Rep2) tptp.top_top_set_nat) A))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.nat tptp.nat)) (Abs2 (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (=> (@ (@ (@ tptp.type_d6250493948777748686at_nat Rep2) Abs2) A) (= (@ (@ tptp.image_nat_nat2 Rep2) tptp.top_top_set_nat) A))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.nat tptp.code_integer)) (Abs2 (-> tptp.code_integer tptp.nat)) (A tptp.set_Code_integer)) (=> (@ (@ (@ tptp.type_d8633139899873770843nteger Rep2) Abs2) A) (= (@ (@ tptp.image_1215581382706833972nteger Rep2) tptp.top_top_set_nat) A))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.assn tptp.produc3658429121746597890et_nat Bool)) (Abs2 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.assn)) (A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ (@ tptp.type_d3909072315231072503_nat_o Rep2) Abs2) A) (= (@ (@ tptp.image_5465535159827709278_nat_o Rep2) tptp.top_top_set_assn) A))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (A tptp.set_int)) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) A) (= (@ (@ tptp.image_948535463418740880er_int Rep2) tptp.top_to4645266643341252675nteger) A))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.product_unit Bool)) (Abs2 (-> Bool tptp.product_unit)) (A tptp.set_o)) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep2) Abs2) A) (= (@ (@ tptp.image_Product_unit_o2 Rep2) tptp.top_to1996260823553986621t_unit) A))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_natural tptp.nat)) (Abs2 (-> tptp.nat tptp.code_natural)) (A tptp.set_nat)) (=> (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep2) Abs2) A) (= (@ (@ tptp.image_6215854944615398399al_nat Rep2) tptp.top_to9103716463852441742atural) A))))
% 5.65/5.93 (assert (@ (@ tptp.refl_on_Product_unit tptp.top_to1996260823553986621t_unit) tptp.id_Product_unit))
% 5.65/5.93 (assert (@ (@ tptp.refl_on_o tptp.top_top_set_o) tptp.id_o2))
% 5.65/5.93 (assert (@ (@ tptp.refl_on_nat tptp.top_top_set_nat) tptp.id_nat))
% 5.65/5.93 (assert (@ (@ tptp.refl_on_int tptp.top_top_set_int) tptp.id_int))
% 5.65/5.93 (assert (forall ((A2 tptp.product_unit) (X tptp.product_unit) (Y tptp.product_unit)) (let ((_let_1 (@ tptp.sup_sup_Product_unit A2))) (let ((_let_2 (@ tptp.inf_inf_Product_unit A2))) (=> (= (@ _let_2 X) tptp.bot_bot_Product_unit) (=> (= (@ _let_1 X) tptp.top_top_Product_unit) (=> (= (@ _let_2 Y) tptp.bot_bot_Product_unit) (=> (= (@ _let_1 Y) tptp.top_top_Product_unit) (= X Y)))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_Pr4532377907799695533_nat_o) (X tptp.set_Pr4532377907799695533_nat_o) (Y tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.sup_su5209123915105501825_nat_o A2))) (let ((_let_2 (@ tptp.inf_in1906310914598751387_nat_o A2))) (=> (= (@ _let_2 X) tptp.bot_bo7824918357723582233_nat_o) (=> (= (@ _let_1 X) tptp.top_to4869887016220417533_nat_o) (=> (= (@ _let_2 Y) tptp.bot_bo7824918357723582233_nat_o) (=> (= (@ _let_1 Y) tptp.top_to4869887016220417533_nat_o) (= X Y)))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.assn) (X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn A2))) (let ((_let_2 (@ tptp.inf_inf_assn A2))) (=> (= (@ _let_2 X) tptp.bot_bot_assn) (=> (= (@ _let_1 X) tptp.top_top_assn) (=> (= (@ _let_2 Y) tptp.bot_bot_assn) (=> (= (@ _let_1 Y) tptp.top_top_assn) (= X Y)))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_Product_unit) (X tptp.set_Product_unit) (Y tptp.set_Product_unit)) (let ((_let_1 (@ tptp.sup_su793286257634532545t_unit A2))) (let ((_let_2 (@ tptp.inf_in4660618365625256667t_unit A2))) (=> (= (@ _let_2 X) tptp.bot_bo3957492148770167129t_unit) (=> (= (@ _let_1 X) tptp.top_to1996260823553986621t_unit) (=> (= (@ _let_2 Y) tptp.bot_bo3957492148770167129t_unit) (=> (= (@ _let_1 Y) tptp.top_to1996260823553986621t_unit) (= X Y)))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_o) (X tptp.set_o) (Y tptp.set_o)) (let ((_let_1 (@ tptp.sup_sup_set_o A2))) (let ((_let_2 (@ tptp.inf_inf_set_o A2))) (=> (= (@ _let_2 X) tptp.bot_bot_set_o) (=> (= (@ _let_1 X) tptp.top_top_set_o) (=> (= (@ _let_2 Y) tptp.bot_bot_set_o) (=> (= (@ _let_1 Y) tptp.top_top_set_o) (= X Y)))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_nat) (X tptp.set_nat) (Y tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A2))) (let ((_let_2 (@ tptp.inf_inf_set_nat A2))) (=> (= (@ _let_2 X) tptp.bot_bot_set_nat) (=> (= (@ _let_1 X) tptp.top_top_set_nat) (=> (= (@ _let_2 Y) tptp.bot_bot_set_nat) (=> (= (@ _let_1 Y) tptp.top_top_set_nat) (= X Y)))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_int) (X tptp.set_int) (Y tptp.set_int)) (let ((_let_1 (@ tptp.sup_sup_set_int A2))) (let ((_let_2 (@ tptp.inf_inf_set_int A2))) (=> (= (@ _let_2 X) tptp.bot_bot_set_int) (=> (= (@ _let_1 X) tptp.top_top_set_int) (=> (= (@ _let_2 Y) tptp.bot_bot_set_int) (=> (= (@ _let_1 Y) tptp.top_top_set_int) (= X Y)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (=> (@ tptp.finite_finite_int A) (= (@ (@ tptp.sup_sup_set_int A) B4) (@ (@ (@ tptp.finite1723285575846220376et_int tptp.insert_int) B4) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (=> (@ tptp.finite_finite_o A) (= (@ (@ tptp.sup_sup_set_o A) B4) (@ (@ (@ tptp.finite_fold_o_set_o tptp.insert_o) B4) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (= (@ (@ tptp.sup_su793286257634532545t_unit A) B4) (@ (@ (@ tptp.finite2740360166580943592t_unit tptp.insert_Product_unit) B4) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ (@ tptp.sup_su848401254843788991nteger A) B4) (@ (@ (@ tptp.finite7486036041278456378nteger tptp.insert_Code_integer) B4) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (= (@ (@ tptp.sup_sup_set_nat A) B4) (@ (@ (@ tptp.finite5529483035118572448et_nat tptp.insert_nat) B4) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (P (-> tptp.set_Product_unit Bool))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ P tptp.bot_bo3957492148770167129t_unit) (=> (forall ((B2 tptp.product_unit) (A9 tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A9) (=> (forall ((X6 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X6) A9) (@ (@ tptp.ord_le361264281704409273t_unit B2) X6))) (=> (@ P A9) (@ P (@ (@ tptp.insert_Product_unit B2) A9)))))) (@ P A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o A) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((B2 Bool) (A9 tptp.set_o)) (=> (@ tptp.finite_finite_o A9) (=> (forall ((X6 Bool)) (=> (@ (@ tptp.member_o X6) A9) (@ (@ tptp.ord_less_o B2) X6))) (=> (@ P A9) (@ P (@ (@ tptp.insert_o B2) A9)))))) (@ P A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B2 tptp.nat) (A9 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A9) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A9) (@ (@ tptp.ord_less_nat B2) X6))) (=> (@ P A9) (@ P (@ (@ tptp.insert_nat B2) A9)))))) (@ P A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B2 tptp.int) (A9 tptp.set_int)) (=> (@ tptp.finite_finite_int A9) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A9) (@ (@ tptp.ord_less_int B2) X6))) (=> (@ P A9) (@ P (@ (@ tptp.insert_int B2) A9)))))) (@ P A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (forall ((B2 tptp.code_integer) (A9 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A9) (=> (forall ((X6 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X6) A9) (@ (@ tptp.ord_le6747313008572928689nteger B2) X6))) (=> (@ P A9) (@ P (@ (@ tptp.insert_Code_integer B2) A9)))))) (@ P A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_rat) (P (-> tptp.set_rat Bool))) (=> (@ tptp.finite_finite_rat A) (=> (@ P tptp.bot_bot_set_rat) (=> (forall ((B2 tptp.rat) (A9 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A9) (=> (forall ((X6 tptp.rat)) (=> (@ (@ tptp.member_rat X6) A9) (@ (@ tptp.ord_less_rat B2) X6))) (=> (@ P A9) (@ P (@ (@ tptp.insert_rat B2) A9)))))) (@ P A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (P (-> tptp.set_Product_unit Bool))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ P tptp.bot_bo3957492148770167129t_unit) (=> (forall ((B2 tptp.product_unit) (A9 tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A9) (=> (forall ((X6 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X6) A9) (@ (@ tptp.ord_le361264281704409273t_unit X6) B2))) (=> (@ P A9) (@ P (@ (@ tptp.insert_Product_unit B2) A9)))))) (@ P A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (P (-> tptp.set_o Bool))) (=> (@ tptp.finite_finite_o A) (=> (@ P tptp.bot_bot_set_o) (=> (forall ((B2 Bool) (A9 tptp.set_o)) (=> (@ tptp.finite_finite_o A9) (=> (forall ((X6 Bool)) (=> (@ (@ tptp.member_o X6) A9) (@ (@ tptp.ord_less_o X6) B2))) (=> (@ P A9) (@ P (@ (@ tptp.insert_o B2) A9)))))) (@ P A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B2 tptp.nat) (A9 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A9) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A9) (@ (@ tptp.ord_less_nat X6) B2))) (=> (@ P A9) (@ P (@ (@ tptp.insert_nat B2) A9)))))) (@ P A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B2 tptp.int) (A9 tptp.set_int)) (=> (@ tptp.finite_finite_int A9) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A9) (@ (@ tptp.ord_less_int X6) B2))) (=> (@ P A9) (@ P (@ (@ tptp.insert_int B2) A9)))))) (@ P A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ P tptp.bot_bo3990330152332043303nteger) (=> (forall ((B2 tptp.code_integer) (A9 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A9) (=> (forall ((X6 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X6) A9) (@ (@ tptp.ord_le6747313008572928689nteger X6) B2))) (=> (@ P A9) (@ P (@ (@ tptp.insert_Code_integer B2) A9)))))) (@ P A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_rat) (P (-> tptp.set_rat Bool))) (=> (@ tptp.finite_finite_rat A) (=> (@ P tptp.bot_bot_set_rat) (=> (forall ((B2 tptp.rat) (A9 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A9) (=> (forall ((X6 tptp.rat)) (=> (@ (@ tptp.member_rat X6) A9) (@ (@ tptp.ord_less_rat X6) B2))) (=> (@ P A9) (@ P (@ (@ tptp.insert_rat B2) A9)))))) (@ P A))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_int) (A2 tptp.int)) (=> (@ tptp.finite_finite_int X4) (=> (not (= X4 tptp.bot_bot_set_int)) (= (@ (@ tptp.ord_less_int (@ tptp.complete_Sup_Sup_int X4)) A2) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) X4) (@ (@ tptp.ord_less_int X2) A2))))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_nat) (A2 tptp.nat)) (=> (@ tptp.finite_finite_nat X4) (=> (not (= X4 tptp.bot_bot_set_nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.complete_Sup_Sup_nat X4)) A2) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) X4) (@ (@ tptp.ord_less_nat X2) A2))))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_Product_unit) (A2 tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit X4) (=> (not (= X4 tptp.bot_bo3957492148770167129t_unit)) (= (@ (@ tptp.ord_le361264281704409273t_unit (@ tptp.comple4687483117567863418t_unit X4)) A2) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) X4) (@ (@ tptp.ord_le361264281704409273t_unit X2) A2))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (M4 tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (= (= (@ tptp.lattic4901227151466704046nteger A) M4) (and (@ (@ tptp.member_Code_integer M4) A) (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X2) A) (@ (@ tptp.ord_le3102999989581377725nteger X2) M4)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (M4 tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (= (@ tptp.lattic1210392890313158908t_unit A) M4) (and (@ (@ tptp.member_Product_unit M4) A) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) A) (@ (@ tptp.ord_le3221252021190050221t_unit X2) M4)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (M4 Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (= (= (@ tptp.lattic1921953407002678535_Max_o A) M4) (and (@ (@ tptp.member_o M4) A) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A) (@ (@ tptp.ord_less_eq_o X2) M4)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_rat) (M4 tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (= (= (@ tptp.lattic7630753665789217321ax_rat A) M4) (and (@ (@ tptp.member_rat M4) A) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.member_rat X2) A) (@ (@ tptp.ord_less_eq_rat X2) M4)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (M4 tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (= (= (@ tptp.lattic8263393255366662781ax_int A) M4) (and (@ (@ tptp.member_int M4) A) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A) (@ (@ tptp.ord_less_eq_int X2) M4)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (M4 tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (= (= (@ tptp.lattic8265883725875713057ax_nat A) M4) (and (@ (@ tptp.member_nat M4) A) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.ord_less_eq_nat X2) M4)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (= (@ (@ tptp.ord_le3102999989581377725nteger X) (@ tptp.lattic4901227151466704046nteger A)) (exists ((X2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X2) A) (@ (@ tptp.ord_le3102999989581377725nteger X) X2))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (@ (@ tptp.ord_le3221252021190050221t_unit X) (@ tptp.lattic1210392890313158908t_unit A)) (exists ((X2 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X2) A) (@ (@ tptp.ord_le3221252021190050221t_unit X) X2))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (= (@ (@ tptp.ord_less_eq_o X) (@ tptp.lattic1921953407002678535_Max_o A)) (exists ((X2 Bool)) (and (@ (@ tptp.member_o X2) A) (@ (@ tptp.ord_less_eq_o X) X2))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_rat) (X tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (= (@ (@ tptp.ord_less_eq_rat X) (@ tptp.lattic7630753665789217321ax_rat A)) (exists ((X2 tptp.rat)) (and (@ (@ tptp.member_rat X2) A) (@ (@ tptp.ord_less_eq_rat X) X2))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (= (@ (@ tptp.ord_less_eq_int X) (@ tptp.lattic8263393255366662781ax_int A)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A) (@ (@ tptp.ord_less_eq_int X) X2))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (= (@ (@ tptp.ord_less_eq_nat X) (@ tptp.lattic8265883725875713057ax_nat A)) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A) (@ (@ tptp.ord_less_eq_nat X) X2))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (M4 tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (= (= M4 (@ tptp.lattic4901227151466704046nteger A)) (and (@ (@ tptp.member_Code_integer M4) A) (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X2) A) (@ (@ tptp.ord_le3102999989581377725nteger X2) M4)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (M4 tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (= M4 (@ tptp.lattic1210392890313158908t_unit A)) (and (@ (@ tptp.member_Product_unit M4) A) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) A) (@ (@ tptp.ord_le3221252021190050221t_unit X2) M4)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (M4 Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (= (= M4 (@ tptp.lattic1921953407002678535_Max_o A)) (and (@ (@ tptp.member_o M4) A) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A) (@ (@ tptp.ord_less_eq_o X2) M4)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_rat) (M4 tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (= (= M4 (@ tptp.lattic7630753665789217321ax_rat A)) (and (@ (@ tptp.member_rat M4) A) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.member_rat X2) A) (@ (@ tptp.ord_less_eq_rat X2) M4)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (M4 tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (= (= M4 (@ tptp.lattic8263393255366662781ax_int A)) (and (@ (@ tptp.member_int M4) A) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A) (@ (@ tptp.ord_less_eq_int X2) M4)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (M4 tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (= (= M4 (@ tptp.lattic8265883725875713057ax_nat A)) (and (@ (@ tptp.member_nat M4) A) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.ord_less_eq_nat X2) M4)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.lattic4901227151466704046nteger A)) X) (forall ((A10 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A10) A) (@ (@ tptp.ord_le3102999989581377725nteger A10) X))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.lattic1210392890313158908t_unit A)) X) (forall ((A10 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A10) A) (@ (@ tptp.ord_le3221252021190050221t_unit A10) X))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ (@ tptp.ord_less_eq_o (@ tptp.lattic1921953407002678535_Max_o A)) X) (forall ((A10 Bool)) (=> (@ (@ tptp.member_o A10) A) (@ (@ tptp.ord_less_eq_o A10) X))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_rat) (X tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.lattic7630753665789217321ax_rat A)) X) (forall ((A10 tptp.rat)) (=> (@ (@ tptp.member_rat A10) A) (@ (@ tptp.ord_less_eq_rat A10) X))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.lattic8263393255366662781ax_int A)) X) (forall ((A10 tptp.int)) (=> (@ (@ tptp.member_int A10) A) (@ (@ tptp.ord_less_eq_int A10) X))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.lattic8265883725875713057ax_nat A)) X) (forall ((A10 tptp.nat)) (=> (@ (@ tptp.member_nat A10) A) (@ (@ tptp.ord_less_eq_nat A10) X))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) A) (@ (@ tptp.ord_le3102999989581377725nteger A4) X))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.lattic4901227151466704046nteger A)) X))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) A) (@ (@ tptp.ord_le3221252021190050221t_unit A4) X))) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.lattic1210392890313158908t_unit A)) X))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) A) (@ (@ tptp.ord_less_eq_o A4) X))) (@ (@ tptp.ord_less_eq_o (@ tptp.lattic1921953407002678535_Max_o A)) X))))))
% 5.65/5.93 (assert (forall ((A tptp.set_rat) (X tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (=> (forall ((A4 tptp.rat)) (=> (@ (@ tptp.member_rat A4) A) (@ (@ tptp.ord_less_eq_rat A4) X))) (@ (@ tptp.ord_less_eq_rat (@ tptp.lattic7630753665789217321ax_rat A)) X))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A) (@ (@ tptp.ord_less_eq_int A4) X))) (@ (@ tptp.ord_less_eq_int (@ tptp.lattic8263393255366662781ax_int A)) X))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A) (@ (@ tptp.ord_less_eq_nat A4) X))) (@ (@ tptp.ord_less_eq_nat (@ tptp.lattic8265883725875713057ax_nat A)) X))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (A2 Bool)) (=> (@ tptp.finite_finite_o A) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) A) (@ (@ tptp.ord_less_eq_o B2) A2))) (= (@ tptp.lattic1921953407002678535_Max_o (@ (@ tptp.insert_o A2) A)) A2)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (A2 tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (forall ((B2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit B2) A) (@ (@ tptp.ord_le3221252021190050221t_unit B2) A2))) (= (@ tptp.lattic1210392890313158908t_unit (@ (@ tptp.insert_Product_unit A2) A)) A2)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (A2 tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) A) (@ (@ tptp.ord_le3102999989581377725nteger B2) A2))) (= (@ tptp.lattic4901227151466704046nteger (@ (@ tptp.insert_Code_integer A2) A)) A2)))))
% 5.65/5.93 (assert (forall ((A tptp.set_rat) (A2 tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (forall ((B2 tptp.rat)) (=> (@ (@ tptp.member_rat B2) A) (@ (@ tptp.ord_less_eq_rat B2) A2))) (= (@ tptp.lattic7630753665789217321ax_rat (@ (@ tptp.insert_rat A2) A)) A2)))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (A2 tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) A) (@ (@ tptp.ord_less_eq_int B2) A2))) (= (@ tptp.lattic8263393255366662781ax_int (@ (@ tptp.insert_int A2) A)) A2)))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (A2 tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) A) (@ (@ tptp.ord_less_eq_nat B2) A2))) (= (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.insert_nat A2) A)) A2)))))
% 5.65/5.93 (assert (forall ((X tptp.product_unit) (S tptp.set_Product_unit)) (=> (@ (@ tptp.member_Product_unit X) S) (@ (@ tptp.ord_le8056459307392131481t_unit (@ (@ tptp.minus_6452836326544984404t_unit S) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit))) S))))
% 5.65/5.93 (assert (forall ((X Bool) (S tptp.set_o)) (=> (@ (@ tptp.member_o X) S) (@ (@ tptp.ord_less_set_o (@ (@ tptp.minus_minus_set_o S) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))) S))))
% 5.65/5.93 (assert (forall ((X tptp.int) (S tptp.set_int)) (=> (@ (@ tptp.member_int X) S) (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int S) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) S))))
% 5.65/5.93 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (S tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o X) S) (@ (@ tptp.ord_le2453136405763929_nat_o (@ (@ tptp.minus_1801376950450012436_nat_o S) (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o))) S))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (S tptp.set_nat)) (=> (@ (@ tptp.member_nat X) S) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat S) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) S))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_int)) (=> (@ tptp.finite_finite_int X4) (=> (not (= X4 tptp.bot_bot_set_int)) (= (@ tptp.complete_Sup_Sup_int X4) (@ tptp.lattic8263393255366662781ax_int X4))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit X4) (=> (not (= X4 tptp.bot_bo3957492148770167129t_unit)) (= (@ tptp.comple4687483117567863418t_unit X4) (@ tptp.lattic1210392890313158908t_unit X4))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat X4) (=> (not (= X4 tptp.bot_bot_set_nat)) (= (@ tptp.complete_Sup_Sup_nat X4) (@ tptp.lattic8265883725875713057ax_nat X4))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (@ tptp.lattic1210392890313158908t_unit A) (@ tptp.comple4687483117567863418t_unit A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (= (@ (@ tptp.ord_le8056459307392131481t_unit (@ (@ tptp.minus_6452836326544984404t_unit A) B4)) A) (not (= (@ (@ tptp.inf_in4660618365625256667t_unit A) B4) tptp.bot_bo3957492148770167129t_unit)))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (= (@ (@ tptp.ord_less_set_o (@ (@ tptp.minus_minus_set_o A) B4)) A) (not (= (@ (@ tptp.inf_inf_set_o A) B4) tptp.bot_bot_set_o)))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A) B4)) A) (not (= (@ (@ tptp.inf_inf_set_int A) B4) tptp.bot_bot_set_int)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.ord_le2453136405763929_nat_o (@ (@ tptp.minus_1801376950450012436_nat_o A) B4)) A) (not (= (@ (@ tptp.inf_in1906310914598751387_nat_o A) B4) tptp.bot_bo7824918357723582233_nat_o)))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A) B4)) A) (not (= (@ (@ tptp.inf_inf_set_nat A) B4) tptp.bot_bot_set_nat)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A2 tptp.code_integer) (X tptp.code_integer)) (=> (= (@ (@ tptp.image_4470545334726330049nteger F) tptp.top_to4645266643341252675nteger) (@ (@ tptp.insert_Code_integer A2) tptp.bot_bo3990330152332043303nteger)) (= (@ F X) A2))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.product_unit)) (A2 tptp.product_unit) (X tptp.product_unit)) (=> (= (@ (@ tptp.image_405062704495631173t_unit F) tptp.top_to1996260823553986621t_unit) (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit)) (= (@ F X) A2))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit Bool)) (A2 Bool) (X tptp.product_unit)) (=> (= (@ (@ tptp.image_Product_unit_o2 F) tptp.top_to1996260823553986621t_unit) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o)) (= (@ F X) A2))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.nat)) (A2 tptp.nat) (X tptp.product_unit)) (=> (= (@ (@ tptp.image_875570014554754200it_nat F) tptp.top_to1996260823553986621t_unit) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat)) (= (@ F X) A2))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.int)) (A2 tptp.int) (X tptp.product_unit)) (=> (= (@ (@ tptp.image_873079544045703924it_int F) tptp.top_to1996260823553986621t_unit) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int)) (= (@ F X) A2))))
% 5.65/5.93 (assert (forall ((F (-> Bool tptp.product_unit)) (A2 tptp.product_unit) (X Bool)) (=> (= (@ (@ tptp.image_o_Product_unit2 F) tptp.top_top_set_o) (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit)) (= (@ F X) A2))))
% 5.65/5.93 (assert (forall ((F (-> Bool Bool)) (A2 Bool) (X Bool)) (=> (= (@ (@ tptp.image_o_o2 F) tptp.top_top_set_o) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o)) (= (@ F X) A2))))
% 5.65/5.93 (assert (forall ((F (-> Bool tptp.nat)) (A2 tptp.nat) (X Bool)) (=> (= (@ (@ tptp.image_o_nat2 F) tptp.top_top_set_o) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat)) (= (@ F X) A2))))
% 5.65/5.93 (assert (forall ((F (-> Bool tptp.int)) (A2 tptp.int) (X Bool)) (=> (= (@ (@ tptp.image_o_int2 F) tptp.top_top_set_o) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int)) (= (@ F X) A2))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A2 tptp.code_integer) (X tptp.nat)) (=> (= (@ (@ tptp.image_1215581382706833972nteger F) tptp.top_top_set_nat) (@ (@ tptp.insert_Code_integer A2) tptp.bot_bo3990330152332043303nteger)) (= (@ F X) A2))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_int) (Y tptp.int)) (=> (not (= X4 tptp.bot_bot_set_int)) (=> (@ tptp.condit2212336002400062152ve_int X4) (= (@ (@ tptp.ord_less_int Y) (@ tptp.complete_Sup_Sup_int X4)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) X4) (@ (@ tptp.ord_less_int Y) X2))))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_nat) (Y tptp.nat)) (=> (not (= X4 tptp.bot_bot_set_nat)) (=> (@ tptp.condit2214826472909112428ve_nat X4) (= (@ (@ tptp.ord_less_nat Y) (@ tptp.complete_Sup_Sup_nat X4)) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) X4) (@ (@ tptp.ord_less_nat Y) X2))))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_Product_unit) (Y tptp.product_unit)) (=> (not (= X4 tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit2080475194861589617t_unit X4) (= (@ (@ tptp.ord_le361264281704409273t_unit Y) (@ tptp.comple4687483117567863418t_unit X4)) (exists ((X2 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X2) X4) (@ (@ tptp.ord_le361264281704409273t_unit Y) X2))))))))
% 5.65/5.93 (assert (forall ((R2 tptp.set_Pr5094982260447487303t_unit) (A2 tptp.product_unit)) (let ((_let_1 (@ tptp.field_Product_unit R2))) (=> (not (= _let_1 tptp.bot_bo3957492148770167129t_unit)) (@ (@ tptp.ord_le8056459307392131481t_unit (@ (@ tptp.order_5809128134054296019t_unit R2) A2)) _let_1)))))
% 5.65/5.93 (assert (forall ((R2 tptp.set_Product_prod_o_o) (A2 Bool)) (let ((_let_1 (@ tptp.field_o R2))) (=> (not (= _let_1 tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_set_o (@ (@ tptp.order_underS_o R2) A2)) _let_1)))))
% 5.65/5.93 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.field_nat R2))) (=> (not (= _let_1 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.order_underS_nat R2) A2)) _let_1)))))
% 5.65/5.93 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (A2 tptp.int)) (let ((_let_1 (@ tptp.field_int R2))) (=> (not (= _let_1 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int (@ (@ tptp.order_underS_int R2) A2)) _let_1)))))
% 5.65/5.93 (assert (forall ((R2 tptp.set_Pr2161125870931222855_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.field_81821745747897882_nat_o R2))) (=> (not (= _let_1 tptp.bot_bo7824918357723582233_nat_o)) (@ (@ tptp.ord_le2453136405763929_nat_o (@ (@ tptp.order_7262550146012401043_nat_o R2) A2)) _let_1)))))
% 5.65/5.93 (assert (forall ((S tptp.set_Code_integer) (F (-> tptp.code_integer tptp.assn))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (not (= S tptp.bot_bo3990330152332043303nteger)) (not (exists ((X6 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X6) S) (@ (@ tptp.ord_less_assn (@ F X6)) (@ F (@ (@ tptp.lattic4682378690128378784r_assn F) S))))))))))
% 5.65/5.93 (assert (forall ((S tptp.set_Product_unit) (F (-> tptp.product_unit tptp.assn))) (=> (@ tptp.finite4290736615968046902t_unit S) (=> (not (= S tptp.bot_bo3957492148770167129t_unit)) (not (exists ((X6 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X6) S) (@ (@ tptp.ord_less_assn (@ F X6)) (@ F (@ (@ tptp.lattic4376901495776413404t_assn F) S))))))))))
% 5.65/5.93 (assert (forall ((S tptp.set_o) (F (-> Bool tptp.assn))) (=> (@ tptp.finite_finite_o S) (=> (not (= S tptp.bot_bot_set_o)) (not (exists ((X6 Bool)) (and (@ (@ tptp.member_o X6) S) (@ (@ tptp.ord_less_assn (@ F X6)) (@ F (@ (@ tptp.lattic7708394068118247271o_assn F) S))))))))))
% 5.65/5.93 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.assn))) (=> (@ tptp.finite_finite_nat S) (=> (not (= S tptp.bot_bot_set_nat)) (not (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) S) (@ (@ tptp.ord_less_assn (@ F X6)) (@ F (@ (@ tptp.lattic2187264146484958483t_assn F) S))))))))))
% 5.65/5.93 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.assn))) (=> (@ tptp.finite_finite_int S) (=> (not (= S tptp.bot_bot_set_int)) (not (exists ((X6 tptp.int)) (and (@ (@ tptp.member_int X6) S) (@ (@ tptp.ord_less_assn (@ F X6)) (@ F (@ (@ tptp.lattic3162799611691135855t_assn F) S))))))))))
% 5.65/5.93 (assert (forall ((S tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (not (= S tptp.bot_bo3990330152332043303nteger)) (not (exists ((X6 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X6) S) (@ (@ tptp.ord_less_nat (@ F X6)) (@ F (@ (@ tptp.lattic6074936555552774728er_nat F) S))))))))))
% 5.65/5.93 (assert (forall ((S tptp.set_Product_unit) (F (-> tptp.product_unit tptp.nat))) (=> (@ tptp.finite4290736615968046902t_unit S) (=> (not (= S tptp.bot_bo3957492148770167129t_unit)) (not (exists ((X6 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X6) S) (@ (@ tptp.ord_less_nat (@ F X6)) (@ F (@ (@ tptp.lattic1360832392136924548it_nat F) S))))))))))
% 5.65/5.93 (assert (forall ((S tptp.set_o) (F (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o S) (=> (not (= S tptp.bot_bot_set_o)) (not (exists ((X6 Bool)) (and (@ (@ tptp.member_o X6) S) (@ (@ tptp.ord_less_nat (@ F X6)) (@ F (@ (@ tptp.lattic2775856028456453135_o_nat F) S))))))))))
% 5.65/5.93 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S) (=> (not (= S tptp.bot_bot_set_nat)) (not (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) S) (@ (@ tptp.ord_less_nat (@ F X6)) (@ F (@ (@ tptp.lattic7446932960582359483at_nat F) S))))))))))
% 5.65/5.93 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int S) (=> (not (= S tptp.bot_bot_set_int)) (not (exists ((X6 tptp.int)) (and (@ (@ tptp.member_int X6) S) (@ (@ tptp.ord_less_nat (@ F X6)) (@ F (@ (@ tptp.lattic8446286672483414039nt_nat F) S))))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_set_Product_unit)) (=> (@ tptp.finite1772178364199683094t_unit A) (= (@ tptp.comple3349607820504768346t_unit A) (@ (@ (@ tptp.finite4243028863286625800t_unit tptp.sup_su793286257634532545t_unit) tptp.bot_bo3957492148770167129t_unit) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_set_o)) (=> (@ tptp.finite_finite_set_o A) (= (@ tptp.comple90263536869209701_set_o A) (@ (@ (@ tptp.finite4337638375924247368_set_o tptp.sup_sup_set_o) tptp.bot_bot_set_o) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (= (@ tptp.comple7399068483239264473et_nat A) (@ (@ (@ tptp.finite677925301803182934et_nat tptp.sup_sup_set_nat) tptp.bot_bot_set_nat) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_set_int)) (=> (@ tptp.finite6197958912794628473et_int A) (= (@ tptp.comple3221217463730067765et_int A) (@ (@ (@ tptp.finite2508883933289561102et_int tptp.sup_sup_set_int) tptp.bot_bot_set_int) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_se1353816476878259085_nat_o)) (=> (@ tptp.finite6069017635265841110_nat_o A) (= (@ tptp.comple3382087578465172250_nat_o A) (@ (@ (@ tptp.finite8456856254070787592_nat_o tptp.sup_su5209123915105501825_nat_o) tptp.bot_bo7824918357723582233_nat_o) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (= (@ tptp.comple4687483117567863418t_unit A) (@ (@ (@ tptp.finite8834431295148555784t_unit tptp.sup_sup_Product_unit) tptp.bot_bot_Product_unit) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.product_unit))) (=> (@ tptp.finite_finite_nat A) (= (@ tptp.comple4687483117567863418t_unit (@ (@ tptp.image_8730104196221521654t_unit F) A)) (@ (@ (@ tptp.finite6602901031542678131t_unit (@ (@ tptp.comp_P6204500334276302049it_nat tptp.sup_sup_Product_unit) F)) tptp.bot_bot_Product_unit) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.product_unit))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ tptp.comple4687483117567863418t_unit (@ (@ tptp.image_7182656606676592809t_unit F) A)) (@ (@ (@ tptp.finite2281032298429728806t_unit (@ (@ tptp.comp_P4558236313141964142nteger tptp.sup_sup_Product_unit) F)) tptp.bot_bot_Product_unit) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.set_Product_unit))) (=> (@ tptp.finite_finite_nat A) (= (@ tptp.comple3349607820504768346t_unit (@ (@ tptp.image_4824033694279209942t_unit F) A)) (@ (@ (@ tptp.finite9145781422887121747t_unit (@ (@ tptp.comp_s6943286182646368705it_nat tptp.sup_su793286257634532545t_unit) F)) tptp.bot_bo3957492148770167129t_unit) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.set_Product_unit))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ tptp.comple3349607820504768346t_unit (@ (@ tptp.image_5870443399019143561t_unit F) A)) (@ (@ (@ tptp.finite3687622995246107910t_unit (@ (@ tptp.comp_s3199726385246003790nteger tptp.sup_su793286257634532545t_unit) F)) tptp.bot_bo3957492148770167129t_unit) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.set_o))) (=> (@ tptp.finite_finite_nat A) (= (@ tptp.comple90263536869209701_set_o (@ (@ tptp.image_nat_set_o F) A)) (@ (@ (@ tptp.finite3217087857726763998_set_o (@ (@ tptp.comp_s4424444925706540684_o_nat tptp.sup_sup_set_o) F)) tptp.bot_bot_set_o) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.set_o))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ tptp.comple90263536869209701_set_o (@ (@ tptp.image_1867029960091478804_set_o F) A)) (@ (@ (@ tptp.finite1928688952044918289_set_o (@ (@ tptp.comp_s90868338361139993nteger tptp.sup_sup_set_o) F)) tptp.bot_bot_set_o) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.set_nat))) (=> (@ tptp.finite_finite_nat A) (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat F) A)) (@ (@ (@ tptp.finite5529483035118572448et_nat (@ (@ tptp.comp_s2351873599094224870at_nat tptp.sup_sup_set_nat) F)) tptp.bot_bot_set_nat) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.set_nat))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_8829277216472192490et_nat F) A)) (@ (@ (@ tptp.finite1590314701948642349et_nat (@ (@ tptp.comp_s3169385134670675059nteger tptp.sup_sup_set_nat) F)) tptp.bot_bot_set_nat) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.set_int))) (=> (@ tptp.finite_finite_nat A) (= (@ tptp.comple3221217463730067765et_int (@ (@ tptp.image_nat_set_int F) A)) (@ (@ (@ tptp.finite1351632015609375740et_int (@ (@ tptp.comp_s6689493721604790522nt_nat tptp.sup_sup_set_int) F)) tptp.bot_bot_set_int) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.set_int))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ tptp.comple3221217463730067765et_int (@ (@ tptp.image_4651426196962995782et_int F) A)) (@ (@ (@ tptp.finite6635835719294221449et_int (@ (@ tptp.comp_s3634918272309710215nteger tptp.sup_sup_set_int) F)) tptp.bot_bot_set_int) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (B9 tptp.set_set_Code_integer) (A11 tptp.set_set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) (@ tptp.comple739944243200306918nteger B9)) (=> (not (= B9 tptp.bot_bo9204850693367297629nteger)) (=> (@ (@ (@ tptp.pred_c5891848916688490280nteger A11) tptp.ord_le1307284697595431911nteger) B9) (not (forall ((B5 tptp.set_Code_integer)) (=> (@ (@ tptp.member1834298987299537450nteger B5) B9) (not (@ (@ tptp.ord_le7084787975880047091nteger A) B5)))))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (B9 tptp.set_set_nat) (A11 tptp.set_set_nat)) (=> (@ tptp.finite_finite_nat A) (=> (@ (@ tptp.ord_less_eq_set_nat A) (@ tptp.comple7399068483239264473et_nat B9)) (=> (not (= B9 tptp.bot_bot_set_set_nat)) (=> (@ (@ (@ tptp.pred_chain_set_nat A11) tptp.ord_less_set_nat) B9) (not (forall ((B5 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat B5) B9) (not (@ (@ tptp.ord_less_eq_set_nat A) B5)))))))))))
% 5.65/5.93 (assert (= (@ (@ tptp.times_times_assn tptp.top_top_assn) tptp.top_top_assn) tptp.top_top_assn))
% 5.65/5.93 (assert (not (= tptp.top_top_assn tptp.bot_bot_assn)))
% 5.65/5.93 (assert (not (= tptp.top_top_assn tptp.one_one_assn)))
% 5.65/5.93 (assert (forall ((H2 tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn tptp.top_top_assn) H2) (@ tptp.in_range H2))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer)) (Fg (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger))) (= (= (@ (@ tptp.comp_C1593894019821074884nteger F) G) Fg) (forall ((X2 tptp.code_integer)) (= (@ F (@ G X2)) (@ Fg X2))))))
% 5.65/5.93 (assert (forall ((F (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (Fg (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger))) (= (= (@ (@ tptp.comp_C8797469213163452608nteger F) G) Fg) (forall ((X2 tptp.code_integer)) (= (@ F (@ G X2)) (@ Fg X2))))))
% 5.65/5.93 (assert (forall ((X (-> tptp.code_integer tptp.code_integer)) (Y (-> tptp.code_integer tptp.code_integer)) (F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger))) (let ((_let_1 (@ tptp.comp_C1593894019821074884nteger F))) (=> (= X Y) (= (@ _let_1 X) (@ _let_1 Y))))))
% 5.65/5.93 (assert (forall ((X (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (Y (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (F (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger))) (let ((_let_1 (@ tptp.comp_C8797469213163452608nteger F))) (=> (= X Y) (= (@ _let_1 X) (@ _let_1 Y))))))
% 5.65/5.93 (assert (forall ((X (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (Y (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (F (-> tptp.code_integer tptp.code_integer))) (=> (= X Y) (= (@ (@ tptp.comp_C1593894019821074884nteger X) F) (@ (@ tptp.comp_C1593894019821074884nteger Y) F)))))
% 5.65/5.93 (assert (forall ((X (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (Y (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (F (-> tptp.code_integer tptp.code_integer tptp.code_integer))) (=> (= X Y) (= (@ (@ tptp.comp_C8797469213163452608nteger X) F) (@ (@ tptp.comp_C8797469213163452608nteger Y) F)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer)) (X tptp.code_integer) (H2 (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (K3 (-> tptp.code_integer tptp.code_integer))) (=> (= (@ F (@ G X)) (@ H2 (@ K3 X))) (= (@ (@ (@ tptp.comp_C1593894019821074884nteger F) G) X) (@ (@ (@ tptp.comp_C1593894019821074884nteger H2) K3) X)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer)) (X tptp.code_integer) (H2 (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (K3 (-> tptp.code_integer tptp.code_integer tptp.code_integer))) (=> (= (@ F (@ G X)) (@ H2 (@ K3 X))) (= (@ (@ (@ tptp.comp_C1593894019821074884nteger F) G) X) (@ (@ (@ tptp.comp_C8797469213163452608nteger H2) K3) X)))))
% 5.65/5.93 (assert (forall ((F (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (X tptp.code_integer) (H2 (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (K3 (-> tptp.code_integer tptp.code_integer))) (=> (= (@ F (@ G X)) (@ H2 (@ K3 X))) (= (@ (@ (@ tptp.comp_C8797469213163452608nteger F) G) X) (@ (@ (@ tptp.comp_C1593894019821074884nteger H2) K3) X)))))
% 5.65/5.93 (assert (forall ((F (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (X tptp.code_integer) (H2 (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (K3 (-> tptp.code_integer tptp.code_integer tptp.code_integer))) (=> (= (@ F (@ G X)) (@ H2 (@ K3 X))) (= (@ (@ (@ tptp.comp_C8797469213163452608nteger F) G) X) (@ (@ (@ tptp.comp_C8797469213163452608nteger H2) K3) X)))))
% 5.65/5.93 (assert (forall ((Rep2 (-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.code_integer)) (Abs2 (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (S (-> tptp.code_integer tptp.set_nat)) (M (-> tptp.code_integer tptp.code_integer)) (F (-> tptp.nat tptp.nat)) (S4 (-> tptp.code_integer tptp.set_nat)) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.comp_s4605850120322998606nteger (@ tptp.image_nat_nat2 F)))) (=> (@ (@ (@ tptp.type_d6544512618915850416nteger Rep2) Abs2) tptp.top_to4645266643341252675nteger) (=> (= (@ (@ tptp.comp_C6537567860429791781nteger S) M) (@ _let_1 S4)) (= (@ (@ tptp.comp_P8262219321096090349nteger (@ (@ tptp.comp_C3184339336801759213nteger S) Rep2)) (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C1593894019821074884nteger Abs2) M)) G)) (@ _let_1 (@ (@ tptp.comp_C6537567860429791781nteger S4) G))))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.code_integer)) (Abs2 (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (S (-> tptp.code_integer tptp.set_Code_integer)) (M (-> tptp.code_integer tptp.code_integer)) (F (-> tptp.code_integer tptp.code_integer)) (S4 (-> tptp.code_integer tptp.set_Code_integer)) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.comp_s956550612328592744nteger (@ tptp.image_4470545334726330049nteger F)))) (=> (@ (@ (@ tptp.type_d6544512618915850416nteger Rep2) Abs2) tptp.top_to4645266643341252675nteger) (=> (= (@ (@ tptp.comp_C8186931911283765298nteger S) M) (@ _let_1 S4)) (= (@ (@ tptp.comp_P4885729792186999034nteger (@ (@ tptp.comp_C6344129587964912378nteger S) Rep2)) (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C1593894019821074884nteger Abs2) M)) G)) (@ _let_1 (@ (@ tptp.comp_C8186931911283765298nteger S4) G))))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.code_integer)) (Abs2 (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (S (-> tptp.code_integer tptp.set_Code_integer)) (M (-> tptp.code_integer tptp.code_integer)) (F (-> tptp.nat tptp.code_integer)) (S4 (-> tptp.code_integer tptp.set_nat)) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.comp_s8292494440407567195nteger (@ tptp.image_1215581382706833972nteger F)))) (=> (@ (@ (@ tptp.type_d6544512618915850416nteger Rep2) Abs2) tptp.top_to4645266643341252675nteger) (=> (= (@ (@ tptp.comp_C8186931911283765298nteger S) M) (@ _let_1 S4)) (= (@ (@ tptp.comp_P4885729792186999034nteger (@ (@ tptp.comp_C6344129587964912378nteger S) Rep2)) (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C1593894019821074884nteger Abs2) M)) G)) (@ _let_1 (@ (@ tptp.comp_C6537567860429791781nteger S4) G))))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.product_unit)) (Abs2 (-> tptp.product_unit tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (S (-> tptp.product_unit tptp.set_nat)) (M (-> tptp.code_integer tptp.product_unit)) (F (-> tptp.nat tptp.nat)) (S4 (-> tptp.code_integer tptp.set_nat)) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.comp_s4605850120322998606nteger (@ tptp.image_nat_nat2 F)))) (=> (@ (@ (@ tptp.type_d6996789741066924922t_unit Rep2) Abs2) tptp.top_to1996260823553986621t_unit) (=> (= (@ (@ tptp.comp_P5878433733084393551nteger S) M) (@ _let_1 S4)) (= (@ (@ tptp.comp_P8262219321096090349nteger (@ (@ tptp.comp_P6101996899264665623nteger S) Rep2)) (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_P4511551582283981294nteger Abs2) M)) G)) (@ _let_1 (@ (@ tptp.comp_C6537567860429791781nteger S4) G))))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.product_unit)) (Abs2 (-> tptp.product_unit tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (S (-> tptp.product_unit tptp.set_Code_integer)) (M (-> tptp.code_integer tptp.product_unit)) (F (-> tptp.code_integer tptp.code_integer)) (S4 (-> tptp.code_integer tptp.set_Code_integer)) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.comp_s956550612328592744nteger (@ tptp.image_4470545334726330049nteger F)))) (=> (@ (@ (@ tptp.type_d6996789741066924922t_unit Rep2) Abs2) tptp.top_to1996260823553986621t_unit) (=> (= (@ (@ tptp.comp_P4767411901762164316nteger S) M) (@ _let_1 S4)) (= (@ (@ tptp.comp_P4885729792186999034nteger (@ (@ tptp.comp_P4635212033913086756nteger S) Rep2)) (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_P4511551582283981294nteger Abs2) M)) G)) (@ _let_1 (@ (@ tptp.comp_C8186931911283765298nteger S4) G))))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.product_unit)) (Abs2 (-> tptp.product_unit tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (S (-> tptp.product_unit tptp.set_Code_integer)) (M (-> tptp.code_integer tptp.product_unit)) (F (-> tptp.nat tptp.code_integer)) (S4 (-> tptp.code_integer tptp.set_nat)) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.comp_s8292494440407567195nteger (@ tptp.image_1215581382706833972nteger F)))) (=> (@ (@ (@ tptp.type_d6996789741066924922t_unit Rep2) Abs2) tptp.top_to1996260823553986621t_unit) (=> (= (@ (@ tptp.comp_P4767411901762164316nteger S) M) (@ _let_1 S4)) (= (@ (@ tptp.comp_P4885729792186999034nteger (@ (@ tptp.comp_P4635212033913086756nteger S) Rep2)) (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_P4511551582283981294nteger Abs2) M)) G)) (@ _let_1 (@ (@ tptp.comp_C6537567860429791781nteger S4) G))))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) Bool)) (Abs2 (-> Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (S (-> Bool tptp.set_nat)) (M (-> tptp.code_integer Bool)) (F (-> tptp.nat tptp.nat)) (S4 (-> tptp.code_integer tptp.set_nat)) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.comp_s4605850120322998606nteger (@ tptp.image_nat_nat2 F)))) (=> (@ (@ (@ tptp.type_d5661033022651575429eger_o Rep2) Abs2) tptp.top_top_set_o) (=> (= (@ (@ tptp.comp_o172754640513974618nteger S) M) (@ _let_1 S4)) (= (@ (@ tptp.comp_P8262219321096090349nteger (@ (@ tptp.comp_o1289984117834210338nteger S) Rep2)) (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_o8922910837708301817nteger Abs2) M)) G)) (@ _let_1 (@ (@ tptp.comp_C6537567860429791781nteger S4) G))))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) Bool)) (Abs2 (-> Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (S (-> Bool tptp.set_Code_integer)) (M (-> tptp.code_integer Bool)) (F (-> tptp.code_integer tptp.code_integer)) (S4 (-> tptp.code_integer tptp.set_Code_integer)) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.comp_s956550612328592744nteger (@ tptp.image_4470545334726330049nteger F)))) (=> (@ (@ (@ tptp.type_d5661033022651575429eger_o Rep2) Abs2) tptp.top_top_set_o) (=> (= (@ (@ tptp.comp_o4291842030903409511nteger S) M) (@ _let_1 S4)) (= (@ (@ tptp.comp_P4885729792186999034nteger (@ (@ tptp.comp_o7929101295636871983nteger S) Rep2)) (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_o8922910837708301817nteger Abs2) M)) G)) (@ _let_1 (@ (@ tptp.comp_C8186931911283765298nteger S4) G))))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) Bool)) (Abs2 (-> Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (S (-> Bool tptp.set_Code_integer)) (M (-> tptp.code_integer Bool)) (F (-> tptp.nat tptp.code_integer)) (S4 (-> tptp.code_integer tptp.set_nat)) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.comp_s8292494440407567195nteger (@ tptp.image_1215581382706833972nteger F)))) (=> (@ (@ (@ tptp.type_d5661033022651575429eger_o Rep2) Abs2) tptp.top_top_set_o) (=> (= (@ (@ tptp.comp_o4291842030903409511nteger S) M) (@ _let_1 S4)) (= (@ (@ tptp.comp_P4885729792186999034nteger (@ (@ tptp.comp_o7929101295636871983nteger S) Rep2)) (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_o8922910837708301817nteger Abs2) M)) G)) (@ _let_1 (@ (@ tptp.comp_C6537567860429791781nteger S4) G))))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> (-> tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.nat)) (Abs2 (-> tptp.nat tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (S (-> tptp.nat tptp.set_nat)) (M (-> tptp.code_integer tptp.nat)) (F (-> tptp.nat tptp.nat)) (S4 (-> tptp.code_integer tptp.set_nat)) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.comp_s4605850120322998606nteger (@ tptp.image_nat_nat2 F)))) (=> (@ (@ (@ tptp.type_d6278479724763174947er_nat Rep2) Abs2) tptp.top_top_set_nat) (=> (= (@ (@ tptp.comp_n5963683855531483544nteger S) M) (@ _let_1 S4)) (= (@ (@ tptp.comp_P8262219321096090349nteger (@ (@ tptp.comp_n3623798160786426464nteger S) Rep2)) (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_n2033352843805742135nteger Abs2) M)) G)) (@ _let_1 (@ (@ tptp.comp_C6537567860429791781nteger S4) G))))))))
% 5.65/5.93 (assert (= tptp.top_to2462227307520033056at_o_o (lambda ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o X2) tptp.top_to4869887016220417533_nat_o))))
% 5.65/5.93 (assert (= tptp.top_to2465898995584390880unit_o (lambda ((X2 tptp.product_unit)) (@ (@ tptp.member_Product_unit X2) tptp.top_to1996260823553986621t_unit))))
% 5.65/5.93 (assert (= tptp.top_top_o_o (lambda ((X2 Bool)) (@ (@ tptp.member_o X2) tptp.top_top_set_o))))
% 5.65/5.93 (assert (= tptp.top_top_nat_o (lambda ((X2 tptp.nat)) (@ (@ tptp.member_nat X2) tptp.top_top_set_nat))))
% 5.65/5.93 (assert (= tptp.top_top_int_o (lambda ((X2 tptp.int)) (@ (@ tptp.member_int X2) tptp.top_top_set_int))))
% 5.65/5.93 (assert (= tptp.top_to4869887016220417533_nat_o (@ tptp.collec939566748876313656_nat_o tptp.top_to2462227307520033056at_o_o)))
% 5.65/5.93 (assert (= tptp.top_to1996260823553986621t_unit (@ tptp.collect_Product_unit tptp.top_to2465898995584390880unit_o)))
% 5.65/5.93 (assert (= tptp.top_top_set_o (@ tptp.collect_o tptp.top_top_o_o)))
% 5.65/5.93 (assert (= tptp.top_top_set_nat (@ tptp.collect_nat tptp.top_top_nat_o)))
% 5.65/5.93 (assert (= tptp.top_top_set_int (@ tptp.collect_int tptp.top_top_int_o)))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (P (-> tptp.product_unit tptp.product_unit Bool))) (@ (@ (@ tptp.pred_c6915491785556283576t_unit A) P) tptp.bot_bo3957492148770167129t_unit)))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (P (-> Bool Bool Bool))) (@ (@ (@ tptp.pred_chain_o A) P) tptp.bot_bot_set_o)))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (P (-> tptp.nat tptp.nat Bool))) (@ (@ (@ tptp.pred_chain_nat A) P) tptp.bot_bot_set_nat)))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (P (-> tptp.int tptp.int Bool))) (@ (@ (@ tptp.pred_chain_int A) P) tptp.bot_bot_set_int)))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (@ (@ (@ tptp.pred_c177362287423414904_nat_o A) P) tptp.bot_bo7824918357723582233_nat_o)))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (X4 tptp.set_Code_integer) (G1 (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G2 (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger))) (=> (= (@ (@ tptp.image_2177946750938214461nteger F) X4) tptp.top_to3804862627464599871nteger) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) X4) (= (@ (@ (@ tptp.comp_C8797469213163452608nteger G1) F) X3) (@ (@ (@ tptp.comp_C8797469213163452608nteger G2) F) X3)))) (= G1 G2)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (X4 tptp.set_Code_integer) (G1 (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G2 (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger))) (=> (= (@ (@ tptp.image_4470545334726330049nteger F) X4) tptp.top_to4645266643341252675nteger) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) X4) (= (@ (@ (@ tptp.comp_C1593894019821074884nteger G1) F) X3) (@ (@ (@ tptp.comp_C1593894019821074884nteger G2) F) X3)))) (= G1 G2)))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.code_integer)) (Abs2 (-> tptp.code_integer tptp.code_integer)) (M (-> tptp.code_integer tptp.code_integer)) (M1 (-> tptp.code_integer tptp.code_integer)) (M22 (-> tptp.code_integer tptp.code_integer)) (F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.comp_C1593894019821074884nteger F))) (=> (@ (@ (@ tptp.type_d4796611474492816872nteger Rep2) Abs2) tptp.top_to4645266643341252675nteger) (=> (= M (@ (@ tptp.comp_C7449957260575251196nteger M1) M22)) (= (@ (@ tptp.comp_C1593894019821074884nteger (@ _let_1 M)) G) (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C1593894019821074884nteger (@ _let_1 M1)) Rep2)) (@ (@ tptp.comp_C7449957260575251196nteger (@ (@ tptp.comp_C7449957260575251196nteger Abs2) M22)) G))))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.product_unit)) (Abs2 (-> tptp.product_unit tptp.code_integer)) (M (-> tptp.code_integer tptp.code_integer)) (M1 (-> tptp.product_unit tptp.code_integer)) (M22 (-> tptp.code_integer tptp.product_unit)) (F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer))) (=> (@ (@ (@ tptp.type_d9006111508436661314t_unit Rep2) Abs2) tptp.top_to1996260823553986621t_unit) (=> (= M (@ (@ tptp.comp_P6790823133229852966nteger M1) M22)) (= (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C1593894019821074884nteger F) M)) G) (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_P4511551582283981294nteger (@ (@ tptp.comp_C5854136495726678886t_unit F) M1)) Rep2)) (@ (@ tptp.comp_C7449957260575251196nteger (@ (@ tptp.comp_P6790823133229852966nteger Abs2) M22)) G)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer Bool)) (Abs2 (-> Bool tptp.code_integer)) (M (-> tptp.code_integer tptp.code_integer)) (M1 (-> Bool tptp.code_integer)) (M22 (-> tptp.code_integer Bool)) (F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer))) (=> (@ (@ (@ tptp.type_d6812736842639505741eger_o Rep2) Abs2) tptp.top_top_set_o) (=> (= M (@ (@ tptp.comp_o1085144040659434033nteger M1) M22)) (= (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C1593894019821074884nteger F) M)) G) (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_o8922910837708301817nteger (@ (@ tptp.comp_C5733264393235242609eger_o F) M1)) Rep2)) (@ (@ tptp.comp_C7449957260575251196nteger (@ (@ tptp.comp_o1085144040659434033nteger Abs2) M22)) G)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.nat)) (Abs2 (-> tptp.nat tptp.code_integer)) (M (-> tptp.code_integer tptp.code_integer)) (M1 (-> tptp.nat tptp.code_integer)) (M22 (-> tptp.code_integer tptp.nat)) (F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer))) (=> (@ (@ (@ tptp.type_d8368584451094728027er_nat Rep2) Abs2) tptp.top_top_set_nat) (=> (= M (@ (@ tptp.comp_n6876073255676942959nteger M1) M22)) (= (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C1593894019821074884nteger F) M)) G) (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_n2033352843805742135nteger (@ (@ tptp.comp_C836733381939181879er_nat F) M1)) Rep2)) (@ (@ tptp.comp_C7449957260575251196nteger (@ (@ tptp.comp_n6876073255676942959nteger Abs2) M22)) G)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (M (-> tptp.code_integer tptp.code_integer)) (M1 (-> tptp.int tptp.code_integer)) (M22 (-> tptp.code_integer tptp.int)) (F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer))) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) tptp.top_top_set_int) (=> (= M (@ (@ tptp.comp_i6014793192326455499nteger M1) M22)) (= (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C1593894019821074884nteger F) M)) G) (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_i2874689474467862163nteger (@ (@ tptp.comp_C834242911430131603er_int F) M1)) Rep2)) (@ (@ tptp.comp_C7449957260575251196nteger (@ (@ tptp.comp_i6014793192326455499nteger Abs2) M22)) G)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.product_unit Bool)) (Abs2 (-> Bool tptp.product_unit)) (M (-> tptp.code_integer tptp.code_integer)) (M1 (-> Bool tptp.code_integer)) (M22 (-> tptp.code_integer Bool)) (F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer))) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep2) Abs2) tptp.top_top_set_o) (=> (= M (@ (@ tptp.comp_o1085144040659434033nteger M1) M22)) (= (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C1593894019821074884nteger F) M)) G) (@ (@ tptp.comp_P4511551582283981294nteger (@ (@ tptp.comp_o6961622296474427249t_unit (@ (@ tptp.comp_C5733264393235242609eger_o F) M1)) Rep2)) (@ (@ tptp.comp_C8146212659816229034nteger (@ (@ tptp.comp_o6635994240230588853nteger Abs2) M22)) G)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_natural tptp.nat)) (Abs2 (-> tptp.nat tptp.code_natural)) (M (-> tptp.code_integer tptp.code_integer)) (M1 (-> tptp.nat tptp.code_integer)) (M22 (-> tptp.code_integer tptp.nat)) (F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer))) (=> (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep2) Abs2) tptp.top_top_set_nat) (=> (= M (@ (@ tptp.comp_n6876073255676942959nteger M1) M22)) (= (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C1593894019821074884nteger F) M)) G) (@ (@ tptp.comp_C456341964420721295nteger (@ (@ tptp.comp_n856947995562459650atural (@ (@ tptp.comp_C836733381939181879er_nat F) M1)) Rep2)) (@ (@ tptp.comp_C1891057325546811591nteger (@ (@ tptp.comp_n1317173320648503354nteger Abs2) M22)) G)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (Abs2 (-> (-> tptp.code_integer tptp.code_integer) tptp.code_integer)) (M (-> tptp.code_integer tptp.code_integer)) (M1 (-> (-> tptp.code_integer tptp.code_integer) tptp.code_integer)) (M22 (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer))) (=> (@ (@ (@ tptp.type_d669523880323286244nteger Rep2) Abs2) tptp.top_to3804862627464599871nteger) (=> (= M (@ (@ tptp.comp_C5076291335850163704nteger M1) M22)) (= (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C1593894019821074884nteger F) M)) G) (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C8797469213163452608nteger (@ (@ tptp.comp_C95226695241045696nteger F) M1)) Rep2)) (@ (@ tptp.comp_C7449957260575251196nteger (@ (@ tptp.comp_C5076291335850163704nteger Abs2) M22)) G)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> (-> tptp.code_integer tptp.code_integer) tptp.code_integer)) (Abs2 (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (M (-> tptp.code_integer tptp.code_integer)) (M1 (-> tptp.code_integer tptp.code_integer)) (M22 (-> tptp.code_integer tptp.code_integer)) (F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.comp_C1593894019821074884nteger F))) (=> (@ (@ (@ tptp.type_d5515310227294319076nteger Rep2) Abs2) tptp.top_to4645266643341252675nteger) (=> (= M (@ (@ tptp.comp_C7449957260575251196nteger M1) M22)) (= (@ (@ tptp.comp_C1593894019821074884nteger (@ _let_1 M)) G) (@ (@ tptp.comp_C8797469213163452608nteger (@ (@ tptp.comp_C95226695241045696nteger (@ _let_1 M1)) Rep2)) (@ (@ tptp.comp_C2931745410781319416nteger (@ (@ tptp.comp_C2931745410781319416nteger Abs2) M22)) G))))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.code_integer)) (Abs2 (-> tptp.code_integer tptp.code_integer)) (M (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (M1 (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (M22 (-> tptp.code_integer tptp.code_integer)) (F (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.comp_C8797469213163452608nteger F))) (=> (@ (@ (@ tptp.type_d4796611474492816872nteger Rep2) Abs2) tptp.top_to4645266643341252675nteger) (=> (= M (@ (@ tptp.comp_C2931745410781319416nteger M1) M22)) (= (@ (@ tptp.comp_C1593894019821074884nteger (@ _let_1 M)) G) (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C1593894019821074884nteger (@ _let_1 M1)) Rep2)) (@ (@ tptp.comp_C7449957260575251196nteger (@ (@ tptp.comp_C7449957260575251196nteger Abs2) M22)) G))))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (Rep3 (-> tptp.code_integer tptp.int)) (Abs3 (-> tptp.int tptp.code_integer)) (Rep4 (-> tptp.code_integer tptp.int)) (Abs4 (-> tptp.int tptp.code_integer)) (M (-> tptp.int tptp.int)) (M1 (-> tptp.int tptp.int)) (M22 (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.comp_i1585864551200866970er_int Abs3))) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) tptp.top_top_set_int) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep3) Abs3) tptp.top_top_set_int) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep4) Abs4) tptp.top_top_set_int) (=> (= (@ (@ tptp.comp_i6014793192326455499nteger (@ _let_1 M)) Rep4) (@ (@ tptp.comp_C7449957260575251196nteger (@ (@ tptp.comp_i6014793192326455499nteger (@ _let_1 M1)) Rep2)) (@ (@ tptp.comp_i6014793192326455499nteger (@ (@ tptp.comp_i1585864551200866970er_int Abs2) M22)) Rep4))) (= (@ (@ tptp.comp_int_int_int M1) M22) M))))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (Rep3 (-> tptp.code_integer tptp.int)) (Abs3 (-> tptp.int tptp.code_integer)) (Rep4 (-> tptp.product_unit Bool)) (Abs4 (-> Bool tptp.product_unit)) (M (-> Bool tptp.int)) (M1 (-> tptp.int tptp.int)) (M22 (-> Bool tptp.int))) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) tptp.top_top_set_int) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep3) Abs3) tptp.top_top_set_int) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep4) Abs4) tptp.top_top_set_o) (=> (= (@ (@ tptp.comp_o780160699970281785t_unit (@ (@ tptp.comp_i5286552343147518890eger_o Abs3) M)) Rep4) (@ (@ tptp.comp_C2290379119555921966t_unit (@ (@ tptp.comp_i6014793192326455499nteger (@ (@ tptp.comp_i1585864551200866970er_int Abs3) M1)) Rep2)) (@ (@ tptp.comp_o780160699970281785t_unit (@ (@ tptp.comp_i5286552343147518890eger_o Abs2) M22)) Rep4))) (= (@ (@ tptp.comp_int_int_o M1) M22) M)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (Rep3 (-> tptp.code_integer tptp.int)) (Abs3 (-> tptp.int tptp.code_integer)) (Rep4 (-> tptp.code_natural tptp.nat)) (Abs4 (-> tptp.nat tptp.code_natural)) (M (-> tptp.nat tptp.int)) (M1 (-> tptp.int tptp.int)) (M22 (-> tptp.nat tptp.int))) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) tptp.top_top_set_int) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep3) Abs3) tptp.top_top_set_int) (=> (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep4) Abs4) tptp.top_top_set_nat) (=> (= (@ (@ tptp.comp_n5699668407433660474atural (@ (@ tptp.comp_i1588355021709917246er_nat Abs3) M)) Rep4) (@ (@ tptp.comp_C6273552412331968711atural (@ (@ tptp.comp_i6014793192326455499nteger (@ (@ tptp.comp_i1585864551200866970er_int Abs3) M1)) Rep2)) (@ (@ tptp.comp_n5699668407433660474atural (@ (@ tptp.comp_i1588355021709917246er_nat Abs2) M22)) Rep4))) (= (@ (@ tptp.comp_int_int_nat M1) M22) M)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (Rep3 (-> tptp.product_unit Bool)) (Abs3 (-> Bool tptp.product_unit)) (Rep4 (-> tptp.code_integer tptp.int)) (Abs4 (-> tptp.int tptp.code_integer)) (M (-> tptp.int Bool)) (M1 (-> tptp.int Bool)) (M22 (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.comp_o7049022088938261380it_int Abs3))) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) tptp.top_top_set_int) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep3) Abs3) tptp.top_top_set_o) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep4) Abs4) tptp.top_top_set_int) (=> (= (@ (@ tptp.comp_i8439899303502915483nteger (@ _let_1 M)) Rep4) (@ (@ tptp.comp_C8146212659816229034nteger (@ (@ tptp.comp_i8439899303502915483nteger (@ _let_1 M1)) Rep2)) (@ (@ tptp.comp_i6014793192326455499nteger (@ (@ tptp.comp_i1585864551200866970er_int Abs2) M22)) Rep4))) (= (@ (@ tptp.comp_int_o_int M1) M22) M))))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (Rep3 (-> tptp.product_unit Bool)) (Abs3 (-> Bool tptp.product_unit)) (Rep4 (-> tptp.product_unit Bool)) (Abs4 (-> Bool tptp.product_unit)) (M (-> Bool Bool)) (M1 (-> tptp.int Bool)) (M22 (-> Bool tptp.int))) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) tptp.top_top_set_int) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep3) Abs3) tptp.top_top_set_o) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep4) Abs4) tptp.top_top_set_o) (=> (= (@ (@ tptp.comp_o7724735231917782709t_unit (@ (@ tptp.comp_o3916225744453444672unit_o Abs3) M)) Rep4) (@ (@ tptp.comp_C2408090164605745152t_unit (@ (@ tptp.comp_i8439899303502915483nteger (@ (@ tptp.comp_o7049022088938261380it_int Abs3) M1)) Rep2)) (@ (@ tptp.comp_o780160699970281785t_unit (@ (@ tptp.comp_i5286552343147518890eger_o Abs2) M22)) Rep4))) (= (@ (@ tptp.comp_int_o_o M1) M22) M)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (Rep3 (-> tptp.product_unit Bool)) (Abs3 (-> Bool tptp.product_unit)) (Rep4 (-> tptp.code_natural tptp.nat)) (Abs4 (-> tptp.nat tptp.code_natural)) (M (-> tptp.nat Bool)) (M1 (-> tptp.int Bool)) (M22 (-> tptp.nat tptp.int))) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) tptp.top_top_set_int) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep3) Abs3) tptp.top_top_set_o) (=> (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep4) Abs4) tptp.top_top_set_nat) (=> (= (@ (@ tptp.comp_n8360577435903631554atural (@ (@ tptp.comp_o7051512559447311656it_nat Abs3) M)) Rep4) (@ (@ tptp.comp_C6969807811572946549atural (@ (@ tptp.comp_i8439899303502915483nteger (@ (@ tptp.comp_o7049022088938261380it_int Abs3) M1)) Rep2)) (@ (@ tptp.comp_n5699668407433660474atural (@ (@ tptp.comp_i1588355021709917246er_nat Abs2) M22)) Rep4))) (= (@ (@ tptp.comp_int_o_nat M1) M22) M)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (Rep3 (-> tptp.code_natural tptp.nat)) (Abs3 (-> tptp.nat tptp.code_natural)) (Rep4 (-> tptp.code_integer tptp.int)) (Abs4 (-> tptp.int tptp.code_integer)) (M (-> tptp.int tptp.nat)) (M1 (-> tptp.int tptp.nat)) (M22 (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.comp_n9160511493981425161al_int Abs3))) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) tptp.top_top_set_int) (=> (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep3) Abs3) tptp.top_top_set_nat) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep4) Abs4) tptp.top_top_set_int) (=> (= (@ (@ tptp.comp_i455893257298015894nteger (@ _let_1 M)) Rep4) (@ (@ tptp.comp_C1891057325546811591nteger (@ (@ tptp.comp_i455893257298015894nteger (@ _let_1 M1)) Rep2)) (@ (@ tptp.comp_i6014793192326455499nteger (@ (@ tptp.comp_i1585864551200866970er_int Abs2) M22)) Rep4))) (= (@ (@ tptp.comp_int_nat_int M1) M22) M))))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (Rep3 (-> tptp.code_natural tptp.nat)) (Abs3 (-> tptp.nat tptp.code_natural)) (Rep4 (-> tptp.product_unit Bool)) (Abs4 (-> Bool tptp.product_unit)) (M (-> Bool tptp.nat)) (M1 (-> tptp.int tptp.nat)) (M22 (-> Bool tptp.int))) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) tptp.top_top_set_int) (=> (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep3) Abs3) tptp.top_top_set_nat) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep4) Abs4) tptp.top_top_set_o) (=> (= (@ (@ tptp.comp_o2643362028263920430t_unit (@ (@ tptp.comp_n2857367870785791611ural_o Abs3) M)) Rep4) (@ (@ tptp.comp_C4153580447849560611t_unit (@ (@ tptp.comp_i455893257298015894nteger (@ (@ tptp.comp_n9160511493981425161al_int Abs3) M1)) Rep2)) (@ (@ tptp.comp_o780160699970281785t_unit (@ (@ tptp.comp_i5286552343147518890eger_o Abs2) M22)) Rep4))) (= (@ (@ tptp.comp_int_nat_o M1) M22) M)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (Rep3 (-> tptp.code_natural tptp.nat)) (Abs3 (-> tptp.nat tptp.code_natural)) (Rep4 (-> tptp.code_natural tptp.nat)) (Abs4 (-> tptp.nat tptp.code_natural)) (M (-> tptp.nat tptp.nat)) (M1 (-> tptp.int tptp.nat)) (M22 (-> tptp.nat tptp.int))) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) tptp.top_top_set_int) (=> (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep3) Abs3) tptp.top_top_set_nat) (=> (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep4) Abs4) tptp.top_top_set_nat) (=> (= (@ (@ tptp.comp_n140768472405220869atural (@ (@ tptp.comp_n9163001964490475437al_nat Abs3) M)) Rep4) (@ (@ tptp.comp_C714652477303529106atural (@ (@ tptp.comp_i455893257298015894nteger (@ (@ tptp.comp_n9160511493981425161al_int Abs3) M1)) Rep2)) (@ (@ tptp.comp_n5699668407433660474atural (@ (@ tptp.comp_i1588355021709917246er_nat Abs2) M22)) Rep4))) (= (@ (@ tptp.comp_int_nat_nat M1) M22) M)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.product_unit Bool)) (Abs2 (-> Bool tptp.product_unit)) (Rep3 (-> tptp.code_integer tptp.int)) (Abs3 (-> tptp.int tptp.code_integer)) (Rep4 (-> tptp.code_integer tptp.int)) (Abs4 (-> tptp.int tptp.code_integer)) (M (-> tptp.int tptp.int)) (M1 (-> Bool tptp.int)) (M22 (-> tptp.int Bool))) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep2) Abs2) tptp.top_top_set_o) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep3) Abs3) tptp.top_top_set_int) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep4) Abs4) tptp.top_top_set_int) (=> (= (@ (@ tptp.comp_i6014793192326455499nteger (@ (@ tptp.comp_i1585864551200866970er_int Abs3) M)) Rep4) (@ (@ tptp.comp_P6790823133229852966nteger (@ (@ tptp.comp_o780160699970281785t_unit (@ (@ tptp.comp_i5286552343147518890eger_o Abs3) M1)) Rep2)) (@ (@ tptp.comp_i8439899303502915483nteger (@ (@ tptp.comp_o7049022088938261380it_int Abs2) M22)) Rep4))) (= (@ (@ tptp.comp_o_int_int M1) M22) M)))))))
% 5.65/5.93 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (Ub (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.nat))) (=> (forall ((A4 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ F B2))) (let ((_let_2 (@ Ub A4))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat B2) A4)) R2) (and (@ (@ tptp.ord_less_eq_nat (@ Ub B2)) _let_2) (@ (@ tptp.ord_less_eq_nat _let_1) _let_2) (@ (@ tptp.ord_less_nat (@ F A4)) _let_1)))))) (@ tptp.wf_nat R2))))
% 5.65/5.93 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (Ub (-> tptp.int tptp.nat)) (F (-> tptp.int tptp.nat))) (=> (forall ((A4 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ F B2))) (let ((_let_2 (@ Ub A4))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int B2) A4)) R2) (and (@ (@ tptp.ord_less_eq_nat (@ Ub B2)) _let_2) (@ (@ tptp.ord_less_eq_nat _let_1) _let_2) (@ (@ tptp.ord_less_nat (@ F A4)) _let_1)))))) (@ tptp.wf_int R2))))
% 5.65/5.93 (assert (= tptp.ord_less_assn (lambda ((A6 tptp.assn) (B6 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn A6) B6) (not (= A6 B6))))))
% 5.65/5.93 (assert (= tptp.top_top_assn (@ tptp.abs_assn tptp.in_range)))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (P (-> tptp.product_unit tptp.product_unit Bool)) (C5 tptp.set_Product_unit) (Z tptp.product_unit)) (let ((_let_1 (@ (@ tptp.pred_c6915491785556283576t_unit A) P))) (=> (@ _let_1 C5) (=> (@ (@ tptp.member_Product_unit Z) A) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) C5) (@ (@ (@ (@ tptp.sup_su3411595859437804162unit_o P) (lambda ((Y4 tptp.product_unit) (Z4 tptp.product_unit)) (= Y4 Z4))) X3) Z))) (@ _let_1 (@ (@ tptp.sup_su793286257634532545t_unit (@ (@ tptp.insert_Product_unit Z) tptp.bot_bo3957492148770167129t_unit)) C5))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (P (-> Bool Bool Bool)) (C5 tptp.set_o) (Z Bool)) (let ((_let_1 (@ (@ tptp.pred_chain_o A) P))) (=> (@ _let_1 C5) (=> (@ (@ tptp.member_o Z) A) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) C5) (@ (@ (@ (@ tptp.sup_sup_o_o_o P) (lambda ((Y4 Bool) (Z4 Bool)) (= Y4 Z4))) X3) Z))) (@ _let_1 (@ (@ tptp.sup_sup_set_o (@ (@ tptp.insert_o Z) tptp.bot_bot_set_o)) C5))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (P (-> tptp.nat tptp.nat Bool)) (C5 tptp.set_nat) (Z tptp.nat)) (let ((_let_1 (@ (@ tptp.pred_chain_nat A) P))) (=> (@ _let_1 C5) (=> (@ (@ tptp.member_nat Z) A) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) C5) (@ (@ (@ (@ tptp.sup_sup_nat_nat_o P) (lambda ((Y4 tptp.nat) (Z4 tptp.nat)) (= Y4 Z4))) X3) Z))) (@ _let_1 (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.insert_nat Z) tptp.bot_bot_set_nat)) C5))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (P (-> tptp.int tptp.int Bool)) (C5 tptp.set_int) (Z tptp.int)) (let ((_let_1 (@ (@ tptp.pred_chain_int A) P))) (=> (@ _let_1 C5) (=> (@ (@ tptp.member_int Z) A) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) C5) (@ (@ (@ (@ tptp.sup_sup_int_int_o P) (lambda ((Y4 tptp.int) (Z4 tptp.int)) (= Y4 Z4))) X3) Z))) (@ _let_1 (@ (@ tptp.sup_sup_set_int (@ (@ tptp.insert_int Z) tptp.bot_bot_set_int)) C5))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (C5 tptp.set_Pr4532377907799695533_nat_o) (Z (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ tptp.pred_c177362287423414904_nat_o A) P))) (=> (@ _let_1 C5) (=> (@ (@ tptp.member6576561426505652726_nat_o Z) A) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) C5) (@ (@ (@ (@ tptp.sup_su1942872429929737346at_o_o P) (lambda ((Y4 (-> tptp.produc3658429121746597890et_nat Bool)) (Z4 (-> tptp.produc3658429121746597890et_nat Bool))) (= Y4 Z4))) X3) Z))) (@ _let_1 (@ (@ tptp.sup_su5209123915105501825_nat_o (@ (@ tptp.insert5175938949040314269_nat_o Z) tptp.bot_bo7824918357723582233_nat_o)) C5))))))))
% 5.65/5.93 (assert (forall ((A11 tptp.set_set_nat)) (=> (not (= A11 tptp.bot_bot_set_set_nat)) (=> (forall ((C7 tptp.set_set_nat)) (=> (not (= C7 tptp.bot_bot_set_set_nat)) (=> (@ (@ (@ tptp.pred_chain_set_nat A11) tptp.ord_less_set_nat) C7) (@ (@ tptp.member_set_nat (@ tptp.comple7399068483239264473et_nat C7)) A11)))) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A11) (forall ((Xa2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa2) A11) (=> (@ (@ tptp.ord_less_eq_set_nat X3) Xa2) (= Xa2 X3))))))))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat) (F (-> tptp.nat tptp.nat))) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.measure_nat F)) (@ (@ tptp.ord_less_nat (@ F X)) (@ F Y)))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int) (F (-> tptp.int tptp.nat))) (= (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ tptp.measure_int F)) (@ (@ tptp.ord_less_nat (@ F X)) (@ F Y)))))
% 5.65/5.93 (assert (@ (@ (@ tptp.orderi2935705153647960990t_unit tptp.ord_le3507040750410214029t_unit) tptp.ord_le8056459307392131481t_unit) tptp.top_to1996260823553986621t_unit))
% 5.65/5.93 (assert (@ (@ (@ tptp.ordering_top_set_o tptp.ord_less_eq_set_o) tptp.ord_less_set_o) tptp.top_top_set_o))
% 5.65/5.93 (assert (@ (@ (@ tptp.ordering_top_set_int tptp.ord_less_eq_set_int) tptp.ord_less_set_int) tptp.top_top_set_int))
% 5.65/5.93 (assert (@ (@ (@ tptp.ordering_top_assn tptp.ord_less_eq_assn) tptp.ord_less_assn) tptp.top_top_assn))
% 5.65/5.93 (assert (@ (@ (@ tptp.orderi2807725203697798511er_nat tptp.ord_le2510731241096832064er_nat) tptp.ord_less_filter_nat) tptp.top_top_filter_nat))
% 5.65/5.93 (assert (@ (@ (@ tptp.ordering_top_set_nat tptp.ord_less_eq_set_nat) tptp.ord_less_set_nat) tptp.top_top_set_nat))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (let ((_let_1 (@ tptp.insert_Code_integer X))) (let ((_let_2 (@ (@ tptp.minus_2355218937544613996nteger A) (@ _let_1 tptp.bot_bo3990330152332043303nteger)))) (let ((_let_3 (@ tptp.lattic4901227151466704046nteger (@ _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bo3990330152332043303nteger))) (=> (@ tptp.finite6017078050557962740nteger A) (and (=> _let_4 (= _let_3 X)) (=> (not _let_4) (= _let_3 (@ (@ tptp.ord_max_Code_integer X) (@ tptp.lattic4901227151466704046nteger _let_2))))))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit X))) (let ((_let_2 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ _let_1 tptp.bot_bo3957492148770167129t_unit)))) (let ((_let_3 (@ tptp.lattic1210392890313158908t_unit (@ _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bo3957492148770167129t_unit))) (=> (@ tptp.finite4290736615968046902t_unit A) (and (=> _let_4 (= _let_3 X)) (=> (not _let_4) (= _let_3 (@ (@ tptp.ord_max_Product_unit X) (@ tptp.lattic1210392890313158908t_unit _let_2))))))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (X Bool)) (let ((_let_1 (@ tptp.insert_o X))) (let ((_let_2 (@ (@ tptp.minus_minus_set_o A) (@ _let_1 tptp.bot_bot_set_o)))) (let ((_let_3 (= _let_2 tptp.bot_bot_set_o))) (=> (@ tptp.finite_finite_o A) (= (@ tptp.lattic1921953407002678535_Max_o (@ _let_1 A)) (and (=> _let_3 X) (=> (not _let_3) (@ (@ tptp.ord_max_o X) (@ tptp.lattic1921953407002678535_Max_o _let_2)))))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ (@ tptp.minus_minus_set_int A) (@ _let_1 tptp.bot_bot_set_int)))) (let ((_let_3 (@ tptp.lattic8263393255366662781ax_int (@ _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bot_set_int))) (=> (@ tptp.finite_finite_int A) (and (=> _let_4 (= _let_3 X)) (=> (not _let_4) (= _let_3 (@ (@ tptp.ord_max_int X) (@ tptp.lattic8263393255366662781ax_int _let_2))))))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ (@ tptp.minus_minus_set_nat A) (@ _let_1 tptp.bot_bot_set_nat)))) (let ((_let_3 (@ tptp.lattic8265883725875713057ax_nat (@ _let_1 A)))) (let ((_let_4 (= _let_2 tptp.bot_bot_set_nat))) (=> (@ tptp.finite_finite_nat A) (and (=> _let_4 (= _let_3 X)) (=> (not _let_4) (= _let_3 (@ (@ tptp.ord_max_nat X) (@ tptp.lattic8265883725875713057ax_nat _let_2))))))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (let ((_let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer X) tptp.bot_bo3990330152332043303nteger)))) (let ((_let_2 (@ tptp.lattic4901227151466704046nteger A))) (let ((_let_3 (= _let_1 tptp.bot_bo3990330152332043303nteger))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ (@ tptp.member_Code_integer X) A) (and (=> _let_3 (= _let_2 X)) (=> (not _let_3) (= _let_2 (@ (@ tptp.ord_max_Code_integer X) (@ tptp.lattic4901227151466704046nteger _let_1))))))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (let ((_let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)))) (let ((_let_2 (@ tptp.lattic1210392890313158908t_unit A))) (let ((_let_3 (= _let_1 tptp.bot_bo3957492148770167129t_unit))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ (@ tptp.member_Product_unit X) A) (and (=> _let_3 (= _let_2 X)) (=> (not _let_3) (= _let_2 (@ (@ tptp.ord_max_Product_unit X) (@ tptp.lattic1210392890313158908t_unit _let_1))))))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (X Bool)) (let ((_let_1 (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)))) (let ((_let_2 (= _let_1 tptp.bot_bot_set_o))) (=> (@ tptp.finite_finite_o A) (=> (@ (@ tptp.member_o X) A) (= (@ tptp.lattic1921953407002678535_Max_o A) (and (=> _let_2 X) (=> (not _let_2) (@ (@ tptp.ord_max_o X) (@ tptp.lattic1921953407002678535_Max_o _let_1)))))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))) (let ((_let_2 (@ tptp.lattic8263393255366662781ax_int A))) (let ((_let_3 (= _let_1 tptp.bot_bot_set_int))) (=> (@ tptp.finite_finite_int A) (=> (@ (@ tptp.member_int X) A) (and (=> _let_3 (= _let_2 X)) (=> (not _let_3) (= _let_2 (@ (@ tptp.ord_max_int X) (@ tptp.lattic8263393255366662781ax_int _let_1))))))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))) (let ((_let_2 (@ tptp.lattic8265883725875713057ax_nat A))) (let ((_let_3 (= _let_1 tptp.bot_bot_set_nat))) (=> (@ tptp.finite_finite_nat A) (=> (@ (@ tptp.member_nat X) A) (and (=> _let_3 (= _let_2 X)) (=> (not _let_3) (= _let_2 (@ (@ tptp.ord_max_nat X) (@ tptp.lattic8265883725875713057ax_nat _let_1))))))))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer) (B4 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.image_4470545334726330049nteger F))) (let ((_let_2 (@ tptp.inj_on1158064722259180589nteger F))) (= (@ _let_2 (@ (@ tptp.sup_su848401254843788991nteger A) B4)) (and (@ _let_2 A) (@ _let_2 B4) (= (@ (@ tptp.inf_in1364745209274528805nteger (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B4))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B4) A))) tptp.bot_bo3990330152332043303nteger)))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_set_nat F))) (let ((_let_2 (@ tptp.inj_on_nat_set_nat F))) (= (@ _let_2 (@ (@ tptp.sup_sup_set_nat A) B4)) (and (@ _let_2 A) (@ _let_2 B4) (= (@ (@ tptp.inf_inf_set_set_nat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B4) A))) tptp.bot_bot_set_set_nat)))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_1215581382706833972nteger F))) (let ((_let_2 (@ tptp.inj_on2245834603434889120nteger F))) (= (@ _let_2 (@ (@ tptp.sup_sup_set_nat A) B4)) (and (@ _let_2 A) (@ _let_2 B4) (= (@ (@ tptp.inf_in1364745209274528805nteger (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B4) A))) tptp.bot_bo3990330152332043303nteger)))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat tptp.product_unit)) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_8730104196221521654t_unit F))) (let ((_let_2 (@ tptp.inj_on7061601236592826506t_unit F))) (= (@ _let_2 (@ (@ tptp.sup_sup_set_nat A) B4)) (and (@ _let_2 A) (@ _let_2 B4) (= (@ (@ tptp.inf_in4660618365625256667t_unit (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B4) A))) tptp.bot_bo3957492148770167129t_unit)))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat Bool)) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_o2 F))) (let ((_let_2 (@ tptp.inj_on_nat_o F))) (= (@ _let_2 (@ (@ tptp.sup_sup_set_nat A) B4)) (and (@ _let_2 A) (@ _let_2 B4) (= (@ (@ tptp.inf_inf_set_o (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B4) A))) tptp.bot_bot_set_o)))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_nat2 F))) (let ((_let_2 (@ tptp.inj_on_nat_nat F))) (= (@ _let_2 (@ (@ tptp.sup_sup_set_nat A) B4)) (and (@ _let_2 A) (@ _let_2 B4) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B4) A))) tptp.bot_bot_set_nat)))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_int2 F))) (let ((_let_2 (@ tptp.inj_on_nat_int F))) (= (@ _let_2 (@ (@ tptp.sup_sup_set_nat A) B4)) (and (@ _let_2 A) (@ _let_2 B4) (= (@ (@ tptp.inf_inf_set_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B4) A))) tptp.bot_bot_set_int)))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_4682239675366380726_nat_o F))) (let ((_let_2 (@ tptp.inj_on7779444506608719434_nat_o F))) (= (@ _let_2 (@ (@ tptp.sup_sup_set_nat A) B4)) (and (@ _let_2 A) (@ _let_2 B4) (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B4) A))) tptp.bot_bo7824918357723582233_nat_o)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (= (@ tptp.lattic4901227151466704046nteger (@ (@ tptp.insert_Code_integer X) A)) (@ (@ tptp.ord_max_Code_integer X) (@ tptp.lattic4901227151466704046nteger A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (@ tptp.lattic1210392890313158908t_unit (@ (@ tptp.insert_Product_unit X) A)) (@ (@ tptp.ord_max_Product_unit X) (@ tptp.lattic1210392890313158908t_unit A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (= (@ tptp.lattic1921953407002678535_Max_o (@ (@ tptp.insert_o X) A)) (@ (@ tptp.ord_max_o X) (@ tptp.lattic1921953407002678535_Max_o A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (= (@ tptp.lattic8263393255366662781ax_int (@ (@ tptp.insert_int X) A)) (@ (@ tptp.ord_max_int X) (@ tptp.lattic8263393255366662781ax_int A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (= (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.insert_nat X) A)) (@ (@ tptp.ord_max_nat X) (@ tptp.lattic8265883725875713057ax_nat A)))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer))) (=> (= (@ (@ tptp.image_4470545334726330049nteger F) tptp.top_to4645266643341252675nteger) tptp.top_to4645266643341252675nteger) (=> (= (@ (@ tptp.image_4470545334726330049nteger G) tptp.top_to4645266643341252675nteger) tptp.top_to4645266643341252675nteger) (= (@ (@ tptp.image_7082141833288935621nteger (@ (@ tptp.produc1802105962441033582nteger F) G)) tptp.top_to2363841527343591755nteger) tptp.top_to2363841527343591755nteger)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.product_unit tptp.product_unit))) (=> (= (@ (@ tptp.image_4470545334726330049nteger F) tptp.top_to4645266643341252675nteger) tptp.top_to4645266643341252675nteger) (=> (= (@ (@ tptp.image_405062704495631173t_unit G) tptp.top_to1996260823553986621t_unit) tptp.top_to1996260823553986621t_unit) (= (@ (@ tptp.image_3456600171786721233t_unit (@ (@ tptp.produc3346700480963112818t_unit F) G)) tptp.top_to3244471725241573579t_unit) tptp.top_to3244471725241573579t_unit)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.product_unit Bool))) (=> (= (@ (@ tptp.image_4470545334726330049nteger F) tptp.top_to4645266643341252675nteger) tptp.top_to4645266643341252675nteger) (=> (= (@ (@ tptp.image_Product_unit_o2 G) tptp.top_to1996260823553986621t_unit) tptp.top_top_set_o) (= (@ (@ tptp.image_7060974388358999388eger_o (@ (@ tptp.produc8116347370398923901unit_o F) G)) tptp.top_to3244471725241573579t_unit) tptp.top_to2658285827425157974eger_o)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.product_unit tptp.nat))) (=> (= (@ (@ tptp.image_4470545334726330049nteger F) tptp.top_to4645266643341252675nteger) tptp.top_to4645266643341252675nteger) (=> (= (@ (@ tptp.image_875570014554754200it_nat G) tptp.top_to1996260823553986621t_unit) tptp.top_top_set_nat) (= (@ (@ tptp.image_8236373689398998434er_nat (@ (@ tptp.produc4022400886476617259it_nat F) G)) tptp.top_to3244471725241573579t_unit) tptp.top_to8760411888770933182er_nat)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.product_unit tptp.int))) (=> (= (@ (@ tptp.image_4470545334726330049nteger F) tptp.top_to4645266643341252675nteger) tptp.top_to4645266643341252675nteger) (=> (= (@ (@ tptp.image_873079544045703924it_int G) tptp.top_to1996260823553986621t_unit) tptp.top_top_set_int) (= (@ (@ tptp.image_4058522669889801726er_int (@ (@ tptp.produc4019910415967566983it_int F) G)) tptp.top_to3244471725241573579t_unit) tptp.top_to6270328743839206426er_int)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (G (-> Bool tptp.product_unit))) (=> (= (@ (@ tptp.image_4470545334726330049nteger F) tptp.top_to4645266643341252675nteger) tptp.top_to4645266643341252675nteger) (=> (= (@ (@ tptp.image_o_Product_unit2 G) tptp.top_top_set_o) tptp.top_to1996260823553986621t_unit) (= (@ (@ tptp.image_2425804817718344284t_unit (@ (@ tptp.produc3530376873132787239t_unit F) G)) tptp.top_to2658285827425157974eger_o) tptp.top_to3244471725241573579t_unit)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (G (-> Bool Bool))) (=> (= (@ (@ tptp.image_4470545334726330049nteger F) tptp.top_to4645266643341252675nteger) tptp.top_to4645266643341252675nteger) (=> (= (@ (@ tptp.image_o_o2 G) tptp.top_top_set_o) tptp.top_top_set_o) (= (@ (@ tptp.image_227735840630799463eger_o (@ (@ tptp.produc1084426483498010290er_o_o F) G)) tptp.top_to2658285827425157974eger_o) tptp.top_to2658285827425157974eger_o)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (G (-> Bool tptp.nat))) (=> (= (@ (@ tptp.image_4470545334726330049nteger F) tptp.top_to4645266643341252675nteger) tptp.top_to4645266643341252675nteger) (=> (= (@ (@ tptp.image_o_nat2 G) tptp.top_top_set_o) tptp.top_top_set_nat) (= (@ (@ tptp.image_1252617143230709591er_nat (@ (@ tptp.produc7550393335539917622_o_nat F) G)) tptp.top_to2658285827425157974eger_o) tptp.top_to8760411888770933182er_nat)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (G (-> Bool tptp.int))) (=> (= (@ (@ tptp.image_4470545334726330049nteger F) tptp.top_to4645266643341252675nteger) tptp.top_to4645266643341252675nteger) (=> (= (@ (@ tptp.image_o_int2 G) tptp.top_top_set_o) tptp.top_top_set_int) (= (@ (@ tptp.image_6298138160576288691er_int (@ (@ tptp.produc7547902865030867346_o_int F) G)) tptp.top_to2658285827425157974eger_o) tptp.top_to6270328743839206426er_int)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.nat tptp.code_integer))) (=> (= (@ (@ tptp.image_4470545334726330049nteger F) tptp.top_to4645266643341252675nteger) tptp.top_to4645266643341252675nteger) (=> (= (@ (@ tptp.image_1215581382706833972nteger G) tptp.top_top_set_nat) tptp.top_to4645266643341252675nteger) (= (@ (@ tptp.image_4921214744877245202nteger (@ (@ tptp.produc1622059938646302433nteger F) G)) tptp.top_to8760411888770933182er_nat) tptp.top_to2363841527343591755nteger)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A2 tptp.code_integer) (A tptp.set_Code_integer)) (let ((_let_1 (@ tptp.insert_Code_integer A2))) (let ((_let_2 (@ tptp.inj_on1158064722259180589nteger F))) (= (@ _let_2 (@ _let_1 A)) (and (@ _let_2 A) (not (@ (@ tptp.member_Code_integer (@ F A2)) (@ (@ tptp.image_4470545334726330049nteger F) (@ (@ tptp.minus_2355218937544613996nteger A) (@ _let_1 tptp.bot_bo3990330152332043303nteger)))))))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.nat)) (A2 tptp.product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit A2))) (let ((_let_2 (@ tptp.inj_on8430439091780834860it_nat F))) (= (@ _let_2 (@ _let_1 A)) (and (@ _let_2 A) (not (@ (@ tptp.member_nat (@ F A2)) (@ (@ tptp.image_875570014554754200it_nat F) (@ (@ tptp.minus_6452836326544984404t_unit A) (@ _let_1 tptp.bot_bo3957492148770167129t_unit)))))))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.int)) (A2 tptp.product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit A2))) (let ((_let_2 (@ tptp.inj_on8427948621271784584it_int F))) (= (@ _let_2 (@ _let_1 A)) (and (@ _let_2 A) (not (@ (@ tptp.member_int (@ F A2)) (@ (@ tptp.image_873079544045703924it_int F) (@ (@ tptp.minus_6452836326544984404t_unit A) (@ _let_1 tptp.bot_bo3957492148770167129t_unit)))))))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit Bool)) (A2 tptp.product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit A2))) (let ((_let_2 (@ tptp.inj_on8854722734121536060unit_o F))) (= (@ _let_2 (@ _let_1 A)) (and (@ _let_2 A) (not (@ (@ tptp.member_o (@ F A2)) (@ (@ tptp.image_Product_unit_o2 F) (@ (@ tptp.minus_6452836326544984404t_unit A) (@ _let_1 tptp.bot_bo3957492148770167129t_unit)))))))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.product_unit)) (A2 tptp.product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit A2))) (let ((_let_2 (@ tptp.inj_on8151373323710067377t_unit F))) (= (@ _let_2 (@ _let_1 A)) (and (@ _let_2 A) (not (@ (@ tptp.member_Product_unit (@ F A2)) (@ (@ tptp.image_405062704495631173t_unit F) (@ (@ tptp.minus_6452836326544984404t_unit A) (@ _let_1 tptp.bot_bo3957492148770167129t_unit)))))))))))
% 5.65/5.93 (assert (forall ((F (-> Bool tptp.nat)) (A2 Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A2))) (let ((_let_2 (@ tptp.inj_on_o_nat F))) (= (@ _let_2 (@ _let_1 A)) (and (@ _let_2 A) (not (@ (@ tptp.member_nat (@ F A2)) (@ (@ tptp.image_o_nat2 F) (@ (@ tptp.minus_minus_set_o A) (@ _let_1 tptp.bot_bot_set_o)))))))))))
% 5.65/5.93 (assert (forall ((F (-> Bool tptp.int)) (A2 Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A2))) (let ((_let_2 (@ tptp.inj_on_o_int F))) (= (@ _let_2 (@ _let_1 A)) (and (@ _let_2 A) (not (@ (@ tptp.member_int (@ F A2)) (@ (@ tptp.image_o_int2 F) (@ (@ tptp.minus_minus_set_o A) (@ _let_1 tptp.bot_bot_set_o)))))))))))
% 5.65/5.93 (assert (forall ((F (-> Bool Bool)) (A2 Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A2))) (let ((_let_2 (@ tptp.inj_on_o_o F))) (= (@ _let_2 (@ _let_1 A)) (and (@ _let_2 A) (not (@ (@ tptp.member_o (@ F A2)) (@ (@ tptp.image_o_o2 F) (@ (@ tptp.minus_minus_set_o A) (@ _let_1 tptp.bot_bot_set_o)))))))))))
% 5.65/5.93 (assert (forall ((F (-> Bool tptp.product_unit)) (A2 Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.insert_o A2))) (let ((_let_2 (@ tptp.inj_on4268752236855399398t_unit F))) (= (@ _let_2 (@ _let_1 A)) (and (@ _let_2 A) (not (@ (@ tptp.member_Product_unit (@ F A2)) (@ (@ tptp.image_o_Product_unit2 F) (@ (@ tptp.minus_minus_set_o A) (@ _let_1 tptp.bot_bot_set_o)))))))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.nat)) (A2 tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A2))) (let ((_let_2 (@ tptp.inj_on_int_nat F))) (= (@ _let_2 (@ _let_1 A)) (and (@ _let_2 A) (not (@ (@ tptp.member_nat (@ F A2)) (@ (@ tptp.image_int_nat2 F) (@ (@ tptp.minus_minus_set_int A) (@ _let_1 tptp.bot_bot_set_int)))))))))))
% 5.65/5.93 (assert (forall ((X tptp.set_Product_unit)) (= (@ (@ tptp.ord_ma508538259134630082t_unit tptp.bot_bo3957492148770167129t_unit) X) X)))
% 5.65/5.93 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.ord_max_set_o tptp.bot_bot_set_o) X) X)))
% 5.65/5.93 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat tptp.bot_bot_set_nat) X) X)))
% 5.65/5.93 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int tptp.bot_bot_set_int) X) X)))
% 5.65/5.93 (assert (forall ((X tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.ord_ma8206644353667601538_nat_o tptp.bot_bo7824918357723582233_nat_o) X) X)))
% 5.65/5.93 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.bot_bot_nat) X) X)))
% 5.65/5.93 (assert (forall ((X tptp.set_Product_unit)) (= (@ (@ tptp.ord_ma508538259134630082t_unit X) tptp.bot_bo3957492148770167129t_unit) X)))
% 5.65/5.93 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.ord_max_set_o X) tptp.bot_bot_set_o) X)))
% 5.65/5.93 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat X) tptp.bot_bot_set_nat) X)))
% 5.65/5.93 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int X) tptp.bot_bot_set_int) X)))
% 5.65/5.93 (assert (forall ((X tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.ord_ma8206644353667601538_nat_o X) tptp.bot_bo7824918357723582233_nat_o) X)))
% 5.65/5.93 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_max_nat X) tptp.bot_bot_nat) X)))
% 5.65/5.93 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.ord_max_assn tptp.top_top_assn) X) tptp.top_top_assn)))
% 5.65/5.93 (assert (forall ((X tptp.set_Product_unit)) (= (@ (@ tptp.ord_ma508538259134630082t_unit tptp.top_to1996260823553986621t_unit) X) tptp.top_to1996260823553986621t_unit)))
% 5.65/5.93 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.ord_max_set_o tptp.top_top_set_o) X) tptp.top_top_set_o)))
% 5.65/5.93 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat tptp.top_top_set_nat) X) tptp.top_top_set_nat)))
% 5.65/5.93 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int tptp.top_top_set_int) X) tptp.top_top_set_int)))
% 5.65/5.93 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.ord_max_assn X) tptp.top_top_assn) tptp.top_top_assn)))
% 5.65/5.93 (assert (forall ((X tptp.set_Product_unit)) (= (@ (@ tptp.ord_ma508538259134630082t_unit X) tptp.top_to1996260823553986621t_unit) tptp.top_to1996260823553986621t_unit)))
% 5.65/5.93 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.ord_max_set_o X) tptp.top_top_set_o) tptp.top_top_set_o)))
% 5.65/5.93 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat X) tptp.top_top_set_nat) tptp.top_top_set_nat)))
% 5.65/5.93 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.ord_max_set_int X) tptp.top_top_set_int) tptp.top_top_set_int)))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat)) (A2 tptp.nat) (B tptp.nat)) (= (@ (@ (@ tptp.produc6977886695330630970at_nat F) G) (@ (@ tptp.product_Pair_nat_nat A2) B)) (@ (@ tptp.product_Pair_nat_nat (@ F A2)) (@ G B)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int)) (A2 tptp.nat) (B tptp.nat)) (= (@ (@ (@ tptp.produc7347049785058425330at_int F) G) (@ (@ tptp.product_Pair_nat_nat A2) B)) (@ (@ tptp.product_Pair_int_int (@ F A2)) (@ G B)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat)) (A2 tptp.int) (B tptp.int)) (= (@ (@ (@ tptp.produc5667422475138734578nt_nat F) G) (@ (@ tptp.product_Pair_int_int A2) B)) (@ (@ tptp.product_Pair_nat_nat (@ F A2)) (@ G B)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int)) (A2 tptp.int) (B tptp.int)) (= (@ (@ (@ tptp.produc6036585564866528938nt_int F) G) (@ (@ tptp.product_Pair_int_int A2) B)) (@ (@ tptp.product_Pair_int_int (@ F A2)) (@ G B)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.nat)) (G (-> tptp.set_nat tptp.nat)) (A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat)) (= (@ (@ (@ tptp.produc8285742784527409791at_nat F) G) (@ (@ tptp.produc7507926704131184380et_nat A2) B)) (@ (@ tptp.product_Pair_nat_nat (@ F A2)) (@ G B)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.int)) (G (-> tptp.set_nat tptp.int)) (A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat)) (= (@ (@ (@ tptp.produc5973434381925408567at_int F) G) (@ (@ tptp.produc7507926704131184380et_nat A2) B)) (@ (@ tptp.product_Pair_int_int (@ F A2)) (@ G B)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat tptp.heap_e7401611519738050253t_unit)) (G (-> tptp.nat tptp.set_nat)) (A2 tptp.nat) (B tptp.nat)) (= (@ (@ (@ tptp.produc2064153442785501et_nat F) G) (@ (@ tptp.product_Pair_nat_nat A2) B)) (@ (@ tptp.produc7507926704131184380et_nat (@ F A2)) (@ G B)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.heap_e7401611519738050253t_unit)) (G (-> tptp.int tptp.set_nat)) (A2 tptp.int) (B tptp.int)) (= (@ (@ (@ tptp.produc3152090231653401565et_nat F) G) (@ (@ tptp.product_Pair_int_int A2) B)) (@ (@ tptp.produc7507926704131184380et_nat (@ F A2)) (@ G B)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit)) (G (-> tptp.set_nat tptp.set_nat)) (A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat)) (= (@ (@ (@ tptp.produc8234977478398262212et_nat F) G) (@ (@ tptp.produc7507926704131184380et_nat A2) B)) (@ (@ tptp.produc7507926704131184380et_nat (@ F A2)) (@ G B)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat tptp.produc3658429121746597890et_nat Bool)) (G (-> tptp.nat tptp.produc3658429121746597890et_nat)) (A2 tptp.nat) (B tptp.nat)) (= (@ (@ (@ tptp.produc79747477514316377et_nat F) G) (@ (@ tptp.product_Pair_nat_nat A2) B)) (@ (@ tptp.produc5001842942810119800et_nat (@ F A2)) (@ G B)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit)) (G (-> tptp.set_nat tptp.set_nat))) (= (@ (@ tptp.comp_P2930521774885306735et_nat tptp.produc8586169260539613262et_nat) (@ (@ tptp.produc8234977478398262212et_nat F) G)) (@ (@ tptp.comp_s5696514601250091763et_nat G) tptp.produc8586169260539613262et_nat))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.heap_e7401611519738050253t_unit)) (G (-> tptp.int tptp.set_nat))) (= (@ (@ tptp.comp_P8606889026643445772nt_int tptp.produc8586169260539613262et_nat) (@ (@ tptp.produc3152090231653401565et_nat F) G)) (@ (@ tptp.comp_i6200299785623974754nt_int G) tptp.product_snd_int_int))))
% 5.65/5.93 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.int)) (G (-> tptp.set_nat tptp.int))) (= (@ (@ tptp.comp_P8308861049717174982et_nat tptp.product_snd_int_int) (@ (@ tptp.produc5973434381925408567at_int F) G)) (@ (@ tptp.comp_s1601710177542341017et_nat G) tptp.produc8586169260539613262et_nat))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (= (@ (@ tptp.comp_P5356232565778667509nt_int tptp.product_snd_int_int) (@ (@ tptp.produc6036585564866528938nt_int F) G)) (@ (@ tptp.comp_i4330622015127193916nt_int G) tptp.product_snd_int_int))))
% 5.65/5.93 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit)) (G (-> tptp.set_nat tptp.set_nat)) (X tptp.produc3658429121746597890et_nat)) (= (@ tptp.produc8586169260539613262et_nat (@ (@ (@ tptp.produc8234977478398262212et_nat F) G) X)) (@ G (@ tptp.produc8586169260539613262et_nat X)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.heap_e7401611519738050253t_unit)) (G (-> tptp.int tptp.set_nat)) (X tptp.product_prod_int_int)) (= (@ tptp.produc8586169260539613262et_nat (@ (@ (@ tptp.produc3152090231653401565et_nat F) G) X)) (@ G (@ tptp.product_snd_int_int X)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.int)) (G (-> tptp.set_nat tptp.int)) (X tptp.produc3658429121746597890et_nat)) (= (@ tptp.product_snd_int_int (@ (@ (@ tptp.produc5973434381925408567at_int F) G) X)) (@ G (@ tptp.produc8586169260539613262et_nat X)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int)) (X tptp.product_prod_int_int)) (= (@ tptp.product_snd_int_int (@ (@ (@ tptp.produc6036585564866528938nt_int F) G) X)) (@ G (@ tptp.product_snd_int_int X)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R3) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat (@ F A2)) (@ G B))) (@ (@ tptp.image_5168914502847457605at_nat (@ (@ tptp.produc6977886695330630970at_nat F) G)) R3)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R3) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int (@ F A2)) (@ G B))) (@ (@ tptp.image_1990417195239315453nt_int (@ (@ tptp.produc7347049785058425330at_int F) G)) R3)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (R3 tptp.set_Pr958786334691620121nt_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R3) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat (@ F A2)) (@ G B))) (@ (@ tptp.image_5831868185956570253at_nat (@ (@ tptp.produc5667422475138734578nt_nat F) G)) R3)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (R3 tptp.set_Pr958786334691620121nt_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R3) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int (@ F A2)) (@ G B))) (@ (@ tptp.image_2653370878348428101nt_int (@ (@ tptp.produc6036585564866528938nt_int F) G)) R3)))))
% 5.65/5.93 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat) (R3 tptp.set_Pr3948176798113811640et_nat) (F (-> tptp.heap_e7401611519738050253t_unit tptp.nat)) (G (-> tptp.set_nat tptp.nat))) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) B)) R3) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat (@ F A2)) (@ G B))) (@ (@ tptp.image_7757775281999735736at_nat (@ (@ tptp.produc8285742784527409791at_nat F) G)) R3)))))
% 5.65/5.93 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat) (R3 tptp.set_Pr3948176798113811640et_nat) (F (-> tptp.heap_e7401611519738050253t_unit tptp.int)) (G (-> tptp.set_nat tptp.int))) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) B)) R3) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int (@ F A2)) (@ G B))) (@ (@ tptp.image_4579277974391593584nt_int (@ (@ tptp.produc5973434381925408567at_int F) G)) R3)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.nat tptp.heap_e7401611519738050253t_unit)) (G (-> tptp.nat tptp.set_nat))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R3) (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat (@ F A2)) (@ G B))) (@ (@ tptp.image_9068448769188195518et_nat (@ (@ tptp.produc2064153442785501et_nat F) G)) R3)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (R3 tptp.set_Pr958786334691620121nt_int) (F (-> tptp.int tptp.heap_e7401611519738050253t_unit)) (G (-> tptp.int tptp.set_nat))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) R3) (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat (@ F A2)) (@ G B))) (@ (@ tptp.image_2127501072796355446et_nat (@ (@ tptp.produc3152090231653401565et_nat F) G)) R3)))))
% 5.65/5.93 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat) (R3 tptp.set_Pr3948176798113811640et_nat) (F (-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit)) (G (-> tptp.set_nat tptp.set_nat))) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) B)) R3) (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat (@ F A2)) (@ G B))) (@ (@ tptp.image_7426123528223433739et_nat (@ (@ tptp.produc8234977478398262212et_nat F) G)) R3)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (R3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.nat tptp.produc3658429121746597890et_nat Bool)) (G (-> tptp.nat tptp.produc3658429121746597890et_nat))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) R3) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat (@ F A2)) (@ G B))) (@ (@ tptp.image_5744643625575355962et_nat (@ (@ tptp.produc79747477514316377et_nat F) G)) R3)))))
