TSTP Solution File: ITP036^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP036^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:17:40 EDT 2023
% Result : Theorem 0.77s 0.98s
% Output : Proof 0.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.16/0.18 % Problem : ITP036^1 : TPTP v8.1.2. Released v7.5.0.
% 0.16/0.19 % Command : do_cvc5 %s %d
% 0.18/0.39 % Computer : n010.cluster.edu
% 0.18/0.39 % Model : x86_64 x86_64
% 0.18/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39 % Memory : 8042.1875MB
% 0.18/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39 % CPULimit : 300
% 0.18/0.39 % WCLimit : 300
% 0.18/0.39 % DateTime : Sun Aug 27 12:08:49 EDT 2023
% 0.18/0.39 % CPUTime :
% 0.25/0.57 %----Proving TH0
% 0.25/0.58 %------------------------------------------------------------------------------
% 0.25/0.58 % File : ITP036^1 : TPTP v8.1.2. Released v7.5.0.
% 0.25/0.58 % Domain : Interactive Theorem Proving
% 0.25/0.58 % Problem : Sledgehammer Coincidence problem prob_1096__7244526_1
% 0.25/0.58 % Version : Especial.
% 0.25/0.58 % English :
% 0.25/0.58
% 0.25/0.58 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.25/0.58 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.25/0.58 % Source : [Des21]
% 0.25/0.58 % Names : Coincidence/prob_1096__7244526_1 [Des21]
% 0.25/0.58
% 0.25/0.58 % Status : Theorem
% 0.25/0.58 % Rating : 0.15 v8.1.0, 0.18 v7.5.0
% 0.25/0.58 % Syntax : Number of formulae : 468 ( 195 unt; 113 typ; 0 def)
% 0.25/0.58 % Number of atoms : 826 ( 271 equ; 0 cnn)
% 0.25/0.58 % Maximal formula atoms : 7 ( 2 avg)
% 0.25/0.58 % Number of connectives : 2724 ( 36 ~; 7 |; 43 &;2295 @)
% 0.25/0.58 % ( 0 <=>; 343 =>; 0 <=; 0 <~>)
% 0.25/0.58 % Maximal formula depth : 18 ( 6 avg)
% 0.25/0.58 % Number of types : 22 ( 21 usr)
% 0.25/0.58 % Number of type conns : 214 ( 214 >; 0 *; 0 +; 0 <<)
% 0.25/0.58 % Number of symbols : 93 ( 92 usr; 12 con; 0-3 aty)
% 0.25/0.58 % Number of variables : 997 ( 101 ^; 881 !; 15 ?; 997 :)
% 0.25/0.58 % SPC : TH0_THM_EQU_NAR
% 0.25/0.58
% 0.25/0.58 % Comments : This file was generated by Sledgehammer 2021-02-23 15:47:10.370
% 0.25/0.58 %------------------------------------------------------------------------------
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% 0.25/0.58 produc350724343real_c: produc640052711real_c > produc640052711real_c ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 0.25/0.58 collec1126017874real_c: ( produc640052711real_c > $o ) > set_Pr754230471real_c ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_OCollect_001t__Sum____Type__Osum_Itf__a_Mt__Sum____Type__Osum_Itf__b_Mtf__c_J_J,type,
% 0.25/0.58 collec2086029184um_b_c: ( sum_su737395349um_b_c > $o ) > set_Su1783761653um_b_c ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_OCollect_001t__Sum____Type__Osum_Itf__c_Mtf__c_J,type,
% 0.25/0.58 collect_Sum_sum_c_c: ( sum_sum_c_c > $o ) > set_Sum_sum_c_c ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Static__Semantics_OFVP_001tf__a_001tf__b_001tf__c,type,
% 0.25/0.58 static_FVP_a_b_c: hp_a_b_c > set_Sum_sum_c_c ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Static__Semantics_OMBV_001tf__a_001tf__b_001tf__c,type,
% 0.25/0.58 static_MBV_a_b_c: hp_a_b_c > set_Sum_sum_c_c ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Static__Semantics_OSIGP_001tf__a_001tf__b_001tf__c,type,
% 0.25/0.58 static_SIGP_a_b_c: hp_a_b_c > set_Su1783761653um_b_c ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Syntax_Ohp_OChoice_001tf__a_001tf__b_001tf__c,type,
% 0.25/0.58 choice_a_b_c: hp_a_b_c > hp_a_b_c > hp_a_b_c ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Syntax_Ohpsafe_001tf__a_001tf__b_001tf__c,type,
% 0.25/0.58 hpsafe_a_b_c: hp_a_b_c > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Wfrec_Osame__fst_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_001t__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J,type,
% 0.25/0.58 same_f1974156740real_c: ( finite1398487019real_c > $o ) > ( finite1398487019real_c > set_Pr1389752855real_c ) > set_Pr754230471real_c ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Wfrec_Osame__fst_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 0.25/0.58 same_f598810924real_c: ( produc190496183real_c > $o ) > ( produc190496183real_c > set_Pr754230471real_c ) > set_Pr242060487real_c ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_member_001t__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J,type,
% 0.25/0.58 member1895684704real_c: produc190496183real_c > set_Pr1389752855real_c > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J,type,
% 0.25/0.58 member346808080real_c: produc640052711real_c > set_Pr754230471real_c > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_Mt__Product____Type__Oprod_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_Mt__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__c_J_J_J_J,type,
% 0.25/0.58 member616151824real_c: produc1037099239real_c > set_Pr242060487real_c > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_member_001t__Sum____Type__Osum_Itf__a_Mt__Sum____Type__Osum_Itf__b_Mtf__c_J_J,type,
% 0.25/0.58 member1893232190um_b_c: sum_su737395349um_b_c > set_Su1783761653um_b_c > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_member_001t__Sum____Type__Osum_Itf__c_Mtf__c_J,type,
% 0.25/0.58 member_Sum_sum_c_c: sum_sum_c_c > set_Sum_sum_c_c > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_I____,type,
% 0.25/0.58 i: denota231621370t_unit ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_J____,type,
% 0.25/0.58 j: denota231621370t_unit ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_V____,type,
% 0.25/0.58 v: set_Sum_sum_c_c ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v__092_060mu_062_H_H____,type,
% 0.25/0.58 mu: produc190496183real_c ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v__092_060mu_062_H____,type,
% 0.25/0.58 mu2: finite1398487019real_c ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v__092_060mu_062____,type,
% 0.25/0.58 mu3: finite1398487019real_c ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v__092_060nu_0621_H____,type,
% 0.25/0.58 nu_1: finite1398487019real_c ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v__092_060nu_0621____,type,
% 0.25/0.58 nu_12: finite1398487019real_c ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v__092_060nu_0622_H____,type,
% 0.25/0.58 nu_2: finite1398487019real_c ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v__092_060nu_0622____,type,
% 0.25/0.58 nu_22: finite1398487019real_c ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_a____,type,
% 0.25/0.58 a: hp_a_b_c ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_b____,type,
% 0.25/0.58 b: hp_a_b_c ).
% 0.25/0.58
% 0.25/0.58 % Relevant facts (354)
% 0.25/0.58 thf(fact_0_hpsafe__Choice_OIH_I2_J,axiom,
% 0.25/0.58 coinci1852866155_a_b_c @ b ).
% 0.25/0.58
% 0.25/0.58 % hpsafe_Choice.IH(2)
% 0.25/0.58 thf(fact_1_hpsafe__Choice_OIH_I1_J,axiom,
% 0.25/0.58 coinci1852866155_a_b_c @ a ).
% 0.25/0.58
% 0.25/0.58 % hpsafe_Choice.IH(1)
% 0.25/0.58 thf(fact_2_prog__sem_H,axiom,
% 0.25/0.58 member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ mu ) @ ( denota904684656_a_b_c @ j @ ( choice_a_b_c @ a @ b ) ) ).
% 0.25/0.58
% 0.25/0.58 % prog_sem'
% 0.25/0.58 thf(fact_3_agree_H,axiom,
% 0.25/0.58 denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ mu @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ ( choice_a_b_c @ a @ b ) ) @ v ) ).
% 0.25/0.58
% 0.25/0.58 % agree'
% 0.25/0.58 thf(fact_4_prog__sem,axiom,
% 0.25/0.58 member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ mu ) @ ( denota904684656_a_b_c @ j @ b ) ).
% 0.25/0.58
% 0.25/0.58 % prog_sem
% 0.25/0.58 thf(fact_5_safe_I2_J,axiom,
% 0.25/0.58 hpsafe_a_b_c @ b ).
% 0.25/0.58
% 0.25/0.58 % safe(2)
% 0.25/0.58 thf(fact_6_safe_I1_J,axiom,
% 0.25/0.58 hpsafe_a_b_c @ a ).
% 0.25/0.58
% 0.25/0.58 % safe(1)
% 0.25/0.58 thf(fact_7_agree,axiom,
% 0.25/0.58 denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ mu @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ b ) @ v ) ).
% 0.25/0.58
% 0.25/0.58 % agree
% 0.25/0.58 thf(fact_8__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062_092_060mu_062_H_H_O_A_092_060lbrakk_062_I_I_092_060nu_0622_M_A_092_060nu_0622_H_J_M_A_092_060mu_062_H_H_J_A_092_060in_062_Aprog__sem_AJ_Ab_059_AVagree_A_I_092_060mu_062_M_A_092_060mu_062_H_J_A_092_060mu_062_H_H_A_IMBV_Ab_A_092_060union_062_AV_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.25/0.58 ~ ! [Mu: produc190496183real_c] :
% 0.25/0.58 ( ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ Mu ) @ ( denota904684656_a_b_c @ j @ b ) )
% 0.25/0.58 => ~ ( denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ Mu @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ b ) @ v ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % \<open>\<And>thesis. (\<And>\<mu>''. \<lbrakk>((\<nu>2, \<nu>2'), \<mu>'') \<in> prog_sem J b; Vagree (\<mu>, \<mu>') \<mu>'' (MBV b \<union> V)\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.25/0.58 thf(fact_9_VA,axiom,
% 0.25/0.58 denota1997846518gree_c @ ( produc394644079real_c @ nu_12 @ nu_1 ) @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ v ).
% 0.25/0.58
% 0.25/0.58 % VA
% 0.25/0.58 thf(fact_10_sup__Pair__Pair,axiom,
% 0.25/0.58 ! [A: finite1398487019real_c,B: finite1398487019real_c,C: finite1398487019real_c,D: finite1398487019real_c] :
% 0.25/0.58 ( ( sup_su1639086475real_c @ ( produc394644079real_c @ A @ B ) @ ( produc394644079real_c @ C @ D ) )
% 0.25/0.58 = ( produc394644079real_c @ ( sup_su2141622551real_c @ A @ C ) @ ( sup_su2141622551real_c @ B @ D ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup_Pair_Pair
% 0.25/0.58 thf(fact_11_sup__Pair__Pair,axiom,
% 0.25/0.58 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c,D: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( sup_su1672617323um_c_c @ ( produc1439061071um_c_c @ A @ B ) @ ( produc1439061071um_c_c @ C @ D ) )
% 0.25/0.58 = ( produc1439061071um_c_c @ ( sup_su1349021703um_c_c @ A @ C ) @ ( sup_su1349021703um_c_c @ B @ D ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup_Pair_Pair
% 0.25/0.58 thf(fact_12_sup__Pair__Pair,axiom,
% 0.25/0.58 ! [A: produc190496183real_c,B: produc190496183real_c,C: produc190496183real_c,D: produc190496183real_c] :
% 0.25/0.58 ( ( sup_su1399591867real_c @ ( produc1687028567real_c @ A @ B ) @ ( produc1687028567real_c @ C @ D ) )
% 0.25/0.58 = ( produc1687028567real_c @ ( sup_su1639086475real_c @ A @ C ) @ ( sup_su1639086475real_c @ B @ D ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup_Pair_Pair
% 0.25/0.58 thf(fact_13_sup__Pair__Pair,axiom,
% 0.25/0.58 ! [A: set_Sum_sum_c_c,B: set_Su1783761653um_b_c,C: set_Sum_sum_c_c,D: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( sup_su421398139um_b_c @ ( produc919784577um_b_c @ A @ B ) @ ( produc919784577um_b_c @ C @ D ) )
% 0.25/0.58 = ( produc919784577um_b_c @ ( sup_su1349021703um_c_c @ A @ C ) @ ( sup_su1968964297um_b_c @ B @ D ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup_Pair_Pair
% 0.25/0.58 thf(fact_14_sup__Pair__Pair,axiom,
% 0.25/0.58 ! [A: set_Su1783761653um_b_c,B: set_Sum_sum_c_c,C: set_Su1783761653um_b_c,D: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( sup_su1731217579um_c_c @ ( produc616453753um_c_c @ A @ B ) @ ( produc616453753um_c_c @ C @ D ) )
% 0.25/0.58 = ( produc616453753um_c_c @ ( sup_su1968964297um_b_c @ A @ C ) @ ( sup_su1349021703um_c_c @ B @ D ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup_Pair_Pair
% 0.25/0.58 thf(fact_15_sup__Pair__Pair,axiom,
% 0.25/0.58 ! [A: set_Sum_sum_c_c,B: produc190496183real_c,C: set_Sum_sum_c_c,D: produc190496183real_c] :
% 0.25/0.58 ( ( sup_su2023888701real_c @ ( produc439851843real_c @ A @ B ) @ ( produc439851843real_c @ C @ D ) )
% 0.25/0.58 = ( produc439851843real_c @ ( sup_su1349021703um_c_c @ A @ C ) @ ( sup_su1639086475real_c @ B @ D ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup_Pair_Pair
% 0.25/0.58 thf(fact_16_sup__Pair__Pair,axiom,
% 0.25/0.58 ! [A: produc190496183real_c,B: set_Sum_sum_c_c,C: produc190496183real_c,D: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( sup_su1347303021um_c_c @ ( produc639456571um_c_c @ A @ B ) @ ( produc639456571um_c_c @ C @ D ) )
% 0.25/0.58 = ( produc639456571um_c_c @ ( sup_su1639086475real_c @ A @ C ) @ ( sup_su1349021703um_c_c @ B @ D ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup_Pair_Pair
% 0.25/0.58 thf(fact_17_sup__Pair__Pair,axiom,
% 0.25/0.58 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c,D: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( sup_su1580927803um_b_c @ ( produc754249687um_b_c @ A @ B ) @ ( produc754249687um_b_c @ C @ D ) )
% 0.25/0.58 = ( produc754249687um_b_c @ ( sup_su1968964297um_b_c @ A @ C ) @ ( sup_su1968964297um_b_c @ B @ D ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup_Pair_Pair
% 0.25/0.58 thf(fact_18_sup__Pair__Pair,axiom,
% 0.25/0.58 ! [A: set_Sum_sum_c_c,B: produc214722967um_c_c,C: set_Sum_sum_c_c,D: produc214722967um_c_c] :
% 0.25/0.58 ( ( sup_su505296157um_c_c @ ( produc1333497635um_c_c @ A @ B ) @ ( produc1333497635um_c_c @ C @ D ) )
% 0.25/0.58 = ( produc1333497635um_c_c @ ( sup_su1349021703um_c_c @ A @ C ) @ ( sup_su1672617323um_c_c @ B @ D ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup_Pair_Pair
% 0.25/0.58 thf(fact_19_sup__Pair__Pair,axiom,
% 0.25/0.58 ! [A: produc190496183real_c,B: set_Su1783761653um_b_c,C: produc190496183real_c,D: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( sup_su1009753337um_b_c @ ( produc2010919061um_b_c @ A @ B ) @ ( produc2010919061um_b_c @ C @ D ) )
% 0.25/0.58 = ( produc2010919061um_b_c @ ( sup_su1639086475real_c @ A @ C ) @ ( sup_su1968964297um_b_c @ B @ D ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup_Pair_Pair
% 0.25/0.58 thf(fact_20_sem,axiom,
% 0.25/0.58 member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_12 @ nu_1 ) @ ( produc394644079real_c @ mu3 @ mu2 ) ) @ ( denota904684656_a_b_c @ i @ ( choice_a_b_c @ a @ b ) ) ).
% 0.25/0.58
% 0.25/0.58 % sem
% 0.25/0.58 thf(fact_21_sub,axiom,
% 0.25/0.58 ord_le1772180283um_c_c @ ( static_FVP_a_b_c @ ( choice_a_b_c @ a @ b ) ) @ v ).
% 0.25/0.58
% 0.25/0.58 % sub
% 0.25/0.58 thf(fact_22_False,axiom,
% 0.25/0.58 ~ ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_12 @ nu_1 ) @ ( produc394644079real_c @ mu3 @ mu2 ) ) @ ( denota904684656_a_b_c @ i @ a ) ) ).
% 0.25/0.58
% 0.25/0.58 % False
% 0.25/0.58 thf(fact_23_hp_Oinject_I6_J,axiom,
% 0.25/0.58 ! [X61: hp_a_b_c,X62: hp_a_b_c,Y61: hp_a_b_c,Y62: hp_a_b_c] :
% 0.25/0.58 ( ( ( choice_a_b_c @ X61 @ X62 )
% 0.25/0.58 = ( choice_a_b_c @ Y61 @ Y62 ) )
% 0.25/0.58 = ( ( X61 = Y61 )
% 0.25/0.58 & ( X62 = Y62 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % hp.inject(6)
% 0.25/0.58 thf(fact_24_UnCI,axiom,
% 0.25/0.58 ! [C: produc190496183real_c,B2: set_Pr1389752855real_c,A2: set_Pr1389752855real_c] :
% 0.25/0.58 ( ( ~ ( member1895684704real_c @ C @ B2 )
% 0.25/0.58 => ( member1895684704real_c @ C @ A2 ) )
% 0.25/0.58 => ( member1895684704real_c @ C @ ( sup_su1857314283real_c @ A2 @ B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % UnCI
% 0.25/0.58 thf(fact_25_UnCI,axiom,
% 0.25/0.58 ! [C: produc1037099239real_c,B2: set_Pr242060487real_c,A2: set_Pr242060487real_c] :
% 0.25/0.58 ( ( ~ ( member616151824real_c @ C @ B2 )
% 0.25/0.58 => ( member616151824real_c @ C @ A2 ) )
% 0.25/0.58 => ( member616151824real_c @ C @ ( sup_su880588443real_c @ A2 @ B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % UnCI
% 0.25/0.58 thf(fact_26_UnCI,axiom,
% 0.25/0.58 ! [C: sum_su737395349um_b_c,B2: set_Su1783761653um_b_c,A2: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( ~ ( member1893232190um_b_c @ C @ B2 )
% 0.25/0.58 => ( member1893232190um_b_c @ C @ A2 ) )
% 0.25/0.58 => ( member1893232190um_b_c @ C @ ( sup_su1968964297um_b_c @ A2 @ B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % UnCI
% 0.25/0.58 thf(fact_27_UnCI,axiom,
% 0.25/0.58 ! [C: produc640052711real_c,B2: set_Pr754230471real_c,A2: set_Pr754230471real_c] :
% 0.25/0.58 ( ( ~ ( member346808080real_c @ C @ B2 )
% 0.25/0.58 => ( member346808080real_c @ C @ A2 ) )
% 0.25/0.58 => ( member346808080real_c @ C @ ( sup_su588839579real_c @ A2 @ B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % UnCI
% 0.25/0.58 thf(fact_28_UnCI,axiom,
% 0.25/0.58 ! [C: sum_sum_c_c,B2: set_Sum_sum_c_c,A2: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( ~ ( member_Sum_sum_c_c @ C @ B2 )
% 0.25/0.58 => ( member_Sum_sum_c_c @ C @ A2 ) )
% 0.25/0.58 => ( member_Sum_sum_c_c @ C @ ( sup_su1349021703um_c_c @ A2 @ B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % UnCI
% 0.25/0.58 thf(fact_29_Un__iff,axiom,
% 0.25/0.58 ! [C: produc190496183real_c,A2: set_Pr1389752855real_c,B2: set_Pr1389752855real_c] :
% 0.25/0.58 ( ( member1895684704real_c @ C @ ( sup_su1857314283real_c @ A2 @ B2 ) )
% 0.25/0.58 = ( ( member1895684704real_c @ C @ A2 )
% 0.25/0.58 | ( member1895684704real_c @ C @ B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Un_iff
% 0.25/0.58 thf(fact_30_Un__iff,axiom,
% 0.25/0.58 ! [C: produc1037099239real_c,A2: set_Pr242060487real_c,B2: set_Pr242060487real_c] :
% 0.25/0.58 ( ( member616151824real_c @ C @ ( sup_su880588443real_c @ A2 @ B2 ) )
% 0.25/0.58 = ( ( member616151824real_c @ C @ A2 )
% 0.25/0.58 | ( member616151824real_c @ C @ B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Un_iff
% 0.25/0.58 thf(fact_31_Un__iff,axiom,
% 0.25/0.58 ! [C: sum_su737395349um_b_c,A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( member1893232190um_b_c @ C @ ( sup_su1968964297um_b_c @ A2 @ B2 ) )
% 0.25/0.58 = ( ( member1893232190um_b_c @ C @ A2 )
% 0.25/0.58 | ( member1893232190um_b_c @ C @ B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Un_iff
% 0.25/0.58 thf(fact_32_Un__iff,axiom,
% 0.25/0.58 ! [C: produc640052711real_c,A2: set_Pr754230471real_c,B2: set_Pr754230471real_c] :
% 0.25/0.58 ( ( member346808080real_c @ C @ ( sup_su588839579real_c @ A2 @ B2 ) )
% 0.25/0.58 = ( ( member346808080real_c @ C @ A2 )
% 0.25/0.58 | ( member346808080real_c @ C @ B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Un_iff
% 0.25/0.58 thf(fact_33_Un__iff,axiom,
% 0.25/0.58 ! [C: sum_sum_c_c,A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( member_Sum_sum_c_c @ C @ ( sup_su1349021703um_c_c @ A2 @ B2 ) )
% 0.25/0.58 = ( ( member_Sum_sum_c_c @ C @ A2 )
% 0.25/0.58 | ( member_Sum_sum_c_c @ C @ B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Un_iff
% 0.25/0.58 thf(fact_34_sup_Oidem,axiom,
% 0.25/0.58 ! [A: produc190496183real_c] :
% 0.25/0.58 ( ( sup_su1639086475real_c @ A @ A )
% 0.25/0.58 = A ) ).
% 0.25/0.58
% 0.25/0.58 % sup.idem
% 0.25/0.58 thf(fact_35_sup_Oidem,axiom,
% 0.25/0.58 ! [A: produc640052711real_c] :
% 0.25/0.58 ( ( sup_su1399591867real_c @ A @ A )
% 0.25/0.58 = A ) ).
% 0.25/0.58
% 0.25/0.58 % sup.idem
% 0.25/0.58 thf(fact_36_sup_Oidem,axiom,
% 0.25/0.58 ! [A: produc214722967um_c_c] :
% 0.25/0.58 ( ( sup_su1672617323um_c_c @ A @ A )
% 0.25/0.58 = A ) ).
% 0.25/0.58
% 0.25/0.58 % sup.idem
% 0.25/0.58 thf(fact_37_sup_Oidem,axiom,
% 0.25/0.58 ! [A: set_Pr754230471real_c] :
% 0.25/0.58 ( ( sup_su588839579real_c @ A @ A )
% 0.25/0.58 = A ) ).
% 0.25/0.58
% 0.25/0.58 % sup.idem
% 0.25/0.58 thf(fact_38_sup_Oidem,axiom,
% 0.25/0.58 ! [A: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( sup_su1968964297um_b_c @ A @ A )
% 0.25/0.58 = A ) ).
% 0.25/0.58
% 0.25/0.58 % sup.idem
% 0.25/0.58 thf(fact_39_sup_Oidem,axiom,
% 0.25/0.58 ! [A: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( sup_su1349021703um_c_c @ A @ A )
% 0.25/0.58 = A ) ).
% 0.25/0.58
% 0.25/0.58 % sup.idem
% 0.25/0.58 thf(fact_40_sup__idem,axiom,
% 0.25/0.58 ! [X: produc190496183real_c] :
% 0.25/0.58 ( ( sup_su1639086475real_c @ X @ X )
% 0.25/0.58 = X ) ).
% 0.25/0.58
% 0.25/0.58 % sup_idem
% 0.25/0.58 thf(fact_41_sup__idem,axiom,
% 0.25/0.58 ! [X: produc640052711real_c] :
% 0.25/0.58 ( ( sup_su1399591867real_c @ X @ X )
% 0.25/0.58 = X ) ).
% 0.25/0.58
% 0.25/0.58 % sup_idem
% 0.25/0.58 thf(fact_42_sup__idem,axiom,
% 0.25/0.58 ! [X: produc214722967um_c_c] :
% 0.25/0.58 ( ( sup_su1672617323um_c_c @ X @ X )
% 0.25/0.58 = X ) ).
% 0.25/0.58
% 0.25/0.58 % sup_idem
% 0.25/0.58 thf(fact_43_sup__idem,axiom,
% 0.25/0.58 ! [X: set_Pr754230471real_c] :
% 0.25/0.58 ( ( sup_su588839579real_c @ X @ X )
% 0.25/0.58 = X ) ).
% 0.25/0.58
% 0.25/0.58 % sup_idem
% 0.25/0.58 thf(fact_44_sup__idem,axiom,
% 0.25/0.58 ! [X: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( sup_su1968964297um_b_c @ X @ X )
% 0.25/0.58 = X ) ).
% 0.25/0.58
% 0.25/0.58 % sup_idem
% 0.25/0.58 thf(fact_45_sup__idem,axiom,
% 0.25/0.58 ! [X: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( sup_su1349021703um_c_c @ X @ X )
% 0.25/0.58 = X ) ).
% 0.25/0.58
% 0.25/0.58 % sup_idem
% 0.25/0.58 thf(fact_46_sup_Oleft__idem,axiom,
% 0.25/0.58 ! [A: produc190496183real_c,B: produc190496183real_c] :
% 0.25/0.58 ( ( sup_su1639086475real_c @ A @ ( sup_su1639086475real_c @ A @ B ) )
% 0.25/0.58 = ( sup_su1639086475real_c @ A @ B ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.left_idem
% 0.25/0.58 thf(fact_47_sup_Oleft__idem,axiom,
% 0.25/0.58 ! [A: produc640052711real_c,B: produc640052711real_c] :
% 0.25/0.58 ( ( sup_su1399591867real_c @ A @ ( sup_su1399591867real_c @ A @ B ) )
% 0.25/0.58 = ( sup_su1399591867real_c @ A @ B ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.left_idem
% 0.25/0.58 thf(fact_48_sup_Oleft__idem,axiom,
% 0.25/0.58 ! [A: produc214722967um_c_c,B: produc214722967um_c_c] :
% 0.25/0.58 ( ( sup_su1672617323um_c_c @ A @ ( sup_su1672617323um_c_c @ A @ B ) )
% 0.25/0.58 = ( sup_su1672617323um_c_c @ A @ B ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.left_idem
% 0.25/0.58 thf(fact_49_sup_Oleft__idem,axiom,
% 0.25/0.58 ! [A: set_Pr754230471real_c,B: set_Pr754230471real_c] :
% 0.25/0.58 ( ( sup_su588839579real_c @ A @ ( sup_su588839579real_c @ A @ B ) )
% 0.25/0.58 = ( sup_su588839579real_c @ A @ B ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.left_idem
% 0.25/0.58 thf(fact_50_sup_Oleft__idem,axiom,
% 0.25/0.58 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( sup_su1968964297um_b_c @ A @ ( sup_su1968964297um_b_c @ A @ B ) )
% 0.25/0.58 = ( sup_su1968964297um_b_c @ A @ B ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.left_idem
% 0.25/0.58 thf(fact_51_sup_Oleft__idem,axiom,
% 0.25/0.58 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( sup_su1349021703um_c_c @ A @ ( sup_su1349021703um_c_c @ A @ B ) )
% 0.25/0.58 = ( sup_su1349021703um_c_c @ A @ B ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.left_idem
% 0.25/0.58 thf(fact_52_subsetI,axiom,
% 0.25/0.58 ! [A2: set_Pr1389752855real_c,B2: set_Pr1389752855real_c] :
% 0.25/0.58 ( ! [X2: produc190496183real_c] :
% 0.25/0.58 ( ( member1895684704real_c @ X2 @ A2 )
% 0.25/0.58 => ( member1895684704real_c @ X2 @ B2 ) )
% 0.25/0.58 => ( ord_le977353143real_c @ A2 @ B2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % subsetI
% 0.25/0.58 thf(fact_53_subsetI,axiom,
% 0.25/0.58 ! [A2: set_Pr242060487real_c,B2: set_Pr242060487real_c] :
% 0.25/0.58 ( ! [X2: produc1037099239real_c] :
% 0.25/0.58 ( ( member616151824real_c @ X2 @ A2 )
% 0.25/0.58 => ( member616151824real_c @ X2 @ B2 ) )
% 0.25/0.58 => ( ord_le100418663real_c @ A2 @ B2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % subsetI
% 0.25/0.58 thf(fact_54_subsetI,axiom,
% 0.25/0.58 ! [A2: set_Pr754230471real_c,B2: set_Pr754230471real_c] :
% 0.25/0.58 ( ! [X2: produc640052711real_c] :
% 0.25/0.58 ( ( member346808080real_c @ X2 @ A2 )
% 0.25/0.58 => ( member346808080real_c @ X2 @ B2 ) )
% 0.25/0.58 => ( ord_le1988344935real_c @ A2 @ B2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % subsetI
% 0.25/0.58 thf(fact_55_subsetI,axiom,
% 0.25/0.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.25/0.58 ( ! [X2: sum_sum_c_c] :
% 0.25/0.58 ( ( member_Sum_sum_c_c @ X2 @ A2 )
% 0.25/0.58 => ( member_Sum_sum_c_c @ X2 @ B2 ) )
% 0.25/0.58 => ( ord_le1772180283um_c_c @ A2 @ B2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % subsetI
% 0.25/0.58 thf(fact_56_subsetI,axiom,
% 0.25/0.58 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ! [X2: sum_su737395349um_b_c] :
% 0.25/0.58 ( ( member1893232190um_b_c @ X2 @ A2 )
% 0.25/0.58 => ( member1893232190um_b_c @ X2 @ B2 ) )
% 0.25/0.58 => ( ord_le929608341um_b_c @ A2 @ B2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % subsetI
% 0.25/0.58 thf(fact_57_subset__antisym,axiom,
% 0.25/0.58 ! [A2: set_Pr754230471real_c,B2: set_Pr754230471real_c] :
% 0.25/0.58 ( ( ord_le1988344935real_c @ A2 @ B2 )
% 0.25/0.58 => ( ( ord_le1988344935real_c @ B2 @ A2 )
% 0.25/0.58 => ( A2 = B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % subset_antisym
% 0.25/0.58 thf(fact_58_subset__antisym,axiom,
% 0.25/0.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( ord_le1772180283um_c_c @ A2 @ B2 )
% 0.25/0.58 => ( ( ord_le1772180283um_c_c @ B2 @ A2 )
% 0.25/0.58 => ( A2 = B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % subset_antisym
% 0.25/0.58 thf(fact_59_subset__antisym,axiom,
% 0.25/0.58 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( ord_le929608341um_b_c @ A2 @ B2 )
% 0.25/0.58 => ( ( ord_le929608341um_b_c @ B2 @ A2 )
% 0.25/0.58 => ( A2 = B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % subset_antisym
% 0.25/0.58 thf(fact_60_sup_Oright__idem,axiom,
% 0.25/0.58 ! [A: produc190496183real_c,B: produc190496183real_c] :
% 0.25/0.58 ( ( sup_su1639086475real_c @ ( sup_su1639086475real_c @ A @ B ) @ B )
% 0.25/0.58 = ( sup_su1639086475real_c @ A @ B ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.right_idem
% 0.25/0.58 thf(fact_61_sup_Oright__idem,axiom,
% 0.25/0.58 ! [A: produc640052711real_c,B: produc640052711real_c] :
% 0.25/0.58 ( ( sup_su1399591867real_c @ ( sup_su1399591867real_c @ A @ B ) @ B )
% 0.25/0.58 = ( sup_su1399591867real_c @ A @ B ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.right_idem
% 0.25/0.58 thf(fact_62_sup_Oright__idem,axiom,
% 0.25/0.58 ! [A: produc214722967um_c_c,B: produc214722967um_c_c] :
% 0.25/0.58 ( ( sup_su1672617323um_c_c @ ( sup_su1672617323um_c_c @ A @ B ) @ B )
% 0.25/0.58 = ( sup_su1672617323um_c_c @ A @ B ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.right_idem
% 0.25/0.58 thf(fact_63_sup_Oright__idem,axiom,
% 0.25/0.58 ! [A: set_Pr754230471real_c,B: set_Pr754230471real_c] :
% 0.25/0.58 ( ( sup_su588839579real_c @ ( sup_su588839579real_c @ A @ B ) @ B )
% 0.25/0.58 = ( sup_su588839579real_c @ A @ B ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.right_idem
% 0.25/0.58 thf(fact_64_sup_Oright__idem,axiom,
% 0.25/0.58 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( sup_su1968964297um_b_c @ ( sup_su1968964297um_b_c @ A @ B ) @ B )
% 0.25/0.58 = ( sup_su1968964297um_b_c @ A @ B ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.right_idem
% 0.25/0.58 thf(fact_65_sup_Oright__idem,axiom,
% 0.25/0.58 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( sup_su1349021703um_c_c @ ( sup_su1349021703um_c_c @ A @ B ) @ B )
% 0.25/0.58 = ( sup_su1349021703um_c_c @ A @ B ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.right_idem
% 0.25/0.58 thf(fact_66_sup__left__idem,axiom,
% 0.25/0.58 ! [X: produc190496183real_c,Y: produc190496183real_c] :
% 0.25/0.58 ( ( sup_su1639086475real_c @ X @ ( sup_su1639086475real_c @ X @ Y ) )
% 0.25/0.58 = ( sup_su1639086475real_c @ X @ Y ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup_left_idem
% 0.25/0.58 thf(fact_67_sup__left__idem,axiom,
% 0.25/0.58 ! [X: produc640052711real_c,Y: produc640052711real_c] :
% 0.25/0.58 ( ( sup_su1399591867real_c @ X @ ( sup_su1399591867real_c @ X @ Y ) )
% 0.25/0.58 = ( sup_su1399591867real_c @ X @ Y ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup_left_idem
% 0.25/0.58 thf(fact_68_sup__left__idem,axiom,
% 0.25/0.58 ! [X: produc214722967um_c_c,Y: produc214722967um_c_c] :
% 0.25/0.58 ( ( sup_su1672617323um_c_c @ X @ ( sup_su1672617323um_c_c @ X @ Y ) )
% 0.25/0.58 = ( sup_su1672617323um_c_c @ X @ Y ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup_left_idem
% 0.25/0.58 thf(fact_69_sup__left__idem,axiom,
% 0.25/0.58 ! [X: set_Pr754230471real_c,Y: set_Pr754230471real_c] :
% 0.25/0.58 ( ( sup_su588839579real_c @ X @ ( sup_su588839579real_c @ X @ Y ) )
% 0.25/0.58 = ( sup_su588839579real_c @ X @ Y ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup_left_idem
% 0.25/0.58 thf(fact_70_sup__left__idem,axiom,
% 0.25/0.58 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( sup_su1968964297um_b_c @ X @ ( sup_su1968964297um_b_c @ X @ Y ) )
% 0.25/0.58 = ( sup_su1968964297um_b_c @ X @ Y ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup_left_idem
% 0.25/0.58 thf(fact_71_sup__left__idem,axiom,
% 0.25/0.58 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( sup_su1349021703um_c_c @ X @ ( sup_su1349021703um_c_c @ X @ Y ) )
% 0.25/0.58 = ( sup_su1349021703um_c_c @ X @ Y ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup_left_idem
% 0.25/0.58 thf(fact_72_sub2,axiom,
% 0.25/0.58 ord_le1772180283um_c_c @ ( static_FVP_a_b_c @ b ) @ v ).
% 0.25/0.58
% 0.25/0.58 % sub2
% 0.25/0.58 thf(fact_73_sub1,axiom,
% 0.25/0.58 ord_le1772180283um_c_c @ ( static_FVP_a_b_c @ a ) @ v ).
% 0.25/0.58
% 0.25/0.58 % sub1
% 0.25/0.58 thf(fact_74_Pair__le,axiom,
% 0.25/0.58 ! [A: produc190496183real_c,B: produc190496183real_c,C: produc190496183real_c,D: produc190496183real_c] :
% 0.25/0.58 ( ( ord_le652477831real_c @ ( produc1687028567real_c @ A @ B ) @ ( produc1687028567real_c @ C @ D ) )
% 0.25/0.58 = ( ( ord_le850691415real_c @ A @ C )
% 0.25/0.58 & ( ord_le850691415real_c @ B @ D ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Pair_le
% 0.25/0.58 thf(fact_75_Pair__le,axiom,
% 0.25/0.58 ! [A: finite1398487019real_c,B: finite1398487019real_c,C: finite1398487019real_c,D: finite1398487019real_c] :
% 0.25/0.58 ( ( ord_le850691415real_c @ ( produc394644079real_c @ A @ B ) @ ( produc394644079real_c @ C @ D ) )
% 0.25/0.58 = ( ( ord_le775706699real_c @ A @ C )
% 0.25/0.58 & ( ord_le775706699real_c @ B @ D ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Pair_le
% 0.25/0.58 thf(fact_76_Pair__le,axiom,
% 0.25/0.58 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c,D: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( ord_le684454199um_c_c @ ( produc1439061071um_c_c @ A @ B ) @ ( produc1439061071um_c_c @ C @ D ) )
% 0.25/0.58 = ( ( ord_le1772180283um_c_c @ A @ C )
% 0.25/0.58 & ( ord_le1772180283um_c_c @ B @ D ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Pair_le
% 0.25/0.58 thf(fact_77_Pair__le,axiom,
% 0.25/0.58 ! [A: set_Sum_sum_c_c,B: set_Su1783761653um_b_c,C: set_Sum_sum_c_c,D: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( ord_le542695343um_b_c @ ( produc919784577um_b_c @ A @ B ) @ ( produc919784577um_b_c @ C @ D ) )
% 0.25/0.58 = ( ( ord_le1772180283um_c_c @ A @ C )
% 0.25/0.58 & ( ord_le929608341um_b_c @ B @ D ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Pair_le
% 0.25/0.58 thf(fact_78_Pair__le,axiom,
% 0.25/0.58 ! [A: set_Su1783761653um_b_c,B: set_Sum_sum_c_c,C: set_Su1783761653um_b_c,D: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( ord_le1852514783um_c_c @ ( produc616453753um_c_c @ A @ B ) @ ( produc616453753um_c_c @ C @ D ) )
% 0.25/0.58 = ( ( ord_le929608341um_b_c @ A @ C )
% 0.25/0.58 & ( ord_le1772180283um_c_c @ B @ D ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Pair_le
% 0.25/0.58 thf(fact_79_Pair__le,axiom,
% 0.25/0.58 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c,D: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( ord_le907560199um_b_c @ ( produc754249687um_b_c @ A @ B ) @ ( produc754249687um_b_c @ C @ D ) )
% 0.25/0.58 = ( ( ord_le929608341um_b_c @ A @ C )
% 0.25/0.58 & ( ord_le929608341um_b_c @ B @ D ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Pair_le
% 0.25/0.58 thf(fact_80_sup_Obounded__iff,axiom,
% 0.25/0.58 ! [B: set_Sum_sum_c_c,C: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ B @ C ) @ A )
% 0.25/0.58 = ( ( ord_le1772180283um_c_c @ B @ A )
% 0.25/0.58 & ( ord_le1772180283um_c_c @ C @ A ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.bounded_iff
% 0.25/0.58 thf(fact_81_sup_Obounded__iff,axiom,
% 0.25/0.58 ! [B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ B @ C ) @ A )
% 0.25/0.58 = ( ( ord_le929608341um_b_c @ B @ A )
% 0.25/0.58 & ( ord_le929608341um_b_c @ C @ A ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.bounded_iff
% 0.25/0.58 thf(fact_82_le__sup__iff,axiom,
% 0.25/0.58 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c,Z: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ X @ Y ) @ Z )
% 0.25/0.58 = ( ( ord_le1772180283um_c_c @ X @ Z )
% 0.25/0.58 & ( ord_le1772180283um_c_c @ Y @ Z ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % le_sup_iff
% 0.25/0.58 thf(fact_83_le__sup__iff,axiom,
% 0.25/0.58 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c,Z: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ X @ Y ) @ Z )
% 0.25/0.58 = ( ( ord_le929608341um_b_c @ X @ Z )
% 0.25/0.58 & ( ord_le929608341um_b_c @ Y @ Z ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % le_sup_iff
% 0.25/0.58 thf(fact_84_Un__subset__iff,axiom,
% 0.25/0.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,C2: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ A2 @ B2 ) @ C2 )
% 0.25/0.58 = ( ( ord_le1772180283um_c_c @ A2 @ C2 )
% 0.25/0.58 & ( ord_le1772180283um_c_c @ B2 @ C2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Un_subset_iff
% 0.25/0.58 thf(fact_85_Un__subset__iff,axiom,
% 0.25/0.58 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c,C2: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ A2 @ B2 ) @ C2 )
% 0.25/0.58 = ( ( ord_le929608341um_b_c @ A2 @ C2 )
% 0.25/0.58 & ( ord_le929608341um_b_c @ B2 @ C2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Un_subset_iff
% 0.25/0.58 thf(fact_86_hpsafe__Choice__simps,axiom,
% 0.25/0.58 ! [A: hp_a_b_c,B: hp_a_b_c] :
% 0.25/0.58 ( ( hpsafe_a_b_c @ ( choice_a_b_c @ A @ B ) )
% 0.25/0.58 = ( ( hpsafe_a_b_c @ A )
% 0.25/0.58 & ( hpsafe_a_b_c @ B ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % hpsafe_Choice_simps
% 0.25/0.58 thf(fact_87_sem2,axiom,
% 0.25/0.58 member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_12 @ nu_1 ) @ ( produc394644079real_c @ mu3 @ mu2 ) ) @ ( denota904684656_a_b_c @ i @ b ) ).
% 0.25/0.58
% 0.25/0.58 % sem2
% 0.25/0.58 thf(fact_88_eitherSem,axiom,
% 0.25/0.58 ( ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_12 @ nu_1 ) @ ( produc394644079real_c @ mu3 @ mu2 ) ) @ ( denota904684656_a_b_c @ i @ a ) )
% 0.25/0.58 | ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_12 @ nu_1 ) @ ( produc394644079real_c @ mu3 @ mu2 ) ) @ ( denota904684656_a_b_c @ i @ b ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % eitherSem
% 0.25/0.58 thf(fact_89_in__mono,axiom,
% 0.25/0.58 ! [A2: set_Pr754230471real_c,B2: set_Pr754230471real_c,X: produc640052711real_c] :
% 0.25/0.58 ( ( ord_le1988344935real_c @ A2 @ B2 )
% 0.25/0.58 => ( ( member346808080real_c @ X @ A2 )
% 0.25/0.58 => ( member346808080real_c @ X @ B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % in_mono
% 0.25/0.58 thf(fact_90_in__mono,axiom,
% 0.25/0.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,X: sum_sum_c_c] :
% 0.25/0.58 ( ( ord_le1772180283um_c_c @ A2 @ B2 )
% 0.25/0.58 => ( ( member_Sum_sum_c_c @ X @ A2 )
% 0.25/0.58 => ( member_Sum_sum_c_c @ X @ B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % in_mono
% 0.25/0.58 thf(fact_91_in__mono,axiom,
% 0.25/0.58 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c,X: sum_su737395349um_b_c] :
% 0.25/0.58 ( ( ord_le929608341um_b_c @ A2 @ B2 )
% 0.25/0.58 => ( ( member1893232190um_b_c @ X @ A2 )
% 0.25/0.58 => ( member1893232190um_b_c @ X @ B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % in_mono
% 0.25/0.58 thf(fact_92_subsetD,axiom,
% 0.25/0.58 ! [A2: set_Pr754230471real_c,B2: set_Pr754230471real_c,C: produc640052711real_c] :
% 0.25/0.58 ( ( ord_le1988344935real_c @ A2 @ B2 )
% 0.25/0.58 => ( ( member346808080real_c @ C @ A2 )
% 0.25/0.58 => ( member346808080real_c @ C @ B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % subsetD
% 0.25/0.58 thf(fact_93_subsetD,axiom,
% 0.25/0.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,C: sum_sum_c_c] :
% 0.25/0.58 ( ( ord_le1772180283um_c_c @ A2 @ B2 )
% 0.25/0.58 => ( ( member_Sum_sum_c_c @ C @ A2 )
% 0.25/0.58 => ( member_Sum_sum_c_c @ C @ B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % subsetD
% 0.25/0.58 thf(fact_94_subsetD,axiom,
% 0.25/0.58 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c,C: sum_su737395349um_b_c] :
% 0.25/0.58 ( ( ord_le929608341um_b_c @ A2 @ B2 )
% 0.25/0.58 => ( ( member1893232190um_b_c @ C @ A2 )
% 0.25/0.58 => ( member1893232190um_b_c @ C @ B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % subsetD
% 0.25/0.58 thf(fact_95_equalityE,axiom,
% 0.25/0.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( A2 = B2 )
% 0.25/0.58 => ~ ( ( ord_le1772180283um_c_c @ A2 @ B2 )
% 0.25/0.58 => ~ ( ord_le1772180283um_c_c @ B2 @ A2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % equalityE
% 0.25/0.58 thf(fact_96_equalityE,axiom,
% 0.25/0.58 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( A2 = B2 )
% 0.25/0.58 => ~ ( ( ord_le929608341um_b_c @ A2 @ B2 )
% 0.25/0.58 => ~ ( ord_le929608341um_b_c @ B2 @ A2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % equalityE
% 0.25/0.58 thf(fact_97_subset__eq,axiom,
% 0.25/0.58 ( ord_le1988344935real_c
% 0.25/0.58 = ( ^ [A3: set_Pr754230471real_c,B3: set_Pr754230471real_c] :
% 0.25/0.58 ! [X3: produc640052711real_c] :
% 0.25/0.58 ( ( member346808080real_c @ X3 @ A3 )
% 0.25/0.58 => ( member346808080real_c @ X3 @ B3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % subset_eq
% 0.25/0.58 thf(fact_98_subset__eq,axiom,
% 0.25/0.58 ( ord_le1772180283um_c_c
% 0.25/0.58 = ( ^ [A3: set_Sum_sum_c_c,B3: set_Sum_sum_c_c] :
% 0.25/0.58 ! [X3: sum_sum_c_c] :
% 0.25/0.58 ( ( member_Sum_sum_c_c @ X3 @ A3 )
% 0.25/0.58 => ( member_Sum_sum_c_c @ X3 @ B3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % subset_eq
% 0.25/0.58 thf(fact_99_subset__eq,axiom,
% 0.25/0.58 ( ord_le929608341um_b_c
% 0.25/0.58 = ( ^ [A3: set_Su1783761653um_b_c,B3: set_Su1783761653um_b_c] :
% 0.25/0.58 ! [X3: sum_su737395349um_b_c] :
% 0.25/0.58 ( ( member1893232190um_b_c @ X3 @ A3 )
% 0.25/0.58 => ( member1893232190um_b_c @ X3 @ B3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % subset_eq
% 0.25/0.58 thf(fact_100_equalityD1,axiom,
% 0.25/0.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( A2 = B2 )
% 0.25/0.58 => ( ord_le1772180283um_c_c @ A2 @ B2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % equalityD1
% 0.25/0.58 thf(fact_101_equalityD1,axiom,
% 0.25/0.58 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( A2 = B2 )
% 0.25/0.58 => ( ord_le929608341um_b_c @ A2 @ B2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % equalityD1
% 0.25/0.58 thf(fact_102_equalityD2,axiom,
% 0.25/0.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( A2 = B2 )
% 0.25/0.58 => ( ord_le1772180283um_c_c @ B2 @ A2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % equalityD2
% 0.25/0.58 thf(fact_103_equalityD2,axiom,
% 0.25/0.58 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( A2 = B2 )
% 0.25/0.58 => ( ord_le929608341um_b_c @ B2 @ A2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % equalityD2
% 0.25/0.58 thf(fact_104_subset__iff,axiom,
% 0.25/0.58 ( ord_le1988344935real_c
% 0.25/0.58 = ( ^ [A3: set_Pr754230471real_c,B3: set_Pr754230471real_c] :
% 0.25/0.58 ! [T: produc640052711real_c] :
% 0.25/0.58 ( ( member346808080real_c @ T @ A3 )
% 0.25/0.58 => ( member346808080real_c @ T @ B3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % subset_iff
% 0.25/0.58 thf(fact_105_subset__iff,axiom,
% 0.25/0.58 ( ord_le1772180283um_c_c
% 0.25/0.58 = ( ^ [A3: set_Sum_sum_c_c,B3: set_Sum_sum_c_c] :
% 0.25/0.58 ! [T: sum_sum_c_c] :
% 0.25/0.58 ( ( member_Sum_sum_c_c @ T @ A3 )
% 0.25/0.58 => ( member_Sum_sum_c_c @ T @ B3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % subset_iff
% 0.25/0.58 thf(fact_106_subset__iff,axiom,
% 0.25/0.58 ( ord_le929608341um_b_c
% 0.25/0.58 = ( ^ [A3: set_Su1783761653um_b_c,B3: set_Su1783761653um_b_c] :
% 0.25/0.58 ! [T: sum_su737395349um_b_c] :
% 0.25/0.58 ( ( member1893232190um_b_c @ T @ A3 )
% 0.25/0.58 => ( member1893232190um_b_c @ T @ B3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % subset_iff
% 0.25/0.58 thf(fact_107_subset__refl,axiom,
% 0.25/0.58 ! [A2: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ A2 @ A2 ) ).
% 0.25/0.58
% 0.25/0.58 % subset_refl
% 0.25/0.58 thf(fact_108_subset__refl,axiom,
% 0.25/0.58 ! [A2: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ A2 @ A2 ) ).