% 5.65/5.93 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (=> (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N5) N2) (not (@ P N5)))) (@ P N2)) (exists ((N6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat N6) N2) (@ P N6))))))
% 5.65/5.93 (assert (= tptp.ord_max_filter_nat (lambda ((A6 tptp.filter_nat) (B6 tptp.filter_nat)) (@ (@ (@ tptp.if_filter_nat (@ (@ tptp.ord_le2510731241096832064er_nat A6) B6)) B6) A6))))
% 5.65/5.93 (assert (= tptp.ord_max_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A6) B6)) B6) A6))))
% 5.65/5.93 (assert (= tptp.ord_max_rat (lambda ((A6 tptp.rat) (B6 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A6) B6)) B6) A6))))
% 5.65/5.93 (assert (= tptp.ord_max_nat (lambda ((A6 tptp.nat) (B6 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A6) B6)) B6) A6))))
% 5.65/5.93 (assert (= tptp.ord_max_int (lambda ((A6 tptp.int) (B6 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A6) B6)) B6) A6))))
% 5.65/5.93 (assert (forall ((Y tptp.filter_nat) (X tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat Y) X) (= (@ (@ tptp.ord_max_filter_nat X) Y) X))))
% 5.65/5.93 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (= (@ (@ tptp.ord_max_set_nat X) Y) X))))
% 5.65/5.93 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.ord_max_rat X) Y) X))))
% 5.65/5.93 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_max_nat X) Y) X))))
% 5.65/5.93 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_max_int X) Y) X))))
% 5.65/5.93 (assert (forall ((X tptp.filter_nat) (Y tptp.filter_nat)) (=> (@ (@ tptp.ord_le2510731241096832064er_nat X) Y) (= (@ (@ tptp.ord_max_filter_nat X) Y) Y))))
% 5.65/5.93 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X) Y) (= (@ (@ tptp.ord_max_set_nat X) Y) Y))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (@ (@ tptp.ord_max_rat X) Y) Y))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.ord_max_nat X) Y) Y))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.ord_max_int X) Y) Y))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.ord_max_rat X) Y)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.minus_minus_rat X) Z)) (@ (@ tptp.minus_minus_rat Y) Z)))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X) Y)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X) Z)) (@ (@ tptp.minus_minus_int Y) Z)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (H2 (-> tptp.code_integer tptp.code_integer)) (I2 (-> tptp.code_integer tptp.code_integer))) (= (@ (@ tptp.comp_P234064951390806312nteger (@ (@ tptp.produc5081366107664765182nteger F) G)) (@ (@ tptp.produc1802105962441033582nteger H2) I2)) (@ (@ tptp.produc5081366107664765182nteger (@ (@ tptp.comp_C1593894019821074884nteger F) H2)) (@ (@ tptp.comp_C1593894019821074884nteger G) I2)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (H2 (-> tptp.code_integer tptp.code_integer)) (I2 (-> tptp.code_integer tptp.code_integer tptp.code_integer))) (= (@ (@ tptp.comp_P6312383820422015140nteger (@ (@ tptp.produc3090791198996863994nteger F) G)) (@ (@ tptp.produc6023007152014423402nteger H2) I2)) (@ (@ tptp.produc5081366107664765182nteger (@ (@ tptp.comp_C1593894019821074884nteger F) H2)) (@ (@ tptp.comp_C8797469213163452608nteger G) I2)))))
% 5.65/5.93 (assert (forall ((F (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (H2 (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (I2 (-> tptp.code_integer tptp.code_integer))) (= (@ (@ tptp.comp_P1414880308642389412nteger (@ (@ tptp.produc6158254626097298938nteger F) G)) (@ (@ tptp.produc3789967387199524714nteger H2) I2)) (@ (@ tptp.produc5081366107664765182nteger (@ (@ tptp.comp_C8797469213163452608nteger F) H2)) (@ (@ tptp.comp_C1593894019821074884nteger G) I2)))))
% 5.65/5.93 (assert (forall ((F (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (H2 (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (I2 (-> tptp.code_integer tptp.code_integer tptp.code_integer))) (= (@ (@ tptp.comp_P5544053077415136032nteger (@ (@ tptp.produc4724772261320961782nteger F) G)) (@ (@ tptp.produc7818937854452556646nteger H2) I2)) (@ (@ tptp.produc5081366107664765182nteger (@ (@ tptp.comp_C8797469213163452608nteger F) H2)) (@ (@ tptp.comp_C8797469213163452608nteger G) I2)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (H2 (-> tptp.code_integer tptp.code_integer)) (I2 (-> tptp.code_integer tptp.code_integer)) (Prod tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.produc5081366107664765182nteger F) G) (@ (@ (@ tptp.produc1802105962441033582nteger H2) I2) Prod)) (@ (@ (@ tptp.produc5081366107664765182nteger (@ (@ tptp.comp_C1593894019821074884nteger F) H2)) (@ (@ tptp.comp_C1593894019821074884nteger G) I2)) Prod))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (H2 (-> tptp.code_integer tptp.code_integer)) (I2 (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (Prod tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.produc3090791198996863994nteger F) G) (@ (@ (@ tptp.produc6023007152014423402nteger H2) I2) Prod)) (@ (@ (@ tptp.produc5081366107664765182nteger (@ (@ tptp.comp_C1593894019821074884nteger F) H2)) (@ (@ tptp.comp_C8797469213163452608nteger G) I2)) Prod))))
% 5.65/5.93 (assert (forall ((F (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (H2 (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (I2 (-> tptp.code_integer tptp.code_integer)) (Prod tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.produc6158254626097298938nteger F) G) (@ (@ (@ tptp.produc3789967387199524714nteger H2) I2) Prod)) (@ (@ (@ tptp.produc5081366107664765182nteger (@ (@ tptp.comp_C8797469213163452608nteger F) H2)) (@ (@ tptp.comp_C1593894019821074884nteger G) I2)) Prod))))
% 5.65/5.93 (assert (forall ((F (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (H2 (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (I2 (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (Prod tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.produc4724772261320961782nteger F) G) (@ (@ (@ tptp.produc7818937854452556646nteger H2) I2) Prod)) (@ (@ (@ tptp.produc5081366107664765182nteger (@ (@ tptp.comp_C8797469213163452608nteger F) H2)) (@ (@ tptp.comp_C8797469213163452608nteger G) I2)) Prod))))
% 5.65/5.93 (assert (forall ((F1 (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (F22 (-> tptp.code_integer tptp.code_integer)) (G1 (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G2 (-> tptp.code_integer tptp.code_integer))) (= (@ (@ tptp.produc5081366107664765182nteger (@ (@ tptp.comp_C1593894019821074884nteger F1) F22)) (@ (@ tptp.comp_C1593894019821074884nteger G1) G2)) (@ (@ tptp.comp_P234064951390806312nteger (@ (@ tptp.produc5081366107664765182nteger F1) G1)) (@ (@ tptp.produc1802105962441033582nteger F22) G2)))))
% 5.65/5.93 (assert (forall ((F1 (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (F22 (-> tptp.code_integer tptp.code_integer)) (G1 (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G2 (-> tptp.code_integer tptp.code_integer tptp.code_integer))) (= (@ (@ tptp.produc5081366107664765182nteger (@ (@ tptp.comp_C1593894019821074884nteger F1) F22)) (@ (@ tptp.comp_C8797469213163452608nteger G1) G2)) (@ (@ tptp.comp_P6312383820422015140nteger (@ (@ tptp.produc3090791198996863994nteger F1) G1)) (@ (@ tptp.produc6023007152014423402nteger F22) G2)))))
% 5.65/5.93 (assert (forall ((F1 (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (F22 (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (G1 (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G2 (-> tptp.code_integer tptp.code_integer))) (= (@ (@ tptp.produc5081366107664765182nteger (@ (@ tptp.comp_C8797469213163452608nteger F1) F22)) (@ (@ tptp.comp_C1593894019821074884nteger G1) G2)) (@ (@ tptp.comp_P1414880308642389412nteger (@ (@ tptp.produc6158254626097298938nteger F1) G1)) (@ (@ tptp.produc3789967387199524714nteger F22) G2)))))
% 5.65/5.93 (assert (forall ((F1 (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (F22 (-> tptp.code_integer tptp.code_integer tptp.code_integer)) (G1 (-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G2 (-> tptp.code_integer tptp.code_integer tptp.code_integer))) (= (@ (@ tptp.produc5081366107664765182nteger (@ (@ tptp.comp_C8797469213163452608nteger F1) F22)) (@ (@ tptp.comp_C8797469213163452608nteger G1) G2)) (@ (@ tptp.comp_P5544053077415136032nteger (@ (@ tptp.produc4724772261320961782nteger F1) G1)) (@ (@ tptp.produc7818937854452556646nteger F22) G2)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer) (X tptp.code_integer) (B4 tptp.set_Code_integer)) (=> (@ (@ tptp.inj_on1158064722259180589nteger F) A) (=> (not (@ (@ tptp.member_Code_integer X) B4)) (=> (= (@ (@ tptp.insert_Code_integer X) B4) (@ (@ tptp.image_4470545334726330049nteger F) A)) (not (forall ((X10 tptp.code_integer) (A7 tptp.set_Code_integer)) (=> (not (@ (@ tptp.member_Code_integer X10) A7)) (=> (= A (@ (@ tptp.insert_Code_integer X10) A7)) (=> (= X (@ F X10)) (not (= B4 (@ (@ tptp.image_4470545334726330049nteger F) A7)))))))))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.set_nat) (X tptp.code_integer) (B4 tptp.set_Code_integer)) (=> (@ (@ tptp.inj_on2245834603434889120nteger F) A) (=> (not (@ (@ tptp.member_Code_integer X) B4)) (=> (= (@ (@ tptp.insert_Code_integer X) B4) (@ (@ tptp.image_1215581382706833972nteger F) A)) (not (forall ((X10 tptp.nat) (A7 tptp.set_nat)) (=> (not (@ (@ tptp.member_nat X10) A7)) (=> (= A (@ (@ tptp.insert_nat X10) A7)) (=> (= X (@ F X10)) (not (= B4 (@ (@ tptp.image_1215581382706833972nteger F) A7)))))))))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (X tptp.nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.inj_on_nat_nat F) A) (=> (not (@ (@ tptp.member_nat X) B4)) (=> (= (@ (@ tptp.insert_nat X) B4) (@ (@ tptp.image_nat_nat2 F) A)) (not (forall ((X10 tptp.nat) (A7 tptp.set_nat)) (=> (not (@ (@ tptp.member_nat X10) A7)) (=> (= A (@ (@ tptp.insert_nat X10) A7)) (=> (= X (@ F X10)) (not (= B4 (@ (@ tptp.image_nat_nat2 F) A7)))))))))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.nat)) (A tptp.set_int) (X tptp.nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.inj_on_int_nat F) A) (=> (not (@ (@ tptp.member_nat X) B4)) (=> (= (@ (@ tptp.insert_nat X) B4) (@ (@ tptp.image_int_nat2 F) A)) (not (forall ((X10 tptp.int) (A7 tptp.set_int)) (=> (not (@ (@ tptp.member_int X10) A7)) (=> (= A (@ (@ tptp.insert_int X10) A7)) (=> (= X (@ F X10)) (not (= B4 (@ (@ tptp.image_int_nat2 F) A7)))))))))))))
% 5.65/5.93 (assert (forall ((F (-> Bool tptp.nat)) (A tptp.set_o) (X tptp.nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.inj_on_o_nat F) A) (=> (not (@ (@ tptp.member_nat X) B4)) (=> (= (@ (@ tptp.insert_nat X) B4) (@ (@ tptp.image_o_nat2 F) A)) (not (forall ((X10 Bool) (A7 tptp.set_o)) (=> (not (@ (@ tptp.member_o X10) A7)) (=> (= A (@ (@ tptp.insert_o X10) A7)) (=> (= X (@ F X10)) (not (= B4 (@ (@ tptp.image_o_nat2 F) A7)))))))))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.nat)) (A tptp.set_Product_unit) (X tptp.nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.inj_on8430439091780834860it_nat F) A) (=> (not (@ (@ tptp.member_nat X) B4)) (=> (= (@ (@ tptp.insert_nat X) B4) (@ (@ tptp.image_875570014554754200it_nat F) A)) (not (forall ((X10 tptp.product_unit) (A7 tptp.set_Product_unit)) (=> (not (@ (@ tptp.member_Product_unit X10) A7)) (=> (= A (@ (@ tptp.insert_Product_unit X10) A7)) (=> (= X (@ F X10)) (not (= B4 (@ (@ tptp.image_875570014554754200it_nat F) A7)))))))))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.set_nat) (X tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.inj_on_nat_int F) A) (=> (not (@ (@ tptp.member_int X) B4)) (=> (= (@ (@ tptp.insert_int X) B4) (@ (@ tptp.image_nat_int2 F) A)) (not (forall ((X10 tptp.nat) (A7 tptp.set_nat)) (=> (not (@ (@ tptp.member_nat X10) A7)) (=> (= A (@ (@ tptp.insert_nat X10) A7)) (=> (= X (@ F X10)) (not (= B4 (@ (@ tptp.image_nat_int2 F) A7)))))))))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.set_int) (X tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.inj_on_int_int F) A) (=> (not (@ (@ tptp.member_int X) B4)) (=> (= (@ (@ tptp.insert_int X) B4) (@ (@ tptp.image_int_int2 F) A)) (not (forall ((X10 tptp.int) (A7 tptp.set_int)) (=> (not (@ (@ tptp.member_int X10) A7)) (=> (= A (@ (@ tptp.insert_int X10) A7)) (=> (= X (@ F X10)) (not (= B4 (@ (@ tptp.image_int_int2 F) A7)))))))))))))
% 5.65/5.93 (assert (forall ((F (-> Bool tptp.int)) (A tptp.set_o) (X tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.inj_on_o_int F) A) (=> (not (@ (@ tptp.member_int X) B4)) (=> (= (@ (@ tptp.insert_int X) B4) (@ (@ tptp.image_o_int2 F) A)) (not (forall ((X10 Bool) (A7 tptp.set_o)) (=> (not (@ (@ tptp.member_o X10) A7)) (=> (= A (@ (@ tptp.insert_o X10) A7)) (=> (= X (@ F X10)) (not (= B4 (@ (@ tptp.image_o_int2 F) A7)))))))))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.int)) (A tptp.set_Product_unit) (X tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.inj_on8427948621271784584it_int F) A) (=> (not (@ (@ tptp.member_int X) B4)) (=> (= (@ (@ tptp.insert_int X) B4) (@ (@ tptp.image_873079544045703924it_int F) A)) (not (forall ((X10 tptp.product_unit) (A7 tptp.set_Product_unit)) (=> (not (@ (@ tptp.member_Product_unit X10) A7)) (=> (= A (@ (@ tptp.insert_Product_unit X10) A7)) (=> (= X (@ F X10)) (not (= B4 (@ (@ tptp.image_873079544045703924it_int F) A7)))))))))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (X tptp.nat) (S (-> tptp.int tptp.set_nat)) (Y tptp.int)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) tptp.top_top_set_int) (=> (@ _let_1 (@ (@ (@ tptp.comp_i5102403792180996084nteger S) Rep2) (@ Abs2 Y))) (@ _let_1 (@ S Y)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (X tptp.int) (S (-> tptp.int tptp.set_int)) (Y tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) tptp.top_top_set_int) (=> (@ _let_1 (@ (@ (@ tptp.comp_i1887841406321795152nteger S) Rep2) (@ Abs2 Y))) (@ _let_1 (@ S Y)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (X Bool) (S (-> tptp.int tptp.set_o)) (Y tptp.int)) (let ((_let_1 (@ tptp.member_o X))) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) tptp.top_top_set_int) (=> (@ _let_1 (@ (@ (@ tptp.comp_i5479505385629679622nteger S) Rep2) (@ Abs2 Y))) (@ _let_1 (@ S Y)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_integer tptp.int)) (Abs2 (-> tptp.int tptp.code_integer)) (X tptp.product_unit) (S (-> tptp.int tptp.set_Product_unit)) (Y tptp.int)) (let ((_let_1 (@ tptp.member_Product_unit X))) (=> (@ (@ (@ tptp.type_d8366093980585677751er_int Rep2) Abs2) tptp.top_top_set_int) (=> (@ _let_1 (@ (@ (@ tptp.comp_i3319814986458681467nteger S) Rep2) (@ Abs2 Y))) (@ _let_1 (@ S Y)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.product_unit Bool)) (Abs2 (-> Bool tptp.product_unit)) (X tptp.nat) (S (-> Bool tptp.set_nat)) (Y Bool)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep2) Abs2) tptp.top_top_set_o) (=> (@ _let_1 (@ (@ (@ tptp.comp_o9190160103024335696t_unit S) Rep2) (@ Abs2 Y))) (@ _let_1 (@ S Y)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.product_unit Bool)) (Abs2 (-> Bool tptp.product_unit)) (X tptp.int) (S (-> Bool tptp.set_int)) (Y Bool)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep2) Abs2) tptp.top_top_set_o) (=> (@ _let_1 (@ (@ (@ tptp.comp_o1521574261646630388t_unit S) Rep2) (@ Abs2 Y))) (@ _let_1 (@ S Y)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.product_unit Bool)) (Abs2 (-> Bool tptp.product_unit)) (X Bool) (S (-> Bool tptp.set_o)) (Y Bool)) (let ((_let_1 (@ tptp.member_o X))) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep2) Abs2) tptp.top_top_set_o) (=> (@ _let_1 (@ (@ (@ tptp.comp_o6895741221744486154t_unit S) Rep2) (@ Abs2 Y))) (@ _let_1 (@ S Y)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.product_unit Bool)) (Abs2 (-> Bool tptp.product_unit)) (X tptp.product_unit) (S (-> Bool tptp.set_Product_unit)) (Y Bool)) (let ((_let_1 (@ tptp.member_Product_unit X))) (=> (@ (@ (@ tptp.type_d6188575255521822967unit_o Rep2) Abs2) tptp.top_top_set_o) (=> (@ _let_1 (@ (@ (@ tptp.comp_o2086126948152544725t_unit S) Rep2) (@ Abs2 Y))) (@ _let_1 (@ S Y)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_natural tptp.nat)) (Abs2 (-> tptp.nat tptp.code_natural)) (X tptp.nat) (S (-> tptp.nat tptp.set_nat)) (Y tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep2) Abs2) tptp.top_top_set_nat) (=> (@ _let_1 (@ (@ (@ tptp.comp_n4787279007288201059atural S) Rep2) (@ Abs2 Y))) (@ _let_1 (@ S Y)))))))
% 5.65/5.93 (assert (forall ((Rep2 (-> tptp.code_natural tptp.nat)) (Abs2 (-> tptp.nat tptp.code_natural)) (X tptp.int) (S (-> tptp.nat tptp.set_int)) (Y tptp.nat)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ (@ (@ tptp.type_d4410041424927559462al_nat Rep2) Abs2) tptp.top_top_set_nat) (=> (@ _let_1 (@ (@ (@ tptp.comp_n1572716621429000127atural S) Rep2) (@ Abs2 Y))) (@ _let_1 (@ S Y)))))))
% 5.65/5.93 (assert (forall ((C tptp.product_prod_nat_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat)) (R3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat C) (@ (@ tptp.image_5168914502847457605at_nat (@ (@ tptp.produc6977886695330630970at_nat F) G)) R3)) (not (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (= C (@ (@ tptp.product_Pair_nat_nat (@ F X3)) (@ G Y2))) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)) R3))))))))
% 5.65/5.93 (assert (forall ((C tptp.product_prod_nat_nat) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat)) (R3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member8440522571783428010at_nat C) (@ (@ tptp.image_5831868185956570253at_nat (@ (@ tptp.produc5667422475138734578nt_nat F) G)) R3)) (not (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (= C (@ (@ tptp.product_Pair_nat_nat (@ F X3)) (@ G Y2))) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y2)) R3))))))))
% 5.65/5.93 (assert (forall ((C tptp.product_prod_int_int) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int)) (R3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member5262025264175285858nt_int C) (@ (@ tptp.image_1990417195239315453nt_int (@ (@ tptp.produc7347049785058425330at_int F) G)) R3)) (not (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (= C (@ (@ tptp.product_Pair_int_int (@ F X3)) (@ G Y2))) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)) R3))))))))
% 5.65/5.93 (assert (forall ((C tptp.product_prod_int_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int)) (R3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int C) (@ (@ tptp.image_2653370878348428101nt_int (@ (@ tptp.produc6036585564866528938nt_int F) G)) R3)) (not (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (= C (@ (@ tptp.product_Pair_int_int (@ F X3)) (@ G Y2))) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y2)) R3))))))))
% 5.65/5.93 (assert (forall ((C tptp.produc3658429121746597890et_nat) (F (-> tptp.nat tptp.heap_e7401611519738050253t_unit)) (G (-> tptp.nat tptp.set_nat)) (R3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member6260224972018164377et_nat C) (@ (@ tptp.image_9068448769188195518et_nat (@ (@ tptp.produc2064153442785501et_nat F) G)) R3)) (not (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (= C (@ (@ tptp.produc7507926704131184380et_nat (@ F X3)) (@ G Y2))) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y2)) R3))))))))
% 5.65/5.93 (assert (forall ((C tptp.produc3658429121746597890et_nat) (F (-> tptp.int tptp.heap_e7401611519738050253t_unit)) (G (-> tptp.int tptp.set_nat)) (R3 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member6260224972018164377et_nat C) (@ (@ tptp.image_2127501072796355446et_nat (@ (@ tptp.produc3152090231653401565et_nat F) G)) R3)) (not (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (= C (@ (@ tptp.produc7507926704131184380et_nat (@ F X3)) (@ G Y2))) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X3) Y2)) R3))))))))
% 5.65/5.93 (assert (forall ((C tptp.product_prod_nat_nat) (F (-> tptp.heap_e7401611519738050253t_unit tptp.nat)) (G (-> tptp.set_nat tptp.nat)) (R3 tptp.set_Pr3948176798113811640et_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat C) (@ (@ tptp.image_7757775281999735736at_nat (@ (@ tptp.produc8285742784527409791at_nat F) G)) R3)) (not (forall ((X3 tptp.heap_e7401611519738050253t_unit) (Y2 tptp.set_nat)) (=> (= C (@ (@ tptp.product_Pair_nat_nat (@ F X3)) (@ G Y2))) (not (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat X3) Y2)) R3))))))))
% 5.65/5.93 (assert (forall ((C tptp.product_prod_int_int) (F (-> tptp.heap_e7401611519738050253t_unit tptp.int)) (G (-> tptp.set_nat tptp.int)) (R3 tptp.set_Pr3948176798113811640et_nat)) (=> (@ (@ tptp.member5262025264175285858nt_int C) (@ (@ tptp.image_4579277974391593584nt_int (@ (@ tptp.produc5973434381925408567at_int F) G)) R3)) (not (forall ((X3 tptp.heap_e7401611519738050253t_unit) (Y2 tptp.set_nat)) (=> (= C (@ (@ tptp.product_Pair_int_int (@ F X3)) (@ G Y2))) (not (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat X3) Y2)) R3))))))))
% 5.65/5.93 (assert (forall ((C tptp.produc3658429121746597890et_nat) (F (-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit)) (G (-> tptp.set_nat tptp.set_nat)) (R3 tptp.set_Pr3948176798113811640et_nat)) (=> (@ (@ tptp.member6260224972018164377et_nat C) (@ (@ tptp.image_7426123528223433739et_nat (@ (@ tptp.produc8234977478398262212et_nat F) G)) R3)) (not (forall ((X3 tptp.heap_e7401611519738050253t_unit) (Y2 tptp.set_nat)) (=> (= C (@ (@ tptp.produc7507926704131184380et_nat (@ F X3)) (@ G Y2))) (not (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat X3) Y2)) R3))))))))
% 5.65/5.93 (assert (forall ((C tptp.product_prod_nat_nat) (F (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.nat)) (G (-> tptp.produc3658429121746597890et_nat tptp.nat)) (R3 tptp.set_Pr3286484037609594932et_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat C) (@ (@ tptp.image_7073998564157519676at_nat (@ (@ tptp.produc2784369760062397435at_nat F) G)) R3)) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3658429121746597890et_nat)) (=> (= C (@ (@ tptp.product_Pair_nat_nat (@ F X3)) (@ G Y2))) (not (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X3) Y2)) R3))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (A8 tptp.set_Code_integer)) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (= (exists ((F4 (-> tptp.code_integer tptp.code_integer))) (and (@ (@ tptp.inj_on1158064722259180589nteger F4) A) (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.image_4470545334726330049nteger F4) A)) A8))) (exists ((G3 (-> tptp.code_integer tptp.code_integer))) (= (@ (@ tptp.image_4470545334726330049nteger G3) A8) A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (A8 tptp.set_set_nat)) (=> (not (= A tptp.bot_bot_set_nat)) (= (exists ((F4 (-> tptp.nat tptp.set_nat))) (and (@ (@ tptp.inj_on_nat_set_nat F4) A) (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.image_nat_set_nat F4) A)) A8))) (exists ((G3 (-> tptp.set_nat tptp.nat))) (= (@ (@ tptp.image_set_nat_nat G3) A8) A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (A8 tptp.set_Code_integer)) (=> (not (= A tptp.bot_bot_set_nat)) (= (exists ((F4 (-> tptp.nat tptp.code_integer))) (and (@ (@ tptp.inj_on2245834603434889120nteger F4) A) (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.image_1215581382706833972nteger F4) A)) A8))) (exists ((G3 (-> tptp.code_integer tptp.nat))) (= (@ (@ tptp.image_951025933927791156er_nat G3) A8) A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_set_nat) (A8 tptp.set_nat)) (=> (not (= A tptp.bot_bot_set_set_nat)) (= (exists ((F4 (-> tptp.set_nat tptp.nat))) (and (@ (@ tptp.inj_on_set_nat_nat F4) A) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_set_nat_nat F4) A)) A8))) (exists ((G3 (-> tptp.nat tptp.set_nat))) (= (@ (@ tptp.image_nat_set_nat G3) A8) A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (A8 tptp.set_nat)) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (= (exists ((F4 (-> tptp.code_integer tptp.nat))) (and (@ (@ tptp.inj_on1981279154655846304er_nat F4) A) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_951025933927791156er_nat F4) A)) A8))) (exists ((G3 (-> tptp.nat tptp.code_integer))) (= (@ (@ tptp.image_1215581382706833972nteger G3) A8) A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (A8 tptp.set_nat)) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (exists ((F4 (-> tptp.product_unit tptp.nat))) (and (@ (@ tptp.inj_on8430439091780834860it_nat F4) A) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_875570014554754200it_nat F4) A)) A8))) (exists ((G3 (-> tptp.nat tptp.product_unit))) (= (@ (@ tptp.image_8730104196221521654t_unit G3) A8) A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (A8 tptp.set_nat)) (=> (not (= A tptp.bot_bot_set_o)) (= (exists ((F4 (-> Bool tptp.nat))) (and (@ (@ tptp.inj_on_o_nat F4) A) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_o_nat2 F4) A)) A8))) (exists ((G3 (-> tptp.nat Bool))) (= (@ (@ tptp.image_nat_o2 G3) A8) A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (A8 tptp.set_nat)) (=> (not (= A tptp.bot_bot_set_nat)) (= (exists ((F4 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.inj_on_nat_nat F4) A) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat2 F4) A)) A8))) (exists ((G3 (-> tptp.nat tptp.nat))) (= (@ (@ tptp.image_nat_nat2 G3) A8) A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (A8 tptp.set_nat)) (=> (not (= A tptp.bot_bot_set_int)) (= (exists ((F4 (-> tptp.int tptp.nat))) (and (@ (@ tptp.inj_on_int_nat F4) A) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_int_nat2 F4) A)) A8))) (exists ((G3 (-> tptp.nat tptp.int))) (= (@ (@ tptp.image_nat_int2 G3) A8) A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (A8 tptp.set_nat)) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (= (exists ((F4 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.nat))) (and (@ (@ tptp.inj_on5271586719803267564_o_nat F4) A) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_2174381888560928856_o_nat F4) A)) A8))) (exists ((G3 (-> tptp.nat tptp.produc3658429121746597890et_nat Bool))) (= (@ (@ tptp.image_4682239675366380726_nat_o G3) A8) A))))))
% 5.65/5.93 (assert (forall ((S tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.complete_Sup_Sup_int (@ (@ tptp.insert_int X) S)))) (let ((_let_2 (= S tptp.bot_bot_set_int))) (=> (@ tptp.finite_finite_int S) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.ord_max_int X) (@ tptp.complete_Sup_Sup_int S))))))))))
% 5.65/5.93 (assert (forall ((S tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.complete_Sup_Sup_nat (@ (@ tptp.insert_nat X) S)))) (let ((_let_2 (= S tptp.bot_bot_set_nat))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.ord_max_nat X) (@ tptp.complete_Sup_Sup_nat S))))))))))
% 5.65/5.93 (assert (forall ((S tptp.set_Product_unit) (X tptp.product_unit)) (let ((_let_1 (@ tptp.comple4687483117567863418t_unit (@ (@ tptp.insert_Product_unit X) S)))) (let ((_let_2 (= S tptp.bot_bo3957492148770167129t_unit))) (=> (@ tptp.finite4290736615968046902t_unit S) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (@ (@ tptp.ord_max_Product_unit X) (@ tptp.comple4687483117567863418t_unit S))))))))))
% 5.65/5.93 (assert (forall ((H2 (-> tptp.code_integer tptp.code_integer)) (N tptp.set_Code_integer)) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (= (@ H2 (@ (@ tptp.ord_max_Code_integer X3) Y2)) (@ (@ tptp.ord_max_Code_integer (@ H2 X3)) (@ H2 Y2)))) (=> (@ tptp.finite6017078050557962740nteger N) (=> (not (= N tptp.bot_bo3990330152332043303nteger)) (= (@ H2 (@ tptp.lattic4901227151466704046nteger N)) (@ tptp.lattic4901227151466704046nteger (@ (@ tptp.image_4470545334726330049nteger H2) N))))))))
% 5.65/5.93 (assert (forall ((H2 (-> tptp.product_unit tptp.product_unit)) (N tptp.set_Product_unit)) (=> (forall ((X3 tptp.product_unit) (Y2 tptp.product_unit)) (= (@ H2 (@ (@ tptp.ord_max_Product_unit X3) Y2)) (@ (@ tptp.ord_max_Product_unit (@ H2 X3)) (@ H2 Y2)))) (=> (@ tptp.finite4290736615968046902t_unit N) (=> (not (= N tptp.bot_bo3957492148770167129t_unit)) (= (@ H2 (@ tptp.lattic1210392890313158908t_unit N)) (@ tptp.lattic1210392890313158908t_unit (@ (@ tptp.image_405062704495631173t_unit H2) N))))))))
% 5.65/5.93 (assert (forall ((H2 (-> Bool Bool)) (N tptp.set_o)) (=> (forall ((X3 Bool) (Y2 Bool)) (= (@ H2 (@ (@ tptp.ord_max_o X3) Y2)) (@ (@ tptp.ord_max_o (@ H2 X3)) (@ H2 Y2)))) (=> (@ tptp.finite_finite_o N) (=> (not (= N tptp.bot_bot_set_o)) (= (@ H2 (@ tptp.lattic1921953407002678535_Max_o N)) (@ tptp.lattic1921953407002678535_Max_o (@ (@ tptp.image_o_o2 H2) N))))))))
% 5.65/5.93 (assert (forall ((H2 (-> tptp.int tptp.int)) (N tptp.set_int)) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (= (@ H2 (@ (@ tptp.ord_max_int X3) Y2)) (@ (@ tptp.ord_max_int (@ H2 X3)) (@ H2 Y2)))) (=> (@ tptp.finite_finite_int N) (=> (not (= N tptp.bot_bot_set_int)) (= (@ H2 (@ tptp.lattic8263393255366662781ax_int N)) (@ tptp.lattic8263393255366662781ax_int (@ (@ tptp.image_int_int2 H2) N))))))))
% 5.65/5.93 (assert (forall ((H2 (-> tptp.nat tptp.nat)) (N tptp.set_nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (= (@ H2 (@ (@ tptp.ord_max_nat X3) Y2)) (@ (@ tptp.ord_max_nat (@ H2 X3)) (@ H2 Y2)))) (=> (@ tptp.finite_finite_nat N) (=> (not (= N tptp.bot_bot_set_nat)) (= (@ H2 (@ tptp.lattic8265883725875713057ax_nat N)) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_nat_nat2 H2) N))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.lattic4901227151466704046nteger A))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= B4 tptp.bot_bo3990330152332043303nteger)) (=> (@ (@ tptp.ord_le7084787975880047091nteger B4) A) (= (@ (@ tptp.ord_max_Code_integer (@ tptp.lattic4901227151466704046nteger B4)) _let_1) _let_1)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.lattic1210392890313158908t_unit A))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= B4 tptp.bot_bo3957492148770167129t_unit)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit B4) A) (= (@ (@ tptp.ord_max_Product_unit (@ tptp.lattic1210392890313158908t_unit B4)) _let_1) _let_1)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.lattic1921953407002678535_Max_o A))) (=> (@ tptp.finite_finite_o A) (=> (not (= B4 tptp.bot_bot_set_o)) (=> (@ (@ tptp.ord_less_eq_set_o B4) A) (= (@ (@ tptp.ord_max_o (@ tptp.lattic1921953407002678535_Max_o B4)) _let_1) _let_1)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.lattic8263393255366662781ax_int A))) (=> (@ tptp.finite_finite_int A) (=> (not (= B4 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B4) A) (= (@ (@ tptp.ord_max_int (@ tptp.lattic8263393255366662781ax_int B4)) _let_1) _let_1)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.lattic8265883725875713057ax_nat A))) (=> (@ tptp.finite_finite_nat A) (=> (not (= B4 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A) (= (@ (@ tptp.ord_max_nat (@ tptp.lattic8265883725875713057ax_nat B4)) _let_1) _let_1)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (@ (@ tptp.member_Code_integer X) A)) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (= (@ tptp.lattic4901227151466704046nteger (@ (@ tptp.insert_Code_integer X) A)) (@ (@ tptp.ord_max_Code_integer X) (@ tptp.lattic4901227151466704046nteger A))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (@ (@ tptp.member_Product_unit X) A)) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (@ tptp.lattic1210392890313158908t_unit (@ (@ tptp.insert_Product_unit X) A)) (@ (@ tptp.ord_max_Product_unit X) (@ tptp.lattic1210392890313158908t_unit A))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (@ (@ tptp.member_o X) A)) (=> (not (= A tptp.bot_bot_set_o)) (= (@ tptp.lattic1921953407002678535_Max_o (@ (@ tptp.insert_o X) A)) (@ (@ tptp.ord_max_o X) (@ tptp.lattic1921953407002678535_Max_o A))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (@ (@ tptp.member_int X) A)) (=> (not (= A tptp.bot_bot_set_int)) (= (@ tptp.lattic8263393255366662781ax_int (@ (@ tptp.insert_int X) A)) (@ (@ tptp.ord_max_int X) (@ tptp.lattic8263393255366662781ax_int A))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (@ (@ tptp.member_nat X) A)) (=> (not (= A tptp.bot_bot_set_nat)) (= (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.insert_nat X) A)) (@ (@ tptp.ord_max_nat X) (@ tptp.lattic8265883725875713057ax_nat A))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (@ (@ tptp.member_Code_integer (@ (@ tptp.ord_max_Code_integer X3) Y2)) (@ (@ tptp.insert_Code_integer X3) (@ (@ tptp.insert_Code_integer Y2) tptp.bot_bo3990330152332043303nteger)))) (@ (@ tptp.member_Code_integer (@ tptp.lattic4901227151466704046nteger A)) A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((X3 tptp.product_unit) (Y2 tptp.product_unit)) (@ (@ tptp.member_Product_unit (@ (@ tptp.ord_max_Product_unit X3) Y2)) (@ (@ tptp.insert_Product_unit X3) (@ (@ tptp.insert_Product_unit Y2) tptp.bot_bo3957492148770167129t_unit)))) (@ (@ tptp.member_Product_unit (@ tptp.lattic1210392890313158908t_unit A)) A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (=> (forall ((X3 Bool) (Y2 Bool)) (@ (@ tptp.member_o (@ (@ tptp.ord_max_o X3) Y2)) (@ (@ tptp.insert_o X3) (@ (@ tptp.insert_o Y2) tptp.bot_bot_set_o)))) (@ (@ tptp.member_o (@ tptp.lattic1921953407002678535_Max_o A)) A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int) (Y2 tptp.int)) (@ (@ tptp.member_int (@ (@ tptp.ord_max_int X3) Y2)) (@ (@ tptp.insert_int X3) (@ (@ tptp.insert_int Y2) tptp.bot_bot_set_int)))) (@ (@ tptp.member_int (@ tptp.lattic8263393255366662781ax_int A)) A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (@ (@ tptp.member_nat (@ (@ tptp.ord_max_nat X3) Y2)) (@ (@ tptp.insert_nat X3) (@ (@ tptp.insert_nat Y2) tptp.bot_bot_set_nat)))) (@ (@ tptp.member_nat (@ tptp.lattic8265883725875713057ax_nat A)) A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (=> (@ tptp.finite6017078050557962740nteger B4) (=> (not (= B4 tptp.bot_bo3990330152332043303nteger)) (= (@ tptp.lattic4901227151466704046nteger (@ (@ tptp.sup_su848401254843788991nteger A) B4)) (@ (@ tptp.ord_max_Code_integer (@ tptp.lattic4901227151466704046nteger A)) (@ tptp.lattic4901227151466704046nteger B4)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.finite4290736615968046902t_unit B4) (=> (not (= B4 tptp.bot_bo3957492148770167129t_unit)) (= (@ tptp.lattic1210392890313158908t_unit (@ (@ tptp.sup_su793286257634532545t_unit A) B4)) (@ (@ tptp.ord_max_Product_unit (@ tptp.lattic1210392890313158908t_unit A)) (@ tptp.lattic1210392890313158908t_unit B4)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.finite_finite_o B4) (=> (not (= B4 tptp.bot_bot_set_o)) (= (@ tptp.lattic1921953407002678535_Max_o (@ (@ tptp.sup_sup_set_o A) B4)) (@ (@ tptp.ord_max_o (@ tptp.lattic1921953407002678535_Max_o A)) (@ tptp.lattic1921953407002678535_Max_o B4)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.finite_finite_int B4) (=> (not (= B4 tptp.bot_bot_set_int)) (= (@ tptp.lattic8263393255366662781ax_int (@ (@ tptp.sup_sup_set_int A) B4)) (@ (@ tptp.ord_max_int (@ tptp.lattic8263393255366662781ax_int A)) (@ tptp.lattic8263393255366662781ax_int B4)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.finite_finite_nat B4) (=> (not (= B4 tptp.bot_bot_set_nat)) (= (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.ord_max_nat (@ tptp.lattic8265883725875713057ax_nat A)) (@ tptp.lattic8265883725875713057ax_nat B4)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (= (@ tptp.lattic1921953407002678535_Max_o (@ (@ tptp.insert_o X) A)) (@ (@ (@ tptp.finite_fold_o_o tptp.ord_max_o) X) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (= (@ tptp.lattic1210392890313158908t_unit (@ (@ tptp.insert_Product_unit X) A)) (@ (@ (@ tptp.finite8834431295148555784t_unit tptp.ord_max_Product_unit) X) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ tptp.lattic4901227151466704046nteger (@ (@ tptp.insert_Code_integer X) A)) (@ (@ (@ tptp.finite6454954857057555716nteger tptp.ord_max_Code_integer) X) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (= (@ tptp.lattic8263393255366662781ax_int (@ (@ tptp.insert_int X) A)) (@ (@ (@ tptp.finite_fold_int_int tptp.ord_max_int) X) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (= (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.insert_nat X) A)) (@ (@ (@ tptp.finite_fold_nat_nat tptp.ord_max_nat) X) A)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.produc2591615631378489102nteger))) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_951025933927791156er_nat (@ (@ tptp.comp_P5725896914063526938nteger tptp.produc8897218493789310642nteger) F)) tptp.top_to4645266643341252675nteger)) (=> (@ tptp.finite6017078050557962740nteger (@ (@ tptp.image_4470545334726330049nteger (@ (@ tptp.comp_P6122662217367900327nteger tptp.produc1781891006948753140nteger) F)) tptp.top_to4645266643341252675nteger)) (@ tptp.finite1154042800025562295nteger (@ (@ tptp.image_3408592110290467754nteger F) tptp.top_to4645266643341252675nteger))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.produc6433947425880249742er_nat))) (=> (@ tptp.finite6017078050557962740nteger (@ (@ tptp.image_4470545334726330049nteger (@ (@ tptp.comp_P7101464685127059239nteger tptp.produc8632663045010267826er_nat) F)) tptp.top_to4645266643341252675nteger)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_951025933927791156er_nat (@ (@ tptp.comp_P5964733648194011802nteger tptp.produc1517335558169710324er_nat) F)) tptp.top_to4645266643341252675nteger)) (@ tptp.finite4996374594527322935er_nat (@ (@ tptp.image_7250923904792228394er_nat F) tptp.top_to4645266643341252675nteger))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.produc8923325533196201883nteger))) (=> (@ tptp.finite6017078050557962740nteger (@ (@ tptp.image_4470545334726330049nteger (@ (@ tptp.comp_P7111796090210262324nteger tptp.produc8508995932063986495nteger) F)) tptp.top_to4645266643341252675nteger)) (=> (@ tptp.finite6017078050557962740nteger (@ (@ tptp.image_4470545334726330049nteger (@ (@ tptp.comp_P7111796090210262324nteger tptp.produc6174133586879617921nteger) F)) tptp.top_to4645266643341252675nteger)) (@ tptp.finite2154694888287295812nteger (@ (@ tptp.image_8049062792287394871nteger F) tptp.top_to4645266643341252675nteger))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.product_prod_nat_nat))) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_875570014554754200it_nat (@ (@ tptp.comp_P2980510830910040157t_unit tptp.product_fst_nat_nat) F)) tptp.top_to1996260823553986621t_unit)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_875570014554754200it_nat (@ (@ tptp.comp_P2980510830910040157t_unit tptp.product_snd_nat_nat) F)) tptp.top_to1996260823553986621t_unit)) (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.image_7281959405765017145at_nat F) tptp.top_to1996260823553986621t_unit))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.produc2591615631378489102nteger))) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_875570014554754200it_nat (@ (@ tptp.comp_P7621350044865347728t_unit tptp.produc8897218493789310642nteger) F)) tptp.top_to1996260823553986621t_unit)) (=> (@ tptp.finite6017078050557962740nteger (@ (@ tptp.image_3815118110082124069nteger (@ (@ tptp.comp_P7320554561093743171t_unit tptp.produc1781891006948753140nteger) F)) tptp.top_to1996260823553986621t_unit)) (@ tptp.finite1154042800025562295nteger (@ (@ tptp.image_4946983642536848454nteger F) tptp.top_to1996260823553986621t_unit))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.produc6433947425880249742er_nat))) (=> (@ tptp.finite6017078050557962740nteger (@ (@ tptp.image_3815118110082124069nteger (@ (@ tptp.comp_P7581484221039074243t_unit tptp.produc8632663045010267826er_nat) F)) tptp.top_to1996260823553986621t_unit)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_875570014554754200it_nat (@ (@ tptp.comp_P6821003776282389008t_unit tptp.produc1517335558169710324er_nat) F)) tptp.top_to1996260823553986621t_unit)) (@ tptp.finite4996374594527322935er_nat (@ (@ tptp.image_8789315437038609094er_nat F) tptp.top_to1996260823553986621t_unit))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.produc8923325533196201883nteger))) (=> (@ tptp.finite6017078050557962740nteger (@ (@ tptp.image_3815118110082124069nteger (@ (@ tptp.comp_P659088277599099894t_unit tptp.produc8508995932063986495nteger) F)) tptp.top_to1996260823553986621t_unit)) (=> (@ tptp.finite6017078050557962740nteger (@ (@ tptp.image_3815118110082124069nteger (@ (@ tptp.comp_P659088277599099894t_unit tptp.produc6174133586879617921nteger) F)) tptp.top_to1996260823553986621t_unit)) (@ tptp.finite2154694888287295812nteger (@ (@ tptp.image_8089323762101378259nteger F) tptp.top_to1996260823553986621t_unit))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.product_prod_int_int))) (=> (@ tptp.finite_finite_int (@ (@ tptp.image_873079544045703924it_int (@ (@ tptp.comp_P6796073005956588617t_unit tptp.product_fst_int_int) F)) tptp.top_to1996260823553986621t_unit)) (=> (@ tptp.finite_finite_int (@ (@ tptp.image_873079544045703924it_int (@ (@ tptp.comp_P6796073005956588617t_unit tptp.product_snd_int_int) F)) tptp.top_to1996260823553986621t_unit)) (@ tptp.finite2998713641127702882nt_int (@ (@ tptp.image_4103462098156874993nt_int F) tptp.top_to1996260823553986621t_unit))))))
% 5.65/5.93 (assert (forall ((F (-> Bool tptp.product_prod_nat_nat))) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_o_nat2 (@ (@ tptp.comp_P4394204175247225320_nat_o tptp.product_fst_nat_nat) F)) tptp.top_top_set_o)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_o_nat2 (@ (@ tptp.comp_P4394204175247225320_nat_o tptp.product_snd_nat_nat) F)) tptp.top_top_set_o)) (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.image_3855930084881510382at_nat F) tptp.top_top_set_o))))))
% 5.65/5.93 (assert (forall ((F (-> Bool tptp.produc2591615631378489102nteger))) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_o_nat2 (@ (@ tptp.comp_P7179991235626930843_nat_o tptp.produc8897218493789310642nteger) F)) tptp.top_top_set_o)) (=> (@ tptp.finite6017078050557962740nteger (@ (@ tptp.image_o_Code_integer (@ (@ tptp.comp_P7177471617286032590eger_o tptp.produc1781891006948753140nteger) F)) tptp.top_top_set_o)) (@ tptp.finite1154042800025562295nteger (@ (@ tptp.image_8407096251609565691nteger F) tptp.top_top_set_o))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer))) (= (@ (@ tptp.inj_on20428373856169009nteger (@ tptp.produc6499014454317279255nteger F)) tptp.top_to2363841527343591755nteger) (@ (@ tptp.inj_on1158064722259180589nteger F) tptp.top_to4645266643341252675nteger))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.product_unit)) (R2 tptp.set_Pr5094982260447487303t_unit)) (let ((_let_1 (@ tptp.total_5665700600833547665t_unit tptp.top_to1996260823553986621t_unit))) (=> (@ (@ tptp.inj_on8151373323710067377t_unit F) tptp.top_to1996260823553986621t_unit) (=> (@ _let_1 R2) (@ _let_1 (@ (@ tptp.inv_im8770536620514187154t_unit R2) F)))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit Bool)) (R2 tptp.set_Product_prod_o_o)) (=> (@ (@ tptp.inj_on8854722734121536060unit_o F) tptp.top_to1996260823553986621t_unit) (=> (@ (@ tptp.total_on_o tptp.top_top_set_o) R2) (@ (@ tptp.total_5665700600833547665t_unit tptp.top_to1996260823553986621t_unit) (@ (@ tptp.inv_im4602722609573551687t_unit R2) F))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.nat)) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.inj_on8430439091780834860it_nat F) tptp.top_to1996260823553986621t_unit) (=> (@ (@ tptp.total_on_nat tptp.top_top_set_nat) R2) (@ (@ tptp.total_5665700600833547665t_unit tptp.top_to1996260823553986621t_unit) (@ (@ tptp.inv_im7624054837341743209t_unit R2) F))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.product_unit tptp.int)) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.inj_on8427948621271784584it_int F) tptp.top_to1996260823553986621t_unit) (=> (@ (@ tptp.total_on_int tptp.top_top_set_int) R2) (@ (@ tptp.total_5665700600833547665t_unit tptp.top_to1996260823553986621t_unit) (@ (@ tptp.inv_im4740476784543923469t_unit R2) F))))))
% 5.65/5.93 (assert (forall ((F (-> Bool tptp.product_unit)) (R2 tptp.set_Pr5094982260447487303t_unit)) (=> (@ (@ tptp.inj_on4268752236855399398t_unit F) tptp.top_top_set_o) (=> (@ (@ tptp.total_5665700600833547665t_unit tptp.top_to1996260823553986621t_unit) R2) (@ (@ tptp.total_on_o tptp.top_top_set_o) (@ (@ tptp.inv_im9188693106839688349unit_o R2) F))))))
% 5.65/5.93 (assert (forall ((F (-> Bool Bool)) (R2 tptp.set_Product_prod_o_o)) (let ((_let_1 (@ tptp.total_on_o tptp.top_top_set_o))) (=> (@ (@ tptp.inj_on_o_o F) tptp.top_top_set_o) (=> (@ _let_1 R2) (@ _let_1 (@ (@ tptp.inv_image_o_o R2) F)))))))
% 5.65/5.93 (assert (forall ((F (-> Bool tptp.nat)) (R2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.inj_on_o_nat F) tptp.top_top_set_o) (=> (@ (@ tptp.total_on_nat tptp.top_top_set_nat) R2) (@ (@ tptp.total_on_o tptp.top_top_set_o) (@ (@ tptp.inv_image_nat_o R2) F))))))
% 5.65/5.93 (assert (forall ((F (-> Bool tptp.int)) (R2 tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.inj_on_o_int F) tptp.top_top_set_o) (=> (@ (@ tptp.total_on_int tptp.top_top_set_int) R2) (@ (@ tptp.total_on_o tptp.top_top_set_o) (@ (@ tptp.inv_image_int_o R2) F))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat tptp.product_unit)) (R2 tptp.set_Pr5094982260447487303t_unit)) (=> (@ (@ tptp.inj_on7061601236592826506t_unit F) tptp.top_top_set_nat) (=> (@ (@ tptp.total_5665700600833547665t_unit tptp.top_to1996260823553986621t_unit) R2) (@ (@ tptp.total_on_nat tptp.top_top_set_nat) (@ (@ tptp.inv_im8992892692529751563it_nat R2) F))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat Bool)) (R2 tptp.set_Product_prod_o_o)) (=> (@ (@ tptp.inj_on_nat_o F) tptp.top_top_set_nat) (=> (@ (@ tptp.total_on_o tptp.top_top_set_o) R2) (@ (@ tptp.total_on_nat tptp.top_top_set_nat) (@ (@ tptp.inv_image_o_nat R2) F))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ (@ tptp.member_Code_integer X) A) (@ (@ tptp.ord_less_nat (@ tptp.finite4902975817058060853nteger (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer X) tptp.bot_bo3990330152332043303nteger)))) (@ tptp.finite4902975817058060853nteger A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ (@ tptp.member_Product_unit X) A) (@ (@ tptp.ord_less_nat (@ tptp.finite410649719033368117t_unit (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)))) (@ tptp.finite410649719033368117t_unit A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (@ (@ tptp.member_o X) A) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)))) (@ tptp.finite_card_o A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (@ (@ tptp.member_int X) A) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))) (@ tptp.finite_card_int A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (@ (@ tptp.member6576561426505652726_nat_o X) A) (@ (@ tptp.ord_less_nat (@ tptp.finite1363419556375932405_nat_o (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)))) (@ tptp.finite1363419556375932405_nat_o A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (@ (@ tptp.member_nat X) A) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))) (@ tptp.finite_card_nat A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ (@ tptp.member_Code_integer X) A) (=> (@ (@ tptp.member_Code_integer Y) A) (@ (@ tptp.ord_less_nat (@ tptp.finite4902975817058060853nteger (@ (@ tptp.minus_2355218937544613996nteger (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer X) tptp.bot_bo3990330152332043303nteger))) (@ (@ tptp.insert_Code_integer Y) tptp.bot_bo3990330152332043303nteger)))) (@ tptp.finite4902975817058060853nteger A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit) (Y tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ (@ tptp.member_Product_unit X) A) (=> (@ (@ tptp.member_Product_unit Y) A) (@ (@ tptp.ord_less_nat (@ tptp.finite410649719033368117t_unit (@ (@ tptp.minus_6452836326544984404t_unit (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit))) (@ (@ tptp.insert_Product_unit Y) tptp.bot_bo3957492148770167129t_unit)))) (@ tptp.finite410649719033368117t_unit A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (X Bool) (Y Bool)) (=> (@ tptp.finite_finite_o A) (=> (@ (@ tptp.member_o X) A) (=> (@ (@ tptp.member_o Y) A) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))) (@ (@ tptp.insert_o Y) tptp.bot_bot_set_o)))) (@ tptp.finite_card_o A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (X tptp.int) (Y tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (@ (@ tptp.member_int X) A) (=> (@ (@ tptp.member_int Y) A) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (@ (@ tptp.insert_int Y) tptp.bot_bot_set_int)))) (@ tptp.finite_card_int A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (@ (@ tptp.member6576561426505652726_nat_o X) A) (=> (@ (@ tptp.member6576561426505652726_nat_o Y) A) (@ (@ tptp.ord_less_nat (@ tptp.finite1363419556375932405_nat_o (@ (@ tptp.minus_1801376950450012436_nat_o (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o))) (@ (@ tptp.insert5175938949040314269_nat_o Y) tptp.bot_bo7824918357723582233_nat_o)))) (@ tptp.finite1363419556375932405_nat_o A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (@ (@ tptp.member_nat X) A) (=> (@ (@ tptp.member_nat Y) A) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.minus_minus_set_nat A) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (@ (@ tptp.insert_nat Y) tptp.bot_bot_set_nat)))) (@ tptp.finite_card_nat A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite4902975817058060853nteger (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer X) tptp.bot_bo3990330152332043303nteger)))) (@ tptp.finite4902975817058060853nteger A)) (and (@ tptp.finite6017078050557962740nteger A) (@ (@ tptp.member_Code_integer X) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite410649719033368117t_unit (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)))) (@ tptp.finite410649719033368117t_unit A)) (and (@ tptp.finite4290736615968046902t_unit A) (@ (@ tptp.member_Product_unit X) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (X Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)))) (@ tptp.finite_card_o A)) (and (@ tptp.finite_finite_o A) (@ (@ tptp.member_o X) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (X tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))) (@ tptp.finite_card_int A)) (and (@ tptp.finite_finite_int A) (@ (@ tptp.member_int X) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (= (@ (@ tptp.ord_less_nat (@ tptp.finite1363419556375932405_nat_o (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)))) (@ tptp.finite1363419556375932405_nat_o A)) (and (@ tptp.finite3252695134891459830_nat_o A) (@ (@ tptp.member6576561426505652726_nat_o X) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))) (@ tptp.finite_card_nat A)) (and (@ tptp.finite_finite_nat A) (@ (@ tptp.member_nat X) A)))))
% 5.65/5.93 (assert (forall ((B9 tptp.set_set_nat) (A11 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B9) (=> (not (= B9 tptp.bot_bot_set_set_nat)) (=> (@ (@ (@ tptp.pred_chain_set_nat A11) tptp.ord_less_set_nat) B9) (@ (@ tptp.member_set_nat (@ tptp.comple7806235888213564991et_nat B9)) B9))))))
% 5.65/5.93 (assert (forall ((S tptp.set_Product_unit)) (= (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) (@ tptp.finite410649719033368117t_unit S)) (= S tptp.top_to1996260823553986621t_unit))))
% 5.65/5.93 (assert (forall ((S tptp.set_o)) (= (= (@ tptp.finite_card_o tptp.top_top_set_o) (@ tptp.finite_card_o S)) (= S tptp.top_top_set_o))))
% 5.65/5.93 (assert (forall ((S tptp.set_Product_unit)) (= (= (@ tptp.finite410649719033368117t_unit S) (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit)) (= S tptp.top_to1996260823553986621t_unit))))
% 5.65/5.93 (assert (forall ((S tptp.set_o)) (= (= (@ tptp.finite_card_o S) (@ tptp.finite_card_o tptp.top_top_set_o)) (= S tptp.top_top_set_o))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int)) (X tptp.product_prod_int_int)) (= (@ tptp.product_fst_int_int (@ (@ (@ tptp.produc6036585564866528938nt_int F) G) X)) (@ F (@ tptp.product_fst_int_int X)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit)) (X tptp.heap_e7401611519738050253t_unit) (Y tptp.set_nat)) (= (@ (@ tptp.produc4172003873565521026et_nat F) (@ (@ tptp.produc7507926704131184380et_nat X) Y)) (@ (@ tptp.produc7507926704131184380et_nat (@ F X)) Y))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.produc986720760941809198at_nat F) (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ tptp.product_Pair_nat_nat (@ F X)) Y))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.int)) (X tptp.int) (Y tptp.int)) (= (@ (@ tptp.produc2355237562570658114nt_int F) (@ (@ tptp.product_Pair_int_int X) Y)) (@ (@ tptp.product_Pair_int_int (@ F X)) Y))))
% 5.65/5.93 (assert (forall ((F (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool)) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.produc3198230245617193214et_nat F) (@ (@ tptp.produc5001842942810119800et_nat X) Y)) (@ (@ tptp.produc5001842942810119800et_nat (@ F X)) Y))))
% 5.65/5.93 (assert (forall ((F (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool)) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3925858234332021118et_nat)) (= (@ (@ tptp.produc1442628905706551930et_nat F) (@ (@ tptp.produc2245416461498447860et_nat X) Y)) (@ (@ tptp.produc2245416461498447860et_nat (@ F X)) Y))))
% 5.65/5.93 (assert (forall ((F (-> tptp.set_nat tptp.set_nat)) (X tptp.heap_e7401611519738050253t_unit) (Y tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat X))) (= (@ (@ tptp.produc3286488329990770625t_unit F) (@ _let_1 Y)) (@ _let_1 (@ F Y))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X))) (= (@ (@ tptp.produc3094765310956027504at_nat F) (@ _let_1 Y)) (@ _let_1 (@ F Y))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.int)) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int X))) (= (@ (@ tptp.produc4463282112584876420nt_int F) (@ _let_1 Y)) (@ _let_1 (@ F Y))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat)) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.produc5001842942810119800et_nat X))) (= (@ (@ tptp.produc8750854537940449737_nat_o F) (@ _let_1 Y)) (@ _let_1 (@ F Y))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat)) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.produc7714581247149323085_nat_o F) (@ (@ tptp.produc5001842942810119800et_nat X) Y)) (@ (@ tptp.produc2245416461498447860et_nat X) (@ F Y)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.produc3925858234332021118et_nat tptp.produc3658429121746597890et_nat)) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3925858234332021118et_nat)) (= (@ (@ tptp.produc1515462096303866701_nat_o F) (@ (@ tptp.produc2245416461498447860et_nat X) Y)) (@ (@ tptp.produc5001842942810119800et_nat X) (@ F Y)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.produc3925858234332021118et_nat tptp.produc3925858234332021118et_nat)) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ tptp.produc2245416461498447860et_nat X))) (= (@ (@ tptp.produc969530845752564945_nat_o F) (@ _let_1 Y)) (@ _let_1 (@ F Y))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.produc1086072967326762835nteger X))) (= (@ (@ tptp.produc6499014454317279255nteger F) (@ _let_1 Y)) (@ _let_1 (@ F Y))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.int)) (X tptp.product_prod_int_int)) (= (@ tptp.product_fst_int_int (@ (@ tptp.produc2355237562570658114nt_int F) X)) (@ F (@ tptp.product_fst_int_int X)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit)) (X tptp.produc3658429121746597890et_nat)) (= (@ tptp.produc8586169260539613262et_nat (@ (@ tptp.produc4172003873565521026et_nat F) X)) (@ tptp.produc8586169260539613262et_nat X))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.int)) (X tptp.product_prod_int_int)) (= (@ tptp.product_snd_int_int (@ (@ tptp.produc2355237562570658114nt_int F) X)) (@ tptp.product_snd_int_int X))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat) (R2 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.nat tptp.nat))) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ tptp.inv_image_nat_nat R2) F)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat (@ F X)) (@ F Y))) R2))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat) (R2 tptp.set_Pr958786334691620121nt_int) (F (-> tptp.nat tptp.int))) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ tptp.inv_image_int_nat R2) F)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int (@ F X)) (@ F Y))) R2))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int) (R2 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.int tptp.nat))) (= (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ (@ tptp.inv_image_nat_int R2) F)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat (@ F X)) (@ F Y))) R2))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int) (R2 tptp.set_Pr958786334691620121nt_int) (F (-> tptp.int tptp.int))) (= (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) (@ (@ tptp.inv_image_int_int R2) F)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int (@ F X)) (@ F Y))) R2))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (X tptp.produc8923325533196201883nteger)) (= (@ tptp.produc8508995932063986495nteger (@ (@ tptp.produc6499014454317279255nteger F) X)) (@ tptp.produc8508995932063986495nteger X))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.int)) (X tptp.product_prod_int_int)) (= (@ tptp.product_fst_int_int (@ (@ tptp.produc4463282112584876420nt_int F) X)) (@ tptp.product_fst_int_int X))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (X tptp.produc8923325533196201883nteger) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.produc6174133586879617921nteger X))) (= (= (@ (@ tptp.produc6499014454317279255nteger F) X) (@ (@ tptp.produc6499014454317279255nteger G) X)) (= (@ F _let_1) (@ G _let_1))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (X tptp.produc8923325533196201883nteger)) (= (@ tptp.produc6174133586879617921nteger (@ (@ tptp.produc6499014454317279255nteger F) X)) (@ F (@ tptp.produc6174133586879617921nteger X)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.set_nat tptp.set_nat)) (X tptp.produc3658429121746597890et_nat)) (= (@ tptp.produc8586169260539613262et_nat (@ (@ tptp.produc3286488329990770625t_unit F) X)) (@ F (@ tptp.produc8586169260539613262et_nat X)))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.int)) (X tptp.product_prod_int_int)) (= (@ tptp.product_snd_int_int (@ (@ tptp.produc4463282112584876420nt_int F) X)) (@ F (@ tptp.product_snd_int_int X)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit)) (= (= (@ tptp.comple2584293577114468500t_unit A) tptp.bot_bot_Product_unit) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.ord_le361264281704409273t_unit tptp.bot_bot_Product_unit) X2) (exists ((Y3 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit Y3) A) (@ (@ tptp.ord_le361264281704409273t_unit Y3) X2))))))))
% 5.65/5.93 (assert (= (@ tptp.complete_Inf_Inf_o tptp.bot_bot_set_o) tptp.top_top_o))
% 5.65/5.93 (assert (= (@ tptp.comple90455603224345172_nat_o tptp.bot_bo7824918357723582233_nat_o) tptp.top_to5213382387105117981_nat_o))
% 5.65/5.93 (assert (= (@ tptp.comple7216939928495492468t_unit tptp.bot_bo6284674557190688313t_unit) tptp.top_to1996260823553986621t_unit))
% 5.65/5.93 (assert (= (@ tptp.comple3063163877087187839_set_o tptp.bot_bot_set_set_o) tptp.top_top_set_o))
% 5.65/5.93 (assert (= (@ tptp.comple3628384868704368283et_int tptp.bot_bot_set_set_int) tptp.top_top_set_int))
% 5.65/5.93 (assert (= (@ tptp.comple7806235888213564991et_nat tptp.bot_bot_set_set_nat) tptp.top_top_set_nat))
% 5.65/5.93 (assert (= (@ tptp.comple2584293577114468500t_unit tptp.bot_bo3957492148770167129t_unit) tptp.top_top_Product_unit))
% 5.65/5.93 (assert (= (@ tptp.comple7216939928495492468t_unit tptp.top_to1767297665138865437t_unit) tptp.bot_bo3957492148770167129t_unit))
% 5.65/5.93 (assert (= (@ tptp.comple3063163877087187839_set_o tptp.top_top_set_set_o) tptp.bot_bot_set_o))
% 5.65/5.93 (assert (= (@ tptp.comple3628384868704368283et_int tptp.top_top_set_set_int) tptp.bot_bot_set_int))
% 5.65/5.93 (assert (= (@ tptp.comple79274577958421812_nat_o tptp.top_to8515903933492314333_nat_o) tptp.bot_bo7824918357723582233_nat_o))
% 5.65/5.93 (assert (= (@ tptp.complete_Inf_Inf_o tptp.top_top_set_o) tptp.bot_bot_o))
% 5.65/5.93 (assert (= (@ tptp.comple7806235888213564991et_nat tptp.top_top_set_set_nat) tptp.bot_bot_set_nat))
% 5.65/5.93 (assert (= (@ tptp.comple2584293577114468500t_unit tptp.top_to1996260823553986621t_unit) tptp.bot_bot_Product_unit))
% 5.65/5.93 (assert (forall ((X Bool)) (= (@ tptp.complete_Inf_Inf_o (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)) X)))
% 5.65/5.93 (assert (forall ((X tptp.int)) (= (@ tptp.complete_Inf_Inf_int (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)) X)))
% 5.65/5.93 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool))) (= (@ tptp.comple90455603224345172_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)) X)))
% 5.65/5.93 (assert (forall ((X tptp.nat)) (= (@ tptp.complete_Inf_Inf_nat (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)) X)))
% 5.65/5.93 (assert (forall ((X tptp.set_nat)) (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.insert_set_nat X) tptp.bot_bot_set_set_nat)) X)))
% 5.65/5.93 (assert (forall ((X tptp.product_unit)) (= (@ tptp.comple2584293577114468500t_unit (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)) X)))
% 5.65/5.93 (assert (forall ((A2 Bool) (A tptp.set_o)) (= (@ tptp.complete_Inf_Inf_o (@ (@ tptp.insert_o A2) A)) (@ (@ tptp.inf_inf_o A2) (@ tptp.complete_Inf_Inf_o A)))))
% 5.65/5.93 (assert (forall ((A2 tptp.set_nat) (A tptp.set_set_nat)) (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.insert_set_nat A2) A)) (@ (@ tptp.inf_inf_set_nat A2) (@ tptp.comple7806235888213564991et_nat A)))))
% 5.65/5.93 (assert (forall ((A2 tptp.product_unit) (A tptp.set_Product_unit)) (= (@ tptp.comple2584293577114468500t_unit (@ (@ tptp.insert_Product_unit A2) A)) (@ (@ tptp.inf_inf_Product_unit A2) (@ tptp.comple2584293577114468500t_unit A)))))
% 5.65/5.93 (assert (forall ((Prod tptp.product_prod_nat_nat)) (= (@ (@ tptp.product_Pair_nat_nat (@ tptp.product_fst_nat_nat Prod)) (@ tptp.product_snd_nat_nat Prod)) Prod)))
% 5.65/5.93 (assert (forall ((Prod tptp.produc3925858234332021118et_nat)) (= (@ (@ tptp.produc5001842942810119800et_nat (@ tptp.produc995936583742144908et_nat Prod)) (@ tptp.produc4011572625026189258et_nat Prod)) Prod)))
% 5.65/5.93 (assert (forall ((Prod tptp.produc2732055786443039994et_nat)) (= (@ (@ tptp.produc2245416461498447860et_nat (@ tptp.produc180342877477747464et_nat Prod)) (@ tptp.produc5374455773327741254et_nat Prod)) Prod)))
% 5.65/5.93 (assert (forall ((Prod tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.produc7507926704131184380et_nat (@ tptp.produc1824681642469235216et_nat Prod)) (@ tptp.produc8586169260539613262et_nat Prod)) Prod)))
% 5.65/5.93 (assert (forall ((Prod tptp.product_prod_int_int)) (= (@ (@ tptp.product_Pair_int_int (@ tptp.product_fst_int_int Prod)) (@ tptp.product_snd_int_int Prod)) Prod)))
% 5.65/5.93 (assert (forall ((S tptp.set_Product_unit)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit)) (@ tptp.finite410649719033368117t_unit S)) (= S tptp.top_to1996260823553986621t_unit))))
% 5.65/5.93 (assert (forall ((S tptp.set_o)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o tptp.top_top_set_o)) (@ tptp.finite_card_o S)) (= S tptp.top_top_set_o))))
% 5.65/5.93 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.minus_1801376950450012436_nat_o A))) (let ((_let_2 (@ tptp.member6576561426505652726_nat_o A2))) (=> (@ _let_2 A) (=> (not (@ _let_2 B4)) (= (@ tptp.finite1363419556375932405_nat_o (@ _let_1 (@ (@ tptp.insert5175938949040314269_nat_o A2) B4))) (@ (@ tptp.minus_minus_nat (@ tptp.finite1363419556375932405_nat_o (@ _let_1 B4))) tptp.one_one_nat))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int A))) (let ((_let_2 (@ tptp.member_int A2))) (=> (@ _let_2 A) (=> (not (@ _let_2 B4)) (= (@ tptp.finite_card_int (@ _let_1 (@ (@ tptp.insert_int A2) B4))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_int (@ _let_1 B4))) tptp.one_one_nat))))))))
% 5.65/5.93 (assert (forall ((A2 Bool) (A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.minus_minus_set_o A))) (let ((_let_2 (@ tptp.member_o A2))) (=> (@ _let_2 A) (=> (not (@ _let_2 B4)) (= (@ tptp.finite_card_o (@ _let_1 (@ (@ tptp.insert_o A2) B4))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_o (@ _let_1 B4))) tptp.one_one_nat))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.minus_6452836326544984404t_unit A))) (let ((_let_2 (@ tptp.member_Product_unit A2))) (=> (@ _let_2 A) (=> (not (@ _let_2 B4)) (= (@ tptp.finite410649719033368117t_unit (@ _let_1 (@ (@ tptp.insert_Product_unit A2) B4))) (@ (@ tptp.minus_minus_nat (@ tptp.finite410649719033368117t_unit (@ _let_1 B4))) tptp.one_one_nat))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A))) (let ((_let_2 (@ tptp.member_nat A2))) (=> (@ _let_2 A) (=> (not (@ _let_2 B4)) (= (@ tptp.finite_card_nat (@ _let_1 (@ (@ tptp.insert_nat A2) B4))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_nat (@ _let_1 B4))) tptp.one_one_nat))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat) (S tptp.set_Pr3948176798113811640et_nat)) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat A2) B)) S) (@ (@ tptp.member242389114213480694t_unit A2) (@ (@ tptp.image_6824039242672219652t_unit tptp.produc1824681642469235216et_nat) S)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (S tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A2) B)) S) (@ (@ tptp.member_nat A2) (@ (@ tptp.image_2486076414777270412at_nat tptp.product_fst_nat_nat) S)))))
% 5.65/5.93 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (S tptp.set_Pr3286484037609594932et_nat)) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A2) B)) S) (@ (@ tptp.member6576561426505652726_nat_o A2) (@ (@ tptp.image_6802380912191114376_nat_o tptp.produc995936583742144908et_nat) S)))))
% 5.65/5.93 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (S tptp.set_Pr8536935166611901872et_nat)) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A2) B)) S) (@ (@ tptp.member6576561426505652726_nat_o A2) (@ (@ tptp.image_2517677226577294348_nat_o tptp.produc180342877477747464et_nat) S)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (S tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A2) B)) S) (@ (@ tptp.member_int A2) (@ (@ tptp.image_5042161079198086560nt_int tptp.product_fst_int_int) S)))))
% 5.65/5.93 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (= (@ tptp.produc6012101397789842562t_unit (@ tptp.produc6300697153377358172et_nat X)) (@ tptp.produc8586169260539613262et_nat X))))
% 5.65/5.93 (assert (forall ((X tptp.product_prod_int_int)) (= (@ tptp.product_fst_int_int (@ tptp.product_swap_int_int X)) (@ tptp.product_snd_int_int X))))
% 5.65/5.93 (assert (forall ((X tptp.produc7348995623955488188t_unit)) (= (@ tptp.produc8586169260539613262et_nat (@ tptp.produc1264744871843189710t_unit X)) (@ tptp.produc6012101397789842562t_unit X))))
% 5.65/5.93 (assert (forall ((X tptp.product_prod_int_int)) (= (@ tptp.product_snd_int_int (@ tptp.product_swap_int_int X)) (@ tptp.product_fst_int_int X))))
% 5.65/5.93 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit))) (= (@ (@ tptp.comp_P2930521774885306735et_nat tptp.produc8586169260539613262et_nat) (@ tptp.produc4172003873565521026et_nat F)) tptp.produc8586169260539613262et_nat)))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.int))) (= (@ (@ tptp.comp_P5356232565778667509nt_int tptp.product_snd_int_int) (@ tptp.produc2355237562570658114nt_int F)) tptp.product_snd_int_int)))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer))) (= (@ (@ tptp.comp_P3428181540658402820nteger tptp.produc8508995932063986495nteger) (@ tptp.produc6499014454317279255nteger F)) tptp.produc8508995932063986495nteger)))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.int))) (= (@ (@ tptp.comp_P5356232565778667509nt_int tptp.product_fst_int_int) (@ tptp.produc4463282112584876420nt_int F)) tptp.product_fst_int_int)))
% 5.65/5.93 (assert (= (@ (@ tptp.image_5042161079198086560nt_int tptp.product_fst_int_int) tptp.top_to4366644338036079209nt_int) tptp.top_top_set_int))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (= (@ (@ tptp.comp_P5356232565778667509nt_int tptp.product_fst_int_int) (@ (@ tptp.produc6036585564866528938nt_int F) G)) (@ (@ tptp.comp_i4330622015127193916nt_int F) tptp.product_fst_int_int))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.int))) (= (@ (@ tptp.comp_P5356232565778667509nt_int tptp.product_fst_int_int) (@ tptp.produc2355237562570658114nt_int F)) (@ (@ tptp.comp_i4330622015127193916nt_int F) tptp.product_fst_int_int))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer))) (= (@ (@ tptp.comp_P3428181540658402820nteger tptp.produc6174133586879617921nteger) (@ tptp.produc6499014454317279255nteger F)) (@ (@ tptp.comp_C1043215000170864188nteger F) tptp.produc6174133586879617921nteger))))
% 5.65/5.93 (assert (forall ((F (-> tptp.set_nat tptp.set_nat))) (= (@ (@ tptp.comp_P2930521774885306735et_nat tptp.produc8586169260539613262et_nat) (@ tptp.produc3286488329990770625t_unit F)) (@ (@ tptp.comp_s5696514601250091763et_nat F) tptp.produc8586169260539613262et_nat))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.int))) (= (@ (@ tptp.comp_P5356232565778667509nt_int tptp.product_snd_int_int) (@ tptp.produc4463282112584876420nt_int F)) (@ (@ tptp.comp_i4330622015127193916nt_int F) tptp.product_snd_int_int))))
% 5.65/5.93 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit)) (G (-> tptp.set_nat tptp.set_nat)) (X tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.produc4172003873565521026et_nat F) (@ (@ tptp.produc3286488329990770625t_unit G) X)) (@ (@ tptp.produc7507926704131184380et_nat (@ F (@ tptp.produc1824681642469235216et_nat X))) (@ G (@ tptp.produc8586169260539613262et_nat X))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.nat)) (G (-> tptp.set_nat tptp.nat)) (X tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.produc8233931525780029747at_nat F) (@ (@ tptp.produc8442695800884449271t_unit G) X)) (@ (@ tptp.product_Pair_nat_nat (@ F (@ tptp.produc1824681642469235216et_nat X))) (@ G (@ tptp.produc8586169260539613262et_nat X))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.int)) (G (-> tptp.set_nat tptp.int)) (X tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.produc7422730317258219nt_int F) (@ (@ tptp.produc7345612820240450715t_unit G) X)) (@ (@ tptp.product_Pair_int_int (@ F (@ tptp.produc1824681642469235216et_nat X))) (@ G (@ tptp.produc8586169260539613262et_nat X))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.produc3658429121746597890et_nat Bool)) (G (-> tptp.set_nat tptp.produc3658429121746597890et_nat)) (X tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.produc6095824665904122878et_nat F) (@ (@ tptp.produc7441988914112407621t_unit G) X)) (@ (@ tptp.produc5001842942810119800et_nat (@ F (@ tptp.produc1824681642469235216et_nat X))) (@ G (@ tptp.produc8586169260539613262et_nat X))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.produc3658429121746597890et_nat Bool)) (G (-> tptp.set_nat tptp.produc3925858234332021118et_nat)) (X tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.produc4273547285574235514et_nat F) (@ (@ tptp.produc7176435795764513225t_unit G) X)) (@ (@ tptp.produc2245416461498447860et_nat (@ F (@ tptp.produc1824681642469235216et_nat X))) (@ G (@ tptp.produc8586169260539613262et_nat X))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.heap_e7401611519738050253t_unit)) (G (-> tptp.int tptp.set_nat)) (X tptp.product_prod_int_int)) (= (@ (@ tptp.produc7086134074927288299et_nat F) (@ (@ tptp.produc1253519502038700766at_int G) X)) (@ (@ tptp.produc7507926704131184380et_nat (@ F (@ tptp.product_fst_int_int X))) (@ G (@ tptp.product_snd_int_int X))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat)) (X tptp.product_prod_int_int)) (= (@ (@ tptp.produc1358374321178653834at_nat F) (@ (@ tptp.produc3463928400683821864at_int G) X)) (@ (@ tptp.product_Pair_nat_nat (@ F (@ tptp.product_fst_int_int X))) (@ G (@ tptp.product_snd_int_int X))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int)) (X tptp.product_prod_int_int)) (= (@ (@ tptp.produc2355237562570658114nt_int F) (@ (@ tptp.produc4463282112584876420nt_int G) X)) (@ (@ tptp.product_Pair_int_int (@ F (@ tptp.product_fst_int_int X))) (@ G (@ tptp.product_snd_int_int X))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.produc3658429121746597890et_nat Bool)) (G (-> tptp.int tptp.produc3658429121746597890et_nat)) (X tptp.product_prod_int_int)) (= (@ (@ tptp.produc5259063908904861543et_nat F) (@ (@ tptp.produc9121118195053341018at_int G) X)) (@ (@ tptp.produc5001842942810119800et_nat (@ F (@ tptp.product_fst_int_int X))) (@ G (@ tptp.product_snd_int_int X))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.produc3658429121746597890et_nat Bool)) (G (-> tptp.int tptp.produc3925858234332021118et_nat)) (X tptp.product_prod_int_int)) (= (@ (@ tptp.produc3602029435013415139et_nat F) (@ (@ tptp.produc2878475440847162070at_int G) X)) (@ (@ tptp.produc2245416461498447860et_nat (@ F (@ tptp.product_fst_int_int X))) (@ G (@ tptp.product_snd_int_int X))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.set_nat tptp.set_nat)) (G (-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit)) (X tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.produc3286488329990770625t_unit F) (@ (@ tptp.produc4172003873565521026et_nat G) X)) (@ (@ tptp.produc7507926704131184380et_nat (@ G (@ tptp.produc1824681642469235216et_nat X))) (@ F (@ tptp.produc8586169260539613262et_nat X))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.set_nat tptp.nat)) (G (-> tptp.heap_e7401611519738050253t_unit tptp.nat)) (X tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.produc1747169720485888550at_nat F) (@ (@ tptp.produc2974404638222180585et_nat G) X)) (@ (@ tptp.product_Pair_nat_nat (@ G (@ tptp.produc1824681642469235216et_nat X))) (@ F (@ tptp.produc8586169260539613262et_nat X))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.set_nat tptp.int)) (G (-> tptp.heap_e7401611519738050253t_unit tptp.int)) (X tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.produc2744032961877892830nt_int F) (@ (@ tptp.produc3346058198459025221et_nat G) X)) (@ (@ tptp.product_Pair_int_int (@ G (@ tptp.produc1824681642469235216et_nat X))) (@ F (@ tptp.produc8586169260539613262et_nat X))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.set_nat tptp.produc3658429121746597890et_nat)) (G (-> tptp.heap_e7401611519738050253t_unit tptp.produc3658429121746597890et_nat Bool)) (X tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.produc1718959742329256773_nat_o F) (@ (@ tptp.produc962520821680634754et_nat G) X)) (@ (@ tptp.produc5001842942810119800et_nat (@ G (@ tptp.produc1824681642469235216et_nat X))) (@ F (@ tptp.produc8586169260539613262et_nat X))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.set_nat tptp.produc3925858234332021118et_nat)) (G (-> tptp.heap_e7401611519738050253t_unit tptp.produc3658429121746597890et_nat Bool)) (X tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.produc3009152965630989513_nat_o F) (@ (@ tptp.produc962520821680634754et_nat G) X)) (@ (@ tptp.produc2245416461498447860et_nat (@ G (@ tptp.produc1824681642469235216et_nat X))) (@ F (@ tptp.produc8586169260539613262et_nat X))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.set_nat)) (G (-> tptp.int tptp.heap_e7401611519738050253t_unit)) (X tptp.product_prod_int_int)) (= (@ (@ tptp.produc2122153897363312795t_unit F) (@ (@ tptp.produc1158806734383251089it_int G) X)) (@ (@ tptp.produc7507926704131184380et_nat (@ G (@ tptp.product_fst_int_int X))) (@ F (@ tptp.product_snd_int_int X))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat)) (X tptp.product_prod_int_int)) (= (@ (@ tptp.produc3466418871192872140at_nat F) (@ (@ tptp.produc1355883850669603558at_int G) X)) (@ (@ tptp.product_Pair_nat_nat (@ G (@ tptp.product_fst_int_int X))) (@ F (@ tptp.product_snd_int_int X))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int)) (X tptp.product_prod_int_int)) (= (@ (@ tptp.produc4463282112584876420nt_int F) (@ (@ tptp.produc2355237562570658114nt_int G) X)) (@ (@ tptp.product_Pair_int_int (@ G (@ tptp.product_fst_int_int X))) (@ F (@ tptp.product_snd_int_int X))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.produc3658429121746597890et_nat)) (G (-> tptp.int tptp.produc3658429121746597890et_nat Bool)) (X tptp.product_prod_int_int)) (= (@ (@ tptp.produc3447581998352395295_nat_o F) (@ (@ tptp.produc1933289243015553937_o_int G) X)) (@ (@ tptp.produc5001842942810119800et_nat (@ G (@ tptp.product_fst_int_int X))) (@ F (@ tptp.product_snd_int_int X))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.int tptp.produc3925858234332021118et_nat)) (G (-> tptp.int tptp.produc3658429121746597890et_nat Bool)) (X tptp.product_prod_int_int)) (= (@ (@ tptp.produc1783401272518604195_nat_o F) (@ (@ tptp.produc1933289243015553937_o_int G) X)) (@ (@ tptp.produc2245416461498447860et_nat (@ G (@ tptp.product_fst_int_int X))) (@ F (@ tptp.product_snd_int_int X))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer)) (P3 tptp.produc8923325533196201883nteger)) (let ((_let_1 (@ tptp.produc6499014454317279255nteger F))) (let ((_let_2 (@ tptp.produc3195571438000033749nteger G))) (= (@ _let_1 (@ _let_2 P3)) (@ _let_2 (@ _let_1 P3)))))))
% 5.65/5.93 (assert (forall ((X tptp.produc3658429121746597890et_nat) (Y tptp.heap_e7401611519738050253t_unit) (Z tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat Y) Z)) (= (@ tptp.produc1824681642469235216et_nat X) Y))))
% 5.65/5.93 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.nat) (Z tptp.nat)) (=> (= X (@ (@ tptp.product_Pair_nat_nat Y) Z)) (= (@ tptp.product_fst_nat_nat X) Y))))
% 5.65/5.93 (assert (forall ((X tptp.produc3925858234332021118et_nat) (Y (-> tptp.produc3658429121746597890et_nat Bool)) (Z tptp.produc3658429121746597890et_nat)) (=> (= X (@ (@ tptp.produc5001842942810119800et_nat Y) Z)) (= (@ tptp.produc995936583742144908et_nat X) Y))))
% 5.65/5.93 (assert (forall ((X tptp.produc2732055786443039994et_nat) (Y (-> tptp.produc3658429121746597890et_nat Bool)) (Z tptp.produc3925858234332021118et_nat)) (=> (= X (@ (@ tptp.produc2245416461498447860et_nat Y) Z)) (= (@ tptp.produc180342877477747464et_nat X) Y))))
% 5.65/5.93 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.int) (Z tptp.int)) (=> (= X (@ (@ tptp.product_Pair_int_int Y) Z)) (= (@ tptp.product_fst_int_int X) Y))))
% 5.65/5.93 (assert (forall ((X tptp.heap_e7401611519738050253t_unit) (Y tptp.set_nat) (A2 tptp.heap_e7401611519738050253t_unit)) (=> (= (@ tptp.produc1824681642469235216et_nat (@ (@ tptp.produc7507926704131184380et_nat X) Y)) A2) (= X A2))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat) (A2 tptp.nat)) (=> (= (@ tptp.product_fst_nat_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) A2) (= X A2))))
% 5.65/5.93 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3658429121746597890et_nat) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (= (@ tptp.produc995936583742144908et_nat (@ (@ tptp.produc5001842942810119800et_nat X) Y)) A2) (= X A2))))
% 5.65/5.93 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3925858234332021118et_nat) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (= (@ tptp.produc180342877477747464et_nat (@ (@ tptp.produc2245416461498447860et_nat X) Y)) A2) (= X A2))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int) (A2 tptp.int)) (=> (= (@ tptp.product_fst_int_int (@ (@ tptp.product_Pair_int_int X) Y)) A2) (= X A2))))
% 5.65/5.93 (assert (forall ((X1 tptp.heap_e7401611519738050253t_unit) (X22 tptp.set_nat)) (= (@ tptp.produc1824681642469235216et_nat (@ (@ tptp.produc7507926704131184380et_nat X1) X22)) X1)))
% 5.65/5.93 (assert (forall ((X1 tptp.nat) (X22 tptp.nat)) (= (@ tptp.product_fst_nat_nat (@ (@ tptp.product_Pair_nat_nat X1) X22)) X1)))
% 5.65/5.93 (assert (forall ((X1 (-> tptp.produc3658429121746597890et_nat Bool)) (X22 tptp.produc3658429121746597890et_nat)) (= (@ tptp.produc995936583742144908et_nat (@ (@ tptp.produc5001842942810119800et_nat X1) X22)) X1)))
% 5.65/5.93 (assert (forall ((X1 (-> tptp.produc3658429121746597890et_nat Bool)) (X22 tptp.produc3925858234332021118et_nat)) (= (@ tptp.produc180342877477747464et_nat (@ (@ tptp.produc2245416461498447860et_nat X1) X22)) X1)))
% 5.65/5.93 (assert (forall ((X1 tptp.int) (X22 tptp.int)) (= (@ tptp.product_fst_int_int (@ (@ tptp.product_Pair_int_int X1) X22)) X1)))
% 5.65/5.93 (assert (forall ((A2 tptp.heap_e7401611519738050253t_unit) (P3 tptp.produc3658429121746597890et_nat)) (= (= A2 (@ tptp.produc1824681642469235216et_nat P3)) (exists ((B6 tptp.set_nat)) (= P3 (@ (@ tptp.produc7507926704131184380et_nat A2) B6))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (P3 tptp.product_prod_nat_nat)) (= (= A2 (@ tptp.product_fst_nat_nat P3)) (exists ((B6 tptp.nat)) (= P3 (@ (@ tptp.product_Pair_nat_nat A2) B6))))))
% 5.65/5.93 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (P3 tptp.produc3925858234332021118et_nat)) (= (= A2 (@ tptp.produc995936583742144908et_nat P3)) (exists ((B6 tptp.produc3658429121746597890et_nat)) (= P3 (@ (@ tptp.produc5001842942810119800et_nat A2) B6))))))
% 5.65/5.93 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (P3 tptp.produc2732055786443039994et_nat)) (= (= A2 (@ tptp.produc180342877477747464et_nat P3)) (exists ((B6 tptp.produc3925858234332021118et_nat)) (= P3 (@ (@ tptp.produc2245416461498447860et_nat A2) B6))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (P3 tptp.product_prod_int_int)) (= (= A2 (@ tptp.product_fst_int_int P3)) (exists ((B6 tptp.int)) (= P3 (@ (@ tptp.product_Pair_int_int A2) B6))))))
% 5.65/5.93 (assert (forall ((X tptp.produc3658429121746597890et_nat) (A2 tptp.heap_e7401611519738050253t_unit) (B tptp.set_nat) (P (-> tptp.heap_e7401611519738050253t_unit Bool))) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat A2) B)) (=> (@ P (@ tptp.produc1824681642469235216et_nat X)) (@ P A2)))))
% 5.65/5.93 (assert (forall ((X tptp.product_prod_nat_nat) (A2 tptp.nat) (B tptp.nat) (P (-> tptp.nat Bool))) (=> (= X (@ (@ tptp.product_Pair_nat_nat A2) B)) (=> (@ P (@ tptp.product_fst_nat_nat X)) (@ P A2)))))
% 5.65/5.93 (assert (forall ((X tptp.produc3925858234332021118et_nat) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (= X (@ (@ tptp.produc5001842942810119800et_nat A2) B)) (=> (@ P (@ tptp.produc995936583742144908et_nat X)) (@ P A2)))))
% 5.65/5.93 (assert (forall ((X tptp.produc2732055786443039994et_nat) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool))) (=> (= X (@ (@ tptp.produc2245416461498447860et_nat A2) B)) (=> (@ P (@ tptp.produc180342877477747464et_nat X)) (@ P A2)))))
% 5.65/5.93 (assert (forall ((X tptp.product_prod_int_int) (A2 tptp.int) (B tptp.int) (P (-> tptp.int Bool))) (=> (= X (@ (@ tptp.product_Pair_int_int A2) B)) (=> (@ P (@ tptp.product_fst_int_int X)) (@ P A2)))))
% 5.65/5.93 (assert (= (lambda ((Y4 tptp.produc3658429121746597890et_nat) (Z4 tptp.produc3658429121746597890et_nat)) (= Y4 Z4)) (lambda ((S7 tptp.produc3658429121746597890et_nat) (T tptp.produc3658429121746597890et_nat)) (and (= (@ tptp.produc1824681642469235216et_nat S7) (@ tptp.produc1824681642469235216et_nat T)) (= (@ tptp.produc8586169260539613262et_nat S7) (@ tptp.produc8586169260539613262et_nat T))))))
% 5.65/5.93 (assert (= (lambda ((Y4 tptp.product_prod_int_int) (Z4 tptp.product_prod_int_int)) (= Y4 Z4)) (lambda ((S7 tptp.product_prod_int_int) (T tptp.product_prod_int_int)) (and (= (@ tptp.product_fst_int_int S7) (@ tptp.product_fst_int_int T)) (= (@ tptp.product_snd_int_int S7) (@ tptp.product_snd_int_int T))))))
% 5.65/5.93 (assert (forall ((P3 tptp.produc3658429121746597890et_nat) (Q4 tptp.produc3658429121746597890et_nat)) (=> (= (@ tptp.produc1824681642469235216et_nat P3) (@ tptp.produc1824681642469235216et_nat Q4)) (=> (= (@ tptp.produc8586169260539613262et_nat P3) (@ tptp.produc8586169260539613262et_nat Q4)) (= P3 Q4)))))
% 5.65/5.93 (assert (forall ((P3 tptp.product_prod_int_int) (Q4 tptp.product_prod_int_int)) (=> (= (@ tptp.product_fst_int_int P3) (@ tptp.product_fst_int_int Q4)) (=> (= (@ tptp.product_snd_int_int P3) (@ tptp.product_snd_int_int Q4)) (= P3 Q4)))))
% 5.65/5.93 (assert (forall ((Prod tptp.produc3658429121746597890et_nat) (Prod2 tptp.produc3658429121746597890et_nat)) (=> (and (= (@ tptp.produc1824681642469235216et_nat Prod) (@ tptp.produc1824681642469235216et_nat Prod2)) (= (@ tptp.produc8586169260539613262et_nat Prod) (@ tptp.produc8586169260539613262et_nat Prod2))) (= Prod Prod2))))
% 5.65/5.93 (assert (forall ((Prod tptp.product_prod_int_int) (Prod2 tptp.product_prod_int_int)) (=> (and (= (@ tptp.product_fst_int_int Prod) (@ tptp.product_fst_int_int Prod2)) (= (@ tptp.product_snd_int_int Prod) (@ tptp.product_snd_int_int Prod2))) (= Prod Prod2))))
% 5.65/5.93 (assert (forall ((P (-> tptp.heap_e7401611519738050253t_unit tptp.set_nat Bool))) (= (forall ((A6 tptp.heap_e7401611519738050253t_unit) (X7 tptp.set_nat)) (@ (@ P A6) X7)) (forall ((Z2 tptp.produc3658429121746597890et_nat)) (@ (@ P (@ tptp.produc1824681642469235216et_nat Z2)) (@ tptp.produc8586169260539613262et_nat Z2))))))
% 5.65/5.93 (assert (forall ((P (-> tptp.int tptp.int Bool))) (= (forall ((A6 tptp.int) (X7 tptp.int)) (@ (@ P A6) X7)) (forall ((Z2 tptp.product_prod_int_int)) (@ (@ P (@ tptp.product_fst_int_int Z2)) (@ tptp.product_snd_int_int Z2))))))
% 5.65/5.93 (assert (forall ((P (-> tptp.heap_e7401611519738050253t_unit tptp.set_nat Bool))) (= (exists ((A6 tptp.heap_e7401611519738050253t_unit) (X7 tptp.set_nat)) (@ (@ P A6) X7)) (exists ((Z2 tptp.produc3658429121746597890et_nat)) (@ (@ P (@ tptp.produc1824681642469235216et_nat Z2)) (@ tptp.produc8586169260539613262et_nat Z2))))))
% 5.65/5.93 (assert (forall ((P (-> tptp.int tptp.int Bool))) (= (exists ((A6 tptp.int) (X7 tptp.int)) (@ (@ P A6) X7)) (exists ((Z2 tptp.product_prod_int_int)) (@ (@ P (@ tptp.product_fst_int_int Z2)) (@ tptp.product_snd_int_int Z2))))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger)) (G (-> tptp.code_integer tptp.code_integer)) (X tptp.produc8923325533196201883nteger)) (= (@ (@ tptp.produc9020447175693601247nteger F) (@ (@ tptp.produc6499014454317279255nteger G) X)) (@ (@ tptp.produc9020447175693601247nteger (@ (@ tptp.comp_C1593894019821074884nteger F) G)) X))))
% 5.65/5.93 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer)) (X tptp.produc8923325533196201883nteger)) (= (@ (@ tptp.produc6499014454317279255nteger F) (@ (@ tptp.produc6499014454317279255nteger G) X)) (@ (@ tptp.produc6499014454317279255nteger (@ (@ tptp.comp_C7449957260575251196nteger F) G)) X))))
% 5.65/5.93 (assert (forall ((S tptp.set_nat) (A (-> tptp.nat tptp.set_nat)) (R2 (-> tptp.nat tptp.set_Pr1261947904930325089at_nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (@ (@ tptp.refl_on_nat (@ A X3)) (@ R2 X3)))) (@ (@ tptp.refl_on_nat (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat A) S))) (@ tptp.comple1930127330929219688at_nat (@ (@ tptp.image_7178329752028323786at_nat R2) S))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_o) (A2 Bool)) (=> (not (= X4 tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) X4) (@ (@ tptp.ord_less_eq_o A2) X3))) (=> (forall ((Y2 Bool)) (=> (forall ((X6 Bool)) (=> (@ (@ tptp.member_o X6) X4) (@ (@ tptp.ord_less_eq_o Y2) X6))) (@ (@ tptp.ord_less_eq_o Y2) A2))) (= (@ tptp.complete_Inf_Inf_o X4) A2))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (not (= X4 tptp.bot_bo7824918357723582233_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) X4) (@ (@ tptp.ord_le729326519192465773_nat_o A2) X3))) (=> (forall ((Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (forall ((X6 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X6) X4) (@ (@ tptp.ord_le729326519192465773_nat_o Y2) X6))) (@ (@ tptp.ord_le729326519192465773_nat_o Y2) A2))) (= (@ tptp.comple90455603224345172_nat_o X4) A2))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_filter_nat) (A2 tptp.filter_nat)) (=> (not (= X4 tptp.bot_bo498966703094740906er_nat)) (=> (forall ((X3 tptp.filter_nat)) (=> (@ (@ tptp.member_filter_nat X3) X4) (@ (@ tptp.ord_le2510731241096832064er_nat A2) X3))) (=> (forall ((Y2 tptp.filter_nat)) (=> (forall ((X6 tptp.filter_nat)) (=> (@ (@ tptp.member_filter_nat X6) X4) (@ (@ tptp.ord_le2510731241096832064er_nat Y2) X6))) (@ (@ tptp.ord_le2510731241096832064er_nat Y2) A2))) (= (@ tptp.comple6612786467464916249er_nat X4) A2))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_int) (A2 tptp.int)) (=> (not (= X4 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) X4) (@ (@ tptp.ord_less_eq_int A2) X3))) (=> (forall ((Y2 tptp.int)) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) X4) (@ (@ tptp.ord_less_eq_int Y2) X6))) (@ (@ tptp.ord_less_eq_int Y2) A2))) (= (@ tptp.complete_Inf_Inf_int X4) A2))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_nat) (A2 tptp.nat)) (=> (not (= X4 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) X4) (@ (@ tptp.ord_less_eq_nat A2) X3))) (=> (forall ((Y2 tptp.nat)) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) X4) (@ (@ tptp.ord_less_eq_nat Y2) X6))) (@ (@ tptp.ord_less_eq_nat Y2) A2))) (= (@ tptp.complete_Inf_Inf_nat X4) A2))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_set_nat) (A2 tptp.set_nat)) (=> (not (= X4 tptp.bot_bot_set_set_nat)) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) X4) (@ (@ tptp.ord_less_eq_set_nat A2) X3))) (=> (forall ((Y2 tptp.set_nat)) (=> (forall ((X6 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X6) X4) (@ (@ tptp.ord_less_eq_set_nat Y2) X6))) (@ (@ tptp.ord_less_eq_set_nat Y2) A2))) (= (@ tptp.comple7806235888213564991et_nat X4) A2))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_Product_unit) (A2 tptp.product_unit)) (=> (not (= X4 tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) X4) (@ (@ tptp.ord_le3221252021190050221t_unit A2) X3))) (=> (forall ((Y2 tptp.product_unit)) (=> (forall ((X6 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X6) X4) (@ (@ tptp.ord_le3221252021190050221t_unit Y2) X6))) (@ (@ tptp.ord_le3221252021190050221t_unit Y2) A2))) (= (@ tptp.comple2584293577114468500t_unit X4) A2))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_o) (Z Bool)) (=> (not (= X4 tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) X4) (@ (@ tptp.ord_less_eq_o Z) X3))) (@ (@ tptp.ord_less_eq_o Z) (@ tptp.complete_Inf_Inf_o X4))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_Pr4532377907799695533_nat_o) (Z (-> tptp.produc3658429121746597890et_nat Bool))) (=> (not (= X4 tptp.bot_bo7824918357723582233_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) X4) (@ (@ tptp.ord_le729326519192465773_nat_o Z) X3))) (@ (@ tptp.ord_le729326519192465773_nat_o Z) (@ tptp.comple90455603224345172_nat_o X4))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_filter_nat) (Z tptp.filter_nat)) (=> (not (= X4 tptp.bot_bo498966703094740906er_nat)) (=> (forall ((X3 tptp.filter_nat)) (=> (@ (@ tptp.member_filter_nat X3) X4) (@ (@ tptp.ord_le2510731241096832064er_nat Z) X3))) (@ (@ tptp.ord_le2510731241096832064er_nat Z) (@ tptp.comple6612786467464916249er_nat X4))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_int) (Z tptp.int)) (=> (not (= X4 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) X4) (@ (@ tptp.ord_less_eq_int Z) X3))) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.complete_Inf_Inf_int X4))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_nat) (Z tptp.nat)) (=> (not (= X4 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) X4) (@ (@ tptp.ord_less_eq_nat Z) X3))) (@ (@ tptp.ord_less_eq_nat Z) (@ tptp.complete_Inf_Inf_nat X4))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_set_nat) (Z tptp.set_nat)) (=> (not (= X4 tptp.bot_bot_set_set_nat)) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) X4) (@ (@ tptp.ord_less_eq_set_nat Z) X3))) (@ (@ tptp.ord_less_eq_set_nat Z) (@ tptp.comple7806235888213564991et_nat X4))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_Product_unit) (Z tptp.product_unit)) (=> (not (= X4 tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) X4) (@ (@ tptp.ord_le3221252021190050221t_unit Z) X3))) (@ (@ tptp.ord_le3221252021190050221t_unit Z) (@ tptp.comple2584293577114468500t_unit X4))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (U Bool)) (=> (forall ((V3 Bool)) (=> (@ (@ tptp.member_o V3) A) (@ (@ tptp.ord_less_eq_o V3) U))) (=> (not (= A tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_eq_o (@ tptp.complete_Inf_Inf_o A)) U)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (U (-> tptp.produc3658429121746597890et_nat Bool))) (=> (forall ((V3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o V3) A) (@ (@ tptp.ord_le729326519192465773_nat_o V3) U))) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (@ (@ tptp.ord_le729326519192465773_nat_o (@ tptp.comple90455603224345172_nat_o A)) U)))))
% 5.65/5.93 (assert (forall ((A tptp.set_filter_nat) (U tptp.filter_nat)) (=> (forall ((V3 tptp.filter_nat)) (=> (@ (@ tptp.member_filter_nat V3) A) (@ (@ tptp.ord_le2510731241096832064er_nat V3) U))) (=> (not (= A tptp.bot_bo498966703094740906er_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ tptp.comple6612786467464916249er_nat A)) U)))))
% 5.65/5.93 (assert (forall ((A tptp.set_set_nat) (U tptp.set_nat)) (=> (forall ((V3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat V3) A) (@ (@ tptp.ord_less_eq_set_nat V3) U))) (=> (not (= A tptp.bot_bot_set_set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7806235888213564991et_nat A)) U)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (U tptp.product_unit)) (=> (forall ((V3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit V3) A) (@ (@ tptp.ord_le3221252021190050221t_unit V3) U))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.comple2584293577114468500t_unit A)) U)))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_int) (Z tptp.int)) (=> (not (= X4 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_int (@ tptp.complete_Inf_Inf_int X4)) Z) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) X4) (@ (@ tptp.ord_less_int X3) Z)))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_nat) (Z tptp.nat)) (=> (not (= X4 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.complete_Inf_Inf_nat X4)) Z) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) X4) (@ (@ tptp.ord_less_nat X3) Z)))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_Product_unit) (Z tptp.product_unit)) (=> (not (= X4 tptp.bot_bo3957492148770167129t_unit)) (=> (@ (@ tptp.ord_le361264281704409273t_unit (@ tptp.comple2584293577114468500t_unit X4)) Z) (exists ((X3 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X3) X4) (@ (@ tptp.ord_le361264281704409273t_unit X3) Z)))))))
% 5.65/5.93 (assert (forall ((I tptp.set_Product_unit) (F (-> tptp.product_unit tptp.set_nat)) (X tptp.set_nat)) (=> (not (= I tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) I) (= (@ F I3) X))) (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_8173849991827986510et_nat F) I)) X)))))
% 5.65/5.93 (assert (forall ((I tptp.set_o) (F (-> Bool tptp.set_nat)) (X tptp.set_nat)) (=> (not (= I tptp.bot_bot_set_o)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I) (= (@ F I3) X))) (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_o_set_nat F) I)) X)))))
% 5.65/5.93 (assert (forall ((I tptp.set_nat) (F (-> tptp.nat tptp.set_nat)) (X tptp.set_nat)) (=> (not (= I tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I) (= (@ F I3) X))) (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat F) I)) X)))))
% 5.65/5.93 (assert (forall ((I tptp.set_int) (F (-> tptp.int tptp.set_nat)) (X tptp.set_nat)) (=> (not (= I tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I) (= (@ F I3) X))) (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_int_set_nat F) I)) X)))))
% 5.65/5.93 (assert (forall ((I tptp.set_Pr4532377907799695533_nat_o) (F (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.set_nat)) (X tptp.set_nat)) (=> (not (= I tptp.bot_bo7824918357723582233_nat_o)) (=> (forall ((I3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o I3) I) (= (@ F I3) X))) (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_6888641473154130958et_nat F) I)) X)))))
% 5.65/5.93 (assert (forall ((I tptp.set_Product_unit) (F (-> tptp.product_unit tptp.product_unit)) (X tptp.product_unit)) (=> (not (= I tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) I) (= (@ F I3) X))) (= (@ tptp.comple2584293577114468500t_unit (@ (@ tptp.image_405062704495631173t_unit F) I)) X)))))
% 5.65/5.93 (assert (forall ((I tptp.set_o) (F (-> Bool tptp.product_unit)) (X tptp.product_unit)) (=> (not (= I tptp.bot_bot_set_o)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I) (= (@ F I3) X))) (= (@ tptp.comple2584293577114468500t_unit (@ (@ tptp.image_o_Product_unit2 F) I)) X)))))
% 5.65/5.93 (assert (forall ((I tptp.set_nat) (F (-> tptp.nat tptp.product_unit)) (X tptp.product_unit)) (=> (not (= I tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I) (= (@ F I3) X))) (= (@ tptp.comple2584293577114468500t_unit (@ (@ tptp.image_8730104196221521654t_unit F) I)) X)))))
% 5.65/5.93 (assert (forall ((I tptp.set_int) (F (-> tptp.int tptp.product_unit)) (X tptp.product_unit)) (=> (not (= I tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I) (= (@ F I3) X))) (= (@ tptp.comple2584293577114468500t_unit (@ (@ tptp.image_5846526143423701914t_unit F) I)) X)))))
% 5.65/5.93 (assert (forall ((I tptp.set_Pr4532377907799695533_nat_o) (F (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.product_unit)) (X tptp.product_unit)) (=> (not (= I tptp.bot_bo7824918357723582233_nat_o)) (=> (forall ((I3 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o I3) I) (= (@ F I3) X))) (= (@ tptp.comple2584293577114468500t_unit (@ (@ tptp.image_8451000719036923781t_unit F) I)) X)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit)) (=> (= (@ tptp.finite410649719033368117t_unit A) tptp.one_one_nat) (not (forall ((X3 tptp.product_unit)) (not (= A (@ (@ tptp.insert_Product_unit X3) tptp.bot_bo3957492148770167129t_unit))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o)) (=> (= (@ tptp.finite_card_o A) tptp.one_one_nat) (not (forall ((X3 Bool)) (not (= A (@ (@ tptp.insert_o X3) tptp.bot_bot_set_o))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat)) (=> (= (@ tptp.finite_card_nat A) tptp.one_one_nat) (not (forall ((X3 tptp.nat)) (not (= A (@ (@ tptp.insert_nat X3) tptp.bot_bot_set_nat))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int)) (=> (= (@ tptp.finite_card_int A) tptp.one_one_nat) (not (forall ((X3 tptp.int)) (not (= A (@ (@ tptp.insert_int X3) tptp.bot_bot_set_int))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (= (@ tptp.finite1363419556375932405_nat_o A) tptp.one_one_nat) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool))) (not (= A (@ (@ tptp.insert5175938949040314269_nat_o X3) tptp.bot_bo7824918357723582233_nat_o))))))))
% 5.65/5.93 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (X tptp.nat) (Y tptp.nat) (A2 tptp.product_prod_nat_nat)) (=> (@ (@ P X) Y) (=> (= A2 (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ P (@ tptp.product_fst_nat_nat A2)) (@ tptp.product_snd_nat_nat A2))))))
% 5.65/5.93 (assert (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool)) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3658429121746597890et_nat) (A2 tptp.produc3925858234332021118et_nat)) (=> (@ (@ P X) Y) (=> (= A2 (@ (@ tptp.produc5001842942810119800et_nat X) Y)) (@ (@ P (@ tptp.produc995936583742144908et_nat A2)) (@ tptp.produc4011572625026189258et_nat A2))))))
% 5.65/5.93 (assert (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool)) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3925858234332021118et_nat) (A2 tptp.produc2732055786443039994et_nat)) (=> (@ (@ P X) Y) (=> (= A2 (@ (@ tptp.produc2245416461498447860et_nat X) Y)) (@ (@ P (@ tptp.produc180342877477747464et_nat A2)) (@ tptp.produc5374455773327741254et_nat A2))))))
% 5.65/5.93 (assert (forall ((P (-> tptp.heap_e7401611519738050253t_unit tptp.set_nat Bool)) (X tptp.heap_e7401611519738050253t_unit) (Y tptp.set_nat) (A2 tptp.produc3658429121746597890et_nat)) (=> (@ (@ P X) Y) (=> (= A2 (@ (@ tptp.produc7507926704131184380et_nat X) Y)) (@ (@ P (@ tptp.produc1824681642469235216et_nat A2)) (@ tptp.produc8586169260539613262et_nat A2))))))
% 5.65/5.93 (assert (forall ((P (-> tptp.int tptp.int Bool)) (X tptp.int) (Y tptp.int) (A2 tptp.product_prod_int_int)) (=> (@ (@ P X) Y) (=> (= A2 (@ (@ tptp.product_Pair_int_int X) Y)) (@ (@ P (@ tptp.product_fst_int_int A2)) (@ tptp.product_snd_int_int A2))))))
% 5.65/5.93 (assert (forall ((Prod tptp.product_prod_nat_nat)) (= Prod (@ (@ tptp.product_Pair_nat_nat (@ tptp.product_fst_nat_nat Prod)) (@ tptp.product_snd_nat_nat Prod)))))
% 5.65/5.93 (assert (forall ((Prod tptp.produc3925858234332021118et_nat)) (= Prod (@ (@ tptp.produc5001842942810119800et_nat (@ tptp.produc995936583742144908et_nat Prod)) (@ tptp.produc4011572625026189258et_nat Prod)))))
% 5.65/5.93 (assert (forall ((Prod tptp.produc2732055786443039994et_nat)) (= Prod (@ (@ tptp.produc2245416461498447860et_nat (@ tptp.produc180342877477747464et_nat Prod)) (@ tptp.produc5374455773327741254et_nat Prod)))))
% 5.65/5.93 (assert (forall ((Prod tptp.produc3658429121746597890et_nat)) (= Prod (@ (@ tptp.produc7507926704131184380et_nat (@ tptp.produc1824681642469235216et_nat Prod)) (@ tptp.produc8586169260539613262et_nat Prod)))))
% 5.65/5.93 (assert (forall ((Prod tptp.product_prod_int_int)) (= Prod (@ (@ tptp.product_Pair_int_int (@ tptp.product_fst_int_int Prod)) (@ tptp.product_snd_int_int Prod)))))
% 5.65/5.93 (assert (forall ((T4 tptp.product_prod_nat_nat)) (= T4 (@ (@ tptp.product_Pair_nat_nat (@ tptp.product_fst_nat_nat T4)) (@ tptp.product_snd_nat_nat T4)))))
% 5.65/5.93 (assert (forall ((T4 tptp.produc3925858234332021118et_nat)) (= T4 (@ (@ tptp.produc5001842942810119800et_nat (@ tptp.produc995936583742144908et_nat T4)) (@ tptp.produc4011572625026189258et_nat T4)))))
% 5.65/5.93 (assert (forall ((T4 tptp.produc2732055786443039994et_nat)) (= T4 (@ (@ tptp.produc2245416461498447860et_nat (@ tptp.produc180342877477747464et_nat T4)) (@ tptp.produc5374455773327741254et_nat T4)))))
% 5.65/5.93 (assert (forall ((T4 tptp.produc3658429121746597890et_nat)) (= T4 (@ (@ tptp.produc7507926704131184380et_nat (@ tptp.produc1824681642469235216et_nat T4)) (@ tptp.produc8586169260539613262et_nat T4)))))
% 5.65/5.93 (assert (forall ((T4 tptp.product_prod_int_int)) (= T4 (@ (@ tptp.product_Pair_int_int (@ tptp.product_fst_int_int T4)) (@ tptp.product_snd_int_int T4)))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A)) (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (X tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A)) (@ tptp.finite_card_int (@ (@ tptp.insert_int X) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (X Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o A)) (@ tptp.finite_card_o (@ (@ tptp.insert_o X) A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite410649719033368117t_unit A)) (@ tptp.finite410649719033368117t_unit (@ (@ tptp.insert_Product_unit X) A)))))
% 5.65/5.93 (assert (forall ((X tptp.heap_e7401611519738050253t_unit) (S tptp.set_Pr3948176798113811640et_nat)) (=> (@ (@ tptp.member242389114213480694t_unit X) (@ (@ tptp.image_6824039242672219652t_unit tptp.produc1824681642469235216et_nat) S)) (not (forall ((Y2 tptp.set_nat)) (not (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat X) Y2)) S)))))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (S tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.image_2486076414777270412at_nat tptp.product_fst_nat_nat) S)) (not (forall ((Y2 tptp.nat)) (not (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y2)) S)))))))
% 5.65/5.93 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (S tptp.set_Pr3286484037609594932et_nat)) (=> (@ (@ tptp.member6576561426505652726_nat_o X) (@ (@ tptp.image_6802380912191114376_nat_o tptp.produc995936583742144908et_nat) S)) (not (forall ((Y2 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X) Y2)) S)))))))
% 5.65/5.93 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (S tptp.set_Pr8536935166611901872et_nat)) (=> (@ (@ tptp.member6576561426505652726_nat_o X) (@ (@ tptp.image_2517677226577294348_nat_o tptp.produc180342877477747464et_nat) S)) (not (forall ((Y2 tptp.produc3925858234332021118et_nat)) (not (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X) Y2)) S)))))))
% 5.65/5.93 (assert (forall ((X tptp.int) (S tptp.set_Pr958786334691620121nt_int)) (=> (@ (@ tptp.member_int X) (@ (@ tptp.image_5042161079198086560nt_int tptp.product_fst_int_int) S)) (not (forall ((Y2 tptp.int)) (not (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y2)) S)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_set_nat) (B4 tptp.set_nat)) (=> (forall ((X8 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X8) A) (@ (@ tptp.ord_less_eq_set_nat X8) B4))) (=> (not (= A tptp.bot_bot_set_set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7806235888213564991et_nat A)) B4)))))
% 5.65/5.93 (assert (= (@ tptp.comple7216939928495492468t_unit tptp.bot_bo6284674557190688313t_unit) tptp.top_to1996260823553986621t_unit))
% 5.65/5.93 (assert (= (@ tptp.comple3063163877087187839_set_o tptp.bot_bot_set_set_o) tptp.top_top_set_o))
% 5.65/5.93 (assert (= (@ tptp.comple3628384868704368283et_int tptp.bot_bot_set_set_int) tptp.top_top_set_int))
% 5.65/5.93 (assert (= (@ tptp.comple7806235888213564991et_nat tptp.bot_bot_set_set_nat) tptp.top_top_set_nat))
% 5.65/5.93 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.image_5042161079198086560nt_int tptp.product_fst_int_int) R3) (@ tptp.domain_int_int R3))))
% 5.65/5.93 (assert (= tptp.domain_int_int (@ tptp.image_5042161079198086560nt_int tptp.product_fst_int_int)))
% 5.65/5.93 (assert (forall ((C5 tptp.set_set_Code_integer) (K3 tptp.nat)) (let ((_let_1 (@ tptp.comple739944243200306918nteger C5))) (=> (@ tptp.finite6931041176100689706nteger C5) (=> (@ tptp.finite6017078050557962740nteger _let_1) (=> (forall ((C2 tptp.set_Code_integer)) (=> (@ (@ tptp.member1834298987299537450nteger C2) C5) (= (@ tptp.finite4902975817058060853nteger C2) K3))) (=> (forall ((C1 tptp.set_Code_integer) (C22 tptp.set_Code_integer)) (=> (@ (@ tptp.member1834298987299537450nteger C1) C5) (=> (@ (@ tptp.member1834298987299537450nteger C22) C5) (=> (not (= C1 C22)) (= (@ (@ tptp.inf_in1364745209274528805nteger C1) C22) tptp.bot_bo3990330152332043303nteger))))) (= (@ (@ tptp.times_times_nat K3) (@ tptp.finite1340570857867686763nteger C5)) (@ tptp.finite4902975817058060853nteger _let_1)))))))))
% 5.65/5.93 (assert (forall ((C5 tptp.set_set_Product_unit) (K3 tptp.nat)) (let ((_let_1 (@ tptp.comple3349607820504768346t_unit C5))) (=> (@ tptp.finite1772178364199683094t_unit C5) (=> (@ tptp.finite4290736615968046902t_unit _let_1) (=> (forall ((C2 tptp.set_Product_unit)) (=> (@ (@ tptp.member5877623283571906838t_unit C2) C5) (= (@ tptp.finite410649719033368117t_unit C2) K3))) (=> (forall ((C1 tptp.set_Product_unit) (C22 tptp.set_Product_unit)) (=> (@ (@ tptp.member5877623283571906838t_unit C1) C5) (=> (@ (@ tptp.member5877623283571906838t_unit C22) C5) (=> (not (= C1 C22)) (= (@ (@ tptp.inf_in4660618365625256667t_unit C1) C22) tptp.bot_bo3957492148770167129t_unit))))) (= (@ (@ tptp.times_times_nat K3) (@ tptp.finite22775419188893461t_unit C5)) (@ tptp.finite410649719033368117t_unit _let_1)))))))))
% 5.65/5.93 (assert (forall ((C5 tptp.set_set_o) (K3 tptp.nat)) (let ((_let_1 (@ tptp.comple90263536869209701_set_o C5))) (=> (@ tptp.finite_finite_set_o C5) (=> (@ tptp.finite_finite_o _let_1) (=> (forall ((C2 tptp.set_o)) (=> (@ (@ tptp.member_set_o C2) C5) (= (@ tptp.finite_card_o C2) K3))) (=> (forall ((C1 tptp.set_o) (C22 tptp.set_o)) (=> (@ (@ tptp.member_set_o C1) C5) (=> (@ (@ tptp.member_set_o C22) C5) (=> (not (= C1 C22)) (= (@ (@ tptp.inf_inf_set_o C1) C22) tptp.bot_bot_set_o))))) (= (@ (@ tptp.times_times_nat K3) (@ tptp.finite_card_set_o C5)) (@ tptp.finite_card_o _let_1)))))))))
% 5.65/5.93 (assert (forall ((C5 tptp.set_set_nat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.comple7399068483239264473et_nat C5))) (=> (@ tptp.finite1152437895449049373et_nat C5) (=> (@ tptp.finite_finite_nat _let_1) (=> (forall ((C2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat C2) C5) (= (@ tptp.finite_card_nat C2) K3))) (=> (forall ((C1 tptp.set_nat) (C22 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat C1) C5) (=> (@ (@ tptp.member_set_nat C22) C5) (=> (not (= C1 C22)) (= (@ (@ tptp.inf_inf_set_nat C1) C22) tptp.bot_bot_set_nat))))) (= (@ (@ tptp.times_times_nat K3) (@ tptp.finite_card_set_nat C5)) (@ tptp.finite_card_nat _let_1)))))))))
% 5.65/5.93 (assert (forall ((C5 tptp.set_set_int) (K3 tptp.nat)) (let ((_let_1 (@ tptp.comple3221217463730067765et_int C5))) (=> (@ tptp.finite6197958912794628473et_int C5) (=> (@ tptp.finite_finite_int _let_1) (=> (forall ((C2 tptp.set_int)) (=> (@ (@ tptp.member_set_int C2) C5) (= (@ tptp.finite_card_int C2) K3))) (=> (forall ((C1 tptp.set_int) (C22 tptp.set_int)) (=> (@ (@ tptp.member_set_int C1) C5) (=> (@ (@ tptp.member_set_int C22) C5) (=> (not (= C1 C22)) (= (@ (@ tptp.inf_inf_set_int C1) C22) tptp.bot_bot_set_int))))) (= (@ (@ tptp.times_times_nat K3) (@ tptp.finite_card_set_int C5)) (@ tptp.finite_card_int _let_1)))))))))
% 5.65/5.93 (assert (forall ((C5 tptp.set_se1353816476878259085_nat_o) (K3 tptp.nat)) (let ((_let_1 (@ tptp.comple3382087578465172250_nat_o C5))) (=> (@ tptp.finite6069017635265841110_nat_o C5) (=> (@ tptp.finite3252695134891459830_nat_o _let_1) (=> (forall ((C2 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member1452989533377600726_nat_o C2) C5) (= (@ tptp.finite1363419556375932405_nat_o C2) K3))) (=> (forall ((C1 tptp.set_Pr4532377907799695533_nat_o) (C22 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member1452989533377600726_nat_o C1) C5) (=> (@ (@ tptp.member1452989533377600726_nat_o C22) C5) (=> (not (= C1 C22)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o C1) C22) tptp.bot_bo7824918357723582233_nat_o))))) (= (@ (@ tptp.times_times_nat K3) (@ tptp.finite4731484169140532437_nat_o C5)) (@ tptp.finite1363419556375932405_nat_o _let_1)))))))))
% 5.65/5.93 (assert (= (@ tptp.comple7216939928495492468t_unit tptp.top_to1767297665138865437t_unit) tptp.bot_bo3957492148770167129t_unit))
% 5.65/5.93 (assert (= (@ tptp.comple3063163877087187839_set_o tptp.top_top_set_set_o) tptp.bot_bot_set_o))
% 5.65/5.93 (assert (= (@ tptp.comple3628384868704368283et_int tptp.top_top_set_set_int) tptp.bot_bot_set_int))
% 5.65/5.93 (assert (= (@ tptp.comple79274577958421812_nat_o tptp.top_to8515903933492314333_nat_o) tptp.bot_bo7824918357723582233_nat_o))
% 5.65/5.93 (assert (= (@ tptp.comple7806235888213564991et_nat tptp.top_top_set_set_nat) tptp.bot_bot_set_nat))
% 5.65/5.93 (assert (forall ((Y tptp.code_integer) (F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer)) (=> (@ (@ tptp.member_Code_integer Y) (@ (@ tptp.image_4470545334726330049nteger F) A)) (@ (@ tptp.member_Code_integer (@ (@ (@ tptp.inv_on4869000451854154612nteger F) A) Y)) A))))
% 5.65/5.93 (assert (forall ((Y tptp.code_integer) (F (-> tptp.nat tptp.code_integer)) (A tptp.set_nat)) (=> (@ (@ tptp.member_Code_integer Y) (@ (@ tptp.image_1215581382706833972nteger F) A)) (@ (@ tptp.member_nat (@ (@ (@ tptp.inv_on1369624593536199399nteger F) A) Y)) A))))
% 5.65/5.93 (assert (forall ((Y tptp.nat) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat Y) (@ (@ tptp.image_nat_nat2 F) A)) (@ (@ tptp.member_nat (@ (@ (@ tptp.inv_on_nat_nat F) A) Y)) A))))
% 5.65/5.93 (assert (forall ((Y tptp.nat) (F (-> tptp.int tptp.nat)) (A tptp.set_int)) (=> (@ (@ tptp.member_nat Y) (@ (@ tptp.image_int_nat2 F) A)) (@ (@ tptp.member_int (@ (@ (@ tptp.inv_on_int_nat F) A) Y)) A))))
% 5.65/5.93 (assert (forall ((Y tptp.nat) (F (-> Bool tptp.nat)) (A tptp.set_o)) (=> (@ (@ tptp.member_nat Y) (@ (@ tptp.image_o_nat2 F) A)) (@ (@ tptp.member_o (@ (@ (@ tptp.inv_on_o_nat F) A) Y)) A))))
% 5.65/5.93 (assert (forall ((Y tptp.nat) (F (-> tptp.product_unit tptp.nat)) (A tptp.set_Product_unit)) (=> (@ (@ tptp.member_nat Y) (@ (@ tptp.image_875570014554754200it_nat F) A)) (@ (@ tptp.member_Product_unit (@ (@ (@ tptp.inv_on7727615724625388965it_nat F) A) Y)) A))))
% 5.65/5.93 (assert (forall ((Y tptp.int) (F (-> tptp.nat tptp.int)) (A tptp.set_nat)) (=> (@ (@ tptp.member_int Y) (@ (@ tptp.image_nat_int2 F) A)) (@ (@ tptp.member_nat (@ (@ (@ tptp.inv_on_nat_int F) A) Y)) A))))
% 5.65/5.93 (assert (forall ((Y tptp.int) (F (-> tptp.int tptp.int)) (A tptp.set_int)) (=> (@ (@ tptp.member_int Y) (@ (@ tptp.image_int_int2 F) A)) (@ (@ tptp.member_int (@ (@ (@ tptp.inv_on_int_int F) A) Y)) A))))
% 5.65/5.93 (assert (forall ((Y tptp.int) (F (-> Bool tptp.int)) (A tptp.set_o)) (=> (@ (@ tptp.member_int Y) (@ (@ tptp.image_o_int2 F) A)) (@ (@ tptp.member_o (@ (@ (@ tptp.inv_on_o_int F) A) Y)) A))))
% 5.65/5.93 (assert (forall ((Y tptp.int) (F (-> tptp.product_unit tptp.int)) (A tptp.set_Product_unit)) (=> (@ (@ tptp.member_int Y) (@ (@ tptp.image_873079544045703924it_int F) A)) (@ (@ tptp.member_Product_unit (@ (@ (@ tptp.inv_on7725125254116338689it_int F) A) Y)) A))))
% 5.65/5.93 (assert (forall ((Y tptp.set_nat) (F (-> tptp.nat tptp.set_nat)) (A tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Y) (@ (@ tptp.image_nat_set_nat F) A)) (= (@ F (@ (@ (@ tptp.inv_on_nat_set_nat F) A) Y)) Y))))
% 5.65/5.93 (assert (forall ((Y tptp.code_integer) (F (-> tptp.code_integer tptp.code_integer)) (A tptp.set_Code_integer)) (=> (@ (@ tptp.member_Code_integer Y) (@ (@ tptp.image_4470545334726330049nteger F) A)) (= (@ F (@ (@ (@ tptp.inv_on4869000451854154612nteger F) A) Y)) Y))))
% 5.65/5.93 (assert (forall ((Y tptp.code_integer) (F (-> tptp.nat tptp.code_integer)) (A tptp.set_nat)) (=> (@ (@ tptp.member_Code_integer Y) (@ (@ tptp.image_1215581382706833972nteger F) A)) (= (@ F (@ (@ (@ tptp.inv_on1369624593536199399nteger F) A) Y)) Y))))
% 5.65/5.93 (assert (forall ((Y tptp.nat) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat Y) (@ (@ tptp.image_nat_nat2 F) A)) (= (@ F (@ (@ (@ tptp.inv_on_nat_nat F) A) Y)) Y))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (M4 tptp.int) (F (-> tptp.product_unit tptp.int))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) A) (@ (@ tptp.ord_less_eq_int M4) (@ F X3)))) (@ (@ tptp.ord_less_eq_int M4) (@ tptp.complete_Inf_Inf_int (@ (@ tptp.image_873079544045703924it_int F) A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (M4 tptp.int) (F (-> Bool tptp.int))) (=> (not (= A tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (@ (@ tptp.ord_less_eq_int M4) (@ F X3)))) (@ (@ tptp.ord_less_eq_int M4) (@ tptp.complete_Inf_Inf_int (@ (@ tptp.image_o_int2 F) A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (M4 tptp.int) (F (-> tptp.nat tptp.int))) (=> (not (= A tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (@ (@ tptp.ord_less_eq_int M4) (@ F X3)))) (@ (@ tptp.ord_less_eq_int M4) (@ tptp.complete_Inf_Inf_int (@ (@ tptp.image_nat_int2 F) A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (M4 tptp.int) (F (-> tptp.int tptp.int))) (=> (not (= A tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (@ (@ tptp.ord_less_eq_int M4) (@ F X3)))) (@ (@ tptp.ord_less_eq_int M4) (@ tptp.complete_Inf_Inf_int (@ (@ tptp.image_int_int2 F) A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (M4 tptp.nat) (F (-> tptp.product_unit tptp.nat))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) A) (@ (@ tptp.ord_less_eq_nat M4) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat M4) (@ tptp.complete_Inf_Inf_nat (@ (@ tptp.image_875570014554754200it_nat F) A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (M4 tptp.nat) (F (-> Bool tptp.nat))) (=> (not (= A tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (@ (@ tptp.ord_less_eq_nat M4) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat M4) (@ tptp.complete_Inf_Inf_nat (@ (@ tptp.image_o_nat2 F) A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (M4 tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (not (= A tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (@ (@ tptp.ord_less_eq_nat M4) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat M4) (@ tptp.complete_Inf_Inf_nat (@ (@ tptp.image_nat_nat2 F) A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (M4 tptp.nat) (F (-> tptp.int tptp.nat))) (=> (not (= A tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (@ (@ tptp.ord_less_eq_nat M4) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat M4) (@ tptp.complete_Inf_Inf_nat (@ (@ tptp.image_int_nat2 F) A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (M4 tptp.product_unit) (F (-> tptp.product_unit tptp.product_unit))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) A) (@ (@ tptp.ord_le3221252021190050221t_unit M4) (@ F X3)))) (@ (@ tptp.ord_le3221252021190050221t_unit M4) (@ tptp.comple2584293577114468500t_unit (@ (@ tptp.image_405062704495631173t_unit F) A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (M4 tptp.product_unit) (F (-> Bool tptp.product_unit))) (=> (not (= A tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (@ (@ tptp.ord_le3221252021190050221t_unit M4) (@ F X3)))) (@ (@ tptp.ord_le3221252021190050221t_unit M4) (@ tptp.comple2584293577114468500t_unit (@ (@ tptp.image_o_Product_unit2 F) A)))))))
% 5.65/5.93 (assert (forall ((I tptp.set_Product_unit) (F (-> tptp.product_unit tptp.product_unit)) (C tptp.product_unit)) (=> (not (= I tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) I) (@ (@ tptp.ord_le3221252021190050221t_unit (@ F I3)) C))) (= (= (@ tptp.comple2584293577114468500t_unit (@ (@ tptp.image_405062704495631173t_unit F) I)) C) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) I) (= (@ F X2) C))))))))
% 5.65/5.93 (assert (forall ((I tptp.set_o) (F (-> Bool tptp.product_unit)) (C tptp.product_unit)) (=> (not (= I tptp.bot_bot_set_o)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I) (@ (@ tptp.ord_le3221252021190050221t_unit (@ F I3)) C))) (= (= (@ tptp.comple2584293577114468500t_unit (@ (@ tptp.image_o_Product_unit2 F) I)) C) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) I) (= (@ F X2) C))))))))
% 5.65/5.93 (assert (forall ((I tptp.set_nat) (F (-> tptp.nat tptp.product_unit)) (C tptp.product_unit)) (=> (not (= I tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I) (@ (@ tptp.ord_le3221252021190050221t_unit (@ F I3)) C))) (= (= (@ tptp.comple2584293577114468500t_unit (@ (@ tptp.image_8730104196221521654t_unit F) I)) C) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) I) (= (@ F X2) C))))))))
% 5.65/5.93 (assert (forall ((I tptp.set_int) (F (-> tptp.int tptp.product_unit)) (C tptp.product_unit)) (=> (not (= I tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I) (@ (@ tptp.ord_le3221252021190050221t_unit (@ F I3)) C))) (= (= (@ tptp.comple2584293577114468500t_unit (@ (@ tptp.image_5846526143423701914t_unit F) I)) C) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) I) (= (@ F X2) C))))))))
% 5.65/5.93 (assert (forall ((I tptp.set_Product_unit) (F (-> tptp.product_unit tptp.filter_nat)) (C tptp.filter_nat)) (=> (not (= I tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) I) (@ (@ tptp.ord_le2510731241096832064er_nat (@ F I3)) C))) (= (= (@ tptp.comple6612786467464916249er_nat (@ (@ tptp.image_1853478764106424488er_nat F) I)) C) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) I) (= (@ F X2) C))))))))
% 5.65/5.93 (assert (forall ((I tptp.set_o) (F (-> Bool tptp.filter_nat)) (C tptp.filter_nat)) (=> (not (= I tptp.bot_bot_set_o)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I) (@ (@ tptp.ord_le2510731241096832064er_nat (@ F I3)) C))) (= (= (@ tptp.comple6612786467464916249er_nat (@ (@ tptp.image_o_filter_nat F) I)) C) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) I) (= (@ F X2) C))))))))
% 5.65/5.93 (assert (forall ((I tptp.set_nat) (F (-> tptp.nat tptp.filter_nat)) (C tptp.filter_nat)) (=> (not (= I tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I) (@ (@ tptp.ord_le2510731241096832064er_nat (@ F I3)) C))) (= (= (@ tptp.comple6612786467464916249er_nat (@ (@ tptp.image_nat_filter_nat F) I)) C) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) I) (= (@ F X2) C))))))))
% 5.65/5.93 (assert (forall ((I tptp.set_int) (F (-> tptp.int tptp.filter_nat)) (C tptp.filter_nat)) (=> (not (= I tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I) (@ (@ tptp.ord_le2510731241096832064er_nat (@ F I3)) C))) (= (= (@ tptp.comple6612786467464916249er_nat (@ (@ tptp.image_int_filter_nat F) I)) C) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) I) (= (@ F X2) C))))))))
% 5.65/5.93 (assert (forall ((I tptp.set_Product_unit) (F (-> tptp.product_unit tptp.set_nat)) (C tptp.set_nat)) (=> (not (= I tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) I) (@ (@ tptp.ord_less_eq_set_nat (@ F I3)) C))) (= (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_8173849991827986510et_nat F) I)) C) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) I) (= (@ F X2) C))))))))
% 5.65/5.93 (assert (forall ((I tptp.set_o) (F (-> Bool tptp.set_nat)) (C tptp.set_nat)) (=> (not (= I tptp.bot_bot_set_o)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I) (@ (@ tptp.ord_less_eq_set_nat (@ F I3)) C))) (= (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_o_set_nat F) I)) C) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) I) (= (@ F X2) C))))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_int) (A2 tptp.int)) (=> (@ tptp.finite_finite_int X4) (=> (not (= X4 tptp.bot_bot_set_int)) (= (@ (@ tptp.ord_less_int A2) (@ tptp.complete_Inf_Inf_int X4)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) X4) (@ (@ tptp.ord_less_int A2) X2))))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_nat) (A2 tptp.nat)) (=> (@ tptp.finite_finite_nat X4) (=> (not (= X4 tptp.bot_bot_set_nat)) (= (@ (@ tptp.ord_less_nat A2) (@ tptp.complete_Inf_Inf_nat X4)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) X4) (@ (@ tptp.ord_less_nat A2) X2))))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_Product_unit) (A2 tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit X4) (=> (not (= X4 tptp.bot_bo3957492148770167129t_unit)) (= (@ (@ tptp.ord_le361264281704409273t_unit A2) (@ tptp.comple2584293577114468500t_unit X4)) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) X4) (@ (@ tptp.ord_le361264281704409273t_unit A2) X2))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o)) (=> (not (= A tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_eq_o (@ tptp.complete_Inf_Inf_o A)) (@ tptp.complete_Sup_Sup_o A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (@ (@ tptp.ord_le729326519192465773_nat_o (@ tptp.comple90455603224345172_nat_o A)) (@ tptp.comple4225350640907012154_nat_o A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_filter_nat)) (=> (not (= A tptp.bot_bo498966703094740906er_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ tptp.comple6612786467464916249er_nat A)) (@ tptp.comple2454491259644266675er_nat A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_set_nat)) (=> (not (= A tptp.bot_bot_set_set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7806235888213564991et_nat A)) (@ tptp.comple7399068483239264473et_nat A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit)) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.comple2584293577114468500t_unit A)) (@ tptp.comple4687483117567863418t_unit A)))))
% 5.65/5.93 (assert (forall ((A tptp.set_o)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (=> (forall ((X3 Bool) (Y2 Bool)) (=> (@ (@ tptp.member_o X3) A) (=> (@ (@ tptp.member_o Y2) A) (@ (@ tptp.member_o (@ (@ tptp.inf_inf_o X3) Y2)) A)))) (@ (@ tptp.member_o (@ tptp.complete_Inf_Inf_o A)) A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X3) A) (=> (@ (@ tptp.member6576561426505652726_nat_o Y2) A) (@ (@ tptp.member6576561426505652726_nat_o (@ (@ tptp.inf_in1318976480646536635_nat_o X3) Y2)) A)))) (@ (@ tptp.member6576561426505652726_nat_o (@ tptp.comple90455603224345172_nat_o A)) A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (not (= A tptp.bot_bot_set_set_nat)) (=> (forall ((X3 tptp.set_nat) (Y2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) A) (=> (@ (@ tptp.member_set_nat Y2) A) (@ (@ tptp.member_set_nat (@ (@ tptp.inf_inf_set_nat X3) Y2)) A)))) (@ (@ tptp.member_set_nat (@ tptp.comple7806235888213564991et_nat A)) A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((X3 tptp.product_unit) (Y2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) A) (=> (@ (@ tptp.member_Product_unit Y2) A) (@ (@ tptp.member_Product_unit (@ (@ tptp.inf_inf_Product_unit X3) Y2)) A)))) (@ (@ tptp.member_Product_unit (@ tptp.comple2584293577114468500t_unit A)) A))))))
% 5.65/5.93 (assert (forall ((S tptp.set_Code_integer) (X tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger S) (=> (= (@ tptp.finite4902975817058060853nteger S) tptp.one_one_nat) (=> (@ (@ tptp.member_Code_integer X) S) (= S (@ (@ tptp.insert_Code_integer X) tptp.bot_bo3990330152332043303nteger)))))))
% 5.65/5.93 (assert (forall ((S tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit S) (=> (= (@ tptp.finite410649719033368117t_unit S) tptp.one_one_nat) (=> (@ (@ tptp.member_Product_unit X) S) (= S (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)))))))
% 5.65/5.93 (assert (forall ((S tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o S) (=> (= (@ tptp.finite_card_o S) tptp.one_one_nat) (=> (@ (@ tptp.member_o X) S) (= S (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)))))))
% 5.65/5.93 (assert (forall ((S tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat S) (=> (= (@ tptp.finite_card_nat S) tptp.one_one_nat) (=> (@ (@ tptp.member_nat X) S) (= S (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))))))
% 5.65/5.93 (assert (forall ((S tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (= (@ tptp.finite_card_int S) tptp.one_one_nat) (=> (@ (@ tptp.member_int X) S) (= S (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))))))
% 5.65/5.93 (assert (forall ((S tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.finite3252695134891459830_nat_o S) (=> (= (@ tptp.finite1363419556375932405_nat_o S) tptp.one_one_nat) (=> (@ (@ tptp.member6576561426505652726_nat_o X) S) (= S (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)))))))
% 5.65/5.93 (assert (forall ((X tptp.product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ tptp.finite410649719033368117t_unit A))) (let ((_let_2 (@ tptp.finite410649719033368117t_unit (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit))))) (let ((_let_3 (@ (@ tptp.member_Product_unit X) A))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.65/5.93 (assert (forall ((X Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.finite_card_o A))) (let ((_let_2 (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))))) (let ((_let_3 (@ (@ tptp.member_o X) A))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.65/5.93 (assert (forall ((X tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.finite_card_int A))) (let ((_let_2 (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))) (let ((_let_3 (@ (@ tptp.member_int X) A))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.65/5.93 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.finite1363419556375932405_nat_o A))) (let ((_let_2 (@ tptp.finite1363419556375932405_nat_o (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o))))) (let ((_let_3 (@ (@ tptp.member6576561426505652726_nat_o X) A))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.finite_card_nat A))) (let ((_let_2 (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))) (let ((_let_3 (@ (@ tptp.member_nat X) A))) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1))))))))
% 5.65/5.93 (assert (forall ((X tptp.product_unit) (A tptp.set_Product_unit)) (=> (@ (@ tptp.member_Product_unit X) A) (= (@ tptp.finite410649719033368117t_unit (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit))) (@ (@ tptp.minus_minus_nat (@ tptp.finite410649719033368117t_unit A)) tptp.one_one_nat)))))
% 5.65/5.93 (assert (forall ((X Bool) (A tptp.set_o)) (=> (@ (@ tptp.member_o X) A) (= (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_o A)) tptp.one_one_nat)))))
% 5.65/5.93 (assert (forall ((X tptp.int) (A tptp.set_int)) (=> (@ (@ tptp.member_int X) A) (= (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_int A)) tptp.one_one_nat)))))
% 5.65/5.93 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member6576561426505652726_nat_o X) A) (= (@ tptp.finite1363419556375932405_nat_o (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o))) (@ (@ tptp.minus_minus_nat (@ tptp.finite1363419556375932405_nat_o A)) tptp.one_one_nat)))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat X) A) (= (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_nat A)) tptp.one_one_nat)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr3948176798113811640et_nat) (B4 tptp.set_he8644174446132254637t_unit) (X tptp.heap_e7401611519738050253t_unit) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_le4903435234951335757t_unit (@ (@ tptp.image_6824039242672219652t_unit tptp.produc1824681642469235216et_nat) A)) B4) (=> (@ (@ tptp.member6260224972018164377et_nat (@ (@ tptp.produc7507926704131184380et_nat X) Y)) A) (@ (@ tptp.member242389114213480694t_unit X) B4)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr3286484037609594932et_nat) (B4 tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o (@ (@ tptp.image_6802380912191114376_nat_o tptp.produc995936583742144908et_nat) A)) B4) (=> (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X) Y)) A) (@ (@ tptp.member6576561426505652726_nat_o X) B4)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr8536935166611901872et_nat) (B4 tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool)) (Y tptp.produc3925858234332021118et_nat)) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o (@ (@ tptp.image_2517677226577294348_nat_o tptp.produc180342877477747464et_nat) A)) B4) (=> (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X) Y)) A) (@ (@ tptp.member6576561426505652726_nat_o X) B4)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr958786334691620121nt_int) (B4 tptp.set_int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_5042161079198086560nt_int tptp.product_fst_int_int) A)) B4) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) A) (@ (@ tptp.member_int X) B4)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_2486076414777270412at_nat tptp.product_fst_nat_nat) A)) B4) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) A) (@ (@ tptp.member_nat X) B4)))))
% 5.65/5.93 (assert (forall ((R3 tptp.set_Pr958786334691620121nt_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_5042161079198086560nt_int tptp.product_fst_int_int) R3)) (@ tptp.field_int R3))))
% 5.65/5.93 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_2486076414777270412at_nat tptp.product_fst_nat_nat) R3)) (@ tptp.field_nat R3))))
% 5.65/5.93 (assert (forall ((A tptp.set_o)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (= (@ tptp.lattic4107685809792843317_fin_o A) (@ tptp.complete_Inf_Inf_o A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (= (@ tptp.lattic956194824204696298_nat_o A) (@ tptp.comple90455603224345172_nat_o A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A) (=> (not (= A tptp.bot_bot_set_set_nat)) (= (@ tptp.lattic3014633134055518761et_nat A) (@ tptp.comple7806235888213564991et_nat A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (@ tptp.lattic1263872656861969706t_unit A) (@ tptp.comple2584293577114468500t_unit A))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_o)) (=> (@ tptp.finite_finite_o X4) (=> (not (= X4 tptp.bot_bot_set_o)) (= (@ tptp.complete_Inf_Inf_o X4) (@ tptp.lattic4107685809792843317_fin_o X4))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_int)) (=> (@ tptp.finite_finite_int X4) (=> (not (= X4 tptp.bot_bot_set_int)) (= (@ tptp.complete_Inf_Inf_int X4) (@ tptp.lattic5235898064620869839in_int X4))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o X4) (=> (not (= X4 tptp.bot_bo7824918357723582233_nat_o)) (= (@ tptp.comple90455603224345172_nat_o X4) (@ tptp.lattic956194824204696298_nat_o X4))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat X4) (=> (not (= X4 tptp.bot_bot_set_nat)) (= (@ tptp.complete_Inf_Inf_nat X4) (@ tptp.lattic5238388535129920115in_nat X4))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat X4) (=> (not (= X4 tptp.bot_bot_set_set_nat)) (= (@ tptp.comple7806235888213564991et_nat X4) (@ tptp.lattic3014633134055518761et_nat X4))))))
% 5.65/5.93 (assert (forall ((X4 tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit X4) (=> (not (= X4 tptp.bot_bo3957492148770167129t_unit)) (= (@ tptp.comple2584293577114468500t_unit X4) (@ tptp.lattic1263872656861969706t_unit X4))))))
% 5.65/5.93 (assert (= tptp.basic_fsts_int_int (lambda ((P5 tptp.product_prod_int_int)) (@ (@ tptp.insert_int (@ tptp.product_fst_int_int P5)) tptp.bot_bot_set_int))))
% 5.65/5.93 (assert (= tptp.produc1264744871843189710t_unit (lambda ((P5 tptp.produc7348995623955488188t_unit)) (@ (@ tptp.produc7507926704131184380et_nat (@ tptp.produc3550216979005444800t_unit P5)) (@ tptp.produc6012101397789842562t_unit P5)))))
% 5.65/5.93 (assert (= tptp.product_swap_nat_nat (lambda ((P5 tptp.product_prod_nat_nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.product_snd_nat_nat P5)) (@ tptp.product_fst_nat_nat P5)))))
% 5.65/5.93 (assert (= tptp.produc1078497009909708626_nat_o (lambda ((P5 tptp.produc6907119039986491712_nat_o)) (@ (@ tptp.produc5001842942810119800et_nat (@ tptp.produc1838968430882301508_nat_o P5)) (@ tptp.produc8046704426453032966_nat_o P5)))))
% 5.65/5.93 (assert (= tptp.produc2580581461503396054_nat_o (lambda ((P5 tptp.produc4962441903510821572_nat_o)) (@ (@ tptp.produc2245416461498447860et_nat (@ tptp.produc6803565743942592456_nat_o P5)) (@ tptp.produc1609452848092598666_nat_o P5)))))
% 5.65/5.93 (assert (= tptp.produc6300697153377358172et_nat (lambda ((P5 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.produc2471974422597015918t_unit (@ tptp.produc8586169260539613262et_nat P5)) (@ tptp.produc1824681642469235216et_nat P5)))))
% 5.65/5.93 (assert (= tptp.product_swap_int_int (lambda ((P5 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.product_snd_int_int P5)) (@ tptp.product_fst_int_int P5)))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (R3 tptp.set_Pr958786334691620121nt_int) (Z tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.comp_i5103216804979976198nt_int (@ tptp.equiv_proj_int_int R3)))) (=> (@ (@ tptp.equiv_equiv_int A) R3) (=> (@ (@ tptp.member5262025264175285858nt_int Z) R3) (= (@ (@ _let_1 tptp.product_fst_int_int) Z) (@ (@ _let_1 tptp.product_snd_int_int) Z)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.product_unit))) (let ((_let_1 (@ (@ tptp.image_405062704495631173t_unit F) A))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.comple2584293577114468500t_unit _let_1)) (@ tptp.comple4687483117567863418t_unit _let_1))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.product_unit))) (let ((_let_1 (@ (@ tptp.image_o_Product_unit2 F) A))) (=> (not (= A tptp.bot_bot_set_o)) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.comple2584293577114468500t_unit _let_1)) (@ tptp.comple4687483117567863418t_unit _let_1))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.product_unit))) (let ((_let_1 (@ (@ tptp.image_8730104196221521654t_unit F) A))) (=> (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.comple2584293577114468500t_unit _let_1)) (@ tptp.comple4687483117567863418t_unit _let_1))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.product_unit))) (let ((_let_1 (@ (@ tptp.image_5846526143423701914t_unit F) A))) (=> (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.comple2584293577114468500t_unit _let_1)) (@ tptp.comple4687483117567863418t_unit _let_1))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.filter_nat))) (let ((_let_1 (@ (@ tptp.image_1853478764106424488er_nat F) A))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ tptp.comple6612786467464916249er_nat _let_1)) (@ tptp.comple2454491259644266675er_nat _let_1))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.filter_nat))) (let ((_let_1 (@ (@ tptp.image_o_filter_nat F) A))) (=> (not (= A tptp.bot_bot_set_o)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ tptp.comple6612786467464916249er_nat _let_1)) (@ tptp.comple2454491259644266675er_nat _let_1))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.filter_nat))) (let ((_let_1 (@ (@ tptp.image_nat_filter_nat F) A))) (=> (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ tptp.comple6612786467464916249er_nat _let_1)) (@ tptp.comple2454491259644266675er_nat _let_1))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.filter_nat))) (let ((_let_1 (@ (@ tptp.image_int_filter_nat F) A))) (=> (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ tptp.comple6612786467464916249er_nat _let_1)) (@ tptp.comple2454491259644266675er_nat _let_1))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.set_nat))) (let ((_let_1 (@ (@ tptp.image_8173849991827986510et_nat F) A))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7806235888213564991et_nat _let_1)) (@ tptp.comple7399068483239264473et_nat _let_1))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.set_nat))) (let ((_let_1 (@ (@ tptp.image_o_set_nat F) A))) (=> (not (= A tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7806235888213564991et_nat _let_1)) (@ tptp.comple7399068483239264473et_nat _let_1))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite410649719033368117t_unit (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)))) (@ tptp.finite410649719033368117t_unit A))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (X Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)))) (@ tptp.finite_card_o A))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (X tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))) (@ tptp.finite_card_int A))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1363419556375932405_nat_o (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)))) (@ tptp.finite1363419556375932405_nat_o A))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))) (@ tptp.finite_card_nat A))))
% 5.65/5.93 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat X) Y))) (=> (@ (@ P Y) X) (@ (@ P (@ tptp.product_snd_nat_nat _let_1)) (@ tptp.product_fst_nat_nat _let_1))))))
% 5.65/5.93 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (Y tptp.produc3658429121746597890et_nat) (X (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ tptp.produc5001842942810119800et_nat X) Y))) (=> (@ (@ P Y) X) (@ (@ P (@ tptp.produc4011572625026189258et_nat _let_1)) (@ tptp.produc995936583742144908et_nat _let_1))))))
% 5.65/5.93 (assert (forall ((P (-> tptp.produc3925858234332021118et_nat (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (Y tptp.produc3925858234332021118et_nat) (X (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ tptp.produc2245416461498447860et_nat X) Y))) (=> (@ (@ P Y) X) (@ (@ P (@ tptp.produc5374455773327741254et_nat _let_1)) (@ tptp.produc180342877477747464et_nat _let_1))))))
% 5.65/5.93 (assert (forall ((P (-> tptp.set_nat tptp.heap_e7401611519738050253t_unit Bool)) (Y tptp.set_nat) (X tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat X) Y))) (=> (@ (@ P Y) X) (@ (@ P (@ tptp.produc8586169260539613262et_nat _let_1)) (@ tptp.produc1824681642469235216et_nat _let_1))))))
% 5.65/5.93 (assert (forall ((P (-> tptp.int tptp.int Bool)) (Y tptp.int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.product_Pair_int_int X) Y))) (=> (@ (@ P Y) X) (@ (@ P (@ tptp.product_snd_int_int _let_1)) (@ tptp.product_fst_int_int _let_1))))))
% 5.65/5.93 (assert (forall ((P (-> tptp.nat Bool)) (P3 tptp.nat) (Q2 (-> tptp.nat Bool)) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat P3) Q4))) (=> (@ P P3) (=> (@ Q2 Q4) (and (@ P (@ tptp.product_fst_nat_nat _let_1)) (@ Q2 (@ tptp.product_snd_nat_nat _let_1))))))))
% 5.65/5.93 (assert (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (P3 (-> tptp.produc3658429121746597890et_nat Bool)) (Q2 (-> tptp.produc3658429121746597890et_nat Bool)) (Q4 tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ (@ tptp.produc5001842942810119800et_nat P3) Q4))) (=> (@ P P3) (=> (@ Q2 Q4) (and (@ P (@ tptp.produc995936583742144908et_nat _let_1)) (@ Q2 (@ tptp.produc4011572625026189258et_nat _let_1))))))))
% 5.65/5.93 (assert (forall ((P (-> (-> tptp.produc3658429121746597890et_nat Bool) Bool)) (P3 (-> tptp.produc3658429121746597890et_nat Bool)) (Q2 (-> tptp.produc3925858234332021118et_nat Bool)) (Q4 tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ (@ tptp.produc2245416461498447860et_nat P3) Q4))) (=> (@ P P3) (=> (@ Q2 Q4) (and (@ P (@ tptp.produc180342877477747464et_nat _let_1)) (@ Q2 (@ tptp.produc5374455773327741254et_nat _let_1))))))))
% 5.65/5.93 (assert (forall ((P (-> tptp.heap_e7401611519738050253t_unit Bool)) (P3 tptp.heap_e7401611519738050253t_unit) (Q2 (-> tptp.set_nat Bool)) (Q4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat P3) Q4))) (=> (@ P P3) (=> (@ Q2 Q4) (and (@ P (@ tptp.produc1824681642469235216et_nat _let_1)) (@ Q2 (@ tptp.produc8586169260539613262et_nat _let_1))))))))
% 5.65/5.93 (assert (forall ((P (-> tptp.int Bool)) (P3 tptp.int) (Q2 (-> tptp.int Bool)) (Q4 tptp.int)) (let ((_let_1 (@ (@ tptp.product_Pair_int_int P3) Q4))) (=> (@ P P3) (=> (@ Q2 Q4) (and (@ P (@ tptp.product_fst_int_int _let_1)) (@ Q2 (@ tptp.product_snd_int_int _let_1))))))))
% 5.65/5.93 (assert (forall ((Q4 tptp.produc3658429121746597890et_nat) (F (-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit)) (P3 tptp.produc3658429121746597890et_nat)) (=> (= Q4 (@ (@ tptp.produc4172003873565521026et_nat F) P3)) (not (forall ((X3 tptp.heap_e7401611519738050253t_unit) (Y2 tptp.set_nat)) (=> (= P3 (@ (@ tptp.produc7507926704131184380et_nat X3) Y2)) (not (= Q4 (@ (@ tptp.produc7507926704131184380et_nat (@ F X3)) Y2)))))))))
% 5.65/5.93 (assert (forall ((Q4 tptp.product_prod_nat_nat) (F (-> tptp.nat tptp.nat)) (P3 tptp.product_prod_nat_nat)) (=> (= Q4 (@ (@ tptp.produc986720760941809198at_nat F) P3)) (not (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (= P3 (@ (@ tptp.product_Pair_nat_nat X3) Y2)) (not (= Q4 (@ (@ tptp.product_Pair_nat_nat (@ F X3)) Y2)))))))))
% 5.65/5.93 (assert (forall ((Q4 tptp.product_prod_int_int) (F (-> tptp.int tptp.int)) (P3 tptp.product_prod_int_int)) (=> (= Q4 (@ (@ tptp.produc2355237562570658114nt_int F) P3)) (not (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (= P3 (@ (@ tptp.product_Pair_int_int X3) Y2)) (not (= Q4 (@ (@ tptp.product_Pair_int_int (@ F X3)) Y2)))))))))
% 5.65/5.93 (assert (forall ((Q4 tptp.produc3925858234332021118et_nat) (F (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool)) (P3 tptp.produc3925858234332021118et_nat)) (=> (= Q4 (@ (@ tptp.produc3198230245617193214et_nat F) P3)) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3658429121746597890et_nat)) (=> (= P3 (@ (@ tptp.produc5001842942810119800et_nat X3) Y2)) (not (= Q4 (@ (@ tptp.produc5001842942810119800et_nat (@ F X3)) Y2)))))))))
% 5.65/5.93 (assert (forall ((Q4 tptp.produc2732055786443039994et_nat) (F (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool)) (P3 tptp.produc2732055786443039994et_nat)) (=> (= Q4 (@ (@ tptp.produc1442628905706551930et_nat F) P3)) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3925858234332021118et_nat)) (=> (= P3 (@ (@ tptp.produc2245416461498447860et_nat X3) Y2)) (not (= Q4 (@ (@ tptp.produc2245416461498447860et_nat (@ F X3)) Y2)))))))))
% 5.65/5.93 (assert (forall ((P (-> tptp.set_nat tptp.heap_e7401611519738050253t_unit Bool)) (P3 tptp.produc3658429121746597890et_nat)) (=> (@ (@ P (@ tptp.produc8586169260539613262et_nat P3)) (@ tptp.produc1824681642469235216et_nat P3)) (not (forall ((X3 tptp.heap_e7401611519738050253t_unit) (Y2 tptp.set_nat)) (not (@ (@ P Y2) X3)))))))
% 5.65/5.93 (assert (forall ((P (-> tptp.int tptp.int Bool)) (P3 tptp.product_prod_int_int)) (=> (@ (@ P (@ tptp.product_snd_int_int P3)) (@ tptp.product_fst_int_int P3)) (not (forall ((X3 tptp.int) (Y2 tptp.int)) (not (@ (@ P Y2) X3)))))))
% 5.65/5.93 (assert (forall ((P (-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit Bool)) (Q2 (-> tptp.heap_e7401611519738050253t_unit tptp.set_nat Bool))) (= tptp.produc8586169260539613262et_nat (@ (@ tptp.comp_P2930521774885306735et_nat tptp.produc8586169260539613262et_nat) (@ (@ tptp.bNF_sn4039337771197282234et_nat P) Q2)))))
% 5.65/5.93 (assert (forall ((P (-> tptp.int tptp.int Bool)) (Q2 (-> tptp.int tptp.int Bool))) (= tptp.product_snd_int_int (@ (@ tptp.comp_P5356232565778667509nt_int tptp.product_snd_int_int) (@ (@ tptp.bNF_sn1062102010912252026nt_int P) Q2)))))
% 5.65/5.93 (assert (forall ((P (-> tptp.int tptp.int Bool)) (Q2 (-> tptp.int tptp.int Bool))) (= tptp.product_fst_int_int (@ (@ tptp.comp_P5356232565778667509nt_int tptp.product_fst_int_int) (@ (@ tptp.bNF_fs8167890477030535480nt_int P) Q2)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite6017078050557962740nteger B4) (=> (= (@ (@ tptp.inf_in1364745209274528805nteger A) B4) tptp.bot_bo3990330152332043303nteger) (= (@ tptp.finite4902975817058060853nteger (@ (@ tptp.sup_su848401254843788991nteger A) B4)) (@ (@ tptp.plus_plus_nat (@ tptp.finite4902975817058060853nteger A)) (@ tptp.finite4902975817058060853nteger B4))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ tptp.finite4290736615968046902t_unit B4) (=> (= (@ (@ tptp.inf_in4660618365625256667t_unit A) B4) tptp.bot_bo3957492148770167129t_unit) (= (@ tptp.finite410649719033368117t_unit (@ (@ tptp.sup_su793286257634532545t_unit A) B4)) (@ (@ tptp.plus_plus_nat (@ tptp.finite410649719033368117t_unit A)) (@ tptp.finite410649719033368117t_unit B4))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (=> (@ tptp.finite_finite_o A) (=> (@ tptp.finite_finite_o B4) (=> (= (@ (@ tptp.inf_inf_set_o A) B4) tptp.bot_bot_set_o) (= (@ tptp.finite_card_o (@ (@ tptp.sup_sup_set_o A) B4)) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_o A)) (@ tptp.finite_card_o B4))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (=> (@ tptp.finite_finite_nat B4) (=> (= (@ (@ tptp.inf_inf_set_nat A) B4) tptp.bot_bot_set_nat) (= (@ tptp.finite_card_nat (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_nat A)) (@ tptp.finite_card_nat B4))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (=> (@ tptp.finite_finite_int A) (=> (@ tptp.finite_finite_int B4) (=> (= (@ (@ tptp.inf_inf_set_int A) B4) tptp.bot_bot_set_int) (= (@ tptp.finite_card_int (@ (@ tptp.sup_sup_set_int A) B4)) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_int A)) (@ tptp.finite_card_int B4))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (@ tptp.finite3252695134891459830_nat_o B4) (=> (= (@ (@ tptp.inf_in1906310914598751387_nat_o A) B4) tptp.bot_bo7824918357723582233_nat_o) (= (@ tptp.finite1363419556375932405_nat_o (@ (@ tptp.sup_su5209123915105501825_nat_o A) B4)) (@ (@ tptp.plus_plus_nat (@ tptp.finite1363419556375932405_nat_o A)) (@ tptp.finite1363419556375932405_nat_o B4))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ (@ tptp.member_Code_integer X) A) (= (@ tptp.suc (@ tptp.finite4902975817058060853nteger (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer X) tptp.bot_bo3990330152332043303nteger)))) (@ tptp.finite4902975817058060853nteger A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ (@ tptp.member_Product_unit X) A) (= (@ tptp.suc (@ tptp.finite410649719033368117t_unit (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)))) (@ tptp.finite410649719033368117t_unit A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (@ (@ tptp.member_o X) A) (= (@ tptp.suc (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)))) (@ tptp.finite_card_o A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (@ (@ tptp.member_int X) A) (= (@ tptp.suc (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))) (@ tptp.finite_card_int A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (@ (@ tptp.member6576561426505652726_nat_o X) A) (= (@ tptp.suc (@ tptp.finite1363419556375932405_nat_o (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)))) (@ tptp.finite1363419556375932405_nat_o A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (@ (@ tptp.member_nat X) A) (= (@ tptp.suc (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))) (@ tptp.finite_card_nat A))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A2))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.65/5.93 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger B) A2) (@ (@ tptp.plus_p5714425477246183910nteger C) A2)) (= B C))))
% 5.65/5.93 (assert (forall ((B tptp.rat) (A2 tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A2) (@ (@ tptp.plus_plus_rat C) A2)) (= B C))))
% 5.65/5.93 (assert (forall ((B tptp.nat) (A2 tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A2) (@ (@ tptp.plus_plus_nat C) A2)) (= B C))))
% 5.65/5.93 (assert (forall ((B tptp.int) (A2 tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A2) (@ (@ tptp.plus_plus_int C) A2)) (= B C))))
% 5.65/5.93 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger C))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_le3102999989581377725nteger A2) B)))))
% 5.65/5.93 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A2) B)))))
% 5.65/5.93 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A2) B)))))
% 5.65/5.93 (assert (forall ((C tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A2) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.ord_le3102999989581377725nteger A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_eq_rat A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_eq_int A2) B))))
% 5.65/5.93 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A2) B)))))
% 5.65/5.93 (assert (forall ((C tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A2) B)))))
% 5.65/5.93 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger C))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_le6747313008572928689nteger A2) B)))))
% 5.65/5.93 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A2) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_int A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.ord_le6747313008572928689nteger A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_rat A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B)) B) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) B)) B) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) B)) B) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B)) B) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A2) B)) B) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A2) B)) B) A2)))
% 5.65/5.93 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger C))) (= (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.minus_8373710615458151222nteger A2) B)))))
% 5.65/5.93 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.minus_minus_rat A2) B)))))
% 5.65/5.93 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.minus_minus_nat A2) B)))))
% 5.65/5.93 (assert (forall ((C tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.minus_minus_int A2) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B)) A2) B)))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) B)) A2) B)))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A2) B)) A2) B)))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) B)) A2) B)))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.minus_minus_rat A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.minus_minus_nat A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.minus_minus_int A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B)) B) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) B)) B) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A2) B)) B) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) B)) B) A2)))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) A)) (= (@ tptp.finite1363419556375932405_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) A)) (@ tptp.suc (@ tptp.finite1363419556375932405_nat_o A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (@ (@ tptp.member_int X) A)) (= (@ tptp.finite_card_int (@ (@ tptp.insert_int X) A)) (@ tptp.suc (@ tptp.finite_card_int A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (@ (@ tptp.member_o X) A)) (= (@ tptp.finite_card_o (@ (@ tptp.insert_o X) A)) (@ tptp.suc (@ tptp.finite_card_o A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (@ (@ tptp.member_Product_unit X) A)) (= (@ tptp.finite410649719033368117t_unit (@ (@ tptp.insert_Product_unit X) A)) (@ tptp.suc (@ tptp.finite410649719033368117t_unit A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (@ (@ tptp.member_nat X) A)) (= (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X) A)) (@ tptp.suc (@ tptp.finite_card_nat A)))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (@ (@ tptp.member_Code_integer X) A)) (= (@ tptp.finite4902975817058060853nteger (@ (@ tptp.insert_Code_integer X) A)) (@ tptp.suc (@ tptp.finite4902975817058060853nteger A)))))))
% 5.65/5.93 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M4) (= (@ tptp.suc (@ _let_1 M4)) (@ _let_1 (@ (@ tptp.minus_minus_nat M4) tptp.one_one_nat))))))))
% 5.65/5.93 (assert (forall ((I2 tptp.code_integer) (J tptp.code_integer) (K3 tptp.code_integer) (L tptp.code_integer)) (=> (and (= I2 J) (= K3 L)) (= (@ (@ tptp.plus_p5714425477246183910nteger I2) K3) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (= I2 J) (= K3 L)) (= (@ (@ tptp.plus_plus_rat I2) K3) (@ (@ tptp.plus_plus_rat J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (= I2 J) (= K3 L)) (= (@ (@ tptp.plus_plus_nat I2) K3) (@ (@ tptp.plus_plus_nat J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (= I2 J) (= K3 L)) (= (@ (@ tptp.plus_plus_int I2) K3) (@ (@ tptp.plus_plus_int J) L)))))
% 5.65/5.93 (assert (forall ((A tptp.code_integer) (K3 tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger K3))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) B)))))))
% 5.65/5.93 (assert (forall ((A tptp.rat) (K3 tptp.rat) (A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K3))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.plus_plus_rat A) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B)))))))
% 5.65/5.93 (assert (forall ((A tptp.nat) (K3 tptp.nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K3))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.plus_plus_nat A) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B)))))))
% 5.65/5.93 (assert (forall ((A tptp.int) (K3 tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K3))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.plus_plus_int A) B) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B)))))))
% 5.65/5.93 (assert (forall ((B4 tptp.code_integer) (K3 tptp.code_integer) (B tptp.code_integer) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A2))) (let ((_let_2 (@ tptp.plus_p5714425477246183910nteger K3))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 5.65/5.93 (assert (forall ((B4 tptp.rat) (K3 tptp.rat) (B tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (let ((_let_2 (@ tptp.plus_plus_rat K3))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 5.65/5.93 (assert (forall ((B4 tptp.nat) (K3 tptp.nat) (B tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (let ((_let_2 (@ tptp.plus_plus_nat K3))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 5.65/5.93 (assert (forall ((B4 tptp.int) (K3 tptp.int) (B tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (let ((_let_2 (@ tptp.plus_plus_int K3))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A2))) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A2))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.65/5.93 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger B) A2) (@ (@ tptp.plus_p5714425477246183910nteger C) A2)) (= B C))))
% 5.65/5.93 (assert (forall ((B tptp.rat) (A2 tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A2) (@ (@ tptp.plus_plus_rat C) A2)) (= B C))))
% 5.65/5.93 (assert (forall ((B tptp.int) (A2 tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A2) (@ (@ tptp.plus_plus_int C) A2)) (= B C))))
% 5.65/5.93 (assert (= tptp.plus_p5714425477246183910nteger (lambda ((A6 tptp.code_integer) (B6 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger B6) A6))))
% 5.65/5.93 (assert (= tptp.plus_plus_rat (lambda ((A6 tptp.rat) (B6 tptp.rat)) (@ (@ tptp.plus_plus_rat B6) A6))))
% 5.65/5.93 (assert (= tptp.plus_plus_nat (lambda ((A6 tptp.nat) (B6 tptp.nat)) (@ (@ tptp.plus_plus_nat B6) A6))))
% 5.65/5.93 (assert (= tptp.plus_plus_int (lambda ((A6 tptp.int) (B6 tptp.int)) (@ (@ tptp.plus_plus_int B6) A6))))
% 5.65/5.93 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger B))) (let ((_let_2 (@ tptp.plus_p5714425477246183910nteger A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.65/5.93 (assert (forall ((B tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat B))) (let ((_let_2 (@ tptp.plus_plus_rat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.65/5.93 (assert (forall ((B tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B))) (let ((_let_2 (@ tptp.plus_plus_nat A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.65/5.93 (assert (forall ((B tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int B))) (let ((_let_2 (@ tptp.plus_plus_int A2))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A2))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A2))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 5.65/5.93 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger B) A2) (@ (@ tptp.plus_p5714425477246183910nteger C) A2)) (= B C))))
% 5.65/5.93 (assert (forall ((B tptp.rat) (A2 tptp.rat) (C tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat B) A2) (@ (@ tptp.plus_plus_rat C) A2)) (= B C))))
% 5.65/5.93 (assert (forall ((B tptp.nat) (A2 tptp.nat) (C tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B) A2) (@ (@ tptp.plus_plus_nat C) A2)) (= B C))))
% 5.65/5.93 (assert (forall ((B tptp.int) (A2 tptp.int) (C tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B) A2) (@ (@ tptp.plus_plus_int C) A2)) (= B C))))
% 5.65/5.93 (assert (forall ((I2 tptp.code_integer) (J tptp.code_integer) (K3 tptp.code_integer) (L tptp.code_integer)) (=> (and (@ (@ tptp.ord_le3102999989581377725nteger I2) J) (= K3 L)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger I2) K3)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J) (= K3 L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K3)) (@ (@ tptp.plus_plus_rat J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (= K3 L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K3)) (@ (@ tptp.plus_plus_nat J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (= K3 L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K3)) (@ (@ tptp.plus_plus_int J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.code_integer) (J tptp.code_integer) (K3 tptp.code_integer) (L tptp.code_integer)) (=> (and (= I2 J) (@ (@ tptp.ord_le3102999989581377725nteger K3) L)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger I2) K3)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_rat K3) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K3)) (@ (@ tptp.plus_plus_rat J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_nat K3) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K3)) (@ (@ tptp.plus_plus_nat J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_int K3) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K3)) (@ (@ tptp.plus_plus_int J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.code_integer) (J tptp.code_integer) (K3 tptp.code_integer) (L tptp.code_integer)) (=> (and (@ (@ tptp.ord_le3102999989581377725nteger I2) J) (@ (@ tptp.ord_le3102999989581377725nteger K3) L)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger I2) K3)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J) (@ (@ tptp.ord_less_eq_rat K3) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K3)) (@ (@ tptp.plus_plus_rat J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat K3) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K3)) (@ (@ tptp.plus_plus_nat J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (@ (@ tptp.ord_less_eq_int K3) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K3)) (@ (@ tptp.plus_plus_int J) L)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B) D2))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int A2) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (not (forall ((C2 tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A2) C2))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B) C)))))
% 5.65/5.93 (assert (= tptp.ord_less_eq_nat (lambda ((A6 tptp.nat) (B6 tptp.nat)) (exists ((C4 tptp.nat)) (= B6 (@ (@ tptp.plus_plus_nat A6) C4))))))
% 5.65/5.93 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_le3102999989581377725nteger A2) B)))))
% 5.65/5.93 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A2) B)))))
% 5.65/5.93 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A2) B)))))
% 5.65/5.93 (assert (forall ((C tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A2) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.ord_le3102999989581377725nteger A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_eq_rat A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_eq_int A2) B))))
% 5.65/5.93 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat K3) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K3)) (@ (@ tptp.plus_plus_nat J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (@ (@ tptp.ord_less_int K3) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K3)) (@ (@ tptp.plus_plus_int J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.code_integer) (J tptp.code_integer) (K3 tptp.code_integer) (L tptp.code_integer)) (=> (and (@ (@ tptp.ord_le6747313008572928689nteger I2) J) (@ (@ tptp.ord_le6747313008572928689nteger K3) L)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger I2) K3)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J) (@ (@ tptp.ord_less_rat K3) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K3)) (@ (@ tptp.plus_plus_rat J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_nat K3) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K3)) (@ (@ tptp.plus_plus_nat J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (= I2 J) (@ (@ tptp.ord_less_int K3) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K3)) (@ (@ tptp.plus_plus_int J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.code_integer) (J tptp.code_integer) (K3 tptp.code_integer) (L tptp.code_integer)) (=> (and (= I2 J) (@ (@ tptp.ord_le6747313008572928689nteger K3) L)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger I2) K3)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_rat K3) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K3)) (@ (@ tptp.plus_plus_rat J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (= K3 L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K3)) (@ (@ tptp.plus_plus_nat J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (= K3 L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K3)) (@ (@ tptp.plus_plus_int J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.code_integer) (J tptp.code_integer) (K3 tptp.code_integer) (L tptp.code_integer)) (=> (and (@ (@ tptp.ord_le6747313008572928689nteger I2) J) (= K3 L)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger I2) K3)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J) (= K3 L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K3)) (@ (@ tptp.plus_plus_rat J) L)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (@ (@ tptp.ord_less_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B) (=> (@ (@ tptp.ord_less_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B) D2))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B) (=> (@ (@ tptp.ord_less_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat A2) B) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int A2) B) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat A2) B) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B) C)))))
% 5.65/5.93 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A2) B)))))
% 5.65/5.93 (assert (forall ((C tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A2) B)))))
% 5.65/5.93 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_le6747313008572928689nteger A2) B)))))
% 5.65/5.93 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A2) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_int A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.ord_le6747313008572928689nteger A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_rat A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (E2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) E2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E2)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B)) E2)) C))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (E2 tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A2) B)) E2)) C))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (E2 tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) E2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) E2)) C)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A2) B)) E2)) C))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (E2 tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A2) B)) E2)) C))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A2) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A2) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A2) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A2))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B)) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A2) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A2) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A2) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A2))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B)) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A2) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A2) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B) C)))))
% 5.65/5.93 (assert (forall ((A tptp.code_integer) (K3 tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger K3))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.minus_8373710615458151222nteger A) B) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger A2) B)))))))
% 5.65/5.93 (assert (forall ((A tptp.rat) (K3 tptp.rat) (A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K3))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.minus_minus_rat A) B) (@ _let_1 (@ (@ tptp.minus_minus_rat A2) B)))))))
% 5.65/5.93 (assert (forall ((A tptp.int) (K3 tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K3))) (=> (= A (@ _let_1 A2)) (= (@ (@ tptp.minus_minus_int A) B) (@ _let_1 (@ (@ tptp.minus_minus_int A2) B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (= (@ (@ tptp.minus_8373710615458151222nteger A2) B) C) (= A2 (@ (@ tptp.plus_p5714425477246183910nteger C) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.minus_minus_rat A2) B) C) (= A2 (@ (@ tptp.plus_plus_rat C) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (= (= (@ (@ tptp.minus_minus_int A2) B) C) (= A2 (@ (@ tptp.plus_plus_int C) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (= A2 (@ (@ tptp.minus_8373710615458151222nteger C) B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A2) B) C))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= A2 (@ (@ tptp.minus_minus_rat C) B)) (= (@ (@ tptp.plus_plus_rat A2) B) C))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (C tptp.int) (B tptp.int)) (= (= A2 (@ (@ tptp.minus_minus_int C) B)) (= (@ (@ tptp.plus_plus_int A2) B) C))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A2))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A2) (@ (@ tptp.minus_8373710615458151222nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) C)) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.minus_minus_int A2) (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) C)) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A2) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) C)) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A2) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A2) C)) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A2))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 C)) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 C)) B)))))
% 5.65/5.93 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A2 tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger C) B) A2) (= C (@ (@ tptp.minus_8373710615458151222nteger A2) B)))))
% 5.65/5.93 (assert (forall ((C tptp.rat) (B tptp.rat) (A2 tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat C) B) A2) (= C (@ (@ tptp.minus_minus_rat A2) B)))))
% 5.65/5.93 (assert (forall ((C tptp.nat) (B tptp.nat) (A2 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat C) B) A2) (= C (@ (@ tptp.minus_minus_nat A2) B)))))
% 5.65/5.93 (assert (forall ((C tptp.int) (B tptp.int) (A2 tptp.int)) (=> (= (@ (@ tptp.plus_plus_int C) B) A2) (= C (@ (@ tptp.minus_minus_int A2) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A2))) (= (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) A) (=> (@ (@ tptp.ord_less_nat B) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) N)) B)) (@ (@ tptp.times_times_nat A) N))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (A5 tptp.nat) (B tptp.nat) (N tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) A5) (=> (@ (@ tptp.ord_less_nat B) N) (=> (@ (@ tptp.ord_less_nat B3) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) N)) B)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A5) N)) B3)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (A5 tptp.nat) (B tptp.nat) (B3 tptp.nat) (N tptp.nat)) (=> (= A2 A5) (=> (@ (@ tptp.ord_less_nat B) B3) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) N)) B)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A5) N)) B3))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (A5 tptp.nat) (B tptp.nat) (B3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) A5) (=> (@ (@ tptp.ord_less_eq_nat B) B3) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) N)) B)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A5) N)) B3))))))
% 5.65/5.93 (assert (forall ((K4 tptp.set_nat)) (=> (not (= K4 tptp.bot_bot_set_nat)) (@ (@ tptp.member_nat (@ tptp.complete_Inf_Inf_nat K4)) K4))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.ord_max_Code_integer X) Y)) Z) (@ (@ tptp.ord_max_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger X) Z)) (@ (@ tptp.plus_p5714425477246183910nteger Y) Z)))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.ord_max_rat X) Y)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.plus_plus_rat X) Z)) (@ (@ tptp.plus_plus_rat Y) Z)))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X) Y)) Z) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X) Z)) (@ (@ tptp.plus_plus_nat Y) Z)))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X) Y)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X) Z)) (@ (@ tptp.plus_plus_int Y) Z)))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger X))) (= (@ _let_1 (@ (@ tptp.ord_max_Code_integer Y) Z)) (@ (@ tptp.ord_max_Code_integer (@ _let_1 Y)) (@ _let_1 Z))))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat X))) (= (@ _let_1 (@ (@ tptp.ord_max_rat Y) Z)) (@ (@ tptp.ord_max_rat (@ _let_1 Y)) (@ _let_1 Z))))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y) Z)) (@ (@ tptp.ord_max_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y) Z)) (@ (@ tptp.ord_max_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 5.65/5.93 (assert (forall ((I2 tptp.code_integer) (J tptp.code_integer) (K3 tptp.code_integer) (L tptp.code_integer)) (=> (and (@ (@ tptp.ord_le3102999989581377725nteger I2) J) (@ (@ tptp.ord_le6747313008572928689nteger K3) L)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger I2) K3)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J) (@ (@ tptp.ord_less_rat K3) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K3)) (@ (@ tptp.plus_plus_rat J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_nat K3) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K3)) (@ (@ tptp.plus_plus_nat J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (@ (@ tptp.ord_less_int K3) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K3)) (@ (@ tptp.plus_plus_int J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.code_integer) (J tptp.code_integer) (K3 tptp.code_integer) (L tptp.code_integer)) (=> (and (@ (@ tptp.ord_le6747313008572928689nteger I2) J) (@ (@ tptp.ord_le3102999989581377725nteger K3) L)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger I2) K3)) (@ (@ tptp.plus_p5714425477246183910nteger J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K3 tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J) (@ (@ tptp.ord_less_eq_rat K3) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K3)) (@ (@ tptp.plus_plus_rat J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_nat K3) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K3)) (@ (@ tptp.plus_plus_nat J) L)))))
% 5.65/5.93 (assert (forall ((I2 tptp.int) (J tptp.int) (K3 tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (@ (@ tptp.ord_less_eq_int K3) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K3)) (@ (@ tptp.plus_plus_int J) L)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B) D2))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (@ (@ tptp.ord_less_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (@ (@ tptp.ord_less_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B) (=> (@ (@ tptp.ord_less_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) (@ (@ tptp.plus_p5714425477246183910nteger B) D2))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat A2) B))) (=> _let_1 (=> _let_1 (= (= (@ (@ tptp.minus_minus_nat B) A2) C) (= B (@ (@ tptp.plus_plus_nat C) A2))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (= (@ (@ tptp.plus_plus_nat A2) (@ (@ tptp.minus_minus_nat B) A2)) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (= (@ (@ tptp.minus_minus_nat C) (@ (@ tptp.minus_minus_nat B) A2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat C) A2)) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A2)) C)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A2)) C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A2) (@ _let_1 (@ (@ tptp.minus_minus_nat B) A2)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) A2)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A2))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (= (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat B) A2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat C) A2)) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A2)) A2) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ (@ tptp.minus_8373710615458151222nteger C) B)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B)) C))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.minus_minus_rat C) B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) B)) C))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.minus_minus_int C) B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) B)) C))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B)) C) (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger C) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A2) B)) C) (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.plus_plus_rat C) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A2) B)) C) (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.plus_plus_int C) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_natural)) (@ (@ tptp.ord_le5570908160329646204atural A2) (@ (@ tptp.plus_p4538020629002901425atural A2) tptp.one_one_Code_natural))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_nat A2) (@ (@ tptp.plus_plus_nat A2) tptp.one_one_nat))))
% 5.65/5.93 (assert (forall ((A2 tptp.int)) (@ (@ tptp.ord_less_int A2) (@ (@ tptp.plus_plus_int A2) tptp.one_one_int))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger A2) tptp.one_one_Code_integer))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat)) (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.plus_plus_rat A2) tptp.one_one_rat))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.ord_le5570908160329646204atural A2) B) (@ (@ tptp.ord_le5570908160329646204atural (@ (@ tptp.plus_p4538020629002901425atural A2) tptp.one_one_Code_natural)) (@ (@ tptp.plus_p4538020629002901425atural B) tptp.one_one_Code_natural)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat B) tptp.one_one_nat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) tptp.one_one_int)) (@ (@ tptp.plus_plus_int B) tptp.one_one_int)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) tptp.one_one_Code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger B) tptp.one_one_Code_integer)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat B) tptp.one_one_rat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A2) B)) C) (@ (@ tptp.ord_less_int A2) (@ (@ tptp.plus_plus_int C) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B)) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger C) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A2) B)) C) (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.plus_plus_rat C) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A2) (@ (@ tptp.minus_minus_int C) B)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B)) C))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ (@ tptp.minus_8373710615458151222nteger C) B)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B)) C))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.minus_minus_rat C) B)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B)) C))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger X) Y)) (@ (@ tptp.minus_8373710615458151222nteger X) Y)))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ (@ tptp.minus_minus_rat X) Y)))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) Y)) (@ (@ tptp.minus_minus_int X) Y)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (E2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) E2)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E2)) D2)) (= C (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B) A2)) E2)) D2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D2)) (= C (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A2)) E2)) D2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D2)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A2)) E2)) D2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (E2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) E2)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E2)) D2)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B)) E2)) C) D2))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D2)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A2) B)) E2)) C) D2))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D2)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A2) B)) E2)) C) D2))))
% 5.65/5.93 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) M4) (= (@ tptp.suc (@ _let_1 M4)) (@ _let_1 (@ (@ tptp.minus_minus_nat M4) tptp.one_one_nat))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc A2))) (= (and (@ (@ tptp.ord_less_nat A2) B) (@ (@ tptp.ord_less_eq_nat B) _let_1)) (= B _let_1)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (= (and (@ (@ tptp.ord_less_eq_nat A2) B) (@ (@ tptp.ord_less_nat B) (@ tptp.suc A2))) (= B A2))))
% 5.65/5.93 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.wf_nat R2) (not (forall ((K tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat (@ F (@ tptp.suc K))) (@ F K))) R2))))))
% 5.65/5.93 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (F (-> tptp.nat tptp.int))) (=> (@ tptp.wf_int R2) (not (forall ((K tptp.nat)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int (@ F (@ tptp.suc K))) (@ F K))) R2))))))
% 5.65/5.93 (assert (= tptp.wf_nat (lambda ((R4 tptp.set_Pr1261947904930325089at_nat)) (not (exists ((F4 (-> tptp.nat tptp.nat))) (forall ((I4 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat (@ F4 (@ tptp.suc I4))) (@ F4 I4))) R4)))))))
% 5.65/5.93 (assert (= tptp.wf_int (lambda ((R4 tptp.set_Pr958786334691620121nt_int)) (not (exists ((F4 (-> tptp.nat tptp.int))) (forall ((I4 tptp.nat)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int (@ F4 (@ tptp.suc I4))) (@ F4 I4))) R4)))))))
% 5.65/5.93 (assert (= tptp.comple4605987646318907561at_o_o (lambda ((S6 tptp.set_Pr6409761941060870310at_o_o) (X2 (-> tptp.produc3658429121746597890et_nat Bool))) (@ (@ tptp.member6576561426505652726_nat_o X2) (@ tptp.comple79274577958421812_nat_o (@ (@ tptp.image_8639947063239330806_nat_o tptp.collec939566748876313656_nat_o) S6))))))
% 5.65/5.93 (assert (= tptp.comple4393433247856107946_int_o (lambda ((S6 tptp.set_int_o) (X2 tptp.int)) (@ (@ tptp.member_int X2) (@ tptp.comple3628384868704368283et_int (@ (@ tptp.image_int_o_set_int tptp.collect_int) S6))))))
% 5.65/5.93 (assert (= tptp.complete_Inf_Inf_o_o (lambda ((S6 tptp.set_o_o) (X2 Bool)) (@ (@ tptp.member_o X2) (@ tptp.comple3063163877087187839_set_o (@ (@ tptp.image_o_o_set_o tptp.collect_o) S6))))))
% 5.65/5.93 (assert (= tptp.comple2092403528524206185unit_o (lambda ((S6 tptp.set_Product_unit_o) (X2 tptp.product_unit)) (@ (@ tptp.member_Product_unit X2) (@ tptp.comple7216939928495492468t_unit (@ (@ tptp.image_5138372075374782070t_unit tptp.collect_Product_unit) S6))))))
% 5.65/5.93 (assert (= tptp.comple6214475593288795910_nat_o (lambda ((S6 tptp.set_nat_o) (X2 tptp.nat)) (@ (@ tptp.member_nat X2) (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_o_set_nat tptp.collect_nat) S6))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (E2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) E2)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E2)) D2)) (@ (@ tptp.ord_le3102999989581377725nteger C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B) A2)) E2)) D2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D2)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A2)) E2)) D2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D2)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A2)) E2)) D2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (E2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) E2)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E2)) D2)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B)) E2)) C)) D2))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A2) B)) E2)) C)) D2))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A2) B)) E2)) C)) D2))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D2)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A2)) E2)) D2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (E2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) E2)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E2)) D2)) (@ (@ tptp.ord_le6747313008572928689nteger C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B) A2)) E2)) D2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D2)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A2)) E2)) D2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A2) B)) E2)) C)) D2))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (E2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A2) E2)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E2)) D2)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B)) E2)) C)) D2))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A2) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A2) B)) E2)) C)) D2))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger X) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger X) tptp.one_one_Code_integer)))))
% 5.65/5.93 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) X)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)))))
% 5.65/5.93 (assert (forall ((X tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X) tptp.one_one_int)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (K3 tptp.nat)) (= (= (@ tptp.finite1363419556375932405_nat_o A) (@ tptp.suc K3)) (exists ((B6 (-> tptp.produc3658429121746597890et_nat Bool)) (B7 tptp.set_Pr4532377907799695533_nat_o)) (and (= A (@ (@ tptp.insert5175938949040314269_nat_o B6) B7)) (not (@ (@ tptp.member6576561426505652726_nat_o B6) B7)) (= (@ tptp.finite1363419556375932405_nat_o B7) K3) (@ tptp.finite3252695134891459830_nat_o B7))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (K3 tptp.nat)) (= (= (@ tptp.finite_card_int A) (@ tptp.suc K3)) (exists ((B6 tptp.int) (B7 tptp.set_int)) (and (= A (@ (@ tptp.insert_int B6) B7)) (not (@ (@ tptp.member_int B6) B7)) (= (@ tptp.finite_card_int B7) K3) (@ tptp.finite_finite_int B7))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (K3 tptp.nat)) (= (= (@ tptp.finite_card_o A) (@ tptp.suc K3)) (exists ((B6 Bool) (B7 tptp.set_o)) (and (= A (@ (@ tptp.insert_o B6) B7)) (not (@ (@ tptp.member_o B6) B7)) (= (@ tptp.finite_card_o B7) K3) (@ tptp.finite_finite_o B7))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (K3 tptp.nat)) (= (= (@ tptp.finite410649719033368117t_unit A) (@ tptp.suc K3)) (exists ((B6 tptp.product_unit) (B7 tptp.set_Product_unit)) (and (= A (@ (@ tptp.insert_Product_unit B6) B7)) (not (@ (@ tptp.member_Product_unit B6) B7)) (= (@ tptp.finite410649719033368117t_unit B7) K3) (@ tptp.finite4290736615968046902t_unit B7))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (K3 tptp.nat)) (= (= (@ tptp.finite_card_nat A) (@ tptp.suc K3)) (exists ((B6 tptp.nat) (B7 tptp.set_nat)) (and (= A (@ (@ tptp.insert_nat B6) B7)) (not (@ (@ tptp.member_nat B6) B7)) (= (@ tptp.finite_card_nat B7) K3) (@ tptp.finite_finite_nat B7))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (K3 tptp.nat)) (= (= (@ tptp.finite4902975817058060853nteger A) (@ tptp.suc K3)) (exists ((B6 tptp.code_integer) (B7 tptp.set_Code_integer)) (and (= A (@ (@ tptp.insert_Code_integer B6) B7)) (not (@ (@ tptp.member_Code_integer B6) B7)) (= (@ tptp.finite4902975817058060853nteger B7) K3) (@ tptp.finite6017078050557962740nteger B7))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.finite1363419556375932405_nat_o A))) (let ((_let_2 (@ tptp.finite1363419556375932405_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) A)))) (let ((_let_3 (@ (@ tptp.member6576561426505652726_nat_o X) A))) (=> (@ tptp.finite3252695134891459830_nat_o A) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.finite_card_int A))) (let ((_let_2 (@ tptp.finite_card_int (@ (@ tptp.insert_int X) A)))) (let ((_let_3 (@ (@ tptp.member_int X) A))) (=> (@ tptp.finite_finite_int A) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (X Bool)) (let ((_let_1 (@ tptp.finite_card_o A))) (let ((_let_2 (@ tptp.finite_card_o (@ (@ tptp.insert_o X) A)))) (let ((_let_3 (@ (@ tptp.member_o X) A))) (=> (@ tptp.finite_finite_o A) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (let ((_let_1 (@ tptp.finite410649719033368117t_unit A))) (let ((_let_2 (@ tptp.finite410649719033368117t_unit (@ (@ tptp.insert_Product_unit X) A)))) (let ((_let_3 (@ (@ tptp.member_Product_unit X) A))) (=> (@ tptp.finite4290736615968046902t_unit A) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.finite_card_nat A))) (let ((_let_2 (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X) A)))) (let ((_let_3 (@ (@ tptp.member_nat X) A))) (=> (@ tptp.finite_finite_nat A) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (let ((_let_1 (@ tptp.finite4902975817058060853nteger A))) (let ((_let_2 (@ tptp.finite4902975817058060853nteger (@ (@ tptp.insert_Code_integer X) A)))) (let ((_let_3 (@ (@ tptp.member_Code_integer X) A))) (=> (@ tptp.finite6017078050557962740nteger A) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 5.65/5.93 (assert (forall ((N2 tptp.nat) (A tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.finite1363419556375932405_nat_o A)) (exists ((A6 (-> tptp.produc3658429121746597890et_nat Bool)) (B7 tptp.set_Pr4532377907799695533_nat_o)) (and (= A (@ (@ tptp.insert5175938949040314269_nat_o A6) B7)) (not (@ (@ tptp.member6576561426505652726_nat_o A6) B7)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.finite1363419556375932405_nat_o B7)) (@ tptp.finite3252695134891459830_nat_o B7))))))
% 5.65/5.93 (assert (forall ((N2 tptp.nat) (A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.finite_card_int A)) (exists ((A6 tptp.int) (B7 tptp.set_int)) (and (= A (@ (@ tptp.insert_int A6) B7)) (not (@ (@ tptp.member_int A6) B7)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.finite_card_int B7)) (@ tptp.finite_finite_int B7))))))
% 5.65/5.93 (assert (forall ((N2 tptp.nat) (A tptp.set_o)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.finite_card_o A)) (exists ((A6 Bool) (B7 tptp.set_o)) (and (= A (@ (@ tptp.insert_o A6) B7)) (not (@ (@ tptp.member_o A6) B7)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.finite_card_o B7)) (@ tptp.finite_finite_o B7))))))
% 5.65/5.93 (assert (forall ((N2 tptp.nat) (A tptp.set_Product_unit)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.finite410649719033368117t_unit A)) (exists ((A6 tptp.product_unit) (B7 tptp.set_Product_unit)) (and (= A (@ (@ tptp.insert_Product_unit A6) B7)) (not (@ (@ tptp.member_Product_unit A6) B7)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.finite410649719033368117t_unit B7)) (@ tptp.finite4290736615968046902t_unit B7))))))
% 5.65/5.93 (assert (forall ((N2 tptp.nat) (A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.finite_card_nat A)) (exists ((A6 tptp.nat) (B7 tptp.set_nat)) (and (= A (@ (@ tptp.insert_nat A6) B7)) (not (@ (@ tptp.member_nat A6) B7)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.finite_card_nat B7)) (@ tptp.finite_finite_nat B7))))))
% 5.65/5.93 (assert (forall ((N2 tptp.nat) (A tptp.set_Code_integer)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.finite4902975817058060853nteger A)) (exists ((A6 tptp.code_integer) (B7 tptp.set_Code_integer)) (and (= A (@ (@ tptp.insert_Code_integer A6) B7)) (not (@ (@ tptp.member_Code_integer A6) B7)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.finite4902975817058060853nteger B7)) (@ tptp.finite6017078050557962740nteger B7))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ (@ tptp.member_Code_integer X) A) (= (@ tptp.finite4902975817058060853nteger A) (@ tptp.suc (@ tptp.finite4902975817058060853nteger (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer X) tptp.bot_bo3990330152332043303nteger)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ (@ tptp.member_Product_unit X) A) (= (@ tptp.finite410649719033368117t_unit A) (@ tptp.suc (@ tptp.finite410649719033368117t_unit (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (@ (@ tptp.member_o X) A) (= (@ tptp.finite_card_o A) (@ tptp.suc (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (@ (@ tptp.member_int X) A) (= (@ tptp.finite_card_int A) (@ tptp.suc (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (@ (@ tptp.member6576561426505652726_nat_o X) A) (= (@ tptp.finite1363419556375932405_nat_o A) (@ tptp.suc (@ tptp.finite1363419556375932405_nat_o (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ (@ tptp.insert5175938949040314269_nat_o X) tptp.bot_bo7824918357723582233_nat_o)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (@ (@ tptp.member_nat X) A) (= (@ tptp.finite_card_nat A) (@ tptp.suc (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (let ((_let_1 (@ tptp.insert_Code_integer X))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ tptp.finite4902975817058060853nteger (@ _let_1 A)) (@ tptp.suc (@ tptp.finite4902975817058060853nteger (@ (@ tptp.minus_2355218937544613996nteger A) (@ _let_1 tptp.bot_bo3990330152332043303nteger)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit X))) (=> (@ tptp.finite4290736615968046902t_unit A) (= (@ tptp.finite410649719033368117t_unit (@ _let_1 A)) (@ tptp.suc (@ tptp.finite410649719033368117t_unit (@ (@ tptp.minus_6452836326544984404t_unit A) (@ _let_1 tptp.bot_bo3957492148770167129t_unit)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (X Bool)) (let ((_let_1 (@ tptp.insert_o X))) (=> (@ tptp.finite_finite_o A) (= (@ tptp.finite_card_o (@ _let_1 A)) (@ tptp.suc (@ tptp.finite_card_o (@ (@ tptp.minus_minus_set_o A) (@ _let_1 tptp.bot_bot_set_o)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (=> (@ tptp.finite_finite_int A) (= (@ tptp.finite_card_int (@ _let_1 A)) (@ tptp.suc (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A) (@ _let_1 tptp.bot_bot_set_int)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.insert5175938949040314269_nat_o X))) (=> (@ tptp.finite3252695134891459830_nat_o A) (= (@ tptp.finite1363419556375932405_nat_o (@ _let_1 A)) (@ tptp.suc (@ tptp.finite1363419556375932405_nat_o (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ _let_1 tptp.bot_bo7824918357723582233_nat_o)))))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X))) (=> (@ tptp.finite_finite_nat A) (= (@ tptp.finite_card_nat (@ _let_1 A)) (@ tptp.suc (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A) (@ _let_1 tptp.bot_bot_set_nat)))))))))
% 5.65/5.93 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M4))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.plus_plus_nat M4) (@ _let_1 N2))))))
% 5.65/5.93 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M4) N2) tptp.one_one_nat) (and (= M4 tptp.one_one_nat) (= N2 tptp.one_one_nat)))))
% 5.65/5.93 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M4) N2)) (and (= M4 tptp.one_one_nat) (= N2 tptp.one_one_nat)))))
% 5.65/5.93 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M4)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M4)) N2)))))
% 5.65/5.93 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M4)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_nat M4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))))
% 5.65/5.93 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M4)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.minus_minus_nat M4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))))
% 5.65/5.93 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M4)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M4)) N2)))))
% 5.65/5.93 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M4)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_eq_nat M4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))))
% 5.65/5.93 (assert (forall ((M4 tptp.nat) (N2 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M4))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N2) Q4)) (@ (@ tptp.ord_max_nat (@ _let_1 N2)) (@ _let_1 Q4))))))
% 5.65/5.93 (assert (forall ((M4 tptp.nat) (N2 tptp.nat) (Q4 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M4) N2)) Q4) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M4) Q4)) (@ (@ tptp.times_times_nat N2) Q4)))))
% 5.65/5.93 (assert (forall ((K3 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K3)))) (= (= (@ _let_1 M4) (@ _let_1 N2)) (= M4 N2)))))
% 5.65/5.93 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J))))))
% 5.65/5.93 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K3)) (@ (@ tptp.times_times_nat J) K3)))))
% 5.65/5.93 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K3 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_eq_nat K3) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K3)) (@ (@ tptp.times_times_nat J) L))))))
% 5.65/5.93 (assert (forall ((M4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat M4) (@ (@ tptp.times_times_nat M4) M4))))
% 5.65/5.93 (assert (forall ((M4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M4))) (@ (@ tptp.ord_less_eq_nat M4) (@ _let_1 (@ _let_1 M4))))))
% 5.65/5.93 (assert (forall ((M4 tptp.nat) (N2 tptp.nat) (K3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M4) N2)) K3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M4) K3)) (@ (@ tptp.times_times_nat N2) K3)))))
% 5.65/5.93 (assert (forall ((K3 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M4) N2)) (@ (@ tptp.plus_plus_nat (@ _let_1 M4)) (@ _let_1 N2))))))
% 5.65/5.93 (assert (forall ((I2 tptp.nat) (U tptp.nat) (J tptp.nat) (K3 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) K3)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I2) J)) U)) K3))))
% 5.65/5.93 (assert (forall ((M4 tptp.nat) (N2 tptp.nat) (K3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M4) N2)) K3) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M4) K3)) (@ (@ tptp.times_times_nat N2) K3)))))
% 5.65/5.93 (assert (forall ((K3 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M4) N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 M4)) (@ _let_1 N2))))))
% 5.65/5.93 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N2) N2)))
% 5.65/5.93 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat N2) tptp.one_one_nat) N2)))
% 5.65/5.93 (assert (forall ((K3 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K3)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M4) N2)))))
% 5.65/5.93 (assert (forall ((K3 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K3)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M4) N2)))))
% 5.65/5.93 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M4)) N2) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat M4) N2)))))
% 5.65/5.93 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M4) N2)))))
% 5.65/5.93 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (= M4 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))))
% 5.65/5.93 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M4)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M4)) N2)))))
% 5.65/5.93 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((A6 tptp.code_integer) (__flatten_var_0 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A6) tptp.one_one_Code_integer)) __flatten_var_0))))
% 5.65/5.93 (assert (= tptp.ord_less_nat (lambda ((A6 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A6) tptp.one_one_nat)) __flatten_var_0))))
% 5.65/5.93 (assert (= tptp.ord_less_int (lambda ((A6 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A6) tptp.one_one_int)) __flatten_var_0))))
% 5.65/5.93 (assert (= tptp.bNF_fs3871268833404974121et_nat (lambda ((P2 (-> tptp.heap_e7401611519738050253t_unit tptp.set_nat Bool)) (Q (-> tptp.set_nat tptp.set_nat Bool)) (Ac tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.produc1824681642469235216et_nat Ac))) (@ (@ tptp.produc7507926704131184380et_nat _let_1) (@ (@ (@ (@ tptp.bNF_pi4042512755101277815et_nat P2) Q) _let_1) (@ tptp.produc8586169260539613262et_nat Ac)))))))
% 5.65/5.93 (assert (= tptp.bNF_fs8167890477030535480nt_int (lambda ((P2 (-> tptp.int tptp.int Bool)) (Q (-> tptp.int tptp.int Bool)) (Ac tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int Ac))) (@ (@ tptp.product_Pair_int_int _let_1) (@ (@ (@ (@ tptp.bNF_pi8853482479757052266nt_int P2) Q) _let_1) (@ tptp.product_snd_int_int Ac)))))))
% 5.65/5.93 (assert (= tptp.bNF_sn4039337771197282234et_nat (lambda ((P2 (-> tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit Bool)) (Q (-> tptp.heap_e7401611519738050253t_unit tptp.set_nat Bool)) (Ac tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.produc8586169260539613262et_nat Ac))) (@ (@ tptp.produc7507926704131184380et_nat (@ (@ (@ (@ tptp.bNF_pi3450177011487049898et_nat P2) Q) (@ tptp.produc1824681642469235216et_nat Ac)) _let_1)) _let_1)))))
% 5.65/5.93 (assert (= tptp.bNF_sn1062102010912252026nt_int (lambda ((P2 (-> tptp.int tptp.int Bool)) (Q (-> tptp.int tptp.int Bool)) (Ac tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Ac))) (@ (@ tptp.product_Pair_int_int (@ (@ (@ (@ tptp.bNF_pi8853482479757052266nt_int P2) Q) (@ tptp.product_fst_int_int Ac)) _let_1)) _let_1)))))
% 5.65/5.93 (assert (forall ((N2 tptp.nat) (Y tptp.set_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat Y)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X) Y))) N2)))))
% 5.65/5.93 (assert (forall ((N2 tptp.nat) (Y tptp.set_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int Y)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.insert_int X) Y))) N2)))))
% 5.65/5.93 (assert (forall ((N2 tptp.nat) (Y tptp.set_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o Y)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o (@ (@ tptp.insert_o X) Y))) N2)))))
% 5.65/5.93 (assert (forall ((N2 tptp.nat) (Y tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite410649719033368117t_unit Y)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite410649719033368117t_unit (@ (@ tptp.insert_Product_unit X) Y))) N2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger B))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger A2))) (= (and (not (= A2 B)) (not (= C D2))) (not (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 D2)) (@ _let_1 C)))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A2))) (= (and (not (= A2 B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_rat (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_rat (@ _let_2 D2)) (@ _let_1 C)))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A2))) (= (and (not (= A2 B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_nat (@ _let_2 D2)) (@ _let_1 C)))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A2))) (= (and (not (= A2 B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_int (@ _let_2 D2)) (@ _let_1 C)))))))))
% 5.65/5.93 (assert (forall ((W tptp.code_integer) (Y tptp.code_integer) (X tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger X))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger W))) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 5.65/5.93 (assert (forall ((W tptp.rat) (Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X))) (let ((_let_2 (@ tptp.times_times_rat W))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 5.65/5.93 (assert (forall ((W tptp.nat) (Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X))) (let ((_let_2 (@ tptp.times_times_nat W))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 5.65/5.93 (assert (forall ((W tptp.int) (Y tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (let ((_let_2 (@ tptp.times_times_int W))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_int (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 5.65/5.93 (assert (= tptp.neg_nu7757733837767384882nteger (lambda ((X2 tptp.code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger X2) X2)) tptp.one_one_Code_integer))))
% 5.65/5.93 (assert (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))
% 5.65/5.93 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X2 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (X (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.finite3252695134891459830_nat_o A) (=> (not (@ (@ tptp.member6576561426505652726_nat_o X) A)) (= (@ (@ tptp.minus_minus_nat (@ tptp.finite1363419556375932405_nat_o (@ (@ tptp.insert5175938949040314269_nat_o X) A))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.finite1363419556375932405_nat_o A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (@ (@ tptp.member_int X) A)) (= (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_int (@ (@ tptp.insert_int X) A))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.finite_card_int A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (@ (@ tptp.member_o X) A)) (= (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_o (@ (@ tptp.insert_o X) A))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.finite_card_o A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (@ (@ tptp.member_Product_unit X) A)) (= (@ (@ tptp.minus_minus_nat (@ tptp.finite410649719033368117t_unit (@ (@ tptp.insert_Product_unit X) A))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.finite410649719033368117t_unit A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (@ (@ tptp.member_nat X) A)) (= (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X) A))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.finite_card_nat A))))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (@ (@ tptp.member_Code_integer X) A)) (= (@ (@ tptp.minus_minus_nat (@ tptp.finite4902975817058060853nteger (@ (@ tptp.insert_Code_integer X) A))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.finite4902975817058060853nteger A))))))