% 0.25/0.58
% 0.25/0.58 % subset_refl
% 0.25/0.58 thf(fact_109_Collect__mono,axiom,
% 0.25/0.58 ! [P: sum_sum_c_c > $o,Q: sum_sum_c_c > $o] :
% 0.25/0.58 ( ! [X2: sum_sum_c_c] :
% 0.25/0.58 ( ( P @ X2 )
% 0.25/0.58 => ( Q @ X2 ) )
% 0.25/0.58 => ( ord_le1772180283um_c_c @ ( collect_Sum_sum_c_c @ P ) @ ( collect_Sum_sum_c_c @ Q ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Collect_mono
% 0.25/0.58 thf(fact_110_Collect__mono,axiom,
% 0.25/0.58 ! [P: sum_su737395349um_b_c > $o,Q: sum_su737395349um_b_c > $o] :
% 0.25/0.58 ( ! [X2: sum_su737395349um_b_c] :
% 0.25/0.58 ( ( P @ X2 )
% 0.25/0.58 => ( Q @ X2 ) )
% 0.25/0.58 => ( ord_le929608341um_b_c @ ( collec2086029184um_b_c @ P ) @ ( collec2086029184um_b_c @ Q ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Collect_mono
% 0.25/0.58 thf(fact_111_subset__trans,axiom,
% 0.25/0.58 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,C2: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( ord_le1772180283um_c_c @ A2 @ B2 )
% 0.25/0.58 => ( ( ord_le1772180283um_c_c @ B2 @ C2 )
% 0.25/0.58 => ( ord_le1772180283um_c_c @ A2 @ C2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % subset_trans
% 0.25/0.58 thf(fact_112_subset__trans,axiom,
% 0.25/0.58 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c,C2: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( ord_le929608341um_b_c @ A2 @ B2 )
% 0.25/0.58 => ( ( ord_le929608341um_b_c @ B2 @ C2 )
% 0.25/0.58 => ( ord_le929608341um_b_c @ A2 @ C2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % subset_trans
% 0.25/0.58 thf(fact_113_set__eq__subset,axiom,
% 0.25/0.58 ( ( ^ [Y2: set_Sum_sum_c_c,Z2: set_Sum_sum_c_c] : ( Y2 = Z2 ) )
% 0.25/0.58 = ( ^ [A3: set_Sum_sum_c_c,B3: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( ord_le1772180283um_c_c @ A3 @ B3 )
% 0.25/0.58 & ( ord_le1772180283um_c_c @ B3 @ A3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % set_eq_subset
% 0.25/0.58 thf(fact_114_set__eq__subset,axiom,
% 0.25/0.58 ( ( ^ [Y2: set_Su1783761653um_b_c,Z2: set_Su1783761653um_b_c] : ( Y2 = Z2 ) )
% 0.25/0.58 = ( ^ [A3: set_Su1783761653um_b_c,B3: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( ord_le929608341um_b_c @ A3 @ B3 )
% 0.25/0.58 & ( ord_le929608341um_b_c @ B3 @ A3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % set_eq_subset
% 0.25/0.58 thf(fact_115_mem__Collect__eq,axiom,
% 0.25/0.58 ! [A: produc640052711real_c,P: produc640052711real_c > $o] :
% 0.25/0.58 ( ( member346808080real_c @ A @ ( collec1126017874real_c @ P ) )
% 0.25/0.58 = ( P @ A ) ) ).
% 0.25/0.58
% 0.25/0.58 % mem_Collect_eq
% 0.25/0.58 thf(fact_116_Collect__mem__eq,axiom,
% 0.25/0.58 ! [A2: set_Pr754230471real_c] :
% 0.25/0.58 ( ( collec1126017874real_c
% 0.25/0.58 @ ^ [X3: produc640052711real_c] : ( member346808080real_c @ X3 @ A2 ) )
% 0.25/0.58 = A2 ) ).
% 0.25/0.58
% 0.25/0.58 % Collect_mem_eq
% 0.25/0.58 thf(fact_117_Collect__mono__iff,axiom,
% 0.25/0.58 ! [P: sum_sum_c_c > $o,Q: sum_sum_c_c > $o] :
% 0.25/0.58 ( ( ord_le1772180283um_c_c @ ( collect_Sum_sum_c_c @ P ) @ ( collect_Sum_sum_c_c @ Q ) )
% 0.25/0.58 = ( ! [X3: sum_sum_c_c] :
% 0.25/0.58 ( ( P @ X3 )
% 0.25/0.58 => ( Q @ X3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Collect_mono_iff
% 0.25/0.58 thf(fact_118_Collect__mono__iff,axiom,
% 0.25/0.58 ! [P: sum_su737395349um_b_c > $o,Q: sum_su737395349um_b_c > $o] :
% 0.25/0.58 ( ( ord_le929608341um_b_c @ ( collec2086029184um_b_c @ P ) @ ( collec2086029184um_b_c @ Q ) )
% 0.25/0.58 = ( ! [X3: sum_su737395349um_b_c] :
% 0.25/0.58 ( ( P @ X3 )
% 0.25/0.58 => ( Q @ X3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Collect_mono_iff
% 0.25/0.58 thf(fact_119_Pair__mono,axiom,
% 0.25/0.58 ! [X: produc190496183real_c,X4: produc190496183real_c,Y: produc190496183real_c,Y3: produc190496183real_c] :
% 0.25/0.58 ( ( ord_le850691415real_c @ X @ X4 )
% 0.25/0.58 => ( ( ord_le850691415real_c @ Y @ Y3 )
% 0.25/0.58 => ( ord_le652477831real_c @ ( produc1687028567real_c @ X @ Y ) @ ( produc1687028567real_c @ X4 @ Y3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Pair_mono
% 0.25/0.58 thf(fact_120_Pair__mono,axiom,
% 0.25/0.58 ! [X: finite1398487019real_c,X4: finite1398487019real_c,Y: finite1398487019real_c,Y3: finite1398487019real_c] :
% 0.25/0.58 ( ( ord_le775706699real_c @ X @ X4 )
% 0.25/0.58 => ( ( ord_le775706699real_c @ Y @ Y3 )
% 0.25/0.58 => ( ord_le850691415real_c @ ( produc394644079real_c @ X @ Y ) @ ( produc394644079real_c @ X4 @ Y3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Pair_mono
% 0.25/0.58 thf(fact_121_Pair__mono,axiom,
% 0.25/0.58 ! [X: set_Sum_sum_c_c,X4: set_Sum_sum_c_c,Y: set_Sum_sum_c_c,Y3: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( ord_le1772180283um_c_c @ X @ X4 )
% 0.25/0.58 => ( ( ord_le1772180283um_c_c @ Y @ Y3 )
% 0.25/0.58 => ( ord_le684454199um_c_c @ ( produc1439061071um_c_c @ X @ Y ) @ ( produc1439061071um_c_c @ X4 @ Y3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Pair_mono
% 0.25/0.58 thf(fact_122_Pair__mono,axiom,
% 0.25/0.58 ! [X: set_Sum_sum_c_c,X4: set_Sum_sum_c_c,Y: set_Su1783761653um_b_c,Y3: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( ord_le1772180283um_c_c @ X @ X4 )
% 0.25/0.58 => ( ( ord_le929608341um_b_c @ Y @ Y3 )
% 0.25/0.58 => ( ord_le542695343um_b_c @ ( produc919784577um_b_c @ X @ Y ) @ ( produc919784577um_b_c @ X4 @ Y3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Pair_mono
% 0.25/0.58 thf(fact_123_Pair__mono,axiom,
% 0.25/0.58 ! [X: set_Su1783761653um_b_c,X4: set_Su1783761653um_b_c,Y: set_Sum_sum_c_c,Y3: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( ord_le929608341um_b_c @ X @ X4 )
% 0.25/0.58 => ( ( ord_le1772180283um_c_c @ Y @ Y3 )
% 0.25/0.58 => ( ord_le1852514783um_c_c @ ( produc616453753um_c_c @ X @ Y ) @ ( produc616453753um_c_c @ X4 @ Y3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Pair_mono
% 0.25/0.58 thf(fact_124_Pair__mono,axiom,
% 0.25/0.58 ! [X: set_Su1783761653um_b_c,X4: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c,Y3: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( ord_le929608341um_b_c @ X @ X4 )
% 0.25/0.58 => ( ( ord_le929608341um_b_c @ Y @ Y3 )
% 0.25/0.58 => ( ord_le907560199um_b_c @ ( produc754249687um_b_c @ X @ Y ) @ ( produc754249687um_b_c @ X4 @ Y3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Pair_mono
% 0.25/0.58 thf(fact_125_sup_OcoboundedI2,axiom,
% 0.25/0.58 ! [C: set_Sum_sum_c_c,B: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( ord_le1772180283um_c_c @ C @ B )
% 0.25/0.58 => ( ord_le1772180283um_c_c @ C @ ( sup_su1349021703um_c_c @ A @ B ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.coboundedI2
% 0.25/0.58 thf(fact_126_sup_OcoboundedI2,axiom,
% 0.25/0.58 ! [C: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( ord_le929608341um_b_c @ C @ B )
% 0.25/0.58 => ( ord_le929608341um_b_c @ C @ ( sup_su1968964297um_b_c @ A @ B ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.coboundedI2
% 0.25/0.58 thf(fact_127_sup_OcoboundedI1,axiom,
% 0.25/0.58 ! [C: set_Sum_sum_c_c,A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( ord_le1772180283um_c_c @ C @ A )
% 0.25/0.58 => ( ord_le1772180283um_c_c @ C @ ( sup_su1349021703um_c_c @ A @ B ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.coboundedI1
% 0.25/0.58 thf(fact_128_sup_OcoboundedI1,axiom,
% 0.25/0.58 ! [C: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( ord_le929608341um_b_c @ C @ A )
% 0.25/0.58 => ( ord_le929608341um_b_c @ C @ ( sup_su1968964297um_b_c @ A @ B ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.coboundedI1
% 0.25/0.58 thf(fact_129_sup_Oabsorb__iff2,axiom,
% 0.25/0.58 ( ord_le1772180283um_c_c
% 0.25/0.58 = ( ^ [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( sup_su1349021703um_c_c @ A4 @ B4 )
% 0.25/0.58 = B4 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.absorb_iff2
% 0.25/0.58 thf(fact_130_sup_Oabsorb__iff2,axiom,
% 0.25/0.58 ( ord_le929608341um_b_c
% 0.25/0.58 = ( ^ [A4: set_Su1783761653um_b_c,B4: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( sup_su1968964297um_b_c @ A4 @ B4 )
% 0.25/0.58 = B4 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.absorb_iff2
% 0.25/0.58 thf(fact_131_sup_Oabsorb__iff1,axiom,
% 0.25/0.58 ( ord_le1772180283um_c_c
% 0.25/0.58 = ( ^ [B4: set_Sum_sum_c_c,A4: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( sup_su1349021703um_c_c @ A4 @ B4 )
% 0.25/0.58 = A4 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.absorb_iff1
% 0.25/0.58 thf(fact_132_sup_Oabsorb__iff1,axiom,
% 0.25/0.58 ( ord_le929608341um_b_c
% 0.25/0.58 = ( ^ [B4: set_Su1783761653um_b_c,A4: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( sup_su1968964297um_b_c @ A4 @ B4 )
% 0.25/0.58 = A4 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.absorb_iff1
% 0.25/0.58 thf(fact_133_sup_Ocobounded2,axiom,
% 0.25/0.58 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ B @ ( sup_su1349021703um_c_c @ A @ B ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.cobounded2
% 0.25/0.58 thf(fact_134_sup_Ocobounded2,axiom,
% 0.25/0.58 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ B @ ( sup_su1968964297um_b_c @ A @ B ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.cobounded2
% 0.25/0.58 thf(fact_135_sup_Ocobounded1,axiom,
% 0.25/0.58 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ A @ ( sup_su1349021703um_c_c @ A @ B ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.cobounded1
% 0.25/0.58 thf(fact_136_sup_Ocobounded1,axiom,
% 0.25/0.58 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ A @ ( sup_su1968964297um_b_c @ A @ B ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.cobounded1
% 0.25/0.58 thf(fact_137_sup_Oorder__iff,axiom,
% 0.25/0.58 ( ord_le1772180283um_c_c
% 0.25/0.58 = ( ^ [B4: set_Sum_sum_c_c,A4: set_Sum_sum_c_c] :
% 0.25/0.58 ( A4
% 0.25/0.58 = ( sup_su1349021703um_c_c @ A4 @ B4 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.order_iff
% 0.25/0.58 thf(fact_138_sup_Oorder__iff,axiom,
% 0.25/0.58 ( ord_le929608341um_b_c
% 0.25/0.58 = ( ^ [B4: set_Su1783761653um_b_c,A4: set_Su1783761653um_b_c] :
% 0.25/0.58 ( A4
% 0.25/0.58 = ( sup_su1968964297um_b_c @ A4 @ B4 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.order_iff
% 0.25/0.58 thf(fact_139_sup_OboundedI,axiom,
% 0.25/0.58 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( ord_le1772180283um_c_c @ B @ A )
% 0.25/0.58 => ( ( ord_le1772180283um_c_c @ C @ A )
% 0.25/0.58 => ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ B @ C ) @ A ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.boundedI
% 0.25/0.58 thf(fact_140_sup_OboundedI,axiom,
% 0.25/0.58 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( ord_le929608341um_b_c @ B @ A )
% 0.25/0.58 => ( ( ord_le929608341um_b_c @ C @ A )
% 0.25/0.58 => ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ B @ C ) @ A ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.boundedI
% 0.25/0.58 thf(fact_141_sup_OboundedE,axiom,
% 0.25/0.58 ! [B: set_Sum_sum_c_c,C: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ B @ C ) @ A )
% 0.25/0.58 => ~ ( ( ord_le1772180283um_c_c @ B @ A )
% 0.25/0.58 => ~ ( ord_le1772180283um_c_c @ C @ A ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.boundedE
% 0.25/0.58 thf(fact_142_sup_OboundedE,axiom,
% 0.25/0.58 ! [B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ B @ C ) @ A )
% 0.25/0.58 => ~ ( ( ord_le929608341um_b_c @ B @ A )
% 0.25/0.58 => ~ ( ord_le929608341um_b_c @ C @ A ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.boundedE
% 0.25/0.58 thf(fact_143_sup__absorb2,axiom,
% 0.25/0.58 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( ord_le1772180283um_c_c @ X @ Y )
% 0.25/0.58 => ( ( sup_su1349021703um_c_c @ X @ Y )
% 0.25/0.58 = Y ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup_absorb2
% 0.25/0.58 thf(fact_144_sup__absorb2,axiom,
% 0.25/0.58 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( ord_le929608341um_b_c @ X @ Y )
% 0.25/0.58 => ( ( sup_su1968964297um_b_c @ X @ Y )
% 0.25/0.58 = Y ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup_absorb2
% 0.25/0.58 thf(fact_145_sup__absorb1,axiom,
% 0.25/0.58 ! [Y: set_Sum_sum_c_c,X: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( ord_le1772180283um_c_c @ Y @ X )
% 0.25/0.58 => ( ( sup_su1349021703um_c_c @ X @ Y )
% 0.25/0.58 = X ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup_absorb1
% 0.25/0.58 thf(fact_146_sup__absorb1,axiom,
% 0.25/0.58 ! [Y: set_Su1783761653um_b_c,X: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( ord_le929608341um_b_c @ Y @ X )
% 0.25/0.58 => ( ( sup_su1968964297um_b_c @ X @ Y )
% 0.25/0.58 = X ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup_absorb1
% 0.25/0.58 thf(fact_147_sup_Oabsorb2,axiom,
% 0.25/0.58 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( ord_le1772180283um_c_c @ A @ B )
% 0.25/0.58 => ( ( sup_su1349021703um_c_c @ A @ B )
% 0.25/0.58 = B ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.absorb2
% 0.25/0.58 thf(fact_148_sup_Oabsorb2,axiom,
% 0.25/0.58 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( ord_le929608341um_b_c @ A @ B )
% 0.25/0.58 => ( ( sup_su1968964297um_b_c @ A @ B )
% 0.25/0.58 = B ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.absorb2
% 0.25/0.58 thf(fact_149_sup_Oabsorb1,axiom,
% 0.25/0.58 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( ord_le1772180283um_c_c @ B @ A )
% 0.25/0.58 => ( ( sup_su1349021703um_c_c @ A @ B )
% 0.25/0.58 = A ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.absorb1
% 0.25/0.58 thf(fact_150_sup_Oabsorb1,axiom,
% 0.25/0.58 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( ord_le929608341um_b_c @ B @ A )
% 0.25/0.58 => ( ( sup_su1968964297um_b_c @ A @ B )
% 0.25/0.58 = A ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.absorb1
% 0.25/0.58 thf(fact_151_sup__unique,axiom,
% 0.25/0.58 ! [F: set_Sum_sum_c_c > set_Sum_sum_c_c > set_Sum_sum_c_c,X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 0.25/0.58 ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ X2 @ ( F @ X2 @ Y4 ) )
% 0.25/0.58 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ Y4 @ ( F @ X2 @ Y4 ) )
% 0.25/0.58 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c,Z3: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( ord_le1772180283um_c_c @ Y4 @ X2 )
% 0.25/0.58 => ( ( ord_le1772180283um_c_c @ Z3 @ X2 )
% 0.25/0.58 => ( ord_le1772180283um_c_c @ ( F @ Y4 @ Z3 ) @ X2 ) ) )
% 0.25/0.58 => ( ( sup_su1349021703um_c_c @ X @ Y )
% 0.25/0.58 = ( F @ X @ Y ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup_unique
% 0.25/0.58 thf(fact_152_sup__unique,axiom,
% 0.25/0.58 ! [F: set_Su1783761653um_b_c > set_Su1783761653um_b_c > set_Su1783761653um_b_c,X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ X2 @ ( F @ X2 @ Y4 ) )
% 0.25/0.58 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ Y4 @ ( F @ X2 @ Y4 ) )
% 0.25/0.58 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c,Z3: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( ord_le929608341um_b_c @ Y4 @ X2 )
% 0.25/0.58 => ( ( ord_le929608341um_b_c @ Z3 @ X2 )
% 0.25/0.58 => ( ord_le929608341um_b_c @ ( F @ Y4 @ Z3 ) @ X2 ) ) )
% 0.25/0.58 => ( ( sup_su1968964297um_b_c @ X @ Y )
% 0.25/0.58 = ( F @ X @ Y ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup_unique
% 0.25/0.58 thf(fact_153_sup_OorderI,axiom,
% 0.25/0.58 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( A
% 0.25/0.58 = ( sup_su1349021703um_c_c @ A @ B ) )
% 0.25/0.58 => ( ord_le1772180283um_c_c @ B @ A ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.orderI
% 0.25/0.58 thf(fact_154_sup_OorderI,axiom,
% 0.25/0.58 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( A
% 0.25/0.58 = ( sup_su1968964297um_b_c @ A @ B ) )
% 0.25/0.58 => ( ord_le929608341um_b_c @ B @ A ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.orderI
% 0.25/0.58 thf(fact_155_sup_OorderE,axiom,
% 0.25/0.58 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 0.25/0.58 ( ( ord_le1772180283um_c_c @ B @ A )
% 0.25/0.58 => ( A
% 0.25/0.58 = ( sup_su1349021703um_c_c @ A @ B ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.orderE
% 0.25/0.58 thf(fact_156_sup_OorderE,axiom,
% 0.25/0.58 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] :
% 0.25/0.58 ( ( ord_le929608341um_b_c @ B @ A )
% 0.25/0.58 => ( A
% 0.25/0.58 = ( sup_su1968964297um_b_c @ A @ B ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % sup.orderE
% 0.25/0.58 thf(fact_157_le__iff__sup,axiom,
% 0.25/0.58 ( ord_le1772180283um_c_c
% 0.25/0.58 = ( ^ [X3: set_Sum_sum_c_c,Y5: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( sup_su1349021703um_c_c @ X3 @ Y5 )
% 0.25/0.59 = Y5 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % le_iff_sup
% 0.25/0.59 thf(fact_158_le__iff__sup,axiom,
% 0.25/0.59 ( ord_le929608341um_b_c
% 0.25/0.59 = ( ^ [X3: set_Su1783761653um_b_c,Y5: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( sup_su1968964297um_b_c @ X3 @ Y5 )
% 0.25/0.59 = Y5 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % le_iff_sup
% 0.25/0.59 thf(fact_159_sup__least,axiom,
% 0.25/0.59 ! [Y: set_Sum_sum_c_c,X: set_Sum_sum_c_c,Z: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ Y @ X )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ Z @ X )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ Y @ Z ) @ X ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % sup_least
% 0.25/0.59 thf(fact_160_sup__least,axiom,
% 0.25/0.59 ! [Y: set_Su1783761653um_b_c,X: set_Su1783761653um_b_c,Z: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ Y @ X )
% 0.25/0.59 => ( ( ord_le929608341um_b_c @ Z @ X )
% 0.25/0.59 => ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ Y @ Z ) @ X ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % sup_least
% 0.25/0.59 thf(fact_161_sup__mono,axiom,
% 0.25/0.59 ! [A: set_Sum_sum_c_c,C: set_Sum_sum_c_c,B: set_Sum_sum_c_c,D: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ A @ C )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ B @ D )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ A @ B ) @ ( sup_su1349021703um_c_c @ C @ D ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % sup_mono
% 0.25/0.59 thf(fact_162_sup__mono,axiom,
% 0.25/0.59 ! [A: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,D: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ A @ C )
% 0.25/0.59 => ( ( ord_le929608341um_b_c @ B @ D )
% 0.25/0.59 => ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ A @ B ) @ ( sup_su1968964297um_b_c @ C @ D ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % sup_mono
% 0.25/0.59 thf(fact_163_sup_Omono,axiom,
% 0.25/0.59 ! [C: set_Sum_sum_c_c,A: set_Sum_sum_c_c,D: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ C @ A )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ D @ B )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ C @ D ) @ ( sup_su1349021703um_c_c @ A @ B ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % sup.mono
% 0.25/0.59 thf(fact_164_sup_Omono,axiom,
% 0.25/0.59 ! [C: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c,D: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ C @ A )
% 0.25/0.59 => ( ( ord_le929608341um_b_c @ D @ B )
% 0.25/0.59 => ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ C @ D ) @ ( sup_su1968964297um_b_c @ A @ B ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % sup.mono
% 0.25/0.59 thf(fact_165_le__supI2,axiom,
% 0.25/0.59 ! [X: set_Sum_sum_c_c,B: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ X @ B )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ X @ ( sup_su1349021703um_c_c @ A @ B ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % le_supI2
% 0.25/0.59 thf(fact_166_le__supI2,axiom,
% 0.25/0.59 ! [X: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ X @ B )
% 0.25/0.59 => ( ord_le929608341um_b_c @ X @ ( sup_su1968964297um_b_c @ A @ B ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % le_supI2
% 0.25/0.59 thf(fact_167_le__supI1,axiom,
% 0.25/0.59 ! [X: set_Sum_sum_c_c,A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ X @ A )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ X @ ( sup_su1349021703um_c_c @ A @ B ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % le_supI1
% 0.25/0.59 thf(fact_168_le__supI1,axiom,
% 0.25/0.59 ! [X: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ X @ A )
% 0.25/0.59 => ( ord_le929608341um_b_c @ X @ ( sup_su1968964297um_b_c @ A @ B ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % le_supI1
% 0.25/0.59 thf(fact_169_sup__ge2,axiom,
% 0.25/0.59 ! [Y: set_Sum_sum_c_c,X: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ Y @ ( sup_su1349021703um_c_c @ X @ Y ) ) ).
% 0.25/0.59
% 0.25/0.59 % sup_ge2
% 0.25/0.59 thf(fact_170_sup__ge2,axiom,
% 0.25/0.59 ! [Y: set_Su1783761653um_b_c,X: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ Y @ ( sup_su1968964297um_b_c @ X @ Y ) ) ).
% 0.25/0.59
% 0.25/0.59 % sup_ge2
% 0.25/0.59 thf(fact_171_sup__ge1,axiom,
% 0.25/0.59 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ X @ ( sup_su1349021703um_c_c @ X @ Y ) ) ).
% 0.25/0.59
% 0.25/0.59 % sup_ge1
% 0.25/0.59 thf(fact_172_sup__ge1,axiom,
% 0.25/0.59 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ X @ ( sup_su1968964297um_b_c @ X @ Y ) ) ).
% 0.25/0.59
% 0.25/0.59 % sup_ge1
% 0.25/0.59 thf(fact_173_le__supI,axiom,
% 0.25/0.59 ! [A: set_Sum_sum_c_c,X: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ A @ X )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ B @ X )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ A @ B ) @ X ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % le_supI
% 0.25/0.59 thf(fact_174_le__supI,axiom,
% 0.25/0.59 ! [A: set_Su1783761653um_b_c,X: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ A @ X )
% 0.25/0.59 => ( ( ord_le929608341um_b_c @ B @ X )
% 0.25/0.59 => ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ A @ B ) @ X ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % le_supI
% 0.25/0.59 thf(fact_175_le__supE,axiom,
% 0.25/0.59 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,X: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ A @ B ) @ X )
% 0.25/0.59 => ~ ( ( ord_le1772180283um_c_c @ A @ X )
% 0.25/0.59 => ~ ( ord_le1772180283um_c_c @ B @ X ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % le_supE
% 0.25/0.59 thf(fact_176_le__supE,axiom,
% 0.25/0.59 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,X: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ A @ B ) @ X )
% 0.25/0.59 => ~ ( ( ord_le929608341um_b_c @ A @ X )
% 0.25/0.59 => ~ ( ord_le929608341um_b_c @ B @ X ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % le_supE
% 0.25/0.59 thf(fact_177_inf__sup__ord_I3_J,axiom,
% 0.25/0.59 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ X @ ( sup_su1349021703um_c_c @ X @ Y ) ) ).
% 0.25/0.59
% 0.25/0.59 % inf_sup_ord(3)
% 0.25/0.59 thf(fact_178_inf__sup__ord_I3_J,axiom,
% 0.25/0.59 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ X @ ( sup_su1968964297um_b_c @ X @ Y ) ) ).
% 0.25/0.59
% 0.25/0.59 % inf_sup_ord(3)
% 0.25/0.59 thf(fact_179_inf__sup__ord_I4_J,axiom,
% 0.25/0.59 ! [Y: set_Sum_sum_c_c,X: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ Y @ ( sup_su1349021703um_c_c @ X @ Y ) ) ).
% 0.25/0.59
% 0.25/0.59 % inf_sup_ord(4)
% 0.25/0.59 thf(fact_180_inf__sup__ord_I4_J,axiom,
% 0.25/0.59 ! [Y: set_Su1783761653um_b_c,X: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ Y @ ( sup_su1968964297um_b_c @ X @ Y ) ) ).
% 0.25/0.59
% 0.25/0.59 % inf_sup_ord(4)
% 0.25/0.59 thf(fact_181_subset__Un__eq,axiom,
% 0.25/0.59 ( ord_le1772180283um_c_c
% 0.25/0.59 = ( ^ [A3: set_Sum_sum_c_c,B3: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( sup_su1349021703um_c_c @ A3 @ B3 )
% 0.25/0.59 = B3 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % subset_Un_eq
% 0.25/0.59 thf(fact_182_subset__Un__eq,axiom,
% 0.25/0.59 ( ord_le929608341um_b_c
% 0.25/0.59 = ( ^ [A3: set_Su1783761653um_b_c,B3: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( sup_su1968964297um_b_c @ A3 @ B3 )
% 0.25/0.59 = B3 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % subset_Un_eq
% 0.25/0.59 thf(fact_183_subset__UnE,axiom,
% 0.25/0.59 ! [C2: set_Sum_sum_c_c,A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ C2 @ ( sup_su1349021703um_c_c @ A2 @ B2 ) )
% 0.25/0.59 => ~ ! [A5: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ A5 @ A2 )
% 0.25/0.59 => ! [B5: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ B5 @ B2 )
% 0.25/0.59 => ( C2
% 0.25/0.59 != ( sup_su1349021703um_c_c @ A5 @ B5 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % subset_UnE
% 0.25/0.59 thf(fact_184_subset__UnE,axiom,
% 0.25/0.59 ! [C2: set_Su1783761653um_b_c,A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ C2 @ ( sup_su1968964297um_b_c @ A2 @ B2 ) )
% 0.25/0.59 => ~ ! [A5: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ A5 @ A2 )
% 0.25/0.59 => ! [B5: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ B5 @ B2 )
% 0.25/0.59 => ( C2
% 0.25/0.59 != ( sup_su1968964297um_b_c @ A5 @ B5 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % subset_UnE
% 0.25/0.59 thf(fact_185_Un__absorb2,axiom,
% 0.25/0.59 ! [B2: set_Sum_sum_c_c,A2: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ B2 @ A2 )
% 0.25/0.59 => ( ( sup_su1349021703um_c_c @ A2 @ B2 )
% 0.25/0.59 = A2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % Un_absorb2
% 0.25/0.59 thf(fact_186_Un__absorb2,axiom,
% 0.25/0.59 ! [B2: set_Su1783761653um_b_c,A2: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ B2 @ A2 )
% 0.25/0.59 => ( ( sup_su1968964297um_b_c @ A2 @ B2 )
% 0.25/0.59 = A2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % Un_absorb2
% 0.25/0.59 thf(fact_187_Un__absorb1,axiom,
% 0.25/0.59 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ A2 @ B2 )
% 0.25/0.59 => ( ( sup_su1349021703um_c_c @ A2 @ B2 )
% 0.25/0.59 = B2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % Un_absorb1
% 0.25/0.59 thf(fact_188_Un__absorb1,axiom,
% 0.25/0.59 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ A2 @ B2 )
% 0.25/0.59 => ( ( sup_su1968964297um_b_c @ A2 @ B2 )
% 0.25/0.59 = B2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % Un_absorb1
% 0.25/0.59 thf(fact_189_Un__upper2,axiom,
% 0.25/0.59 ! [B2: set_Sum_sum_c_c,A2: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ B2 @ ( sup_su1349021703um_c_c @ A2 @ B2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % Un_upper2
% 0.25/0.59 thf(fact_190_Un__upper2,axiom,
% 0.25/0.59 ! [B2: set_Su1783761653um_b_c,A2: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ B2 @ ( sup_su1968964297um_b_c @ A2 @ B2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % Un_upper2
% 0.25/0.59 thf(fact_191_Un__upper1,axiom,
% 0.25/0.59 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ A2 @ ( sup_su1349021703um_c_c @ A2 @ B2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % Un_upper1
% 0.25/0.59 thf(fact_192_Un__upper1,axiom,
% 0.25/0.59 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ A2 @ ( sup_su1968964297um_b_c @ A2 @ B2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % Un_upper1
% 0.25/0.59 thf(fact_193_Un__least,axiom,
% 0.25/0.59 ! [A2: set_Sum_sum_c_c,C2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ A2 @ C2 )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ B2 @ C2 )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ A2 @ B2 ) @ C2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Un_least
% 0.25/0.59 thf(fact_194_Un__least,axiom,
% 0.25/0.59 ! [A2: set_Su1783761653um_b_c,C2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ A2 @ C2 )
% 0.25/0.59 => ( ( ord_le929608341um_b_c @ B2 @ C2 )
% 0.25/0.59 => ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ A2 @ B2 ) @ C2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Un_least
% 0.25/0.59 thf(fact_195_Un__mono,axiom,
% 0.25/0.59 ! [A2: set_Sum_sum_c_c,C2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,D2: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ A2 @ C2 )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ B2 @ D2 )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ ( sup_su1349021703um_c_c @ A2 @ B2 ) @ ( sup_su1349021703um_c_c @ C2 @ D2 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Un_mono
% 0.25/0.59 thf(fact_196_Un__mono,axiom,
% 0.25/0.59 ! [A2: set_Su1783761653um_b_c,C2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c,D2: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ A2 @ C2 )
% 0.25/0.59 => ( ( ord_le929608341um_b_c @ B2 @ D2 )
% 0.25/0.59 => ( ord_le929608341um_b_c @ ( sup_su1968964297um_b_c @ A2 @ B2 ) @ ( sup_su1968964297um_b_c @ C2 @ D2 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Un_mono
% 0.25/0.59 thf(fact_197_hpsafe__fsafe_Ohpsafe__Choice,axiom,
% 0.25/0.59 ! [A: hp_a_b_c,B: hp_a_b_c] :
% 0.25/0.59 ( ( hpsafe_a_b_c @ A )
% 0.25/0.59 => ( ( hpsafe_a_b_c @ B )
% 0.25/0.59 => ( hpsafe_a_b_c @ ( choice_a_b_c @ A @ B ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % hpsafe_fsafe.hpsafe_Choice
% 0.25/0.59 thf(fact_198_sup__left__commute,axiom,
% 0.25/0.59 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c,Z: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( sup_su1349021703um_c_c @ X @ ( sup_su1349021703um_c_c @ Y @ Z ) )
% 0.25/0.59 = ( sup_su1349021703um_c_c @ Y @ ( sup_su1349021703um_c_c @ X @ Z ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % sup_left_commute
% 0.25/0.59 thf(fact_199_sup_Oleft__commute,axiom,
% 0.25/0.59 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( sup_su1349021703um_c_c @ B @ ( sup_su1349021703um_c_c @ A @ C ) )
% 0.25/0.59 = ( sup_su1349021703um_c_c @ A @ ( sup_su1349021703um_c_c @ B @ C ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % sup.left_commute
% 0.25/0.59 thf(fact_200_sup__commute,axiom,
% 0.25/0.59 ( sup_su1349021703um_c_c
% 0.25/0.59 = ( ^ [X3: set_Sum_sum_c_c,Y5: set_Sum_sum_c_c] : ( sup_su1349021703um_c_c @ Y5 @ X3 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % sup_commute
% 0.25/0.59 thf(fact_201_sup_Ocommute,axiom,
% 0.25/0.59 ( sup_su1349021703um_c_c
% 0.25/0.59 = ( ^ [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c] : ( sup_su1349021703um_c_c @ B4 @ A4 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % sup.commute
% 0.25/0.59 thf(fact_202_sup__assoc,axiom,
% 0.25/0.59 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c,Z: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( sup_su1349021703um_c_c @ ( sup_su1349021703um_c_c @ X @ Y ) @ Z )
% 0.25/0.59 = ( sup_su1349021703um_c_c @ X @ ( sup_su1349021703um_c_c @ Y @ Z ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % sup_assoc
% 0.25/0.59 thf(fact_203_sup_Oassoc,axiom,
% 0.25/0.59 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( sup_su1349021703um_c_c @ ( sup_su1349021703um_c_c @ A @ B ) @ C )
% 0.25/0.59 = ( sup_su1349021703um_c_c @ A @ ( sup_su1349021703um_c_c @ B @ C ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % sup.assoc
% 0.25/0.59 thf(fact_204_boolean__algebra__cancel_Osup2,axiom,
% 0.25/0.59 ! [B2: set_Sum_sum_c_c,K: set_Sum_sum_c_c,B: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( B2
% 0.25/0.59 = ( sup_su1349021703um_c_c @ K @ B ) )
% 0.25/0.59 => ( ( sup_su1349021703um_c_c @ A @ B2 )
% 0.25/0.59 = ( sup_su1349021703um_c_c @ K @ ( sup_su1349021703um_c_c @ A @ B ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % boolean_algebra_cancel.sup2
% 0.25/0.59 thf(fact_205_boolean__algebra__cancel_Osup1,axiom,
% 0.25/0.59 ! [A2: set_Sum_sum_c_c,K: set_Sum_sum_c_c,A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( A2
% 0.25/0.59 = ( sup_su1349021703um_c_c @ K @ A ) )
% 0.25/0.59 => ( ( sup_su1349021703um_c_c @ A2 @ B )
% 0.25/0.59 = ( sup_su1349021703um_c_c @ K @ ( sup_su1349021703um_c_c @ A @ B ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % boolean_algebra_cancel.sup1
% 0.25/0.59 thf(fact_206_inf__sup__aci_I5_J,axiom,
% 0.25/0.59 ( sup_su1349021703um_c_c
% 0.25/0.59 = ( ^ [X3: set_Sum_sum_c_c,Y5: set_Sum_sum_c_c] : ( sup_su1349021703um_c_c @ Y5 @ X3 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % inf_sup_aci(5)
% 0.25/0.59 thf(fact_207_inf__sup__aci_I6_J,axiom,
% 0.25/0.59 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c,Z: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( sup_su1349021703um_c_c @ ( sup_su1349021703um_c_c @ X @ Y ) @ Z )
% 0.25/0.59 = ( sup_su1349021703um_c_c @ X @ ( sup_su1349021703um_c_c @ Y @ Z ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % inf_sup_aci(6)
% 0.25/0.59 thf(fact_208_inf__sup__aci_I7_J,axiom,
% 0.25/0.59 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c,Z: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( sup_su1349021703um_c_c @ X @ ( sup_su1349021703um_c_c @ Y @ Z ) )
% 0.25/0.59 = ( sup_su1349021703um_c_c @ Y @ ( sup_su1349021703um_c_c @ X @ Z ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % inf_sup_aci(7)
% 0.25/0.59 thf(fact_209_inf__sup__aci_I8_J,axiom,
% 0.25/0.59 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( sup_su1349021703um_c_c @ X @ ( sup_su1349021703um_c_c @ X @ Y ) )
% 0.25/0.59 = ( sup_su1349021703um_c_c @ X @ Y ) ) ).
% 0.25/0.59
% 0.25/0.59 % inf_sup_aci(8)
% 0.25/0.59 thf(fact_210_Un__left__commute,axiom,
% 0.25/0.59 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,C2: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( sup_su1349021703um_c_c @ A2 @ ( sup_su1349021703um_c_c @ B2 @ C2 ) )
% 0.25/0.59 = ( sup_su1349021703um_c_c @ B2 @ ( sup_su1349021703um_c_c @ A2 @ C2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Un_left_commute
% 0.25/0.59 thf(fact_211_Un__left__absorb,axiom,
% 0.25/0.59 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( sup_su1349021703um_c_c @ A2 @ ( sup_su1349021703um_c_c @ A2 @ B2 ) )
% 0.25/0.59 = ( sup_su1349021703um_c_c @ A2 @ B2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % Un_left_absorb
% 0.25/0.59 thf(fact_212_Un__commute,axiom,
% 0.25/0.59 ( sup_su1349021703um_c_c
% 0.25/0.59 = ( ^ [A3: set_Sum_sum_c_c,B3: set_Sum_sum_c_c] : ( sup_su1349021703um_c_c @ B3 @ A3 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Un_commute
% 0.25/0.59 thf(fact_213_Un__absorb,axiom,
% 0.25/0.59 ! [A2: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( sup_su1349021703um_c_c @ A2 @ A2 )
% 0.25/0.59 = A2 ) ).
% 0.25/0.59
% 0.25/0.59 % Un_absorb
% 0.25/0.59 thf(fact_214_Un__assoc,axiom,
% 0.25/0.59 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,C2: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( sup_su1349021703um_c_c @ ( sup_su1349021703um_c_c @ A2 @ B2 ) @ C2 )
% 0.25/0.59 = ( sup_su1349021703um_c_c @ A2 @ ( sup_su1349021703um_c_c @ B2 @ C2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Un_assoc
% 0.25/0.59 thf(fact_215_ball__Un,axiom,
% 0.25/0.59 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,P: sum_sum_c_c > $o] :
% 0.25/0.59 ( ( ! [X3: sum_sum_c_c] :
% 0.25/0.59 ( ( member_Sum_sum_c_c @ X3 @ ( sup_su1349021703um_c_c @ A2 @ B2 ) )
% 0.25/0.59 => ( P @ X3 ) ) )
% 0.25/0.59 = ( ! [X3: sum_sum_c_c] :
% 0.25/0.59 ( ( member_Sum_sum_c_c @ X3 @ A2 )
% 0.25/0.59 => ( P @ X3 ) )
% 0.25/0.59 & ! [X3: sum_sum_c_c] :
% 0.25/0.59 ( ( member_Sum_sum_c_c @ X3 @ B2 )
% 0.25/0.59 => ( P @ X3 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % ball_Un
% 0.25/0.59 thf(fact_216_bex__Un,axiom,
% 0.25/0.59 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,P: sum_sum_c_c > $o] :
% 0.25/0.59 ( ( ? [X3: sum_sum_c_c] :
% 0.25/0.59 ( ( member_Sum_sum_c_c @ X3 @ ( sup_su1349021703um_c_c @ A2 @ B2 ) )
% 0.25/0.59 & ( P @ X3 ) ) )
% 0.25/0.59 = ( ? [X3: sum_sum_c_c] :
% 0.25/0.59 ( ( member_Sum_sum_c_c @ X3 @ A2 )
% 0.25/0.59 & ( P @ X3 ) )
% 0.25/0.59 | ? [X3: sum_sum_c_c] :
% 0.25/0.59 ( ( member_Sum_sum_c_c @ X3 @ B2 )
% 0.25/0.59 & ( P @ X3 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % bex_Un
% 0.25/0.59 thf(fact_217_UnI2,axiom,
% 0.25/0.59 ! [C: produc640052711real_c,B2: set_Pr754230471real_c,A2: set_Pr754230471real_c] :
% 0.25/0.59 ( ( member346808080real_c @ C @ B2 )
% 0.25/0.59 => ( member346808080real_c @ C @ ( sup_su588839579real_c @ A2 @ B2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % UnI2
% 0.25/0.59 thf(fact_218_UnI2,axiom,
% 0.25/0.59 ! [C: sum_sum_c_c,B2: set_Sum_sum_c_c,A2: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( member_Sum_sum_c_c @ C @ B2 )
% 0.25/0.59 => ( member_Sum_sum_c_c @ C @ ( sup_su1349021703um_c_c @ A2 @ B2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % UnI2
% 0.25/0.59 thf(fact_219_UnI1,axiom,
% 0.25/0.59 ! [C: produc640052711real_c,A2: set_Pr754230471real_c,B2: set_Pr754230471real_c] :
% 0.25/0.59 ( ( member346808080real_c @ C @ A2 )
% 0.25/0.59 => ( member346808080real_c @ C @ ( sup_su588839579real_c @ A2 @ B2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % UnI1
% 0.25/0.59 thf(fact_220_UnI1,axiom,
% 0.25/0.59 ! [C: sum_sum_c_c,A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( member_Sum_sum_c_c @ C @ A2 )
% 0.25/0.59 => ( member_Sum_sum_c_c @ C @ ( sup_su1349021703um_c_c @ A2 @ B2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % UnI1
% 0.25/0.59 thf(fact_221_UnE,axiom,
% 0.25/0.59 ! [C: produc640052711real_c,A2: set_Pr754230471real_c,B2: set_Pr754230471real_c] :
% 0.25/0.59 ( ( member346808080real_c @ C @ ( sup_su588839579real_c @ A2 @ B2 ) )
% 0.25/0.59 => ( ~ ( member346808080real_c @ C @ A2 )
% 0.25/0.59 => ( member346808080real_c @ C @ B2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % UnE
% 0.25/0.59 thf(fact_222_UnE,axiom,
% 0.25/0.59 ! [C: sum_sum_c_c,A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( member_Sum_sum_c_c @ C @ ( sup_su1349021703um_c_c @ A2 @ B2 ) )
% 0.25/0.59 => ( ~ ( member_Sum_sum_c_c @ C @ A2 )
% 0.25/0.59 => ( member_Sum_sum_c_c @ C @ B2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % UnE
% 0.25/0.59 thf(fact_223_IA,axiom,
% 0.25/0.59 denota69106024_a_b_c @ i @ j @ ( static_SIGP_a_b_c @ ( choice_a_b_c @ a @ b ) ) ).
% 0.25/0.59
% 0.25/0.59 % IA
% 0.25/0.59 thf(fact_224_IH1,axiom,
% 0.25/0.59 ! [I: denota231621370t_unit,J: denota231621370t_unit] :
% 0.25/0.59 ( ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,Mu2: produc190496183real_c,V: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( denota69106024_a_b_c @ I @ J @ ( static_SIGP_a_b_c @ a ) )
% 0.25/0.59 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ V )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ ( static_FVP_a_b_c @ a ) @ V )
% 0.25/0.59 => ( ( member346808080real_c @ ( produc1687028567real_c @ Nu @ Mu2 ) @ ( denota904684656_a_b_c @ I @ a ) )
% 0.25/0.59 => ? [Mu3: produc190496183real_c] :
% 0.25/0.59 ( ( member346808080real_c @ ( produc1687028567real_c @ Nu2 @ Mu3 ) @ ( denota904684656_a_b_c @ J @ a ) )
% 0.25/0.59 & ( denota1997846518gree_c @ Mu2 @ Mu3 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ a ) @ V ) ) ) ) ) ) )
% 0.25/0.59 & ( coinci772602909_a_b_c @ a @ I ) ) ).
% 0.25/0.59
% 0.25/0.59 % IH1
% 0.25/0.59 thf(fact_225_IH2,axiom,
% 0.25/0.59 ! [I: denota231621370t_unit,J: denota231621370t_unit] :
% 0.25/0.59 ( ! [Nu: produc190496183real_c,Nu2: produc190496183real_c,Mu2: produc190496183real_c,V: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( denota69106024_a_b_c @ I @ J @ ( static_SIGP_a_b_c @ b ) )
% 0.25/0.59 => ( ( denota1997846518gree_c @ Nu @ Nu2 @ V )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ ( static_FVP_a_b_c @ b ) @ V )
% 0.25/0.59 => ( ( member346808080real_c @ ( produc1687028567real_c @ Nu @ Mu2 ) @ ( denota904684656_a_b_c @ I @ b ) )
% 0.25/0.59 => ? [Mu3: produc190496183real_c] :
% 0.25/0.59 ( ( member346808080real_c @ ( produc1687028567real_c @ Nu2 @ Mu3 ) @ ( denota904684656_a_b_c @ J @ b ) )
% 0.25/0.59 & ( denota1997846518gree_c @ Mu2 @ Mu3 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ b ) @ V ) ) ) ) ) ) )
% 0.25/0.59 & ( coinci772602909_a_b_c @ b @ I ) ) ).
% 0.25/0.59
% 0.25/0.59 % IH2
% 0.25/0.59 thf(fact_226_coincide__hp_H__def,axiom,
% 0.25/0.59 ( coinci1852866155_a_b_c
% 0.25/0.59 = ( ^ [Alpha: hp_a_b_c] :
% 0.25/0.59 ! [I2: denota231621370t_unit,J2: denota231621370t_unit] :
% 0.25/0.59 ( ( coinci354700372_a_b_c @ Alpha @ I2 @ J2 )
% 0.25/0.59 & ( coinci772602909_a_b_c @ Alpha @ I2 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % coincide_hp'_def
% 0.25/0.59 thf(fact_227_FVP_Osimps_I6_J,axiom,
% 0.25/0.59 ! [Alpha2: hp_a_b_c,Beta: hp_a_b_c] :
% 0.25/0.59 ( ( static_FVP_a_b_c @ ( choice_a_b_c @ Alpha2 @ Beta ) )
% 0.25/0.59 = ( sup_su1349021703um_c_c @ ( static_FVP_a_b_c @ Alpha2 ) @ ( static_FVP_a_b_c @ Beta ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % FVP.simps(6)
% 0.25/0.59 thf(fact_228_agree__supset,axiom,
% 0.25/0.59 ! [B2: set_Sum_sum_c_c,A2: set_Sum_sum_c_c,Nu3: produc190496183real_c,Nu4: produc190496183real_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ B2 @ A2 )
% 0.25/0.59 => ( ( denota1997846518gree_c @ Nu3 @ Nu4 @ A2 )
% 0.25/0.59 => ( denota1997846518gree_c @ Nu3 @ Nu4 @ B2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % agree_supset
% 0.25/0.59 thf(fact_229_agree__sub,axiom,
% 0.25/0.59 ! [A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c,Nu3: produc190496183real_c,Omega: produc190496183real_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ A2 @ B2 )
% 0.25/0.59 => ( ( denota1997846518gree_c @ Nu3 @ Omega @ B2 )
% 0.25/0.59 => ( denota1997846518gree_c @ Nu3 @ Omega @ A2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % agree_sub
% 0.25/0.59 thf(fact_230_old_Oprod_Oinject,axiom,
% 0.25/0.59 ! [A: produc190496183real_c,B: produc190496183real_c,A6: produc190496183real_c,B6: produc190496183real_c] :
% 0.25/0.59 ( ( ( produc1687028567real_c @ A @ B )
% 0.25/0.59 = ( produc1687028567real_c @ A6 @ B6 ) )
% 0.25/0.59 = ( ( A = A6 )
% 0.25/0.59 & ( B = B6 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % old.prod.inject
% 0.25/0.59 thf(fact_231_old_Oprod_Oinject,axiom,
% 0.25/0.59 ! [A: finite1398487019real_c,B: finite1398487019real_c,A6: finite1398487019real_c,B6: finite1398487019real_c] :
% 0.25/0.59 ( ( ( produc394644079real_c @ A @ B )
% 0.25/0.59 = ( produc394644079real_c @ A6 @ B6 ) )
% 0.25/0.59 = ( ( A = A6 )
% 0.25/0.59 & ( B = B6 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % old.prod.inject
% 0.25/0.59 thf(fact_232_prod_Oinject,axiom,
% 0.25/0.59 ! [X1: produc190496183real_c,X22: produc190496183real_c,Y1: produc190496183real_c,Y22: produc190496183real_c] :
% 0.25/0.59 ( ( ( produc1687028567real_c @ X1 @ X22 )
% 0.25/0.59 = ( produc1687028567real_c @ Y1 @ Y22 ) )
% 0.25/0.59 = ( ( X1 = Y1 )
% 0.25/0.59 & ( X22 = Y22 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % prod.inject
% 0.25/0.59 thf(fact_233_prod_Oinject,axiom,
% 0.25/0.59 ! [X1: finite1398487019real_c,X22: finite1398487019real_c,Y1: finite1398487019real_c,Y22: finite1398487019real_c] :
% 0.25/0.59 ( ( ( produc394644079real_c @ X1 @ X22 )
% 0.25/0.59 = ( produc394644079real_c @ Y1 @ Y22 ) )
% 0.25/0.59 = ( ( X1 = Y1 )
% 0.25/0.59 & ( X22 = Y22 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % prod.inject
% 0.25/0.59 thf(fact_234_order__refl,axiom,
% 0.25/0.59 ! [X: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ X @ X ) ).
% 0.25/0.59
% 0.25/0.59 % order_refl
% 0.25/0.59 thf(fact_235_order__refl,axiom,
% 0.25/0.59 ! [X: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ X @ X ) ).
% 0.25/0.59
% 0.25/0.59 % order_refl
% 0.25/0.59 thf(fact_236_Ssub_I2_J,axiom,
% 0.25/0.59 ord_le929608341um_b_c @ ( static_SIGP_a_b_c @ b ) @ ( static_SIGP_a_b_c @ ( choice_a_b_c @ a @ b ) ) ).
% 0.25/0.59
% 0.25/0.59 % Ssub(2)
% 0.25/0.59 thf(fact_237_Ssub_I1_J,axiom,
% 0.25/0.59 ord_le929608341um_b_c @ ( static_SIGP_a_b_c @ a ) @ ( static_SIGP_a_b_c @ ( choice_a_b_c @ a @ b ) ) ).
% 0.25/0.59
% 0.25/0.59 % Ssub(1)
% 0.25/0.59 thf(fact_238_IA2,axiom,
% 0.25/0.59 denota69106024_a_b_c @ i @ j @ ( static_SIGP_a_b_c @ b ) ).
% 0.25/0.59
% 0.25/0.59 % IA2
% 0.25/0.59 thf(fact_239_IA1,axiom,
% 0.25/0.59 denota69106024_a_b_c @ i @ j @ ( static_SIGP_a_b_c @ a ) ).
% 0.25/0.59
% 0.25/0.59 % IA1
% 0.25/0.59 thf(fact_240_coincide__hp__def,axiom,
% 0.25/0.59 ( coinci354700372_a_b_c
% 0.25/0.59 = ( ^ [Alpha: hp_a_b_c,I2: denota231621370t_unit,J2: denota231621370t_unit] :
% 0.25/0.59 ! [Nu5: produc190496183real_c,Nu6: produc190496183real_c,Mu4: produc190496183real_c,V2: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( denota69106024_a_b_c @ I2 @ J2 @ ( static_SIGP_a_b_c @ Alpha ) )
% 0.25/0.59 => ( ( denota1997846518gree_c @ Nu5 @ Nu6 @ V2 )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ ( static_FVP_a_b_c @ Alpha ) @ V2 )
% 0.25/0.59 => ( ( member346808080real_c @ ( produc1687028567real_c @ Nu5 @ Mu4 ) @ ( denota904684656_a_b_c @ I2 @ Alpha ) )
% 0.25/0.59 => ? [Mu5: produc190496183real_c] :
% 0.25/0.59 ( ( member346808080real_c @ ( produc1687028567real_c @ Nu6 @ Mu5 ) @ ( denota904684656_a_b_c @ J2 @ Alpha ) )
% 0.25/0.59 & ( denota1997846518gree_c @ Mu4 @ Mu5 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ Alpha ) @ V2 ) ) ) ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % coincide_hp_def
% 0.25/0.59 thf(fact_241_Iagree__sub,axiom,
% 0.25/0.59 ! [A2: set_Su1783761653um_b_c,B2: set_Su1783761653um_b_c,I3: denota231621370t_unit,J3: denota231621370t_unit] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ A2 @ B2 )
% 0.25/0.59 => ( ( denota69106024_a_b_c @ I3 @ J3 @ B2 )
% 0.25/0.59 => ( denota69106024_a_b_c @ I3 @ J3 @ A2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Iagree_sub
% 0.25/0.59 thf(fact_242_Iagree__refl,axiom,
% 0.25/0.59 ! [I3: denota231621370t_unit,A2: set_Su1783761653um_b_c] : ( denota69106024_a_b_c @ I3 @ I3 @ A2 ) ).