% 5.65/5.93 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 5.65/5.93 (assert (forall ((N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= N2 tptp.zero_zero_nat))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat A2) tptp.zero_zero_rat) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A2) tptp.zero_zero_nat) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int A2) tptp.zero_zero_int) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A2) tptp.zero_z3403309356797280102nteger) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A2) A2)) (= A2 tptp.zero_zero_rat))))
% 5.65/5.93 (assert (forall ((A2 tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A2) A2)) (= A2 tptp.zero_zero_int))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) A2)) (= A2 tptp.zero_z3403309356797280102nteger))))
% 5.65/5.93 (assert (forall ((B tptp.rat) (A2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A2) A2) (= B tptp.zero_zero_rat))))
% 5.65/5.93 (assert (forall ((B tptp.nat) (A2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A2) A2) (= B tptp.zero_zero_nat))))
% 5.65/5.93 (assert (forall ((B tptp.int) (A2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A2) A2) (= B tptp.zero_zero_int))))
% 5.65/5.93 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger B) A2) A2) (= B tptp.zero_z3403309356797280102nteger))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A2) B) A2) (= B tptp.zero_zero_rat))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A2) B) A2) (= B tptp.zero_zero_nat))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A2) B) A2) (= B tptp.zero_zero_int))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A2) B) A2) (= B tptp.zero_z3403309356797280102nteger))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (= A2 (@ (@ tptp.plus_plus_rat B) A2)) (= B tptp.zero_zero_rat))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (= (= A2 (@ (@ tptp.plus_plus_nat B) A2)) (= B tptp.zero_zero_nat))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (= A2 (@ (@ tptp.plus_plus_int B) A2)) (= B tptp.zero_zero_int))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (= A2 (@ (@ tptp.plus_p5714425477246183910nteger B) A2)) (= B tptp.zero_z3403309356797280102nteger))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (= A2 (@ (@ tptp.plus_plus_rat A2) B)) (= B tptp.zero_zero_rat))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (= (= A2 (@ (@ tptp.plus_plus_nat A2) B)) (= B tptp.zero_zero_nat))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (= A2 (@ (@ tptp.plus_plus_int A2) B)) (= B tptp.zero_zero_int))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (= A2 (@ (@ tptp.plus_p5714425477246183910nteger A2) B)) (= B tptp.zero_z3403309356797280102nteger))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X) Y)) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A2) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A2) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A2) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) A2) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A2) C) (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (= C tptp.zero_z3403309356797280102nteger) (= A2 B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A2) C) (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= A2 B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A2) C) (@ (@ tptp.times_times_nat B) C)) (or (= C tptp.zero_zero_nat) (= A2 B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (C tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A2) C) (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= A2 B)))))
% 5.65/5.93 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (= (@ _let_1 A2) (@ _let_1 B)) (or (= C tptp.zero_z3403309356797280102nteger) (= A2 B))))))
% 5.65/5.93 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (= (@ _let_1 A2) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (= A2 B))))))
% 5.65/5.93 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (= (@ _let_1 A2) (@ _let_1 B)) (or (= C tptp.zero_zero_nat) (= A2 B))))))
% 5.65/5.93 (assert (forall ((C tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (= (@ _let_1 A2) (@ _let_1 B)) (or (= C tptp.zero_zero_int) (= A2 B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A2) B) tptp.zero_z3403309356797280102nteger) (or (= A2 tptp.zero_z3403309356797280102nteger) (= B tptp.zero_z3403309356797280102nteger)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A2) B) tptp.zero_zero_rat) (or (= A2 tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A2) B) tptp.zero_zero_nat) (or (= A2 tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A2) B) tptp.zero_zero_int) (or (= A2 tptp.zero_zero_int) (= B tptp.zero_zero_int)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A2) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 5.65/5.93 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat A2) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 5.65/5.93 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat A2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 5.65/5.93 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int A2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) A2) tptp.zero_z3403309356797280102nteger)))
% 5.65/5.93 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A2) tptp.zero_zero_rat)))
% 5.65/5.93 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A2) tptp.zero_zero_nat)))
% 5.65/5.93 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A2) tptp.zero_zero_int)))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A2) A2) tptp.zero_z3403309356797280102nteger)))
% 5.65/5.93 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) A2) tptp.zero_zero_rat)))
% 5.65/5.93 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) A2) tptp.zero_zero_int)))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A2) tptp.zero_z3403309356797280102nteger) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) tptp.zero_zero_rat) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) tptp.zero_zero_int) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A2) tptp.zero_zero_nat)))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A2) tptp.zero_z3403309356797280102nteger) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) tptp.zero_zero_rat) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) tptp.zero_zero_nat) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) tptp.zero_zero_int) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A2) A2) tptp.zero_z3403309356797280102nteger)))
% 5.65/5.93 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) A2) tptp.zero_zero_rat)))
% 5.65/5.93 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) A2) tptp.zero_zero_nat)))
% 5.65/5.93 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.minus_minus_int A2) A2) tptp.zero_zero_int)))
% 5.65/5.93 (assert (forall ((M4 tptp.nat) (K3 tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M4) K3) (@ (@ tptp.times_times_nat N2) K3)) (or (= M4 N2) (= K3 tptp.zero_zero_nat)))))
% 5.65/5.93 (assert (forall ((K3 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (= (= (@ _let_1 M4) (@ _let_1 N2)) (or (= M4 N2) (= K3 tptp.zero_zero_nat))))))
% 5.65/5.93 (assert (forall ((M4 tptp.nat)) (= (@ (@ tptp.times_times_nat M4) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 5.65/5.93 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M4) N2) tptp.zero_zero_nat) (or (= M4 tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat)))))
% 5.65/5.93 (assert (= (@ tptp.complete_Sup_Sup_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 5.65/5.93 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int))
% 5.65/5.93 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) A2)) (@ _let_1 A2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A2) A2)) (@ _let_1 A2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A2) A2)) (@ _let_1 A2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) A2)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) A2)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat))))
% 5.65/5.93 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) A2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger B) A2)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.plus_plus_rat B) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A2) (@ (@ tptp.plus_plus_nat B) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.plus_plus_int B) A2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger A2) B)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.plus_plus_rat A2) B)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A2) (@ (@ tptp.plus_plus_nat A2) B)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.plus_plus_int A2) B)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B)) B) (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) B)) B) (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) B)) B) (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) B)) B) (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int))))
% 5.65/5.93 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A2)) B) (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger))))
% 5.65/5.93 (assert (forall ((B tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat B) A2)) B) (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat))))
% 5.65/5.93 (assert (forall ((B tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat B) A2)) B) (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat))))
% 5.65/5.93 (assert (forall ((B tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int B) A2)) B) (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger A2) B)) (@ (@ tptp.ord_le3102999989581377725nteger B) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A2) B)) (@ (@ tptp.ord_less_eq_rat B) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A2) B)) (@ (@ tptp.ord_less_eq_int B) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger A2) B)) (@ (@ tptp.ord_le3102999989581377725nteger B) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A2) B)) (@ (@ tptp.ord_less_eq_rat B) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A2) B)) (@ (@ tptp.ord_less_eq_int B) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A2) A2)) (@ _let_1 A2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) A2)) (@ _let_1 A2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A2) A2)) (@ _let_1 A2)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) A2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) A2)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) A2)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat A2) (@ (@ tptp.plus_plus_nat B) A2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A2) (@ (@ tptp.plus_plus_int B) A2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger B) A2)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.plus_plus_rat B) A2)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat A2) (@ (@ tptp.plus_plus_nat A2) B)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A2) (@ (@ tptp.plus_plus_int A2) B)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger A2) B)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A2) (@ (@ tptp.plus_plus_rat A2) B)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) B)) B) (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B)) B) (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B)) B) (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B)) B) (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat))))
% 5.65/5.93 (assert (forall ((B tptp.nat) (A2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat B) A2)) B) (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat))))
% 5.65/5.93 (assert (forall ((B tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int B) A2)) B) (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int))))
% 5.65/5.93 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A2)) B) (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger))))
% 5.65/5.93 (assert (forall ((B tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat B) A2)) B) (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A2) B)) (@ (@ tptp.ord_less_int B) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger A2) B)) (@ (@ tptp.ord_le6747313008572928689nteger B) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A2) B)) (@ (@ tptp.ord_less_rat B) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A2) B)) (@ (@ tptp.ord_less_int B) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger A2) B)) (@ (@ tptp.ord_le6747313008572928689nteger B) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A2) B)) (@ (@ tptp.ord_less_rat B) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A2) (@ (@ tptp.plus_plus_nat A2) B)) tptp.zero_zero_nat)))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A2) C) C) (or (= C tptp.zero_z3403309356797280102nteger) (= A2 tptp.one_one_Code_integer)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.times_times_rat A2) C) C) (or (= C tptp.zero_zero_rat) (= A2 tptp.one_one_rat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (C tptp.int)) (= (= (@ (@ tptp.times_times_int A2) C) C) (or (= C tptp.zero_zero_int) (= A2 tptp.one_one_int)))))
% 5.65/5.93 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (= C (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (= C tptp.zero_z3403309356797280102nteger) (= B tptp.one_one_Code_integer)))))
% 5.65/5.93 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (= C (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))))
% 5.65/5.93 (assert (forall ((C tptp.int) (B tptp.int)) (= (= C (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))))
% 5.65/5.93 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger C) A2) C) (or (= C tptp.zero_z3403309356797280102nteger) (= A2 tptp.one_one_Code_integer)))))
% 5.65/5.93 (assert (forall ((C tptp.rat) (A2 tptp.rat)) (= (= (@ (@ tptp.times_times_rat C) A2) C) (or (= C tptp.zero_zero_rat) (= A2 tptp.one_one_rat)))))
% 5.65/5.93 (assert (forall ((C tptp.int) (A2 tptp.int)) (= (= (@ (@ tptp.times_times_int C) A2) C) (or (= C tptp.zero_zero_int) (= A2 tptp.one_one_int)))))
% 5.65/5.93 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (= C (@ (@ tptp.times_3573771949741848930nteger C) B)) (or (= C tptp.zero_z3403309356797280102nteger) (= B tptp.one_one_Code_integer)))))
% 5.65/5.93 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (= C (@ (@ tptp.times_times_rat C) B)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))))
% 5.65/5.93 (assert (forall ((C tptp.int) (B tptp.int)) (= (= C (@ (@ tptp.times_times_int C) B)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))))
% 5.65/5.93 (assert (forall ((S tptp.set_rat)) (= (@ (@ tptp.image_rat_rat (@ tptp.plus_plus_rat tptp.zero_zero_rat)) S) S)))
% 5.65/5.93 (assert (forall ((S tptp.set_nat)) (= (@ (@ tptp.image_nat_nat2 (@ tptp.plus_plus_nat tptp.zero_zero_nat)) S) S)))
% 5.65/5.93 (assert (forall ((S tptp.set_int)) (= (@ (@ tptp.image_int_int2 (@ tptp.plus_plus_int tptp.zero_zero_int)) S) S)))
% 5.65/5.93 (assert (forall ((S tptp.set_Code_integer)) (= (@ (@ tptp.image_4470545334726330049nteger (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger)) S) S)))
% 5.65/5.93 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 5.65/5.93 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 5.65/5.93 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 5.65/5.93 (assert (= (@ (@ tptp.ord_max_Code_natural tptp.one_one_Code_natural) tptp.zero_z2226904508553997617atural) tptp.one_one_Code_natural))
% 5.65/5.93 (assert (= (@ (@ tptp.ord_max_Code_integer tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 5.65/5.93 (assert (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat))
% 5.65/5.93 (assert (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int))
% 5.65/5.93 (assert (= (@ (@ tptp.ord_max_Code_natural tptp.zero_z2226904508553997617atural) tptp.one_one_Code_natural) tptp.one_one_Code_natural))
% 5.65/5.93 (assert (= (@ (@ tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 5.65/5.93 (assert (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat))
% 5.65/5.93 (assert (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int))
% 5.65/5.93 (assert (= (@ tptp.finite410649719033368117t_unit tptp.bot_bo3957492148770167129t_unit) tptp.zero_zero_nat))
% 5.65/5.93 (assert (= (@ tptp.finite_card_o tptp.bot_bot_set_o) tptp.zero_zero_nat))
% 5.65/5.93 (assert (= (@ tptp.finite_card_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 5.65/5.93 (assert (= (@ tptp.finite_card_int tptp.bot_bot_set_int) tptp.zero_zero_nat))
% 5.65/5.93 (assert (= (@ tptp.finite1363419556375932405_nat_o tptp.bot_bo7824918357723582233_nat_o) tptp.zero_zero_nat))
% 5.65/5.93 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.times_times_nat M4) N2)) (and (= M4 _let_1) (= N2 _let_1))))))
% 5.65/5.93 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M4) N2) _let_1) (and (= M4 _let_1) (= N2 _let_1))))))
% 5.65/5.93 (assert (forall ((K3 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M4)) (@ _let_1 N2)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.ord_less_nat M4) N2))))))
% 5.65/5.93 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M4) N2)) (and (@ _let_1 M4) (@ _let_1 N2))))))
% 5.65/5.93 (assert (forall ((M4 tptp.nat) (K3 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M4) K3)) (@ (@ tptp.times_times_nat N2) K3)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.ord_less_nat M4) N2)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (= (= (@ tptp.finite4902975817058060853nteger A) tptp.zero_zero_nat) (= A tptp.bot_bo3990330152332043303nteger)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (= (= (@ tptp.finite410649719033368117t_unit A) tptp.zero_zero_nat) (= A tptp.bot_bo3957492148770167129t_unit)))))
% 5.65/5.93 (assert (forall ((A tptp.set_o)) (=> (@ tptp.finite_finite_o A) (= (= (@ tptp.finite_card_o A) tptp.zero_zero_nat) (= A tptp.bot_bot_set_o)))))
% 5.65/5.93 (assert (forall ((A tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (= (= (@ tptp.finite_card_nat A) tptp.zero_zero_nat) (= A tptp.bot_bot_set_nat)))))
% 5.65/5.93 (assert (forall ((A tptp.set_int)) (=> (@ tptp.finite_finite_int A) (= (= (@ tptp.finite_card_int A) tptp.zero_zero_nat) (= A tptp.bot_bot_set_int)))))
% 5.65/5.93 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (@ tptp.finite3252695134891459830_nat_o A) (= (= (@ tptp.finite1363419556375932405_nat_o A) tptp.zero_zero_nat) (= A tptp.bot_bo7824918357723582233_nat_o)))))
% 5.65/5.93 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (= (@ _let_1 (@ (@ tptp.times_times_nat M4) N2)) (and (@ _let_1 M4) (@ _let_1 N2))))))
% 5.65/5.93 (assert (forall ((M4 tptp.nat) (K3 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M4) K3)) (@ (@ tptp.times_times_nat N2) K3)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.ord_less_eq_nat M4) N2)))))
% 5.65/5.93 (assert (forall ((K3 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M4)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.ord_less_eq_nat M4) N2))))))
% 5.65/5.93 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 5.65/5.93 (assert (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))))
% 5.65/5.93 (assert (forall ((X tptp.int)) (= (= tptp.zero_zero_int X) (= X tptp.zero_zero_int))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger X) (= X tptp.zero_z3403309356797280102nteger))))
% 5.65/5.93 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)))
% 5.65/5.93 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 5.65/5.93 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 5.65/5.93 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M4) N2) (not (= N2 tptp.zero_zero_nat)))))
% 5.65/5.93 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (not (= N2 tptp.zero_zero_nat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A2) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A2) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A2) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) A2) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat A2) tptp.zero_zero_rat) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A2) tptp.zero_zero_nat) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int A2) tptp.zero_zero_int) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A2) tptp.zero_z3403309356797280102nteger) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A2) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A2) A2)))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) A2) A2)))
% 5.65/5.93 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (= (@ (@ tptp.times_3573771949741848930nteger A2) C) (@ (@ tptp.times_3573771949741848930nteger B) C)) (= A2 B)))))
% 5.65/5.93 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.times_times_rat A2) C) (@ (@ tptp.times_times_rat B) C)) (= A2 B)))))
% 5.65/5.93 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ (@ tptp.times_times_nat A2) C) (@ (@ tptp.times_times_nat B) C)) (= A2 B)))))
% 5.65/5.93 (assert (forall ((C tptp.int) (A2 tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (= (@ (@ tptp.times_times_int A2) C) (@ (@ tptp.times_times_int B) C)) (= A2 B)))))
% 5.65/5.93 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (= (@ _let_1 A2) (@ _let_1 B)) (= A2 B))))))
% 5.65/5.93 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ _let_1 A2) (@ _let_1 B)) (= A2 B))))))
% 5.65/5.93 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ _let_1 A2) (@ _let_1 B)) (= A2 B))))))
% 5.65/5.93 (assert (forall ((C tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (= (@ _let_1 A2) (@ _let_1 B)) (= A2 B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (not (= A2 tptp.zero_z3403309356797280102nteger)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (not (= (@ (@ tptp.times_3573771949741848930nteger A2) B) tptp.zero_z3403309356797280102nteger))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (not (= A2 tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (not (= (@ (@ tptp.times_times_rat A2) B) tptp.zero_zero_rat))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (not (= A2 tptp.zero_zero_nat)) (=> (not (= B tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A2) B) tptp.zero_zero_nat))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (not (= A2 tptp.zero_zero_int)) (=> (not (= B tptp.zero_zero_int)) (not (= (@ (@ tptp.times_times_int A2) B) tptp.zero_zero_int))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.times_3573771949741848930nteger A2) B) tptp.zero_z3403309356797280102nteger) (or (= A2 tptp.zero_z3403309356797280102nteger) (= B tptp.zero_z3403309356797280102nteger)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A2) B) tptp.zero_zero_rat) (or (= A2 tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A2) B) tptp.zero_zero_nat) (or (= A2 tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.times_times_int A2) B) tptp.zero_zero_int) (or (= A2 tptp.zero_zero_int) (= B tptp.zero_zero_int)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (not (= (@ (@ tptp.times_3573771949741848930nteger A2) B) tptp.zero_z3403309356797280102nteger)) (and (not (= A2 tptp.zero_z3403309356797280102nteger)) (not (= B tptp.zero_z3403309356797280102nteger))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (not (= (@ (@ tptp.times_times_rat A2) B) tptp.zero_zero_rat)) (and (not (= A2 tptp.zero_zero_rat)) (not (= B tptp.zero_zero_rat))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (not (= (@ (@ tptp.times_times_nat A2) B) tptp.zero_zero_nat)) (and (not (= A2 tptp.zero_zero_nat)) (not (= B tptp.zero_zero_nat))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (not (= (@ (@ tptp.times_times_int A2) B) tptp.zero_zero_int)) (and (not (= A2 tptp.zero_zero_int)) (not (= B tptp.zero_zero_int))))))
% 5.65/5.93 (assert (not (= tptp.zero_z2226904508553997617atural tptp.one_one_Code_natural)))
% 5.65/5.93 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 5.65/5.93 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 5.65/5.93 (assert (not (= tptp.zero_z3403309356797280102nteger tptp.one_one_Code_integer)))
% 5.65/5.93 (assert (= (lambda ((Y4 tptp.code_integer) (Z4 tptp.code_integer)) (= Y4 Z4)) (lambda ((A6 tptp.code_integer) (B6 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A6) B6) tptp.zero_z3403309356797280102nteger))))
% 5.65/5.93 (assert (= (lambda ((Y4 tptp.rat) (Z4 tptp.rat)) (= Y4 Z4)) (lambda ((A6 tptp.rat) (B6 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A6) B6) tptp.zero_zero_rat))))
% 5.65/5.93 (assert (= (lambda ((Y4 tptp.int) (Z4 tptp.int)) (= Y4 Z4)) (lambda ((A6 tptp.int) (B6 tptp.int)) (= (@ (@ tptp.minus_minus_int A6) B6) tptp.zero_zero_int))))
% 5.65/5.93 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 5.65/5.93 (assert (forall ((K3 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (= (= (@ _let_1 M4) (@ _let_1 N2)) (or (= K3 tptp.zero_zero_nat) (= M4 N2))))))
% 5.65/5.93 (assert (forall ((R2 tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger R2))) (=> (not (= R2 tptp.zero_z3403309356797280102nteger)) (=> (and (= A2 B) (not (= C D2))) (not (= (@ (@ tptp.plus_p5714425477246183910nteger A2) (@ _let_1 C)) (@ (@ tptp.plus_p5714425477246183910nteger B) (@ _let_1 D2)))))))))
% 5.65/5.93 (assert (forall ((R2 tptp.rat) (A2 tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R2))) (=> (not (= R2 tptp.zero_zero_rat)) (=> (and (= A2 B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_rat A2) (@ _let_1 C)) (@ (@ tptp.plus_plus_rat B) (@ _let_1 D2)))))))))
% 5.65/5.93 (assert (forall ((R2 tptp.nat) (A2 tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R2))) (=> (not (= R2 tptp.zero_zero_nat)) (=> (and (= A2 B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_nat A2) (@ _let_1 C)) (@ (@ tptp.plus_plus_nat B) (@ _let_1 D2)))))))))
% 5.65/5.93 (assert (forall ((R2 tptp.int) (A2 tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int R2))) (=> (not (= R2 tptp.zero_zero_int)) (=> (and (= A2 B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_int A2) (@ _let_1 C)) (@ (@ tptp.plus_plus_int B) (@ _let_1 D2)))))))))
% 5.65/5.93 (assert (= tptp.complete_Sup_Sup_nat (lambda ((X7 tptp.set_nat)) (@ (@ (@ tptp.if_nat (= X7 tptp.bot_bot_set_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat X7)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat C) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int C) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) B)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A2) C)))))))
% 5.65/5.93 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) C)) B)))))
% 5.65/5.93 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) C)) B)))))
% 5.65/5.93 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) C)) B)))))
% 5.65/5.93 (assert (forall ((C tptp.int) (A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int A2) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) C)) B)))))
% 5.65/5.93 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) C)))))))
% 5.65/5.93 (assert (forall ((C tptp.rat) (B tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) C)))))))
% 5.65/5.93 (assert (forall ((C tptp.nat) (B tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) C)))))))
% 5.65/5.93 (assert (forall ((C tptp.int) (B tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.plus_plus_int A2) C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B)) tptp.zero_z3403309356797280102nteger)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A2) B)) tptp.zero_zero_rat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A2) B)) tptp.zero_zero_nat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A2) B)) tptp.zero_zero_int)))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_p5714425477246183910nteger X) Y) tptp.zero_z3403309356797280102nteger) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger))))))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))))
% 5.65/5.93 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) tptp.zero_z3403309356797280102nteger) (= (= (@ (@ tptp.plus_p5714425477246183910nteger X) Y) tptp.zero_z3403309356797280102nteger) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger)))))))
% 5.65/5.93 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))))
% 5.65/5.93 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))))
% 5.65/5.93 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A2) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A2) B)) (or (and (@ _let_1 A2) (@ _let_1 B)) (and (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A2) B)) (or (and (@ _let_1 A2) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A2) B)) (or (and (@ _let_1 A2) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger B) A2)) tptp.zero_z3403309356797280102nteger)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat B) A2)) tptp.zero_zero_rat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B) A2)) tptp.zero_zero_nat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int B) A2)) tptp.zero_zero_int)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) B)) tptp.zero_z3403309356797280102nteger)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B)) tptp.zero_zero_rat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) B)) tptp.zero_zero_nat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B)) tptp.zero_zero_int)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) B)) tptp.zero_z3403309356797280102nteger)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B)) tptp.zero_zero_rat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) B)) tptp.zero_zero_nat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B)) tptp.zero_zero_int)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A2) B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A2) B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat A2) B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int A2) B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (or (and (@ _let_1 A2) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger)) (and (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (@ _let_1 B))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) B)) tptp.zero_z3403309356797280102nteger)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B)) tptp.zero_zero_rat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat)) (and (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) B)) tptp.zero_zero_nat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B)) tptp.zero_zero_int)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) B)) tptp.zero_z3403309356797280102nteger) (or (and (@ _let_1 A2) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger)) (and (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (@ _let_1 B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B)) tptp.zero_zero_int) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (@ _let_1 B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B) C))))))
% 5.65/5.93 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 5.65/5.93 (assert (forall ((B tptp.rat) (A2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A2) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B) C))))))
% 5.65/5.93 (assert (forall ((B tptp.int) (A2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A2) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B) C))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A2) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.times_3573771949741848930nteger A2) B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A2) B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A2) B))))))
% 5.65/5.93 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.65/5.93 (assert (forall ((B tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A2) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.65/5.93 (assert (forall ((B tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A2) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (or (and (@ _let_1 A2) (@ _let_1 B)) (and (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger))) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A2) B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A2) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (@ _let_1 (@ (@ tptp.times_times_rat A2) B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A2) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int))) (@ _let_1 (@ (@ tptp.times_times_int A2) B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.times_3573771949741848930nteger A2) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A2) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A2) A2))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2)))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B) D2)))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B) D2)))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A2) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B) D2)))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2)))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B) D2)))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B) D2)))))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A2) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B) D2)))))))))
% 5.65/5.93 (assert (not (@ (@ tptp.ord_le1926595141338095240atural tptp.one_one_Code_natural) tptp.zero_z2226904508553997617atural)))
% 5.65/5.93 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 5.65/5.93 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 5.65/5.93 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 5.65/5.93 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 5.65/5.93 (assert (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) tptp.one_one_Code_natural))
% 5.65/5.93 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 5.65/5.93 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 5.65/5.93 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 5.65/5.93 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 5.65/5.93 (assert (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) tptp.one_one_Code_natural))
% 5.65/5.93 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 5.65/5.93 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 5.65/5.93 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 5.65/5.93 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 5.65/5.93 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((A6 tptp.code_integer) (B6 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A6) B6)) tptp.zero_z3403309356797280102nteger))))
% 5.65/5.93 (assert (= tptp.ord_less_eq_rat (lambda ((A6 tptp.rat) (B6 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A6) B6)) tptp.zero_zero_rat))))
% 5.65/5.93 (assert (= tptp.ord_less_eq_int (lambda ((A6 tptp.int) (B6 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A6) B6)) tptp.zero_zero_int))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A2) C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) C)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (not (forall ((C2 tptp.nat)) (=> (= B (@ (@ tptp.plus_plus_nat A2) C2)) (= C2 tptp.zero_zero_nat)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) B)) tptp.zero_zero_nat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B)) tptp.zero_zero_int)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B)) tptp.zero_z3403309356797280102nteger)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B)) tptp.zero_zero_rat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A2) B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.times_3573771949741848930nteger A2) B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A2) B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) A2)) tptp.zero_zero_int))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) A2)) tptp.zero_z3403309356797280102nteger))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) A2)) tptp.zero_zero_rat))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) B)) tptp.zero_zero_int) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (@ _let_1 B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) B)) tptp.zero_z3403309356797280102nteger) (or (and (@ _let_1 A2) (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger)) (and (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger) (@ _let_1 B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A2) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) B)) tptp.zero_zero_nat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) B)) tptp.zero_zero_int)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) B)) tptp.zero_z3403309356797280102nteger)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) B)) tptp.zero_zero_rat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) B)) tptp.zero_zero_nat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) B)) tptp.zero_zero_int)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) B)) tptp.zero_z3403309356797280102nteger)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) B)) tptp.zero_zero_rat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat A2) B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int A2) B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A2) B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A2) B)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat B) A2)) tptp.zero_zero_nat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int B) A2)) tptp.zero_zero_int)))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger B) A2)) tptp.zero_z3403309356797280102nteger)))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat B) A2)) tptp.zero_zero_rat)))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A2) B)) (or (and (@ _let_1 A2) (@ _let_1 B)) (and (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.zero_zero_int)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A2) B)) (or (and (@ _let_1 A2) (@ _let_1 B)) (and (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A2) B)) (or (and (@ _let_1 A2) (@ _let_1 B)) (and (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)))))))
% 5.65/5.93 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat A2) B)) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int A2) B)) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A2) B)) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 5.65/5.93 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat A2) B)) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 5.65/5.93 (assert (forall ((B tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat B) A2)) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 5.65/5.93 (assert (forall ((B tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int B) A2)) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 5.65/5.93 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) A2)) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 5.65/5.93 (assert (forall ((B tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat B) A2)) (=> (@ _let_1 A2) (@ _let_1 B))))))
% 5.65/5.93 (assert (forall ((C tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_less_int B) A2))))))
% 5.65/5.93 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_le6747313008572928689nteger B) A2))))))
% 5.65/5.93 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat B) A2))))))
% 5.65/5.93 (assert (forall ((C tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A2) B))))))
% 5.65/5.93 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_le6747313008572928689nteger A2) B))))))
% 5.65/5.93 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A2) B))))))
% 5.65/5.93 (assert (forall ((B tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int B) A2) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.65/5.94 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.65/5.94 (assert (forall ((B tptp.rat) (A2 tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat B) A2) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A2) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A2) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.65/5.94 (assert (forall ((C tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A2)))))))
% 5.65/5.94 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) B)) (and (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) A2)))))))
% 5.65/5.94 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A2)))))))
% 5.65/5.94 (assert (forall ((B tptp.int) (A2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B) A2) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B) C))))))
% 5.65/5.94 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 5.65/5.94 (assert (forall ((B tptp.rat) (A2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A2) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B) C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B) C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B) C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B) C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B) C)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (and (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) B)) (and (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) A2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B) C)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A2) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A2) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B)))))))
% 5.65/5.94 (assert (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) tptp.one_one_Code_natural))
% 5.65/5.94 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 5.65/5.94 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 5.65/5.94 (assert (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 5.65/5.94 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 5.65/5.94 (assert (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) tptp.one_one_Code_natural))
% 5.65/5.94 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 5.65/5.94 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 5.65/5.94 (assert (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 5.65/5.94 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 5.65/5.94 (assert (not (@ (@ tptp.ord_le5570908160329646204atural tptp.one_one_Code_natural) tptp.zero_z2226904508553997617atural)))
% 5.65/5.94 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 5.65/5.94 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 5.65/5.94 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 5.65/5.94 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 5.65/5.94 (assert (= tptp.ord_less_int (lambda ((A6 tptp.int) (B6 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A6) B6)) tptp.zero_zero_int))))
% 5.65/5.94 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((A6 tptp.code_integer) (B6 tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A6) B6)) tptp.zero_z3403309356797280102nteger))))
% 5.65/5.94 (assert (= tptp.ord_less_rat (lambda ((A6 tptp.rat) (B6 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A6) B6)) tptp.zero_zero_rat))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (A tptp.set_Code_integer)) (=> (not (= A2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.inj_on1158064722259180589nteger (@ tptp.times_3573771949741848930nteger A2)) A))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (A tptp.set_rat)) (=> (not (= A2 tptp.zero_zero_rat)) (@ (@ tptp.inj_on_rat_rat (@ tptp.times_times_rat A2)) A))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (A tptp.set_nat)) (=> (not (= A2 tptp.zero_zero_nat)) (@ (@ tptp.inj_on_nat_nat (@ tptp.times_times_nat A2)) A))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (A tptp.set_int)) (=> (not (= A2 tptp.zero_zero_int)) (@ (@ tptp.inj_on_int_int (@ tptp.times_times_int A2)) A))))
% 5.65/5.94 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (forall ((Nn tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Nn) N3) (@ P Nn))) (@ P (@ tptp.suc N3)))) (@ P N2)))))
% 5.65/5.94 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (forall ((Nn tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Nn) N3) (@ P Nn))) (@ P (@ tptp.suc N3)))) (@ P N2)))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (M4 tptp.nat)) (=> (= (@ tptp.suc N2) M4) (= N2 (@ (@ tptp.minus_minus_nat M4) (@ tptp.suc tptp.zero_zero_nat))))))
% 5.65/5.94 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I2) K3)) (@ (@ tptp.times_times_nat J) K3))))))
% 5.65/5.94 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.ord_less_nat (@ _let_1 I2)) (@ _let_1 J)))))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (= (@ _let_1 M4) (@ _let_1 N2)) (= M4 N2))))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.ord_less_nat (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M4) N2))))))
% 5.65/5.94 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) X) (not (= X tptp.zero_zero_nat)))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (= M4 (@ (@ tptp.times_times_nat M4) N2)) (or (= N2 tptp.one_one_nat) (= M4 tptp.zero_zero_nat)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) C)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) C)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) C)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A2) C)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) C) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ (@ tptp.plus_p5714425477246183910nteger A2) C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.plus_plus_rat A2) C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_nat B) (@ (@ tptp.plus_plus_nat A2) C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ (@ tptp.ord_less_int B) (@ (@ tptp.plus_plus_int A2) C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) B)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B)) tptp.zero_z3403309356797280102nteger)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B)) tptp.zero_zero_rat)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) B)) tptp.zero_zero_nat)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B)) tptp.zero_zero_int)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A2) B)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A2) B)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A2) B)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A2) B)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B)) tptp.zero_z3403309356797280102nteger)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A2) B)) tptp.zero_zero_rat)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A2) B)) tptp.zero_zero_nat)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A2) B)) tptp.zero_zero_int)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B) D2))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B) D2))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B) D2))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B) D2))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B) D2))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B) D2))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A2) B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B) C)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B) C)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A2) B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B) C)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) B)))))
% 5.65/5.94 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A2) B))))))
% 5.65/5.94 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) B))))))
% 5.65/5.94 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A2) B))))))
% 5.65/5.94 (assert (forall ((C tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) B))))))
% 5.65/5.94 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_le3102999989581377725nteger A2) B))))))
% 5.65/5.94 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A2) B))))))
% 5.65/5.94 (assert (forall ((C tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A2) B))))))
% 5.65/5.94 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_le3102999989581377725nteger B) A2))))))
% 5.65/5.94 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat B) A2))))))
% 5.65/5.94 (assert (forall ((C tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int B) A2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) A2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2)))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat A2) B) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B) D2)))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B) D2)))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int A2) B) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ _let_1 A2) (=> (@ _let_1 C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B) D2)))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B) C)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B) C)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A2) B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B) C)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B)))))
% 5.65/5.94 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) A2)))))))
% 5.65/5.94 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A2)))))))
% 5.65/5.94 (assert (forall ((C tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A2)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A2) B) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B) D2))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B) D2))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B) D2))))))))
% 5.65/5.94 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A2)) (@ _let_1 B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) B))))))
% 5.65/5.94 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) B))))))
% 5.65/5.94 (assert (forall ((C tptp.nat) (A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A2) B))))))
% 5.65/5.94 (assert (forall ((C tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) B))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A2) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) A2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A2))))))
% 5.65/5.94 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A2)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A2) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) A2)))))))
% 5.65/5.94 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A2)))))))
% 5.65/5.94 (assert (forall ((C tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A2)))))))
% 5.65/5.94 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y)))))
% 5.65/5.94 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)))))
% 5.65/5.94 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)))))
% 5.65/5.94 (assert (forall ((C tptp.code_natural) (A2 tptp.code_natural)) (=> (@ (@ tptp.ord_le1926595141338095240atural C) tptp.one_one_Code_natural) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) A2) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.times_2397367101498566445atural A2) C)) A2)))))
% 5.65/5.94 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.one_one_Code_integer) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) A2)))))
% 5.65/5.94 (assert (forall ((C tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) A2)))))
% 5.65/5.94 (assert (forall ((C tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) C)) A2)))))
% 5.65/5.94 (assert (forall ((C tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.ord_le1926595141338095240atural A2) tptp.one_one_Code_natural) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) B) (=> (@ (@ tptp.ord_le1926595141338095240atural B) tptp.one_one_Code_natural) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.times_2397367101498566445atural A2) B)) tptp.one_one_Code_natural))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.one_one_Code_integer) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) B)) tptp.one_one_Code_integer))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) B)) tptp.one_one_rat))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A2) B)) tptp.one_one_nat))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) B)) tptp.one_one_int))))))
% 5.65/5.94 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger X) Y)) X)))))))
% 5.65/5.94 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Y)) X)))))))
% 5.65/5.94 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Y)) X)))))))
% 5.65/5.94 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger Y) X)) X)))))))
% 5.65/5.94 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y) X)) X)))))))
% 5.65/5.94 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y) X)) X)))))))
% 5.65/5.94 (assert (forall ((X tptp.int) (Y tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int))))
% 5.65/5.94 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y))) tptp.zero_z3403309356797280102nteger))))
% 5.65/5.94 (assert (forall ((X tptp.rat) (Y tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat))))
% 5.65/5.94 (assert (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) tptp.one_one_Code_natural)))
% 5.65/5.94 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 5.65/5.94 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 5.65/5.94 (assert (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer)))
% 5.65/5.94 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer)) (= (= (@ tptp.finite4902975817058060853nteger A) tptp.zero_zero_nat) (or (= A tptp.bot_bo3990330152332043303nteger) (not (@ tptp.finite6017078050557962740nteger A))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit)) (= (= (@ tptp.finite410649719033368117t_unit A) tptp.zero_zero_nat) (or (= A tptp.bot_bo3957492148770167129t_unit) (not (@ tptp.finite4290736615968046902t_unit A))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o)) (= (= (@ tptp.finite_card_o A) tptp.zero_zero_nat) (or (= A tptp.bot_bot_set_o) (not (@ tptp.finite_finite_o A))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat)) (= (= (@ tptp.finite_card_nat A) tptp.zero_zero_nat) (or (= A tptp.bot_bot_set_nat) (not (@ tptp.finite_finite_nat A))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int)) (= (= (@ tptp.finite_card_int A) tptp.zero_zero_nat) (or (= A tptp.bot_bot_set_int) (not (@ tptp.finite_finite_int A))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (= (= (@ tptp.finite1363419556375932405_nat_o A) tptp.zero_zero_nat) (or (= A tptp.bot_bo7824918357723582233_nat_o) (not (@ tptp.finite3252695134891459830_nat_o A))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (M4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N2) (=> (@ _let_1 M4) (@ _let_1 (@ (@ tptp.times_times_nat M4) N2)))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M4) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat M4) N2))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M4) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat N2) M4))))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M4) N2))))))
% 5.65/5.94 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger C) (@ (@ tptp.times_3573771949741848930nteger C) B)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.one_one_Code_integer))))))
% 5.65/5.94 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat C) B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 5.65/5.94 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int C) B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 5.65/5.94 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger C) A2)) C) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A2))))))
% 5.65/5.94 (assert (forall ((C tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat C) A2)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A2))))))
% 5.65/5.94 (assert (forall ((C tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int C) A2)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A2))))))
% 5.65/5.94 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger C) (@ (@ tptp.times_3573771949741848930nteger B) C)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.one_one_Code_integer))))))
% 5.65/5.94 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 5.65/5.94 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) C) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A2) C)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A2) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A2) C)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A2) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A2))))))
% 5.65/5.94 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger C) (@ (@ tptp.times_3573771949741848930nteger C) B)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer))))))
% 5.65/5.94 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat C) B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 5.65/5.94 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int C) B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 5.65/5.94 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger C) A2)) C) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A2))))))
% 5.65/5.94 (assert (forall ((C tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat C) A2)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2))))))
% 5.65/5.94 (assert (forall ((C tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int C) A2)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A2))))))
% 5.65/5.94 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger C) (@ (@ tptp.times_3573771949741848930nteger B) C)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer))))))
% 5.65/5.94 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 5.65/5.94 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) C)) C) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) C)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A2) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) C)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A2) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A2))))))
% 5.65/5.94 (assert (forall ((X tptp.code_integer) (A2 tptp.code_integer) (Y tptp.code_integer) (U tptp.code_integer) (V tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) A2) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger U) V) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger U) X)) (@ (@ tptp.times_3573771949741848930nteger V) Y))) A2)))))))))
% 5.65/5.94 (assert (forall ((X tptp.rat) (A2 tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat X) A2) (=> (@ (@ tptp.ord_less_eq_rat Y) A2) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X)) (@ (@ tptp.times_times_rat V) Y))) A2)))))))))
% 5.65/5.94 (assert (forall ((X tptp.int) (A2 tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int X) A2) (=> (@ (@ tptp.ord_less_eq_int Y) A2) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V) Y))) A2)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite4902975817058060853nteger A)) (and (not (= A tptp.bot_bo3990330152332043303nteger)) (@ tptp.finite6017078050557962740nteger A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite410649719033368117t_unit A)) (and (not (= A tptp.bot_bo3957492148770167129t_unit)) (@ tptp.finite4290736615968046902t_unit A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_o A)) (and (not (= A tptp.bot_bot_set_o)) (@ tptp.finite_finite_o A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat A)) (and (not (= A tptp.bot_bot_set_nat)) (@ tptp.finite_finite_nat A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_int A)) (and (not (= A tptp.bot_bot_set_int)) (@ tptp.finite_finite_int A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite1363419556375932405_nat_o A)) (and (not (= A tptp.bot_bo7824918357723582233_nat_o)) (@ tptp.finite3252695134891459830_nat_o A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit)) (= (= (@ tptp.finite410649719033368117t_unit A) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X2 tptp.product_unit)) (= A (@ (@ tptp.insert_Product_unit X2) tptp.bot_bo3957492148770167129t_unit))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o)) (= (= (@ tptp.finite_card_o A) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X2 Bool)) (= A (@ (@ tptp.insert_o X2) tptp.bot_bot_set_o))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat)) (= (= (@ tptp.finite_card_nat A) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X2 tptp.nat)) (= A (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int)) (= (= (@ tptp.finite_card_int A) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X2 tptp.int)) (= A (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (= (= (@ tptp.finite1363419556375932405_nat_o A) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (= A (@ (@ tptp.insert5175938949040314269_nat_o X2) tptp.bot_bo7824918357723582233_nat_o))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (K3 tptp.nat)) (=> (= (@ tptp.finite410649719033368117t_unit A) (@ tptp.suc K3)) (exists ((B2 tptp.product_unit) (B5 tptp.set_Product_unit)) (and (= A (@ (@ tptp.insert_Product_unit B2) B5)) (not (@ (@ tptp.member_Product_unit B2) B5)) (= (@ tptp.finite410649719033368117t_unit B5) K3) (=> (= K3 tptp.zero_zero_nat) (= B5 tptp.bot_bo3957492148770167129t_unit)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (K3 tptp.nat)) (=> (= (@ tptp.finite_card_o A) (@ tptp.suc K3)) (exists ((B2 Bool) (B5 tptp.set_o)) (and (= A (@ (@ tptp.insert_o B2) B5)) (not (@ (@ tptp.member_o B2) B5)) (= (@ tptp.finite_card_o B5) K3) (=> (= K3 tptp.zero_zero_nat) (= B5 tptp.bot_bot_set_o)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (K3 tptp.nat)) (=> (= (@ tptp.finite_card_nat A) (@ tptp.suc K3)) (exists ((B2 tptp.nat) (B5 tptp.set_nat)) (and (= A (@ (@ tptp.insert_nat B2) B5)) (not (@ (@ tptp.member_nat B2) B5)) (= (@ tptp.finite_card_nat B5) K3) (=> (= K3 tptp.zero_zero_nat) (= B5 tptp.bot_bot_set_nat)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (K3 tptp.nat)) (=> (= (@ tptp.finite_card_int A) (@ tptp.suc K3)) (exists ((B2 tptp.int) (B5 tptp.set_int)) (and (= A (@ (@ tptp.insert_int B2) B5)) (not (@ (@ tptp.member_int B2) B5)) (= (@ tptp.finite_card_int B5) K3) (=> (= K3 tptp.zero_zero_nat) (= B5 tptp.bot_bot_set_int)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (K3 tptp.nat)) (=> (= (@ tptp.finite1363419556375932405_nat_o A) (@ tptp.suc K3)) (exists ((B2 (-> tptp.produc3658429121746597890et_nat Bool)) (B5 tptp.set_Pr4532377907799695533_nat_o)) (and (= A (@ (@ tptp.insert5175938949040314269_nat_o B2) B5)) (not (@ (@ tptp.member6576561426505652726_nat_o B2) B5)) (= (@ tptp.finite1363419556375932405_nat_o B5) K3) (=> (= K3 tptp.zero_zero_nat) (= B5 tptp.bot_bo7824918357723582233_nat_o)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (K3 tptp.nat)) (= (= (@ tptp.finite410649719033368117t_unit A) (@ tptp.suc K3)) (exists ((B6 tptp.product_unit) (B7 tptp.set_Product_unit)) (and (= A (@ (@ tptp.insert_Product_unit B6) B7)) (not (@ (@ tptp.member_Product_unit B6) B7)) (= (@ tptp.finite410649719033368117t_unit B7) K3) (=> (= K3 tptp.zero_zero_nat) (= B7 tptp.bot_bo3957492148770167129t_unit)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (K3 tptp.nat)) (= (= (@ tptp.finite_card_o A) (@ tptp.suc K3)) (exists ((B6 Bool) (B7 tptp.set_o)) (and (= A (@ (@ tptp.insert_o B6) B7)) (not (@ (@ tptp.member_o B6) B7)) (= (@ tptp.finite_card_o B7) K3) (=> (= K3 tptp.zero_zero_nat) (= B7 tptp.bot_bot_set_o)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (K3 tptp.nat)) (= (= (@ tptp.finite_card_nat A) (@ tptp.suc K3)) (exists ((B6 tptp.nat) (B7 tptp.set_nat)) (and (= A (@ (@ tptp.insert_nat B6) B7)) (not (@ (@ tptp.member_nat B6) B7)) (= (@ tptp.finite_card_nat B7) K3) (=> (= K3 tptp.zero_zero_nat) (= B7 tptp.bot_bot_set_nat)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (K3 tptp.nat)) (= (= (@ tptp.finite_card_int A) (@ tptp.suc K3)) (exists ((B6 tptp.int) (B7 tptp.set_int)) (and (= A (@ (@ tptp.insert_int B6) B7)) (not (@ (@ tptp.member_int B6) B7)) (= (@ tptp.finite_card_int B7) K3) (=> (= K3 tptp.zero_zero_nat) (= B7 tptp.bot_bot_set_int)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (K3 tptp.nat)) (= (= (@ tptp.finite1363419556375932405_nat_o A) (@ tptp.suc K3)) (exists ((B6 (-> tptp.produc3658429121746597890et_nat Bool)) (B7 tptp.set_Pr4532377907799695533_nat_o)) (and (= A (@ (@ tptp.insert5175938949040314269_nat_o B6) B7)) (not (@ (@ tptp.member6576561426505652726_nat_o B6) B7)) (= (@ tptp.finite1363419556375932405_nat_o B7) K3) (=> (= K3 tptp.zero_zero_nat) (= B7 tptp.bot_bo7824918357723582233_nat_o)))))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (=> (@ (@ tptp.ord_less_eq_nat K3) M4) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat K3) (@ tptp.suc tptp.zero_zero_nat))) M4)))))
% 5.65/5.94 (assert (= tptp.times_times_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N4) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)) N4))))))
% 5.65/5.94 (assert (forall ((X tptp.code_integer) (A2 tptp.code_integer) (Y tptp.code_integer) (U tptp.code_integer) (V tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger Y) A2) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger U) V) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger U) X)) (@ (@ tptp.times_3573771949741848930nteger V) Y))) A2)))))))))
% 5.65/5.94 (assert (forall ((X tptp.rat) (A2 tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat X) A2) (=> (@ (@ tptp.ord_less_rat Y) A2) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X)) (@ (@ tptp.times_times_rat V) Y))) A2)))))))))
% 5.65/5.94 (assert (forall ((X tptp.int) (A2 tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X) A2) (=> (@ (@ tptp.ord_less_int Y) A2) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V) Y))) A2)))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.inj_on1158064722259180589nteger (@ tptp.times_3573771949741848930nteger A2)) tptp.top_to4645266643341252675nteger) (not (= A2 tptp.zero_z3403309356797280102nteger)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.inj_on_rat_rat (@ tptp.times_times_rat A2)) tptp.top_top_set_rat) (not (= A2 tptp.zero_zero_rat)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.inj_on_int_int (@ tptp.times_times_int A2)) tptp.top_top_set_int) (not (= A2 tptp.zero_zero_int)))))
% 5.65/5.94 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z3) (=> (@ (@ tptp.ord_less_rat Z3) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z3) X)) Y)))) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 5.65/5.94 (assert (= tptp.basic_5567952622663070111et_nat (lambda ((F4 (-> tptp.heap_e7401611519738050253t_unit tptp.nat)) (G3 (-> tptp.set_nat tptp.nat)) (P5 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ F4 (@ tptp.produc1824681642469235216et_nat P5))) (@ G3 (@ tptp.produc8586169260539613262et_nat P5)))) (@ tptp.suc tptp.zero_zero_nat)))))
% 5.65/5.94 (assert (= tptp.basic_1872990034501187214nt_int (lambda ((F4 (-> tptp.int tptp.nat)) (G3 (-> tptp.int tptp.nat)) (P5 tptp.product_prod_int_int)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ F4 (@ tptp.product_fst_int_int P5))) (@ G3 (@ tptp.product_snd_int_int P5)))) (@ tptp.suc tptp.zero_zero_nat)))))
% 5.65/5.94 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))))
% 5.65/5.94 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y))) (or (not (= X tptp.zero_z3403309356797280102nteger)) (not (= Y tptp.zero_z3403309356797280102nteger))))))
% 5.65/5.94 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) (or (not (= X tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat))))))
% 5.65/5.94 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y))) tptp.zero_z3403309356797280102nteger) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger)))))
% 5.65/5.94 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 5.65/5.94 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 5.65/5.94 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger Z))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_le3102999989581377725nteger X) Y))))))
% 5.65/5.94 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat Z))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_rat X) Y))))))
% 5.65/5.94 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X) Y))))))
% 5.65/5.94 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger X) Z)) (@ (@ tptp.times_3573771949741848930nteger Y) Z)) (@ (@ tptp.ord_le3102999989581377725nteger X) Y)))))
% 5.65/5.94 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_eq_rat X) Y)))))
% 5.65/5.94 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_eq_int X) Y)))))
% 5.65/5.94 (assert (forall ((Q4 tptp.nat) (R2 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q4) R2)) (= R2 tptp.zero_zero_nat))))
% 5.65/5.94 (assert (forall ((Q4 tptp.int) (R2 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q4) R2)) (= R2 tptp.zero_zero_int))))
% 5.65/5.94 (assert (forall ((Q4 tptp.code_integer) (R2 tptp.code_integer)) (= (@ tptp.unique5706413561485394159nteger (@ (@ tptp.produc1086072967326762835nteger Q4) R2)) (= R2 tptp.zero_z3403309356797280102nteger))))
% 5.65/5.94 (assert (= tptp.unique6322359934112328802ux_nat (lambda ((Qr tptp.product_prod_nat_nat)) (= (@ tptp.product_snd_nat_nat Qr) tptp.zero_zero_nat))))
% 5.65/5.94 (assert (= tptp.unique6319869463603278526ux_int (lambda ((Qr tptp.product_prod_int_int)) (= (@ tptp.product_snd_int_int Qr) tptp.zero_zero_int))))
% 5.65/5.94 (assert (= tptp.unique5706413561485394159nteger (lambda ((Qr tptp.produc8923325533196201883nteger)) (= (@ tptp.produc6174133586879617921nteger Qr) tptp.zero_z3403309356797280102nteger))))
% 5.65/5.94 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_int X) Y)))))
% 5.65/5.94 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger X) Z)) (@ (@ tptp.times_3573771949741848930nteger Y) Z)) (@ (@ tptp.ord_le6747313008572928689nteger X) Y)))))
% 5.65/5.94 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_rat X) Y)))))
% 5.65/5.94 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y)) tptp.zero_z3403309356797280102nteger) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger)))))
% 5.65/5.94 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 5.65/5.94 (assert (forall ((X tptp.int) (Y tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 5.65/5.94 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 5.65/5.94 (assert (= (@ tptp.neg_nu5831290666863070958nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 5.65/5.94 (assert (forall ((S tptp.set_Product_unit) (N2 tptp.nat)) (let ((_let_1 (@ tptp.infini7930543730640340914t_unit S))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.infini7930543730640340914t_unit (@ (@ tptp.minus_6452836326544984404t_unit S) (@ (@ tptp.insert_Product_unit (@ _let_1 tptp.zero_zero_nat)) tptp.bot_bo3957492148770167129t_unit))) N2)))))
% 5.65/5.94 (assert (forall ((S tptp.set_nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.infini8530281810654367211te_nat S))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.infini8530281810654367211te_nat (@ (@ tptp.minus_minus_set_nat S) (@ (@ tptp.insert_nat (@ _let_1 tptp.zero_zero_nat)) tptp.bot_bot_set_nat))) N2)))))
% 5.65/5.94 (assert (forall ((B tptp.code_natural) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural B))) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) B) (=> (@ (@ tptp.ord_le5570908160329646204atural B) tptp.one_one_Code_natural) (= (@ (@ tptp.ord_le1926595141338095240atural (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M4)))))))
% 5.65/5.94 (assert (forall ((B tptp.code_integer) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M4)))))))
% 5.65/5.94 (assert (forall ((B tptp.rat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M4)))))))
% 5.65/5.94 (assert (forall ((B tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M4)))))))
% 5.65/5.94 (assert (forall ((B tptp.int) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M4)))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_set_Code_integer) (K3 tptp.nat)) (let ((_let_1 (@ tptp.comple739944243200306918nteger C5))) (=> (@ tptp.finite6017078050557962740nteger _let_1) (=> (forall ((X3 tptp.set_Code_integer)) (=> (@ (@ tptp.member1834298987299537450nteger X3) C5) (@ (@ tptp.dvd_dvd_nat K3) (@ tptp.finite4902975817058060853nteger X3)))) (=> (forall ((X3 tptp.set_Code_integer)) (=> (@ (@ tptp.member1834298987299537450nteger X3) C5) (forall ((Xa3 tptp.set_Code_integer)) (=> (@ (@ tptp.member1834298987299537450nteger Xa3) C5) (=> (not (= X3 Xa3)) (= (@ (@ tptp.inf_in1364745209274528805nteger X3) Xa3) tptp.bot_bo3990330152332043303nteger)))))) (@ (@ tptp.dvd_dvd_nat K3) (@ tptp.finite4902975817058060853nteger _let_1))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_set_Product_unit) (K3 tptp.nat)) (let ((_let_1 (@ tptp.comple3349607820504768346t_unit C5))) (=> (@ tptp.finite4290736615968046902t_unit _let_1) (=> (forall ((X3 tptp.set_Product_unit)) (=> (@ (@ tptp.member5877623283571906838t_unit X3) C5) (@ (@ tptp.dvd_dvd_nat K3) (@ tptp.finite410649719033368117t_unit X3)))) (=> (forall ((X3 tptp.set_Product_unit)) (=> (@ (@ tptp.member5877623283571906838t_unit X3) C5) (forall ((Xa3 tptp.set_Product_unit)) (=> (@ (@ tptp.member5877623283571906838t_unit Xa3) C5) (=> (not (= X3 Xa3)) (= (@ (@ tptp.inf_in4660618365625256667t_unit X3) Xa3) tptp.bot_bo3957492148770167129t_unit)))))) (@ (@ tptp.dvd_dvd_nat K3) (@ tptp.finite410649719033368117t_unit _let_1))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_set_o) (K3 tptp.nat)) (let ((_let_1 (@ tptp.comple90263536869209701_set_o C5))) (=> (@ tptp.finite_finite_o _let_1) (=> (forall ((X3 tptp.set_o)) (=> (@ (@ tptp.member_set_o X3) C5) (@ (@ tptp.dvd_dvd_nat K3) (@ tptp.finite_card_o X3)))) (=> (forall ((X3 tptp.set_o)) (=> (@ (@ tptp.member_set_o X3) C5) (forall ((Xa3 tptp.set_o)) (=> (@ (@ tptp.member_set_o Xa3) C5) (=> (not (= X3 Xa3)) (= (@ (@ tptp.inf_inf_set_o X3) Xa3) tptp.bot_bot_set_o)))))) (@ (@ tptp.dvd_dvd_nat K3) (@ tptp.finite_card_o _let_1))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_set_nat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.comple7399068483239264473et_nat C5))) (=> (@ tptp.finite_finite_nat _let_1) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) C5) (@ (@ tptp.dvd_dvd_nat K3) (@ tptp.finite_card_nat X3)))) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) C5) (forall ((Xa3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa3) C5) (=> (not (= X3 Xa3)) (= (@ (@ tptp.inf_inf_set_nat X3) Xa3) tptp.bot_bot_set_nat)))))) (@ (@ tptp.dvd_dvd_nat K3) (@ tptp.finite_card_nat _let_1))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_set_int) (K3 tptp.nat)) (let ((_let_1 (@ tptp.comple3221217463730067765et_int C5))) (=> (@ tptp.finite_finite_int _let_1) (=> (forall ((X3 tptp.set_int)) (=> (@ (@ tptp.member_set_int X3) C5) (@ (@ tptp.dvd_dvd_nat K3) (@ tptp.finite_card_int X3)))) (=> (forall ((X3 tptp.set_int)) (=> (@ (@ tptp.member_set_int X3) C5) (forall ((Xa3 tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa3) C5) (=> (not (= X3 Xa3)) (= (@ (@ tptp.inf_inf_set_int X3) Xa3) tptp.bot_bot_set_int)))))) (@ (@ tptp.dvd_dvd_nat K3) (@ tptp.finite_card_int _let_1))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_se1353816476878259085_nat_o) (K3 tptp.nat)) (let ((_let_1 (@ tptp.comple3382087578465172250_nat_o C5))) (=> (@ tptp.finite3252695134891459830_nat_o _let_1) (=> (forall ((X3 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member1452989533377600726_nat_o X3) C5) (@ (@ tptp.dvd_dvd_nat K3) (@ tptp.finite1363419556375932405_nat_o X3)))) (=> (forall ((X3 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member1452989533377600726_nat_o X3) C5) (forall ((Xa3 tptp.set_Pr4532377907799695533_nat_o)) (=> (@ (@ tptp.member1452989533377600726_nat_o Xa3) C5) (=> (not (= X3 Xa3)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o X3) Xa3) tptp.bot_bo7824918357723582233_nat_o)))))) (@ (@ tptp.dvd_dvd_nat K3) (@ tptp.finite1363419556375932405_nat_o _let_1))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o)) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit5488710616941104124bove_o A) (=> (@ tptp.condit5413489452508810728elow_o A) (@ (@ tptp.ord_less_eq_o (@ tptp.complete_Inf_Inf_o A)) (@ tptp.complete_Sup_Sup_o A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (=> (@ tptp.condit4352657709669162033_nat_o A) (=> (@ tptp.condit8399017556247434269_nat_o A) (@ (@ tptp.ord_le729326519192465773_nat_o (@ tptp.comple90455603224345172_nat_o A)) (@ tptp.comple4225350640907012154_nat_o A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_filter_nat)) (=> (not (= A tptp.bot_bo498966703094740906er_nat)) (=> (@ tptp.condit4029664723990530684er_nat A) (=> (@ tptp.condit3133331395780078992er_nat A) (@ (@ tptp.ord_le2510731241096832064er_nat (@ tptp.comple6612786467464916249er_nat A)) (@ tptp.comple2454491259644266675er_nat A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int)) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit2212336002400062152ve_int A) (=> (@ tptp.condit1735850657277959132ow_int A) (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Inf_Inf_int A)) (@ tptp.complete_Sup_Sup_int A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_set_nat)) (=> (not (= A tptp.bot_bot_set_set_nat)) (=> (@ tptp.condit5477540289124974626et_nat A) (=> (@ tptp.condit68592940725977398et_nat A) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7806235888213564991et_nat A)) (@ tptp.comple7399068483239264473et_nat A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat)) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit2214826472909112428ve_nat A) (=> (@ tptp.condit1738341127787009408ow_nat A) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Inf_Inf_nat A)) (@ tptp.complete_Sup_Sup_nat A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit)) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit2080475194861589617t_unit A) (=> (@ tptp.condit9161856309968323677t_unit A) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.comple2584293577114468500t_unit A)) (@ tptp.comple4687483117567863418t_unit A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups7237345082560585321er_nat F) A)) (@ (@ tptp.times_times_nat (@ tptp.finite4902975817058060853nteger A)) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_951025933927791156er_nat F) A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) A)) (@ (@ tptp.times_times_nat (@ tptp.finite_card_nat A)) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_nat_nat2 F) A)))))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A2) tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.gbinomial_rat A2) K3) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))) (@ _let_1 K3)))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_assn tptp.one_one_assn) N2) tptp.one_one_assn)))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger tptp.one_one_Code_integer) N2) tptp.one_one_Code_integer)))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_7079662738309270450atural tptp.one_one_Code_natural) N2) tptp.one_one_Code_natural)))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N2) tptp.one_one_int)))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N2) tptp.one_one_nat)))
% 5.65/5.94 (assert (@ tptp.condit9161856309968323677t_unit tptp.bot_bo3957492148770167129t_unit))
% 5.65/5.94 (assert (@ tptp.condit5413489452508810728elow_o tptp.bot_bot_set_o))
% 5.65/5.94 (assert (@ tptp.condit1738341127787009408ow_nat tptp.bot_bot_set_nat))
% 5.65/5.94 (assert (@ tptp.condit1735850657277959132ow_int tptp.bot_bot_set_int))
% 5.65/5.94 (assert (@ tptp.condit8399017556247434269_nat_o tptp.bot_bo7824918357723582233_nat_o))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (A tptp.set_nat)) (= (@ tptp.condit1738341127787009408ow_nat (@ (@ tptp.insert_nat A2) A)) (@ tptp.condit1738341127787009408ow_nat A))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (A tptp.set_int)) (= (@ tptp.condit1735850657277959132ow_int (@ (@ tptp.insert_int A2) A)) (@ tptp.condit1735850657277959132ow_int A))))
% 5.65/5.94 (assert (forall ((A2 Bool) (A tptp.set_o)) (= (@ tptp.condit5413489452508810728elow_o (@ (@ tptp.insert_o A2) A)) (@ tptp.condit5413489452508810728elow_o A))))
% 5.65/5.94 (assert (forall ((A2 tptp.product_unit) (A tptp.set_Product_unit)) (= (@ tptp.condit9161856309968323677t_unit (@ (@ tptp.insert_Product_unit A2) A)) (@ tptp.condit9161856309968323677t_unit A))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A2 tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger B) A2)) (@ (@ tptp.times_3573771949741848930nteger C) A2)) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A2 tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat B) A2)) (@ (@ tptp.times_times_nat C) A2)) (@ (@ tptp.dvd_dvd_nat B) C)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A2 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int B) A2)) (@ (@ tptp.times_times_int C) A2)) (@ (@ tptp.dvd_dvd_int B) C)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A2))) (=> (not (= A2 tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_Code_integer B) C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (=> (not (= A2 tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_nat B) C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (=> (not (= A2 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_int B) C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A2) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A2) B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A2) B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A2) B)))))
% 5.65/5.94 (assert (forall ((C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 A2)) (@ _let_1 B)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A2) B))))))
% 5.65/5.94 (assert (forall ((C tptp.rat) (A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.dvd_dvd_rat (@ _let_1 A2)) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A2) B))))))
% 5.65/5.94 (assert (forall ((C tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 A2)) (@ _let_1 B)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A2) B))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A2))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) A2)) B)) (@ _let_1 B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat C) A2)) B)) (@ _let_1 B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) A2)) B)) (@ _let_1 B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) A2)) B)) (@ _let_1 B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A2))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) (@ (@ tptp.times_3573771949741848930nteger C) A2))) (@ _let_1 B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.times_times_rat C) A2))) (@ _let_1 B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.times_times_nat C) A2))) (@ _let_1 B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) (@ (@ tptp.times_times_int C) A2))) (@ _let_1 B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A2) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A2) B)) tptp.one_one_Code_integer)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A2) tptp.one_one_Code_natural) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (@ (@ tptp.dvd_dvd_Code_natural (@ (@ tptp.times_2397367101498566445atural A2) B)) tptp.one_one_Code_natural)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A2) B)) tptp.one_one_nat)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A2) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A2) B)) tptp.one_one_int)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural A2))) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.one_one_Code_natural) A2) (= (= (@ _let_1 M4) (@ _let_1 N2)) (= M4 N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A2) (= (= (@ _let_1 M4) (@ _let_1 N2)) (= M4 N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A2) (= (= (@ _let_1 M4) (@ _let_1 N2)) (= M4 N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A2) (= (= (@ _let_1 M4) (@ _let_1 N2)) (= M4 N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2) (= (= (@ _let_1 M4) (@ _let_1 N2)) (= M4 N2))))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M4)) (@ _let_1 N2)) (or (= K3 tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M4) N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.gbinomial_nat A2) tptp.zero_zero_nat) tptp.one_one_nat)))
% 5.65/5.94 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.gbinomial_int A2) tptp.zero_zero_nat) tptp.one_one_int)))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.gbinom8545251970709558553nteger A2) tptp.zero_zero_nat) tptp.one_one_Code_integer)))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural)) (= (@ (@ tptp.gbinom7368847122466276068atural A2) tptp.zero_zero_nat) tptp.one_one_Code_natural)))
% 5.65/5.94 (assert (forall ((B tptp.code_natural) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural B))) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.one_one_Code_natural) B) (= (@ (@ tptp.ord_le5570908160329646204atural (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 5.65/5.94 (assert (forall ((B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 5.65/5.94 (assert (forall ((B tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 5.65/5.94 (assert (forall ((B tptp.code_integer) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 5.65/5.94 (assert (forall ((B tptp.rat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 5.65/5.94 (assert (forall ((B tptp.code_natural) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural B))) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) B) (=> (@ (@ tptp.ord_le5570908160329646204atural B) tptp.one_one_Code_natural) (= (@ (@ tptp.ord_le5570908160329646204atural (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M4)))))))
% 5.65/5.94 (assert (forall ((B tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_nat (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M4)))))))
% 5.65/5.94 (assert (forall ((B tptp.int) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_int (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M4)))))))
% 5.65/5.94 (assert (forall ((B tptp.code_integer) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M4)))))))
% 5.65/5.94 (assert (forall ((B tptp.rat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M4)))))))
% 5.65/5.94 (assert (forall ((B tptp.code_natural) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural B))) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.one_one_Code_natural) B) (= (@ (@ tptp.ord_le1926595141338095240atural (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 5.65/5.94 (assert (forall ((B tptp.code_integer) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 5.65/5.94 (assert (forall ((B tptp.rat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 5.65/5.94 (assert (forall ((B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 5.65/5.94 (assert (forall ((B tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger A2) N2)) tptp.one_one_Code_integer) (or (@ (@ tptp.dvd_dvd_Code_integer A2) tptp.one_one_Code_integer) (= N2 tptp.zero_zero_nat)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_natural (@ (@ tptp.power_7079662738309270450atural A2) N2)) tptp.one_one_Code_natural) (or (@ (@ tptp.dvd_dvd_Code_natural A2) tptp.one_one_Code_natural) (= N2 tptp.zero_zero_nat)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A2) N2)) tptp.one_one_int) (or (@ (@ tptp.dvd_dvd_int A2) tptp.one_one_int) (= N2 tptp.zero_zero_nat)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A2) N2)) tptp.one_one_nat) (or (@ (@ tptp.dvd_dvd_nat A2) tptp.one_one_nat) (= N2 tptp.zero_zero_nat)))))
% 5.65/5.94 (assert (forall ((X tptp.assn) (Y tptp.assn) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_assn X) N2))) (let ((_let_2 (@ tptp.times_times_assn Y))) (=> (= (@ (@ tptp.times_times_assn X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_assn _let_1) Y) (@ _let_2 _let_1)))))))
% 5.65/5.94 (assert (forall ((X tptp.rat) (Y tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X) N2))) (let ((_let_2 (@ tptp.times_times_rat Y))) (=> (= (@ (@ tptp.times_times_rat X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ _let_2 _let_1)))))))
% 5.65/5.94 (assert (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X) N2))) (let ((_let_2 (@ tptp.times_times_nat Y))) (=> (= (@ (@ tptp.times_times_nat X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ _let_2 _let_1)))))))
% 5.65/5.94 (assert (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X) N2))) (let ((_let_2 (@ tptp.times_times_int Y))) (=> (= (@ (@ tptp.times_times_int X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_int _let_1) Y) (@ _let_2 _let_1)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.assn) (B tptp.assn) (N2 tptp.nat)) (= (@ (@ tptp.power_power_assn (@ (@ tptp.times_times_assn A2) B)) N2) (@ (@ tptp.times_times_assn (@ (@ tptp.power_power_assn A2) N2)) (@ (@ tptp.power_power_assn B) N2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.times_times_rat A2) B)) N2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat A2) N2)) (@ (@ tptp.power_power_rat B) N2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A2) B)) N2) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A2) N2)) (@ (@ tptp.power_power_nat B) N2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A2) B)) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A2) N2)) (@ (@ tptp.power_power_int B) N2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.assn) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_assn A2) N2))) (= (@ (@ tptp.times_times_assn _let_1) A2) (@ (@ tptp.times_times_assn A2) _let_1)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A2) N2))) (= (@ (@ tptp.times_times_rat _let_1) A2) (@ (@ tptp.times_times_rat A2) _let_1)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A2) N2))) (= (@ (@ tptp.times_times_nat _let_1) A2) (@ (@ tptp.times_times_nat A2) _let_1)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A2) N2))) (= (@ (@ tptp.times_times_int _let_1) A2) (@ (@ tptp.times_times_int A2) _let_1)))))
% 5.65/5.94 (assert (forall ((A2 tptp.assn) (B tptp.assn)) (@ (@ tptp.dvd_dvd_assn A2) (@ (@ tptp.times_times_assn B) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A2) (@ (@ tptp.times_times_rat B) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A2) (@ (@ tptp.times_times_nat B) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A2) (@ (@ tptp.times_times_int B) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.assn) (B tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.dvd_dvd_assn (@ (@ tptp.times_times_assn A2) B)) C) (@ (@ tptp.dvd_dvd_assn B) C))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A2) B)) C) (@ (@ tptp.dvd_dvd_rat B) C))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A2) B)) C) (@ (@ tptp.dvd_dvd_nat B) C))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A2) B)) C) (@ (@ tptp.dvd_dvd_int B) C))))
% 5.65/5.94 (assert (forall ((A2 tptp.assn) (B tptp.assn) (C tptp.assn) (D2 tptp.assn)) (=> (@ (@ tptp.dvd_dvd_assn A2) B) (=> (@ (@ tptp.dvd_dvd_assn C) D2) (@ (@ tptp.dvd_dvd_assn (@ (@ tptp.times_times_assn A2) C)) (@ (@ tptp.times_times_assn B) D2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat A2) B) (=> (@ (@ tptp.dvd_dvd_rat C) D2) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A2) C)) (@ (@ tptp.times_times_rat B) D2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) B) (=> (@ (@ tptp.dvd_dvd_nat C) D2) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A2) C)) (@ (@ tptp.times_times_nat B) D2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A2) B) (=> (@ (@ tptp.dvd_dvd_int C) D2) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B) D2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.assn) (B tptp.assn)) (@ (@ tptp.dvd_dvd_assn A2) (@ (@ tptp.times_times_assn A2) B))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A2) (@ (@ tptp.times_times_rat A2) B))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A2) (@ (@ tptp.times_times_nat A2) B))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A2) (@ (@ tptp.times_times_int A2) B))))
% 5.65/5.94 (assert (forall ((A2 tptp.assn) (B tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.dvd_dvd_assn (@ (@ tptp.times_times_assn A2) B)) C) (@ (@ tptp.dvd_dvd_assn A2) C))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A2) B)) C) (@ (@ tptp.dvd_dvd_rat A2) C))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A2) B)) C) (@ (@ tptp.dvd_dvd_nat A2) C))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A2) B)) C) (@ (@ tptp.dvd_dvd_int A2) C))))
% 5.65/5.94 (assert (forall ((A2 tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.dvd_dvd_assn A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_assn B) C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.assn) (C tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.dvd_dvd_assn A2))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_assn B) C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A2))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A2))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A2))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 5.65/5.94 (assert (= tptp.dvd_dvd_assn (lambda ((B6 tptp.assn) (A6 tptp.assn)) (exists ((K5 tptp.assn)) (= A6 (@ (@ tptp.times_times_assn B6) K5))))))
% 5.65/5.94 (assert (= tptp.dvd_dvd_rat (lambda ((B6 tptp.rat) (A6 tptp.rat)) (exists ((K5 tptp.rat)) (= A6 (@ (@ tptp.times_times_rat B6) K5))))))
% 5.65/5.94 (assert (= tptp.dvd_dvd_nat (lambda ((B6 tptp.nat) (A6 tptp.nat)) (exists ((K5 tptp.nat)) (= A6 (@ (@ tptp.times_times_nat B6) K5))))))
% 5.65/5.94 (assert (= tptp.dvd_dvd_int (lambda ((B6 tptp.int) (A6 tptp.int)) (exists ((K5 tptp.int)) (= A6 (@ (@ tptp.times_times_int B6) K5))))))
% 5.65/5.94 (assert (forall ((A2 tptp.assn) (B tptp.assn) (K3 tptp.assn)) (=> (= A2 (@ (@ tptp.times_times_assn B) K3)) (@ (@ tptp.dvd_dvd_assn B) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat) (K3 tptp.rat)) (=> (= A2 (@ (@ tptp.times_times_rat B) K3)) (@ (@ tptp.dvd_dvd_rat B) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (K3 tptp.nat)) (=> (= A2 (@ (@ tptp.times_times_nat B) K3)) (@ (@ tptp.dvd_dvd_nat B) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (K3 tptp.int)) (=> (= A2 (@ (@ tptp.times_times_int B) K3)) (@ (@ tptp.dvd_dvd_int B) A2))))
% 5.65/5.94 (assert (forall ((B tptp.assn) (A2 tptp.assn)) (=> (@ (@ tptp.dvd_dvd_assn B) A2) (not (forall ((K tptp.assn)) (not (= A2 (@ (@ tptp.times_times_assn B) K))))))))
% 5.65/5.94 (assert (forall ((B tptp.rat) (A2 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A2) (not (forall ((K tptp.rat)) (not (= A2 (@ (@ tptp.times_times_rat B) K))))))))
% 5.65/5.94 (assert (forall ((B tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A2) (not (forall ((K tptp.nat)) (not (= A2 (@ (@ tptp.times_times_nat B) K))))))))
% 5.65/5.94 (assert (forall ((B tptp.int) (A2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A2) (not (forall ((K tptp.int)) (not (= A2 (@ (@ tptp.times_times_int B) K))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ _let_1 tptp.one_one_int))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ _let_1 tptp.one_one_Code_integer))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (@ _let_1 tptp.one_one_Code_natural))))))
% 5.65/5.94 (assert (forall ((B tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat B))) (=> (@ _let_1 tptp.one_one_nat) (@ _let_1 A2)))))
% 5.65/5.94 (assert (forall ((B tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int B))) (=> (@ _let_1 tptp.one_one_int) (@ _let_1 A2)))))
% 5.65/5.94 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer B))) (=> (@ _let_1 tptp.one_one_Code_integer) (@ _let_1 A2)))))
% 5.65/5.94 (assert (forall ((B tptp.code_natural) (A2 tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural B))) (=> (@ _let_1 tptp.one_one_Code_natural) (@ _let_1 A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.assn)) (@ (@ tptp.dvd_dvd_assn tptp.one_one_assn) A2)))
% 5.65/5.94 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A2)))
% 5.65/5.94 (assert (forall ((A2 tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A2)))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer tptp.one_one_Code_integer) A2)))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural)) (@ (@ tptp.dvd_dvd_Code_natural tptp.one_one_Code_natural) A2)))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (= (@ _let_1 (@ (@ tptp.times_times_nat M4) N2)) (@ (@ tptp.power_power_int (@ _let_1 M4)) N2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (= (@ _let_1 (@ (@ tptp.times_times_nat M4) N2)) (@ (@ tptp.power_power_nat (@ _let_1 M4)) N2)))))
% 5.65/5.94 (assert (forall ((X tptp.code_natural) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural X))) (=> (not (= X tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.dvd_dvd_Code_natural (@ _let_1 M4)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_Code_natural X) tptp.one_one_Code_natural) (@ (@ tptp.ord_less_eq_nat M4) N2)))))))
% 5.65/5.94 (assert (forall ((X tptp.code_integer) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (=> (not (= X tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M4)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_Code_integer X) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M4) N2)))))))
% 5.65/5.94 (assert (forall ((X tptp.int) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (not (= X tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M4)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M4) N2)))))))
% 5.65/5.94 (assert (forall ((X tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X))) (=> (not (= X tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M4)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_nat X) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M4) N2)))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (X tptp.code_integer)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_Code_integer)) (@ (@ tptp.dvd_dvd_Code_integer X) (@ (@ tptp.power_8256067586552552935nteger X) N2)))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (X tptp.code_natural)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_Code_natural)) (@ (@ tptp.dvd_dvd_Code_natural X) (@ (@ tptp.power_7079662738309270450atural X) N2)))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (X tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X) (@ (@ tptp.power_power_int X) N2)))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X) (@ (@ tptp.power_power_nat X) N2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (let ((_let_2 (@ tptp.gbinomial_rat A2))) (= (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat A2) tptp.one_one_rat)) _let_1) (@ (@ tptp.plus_plus_rat (@ _let_2 K3)) (@ _let_2 _let_1)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A2) N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le1926595141338095240atural tptp.one_one_Code_natural))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_7079662738309270450atural A2) N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_rat A2) N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_nat A2) N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_int A2) N2))))))
% 5.65/5.94 (assert (not (@ (@ tptp.dvd_dvd_Code_natural tptp.zero_z2226904508553997617atural) tptp.one_one_Code_natural)))
% 5.65/5.94 (assert (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)))
% 5.65/5.94 (assert (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)))
% 5.65/5.94 (assert (not (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer)))
% 5.65/5.94 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_3573771949741848930nteger X) Y) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger X) N2)) (@ (@ tptp.power_8256067586552552935nteger Y) N2)) tptp.one_one_Code_integer))))
% 5.65/5.94 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_2397367101498566445atural X) Y) tptp.one_one_Code_natural) (= (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.power_7079662738309270450atural X) N2)) (@ (@ tptp.power_7079662738309270450atural Y) N2)) tptp.one_one_Code_natural))))
% 5.65/5.94 (assert (forall ((X tptp.assn) (Y tptp.assn) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_assn X) Y) tptp.one_one_assn) (= (@ (@ tptp.times_times_assn (@ (@ tptp.power_power_assn X) N2)) (@ (@ tptp.power_power_assn Y) N2)) tptp.one_one_assn))))
% 5.65/5.94 (assert (forall ((X tptp.rat) (Y tptp.rat) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X) Y) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X) N2)) (@ (@ tptp.power_power_rat Y) N2)) tptp.one_one_rat))))
% 5.65/5.94 (assert (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X) Y) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X) N2)) (@ (@ tptp.power_power_nat Y) N2)) tptp.one_one_nat))))
% 5.65/5.94 (assert (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_int X) Y) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) N2)) tptp.one_one_int))))
% 5.65/5.94 (assert (forall ((A2 tptp.assn) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_assn A2))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_assn (@ _let_1 N2)) A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ _let_1 N2)) A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.assn) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_assn A2))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_assn A2) (@ _let_1 N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_rat A2) (@ _let_1 N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat A2) (@ _let_1 N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int A2) (@ _let_1 N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A2) tptp.one_one_Code_integer) (= (= (@ (@ tptp.times_3573771949741848930nteger B) A2) (@ (@ tptp.times_3573771949741848930nteger C) A2)) (= B C)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A2) tptp.one_one_Code_natural) (= (= (@ (@ tptp.times_2397367101498566445atural B) A2) (@ (@ tptp.times_2397367101498566445atural C) A2)) (= B C)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) tptp.one_one_nat) (= (= (@ (@ tptp.times_times_nat B) A2) (@ (@ tptp.times_times_nat C) A2)) (= B C)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A2) tptp.one_one_int) (= (= (@ (@ tptp.times_times_int B) A2) (@ (@ tptp.times_times_int C) A2)) (= B C)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A2))) (=> (@ (@ tptp.dvd_dvd_Code_integer A2) tptp.one_one_Code_integer) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A2))) (=> (@ (@ tptp.dvd_dvd_Code_natural A2) tptp.one_one_Code_natural) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (=> (@ (@ tptp.dvd_dvd_nat A2) tptp.one_one_nat) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (=> (@ (@ tptp.dvd_dvd_int A2) tptp.one_one_int) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A2) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A2) B)) C) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A2) tptp.one_one_Code_natural) (= (@ (@ tptp.dvd_dvd_Code_natural (@ (@ tptp.times_2397367101498566445atural A2) B)) C) (@ (@ tptp.dvd_dvd_Code_natural B) C)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A2) B)) C) (@ (@ tptp.dvd_dvd_nat B) C)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A2) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A2) B)) C) (@ (@ tptp.dvd_dvd_int B) C)))))