% 0.25/0.59
% 0.25/0.59 % Iagree_refl
% 0.25/0.59 thf(fact_243_Iagree__comm,axiom,
% 0.25/0.59 ! [A2: denota231621370t_unit,B2: denota231621370t_unit,V3: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( denota69106024_a_b_c @ A2 @ B2 @ V3 )
% 0.25/0.59 => ( denota69106024_a_b_c @ B2 @ A2 @ V3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % Iagree_comm
% 0.25/0.59 thf(fact_244_SIGP_Osimps_I6_J,axiom,
% 0.25/0.59 ! [A: hp_a_b_c,B: hp_a_b_c] :
% 0.25/0.59 ( ( static_SIGP_a_b_c @ ( choice_a_b_c @ A @ B ) )
% 0.25/0.59 = ( sup_su1968964297um_b_c @ ( static_SIGP_a_b_c @ A ) @ ( static_SIGP_a_b_c @ B ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % SIGP.simps(6)
% 0.25/0.59 thf(fact_245_dual__order_Oantisym,axiom,
% 0.25/0.59 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ B @ A )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ A @ B )
% 0.25/0.59 => ( A = B ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % dual_order.antisym
% 0.25/0.59 thf(fact_246_dual__order_Oantisym,axiom,
% 0.25/0.59 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ B @ A )
% 0.25/0.59 => ( ( ord_le929608341um_b_c @ A @ B )
% 0.25/0.59 => ( A = B ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % dual_order.antisym
% 0.25/0.59 thf(fact_247_dual__order_Oeq__iff,axiom,
% 0.25/0.59 ( ( ^ [Y2: set_Sum_sum_c_c,Z2: set_Sum_sum_c_c] : ( Y2 = Z2 ) )
% 0.25/0.59 = ( ^ [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ B4 @ A4 )
% 0.25/0.59 & ( ord_le1772180283um_c_c @ A4 @ B4 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % dual_order.eq_iff
% 0.25/0.59 thf(fact_248_dual__order_Oeq__iff,axiom,
% 0.25/0.59 ( ( ^ [Y2: set_Su1783761653um_b_c,Z2: set_Su1783761653um_b_c] : ( Y2 = Z2 ) )
% 0.25/0.59 = ( ^ [A4: set_Su1783761653um_b_c,B4: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ B4 @ A4 )
% 0.25/0.59 & ( ord_le929608341um_b_c @ A4 @ B4 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % dual_order.eq_iff
% 0.25/0.59 thf(fact_249_dual__order_Otrans,axiom,
% 0.25/0.59 ! [B: set_Sum_sum_c_c,A: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ B @ A )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ C @ B )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ C @ A ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % dual_order.trans
% 0.25/0.59 thf(fact_250_dual__order_Otrans,axiom,
% 0.25/0.59 ! [B: set_Su1783761653um_b_c,A: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ B @ A )
% 0.25/0.59 => ( ( ord_le929608341um_b_c @ C @ B )
% 0.25/0.59 => ( ord_le929608341um_b_c @ C @ A ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % dual_order.trans
% 0.25/0.59 thf(fact_251_dual__order_Orefl,axiom,
% 0.25/0.59 ! [A: set_Sum_sum_c_c] : ( ord_le1772180283um_c_c @ A @ A ) ).
% 0.25/0.59
% 0.25/0.59 % dual_order.refl
% 0.25/0.59 thf(fact_252_dual__order_Orefl,axiom,
% 0.25/0.59 ! [A: set_Su1783761653um_b_c] : ( ord_le929608341um_b_c @ A @ A ) ).
% 0.25/0.59
% 0.25/0.59 % dual_order.refl
% 0.25/0.59 thf(fact_253_order__trans,axiom,
% 0.25/0.59 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c,Z: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ X @ Y )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ Y @ Z )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ X @ Z ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % order_trans
% 0.25/0.59 thf(fact_254_order__trans,axiom,
% 0.25/0.59 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c,Z: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ X @ Y )
% 0.25/0.59 => ( ( ord_le929608341um_b_c @ Y @ Z )
% 0.25/0.59 => ( ord_le929608341um_b_c @ X @ Z ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % order_trans
% 0.25/0.59 thf(fact_255_order__class_Oorder_Oantisym,axiom,
% 0.25/0.59 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ A @ B )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ B @ A )
% 0.25/0.59 => ( A = B ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % order_class.order.antisym
% 0.25/0.59 thf(fact_256_order__class_Oorder_Oantisym,axiom,
% 0.25/0.59 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ A @ B )
% 0.25/0.59 => ( ( ord_le929608341um_b_c @ B @ A )
% 0.25/0.59 => ( A = B ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % order_class.order.antisym
% 0.25/0.59 thf(fact_257_ord__le__eq__trans,axiom,
% 0.25/0.59 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ A @ B )
% 0.25/0.59 => ( ( B = C )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ A @ C ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % ord_le_eq_trans
% 0.25/0.59 thf(fact_258_ord__le__eq__trans,axiom,
% 0.25/0.59 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ A @ B )
% 0.25/0.59 => ( ( B = C )
% 0.25/0.59 => ( ord_le929608341um_b_c @ A @ C ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % ord_le_eq_trans
% 0.25/0.59 thf(fact_259_ord__eq__le__trans,axiom,
% 0.25/0.59 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( A = B )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ B @ C )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ A @ C ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % ord_eq_le_trans
% 0.25/0.59 thf(fact_260_ord__eq__le__trans,axiom,
% 0.25/0.59 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( A = B )
% 0.25/0.59 => ( ( ord_le929608341um_b_c @ B @ C )
% 0.25/0.59 => ( ord_le929608341um_b_c @ A @ C ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % ord_eq_le_trans
% 0.25/0.59 thf(fact_261_order__class_Oorder_Oeq__iff,axiom,
% 0.25/0.59 ( ( ^ [Y2: set_Sum_sum_c_c,Z2: set_Sum_sum_c_c] : ( Y2 = Z2 ) )
% 0.25/0.59 = ( ^ [A4: set_Sum_sum_c_c,B4: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ A4 @ B4 )
% 0.25/0.59 & ( ord_le1772180283um_c_c @ B4 @ A4 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % order_class.order.eq_iff
% 0.25/0.59 thf(fact_262_order__class_Oorder_Oeq__iff,axiom,
% 0.25/0.59 ( ( ^ [Y2: set_Su1783761653um_b_c,Z2: set_Su1783761653um_b_c] : ( Y2 = Z2 ) )
% 0.25/0.59 = ( ^ [A4: set_Su1783761653um_b_c,B4: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ A4 @ B4 )
% 0.25/0.59 & ( ord_le929608341um_b_c @ B4 @ A4 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % order_class.order.eq_iff
% 0.25/0.59 thf(fact_263_antisym__conv,axiom,
% 0.25/0.59 ! [Y: set_Sum_sum_c_c,X: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ Y @ X )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ X @ Y )
% 0.25/0.59 = ( X = Y ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % antisym_conv
% 0.25/0.59 thf(fact_264_antisym__conv,axiom,
% 0.25/0.59 ! [Y: set_Su1783761653um_b_c,X: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ Y @ X )
% 0.25/0.59 => ( ( ord_le929608341um_b_c @ X @ Y )
% 0.25/0.59 = ( X = Y ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % antisym_conv
% 0.25/0.59 thf(fact_265_order_Otrans,axiom,
% 0.25/0.59 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ A @ B )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ B @ C )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ A @ C ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % order.trans
% 0.25/0.59 thf(fact_266_order_Otrans,axiom,
% 0.25/0.59 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ A @ B )
% 0.25/0.59 => ( ( ord_le929608341um_b_c @ B @ C )
% 0.25/0.59 => ( ord_le929608341um_b_c @ A @ C ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % order.trans
% 0.25/0.59 thf(fact_267_eq__refl,axiom,
% 0.25/0.59 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( X = Y )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ X @ Y ) ) ).
% 0.25/0.59
% 0.25/0.59 % eq_refl
% 0.25/0.59 thf(fact_268_eq__refl,axiom,
% 0.25/0.59 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( X = Y )
% 0.25/0.59 => ( ord_le929608341um_b_c @ X @ Y ) ) ).
% 0.25/0.59
% 0.25/0.59 % eq_refl
% 0.25/0.59 thf(fact_269_antisym,axiom,
% 0.25/0.59 ! [X: set_Sum_sum_c_c,Y: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ X @ Y )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ Y @ X )
% 0.25/0.59 => ( X = Y ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % antisym
% 0.25/0.59 thf(fact_270_antisym,axiom,
% 0.25/0.59 ! [X: set_Su1783761653um_b_c,Y: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ X @ Y )
% 0.25/0.59 => ( ( ord_le929608341um_b_c @ Y @ X )
% 0.25/0.59 => ( X = Y ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % antisym
% 0.25/0.59 thf(fact_271_eq__iff,axiom,
% 0.25/0.59 ( ( ^ [Y2: set_Sum_sum_c_c,Z2: set_Sum_sum_c_c] : ( Y2 = Z2 ) )
% 0.25/0.59 = ( ^ [X3: set_Sum_sum_c_c,Y5: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ X3 @ Y5 )
% 0.25/0.59 & ( ord_le1772180283um_c_c @ Y5 @ X3 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % eq_iff
% 0.25/0.59 thf(fact_272_eq__iff,axiom,
% 0.25/0.59 ( ( ^ [Y2: set_Su1783761653um_b_c,Z2: set_Su1783761653um_b_c] : ( Y2 = Z2 ) )
% 0.25/0.59 = ( ^ [X3: set_Su1783761653um_b_c,Y5: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ X3 @ Y5 )
% 0.25/0.59 & ( ord_le929608341um_b_c @ Y5 @ X3 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % eq_iff
% 0.25/0.59 thf(fact_273_ord__le__eq__subst,axiom,
% 0.25/0.59 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,F: set_Sum_sum_c_c > set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ A @ B )
% 0.25/0.59 => ( ( ( F @ B )
% 0.25/0.59 = C )
% 0.25/0.59 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ ( F @ A ) @ C ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % ord_le_eq_subst
% 0.25/0.59 thf(fact_274_ord__le__eq__subst,axiom,
% 0.25/0.59 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,F: set_Sum_sum_c_c > set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ A @ B )
% 0.25/0.59 => ( ( ( F @ B )
% 0.25/0.59 = C )
% 0.25/0.59 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 0.25/0.59 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.25/0.59 => ( ord_le929608341um_b_c @ ( F @ A ) @ C ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % ord_le_eq_subst
% 0.25/0.59 thf(fact_275_ord__le__eq__subst,axiom,
% 0.25/0.59 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,F: set_Su1783761653um_b_c > set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ A @ B )
% 0.25/0.59 => ( ( ( F @ B )
% 0.25/0.59 = C )
% 0.25/0.59 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ ( F @ A ) @ C ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % ord_le_eq_subst
% 0.25/0.59 thf(fact_276_ord__le__eq__subst,axiom,
% 0.25/0.59 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,F: set_Su1783761653um_b_c > set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ A @ B )
% 0.25/0.59 => ( ( ( F @ B )
% 0.25/0.59 = C )
% 0.25/0.59 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 0.25/0.59 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.25/0.59 => ( ord_le929608341um_b_c @ ( F @ A ) @ C ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % ord_le_eq_subst
% 0.25/0.59 thf(fact_277_ord__eq__le__subst,axiom,
% 0.25/0.59 ! [A: set_Sum_sum_c_c,F: set_Sum_sum_c_c > set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( A
% 0.25/0.59 = ( F @ B ) )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ B @ C )
% 0.25/0.59 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ A @ ( F @ C ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % ord_eq_le_subst
% 0.25/0.59 thf(fact_278_ord__eq__le__subst,axiom,
% 0.25/0.59 ! [A: set_Su1783761653um_b_c,F: set_Sum_sum_c_c > set_Su1783761653um_b_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( A
% 0.25/0.59 = ( F @ B ) )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ B @ C )
% 0.25/0.59 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 0.25/0.59 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.25/0.59 => ( ord_le929608341um_b_c @ A @ ( F @ C ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % ord_eq_le_subst
% 0.25/0.59 thf(fact_279_ord__eq__le__subst,axiom,
% 0.25/0.59 ! [A: set_Sum_sum_c_c,F: set_Su1783761653um_b_c > set_Sum_sum_c_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( A
% 0.25/0.59 = ( F @ B ) )
% 0.25/0.59 => ( ( ord_le929608341um_b_c @ B @ C )
% 0.25/0.59 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ A @ ( F @ C ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % ord_eq_le_subst
% 0.25/0.59 thf(fact_280_ord__eq__le__subst,axiom,
% 0.25/0.59 ! [A: set_Su1783761653um_b_c,F: set_Su1783761653um_b_c > set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( A
% 0.25/0.59 = ( F @ B ) )
% 0.25/0.59 => ( ( ord_le929608341um_b_c @ B @ C )
% 0.25/0.59 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 0.25/0.59 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.25/0.59 => ( ord_le929608341um_b_c @ A @ ( F @ C ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % ord_eq_le_subst
% 0.25/0.59 thf(fact_281_order__subst2,axiom,
% 0.25/0.59 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,F: set_Sum_sum_c_c > set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ A @ B )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ ( F @ B ) @ C )
% 0.25/0.59 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ ( F @ A ) @ C ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % order_subst2
% 0.25/0.59 thf(fact_282_order__subst2,axiom,
% 0.25/0.59 ! [A: set_Sum_sum_c_c,B: set_Sum_sum_c_c,F: set_Sum_sum_c_c > set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ A @ B )
% 0.25/0.59 => ( ( ord_le929608341um_b_c @ ( F @ B ) @ C )
% 0.25/0.59 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 0.25/0.59 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.25/0.59 => ( ord_le929608341um_b_c @ ( F @ A ) @ C ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % order_subst2
% 0.25/0.59 thf(fact_283_order__subst2,axiom,
% 0.25/0.59 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,F: set_Su1783761653um_b_c > set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ A @ B )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ ( F @ B ) @ C )
% 0.25/0.59 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ ( F @ A ) @ C ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % order_subst2
% 0.25/0.59 thf(fact_284_order__subst2,axiom,
% 0.25/0.59 ! [A: set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,F: set_Su1783761653um_b_c > set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ A @ B )
% 0.25/0.59 => ( ( ord_le929608341um_b_c @ ( F @ B ) @ C )
% 0.25/0.59 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 0.25/0.59 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.25/0.59 => ( ord_le929608341um_b_c @ ( F @ A ) @ C ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % order_subst2
% 0.25/0.59 thf(fact_285_order__subst1,axiom,
% 0.25/0.59 ! [A: set_Sum_sum_c_c,F: set_Sum_sum_c_c > set_Sum_sum_c_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ A @ ( F @ B ) )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ B @ C )
% 0.25/0.59 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ A @ ( F @ C ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % order_subst1
% 0.25/0.59 thf(fact_286_order__subst1,axiom,
% 0.25/0.59 ! [A: set_Sum_sum_c_c,F: set_Su1783761653um_b_c > set_Sum_sum_c_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ A @ ( F @ B ) )
% 0.25/0.59 => ( ( ord_le929608341um_b_c @ B @ C )
% 0.25/0.59 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ A @ ( F @ C ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % order_subst1
% 0.25/0.59 thf(fact_287_order__subst1,axiom,
% 0.25/0.59 ! [A: set_Su1783761653um_b_c,F: set_Sum_sum_c_c > set_Su1783761653um_b_c,B: set_Sum_sum_c_c,C: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ A @ ( F @ B ) )
% 0.25/0.59 => ( ( ord_le1772180283um_c_c @ B @ C )
% 0.25/0.59 => ( ! [X2: set_Sum_sum_c_c,Y4: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ X2 @ Y4 )
% 0.25/0.59 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.25/0.59 => ( ord_le929608341um_b_c @ A @ ( F @ C ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % order_subst1
% 0.25/0.59 thf(fact_288_order__subst1,axiom,
% 0.25/0.59 ! [A: set_Su1783761653um_b_c,F: set_Su1783761653um_b_c > set_Su1783761653um_b_c,B: set_Su1783761653um_b_c,C: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ A @ ( F @ B ) )
% 0.25/0.59 => ( ( ord_le929608341um_b_c @ B @ C )
% 0.25/0.59 => ( ! [X2: set_Su1783761653um_b_c,Y4: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ X2 @ Y4 )
% 0.25/0.59 => ( ord_le929608341um_b_c @ ( F @ X2 ) @ ( F @ Y4 ) ) )
% 0.25/0.59 => ( ord_le929608341um_b_c @ A @ ( F @ C ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % order_subst1
% 0.25/0.59 thf(fact_289_surj__pair,axiom,
% 0.25/0.59 ! [P2: produc640052711real_c] :
% 0.25/0.59 ? [X2: produc190496183real_c,Y4: produc190496183real_c] :
% 0.25/0.59 ( P2
% 0.25/0.59 = ( produc1687028567real_c @ X2 @ Y4 ) ) ).
% 0.25/0.59
% 0.25/0.59 % surj_pair
% 0.25/0.59 thf(fact_290_surj__pair,axiom,
% 0.25/0.59 ! [P2: produc190496183real_c] :
% 0.25/0.59 ? [X2: finite1398487019real_c,Y4: finite1398487019real_c] :
% 0.25/0.59 ( P2
% 0.25/0.59 = ( produc394644079real_c @ X2 @ Y4 ) ) ).
% 0.25/0.59
% 0.25/0.59 % surj_pair
% 0.25/0.59 thf(fact_291_prod__cases,axiom,
% 0.25/0.59 ! [P: produc640052711real_c > $o,P2: produc640052711real_c] :
% 0.25/0.59 ( ! [A7: produc190496183real_c,B7: produc190496183real_c] : ( P @ ( produc1687028567real_c @ A7 @ B7 ) )
% 0.25/0.59 => ( P @ P2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % prod_cases
% 0.25/0.59 thf(fact_292_prod__cases,axiom,
% 0.25/0.59 ! [P: produc190496183real_c > $o,P2: produc190496183real_c] :
% 0.25/0.59 ( ! [A7: finite1398487019real_c,B7: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A7 @ B7 ) )
% 0.25/0.59 => ( P @ P2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % prod_cases
% 0.25/0.59 thf(fact_293_Pair__inject,axiom,
% 0.25/0.59 ! [A: produc190496183real_c,B: produc190496183real_c,A6: produc190496183real_c,B6: produc190496183real_c] :
% 0.25/0.59 ( ( ( produc1687028567real_c @ A @ B )
% 0.25/0.59 = ( produc1687028567real_c @ A6 @ B6 ) )
% 0.25/0.59 => ~ ( ( A = A6 )
% 0.25/0.59 => ( B != B6 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Pair_inject
% 0.25/0.59 thf(fact_294_Pair__inject,axiom,
% 0.25/0.59 ! [A: finite1398487019real_c,B: finite1398487019real_c,A6: finite1398487019real_c,B6: finite1398487019real_c] :
% 0.25/0.59 ( ( ( produc394644079real_c @ A @ B )
% 0.25/0.59 = ( produc394644079real_c @ A6 @ B6 ) )
% 0.25/0.59 => ~ ( ( A = A6 )
% 0.25/0.59 => ( B != B6 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Pair_inject
% 0.25/0.59 thf(fact_295_old_Oprod_Oexhaust,axiom,
% 0.25/0.59 ! [Y: produc640052711real_c] :
% 0.25/0.59 ~ ! [A7: produc190496183real_c,B7: produc190496183real_c] :
% 0.25/0.59 ( Y
% 0.25/0.59 != ( produc1687028567real_c @ A7 @ B7 ) ) ).
% 0.25/0.59
% 0.25/0.59 % old.prod.exhaust
% 0.25/0.59 thf(fact_296_old_Oprod_Oexhaust,axiom,
% 0.25/0.59 ! [Y: produc190496183real_c] :
% 0.25/0.59 ~ ! [A7: finite1398487019real_c,B7: finite1398487019real_c] :
% 0.25/0.59 ( Y
% 0.25/0.59 != ( produc394644079real_c @ A7 @ B7 ) ) ).
% 0.25/0.59
% 0.25/0.59 % old.prod.exhaust
% 0.25/0.59 thf(fact_297_old_Oprod_Oinducts,axiom,
% 0.25/0.59 ! [P: produc640052711real_c > $o,Prod: produc640052711real_c] :
% 0.25/0.59 ( ! [A7: produc190496183real_c,B7: produc190496183real_c] : ( P @ ( produc1687028567real_c @ A7 @ B7 ) )
% 0.25/0.59 => ( P @ Prod ) ) ).
% 0.25/0.59
% 0.25/0.59 % old.prod.inducts
% 0.25/0.59 thf(fact_298_old_Oprod_Oinducts,axiom,
% 0.25/0.59 ! [P: produc190496183real_c > $o,Prod: produc190496183real_c] :
% 0.25/0.59 ( ! [A7: finite1398487019real_c,B7: finite1398487019real_c] : ( P @ ( produc394644079real_c @ A7 @ B7 ) )
% 0.25/0.59 => ( P @ Prod ) ) ).
% 0.25/0.59
% 0.25/0.59 % old.prod.inducts
% 0.25/0.59 thf(fact_299_agree__comm,axiom,
% 0.25/0.59 ! [A2: produc190496183real_c,B2: produc190496183real_c,V3: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( denota1997846518gree_c @ A2 @ B2 @ V3 )
% 0.25/0.59 => ( denota1997846518gree_c @ B2 @ A2 @ V3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % agree_comm
% 0.25/0.59 thf(fact_300_agree__refl,axiom,
% 0.25/0.59 ! [Nu3: produc190496183real_c,A2: set_Sum_sum_c_c] : ( denota1997846518gree_c @ Nu3 @ Nu3 @ A2 ) ).
% 0.25/0.59
% 0.25/0.59 % agree_refl
% 0.25/0.59 thf(fact_301_prod__cases3,axiom,
% 0.25/0.59 ! [Y: produc640052711real_c] :
% 0.25/0.59 ~ ! [A7: produc190496183real_c,B7: finite1398487019real_c,C3: finite1398487019real_c] :
% 0.25/0.59 ( Y
% 0.25/0.59 != ( produc1687028567real_c @ A7 @ ( produc394644079real_c @ B7 @ C3 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % prod_cases3
% 0.25/0.59 thf(fact_302_prod__induct3,axiom,
% 0.25/0.59 ! [P: produc640052711real_c > $o,X: produc640052711real_c] :
% 0.25/0.59 ( ! [A7: produc190496183real_c,B7: finite1398487019real_c,C3: finite1398487019real_c] : ( P @ ( produc1687028567real_c @ A7 @ ( produc394644079real_c @ B7 @ C3 ) ) )
% 0.25/0.59 => ( P @ X ) ) ).
% 0.25/0.59
% 0.25/0.59 % prod_induct3
% 0.25/0.59 thf(fact_303_agree__union,axiom,
% 0.25/0.59 ! [Nu3: produc190496183real_c,Omega: produc190496183real_c,A2: set_Sum_sum_c_c,B2: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( denota1997846518gree_c @ Nu3 @ Omega @ A2 )
% 0.25/0.59 => ( ( denota1997846518gree_c @ Nu3 @ Omega @ B2 )
% 0.25/0.59 => ( denota1997846518gree_c @ Nu3 @ Omega @ ( sup_su1349021703um_c_c @ A2 @ B2 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % agree_union
% 0.25/0.59 thf(fact_304_prog__sem_Osimps_I5_J,axiom,
% 0.25/0.59 ! [I3: denota231621370t_unit,Alpha2: hp_a_b_c,Beta: hp_a_b_c] :
% 0.25/0.59 ( ( denota904684656_a_b_c @ I3 @ ( choice_a_b_c @ Alpha2 @ Beta ) )
% 0.25/0.59 = ( sup_su588839579real_c @ ( denota904684656_a_b_c @ I3 @ Alpha2 ) @ ( denota904684656_a_b_c @ I3 @ Beta ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % prog_sem.simps(5)
% 0.25/0.59 thf(fact_305_same__fstI,axiom,
% 0.25/0.59 ! [P: produc190496183real_c > $o,X: produc190496183real_c,Y3: produc190496183real_c,Y: produc190496183real_c,R: produc190496183real_c > set_Pr754230471real_c] :
% 0.25/0.59 ( ( P @ X )
% 0.25/0.59 => ( ( member346808080real_c @ ( produc1687028567real_c @ Y3 @ Y ) @ ( R @ X ) )
% 0.25/0.59 => ( member616151824real_c @ ( produc544496471real_c @ ( produc1687028567real_c @ X @ Y3 ) @ ( produc1687028567real_c @ X @ Y ) ) @ ( same_f598810924real_c @ P @ R ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % same_fstI
% 0.25/0.59 thf(fact_306_same__fstI,axiom,
% 0.25/0.59 ! [P: finite1398487019real_c > $o,X: finite1398487019real_c,Y3: finite1398487019real_c,Y: finite1398487019real_c,R: finite1398487019real_c > set_Pr1389752855real_c] :
% 0.25/0.59 ( ( P @ X )
% 0.25/0.59 => ( ( member1895684704real_c @ ( produc394644079real_c @ Y3 @ Y ) @ ( R @ X ) )
% 0.25/0.59 => ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ X @ Y3 ) @ ( produc394644079real_c @ X @ Y ) ) @ ( same_f1974156740real_c @ P @ R ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % same_fstI
% 0.25/0.59 thf(fact_307_relChain__def,axiom,
% 0.25/0.59 ( bNF_Ca1667803246um_c_c
% 0.25/0.59 = ( ^ [R2: set_Pr754230471real_c,As: produc190496183real_c > set_Sum_sum_c_c] :
% 0.25/0.59 ! [I4: produc190496183real_c,J4: produc190496183real_c] :
% 0.25/0.59 ( ( member346808080real_c @ ( produc1687028567real_c @ I4 @ J4 ) @ R2 )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ ( As @ I4 ) @ ( As @ J4 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % relChain_def
% 0.25/0.59 thf(fact_308_relChain__def,axiom,
% 0.25/0.59 ( bNF_Ca1693016812um_c_c
% 0.25/0.59 = ( ^ [R2: set_Pr1389752855real_c,As: finite1398487019real_c > set_Sum_sum_c_c] :
% 0.25/0.59 ! [I4: finite1398487019real_c,J4: finite1398487019real_c] :
% 0.25/0.59 ( ( member1895684704real_c @ ( produc394644079real_c @ I4 @ J4 ) @ R2 )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ ( As @ I4 ) @ ( As @ J4 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % relChain_def
% 0.25/0.59 thf(fact_309_relChain__def,axiom,
% 0.25/0.59 ( bNF_Ca419199138um_b_c
% 0.25/0.59 = ( ^ [R2: set_Pr754230471real_c,As: produc190496183real_c > set_Su1783761653um_b_c] :
% 0.25/0.59 ! [I4: produc190496183real_c,J4: produc190496183real_c] :
% 0.25/0.59 ( ( member346808080real_c @ ( produc1687028567real_c @ I4 @ J4 ) @ R2 )
% 0.25/0.59 => ( ord_le929608341um_b_c @ ( As @ I4 ) @ ( As @ J4 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % relChain_def
% 0.25/0.59 thf(fact_310_relChain__def,axiom,
% 0.25/0.59 ( bNF_Ca318582436um_b_c
% 0.25/0.59 = ( ^ [R2: set_Pr1389752855real_c,As: finite1398487019real_c > set_Su1783761653um_b_c] :
% 0.25/0.59 ! [I4: finite1398487019real_c,J4: finite1398487019real_c] :
% 0.25/0.59 ( ( member1895684704real_c @ ( produc394644079real_c @ I4 @ J4 ) @ R2 )
% 0.25/0.59 => ( ord_le929608341um_b_c @ ( As @ I4 ) @ ( As @ J4 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % relChain_def
% 0.25/0.59 thf(fact_311_GreatestI2__order,axiom,
% 0.25/0.59 ! [P: set_Sum_sum_c_c > $o,X: set_Sum_sum_c_c,Q: set_Sum_sum_c_c > $o] :
% 0.25/0.59 ( ( P @ X )
% 0.25/0.59 => ( ! [Y4: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( P @ Y4 )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ Y4 @ X ) )
% 0.25/0.59 => ( ! [X2: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( P @ X2 )
% 0.25/0.59 => ( ! [Y6: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( P @ Y6 )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ Y6 @ X2 ) )
% 0.25/0.59 => ( Q @ X2 ) ) )
% 0.25/0.59 => ( Q @ ( order_1776530114um_c_c @ P ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % GreatestI2_order
% 0.25/0.59 thf(fact_312_GreatestI2__order,axiom,
% 0.25/0.59 ! [P: set_Su1783761653um_b_c > $o,X: set_Su1783761653um_b_c,Q: set_Su1783761653um_b_c > $o] :
% 0.25/0.59 ( ( P @ X )
% 0.25/0.59 => ( ! [Y4: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( P @ Y4 )
% 0.25/0.59 => ( ord_le929608341um_b_c @ Y4 @ X ) )
% 0.25/0.59 => ( ! [X2: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( P @ X2 )
% 0.25/0.59 => ( ! [Y6: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( P @ Y6 )
% 0.25/0.59 => ( ord_le929608341um_b_c @ Y6 @ X2 ) )
% 0.25/0.59 => ( Q @ X2 ) ) )
% 0.25/0.59 => ( Q @ ( order_365181262um_b_c @ P ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % GreatestI2_order
% 0.25/0.59 thf(fact_313_Greatest__equality,axiom,
% 0.25/0.59 ! [P: set_Sum_sum_c_c > $o,X: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( P @ X )
% 0.25/0.59 => ( ! [Y4: set_Sum_sum_c_c] :
% 0.25/0.59 ( ( P @ Y4 )
% 0.25/0.59 => ( ord_le1772180283um_c_c @ Y4 @ X ) )
% 0.25/0.59 => ( ( order_1776530114um_c_c @ P )
% 0.25/0.59 = X ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Greatest_equality
% 0.25/0.59 thf(fact_314_Greatest__equality,axiom,
% 0.25/0.59 ! [P: set_Su1783761653um_b_c > $o,X: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( P @ X )
% 0.25/0.59 => ( ! [Y4: set_Su1783761653um_b_c] :
% 0.25/0.59 ( ( P @ Y4 )
% 0.25/0.59 => ( ord_le929608341um_b_c @ Y4 @ X ) )
% 0.25/0.59 => ( ( order_365181262um_b_c @ P )
% 0.25/0.59 = X ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Greatest_equality
% 0.25/0.59 thf(fact_315_prod_Ocollapse,axiom,
% 0.25/0.59 ! [Prod: produc640052711real_c] :
% 0.25/0.59 ( ( produc1687028567real_c @ ( produc876006723real_c @ Prod ) @ ( produc415593093real_c @ Prod ) )
% 0.25/0.59 = Prod ) ).
% 0.25/0.59
% 0.25/0.59 % prod.collapse
% 0.25/0.59 thf(fact_316_prod_Ocollapse,axiom,
% 0.25/0.59 ! [Prod: produc190496183real_c] :
% 0.25/0.59 ( ( produc394644079real_c @ ( produc2010422875real_c @ Prod ) @ ( produc314122909real_c @ Prod ) )
% 0.25/0.59 = Prod ) ).
% 0.25/0.59
% 0.25/0.59 % prod.collapse
% 0.25/0.59 thf(fact_317_less__eq__prod__def,axiom,
% 0.25/0.59 ( ord_le684454199um_c_c
% 0.25/0.59 = ( ^ [X3: produc214722967um_c_c,Y5: produc214722967um_c_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ ( produc1983230011um_c_c @ X3 ) @ ( produc1983230011um_c_c @ Y5 ) )
% 0.25/0.59 & ( ord_le1772180283um_c_c @ ( produc1132019837um_c_c @ X3 ) @ ( produc1132019837um_c_c @ Y5 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % less_eq_prod_def
% 0.25/0.59 thf(fact_318_less__eq__prod__def,axiom,
% 0.25/0.59 ( ord_le542695343um_b_c
% 0.25/0.59 = ( ^ [X3: produc263671631um_b_c,Y5: produc263671631um_b_c] :
% 0.25/0.59 ( ( ord_le1772180283um_c_c @ ( produc1758795157um_b_c @ X3 ) @ ( produc1758795157um_b_c @ Y5 ) )
% 0.25/0.59 & ( ord_le929608341um_b_c @ ( produc1193764051um_b_c @ X3 ) @ ( produc1193764051um_b_c @ Y5 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % less_eq_prod_def
% 0.25/0.59 thf(fact_319_less__eq__prod__def,axiom,
% 0.25/0.59 ( ord_le1852514783um_c_c
% 0.25/0.59 = ( ^ [X3: produc1573491071um_c_c,Y5: produc1573491071um_c_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ ( produc1455464333um_c_c @ X3 ) @ ( produc1455464333um_c_c @ Y5 ) )
% 0.25/0.59 & ( ord_le1772180283um_c_c @ ( produc890433227um_c_c @ X3 ) @ ( produc890433227um_c_c @ Y5 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % less_eq_prod_def
% 0.25/0.59 thf(fact_320_less__eq__prod__def,axiom,
% 0.25/0.59 ( ord_le907560199um_b_c
% 0.25/0.59 = ( ^ [X3: produc1415638375um_b_c,Y5: produc1415638375um_b_c] :
% 0.25/0.59 ( ( ord_le929608341um_b_c @ ( produc1961869763um_b_c @ X3 ) @ ( produc1961869763um_b_c @ Y5 ) )
% 0.25/0.59 & ( ord_le929608341um_b_c @ ( produc932426501um_b_c @ X3 ) @ ( produc932426501um_b_c @ Y5 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % less_eq_prod_def
% 0.25/0.59 thf(fact_321_sup__prod__def,axiom,
% 0.25/0.59 ( sup_su1399591867real_c
% 0.25/0.59 = ( ^ [X3: produc640052711real_c,Y5: produc640052711real_c] : ( produc1687028567real_c @ ( sup_su1639086475real_c @ ( produc876006723real_c @ X3 ) @ ( produc876006723real_c @ Y5 ) ) @ ( sup_su1639086475real_c @ ( produc415593093real_c @ X3 ) @ ( produc415593093real_c @ Y5 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % sup_prod_def
% 0.25/0.59 thf(fact_322_sup__prod__def,axiom,
% 0.25/0.59 ( sup_su1639086475real_c
% 0.25/0.59 = ( ^ [X3: produc190496183real_c,Y5: produc190496183real_c] : ( produc394644079real_c @ ( sup_su2141622551real_c @ ( produc2010422875real_c @ X3 ) @ ( produc2010422875real_c @ Y5 ) ) @ ( sup_su2141622551real_c @ ( produc314122909real_c @ X3 ) @ ( produc314122909real_c @ Y5 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % sup_prod_def
% 0.25/0.59 thf(fact_323_sup__prod__def,axiom,
% 0.25/0.59 ( sup_su1672617323um_c_c
% 0.25/0.59 = ( ^ [X3: produc214722967um_c_c,Y5: produc214722967um_c_c] : ( produc1439061071um_c_c @ ( sup_su1349021703um_c_c @ ( produc1983230011um_c_c @ X3 ) @ ( produc1983230011um_c_c @ Y5 ) ) @ ( sup_su1349021703um_c_c @ ( produc1132019837um_c_c @ X3 ) @ ( produc1132019837um_c_c @ Y5 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % sup_prod_def
% 0.25/0.59 thf(fact_324_fst__conv,axiom,
% 0.25/0.59 ! [X1: produc190496183real_c,X22: produc190496183real_c] :
% 0.25/0.59 ( ( produc876006723real_c @ ( produc1687028567real_c @ X1 @ X22 ) )
% 0.25/0.59 = X1 ) ).
% 0.25/0.59
% 0.25/0.59 % fst_conv
% 0.25/0.59 thf(fact_325_fst__conv,axiom,
% 0.25/0.59 ! [X1: finite1398487019real_c,X22: finite1398487019real_c] :
% 0.25/0.59 ( ( produc2010422875real_c @ ( produc394644079real_c @ X1 @ X22 ) )
% 0.25/0.59 = X1 ) ).
% 0.25/0.59
% 0.25/0.59 % fst_conv
% 0.25/0.59 thf(fact_326_fst__eqD,axiom,
% 0.25/0.59 ! [X: produc190496183real_c,Y: produc190496183real_c,A: produc190496183real_c] :
% 0.25/0.59 ( ( ( produc876006723real_c @ ( produc1687028567real_c @ X @ Y ) )
% 0.25/0.59 = A )
% 0.25/0.59 => ( X = A ) ) ).
% 0.25/0.59
% 0.25/0.59 % fst_eqD
% 0.25/0.59 thf(fact_327_fst__eqD,axiom,
% 0.25/0.59 ! [X: finite1398487019real_c,Y: finite1398487019real_c,A: finite1398487019real_c] :
% 0.25/0.59 ( ( ( produc2010422875real_c @ ( produc394644079real_c @ X @ Y ) )
% 0.25/0.59 = A )
% 0.25/0.59 => ( X = A ) ) ).
% 0.25/0.59
% 0.25/0.59 % fst_eqD
% 0.25/0.59 thf(fact_328_snd__conv,axiom,
% 0.25/0.59 ! [X1: produc190496183real_c,X22: produc190496183real_c] :
% 0.25/0.59 ( ( produc415593093real_c @ ( produc1687028567real_c @ X1 @ X22 ) )
% 0.25/0.59 = X22 ) ).
% 0.25/0.59
% 0.25/0.59 % snd_conv
% 0.25/0.59 thf(fact_329_snd__conv,axiom,
% 0.25/0.59 ! [X1: finite1398487019real_c,X22: finite1398487019real_c] :
% 0.25/0.59 ( ( produc314122909real_c @ ( produc394644079real_c @ X1 @ X22 ) )
% 0.25/0.59 = X22 ) ).
% 0.25/0.59
% 0.25/0.59 % snd_conv
% 0.25/0.59 thf(fact_330_snd__eqD,axiom,
% 0.25/0.59 ! [X: produc190496183real_c,Y: produc190496183real_c,A: produc190496183real_c] :
% 0.25/0.59 ( ( ( produc415593093real_c @ ( produc1687028567real_c @ X @ Y ) )
% 0.25/0.59 = A )
% 0.25/0.59 => ( Y = A ) ) ).
% 0.25/0.59
% 0.25/0.59 % snd_eqD
% 0.25/0.59 thf(fact_331_snd__eqD,axiom,
% 0.25/0.59 ! [X: finite1398487019real_c,Y: finite1398487019real_c,A: finite1398487019real_c] :
% 0.25/0.59 ( ( ( produc314122909real_c @ ( produc394644079real_c @ X @ Y ) )
% 0.25/0.59 = A )
% 0.25/0.59 => ( Y = A ) ) ).
% 0.25/0.59
% 0.25/0.59 % snd_eqD
% 0.25/0.59 thf(fact_332_surjective__pairing,axiom,
% 0.25/0.59 ! [T2: produc640052711real_c] :
% 0.25/0.59 ( T2
% 0.25/0.59 = ( produc1687028567real_c @ ( produc876006723real_c @ T2 ) @ ( produc415593093real_c @ T2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % surjective_pairing
% 0.25/0.59 thf(fact_333_surjective__pairing,axiom,
% 0.25/0.59 ! [T2: produc190496183real_c] :
% 0.25/0.59 ( T2
% 0.25/0.59 = ( produc394644079real_c @ ( produc2010422875real_c @ T2 ) @ ( produc314122909real_c @ T2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % surjective_pairing
% 0.25/0.59 thf(fact_334_prod_Oexhaust__sel,axiom,
% 0.25/0.59 ! [Prod: produc640052711real_c] :
% 0.25/0.59 ( Prod
% 0.25/0.59 = ( produc1687028567real_c @ ( produc876006723real_c @ Prod ) @ ( produc415593093real_c @ Prod ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % prod.exhaust_sel
% 0.25/0.59 thf(fact_335_prod_Oexhaust__sel,axiom,
% 0.25/0.59 ! [Prod: produc190496183real_c] :
% 0.25/0.59 ( Prod
% 0.25/0.59 = ( produc394644079real_c @ ( produc2010422875real_c @ Prod ) @ ( produc314122909real_c @ Prod ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % prod.exhaust_sel
% 0.25/0.59 thf(fact_336_exI__realizer,axiom,
% 0.25/0.59 ! [P: produc190496183real_c > produc190496183real_c > $o,Y: produc190496183real_c,X: produc190496183real_c] :
% 0.25/0.59 ( ( P @ Y @ X )
% 0.25/0.59 => ( P @ ( produc415593093real_c @ ( produc1687028567real_c @ X @ Y ) ) @ ( produc876006723real_c @ ( produc1687028567real_c @ X @ Y ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % exI_realizer
% 0.25/0.59 thf(fact_337_exI__realizer,axiom,
% 0.25/0.59 ! [P: finite1398487019real_c > finite1398487019real_c > $o,Y: finite1398487019real_c,X: finite1398487019real_c] :
% 0.25/0.59 ( ( P @ Y @ X )
% 0.25/0.59 => ( P @ ( produc314122909real_c @ ( produc394644079real_c @ X @ Y ) ) @ ( produc2010422875real_c @ ( produc394644079real_c @ X @ Y ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % exI_realizer
% 0.25/0.59 thf(fact_338_conjI__realizer,axiom,
% 0.25/0.59 ! [P: produc190496183real_c > $o,P2: produc190496183real_c,Q: produc190496183real_c > $o,Q2: produc190496183real_c] :
% 0.25/0.59 ( ( P @ P2 )
% 0.25/0.59 => ( ( Q @ Q2 )
% 0.25/0.59 => ( ( P @ ( produc876006723real_c @ ( produc1687028567real_c @ P2 @ Q2 ) ) )
% 0.25/0.59 & ( Q @ ( produc415593093real_c @ ( produc1687028567real_c @ P2 @ Q2 ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % conjI_realizer
% 0.25/0.59 thf(fact_339_conjI__realizer,axiom,
% 0.25/0.59 ! [P: finite1398487019real_c > $o,P2: finite1398487019real_c,Q: finite1398487019real_c > $o,Q2: finite1398487019real_c] :
% 0.25/0.59 ( ( P @ P2 )
% 0.25/0.59 => ( ( Q @ Q2 )
% 0.25/0.59 => ( ( P @ ( produc2010422875real_c @ ( produc394644079real_c @ P2 @ Q2 ) ) )
% 0.25/0.59 & ( Q @ ( produc314122909real_c @ ( produc394644079real_c @ P2 @ Q2 ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % conjI_realizer
% 0.25/0.59 thf(fact_340_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.25/0.59 ! [P: produc190496183real_c > produc190496183real_c > $o,X: produc190496183real_c,Y: produc190496183real_c,A: produc640052711real_c] :
% 0.25/0.59 ( ( P @ X @ Y )
% 0.25/0.59 => ( ( A
% 0.25/0.59 = ( produc1687028567real_c @ X @ Y ) )
% 0.25/0.59 => ( P @ ( produc876006723real_c @ A ) @ ( produc415593093real_c @ A ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % BNF_Greatest_Fixpoint.subst_Pair
% 0.25/0.59 thf(fact_341_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.25/0.59 ! [P: finite1398487019real_c > finite1398487019real_c > $o,X: finite1398487019real_c,Y: finite1398487019real_c,A: produc190496183real_c] :
% 0.25/0.59 ( ( P @ X @ Y )
% 0.25/0.59 => ( ( A
% 0.25/0.59 = ( produc394644079real_c @ X @ Y ) )
% 0.25/0.59 => ( P @ ( produc2010422875real_c @ A ) @ ( produc314122909real_c @ A ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % BNF_Greatest_Fixpoint.subst_Pair
% 0.25/0.59 thf(fact_342_sndI,axiom,
% 0.25/0.59 ! [X: produc640052711real_c,Y: produc190496183real_c,Z: produc190496183real_c] :
% 0.25/0.59 ( ( X
% 0.25/0.59 = ( produc1687028567real_c @ Y @ Z ) )
% 0.25/0.59 => ( ( produc415593093real_c @ X )
% 0.25/0.59 = Z ) ) ).
% 0.25/0.59
% 0.25/0.59 % sndI
% 0.25/0.59 thf(fact_343_sndI,axiom,
% 0.25/0.59 ! [X: produc190496183real_c,Y: finite1398487019real_c,Z: finite1398487019real_c] :
% 0.25/0.59 ( ( X
% 0.25/0.59 = ( produc394644079real_c @ Y @ Z ) )
% 0.25/0.59 => ( ( produc314122909real_c @ X )
% 0.25/0.59 = Z ) ) ).
% 0.25/0.59
% 0.25/0.59 % sndI
% 0.25/0.59 thf(fact_344_fstI,axiom,
% 0.25/0.59 ! [X: produc640052711real_c,Y: produc190496183real_c,Z: produc190496183real_c] :
% 0.25/0.59 ( ( X
% 0.25/0.59 = ( produc1687028567real_c @ Y @ Z ) )
% 0.25/0.59 => ( ( produc876006723real_c @ X )
% 0.25/0.59 = Y ) ) ).
% 0.25/0.59
% 0.25/0.59 % fstI
% 0.25/0.59 thf(fact_345_fstI,axiom,
% 0.25/0.59 ! [X: produc190496183real_c,Y: finite1398487019real_c,Z: finite1398487019real_c] :
% 0.25/0.59 ( ( X
% 0.25/0.59 = ( produc394644079real_c @ Y @ Z ) )
% 0.25/0.59 => ( ( produc2010422875real_c @ X )
% 0.25/0.59 = Y ) ) ).
% 0.25/0.59
% 0.25/0.59 % fstI
% 0.25/0.59 thf(fact_346_eq__snd__iff,axiom,
% 0.25/0.59 ! [B: produc190496183real_c,P2: produc640052711real_c] :
% 0.25/0.59 ( ( B
% 0.25/0.59 = ( produc415593093real_c @ P2 ) )
% 0.25/0.59 = ( ? [A4: produc190496183real_c] :
% 0.25/0.59 ( P2
% 0.25/0.59 = ( produc1687028567real_c @ A4 @ B ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % eq_snd_iff
% 0.25/0.59 thf(fact_347_eq__snd__iff,axiom,
% 0.25/0.59 ! [B: finite1398487019real_c,P2: produc190496183real_c] :
% 0.25/0.59 ( ( B
% 0.25/0.59 = ( produc314122909real_c @ P2 ) )
% 0.25/0.59 = ( ? [A4: finite1398487019real_c] :
% 0.25/0.59 ( P2
% 0.25/0.59 = ( produc394644079real_c @ A4 @ B ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % eq_snd_iff
% 0.25/0.59 thf(fact_348_eq__fst__iff,axiom,
% 0.25/0.59 ! [A: produc190496183real_c,P2: produc640052711real_c] :
% 0.25/0.59 ( ( A
% 0.25/0.59 = ( produc876006723real_c @ P2 ) )
% 0.25/0.59 = ( ? [B4: produc190496183real_c] :
% 0.25/0.59 ( P2
% 0.25/0.59 = ( produc1687028567real_c @ A @ B4 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % eq_fst_iff
% 0.25/0.59 thf(fact_349_eq__fst__iff,axiom,
% 0.25/0.59 ! [A: finite1398487019real_c,P2: produc190496183real_c] :
% 0.25/0.59 ( ( A
% 0.25/0.59 = ( produc2010422875real_c @ P2 ) )
% 0.25/0.59 = ( ? [B4: finite1398487019real_c] :
% 0.25/0.66 ( P2
% 0.25/0.66 = ( produc394644079real_c @ A @ B4 ) ) ) ) ).
% 0.25/0.66
% 0.25/0.66 % eq_fst_iff
% 0.25/0.66 thf(fact_350_prod_Oswap__def,axiom,
% 0.25/0.66 ( produc350724343real_c
% 0.25/0.66 = ( ^ [P3: produc640052711real_c] : ( produc1687028567real_c @ ( produc415593093real_c @ P3 ) @ ( produc876006723real_c @ P3 ) ) ) ) ).
% 0.25/0.66
% 0.25/0.66 % prod.swap_def
% 0.25/0.66 thf(fact_351_prod_Oswap__def,axiom,
% 0.25/0.66 ( produc704157711real_c
% 0.25/0.66 = ( ^ [P3: produc190496183real_c] : ( produc394644079real_c @ ( produc314122909real_c @ P3 ) @ ( produc2010422875real_c @ P3 ) ) ) ) ).
% 0.25/0.66
% 0.25/0.66 % prod.swap_def
% 0.25/0.66 thf(fact_352_swap__simp,axiom,
% 0.25/0.66 ! [X: produc190496183real_c,Y: produc190496183real_c] :
% 0.25/0.66 ( ( produc350724343real_c @ ( produc1687028567real_c @ X @ Y ) )
% 0.25/0.66 = ( produc1687028567real_c @ Y @ X ) ) ).
% 0.25/0.66
% 0.25/0.66 % swap_simp
% 0.25/0.66 thf(fact_353_swap__simp,axiom,
% 0.25/0.66 ! [X: finite1398487019real_c,Y: finite1398487019real_c] :
% 0.25/0.66 ( ( produc704157711real_c @ ( produc394644079real_c @ X @ Y ) )
% 0.25/0.66 = ( produc394644079real_c @ Y @ X ) ) ).
% 0.25/0.66
% 0.25/0.66 % swap_simp
% 0.25/0.66
% 0.25/0.66 % Conjectures (1)
% 0.25/0.66 thf(conj_0,conjecture,
% 0.25/0.66 ? [Mu6: produc190496183real_c] :
% 0.25/0.66 ( ( member346808080real_c @ ( produc1687028567real_c @ ( produc394644079real_c @ nu_22 @ nu_2 ) @ Mu6 ) @ ( denota904684656_a_b_c @ j @ ( choice_a_b_c @ a @ b ) ) )
% 0.25/0.66 & ( denota1997846518gree_c @ ( produc394644079real_c @ mu3 @ mu2 ) @ Mu6 @ ( sup_su1349021703um_c_c @ ( static_MBV_a_b_c @ ( choice_a_b_c @ a @ b ) ) @ v ) ) ) ).
% 0.25/0.66
% 0.25/0.66 %------------------------------------------------------------------------------
% 0.25/0.66 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.plrVdivEIP/cvc5---1.0.5_22994.p...