% 5.65/5.94 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A2))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ _let_1 C))))))
% 5.65/5.94 (assert (forall ((B tptp.code_natural) (A2 tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural A2))) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (@ _let_1 (@ (@ tptp.times_2397367101498566445atural B) C)) (@ _let_1 C))))))
% 5.65/5.94 (assert (forall ((B tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A2))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ _let_1 C))))))
% 5.65/5.94 (assert (forall ((B tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A2))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ _let_1 C))))))
% 5.65/5.94 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A2) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A2) C)))))
% 5.65/5.94 (assert (forall ((B tptp.code_natural) (A2 tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (@ (@ tptp.dvd_dvd_Code_natural (@ (@ tptp.times_2397367101498566445atural A2) B)) C) (@ (@ tptp.dvd_dvd_Code_natural A2) C)))))
% 5.65/5.94 (assert (forall ((B tptp.nat) (A2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A2) B)) C) (@ (@ tptp.dvd_dvd_nat A2) C)))))
% 5.65/5.94 (assert (forall ((B tptp.int) (A2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A2) B)) C) (@ (@ tptp.dvd_dvd_int A2) C)))))
% 5.65/5.94 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A2))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger C) B)) (@ _let_1 C))))))
% 5.65/5.94 (assert (forall ((B tptp.code_natural) (A2 tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural A2))) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (@ _let_1 (@ (@ tptp.times_2397367101498566445atural C) B)) (@ _let_1 C))))))
% 5.65/5.94 (assert (forall ((B tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A2))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat C) B)) (@ _let_1 C))))))
% 5.65/5.94 (assert (forall ((B tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A2))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int C) B)) (@ _let_1 C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A2) B)) tptp.one_one_Code_integer) (and (@ (@ tptp.dvd_dvd_Code_integer A2) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.dvd_dvd_Code_natural (@ (@ tptp.times_2397367101498566445atural A2) B)) tptp.one_one_Code_natural) (and (@ (@ tptp.dvd_dvd_Code_natural A2) tptp.one_one_Code_natural) (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A2) B)) tptp.one_one_nat) (and (@ (@ tptp.dvd_dvd_nat A2) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A2) B)) tptp.one_one_int) (and (@ (@ tptp.dvd_dvd_int A2) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int)))))
% 5.65/5.94 (assert (forall ((A2 tptp.assn)) (= (@ (@ tptp.power_power_assn A2) tptp.zero_zero_nat) tptp.one_one_assn)))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.power_8256067586552552935nteger A2) tptp.zero_zero_nat) tptp.one_one_Code_integer)))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural)) (= (@ (@ tptp.power_7079662738309270450atural A2) tptp.zero_zero_nat) tptp.one_one_Code_natural)))
% 5.65/5.94 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.power_power_int A2) tptp.zero_zero_nat) tptp.one_one_int)))
% 5.65/5.94 (assert (forall ((A2 tptp.nat)) (= (@ (@ tptp.power_power_nat A2) tptp.zero_zero_nat) tptp.one_one_nat)))
% 5.65/5.94 (assert (forall ((A2 tptp.assn) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_assn A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M4) N2)) (@ (@ tptp.times_times_assn (@ _let_1 M4)) (@ _let_1 N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M4) N2)) (@ (@ tptp.times_times_rat (@ _let_1 M4)) (@ _let_1 N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M4) N2)) (@ (@ tptp.times_times_nat (@ _let_1 M4)) (@ _let_1 N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M4) N2)) (@ (@ tptp.times_times_int (@ _let_1 M4)) (@ _let_1 N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A2) tptp.one_one_rat)))) (let ((_let_2 (@ tptp.suc K3))) (= (@ (@ tptp.gbinomial_rat A2) _let_2) (@ (@ tptp.plus_plus_rat (@ _let_1 _let_2)) (@ _let_1 K3)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural) (N2 tptp.nat)) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) A2) (=> (@ (@ tptp.ord_le1926595141338095240atural A2) tptp.one_one_Code_natural) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.power_7079662738309270450atural A2) N2)) tptp.one_one_Code_natural)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A2) N2)) tptp.one_one_Code_integer)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A2) N2)) tptp.one_one_rat)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A2) N2)) tptp.one_one_nat)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A2) N2)) tptp.one_one_int)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_7079662738309270450atural A2) N2))) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.one_one_Code_natural) A2) (@ (@ tptp.ord_le5570908160329646204atural _let_1) (@ (@ tptp.times_2397367101498566445atural A2) _let_1))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A2) N2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A2) (@ (@ tptp.ord_less_nat _let_1) (@ (@ tptp.times_times_nat A2) _let_1))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A2) N2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A2) (@ (@ tptp.ord_less_int _let_1) (@ (@ tptp.times_times_int A2) _let_1))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A2) N2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A2) (@ (@ tptp.ord_le6747313008572928689nteger _let_1) (@ (@ tptp.times_3573771949741848930nteger A2) _let_1))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A2) N2))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2) (@ (@ tptp.ord_less_rat _let_1) (@ (@ tptp.times_times_rat A2) _let_1))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le5570908160329646204atural tptp.one_one_Code_natural))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.times_2397367101498566445atural A2) (@ (@ tptp.power_7079662738309270450atural A2) N2)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.times_times_nat A2) (@ (@ tptp.power_power_nat A2) N2)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.times_times_int A2) (@ (@ tptp.power_power_int A2) N2)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A2) (@ (@ tptp.power_8256067586552552935nteger A2) N2)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.times_times_rat A2) (@ (@ tptp.power_power_rat A2) N2)))))))
% 5.65/5.94 (assert (forall ((P (-> tptp.code_integer Bool)) (L tptp.code_integer)) (= (exists ((X2 tptp.code_integer)) (@ P (@ (@ tptp.times_3573771949741848930nteger L) X2))) (exists ((X2 tptp.code_integer)) (and (@ (@ tptp.dvd_dvd_Code_integer L) (@ (@ tptp.plus_p5714425477246183910nteger X2) tptp.zero_z3403309356797280102nteger)) (@ P X2))))))
% 5.65/5.94 (assert (forall ((P (-> tptp.rat Bool)) (L tptp.rat)) (= (exists ((X2 tptp.rat)) (@ P (@ (@ tptp.times_times_rat L) X2))) (exists ((X2 tptp.rat)) (and (@ (@ tptp.dvd_dvd_rat L) (@ (@ tptp.plus_plus_rat X2) tptp.zero_zero_rat)) (@ P X2))))))
% 5.65/5.94 (assert (forall ((P (-> tptp.nat Bool)) (L tptp.nat)) (= (exists ((X2 tptp.nat)) (@ P (@ (@ tptp.times_times_nat L) X2))) (exists ((X2 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L) (@ (@ tptp.plus_plus_nat X2) tptp.zero_zero_nat)) (@ P X2))))))
% 5.65/5.94 (assert (forall ((P (-> tptp.int Bool)) (L tptp.int)) (= (exists ((X2 tptp.int)) (@ P (@ (@ tptp.times_times_int L) X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.dvd_dvd_int L) (@ (@ tptp.plus_plus_int X2) tptp.zero_zero_int)) (@ P X2))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_7079662738309270450atural tptp.zero_z2226904508553997617atural) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_Code_natural)) (=> (not _let_2) (= _let_1 tptp.zero_z2226904508553997617atural)))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger tptp.zero_z3403309356797280102nteger) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_Code_integer)) (=> (not _let_2) (= _let_1 tptp.zero_z3403309356797280102nteger)))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int tptp.zero_zero_int) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A2) tptp.one_one_Code_natural) (not (=> (not (= A2 tptp.zero_z2226904508553997617atural)) (forall ((C2 tptp.code_natural)) (not (= B (@ (@ tptp.times_2397367101498566445atural A2) C2)))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A2) tptp.one_one_Code_integer) (not (=> (not (= A2 tptp.zero_z3403309356797280102nteger)) (forall ((C2 tptp.code_integer)) (not (= B (@ (@ tptp.times_3573771949741848930nteger A2) C2)))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) tptp.one_one_nat) (not (=> (not (= A2 tptp.zero_zero_nat)) (forall ((C2 tptp.nat)) (not (= B (@ (@ tptp.times_times_nat A2) C2)))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A2) tptp.one_one_int) (not (=> (not (= A2 tptp.zero_zero_int)) (forall ((C2 tptp.int)) (not (= B (@ (@ tptp.times_times_int A2) C2)))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le5570908160329646204atural tptp.one_one_Code_natural))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_7079662738309270450atural A2) (@ tptp.suc N2)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_nat A2) (@ tptp.suc N2)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_int A2) (@ tptp.suc N2)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A2) (@ tptp.suc N2)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.power_power_rat A2) (@ tptp.suc N2)))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (N tptp.nat) (A2 tptp.code_natural)) (let ((_let_1 (@ tptp.power_7079662738309270450atural A2))) (=> (@ (@ tptp.ord_less_nat N2) N) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.one_one_Code_natural) A2) (@ (@ tptp.ord_le5570908160329646204atural (@ _let_1 N2)) (@ _let_1 N)))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (N tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_nat N2) N) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A2) (@ (@ tptp.ord_less_nat (@ _let_1 N2)) (@ _let_1 N)))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (N tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_nat N2) N) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A2) (@ (@ tptp.ord_less_int (@ _let_1 N2)) (@ _let_1 N)))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (N tptp.nat) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (=> (@ (@ tptp.ord_less_nat N2) N) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A2) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 N2)) (@ _let_1 N)))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (N tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (@ (@ tptp.ord_less_nat N2) N) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2) (@ (@ tptp.ord_less_rat (@ _let_1 N2)) (@ _let_1 N)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural A2))) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.one_one_Code_natural) A2) (=> (@ (@ tptp.ord_le5570908160329646204atural (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M4) N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A2) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M4) N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A2) (=> (@ (@ tptp.ord_less_int (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M4) N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M4) N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2) (=> (@ (@ tptp.ord_less_rat (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M4) N2))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (N tptp.nat) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (=> (@ (@ tptp.ord_less_eq_nat N2) N) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A2) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 N2)) (@ _let_1 N)))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (N tptp.nat) (A2 tptp.code_natural)) (let ((_let_1 (@ tptp.power_7079662738309270450atural A2))) (=> (@ (@ tptp.ord_less_eq_nat N2) N) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.one_one_Code_natural) A2) (@ (@ tptp.ord_le1926595141338095240atural (@ _let_1 N2)) (@ _let_1 N)))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (N tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (@ (@ tptp.ord_less_eq_nat N2) N) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A2) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N2)) (@ _let_1 N)))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (N tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_eq_nat N2) N) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 N)))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (N tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_eq_nat N2) N) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A2) (@ (@ tptp.ord_less_eq_int (@ _let_1 N2)) (@ _let_1 N)))))))
% 5.65/5.94 (assert (forall ((D2 tptp.code_integer) (D3 tptp.code_integer) (T4 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D2) D3) (forall ((X6 tptp.code_integer) (K2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D2))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X6) T4)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X6) (@ (@ tptp.times_3573771949741848930nteger K2) D3))) T4))))))))
% 5.65/5.94 (assert (forall ((D2 tptp.rat) (D3 tptp.rat) (T4 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D2) D3) (forall ((X6 tptp.rat) (K2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat X6) T4)) (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X6) (@ (@ tptp.times_times_rat K2) D3))) T4))))))))
% 5.65/5.94 (assert (forall ((D2 tptp.int) (D3 tptp.int) (T4 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D3) (forall ((X6 tptp.int) (K2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X6) T4)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K2) D3))) T4))))))))
% 5.65/5.94 (assert (forall ((D2 tptp.code_integer) (D3 tptp.code_integer) (T4 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D2) D3) (forall ((X6 tptp.code_integer) (K2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D2))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X6) T4))) (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X6) (@ (@ tptp.times_3573771949741848930nteger K2) D3))) T4)))))))))
% 5.65/5.94 (assert (forall ((D2 tptp.rat) (D3 tptp.rat) (T4 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D2) D3) (forall ((X6 tptp.rat) (K2 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D2))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_rat X6) T4))) (not (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X6) (@ (@ tptp.times_times_rat K2) D3))) T4)))))))))
% 5.65/5.94 (assert (forall ((D2 tptp.int) (D3 tptp.int) (T4 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D3) (forall ((X6 tptp.int) (K2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X6) T4))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K2) D3))) T4)))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_o) (A tptp.set_o)) (=> (not (= B4 tptp.bot_bot_set_o)) (=> (@ tptp.condit5413489452508810728elow_o A) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) B4) (exists ((X6 Bool)) (and (@ (@ tptp.member_o X6) A) (@ (@ tptp.ord_less_eq_o X6) B2))))) (@ (@ tptp.ord_less_eq_o (@ tptp.complete_Inf_Inf_o A)) (@ tptp.complete_Inf_Inf_o B4)))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_Pr4532377907799695533_nat_o) (A tptp.set_Pr4532377907799695533_nat_o)) (=> (not (= B4 tptp.bot_bo7824918357723582233_nat_o)) (=> (@ tptp.condit8399017556247434269_nat_o A) (=> (forall ((B2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o B2) B4) (exists ((X6 (-> tptp.produc3658429121746597890et_nat Bool))) (and (@ (@ tptp.member6576561426505652726_nat_o X6) A) (@ (@ tptp.ord_le729326519192465773_nat_o X6) B2))))) (@ (@ tptp.ord_le729326519192465773_nat_o (@ tptp.comple90455603224345172_nat_o A)) (@ tptp.comple90455603224345172_nat_o B4)))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_filter_nat) (A tptp.set_filter_nat)) (=> (not (= B4 tptp.bot_bo498966703094740906er_nat)) (=> (@ tptp.condit3133331395780078992er_nat A) (=> (forall ((B2 tptp.filter_nat)) (=> (@ (@ tptp.member_filter_nat B2) B4) (exists ((X6 tptp.filter_nat)) (and (@ (@ tptp.member_filter_nat X6) A) (@ (@ tptp.ord_le2510731241096832064er_nat X6) B2))))) (@ (@ tptp.ord_le2510731241096832064er_nat (@ tptp.comple6612786467464916249er_nat A)) (@ tptp.comple6612786467464916249er_nat B4)))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_int) (A tptp.set_int)) (=> (not (= B4 tptp.bot_bot_set_int)) (=> (@ tptp.condit1735850657277959132ow_int A) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) B4) (exists ((X6 tptp.int)) (and (@ (@ tptp.member_int X6) A) (@ (@ tptp.ord_less_eq_int X6) B2))))) (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Inf_Inf_int A)) (@ tptp.complete_Inf_Inf_int B4)))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_nat) (A tptp.set_nat)) (=> (not (= B4 tptp.bot_bot_set_nat)) (=> (@ tptp.condit1738341127787009408ow_nat A) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) B4) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) A) (@ (@ tptp.ord_less_eq_nat X6) B2))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Inf_Inf_nat A)) (@ tptp.complete_Inf_Inf_nat B4)))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_set_nat) (A tptp.set_set_nat)) (=> (not (= B4 tptp.bot_bot_set_set_nat)) (=> (@ tptp.condit68592940725977398et_nat A) (=> (forall ((B2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat B2) B4) (exists ((X6 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X6) A) (@ (@ tptp.ord_less_eq_set_nat X6) B2))))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7806235888213564991et_nat A)) (@ tptp.comple7806235888213564991et_nat B4)))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_Product_unit) (A tptp.set_Product_unit)) (=> (not (= B4 tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit9161856309968323677t_unit A) (=> (forall ((B2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit B2) B4) (exists ((X6 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X6) A) (@ (@ tptp.ord_le3221252021190050221t_unit X6) B2))))) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.comple2584293577114468500t_unit A)) (@ tptp.comple2584293577114468500t_unit B4)))))))
% 5.65/5.94 (assert (forall ((S tptp.set_o) (A2 Bool)) (=> (not (= S tptp.bot_bot_set_o)) (=> (@ tptp.condit5413489452508810728elow_o S) (= (@ (@ tptp.ord_less_eq_o A2) (@ tptp.complete_Inf_Inf_o S)) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) S) (@ (@ tptp.ord_less_eq_o A2) X2))))))))
% 5.65/5.94 (assert (forall ((S tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (not (= S tptp.bot_bo7824918357723582233_nat_o)) (=> (@ tptp.condit8399017556247434269_nat_o S) (= (@ (@ tptp.ord_le729326519192465773_nat_o A2) (@ tptp.comple90455603224345172_nat_o S)) (forall ((X2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o X2) S) (@ (@ tptp.ord_le729326519192465773_nat_o A2) X2))))))))
% 5.65/5.94 (assert (forall ((S tptp.set_filter_nat) (A2 tptp.filter_nat)) (=> (not (= S tptp.bot_bo498966703094740906er_nat)) (=> (@ tptp.condit3133331395780078992er_nat S) (= (@ (@ tptp.ord_le2510731241096832064er_nat A2) (@ tptp.comple6612786467464916249er_nat S)) (forall ((X2 tptp.filter_nat)) (=> (@ (@ tptp.member_filter_nat X2) S) (@ (@ tptp.ord_le2510731241096832064er_nat A2) X2))))))))
% 5.65/5.94 (assert (forall ((S tptp.set_int) (A2 tptp.int)) (=> (not (= S tptp.bot_bot_set_int)) (=> (@ tptp.condit1735850657277959132ow_int S) (= (@ (@ tptp.ord_less_eq_int A2) (@ tptp.complete_Inf_Inf_int S)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) S) (@ (@ tptp.ord_less_eq_int A2) X2))))))))
% 5.65/5.94 (assert (forall ((S tptp.set_nat) (A2 tptp.nat)) (=> (not (= S tptp.bot_bot_set_nat)) (=> (@ tptp.condit1738341127787009408ow_nat S) (= (@ (@ tptp.ord_less_eq_nat A2) (@ tptp.complete_Inf_Inf_nat S)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) S) (@ (@ tptp.ord_less_eq_nat A2) X2))))))))
% 5.65/5.94 (assert (forall ((S tptp.set_set_nat) (A2 tptp.set_nat)) (=> (not (= S tptp.bot_bot_set_set_nat)) (=> (@ tptp.condit68592940725977398et_nat S) (= (@ (@ tptp.ord_less_eq_set_nat A2) (@ tptp.comple7806235888213564991et_nat S)) (forall ((X2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X2) S) (@ (@ tptp.ord_less_eq_set_nat A2) X2))))))))
% 5.65/5.94 (assert (forall ((S tptp.set_Product_unit) (A2 tptp.product_unit)) (=> (not (= S tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit9161856309968323677t_unit S) (= (@ (@ tptp.ord_le3221252021190050221t_unit A2) (@ tptp.comple2584293577114468500t_unit S)) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) S) (@ (@ tptp.ord_le3221252021190050221t_unit A2) X2))))))))
% 5.65/5.94 (assert (forall ((X4 tptp.set_int) (Y tptp.int)) (=> (not (= X4 tptp.bot_bot_set_int)) (=> (@ tptp.condit1735850657277959132ow_int X4) (= (@ (@ tptp.ord_less_int (@ tptp.complete_Inf_Inf_int X4)) Y) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) X4) (@ (@ tptp.ord_less_int X2) Y))))))))
% 5.65/5.94 (assert (forall ((X4 tptp.set_nat) (Y tptp.nat)) (=> (not (= X4 tptp.bot_bot_set_nat)) (=> (@ tptp.condit1738341127787009408ow_nat X4) (= (@ (@ tptp.ord_less_nat (@ tptp.complete_Inf_Inf_nat X4)) Y) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) X4) (@ (@ tptp.ord_less_nat X2) Y))))))))
% 5.65/5.94 (assert (forall ((X4 tptp.set_Product_unit) (Y tptp.product_unit)) (=> (not (= X4 tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit9161856309968323677t_unit X4) (= (@ (@ tptp.ord_le361264281704409273t_unit (@ tptp.comple2584293577114468500t_unit X4)) Y) (exists ((X2 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X2) X4) (@ (@ tptp.ord_le361264281704409273t_unit X2) Y))))))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M4)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.dvd_dvd_nat M4) N2))))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.dvd_dvd_nat M4) N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_7079662738309270450atural A2) N2))) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) A2) (=> (@ (@ tptp.ord_le5570908160329646204atural A2) tptp.one_one_Code_natural) (@ (@ tptp.ord_le5570908160329646204atural (@ (@ tptp.times_2397367101498566445atural A2) _let_1)) _let_1))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A2) N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat A2) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A2) _let_1)) _let_1))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A2) N2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int A2) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A2) _let_1)) _let_1))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A2) N2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A2) _let_1)) _let_1))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A2) N2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_rat A2) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A2) _let_1)) _let_1))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural) (N2 tptp.nat)) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) A2) (=> (@ (@ tptp.ord_le1926595141338095240atural A2) tptp.one_one_Code_natural) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.power_7079662738309270450atural A2) (@ tptp.suc N2))) A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A2) (@ tptp.suc N2))) A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A2) (@ tptp.suc N2))) A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A2) (@ tptp.suc N2))) A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A2) (@ tptp.suc N2))) A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural) (N2 tptp.nat)) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) A2) (=> (@ (@ tptp.ord_le5570908160329646204atural A2) tptp.one_one_Code_natural) (@ (@ tptp.ord_le5570908160329646204atural (@ (@ tptp.power_7079662738309270450atural A2) (@ tptp.suc N2))) tptp.one_one_Code_natural)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat A2) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A2) (@ tptp.suc N2))) tptp.one_one_nat)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int A2) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A2) (@ tptp.suc N2))) tptp.one_one_int)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A2) (@ tptp.suc N2))) tptp.one_one_Code_integer)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_rat A2) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A2) (@ tptp.suc N2))) tptp.one_one_rat)))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (N tptp.nat) (A2 tptp.code_natural)) (let ((_let_1 (@ tptp.power_7079662738309270450atural A2))) (=> (@ (@ tptp.ord_less_nat N2) N) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) A2) (=> (@ (@ tptp.ord_le5570908160329646204atural A2) tptp.one_one_Code_natural) (@ (@ tptp.ord_le5570908160329646204atural (@ _let_1 N)) (@ _let_1 N2))))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (N tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_nat N2) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_nat A2) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 N2))))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (N tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_nat N2) N) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_int A2) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N)) (@ _let_1 N2))))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (N tptp.nat) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (=> (@ (@ tptp.ord_less_nat N2) N) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 N)) (@ _let_1 N2))))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (N tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (@ (@ tptp.ord_less_nat N2) N) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_rat A2) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N)) (@ _let_1 N2))))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (N tptp.nat) (A2 tptp.code_natural)) (let ((_let_1 (@ tptp.power_7079662738309270450atural A2))) (=> (@ (@ tptp.ord_less_eq_nat N2) N) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) A2) (=> (@ (@ tptp.ord_le1926595141338095240atural A2) tptp.one_one_Code_natural) (@ (@ tptp.ord_le1926595141338095240atural (@ _let_1 N)) (@ _let_1 N2))))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (N tptp.nat) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (=> (@ (@ tptp.ord_less_eq_nat N2) N) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 N)) (@ _let_1 N2))))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (N tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (@ (@ tptp.ord_less_eq_nat N2) N) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat A2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N)) (@ _let_1 N2))))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (N tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_eq_nat N2) N) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat A2) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 N2))))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (N tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_eq_nat N2) N) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) (@ _let_1 N2))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural A2))) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.one_one_Code_natural) A2) (=> (@ (@ tptp.ord_le1926595141338095240atural (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M4) N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A2) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M4) N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A2) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M4) N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A2) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M4) N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A2) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M4) N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ (@ tptp.power_8256067586552552935nteger A2) N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural) (N2 tptp.nat)) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.one_one_Code_natural) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_le1926595141338095240atural A2) (@ (@ tptp.power_7079662738309270450atural A2) N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_rat A2) (@ (@ tptp.power_power_rat A2) N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat A2) (@ (@ tptp.power_power_nat A2) N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_int A2) (@ (@ tptp.power_power_int A2) N2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_natural) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le5570908160329646204atural tptp.one_one_Code_natural))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_7079662738309270450atural A2) N2)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_nat A2) N2)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_int A2) N2)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A2) N2)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_rat A2) N2)))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_Product_unit) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (G (-> tptp.product_unit tptp.nat))) (let ((_let_1 (@ (@ tptp.image_nat_nat2 F) A))) (=> (not (= B4 tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit1738341127787009408ow_nat _let_1) (=> (forall ((M2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit M2) B4) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) A) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ G M2)))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Inf_Inf_nat _let_1)) (@ tptp.complete_Inf_Inf_nat (@ (@ tptp.image_875570014554754200it_nat G) B4)))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_o) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (G (-> Bool tptp.nat))) (let ((_let_1 (@ (@ tptp.image_nat_nat2 F) A))) (=> (not (= B4 tptp.bot_bot_set_o)) (=> (@ tptp.condit1738341127787009408ow_nat _let_1) (=> (forall ((M2 Bool)) (=> (@ (@ tptp.member_o M2) B4) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) A) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ G M2)))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Inf_Inf_nat _let_1)) (@ tptp.complete_Inf_Inf_nat (@ (@ tptp.image_o_nat2 G) B4)))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.image_nat_nat2 F) A))) (=> (not (= B4 tptp.bot_bot_set_nat)) (=> (@ tptp.condit1738341127787009408ow_nat _let_1) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.member_nat M2) B4) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) A) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ G M2)))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Inf_Inf_nat _let_1)) (@ tptp.complete_Inf_Inf_nat (@ (@ tptp.image_nat_nat2 G) B4)))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_int) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.image_nat_nat2 F) A))) (=> (not (= B4 tptp.bot_bot_set_int)) (=> (@ tptp.condit1738341127787009408ow_nat _let_1) (=> (forall ((M2 tptp.int)) (=> (@ (@ tptp.member_int M2) B4) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) A) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ G M2)))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Inf_Inf_nat _let_1)) (@ tptp.complete_Inf_Inf_nat (@ (@ tptp.image_int_nat2 G) B4)))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_Pr4532377907799695533_nat_o) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (G (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.nat))) (let ((_let_1 (@ (@ tptp.image_nat_nat2 F) A))) (=> (not (= B4 tptp.bot_bo7824918357723582233_nat_o)) (=> (@ tptp.condit1738341127787009408ow_nat _let_1) (=> (forall ((M2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o M2) B4) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) A) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ G M2)))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Inf_Inf_nat _let_1)) (@ tptp.complete_Inf_Inf_nat (@ (@ tptp.image_2174381888560928856_o_nat G) B4)))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_Product_unit) (F (-> tptp.nat tptp.set_nat)) (A tptp.set_nat) (G (-> tptp.product_unit tptp.set_nat))) (let ((_let_1 (@ (@ tptp.image_nat_set_nat F) A))) (=> (not (= B4 tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit68592940725977398et_nat _let_1) (=> (forall ((M2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit M2) B4) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) A) (@ (@ tptp.ord_less_eq_set_nat (@ F X6)) (@ G M2)))))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7806235888213564991et_nat _let_1)) (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_8173849991827986510et_nat G) B4)))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_o) (F (-> tptp.nat tptp.set_nat)) (A tptp.set_nat) (G (-> Bool tptp.set_nat))) (let ((_let_1 (@ (@ tptp.image_nat_set_nat F) A))) (=> (not (= B4 tptp.bot_bot_set_o)) (=> (@ tptp.condit68592940725977398et_nat _let_1) (=> (forall ((M2 Bool)) (=> (@ (@ tptp.member_o M2) B4) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) A) (@ (@ tptp.ord_less_eq_set_nat (@ F X6)) (@ G M2)))))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7806235888213564991et_nat _let_1)) (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_o_set_nat G) B4)))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_nat) (F (-> tptp.nat tptp.set_nat)) (A tptp.set_nat) (G (-> tptp.nat tptp.set_nat))) (let ((_let_1 (@ (@ tptp.image_nat_set_nat F) A))) (=> (not (= B4 tptp.bot_bot_set_nat)) (=> (@ tptp.condit68592940725977398et_nat _let_1) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.member_nat M2) B4) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) A) (@ (@ tptp.ord_less_eq_set_nat (@ F X6)) (@ G M2)))))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7806235888213564991et_nat _let_1)) (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat G) B4)))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_int) (F (-> tptp.nat tptp.set_nat)) (A tptp.set_nat) (G (-> tptp.int tptp.set_nat))) (let ((_let_1 (@ (@ tptp.image_nat_set_nat F) A))) (=> (not (= B4 tptp.bot_bot_set_int)) (=> (@ tptp.condit68592940725977398et_nat _let_1) (=> (forall ((M2 tptp.int)) (=> (@ (@ tptp.member_int M2) B4) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) A) (@ (@ tptp.ord_less_eq_set_nat (@ F X6)) (@ G M2)))))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7806235888213564991et_nat _let_1)) (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_int_set_nat G) B4)))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_Pr4532377907799695533_nat_o) (F (-> tptp.nat tptp.set_nat)) (A tptp.set_nat) (G (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.set_nat))) (let ((_let_1 (@ (@ tptp.image_nat_set_nat F) A))) (=> (not (= B4 tptp.bot_bo7824918357723582233_nat_o)) (=> (@ tptp.condit68592940725977398et_nat _let_1) (=> (forall ((M2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.member6576561426505652726_nat_o M2) B4) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) A) (@ (@ tptp.ord_less_eq_set_nat (@ F X6)) (@ G M2)))))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7806235888213564991et_nat _let_1)) (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_6888641473154130958et_nat G) B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.int)) (U tptp.int)) (let ((_let_1 (@ (@ tptp.image_873079544045703924it_int F) A))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit1735850657277959132ow_int _let_1) (= (@ (@ tptp.ord_less_eq_int U) (@ tptp.complete_Inf_Inf_int _let_1)) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) A) (@ (@ tptp.ord_less_eq_int U) (@ F X2))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.int)) (U tptp.int)) (let ((_let_1 (@ (@ tptp.image_o_int2 F) A))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit1735850657277959132ow_int _let_1) (= (@ (@ tptp.ord_less_eq_int U) (@ tptp.complete_Inf_Inf_int _let_1)) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A) (@ (@ tptp.ord_less_eq_int U) (@ F X2))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.int)) (U tptp.int)) (let ((_let_1 (@ (@ tptp.image_nat_int2 F) A))) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit1735850657277959132ow_int _let_1) (= (@ (@ tptp.ord_less_eq_int U) (@ tptp.complete_Inf_Inf_int _let_1)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.ord_less_eq_int U) (@ F X2))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.int)) (U tptp.int)) (let ((_let_1 (@ (@ tptp.image_int_int2 F) A))) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit1735850657277959132ow_int _let_1) (= (@ (@ tptp.ord_less_eq_int U) (@ tptp.complete_Inf_Inf_int _let_1)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A) (@ (@ tptp.ord_less_eq_int U) (@ F X2))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.nat)) (U tptp.nat)) (let ((_let_1 (@ (@ tptp.image_875570014554754200it_nat F) A))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit1738341127787009408ow_nat _let_1) (= (@ (@ tptp.ord_less_eq_nat U) (@ tptp.complete_Inf_Inf_nat _let_1)) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) A) (@ (@ tptp.ord_less_eq_nat U) (@ F X2))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.nat)) (U tptp.nat)) (let ((_let_1 (@ (@ tptp.image_o_nat2 F) A))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit1738341127787009408ow_nat _let_1) (= (@ (@ tptp.ord_less_eq_nat U) (@ tptp.complete_Inf_Inf_nat _let_1)) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A) (@ (@ tptp.ord_less_eq_nat U) (@ F X2))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat)) (U tptp.nat)) (let ((_let_1 (@ (@ tptp.image_nat_nat2 F) A))) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit1738341127787009408ow_nat _let_1) (= (@ (@ tptp.ord_less_eq_nat U) (@ tptp.complete_Inf_Inf_nat _let_1)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.ord_less_eq_nat U) (@ F X2))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.nat)) (U tptp.nat)) (let ((_let_1 (@ (@ tptp.image_int_nat2 F) A))) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit1738341127787009408ow_nat _let_1) (= (@ (@ tptp.ord_less_eq_nat U) (@ tptp.complete_Inf_Inf_nat _let_1)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A) (@ (@ tptp.ord_less_eq_nat U) (@ F X2))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.product_unit)) (U tptp.product_unit)) (let ((_let_1 (@ (@ tptp.image_405062704495631173t_unit F) A))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit9161856309968323677t_unit _let_1) (= (@ (@ tptp.ord_le3221252021190050221t_unit U) (@ tptp.comple2584293577114468500t_unit _let_1)) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) A) (@ (@ tptp.ord_le3221252021190050221t_unit U) (@ F X2))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.product_unit)) (U tptp.product_unit)) (let ((_let_1 (@ (@ tptp.image_o_Product_unit2 F) A))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit9161856309968323677t_unit _let_1) (= (@ (@ tptp.ord_le3221252021190050221t_unit U) (@ tptp.comple2584293577114468500t_unit _let_1)) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A) (@ (@ tptp.ord_le3221252021190050221t_unit U) (@ F X2))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit5413489452508810728elow_o B4) (=> (@ (@ tptp.ord_less_eq_set_o A) B4) (@ (@ tptp.ord_less_eq_o (@ tptp.complete_Inf_Inf_o B4)) (@ tptp.complete_Inf_Inf_o A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (=> (@ tptp.condit8399017556247434269_nat_o B4) (=> (@ (@ tptp.ord_le2965882846123202637_nat_o A) B4) (@ (@ tptp.ord_le729326519192465773_nat_o (@ tptp.comple90455603224345172_nat_o B4)) (@ tptp.comple90455603224345172_nat_o A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_filter_nat) (B4 tptp.set_filter_nat)) (=> (not (= A tptp.bot_bo498966703094740906er_nat)) (=> (@ tptp.condit3133331395780078992er_nat B4) (=> (@ (@ tptp.ord_le2426478655948331894er_nat A) B4) (@ (@ tptp.ord_le2510731241096832064er_nat (@ tptp.comple6612786467464916249er_nat B4)) (@ tptp.comple6612786467464916249er_nat A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit1735850657277959132ow_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A) B4) (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Inf_Inf_int B4)) (@ tptp.complete_Inf_Inf_int A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit1738341127787009408ow_nat B4) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Inf_Inf_nat B4)) (@ tptp.complete_Inf_Inf_nat A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_set_nat) (B4 tptp.set_set_nat)) (=> (not (= A tptp.bot_bot_set_set_nat)) (=> (@ tptp.condit68592940725977398et_nat B4) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A) B4) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.comple7806235888213564991et_nat B4)) (@ tptp.comple7806235888213564991et_nat A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit9161856309968323677t_unit B4) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) B4) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.comple2584293577114468500t_unit B4)) (@ tptp.comple2584293577114468500t_unit A)))))))
% 5.65/5.94 (assert (forall ((X4 tptp.set_o) (A2 Bool)) (=> (not (= X4 tptp.bot_bot_set_o)) (=> (@ tptp.condit5413489452508810728elow_o X4) (= (@ tptp.complete_Inf_Inf_o (@ (@ tptp.insert_o A2) X4)) (@ (@ tptp.inf_inf_o A2) (@ tptp.complete_Inf_Inf_o X4)))))))
% 5.65/5.94 (assert (forall ((X4 tptp.set_int) (A2 tptp.int)) (=> (not (= X4 tptp.bot_bot_set_int)) (=> (@ tptp.condit1735850657277959132ow_int X4) (= (@ tptp.complete_Inf_Inf_int (@ (@ tptp.insert_int A2) X4)) (@ (@ tptp.inf_inf_int A2) (@ tptp.complete_Inf_Inf_int X4)))))))
% 5.65/5.94 (assert (forall ((X4 tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (not (= X4 tptp.bot_bo7824918357723582233_nat_o)) (=> (@ tptp.condit8399017556247434269_nat_o X4) (= (@ tptp.comple90455603224345172_nat_o (@ (@ tptp.insert5175938949040314269_nat_o A2) X4)) (@ (@ tptp.inf_in1318976480646536635_nat_o A2) (@ tptp.comple90455603224345172_nat_o X4)))))))
% 5.65/5.94 (assert (forall ((X4 tptp.set_nat) (A2 tptp.nat)) (=> (not (= X4 tptp.bot_bot_set_nat)) (=> (@ tptp.condit1738341127787009408ow_nat X4) (= (@ tptp.complete_Inf_Inf_nat (@ (@ tptp.insert_nat A2) X4)) (@ (@ tptp.inf_inf_nat A2) (@ tptp.complete_Inf_Inf_nat X4)))))))
% 5.65/5.94 (assert (forall ((X4 tptp.set_set_nat) (A2 tptp.set_nat)) (=> (not (= X4 tptp.bot_bot_set_set_nat)) (=> (@ tptp.condit68592940725977398et_nat X4) (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.insert_set_nat A2) X4)) (@ (@ tptp.inf_inf_set_nat A2) (@ tptp.comple7806235888213564991et_nat X4)))))))
% 5.65/5.94 (assert (forall ((X4 tptp.set_Product_unit) (A2 tptp.product_unit)) (=> (not (= X4 tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit9161856309968323677t_unit X4) (= (@ tptp.comple2584293577114468500t_unit (@ (@ tptp.insert_Product_unit A2) X4)) (@ (@ tptp.inf_inf_Product_unit A2) (@ tptp.comple2584293577114468500t_unit X4)))))))
% 5.65/5.94 (assert (forall ((X4 tptp.set_o) (A2 Bool)) (let ((_let_1 (= X4 tptp.bot_bot_set_o))) (=> (@ tptp.condit5413489452508810728elow_o X4) (= (@ tptp.complete_Inf_Inf_o (@ (@ tptp.insert_o A2) X4)) (and (=> _let_1 A2) (=> (not _let_1) (@ (@ tptp.inf_inf_o A2) (@ tptp.complete_Inf_Inf_o X4)))))))))
% 5.65/5.94 (assert (forall ((X4 tptp.set_int) (A2 tptp.int)) (let ((_let_1 (@ tptp.complete_Inf_Inf_int (@ (@ tptp.insert_int A2) X4)))) (let ((_let_2 (= X4 tptp.bot_bot_set_int))) (=> (@ tptp.condit1735850657277959132ow_int X4) (and (=> _let_2 (= _let_1 A2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.inf_inf_int A2) (@ tptp.complete_Inf_Inf_int X4))))))))))
% 5.65/5.94 (assert (forall ((X4 tptp.set_Pr4532377907799695533_nat_o) (A2 (-> tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ tptp.comple90455603224345172_nat_o (@ (@ tptp.insert5175938949040314269_nat_o A2) X4)))) (let ((_let_2 (= X4 tptp.bot_bo7824918357723582233_nat_o))) (=> (@ tptp.condit8399017556247434269_nat_o X4) (and (=> _let_2 (= _let_1 A2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.inf_in1318976480646536635_nat_o A2) (@ tptp.comple90455603224345172_nat_o X4))))))))))
% 5.65/5.94 (assert (forall ((X4 tptp.set_nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.complete_Inf_Inf_nat (@ (@ tptp.insert_nat A2) X4)))) (let ((_let_2 (= X4 tptp.bot_bot_set_nat))) (=> (@ tptp.condit1738341127787009408ow_nat X4) (and (=> _let_2 (= _let_1 A2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.inf_inf_nat A2) (@ tptp.complete_Inf_Inf_nat X4))))))))))
% 5.65/5.94 (assert (forall ((X4 tptp.set_set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.insert_set_nat A2) X4)))) (let ((_let_2 (= X4 tptp.bot_bot_set_set_nat))) (=> (@ tptp.condit68592940725977398et_nat X4) (and (=> _let_2 (= _let_1 A2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.inf_inf_set_nat A2) (@ tptp.comple7806235888213564991et_nat X4))))))))))
% 5.65/5.94 (assert (forall ((X4 tptp.set_Product_unit) (A2 tptp.product_unit)) (let ((_let_1 (@ tptp.comple2584293577114468500t_unit (@ (@ tptp.insert_Product_unit A2) X4)))) (let ((_let_2 (= X4 tptp.bot_bo3957492148770167129t_unit))) (=> (@ tptp.condit9161856309968323677t_unit X4) (and (=> _let_2 (= _let_1 A2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.inf_inf_Product_unit A2) (@ tptp.comple2584293577114468500t_unit X4))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit5413489452508810728elow_o A) (=> (not (= B4 tptp.bot_bot_set_o)) (=> (@ tptp.condit5413489452508810728elow_o B4) (= (@ tptp.complete_Inf_Inf_o (@ (@ tptp.sup_sup_set_o A) B4)) (@ (@ tptp.inf_inf_o (@ tptp.complete_Inf_Inf_o A)) (@ tptp.complete_Inf_Inf_o B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit1735850657277959132ow_int A) (=> (not (= B4 tptp.bot_bot_set_int)) (=> (@ tptp.condit1735850657277959132ow_int B4) (= (@ tptp.complete_Inf_Inf_int (@ (@ tptp.sup_sup_set_int A) B4)) (@ (@ tptp.inf_inf_int (@ tptp.complete_Inf_Inf_int A)) (@ tptp.complete_Inf_Inf_int B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (=> (not (= A tptp.bot_bo7824918357723582233_nat_o)) (=> (@ tptp.condit8399017556247434269_nat_o A) (=> (not (= B4 tptp.bot_bo7824918357723582233_nat_o)) (=> (@ tptp.condit8399017556247434269_nat_o B4) (= (@ tptp.comple90455603224345172_nat_o (@ (@ tptp.sup_su5209123915105501825_nat_o A) B4)) (@ (@ tptp.inf_in1318976480646536635_nat_o (@ tptp.comple90455603224345172_nat_o A)) (@ tptp.comple90455603224345172_nat_o B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit1738341127787009408ow_nat A) (=> (not (= B4 tptp.bot_bot_set_nat)) (=> (@ tptp.condit1738341127787009408ow_nat B4) (= (@ tptp.complete_Inf_Inf_nat (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.inf_inf_nat (@ tptp.complete_Inf_Inf_nat A)) (@ tptp.complete_Inf_Inf_nat B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_set_nat) (B4 tptp.set_set_nat)) (=> (not (= A tptp.bot_bot_set_set_nat)) (=> (@ tptp.condit68592940725977398et_nat A) (=> (not (= B4 tptp.bot_bot_set_set_nat)) (=> (@ tptp.condit68592940725977398et_nat B4) (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.sup_sup_set_set_nat A) B4)) (@ (@ tptp.inf_inf_set_nat (@ tptp.comple7806235888213564991et_nat A)) (@ tptp.comple7806235888213564991et_nat B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit9161856309968323677t_unit A) (=> (not (= B4 tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit9161856309968323677t_unit B4) (= (@ tptp.comple2584293577114468500t_unit (@ (@ tptp.sup_su793286257634532545t_unit A) B4)) (@ (@ tptp.inf_inf_Product_unit (@ tptp.comple2584293577114468500t_unit A)) (@ tptp.comple2584293577114468500t_unit B4)))))))))
% 5.65/5.94 (assert (= tptp.neg_nu5831290666863070958nteger (lambda ((X2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger X2) X2)) tptp.one_one_Code_integer))))
% 5.65/5.94 (assert (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X2 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X2) X2)) tptp.one_one_rat))))
% 5.65/5.94 (assert (= tptp.neg_nu5851722552734809277nc_int (lambda ((X2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X2) X2)) tptp.one_one_int))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M4) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M4) N2)) M4) (= N2 tptp.one_one_nat)))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M4) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N2) M4)) M4) (= N2 tptp.one_one_nat)))))
% 5.65/5.94 (assert (forall ((Q4 tptp.nat) (N2 tptp.nat) (R2 tptp.nat) (M4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R2) M4))) (let ((_let_2 (@ tptp.dvd_dvd_nat M4))) (let ((_let_3 (@ tptp.ord_less_eq_nat Q4))) (=> (@ _let_3 N2) (=> (@ _let_3 _let_1) (= (@ _let_2 (@ (@ tptp.minus_minus_nat N2) Q4)) (@ _let_2 (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.minus_minus_nat _let_1) Q4)))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (G (-> tptp.product_unit tptp.int)) (B4 tptp.set_Product_unit) (F (-> tptp.product_unit tptp.int))) (let ((_let_1 (@ (@ tptp.image_873079544045703924it_int G) B4))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit1735850657277959132ow_int _let_1) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) B4) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) B4) (@ (@ tptp.ord_less_eq_int (@ G X3)) (@ F X3)))) (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Inf_Inf_int _let_1)) (@ tptp.complete_Inf_Inf_int (@ (@ tptp.image_873079544045703924it_int F) A))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (G (-> Bool tptp.int)) (B4 tptp.set_o) (F (-> Bool tptp.int))) (let ((_let_1 (@ (@ tptp.image_o_int2 G) B4))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit1735850657277959132ow_int _let_1) (=> (@ (@ tptp.ord_less_eq_set_o A) B4) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) B4) (@ (@ tptp.ord_less_eq_int (@ G X3)) (@ F X3)))) (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Inf_Inf_int _let_1)) (@ tptp.complete_Inf_Inf_int (@ (@ tptp.image_o_int2 F) A))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.int)) (B4 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ (@ tptp.image_int_int2 G) B4))) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit1735850657277959132ow_int _let_1) (=> (@ (@ tptp.ord_less_eq_set_int A) B4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) B4) (@ (@ tptp.ord_less_eq_int (@ G X3)) (@ F X3)))) (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Inf_Inf_int _let_1)) (@ tptp.complete_Inf_Inf_int (@ (@ tptp.image_int_int2 F) A))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.int)) (B4 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.image_nat_int2 G) B4))) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit1735850657277959132ow_int _let_1) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) B4) (@ (@ tptp.ord_less_eq_int (@ G X3)) (@ F X3)))) (@ (@ tptp.ord_less_eq_int (@ tptp.complete_Inf_Inf_int _let_1)) (@ tptp.complete_Inf_Inf_int (@ (@ tptp.image_nat_int2 F) A))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (G (-> tptp.product_unit tptp.nat)) (B4 tptp.set_Product_unit) (F (-> tptp.product_unit tptp.nat))) (let ((_let_1 (@ (@ tptp.image_875570014554754200it_nat G) B4))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit1738341127787009408ow_nat _let_1) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) B4) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) B4) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Inf_Inf_nat _let_1)) (@ tptp.complete_Inf_Inf_nat (@ (@ tptp.image_875570014554754200it_nat F) A))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (G (-> Bool tptp.nat)) (B4 tptp.set_o) (F (-> Bool tptp.nat))) (let ((_let_1 (@ (@ tptp.image_o_nat2 G) B4))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit1738341127787009408ow_nat _let_1) (=> (@ (@ tptp.ord_less_eq_set_o A) B4) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) B4) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Inf_Inf_nat _let_1)) (@ tptp.complete_Inf_Inf_nat (@ (@ tptp.image_o_nat2 F) A))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.nat)) (B4 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.image_int_nat2 G) B4))) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit1738341127787009408ow_nat _let_1) (=> (@ (@ tptp.ord_less_eq_set_int A) B4) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) B4) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Inf_Inf_nat _let_1)) (@ tptp.complete_Inf_Inf_nat (@ (@ tptp.image_int_nat2 F) A))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.nat)) (B4 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.image_nat_nat2 G) B4))) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit1738341127787009408ow_nat _let_1) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) B4) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat (@ tptp.complete_Inf_Inf_nat _let_1)) (@ tptp.complete_Inf_Inf_nat (@ (@ tptp.image_nat_nat2 F) A))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (G (-> tptp.product_unit tptp.product_unit)) (B4 tptp.set_Product_unit) (F (-> tptp.product_unit tptp.product_unit))) (let ((_let_1 (@ (@ tptp.image_405062704495631173t_unit G) B4))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit9161856309968323677t_unit _let_1) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) B4) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) B4) (@ (@ tptp.ord_le3221252021190050221t_unit (@ G X3)) (@ F X3)))) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.comple2584293577114468500t_unit _let_1)) (@ tptp.comple2584293577114468500t_unit (@ (@ tptp.image_405062704495631173t_unit F) A))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (G (-> Bool tptp.product_unit)) (B4 tptp.set_o) (F (-> Bool tptp.product_unit))) (let ((_let_1 (@ (@ tptp.image_o_Product_unit2 G) B4))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit9161856309968323677t_unit _let_1) (=> (@ (@ tptp.ord_less_eq_set_o A) B4) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) B4) (@ (@ tptp.ord_le3221252021190050221t_unit (@ G X3)) (@ F X3)))) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.comple2584293577114468500t_unit _let_1)) (@ tptp.comple2584293577114468500t_unit (@ (@ tptp.image_o_Product_unit2 F) A))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (let ((_let_1 (@ (@ tptp.inf_inf_set_o A) B4))) (=> (@ tptp.condit5413489452508810728elow_o A) (=> (@ tptp.condit5413489452508810728elow_o B4) (=> (not (= _let_1 tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_eq_o (@ (@ tptp.inf_inf_o (@ tptp.complete_Inf_Inf_o A)) (@ tptp.complete_Inf_Inf_o B4))) (@ tptp.complete_Inf_Inf_o _let_1))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ (@ tptp.inf_in1906310914598751387_nat_o A) B4))) (=> (@ tptp.condit8399017556247434269_nat_o A) (=> (@ tptp.condit8399017556247434269_nat_o B4) (=> (not (= _let_1 tptp.bot_bo7824918357723582233_nat_o)) (@ (@ tptp.ord_le729326519192465773_nat_o (@ (@ tptp.inf_in1318976480646536635_nat_o (@ tptp.comple90455603224345172_nat_o A)) (@ tptp.comple90455603224345172_nat_o B4))) (@ tptp.comple90455603224345172_nat_o _let_1))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_filter_nat) (B4 tptp.set_filter_nat)) (let ((_let_1 (@ (@ tptp.inf_in7395780696554941096er_nat A) B4))) (=> (@ tptp.condit3133331395780078992er_nat A) (=> (@ tptp.condit3133331395780078992er_nat B4) (=> (not (= _let_1 tptp.bot_bo498966703094740906er_nat)) (@ (@ tptp.ord_le2510731241096832064er_nat (@ (@ tptp.inf_inf_filter_nat (@ tptp.comple6612786467464916249er_nat A)) (@ tptp.comple6612786467464916249er_nat B4))) (@ tptp.comple6612786467464916249er_nat _let_1))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ (@ tptp.inf_inf_set_int A) B4))) (=> (@ tptp.condit1735850657277959132ow_int A) (=> (@ tptp.condit1735850657277959132ow_int B4) (=> (not (= _let_1 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int (@ tptp.complete_Inf_Inf_int A)) (@ tptp.complete_Inf_Inf_int B4))) (@ tptp.complete_Inf_Inf_int _let_1))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat A) B4))) (=> (@ tptp.condit1738341127787009408ow_nat A) (=> (@ tptp.condit1738341127787009408ow_nat B4) (=> (not (= _let_1 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat (@ tptp.complete_Inf_Inf_nat A)) (@ tptp.complete_Inf_Inf_nat B4))) (@ tptp.complete_Inf_Inf_nat _let_1))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_set_nat) (B4 tptp.set_set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_set_nat A) B4))) (=> (@ tptp.condit68592940725977398et_nat A) (=> (@ tptp.condit68592940725977398et_nat B4) (=> (not (= _let_1 tptp.bot_bot_set_set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat (@ tptp.comple7806235888213564991et_nat A)) (@ tptp.comple7806235888213564991et_nat B4))) (@ tptp.comple7806235888213564991et_nat _let_1))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ (@ tptp.inf_in4660618365625256667t_unit A) B4))) (=> (@ tptp.condit9161856309968323677t_unit A) (=> (@ tptp.condit9161856309968323677t_unit B4) (=> (not (= _let_1 tptp.bot_bo3957492148770167129t_unit)) (@ (@ tptp.ord_le3221252021190050221t_unit (@ (@ tptp.inf_inf_Product_unit (@ tptp.comple2584293577114468500t_unit A)) (@ tptp.comple2584293577114468500t_unit B4))) (@ tptp.comple2584293577114468500t_unit _let_1))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.nat)) (A2 tptp.product_unit)) (let ((_let_1 (@ tptp.image_875570014554754200it_nat F))) (let ((_let_2 (@ _let_1 A))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit1738341127787009408ow_nat _let_2) (= (@ tptp.complete_Inf_Inf_nat (@ _let_1 (@ (@ tptp.insert_Product_unit A2) A))) (@ (@ tptp.inf_inf_nat (@ F A2)) (@ tptp.complete_Inf_Inf_nat _let_2)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.nat)) (A2 Bool)) (let ((_let_1 (@ tptp.image_o_nat2 F))) (let ((_let_2 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit1738341127787009408ow_nat _let_2) (= (@ tptp.complete_Inf_Inf_nat (@ _let_1 (@ (@ tptp.insert_o A2) A))) (@ (@ tptp.inf_inf_nat (@ F A2)) (@ tptp.complete_Inf_Inf_nat _let_2)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat)) (A2 tptp.nat)) (let ((_let_1 (@ tptp.image_nat_nat2 F))) (let ((_let_2 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit1738341127787009408ow_nat _let_2) (= (@ tptp.complete_Inf_Inf_nat (@ _let_1 (@ (@ tptp.insert_nat A2) A))) (@ (@ tptp.inf_inf_nat (@ F A2)) (@ tptp.complete_Inf_Inf_nat _let_2)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.nat)) (A2 tptp.int)) (let ((_let_1 (@ tptp.image_int_nat2 F))) (let ((_let_2 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit1738341127787009408ow_nat _let_2) (= (@ tptp.complete_Inf_Inf_nat (@ _let_1 (@ (@ tptp.insert_int A2) A))) (@ (@ tptp.inf_inf_nat (@ F A2)) (@ tptp.complete_Inf_Inf_nat _let_2)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.product_unit)) (A2 tptp.product_unit)) (let ((_let_1 (@ tptp.image_405062704495631173t_unit F))) (let ((_let_2 (@ _let_1 A))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit9161856309968323677t_unit _let_2) (= (@ tptp.comple2584293577114468500t_unit (@ _let_1 (@ (@ tptp.insert_Product_unit A2) A))) (@ (@ tptp.inf_inf_Product_unit (@ F A2)) (@ tptp.comple2584293577114468500t_unit _let_2)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.product_unit)) (A2 Bool)) (let ((_let_1 (@ tptp.image_o_Product_unit2 F))) (let ((_let_2 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit9161856309968323677t_unit _let_2) (= (@ tptp.comple2584293577114468500t_unit (@ _let_1 (@ (@ tptp.insert_o A2) A))) (@ (@ tptp.inf_inf_Product_unit (@ F A2)) (@ tptp.comple2584293577114468500t_unit _let_2)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.product_unit)) (A2 tptp.nat)) (let ((_let_1 (@ tptp.image_8730104196221521654t_unit F))) (let ((_let_2 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit9161856309968323677t_unit _let_2) (= (@ tptp.comple2584293577114468500t_unit (@ _let_1 (@ (@ tptp.insert_nat A2) A))) (@ (@ tptp.inf_inf_Product_unit (@ F A2)) (@ tptp.comple2584293577114468500t_unit _let_2)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.product_unit)) (A2 tptp.int)) (let ((_let_1 (@ tptp.image_5846526143423701914t_unit F))) (let ((_let_2 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit9161856309968323677t_unit _let_2) (= (@ tptp.comple2584293577114468500t_unit (@ _let_1 (@ (@ tptp.insert_int A2) A))) (@ (@ tptp.inf_inf_Product_unit (@ F A2)) (@ tptp.comple2584293577114468500t_unit _let_2)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.set_nat)) (A2 tptp.product_unit)) (let ((_let_1 (@ tptp.image_8173849991827986510et_nat F))) (let ((_let_2 (@ _let_1 A))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit68592940725977398et_nat _let_2) (= (@ tptp.comple7806235888213564991et_nat (@ _let_1 (@ (@ tptp.insert_Product_unit A2) A))) (@ (@ tptp.inf_inf_set_nat (@ F A2)) (@ tptp.comple7806235888213564991et_nat _let_2)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.set_nat)) (A2 Bool)) (let ((_let_1 (@ tptp.image_o_set_nat F))) (let ((_let_2 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit68592940725977398et_nat _let_2) (= (@ tptp.comple7806235888213564991et_nat (@ _let_1 (@ (@ tptp.insert_o A2) A))) (@ (@ tptp.inf_inf_set_nat (@ F A2)) (@ tptp.comple7806235888213564991et_nat _let_2)))))))))
% 5.65/5.94 (assert (= tptp.power_8256067586552552935nteger (lambda ((P5 tptp.code_integer) (M3 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= M3 tptp.zero_zero_nat)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger P5) (@ (@ tptp.power_8256067586552552935nteger P5) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.65/5.94 (assert (= tptp.power_7079662738309270450atural (lambda ((P5 tptp.code_natural) (M3 tptp.nat)) (@ (@ (@ tptp.if_Code_natural (= M3 tptp.zero_zero_nat)) tptp.one_one_Code_natural) (@ (@ tptp.times_2397367101498566445atural P5) (@ (@ tptp.power_7079662738309270450atural P5) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.65/5.94 (assert (= tptp.power_power_assn (lambda ((P5 tptp.assn) (M3 tptp.nat)) (@ (@ (@ tptp.if_assn (= M3 tptp.zero_zero_nat)) tptp.one_one_assn) (@ (@ tptp.times_times_assn P5) (@ (@ tptp.power_power_assn P5) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.65/5.94 (assert (= tptp.power_power_rat (lambda ((P5 tptp.rat) (M3 tptp.nat)) (@ (@ (@ tptp.if_rat (= M3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P5) (@ (@ tptp.power_power_rat P5) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.65/5.94 (assert (= tptp.power_power_nat (lambda ((P5 tptp.nat) (M3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P5) (@ (@ tptp.power_power_nat P5) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.65/5.94 (assert (= tptp.power_power_int (lambda ((P5 tptp.int) (M3 tptp.nat)) (@ (@ (@ tptp.if_int (= M3 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P5) (@ (@ tptp.power_power_int P5) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (A2 tptp.assn)) (let ((_let_1 (@ tptp.power_power_assn A2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A2) (@ _let_1 N2))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A2) (@ _let_1 N2))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (A2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A2) (@ _let_1 N2))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A2) (@ _let_1 N2))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.nat)) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.image_875570014554754200it_nat F))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ _let_1 A))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit1738341127787009408ow_nat _let_3) (=> (not (= B4 tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit1738341127787009408ow_nat _let_2) (= (@ tptp.complete_Inf_Inf_nat (@ _let_1 (@ (@ tptp.sup_su793286257634532545t_unit A) B4))) (@ (@ tptp.inf_inf_nat (@ tptp.complete_Inf_Inf_nat _let_3)) (@ tptp.complete_Inf_Inf_nat _let_2))))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.nat)) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.image_o_nat2 F))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit1738341127787009408ow_nat _let_3) (=> (not (= B4 tptp.bot_bot_set_o)) (=> (@ tptp.condit1738341127787009408ow_nat _let_2) (= (@ tptp.complete_Inf_Inf_nat (@ _let_1 (@ (@ tptp.sup_sup_set_o A) B4))) (@ (@ tptp.inf_inf_nat (@ tptp.complete_Inf_Inf_nat _let_3)) (@ tptp.complete_Inf_Inf_nat _let_2))))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat)) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_nat2 F))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit1738341127787009408ow_nat _let_3) (=> (not (= B4 tptp.bot_bot_set_nat)) (=> (@ tptp.condit1738341127787009408ow_nat _let_2) (= (@ tptp.complete_Inf_Inf_nat (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4))) (@ (@ tptp.inf_inf_nat (@ tptp.complete_Inf_Inf_nat _let_3)) (@ tptp.complete_Inf_Inf_nat _let_2))))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.nat)) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.image_int_nat2 F))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit1738341127787009408ow_nat _let_3) (=> (not (= B4 tptp.bot_bot_set_int)) (=> (@ tptp.condit1738341127787009408ow_nat _let_2) (= (@ tptp.complete_Inf_Inf_nat (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B4))) (@ (@ tptp.inf_inf_nat (@ tptp.complete_Inf_Inf_nat _let_3)) (@ tptp.complete_Inf_Inf_nat _let_2))))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.product_unit)) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.image_405062704495631173t_unit F))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ _let_1 A))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit9161856309968323677t_unit _let_3) (=> (not (= B4 tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit9161856309968323677t_unit _let_2) (= (@ tptp.comple2584293577114468500t_unit (@ _let_1 (@ (@ tptp.sup_su793286257634532545t_unit A) B4))) (@ (@ tptp.inf_inf_Product_unit (@ tptp.comple2584293577114468500t_unit _let_3)) (@ tptp.comple2584293577114468500t_unit _let_2))))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.product_unit)) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.image_o_Product_unit2 F))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit9161856309968323677t_unit _let_3) (=> (not (= B4 tptp.bot_bot_set_o)) (=> (@ tptp.condit9161856309968323677t_unit _let_2) (= (@ tptp.comple2584293577114468500t_unit (@ _let_1 (@ (@ tptp.sup_sup_set_o A) B4))) (@ (@ tptp.inf_inf_Product_unit (@ tptp.comple2584293577114468500t_unit _let_3)) (@ tptp.comple2584293577114468500t_unit _let_2))))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.product_unit)) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_8730104196221521654t_unit F))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.condit9161856309968323677t_unit _let_3) (=> (not (= B4 tptp.bot_bot_set_nat)) (=> (@ tptp.condit9161856309968323677t_unit _let_2) (= (@ tptp.comple2584293577114468500t_unit (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4))) (@ (@ tptp.inf_inf_Product_unit (@ tptp.comple2584293577114468500t_unit _let_3)) (@ tptp.comple2584293577114468500t_unit _let_2))))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.product_unit)) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.image_5846526143423701914t_unit F))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.condit9161856309968323677t_unit _let_3) (=> (not (= B4 tptp.bot_bot_set_int)) (=> (@ tptp.condit9161856309968323677t_unit _let_2) (= (@ tptp.comple2584293577114468500t_unit (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B4))) (@ (@ tptp.inf_inf_Product_unit (@ tptp.comple2584293577114468500t_unit _let_3)) (@ tptp.comple2584293577114468500t_unit _let_2))))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.set_nat)) (B4 tptp.set_Product_unit)) (let ((_let_1 (@ tptp.image_8173849991827986510et_nat F))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ _let_1 A))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit68592940725977398et_nat _let_3) (=> (not (= B4 tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.condit68592940725977398et_nat _let_2) (= (@ tptp.comple7806235888213564991et_nat (@ _let_1 (@ (@ tptp.sup_su793286257634532545t_unit A) B4))) (@ (@ tptp.inf_inf_set_nat (@ tptp.comple7806235888213564991et_nat _let_3)) (@ tptp.comple7806235888213564991et_nat _let_2))))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.set_nat)) (B4 tptp.set_o)) (let ((_let_1 (@ tptp.image_o_set_nat F))) (let ((_let_2 (@ _let_1 B4))) (let ((_let_3 (@ _let_1 A))) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.condit68592940725977398et_nat _let_3) (=> (not (= B4 tptp.bot_bot_set_o)) (=> (@ tptp.condit68592940725977398et_nat _let_2) (= (@ tptp.comple7806235888213564991et_nat (@ _let_1 (@ (@ tptp.sup_sup_set_o A) B4))) (@ (@ tptp.inf_inf_set_nat (@ tptp.comple7806235888213564991et_nat _let_3)) (@ tptp.comple7806235888213564991et_nat _let_2))))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups7873554091576472773nteger G))) (=> (@ tptp.finite_finite_int A) (=> (not (@ (@ tptp.member_int X) A)) (= (@ _let_1 (@ (@ tptp.insert_int X) A)) (@ (@ tptp.plus_p5714425477246183910nteger (@ G X)) (@ _let_1 A))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (X Bool) (G (-> Bool tptp.code_integer))) (let ((_let_1 (@ tptp.groups4406642042086082107nteger G))) (=> (@ tptp.finite_finite_o A) (=> (not (@ (@ tptp.member_o X) A)) (= (@ _let_1 (@ (@ tptp.insert_o X) A)) (@ (@ tptp.plus_p5714425477246183910nteger (@ G X)) (@ _let_1 A))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit) (G (-> tptp.product_unit tptp.code_integer))) (let ((_let_1 (@ tptp.groups5393439102872367408nteger G))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (@ (@ tptp.member_Product_unit X) A)) (= (@ _let_1 (@ (@ tptp.insert_Product_unit X) A)) (@ (@ tptp.plus_p5714425477246183910nteger (@ G X)) (@ _let_1 A))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups7501900531339628137nteger G))) (=> (@ tptp.finite_finite_nat A) (=> (not (@ (@ tptp.member_nat X) A)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A)) (@ (@ tptp.plus_p5714425477246183910nteger (@ G X)) (@ _let_1 A))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups879477027807139574nteger G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (@ (@ tptp.member_Code_integer X) A)) (= (@ _let_1 (@ (@ tptp.insert_Code_integer X) A)) (@ (@ tptp.plus_p5714425477246183910nteger (@ G X)) (@ _let_1 A))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A) (=> (not (@ (@ tptp.member_int X) A)) (= (@ _let_1 (@ (@ tptp.insert_int X) A)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 A))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (X Bool) (G (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat G))) (=> (@ tptp.finite_finite_o A) (=> (not (@ (@ tptp.member_o X) A)) (= (@ _let_1 (@ (@ tptp.insert_o X) A)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 A))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit) (G (-> tptp.product_unit tptp.rat))) (let ((_let_1 (@ tptp.groups8131667117488461483it_rat G))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (@ (@ tptp.member_Product_unit X) A)) (= (@ _let_1 (@ (@ tptp.insert_Product_unit X) A)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 A))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A) (=> (not (@ (@ tptp.member_nat X) A)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 A))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (@ (@ tptp.member_Code_integer X) A)) (= (@ _let_1 (@ (@ tptp.insert_Code_integer X) A)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 A))))))))
% 5.65/5.94 (assert (forall ((G (-> tptp.product_unit tptp.nat))) (= (@ (@ tptp.groups8766797177574957219it_nat G) tptp.bot_bo3957492148770167129t_unit) tptp.zero_zero_nat)))
% 5.65/5.94 (assert (forall ((G (-> tptp.product_unit tptp.int))) (= (@ (@ tptp.groups8764306707065906943it_int G) tptp.bot_bo3957492148770167129t_unit) tptp.zero_zero_int)))
% 5.65/5.94 (assert (forall ((G (-> tptp.product_unit tptp.code_integer))) (= (@ (@ tptp.groups5393439102872367408nteger G) tptp.bot_bo3957492148770167129t_unit) tptp.zero_z3403309356797280102nteger)))
% 5.65/5.94 (assert (forall ((G (-> Bool tptp.nat))) (= (@ (@ tptp.groups8507830703676809646_o_nat G) tptp.bot_bot_set_o) tptp.zero_zero_nat)))
% 5.65/5.94 (assert (forall ((G (-> Bool tptp.int))) (= (@ (@ tptp.groups8505340233167759370_o_int G) tptp.bot_bot_set_o) tptp.zero_zero_int)))
% 5.65/5.94 (assert (forall ((G (-> Bool tptp.code_integer))) (= (@ (@ tptp.groups4406642042086082107nteger G) tptp.bot_bot_set_o) tptp.zero_z3403309356797280102nteger)))
% 5.65/5.94 (assert (forall ((G (-> tptp.nat tptp.int))) (= (@ (@ tptp.groups3539618377306564664at_int G) tptp.bot_bot_set_nat) tptp.zero_zero_int)))
% 5.65/5.94 (assert (forall ((G (-> tptp.nat tptp.code_integer))) (= (@ (@ tptp.groups7501900531339628137nteger G) tptp.bot_bot_set_nat) tptp.zero_z3403309356797280102nteger)))
% 5.65/5.94 (assert (forall ((G (-> tptp.int tptp.nat))) (= (@ (@ tptp.groups4541462559716669496nt_nat G) tptp.bot_bot_set_int) tptp.zero_zero_nat)))
% 5.65/5.94 (assert (forall ((G (-> tptp.int tptp.code_integer))) (= (@ (@ tptp.groups7873554091576472773nteger G) tptp.bot_bot_set_int) tptp.zero_z3403309356797280102nteger)))
% 5.65/5.94 (assert (forall ((I2 tptp.code_integer) (A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer))) (=> (@ (@ tptp.member_Code_integer I2) A) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer I2) tptp.bot_bo3990330152332043303nteger))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (=> (@ tptp.finite6017078050557962740nteger A) (@ (@ tptp.ord_le3102999989581377725nteger (@ F I2)) (@ (@ tptp.groups879477027807139574nteger F) A)))))))
% 5.65/5.94 (assert (forall ((I2 tptp.product_unit) (A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.code_integer))) (=> (@ (@ tptp.member_Product_unit I2) A) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit I2) tptp.bot_bo3957492148770167129t_unit))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (=> (@ tptp.finite4290736615968046902t_unit A) (@ (@ tptp.ord_le3102999989581377725nteger (@ F I2)) (@ (@ tptp.groups5393439102872367408nteger F) A)))))))
% 5.65/5.94 (assert (forall ((I2 Bool) (A tptp.set_o) (F (-> Bool tptp.code_integer))) (=> (@ (@ tptp.member_o I2) A) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o I2) tptp.bot_bot_set_o))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (=> (@ tptp.finite_finite_o A) (@ (@ tptp.ord_le3102999989581377725nteger (@ F I2)) (@ (@ tptp.groups4406642042086082107nteger F) A)))))))
% 5.65/5.94 (assert (forall ((I2 tptp.int) (A tptp.set_int) (F (-> tptp.int tptp.code_integer))) (=> (@ (@ tptp.member_int I2) A) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int I2) tptp.bot_bot_set_int))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (=> (@ tptp.finite_finite_int A) (@ (@ tptp.ord_le3102999989581377725nteger (@ F I2)) (@ (@ tptp.groups7873554091576472773nteger F) A)))))))
% 5.65/5.94 (assert (forall ((I2 tptp.nat) (A tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (=> (@ (@ tptp.member_nat I2) A) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat A) (@ (@ tptp.insert_nat I2) tptp.bot_bot_set_nat))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (=> (@ tptp.finite_finite_nat A) (@ (@ tptp.ord_le3102999989581377725nteger (@ F I2)) (@ (@ tptp.groups7501900531339628137nteger F) A)))))))
% 5.65/5.94 (assert (forall ((I2 tptp.code_integer) (A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (=> (@ (@ tptp.member_Code_integer I2) A) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer I2) tptp.bot_bo3990330152332043303nteger))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (=> (@ tptp.finite6017078050557962740nteger A) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ (@ tptp.groups6602215022474089585er_rat F) A)))))))
% 5.65/5.94 (assert (forall ((I2 tptp.product_unit) (A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.rat))) (=> (@ (@ tptp.member_Product_unit I2) A) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit I2) tptp.bot_bo3957492148770167129t_unit))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (=> (@ tptp.finite4290736615968046902t_unit A) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ (@ tptp.groups8131667117488461483it_rat F) A)))))))
% 5.65/5.94 (assert (forall ((I2 Bool) (A tptp.set_o) (F (-> Bool tptp.rat))) (=> (@ (@ tptp.member_o I2) A) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o I2) tptp.bot_bot_set_o))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (=> (@ tptp.finite_finite_o A) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ (@ tptp.groups7872700643590313910_o_rat F) A)))))))
% 5.65/5.94 (assert (forall ((I2 tptp.int) (A tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ (@ tptp.member_int I2) A) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int I2) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (=> (@ tptp.finite_finite_int A) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ (@ tptp.groups3906332499630173760nt_rat F) A)))))))
% 5.65/5.94 (assert (forall ((I2 tptp.nat) (A tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.member_nat I2) A) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat A) (@ (@ tptp.insert_nat I2) tptp.bot_bot_set_nat))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (=> (@ tptp.finite_finite_nat A) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ (@ tptp.groups2906978787729119204at_rat F) A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups879477027807139574nteger G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite6017078050557962740nteger B4) (=> (= (@ (@ tptp.inf_in1364745209274528805nteger A) B4) tptp.bot_bo3990330152332043303nteger) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A) B4)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite6017078050557962740nteger B4) (=> (= (@ (@ tptp.inf_in1364745209274528805nteger A) B4) tptp.bot_bo3990330152332043303nteger) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A) B4)) (@ (@ tptp.plus_plus_rat (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite6017078050557962740nteger B4) (=> (= (@ (@ tptp.inf_in1364745209274528805nteger A) B4) tptp.bot_bo3990330152332043303nteger) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A) B4)) (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite6017078050557962740nteger B4) (=> (= (@ (@ tptp.inf_in1364745209274528805nteger A) B4) tptp.bot_bo3990330152332043303nteger) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A) B4)) (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit) (G (-> tptp.product_unit tptp.code_integer))) (let ((_let_1 (@ tptp.groups5393439102872367408nteger G))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ tptp.finite4290736615968046902t_unit B4) (=> (= (@ (@ tptp.inf_in4660618365625256667t_unit A) B4) tptp.bot_bo3957492148770167129t_unit) (= (@ _let_1 (@ (@ tptp.sup_su793286257634532545t_unit A) B4)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit) (G (-> tptp.product_unit tptp.rat))) (let ((_let_1 (@ tptp.groups8131667117488461483it_rat G))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ tptp.finite4290736615968046902t_unit B4) (=> (= (@ (@ tptp.inf_in4660618365625256667t_unit A) B4) tptp.bot_bo3957492148770167129t_unit) (= (@ _let_1 (@ (@ tptp.sup_su793286257634532545t_unit A) B4)) (@ (@ tptp.plus_plus_rat (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit) (G (-> tptp.product_unit tptp.nat))) (let ((_let_1 (@ tptp.groups8766797177574957219it_nat G))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ tptp.finite4290736615968046902t_unit B4) (=> (= (@ (@ tptp.inf_in4660618365625256667t_unit A) B4) tptp.bot_bo3957492148770167129t_unit) (= (@ _let_1 (@ (@ tptp.sup_su793286257634532545t_unit A) B4)) (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit) (G (-> tptp.product_unit tptp.int))) (let ((_let_1 (@ tptp.groups8764306707065906943it_int G))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ tptp.finite4290736615968046902t_unit B4) (=> (= (@ (@ tptp.inf_in4660618365625256667t_unit A) B4) tptp.bot_bo3957492148770167129t_unit) (= (@ _let_1 (@ (@ tptp.sup_su793286257634532545t_unit A) B4)) (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (B4 tptp.set_o) (G (-> Bool tptp.code_integer))) (let ((_let_1 (@ tptp.groups4406642042086082107nteger G))) (=> (@ tptp.finite_finite_o A) (=> (@ tptp.finite_finite_o B4) (=> (= (@ (@ tptp.inf_inf_set_o A) B4) tptp.bot_bot_set_o) (= (@ _let_1 (@ (@ tptp.sup_sup_set_o A) B4)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (B4 tptp.set_o) (G (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat G))) (=> (@ tptp.finite_finite_o A) (=> (@ tptp.finite_finite_o B4) (=> (= (@ (@ tptp.inf_inf_set_o A) B4) tptp.bot_bot_set_o) (= (@ _let_1 (@ (@ tptp.sup_sup_set_o A) B4)) (@ (@ tptp.plus_plus_rat (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (A2 tptp.code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer A2) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_4 (@ (@ tptp.member_Code_integer A2) A))) (=> (@ tptp.finite6017078050557962740nteger A) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (A2 tptp.product_unit) (F (-> tptp.product_unit tptp.rat))) (let ((_let_1 (@ tptp.groups8131667117488461483it_rat F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit))))) (let ((_let_4 (@ (@ tptp.member_Product_unit A2) A))) (=> (@ tptp.finite4290736615968046902t_unit A) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (A2 Bool) (F (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))))) (let ((_let_4 (@ (@ tptp.member_o A2) A))) (=> (@ tptp.finite_finite_o A) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (A2 tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A2) A))) (=> (@ tptp.finite_finite_int A) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (A2 tptp.code_integer) (F (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer A2) tptp.bot_bo3990330152332043303nteger))))) (let ((_let_4 (@ (@ tptp.member_Code_integer A2) A))) (=> (@ tptp.finite6017078050557962740nteger A) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (A2 tptp.product_unit) (F (-> tptp.product_unit tptp.int))) (let ((_let_1 (@ tptp.groups8764306707065906943it_int F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit))))) (let ((_let_4 (@ (@ tptp.member_Product_unit A2) A))) (=> (@ tptp.finite4290736615968046902t_unit A) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (A2 Bool) (F (-> Bool tptp.int))) (let ((_let_1 (@ tptp.groups8505340233167759370_o_int F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))))) (let ((_let_4 (@ (@ tptp.member_o A2) A))) (=> (@ tptp.finite_finite_o A) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (A2 tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A2) A))) (=> (@ tptp.finite_finite_nat A) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_rat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (A2 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A2) A))) (=> (@ tptp.finite_finite_nat A) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (A2 tptp.int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A2) A))) (=> (@ tptp.finite_finite_int A) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_int _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups879477027807139574nteger G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ (@ tptp.member_Code_integer X) A) (= (@ _let_1 A) (@ (@ tptp.plus_p5714425477246183910nteger (@ G X)) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer X) tptp.bot_bo3990330152332043303nteger))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ (@ tptp.member_Code_integer X) A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer X) tptp.bot_bo3990330152332043303nteger))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ (@ tptp.member_Code_integer X) A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer X) tptp.bot_bo3990330152332043303nteger))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ (@ tptp.member_Code_integer X) A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer X) tptp.bot_bo3990330152332043303nteger))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit) (G (-> tptp.product_unit tptp.code_integer))) (let ((_let_1 (@ tptp.groups5393439102872367408nteger G))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ (@ tptp.member_Product_unit X) A) (= (@ _let_1 A) (@ (@ tptp.plus_p5714425477246183910nteger (@ G X)) (@ _let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit) (G (-> tptp.product_unit tptp.rat))) (let ((_let_1 (@ tptp.groups8131667117488461483it_rat G))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ (@ tptp.member_Product_unit X) A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit) (G (-> tptp.product_unit tptp.nat))) (let ((_let_1 (@ tptp.groups8766797177574957219it_nat G))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ (@ tptp.member_Product_unit X) A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit) (G (-> tptp.product_unit tptp.int))) (let ((_let_1 (@ tptp.groups8764306707065906943it_int G))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ (@ tptp.member_Product_unit X) A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (X Bool) (G (-> Bool tptp.code_integer))) (let ((_let_1 (@ tptp.groups4406642042086082107nteger G))) (=> (@ tptp.finite_finite_o A) (=> (@ (@ tptp.member_o X) A) (= (@ _let_1 A) (@ (@ tptp.plus_p5714425477246183910nteger (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (X Bool) (G (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat G))) (=> (@ tptp.finite_finite_o A) (=> (@ (@ tptp.member_o X) A) (= (@ _let_1 A) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer)) (X tptp.code_integer)) (let ((_let_1 (@ tptp.insert_Code_integer X))) (let ((_let_2 (@ tptp.groups879477027807139574nteger G))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.plus_p5714425477246183910nteger (@ G X)) (@ _let_2 (@ (@ tptp.minus_2355218937544613996nteger A) (@ _let_1 tptp.bot_bo3990330152332043303nteger))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (X tptp.code_integer)) (let ((_let_1 (@ tptp.insert_Code_integer X))) (let ((_let_2 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_2 (@ (@ tptp.minus_2355218937544613996nteger A) (@ _let_1 tptp.bot_bo3990330152332043303nteger))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat)) (X tptp.code_integer)) (let ((_let_1 (@ tptp.insert_Code_integer X))) (let ((_let_2 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_2355218937544613996nteger A) (@ _let_1 tptp.bot_bo3990330152332043303nteger))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int)) (X tptp.code_integer)) (let ((_let_1 (@ tptp.insert_Code_integer X))) (let ((_let_2 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_2355218937544613996nteger A) (@ _let_1 tptp.bot_bo3990330152332043303nteger))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (G (-> tptp.product_unit tptp.code_integer)) (X tptp.product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit X))) (let ((_let_2 (@ tptp.groups5393439102872367408nteger G))) (=> (@ tptp.finite4290736615968046902t_unit A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.plus_p5714425477246183910nteger (@ G X)) (@ _let_2 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ _let_1 tptp.bot_bo3957492148770167129t_unit))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (G (-> tptp.product_unit tptp.rat)) (X tptp.product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit X))) (let ((_let_2 (@ tptp.groups8131667117488461483it_rat G))) (=> (@ tptp.finite4290736615968046902t_unit A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_2 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ _let_1 tptp.bot_bo3957492148770167129t_unit))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (G (-> tptp.product_unit tptp.nat)) (X tptp.product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit X))) (let ((_let_2 (@ tptp.groups8766797177574957219it_nat G))) (=> (@ tptp.finite4290736615968046902t_unit A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ _let_1 tptp.bot_bo3957492148770167129t_unit))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (G (-> tptp.product_unit tptp.int)) (X tptp.product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit X))) (let ((_let_2 (@ tptp.groups8764306707065906943it_int G))) (=> (@ tptp.finite4290736615968046902t_unit A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ _let_1 tptp.bot_bo3957492148770167129t_unit))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (G (-> Bool tptp.code_integer)) (X Bool)) (let ((_let_1 (@ tptp.insert_o X))) (let ((_let_2 (@ tptp.groups4406642042086082107nteger G))) (=> (@ tptp.finite_finite_o A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.plus_p5714425477246183910nteger (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_o A) (@ _let_1 tptp.bot_bot_set_o))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (G (-> Bool tptp.rat)) (X Bool)) (let ((_let_1 (@ tptp.insert_o X))) (let ((_let_2 (@ tptp.groups7872700643590313910_o_rat G))) (=> (@ tptp.finite_finite_o A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_o A) (@ _let_1 tptp.bot_bot_set_o))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups7237345082560585321er_nat F) A)) (@ (@ tptp.groups7237345082560585321er_nat G) A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.nat)) (G (-> tptp.product_unit tptp.nat))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) A) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups8766797177574957219it_nat F) A)) (@ (@ tptp.groups8766797177574957219it_nat G) A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.nat)) (G (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups8507830703676809646_o_nat F) A)) (@ (@ tptp.groups8507830703676809646_o_nat G) A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A)) (@ (@ tptp.groups4541462559716669496nt_nat G) A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int)) (G (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A) (@ (@ tptp.ord_less_int (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups7234854612051535045er_int F) A)) (@ (@ tptp.groups7234854612051535045er_int G) A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.int)) (G (-> tptp.product_unit tptp.int))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) A) (@ (@ tptp.ord_less_int (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups8764306707065906943it_int F) A)) (@ (@ tptp.groups8764306707065906943it_int G) A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.int)) (G (-> Bool tptp.int))) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (@ (@ tptp.ord_less_int (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups8505340233167759370_o_int F) A)) (@ (@ tptp.groups8505340233167759370_o_int G) A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (@ (@ tptp.ord_less_int (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) A)) (@ (@ tptp.groups3539618377306564664at_int G) A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A) (@ (@ tptp.ord_le6747313008572928689nteger (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.groups879477027807139574nteger F) A)) (@ (@ tptp.groups879477027807139574nteger G) A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.code_integer)) (G (-> tptp.product_unit tptp.code_integer))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) A) (@ (@ tptp.ord_le6747313008572928689nteger (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.groups5393439102872367408nteger F) A)) (@ (@ tptp.groups5393439102872367408nteger G) A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups7873554091576472773nteger G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A)))) (let ((_let_4 (@ (@ tptp.member_int X) A))) (=> (@ tptp.finite_finite_int A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger (@ G X)) _let_2)))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (X Bool) (G (-> Bool tptp.code_integer))) (let ((_let_1 (@ tptp.groups4406642042086082107nteger G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_o X) A)))) (let ((_let_4 (@ (@ tptp.member_o X) A))) (=> (@ tptp.finite_finite_o A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger (@ G X)) _let_2)))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit) (G (-> tptp.product_unit tptp.code_integer))) (let ((_let_1 (@ tptp.groups5393439102872367408nteger G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Product_unit X) A)))) (let ((_let_4 (@ (@ tptp.member_Product_unit X) A))) (=> (@ tptp.finite4290736615968046902t_unit A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger (@ G X)) _let_2)))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups7501900531339628137nteger G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X) A)))) (let ((_let_4 (@ (@ tptp.member_nat X) A))) (=> (@ tptp.finite_finite_nat A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger (@ G X)) _let_2)))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups879477027807139574nteger G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Code_integer X) A)))) (let ((_let_4 (@ (@ tptp.member_Code_integer X) A))) (=> (@ tptp.finite6017078050557962740nteger A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger (@ G X)) _let_2)))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A)))) (let ((_let_4 (@ (@ tptp.member_int X) A))) (=> (@ tptp.finite_finite_int A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X)) _let_2)))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (X Bool) (G (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_o X) A)))) (let ((_let_4 (@ (@ tptp.member_o X) A))) (=> (@ tptp.finite_finite_o A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X)) _let_2)))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit) (G (-> tptp.product_unit tptp.rat))) (let ((_let_1 (@ tptp.groups8131667117488461483it_rat G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Product_unit X) A)))) (let ((_let_4 (@ (@ tptp.member_Product_unit X) A))) (=> (@ tptp.finite4290736615968046902t_unit A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X)) _let_2)))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X) A)))) (let ((_let_4 (@ (@ tptp.member_nat X) A))) (=> (@ tptp.finite_finite_nat A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X)) _let_2)))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Code_integer X) A)))) (let ((_let_4 (@ (@ tptp.member_Code_integer X) A))) (=> (@ tptp.finite6017078050557962740nteger A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X)) _let_2)))))))))))
% 5.65/5.94 (assert (forall ((I tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger I) (=> (not (= I tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups7237345082560585321er_nat F) I)))))))
% 5.65/5.94 (assert (forall ((I tptp.set_Product_unit) (F (-> tptp.product_unit tptp.nat))) (=> (@ tptp.finite4290736615968046902t_unit I) (=> (not (= I tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) I) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups8766797177574957219it_nat F) I)))))))
% 5.65/5.94 (assert (forall ((I tptp.set_o) (F (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o I) (=> (not (= I tptp.bot_bot_set_o)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups8507830703676809646_o_nat F) I)))))))
% 5.65/5.94 (assert (forall ((I tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int I) (=> (not (= I tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) I)))))))
% 5.65/5.94 (assert (forall ((I tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger I) (=> (not (= I tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I3)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups7234854612051535045er_int F) I)))))))
% 5.65/5.94 (assert (forall ((I tptp.set_Product_unit) (F (-> tptp.product_unit tptp.int))) (=> (@ tptp.finite4290736615968046902t_unit I) (=> (not (= I tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) I) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I3)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups8764306707065906943it_int F) I)))))))
% 5.65/5.94 (assert (forall ((I tptp.set_o) (F (-> Bool tptp.int))) (=> (@ tptp.finite_finite_o I) (=> (not (= I tptp.bot_bot_set_o)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I3)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups8505340233167759370_o_int F) I)))))))
% 5.65/5.94 (assert (forall ((I tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat I) (=> (not (= I tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I3)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups3539618377306564664at_int F) I)))))))
% 5.65/5.94 (assert (forall ((I tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger I) (=> (not (= I tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ F I3)))) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.groups879477027807139574nteger F) I)))))))
% 5.65/5.94 (assert (forall ((I tptp.set_Product_unit) (F (-> tptp.product_unit tptp.code_integer))) (=> (@ tptp.finite4290736615968046902t_unit I) (=> (not (= I tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) I) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ F I3)))) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.groups5393439102872367408nteger F) I)))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_set_nat) (G (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) C5) (@ tptp.finite_finite_nat X3))) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) C5) (forall ((Xa3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa3) C5) (=> (not (= X3 Xa3)) (= (@ (@ tptp.inf_inf_set_nat X3) Xa3) tptp.bot_bot_set_nat)))))) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.comple7399068483239264473et_nat C5)) (@ (@ (@ (@ tptp.comp_s5456809700045850692at_nat tptp.groups8294997508430121362at_nat) tptp.groups3542108847815614940at_nat) G) C5))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_set_int) (G (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.set_int)) (=> (@ (@ tptp.member_set_int X3) C5) (@ tptp.finite_finite_int X3))) (=> (forall ((X3 tptp.set_int)) (=> (@ (@ tptp.member_set_int X3) C5) (forall ((Xa3 tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa3) C5) (=> (not (= X3 Xa3)) (= (@ (@ tptp.inf_inf_set_int X3) Xa3) tptp.bot_bot_set_int)))))) (= (@ (@ tptp.groups4538972089207619220nt_int G) (@ tptp.comple3221217463730067765et_int C5)) (@ (@ (@ (@ tptp.comp_s9098231955081793132nt_int tptp.groups1256056575759317066nt_int) tptp.groups4538972089207619220nt_int) G) C5))))))
% 5.65/5.94 (assert (forall ((A2 tptp.product_unit) (A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.nat))) (let ((_let_1 (@ tptp.groups8766797177574957219it_nat F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit A2) tptp.bot_bo3957492148770167129t_unit))))) (let ((_let_4 (@ (@ tptp.member_Product_unit A2) A))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 5.65/5.94 (assert (forall ((A2 Bool) (A tptp.set_o) (F (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.groups8507830703676809646_o_nat F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o A2) tptp.bot_bot_set_o))))) (let ((_let_4 (@ (@ tptp.member_o A2) A))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (A tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int A2) tptp.bot_bot_set_int))))) (let ((_let_4 (@ (@ tptp.member_int A2) A))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 5.65/5.94 (assert (forall ((A2 (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o) (F (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.nat))) (let ((_let_1 (@ tptp.groups6742167275697360483_o_nat F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_1801376950450012436_nat_o A) (@ (@ tptp.insert5175938949040314269_nat_o A2) tptp.bot_bo7824918357723582233_nat_o))))) (let ((_let_4 (@ (@ tptp.member6576561426505652726_nat_o A2) A))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (A tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) (@ (@ tptp.insert_nat A2) tptp.bot_bot_set_nat))))) (let ((_let_4 (@ (@ tptp.member_nat A2) A))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A2)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (not (= A2 tptp.zero_zero_nat)) (exists ((D tptp.nat) (X3 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D))) (and (@ _let_1 A2) (@ _let_1 B) (= (@ (@ tptp.times_times_nat A2) X3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y2)) D))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (exists ((D tptp.nat) (X3 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D))) (and (@ _let_3 A2) (@ _let_3 B) (or (= (@ (@ tptp.minus_minus_nat (@ _let_1 X3)) (@ _let_2 Y2)) D) (= (@ (@ tptp.minus_minus_nat (@ _let_2 X3)) (@ _let_1 Y2)) D)))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (exists ((D tptp.nat) (X3 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D))) (and (@ _let_3 A2) (@ _let_3 B) (or (= (@ _let_1 X3) (@ (@ tptp.plus_plus_nat (@ _let_2 Y2)) D)) (= (@ _let_2 X3) (@ (@ tptp.plus_plus_nat (@ _let_1 Y2)) D))))))))))
% 5.65/5.94 (assert (forall ((D2 tptp.nat) (A2 tptp.nat) (B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D2))) (=> (@ _let_3 A2) (=> (@ _let_3 B) (=> (or (= (@ _let_1 X) (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) D2)) (= (@ _let_2 X) (@ (@ tptp.plus_plus_nat (@ _let_1 Y)) D2))) (exists ((X3 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A2))) (let ((_let_2 (@ (@ tptp.plus_plus_nat A2) B))) (let ((_let_3 (@ tptp.times_times_nat _let_2))) (let ((_let_4 (@ tptp.dvd_dvd_nat D2))) (and (@ _let_4 A2) (@ _let_4 _let_2) (or (= (@ _let_1 X3) (@ (@ tptp.plus_plus_nat (@ _let_3 Y2)) D2)) (= (@ _let_3 X3) (@ (@ tptp.plus_plus_nat (@ _let_1 Y2)) D2)))))))))))))))))
% 5.65/5.94 (assert (forall ((P3 tptp.nat) (A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat P3) (@ (@ tptp.times_times_nat A2) B)) (not (forall ((X3 tptp.nat) (Y2 tptp.nat)) (=> (= P3 (@ (@ tptp.times_times_nat X3) Y2)) (=> (@ (@ tptp.dvd_dvd_nat X3) A2) (not (@ (@ tptp.dvd_dvd_nat Y2) B)))))))))
% 5.65/5.94 (assert (forall ((P3 tptp.int) (A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int P3) (@ (@ tptp.times_times_int A2) B)) (not (forall ((X3 tptp.int) (Y2 tptp.int)) (=> (= P3 (@ (@ tptp.times_times_int X3) Y2)) (=> (@ (@ tptp.dvd_dvd_int X3) A2) (not (@ (@ tptp.dvd_dvd_int Y2) B)))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) (@ (@ tptp.times_times_nat B) C)) (exists ((B10 tptp.nat) (C8 tptp.nat)) (and (= A2 (@ (@ tptp.times_times_nat B10) C8)) (@ (@ tptp.dvd_dvd_nat B10) B) (@ (@ tptp.dvd_dvd_nat C8) C))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A2) (@ (@ tptp.times_times_int B) C)) (exists ((B10 tptp.int) (C8 tptp.int)) (and (= A2 (@ (@ tptp.times_times_int B10) C8)) (@ (@ tptp.dvd_dvd_int B10) B) (@ (@ tptp.dvd_dvd_int C8) C))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.finite4902975817058060853nteger A)) (@ tptp.lattic8721135487736765967in_nat (@ (@ tptp.image_951025933927791156er_nat F) A)))) (@ (@ tptp.groups7237345082560585321er_nat F) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.finite_card_nat A)) (@ tptp.lattic8721135487736765967in_nat (@ (@ tptp.image_nat_nat2 F) A)))) (@ (@ tptp.groups3542108847815614940at_nat F) A)))))
% 5.65/5.94 (assert (forall ((X tptp.product_unit)) (= (@ tptp.lattic8554435388794137742t_unit (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit)) X)))
% 5.65/5.94 (assert (forall ((X Bool)) (= (@ tptp.lattic1973801136483472281_Min_o (@ (@ tptp.insert_o X) tptp.bot_bot_set_o)) X)))
% 5.65/5.94 (assert (forall ((X tptp.nat)) (= (@ tptp.lattic8721135487736765967in_nat (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)) X)))
% 5.65/5.94 (assert (forall ((X tptp.int)) (= (@ tptp.lattic8718645017227715691in_int (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)) X)))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (= (@ (@ tptp.ord_le3102999989581377725nteger X) (@ tptp.lattic1063845414844153500nteger A)) (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X2) A) (@ (@ tptp.ord_le3102999989581377725nteger X) X2))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (@ (@ tptp.ord_le3221252021190050221t_unit X) (@ tptp.lattic8554435388794137742t_unit A)) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) A) (@ (@ tptp.ord_le3221252021190050221t_unit X) X2))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (= (@ (@ tptp.ord_less_eq_o X) (@ tptp.lattic1973801136483472281_Min_o A)) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A) (@ (@ tptp.ord_less_eq_o X) X2))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_rat) (X tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (= (@ (@ tptp.ord_less_eq_rat X) (@ tptp.lattic8086005427650270231in_rat A)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.member_rat X2) A) (@ (@ tptp.ord_less_eq_rat X) X2))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (= (@ (@ tptp.ord_less_eq_nat X) (@ tptp.lattic8721135487736765967in_nat A)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.ord_less_eq_nat X) X2))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (= (@ (@ tptp.ord_less_eq_int X) (@ tptp.lattic8718645017227715691in_int A)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A) (@ (@ tptp.ord_less_eq_int X) X2))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (@ (@ tptp.ord_le361264281704409273t_unit X) (@ tptp.lattic8554435388794137742t_unit A)) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) A) (@ (@ tptp.ord_le361264281704409273t_unit X) X2))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (= (@ (@ tptp.ord_less_o X) (@ tptp.lattic1973801136483472281_Min_o A)) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A) (@ (@ tptp.ord_less_o X) X2))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (= (@ (@ tptp.ord_less_nat X) (@ tptp.lattic8721135487736765967in_nat A)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.ord_less_nat X) X2))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (= (@ (@ tptp.ord_less_int X) (@ tptp.lattic8718645017227715691in_int A)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A) (@ (@ tptp.ord_less_int X) X2))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (= (@ (@ tptp.ord_le6747313008572928689nteger X) (@ tptp.lattic1063845414844153500nteger A)) (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X2) A) (@ (@ tptp.ord_le6747313008572928689nteger X) X2))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_rat) (X tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (= (@ (@ tptp.ord_less_rat X) (@ tptp.lattic8086005427650270231in_rat A)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.member_rat X2) A) (@ (@ tptp.ord_less_rat X) X2))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (@ (@ tptp.member_Code_integer (@ tptp.lattic1063845414844153500nteger A)) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (@ (@ tptp.member_Product_unit (@ tptp.lattic8554435388794137742t_unit A)) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_o)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (@ (@ tptp.member_o (@ tptp.lattic1973801136483472281_Min_o A)) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.member_nat (@ tptp.lattic8721135487736765967in_nat A)) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.member_int (@ tptp.lattic8718645017227715691in_int A)) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (M4 tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (= (= (@ tptp.lattic1063845414844153500nteger A) M4) (and (@ (@ tptp.member_Code_integer M4) A) (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X2) A) (@ (@ tptp.ord_le3102999989581377725nteger M4) X2)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (M4 tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (= (@ tptp.lattic8554435388794137742t_unit A) M4) (and (@ (@ tptp.member_Product_unit M4) A) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) A) (@ (@ tptp.ord_le3221252021190050221t_unit M4) X2)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (M4 Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (= (= (@ tptp.lattic1973801136483472281_Min_o A) M4) (and (@ (@ tptp.member_o M4) A) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A) (@ (@ tptp.ord_less_eq_o M4) X2)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_rat) (M4 tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (= (= (@ tptp.lattic8086005427650270231in_rat A) M4) (and (@ (@ tptp.member_rat M4) A) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.member_rat X2) A) (@ (@ tptp.ord_less_eq_rat M4) X2)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (M4 tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (= (= (@ tptp.lattic8721135487736765967in_nat A) M4) (and (@ (@ tptp.member_nat M4) A) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.ord_less_eq_nat M4) X2)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (M4 tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (= (= (@ tptp.lattic8718645017227715691in_int A) M4) (and (@ (@ tptp.member_int M4) A) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A) (@ (@ tptp.ord_less_eq_int M4) X2)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.lattic1063845414844153500nteger A)) X) (exists ((X2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X2) A) (@ (@ tptp.ord_le3102999989581377725nteger X2) X))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.lattic8554435388794137742t_unit A)) X) (exists ((X2 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X2) A) (@ (@ tptp.ord_le3221252021190050221t_unit X2) X))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (= (@ (@ tptp.ord_less_eq_o (@ tptp.lattic1973801136483472281_Min_o A)) X) (exists ((X2 Bool)) (and (@ (@ tptp.member_o X2) A) (@ (@ tptp.ord_less_eq_o X2) X))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_rat) (X tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.lattic8086005427650270231in_rat A)) X) (exists ((X2 tptp.rat)) (and (@ (@ tptp.member_rat X2) A) (@ (@ tptp.ord_less_eq_rat X2) X))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.lattic8721135487736765967in_nat A)) X) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A) (@ (@ tptp.ord_less_eq_nat X2) X))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.lattic8718645017227715691in_int A)) X) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A) (@ (@ tptp.ord_less_eq_int X2) X))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (M4 tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (= (= M4 (@ tptp.lattic1063845414844153500nteger A)) (and (@ (@ tptp.member_Code_integer M4) A) (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X2) A) (@ (@ tptp.ord_le3102999989581377725nteger M4) X2)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (M4 tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (= M4 (@ tptp.lattic8554435388794137742t_unit A)) (and (@ (@ tptp.member_Product_unit M4) A) (forall ((X2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X2) A) (@ (@ tptp.ord_le3221252021190050221t_unit M4) X2)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (M4 Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (= (= M4 (@ tptp.lattic1973801136483472281_Min_o A)) (and (@ (@ tptp.member_o M4) A) (forall ((X2 Bool)) (=> (@ (@ tptp.member_o X2) A) (@ (@ tptp.ord_less_eq_o M4) X2)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_rat) (M4 tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (= (= M4 (@ tptp.lattic8086005427650270231in_rat A)) (and (@ (@ tptp.member_rat M4) A) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.member_rat X2) A) (@ (@ tptp.ord_less_eq_rat M4) X2)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (M4 tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (= (= M4 (@ tptp.lattic8721135487736765967in_nat A)) (and (@ (@ tptp.member_nat M4) A) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) A) (@ (@ tptp.ord_less_eq_nat M4) X2)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (M4 tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (= (= M4 (@ tptp.lattic8718645017227715691in_int A)) (and (@ (@ tptp.member_int M4) A) (forall ((X2 tptp.int)) (=> (@ (@ tptp.member_int X2) A) (@ (@ tptp.ord_less_eq_int M4) X2)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) (@ tptp.lattic1063845414844153500nteger A)) (forall ((A10 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A10) A) (@ (@ tptp.ord_le3102999989581377725nteger X) A10))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ (@ tptp.ord_le3221252021190050221t_unit X) (@ tptp.lattic8554435388794137742t_unit A)) (forall ((A10 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A10) A) (@ (@ tptp.ord_le3221252021190050221t_unit X) A10))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ (@ tptp.ord_less_eq_o X) (@ tptp.lattic1973801136483472281_Min_o A)) (forall ((A10 Bool)) (=> (@ (@ tptp.member_o A10) A) (@ (@ tptp.ord_less_eq_o X) A10))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_rat) (X tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (=> (@ (@ tptp.ord_less_eq_rat X) (@ tptp.lattic8086005427650270231in_rat A)) (forall ((A10 tptp.rat)) (=> (@ (@ tptp.member_rat A10) A) (@ (@ tptp.ord_less_eq_rat X) A10))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_nat X) (@ tptp.lattic8721135487736765967in_nat A)) (forall ((A10 tptp.nat)) (=> (@ (@ tptp.member_nat A10) A) (@ (@ tptp.ord_less_eq_nat X) A10))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_int X) (@ tptp.lattic8718645017227715691in_int A)) (forall ((A10 tptp.int)) (=> (@ (@ tptp.member_int A10) A) (@ (@ tptp.ord_less_eq_int X) A10))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) A) (@ (@ tptp.ord_le3102999989581377725nteger X) A4))) (@ (@ tptp.ord_le3102999989581377725nteger X) (@ tptp.lattic1063845414844153500nteger A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) A) (@ (@ tptp.ord_le3221252021190050221t_unit X) A4))) (@ (@ tptp.ord_le3221252021190050221t_unit X) (@ tptp.lattic8554435388794137742t_unit A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) A) (@ (@ tptp.ord_less_eq_o X) A4))) (@ (@ tptp.ord_less_eq_o X) (@ tptp.lattic1973801136483472281_Min_o A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_rat) (X tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (=> (forall ((A4 tptp.rat)) (=> (@ (@ tptp.member_rat A4) A) (@ (@ tptp.ord_less_eq_rat X) A4))) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.lattic8086005427650270231in_rat A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A) (@ (@ tptp.ord_less_eq_nat X) A4))) (@ (@ tptp.ord_less_eq_nat X) (@ tptp.lattic8721135487736765967in_nat A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A) (@ (@ tptp.ord_less_eq_int X) A4))) (@ (@ tptp.ord_less_eq_int X) (@ tptp.lattic8718645017227715691in_int A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (@ (@ tptp.ord_le361264281704409273t_unit (@ tptp.lattic8554435388794137742t_unit A)) X) (exists ((X2 tptp.product_unit)) (and (@ (@ tptp.member_Product_unit X2) A) (@ (@ tptp.ord_le361264281704409273t_unit X2) X))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (X Bool)) (=> (@ tptp.finite_finite_o A) (=> (not (= A tptp.bot_bot_set_o)) (= (@ (@ tptp.ord_less_o (@ tptp.lattic1973801136483472281_Min_o A)) X) (exists ((X2 Bool)) (and (@ (@ tptp.member_o X2) A) (@ (@ tptp.ord_less_o X2) X))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (X tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (not (= A tptp.bot_bot_set_nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.lattic8721135487736765967in_nat A)) X) (exists ((X2 tptp.nat)) (and (@ (@ tptp.member_nat X2) A) (@ (@ tptp.ord_less_nat X2) X))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (X tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (not (= A tptp.bot_bot_set_int)) (= (@ (@ tptp.ord_less_int (@ tptp.lattic8718645017227715691in_int A)) X) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) A) (@ (@ tptp.ord_less_int X2) X))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.lattic1063845414844153500nteger A)) X) (exists ((X2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X2) A) (@ (@ tptp.ord_le6747313008572928689nteger X2) X))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_rat) (X tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (not (= A tptp.bot_bot_set_rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.lattic8086005427650270231in_rat A)) X) (exists ((X2 tptp.rat)) (and (@ (@ tptp.member_rat X2) A) (@ (@ tptp.ord_less_rat X2) X))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (A2 Bool)) (=> (@ tptp.finite_finite_o A) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) A) (@ (@ tptp.ord_less_eq_o A2) B2))) (= (@ tptp.lattic1973801136483472281_Min_o (@ (@ tptp.insert_o A2) A)) A2)))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (A2 tptp.product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (forall ((B2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit B2) A) (@ (@ tptp.ord_le3221252021190050221t_unit A2) B2))) (= (@ tptp.lattic8554435388794137742t_unit (@ (@ tptp.insert_Product_unit A2) A)) A2)))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (A2 tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) A) (@ (@ tptp.ord_le3102999989581377725nteger A2) B2))) (= (@ tptp.lattic1063845414844153500nteger (@ (@ tptp.insert_Code_integer A2) A)) A2)))))
% 5.65/5.94 (assert (forall ((A tptp.set_rat) (A2 tptp.rat)) (=> (@ tptp.finite_finite_rat A) (=> (forall ((B2 tptp.rat)) (=> (@ (@ tptp.member_rat B2) A) (@ (@ tptp.ord_less_eq_rat A2) B2))) (= (@ tptp.lattic8086005427650270231in_rat (@ (@ tptp.insert_rat A2) A)) A2)))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (A2 tptp.nat)) (=> (@ tptp.finite_finite_nat A) (=> (forall ((B2 tptp.nat)) (=> (@ (@ tptp.member_nat B2) A) (@ (@ tptp.ord_less_eq_nat A2) B2))) (= (@ tptp.lattic8721135487736765967in_nat (@ (@ tptp.insert_nat A2) A)) A2)))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (A2 tptp.int)) (=> (@ tptp.finite_finite_int A) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) A) (@ (@ tptp.ord_less_eq_int A2) B2))) (= (@ tptp.lattic8718645017227715691in_int (@ (@ tptp.insert_int A2) A)) A2)))))
% 5.65/5.94 (assert (forall ((X4 tptp.set_int)) (=> (@ tptp.finite_finite_int X4) (=> (not (= X4 tptp.bot_bot_set_int)) (= (@ tptp.complete_Inf_Inf_int X4) (@ tptp.lattic8718645017227715691in_int X4))))))
% 5.65/5.94 (assert (forall ((X4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat X4) (=> (not (= X4 tptp.bot_bot_set_nat)) (= (@ tptp.complete_Inf_Inf_nat X4) (@ tptp.lattic8721135487736765967in_nat X4))))))
% 5.65/5.94 (assert (forall ((X4 tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit X4) (=> (not (= X4 tptp.bot_bo3957492148770167129t_unit)) (= (@ tptp.comple2584293577114468500t_unit X4) (@ tptp.lattic8554435388794137742t_unit X4))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit)) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (= (@ tptp.lattic8554435388794137742t_unit A) (@ tptp.comple2584293577114468500t_unit A))))))
% 5.65/5.94 (assert (forall ((M tptp.set_Code_integer) (N tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le7084787975880047091nteger M) N) (=> (not (= M tptp.bot_bo3990330152332043303nteger)) (=> (@ tptp.finite6017078050557962740nteger N) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.lattic1063845414844153500nteger N)) (@ tptp.lattic1063845414844153500nteger M)))))))
% 5.65/5.94 (assert (forall ((M tptp.set_Product_unit) (N tptp.set_Product_unit)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit M) N) (=> (not (= M tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.finite4290736615968046902t_unit N) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.lattic8554435388794137742t_unit N)) (@ tptp.lattic8554435388794137742t_unit M)))))))
% 5.65/5.94 (assert (forall ((M tptp.set_o) (N tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o M) N) (=> (not (= M tptp.bot_bot_set_o)) (=> (@ tptp.finite_finite_o N) (@ (@ tptp.ord_less_eq_o (@ tptp.lattic1973801136483472281_Min_o N)) (@ tptp.lattic1973801136483472281_Min_o M)))))))
% 5.65/5.94 (assert (forall ((M tptp.set_rat) (N tptp.set_rat)) (=> (@ (@ tptp.ord_less_eq_set_rat M) N) (=> (not (= M tptp.bot_bot_set_rat)) (=> (@ tptp.finite_finite_rat N) (@ (@ tptp.ord_less_eq_rat (@ tptp.lattic8086005427650270231in_rat N)) (@ tptp.lattic8086005427650270231in_rat M)))))))
% 5.65/5.94 (assert (forall ((M tptp.set_int) (N tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int M) N) (=> (not (= M tptp.bot_bot_set_int)) (=> (@ tptp.finite_finite_int N) (@ (@ tptp.ord_less_eq_int (@ tptp.lattic8718645017227715691in_int N)) (@ tptp.lattic8718645017227715691in_int M)))))))
% 5.65/5.94 (assert (forall ((M tptp.set_nat) (N tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat M) N) (=> (not (= M tptp.bot_bot_set_nat)) (=> (@ tptp.finite_finite_nat N) (@ (@ tptp.ord_less_eq_nat (@ tptp.lattic8721135487736765967in_nat N)) (@ tptp.lattic8721135487736765967in_nat M)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) B4) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (=> (@ tptp.finite6017078050557962740nteger B4) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.lattic1063845414844153500nteger B4)) (@ tptp.lattic1063845414844153500nteger A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) B4) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (=> (@ tptp.finite4290736615968046902t_unit B4) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.lattic8554435388794137742t_unit B4)) (@ tptp.lattic8554435388794137742t_unit A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A) B4) (=> (not (= A tptp.bot_bot_set_o)) (=> (@ tptp.finite_finite_o B4) (@ (@ tptp.ord_less_eq_o (@ tptp.lattic1973801136483472281_Min_o B4)) (@ tptp.lattic1973801136483472281_Min_o A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_rat) (B4 tptp.set_rat)) (=> (@ (@ tptp.ord_less_eq_set_rat A) B4) (=> (not (= A tptp.bot_bot_set_rat)) (=> (@ tptp.finite_finite_rat B4) (@ (@ tptp.ord_less_eq_rat (@ tptp.lattic8086005427650270231in_rat B4)) (@ tptp.lattic8086005427650270231in_rat A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B4) (=> (not (= A tptp.bot_bot_set_int)) (=> (@ tptp.finite_finite_int B4) (@ (@ tptp.ord_less_eq_int (@ tptp.lattic8718645017227715691in_int B4)) (@ tptp.lattic8718645017227715691in_int A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (=> (not (= A tptp.bot_bot_set_nat)) (=> (@ tptp.finite_finite_nat B4) (@ (@ tptp.ord_less_eq_nat (@ tptp.lattic8721135487736765967in_nat B4)) (@ tptp.lattic8721135487736765967in_nat A)))))))
% 5.65/5.94 (assert (forall ((S tptp.set_int)) (=> (@ tptp.finite_finite_int S) (=> (not (= S tptp.bot_bot_set_int)) (= (@ tptp.uminus_uminus_int (@ tptp.lattic8718645017227715691in_int S)) (@ tptp.lattic8263393255366662781ax_int (@ (@ tptp.image_int_int2 tptp.uminus_uminus_int) S)))))))
% 5.65/5.94 (assert (forall ((S tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger S) (=> (not (= S tptp.bot_bo3990330152332043303nteger)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.lattic1063845414844153500nteger S)) (@ tptp.lattic4901227151466704046nteger (@ (@ tptp.image_4470545334726330049nteger tptp.uminus1351360451143612070nteger) S)))))))
% 5.65/5.94 (assert (forall ((S tptp.set_int)) (=> (@ tptp.finite_finite_int S) (=> (not (= S tptp.bot_bot_set_int)) (= (@ tptp.uminus_uminus_int (@ tptp.lattic8263393255366662781ax_int S)) (@ tptp.lattic8718645017227715691in_int (@ (@ tptp.image_int_int2 tptp.uminus_uminus_int) S)))))))
% 5.65/5.94 (assert (forall ((S tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger S) (=> (not (= S tptp.bot_bo3990330152332043303nteger)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.lattic4901227151466704046nteger S)) (@ tptp.lattic1063845414844153500nteger (@ (@ tptp.image_4470545334726330049nteger tptp.uminus1351360451143612070nteger) S)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int)) (= (= (@ tptp.gcd_Gcd_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_set_int A) (@ (@ tptp.insert_int tptp.zero_zero_int) tptp.bot_bot_set_int)))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat)) (= (= (@ tptp.gcd_Gcd_nat A) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_set_nat A) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 5.65/5.94 (assert (forall ((A tptp.set_int)) (= (= (@ tptp.semiri4256215615220890538in_int A) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_set_int A) (@ (@ tptp.insert_int tptp.zero_zero_int) tptp.bot_bot_set_int)) (@ tptp.finite_finite_int A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat)) (= (= (@ tptp.semiri4258706085729940814in_nat A) tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_set_nat A) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)) (@ tptp.finite_finite_nat A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.rat)) (K4 tptp.rat)) (let ((_let_1 (@ tptp.finite_card_nat A))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) A) (@ (@ tptp.ord_less_rat (@ F I3)) K4))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) K4)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.rat)) (K4 tptp.rat)) (let ((_let_1 (@ tptp.finite_card_int A))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A) (@ (@ tptp.ord_less_rat (@ F I3)) K4))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) K4)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.rat)) (K4 tptp.rat)) (let ((_let_1 (@ tptp.finite_card_o A))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) A) (@ (@ tptp.ord_less_rat (@ F I3)) K4))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups7872700643590313910_o_rat F) A)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) K4)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.rat)) (K4 tptp.rat)) (let ((_let_1 (@ tptp.finite410649719033368117t_unit A))) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) A) (@ (@ tptp.ord_less_rat (@ F I3)) K4))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups8131667117488461483it_rat F) A)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) K4)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.int)) (K4 tptp.int)) (let ((_let_1 (@ tptp.finite_card_nat A))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) A) (@ (@ tptp.ord_less_int (@ F I3)) K4))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) A)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) K4)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.int)) (K4 tptp.int)) (let ((_let_1 (@ tptp.finite_card_o A))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) A) (@ (@ tptp.ord_less_int (@ F I3)) K4))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.groups8505340233167759370_o_int F) A)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) K4)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.int)) (K4 tptp.int)) (let ((_let_1 (@ tptp.finite410649719033368117t_unit A))) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) A) (@ (@ tptp.ord_less_int (@ F I3)) K4))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.groups8764306707065906943it_int F) A)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) K4)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.nat)) (K4 tptp.nat)) (let ((_let_1 (@ tptp.finite_card_int A))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A) (@ (@ tptp.ord_less_nat (@ F I3)) K4))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) K4)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.nat)) (K4 tptp.nat)) (let ((_let_1 (@ tptp.finite_card_o A))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) A) (@ (@ tptp.ord_less_nat (@ F I3)) K4))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups8507830703676809646_o_nat F) A)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) K4)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.nat)) (K4 tptp.nat)) (let ((_let_1 (@ tptp.finite410649719033368117t_unit A))) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) A) (@ (@ tptp.ord_less_nat (@ F I3)) K4))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups8766797177574957219it_nat F) A)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) K4)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.code_natural)) (N2 tptp.code_natural) (K3 tptp.nat)) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_nat I3) A) (and (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) _let_1) (@ (@ tptp.ord_le1926595141338095240atural _let_1) N2))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A)) K3) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.one_one_Code_natural) N2) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.groups2279045934846249631atural F) A)) (@ (@ tptp.power_7079662738309270450atural N2) K3)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.code_natural)) (N2 tptp.code_natural) (K3 tptp.nat)) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A) (and (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) _let_1) (@ (@ tptp.ord_le1926595141338095240atural _let_1) N2))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A)) K3) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.one_one_Code_natural) N2) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.groups2650699495083094267atural F) A)) (@ (@ tptp.power_7079662738309270450atural N2) K3)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.code_natural)) (N2 tptp.code_natural) (K3 tptp.nat)) (=> (forall ((I3 Bool)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_o I3) A) (and (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) _let_1) (@ (@ tptp.ord_le1926595141338095240atural _let_1) N2))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o A)) K3) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.one_one_Code_natural) N2) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.groups6518289543945209051atural F) A)) (@ (@ tptp.power_7079662738309270450atural N2) K3)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.code_natural)) (N2 tptp.code_natural) (K3 tptp.nat)) (=> (forall ((I3 tptp.product_unit)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_Product_unit I3) A) (and (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) _let_1) (@ (@ tptp.ord_le1926595141338095240atural _let_1) N2))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite410649719033368117t_unit A)) K3) (=> (@ (@ tptp.ord_le1926595141338095240atural tptp.one_one_Code_natural) N2) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.groups7008954963700796496atural F) A)) (@ (@ tptp.power_7079662738309270450atural N2) K3)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.code_integer)) (N2 tptp.code_integer) (K3 tptp.nat)) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_nat I3) A) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) N2))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A)) K3) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) N2) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups3455450783089532116nteger F) A)) (@ (@ tptp.power_8256067586552552935nteger N2) K3)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.code_integer)) (N2 tptp.code_integer) (K3 tptp.nat)) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) N2))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A)) K3) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) N2) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups3827104343326376752nteger F) A)) (@ (@ tptp.power_8256067586552552935nteger N2) K3)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.code_integer)) (N2 tptp.code_integer) (K3 tptp.nat)) (=> (forall ((I3 Bool)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_o I3) A) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) N2))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o A)) K3) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) N2) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7694694392188491536nteger F) A)) (@ (@ tptp.power_8256067586552552935nteger N2) K3)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.code_integer)) (N2 tptp.code_integer) (K3 tptp.nat)) (=> (forall ((I3 tptp.product_unit)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_Product_unit I3) A) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) N2))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite410649719033368117t_unit A)) K3) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) N2) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups8185359811944078981nteger F) A)) (@ (@ tptp.power_8256067586552552935nteger N2) K3)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.rat)) (N2 tptp.rat) (K3 tptp.nat)) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_nat I3) A) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) N2))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A)) K3) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) N2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A)) (@ (@ tptp.power_power_rat N2) K3)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.rat)) (N2 tptp.rat) (K3 tptp.nat)) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) N2))))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A)) K3) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) N2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A)) (@ (@ tptp.power_power_rat N2) K3)))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_int) (A tptp.set_int) (F (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups3827104343326376752nteger F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A) B4) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int B4) A)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F B2)))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F A4)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_o) (A tptp.set_o) (F (-> Bool tptp.code_integer))) (let ((_let_1 (@ tptp.groups7694694392188491536nteger F))) (=> (@ tptp.finite_finite_o B4) (=> (@ (@ tptp.ord_less_eq_set_o A) B4) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) (@ (@ tptp.minus_minus_set_o B4) A)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F B2)))) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F A4)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_Product_unit) (A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.code_integer))) (let ((_let_1 (@ tptp.groups8185359811944078981nteger F))) (=> (@ tptp.finite4290736615968046902t_unit B4) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) B4) (=> (forall ((B2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit B2) (@ (@ tptp.minus_6452836326544984404t_unit B4) A)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F B2)))) (=> (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F A4)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_Code_integer) (A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups3674199335183972705nteger F))) (=> (@ tptp.finite6017078050557962740nteger B4) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) B4) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) (@ (@ tptp.minus_2355218937544613996nteger B4) A)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F B2)))) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F A4)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_int) (A tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A) B4) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int B4) A)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B2)))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A4)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_o) (A tptp.set_o) (F (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups2869687844427037835_o_rat F))) (=> (@ tptp.finite_finite_o B4) (=> (@ (@ tptp.ord_less_eq_set_o A) B4) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) (@ (@ tptp.minus_minus_set_o B4) A)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B2)))) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A4)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_Product_unit) (A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.rat))) (let ((_let_1 (@ tptp.groups8984663225794451456it_rat F))) (=> (@ tptp.finite4290736615968046902t_unit B4) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) B4) (=> (forall ((B2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit B2) (@ (@ tptp.minus_6452836326544984404t_unit B4) A)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B2)))) (=> (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A4)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_Code_integer) (A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat F))) (=> (@ tptp.finite6017078050557962740nteger B4) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) B4) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) (@ (@ tptp.minus_2355218937544613996nteger B4) A)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B2)))) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A4)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_int) (A tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups1705073143266064639nt_int F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A) B4) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int B4) A)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B2)))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A4)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_o) (A tptp.set_o) (F (-> Bool tptp.int))) (let ((_let_1 (@ tptp.groups3502327434004483295_o_int F))) (=> (@ tptp.finite_finite_o B4) (=> (@ (@ tptp.ord_less_eq_set_o A) B4) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) (@ (@ tptp.minus_minus_set_o B4) A)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B2)))) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A4)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A2) (@ tptp.uminus_uminus_int B)) (= A2 B))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A2) (@ tptp.uminus1351360451143612070nteger B)) (= A2 B))))
% 5.65/5.94 (assert (forall ((A2 tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A2)) A2)))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger A2)) A2)))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat A)) (@ tptp.uminus5710092332889474511et_nat B4)) (@ (@ tptp.ord_less_eq_set_nat B4) A))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B4) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat B4)) (@ tptp.uminus5710092332889474511et_nat A)))))
% 5.65/5.94 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A2)) (@ (@ tptp.ord_le3102999989581377725nteger A2) B))))
% 5.65/5.94 (assert (forall ((B tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A2)) (@ (@ tptp.ord_less_eq_rat A2) B))))
% 5.65/5.94 (assert (forall ((B tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A2)) (@ (@ tptp.ord_less_eq_int A2) B))))
% 5.65/5.94 (assert (forall ((A2 tptp.int)) (= (= (@ tptp.uminus_uminus_int A2) A2) (= A2 tptp.zero_zero_int))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A2) A2) (= A2 tptp.zero_z3403309356797280102nteger))))
% 5.65/5.94 (assert (forall ((A2 tptp.int)) (= (= A2 (@ tptp.uminus_uminus_int A2)) (= A2 tptp.zero_zero_int))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer)) (= (= A2 (@ tptp.uminus1351360451143612070nteger A2)) (= A2 tptp.zero_z3403309356797280102nteger))))
% 5.65/5.94 (assert (forall ((A2 tptp.int)) (= (= (@ tptp.uminus_uminus_int A2) tptp.zero_zero_int) (= A2 tptp.zero_zero_int))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A2) tptp.zero_z3403309356797280102nteger) (= A2 tptp.zero_z3403309356797280102nteger))))
% 5.65/5.94 (assert (forall ((A2 tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A2)) (= tptp.zero_zero_int A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger A2)) (= tptp.zero_z3403309356797280102nteger A2))))
% 5.65/5.94 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 5.65/5.94 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 5.65/5.94 (assert (forall ((B tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A2)) (@ (@ tptp.ord_less_rat A2) B))))
% 5.65/5.94 (assert (forall ((B tptp.int) (A2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A2)) (@ (@ tptp.ord_less_int A2) B))))
% 5.65/5.94 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A2)) (@ (@ tptp.ord_le6747313008572928689nteger A2) B))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A2) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A2)) (@ tptp.uminus_uminus_rat B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A2) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A2)) (@ tptp.uminus_uminus_int B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A2)) (@ tptp.uminus1351360451143612070nteger B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A2)) (@ (@ tptp.plus_plus_rat A2) B)) B)))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A2)) (@ (@ tptp.plus_plus_int A2) B)) B)))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A2)) (@ (@ tptp.plus_p5714425477246183910nteger A2) B)) B)))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A2) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A2)) B)) B)))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A2) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A2)) B)) B)))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A2)) B)) B)))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A2)) B) (@ tptp.uminus_uminus_rat (@ (@ tptp.times_times_rat A2) B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A2)) B) (@ tptp.uminus_uminus_int (@ (@ tptp.times_times_int A2) B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A2)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A2) B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A2)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A2) B))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A2)) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.times_times_int A2) B))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A2)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A2) B))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A2))) (= (@ _let_1 (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ _let_1 B))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int A2))) (= (@ _let_1 (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ _let_1 B))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A2))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 B))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A2) B)) (@ (@ tptp.minus_minus_rat B) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A2) B)) (@ (@ tptp.minus_minus_int B) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A2) B)) (@ (@ tptp.minus_8373710615458151222nteger B) A2))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit A) (@ tptp.uminus5944136376168626660t_unit A)) tptp.bot_bo3957492148770167129t_unit)))
% 5.65/5.94 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o A) (@ tptp.uminus_uminus_set_o A)) tptp.bot_bot_set_o)))
% 5.65/5.94 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A) (@ tptp.uminus5710092332889474511et_nat A)) tptp.bot_bot_set_nat)))
% 5.65/5.94 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A) (@ tptp.uminus1532241313380277803et_int A)) tptp.bot_bot_set_int)))
% 5.65/5.94 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o A) (@ tptp.uminus5254974436814262692_nat_o A)) tptp.bot_bo7824918357723582233_nat_o)))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit (@ tptp.uminus5944136376168626660t_unit A)) A) tptp.bot_bo3957492148770167129t_unit)))
% 5.65/5.94 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o (@ tptp.uminus_uminus_set_o A)) A) tptp.bot_bot_set_o)))
% 5.65/5.94 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat A)) A) tptp.bot_bot_set_nat)))
% 5.65/5.94 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int A)) A) tptp.bot_bot_set_int)))
% 5.65/5.94 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ tptp.uminus5254974436814262692_nat_o A)) A) tptp.bot_bo7824918357723582233_nat_o)))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A) (@ tptp.uminus5710092332889474511et_nat B4)) (@ (@ tptp.minus_minus_set_nat A) B4))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A) (@ tptp.uminus5710092332889474511et_nat B4)) (@ (@ tptp.inf_inf_set_nat A) B4))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.minus_minus_set_nat A) B4)) (@ (@ tptp.sup_sup_set_nat (@ tptp.uminus5710092332889474511et_nat A)) B4))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A2)) (@ (@ tptp.ord_le3102999989581377725nteger A2) tptp.zero_z3403309356797280102nteger))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat A2)) (@ (@ tptp.ord_less_eq_rat A2) tptp.zero_zero_rat))))
% 5.65/5.94 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A2)) (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A2)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A2)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A2))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A2)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A2))) (= (@ _let_1 (@ tptp.uminus_uminus_rat A2)) (@ _let_1 tptp.zero_zero_rat)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A2))) (= (@ _let_1 (@ tptp.uminus_uminus_int A2)) (@ _let_1 tptp.zero_zero_int)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A2)) A2) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A2)) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A2)) A2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A2))) (= (@ _let_1 (@ tptp.uminus_uminus_rat A2)) (@ _let_1 tptp.zero_zero_rat)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A2))) (= (@ _let_1 (@ tptp.uminus_uminus_int A2)) (@ _let_1 tptp.zero_zero_int)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A2))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A2)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A2)) A2) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A2)) A2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A2)) A2) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat A2)) (@ (@ tptp.ord_less_rat A2) tptp.zero_zero_rat))))
% 5.65/5.94 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A2)) (@ (@ tptp.ord_less_int A2) tptp.zero_zero_int))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A2)) (@ (@ tptp.ord_le6747313008572928689nteger A2) tptp.zero_z3403309356797280102nteger))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A2)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A2)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A2)) A2) tptp.zero_zero_rat)))
% 5.65/5.94 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A2)) A2) tptp.zero_zero_int)))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A2)) A2) tptp.zero_z3403309356797280102nteger)))
% 5.65/5.94 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat A2) (@ tptp.uminus_uminus_rat A2)) tptp.zero_zero_rat)))
% 5.65/5.94 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int A2) (@ tptp.uminus_uminus_int A2)) tptp.zero_zero_int)))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A2) (@ tptp.uminus1351360451143612070nteger A2)) tptp.zero_z3403309356797280102nteger)))
% 5.65/5.94 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) A2) (@ tptp.uminus_uminus_rat A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A2) (@ tptp.uminus_uminus_int A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) A2) (@ tptp.uminus1351360451143612070nteger A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A2) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A2) B))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A2) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A2) B))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A2) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A2) B))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A2)) B) (@ (@ tptp.minus_minus_rat B) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A2)) B) (@ (@ tptp.minus_minus_int B) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A2)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A2))))
% 5.65/5.94 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (@ tptp.uminus_uminus_rat Z))))
% 5.65/5.94 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z) (@ tptp.uminus_uminus_int Z))))
% 5.65/5.94 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (@ tptp.uminus1351360451143612070nteger Z))))
% 5.65/5.94 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z))))
% 5.65/5.94 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z))))
% 5.65/5.94 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z))))
% 5.65/5.94 (assert (= (@ tptp.uminus5254974436814262692_nat_o tptp.top_to4869887016220417533_nat_o) tptp.bot_bo7824918357723582233_nat_o))
% 5.65/5.94 (assert (= (@ tptp.uminus5944136376168626660t_unit tptp.top_to1996260823553986621t_unit) tptp.bot_bo3957492148770167129t_unit))
% 5.65/5.94 (assert (= (@ tptp.uminus_uminus_set_o tptp.top_top_set_o) tptp.bot_bot_set_o))
% 5.65/5.94 (assert (= (@ tptp.uminus5710092332889474511et_nat tptp.top_top_set_nat) tptp.bot_bot_set_nat))
% 5.65/5.94 (assert (= (@ tptp.uminus1532241313380277803et_int tptp.top_top_set_int) tptp.bot_bot_set_int))
% 5.65/5.94 (assert (= (@ tptp.uminus_uminus_assn tptp.top_top_assn) tptp.bot_bot_assn))
% 5.65/5.94 (assert (= (@ tptp.uminus2952777764628376836t_unit tptp.top_top_Product_unit) tptp.bot_bot_Product_unit))
% 5.65/5.94 (assert (= (@ tptp.uminus5254974436814262692_nat_o tptp.bot_bo7824918357723582233_nat_o) tptp.top_to4869887016220417533_nat_o))
% 5.65/5.94 (assert (= (@ tptp.uminus5944136376168626660t_unit tptp.bot_bo3957492148770167129t_unit) tptp.top_to1996260823553986621t_unit))
% 5.65/5.94 (assert (= (@ tptp.uminus_uminus_set_o tptp.bot_bot_set_o) tptp.top_top_set_o))
% 5.65/5.94 (assert (= (@ tptp.uminus5710092332889474511et_nat tptp.bot_bot_set_nat) tptp.top_top_set_nat))
% 5.65/5.94 (assert (= (@ tptp.uminus1532241313380277803et_int tptp.bot_bot_set_int) tptp.top_top_set_int))
% 5.65/5.94 (assert (= (@ tptp.uminus_uminus_assn tptp.bot_bot_assn) tptp.top_top_assn))
% 5.65/5.94 (assert (= (@ tptp.uminus2952777764628376836t_unit tptp.bot_bot_Product_unit) tptp.top_top_Product_unit))
% 5.65/5.94 (assert (forall ((X tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit X) (@ tptp.uminus5944136376168626660t_unit X)) tptp.bot_bo3957492148770167129t_unit)))
% 5.65/5.94 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o X) (@ tptp.uminus_uminus_set_o X)) tptp.bot_bot_set_o)))
% 5.65/5.94 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) (@ tptp.uminus5710092332889474511et_nat X)) tptp.bot_bot_set_nat)))
% 5.65/5.94 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X) (@ tptp.uminus1532241313380277803et_int X)) tptp.bot_bot_set_int)))
% 5.65/5.94 (assert (forall ((X tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o X) (@ tptp.uminus5254974436814262692_nat_o X)) tptp.bot_bo7824918357723582233_nat_o)))
% 5.65/5.94 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) (@ tptp.uminus_uminus_assn X)) tptp.bot_bot_assn)))
% 5.65/5.94 (assert (forall ((X tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit X) (@ tptp.uminus2952777764628376836t_unit X)) tptp.bot_bot_Product_unit)))
% 5.65/5.94 (assert (forall ((X tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit (@ tptp.uminus5944136376168626660t_unit X)) X) tptp.bot_bo3957492148770167129t_unit)))
% 5.65/5.94 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o (@ tptp.uminus_uminus_set_o X)) X) tptp.bot_bot_set_o)))
% 5.65/5.94 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat X)) X) tptp.bot_bot_set_nat)))
% 5.65/5.94 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int X)) X) tptp.bot_bot_set_int)))
% 5.65/5.94 (assert (forall ((X tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ tptp.uminus5254974436814262692_nat_o X)) X) tptp.bot_bo7824918357723582233_nat_o)))
% 5.65/5.94 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn (@ tptp.uminus_uminus_assn X)) X) tptp.bot_bot_assn)))
% 5.65/5.94 (assert (forall ((X tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit (@ tptp.uminus2952777764628376836t_unit X)) X) tptp.bot_bot_Product_unit)))
% 5.65/5.94 (assert (forall ((X tptp.set_Product_unit) (Y tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit X) (@ (@ tptp.inf_in4660618365625256667t_unit Y) (@ tptp.uminus5944136376168626660t_unit X))) tptp.bot_bo3957492148770167129t_unit)))
% 5.65/5.94 (assert (forall ((X tptp.set_o) (Y tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o X) (@ (@ tptp.inf_inf_set_o Y) (@ tptp.uminus_uminus_set_o X))) tptp.bot_bot_set_o)))
% 5.65/5.94 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) (@ (@ tptp.inf_inf_set_nat Y) (@ tptp.uminus5710092332889474511et_nat X))) tptp.bot_bot_set_nat)))
% 5.65/5.94 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X) (@ (@ tptp.inf_inf_set_int Y) (@ tptp.uminus1532241313380277803et_int X))) tptp.bot_bot_set_int)))
% 5.65/5.94 (assert (forall ((X tptp.set_Pr4532377907799695533_nat_o) (Y tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o X) (@ (@ tptp.inf_in1906310914598751387_nat_o Y) (@ tptp.uminus5254974436814262692_nat_o X))) tptp.bot_bo7824918357723582233_nat_o)))
% 5.65/5.94 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) (@ (@ tptp.inf_inf_assn Y) (@ tptp.uminus_uminus_assn X))) tptp.bot_bot_assn)))
% 5.65/5.94 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit X) (@ (@ tptp.inf_inf_Product_unit Y) (@ tptp.uminus2952777764628376836t_unit X))) tptp.bot_bot_Product_unit)))
% 5.65/5.94 (assert (forall ((X tptp.set_Product_unit) (Y tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit X) (@ (@ tptp.inf_in4660618365625256667t_unit (@ tptp.uminus5944136376168626660t_unit X)) Y)) tptp.bot_bo3957492148770167129t_unit)))
% 5.65/5.94 (assert (forall ((X tptp.set_o) (Y tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o X) (@ (@ tptp.inf_inf_set_o (@ tptp.uminus_uminus_set_o X)) Y)) tptp.bot_bot_set_o)))
% 5.65/5.94 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat X)) Y)) tptp.bot_bot_set_nat)))
% 5.65/5.94 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X) (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int X)) Y)) tptp.bot_bot_set_int)))
% 5.65/5.94 (assert (forall ((X tptp.set_Pr4532377907799695533_nat_o) (Y tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o X) (@ (@ tptp.inf_in1906310914598751387_nat_o (@ tptp.uminus5254974436814262692_nat_o X)) Y)) tptp.bot_bo7824918357723582233_nat_o)))
% 5.65/5.94 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) (@ (@ tptp.inf_inf_assn (@ tptp.uminus_uminus_assn X)) Y)) tptp.bot_bot_assn)))
% 5.65/5.94 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit X) (@ (@ tptp.inf_inf_Product_unit (@ tptp.uminus2952777764628376836t_unit X)) Y)) tptp.bot_bot_Product_unit)))
% 5.65/5.94 (assert (forall ((X tptp.set_Product_unit) (Y tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit (@ tptp.uminus5944136376168626660t_unit X)) (@ (@ tptp.inf_in4660618365625256667t_unit X) Y)) tptp.bot_bo3957492148770167129t_unit)))
% 5.65/5.94 (assert (forall ((X tptp.set_o) (Y tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o (@ tptp.uminus_uminus_set_o X)) (@ (@ tptp.inf_inf_set_o X) Y)) tptp.bot_bot_set_o)))
% 5.65/5.94 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat X)) (@ (@ tptp.inf_inf_set_nat X) Y)) tptp.bot_bot_set_nat)))
% 5.65/5.94 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int X)) (@ (@ tptp.inf_inf_set_int X) Y)) tptp.bot_bot_set_int)))
% 5.65/5.94 (assert (forall ((X tptp.set_Pr4532377907799695533_nat_o) (Y tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ tptp.uminus5254974436814262692_nat_o X)) (@ (@ tptp.inf_in1906310914598751387_nat_o X) Y)) tptp.bot_bo7824918357723582233_nat_o)))
% 5.65/5.94 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.inf_inf_assn (@ tptp.uminus_uminus_assn X)) (@ (@ tptp.inf_inf_assn X) Y)) tptp.bot_bot_assn)))
% 5.65/5.94 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit (@ tptp.uminus2952777764628376836t_unit X)) (@ (@ tptp.inf_inf_Product_unit X) Y)) tptp.bot_bot_Product_unit)))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (B tptp.product_unit)) (= (@ (@ tptp.ord_le3507040750410214029t_unit A) (@ tptp.uminus5944136376168626660t_unit (@ (@ tptp.insert_Product_unit B) tptp.bot_bo3957492148770167129t_unit))) (not (@ (@ tptp.member_Product_unit B) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (B Bool)) (= (@ (@ tptp.ord_less_eq_set_o A) (@ tptp.uminus_uminus_set_o (@ (@ tptp.insert_o B) tptp.bot_bot_set_o))) (not (@ (@ tptp.member_o B) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int A) (@ tptp.uminus1532241313380277803et_int (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (not (@ (@ tptp.member_int B) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B (-> tptp.produc3658429121746597890et_nat Bool))) (= (@ (@ tptp.ord_le2965882846123202637_nat_o A) (@ tptp.uminus5254974436814262692_nat_o (@ (@ tptp.insert5175938949040314269_nat_o B) tptp.bot_bo7824918357723582233_nat_o))) (not (@ (@ tptp.member6576561426505652726_nat_o B) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (not (@ (@ tptp.member_nat B) A)))))
% 5.65/5.94 (assert (forall ((G (-> tptp.product_unit tptp.assn))) (= (@ (@ tptp.groups5360233303959380816t_assn G) tptp.bot_bo3957492148770167129t_unit) tptp.one_one_assn)))
% 5.65/5.94 (assert (forall ((G (-> tptp.product_unit tptp.nat))) (= (@ (@ tptp.groups396421249026171384it_nat G) tptp.bot_bo3957492148770167129t_unit) tptp.one_one_nat)))
% 5.65/5.94 (assert (forall ((G (-> tptp.product_unit tptp.int))) (= (@ (@ tptp.groups393930778517121108it_int G) tptp.bot_bo3957492148770167129t_unit) tptp.one_one_int)))
% 5.65/5.94 (assert (forall ((G (-> tptp.product_unit tptp.code_integer))) (= (@ (@ tptp.groups8185359811944078981nteger G) tptp.bot_bo3957492148770167129t_unit) tptp.one_one_Code_integer)))
% 5.65/5.94 (assert (forall ((G (-> tptp.product_unit tptp.code_natural))) (= (@ (@ tptp.groups7008954963700796496atural G) tptp.bot_bo3957492148770167129t_unit) tptp.one_one_Code_natural)))
% 5.65/5.94 (assert (forall ((G (-> Bool tptp.assn))) (= (@ (@ tptp.groups5301882518646026715o_assn G) tptp.bot_bot_set_o) tptp.one_one_assn)))
% 5.65/5.94 (assert (forall ((G (-> Bool tptp.nat))) (= (@ (@ tptp.groups3504817904513533571_o_nat G) tptp.bot_bot_set_o) tptp.one_one_nat)))
% 5.65/5.94 (assert (forall ((G (-> Bool tptp.int))) (= (@ (@ tptp.groups3502327434004483295_o_int G) tptp.bot_bot_set_o) tptp.one_one_int)))
% 5.65/5.94 (assert (forall ((G (-> Bool tptp.code_integer))) (= (@ (@ tptp.groups7694694392188491536nteger G) tptp.bot_bot_set_o) tptp.one_one_Code_integer)))
% 5.65/5.94 (assert (forall ((G (-> Bool tptp.code_natural))) (= (@ (@ tptp.groups6518289543945209051atural G) tptp.bot_bot_set_o) tptp.one_one_Code_natural)))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.assn))) (=> (not (@ tptp.finite_finite_nat A)) (= (@ (@ tptp.groups6906906614972039071t_assn G) A) tptp.one_one_assn))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (=> (not (@ tptp.finite6017078050557962740nteger A)) (= (@ (@ tptp.groups1304777262505850412r_assn G) A) tptp.one_one_assn))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (=> (not (@ tptp.finite6017078050557962740nteger A)) (= (@ (@ tptp.groups3190895334310489300er_nat G) A) tptp.one_one_nat))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.int))) (=> (not (@ tptp.finite_finite_nat A)) (= (@ (@ tptp.groups705719431365010083at_int G) A) tptp.one_one_int))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (=> (not (@ tptp.finite6017078050557962740nteger A)) (= (@ (@ tptp.groups3188404863801439024er_int G) A) tptp.one_one_int))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (=> (not (@ tptp.finite_finite_nat A)) (= (@ (@ tptp.groups3455450783089532116nteger G) A) tptp.one_one_Code_integer))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (=> (not (@ tptp.finite6017078050557962740nteger A)) (= (@ (@ tptp.groups3674199335183972705nteger G) A) tptp.one_one_Code_integer))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.code_natural))) (=> (not (@ tptp.finite_finite_nat A)) (= (@ (@ tptp.groups2279045934846249631atural G) A) tptp.one_one_Code_natural))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_natural))) (=> (not (@ tptp.finite6017078050557962740nteger A)) (= (@ (@ tptp.groups2497794486940690220atural G) A) tptp.one_one_Code_natural))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.nat))) (=> (not (@ tptp.finite_finite_nat A)) (= (@ (@ tptp.groups708209901874060359at_nat G) A) tptp.one_one_nat))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.times_times_nat M4) N2)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M4)) (@ tptp.semiri681578069525770553at_rat N2)))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat M4) N2)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M4)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.times_times_nat M4) N2)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M4)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.times_times_nat M4) N2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger M4)) (@ tptp.semiri4939895301339042750nteger N2)))))
% 5.65/5.94 (assert (= (@ tptp.semiri3763490453095760265atural tptp.one_one_nat) tptp.one_one_Code_natural))
% 5.65/5.94 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 5.65/5.94 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 5.65/5.94 (assert (= (@ tptp.semiri4939895301339042750nteger tptp.one_one_nat) tptp.one_one_Code_integer))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_Code_natural (@ tptp.semiri3763490453095760265atural N2)) (= N2 tptp.one_one_nat))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N2)) (= N2 tptp.one_one_nat))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N2)) (= N2 tptp.one_one_nat))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_Code_integer (@ tptp.semiri4939895301339042750nteger N2)) (= N2 tptp.one_one_nat))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri3763490453095760265atural N2) tptp.one_one_Code_natural) (= N2 tptp.one_one_nat))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N2) tptp.one_one_int) (= N2 tptp.one_one_nat))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N2) tptp.one_one_nat) (= N2 tptp.one_one_nat))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger N2) tptp.one_one_Code_integer) (= N2 tptp.one_one_nat))))
% 5.65/5.94 (assert (= (@ tptp.gcd_Gcd_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 5.65/5.94 (assert (= (@ tptp.gcd_Gcd_int tptp.bot_bot_set_int) tptp.zero_zero_int))
% 5.65/5.94 (assert (= (@ tptp.gcd_Gcd_nat tptp.top_top_set_nat) tptp.one_one_nat))
% 5.65/5.94 (assert (= (@ tptp.gcd_Gcd_int tptp.top_top_set_int) tptp.one_one_int))
% 5.65/5.94 (assert (= (@ tptp.semiri4258706085729940814in_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 5.65/5.94 (assert (= (@ tptp.semiri4256215615220890538in_int tptp.bot_bot_set_int) tptp.zero_zero_int))
% 5.65/5.94 (assert (forall ((A tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A)) (= (@ tptp.semiri4258706085729940814in_nat A) tptp.one_one_nat))))
% 5.65/5.94 (assert (forall ((A tptp.set_int)) (=> (not (@ tptp.finite_finite_int A)) (= (@ tptp.semiri4256215615220890538in_int A) tptp.one_one_int))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat)) (let ((_let_1 (@ tptp.semiri4258706085729940814in_nat A))) (= (@ (@ tptp.dvd_dvd_nat _let_1) tptp.one_one_nat) (= _let_1 tptp.one_one_nat)))))
% 5.65/5.94 (assert (forall ((A tptp.set_int)) (let ((_let_1 (@ tptp.semiri4256215615220890538in_int A))) (= (@ (@ tptp.dvd_dvd_int _let_1) tptp.one_one_int) (= _let_1 tptp.one_one_int)))))
% 5.65/5.94 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.neg_nu5851722552734809277nc_int _let_1) _let_1)))
% 5.65/5.94 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.neg_nu5831290666863070958nteger _let_1) _let_1)))
% 5.65/5.94 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 5.65/5.94 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 5.65/5.94 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 5.65/5.94 (assert (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) tptp.zero_zero_rat))
% 5.65/5.94 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 5.65/5.94 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 5.65/5.94 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.minus_minus_rat _let_1) _let_1) tptp.zero_zero_rat)))
% 5.65/5.94 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 5.65/5.94 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.minus_8373710615458151222nteger _let_1) _let_1) tptp.zero_z3403309356797280102nteger)))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) tptp.one_one_rat))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2))) (= (@ (@ tptp.times_times_int _let_1) _let_1) tptp.one_one_int))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) tptp.one_one_Code_integer))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2)))) (= (@ _let_1 (@ _let_1 A2)) A2))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (A2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)))) (= (@ _let_1 (@ _let_1 A2)) A2))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)))) (= (@ _let_1 (@ _let_1 A2)) A2))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat)) (= (@ tptp.semiri3763490453095760265atural (@ tptp.suc M4)) (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ tptp.semiri3763490453095760265atural M4)))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M4)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M4)))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M4)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M4)))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M4)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M4)))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.suc M4)) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.semiri4939895301339042750nteger M4)))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int A) (=> (not (@ (@ tptp.member_int X) A)) (= (@ _let_1 (@ (@ tptp.insert_int X) A)) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_1 A))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (X Bool) (G (-> Bool tptp.assn))) (let ((_let_1 (@ tptp.groups5301882518646026715o_assn G))) (=> (@ tptp.finite_finite_o A) (=> (not (@ (@ tptp.member_o X) A)) (= (@ _let_1 (@ (@ tptp.insert_o X) A)) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_1 A))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit) (G (-> tptp.product_unit tptp.assn))) (let ((_let_1 (@ tptp.groups5360233303959380816t_assn G))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (@ (@ tptp.member_Product_unit X) A)) (= (@ _let_1 (@ (@ tptp.insert_Product_unit X) A)) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_1 A))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat A) (=> (not (@ (@ tptp.member_nat X) A)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A)) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_1 A))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (@ (@ tptp.member_Code_integer X) A)) (= (@ _let_1 (@ (@ tptp.insert_Code_integer X) A)) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_1 A))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A) (=> (not (@ (@ tptp.member_int X) A)) (= (@ _let_1 (@ (@ tptp.insert_int X) A)) (@ (@ tptp.times_times_rat (@ G X)) (@ _let_1 A))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (X Bool) (G (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups2869687844427037835_o_rat G))) (=> (@ tptp.finite_finite_o A) (=> (not (@ (@ tptp.member_o X) A)) (= (@ _let_1 (@ (@ tptp.insert_o X) A)) (@ (@ tptp.times_times_rat (@ G X)) (@ _let_1 A))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit) (G (-> tptp.product_unit tptp.rat))) (let ((_let_1 (@ tptp.groups8984663225794451456it_rat G))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (not (@ (@ tptp.member_Product_unit X) A)) (= (@ _let_1 (@ (@ tptp.insert_Product_unit X) A)) (@ (@ tptp.times_times_rat (@ G X)) (@ _let_1 A))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A) (=> (not (@ (@ tptp.member_nat X) A)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A)) (@ (@ tptp.times_times_rat (@ G X)) (@ _let_1 A))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (not (@ (@ tptp.member_Code_integer X) A)) (= (@ _let_1 (@ (@ tptp.insert_Code_integer X) A)) (@ (@ tptp.times_times_rat (@ G X)) (@ _let_1 A))))))))
% 5.65/5.94 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 5.65/5.94 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A2) B) (= (@ tptp.uminus_uminus_int B) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A2) B) (= (@ tptp.uminus1351360451143612070nteger B) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (= A2 (@ tptp.uminus_uminus_int B)) (= B (@ tptp.uminus_uminus_int A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (= A2 (@ tptp.uminus1351360451143612070nteger B)) (= B (@ tptp.uminus1351360451143612070nteger A2)))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (= (@ G X3) tptp.one_one_nat))) (= (@ (@ tptp.groups708209901874060359at_nat G) A) tptp.one_one_nat))))
% 5.65/5.94 (assert (forall ((G (-> tptp.nat tptp.assn)) (A tptp.set_nat)) (=> (not (= (@ (@ tptp.groups6906906614972039071t_assn G) A) tptp.one_one_assn)) (not (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A) (= (@ G A4) tptp.one_one_assn)))))))
% 5.65/5.94 (assert (forall ((G (-> tptp.int tptp.assn)) (A tptp.set_int)) (=> (not (= (@ (@ tptp.groups7882442080178216443t_assn G) A) tptp.one_one_assn)) (not (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A) (= (@ G A4) tptp.one_one_assn)))))))
% 5.65/5.94 (assert (forall ((G (-> Bool tptp.assn)) (A tptp.set_o)) (=> (not (= (@ (@ tptp.groups5301882518646026715o_assn G) A) tptp.one_one_assn)) (not (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) A) (= (@ G A4) tptp.one_one_assn)))))))
% 5.65/5.94 (assert (forall ((G (-> tptp.product_unit tptp.assn)) (A tptp.set_Product_unit)) (=> (not (= (@ (@ tptp.groups5360233303959380816t_assn G) A) tptp.one_one_assn)) (not (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) A) (= (@ G A4) tptp.one_one_assn)))))))
% 5.65/5.94 (assert (forall ((G (-> tptp.int tptp.nat)) (A tptp.set_int)) (=> (not (= (@ (@ tptp.groups1707563613775114915nt_nat G) A) tptp.one_one_nat)) (not (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A) (= (@ G A4) tptp.one_one_nat)))))))
% 5.65/5.94 (assert (forall ((G (-> Bool tptp.nat)) (A tptp.set_o)) (=> (not (= (@ (@ tptp.groups3504817904513533571_o_nat G) A) tptp.one_one_nat)) (not (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) A) (= (@ G A4) tptp.one_one_nat)))))))
% 5.65/5.94 (assert (forall ((G (-> tptp.product_unit tptp.nat)) (A tptp.set_Product_unit)) (=> (not (= (@ (@ tptp.groups396421249026171384it_nat G) A) tptp.one_one_nat)) (not (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) A) (= (@ G A4) tptp.one_one_nat)))))))
% 5.65/5.94 (assert (forall ((G (-> tptp.nat tptp.int)) (A tptp.set_nat)) (=> (not (= (@ (@ tptp.groups705719431365010083at_int G) A) tptp.one_one_int)) (not (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A) (= (@ G A4) tptp.one_one_int)))))))
% 5.65/5.94 (assert (forall ((G (-> tptp.int tptp.int)) (A tptp.set_int)) (=> (not (= (@ (@ tptp.groups1705073143266064639nt_int G) A) tptp.one_one_int)) (not (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A) (= (@ G A4) tptp.one_one_int)))))))
% 5.65/5.94 (assert (forall ((G (-> Bool tptp.int)) (A tptp.set_o)) (=> (not (= (@ (@ tptp.groups3502327434004483295_o_int G) A) tptp.one_one_int)) (not (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) A) (= (@ G A4) tptp.one_one_int)))))))
% 5.65/5.94 (assert (forall ((X tptp.nat) (Y tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat X))) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ (@ tptp.times_times_rat Y) _let_1)))))
% 5.65/5.94 (assert (forall ((X tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))))
% 5.65/5.94 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X))) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ (@ tptp.times_times_nat Y) _let_1)))))
% 5.65/5.94 (assert (forall ((X tptp.nat) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger X))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) Y) (@ (@ tptp.times_3573771949741848930nteger Y) _let_1)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A2) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A2) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A2)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A2)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A2)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A2) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A2) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.ord_less_eq_rat B) (@ tptp.uminus_uminus_rat A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A2) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.ord_less_eq_int B) (@ tptp.uminus_uminus_int A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A2)) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A2)) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A2)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A2))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A2) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.ord_less_rat B) (@ tptp.uminus_uminus_rat A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A2) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.ord_less_int B) (@ tptp.uminus_uminus_int A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A2) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A2) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A2) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A2)))))
% 5.65/5.94 (assert (forall ((A tptp.rat) (K3 tptp.rat) (A2 tptp.rat)) (=> (= A (@ (@ tptp.plus_plus_rat K3) A2)) (= (@ tptp.uminus_uminus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K3)) (@ tptp.uminus_uminus_rat A2))))))
% 5.65/5.94 (assert (forall ((A tptp.int) (K3 tptp.int) (A2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int K3) A2)) (= (@ tptp.uminus_uminus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K3)) (@ tptp.uminus_uminus_int A2))))))
% 5.65/5.94 (assert (forall ((A tptp.code_integer) (K3 tptp.code_integer) (A2 tptp.code_integer)) (=> (= A (@ (@ tptp.plus_p5714425477246183910nteger K3) A2)) (= (@ tptp.uminus1351360451143612070nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K3)) (@ tptp.uminus1351360451143612070nteger A2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A2) A2) (@ (@ tptp.times_times_rat B) B)) (or (= A2 B) (= A2 (@ tptp.uminus_uminus_rat B))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A2) A2) (@ (@ tptp.times_times_int B) B)) (or (= A2 B) (= A2 (@ tptp.uminus_uminus_int B))))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A2) A2) (@ (@ tptp.times_3573771949741848930nteger B) B)) (or (= A2 B) (= A2 (@ tptp.uminus1351360451143612070nteger B))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A2)) B) (@ (@ tptp.times_times_rat A2) (@ tptp.uminus_uminus_rat B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A2)) B) (@ (@ tptp.times_times_int A2) (@ tptp.uminus_uminus_int B)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A2)) B) (@ (@ tptp.times_3573771949741848930nteger A2) (@ tptp.uminus1351360451143612070nteger B)))))
% 5.65/5.94 (assert (not (= tptp.one_one_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 5.65/5.94 (assert (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 5.65/5.94 (assert (forall ((B tptp.rat) (A2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat B)) A2) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A2)) B))))
% 5.65/5.94 (assert (forall ((B tptp.int) (A2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int B)) A2) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A2)) B))))
% 5.65/5.94 (assert (forall ((B tptp.code_integer) (A2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger B)) A2) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A2)) B))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat)) (=> (@ (@ tptp.member_nat tptp.one_one_nat) A) (= (@ tptp.gcd_Gcd_nat A) tptp.one_one_nat))))
% 5.65/5.94 (assert (forall ((A tptp.set_int)) (=> (@ (@ tptp.member_int tptp.one_one_int) A) (= (@ tptp.gcd_Gcd_int A) tptp.one_one_int))))
% 5.65/5.94 (assert (= tptp.minus_minus_assn (lambda ((A6 tptp.assn) (B6 tptp.assn)) (@ (@ tptp.inf_inf_assn A6) (@ tptp.uminus_uminus_assn B6)))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ (@ tptp.groups3455450783089532116nteger F) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.code_integer))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ (@ tptp.groups3827104343326376752nteger F) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.code_integer))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ (@ tptp.groups7694694392188491536nteger F) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.code_integer))) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ (@ tptp.groups8185359811944078981nteger F) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.code_natural))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (@ (@ tptp.ord_le1926595141338095240atural tptp.one_one_Code_natural) (@ F X3)))) (@ (@ tptp.ord_le1926595141338095240atural tptp.one_one_Code_natural) (@ (@ tptp.groups2279045934846249631atural F) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.code_natural))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (@ (@ tptp.ord_le1926595141338095240atural tptp.one_one_Code_natural) (@ F X3)))) (@ (@ tptp.ord_le1926595141338095240atural tptp.one_one_Code_natural) (@ (@ tptp.groups2650699495083094267atural F) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.code_natural))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A) (@ (@ tptp.ord_le1926595141338095240atural tptp.one_one_Code_natural) (@ F X3)))) (@ (@ tptp.ord_le1926595141338095240atural tptp.one_one_Code_natural) (@ (@ tptp.groups6518289543945209051atural F) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.code_natural))) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) A) (@ (@ tptp.ord_le1926595141338095240atural tptp.one_one_Code_natural) (@ F X3)))) (@ (@ tptp.ord_le1926595141338095240atural tptp.one_one_Code_natural) (@ (@ tptp.groups7008954963700796496atural F) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups73079841787564623at_rat F) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups1072433553688619179nt_rat F) A)))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_set_int) (G (-> tptp.int tptp.assn))) (=> (forall ((X3 tptp.set_int)) (=> (@ (@ tptp.member_set_int X3) B4) (@ tptp.finite_finite_int X3))) (=> (forall ((A12 tptp.set_int)) (=> (@ (@ tptp.member_set_int A12) B4) (forall ((A23 tptp.set_int)) (=> (@ (@ tptp.member_set_int A23) B4) (=> (not (= A12 A23)) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 A12) (=> (@ _let_1 A23) (= (@ G X3) tptp.one_one_assn)))))))))) (= (@ (@ tptp.groups7882442080178216443t_assn G) (@ tptp.comple3221217463730067765et_int B4)) (@ (@ (@ (@ tptp.comp_s4595925057662634336t_assn tptp.groups5950967880310095793t_assn) tptp.groups7882442080178216443t_assn) G) B4))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_set_o) (G (-> Bool tptp.assn))) (=> (forall ((X3 tptp.set_o)) (=> (@ (@ tptp.member_set_o X3) B4) (@ tptp.finite_finite_o X3))) (=> (forall ((A12 tptp.set_o)) (=> (@ (@ tptp.member_set_o A12) B4) (forall ((A23 tptp.set_o)) (=> (@ (@ tptp.member_set_o A23) B4) (=> (not (= A12 A23)) (forall ((X3 Bool)) (let ((_let_1 (@ tptp.member_o X3))) (=> (@ _let_1 A12) (=> (@ _let_1 A23) (= (@ G X3) tptp.one_one_assn)))))))))) (= (@ (@ tptp.groups5301882518646026715o_assn G) (@ tptp.comple90263536869209701_set_o B4)) (@ (@ (@ (@ tptp.comp_s518380907012905326o_assn tptp.groups6963733262650904763o_assn) tptp.groups5301882518646026715o_assn) G) B4))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_set_Product_unit) (G (-> tptp.product_unit tptp.assn))) (=> (forall ((X3 tptp.set_Product_unit)) (=> (@ (@ tptp.member5877623283571906838t_unit X3) B4) (@ tptp.finite4290736615968046902t_unit X3))) (=> (forall ((A12 tptp.set_Product_unit)) (=> (@ (@ tptp.member5877623283571906838t_unit A12) B4) (forall ((A23 tptp.set_Product_unit)) (=> (@ (@ tptp.member5877623283571906838t_unit A23) B4) (=> (not (= A12 A23)) (forall ((X3 tptp.product_unit)) (let ((_let_1 (@ tptp.member_Product_unit X3))) (=> (@ _let_1 A12) (=> (@ _let_1 A23) (= (@ G X3) tptp.one_one_assn)))))))))) (= (@ (@ tptp.groups5360233303959380816t_assn G) (@ tptp.comple3349607820504768346t_unit B4)) (@ (@ (@ (@ tptp.comp_s8247530669214396195t_assn tptp.groups2392624107559085104t_assn) tptp.groups5360233303959380816t_assn) G) B4))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_set_nat) (G (-> tptp.nat tptp.assn))) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) B4) (@ tptp.finite_finite_nat X3))) (=> (forall ((A12 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat A12) B4) (forall ((A23 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat A23) B4) (=> (not (= A12 A23)) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 A12) (=> (@ _let_1 A23) (= (@ G X3) tptp.one_one_assn)))))))))) (= (@ (@ tptp.groups6906906614972039071t_assn G) (@ tptp.comple7399068483239264473et_nat B4)) (@ (@ (@ (@ tptp.comp_s2451231738238893644t_assn tptp.groups1535173586962943829t_assn) tptp.groups6906906614972039071t_assn) G) B4))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (=> (forall ((X3 tptp.set_Code_integer)) (=> (@ (@ tptp.member1834298987299537450nteger X3) B4) (@ tptp.finite6017078050557962740nteger X3))) (=> (forall ((A12 tptp.set_Code_integer)) (=> (@ (@ tptp.member1834298987299537450nteger A12) B4) (forall ((A23 tptp.set_Code_integer)) (=> (@ (@ tptp.member1834298987299537450nteger A23) B4) (=> (not (= A12 A23)) (forall ((X3 tptp.code_integer)) (let ((_let_1 (@ tptp.member_Code_integer X3))) (=> (@ _let_1 A12) (=> (@ _let_1 A23) (= (@ G X3) tptp.one_one_assn)))))))))) (= (@ (@ tptp.groups1304777262505850412r_assn G) (@ tptp.comple739944243200306918nteger B4)) (@ (@ (@ (@ tptp.comp_s3531641609786562035r_assn tptp.groups4245288774754739042r_assn) tptp.groups1304777262505850412r_assn) G) B4))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_set_int) (G (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.set_int)) (=> (@ (@ tptp.member_set_int X3) B4) (@ tptp.finite_finite_int X3))) (=> (forall ((A12 tptp.set_int)) (=> (@ (@ tptp.member_set_int A12) B4) (forall ((A23 tptp.set_int)) (=> (@ (@ tptp.member_set_int A23) B4) (=> (not (= A12 A23)) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 A12) (=> (@ _let_1 A23) (= (@ G X3) tptp.one_one_nat)))))))))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) (@ tptp.comple3221217463730067765et_int B4)) (@ (@ (@ (@ tptp.comp_s3237642481825588056nt_nat tptp.groups6435469334873047129nt_nat) tptp.groups1707563613775114915nt_nat) G) B4))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_set_o) (G (-> Bool tptp.nat))) (=> (forall ((X3 tptp.set_o)) (=> (@ (@ tptp.member_set_o X3) B4) (@ tptp.finite_finite_o X3))) (=> (forall ((A12 tptp.set_o)) (=> (@ (@ tptp.member_set_o A12) B4) (forall ((A23 tptp.set_o)) (=> (@ (@ tptp.member_set_o A23) B4) (=> (not (= A12 A23)) (forall ((X3 Bool)) (let ((_let_1 (@ tptp.member_o X3))) (=> (@ _let_1 A12) (=> (@ _let_1 A23) (= (@ G X3) tptp.one_one_nat)))))))))) (= (@ (@ tptp.groups3504817904513533571_o_nat G) (@ tptp.comple90263536869209701_set_o B4)) (@ (@ (@ (@ tptp.comp_s6084864194472624150_o_nat tptp.groups4868773677410035043_o_nat) tptp.groups3504817904513533571_o_nat) G) B4))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_set_Product_unit) (G (-> tptp.product_unit tptp.nat))) (=> (forall ((X3 tptp.set_Product_unit)) (=> (@ (@ tptp.member5877623283571906838t_unit X3) B4) (@ tptp.finite4290736615968046902t_unit X3))) (=> (forall ((A12 tptp.set_Product_unit)) (=> (@ (@ tptp.member5877623283571906838t_unit A12) B4) (forall ((A23 tptp.set_Product_unit)) (=> (@ (@ tptp.member5877623283571906838t_unit A23) B4) (=> (not (= A12 A23)) (forall ((X3 tptp.product_unit)) (let ((_let_1 (@ tptp.member_Product_unit X3))) (=> (@ _let_1 A12) (=> (@ _let_1 A23) (= (@ G X3) tptp.one_one_nat)))))))))) (= (@ (@ tptp.groups396421249026171384it_nat G) (@ tptp.comple3349607820504768346t_unit B4)) (@ (@ (@ (@ tptp.comp_s8928436226432208331it_nat tptp.groups8454329047868613336it_nat) tptp.groups396421249026171384it_nat) G) B4))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (=> (forall ((X3 tptp.set_Code_integer)) (=> (@ (@ tptp.member1834298987299537450nteger X3) B4) (@ tptp.finite6017078050557962740nteger X3))) (=> (forall ((A12 tptp.set_Code_integer)) (=> (@ (@ tptp.member1834298987299537450nteger A12) B4) (forall ((A23 tptp.set_Code_integer)) (=> (@ (@ tptp.member1834298987299537450nteger A23) B4) (=> (not (= A12 A23)) (forall ((X3 tptp.code_integer)) (let ((_let_1 (@ tptp.member_Code_integer X3))) (=> (@ _let_1 A12) (=> (@ _let_1 A23) (= (@ G X3) tptp.one_one_nat)))))))))) (= (@ (@ tptp.groups3190895334310489300er_nat G) (@ tptp.comple739944243200306918nteger B4)) (@ (@ (@ (@ tptp.comp_s8759123648413916139er_nat tptp.groups6044384099095135754er_nat) tptp.groups3190895334310489300er_nat) G) B4))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_set_int) (G (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.set_int)) (=> (@ (@ tptp.member_set_int X3) B4) (@ tptp.finite_finite_int X3))) (=> (forall ((A12 tptp.set_int)) (=> (@ (@ tptp.member_set_int A12) B4) (forall ((A23 tptp.set_int)) (=> (@ (@ tptp.member_set_int A23) B4) (=> (not (= A12 A23)) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 A12) (=> (@ _let_1 A23) (= (@ G X3) tptp.one_one_int)))))))))) (= (@ (@ tptp.groups1705073143266064639nt_int G) (@ tptp.comple3221217463730067765et_int B4)) (@ (@ (@ (@ tptp.comp_s9098231955081793132nt_int tptp.groups6432978864363996853nt_int) tptp.groups1705073143266064639nt_int) G) B4))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A2) B) (= (@ (@ tptp.plus_plus_rat A2) B) tptp.zero_zero_rat))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A2) B) (= (@ (@ tptp.plus_plus_int A2) B) tptp.zero_zero_int))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A2) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A2) B) tptp.zero_z3403309356797280102nteger))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (= A2 (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A2) B) tptp.zero_zero_rat))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (= A2 (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A2) B) tptp.zero_zero_int))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (= A2 (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A2) B) tptp.zero_z3403309356797280102nteger))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A2) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A2) B))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A2) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A2) B))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A2) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A2) B))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A2)) A2) tptp.zero_zero_rat)))
% 5.65/5.94 (assert (forall ((A2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A2)) A2) tptp.zero_zero_int)))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A2)) A2) tptp.zero_z3403309356797280102nteger)))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A2) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A2) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A2) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A2)))))
% 5.65/5.94 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 5.65/5.94 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 5.65/5.94 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 5.65/5.94 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 5.65/5.94 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 5.65/5.94 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 5.65/5.94 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 5.65/5.94 (assert (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 5.65/5.94 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 5.65/5.94 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 5.65/5.94 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 5.65/5.94 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 5.65/5.94 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 5.65/5.94 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 5.65/5.94 (assert (= tptp.minus_minus_rat (lambda ((A6 tptp.rat) (B6 tptp.rat)) (@ (@ tptp.plus_plus_rat A6) (@ tptp.uminus_uminus_rat B6)))))
% 5.65/5.94 (assert (= tptp.minus_minus_int (lambda ((A6 tptp.int) (B6 tptp.int)) (@ (@ tptp.plus_plus_int A6) (@ tptp.uminus_uminus_int B6)))))
% 5.65/5.94 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A6 tptp.code_integer) (B6 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A6) (@ tptp.uminus1351360451143612070nteger B6)))))
% 5.65/5.94 (assert (= tptp.minus_minus_rat (lambda ((A6 tptp.rat) (B6 tptp.rat)) (@ (@ tptp.plus_plus_rat A6) (@ tptp.uminus_uminus_rat B6)))))
% 5.65/5.94 (assert (= tptp.minus_minus_int (lambda ((A6 tptp.int) (B6 tptp.int)) (@ (@ tptp.plus_plus_int A6) (@ tptp.uminus_uminus_int B6)))))
% 5.65/5.94 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A6 tptp.code_integer) (B6 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A6) (@ tptp.uminus1351360451143612070nteger B6)))))
% 5.65/5.94 (assert (forall ((B4 tptp.rat) (K3 tptp.rat) (B tptp.rat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A2))) (=> (= B4 (@ (@ tptp.plus_plus_rat K3) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K3)) (@ _let_1 B)))))))
% 5.65/5.94 (assert (forall ((B4 tptp.int) (K3 tptp.int) (B tptp.int) (A2 tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A2))) (=> (= B4 (@ (@ tptp.plus_plus_int K3) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K3)) (@ _let_1 B)))))))
% 5.65/5.94 (assert (forall ((B4 tptp.code_integer) (K3 tptp.code_integer) (B tptp.code_integer) (A2 tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A2))) (=> (= B4 (@ (@ tptp.plus_p5714425477246183910nteger K3) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K3)) (@ _let_1 B)))))))
% 5.65/5.94 (assert (forall ((X tptp.rat)) (= (= (@ (@ tptp.times_times_rat X) X) tptp.one_one_rat) (or (= X tptp.one_one_rat) (= X (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 5.65/5.94 (assert (forall ((X tptp.int)) (= (= (@ (@ tptp.times_times_int X) X) tptp.one_one_int) (or (= X tptp.one_one_int) (= X (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 5.65/5.94 (assert (forall ((X tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger X) X) tptp.one_one_Code_integer) (or (= X tptp.one_one_Code_integer) (= X (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 5.65/5.94 (assert (forall ((X tptp.set_Product_unit) (A2 tptp.set_Product_unit) (B tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit (@ (@ tptp.inf_in4660618365625256667t_unit (@ tptp.uminus5944136376168626660t_unit X)) A2)) (@ (@ tptp.inf_in4660618365625256667t_unit X) B)) tptp.bot_bo3957492148770167129t_unit)))
% 5.65/5.94 (assert (forall ((X tptp.set_o) (A2 tptp.set_o) (B tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.inf_inf_set_o (@ tptp.uminus_uminus_set_o X)) A2)) (@ (@ tptp.inf_inf_set_o X) B)) tptp.bot_bot_set_o)))
% 5.65/5.94 (assert (forall ((X tptp.set_nat) (A2 tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat X)) A2)) (@ (@ tptp.inf_inf_set_nat X) B)) tptp.bot_bot_set_nat)))
% 5.65/5.94 (assert (forall ((X tptp.set_int) (A2 tptp.set_int) (B tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int X)) A2)) (@ (@ tptp.inf_inf_set_int X) B)) tptp.bot_bot_set_int)))
% 5.65/5.94 (assert (forall ((X tptp.set_Pr4532377907799695533_nat_o) (A2 tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ (@ tptp.inf_in1906310914598751387_nat_o (@ tptp.uminus5254974436814262692_nat_o X)) A2)) (@ (@ tptp.inf_in1906310914598751387_nat_o X) B)) tptp.bot_bo7824918357723582233_nat_o)))
% 5.65/5.94 (assert (forall ((X tptp.assn) (A2 tptp.assn) (B tptp.assn)) (= (@ (@ tptp.inf_inf_assn (@ (@ tptp.inf_inf_assn (@ tptp.uminus_uminus_assn X)) A2)) (@ (@ tptp.inf_inf_assn X) B)) tptp.bot_bot_assn)))
% 5.65/5.94 (assert (forall ((X tptp.product_unit) (A2 tptp.product_unit) (B tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit (@ (@ tptp.inf_inf_Product_unit (@ tptp.uminus2952777764628376836t_unit X)) A2)) (@ (@ tptp.inf_inf_Product_unit X) B)) tptp.bot_bot_Product_unit)))
% 5.65/5.94 (assert (forall ((X tptp.set_Product_unit) (A2 tptp.set_Product_unit) (B tptp.set_Product_unit)) (= (@ (@ tptp.inf_in4660618365625256667t_unit (@ (@ tptp.inf_in4660618365625256667t_unit X) A2)) (@ (@ tptp.inf_in4660618365625256667t_unit (@ tptp.uminus5944136376168626660t_unit X)) B)) tptp.bot_bo3957492148770167129t_unit)))
% 5.65/5.94 (assert (forall ((X tptp.set_o) (A2 tptp.set_o) (B tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.inf_inf_set_o X) A2)) (@ (@ tptp.inf_inf_set_o (@ tptp.uminus_uminus_set_o X)) B)) tptp.bot_bot_set_o)))
% 5.65/5.94 (assert (forall ((X tptp.set_nat) (A2 tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.inf_inf_set_nat X) A2)) (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat X)) B)) tptp.bot_bot_set_nat)))
% 5.65/5.94 (assert (forall ((X tptp.set_int) (A2 tptp.set_int) (B tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.inf_inf_set_int X) A2)) (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int X)) B)) tptp.bot_bot_set_int)))
% 5.65/5.94 (assert (forall ((X tptp.set_Pr4532377907799695533_nat_o) (A2 tptp.set_Pr4532377907799695533_nat_o) (B tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.inf_in1906310914598751387_nat_o (@ (@ tptp.inf_in1906310914598751387_nat_o X) A2)) (@ (@ tptp.inf_in1906310914598751387_nat_o (@ tptp.uminus5254974436814262692_nat_o X)) B)) tptp.bot_bo7824918357723582233_nat_o)))
% 5.65/5.94 (assert (forall ((X tptp.assn) (A2 tptp.assn) (B tptp.assn)) (= (@ (@ tptp.inf_inf_assn (@ (@ tptp.inf_inf_assn X) A2)) (@ (@ tptp.inf_inf_assn (@ tptp.uminus_uminus_assn X)) B)) tptp.bot_bot_assn)))
% 5.65/5.94 (assert (forall ((X tptp.product_unit) (A2 tptp.product_unit) (B tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit (@ (@ tptp.inf_inf_Product_unit X) A2)) (@ (@ tptp.inf_inf_Product_unit (@ tptp.uminus2952777764628376836t_unit X)) B)) tptp.bot_bot_Product_unit)))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit)) (= (@ (@ tptp.ord_le3507040750410214029t_unit A) (@ tptp.uminus5944136376168626660t_unit A)) (= A tptp.bot_bo3957492148770167129t_unit))))
% 5.65/5.94 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o A) (@ tptp.uminus_uminus_set_o A)) (= A tptp.bot_bot_set_o))))
% 5.65/5.94 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A) (@ tptp.uminus1532241313380277803et_int A)) (= A tptp.bot_bot_set_int))))
% 5.65/5.94 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o)) (= (@ (@ tptp.ord_le2965882846123202637_nat_o A) (@ tptp.uminus5254974436814262692_nat_o A)) (= A tptp.bot_bo7824918357723582233_nat_o))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) (@ tptp.uminus5710092332889474511et_nat A)) (= A tptp.bot_bot_set_nat))))
% 5.65/5.94 (assert (= (@ tptp.uminus5254974436814262692_nat_o tptp.top_to4869887016220417533_nat_o) tptp.bot_bo7824918357723582233_nat_o))
% 5.65/5.94 (assert (= (@ tptp.uminus5944136376168626660t_unit tptp.top_to1996260823553986621t_unit) tptp.bot_bo3957492148770167129t_unit))
% 5.65/5.94 (assert (= (@ tptp.uminus_uminus_set_o tptp.top_top_set_o) tptp.bot_bot_set_o))
% 5.65/5.94 (assert (= (@ tptp.uminus5710092332889474511et_nat tptp.top_top_set_nat) tptp.bot_bot_set_nat))
% 5.65/5.94 (assert (= (@ tptp.uminus1532241313380277803et_int tptp.top_top_set_int) tptp.bot_bot_set_int))
% 5.65/5.94 (assert (= (@ tptp.uminus5254974436814262692_nat_o tptp.bot_bo7824918357723582233_nat_o) tptp.top_to4869887016220417533_nat_o))
% 5.65/5.94 (assert (= (@ tptp.uminus5944136376168626660t_unit tptp.bot_bo3957492148770167129t_unit) tptp.top_to1996260823553986621t_unit))
% 5.65/5.94 (assert (= (@ tptp.uminus_uminus_set_o tptp.bot_bot_set_o) tptp.top_top_set_o))
% 5.65/5.94 (assert (= (@ tptp.uminus5710092332889474511et_nat tptp.bot_bot_set_nat) tptp.top_top_set_nat))
% 5.65/5.94 (assert (= (@ tptp.uminus1532241313380277803et_int tptp.bot_bot_set_int) tptp.top_top_set_int))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit)) (= (@ (@ tptp.sup_su793286257634532545t_unit (@ tptp.uminus5944136376168626660t_unit A)) A) tptp.top_to1996260823553986621t_unit)))
% 5.65/5.94 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o (@ tptp.uminus_uminus_set_o A)) A) tptp.top_top_set_o)))
% 5.65/5.94 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ tptp.uminus5710092332889474511et_nat A)) A) tptp.top_top_set_nat)))
% 5.65/5.94 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int (@ tptp.uminus1532241313380277803et_int A)) A) tptp.top_top_set_int)))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit)) (= (@ (@ tptp.sup_su793286257634532545t_unit A) (@ tptp.uminus5944136376168626660t_unit A)) tptp.top_to1996260823553986621t_unit)))
% 5.65/5.94 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o A) (@ tptp.uminus_uminus_set_o A)) tptp.top_top_set_o)))
% 5.65/5.94 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A) (@ tptp.uminus5710092332889474511et_nat A)) tptp.top_top_set_nat)))
% 5.65/5.94 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A) (@ tptp.uminus1532241313380277803et_int A)) tptp.top_top_set_int)))
% 5.65/5.94 (assert (= tptp.uminus5944136376168626660t_unit (@ tptp.minus_6452836326544984404t_unit tptp.top_to1996260823553986621t_unit)))
% 5.65/5.94 (assert (= tptp.uminus_uminus_set_o (@ tptp.minus_minus_set_o tptp.top_top_set_o)))
% 5.65/5.94 (assert (= tptp.uminus1532241313380277803et_int (@ tptp.minus_minus_set_int tptp.top_top_set_int)))
% 5.65/5.94 (assert (= tptp.uminus5710092332889474511et_nat (@ tptp.minus_minus_set_nat tptp.top_top_set_nat)))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.inf_inf_set_nat A) B4)) (@ (@ tptp.sup_sup_set_nat (@ tptp.uminus5710092332889474511et_nat A)) (@ tptp.uminus5710092332889474511et_nat B4)))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat A)) (@ tptp.uminus5710092332889474511et_nat B4)))))
% 5.65/5.94 (assert (= tptp.gbinomial_rat (lambda ((A6 tptp.rat) (K5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K5)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat K5)) A6)) tptp.one_one_rat)) K5)))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (= (@ (@ tptp.times_times_rat (@ _let_1 K3)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) tptp.one_one_rat)) K3)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K3))) tptp.one_one_rat)) N2))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_set_nat) (G (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) C5) (@ tptp.finite_finite_nat X3))) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) C5) (forall ((Xa3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa3) C5) (=> (not (= X3 Xa3)) (= (@ (@ tptp.inf_inf_set_nat X3) Xa3) tptp.bot_bot_set_nat)))))) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.comple7399068483239264473et_nat C5)) (@ (@ (@ (@ tptp.comp_s5456809700045850692at_nat tptp.groups4248547760180025341at_nat) tptp.groups708209901874060359at_nat) G) C5))))))
% 5.65/5.94 (assert (forall ((M tptp.set_nat)) (=> (@ tptp.finite_finite_nat M) (= (@ tptp.gcd_Gcd_nat M) (@ tptp.gcd_Gcd_nat (@ (@ tptp.minus_minus_set_nat M) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (A tptp.set_nat)) (=> (@ (@ tptp.dvd_dvd_nat A2) tptp.one_one_nat) (=> (@ (@ tptp.member_nat A2) A) (= (@ tptp.gcd_Gcd_nat A) tptp.one_one_nat)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (A tptp.set_int)) (=> (@ (@ tptp.dvd_dvd_int A2) tptp.one_one_int) (=> (@ (@ tptp.member_int A2) A) (= (@ tptp.gcd_Gcd_int A) tptp.one_one_int)))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.code_natural))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_nat X3) A) (and (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) _let_1) (@ (@ tptp.ord_le1926595141338095240atural _let_1) tptp.one_one_Code_natural))))) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.groups2279045934846249631atural F) A)) tptp.one_one_Code_natural))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.code_natural))) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_int X3) A) (and (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) _let_1) (@ (@ tptp.ord_le1926595141338095240atural _let_1) tptp.one_one_Code_natural))))) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.groups2650699495083094267atural F) A)) tptp.one_one_Code_natural))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.code_natural))) (=> (forall ((X3 Bool)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_o X3) A) (and (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) _let_1) (@ (@ tptp.ord_le1926595141338095240atural _let_1) tptp.one_one_Code_natural))))) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.groups6518289543945209051atural F) A)) tptp.one_one_Code_natural))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.code_natural))) (=> (forall ((X3 tptp.product_unit)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_Product_unit X3) A) (and (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) _let_1) (@ (@ tptp.ord_le1926595141338095240atural _let_1) tptp.one_one_Code_natural))))) (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.groups7008954963700796496atural F) A)) tptp.one_one_Code_natural))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_nat X3) A) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) tptp.one_one_Code_integer))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups3455450783089532116nteger F) A)) tptp.one_one_Code_integer))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.code_integer))) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_int X3) A) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) tptp.one_one_Code_integer))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups3827104343326376752nteger F) A)) tptp.one_one_Code_integer))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.code_integer))) (=> (forall ((X3 Bool)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_o X3) A) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) tptp.one_one_Code_integer))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7694694392188491536nteger F) A)) tptp.one_one_Code_integer))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.code_integer))) (=> (forall ((X3 tptp.product_unit)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_Product_unit X3) A) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) tptp.one_one_Code_integer))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups8185359811944078981nteger F) A)) tptp.one_one_Code_integer))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_nat X3) A) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A)) tptp.one_one_rat))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_int X3) A) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A)) tptp.one_one_rat))))
% 5.65/5.94 (assert (forall ((R3 (-> tptp.code_integer tptp.code_integer Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.code_integer)) (G (-> tptp.nat tptp.code_integer))) (=> (@ (@ R3 tptp.one_one_Code_integer) tptp.one_one_Code_integer) (=> (forall ((X12 tptp.code_integer) (Y12 tptp.code_integer) (X23 tptp.code_integer) (Y23 tptp.code_integer)) (=> (and (@ (@ R3 X12) X23) (@ (@ R3 Y12) Y23)) (@ (@ R3 (@ (@ tptp.times_3573771949741848930nteger X12) Y12)) (@ (@ tptp.times_3573771949741848930nteger X23) Y23)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (@ (@ R3 (@ H2 X3)) (@ G X3)))) (@ (@ R3 (@ (@ tptp.groups3455450783089532116nteger H2) S)) (@ (@ tptp.groups3455450783089532116nteger G) S))))))))