% 0.25/0.66 (declare-sort $$unsorted 0)
% 0.25/0.66 (declare-sort tptp.set_Pr242060487real_c 0)
% 0.25/0.66 (declare-sort tptp.produc1037099239real_c 0)
% 0.25/0.66 (declare-sort tptp.set_Pr754230471real_c 0)
% 0.25/0.66 (declare-sort tptp.produc640052711real_c 0)
% 0.25/0.66 (declare-sort tptp.produc1360640805um_b_c 0)
% 0.25/0.66 (declare-sort tptp.produc1470506001real_c 0)
% 0.25/0.66 (declare-sort tptp.produc793920321um_c_c 0)
% 0.25/0.66 (declare-sort tptp.produc777402865um_c_c 0)
% 0.25/0.66 (declare-sort tptp.produc1415638375um_b_c 0)
% 0.25/0.66 (declare-sort tptp.set_Pr1389752855real_c 0)
% 0.25/0.66 (declare-sort tptp.produc263671631um_b_c 0)
% 0.25/0.66 (declare-sort tptp.produc1573491071um_c_c 0)
% 0.25/0.66 (declare-sort tptp.produc190496183real_c 0)
% 0.25/0.66 (declare-sort tptp.produc214722967um_c_c 0)
% 0.25/0.66 (declare-sort tptp.denota231621370t_unit 0)
% 0.25/0.66 (declare-sort tptp.set_Su1783761653um_b_c 0)
% 0.25/0.66 (declare-sort tptp.sum_su737395349um_b_c 0)
% 0.25/0.66 (declare-sort tptp.finite1398487019real_c 0)
% 0.25/0.66 (declare-sort tptp.set_Sum_sum_c_c 0)
% 0.25/0.66 (declare-sort tptp.hp_a_b_c 0)
% 0.25/0.66 (declare-sort tptp.sum_sum_c_c 0)
% 0.25/0.66 (declare-fun tptp.bNF_Ca318582436um_b_c (tptp.set_Pr1389752855real_c (-> tptp.finite1398487019real_c tptp.set_Su1783761653um_b_c)) Bool)
% 0.25/0.66 (declare-fun tptp.bNF_Ca1693016812um_c_c (tptp.set_Pr1389752855real_c (-> tptp.finite1398487019real_c tptp.set_Sum_sum_c_c)) Bool)
% 0.25/0.66 (declare-fun tptp.bNF_Ca419199138um_b_c (tptp.set_Pr754230471real_c (-> tptp.produc190496183real_c tptp.set_Su1783761653um_b_c)) Bool)
% 0.25/0.66 (declare-fun tptp.bNF_Ca1667803246um_c_c (tptp.set_Pr754230471real_c (-> tptp.produc190496183real_c tptp.set_Sum_sum_c_c)) Bool)
% 0.25/0.66 (declare-fun tptp.coinci354700372_a_b_c (tptp.hp_a_b_c tptp.denota231621370t_unit tptp.denota231621370t_unit) Bool)
% 0.25/0.66 (declare-fun tptp.coinci1852866155_a_b_c (tptp.hp_a_b_c) Bool)
% 0.25/0.66 (declare-fun tptp.coinci772602909_a_b_c (tptp.hp_a_b_c tptp.denota231621370t_unit) Bool)
% 0.25/0.66 (declare-fun tptp.denota69106024_a_b_c (tptp.denota231621370t_unit tptp.denota231621370t_unit tptp.set_Su1783761653um_b_c) Bool)
% 0.25/0.66 (declare-fun tptp.denota1997846518gree_c (tptp.produc190496183real_c tptp.produc190496183real_c tptp.set_Sum_sum_c_c) Bool)
% 0.25/0.66 (declare-fun tptp.denota904684656_a_b_c (tptp.denota231621370t_unit tptp.hp_a_b_c) tptp.set_Pr754230471real_c)
% 0.25/0.66 (declare-fun tptp.sup_su2141622551real_c (tptp.finite1398487019real_c tptp.finite1398487019real_c) tptp.finite1398487019real_c)
% 0.25/0.66 (declare-fun tptp.sup_su1639086475real_c (tptp.produc190496183real_c tptp.produc190496183real_c) tptp.produc190496183real_c)
% 0.25/0.66 (declare-fun tptp.sup_su1399591867real_c (tptp.produc640052711real_c tptp.produc640052711real_c) tptp.produc640052711real_c)
% 0.25/0.66 (declare-fun tptp.sup_su1009753337um_b_c (tptp.produc1360640805um_b_c tptp.produc1360640805um_b_c) tptp.produc1360640805um_b_c)
% 0.25/0.66 (declare-fun tptp.sup_su1347303021um_c_c (tptp.produc793920321um_c_c tptp.produc793920321um_c_c) tptp.produc793920321um_c_c)
% 0.25/0.66 (declare-fun tptp.sup_su1580927803um_b_c (tptp.produc1415638375um_b_c tptp.produc1415638375um_b_c) tptp.produc1415638375um_b_c)
% 0.25/0.66 (declare-fun tptp.sup_su1731217579um_c_c (tptp.produc1573491071um_c_c tptp.produc1573491071um_c_c) tptp.produc1573491071um_c_c)
% 0.25/0.66 (declare-fun tptp.sup_su2023888701real_c (tptp.produc1470506001real_c tptp.produc1470506001real_c) tptp.produc1470506001real_c)
% 0.25/0.66 (declare-fun tptp.sup_su505296157um_c_c (tptp.produc777402865um_c_c tptp.produc777402865um_c_c) tptp.produc777402865um_c_c)
% 0.25/0.66 (declare-fun tptp.sup_su421398139um_b_c (tptp.produc263671631um_b_c tptp.produc263671631um_b_c) tptp.produc263671631um_b_c)
% 0.25/0.66 (declare-fun tptp.sup_su1672617323um_c_c (tptp.produc214722967um_c_c tptp.produc214722967um_c_c) tptp.produc214722967um_c_c)
% 0.25/0.66 (declare-fun tptp.sup_su1857314283real_c (tptp.set_Pr1389752855real_c tptp.set_Pr1389752855real_c) tptp.set_Pr1389752855real_c)
% 0.25/0.66 (declare-fun tptp.sup_su588839579real_c (tptp.set_Pr754230471real_c tptp.set_Pr754230471real_c) tptp.set_Pr754230471real_c)
% 0.25/0.66 (declare-fun tptp.sup_su880588443real_c (tptp.set_Pr242060487real_c tptp.set_Pr242060487real_c) tptp.set_Pr242060487real_c)
% 0.25/0.66 (declare-fun tptp.sup_su1968964297um_b_c (tptp.set_Su1783761653um_b_c tptp.set_Su1783761653um_b_c) tptp.set_Su1783761653um_b_c)
% 0.25/0.66 (declare-fun tptp.sup_su1349021703um_c_c (tptp.set_Sum_sum_c_c tptp.set_Sum_sum_c_c) tptp.set_Sum_sum_c_c)
% 0.25/0.66 (declare-fun tptp.ord_le775706699real_c (tptp.finite1398487019real_c tptp.finite1398487019real_c) Bool)
% 0.25/0.66 (declare-fun tptp.ord_le850691415real_c (tptp.produc190496183real_c tptp.produc190496183real_c) Bool)
% 0.25/0.66 (declare-fun tptp.ord_le652477831real_c (tptp.produc640052711real_c tptp.produc640052711real_c) Bool)
% 0.25/0.66 (declare-fun tptp.ord_le907560199um_b_c (tptp.produc1415638375um_b_c tptp.produc1415638375um_b_c) Bool)
% 0.25/0.66 (declare-fun tptp.ord_le1852514783um_c_c (tptp.produc1573491071um_c_c tptp.produc1573491071um_c_c) Bool)
% 0.25/0.66 (declare-fun tptp.ord_le542695343um_b_c (tptp.produc263671631um_b_c tptp.produc263671631um_b_c) Bool)
% 0.25/0.66 (declare-fun tptp.ord_le684454199um_c_c (tptp.produc214722967um_c_c tptp.produc214722967um_c_c) Bool)
% 0.25/0.66 (declare-fun tptp.ord_le977353143real_c (tptp.set_Pr1389752855real_c tptp.set_Pr1389752855real_c) Bool)
% 0.25/0.66 (declare-fun tptp.ord_le1988344935real_c (tptp.set_Pr754230471real_c tptp.set_Pr754230471real_c) Bool)
% 0.25/0.66 (declare-fun tptp.ord_le100418663real_c (tptp.set_Pr242060487real_c tptp.set_Pr242060487real_c) Bool)
% 0.25/0.66 (declare-fun tptp.ord_le929608341um_b_c (tptp.set_Su1783761653um_b_c tptp.set_Su1783761653um_b_c) Bool)
% 0.25/0.66 (declare-fun tptp.ord_le1772180283um_c_c (tptp.set_Sum_sum_c_c tptp.set_Sum_sum_c_c) Bool)
% 0.25/0.66 (declare-fun tptp.order_365181262um_b_c ((-> tptp.set_Su1783761653um_b_c Bool)) tptp.set_Su1783761653um_b_c)
% 0.25/0.66 (declare-fun tptp.order_1776530114um_c_c ((-> tptp.set_Sum_sum_c_c Bool)) tptp.set_Sum_sum_c_c)
% 0.25/0.66 (declare-fun tptp.produc394644079real_c (tptp.finite1398487019real_c tptp.finite1398487019real_c) tptp.produc190496183real_c)
% 0.25/0.66 (declare-fun tptp.produc1687028567real_c (tptp.produc190496183real_c tptp.produc190496183real_c) tptp.produc640052711real_c)
% 0.25/0.66 (declare-fun tptp.produc2010919061um_b_c (tptp.produc190496183real_c tptp.set_Su1783761653um_b_c) tptp.produc1360640805um_b_c)
% 0.25/0.66 (declare-fun tptp.produc639456571um_c_c (tptp.produc190496183real_c tptp.set_Sum_sum_c_c) tptp.produc793920321um_c_c)
% 0.25/0.66 (declare-fun tptp.produc544496471real_c (tptp.produc640052711real_c tptp.produc640052711real_c) tptp.produc1037099239real_c)
% 0.25/0.66 (declare-fun tptp.produc754249687um_b_c (tptp.set_Su1783761653um_b_c tptp.set_Su1783761653um_b_c) tptp.produc1415638375um_b_c)
% 0.25/0.66 (declare-fun tptp.produc616453753um_c_c (tptp.set_Su1783761653um_b_c tptp.set_Sum_sum_c_c) tptp.produc1573491071um_c_c)
% 0.25/0.66 (declare-fun tptp.produc439851843real_c (tptp.set_Sum_sum_c_c tptp.produc190496183real_c) tptp.produc1470506001real_c)
% 0.25/0.66 (declare-fun tptp.produc1333497635um_c_c (tptp.set_Sum_sum_c_c tptp.produc214722967um_c_c) tptp.produc777402865um_c_c)
% 0.25/0.66 (declare-fun tptp.produc919784577um_b_c (tptp.set_Sum_sum_c_c tptp.set_Su1783761653um_b_c) tptp.produc263671631um_b_c)
% 0.25/0.66 (declare-fun tptp.produc1439061071um_c_c (tptp.set_Sum_sum_c_c tptp.set_Sum_sum_c_c) tptp.produc214722967um_c_c)
% 0.25/0.66 (declare-fun tptp.produc2010422875real_c (tptp.produc190496183real_c) tptp.finite1398487019real_c)
% 0.25/0.66 (declare-fun tptp.produc876006723real_c (tptp.produc640052711real_c) tptp.produc190496183real_c)
% 0.25/0.66 (declare-fun tptp.produc1961869763um_b_c (tptp.produc1415638375um_b_c) tptp.set_Su1783761653um_b_c)
% 0.25/0.66 (declare-fun tptp.produc1455464333um_c_c (tptp.produc1573491071um_c_c) tptp.set_Su1783761653um_b_c)
% 0.25/0.66 (declare-fun tptp.produc1758795157um_b_c (tptp.produc263671631um_b_c) tptp.set_Sum_sum_c_c)
% 0.25/0.66 (declare-fun tptp.produc1983230011um_c_c (tptp.produc214722967um_c_c) tptp.set_Sum_sum_c_c)
% 0.25/0.66 (declare-fun tptp.produc314122909real_c (tptp.produc190496183real_c) tptp.finite1398487019real_c)
% 0.25/0.66 (declare-fun tptp.produc415593093real_c (tptp.produc640052711real_c) tptp.produc190496183real_c)
% 0.25/0.66 (declare-fun tptp.produc932426501um_b_c (tptp.produc1415638375um_b_c) tptp.set_Su1783761653um_b_c)
% 0.25/0.66 (declare-fun tptp.produc890433227um_c_c (tptp.produc1573491071um_c_c) tptp.set_Sum_sum_c_c)
% 0.25/0.66 (declare-fun tptp.produc1193764051um_b_c (tptp.produc263671631um_b_c) tptp.set_Su1783761653um_b_c)
% 0.25/0.66 (declare-fun tptp.produc1132019837um_c_c (tptp.produc214722967um_c_c) tptp.set_Sum_sum_c_c)
% 0.25/0.66 (declare-fun tptp.produc704157711real_c (tptp.produc190496183real_c) tptp.produc190496183real_c)
% 0.25/0.66 (declare-fun tptp.produc350724343real_c (tptp.produc640052711real_c) tptp.produc640052711real_c)
% 0.25/0.66 (declare-fun tptp.collec1126017874real_c ((-> tptp.produc640052711real_c Bool)) tptp.set_Pr754230471real_c)
% 0.25/0.66 (declare-fun tptp.collec2086029184um_b_c ((-> tptp.sum_su737395349um_b_c Bool)) tptp.set_Su1783761653um_b_c)
% 0.25/0.66 (declare-fun tptp.collect_Sum_sum_c_c ((-> tptp.sum_sum_c_c Bool)) tptp.set_Sum_sum_c_c)
% 0.25/0.66 (declare-fun tptp.static_FVP_a_b_c (tptp.hp_a_b_c) tptp.set_Sum_sum_c_c)
% 0.25/0.66 (declare-fun tptp.static_MBV_a_b_c (tptp.hp_a_b_c) tptp.set_Sum_sum_c_c)
% 0.25/0.66 (declare-fun tptp.static_SIGP_a_b_c (tptp.hp_a_b_c) tptp.set_Su1783761653um_b_c)
% 0.25/0.66 (declare-fun tptp.choice_a_b_c (tptp.hp_a_b_c tptp.hp_a_b_c) tptp.hp_a_b_c)
% 0.25/0.66 (declare-fun tptp.hpsafe_a_b_c (tptp.hp_a_b_c) Bool)
% 0.25/0.66 (declare-fun tptp.same_f1974156740real_c ((-> tptp.finite1398487019real_c Bool) (-> tptp.finite1398487019real_c tptp.set_Pr1389752855real_c)) tptp.set_Pr754230471real_c)
% 0.25/0.66 (declare-fun tptp.same_f598810924real_c ((-> tptp.produc190496183real_c Bool) (-> tptp.produc190496183real_c tptp.set_Pr754230471real_c)) tptp.set_Pr242060487real_c)
% 0.25/0.66 (declare-fun tptp.member1895684704real_c (tptp.produc190496183real_c tptp.set_Pr1389752855real_c) Bool)
% 0.25/0.66 (declare-fun tptp.member346808080real_c (tptp.produc640052711real_c tptp.set_Pr754230471real_c) Bool)
% 0.25/0.66 (declare-fun tptp.member616151824real_c (tptp.produc1037099239real_c tptp.set_Pr242060487real_c) Bool)
% 0.25/0.66 (declare-fun tptp.member1893232190um_b_c (tptp.sum_su737395349um_b_c tptp.set_Su1783761653um_b_c) Bool)
% 0.25/0.66 (declare-fun tptp.member_Sum_sum_c_c (tptp.sum_sum_c_c tptp.set_Sum_sum_c_c) Bool)
% 0.25/0.66 (declare-fun tptp.i () tptp.denota231621370t_unit)
% 0.25/0.66 (declare-fun tptp.j () tptp.denota231621370t_unit)
% 0.25/0.66 (declare-fun tptp.v () tptp.set_Sum_sum_c_c)
% 0.25/0.66 (declare-fun tptp.mu () tptp.produc190496183real_c)
% 0.25/0.66 (declare-fun tptp.mu2 () tptp.finite1398487019real_c)
% 0.25/0.66 (declare-fun tptp.mu3 () tptp.finite1398487019real_c)
% 0.25/0.66 (declare-fun tptp.nu_1 () tptp.finite1398487019real_c)
% 0.25/0.66 (declare-fun tptp.nu_12 () tptp.finite1398487019real_c)
% 0.25/0.66 (declare-fun tptp.nu_2 () tptp.finite1398487019real_c)
% 0.25/0.66 (declare-fun tptp.nu_22 () tptp.finite1398487019real_c)
% 0.25/0.66 (declare-fun tptp.a () tptp.hp_a_b_c)
% 0.25/0.66 (declare-fun tptp.b () tptp.hp_a_b_c)
% 0.25/0.66 (assert (@ tptp.coinci1852866155_a_b_c tptp.b))
% 0.25/0.66 (assert (@ tptp.coinci1852866155_a_b_c tptp.a))
% 0.25/0.66 (assert (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c (@ (@ tptp.produc394644079real_c tptp.nu_22) tptp.nu_2)) tptp.mu)) (@ (@ tptp.denota904684656_a_b_c tptp.j) (@ (@ tptp.choice_a_b_c tptp.a) tptp.b))))
% 0.25/0.66 (assert (@ (@ (@ tptp.denota1997846518gree_c (@ (@ tptp.produc394644079real_c tptp.mu3) tptp.mu2)) tptp.mu) (@ (@ tptp.sup_su1349021703um_c_c (@ tptp.static_MBV_a_b_c (@ (@ tptp.choice_a_b_c tptp.a) tptp.b))) tptp.v)))
% 0.25/0.66 (assert (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c (@ (@ tptp.produc394644079real_c tptp.nu_22) tptp.nu_2)) tptp.mu)) (@ (@ tptp.denota904684656_a_b_c tptp.j) tptp.b)))
% 0.25/0.66 (assert (@ tptp.hpsafe_a_b_c tptp.b))
% 0.25/0.66 (assert (@ tptp.hpsafe_a_b_c tptp.a))
% 0.25/0.66 (assert (@ (@ (@ tptp.denota1997846518gree_c (@ (@ tptp.produc394644079real_c tptp.mu3) tptp.mu2)) tptp.mu) (@ (@ tptp.sup_su1349021703um_c_c (@ tptp.static_MBV_a_b_c tptp.b)) tptp.v)))
% 0.25/0.66 (assert (not (forall ((Mu tptp.produc190496183real_c)) (=> (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c (@ (@ tptp.produc394644079real_c tptp.nu_22) tptp.nu_2)) Mu)) (@ (@ tptp.denota904684656_a_b_c tptp.j) tptp.b)) (not (@ (@ (@ tptp.denota1997846518gree_c (@ (@ tptp.produc394644079real_c tptp.mu3) tptp.mu2)) Mu) (@ (@ tptp.sup_su1349021703um_c_c (@ tptp.static_MBV_a_b_c tptp.b)) tptp.v)))))))
% 0.25/0.66 (assert (@ (@ (@ tptp.denota1997846518gree_c (@ (@ tptp.produc394644079real_c tptp.nu_12) tptp.nu_1)) (@ (@ tptp.produc394644079real_c tptp.nu_22) tptp.nu_2)) tptp.v))
% 0.25/0.66 (assert (forall ((A tptp.finite1398487019real_c) (B tptp.finite1398487019real_c) (C tptp.finite1398487019real_c) (D tptp.finite1398487019real_c)) (= (@ (@ tptp.sup_su1639086475real_c (@ (@ tptp.produc394644079real_c A) B)) (@ (@ tptp.produc394644079real_c C) D)) (@ (@ tptp.produc394644079real_c (@ (@ tptp.sup_su2141622551real_c A) C)) (@ (@ tptp.sup_su2141622551real_c B) D)))))
% 0.25/0.66 (assert (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c) (D tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.sup_su1672617323um_c_c (@ (@ tptp.produc1439061071um_c_c A) B)) (@ (@ tptp.produc1439061071um_c_c C) D)) (@ (@ tptp.produc1439061071um_c_c (@ (@ tptp.sup_su1349021703um_c_c A) C)) (@ (@ tptp.sup_su1349021703um_c_c B) D)))))
% 0.25/0.66 (assert (forall ((A tptp.produc190496183real_c) (B tptp.produc190496183real_c) (C tptp.produc190496183real_c) (D tptp.produc190496183real_c)) (= (@ (@ tptp.sup_su1399591867real_c (@ (@ tptp.produc1687028567real_c A) B)) (@ (@ tptp.produc1687028567real_c C) D)) (@ (@ tptp.produc1687028567real_c (@ (@ tptp.sup_su1639086475real_c A) C)) (@ (@ tptp.sup_su1639086475real_c B) D)))))
% 0.25/0.66 (assert (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Su1783761653um_b_c) (C tptp.set_Sum_sum_c_c) (D tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.sup_su421398139um_b_c (@ (@ tptp.produc919784577um_b_c A) B)) (@ (@ tptp.produc919784577um_b_c C) D)) (@ (@ tptp.produc919784577um_b_c (@ (@ tptp.sup_su1349021703um_c_c A) C)) (@ (@ tptp.sup_su1968964297um_b_c B) D)))))
% 0.25/0.66 (assert (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Sum_sum_c_c) (C tptp.set_Su1783761653um_b_c) (D tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.sup_su1731217579um_c_c (@ (@ tptp.produc616453753um_c_c A) B)) (@ (@ tptp.produc616453753um_c_c C) D)) (@ (@ tptp.produc616453753um_c_c (@ (@ tptp.sup_su1968964297um_b_c A) C)) (@ (@ tptp.sup_su1349021703um_c_c B) D)))))
% 0.25/0.66 (assert (forall ((A tptp.set_Sum_sum_c_c) (B tptp.produc190496183real_c) (C tptp.set_Sum_sum_c_c) (D tptp.produc190496183real_c)) (= (@ (@ tptp.sup_su2023888701real_c (@ (@ tptp.produc439851843real_c A) B)) (@ (@ tptp.produc439851843real_c C) D)) (@ (@ tptp.produc439851843real_c (@ (@ tptp.sup_su1349021703um_c_c A) C)) (@ (@ tptp.sup_su1639086475real_c B) D)))))
% 0.25/0.66 (assert (forall ((A tptp.produc190496183real_c) (B tptp.set_Sum_sum_c_c) (C tptp.produc190496183real_c) (D tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.sup_su1347303021um_c_c (@ (@ tptp.produc639456571um_c_c A) B)) (@ (@ tptp.produc639456571um_c_c C) D)) (@ (@ tptp.produc639456571um_c_c (@ (@ tptp.sup_su1639086475real_c A) C)) (@ (@ tptp.sup_su1349021703um_c_c B) D)))))
% 0.25/0.66 (assert (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c) (D tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.sup_su1580927803um_b_c (@ (@ tptp.produc754249687um_b_c A) B)) (@ (@ tptp.produc754249687um_b_c C) D)) (@ (@ tptp.produc754249687um_b_c (@ (@ tptp.sup_su1968964297um_b_c A) C)) (@ (@ tptp.sup_su1968964297um_b_c B) D)))))
% 0.25/0.66 (assert (forall ((A tptp.set_Sum_sum_c_c) (B tptp.produc214722967um_c_c) (C tptp.set_Sum_sum_c_c) (D tptp.produc214722967um_c_c)) (= (@ (@ tptp.sup_su505296157um_c_c (@ (@ tptp.produc1333497635um_c_c A) B)) (@ (@ tptp.produc1333497635um_c_c C) D)) (@ (@ tptp.produc1333497635um_c_c (@ (@ tptp.sup_su1349021703um_c_c A) C)) (@ (@ tptp.sup_su1672617323um_c_c B) D)))))
% 0.25/0.66 (assert (forall ((A tptp.produc190496183real_c) (B tptp.set_Su1783761653um_b_c) (C tptp.produc190496183real_c) (D tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.sup_su1009753337um_b_c (@ (@ tptp.produc2010919061um_b_c A) B)) (@ (@ tptp.produc2010919061um_b_c C) D)) (@ (@ tptp.produc2010919061um_b_c (@ (@ tptp.sup_su1639086475real_c A) C)) (@ (@ tptp.sup_su1968964297um_b_c B) D)))))
% 0.25/0.66 (assert (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c (@ (@ tptp.produc394644079real_c tptp.nu_12) tptp.nu_1)) (@ (@ tptp.produc394644079real_c tptp.mu3) tptp.mu2))) (@ (@ tptp.denota904684656_a_b_c tptp.i) (@ (@ tptp.choice_a_b_c tptp.a) tptp.b))))
% 0.25/0.66 (assert (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.static_FVP_a_b_c (@ (@ tptp.choice_a_b_c tptp.a) tptp.b))) tptp.v))
% 0.25/0.66 (assert (not (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c (@ (@ tptp.produc394644079real_c tptp.nu_12) tptp.nu_1)) (@ (@ tptp.produc394644079real_c tptp.mu3) tptp.mu2))) (@ (@ tptp.denota904684656_a_b_c tptp.i) tptp.a))))
% 0.25/0.66 (assert (forall ((X61 tptp.hp_a_b_c) (X62 tptp.hp_a_b_c) (Y61 tptp.hp_a_b_c) (Y62 tptp.hp_a_b_c)) (= (= (@ (@ tptp.choice_a_b_c X61) X62) (@ (@ tptp.choice_a_b_c Y61) Y62)) (and (= X61 Y61) (= X62 Y62)))))
% 0.25/0.66 (assert (forall ((C tptp.produc190496183real_c) (B2 tptp.set_Pr1389752855real_c) (A2 tptp.set_Pr1389752855real_c)) (let ((_let_1 (@ tptp.member1895684704real_c C))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A2)) (@ _let_1 (@ (@ tptp.sup_su1857314283real_c A2) B2))))))
% 0.25/0.66 (assert (forall ((C tptp.produc1037099239real_c) (B2 tptp.set_Pr242060487real_c) (A2 tptp.set_Pr242060487real_c)) (let ((_let_1 (@ tptp.member616151824real_c C))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A2)) (@ _let_1 (@ (@ tptp.sup_su880588443real_c A2) B2))))))
% 0.25/0.66 (assert (forall ((C tptp.sum_su737395349um_b_c) (B2 tptp.set_Su1783761653um_b_c) (A2 tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.member1893232190um_b_c C))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A2)) (@ _let_1 (@ (@ tptp.sup_su1968964297um_b_c A2) B2))))))
% 0.25/0.66 (assert (forall ((C tptp.produc640052711real_c) (B2 tptp.set_Pr754230471real_c) (A2 tptp.set_Pr754230471real_c)) (let ((_let_1 (@ tptp.member346808080real_c C))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A2)) (@ _let_1 (@ (@ tptp.sup_su588839579real_c A2) B2))))))
% 0.25/0.66 (assert (forall ((C tptp.sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (A2 tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.member_Sum_sum_c_c C))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A2)) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c A2) B2))))))
% 0.25/0.66 (assert (forall ((C tptp.produc190496183real_c) (A2 tptp.set_Pr1389752855real_c) (B2 tptp.set_Pr1389752855real_c)) (let ((_let_1 (@ tptp.member1895684704real_c C))) (= (@ _let_1 (@ (@ tptp.sup_su1857314283real_c A2) B2)) (or (@ _let_1 A2) (@ _let_1 B2))))))
% 0.25/0.66 (assert (forall ((C tptp.produc1037099239real_c) (A2 tptp.set_Pr242060487real_c) (B2 tptp.set_Pr242060487real_c)) (let ((_let_1 (@ tptp.member616151824real_c C))) (= (@ _let_1 (@ (@ tptp.sup_su880588443real_c A2) B2)) (or (@ _let_1 A2) (@ _let_1 B2))))))
% 0.25/0.66 (assert (forall ((C tptp.sum_su737395349um_b_c) (A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.member1893232190um_b_c C))) (= (@ _let_1 (@ (@ tptp.sup_su1968964297um_b_c A2) B2)) (or (@ _let_1 A2) (@ _let_1 B2))))))