% 5.65/5.94 (assert (forall ((R3 (-> tptp.code_integer tptp.code_integer Bool)) (S tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer))) (=> (@ (@ R3 tptp.one_one_Code_integer) tptp.one_one_Code_integer) (=> (forall ((X12 tptp.code_integer) (Y12 tptp.code_integer) (X23 tptp.code_integer) (Y23 tptp.code_integer)) (=> (and (@ (@ R3 X12) X23) (@ (@ R3 Y12) Y23)) (@ (@ R3 (@ (@ tptp.times_3573771949741848930nteger X12) Y12)) (@ (@ tptp.times_3573771949741848930nteger X23) Y23)))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (@ (@ R3 (@ H2 X3)) (@ G X3)))) (@ (@ R3 (@ (@ tptp.groups3674199335183972705nteger H2) S)) (@ (@ tptp.groups3674199335183972705nteger G) S))))))))
% 5.65/5.94 (assert (forall ((R3 (-> tptp.code_natural tptp.code_natural Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.code_natural)) (G (-> tptp.nat tptp.code_natural))) (=> (@ (@ R3 tptp.one_one_Code_natural) tptp.one_one_Code_natural) (=> (forall ((X12 tptp.code_natural) (Y12 tptp.code_natural) (X23 tptp.code_natural) (Y23 tptp.code_natural)) (=> (and (@ (@ R3 X12) X23) (@ (@ R3 Y12) Y23)) (@ (@ R3 (@ (@ tptp.times_2397367101498566445atural X12) Y12)) (@ (@ tptp.times_2397367101498566445atural X23) Y23)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (@ (@ R3 (@ H2 X3)) (@ G X3)))) (@ (@ R3 (@ (@ tptp.groups2279045934846249631atural H2) S)) (@ (@ tptp.groups2279045934846249631atural G) S))))))))
% 5.65/5.94 (assert (forall ((R3 (-> tptp.code_natural tptp.code_natural Bool)) (S tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.code_natural)) (G (-> tptp.code_integer tptp.code_natural))) (=> (@ (@ R3 tptp.one_one_Code_natural) tptp.one_one_Code_natural) (=> (forall ((X12 tptp.code_natural) (Y12 tptp.code_natural) (X23 tptp.code_natural) (Y23 tptp.code_natural)) (=> (and (@ (@ R3 X12) X23) (@ (@ R3 Y12) Y23)) (@ (@ R3 (@ (@ tptp.times_2397367101498566445atural X12) Y12)) (@ (@ tptp.times_2397367101498566445atural X23) Y23)))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (@ (@ R3 (@ H2 X3)) (@ G X3)))) (@ (@ R3 (@ (@ tptp.groups2497794486940690220atural H2) S)) (@ (@ tptp.groups2497794486940690220atural G) S))))))))
% 5.65/5.94 (assert (forall ((R3 (-> tptp.assn tptp.assn Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.assn)) (G (-> tptp.nat tptp.assn))) (=> (@ (@ R3 tptp.one_one_assn) tptp.one_one_assn) (=> (forall ((X12 tptp.assn) (Y12 tptp.assn) (X23 tptp.assn) (Y23 tptp.assn)) (=> (and (@ (@ R3 X12) X23) (@ (@ R3 Y12) Y23)) (@ (@ R3 (@ (@ tptp.times_times_assn X12) Y12)) (@ (@ tptp.times_times_assn X23) Y23)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (@ (@ R3 (@ H2 X3)) (@ G X3)))) (@ (@ R3 (@ (@ tptp.groups6906906614972039071t_assn H2) S)) (@ (@ tptp.groups6906906614972039071t_assn G) S))))))))
% 5.65/5.94 (assert (forall ((R3 (-> tptp.assn tptp.assn Bool)) (S tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.assn)) (G (-> tptp.code_integer tptp.assn))) (=> (@ (@ R3 tptp.one_one_assn) tptp.one_one_assn) (=> (forall ((X12 tptp.assn) (Y12 tptp.assn) (X23 tptp.assn) (Y23 tptp.assn)) (=> (and (@ (@ R3 X12) X23) (@ (@ R3 Y12) Y23)) (@ (@ R3 (@ (@ tptp.times_times_assn X12) Y12)) (@ (@ tptp.times_times_assn X23) Y23)))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (@ (@ R3 (@ H2 X3)) (@ G X3)))) (@ (@ R3 (@ (@ tptp.groups1304777262505850412r_assn H2) S)) (@ (@ tptp.groups1304777262505850412r_assn G) S))))))))
% 5.65/5.94 (assert (forall ((R3 (-> tptp.rat tptp.rat Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ (@ R3 tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X12 tptp.rat) (Y12 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R3 X12) X23) (@ (@ R3 Y12) Y23)) (@ (@ R3 (@ (@ tptp.times_times_rat X12) Y12)) (@ (@ tptp.times_times_rat X23) Y23)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (@ (@ R3 (@ H2 X3)) (@ G X3)))) (@ (@ R3 (@ (@ tptp.groups73079841787564623at_rat H2) S)) (@ (@ tptp.groups73079841787564623at_rat G) S))))))))
% 5.65/5.94 (assert (forall ((R3 (-> tptp.rat tptp.rat Bool)) (S tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ (@ R3 tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X12 tptp.rat) (Y12 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R3 X12) X23) (@ (@ R3 Y12) Y23)) (@ (@ R3 (@ (@ tptp.times_times_rat X12) Y12)) (@ (@ tptp.times_times_rat X23) Y23)))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (@ (@ R3 (@ H2 X3)) (@ G X3)))) (@ (@ R3 (@ (@ tptp.groups2555765274223993564er_rat H2) S)) (@ (@ tptp.groups2555765274223993564er_rat G) S))))))))
% 5.65/5.94 (assert (forall ((R3 (-> tptp.nat tptp.nat Bool)) (S tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (=> (@ (@ R3 tptp.one_one_nat) tptp.one_one_nat) (=> (forall ((X12 tptp.nat) (Y12 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R3 X12) X23) (@ (@ R3 Y12) Y23)) (@ (@ R3 (@ (@ tptp.times_times_nat X12) Y12)) (@ (@ tptp.times_times_nat X23) Y23)))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (@ (@ R3 (@ H2 X3)) (@ G X3)))) (@ (@ R3 (@ (@ tptp.groups3190895334310489300er_nat H2) S)) (@ (@ tptp.groups3190895334310489300er_nat G) S))))))))
% 5.65/5.94 (assert (forall ((R3 (-> tptp.int tptp.int Bool)) (S tptp.set_nat) (H2 (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ (@ R3 tptp.one_one_int) tptp.one_one_int) (=> (forall ((X12 tptp.int) (Y12 tptp.int) (X23 tptp.int) (Y23 tptp.int)) (=> (and (@ (@ R3 X12) X23) (@ (@ R3 Y12) Y23)) (@ (@ R3 (@ (@ tptp.times_times_int X12) Y12)) (@ (@ tptp.times_times_int X23) Y23)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (@ (@ R3 (@ H2 X3)) (@ G X3)))) (@ (@ R3 (@ (@ tptp.groups705719431365010083at_int H2) S)) (@ (@ tptp.groups705719431365010083at_int G) S))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A)))) (let ((_let_4 (@ (@ tptp.member_int X) A))) (=> (@ tptp.finite_finite_int A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_assn (@ G X)) _let_2)))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (X Bool) (G (-> Bool tptp.assn))) (let ((_let_1 (@ tptp.groups5301882518646026715o_assn G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_o X) A)))) (let ((_let_4 (@ (@ tptp.member_o X) A))) (=> (@ tptp.finite_finite_o A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_assn (@ G X)) _let_2)))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit) (G (-> tptp.product_unit tptp.assn))) (let ((_let_1 (@ tptp.groups5360233303959380816t_assn G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Product_unit X) A)))) (let ((_let_4 (@ (@ tptp.member_Product_unit X) A))) (=> (@ tptp.finite4290736615968046902t_unit A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_assn (@ G X)) _let_2)))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X) A)))) (let ((_let_4 (@ (@ tptp.member_nat X) A))) (=> (@ tptp.finite_finite_nat A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_assn (@ G X)) _let_2)))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Code_integer X) A)))) (let ((_let_4 (@ (@ tptp.member_Code_integer X) A))) (=> (@ tptp.finite6017078050557962740nteger A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_assn (@ G X)) _let_2)))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A)))) (let ((_let_4 (@ (@ tptp.member_int X) A))) (=> (@ tptp.finite_finite_int A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G X)) _let_2)))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (X Bool) (G (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups2869687844427037835_o_rat G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_o X) A)))) (let ((_let_4 (@ (@ tptp.member_o X) A))) (=> (@ tptp.finite_finite_o A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G X)) _let_2)))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit) (G (-> tptp.product_unit tptp.rat))) (let ((_let_1 (@ tptp.groups8984663225794451456it_rat G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Product_unit X) A)))) (let ((_let_4 (@ (@ tptp.member_Product_unit X) A))) (=> (@ tptp.finite4290736615968046902t_unit A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G X)) _let_2)))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X) A)))) (let ((_let_4 (@ (@ tptp.member_nat X) A))) (=> (@ tptp.finite_finite_nat A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G X)) _let_2)))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_Code_integer X) A)))) (let ((_let_4 (@ (@ tptp.member_Code_integer X) A))) (=> (@ tptp.finite6017078050557962740nteger A) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G X)) _let_2)))))))))))
% 5.65/5.94 (assert (forall ((S4 tptp.set_int) (T5 tptp.set_int) (S tptp.set_int) (I2 (-> tptp.int tptp.int)) (J (-> tptp.int tptp.int)) (T2 tptp.set_int) (G (-> tptp.int tptp.assn)) (H2 (-> tptp.int tptp.assn))) (=> (@ tptp.finite_finite_int S4) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int S) S4)) (= (@ I2 (@ J A4)) A4))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int S) S4)) (@ (@ tptp.member_int (@ J A4)) (@ (@ tptp.minus_minus_set_int T2) T5)))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T2) T5)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T2) T5)) (@ (@ tptp.member_int (@ I2 B2)) (@ (@ tptp.minus_minus_set_int S) S4)))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) S4) (= (@ G A4) tptp.one_one_assn))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) T5) (= (@ H2 B2) tptp.one_one_assn))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) S) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups7882442080178216443t_assn G) S) (@ (@ tptp.groups7882442080178216443t_assn H2) T2)))))))))))))
% 5.65/5.94 (assert (forall ((S4 tptp.set_int) (T5 tptp.set_o) (S tptp.set_int) (I2 (-> Bool tptp.int)) (J (-> tptp.int Bool)) (T2 tptp.set_o) (G (-> tptp.int tptp.assn)) (H2 (-> Bool tptp.assn))) (=> (@ tptp.finite_finite_int S4) (=> (@ tptp.finite_finite_o T5) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int S) S4)) (= (@ I2 (@ J A4)) A4))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int S) S4)) (@ (@ tptp.member_o (@ J A4)) (@ (@ tptp.minus_minus_set_o T2) T5)))) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) (@ (@ tptp.minus_minus_set_o T2) T5)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) (@ (@ tptp.minus_minus_set_o T2) T5)) (@ (@ tptp.member_int (@ I2 B2)) (@ (@ tptp.minus_minus_set_int S) S4)))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) S4) (= (@ G A4) tptp.one_one_assn))) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) T5) (= (@ H2 B2) tptp.one_one_assn))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) S) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups7882442080178216443t_assn G) S) (@ (@ tptp.groups5301882518646026715o_assn H2) T2)))))))))))))
% 5.65/5.94 (assert (forall ((S4 tptp.set_int) (T5 tptp.set_Product_unit) (S tptp.set_int) (I2 (-> tptp.product_unit tptp.int)) (J (-> tptp.int tptp.product_unit)) (T2 tptp.set_Product_unit) (G (-> tptp.int tptp.assn)) (H2 (-> tptp.product_unit tptp.assn))) (=> (@ tptp.finite_finite_int S4) (=> (@ tptp.finite4290736615968046902t_unit T5) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int S) S4)) (= (@ I2 (@ J A4)) A4))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int S) S4)) (@ (@ tptp.member_Product_unit (@ J A4)) (@ (@ tptp.minus_6452836326544984404t_unit T2) T5)))) (=> (forall ((B2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit B2) (@ (@ tptp.minus_6452836326544984404t_unit T2) T5)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit B2) (@ (@ tptp.minus_6452836326544984404t_unit T2) T5)) (@ (@ tptp.member_int (@ I2 B2)) (@ (@ tptp.minus_minus_set_int S) S4)))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) S4) (= (@ G A4) tptp.one_one_assn))) (=> (forall ((B2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit B2) T5) (= (@ H2 B2) tptp.one_one_assn))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) S) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups7882442080178216443t_assn G) S) (@ (@ tptp.groups5360233303959380816t_assn H2) T2)))))))))))))
% 5.65/5.94 (assert (forall ((S4 tptp.set_o) (T5 tptp.set_int) (S tptp.set_o) (I2 (-> tptp.int Bool)) (J (-> Bool tptp.int)) (T2 tptp.set_int) (G (-> Bool tptp.assn)) (H2 (-> tptp.int tptp.assn))) (=> (@ tptp.finite_finite_o S4) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o S) S4)) (= (@ I2 (@ J A4)) A4))) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o S) S4)) (@ (@ tptp.member_int (@ J A4)) (@ (@ tptp.minus_minus_set_int T2) T5)))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T2) T5)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T2) T5)) (@ (@ tptp.member_o (@ I2 B2)) (@ (@ tptp.minus_minus_set_o S) S4)))) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) S4) (= (@ G A4) tptp.one_one_assn))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) T5) (= (@ H2 B2) tptp.one_one_assn))) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) S) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups5301882518646026715o_assn G) S) (@ (@ tptp.groups7882442080178216443t_assn H2) T2)))))))))))))
% 5.65/5.94 (assert (forall ((S4 tptp.set_o) (T5 tptp.set_o) (S tptp.set_o) (I2 (-> Bool Bool)) (J (-> Bool Bool)) (T2 tptp.set_o) (G (-> Bool tptp.assn)) (H2 (-> Bool tptp.assn))) (=> (@ tptp.finite_finite_o S4) (=> (@ tptp.finite_finite_o T5) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o S) S4)) (= (@ I2 (@ J A4)) A4))) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o S) S4)) (@ (@ tptp.member_o (@ J A4)) (@ (@ tptp.minus_minus_set_o T2) T5)))) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) (@ (@ tptp.minus_minus_set_o T2) T5)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) (@ (@ tptp.minus_minus_set_o T2) T5)) (@ (@ tptp.member_o (@ I2 B2)) (@ (@ tptp.minus_minus_set_o S) S4)))) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) S4) (= (@ G A4) tptp.one_one_assn))) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) T5) (= (@ H2 B2) tptp.one_one_assn))) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) S) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups5301882518646026715o_assn G) S) (@ (@ tptp.groups5301882518646026715o_assn H2) T2)))))))))))))
% 5.65/5.94 (assert (forall ((S4 tptp.set_o) (T5 tptp.set_Product_unit) (S tptp.set_o) (I2 (-> tptp.product_unit Bool)) (J (-> Bool tptp.product_unit)) (T2 tptp.set_Product_unit) (G (-> Bool tptp.assn)) (H2 (-> tptp.product_unit tptp.assn))) (=> (@ tptp.finite_finite_o S4) (=> (@ tptp.finite4290736615968046902t_unit T5) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o S) S4)) (= (@ I2 (@ J A4)) A4))) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o S) S4)) (@ (@ tptp.member_Product_unit (@ J A4)) (@ (@ tptp.minus_6452836326544984404t_unit T2) T5)))) (=> (forall ((B2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit B2) (@ (@ tptp.minus_6452836326544984404t_unit T2) T5)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit B2) (@ (@ tptp.minus_6452836326544984404t_unit T2) T5)) (@ (@ tptp.member_o (@ I2 B2)) (@ (@ tptp.minus_minus_set_o S) S4)))) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) S4) (= (@ G A4) tptp.one_one_assn))) (=> (forall ((B2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit B2) T5) (= (@ H2 B2) tptp.one_one_assn))) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) S) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups5301882518646026715o_assn G) S) (@ (@ tptp.groups5360233303959380816t_assn H2) T2)))))))))))))
% 5.65/5.94 (assert (forall ((S4 tptp.set_Product_unit) (T5 tptp.set_int) (S tptp.set_Product_unit) (I2 (-> tptp.int tptp.product_unit)) (J (-> tptp.product_unit tptp.int)) (T2 tptp.set_int) (G (-> tptp.product_unit tptp.assn)) (H2 (-> tptp.int tptp.assn))) (=> (@ tptp.finite4290736615968046902t_unit S4) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) (@ (@ tptp.minus_6452836326544984404t_unit S) S4)) (= (@ I2 (@ J A4)) A4))) (=> (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) (@ (@ tptp.minus_6452836326544984404t_unit S) S4)) (@ (@ tptp.member_int (@ J A4)) (@ (@ tptp.minus_minus_set_int T2) T5)))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T2) T5)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int T2) T5)) (@ (@ tptp.member_Product_unit (@ I2 B2)) (@ (@ tptp.minus_6452836326544984404t_unit S) S4)))) (=> (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) S4) (= (@ G A4) tptp.one_one_assn))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) T5) (= (@ H2 B2) tptp.one_one_assn))) (=> (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) S) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups5360233303959380816t_assn G) S) (@ (@ tptp.groups7882442080178216443t_assn H2) T2)))))))))))))
% 5.65/5.94 (assert (forall ((S4 tptp.set_Product_unit) (T5 tptp.set_o) (S tptp.set_Product_unit) (I2 (-> Bool tptp.product_unit)) (J (-> tptp.product_unit Bool)) (T2 tptp.set_o) (G (-> tptp.product_unit tptp.assn)) (H2 (-> Bool tptp.assn))) (=> (@ tptp.finite4290736615968046902t_unit S4) (=> (@ tptp.finite_finite_o T5) (=> (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) (@ (@ tptp.minus_6452836326544984404t_unit S) S4)) (= (@ I2 (@ J A4)) A4))) (=> (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) (@ (@ tptp.minus_6452836326544984404t_unit S) S4)) (@ (@ tptp.member_o (@ J A4)) (@ (@ tptp.minus_minus_set_o T2) T5)))) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) (@ (@ tptp.minus_minus_set_o T2) T5)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) (@ (@ tptp.minus_minus_set_o T2) T5)) (@ (@ tptp.member_Product_unit (@ I2 B2)) (@ (@ tptp.minus_6452836326544984404t_unit S) S4)))) (=> (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) S4) (= (@ G A4) tptp.one_one_assn))) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) T5) (= (@ H2 B2) tptp.one_one_assn))) (=> (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) S) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups5360233303959380816t_assn G) S) (@ (@ tptp.groups5301882518646026715o_assn H2) T2)))))))))))))
% 5.65/5.94 (assert (forall ((S4 tptp.set_Product_unit) (T5 tptp.set_Product_unit) (S tptp.set_Product_unit) (I2 (-> tptp.product_unit tptp.product_unit)) (J (-> tptp.product_unit tptp.product_unit)) (T2 tptp.set_Product_unit) (G (-> tptp.product_unit tptp.assn)) (H2 (-> tptp.product_unit tptp.assn))) (=> (@ tptp.finite4290736615968046902t_unit S4) (=> (@ tptp.finite4290736615968046902t_unit T5) (=> (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) (@ (@ tptp.minus_6452836326544984404t_unit S) S4)) (= (@ I2 (@ J A4)) A4))) (=> (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) (@ (@ tptp.minus_6452836326544984404t_unit S) S4)) (@ (@ tptp.member_Product_unit (@ J A4)) (@ (@ tptp.minus_6452836326544984404t_unit T2) T5)))) (=> (forall ((B2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit B2) (@ (@ tptp.minus_6452836326544984404t_unit T2) T5)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit B2) (@ (@ tptp.minus_6452836326544984404t_unit T2) T5)) (@ (@ tptp.member_Product_unit (@ I2 B2)) (@ (@ tptp.minus_6452836326544984404t_unit S) S4)))) (=> (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) S4) (= (@ G A4) tptp.one_one_assn))) (=> (forall ((B2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit B2) T5) (= (@ H2 B2) tptp.one_one_assn))) (=> (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) S) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups5360233303959380816t_assn G) S) (@ (@ tptp.groups5360233303959380816t_assn H2) T2)))))))))))))
% 5.65/5.94 (assert (forall ((S4 tptp.set_int) (T5 tptp.set_Code_integer) (S tptp.set_int) (I2 (-> tptp.code_integer tptp.int)) (J (-> tptp.int tptp.code_integer)) (T2 tptp.set_Code_integer) (G (-> tptp.int tptp.assn)) (H2 (-> tptp.code_integer tptp.assn))) (=> (@ tptp.finite_finite_int S4) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int S) S4)) (= (@ I2 (@ J A4)) A4))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int S) S4)) (@ (@ tptp.member_Code_integer (@ J A4)) (@ (@ tptp.minus_2355218937544613996nteger T2) T5)))) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) (@ (@ tptp.minus_2355218937544613996nteger T2) T5)) (= (@ J (@ I2 B2)) B2))) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) (@ (@ tptp.minus_2355218937544613996nteger T2) T5)) (@ (@ tptp.member_int (@ I2 B2)) (@ (@ tptp.minus_minus_set_int S) S4)))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) S4) (= (@ G A4) tptp.one_one_assn))) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) T5) (= (@ H2 B2) tptp.one_one_assn))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) S) (= (@ H2 (@ J A4)) (@ G A4)))) (= (@ (@ tptp.groups7882442080178216443t_assn G) S) (@ (@ tptp.groups1304777262505850412r_assn H2) T2)))))))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (K3 tptp.nat)) (= (@ (@ tptp.gbinomial_rat (@ tptp.uminus_uminus_rat A2)) K3) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A2) (@ tptp.semiri681578069525770553at_rat K3))) tptp.one_one_rat)) K3)))))
% 5.65/5.94 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 5.65/5.94 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 5.65/5.94 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 5.65/5.94 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 5.65/5.94 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 5.65/5.94 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 5.65/5.94 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 5.65/5.94 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 5.65/5.94 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 5.65/5.94 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 5.65/5.94 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 5.65/5.94 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 5.65/5.94 (assert (forall ((X tptp.set_Product_unit) (Y tptp.set_Product_unit)) (= (= (@ (@ tptp.inf_in4660618365625256667t_unit X) Y) tptp.bot_bo3957492148770167129t_unit) (@ (@ tptp.ord_le3507040750410214029t_unit X) (@ tptp.uminus5944136376168626660t_unit Y)))))
% 5.65/5.94 (assert (forall ((X tptp.set_o) (Y tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o X) Y) tptp.bot_bot_set_o) (@ (@ tptp.ord_less_eq_set_o X) (@ tptp.uminus_uminus_set_o Y)))))
% 5.65/5.94 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int X) Y) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X) (@ tptp.uminus1532241313380277803et_int Y)))))
% 5.65/5.94 (assert (forall ((X tptp.set_Pr4532377907799695533_nat_o) (Y tptp.set_Pr4532377907799695533_nat_o)) (= (= (@ (@ tptp.inf_in1906310914598751387_nat_o X) Y) tptp.bot_bo7824918357723582233_nat_o) (@ (@ tptp.ord_le2965882846123202637_nat_o X) (@ tptp.uminus5254974436814262692_nat_o Y)))))
% 5.65/5.94 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (= (@ (@ tptp.inf_inf_assn X) Y) tptp.bot_bot_assn) (@ (@ tptp.ord_less_eq_assn X) (@ tptp.uminus_uminus_assn Y)))))
% 5.65/5.94 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (= (@ (@ tptp.inf_inf_Product_unit X) Y) tptp.bot_bot_Product_unit) (@ (@ tptp.ord_le3221252021190050221t_unit X) (@ tptp.uminus2952777764628376836t_unit Y)))))
% 5.65/5.94 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat X) Y) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X) (@ tptp.uminus5710092332889474511et_nat Y)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A2)) N2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2)) (@ (@ tptp.power_power_rat A2) N2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A2)) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)) (@ (@ tptp.power_power_int A2) N2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A2)) N2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)) (@ (@ tptp.power_8256067586552552935nteger A2) N2)))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit)) (= (= (@ (@ tptp.inf_in4660618365625256667t_unit A) B4) tptp.bot_bo3957492148770167129t_unit) (@ (@ tptp.ord_le3507040750410214029t_unit A) (@ tptp.uminus5944136376168626660t_unit B4)))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (B4 tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o A) B4) tptp.bot_bot_set_o) (@ (@ tptp.ord_less_eq_set_o A) (@ tptp.uminus_uminus_set_o B4)))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (B4 tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int A) B4) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A) (@ tptp.uminus1532241313380277803et_int B4)))))
% 5.65/5.94 (assert (forall ((A tptp.set_Pr4532377907799695533_nat_o) (B4 tptp.set_Pr4532377907799695533_nat_o)) (= (= (@ (@ tptp.inf_in1906310914598751387_nat_o A) B4) tptp.bot_bo7824918357723582233_nat_o) (@ (@ tptp.ord_le2965882846123202637_nat_o A) (@ tptp.uminus5254974436814262692_nat_o B4)))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A) B4) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A) (@ tptp.uminus5710092332889474511et_nat B4)))))
% 5.65/5.94 (assert (forall ((X tptp.product_unit) (A tptp.set_Product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit X))) (= (@ tptp.uminus5944136376168626660t_unit (@ _let_1 A)) (@ (@ tptp.minus_6452836326544984404t_unit (@ tptp.uminus5944136376168626660t_unit A)) (@ _let_1 tptp.bot_bo3957492148770167129t_unit))))))
% 5.65/5.94 (assert (forall ((X Bool) (A tptp.set_o)) (let ((_let_1 (@ tptp.insert_o X))) (= (@ tptp.uminus_uminus_set_o (@ _let_1 A)) (@ (@ tptp.minus_minus_set_o (@ tptp.uminus_uminus_set_o A)) (@ _let_1 tptp.bot_bot_set_o))))))
% 5.65/5.94 (assert (forall ((X tptp.int) (A tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X))) (= (@ tptp.uminus1532241313380277803et_int (@ _let_1 A)) (@ (@ tptp.minus_minus_set_int (@ tptp.uminus1532241313380277803et_int A)) (@ _let_1 tptp.bot_bot_set_int))))))
% 5.65/5.94 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (A tptp.set_Pr4532377907799695533_nat_o)) (let ((_let_1 (@ tptp.insert5175938949040314269_nat_o X))) (= (@ tptp.uminus5254974436814262692_nat_o (@ _let_1 A)) (@ (@ tptp.minus_1801376950450012436_nat_o (@ tptp.uminus5254974436814262692_nat_o A)) (@ _let_1 tptp.bot_bo7824918357723582233_nat_o))))))
% 5.65/5.94 (assert (forall ((X tptp.nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X))) (= (@ tptp.uminus5710092332889474511et_nat (@ _let_1 A)) (@ (@ tptp.minus_minus_set_nat (@ tptp.uminus5710092332889474511et_nat A)) (@ _let_1 tptp.bot_bot_set_nat))))))
% 5.65/5.94 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (A tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat R2) A)) B4) (@ (@ tptp.ord_less_eq_set_nat A) (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.image_nat_nat (@ tptp.converse_nat_nat R2)) (@ tptp.uminus5710092332889474511et_nat B4)))))))
% 5.65/5.94 (assert (forall ((I tptp.set_int) (I2 tptp.int) (F (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ tptp.finite_finite_int I) (=> (@ (@ tptp.member_int I2) I) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups3827104343326376752nteger F) I)))))))))
% 5.65/5.94 (assert (forall ((I tptp.set_o) (I2 Bool) (F (-> Bool tptp.code_integer))) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ tptp.finite_finite_o I) (=> (@ (@ tptp.member_o I2) I) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups7694694392188491536nteger F) I)))))))))
% 5.65/5.94 (assert (forall ((I tptp.set_Product_unit) (I2 tptp.product_unit) (F (-> tptp.product_unit tptp.code_integer))) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ tptp.finite4290736615968046902t_unit I) (=> (@ (@ tptp.member_Product_unit I2) I) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) I) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups8185359811944078981nteger F) I)))))))))
% 5.65/5.94 (assert (forall ((I tptp.set_nat) (I2 tptp.nat) (F (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ tptp.finite_finite_nat I) (=> (@ (@ tptp.member_nat I2) I) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups3455450783089532116nteger F) I)))))))))
% 5.65/5.94 (assert (forall ((I tptp.set_Code_integer) (I2 tptp.code_integer) (F (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ tptp.finite6017078050557962740nteger I) (=> (@ (@ tptp.member_Code_integer I2) I) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups3674199335183972705nteger F) I)))))))))
% 5.65/5.94 (assert (forall ((I tptp.set_int) (I2 tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_int I) (=> (@ (@ tptp.member_int I2) I) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups1072433553688619179nt_rat F) I)))))))))
% 5.65/5.94 (assert (forall ((I tptp.set_o) (I2 Bool) (F (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_o I) (=> (@ (@ tptp.member_o I2) I) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups2869687844427037835_o_rat F) I)))))))))
% 5.65/5.94 (assert (forall ((I tptp.set_Product_unit) (I2 tptp.product_unit) (F (-> tptp.product_unit tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite4290736615968046902t_unit I) (=> (@ (@ tptp.member_Product_unit I2) I) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) I) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups8984663225794451456it_rat F) I)))))))))
% 5.65/5.94 (assert (forall ((I tptp.set_nat) (I2 tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_nat I) (=> (@ (@ tptp.member_nat I2) I) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups73079841787564623at_rat F) I)))))))))
% 5.65/5.94 (assert (forall ((I tptp.set_Code_integer) (I2 tptp.code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite6017078050557962740nteger I) (=> (@ (@ tptp.member_Code_integer I2) I) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups2555765274223993564er_rat F) I)))))))))
% 5.65/5.94 (assert (forall ((I tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger I) (=> (not (= I tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I3)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups3188404863801439024er_int F) I)))))))
% 5.65/5.94 (assert (forall ((I tptp.set_Product_unit) (F (-> tptp.product_unit tptp.int))) (=> (@ tptp.finite4290736615968046902t_unit I) (=> (not (= I tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) I) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I3)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups393930778517121108it_int F) I)))))))
% 5.65/5.94 (assert (forall ((I tptp.set_o) (F (-> Bool tptp.int))) (=> (@ tptp.finite_finite_o I) (=> (not (= I tptp.bot_bot_set_o)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I3)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups3502327434004483295_o_int F) I)))))))
% 5.65/5.94 (assert (forall ((I tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat I) (=> (not (= I tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I3)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups705719431365010083at_int F) I)))))))
% 5.65/5.94 (assert (forall ((I tptp.set_int) (F (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int I) (=> (not (= I tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I3)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups1705073143266064639nt_int F) I)))))))
% 5.65/5.94 (assert (forall ((I tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger I) (=> (not (= I tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ F I3)))) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ (@ tptp.groups3674199335183972705nteger F) I)))))))
% 5.65/5.94 (assert (forall ((I tptp.set_Product_unit) (F (-> tptp.product_unit tptp.code_integer))) (=> (@ tptp.finite4290736615968046902t_unit I) (=> (not (= I tptp.bot_bo3957492148770167129t_unit)) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) I) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ F I3)))) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ (@ tptp.groups8185359811944078981nteger F) I)))))))
% 5.65/5.94 (assert (forall ((I tptp.set_o) (F (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o I) (=> (not (= I tptp.bot_bot_set_o)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ F I3)))) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ (@ tptp.groups7694694392188491536nteger F) I)))))))
% 5.65/5.94 (assert (forall ((I tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat I) (=> (not (= I tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ F I3)))) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ (@ tptp.groups3455450783089532116nteger F) I)))))))
% 5.65/5.94 (assert (forall ((I tptp.set_int) (F (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int I) (=> (not (= I tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ F I3)))) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ (@ tptp.groups3827104343326376752nteger F) I)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (H2 (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.assn))) (=> (@ tptp.finite_finite_nat A) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ H2 X3))) (=> (@ (@ tptp.member_nat X3) A) (=> (@ (@ tptp.member_nat Y2) A) (=> (not (= X3 Y2)) (=> (= _let_1 (@ H2 Y2)) (= (@ G _let_1) tptp.one_one_assn))))))) (= (@ (@ tptp.groups6906906614972039071t_assn G) (@ (@ tptp.image_nat_nat2 H2) A)) (@ (@ tptp.groups6906906614972039071t_assn (@ (@ tptp.comp_nat_assn_nat G) H2)) A))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (H2 (-> tptp.nat tptp.code_integer)) (G (-> tptp.code_integer tptp.assn))) (=> (@ tptp.finite_finite_nat A) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ H2 X3))) (=> (@ (@ tptp.member_nat X3) A) (=> (@ (@ tptp.member_nat Y2) A) (=> (not (= X3 Y2)) (=> (= _let_1 (@ H2 Y2)) (= (@ G _let_1) tptp.one_one_assn))))))) (= (@ (@ tptp.groups1304777262505850412r_assn G) (@ (@ tptp.image_1215581382706833972nteger H2) A)) (@ (@ tptp.groups6906906614972039071t_assn (@ (@ tptp.comp_C8462447471145125178sn_nat G) H2)) A))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.assn))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (let ((_let_1 (@ H2 X3))) (=> (@ (@ tptp.member_Code_integer X3) A) (=> (@ (@ tptp.member_Code_integer Y2) A) (=> (not (= X3 Y2)) (=> (= _let_1 (@ H2 Y2)) (= (@ G _let_1) tptp.one_one_assn))))))) (= (@ (@ tptp.groups1304777262505850412r_assn G) (@ (@ tptp.image_4470545334726330049nteger H2) A)) (@ (@ tptp.groups1304777262505850412r_assn (@ (@ tptp.comp_C3026223900822616519nteger G) H2)) A))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (let ((_let_1 (@ H2 X3))) (=> (@ (@ tptp.member_Code_integer X3) A) (=> (@ (@ tptp.member_Code_integer Y2) A) (=> (not (= X3 Y2)) (=> (= _let_1 (@ H2 Y2)) (= (@ G _let_1) tptp.one_one_nat))))))) (= (@ (@ tptp.groups3190895334310489300er_nat G) (@ (@ tptp.image_4470545334726330049nteger H2) A)) (@ (@ tptp.groups3190895334310489300er_nat (@ (@ tptp.comp_C7238605732685392495nteger G) H2)) A))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (H2 (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ H2 X3))) (=> (@ (@ tptp.member_nat X3) A) (=> (@ (@ tptp.member_nat Y2) A) (=> (not (= X3 Y2)) (=> (= _let_1 (@ H2 Y2)) (= (@ G _let_1) tptp.one_one_int))))))) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.image_nat_nat2 H2) A)) (@ (@ tptp.groups705719431365010083at_int (@ (@ tptp.comp_nat_int_nat G) H2)) A))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (H2 (-> tptp.nat tptp.code_integer)) (G (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite_finite_nat A) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ H2 X3))) (=> (@ (@ tptp.member_nat X3) A) (=> (@ (@ tptp.member_nat Y2) A) (=> (not (= X3 Y2)) (=> (= _let_1 (@ H2 Y2)) (= (@ G _let_1) tptp.one_one_int))))))) (= (@ (@ tptp.groups3188404863801439024er_int G) (@ (@ tptp.image_1215581382706833972nteger H2) A)) (@ (@ tptp.groups705719431365010083at_int (@ (@ tptp.comp_C5048910307564104766nt_nat G) H2)) A))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (let ((_let_1 (@ H2 X3))) (=> (@ (@ tptp.member_Code_integer X3) A) (=> (@ (@ tptp.member_Code_integer Y2) A) (=> (not (= X3 Y2)) (=> (= _let_1 (@ H2 Y2)) (= (@ G _let_1) tptp.one_one_int))))))) (= (@ (@ tptp.groups3188404863801439024er_int G) (@ (@ tptp.image_4470545334726330049nteger H2) A)) (@ (@ tptp.groups3188404863801439024er_int (@ (@ tptp.comp_C7610259292922237131nteger G) H2)) A))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (H2 (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat A) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ H2 X3))) (=> (@ (@ tptp.member_nat X3) A) (=> (@ (@ tptp.member_nat Y2) A) (=> (not (= X3 Y2)) (=> (= _let_1 (@ H2 Y2)) (= (@ G _let_1) tptp.one_one_Code_integer))))))) (= (@ (@ tptp.groups3455450783089532116nteger G) (@ (@ tptp.image_nat_nat2 H2) A)) (@ (@ tptp.groups3455450783089532116nteger (@ (@ tptp.comp_n3898172953802868194er_nat G) H2)) A))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (H2 (-> tptp.nat tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite_finite_nat A) (=> (forall ((X3 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ H2 X3))) (=> (@ (@ tptp.member_nat X3) A) (=> (@ (@ tptp.member_nat Y2) A) (=> (not (= X3 Y2)) (=> (= _let_1 (@ H2 Y2)) (= (@ G _let_1) tptp.one_one_Code_integer))))))) (= (@ (@ tptp.groups3674199335183972705nteger G) (@ (@ tptp.image_1215581382706833972nteger H2) A)) (@ (@ tptp.groups3455450783089532116nteger (@ (@ tptp.comp_C6974050283906349679er_nat G) H2)) A))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (forall ((X3 tptp.code_integer) (Y2 tptp.code_integer)) (let ((_let_1 (@ H2 X3))) (=> (@ (@ tptp.member_Code_integer X3) A) (=> (@ (@ tptp.member_Code_integer Y2) A) (=> (not (= X3 Y2)) (=> (= _let_1 (@ H2 Y2)) (= (@ G _let_1) tptp.one_one_Code_integer))))))) (= (@ (@ tptp.groups3674199335183972705nteger G) (@ (@ tptp.image_4470545334726330049nteger H2) A)) (@ (@ tptp.groups3674199335183972705nteger (@ (@ tptp.comp_C7449957260575251196nteger G) H2)) A))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_Code_integer) (A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B4) A) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 A) (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B4))) (@ _let_1 B4))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_Code_integer) (A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B4) A) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 A) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B4))) (@ _let_1 B4))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_Code_integer) (A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B4) A) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 A) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B4))) (@ _let_1 B4))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_Code_integer) (A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B4) A) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 A) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B4))) (@ _let_1 B4))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_nat) (A tptp.set_nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A) (=> (@ tptp.finite_finite_nat A) (= (@ _let_1 A) (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4))) (@ _let_1 B4))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_nat) (A tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A) (=> (@ tptp.finite_finite_nat A) (= (@ _let_1 A) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4))) (@ _let_1 B4))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_nat) (A tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A) (=> (@ tptp.finite_finite_nat A) (= (@ _let_1 A) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4))) (@ _let_1 B4))))))))
% 5.65/5.94 (assert (forall ((B4 tptp.set_nat) (A tptp.set_nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A) (=> (@ tptp.finite_finite_nat A) (= (@ _let_1 A) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4))) (@ _let_1 B4))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_int) (A tptp.set_int) (B4 tptp.set_int) (G (-> tptp.int tptp.assn)) (H2 (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn H2))) (let ((_let_2 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int C5) (=> (@ (@ tptp.ord_less_eq_set_int A) C5) (=> (@ (@ tptp.ord_less_eq_set_int B4) C5) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int C5) A)) (= (@ G A4) tptp.one_one_assn))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C5) B4)) (= (@ H2 B2) tptp.one_one_assn))) (= (= (@ _let_2 A) (@ _let_1 B4)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_o) (A tptp.set_o) (B4 tptp.set_o) (G (-> Bool tptp.assn)) (H2 (-> Bool tptp.assn))) (let ((_let_1 (@ tptp.groups5301882518646026715o_assn H2))) (let ((_let_2 (@ tptp.groups5301882518646026715o_assn G))) (=> (@ tptp.finite_finite_o C5) (=> (@ (@ tptp.ord_less_eq_set_o A) C5) (=> (@ (@ tptp.ord_less_eq_set_o B4) C5) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C5) A)) (= (@ G A4) tptp.one_one_assn))) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) (@ (@ tptp.minus_minus_set_o C5) B4)) (= (@ H2 B2) tptp.one_one_assn))) (= (= (@ _let_2 A) (@ _let_1 B4)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_Product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit) (G (-> tptp.product_unit tptp.assn)) (H2 (-> tptp.product_unit tptp.assn))) (let ((_let_1 (@ tptp.groups5360233303959380816t_assn H2))) (let ((_let_2 (@ tptp.groups5360233303959380816t_assn G))) (=> (@ tptp.finite4290736615968046902t_unit C5) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) C5) (=> (@ (@ tptp.ord_le3507040750410214029t_unit B4) C5) (=> (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) (@ (@ tptp.minus_6452836326544984404t_unit C5) A)) (= (@ G A4) tptp.one_one_assn))) (=> (forall ((B2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit B2) (@ (@ tptp.minus_6452836326544984404t_unit C5) B4)) (= (@ H2 B2) tptp.one_one_assn))) (= (= (@ _let_2 A) (@ _let_1 B4)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_Code_integer) (A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn)) (H2 (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn H2))) (let ((_let_2 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger C5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) C5) (=> (@ (@ tptp.ord_le7084787975880047091nteger B4) C5) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) (@ (@ tptp.minus_2355218937544613996nteger C5) A)) (= (@ G A4) tptp.one_one_assn))) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) (@ (@ tptp.minus_2355218937544613996nteger C5) B4)) (= (@ H2 B2) tptp.one_one_assn))) (= (= (@ _let_2 A) (@ _let_1 B4)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_int) (A tptp.set_int) (B4 tptp.set_int) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat H2))) (let ((_let_2 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int C5) (=> (@ (@ tptp.ord_less_eq_set_int A) C5) (=> (@ (@ tptp.ord_less_eq_set_int B4) C5) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int C5) A)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C5) B4)) (= (@ H2 B2) tptp.one_one_nat))) (= (= (@ _let_2 A) (@ _let_1 B4)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_o) (A tptp.set_o) (B4 tptp.set_o) (G (-> Bool tptp.nat)) (H2 (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.groups3504817904513533571_o_nat H2))) (let ((_let_2 (@ tptp.groups3504817904513533571_o_nat G))) (=> (@ tptp.finite_finite_o C5) (=> (@ (@ tptp.ord_less_eq_set_o A) C5) (=> (@ (@ tptp.ord_less_eq_set_o B4) C5) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C5) A)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) (@ (@ tptp.minus_minus_set_o C5) B4)) (= (@ H2 B2) tptp.one_one_nat))) (= (= (@ _let_2 A) (@ _let_1 B4)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_Product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit) (G (-> tptp.product_unit tptp.nat)) (H2 (-> tptp.product_unit tptp.nat))) (let ((_let_1 (@ tptp.groups396421249026171384it_nat H2))) (let ((_let_2 (@ tptp.groups396421249026171384it_nat G))) (=> (@ tptp.finite4290736615968046902t_unit C5) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) C5) (=> (@ (@ tptp.ord_le3507040750410214029t_unit B4) C5) (=> (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) (@ (@ tptp.minus_6452836326544984404t_unit C5) A)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit B2) (@ (@ tptp.minus_6452836326544984404t_unit C5) B4)) (= (@ H2 B2) tptp.one_one_nat))) (= (= (@ _let_2 A) (@ _let_1 B4)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_Code_integer) (A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat)) (H2 (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat H2))) (let ((_let_2 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ tptp.finite6017078050557962740nteger C5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) C5) (=> (@ (@ tptp.ord_le7084787975880047091nteger B4) C5) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) (@ (@ tptp.minus_2355218937544613996nteger C5) A)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) (@ (@ tptp.minus_2355218937544613996nteger C5) B4)) (= (@ H2 B2) tptp.one_one_nat))) (= (= (@ _let_2 A) (@ _let_1 B4)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_int) (A tptp.set_int) (B4 tptp.set_int) (G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups1705073143266064639nt_int H2))) (let ((_let_2 (@ tptp.groups1705073143266064639nt_int G))) (=> (@ tptp.finite_finite_int C5) (=> (@ (@ tptp.ord_less_eq_set_int A) C5) (=> (@ (@ tptp.ord_less_eq_set_int B4) C5) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int C5) A)) (= (@ G A4) tptp.one_one_int))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C5) B4)) (= (@ H2 B2) tptp.one_one_int))) (= (= (@ _let_2 A) (@ _let_1 B4)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_o) (A tptp.set_o) (B4 tptp.set_o) (G (-> Bool tptp.int)) (H2 (-> Bool tptp.int))) (let ((_let_1 (@ tptp.groups3502327434004483295_o_int H2))) (let ((_let_2 (@ tptp.groups3502327434004483295_o_int G))) (=> (@ tptp.finite_finite_o C5) (=> (@ (@ tptp.ord_less_eq_set_o A) C5) (=> (@ (@ tptp.ord_less_eq_set_o B4) C5) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C5) A)) (= (@ G A4) tptp.one_one_int))) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) (@ (@ tptp.minus_minus_set_o C5) B4)) (= (@ H2 B2) tptp.one_one_int))) (= (= (@ _let_2 A) (@ _let_1 B4)) (= (@ _let_2 C5) (@ _let_1 C5))))))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_int) (A tptp.set_int) (B4 tptp.set_int) (G (-> tptp.int tptp.assn)) (H2 (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn H2))) (let ((_let_2 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int C5) (=> (@ (@ tptp.ord_less_eq_set_int A) C5) (=> (@ (@ tptp.ord_less_eq_set_int B4) C5) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int C5) A)) (= (@ G A4) tptp.one_one_assn))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C5) B4)) (= (@ H2 B2) tptp.one_one_assn))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A) (@ _let_1 B4))))))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_o) (A tptp.set_o) (B4 tptp.set_o) (G (-> Bool tptp.assn)) (H2 (-> Bool tptp.assn))) (let ((_let_1 (@ tptp.groups5301882518646026715o_assn H2))) (let ((_let_2 (@ tptp.groups5301882518646026715o_assn G))) (=> (@ tptp.finite_finite_o C5) (=> (@ (@ tptp.ord_less_eq_set_o A) C5) (=> (@ (@ tptp.ord_less_eq_set_o B4) C5) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C5) A)) (= (@ G A4) tptp.one_one_assn))) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) (@ (@ tptp.minus_minus_set_o C5) B4)) (= (@ H2 B2) tptp.one_one_assn))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A) (@ _let_1 B4))))))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_Product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit) (G (-> tptp.product_unit tptp.assn)) (H2 (-> tptp.product_unit tptp.assn))) (let ((_let_1 (@ tptp.groups5360233303959380816t_assn H2))) (let ((_let_2 (@ tptp.groups5360233303959380816t_assn G))) (=> (@ tptp.finite4290736615968046902t_unit C5) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) C5) (=> (@ (@ tptp.ord_le3507040750410214029t_unit B4) C5) (=> (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) (@ (@ tptp.minus_6452836326544984404t_unit C5) A)) (= (@ G A4) tptp.one_one_assn))) (=> (forall ((B2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit B2) (@ (@ tptp.minus_6452836326544984404t_unit C5) B4)) (= (@ H2 B2) tptp.one_one_assn))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A) (@ _let_1 B4))))))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_Code_integer) (A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn)) (H2 (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn H2))) (let ((_let_2 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger C5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) C5) (=> (@ (@ tptp.ord_le7084787975880047091nteger B4) C5) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) (@ (@ tptp.minus_2355218937544613996nteger C5) A)) (= (@ G A4) tptp.one_one_assn))) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) (@ (@ tptp.minus_2355218937544613996nteger C5) B4)) (= (@ H2 B2) tptp.one_one_assn))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A) (@ _let_1 B4))))))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_int) (A tptp.set_int) (B4 tptp.set_int) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat H2))) (let ((_let_2 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int C5) (=> (@ (@ tptp.ord_less_eq_set_int A) C5) (=> (@ (@ tptp.ord_less_eq_set_int B4) C5) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int C5) A)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C5) B4)) (= (@ H2 B2) tptp.one_one_nat))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A) (@ _let_1 B4))))))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_o) (A tptp.set_o) (B4 tptp.set_o) (G (-> Bool tptp.nat)) (H2 (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.groups3504817904513533571_o_nat H2))) (let ((_let_2 (@ tptp.groups3504817904513533571_o_nat G))) (=> (@ tptp.finite_finite_o C5) (=> (@ (@ tptp.ord_less_eq_set_o A) C5) (=> (@ (@ tptp.ord_less_eq_set_o B4) C5) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C5) A)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) (@ (@ tptp.minus_minus_set_o C5) B4)) (= (@ H2 B2) tptp.one_one_nat))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A) (@ _let_1 B4))))))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_Product_unit) (A tptp.set_Product_unit) (B4 tptp.set_Product_unit) (G (-> tptp.product_unit tptp.nat)) (H2 (-> tptp.product_unit tptp.nat))) (let ((_let_1 (@ tptp.groups396421249026171384it_nat H2))) (let ((_let_2 (@ tptp.groups396421249026171384it_nat G))) (=> (@ tptp.finite4290736615968046902t_unit C5) (=> (@ (@ tptp.ord_le3507040750410214029t_unit A) C5) (=> (@ (@ tptp.ord_le3507040750410214029t_unit B4) C5) (=> (forall ((A4 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit A4) (@ (@ tptp.minus_6452836326544984404t_unit C5) A)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B2 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit B2) (@ (@ tptp.minus_6452836326544984404t_unit C5) B4)) (= (@ H2 B2) tptp.one_one_nat))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A) (@ _let_1 B4))))))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_Code_integer) (A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat)) (H2 (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat H2))) (let ((_let_2 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ tptp.finite6017078050557962740nteger C5) (=> (@ (@ tptp.ord_le7084787975880047091nteger A) C5) (=> (@ (@ tptp.ord_le7084787975880047091nteger B4) C5) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) (@ (@ tptp.minus_2355218937544613996nteger C5) A)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B2) (@ (@ tptp.minus_2355218937544613996nteger C5) B4)) (= (@ H2 B2) tptp.one_one_nat))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A) (@ _let_1 B4))))))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_int) (A tptp.set_int) (B4 tptp.set_int) (G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups1705073143266064639nt_int H2))) (let ((_let_2 (@ tptp.groups1705073143266064639nt_int G))) (=> (@ tptp.finite_finite_int C5) (=> (@ (@ tptp.ord_less_eq_set_int A) C5) (=> (@ (@ tptp.ord_less_eq_set_int B4) C5) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) (@ (@ tptp.minus_minus_set_int C5) A)) (= (@ G A4) tptp.one_one_int))) (=> (forall ((B2 tptp.int)) (=> (@ (@ tptp.member_int B2) (@ (@ tptp.minus_minus_set_int C5) B4)) (= (@ H2 B2) tptp.one_one_int))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A) (@ _let_1 B4))))))))))))
% 5.65/5.94 (assert (forall ((C5 tptp.set_o) (A tptp.set_o) (B4 tptp.set_o) (G (-> Bool tptp.int)) (H2 (-> Bool tptp.int))) (let ((_let_1 (@ tptp.groups3502327434004483295_o_int H2))) (let ((_let_2 (@ tptp.groups3502327434004483295_o_int G))) (=> (@ tptp.finite_finite_o C5) (=> (@ (@ tptp.ord_less_eq_set_o A) C5) (=> (@ (@ tptp.ord_less_eq_set_o B4) C5) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C5) A)) (= (@ G A4) tptp.one_one_int))) (=> (forall ((B2 Bool)) (=> (@ (@ tptp.member_o B2) (@ (@ tptp.minus_minus_set_o C5) B4)) (= (@ H2 B2) tptp.one_one_int))) (=> (= (@ _let_2 C5) (@ _let_1 C5)) (= (@ _let_2 A) (@ _let_1 B4))))))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger T2) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T2) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T2) S)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 S) (@ _let_1 T2))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ tptp.finite6017078050557962740nteger T2) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T2) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T2) S)) (= (@ G X3) tptp.one_one_nat))) (= (@ _let_1 S) (@ _let_1 T2))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int G))) (=> (@ tptp.finite6017078050557962740nteger T2) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T2) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T2) S)) (= (@ G X3) tptp.one_one_int))) (= (@ _let_1 S) (@ _let_1 T2))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups3674199335183972705nteger G))) (=> (@ tptp.finite6017078050557962740nteger T2) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T2) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T2) S)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 S) (@ _let_1 T2))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_natural))) (let ((_let_1 (@ tptp.groups2497794486940690220atural G))) (=> (@ tptp.finite6017078050557962740nteger T2) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T2) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T2) S)) (= (@ G X3) tptp.one_one_Code_natural))) (= (@ _let_1 S) (@ _let_1 T2))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat T2) (=> (@ (@ tptp.ord_less_eq_set_nat S) T2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T2) S)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 S) (@ _let_1 T2))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ tptp.finite_finite_nat T2) (=> (@ (@ tptp.ord_less_eq_set_nat S) T2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T2) S)) (= (@ G X3) tptp.one_one_int))) (= (@ _let_1 S) (@ _let_1 T2))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G))) (=> (@ tptp.finite_finite_nat T2) (=> (@ (@ tptp.ord_less_eq_set_nat S) T2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T2) S)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 S) (@ _let_1 T2))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.code_natural))) (let ((_let_1 (@ tptp.groups2279045934846249631atural G))) (=> (@ tptp.finite_finite_nat T2) (=> (@ (@ tptp.ord_less_eq_set_nat S) T2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T2) S)) (= (@ G X3) tptp.one_one_Code_natural))) (= (@ _let_1 S) (@ _let_1 T2))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ tptp.finite_finite_nat T2) (=> (@ (@ tptp.ord_less_eq_set_nat S) T2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T2) S)) (= (@ G X3) tptp.one_one_nat))) (= (@ _let_1 S) (@ _let_1 T2))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger T2) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T2) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T2) S)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 T2) (@ _let_1 S))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ tptp.finite6017078050557962740nteger T2) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T2) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T2) S)) (= (@ G X3) tptp.one_one_nat))) (= (@ _let_1 T2) (@ _let_1 S))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int G))) (=> (@ tptp.finite6017078050557962740nteger T2) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T2) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T2) S)) (= (@ G X3) tptp.one_one_int))) (= (@ _let_1 T2) (@ _let_1 S))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups3674199335183972705nteger G))) (=> (@ tptp.finite6017078050557962740nteger T2) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T2) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T2) S)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 T2) (@ _let_1 S))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_natural))) (let ((_let_1 (@ tptp.groups2497794486940690220atural G))) (=> (@ tptp.finite6017078050557962740nteger T2) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T2) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T2) S)) (= (@ G X3) tptp.one_one_Code_natural))) (= (@ _let_1 T2) (@ _let_1 S))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat T2) (=> (@ (@ tptp.ord_less_eq_set_nat S) T2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T2) S)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 T2) (@ _let_1 S))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ tptp.finite_finite_nat T2) (=> (@ (@ tptp.ord_less_eq_set_nat S) T2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T2) S)) (= (@ G X3) tptp.one_one_int))) (= (@ _let_1 T2) (@ _let_1 S))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G))) (=> (@ tptp.finite_finite_nat T2) (=> (@ (@ tptp.ord_less_eq_set_nat S) T2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T2) S)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 T2) (@ _let_1 S))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.code_natural))) (let ((_let_1 (@ tptp.groups2279045934846249631atural G))) (=> (@ tptp.finite_finite_nat T2) (=> (@ (@ tptp.ord_less_eq_set_nat S) T2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T2) S)) (= (@ G X3) tptp.one_one_Code_natural))) (= (@ _let_1 T2) (@ _let_1 S))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ tptp.finite_finite_nat T2) (=> (@ (@ tptp.ord_less_eq_set_nat S) T2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T2) S)) (= (@ G X3) tptp.one_one_nat))) (= (@ _let_1 T2) (@ _let_1 S))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_int) (S tptp.set_int) (H2 (-> tptp.int tptp.assn)) (G (-> tptp.int tptp.assn))) (=> (@ tptp.finite_finite_int T2) (=> (@ (@ tptp.ord_less_eq_set_int S) T2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T2) S)) (= (@ H2 X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups7882442080178216443t_assn G) S) (@ (@ tptp.groups7882442080178216443t_assn H2) T2))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_o) (S tptp.set_o) (H2 (-> Bool tptp.assn)) (G (-> Bool tptp.assn))) (=> (@ tptp.finite_finite_o T2) (=> (@ (@ tptp.ord_less_eq_set_o S) T2) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T2) S)) (= (@ H2 X3) tptp.one_one_assn))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5301882518646026715o_assn G) S) (@ (@ tptp.groups5301882518646026715o_assn H2) T2))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_Product_unit) (S tptp.set_Product_unit) (H2 (-> tptp.product_unit tptp.assn)) (G (-> tptp.product_unit tptp.assn))) (=> (@ tptp.finite4290736615968046902t_unit T2) (=> (@ (@ tptp.ord_le3507040750410214029t_unit S) T2) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) (@ (@ tptp.minus_6452836326544984404t_unit T2) S)) (= (@ H2 X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) S) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5360233303959380816t_assn G) S) (@ (@ tptp.groups5360233303959380816t_assn H2) T2))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_Code_integer) (S tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.assn)) (G (-> tptp.code_integer tptp.assn))) (=> (@ tptp.finite6017078050557962740nteger T2) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T2) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T2) S)) (= (@ H2 X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1304777262505850412r_assn G) S) (@ (@ tptp.groups1304777262505850412r_assn H2) T2))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_int) (S tptp.set_int) (H2 (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int T2) (=> (@ (@ tptp.ord_less_eq_set_int S) T2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T2) S)) (= (@ H2 X3) tptp.one_one_nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) S) (@ (@ tptp.groups1707563613775114915nt_nat H2) T2))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_o) (S tptp.set_o) (H2 (-> Bool tptp.nat)) (G (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o T2) (=> (@ (@ tptp.ord_less_eq_set_o S) T2) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T2) S)) (= (@ H2 X3) tptp.one_one_nat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups3504817904513533571_o_nat G) S) (@ (@ tptp.groups3504817904513533571_o_nat H2) T2))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_Product_unit) (S tptp.set_Product_unit) (H2 (-> tptp.product_unit tptp.nat)) (G (-> tptp.product_unit tptp.nat))) (=> (@ tptp.finite4290736615968046902t_unit T2) (=> (@ (@ tptp.ord_le3507040750410214029t_unit S) T2) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) (@ (@ tptp.minus_6452836326544984404t_unit T2) S)) (= (@ H2 X3) tptp.one_one_nat))) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) S) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups396421249026171384it_nat G) S) (@ (@ tptp.groups396421249026171384it_nat H2) T2))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_Code_integer) (S tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger T2) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T2) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T2) S)) (= (@ H2 X3) tptp.one_one_nat))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups3190895334310489300er_nat G) S) (@ (@ tptp.groups3190895334310489300er_nat H2) T2))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_int) (S tptp.set_int) (H2 (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int T2) (=> (@ (@ tptp.ord_less_eq_set_int S) T2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T2) S)) (= (@ H2 X3) tptp.one_one_int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1705073143266064639nt_int G) S) (@ (@ tptp.groups1705073143266064639nt_int H2) T2))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_o) (S tptp.set_o) (H2 (-> Bool tptp.int)) (G (-> Bool tptp.int))) (=> (@ tptp.finite_finite_o T2) (=> (@ (@ tptp.ord_less_eq_set_o S) T2) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T2) S)) (= (@ H2 X3) tptp.one_one_int))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups3502327434004483295_o_int G) S) (@ (@ tptp.groups3502327434004483295_o_int H2) T2))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.assn)) (H2 (-> tptp.int tptp.assn))) (=> (@ tptp.finite_finite_int T2) (=> (@ (@ tptp.ord_less_eq_set_int S) T2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T2) S)) (= (@ G X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups7882442080178216443t_assn G) T2) (@ (@ tptp.groups7882442080178216443t_assn H2) S))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_o) (S tptp.set_o) (G (-> Bool tptp.assn)) (H2 (-> Bool tptp.assn))) (=> (@ tptp.finite_finite_o T2) (=> (@ (@ tptp.ord_less_eq_set_o S) T2) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T2) S)) (= (@ G X3) tptp.one_one_assn))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5301882518646026715o_assn G) T2) (@ (@ tptp.groups5301882518646026715o_assn H2) S))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_Product_unit) (S tptp.set_Product_unit) (G (-> tptp.product_unit tptp.assn)) (H2 (-> tptp.product_unit tptp.assn))) (=> (@ tptp.finite4290736615968046902t_unit T2) (=> (@ (@ tptp.ord_le3507040750410214029t_unit S) T2) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) (@ (@ tptp.minus_6452836326544984404t_unit T2) S)) (= (@ G X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) S) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5360233303959380816t_assn G) T2) (@ (@ tptp.groups5360233303959380816t_assn H2) S))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn)) (H2 (-> tptp.code_integer tptp.assn))) (=> (@ tptp.finite6017078050557962740nteger T2) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T2) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T2) S)) (= (@ G X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1304777262505850412r_assn G) T2) (@ (@ tptp.groups1304777262505850412r_assn H2) S))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.nat)) (H2 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int T2) (=> (@ (@ tptp.ord_less_eq_set_int S) T2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T2) S)) (= (@ G X3) tptp.one_one_nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) T2) (@ (@ tptp.groups1707563613775114915nt_nat H2) S))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_o) (S tptp.set_o) (G (-> Bool tptp.nat)) (H2 (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o T2) (=> (@ (@ tptp.ord_less_eq_set_o S) T2) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T2) S)) (= (@ G X3) tptp.one_one_nat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups3504817904513533571_o_nat G) T2) (@ (@ tptp.groups3504817904513533571_o_nat H2) S))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_Product_unit) (S tptp.set_Product_unit) (G (-> tptp.product_unit tptp.nat)) (H2 (-> tptp.product_unit tptp.nat))) (=> (@ tptp.finite4290736615968046902t_unit T2) (=> (@ (@ tptp.ord_le3507040750410214029t_unit S) T2) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) (@ (@ tptp.minus_6452836326544984404t_unit T2) S)) (= (@ G X3) tptp.one_one_nat))) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) S) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups396421249026171384it_nat G) T2) (@ (@ tptp.groups396421249026171384it_nat H2) S))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat)) (H2 (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger T2) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T2) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T2) S)) (= (@ G X3) tptp.one_one_nat))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups3190895334310489300er_nat G) T2) (@ (@ tptp.groups3190895334310489300er_nat H2) S))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int T2) (=> (@ (@ tptp.ord_less_eq_set_int S) T2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T2) S)) (= (@ G X3) tptp.one_one_int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1705073143266064639nt_int G) T2) (@ (@ tptp.groups1705073143266064639nt_int H2) S))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_o) (S tptp.set_o) (G (-> Bool tptp.int)) (H2 (-> Bool tptp.int))) (=> (@ tptp.finite_finite_o T2) (=> (@ (@ tptp.ord_less_eq_set_o S) T2) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T2) S)) (= (@ G X3) tptp.one_one_int))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups3502327434004483295_o_int G) T2) (@ (@ tptp.groups3502327434004483295_o_int H2) S))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite6017078050557962740nteger B4) (= (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A) B4))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A) B4))) (@ (@ tptp.times_times_assn (@ _let_1 A)) (@ _let_1 B4))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat A) (=> (@ tptp.finite_finite_nat B4) (= (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4))) (@ (@ tptp.times_times_assn (@ _let_1 A)) (@ _let_1 B4))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite6017078050557962740nteger B4) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A) B4))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A) B4))) (@ (@ tptp.times_times_rat (@ _let_1 A)) (@ _let_1 B4))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A) (=> (@ tptp.finite_finite_nat B4) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4))) (@ (@ tptp.times_times_rat (@ _let_1 A)) (@ _let_1 B4))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite6017078050557962740nteger B4) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A) B4))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A) B4))) (@ (@ tptp.times_times_nat (@ _let_1 A)) (@ _let_1 B4))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite6017078050557962740nteger B4) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A) B4))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A) B4))) (@ (@ tptp.times_times_int (@ _let_1 A)) (@ _let_1 B4))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ tptp.finite_finite_nat A) (=> (@ tptp.finite_finite_nat B4) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4))) (@ (@ tptp.times_times_int (@ _let_1 A)) (@ _let_1 B4))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ tptp.finite_finite_nat A) (=> (@ tptp.finite_finite_nat B4) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4))) (@ (@ tptp.times_times_nat (@ _let_1 A)) (@ _let_1 B4))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn)) (B4 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 A) (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A) B4))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B4))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.assn)) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat A) (= (@ _let_1 A) (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (B4 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 A) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A) B4))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B4))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.rat)) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A) (= (@ _let_1 A) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat)) (B4 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 A) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A) B4))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B4))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int)) (B4 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.groups3188404863801439024er_int G))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_1 A) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A) B4))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B4))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.int)) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ tptp.finite_finite_nat A) (= (@ _let_1 A) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.nat)) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ tptp.finite_finite_nat A) (= (@ _let_1 A) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_int) (S tptp.set_int) (H2 (-> tptp.int tptp.assn)) (G (-> tptp.int tptp.assn))) (=> (@ tptp.finite_finite_int T2) (=> (@ tptp.finite_finite_int S) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int T2) S)) (= (@ H2 I3) tptp.one_one_assn))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int S) T2)) (= (@ G I3) tptp.one_one_assn))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int S) T2)) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups7882442080178216443t_assn G) S) (@ (@ tptp.groups7882442080178216443t_assn H2) T2)))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_o) (S tptp.set_o) (H2 (-> Bool tptp.assn)) (G (-> Bool tptp.assn))) (=> (@ tptp.finite_finite_o T2) (=> (@ tptp.finite_finite_o S) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o T2) S)) (= (@ H2 I3) tptp.one_one_assn))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o S) T2)) (= (@ G I3) tptp.one_one_assn))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.inf_inf_set_o S) T2)) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5301882518646026715o_assn G) S) (@ (@ tptp.groups5301882518646026715o_assn H2) T2)))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_Product_unit) (S tptp.set_Product_unit) (H2 (-> tptp.product_unit tptp.assn)) (G (-> tptp.product_unit tptp.assn))) (=> (@ tptp.finite4290736615968046902t_unit T2) (=> (@ tptp.finite4290736615968046902t_unit S) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) (@ (@ tptp.minus_6452836326544984404t_unit T2) S)) (= (@ H2 I3) tptp.one_one_assn))) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) (@ (@ tptp.minus_6452836326544984404t_unit S) T2)) (= (@ G I3) tptp.one_one_assn))) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) (@ (@ tptp.inf_in4660618365625256667t_unit S) T2)) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups5360233303959380816t_assn G) S) (@ (@ tptp.groups5360233303959380816t_assn H2) T2)))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_Code_integer) (S tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.assn)) (G (-> tptp.code_integer tptp.assn))) (=> (@ tptp.finite6017078050557962740nteger T2) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) (@ (@ tptp.minus_2355218937544613996nteger T2) S)) (= (@ H2 I3) tptp.one_one_assn))) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) (@ (@ tptp.minus_2355218937544613996nteger S) T2)) (= (@ G I3) tptp.one_one_assn))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger S) T2)) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1304777262505850412r_assn G) S) (@ (@ tptp.groups1304777262505850412r_assn H2) T2)))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_int) (S tptp.set_int) (H2 (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int T2) (=> (@ tptp.finite_finite_int S) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int T2) S)) (= (@ H2 I3) tptp.one_one_nat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int S) T2)) (= (@ G I3) tptp.one_one_nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int S) T2)) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) S) (@ (@ tptp.groups1707563613775114915nt_nat H2) T2)))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_o) (S tptp.set_o) (H2 (-> Bool tptp.nat)) (G (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o T2) (=> (@ tptp.finite_finite_o S) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o T2) S)) (= (@ H2 I3) tptp.one_one_nat))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o S) T2)) (= (@ G I3) tptp.one_one_nat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.inf_inf_set_o S) T2)) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups3504817904513533571_o_nat G) S) (@ (@ tptp.groups3504817904513533571_o_nat H2) T2)))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_Product_unit) (S tptp.set_Product_unit) (H2 (-> tptp.product_unit tptp.nat)) (G (-> tptp.product_unit tptp.nat))) (=> (@ tptp.finite4290736615968046902t_unit T2) (=> (@ tptp.finite4290736615968046902t_unit S) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) (@ (@ tptp.minus_6452836326544984404t_unit T2) S)) (= (@ H2 I3) tptp.one_one_nat))) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) (@ (@ tptp.minus_6452836326544984404t_unit S) T2)) (= (@ G I3) tptp.one_one_nat))) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) (@ (@ tptp.inf_in4660618365625256667t_unit S) T2)) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups396421249026171384it_nat G) S) (@ (@ tptp.groups396421249026171384it_nat H2) T2)))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_Code_integer) (S tptp.set_Code_integer) (H2 (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger T2) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) (@ (@ tptp.minus_2355218937544613996nteger T2) S)) (= (@ H2 I3) tptp.one_one_nat))) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) (@ (@ tptp.minus_2355218937544613996nteger S) T2)) (= (@ G I3) tptp.one_one_nat))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger S) T2)) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups3190895334310489300er_nat G) S) (@ (@ tptp.groups3190895334310489300er_nat H2) T2)))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_int) (S tptp.set_int) (H2 (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int T2) (=> (@ tptp.finite_finite_int S) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int T2) S)) (= (@ H2 I3) tptp.one_one_int))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int S) T2)) (= (@ G I3) tptp.one_one_int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int S) T2)) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups1705073143266064639nt_int G) S) (@ (@ tptp.groups1705073143266064639nt_int H2) T2)))))))))
% 5.65/5.94 (assert (forall ((T2 tptp.set_o) (S tptp.set_o) (H2 (-> Bool tptp.int)) (G (-> Bool tptp.int))) (=> (@ tptp.finite_finite_o T2) (=> (@ tptp.finite_finite_o S) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o T2) S)) (= (@ H2 I3) tptp.one_one_int))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o S) T2)) (= (@ G I3) tptp.one_one_int))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.inf_inf_set_o S) T2)) (= (@ G X3) (@ H2 X3)))) (= (@ (@ tptp.groups3502327434004483295_o_int G) S) (@ (@ tptp.groups3502327434004483295_o_int H2) T2)))))))))
% 5.65/5.94 (assert (= tptp.groups708209901874060359at_nat (lambda ((G3 (-> tptp.nat tptp.nat)) (__flatten_var_0 tptp.set_nat)) (@ (@ (@ tptp.finite_fold_nat_nat (@ (@ tptp.comp_nat_nat_nat_nat tptp.times_times_nat) G3)) tptp.one_one_nat) __flatten_var_0))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.code_integer)) (K4 tptp.code_integer)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ F I3)) K4))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7501900531339628137nteger F) A)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger (@ tptp.finite_card_nat A))) K4)))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.code_integer)) (K4 tptp.code_integer)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ F I3)) K4))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7873554091576472773nteger F) A)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger (@ tptp.finite_card_int A))) K4)))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.code_integer)) (K4 tptp.code_integer)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ F I3)) K4))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups4406642042086082107nteger F) A)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger (@ tptp.finite_card_o A))) K4)))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.code_integer)) (K4 tptp.code_integer)) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ F I3)) K4))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups5393439102872367408nteger F) A)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger (@ tptp.finite410649719033368117t_unit A))) K4)))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.rat)) (K4 tptp.rat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) A) (@ (@ tptp.ord_less_eq_rat (@ F I3)) K4))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) A)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_nat A))) K4)))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.rat)) (K4 tptp.rat)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A) (@ (@ tptp.ord_less_eq_rat (@ F I3)) K4))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_int A))) K4)))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.rat)) (K4 tptp.rat)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) A) (@ (@ tptp.ord_less_eq_rat (@ F I3)) K4))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups7872700643590313910_o_rat F) A)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_o A))) K4)))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.rat)) (K4 tptp.rat)) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) A) (@ (@ tptp.ord_less_eq_rat (@ F I3)) K4))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups8131667117488461483it_rat F) A)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite410649719033368117t_unit A))) K4)))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.nat)) (K4 tptp.nat)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A) (@ (@ tptp.ord_less_eq_nat (@ F I3)) K4))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_int A))) K4)))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.nat)) (K4 tptp.nat)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) A) (@ (@ tptp.ord_less_eq_nat (@ F I3)) K4))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups8507830703676809646_o_nat F) A)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_o A))) K4)))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (K4 tptp.code_integer) (F (-> tptp.nat tptp.code_integer))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) A) (@ (@ tptp.ord_le3102999989581377725nteger K4) (@ F I3)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger (@ tptp.finite_card_nat A))) K4)) (@ (@ tptp.groups7501900531339628137nteger F) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (K4 tptp.code_integer) (F (-> tptp.int tptp.code_integer))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A) (@ (@ tptp.ord_le3102999989581377725nteger K4) (@ F I3)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger (@ tptp.finite_card_int A))) K4)) (@ (@ tptp.groups7873554091576472773nteger F) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (K4 tptp.code_integer) (F (-> Bool tptp.code_integer))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) A) (@ (@ tptp.ord_le3102999989581377725nteger K4) (@ F I3)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger (@ tptp.finite_card_o A))) K4)) (@ (@ tptp.groups4406642042086082107nteger F) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (K4 tptp.code_integer) (F (-> tptp.product_unit tptp.code_integer))) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) A) (@ (@ tptp.ord_le3102999989581377725nteger K4) (@ F I3)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger (@ tptp.finite410649719033368117t_unit A))) K4)) (@ (@ tptp.groups5393439102872367408nteger F) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (K4 tptp.rat) (F (-> tptp.nat tptp.rat))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) A) (@ (@ tptp.ord_less_eq_rat K4) (@ F I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_nat A))) K4)) (@ (@ tptp.groups2906978787729119204at_rat F) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (K4 tptp.rat) (F (-> tptp.int tptp.rat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A) (@ (@ tptp.ord_less_eq_rat K4) (@ F I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_int A))) K4)) (@ (@ tptp.groups3906332499630173760nt_rat F) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (K4 tptp.rat) (F (-> Bool tptp.rat))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) A) (@ (@ tptp.ord_less_eq_rat K4) (@ F I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_o A))) K4)) (@ (@ tptp.groups7872700643590313910_o_rat F) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (K4 tptp.rat) (F (-> tptp.product_unit tptp.rat))) (=> (forall ((I3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit I3) A) (@ (@ tptp.ord_less_eq_rat K4) (@ F I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite410649719033368117t_unit A))) K4)) (@ (@ tptp.groups8131667117488461483it_rat F) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (K4 tptp.nat) (F (-> tptp.int tptp.nat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A) (@ (@ tptp.ord_less_eq_nat K4) (@ F I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_int A))) K4)) (@ (@ tptp.groups4541462559716669496nt_nat F) A)))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (K4 tptp.nat) (F (-> Bool tptp.nat))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) A) (@ (@ tptp.ord_less_eq_nat K4) (@ F I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_o A))) K4)) (@ (@ tptp.groups8507830703676809646_o_nat F) A)))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat A2))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat K3))) (@ (@ tptp.gbinomial_rat A2) K3)) (@ (@ tptp.times_times_rat A2) (@ (@ tptp.gbinomial_rat (@ _let_1 tptp.one_one_rat)) K3))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (let ((_let_2 (@ tptp.gbinomial_rat A2))) (let ((_let_3 (@ _let_2 K3))) (= (@ (@ tptp.times_times_rat A2) _let_3) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K3)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.rat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (let ((_let_2 (@ tptp.gbinomial_rat A2))) (let ((_let_3 (@ _let_2 K3))) (= (@ (@ tptp.times_times_rat _let_3) A2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K3)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))))
% 5.65/5.94 (assert (forall ((X tptp.set_Pr4532377907799695533_nat_o) (Y tptp.set_Pr4532377907799695533_nat_o)) (=> (= (@ (@ tptp.inf_in1906310914598751387_nat_o X) Y) tptp.bot_bo7824918357723582233_nat_o) (=> (= (@ (@ tptp.sup_su5209123915105501825_nat_o X) Y) tptp.top_to4869887016220417533_nat_o) (= (@ tptp.uminus5254974436814262692_nat_o X) Y)))))
% 5.65/5.94 (assert (forall ((X tptp.set_Product_unit) (Y tptp.set_Product_unit)) (=> (= (@ (@ tptp.inf_in4660618365625256667t_unit X) Y) tptp.bot_bo3957492148770167129t_unit) (=> (= (@ (@ tptp.sup_su793286257634532545t_unit X) Y) tptp.top_to1996260823553986621t_unit) (= (@ tptp.uminus5944136376168626660t_unit X) Y)))))
% 5.65/5.94 (assert (forall ((X tptp.set_o) (Y tptp.set_o)) (=> (= (@ (@ tptp.inf_inf_set_o X) Y) tptp.bot_bot_set_o) (=> (= (@ (@ tptp.sup_sup_set_o X) Y) tptp.top_top_set_o) (= (@ tptp.uminus_uminus_set_o X) Y)))))
% 5.65/5.94 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (=> (= (@ (@ tptp.inf_inf_set_nat X) Y) tptp.bot_bot_set_nat) (=> (= (@ (@ tptp.sup_sup_set_nat X) Y) tptp.top_top_set_nat) (= (@ tptp.uminus5710092332889474511et_nat X) Y)))))
% 5.65/5.94 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (= (@ (@ tptp.inf_inf_set_int X) Y) tptp.bot_bot_set_int) (=> (= (@ (@ tptp.sup_sup_set_int X) Y) tptp.top_top_set_int) (= (@ tptp.uminus1532241313380277803et_int X) Y)))))
% 5.65/5.94 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (= (@ (@ tptp.inf_inf_assn X) Y) tptp.bot_bot_assn) (=> (= (@ (@ tptp.sup_sup_assn X) Y) tptp.top_top_assn) (= (@ tptp.uminus_uminus_assn X) Y)))))
% 5.65/5.94 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (=> (= (@ (@ tptp.inf_inf_Product_unit X) Y) tptp.bot_bot_Product_unit) (=> (= (@ (@ tptp.sup_sup_Product_unit X) Y) tptp.top_top_Product_unit) (= (@ tptp.uminus2952777764628376836t_unit X) Y)))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (forall ((I3 tptp.code_integer)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_Code_integer I3) A) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le6747313008572928689nteger _let_1) (@ G I3)))))) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.groups3674199335183972705nteger F) A)) (@ (@ tptp.groups3674199335183972705nteger G) A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.code_integer)) (G (-> tptp.product_unit tptp.code_integer))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (forall ((I3 tptp.product_unit)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_Product_unit I3) A) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le6747313008572928689nteger _let_1) (@ G I3)))))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.groups8185359811944078981nteger F) A)) (@ (@ tptp.groups8185359811944078981nteger G) A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.code_integer)) (G (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o A) (=> (forall ((I3 Bool)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_o I3) A) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le6747313008572928689nteger _let_1) (@ G I3)))))) (=> (not (= A tptp.bot_bot_set_o)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.groups7694694392188491536nteger F) A)) (@ (@ tptp.groups7694694392188491536nteger G) A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.code_integer)) (G (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat A) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_nat I3) A) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le6747313008572928689nteger _let_1) (@ G I3)))))) (=> (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.groups3455450783089532116nteger F) A)) (@ (@ tptp.groups3455450783089532116nteger G) A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.code_integer)) (G (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int A) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le6747313008572928689nteger _let_1) (@ G I3)))))) (=> (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.groups3827104343326376752nteger F) A)) (@ (@ tptp.groups3827104343326376752nteger G) A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (forall ((I3 tptp.code_integer)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_Code_integer I3) A) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I3)))))) (=> (not (= A tptp.bot_bo3990330152332043303nteger)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2555765274223993564er_rat F) A)) (@ (@ tptp.groups2555765274223993564er_rat G) A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (F (-> tptp.product_unit tptp.rat)) (G (-> tptp.product_unit tptp.rat))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (forall ((I3 tptp.product_unit)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_Product_unit I3) A) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I3)))))) (=> (not (= A tptp.bot_bo3957492148770167129t_unit)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups8984663225794451456it_rat F) A)) (@ (@ tptp.groups8984663225794451456it_rat G) A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (F (-> Bool tptp.rat)) (G (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o A) (=> (forall ((I3 Bool)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_o I3) A) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I3)))))) (=> (not (= A tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2869687844427037835_o_rat F) A)) (@ (@ tptp.groups2869687844427037835_o_rat G) A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_nat I3) A) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I3)))))) (=> (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups73079841787564623at_rat F) A)) (@ (@ tptp.groups73079841787564623at_rat G) A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I3)))))) (=> (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A)) (@ (@ tptp.groups1072433553688619179nt_rat G) A)))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn)) (X tptp.code_integer)) (let ((_let_1 (@ tptp.insert_Code_integer X))) (let ((_let_2 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_2 (@ (@ tptp.minus_2355218937544613996nteger A) (@ _let_1 tptp.bot_bo3990330152332043303nteger))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (G (-> tptp.product_unit tptp.assn)) (X tptp.product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit X))) (let ((_let_2 (@ tptp.groups5360233303959380816t_assn G))) (=> (@ tptp.finite4290736615968046902t_unit A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_2 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ _let_1 tptp.bot_bo3957492148770167129t_unit))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (G (-> Bool tptp.assn)) (X Bool)) (let ((_let_1 (@ tptp.insert_o X))) (let ((_let_2 (@ tptp.groups5301882518646026715o_assn G))) (=> (@ tptp.finite_finite_o A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_o A) (@ _let_1 tptp.bot_bot_set_o))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.assn)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.assn)) (X tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_nat A) (@ _let_1 tptp.bot_bot_set_nat))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (X tptp.code_integer)) (let ((_let_1 (@ tptp.insert_Code_integer X))) (let ((_let_2 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.times_times_rat (@ G X)) (@ _let_2 (@ (@ tptp.minus_2355218937544613996nteger A) (@ _let_1 tptp.bot_bo3990330152332043303nteger))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (G (-> tptp.product_unit tptp.rat)) (X tptp.product_unit)) (let ((_let_1 (@ tptp.insert_Product_unit X))) (let ((_let_2 (@ tptp.groups8984663225794451456it_rat G))) (=> (@ tptp.finite4290736615968046902t_unit A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.times_times_rat (@ G X)) (@ _let_2 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ _let_1 tptp.bot_bo3957492148770167129t_unit))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (G (-> Bool tptp.rat)) (X Bool)) (let ((_let_1 (@ tptp.insert_o X))) (let ((_let_2 (@ tptp.groups2869687844427037835_o_rat G))) (=> (@ tptp.finite_finite_o A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.times_times_rat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_o A) (@ _let_1 tptp.bot_bot_set_o))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (G (-> tptp.int tptp.rat)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.times_times_rat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (G (-> tptp.nat tptp.rat)) (X tptp.nat)) (let ((_let_1 (@ tptp.insert_nat X))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A) (= (@ _let_2 (@ _let_1 A)) (@ (@ tptp.times_times_rat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_nat A) (@ _let_1 tptp.bot_bot_set_nat))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ (@ tptp.member_Code_integer X) A) (= (@ _let_1 A) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer X) tptp.bot_bo3990330152332043303nteger))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit) (G (-> tptp.product_unit tptp.assn))) (let ((_let_1 (@ tptp.groups5360233303959380816t_assn G))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ (@ tptp.member_Product_unit X) A) (= (@ _let_1 A) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (X Bool) (G (-> Bool tptp.assn))) (let ((_let_1 (@ tptp.groups5301882518646026715o_assn G))) (=> (@ tptp.finite_finite_o A) (=> (@ (@ tptp.member_o X) A) (= (@ _let_1 A) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int A) (=> (@ (@ tptp.member_int X) A) (= (@ _let_1 A) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat A) (=> (@ (@ tptp.member_nat X) A) (= (@ _let_1 A) (@ (@ tptp.times_times_assn (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (X tptp.code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ (@ tptp.member_Code_integer X) A) (= (@ _let_1 A) (@ (@ tptp.times_times_rat (@ G X)) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) (@ (@ tptp.insert_Code_integer X) tptp.bot_bo3990330152332043303nteger))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (X tptp.product_unit) (G (-> tptp.product_unit tptp.rat))) (let ((_let_1 (@ tptp.groups8984663225794451456it_rat G))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ (@ tptp.member_Product_unit X) A) (= (@ _let_1 A) (@ (@ tptp.times_times_rat (@ G X)) (@ _let_1 (@ (@ tptp.minus_6452836326544984404t_unit A) (@ (@ tptp.insert_Product_unit X) tptp.bot_bo3957492148770167129t_unit))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (X Bool) (G (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups2869687844427037835_o_rat G))) (=> (@ tptp.finite_finite_o A) (=> (@ (@ tptp.member_o X) A) (= (@ _let_1 A) (@ (@ tptp.times_times_rat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_o A) (@ (@ tptp.insert_o X) tptp.bot_bot_set_o))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A) (=> (@ (@ tptp.member_int X) A) (= (@ _let_1 A) (@ (@ tptp.times_times_rat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A) (=> (@ (@ tptp.member_nat X) A) (= (@ _let_1 A) (@ (@ tptp.times_times_rat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups3674199335183972705nteger G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite6017078050557962740nteger B4) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger A) B4)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A) B4)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_natural))) (let ((_let_1 (@ tptp.groups2497794486940690220atural G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite6017078050557962740nteger B4) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger A) B4)) (= (@ G X3) tptp.one_one_Code_natural))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A) B4)) (@ (@ tptp.times_2397367101498566445atural (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G))) (=> (@ tptp.finite_finite_nat A) (=> (@ tptp.finite_finite_nat B4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A) B4)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (G (-> tptp.nat tptp.code_natural))) (let ((_let_1 (@ tptp.groups2279045934846249631atural G))) (=> (@ tptp.finite_finite_nat A) (=> (@ tptp.finite_finite_nat B4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A) B4)) (= (@ G X3) tptp.one_one_Code_natural))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.times_2397367101498566445atural (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite6017078050557962740nteger B4) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger A) B4)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A) B4)) (@ (@ tptp.times_times_assn (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat A) (=> (@ tptp.finite_finite_nat B4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A) B4)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.times_times_assn (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite6017078050557962740nteger B4) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger A) B4)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A) B4)) (@ (@ tptp.times_times_rat (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A) (=> (@ tptp.finite_finite_nat B4) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A) B4)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.times_times_rat (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite6017078050557962740nteger B4) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger A) B4)) (= (@ G X3) tptp.one_one_nat))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A) B4)) (@ (@ tptp.times_times_nat (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite6017078050557962740nteger B4) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger A) B4)) (= (@ G X3) tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A) B4)) (@ (@ tptp.times_times_int (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite6017078050557962740nteger B4) (=> (= (@ (@ tptp.inf_in1364745209274528805nteger A) B4) tptp.bot_bo3990330152332043303nteger) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A) B4)) (@ (@ tptp.times_times_assn (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit) (G (-> tptp.product_unit tptp.assn))) (let ((_let_1 (@ tptp.groups5360233303959380816t_assn G))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ tptp.finite4290736615968046902t_unit B4) (=> (= (@ (@ tptp.inf_in4660618365625256667t_unit A) B4) tptp.bot_bo3957492148770167129t_unit) (= (@ _let_1 (@ (@ tptp.sup_su793286257634532545t_unit A) B4)) (@ (@ tptp.times_times_assn (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (B4 tptp.set_o) (G (-> Bool tptp.assn))) (let ((_let_1 (@ tptp.groups5301882518646026715o_assn G))) (=> (@ tptp.finite_finite_o A) (=> (@ tptp.finite_finite_o B4) (=> (= (@ (@ tptp.inf_inf_set_o A) B4) tptp.bot_bot_set_o) (= (@ _let_1 (@ (@ tptp.sup_sup_set_o A) B4)) (@ (@ tptp.times_times_assn (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat A) (=> (@ tptp.finite_finite_nat B4) (=> (= (@ (@ tptp.inf_inf_set_nat A) B4) tptp.bot_bot_set_nat) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.times_times_assn (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (B4 tptp.set_int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int A) (=> (@ tptp.finite_finite_int B4) (=> (= (@ (@ tptp.inf_inf_set_int A) B4) tptp.bot_bot_set_int) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B4)) (@ (@ tptp.times_times_assn (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite6017078050557962740nteger B4) (=> (= (@ (@ tptp.inf_in1364745209274528805nteger A) B4) tptp.bot_bo3990330152332043303nteger) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A) B4)) (@ (@ tptp.times_times_rat (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Product_unit) (B4 tptp.set_Product_unit) (G (-> tptp.product_unit tptp.rat))) (let ((_let_1 (@ tptp.groups8984663225794451456it_rat G))) (=> (@ tptp.finite4290736615968046902t_unit A) (=> (@ tptp.finite4290736615968046902t_unit B4) (=> (= (@ (@ tptp.inf_in4660618365625256667t_unit A) B4) tptp.bot_bo3957492148770167129t_unit) (= (@ _let_1 (@ (@ tptp.sup_su793286257634532545t_unit A) B4)) (@ (@ tptp.times_times_rat (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_o) (B4 tptp.set_o) (G (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups2869687844427037835_o_rat G))) (=> (@ tptp.finite_finite_o A) (=> (@ tptp.finite_finite_o B4) (=> (= (@ (@ tptp.inf_inf_set_o A) B4) tptp.bot_bot_set_o) (= (@ _let_1 (@ (@ tptp.sup_sup_set_o A) B4)) (@ (@ tptp.times_times_rat (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A) (=> (@ tptp.finite_finite_nat B4) (=> (= (@ (@ tptp.inf_inf_set_nat A) B4) tptp.bot_bot_set_nat) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.times_times_rat (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_int) (B4 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A) (=> (@ tptp.finite_finite_int B4) (=> (= (@ (@ tptp.inf_inf_set_int A) B4) tptp.bot_bot_set_int) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B4)) (@ (@ tptp.times_times_rat (@ _let_1 A)) (@ _let_1 B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite6017078050557962740nteger B4) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A) B4)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B4))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B4) A)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A) B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat A) (=> (@ tptp.finite_finite_nat B4) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B4) A)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite6017078050557962740nteger B4) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A) B4)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B4))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B4) A)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A) B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A) (=> (@ tptp.finite_finite_nat B4) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B4) A)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite6017078050557962740nteger B4) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A) B4)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B4))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B4) A)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A) B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_Code_integer) (B4 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int G))) (=> (@ tptp.finite6017078050557962740nteger A) (=> (@ tptp.finite6017078050557962740nteger B4) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A) B4)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A) B4))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B4) A)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A) B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ tptp.finite_finite_nat A) (=> (@ tptp.finite_finite_nat B4) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B4) A)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)))))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat) (B4 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ tptp.finite_finite_nat A) (=> (@ tptp.finite_finite_nat B4) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B4)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A) B4))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B4) A)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B4)))))))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A2) tptp.one_one_rat))) (let ((_let_2 (@ tptp.suc K3))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_2)) (@ (@ tptp.gbinomial_rat _let_1) _let_2)) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.gbinomial_rat A2) K3)))))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.suc K3))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ (@ tptp.gbinomial_rat A2) _let_1)) (@ (@ tptp.times_times_rat A2) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A2) tptp.one_one_rat)) K3))))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (M4 tptp.nat) (A2 tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat A2))) (=> (@ (@ tptp.ord_less_eq_nat K3) M4) (= (@ (@ tptp.times_times_rat (@ _let_1 M4)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat M4)) K3)) (@ (@ tptp.times_times_rat (@ _let_1 K3)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A2) (@ tptp.semiri681578069525770553at_rat K3))) (@ (@ tptp.minus_minus_nat M4) K3))))))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)))) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K3)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K3)))))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K3)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K3)))))))
% 5.65/5.94 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat Y) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N3)) X))))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (A2 tptp.rat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.gbinomial_rat A2) K3) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat A2) (@ tptp.semiri681578069525770553at_rat K3))) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A2) tptp.one_one_rat)) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)))))))
% 5.65/5.94 (assert (forall ((B tptp.rat) (K3 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K3) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K3))) tptp.one_one_rat)) K3)))))
% 5.65/5.94 (assert (forall ((B tptp.int) (K3 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B)) K3) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K3)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B) (@ tptp.semiri1314217659103216013at_int K3))) tptp.one_one_int)) K3)))))
% 5.65/5.94 (assert (forall ((B tptp.code_integer) (K3 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger B)) K3) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K3)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger B) (@ tptp.semiri4939895301339042750nteger K3))) tptp.one_one_Code_integer)) K3)))))
% 5.65/5.94 (assert (forall ((B tptp.rat) (K3 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K3))) tptp.one_one_rat)) K3) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K3)))))
% 5.65/5.94 (assert (forall ((B tptp.int) (K3 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B) (@ tptp.semiri1314217659103216013at_int K3))) tptp.one_one_int)) K3) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K3)) (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B)) K3)))))
% 5.65/5.94 (assert (forall ((B tptp.code_integer) (K3 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger B) (@ tptp.semiri4939895301339042750nteger K3))) tptp.one_one_Code_integer)) K3) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K3)) (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger B)) K3)))))
% 5.65/5.94 (assert (forall ((I2 tptp.int) (J tptp.int) (K3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K3)))) (=> (@ (@ tptp.ord_less_int I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J)))))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M4)) (@ _let_1 N2)))) (let ((_let_3 (= K3 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat M4) N2)))))))))
% 5.65/5.94 (assert (forall ((M4 tptp.int) (N2 tptp.int)) (=> (= (@ (@ tptp.times_times_int M4) N2) tptp.one_one_int) (or (= M4 tptp.one_one_int) (= M4 (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 5.65/5.94 (assert (forall ((M4 tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.times_times_int M4) N2) tptp.one_one_int) (or (and (= M4 tptp.one_one_int) (= N2 tptp.one_one_int)) (and (= M4 _let_1) (= N2 _let_1)))))))
% 5.65/5.94 (assert (forall ((K3 tptp.int) (M4 tptp.int) (T4 tptp.int)) (let ((_let_1 (@ tptp.times_times_int K3))) (=> (not (= K3 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int M4) T4) (@ (@ tptp.dvd_dvd_int (@ _let_1 M4)) (@ _let_1 T4)))))))
% 5.65/5.94 (assert (forall ((K3 tptp.int) (M4 tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int K3))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 M4)) (@ _let_1 N2)) (=> (not (= K3 tptp.zero_zero_int)) (@ (@ tptp.dvd_dvd_int M4) N2))))))
% 5.65/5.94 (assert (forall ((K3 tptp.int) (N2 tptp.int) (M4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K3))) (= (@ _let_1 (@ (@ tptp.plus_plus_int N2) (@ (@ tptp.times_times_int K3) M4))) (@ _let_1 N2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (D2 tptp.int) (X tptp.int) (T4 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (let ((_let_2 (@ tptp.dvd_dvd_int A2))) (=> (@ _let_2 D2) (= (@ _let_2 (@ _let_1 T4)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.times_times_int C) D2))) T4))))))))
% 5.65/5.94 (assert (forall ((B tptp.int) (Q5 tptp.int) (R6 tptp.int) (Q4 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_2 Q5)) R6)) (@ (@ tptp.plus_plus_int (@ _let_2 Q4)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ _let_1 R2) (=> (@ _let_1 R6) (@ (@ tptp.ord_less_eq_int Q4) Q5)))))))))
% 5.65/5.94 (assert (forall ((B tptp.int) (Q5 tptp.int) (R6 tptp.int) (Q4 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q5)) R6)) (@ (@ tptp.plus_plus_int (@ _let_1 Q4)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R6) (=> (@ (@ tptp.ord_less_int R6) B) (=> (@ (@ tptp.ord_less_int R2) B) (@ (@ tptp.ord_less_eq_int Q5) Q4))))))))
% 5.65/5.94 (assert (forall ((B tptp.int) (Q4 tptp.int) (R2 tptp.int) (B3 tptp.int) (Q5 tptp.int) (R6 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B3) Q5)) R6))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q4)) R2) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R2) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R6) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (=> (@ (@ tptp.ord_less_eq_int B3) B) (@ (@ tptp.ord_less_eq_int Q5) Q4))))))))))
% 5.65/5.94 (assert (forall ((B tptp.int) (Q4 tptp.int) (R2 tptp.int) (B3 tptp.int) (Q5 tptp.int) (R6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B3) Q5)) R6))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q4)) R2) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R6) B3) (=> (@ _let_1 R2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (=> (@ (@ tptp.ord_less_eq_int B3) B) (@ (@ tptp.ord_less_eq_int Q4) Q5)))))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (Q4 tptp.int) (R2 tptp.int)) (=> (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q4)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B) (= (@ (@ tptp.divide_divide_int A2) B) Q4))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (Q4 tptp.int) (R2 tptp.int)) (=> (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q4)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R2) (= (@ (@ tptp.divide_divide_int A2) B) Q4))))))
% 5.65/5.94 (assert (forall ((B3 tptp.int) (Q5 tptp.int) (R6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B3) Q5)) R6)) (=> (@ (@ tptp.ord_less_int R6) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (@ _let_1 Q5)))))))
% 5.65/5.94 (assert (forall ((P (-> tptp.int Bool)) (N2 tptp.int) (K3 tptp.int)) (= (@ P (@ (@ tptp.divide_divide_int N2) K3)) (and (=> (= K3 tptp.zero_zero_int) (@ P tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K3) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K3) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K3) I4)) J3))) (@ P I4)))) (=> (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K3) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K3) I4)) J3))) (@ P I4))))))))
% 5.65/5.94 (assert (forall ((D2 tptp.int) (P (-> tptp.int Bool)) (K3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D2)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K3) (forall ((X6 tptp.int)) (=> (@ P X6) (@ P (@ (@ tptp.plus_plus_int X6) (@ (@ tptp.times_times_int K3) D2))))))))))
% 5.65/5.94 (assert (forall ((M4 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M4) (= (= (@ (@ tptp.times_times_int M4) N2) tptp.one_one_int) (and (= M4 tptp.one_one_int) (= N2 tptp.one_one_int))))))
% 5.65/5.94 (assert (forall ((I2 tptp.int) (J tptp.int) (K3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int K3))) (=> (@ (@ tptp.ord_less_int I2) J) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K3) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J)))))))
% 5.65/5.94 (assert (forall ((D2 tptp.int) (P1 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P1 X3) (@ P1 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D2))))) (=> (exists ((Z6 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z6) (= (@ P X3) (@ P1 X3))))) (=> (exists ((X_12 tptp.int)) (@ P1 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 5.65/5.94 (assert (forall ((D2 tptp.int) (P7 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P7 X3) (@ P7 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D2))))) (=> (exists ((Z6 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z6) X3) (= (@ P X3) (@ P7 X3))))) (=> (exists ((X_12 tptp.int)) (@ P7 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 5.65/5.94 (assert (forall ((D2 tptp.int) (P (-> tptp.int Bool)) (K3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D2)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K3) (forall ((X6 tptp.int)) (=> (@ P X6) (@ P (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K3) D2))))))))))
% 5.65/5.94 (assert (forall ((L tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) L) tptp.zero_zero_int)))
% 5.65/5.94 (assert (forall ((K3 tptp.int)) (= (@ (@ tptp.times_times_int K3) tptp.zero_zero_int) tptp.zero_zero_int)))
% 5.65/5.94 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z1) Z22)) W) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z22) W)))))
% 5.65/5.94 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z1) Z22)) (@ (@ tptp.plus_plus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 5.65/5.94 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.minus_minus_int Z1) Z22)) (@ (@ tptp.minus_minus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 5.65/5.94 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z1) Z22)) W) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z22) W)))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.divide_divide_nat (@ _let_1 M4)) (@ _let_1 N2)) (@ (@ tptp.divide_divide_nat M4) N2))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M4) N2)) N2) M4))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) M4)) N2) M4))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (N2 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M4))) (= (@ _let_1 (@ (@ tptp.times_times_nat N2) Q4)) (@ (@ tptp.divide_divide_nat (@ _let_1 N2)) Q4)))))
% 5.65/5.94 (assert (forall ((C tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (I2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M4) (@ (@ tptp.times_times_nat I2) N2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M4) N2)) I2))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M4) N2)) N2)) M4)))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (M4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.divide_divide_nat M4) N2))) M4)))
% 5.65/5.94 (assert (forall ((Q4 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q4) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M4) Q4)) N2) (@ (@ tptp.ord_less_nat M4) (@ (@ tptp.times_times_nat N2) Q4))))))
% 5.65/5.94 (assert (forall ((Q4 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q4) (= (@ (@ tptp.ord_less_eq_nat M4) (@ (@ tptp.divide_divide_nat N2) Q4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M4) Q4)) N2)))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (Q4 tptp.nat) (M4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q4)) M4) (=> (@ (@ tptp.ord_less_nat M4) (@ _let_1 (@ tptp.suc Q4))) (= (@ (@ tptp.divide_divide_nat M4) N2) Q4))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat M4) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.divide_divide_nat M4) N2)))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat M4) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M4) N2)) N2))))))
% 5.65/5.94 (assert (forall ((P (-> tptp.nat Bool)) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M4) N2)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N2) (=> (= M4 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I4)) J3)) (@ P I4))))))))))
% 5.65/5.94 (assert (forall ((P (-> tptp.nat Bool)) (M4 tptp.nat) (N2 tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M4) N2)) (or (and (= N2 tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (exists ((Q6 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q6)) M4) (@ (@ tptp.ord_less_nat M4) (@ _let_1 (@ tptp.suc Q6))) (@ P Q6))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat A2) B)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A2)) (@ tptp.semiri1314217659103216013at_int B)))))
% 5.65/5.94 (assert (forall ((K3 tptp.int) (L tptp.int) (Q4 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L))) (let ((_let_2 (@ _let_1 tptp.zero_zero_int))) (let ((_let_3 (@ (@ tptp.ord_less_int tptp.zero_zero_int) L))) (= (@ (@ (@ tptp.eucl_rel_int K3) L) (@ (@ tptp.product_Pair_int_int Q4) R2)) (and (= K3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int L) Q4)) R2)) (=> _let_3 (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (@ (@ tptp.ord_less_int R2) L))) (=> (not _let_3) (and (=> _let_2 (and (@ _let_1 R2) (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int))) (=> (not _let_2) (= Q4 tptp.zero_zero_int)))))))))))
% 5.65/5.94 (assert (forall ((L tptp.int) (K3 tptp.int) (Q4 tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (= K3 (@ (@ tptp.times_times_int Q4) L)) (@ (@ (@ tptp.eucl_rel_int K3) L) (@ (@ tptp.product_Pair_int_int Q4) tptp.zero_zero_int))))))
% 5.65/5.94 (assert (forall ((K3 tptp.int) (P (-> tptp.int tptp.int Bool)) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K3) (= (@ (@ P (@ (@ tptp.divide_divide_int N2) K3)) (@ (@ tptp.modulo_modulo_int N2) K3)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K3) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K3) I4)) J3))) (@ (@ P I4) J3)))))))
% 5.65/5.94 (assert (forall ((K3 tptp.int) (P (-> tptp.int tptp.int Bool)) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int) (= (@ (@ P (@ (@ tptp.divide_divide_int N2) K3)) (@ (@ tptp.modulo_modulo_int N2) K3)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K3) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K3) I4)) J3))) (@ (@ P I4) J3)))))))
% 5.65/5.94 (assert (forall ((D2 tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D2))) Z)))))
% 5.65/5.94 (assert (forall ((D2 tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) Z))) tptp.one_one_int)) D2))))))
% 5.65/5.94 (assert (forall ((M4 tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int M4) D2) tptp.zero_zero_int) (exists ((Q6 tptp.int)) (= M4 (@ (@ tptp.times_times_int D2) Q6))))))
% 5.65/5.94 (assert (forall ((M4 tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int M4) D2) tptp.zero_zero_int) (exists ((Q7 tptp.int)) (= M4 (@ (@ tptp.times_times_int D2) Q7))))))
% 5.65/5.94 (assert (forall ((M4 tptp.int) (N2 tptp.int)) (=> (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int M4) N2)) tptp.one_one_int) (= (@ tptp.abs_abs_int M4) tptp.one_one_int))))
% 5.65/5.94 (assert (forall ((A tptp.int) (N2 tptp.int)) (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) N2)) N2)) (@ (@ tptp.modulo_modulo_int A) N2)))))
% 5.65/5.94 (assert (forall ((M4 tptp.int) (N2 tptp.int)) (=> (not (= M4 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int M4) N2)) M4) (= (@ tptp.abs_abs_int N2) tptp.one_one_int)))))
% 5.65/5.94 (assert (forall ((P (-> tptp.int Bool)) (N2 tptp.int) (K3 tptp.int)) (= (@ P (@ (@ tptp.modulo_modulo_int N2) K3)) (and (=> (= K3 tptp.zero_zero_int) (@ P N2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K3) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K3) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K3) I4)) J3))) (@ P J3)))) (=> (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K3) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K3) I4)) J3))) (@ P J3))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (Q4 tptp.int) (R2 tptp.int)) (=> (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q4)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R2) (= (@ (@ tptp.modulo_modulo_int A2) B) R2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (Q4 tptp.int) (R2 tptp.int)) (=> (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q4)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B) (= (@ (@ tptp.modulo_modulo_int A2) B) R2))))))
% 5.65/5.94 (assert (forall ((C tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A2))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A2) B)) C))) (@ _let_1 B))))))))
% 5.65/5.94 (assert (= tptp.eucl_rel_int (lambda ((A13 tptp.int) (A24 tptp.int) (A32 tptp.product_prod_int_int)) (or (exists ((K5 tptp.int)) (and (= A13 K5) (= A24 tptp.zero_zero_int) (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K5)))) (exists ((L2 tptp.int) (K5 tptp.int) (Q6 tptp.int)) (and (= A13 K5) (= A24 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q6) tptp.zero_zero_int)) (not (= L2 tptp.zero_zero_int)) (= K5 (@ (@ tptp.times_times_int Q6) L2)))) (exists ((R4 tptp.int) (L2 tptp.int) (K5 tptp.int) (Q6 tptp.int)) (and (= A13 K5) (= A24 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q6) R4)) (= (@ tptp.sgn_sgn_int R4) (@ tptp.sgn_sgn_int L2)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R4)) (@ tptp.abs_abs_int L2)) (= K5 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q6) L2)) R4))))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (K3 tptp.nat) (M4 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) K3)) M4))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M4)) N2))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (N2 tptp.nat) (M4 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) N2)) M4))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M4)) N2))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (N2 tptp.nat) (K3 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M4) (@ (@ tptp.times_times_nat N2) K3)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M4)) N2))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (K3 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M4) (@ (@ tptp.times_times_nat K3) N2)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M4)) N2))))
% 5.65/5.94 (assert (forall ((K3 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat K3))) (=> (not (= _let_1 tptp.one_one_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) _let_1) tptp.one_one_nat)))))
% 5.65/5.94 (assert (forall ((L tptp.int) (K3 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L))) (= (@ _let_1 (@ (@ tptp.times_times_int K3) (@ tptp.sgn_sgn_int R2))) (or (@ _let_1 K3) (= R2 tptp.zero_zero_int))))))
% 5.65/5.94 (assert (forall ((L tptp.int) (R2 tptp.int) (K3 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R2)) K3)) (or (@ _let_1 K3) (= R2 tptp.zero_zero_int))))))
% 5.65/5.94 (assert (forall ((L tptp.int) (R2 tptp.int) (K3 tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int L) (@ tptp.sgn_sgn_int R2))) K3) (and (@ (@ tptp.dvd_dvd_int L) K3) (=> (= R2 tptp.zero_zero_int) (= K3 tptp.zero_zero_int))))))
% 5.65/5.94 (assert (forall ((R2 tptp.int) (L tptp.int) (K3 tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R2)) L)) K3) (and (@ (@ tptp.dvd_dvd_int L) K3) (=> (= R2 tptp.zero_zero_int) (= K3 tptp.zero_zero_int))))))
% 5.65/5.94 (assert (forall ((K3 tptp.int)) (not (forall ((N3 tptp.nat) (L3 tptp.int)) (not (= K3 (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int L3)) (@ tptp.semiri1314217659103216013at_int N3))))))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (D2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M4) D2) tptp.zero_zero_nat) (exists ((Q7 tptp.nat)) (= M4 (@ (@ tptp.times_times_nat D2) Q7))))))
% 5.65/5.94 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X) N2) (@ (@ tptp.modulo_modulo_nat Y) N2)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (= (@ (@ tptp.plus_plus_nat X) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y) (@ _let_1 Q22))))))))
% 5.65/5.94 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X) N2) (@ (@ tptp.modulo_modulo_nat Y) N2)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (exists ((Q7 tptp.nat)) (= X (@ (@ tptp.plus_plus_nat Y) (@ (@ tptp.times_times_nat N2) Q7))))))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (Q4 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M4) Q4) (@ (@ tptp.modulo_modulo_nat N2) Q4)) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (not (forall ((S8 tptp.nat)) (not (= N2 (@ (@ tptp.plus_plus_nat M4) (@ (@ tptp.times_times_nat Q4) S8))))))))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (Q4 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M4) Q4) (@ (@ tptp.modulo_modulo_nat N2) Q4)) (=> (@ (@ tptp.ord_less_eq_nat N2) M4) (not (forall ((S8 tptp.nat)) (not (= M4 (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat Q4) S8))))))))))
% 5.65/5.94 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) N2)) N2)) (@ (@ tptp.modulo_modulo_nat A) N2)))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (N2 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M4))) (let ((_let_2 (@ tptp.times_times_nat N2))) (= (@ _let_1 (@ _let_2 Q4)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat M4) N2)) Q4))) (@ _let_1 N2)))))))
% 5.65/5.94 (assert (= tptp.modulo_modulo_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.minus_minus_nat M3) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M3) N4)) N4)))))
% 5.65/5.94 (assert (forall ((V tptp.int) (K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (let ((_let_2 (@ tptp.abs_abs_int K3))) (let ((_let_3 (@ tptp.times_times_int (@ tptp.sgn_sgn_int V)))) (=> (not (= V tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) (@ _let_3 _let_1)) (@ (@ tptp.divide_divide_int _let_2) _let_1))))))))
% 5.65/5.94 (assert (forall ((L tptp.int) (K3 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int L) K3) (= (@ (@ tptp.divide_divide_int K3) L) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int K3)) (@ tptp.sgn_sgn_int L))) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K3)) (@ tptp.abs_abs_int L)))))))
% 5.65/5.94 (assert (forall ((P (-> tptp.nat Bool)) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M4) N2)) (and (=> _let_1 (@ P M4)) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N2) (=> (= M4 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I4)) J3)) (@ P J3))))))))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M4) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M4) N2))) M4) tptp.one_one_nat))))
% 5.65/5.94 (assert (forall ((R2 tptp.int) (L tptp.int) (K3 tptp.int) (Q4 tptp.int)) (=> (= (@ tptp.sgn_sgn_int R2) (@ tptp.sgn_sgn_int L)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R2)) (@ tptp.abs_abs_int L)) (=> (= K3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q4) L)) R2)) (@ (@ (@ tptp.eucl_rel_int K3) L) (@ (@ tptp.product_Pair_int_int Q4) R2)))))))
% 5.65/5.94 (assert (forall ((A1 tptp.int) (A22 tptp.int) (A33 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.eucl_rel_int A1) A22) A33) (=> (=> (= A22 tptp.zero_zero_int) (not (= A33 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A1)))) (=> (forall ((Q7 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q7) tptp.zero_zero_int)) (=> (not (= A22 tptp.zero_zero_int)) (not (= A1 (@ (@ tptp.times_times_int Q7) A22)))))) (not (forall ((R7 tptp.int) (Q7 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q7) R7)) (=> (= (@ tptp.sgn_sgn_int R7) (@ tptp.sgn_sgn_int A22)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R7)) (@ tptp.abs_abs_int A22)) (not (= A1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q7) A22)) R7)))))))))))))
% 5.65/5.94 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa) (@ (@ tptp.modulo_modulo_nat X) Xa)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa) Y) (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa))))))))))))))
% 5.65/5.94 (assert (= tptp.bezw (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y3) (@ (@ tptp.modulo_modulo_nat X2) Y3)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= Y3 tptp.zero_zero_nat)) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X2) Y3)))))))))))
% 5.65/5.94 (assert (forall ((Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y) (@ (@ tptp.modulo_modulo_nat X) Y)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y) (= (@ (@ tptp.bezw X) Y) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Y)))))))))))
% 5.65/5.94 (assert (forall ((L tptp.int) (K3 tptp.int) (N2 tptp.nat) (M4 tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat M4) N2))) (let ((_let_2 (@ tptp.sgn_sgn_int L))) (let ((_let_3 (@ tptp.sgn_sgn_int K3))) (let ((_let_4 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int M4))) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int N2))))) (let ((_let_5 (= _let_3 _let_2))) (let ((_let_6 (or (= _let_2 tptp.zero_zero_int) (= _let_3 tptp.zero_zero_int) (= N2 tptp.zero_zero_nat)))) (and (=> _let_6 (= _let_4 tptp.zero_zero_int)) (=> (not _let_6) (and (=> _let_5 (= _let_4 (@ tptp.semiri1314217659103216013at_int _let_1))) (=> (not _let_5) (= _let_4 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N2) M4)))))))))))))))))))
% 5.65/5.94 (assert (forall ((L tptp.int) (K3 tptp.int) (N2 tptp.nat) (M4 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M4) N2)))) (let ((_let_2 (@ tptp.sgn_sgn_int L))) (let ((_let_3 (@ tptp.times_times_int _let_2))) (let ((_let_4 (@ tptp.sgn_sgn_int K3))) (let ((_let_5 (@ (@ tptp.times_times_int _let_4) (@ tptp.semiri1314217659103216013at_int M4)))) (let ((_let_6 (@ (@ tptp.modulo_modulo_int _let_5) (@ _let_3 (@ tptp.semiri1314217659103216013at_int N2))))) (let ((_let_7 (= _let_4 _let_2))) (let ((_let_8 (or (= _let_2 tptp.zero_zero_int) (= _let_4 tptp.zero_zero_int) (= N2 tptp.zero_zero_nat)))) (and (=> _let_8 (= _let_6 _let_5)) (=> (not _let_8) (and (=> _let_7 (= _let_6 (@ _let_3 _let_1))) (=> (not _let_7) (= _let_6 (@ _let_3 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat N2) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N2) M4)))))) _let_1)))))))))))))))))
% 5.65/5.94 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa)))) (let ((_let_2 (@ (@ tptp.bezw Xa) (@ (@ tptp.modulo_modulo_nat X) Xa)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa) Y) (=> _let_1 (not (=> (and (=> _let_4 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y (@ (@ tptp.product_Pair_int_int _let_3) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_2)) (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa)))))))) (not _let_1)))))))))))
% 5.65/5.94 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N2) N2)))
% 5.65/5.94 (assert (forall ((M4 tptp.num)) (= (@ (@ tptp.times_times_num M4) tptp.one) M4)))
% 5.65/5.94 (assert (forall ((B tptp.int) (A2 tptp.int) (Q4 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.product_Pair_int_int Q4))) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (=> (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int A2) tptp.one_one_int)) B) (@ _let_2 R2)) (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 A2))) (@ _let_1 B)) (@ _let_2 (@ (@ tptp.minus_minus_int (@ _let_1 R2)) tptp.one_one_int)))))))))
% 5.65/5.94 (assert (forall ((M4 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M4)) (@ tptp.bit0 N2)) (@ tptp.bit0 (@ tptp.bit0 (@ (@ tptp.times_times_num M4) N2))))))
% 5.65/5.94 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N2) (@ tptp.bit0 N2))))
% 5.65/5.94 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat N2) _let_1)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ tptp.suc (@ _let_1 M4)) (@ _let_1 N2))))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ _let_1 M4) (@ tptp.suc (@ _let_1 N2)))))))
% 5.65/5.94 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (@ P (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (@ P N2))))))
% 5.65/5.94 (assert (forall ((P (-> tptp.int Bool)) (K3 tptp.int)) (=> (@ P tptp.zero_zero_int) (=> (@ P (@ tptp.uminus_uminus_int tptp.one_one_int)) (=> (forall ((K tptp.int)) (=> (@ P K) (=> (not (= K tptp.zero_zero_int)) (@ P (@ (@ tptp.times_times_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))) (=> (forall ((K tptp.int)) (=> (@ P K) (=> (not (= K (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ P (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))) (@ P K3)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A2)) (@ (@ tptp.divide_divide_int B) A2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A2))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A2) (= (@ (@ tptp.modulo_modulo_int (@ _let_2 (@ _let_1 B))) (@ _let_1 A2)) (@ _let_2 (@ _let_1 (@ (@ tptp.modulo_modulo_int B) A2)))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A2) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A2)) (@ (@ tptp.minus_minus_int (@ _let_1 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A2))) tptp.one_one_int))))))
% 5.65/5.94 (assert (forall ((B tptp.int) (A2 tptp.int) (Q4 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_3 (@ tptp.product_Pair_int_int Q4))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ (@ tptp.eucl_rel_int A2) B) (@ _let_3 R2)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A2))) (@ _let_1 B)) (@ _let_3 (@ _let_2 (@ _let_1 R2)))))))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (K3 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K3))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ tptp.numeral_numeral_int K3))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (K3 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K3)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K3)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K3)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.times_times_int K3) L))))))
% 5.65/5.94 (assert (forall ((X tptp.int) (Xa tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 X)) (not (@ _let_2 Xa)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_5 (and (@ (@ tptp.member_int X) _let_4) (@ (@ tptp.member_int Xa) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa) Y) (and (=> _let_5 (= Y (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_1)) (@ (@ tptp.divide_divide_int Xa) _let_1)))))))))))))))
% 5.65/5.94 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K5 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K5)) (not (@ _let_2 L2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (@ (@ (@ tptp.if_int (and (@ (@ tptp.member_int K5) _let_4) (@ (@ tptp.member_int L2) _let_4))) (@ tptp.uminus_uminus_int _let_3)) (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K5) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (K3 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K3)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K3))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ (@ tptp.bit_concat_bit (@ tptp.suc N2)) K3) L) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ (@ tptp.bit_concat_bit N2) (@ (@ tptp.divide_divide_int K3) _let_1)) L)))))))
% 5.65/5.94 (assert (forall ((M4 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M4)) _let_1) (@ tptp.bit0 (@ (@ tptp.times_times_num M4) _let_1))))))
% 5.65/5.94 (assert (forall ((M4 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.times_times_num (@ tptp.bit1 M4)))) (= (@ _let_1 (@ tptp.bit0 N2)) (@ tptp.bit0 (@ _let_1 N2))))))
% 5.65/5.94 (assert (forall ((M4 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit1 M4)) (@ tptp.bit1 N2)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M4) N2)) (@ tptp.bit0 (@ (@ tptp.times_times_num M4) N2)))))))
% 5.65/5.94 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W)))) tptp.one_one_int))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (K3 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K3))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ tptp.numeral_numeral_int K3))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K3)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.times_times_int K3) L))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (K3 tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K3)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K3)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 5.65/5.94 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K5 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K5)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K5) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 5.65/5.94 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K5 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K5 tptp.zero_zero_int) (= L2 tptp.zero_zero_int))) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= K5 _let_2)) L2) (@ (@ (@ tptp.if_int (= L2 _let_2)) K5) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int K5) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K5) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 5.65/5.94 (assert (forall ((L tptp.num) (K3 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K3)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K3))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 5.65/5.94 (assert (forall ((L tptp.num) (K3 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K3))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K3))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 5.65/5.94 (assert (forall ((K3 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K3)) (not (@ _let_2 L)))))) (let ((_let_4 (@ (@ tptp.bit_se725231765392027082nd_int K3) L))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int K3) _let_5) (@ (@ tptp.member_int L) _let_5)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K3) L)) (and (=> _let_6 (= _let_4 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_6) (= _let_4 (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))))))
% 5.65/5.94 (assert (forall ((X tptp.int) (Xa tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X) Xa)))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_2))) (let ((_let_4 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_3 X)) (not (@ _let_3 Xa)))))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int X) _let_5) (@ (@ tptp.member_int Xa) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa) Y) (=> _let_1 (not (=> (and (=> _let_6 (= Y (@ tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y (@ (@ tptp.plus_plus_int _let_4) (@ (@ tptp.times_times_int _let_2) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_2)) (@ (@ tptp.divide_divide_int Xa) _let_2))))))) (not _let_1)))))))))))))
% 5.65/5.94 (assert (forall ((L tptp.num) (K3 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K3))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K3))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 5.65/5.94 (assert (forall ((L tptp.num) (K3 tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K3)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K3)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 5.65/5.94 (assert (forall ((L tptp.num) (K3 tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K3)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K3)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 5.65/5.94 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M3 tptp.zero_zero_nat) (= N4 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M3) _let_1)) (@ (@ tptp.modulo_modulo_nat N4) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 5.65/5.94 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (@ _let_2 M3)) (not (@ _let_2 N4))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 5.65/5.94 (assert (forall ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((K tptp.int) (L3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K) L3)) (=> (=> (not (and (@ (@ tptp.member_int K) _let_2) (@ (@ tptp.member_int L3) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1))) (@ (@ P K) L3)))))) (@ (@ P A0) A1)))))
% 5.65/5.94 (assert (forall ((L tptp.num) (K3 tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K3)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K3))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (K3 tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K3)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K3))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 5.65/5.94 (assert (= tptp.binomial (lambda ((N4 tptp.nat) (K5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N4) K5))) (let ((_let_2 (@ tptp.ord_less_nat N4))) (@ (@ (@ tptp.if_nat (@ _let_2 K5)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K5))) (@ (@ tptp.binomial N4) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N4) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K5)))))))))
% 5.65/5.94 (assert (= tptp.modulo_modulo_int (lambda ((K5 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 (@ tptp.abs_abs_int K5))) (@ tptp.nat2 _let_1))))) (let ((_let_3 (@ tptp.sgn_sgn_int L2))) (let ((_let_4 (@ tptp.times_times_int _let_3))) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K5) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K5) _let_3)) (@ _let_4 _let_2)) (@ _let_4 (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int _let_1) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L2) K5))))) _let_2)))))))))))
% 5.65/5.94 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K5 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K5 _let_2) (= L2 _let_2))) _let_2) (@ (@ (@ tptp.if_int (= K5 tptp.zero_zero_int)) L2) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K5) (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int (@ (@ tptp.modulo_modulo_int K5) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K5) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N2) K3)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial _let_2) _let_1)) _let_1))))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.suc K3))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial _let_1) _let_2)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N2) K3)))))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (R2 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M4))) (let ((_let_2 (@ _let_1 R2))) (let ((_let_3 (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) K3)))) (let ((_let_4 (@ _let_1 K3))) (= (@ (@ tptp.times_times_nat (@ _let_3 _let_4)) (@ (@ tptp.binomial _let_4) K3)) (@ (@ tptp.times_times_nat (@ _let_3 K3)) (@ (@ tptp.binomial _let_2) M4)))))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat A2) B))))) (let ((_let_2 (@ tptp.suc A2))) (= (@ (@ tptp.times_times_nat _let_2) (@ _let_1 _let_2)) (@ (@ tptp.times_times_nat (@ tptp.suc B)) (@ _let_1 A2)))))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K3)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K3)))) (@ (@ tptp.binomial N2) K3)) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K3) M4) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (= (@ (@ tptp.times_times_nat (@ _let_1 M4)) (@ (@ tptp.binomial M4) K3)) (@ (@ tptp.times_times_nat (@ _let_1 K3)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) K3)) (@ (@ tptp.minus_minus_nat M4) K3)))))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (= (@ (@ tptp.times_times_nat (@ _let_1 K3)) (@ (@ tptp.binomial N2) K3)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.binomial (@ _let_1 tptp.one_one_nat)) K3))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ tptp.binomial _let_2) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N2) K3))) _let_1))))))
% 5.65/5.94 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.times_times_int W) Z))) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.abs_abs_int W))) (@ tptp.nat2 (@ tptp.abs_abs_int Z))))))
% 5.65/5.94 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.times_times_num X))) (= (@ _let_1 (@ tptp.inc Y)) (@ (@ tptp.plus_plus_num (@ _let_1 Y)) X)))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N2) _let_1)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) K3))))))
% 5.65/5.94 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z7)) (@ (@ tptp.times_times_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7))))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N2) (= (@ (@ tptp.binomial N2) K3) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K3)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K3))))))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.times_times_nat K3) (@ (@ tptp.binomial N2) K3)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)))))))
% 5.65/5.94 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z7)) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.uminus_uminus_int Z))) (@ tptp.nat2 (@ tptp.uminus_uminus_int Z7)))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.binomial N2) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) _let_1)))))
% 5.65/5.94 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K5 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (or (not (@ _let_2 K5)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K5) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 5.65/5.94 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (K5 tptp.int)) (let ((_let_1 (@ tptp.suc N4))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int _let_1) K5)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K5) N4))))))))
% 5.65/5.94 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) N4) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) M3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M3) _let_1)) (@ (@ tptp.modulo_modulo_nat N4) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1))))))))))
% 5.65/5.94 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N4 tptp.nat) (K5 tptp.int)) (@ (@ tptp.times_times_int K5) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)))))
% 5.65/5.94 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N4 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.times_times_nat M3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 5.65/5.94 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N4 tptp.nat) (K5 tptp.int)) (@ (@ tptp.plus_plus_int K5) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K5) N4)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4))))))
% 5.65/5.94 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N4 tptp.nat) (K5 tptp.int)) (@ (@ tptp.minus_minus_int K5) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K5) N4))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4))))))
% 5.65/5.94 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (or (not (@ _let_2 M3)) (not (@ _let_2 N4))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 5.65/5.94 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) N4) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) M3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M3) _let_1)) (@ (@ tptp.modulo_modulo_nat N4) _let_1))) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1))))))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (K3 tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N2)))) (@ (@ tptp.bit_se2923211474154528505it_int N2) K3)))))
% 5.65/5.94 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K5 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (not (= (not (@ _let_2 K5)) (not (@ _let_2 L2)))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K5) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 5.65/5.94 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (not (= (not (@ _let_2 M3)) (not (@ _let_2 N4)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 5.65/5.94 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K5 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (= K5 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int L2)) (@ (@ (@ tptp.if_int (= L2 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int K5)) (@ (@ (@ tptp.if_int (= K5 tptp.zero_zero_int)) L2) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K5) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int K5) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1)))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K5) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))))))
% 5.65/5.94 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K5 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int _let_1) K5))) (@ (@ tptp.times_times_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.divide_divide_int K5) _let_1))))))))
% 5.65/5.94 (assert (forall ((M4 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M4))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M4)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))))))))
% 5.65/5.94 (assert (forall ((M4 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M4))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M4)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))))))))
% 5.65/5.94 (assert (forall ((M4 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M4))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M4)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))))))))
% 5.65/5.94 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Q2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.proper P) (=> (@ tptp.proper Q2) (@ tptp.proper (lambda ((H4 tptp.produc3658429121746597890et_nat)) (and (@ P H4) (@ Q2 H4))))))))
% 5.65/5.94 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Q2 (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.proper P) (=> (@ tptp.proper Q2) (@ tptp.proper (lambda ((H4 tptp.produc3658429121746597890et_nat)) (or (@ P H4) (@ Q2 H4))))))))
% 5.65/5.94 (assert (@ tptp.proper (lambda ((Uu tptp.produc3658429121746597890et_nat)) false)))
% 5.65/5.94 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ tptp.proper P) (@ tptp.proper (lambda ((H4 tptp.produc3658429121746597890et_nat)) (and (@ tptp.in_range H4) (not (@ P H4))))))))
% 5.65/5.94 (assert (= tptp.bot_bot_assn (@ tptp.abs_assn (lambda ((Uu tptp.produc3658429121746597890et_nat)) false))))
% 5.65/5.94 (assert (= tptp.sup_sup_assn (lambda ((P2 tptp.assn) (Q tptp.assn)) (@ tptp.abs_assn (lambda ((H4 tptp.produc3658429121746597890et_nat)) (or (@ (@ tptp.rep_assn P2) H4) (@ (@ tptp.rep_assn Q) H4)))))))
% 5.65/5.94 (assert (= tptp.inf_inf_assn (lambda ((P2 tptp.assn) (Q tptp.assn)) (@ tptp.abs_assn (lambda ((H4 tptp.produc3658429121746597890et_nat)) (and (@ (@ tptp.rep_assn P2) H4) (@ (@ tptp.rep_assn Q) H4)))))))
% 5.65/5.94 (assert (= tptp.times_times_nat (lambda ((A6 tptp.nat) (B6 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A6)) (@ tptp.semiri1314217659103216013at_int B6))))))
% 5.65/5.94 (assert (= tptp.divide_divide_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K5) N4)) M3))))))))
% 5.65/5.94 (assert (= tptp.uminus_uminus_assn (lambda ((P2 tptp.assn)) (@ tptp.abs_assn (lambda ((H4 tptp.produc3658429121746597890et_nat)) (and (@ tptp.in_range H4) (not (@ (@ tptp.rep_assn P2) H4))))))))
% 5.65/5.94 (assert (forall ((M tptp.set_nat)) (=> (@ tptp.finite_finite_nat M) (=> (not (= M tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M)) (= (@ tptp.gcd_Gcd_nat M) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat (lambda ((M3 tptp.nat)) (@ tptp.collect_nat (lambda ((D4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D4) M3))))) M)))))))))
% 5.65/5.94 (assert (forall ((M4 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M4))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M4)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))))))
% 5.65/5.94 (assert (forall ((M4 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M4))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M4)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))))))
% 5.65/5.94 (assert (forall ((M4 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M4))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M4)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))))))
% 5.65/5.94 (assert (forall ((M4 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M4))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M4)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))))))
% 5.65/5.94 (assert (forall ((M4 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M4))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M4)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))))))))
% 5.65/5.94 (assert (= (@ tptp.set_ord_atMost_nat tptp.zero_zero_nat) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (N2 tptp.nat) (R2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K5 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M4) K5)) (@ (@ tptp.binomial N2) (@ (@ tptp.minus_minus_nat R2) K5))))) (@ tptp.set_ord_atMost_nat R2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M4) N2)) R2))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat) (M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M4) (= (@ tptp.semiri1408675320244567234ct_nat M4) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N2)) M4)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A2) B)) N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K5 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N2) K5))) (@ (@ tptp.power_power_nat A2) K5))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N2) K5))))) (@ tptp.set_ord_atMost_nat N2)))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K5 tptp.nat)) (@ (@ tptp.power_power_nat (@ (@ tptp.binomial N2) K5)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) N2))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) (@ tptp.suc N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) M4))) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat))) (@ tptp.set_ord_atMost_nat M4)) (@ (@ tptp.power_power_nat _let_1) _let_2))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat I4) (@ (@ tptp.binomial N2) I4)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (D2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A2) (@ (@ tptp.times_times_nat I4) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A2)) (@ (@ tptp.times_times_nat N2) D2)))) _let_1)))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or1269000886237332187st_nat M4) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M4) (@ (@ tptp.minus_minus_nat M4) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.65/5.94 (assert (forall ((D2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D2))))) (= (exists ((X7 tptp.int)) (@ P X7)) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D2)) (@ P X2))))))))
% 5.65/5.94 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J3) I4)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int I4) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J3))))))
% 5.65/5.94 (assert (forall ((D3 tptp.int) (P (-> tptp.int Bool)) (P7 (-> tptp.int Bool)) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (exists ((Z6 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z6) (= (@ P X3) (@ P7 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D3))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P7 X3) (@ P7 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D3))))) (= (exists ((X7 tptp.int)) (@ P X7)) (or (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (@ P7 X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (exists ((Y3 tptp.int)) (and (@ (@ tptp.member_int Y3) B4) (@ P (@ (@ tptp.plus_plus_int Y3) X2))))))))))))))
% 5.65/5.94 (assert (forall ((D3 tptp.int) (P (-> tptp.int Bool)) (P7 (-> tptp.int Bool)) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (exists ((Z6 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z6) X3) (= (@ P X3) (@ P7 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D3))))) (=> (forall ((X3 tptp.int) (K tptp.int)) (= (@ P7 X3) (@ P7 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D3))))) (= (exists ((X7 tptp.int)) (@ P X7)) (or (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (@ P7 X2))) (exists ((X2 tptp.int)) (and (@ (@ tptp.member_int X2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (exists ((Y3 tptp.int)) (and (@ (@ tptp.member_int Y3) A) (@ P (@ (@ tptp.minus_minus_int Y3) X2))))))))))))))
% 5.65/5.94 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q6 tptp.nat) (R4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q6))) (let ((_let_2 (@ tptp.numeral_numeral_nat L2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R4)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R4) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R4)))))) __flatten_var_0))))
% 5.65/5.94 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q6 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q6))) (let ((_let_2 (@ tptp.numeral_numeral_int L2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R4)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R4) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R4)))))) __flatten_var_0))))
% 5.65/5.94 (assert (forall ((M4 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M4) N2) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X2 tptp.int)) X2)) (@ (@ tptp.set_or1266510415728281911st_int M4) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int N2) (@ (@ tptp.plus_plus_int N2) tptp.one_one_int))) (@ (@ tptp.times_times_int M4) (@ (@ tptp.minus_minus_int M4) tptp.one_one_int)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X2 tptp.nat)) X2)) (@ (@ tptp.set_or4665077453230672383an_nat M4) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M4) (@ (@ tptp.minus_minus_nat M4) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M4) (@ tptp.suc M4)) (@ (@ tptp.insert_nat M4) tptp.bot_bot_set_nat))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M4) tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M4))) (let ((_let_2 (@ _let_1 (@ tptp.suc N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat M4) N2))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat N2) (@ _let_1 N2)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (K3 tptp.num)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M4))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat K3)))) (let ((_let_3 (@ tptp.pred_numeral K3))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat M4) _let_3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.insert_nat _let_3) (@ _let_1 _let_3)))) (=> (not _let_4) (= _let_2 tptp.bot_bot_set_nat)))))))))
% 5.65/5.94 (assert (forall ((C tptp.nat) (Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X) Y))) (let ((_let_2 (@ (@ tptp.ord_less_nat X) Y))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat2 (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X) C)) (@ (@ tptp.minus_minus_nat Y) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat2 (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat2 (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) tptp.bot_bot_set_nat))))))))))
% 5.65/5.94 (assert (= tptp.unique4921790084139445826nteger (lambda ((L2 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q6 tptp.code_integer) (R4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q6))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L2))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R4)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R4) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R4)))))) __flatten_var_0))))
% 5.65/5.94 (assert (= tptp.nat_triangle (lambda ((N4 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N4) (@ tptp.suc N4))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 5.65/5.94 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.image_4470545334726330049nteger (lambda ((X2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger X2) L))) (@ (@ tptp.set_or8404916559141939852nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger U) L))) (@ (@ tptp.set_or8404916559141939852nteger L) U))))
% 5.65/5.94 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.set_or8404916559141939852nteger L) (@ (@ tptp.plus_p5714425477246183910nteger U) tptp.one_one_Code_integer)) (@ (@ tptp.set_or189985376899183464nteger L) U))))
% 5.65/5.94 (assert (forall ((L tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) L) tptp.zero_z3403309356797280102nteger)))
% 5.65/5.94 (assert (forall ((K3 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger K3) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 5.65/5.94 (assert (= tptp.code_integer_of_int (lambda ((K5 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int K5) _let_2))))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K5) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.code_integer_of_int (@ tptp.uminus_uminus_int K5)))) (@ (@ (@ tptp.if_Code_integer (= K5 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K5) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 5.65/5.94 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or8404916559141939852nteger L) U))))
% 5.65/5.94 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or189985376899183464nteger L) U))))
% 5.65/5.94 (assert (forall ((U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or8404916559141939852nteger tptp.zero_z3403309356797280102nteger) U))))
% 5.65/5.94 (assert (@ (@ (@ (@ tptp.bNF_re711492959462206631nt_int (lambda ((Y4 tptp.int) (Z4 tptp.int)) (= Y4 Z4))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y4 tptp.int) (Z4 tptp.int)) (= Y4 Z4))) (lambda ((Y4 tptp.int) (Z4 tptp.int)) (= Y4 Z4)))) tptp.times_times_int) tptp.times_times_int))
% 5.65/5.94 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y4 tptp.nat) (Z4 tptp.nat)) (= Y4 Z4))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y4 tptp.nat) (Z4 tptp.nat)) (= Y4 Z4))) (lambda ((Y4 tptp.nat) (Z4 tptp.nat)) (= Y4 Z4)))) tptp.times_times_nat) tptp.times_times_nat))
% 5.65/5.94 (assert (forall ((Xa tptp.int) (X tptp.int)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.times_times_int Xa) X)))))
% 5.65/5.94 (assert (= tptp.code_divmod_integer (lambda ((K5 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K5) L2))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K5 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K5)) (@ (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C8797469213163452608nteger tptp.produc6499014454317279255nteger) tptp.times_3573771949741848930nteger)) tptp.sgn_sgn_Code_integer) L2) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= (@ tptp.sgn_sgn_Code_integer K5) (@ tptp.sgn_sgn_Code_integer L2))) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R4 tptp.code_integer) (S7 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R4))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S7 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer L2)) S7)))))) _let_1))))))))))
% 5.65/5.94 (assert (@ (@ (@ (@ tptp.bNF_re7627151682743391978at_rat tptp.pcr_rat) (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat)) (lambda ((X2 tptp.product_prod_int_int) (Y3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y3))) (let ((_let_2 (@ tptp.product_snd_int_int X2))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y3)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1)))))) tptp.plus_plus_rat))
% 5.65/5.94 (assert (@ (@ (@ (@ tptp.bNF_re7627151682743391978at_rat tptp.pcr_rat) (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat)) (lambda ((X2 tptp.product_prod_int_int) (Y3 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_fst_int_int Y3))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X2)) (@ tptp.product_snd_int_int Y3))))) tptp.times_times_rat))
% 5.65/5.94 (assert (= tptp.code_int_of_integer (lambda ((K5 tptp.code_integer)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_le6747313008572928689nteger K5) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus_uminus_int (@ tptp.code_int_of_integer (@ tptp.uminus1351360451143612070nteger K5)))) (@ (@ (@ tptp.if_int (= K5 tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_int) (@ (@ tptp.produc1553301316500091796er_int (lambda ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.code_int_of_integer L2)))) (@ (@ (@ tptp.if_int (= J3 tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.code_divmod_integer K5) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))))
% 5.65/5.94 (assert (@ (@ (@ (@ tptp.bNF_re1494630372529172596at_o_o tptp.pcr_rat) (lambda ((Y4 Bool) (Z4 Bool)) (= Y4 Z4))) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_snd_int_int X2))))) tptp.positive))
% 5.65/5.94 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U3 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y3))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U3)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U3))))))) __flatten_var_0)))) tptp.times_times_int))
% 5.65/5.94 (assert (forall ((Xa tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.times_times_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U3 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y3))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U3)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U3))))))) __flatten_var_0))) Xa) X)))))
% 5.65/5.94 (assert (forall ((X tptp.code_integer) (Xa tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.times_3573771949741848930nteger X) Xa)) (@ (@ tptp.times_times_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa)))))
% 5.65/5.94 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ tptp.positive X) (=> (@ tptp.positive Y) (@ tptp.positive (@ (@ tptp.times_times_rat X) Y))))))
% 5.65/5.94 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.ord_less_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Y)) (@ (@ tptp.ord_le6747313008572928689nteger X) Y))))
% 5.65/5.94 (assert (@ (@ (@ tptp.type_d8366093980585677751er_int tptp.code_int_of_integer) tptp.code_integer_of_int) tptp.top_top_set_int))
% 5.65/5.94 (assert (= tptp.positive (lambda ((X2 tptp.rat)) (let ((_let_1 (@ tptp.rep_Rat X2))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.product_snd_int_int _let_1)))))))
% 5.65/5.94 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_nat (@ tptp.code_nat_of_integer X)) (@ tptp.code_nat_of_integer Y)) (@ (@ tptp.ord_le6747313008572928689nteger X) Y)))))))
% 5.65/5.94 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U3 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y3))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U3)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U3))))))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U3 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y3))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U3)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U3))))))) __flatten_var_0)))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc A2))) (=> (@ (@ tptp.ord_less_nat A2) B) (= (@ (@ tptp.ord_min_nat _let_1) B) _let_1)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc A2))) (=> (@ (@ tptp.ord_less_nat A2) B) (= (@ (@ tptp.ord_min_nat B) _let_1) _let_1)))))
% 5.65/5.94 (assert (= (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (N2 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M4))) (= (@ _let_1 (@ (@ tptp.ord_min_nat N2) Q4)) (@ (@ tptp.ord_min_nat (@ _let_1 N2)) (@ _let_1 Q4))))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (N2 tptp.nat) (Q4 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_min_nat M4) N2)) Q4) (@ (@ tptp.ord_min_nat (@ (@ tptp.times_times_nat M4) Q4)) (@ (@ tptp.times_times_nat N2) Q4)))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N2) tptp.bot_bot_set_nat) (= N2 tptp.zero_zero_nat))))
% 5.65/5.94 (assert (forall ((U tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) U) (= (@ (@ tptp.set_or8404916559141939852nteger tptp.zero_z3403309356797280102nteger) U) (@ (@ tptp.image_1215581382706833972nteger tptp.semiri4939895301339042750nteger) (@ tptp.set_ord_lessThan_nat (@ tptp.code_nat_of_integer U)))))))
% 5.65/5.94 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw X) Y))) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_gcd_nat X) Y)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int X))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int Y)))))))
% 5.65/5.94 (assert (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat) tptp.top_top_set_nat)) tptp.bot_bot_set_nat))
% 5.65/5.94 (assert (forall ((K3 tptp.nat) (M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K3))) (= (@ _let_1 (@ (@ tptp.gcd_gcd_nat M4) N2)) (@ (@ tptp.gcd_gcd_nat (@ _let_1 M4)) (@ _let_1 N2))))))
% 5.65/5.94 (assert (forall ((A tptp.set_nat)) (=> (forall ((A4 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A) (=> (@ (@ tptp.member_nat B2) A) (@ (@ tptp.member_nat (@ (@ tptp.gcd_gcd_nat A4) B2)) A)))) (=> (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.member_nat (@ tptp.gcd_Gcd_nat A)) A)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (not (= A2 tptp.zero_zero_nat)) (exists ((X3 tptp.nat) (Y2 tptp.nat)) (= (@ (@ tptp.times_times_nat A2) X3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y2)) (@ (@ tptp.gcd_gcd_nat A2) B)))))))
% 5.65/5.94 (assert (forall ((B tptp.nat) (A2 tptp.nat)) (exists ((X3 tptp.nat) (Y2 tptp.nat)) (let ((_let_1 (@ (@ tptp.gcd_gcd_nat A2) B))) (let ((_let_2 (@ tptp.times_times_nat A2))) (let ((_let_3 (@ _let_2 Y2))) (let ((_let_4 (@ tptp.times_times_nat B))) (let ((_let_5 (@ _let_4 X3))) (let ((_let_6 (@ _let_4 Y2))) (let ((_let_7 (@ _let_2 X3))) (or (and (@ (@ tptp.ord_less_eq_nat _let_6) _let_7) (= (@ (@ tptp.minus_minus_nat _let_7) _let_6) _let_1)) (and (@ (@ tptp.ord_less_eq_nat _let_3) _let_5) (= (@ (@ tptp.minus_minus_nat _let_5) _let_3) _let_1)))))))))))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (= (@ tptp.set_or1210151606488870762an_nat _let_1) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_or1210151606488870762an_nat K3)) (@ (@ tptp.insert_nat _let_1) tptp.bot_bot_set_nat))))))
% 5.65/5.94 (assert (@ (@ (@ (@ tptp.bNF_re5228765855967844073nt_int tptp.ratrel) (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel)) (lambda ((X2 tptp.product_prod_int_int) (Y3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y3))) (let ((_let_2 (@ tptp.product_snd_int_int X2))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y3)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1)))))) (lambda ((X2 tptp.product_prod_int_int) (Y3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y3))) (let ((_let_2 (@ tptp.product_snd_int_int X2))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y3)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1)))))))
% 5.65/5.94 (assert (@ (@ (@ (@ tptp.bNF_re8699439704749558557nt_o_o tptp.ratrel) (lambda ((Y4 Bool) (Z4 Bool)) (= Y4 Z4))) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_snd_int_int X2))))) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_snd_int_int X2))))))
% 5.65/5.94 (assert (= tptp.ratrel (lambda ((X2 tptp.product_prod_int_int) (Y3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X2))) (let ((_let_2 (@ tptp.product_snd_int_int Y3))) (and (not (= _let_1 tptp.zero_zero_int)) (not (= _let_2 tptp.zero_zero_int)) (= (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_2) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y3)) _let_1))))))))
% 5.65/5.94 (assert (forall ((X tptp.int) (Y tptp.int)) (exists ((U4 tptp.int) (V3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U4) X)) (@ (@ tptp.times_times_int V3) Y)) (@ (@ tptp.gcd_gcd_int X) Y)))))
% 5.65/5.94 (assert (forall ((K3 tptp.int) (M4 tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int K3))) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int K3)) (@ (@ tptp.gcd_gcd_int M4) N2)) (@ (@ tptp.gcd_gcd_int (@ _let_1 M4)) (@ _let_1 N2))))))
% 5.65/5.94 (assert (= tptp.ratrel (lambda ((X2 tptp.product_prod_int_int) (Y3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X2))) (let ((_let_2 (@ tptp.product_snd_int_int Y3))) (and (not (= _let_1 tptp.zero_zero_int)) (not (= _let_2 tptp.zero_zero_int)) (= (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_2) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y3)) _let_1))))))))
% 5.65/5.94 (assert (@ (@ (@ (@ tptp.bNF_re5228765855967844073nt_int tptp.ratrel) (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel)) (lambda ((X2 tptp.product_prod_int_int) (Y3 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_fst_int_int Y3))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X2)) (@ tptp.product_snd_int_int Y3))))) (lambda ((X2 tptp.product_prod_int_int) (Y3 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_fst_int_int Y3))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X2)) (@ tptp.product_snd_int_int Y3))))))
% 5.65/5.94 (assert (forall ((Xa tptp.product_prod_int_int) (X tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X))) (let ((_let_2 (@ tptp.product_snd_int_int Xa))) (=> (@ (@ tptp.ratrel Xa) Xa) (=> (@ (@ tptp.ratrel X) X) (= (@ (@ tptp.plus_plus_rat (@ tptp.abs_Rat Xa)) (@ tptp.abs_Rat X)) (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Xa)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1))))))))))
% 5.65/5.94 (assert (forall ((X tptp.product_prod_int_int)) (=> (@ (@ tptp.ratrel X) X) (= (@ tptp.positive (@ tptp.abs_Rat X)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) (@ tptp.product_snd_int_int X)))))))
% 5.65/5.94 (assert (forall ((Xa tptp.product_prod_int_int) (X tptp.product_prod_int_int)) (=> (@ (@ tptp.ratrel Xa) Xa) (=> (@ (@ tptp.ratrel X) X) (= (@ (@ tptp.times_times_rat (@ tptp.abs_Rat Xa)) (@ tptp.abs_Rat X)) (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Xa)) (@ tptp.product_fst_int_int X))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int Xa)) (@ tptp.product_snd_int_int X)))))))))
% 5.65/5.94 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or4266950643985792945nteger L) U))))
% 5.65/5.94 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.set_or8404916559141939852nteger (@ (@ tptp.plus_p5714425477246183910nteger L) tptp.one_one_Code_integer)) U) (@ (@ tptp.set_or4266950643985792945nteger L) U))))
% 5.65/5.94 (assert (= tptp.positive (@ (@ (@ tptp.map_fu898904425404107465nt_o_o tptp.rep_Rat) tptp.id_o) (lambda ((X2 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_snd_int_int X2)))))))
% 5.65/5.94 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or2715278749043346189nteger L) U))))
% 5.65/5.94 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.set_or189985376899183464nteger (@ (@ tptp.plus_p5714425477246183910nteger L) tptp.one_one_Code_integer)) U) (@ (@ tptp.set_or2715278749043346189nteger L) U))))
% 5.65/5.94 (assert (forall ((K3 tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K3)) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atLeast_nat K3)) (@ (@ tptp.insert_nat K3) tptp.bot_bot_set_nat)))))
% 5.65/5.94 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I4 tptp.nat)) (@ P (@ tptp.suc I4)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 5.65/5.94 (assert (forall ((P (-> tptp.nat Bool)) (K3 tptp.nat)) (= (@ (@ tptp.eventually_nat (lambda ((N4 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat N4) K3)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 5.65/5.94 (assert (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat))
% 5.65/5.94 (assert (forall ((C tptp.nat) (P (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) X3) (@ P X3))) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 5.65/5.94 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N7 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N4) (@ P N4)))))))
% 5.65/5.94 (assert (forall ((F2 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F2) tptp.at_top_nat) (forall ((N7 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N7)) F2)))))
% 5.65/5.94 (assert (@ (@ (@ tptp.filter3212408913953519116et_nat tptp.set_ord_atMost_nat) (@ tptp.finite3254316476582989077op_nat tptp.top_top_set_nat)) tptp.at_top_nat))
% 5.65/5.94 (assert (@ (@ (@ tptp.filter3212408913953519116et_nat tptp.set_ord_lessThan_nat) (@ tptp.finite3254316476582989077op_nat tptp.top_top_set_nat)) tptp.at_top_nat))
% 5.65/5.94 (assert (not (= tptp.at_top_nat tptp.bot_bot_filter_nat)))
% 5.65/5.94 (assert (not (@ (@ tptp.eventually_nat (lambda ((N4 tptp.nat)) false)) tptp.at_top_nat)))
% 5.65/5.94 (assert (= tptp.plus_plus_rat (@ (@ (@ tptp.map_fu4333342158222067775at_rat tptp.rep_Rat) (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat)) (lambda ((X2 tptp.product_prod_int_int) (Y3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y3))) (let ((_let_2 (@ tptp.product_snd_int_int X2))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y3)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1))))))))
% 5.65/5.94 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.eventu1038000079068216329at_nat P) (@ (@ tptp.prod_filter_nat_nat tptp.at_top_nat) tptp.at_top_nat)) (exists ((N7 tptp.nat)) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) M3) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N4) (@ P (@ (@ tptp.product_Pair_nat_nat N4) M3))))))))))
% 5.65/5.94 (assert (= tptp.times_times_rat (@ (@ (@ tptp.map_fu4333342158222067775at_rat tptp.rep_Rat) (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat)) (lambda ((X2 tptp.product_prod_int_int) (Y3 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_fst_int_int Y3))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X2)) (@ tptp.product_snd_int_int Y3)))))))
% 5.65/5.94 (assert (forall ((B tptp.int) (D2 tptp.int) (A2 tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D2 tptp.zero_zero_int)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.fract A2) B)) (@ (@ tptp.fract C) D2)) (@ (@ tptp.fract (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A2) D2)) (@ (@ tptp.times_times_int C) B))) (@ (@ tptp.times_times_int B) D2)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.fract A2) B)) (@ (@ tptp.fract C) D2)) (@ (@ tptp.fract (@ (@ tptp.times_times_int A2) D2)) (@ (@ tptp.times_times_int B) C)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.fract A2) B)) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A2)) (@ tptp.sgn_sgn_int B))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.fract A2) B)) (@ (@ tptp.fract C) D2)) (@ (@ tptp.fract (@ (@ tptp.times_times_int A2) C)) (@ (@ tptp.times_times_int B) D2)))))
% 5.65/5.94 (assert (forall ((B tptp.int) (D2 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D2))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D2 tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A2) B)) (@ (@ tptp.fract C) D2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A2) D2)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))))
% 5.65/5.94 (assert (forall ((B tptp.int) (D2 tptp.int) (A2 tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D2))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D2 tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A2) B)) (@ (@ tptp.fract C) D2)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A2) D2)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))))
% 5.65/5.94 (assert (forall ((B tptp.int) (D2 tptp.int) (A2 tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D2 tptp.zero_zero_int)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.fract A2) B)) (@ (@ tptp.fract C) D2)) (@ (@ tptp.fract (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A2) D2)) (@ (@ tptp.times_times_int C) B))) (@ (@ tptp.times_times_int B) D2)))))))
% 5.65/5.94 (assert (forall ((B tptp.int) (D2 tptp.int) (A2 tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D2 tptp.zero_zero_int)) (= (= (@ (@ tptp.fract A2) B) (@ (@ tptp.fract C) D2)) (= (@ (@ tptp.times_times_int A2) D2) (@ (@ tptp.times_times_int C) B)))))))
% 5.65/5.94 (assert (forall ((C tptp.int) (A2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.fract (@ _let_1 A2)) (@ _let_1 B)) (@ (@ tptp.fract A2) B))))))
% 5.65/5.94 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N2)))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (B tptp.int)) (= (@ tptp.positive (@ (@ tptp.fract A2) B)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A2) B)))))
% 5.65/5.94 (assert (= (@ tptp.nat_set_encode tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 5.65/5.94 (assert (forall ((Q4 tptp.int) (S2 tptp.int) (P3 tptp.int) (R2 tptp.int)) (=> (not (= Q4 tptp.zero_zero_int)) (=> (not (= S2 tptp.zero_zero_int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P3) Q4)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int R2) S2))) (= (@ (@ tptp.times_times_int P3) S2) (@ (@ tptp.times_times_int R2) Q4)))))))
% 5.65/5.94 (assert (forall ((P3 tptp.rat) (Q4 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.minus_minus_rat P3) Q4)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A6 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B6 tptp.int) (D4 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A6) D4)) (@ (@ tptp.times_times_int B6) C4))) (@ (@ tptp.times_times_int C4) D4))))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P3)))))
% 5.65/5.94 (assert (forall ((P3 tptp.rat) (Q4 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.plus_plus_rat P3) Q4)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A6 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B6 tptp.int) (D4 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A6) D4)) (@ (@ tptp.times_times_int B6) C4))) (@ (@ tptp.times_times_int C4) D4))))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P3)))))
% 5.65/5.94 (assert (forall ((P3 tptp.rat) (Q4 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.times_times_rat P3) Q4)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A6 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B6 tptp.int) (D4 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A6) B6)) (@ (@ tptp.times_times_int C4) D4))))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P3)))))
% 5.65/5.94 (assert (= tptp.ord_less_rat (lambda ((P5 tptp.rat) (Q6 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A6 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B6 tptp.int) (D4 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A6) D4)) (@ (@ tptp.times_times_int C4) B6)))) (@ tptp.quotient_of Q6)))) (@ tptp.quotient_of P5)))))
% 5.65/5.94 (assert (= tptp.ord_less_eq_rat (lambda ((P5 tptp.rat) (Q6 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A6 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B6 tptp.int) (D4 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A6) D4)) (@ (@ tptp.times_times_int C4) B6)))) (@ tptp.quotient_of Q6)))) (@ tptp.quotient_of P5)))))
% 5.65/5.94 (assert (forall ((P3 tptp.rat) (Q4 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.divide_divide_rat P3) Q4)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A6 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B6 tptp.int) (D4 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A6) D4)) (@ (@ tptp.times_times_int C4) B6))))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P3)))))
% 5.65/5.94 (assert (forall ((P3 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P3)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A6 tptp.int) (B6 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= A6 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A6)) B6)) (@ tptp.abs_abs_int A6))))) (@ tptp.quotient_of P3)))))
% 5.65/5.94 (assert (= tptp.divide_divide_rat (lambda ((Q6 tptp.rat) (R4 tptp.rat)) (@ (@ tptp.times_times_rat Q6) (@ tptp.inverse_inverse_rat R4)))))
% 5.65/5.94 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.neg_numeral_sub_int (@ tptp.bitM N2)) tptp.one) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.neg_numeral_sub_int N2) tptp.one)))))
% 5.65/5.94 (assert (= (@ tptp.nat_set_decode tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 5.65/5.94 (assert (= tptp.cofinite_nat tptp.at_top_nat))
% 5.65/5.94 (assert (forall ((P (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (@ P tptp.zero_zero_nat) (=> (forall ((I3 tptp.nat)) (=> (@ P I3) (exists ((J4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) J4) (@ P J4) (@ Q2 J4))))) (@ (@ tptp.frequently_nat Q2) tptp.cofinite_nat)))))
% 5.65/5.94 (assert (= tptp.gcd_lcm_int (lambda ((A6 tptp.int) (B6 tptp.int)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A6)) (@ tptp.abs_abs_int B6))) (@ (@ tptp.gcd_gcd_int A6) B6)))))
% 5.65/5.94 (assert (= tptp.times_times_num (lambda ((M3 tptp.num) (N4 tptp.num)) (@ tptp.num_of_nat (@ (@ tptp.times_times_nat (@ tptp.nat_of_num M3)) (@ tptp.nat_of_num N4))))))
% 5.65/5.94 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ tptp.nat_of_num (@ (@ tptp.times_times_num X) Y)) (@ (@ tptp.times_times_nat (@ tptp.nat_of_num X)) (@ tptp.nat_of_num Y)))))
% 5.65/5.94 (assert (forall ((M4 tptp.int) (N2 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int M4)) (@ tptp.abs_abs_int N2)) (@ (@ tptp.times_times_int (@ (@ tptp.gcd_gcd_int M4) N2)) (@ (@ tptp.gcd_lcm_int M4) N2)))))
% 5.65/5.94 (assert (= tptp.times_times_nat (lambda ((M3 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.gcd_gcd_nat M3) N4)) (@ (@ tptp.gcd_lcm_nat M3) N4)))))
% 5.65/5.94 (assert (= tptp.gcd_lcm_Code_integer (lambda ((A6 tptp.code_integer) (B6 tptp.code_integer)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A6)) (@ tptp.abs_abs_Code_integer B6))) (@ (@ tptp.gcd_gcd_Code_integer A6) B6)))))
% 5.65/5.94 (assert (= tptp.gcd_lcm_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat X2) Y3)) (@ (@ tptp.gcd_gcd_nat X2) Y3)))))
% 5.65/5.94 (assert (forall ((M tptp.set_nat)) (=> (@ tptp.finite_finite_nat M) (=> (not (= M tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M)) (=> (forall ((M2 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.member_nat M2) M) (=> (@ (@ tptp.member_nat N3) M) (@ (@ tptp.member_nat (@ (@ tptp.gcd_lcm_nat M2) N3)) M)))) (= (@ tptp.gcd_Lcm_nat M) (@ tptp.lattic8265883725875713057ax_nat M))))))))
% 5.65/5.94 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.nat_of_num X))) (= (@ tptp.nat_of_num (@ tptp.sqr X)) (@ (@ tptp.times_times_nat _let_1) _let_1)))))
% 5.65/5.94 (assert (= (@ tptp.gcd_Lcm_nat tptp.bot_bot_set_nat) tptp.one_one_nat))
% 5.65/5.94 (assert (= tptp.sqr (lambda ((X2 tptp.num)) (@ (@ tptp.times_times_num X2) X2))))
% 5.65/5.94 (assert (forall ((M tptp.set_nat)) (=> (@ tptp.finite_finite_nat M) (=> (not (= M tptp.bot_bot_set_nat)) (=> (forall ((M2 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.member_nat M2) M) (=> (@ (@ tptp.member_nat N3) M) (@ (@ tptp.member_nat (@ (@ tptp.gcd_lcm_nat M2) N3)) M)))) (@ (@ tptp.member_nat (@ tptp.gcd_Lcm_nat M)) M))))))
% 5.65/5.94 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X))) (= (@ _let_1 (@ tptp.bit1 Y)) (@ (@ tptp.times_times_num (@ tptp.sqr (@ _let_1 Y))) X)))))
% 5.65/5.94 (assert (forall ((A2 tptp.nat) (D2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.algebr934650988132801477me_nat A2) D2) (=> (@ (@ tptp.algebr934650988132801477me_nat B) C) (= (= (@ (@ tptp.times_times_nat A2) C) (@ (@ tptp.times_times_nat B) D2)) (and (= A2 B) (= C D2)))))))
% 5.65/5.94 (assert (forall ((A2 tptp.int) (D2 tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int D2))) (let ((_let_2 (@ tptp.abs_abs_int C))) (let ((_let_3 (@ tptp.abs_abs_int B))) (let ((_let_4 (@ tptp.abs_abs_int A2))) (=> (@ (@ tptp.algebr932160517623751201me_int A2) D2) (=> (@ (@ tptp.algebr932160517623751201me_int B) C) (= (= (@ (@ tptp.times_times_int _let_4) _let_2) (@ (@ tptp.times_times_int _let_3) _let_1)) (and (= _let_4 _let_3) (= _let_2 _let_1)))))))))))
% 5.65/5.94 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (@ tptp.in_range X)) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H) As2)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) As2) (@ (@ tptp.ord_less_nat X3) (@ tptp.lim_Product_unit H))))))))))
% 5.65/5.94 (assert (forall ((H2 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (= (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H2) As)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) As) (@ (@ tptp.ord_less_nat X2) (@ tptp.lim_Product_unit H2)))))))
% 5.65/5.94 (assert (forall ((X tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ tptp.in_range X) Y) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H) As2)) (= Y (not (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) As2) (@ (@ tptp.ord_less_nat X2) (@ tptp.lim_Product_unit H))))))))))))
% 5.65/5.94 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (@ tptp.in_range X) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H) As2)) (not (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) As2) (@ (@ tptp.ord_less_nat X6) (@ tptp.lim_Product_unit H)))))))))))
% 5.65/5.94 (assert (= tptp.top_top_set_o (@ (@ tptp.insert_o false) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o))))
% 5.65/5.94 (assert (forall ((Y Bool) (P (-> Bool Bool))) (=> (@ (@ tptp.member_o Y) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)) (=> (forall ((X3 tptp.product_unit)) (@ P (@ tptp.product_Rep_unit X3))) (@ P Y)))))
% 5.65/5.94 (assert (forall ((X Bool) (Y Bool)) (let ((_let_1 (@ (@ tptp.insert_o true) tptp.bot_bot_set_o))) (=> (@ (@ tptp.member_o X) _let_1) (=> (@ (@ tptp.member_o Y) _let_1) (= (= (@ tptp.product_Abs_unit X) (@ tptp.product_Abs_unit Y)) (= X Y)))))))
% 5.65/5.94 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (= (@ tptp.product_Rep_unit X) (@ tptp.product_Rep_unit Y)) (= X Y))))
% 5.65/5.94 (assert (forall ((X tptp.product_unit)) (= (@ tptp.product_Abs_unit (@ tptp.product_Rep_unit X)) X)))
% 5.65/5.94 (assert (forall ((Y Bool)) (=> (@ (@ tptp.member_o Y) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)) (= (@ tptp.product_Rep_unit (@ tptp.product_Abs_unit Y)) Y))))
% 5.65/5.94 (assert (@ (@ (@ tptp.type_d6188575255521822967unit_o tptp.product_Rep_unit) tptp.product_Abs_unit) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)))
% 5.65/5.94 (assert (forall ((X tptp.product_unit)) (@ (@ tptp.member_o (@ tptp.product_Rep_unit X)) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o))))
% 5.65/5.94 (assert (forall ((X tptp.product_unit)) (not (forall ((Y2 Bool)) (=> (= X (@ tptp.product_Abs_unit Y2)) (not (@ (@ tptp.member_o Y2) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o))))))))
% 5.65/5.94 (assert (forall ((Y Bool)) (=> (@ (@ tptp.member_o Y) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)) (not (forall ((X3 tptp.product_unit)) (= Y (not (@ tptp.product_Rep_unit X3))))))))
% 5.65/5.94 (assert (forall ((P (-> tptp.product_unit Bool)) (X tptp.product_unit)) (=> (forall ((Y2 Bool)) (=> (@ (@ tptp.member_o Y2) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)) (@ P (@ tptp.product_Abs_unit Y2)))) (@ P X))))
% 5.65/5.94 (assert (forall ((B0 Bool) (B1 Bool) (B22 Bool) (B32 Bool) (B42 Bool) (B52 Bool) (B62 Bool) (B72 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ tptp.integer_of_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 B0) B1) B22) B32) B42) B52) B62) B72)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger B72)) _let_1)) (@ tptp.zero_n356916108424825756nteger B62))) _let_1)) (@ tptp.zero_n356916108424825756nteger B52))) _let_1)) (@ tptp.zero_n356916108424825756nteger B42))) _let_1)) (@ tptp.zero_n356916108424825756nteger B32))) _let_1)) (@ tptp.zero_n356916108424825756nteger B22))) _let_1)) (@ tptp.zero_n356916108424825756nteger B1))) _let_1)) (@ tptp.zero_n356916108424825756nteger B0))))))
% 5.65/5.94 (assert (= tptp.nat_sum_encode (@ (@ tptp.sum_ca6763686470577984908at_nat (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (lambda ((B6 tptp.nat)) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B6))))))
% 5.65/5.94 (assert (forall ((J tptp.nat)) (= (= (@ (@ tptp.upt tptp.zero_zero_nat) J) tptp.nil_nat) (= J tptp.zero_zero_nat))))
% 5.65/5.94 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat J) K3)) (= (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.upt J) K3)) (@ _let_1 K3))))))
% 5.65/5.94 (assert (forall ((Ofs tptp.nat) (A2 tptp.nat) (B tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) Ofs))) (@ (@ tptp.upt A2) B)) (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat A2) Ofs)) (@ (@ tptp.plus_plus_nat B) Ofs)))))
% 5.65/5.94 (assert (forall ((I2 tptp.nat) (J tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (= (@ (@ tptp.upt I2) J) (@ (@ tptp.append_nat Xs) Ys)) (exists ((K5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I2) K5) (@ (@ tptp.ord_less_eq_nat K5) J) (= (@ (@ tptp.upt I2) K5) Xs) (= (@ (@ tptp.upt K5) J) Ys)))))))
% 5.65/5.94 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat I2) J) (= (@ (@ tptp.append_nat (@ _let_1 I2)) (@ (@ tptp.upt I2) J)) (@ _let_1 J))))))
% 5.65/5.94 (assert (forall ((M4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.upt M4))) (= (@ tptp.butlast_nat (@ _let_1 N2)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 5.65/5.94 (assert (forall ((L tptp.nat) (H2 tptp.nat) (Is1 tptp.list_nat) (I2 tptp.nat) (Is2 tptp.list_nat)) (let ((_let_1 (@ tptp.upt L))) (= (= (@ _let_1 H2) (@ (@ tptp.append_nat Is1) (@ (@ tptp.cons_nat I2) Is2))) (and (= Is1 (@ _let_1 I2)) (= Is2 (@ (@ tptp.upt (@ tptp.suc I2)) H2)) (@ (@ tptp.ord_less_eq_nat L) I2) (@ (@ tptp.ord_less_nat I2) H2))))))
% 5.65/5.94 (assert (forall ((U tptp.nat) (U5 tptp.nat) (P (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.upt tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.filter_nat2 P))) (=> (@ (@ tptp.ord_less_eq_nat U) U5) (=> (forall ((I3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat U) I3) (@ (@ tptp.ord_less_nat I3) U5)) (not (@ P I3)))) (= (@ _let_2 (@ _let_1 U)) (@ _let_2 (@ _let_1 U5)))))))))
% 5.65/5.94 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (@ tptp.in_range X)) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) X) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) _let_1) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) As2) (@ (@ tptp.ord_less_nat X3) (@ tptp.lim_Product_unit H)))))))))))))
% 5.65/5.94 (assert (forall ((X tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ tptp.in_range X) Y) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) X) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As2))) (=> (= X _let_1) (=> (= Y (forall ((X2 tptp.nat)) (=> (@ (@ tptp.member_nat X2) As2) (@ (@ tptp.ord_less_nat X2) (@ tptp.lim_Product_unit H))))) (not (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) _let_1)))))))))))
% 5.65/5.94 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (@ tptp.in_range X) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) X) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) _let_1) (not (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) As2) (@ (@ tptp.ord_less_nat X6) (@ tptp.lim_Product_unit H))))))))))))))
% 5.65/5.94 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (@ tptp.one_assn_raw X)) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) X) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) _let_1) (= As2 tptp.bot_bot_set_nat))))))))))
% 5.65/5.94 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (@ tptp.one_assn_raw X) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) X) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) _let_1) (not (= As2 tptp.bot_bot_set_nat)))))))))))
% 5.65/5.94 (assert (forall ((X tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ tptp.one_assn_raw X) Y) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) X) (not (forall ((H tptp.heap_e7401611519738050253t_unit) (As2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As2))) (=> (= X _let_1) (=> (= Y (= As2 tptp.bot_bot_set_nat)) (not (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) _let_1)))))))))))
% 5.65/5.94 (assert (= tptp.times_times_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X2 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U3 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y3))) (let ((_let_2 (@ tptp.times_times_nat X2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U3)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U3))))))) __flatten_var_0))))))
% 5.65/5.94 (assert (forall ((V tptp.code_natural) (W tptp.code_natural)) (let ((_let_1 (@ tptp.bit1 tptp.one))) (let ((_let_2 (@ tptp.bit1 _let_1))) (let ((_let_3 (@ tptp.bit0 _let_1))) (let ((_let_4 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_3)))))))))))))))) (let ((_let_5 (@ tptp.bit0 tptp.one))) (let ((_let_6 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_5)))))) (let ((_let_7 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_2)))))))))))))))))))))) (let ((_let_8 (@ (@ (@ tptp.minus_shift (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 _let_7)))))))))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural W) _let_4)) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 _let_6))))))))))))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural W) _let_4)) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_2)))))))))))))) (let ((_let_9 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 _let_3)))))))))))))))) (let ((_let_10 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 _let_7))))))))) (let ((_let_11 (@ (@ (@ tptp.minus_shift (@ tptp.numera5444537566228673987atural (@ tptp.bit1 _let_10))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural V) _let_9)) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 _let_6))))))))))))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural V) _let_9)) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_5))))))))))))))))) (= (@ tptp.next (@ (@ tptp.produc3574140220909816553atural V) W)) (@ (@ tptp.produc6639722614265839536atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ (@ tptp.minus_shift (@ tptp.numera5444537566228673987atural (@ tptp.bit0 _let_10))) _let_11) (@ (@ tptp.plus_p4538020629002901425atural _let_8) tptp.one_one_Code_natural))) tptp.one_one_Code_natural)) (@ (@ tptp.produc3574140220909816553atural _let_11) _let_8))))))))))))))))
% 5.65/5.94 (assert (= tptp.range (lambda ((K5 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ (@ tptp.produc5538323210962509403atural (@ (@ (@ tptp.iterat8892046348760725948atural (@ (@ tptp.log (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one)))))))))))))))))))))))))))))))) K5)) (lambda ((L2 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ (@ tptp.produc5538323210962509403atural tptp.next) (lambda ((V4 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc6639722614265839536atural (@ (@ tptp.plus_p4538020629002901425atural V4) (@ (@ tptp.times_2397367101498566445atural L2) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one)))))))))))))))))))))))))))))))))) __flatten_var_0))) __flatten_var_0))) tptp.one_one_Code_natural)) (lambda ((V4 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc6639722614265839536atural (@ (@ tptp.modulo8411746178871703098atural V4) K5)) __flatten_var_0))) __flatten_var_0))))
% 5.65/5.94 (assert (= tptp.bot_bot_Product_unit tptp.product_Unity))
% 5.65/5.94 (assert (= tptp.sup_sup_Product_unit (lambda ((Uu2 tptp.product_unit) (Uv tptp.product_unit)) tptp.product_Unity)))
% 5.65/5.94 (assert (forall ((Y tptp.product_unit)) (= Y tptp.product_Unity)))
% 5.65/5.94 (assert (= tptp.comple2584293577114468500t_unit (lambda ((Uu2 tptp.set_Product_unit)) tptp.product_Unity)))
% 5.65/5.94 (assert (= tptp.uminus2952777764628376836t_unit (lambda ((Uu2 tptp.product_unit)) tptp.product_Unity)))
% 5.65/5.94 (assert (= tptp.top_top_Product_unit tptp.product_Unity))
% 5.65/5.94 (assert (= tptp.product_Unity (@ tptp.product_Abs_unit true)))
% 5.65/5.94 (assert (= tptp.comple4687483117567863418t_unit (lambda ((Uu2 tptp.set_Product_unit)) tptp.product_Unity)))
% 5.65/5.94 (assert (= tptp.inf_inf_Product_unit (lambda ((Uu2 tptp.product_unit) (Uv tptp.product_unit)) tptp.product_Unity)))
% 5.65/5.94 (assert (= tptp.top_to1996260823553986621t_unit (@ (@ tptp.insert_Product_unit tptp.product_Unity) tptp.bot_bo3957492148770167129t_unit)))
% 5.65/5.94 (assert (= tptp.defaul566961228789861419t_unit tptp.product_Unity))
% 5.65/5.94 (assert (= tptp.bNF_Cardinal_cone (@ tptp.bNF_Ca7083678892733797993t_unit (@ (@ tptp.insert_Product_unit tptp.product_Unity) tptp.bot_bo3957492148770167129t_unit))))
% 5.65/5.94 (assert (forall ((M4 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.code_Pos M4)) (@ tptp.code_Pos N2)) (@ tptp.code_Pos (@ (@ tptp.times_times_num M4) N2)))))
% 5.65/5.94 (assert (forall ((M4 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.code_Neg M4)) (@ tptp.code_Neg N2)) (@ tptp.code_Pos (@ (@ tptp.times_times_num M4) N2)))))
% 5.65/5.94 (assert (forall ((M4 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.code_Neg M4)) (@ tptp.code_Pos N2)) (@ tptp.code_Neg (@ (@ tptp.times_times_num M4) N2)))))
% 5.65/5.94 (assert (forall ((M4 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.code_Pos M4)) (@ tptp.code_Neg N2)) (@ tptp.code_Neg (@ (@ tptp.times_times_num M4) N2)))))
% 5.65/5.94 (assert (forall ((X tptp.code_natural) (Xa tptp.code_natural)) (= (@ tptp.code_nat_of_natural (@ (@ tptp.times_2397367101498566445atural X) Xa)) (@ (@ tptp.times_times_nat (@ tptp.code_nat_of_natural X)) (@ tptp.code_nat_of_natural Xa)))))
% 5.65/5.94 (assert (forall ((M4 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.pos M4)) (@ tptp.pos N2)) (@ tptp.pos (@ (@ tptp.times_times_num M4) N2)))))
% 5.65/5.94 (assert (forall ((M4 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.pos M4)) (@ tptp.neg N2)) (@ tptp.neg (@ (@ tptp.times_times_num M4) N2)))))
% 5.65/5.94 (assert (forall ((M4 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.neg M4)) (@ tptp.pos N2)) (@ tptp.neg (@ (@ tptp.times_times_num M4) N2)))))
% 5.65/5.94 (assert (forall ((M4 tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.neg M4)) (@ tptp.neg N2)) (@ tptp.pos (@ (@ tptp.times_times_num M4) N2)))))
% 5.65/5.94 (assert (@ (@ (@ (@ tptp.bNF_re88643428490162567atural tptp.code_pcr_natural) (@ (@ tptp.bNF_re3704215830270325841atural tptp.code_pcr_natural) tptp.code_pcr_natural)) tptp.times_times_nat) tptp.times_2397367101498566445atural))
% 5.65/5.94 (assert (forall ((Xa tptp.nat) (X tptp.nat)) (= (@ (@ tptp.times_2397367101498566445atural (@ tptp.code_natural_of_nat Xa)) (@ tptp.code_natural_of_nat X)) (@ tptp.code_natural_of_nat (@ (@ tptp.times_times_nat Xa) X)))))
% 5.65/5.94 (assert (@ (@ (@ tptp.type_d4410041424927559462al_nat tptp.code_nat_of_natural) tptp.code_natural_of_nat) tptp.top_top_set_nat))
% 5.65/5.94 (assert (= tptp.times_2397367101498566445atural (@ (@ (@ tptp.map_fu6549440983881763648atural tptp.code_nat_of_natural) (@ (@ tptp.map_fu1239815594074539274atural tptp.code_nat_of_natural) tptp.code_natural_of_nat)) tptp.times_times_nat)))
% 5.65/5.94 (assert (@ (@ (@ (@ tptp.bNF_re398004352372739002nteger tptp.code_pcr_integer) (@ (@ tptp.bNF_re3379532845092657523nteger tptp.code_pcr_integer) tptp.code_pcr_integer)) tptp.times_times_int) tptp.times_3573771949741848930nteger))
% 5.65/5.94 (assert (= tptp.times_3573771949741848930nteger (@ (@ (@ tptp.map_fu8272188784021352819nteger tptp.code_int_of_integer) (@ (@ tptp.map_fu2599414010547811884nteger tptp.code_int_of_integer) tptp.code_integer_of_int)) tptp.times_times_int)))
% 5.65/5.94 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X) Y) Y)))
% 5.65/5.94 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X) Y) X)))
% 5.65/5.94 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y) Y)))
% 5.65/5.94 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y) X)))
% 5.65/5.94 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X) Y) Y)))
% 5.65/5.94 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X) Y) X)))
% 5.65/5.94 (assert (forall ((X t/export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 28705 Alarm clock ( read result; case "$result" in
% 300.03/300.37 unsat)
% 300.03/300.37 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 300.03/300.37 ;;
% 300.03/300.37 sat)
% 300.03/300.37 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 300.03/300.37 ;;
% 300.03/300.37 esac; exit 1 )
% 300.03/300.37 Alarm clock
% 300.03/300.37 % cvc5---1.0.5 exiting
% 300.03/300.38 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------