% 0.25/0.66 (assert (forall ((C tptp.produc640052711real_c) (A2 tptp.set_Pr754230471real_c) (B2 tptp.set_Pr754230471real_c)) (let ((_let_1 (@ tptp.member346808080real_c C))) (= (@ _let_1 (@ (@ tptp.sup_su588839579real_c A2) B2)) (or (@ _let_1 A2) (@ _let_1 B2))))))
% 0.25/0.66 (assert (forall ((C tptp.sum_sum_c_c) (A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.member_Sum_sum_c_c C))) (= (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c A2) B2)) (or (@ _let_1 A2) (@ _let_1 B2))))))
% 0.25/0.66 (assert (forall ((A tptp.produc190496183real_c)) (= (@ (@ tptp.sup_su1639086475real_c A) A) A)))
% 0.25/0.66 (assert (forall ((A tptp.produc640052711real_c)) (= (@ (@ tptp.sup_su1399591867real_c A) A) A)))
% 0.25/0.66 (assert (forall ((A tptp.produc214722967um_c_c)) (= (@ (@ tptp.sup_su1672617323um_c_c A) A) A)))
% 0.25/0.66 (assert (forall ((A tptp.set_Pr754230471real_c)) (= (@ (@ tptp.sup_su588839579real_c A) A) A)))
% 0.25/0.66 (assert (forall ((A tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.sup_su1968964297um_b_c A) A) A)))
% 0.25/0.66 (assert (forall ((A tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.sup_su1349021703um_c_c A) A) A)))
% 0.25/0.66 (assert (forall ((X tptp.produc190496183real_c)) (= (@ (@ tptp.sup_su1639086475real_c X) X) X)))
% 0.25/0.66 (assert (forall ((X tptp.produc640052711real_c)) (= (@ (@ tptp.sup_su1399591867real_c X) X) X)))
% 0.25/0.66 (assert (forall ((X tptp.produc214722967um_c_c)) (= (@ (@ tptp.sup_su1672617323um_c_c X) X) X)))
% 0.25/0.66 (assert (forall ((X tptp.set_Pr754230471real_c)) (= (@ (@ tptp.sup_su588839579real_c X) X) X)))
% 0.25/0.66 (assert (forall ((X tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.sup_su1968964297um_b_c X) X) X)))
% 0.25/0.66 (assert (forall ((X tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.sup_su1349021703um_c_c X) X) X)))
% 0.25/0.66 (assert (forall ((A tptp.produc190496183real_c) (B tptp.produc190496183real_c)) (let ((_let_1 (@ tptp.sup_su1639086475real_c A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.25/0.66 (assert (forall ((A tptp.produc640052711real_c) (B tptp.produc640052711real_c)) (let ((_let_1 (@ tptp.sup_su1399591867real_c A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.25/0.66 (assert (forall ((A tptp.produc214722967um_c_c) (B tptp.produc214722967um_c_c)) (let ((_let_1 (@ tptp.sup_su1672617323um_c_c A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.25/0.66 (assert (forall ((A tptp.set_Pr754230471real_c) (B tptp.set_Pr754230471real_c)) (let ((_let_1 (@ tptp.sup_su588839579real_c A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.25/0.66 (assert (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.sup_su1968964297um_b_c A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.25/0.66 (assert (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Pr1389752855real_c) (B2 tptp.set_Pr1389752855real_c)) (=> (forall ((X2 tptp.produc190496183real_c)) (let ((_let_1 (@ tptp.member1895684704real_c X2))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le977353143real_c A2) B2))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Pr242060487real_c) (B2 tptp.set_Pr242060487real_c)) (=> (forall ((X2 tptp.produc1037099239real_c)) (let ((_let_1 (@ tptp.member616151824real_c X2))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le100418663real_c A2) B2))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Pr754230471real_c) (B2 tptp.set_Pr754230471real_c)) (=> (forall ((X2 tptp.produc640052711real_c)) (let ((_let_1 (@ tptp.member346808080real_c X2))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le1988344935real_c A2) B2))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (=> (forall ((X2 tptp.sum_sum_c_c)) (let ((_let_1 (@ tptp.member_Sum_sum_c_c X2))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le1772180283um_c_c A2) B2))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c)) (=> (forall ((X2 tptp.sum_su737395349um_b_c)) (let ((_let_1 (@ tptp.member1893232190um_b_c X2))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le929608341um_b_c A2) B2))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Pr754230471real_c) (B2 tptp.set_Pr754230471real_c)) (=> (@ (@ tptp.ord_le1988344935real_c A2) B2) (=> (@ (@ tptp.ord_le1988344935real_c B2) A2) (= A2 B2)))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A2) B2) (=> (@ (@ tptp.ord_le1772180283um_c_c B2) A2) (= A2 B2)))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A2) B2) (=> (@ (@ tptp.ord_le929608341um_b_c B2) A2) (= A2 B2)))))
% 0.25/0.66 (assert (forall ((A tptp.produc190496183real_c) (B tptp.produc190496183real_c)) (let ((_let_1 (@ (@ tptp.sup_su1639086475real_c A) B))) (= (@ (@ tptp.sup_su1639086475real_c _let_1) B) _let_1))))
% 0.25/0.66 (assert (forall ((A tptp.produc640052711real_c) (B tptp.produc640052711real_c)) (let ((_let_1 (@ (@ tptp.sup_su1399591867real_c A) B))) (= (@ (@ tptp.sup_su1399591867real_c _let_1) B) _let_1))))
% 0.25/0.66 (assert (forall ((A tptp.produc214722967um_c_c) (B tptp.produc214722967um_c_c)) (let ((_let_1 (@ (@ tptp.sup_su1672617323um_c_c A) B))) (= (@ (@ tptp.sup_su1672617323um_c_c _let_1) B) _let_1))))
% 0.25/0.66 (assert (forall ((A tptp.set_Pr754230471real_c) (B tptp.set_Pr754230471real_c)) (let ((_let_1 (@ (@ tptp.sup_su588839579real_c A) B))) (= (@ (@ tptp.sup_su588839579real_c _let_1) B) _let_1))))
% 0.25/0.66 (assert (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ (@ tptp.sup_su1968964297um_b_c A) B))) (= (@ (@ tptp.sup_su1968964297um_b_c _let_1) B) _let_1))))
% 0.25/0.66 (assert (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ (@ tptp.sup_su1349021703um_c_c A) B))) (= (@ (@ tptp.sup_su1349021703um_c_c _let_1) B) _let_1))))
% 0.25/0.66 (assert (forall ((X tptp.produc190496183real_c) (Y tptp.produc190496183real_c)) (let ((_let_1 (@ tptp.sup_su1639086475real_c X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 0.25/0.66 (assert (forall ((X tptp.produc640052711real_c) (Y tptp.produc640052711real_c)) (let ((_let_1 (@ tptp.sup_su1399591867real_c X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 0.25/0.66 (assert (forall ((X tptp.produc214722967um_c_c) (Y tptp.produc214722967um_c_c)) (let ((_let_1 (@ tptp.sup_su1672617323um_c_c X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 0.25/0.66 (assert (forall ((X tptp.set_Pr754230471real_c) (Y tptp.set_Pr754230471real_c)) (let ((_let_1 (@ tptp.sup_su588839579real_c X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 0.25/0.66 (assert (forall ((X tptp.set_Su1783761653um_b_c) (Y tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.sup_su1968964297um_b_c X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 0.25/0.66 (assert (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 0.25/0.66 (assert (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.static_FVP_a_b_c tptp.b)) tptp.v))
% 0.25/0.66 (assert (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.static_FVP_a_b_c tptp.a)) tptp.v))
% 0.25/0.66 (assert (forall ((A tptp.produc190496183real_c) (B tptp.produc190496183real_c) (C tptp.produc190496183real_c) (D tptp.produc190496183real_c)) (= (@ (@ tptp.ord_le652477831real_c (@ (@ tptp.produc1687028567real_c A) B)) (@ (@ tptp.produc1687028567real_c C) D)) (and (@ (@ tptp.ord_le850691415real_c A) C) (@ (@ tptp.ord_le850691415real_c B) D)))))
% 0.25/0.66 (assert (forall ((A tptp.finite1398487019real_c) (B tptp.finite1398487019real_c) (C tptp.finite1398487019real_c) (D tptp.finite1398487019real_c)) (= (@ (@ tptp.ord_le850691415real_c (@ (@ tptp.produc394644079real_c A) B)) (@ (@ tptp.produc394644079real_c C) D)) (and (@ (@ tptp.ord_le775706699real_c A) C) (@ (@ tptp.ord_le775706699real_c B) D)))))
% 0.25/0.66 (assert (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c) (D tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.ord_le684454199um_c_c (@ (@ tptp.produc1439061071um_c_c A) B)) (@ (@ tptp.produc1439061071um_c_c C) D)) (and (@ (@ tptp.ord_le1772180283um_c_c A) C) (@ (@ tptp.ord_le1772180283um_c_c B) D)))))
% 0.25/0.66 (assert (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Su1783761653um_b_c) (C tptp.set_Sum_sum_c_c) (D tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.ord_le542695343um_b_c (@ (@ tptp.produc919784577um_b_c A) B)) (@ (@ tptp.produc919784577um_b_c C) D)) (and (@ (@ tptp.ord_le1772180283um_c_c A) C) (@ (@ tptp.ord_le929608341um_b_c B) D)))))
% 0.25/0.66 (assert (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Sum_sum_c_c) (C tptp.set_Su1783761653um_b_c) (D tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.ord_le1852514783um_c_c (@ (@ tptp.produc616453753um_c_c A) B)) (@ (@ tptp.produc616453753um_c_c C) D)) (and (@ (@ tptp.ord_le929608341um_b_c A) C) (@ (@ tptp.ord_le1772180283um_c_c B) D)))))
% 0.25/0.66 (assert (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c) (D tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.ord_le907560199um_b_c (@ (@ tptp.produc754249687um_b_c A) B)) (@ (@ tptp.produc754249687um_b_c C) D)) (and (@ (@ tptp.ord_le929608341um_b_c A) C) (@ (@ tptp.ord_le929608341um_b_c B) D)))))
% 0.25/0.66 (assert (forall ((B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c B) C)) A) (and (@ (@ tptp.ord_le1772180283um_c_c B) A) (@ (@ tptp.ord_le1772180283um_c_c C) A)))))
% 0.25/0.66 (assert (forall ((B tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c B) C)) A) (and (@ (@ tptp.ord_le929608341um_b_c B) A) (@ (@ tptp.ord_le929608341um_b_c C) A)))))
% 0.25/0.66 (assert (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c) (Z tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c X) Y)) Z) (and (@ (@ tptp.ord_le1772180283um_c_c X) Z) (@ (@ tptp.ord_le1772180283um_c_c Y) Z)))))
% 0.25/0.66 (assert (forall ((X tptp.set_Su1783761653um_b_c) (Y tptp.set_Su1783761653um_b_c) (Z tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c X) Y)) Z) (and (@ (@ tptp.ord_le929608341um_b_c X) Z) (@ (@ tptp.ord_le929608341um_b_c Y) Z)))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (C2 tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c A2) B2)) C2) (and (@ (@ tptp.ord_le1772180283um_c_c A2) C2) (@ (@ tptp.ord_le1772180283um_c_c B2) C2)))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c) (C2 tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c A2) B2)) C2) (and (@ (@ tptp.ord_le929608341um_b_c A2) C2) (@ (@ tptp.ord_le929608341um_b_c B2) C2)))))
% 0.25/0.66 (assert (forall ((A tptp.hp_a_b_c) (B tptp.hp_a_b_c)) (= (@ tptp.hpsafe_a_b_c (@ (@ tptp.choice_a_b_c A) B)) (and (@ tptp.hpsafe_a_b_c A) (@ tptp.hpsafe_a_b_c B)))))
% 0.25/0.66 (assert (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c (@ (@ tptp.produc394644079real_c tptp.nu_12) tptp.nu_1)) (@ (@ tptp.produc394644079real_c tptp.mu3) tptp.mu2))) (@ (@ tptp.denota904684656_a_b_c tptp.i) tptp.b)))
% 0.25/0.66 (assert (let ((_let_1 (@ tptp.denota904684656_a_b_c tptp.i))) (let ((_let_2 (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c (@ (@ tptp.produc394644079real_c tptp.nu_12) tptp.nu_1)) (@ (@ tptp.produc394644079real_c tptp.mu3) tptp.mu2))))) (or (@ _let_2 (@ _let_1 tptp.a)) (@ _let_2 (@ _let_1 tptp.b))))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Pr754230471real_c) (B2 tptp.set_Pr754230471real_c) (X tptp.produc640052711real_c)) (let ((_let_1 (@ tptp.member346808080real_c X))) (=> (@ (@ tptp.ord_le1988344935real_c A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (X tptp.sum_sum_c_c)) (let ((_let_1 (@ tptp.member_Sum_sum_c_c X))) (=> (@ (@ tptp.ord_le1772180283um_c_c A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c) (X tptp.sum_su737395349um_b_c)) (let ((_let_1 (@ tptp.member1893232190um_b_c X))) (=> (@ (@ tptp.ord_le929608341um_b_c A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Pr754230471real_c) (B2 tptp.set_Pr754230471real_c) (C tptp.produc640052711real_c)) (let ((_let_1 (@ tptp.member346808080real_c C))) (=> (@ (@ tptp.ord_le1988344935real_c A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (C tptp.sum_sum_c_c)) (let ((_let_1 (@ tptp.member_Sum_sum_c_c C))) (=> (@ (@ tptp.ord_le1772180283um_c_c A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c) (C tptp.sum_su737395349um_b_c)) (let ((_let_1 (@ tptp.member1893232190um_b_c C))) (=> (@ (@ tptp.ord_le929608341um_b_c A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (=> (= A2 B2) (not (=> (@ (@ tptp.ord_le1772180283um_c_c A2) B2) (not (@ (@ tptp.ord_le1772180283um_c_c B2) A2)))))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c)) (=> (= A2 B2) (not (=> (@ (@ tptp.ord_le929608341um_b_c A2) B2) (not (@ (@ tptp.ord_le929608341um_b_c B2) A2)))))))
% 0.25/0.66 (assert (= tptp.ord_le1988344935real_c (lambda ((A3 tptp.set_Pr754230471real_c) (B3 tptp.set_Pr754230471real_c)) (forall ((X3 tptp.produc640052711real_c)) (let ((_let_1 (@ tptp.member346808080real_c X3))) (=> (@ _let_1 A3) (@ _let_1 B3)))))))
% 0.25/0.66 (assert (= tptp.ord_le1772180283um_c_c (lambda ((A3 tptp.set_Sum_sum_c_c) (B3 tptp.set_Sum_sum_c_c)) (forall ((X3 tptp.sum_sum_c_c)) (let ((_let_1 (@ tptp.member_Sum_sum_c_c X3))) (=> (@ _let_1 A3) (@ _let_1 B3)))))))
% 0.25/0.66 (assert (= tptp.ord_le929608341um_b_c (lambda ((A3 tptp.set_Su1783761653um_b_c) (B3 tptp.set_Su1783761653um_b_c)) (forall ((X3 tptp.sum_su737395349um_b_c)) (let ((_let_1 (@ tptp.member1893232190um_b_c X3))) (=> (@ _let_1 A3) (@ _let_1 B3)))))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (=> (= A2 B2) (@ (@ tptp.ord_le1772180283um_c_c A2) B2))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c)) (=> (= A2 B2) (@ (@ tptp.ord_le929608341um_b_c A2) B2))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (=> (= A2 B2) (@ (@ tptp.ord_le1772180283um_c_c B2) A2))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c)) (=> (= A2 B2) (@ (@ tptp.ord_le929608341um_b_c B2) A2))))
% 0.25/0.66 (assert (= tptp.ord_le1988344935real_c (lambda ((A3 tptp.set_Pr754230471real_c) (B3 tptp.set_Pr754230471real_c)) (forall ((T tptp.produc640052711real_c)) (let ((_let_1 (@ tptp.member346808080real_c T))) (=> (@ _let_1 A3) (@ _let_1 B3)))))))
% 0.25/0.66 (assert (= tptp.ord_le1772180283um_c_c (lambda ((A3 tptp.set_Sum_sum_c_c) (B3 tptp.set_Sum_sum_c_c)) (forall ((T tptp.sum_sum_c_c)) (let ((_let_1 (@ tptp.member_Sum_sum_c_c T))) (=> (@ _let_1 A3) (@ _let_1 B3)))))))
% 0.25/0.66 (assert (= tptp.ord_le929608341um_b_c (lambda ((A3 tptp.set_Su1783761653um_b_c) (B3 tptp.set_Su1783761653um_b_c)) (forall ((T tptp.sum_su737395349um_b_c)) (let ((_let_1 (@ tptp.member1893232190um_b_c T))) (=> (@ _let_1 A3) (@ _let_1 B3)))))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c A2) A2)))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c A2) A2)))
% 0.25/0.66 (assert (forall ((P (-> tptp.sum_sum_c_c Bool)) (Q (-> tptp.sum_sum_c_c Bool))) (=> (forall ((X2 tptp.sum_sum_c_c)) (=> (@ P X2) (@ Q X2))) (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.collect_Sum_sum_c_c P)) (@ tptp.collect_Sum_sum_c_c Q)))))
% 0.25/0.66 (assert (forall ((P (-> tptp.sum_su737395349um_b_c Bool)) (Q (-> tptp.sum_su737395349um_b_c Bool))) (=> (forall ((X2 tptp.sum_su737395349um_b_c)) (=> (@ P X2) (@ Q X2))) (@ (@ tptp.ord_le929608341um_b_c (@ tptp.collec2086029184um_b_c P)) (@ tptp.collec2086029184um_b_c Q)))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (C2 tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.ord_le1772180283um_c_c A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le1772180283um_c_c B2) C2) (@ _let_1 C2))))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c) (C2 tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.ord_le929608341um_b_c A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le929608341um_b_c B2) C2) (@ _let_1 C2))))))
% 0.25/0.66 (assert (= (lambda ((Y2 tptp.set_Sum_sum_c_c) (Z2 tptp.set_Sum_sum_c_c)) (= Y2 Z2)) (lambda ((A3 tptp.set_Sum_sum_c_c) (B3 tptp.set_Sum_sum_c_c)) (and (@ (@ tptp.ord_le1772180283um_c_c A3) B3) (@ (@ tptp.ord_le1772180283um_c_c B3) A3)))))
% 0.25/0.66 (assert (= (lambda ((Y2 tptp.set_Su1783761653um_b_c) (Z2 tptp.set_Su1783761653um_b_c)) (= Y2 Z2)) (lambda ((A3 tptp.set_Su1783761653um_b_c) (B3 tptp.set_Su1783761653um_b_c)) (and (@ (@ tptp.ord_le929608341um_b_c A3) B3) (@ (@ tptp.ord_le929608341um_b_c B3) A3)))))
% 0.25/0.66 (assert (forall ((A tptp.produc640052711real_c) (P (-> tptp.produc640052711real_c Bool))) (= (@ (@ tptp.member346808080real_c A) (@ tptp.collec1126017874real_c P)) (@ P A))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Pr754230471real_c)) (= (@ tptp.collec1126017874real_c (lambda ((X3 tptp.produc640052711real_c)) (@ (@ tptp.member346808080real_c X3) A2))) A2)))
% 0.25/0.66 (assert (forall ((P (-> tptp.sum_sum_c_c Bool)) (Q (-> tptp.sum_sum_c_c Bool))) (= (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.collect_Sum_sum_c_c P)) (@ tptp.collect_Sum_sum_c_c Q)) (forall ((X3 tptp.sum_sum_c_c)) (=> (@ P X3) (@ Q X3))))))
% 0.25/0.66 (assert (forall ((P (-> tptp.sum_su737395349um_b_c Bool)) (Q (-> tptp.sum_su737395349um_b_c Bool))) (= (@ (@ tptp.ord_le929608341um_b_c (@ tptp.collec2086029184um_b_c P)) (@ tptp.collec2086029184um_b_c Q)) (forall ((X3 tptp.sum_su737395349um_b_c)) (=> (@ P X3) (@ Q X3))))))
% 0.25/0.66 (assert (forall ((X tptp.produc190496183real_c) (X4 tptp.produc190496183real_c) (Y tptp.produc190496183real_c) (Y3 tptp.produc190496183real_c)) (=> (@ (@ tptp.ord_le850691415real_c X) X4) (=> (@ (@ tptp.ord_le850691415real_c Y) Y3) (@ (@ tptp.ord_le652477831real_c (@ (@ tptp.produc1687028567real_c X) Y)) (@ (@ tptp.produc1687028567real_c X4) Y3))))))
% 0.25/0.66 (assert (forall ((X tptp.finite1398487019real_c) (X4 tptp.finite1398487019real_c) (Y tptp.finite1398487019real_c) (Y3 tptp.finite1398487019real_c)) (=> (@ (@ tptp.ord_le775706699real_c X) X4) (=> (@ (@ tptp.ord_le775706699real_c Y) Y3) (@ (@ tptp.ord_le850691415real_c (@ (@ tptp.produc394644079real_c X) Y)) (@ (@ tptp.produc394644079real_c X4) Y3))))))
% 0.25/0.66 (assert (forall ((X tptp.set_Sum_sum_c_c) (X4 tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c) (Y3 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X) X4) (=> (@ (@ tptp.ord_le1772180283um_c_c Y) Y3) (@ (@ tptp.ord_le684454199um_c_c (@ (@ tptp.produc1439061071um_c_c X) Y)) (@ (@ tptp.produc1439061071um_c_c X4) Y3))))))
% 0.25/0.66 (assert (forall ((X tptp.set_Sum_sum_c_c) (X4 tptp.set_Sum_sum_c_c) (Y tptp.set_Su1783761653um_b_c) (Y3 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X) X4) (=> (@ (@ tptp.ord_le929608341um_b_c Y) Y3) (@ (@ tptp.ord_le542695343um_b_c (@ (@ tptp.produc919784577um_b_c X) Y)) (@ (@ tptp.produc919784577um_b_c X4) Y3))))))
% 0.25/0.66 (assert (forall ((X tptp.set_Su1783761653um_b_c) (X4 tptp.set_Su1783761653um_b_c) (Y tptp.set_Sum_sum_c_c) (Y3 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X) X4) (=> (@ (@ tptp.ord_le1772180283um_c_c Y) Y3) (@ (@ tptp.ord_le1852514783um_c_c (@ (@ tptp.produc616453753um_c_c X) Y)) (@ (@ tptp.produc616453753um_c_c X4) Y3))))))
% 0.25/0.66 (assert (forall ((X tptp.set_Su1783761653um_b_c) (X4 tptp.set_Su1783761653um_b_c) (Y tptp.set_Su1783761653um_b_c) (Y3 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X) X4) (=> (@ (@ tptp.ord_le929608341um_b_c Y) Y3) (@ (@ tptp.ord_le907560199um_b_c (@ (@ tptp.produc754249687um_b_c X) Y)) (@ (@ tptp.produc754249687um_b_c X4) Y3))))))
% 0.25/0.66 (assert (forall ((C tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.ord_le1772180283um_c_c C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c A) B))))))
% 0.25/0.66 (assert (forall ((C tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.ord_le929608341um_b_c C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su1968964297um_b_c A) B))))))
% 0.25/0.66 (assert (forall ((C tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.ord_le1772180283um_c_c C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c A) B))))))
% 0.25/0.66 (assert (forall ((C tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.ord_le929608341um_b_c C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su1968964297um_b_c A) B))))))
% 0.25/0.66 (assert (= tptp.ord_le1772180283um_c_c (lambda ((A4 tptp.set_Sum_sum_c_c) (B4 tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.sup_su1349021703um_c_c A4) B4) B4))))
% 0.25/0.66 (assert (= tptp.ord_le929608341um_b_c (lambda ((A4 tptp.set_Su1783761653um_b_c) (B4 tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.sup_su1968964297um_b_c A4) B4) B4))))
% 0.25/0.66 (assert (= tptp.ord_le1772180283um_c_c (lambda ((B4 tptp.set_Sum_sum_c_c) (A4 tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.sup_su1349021703um_c_c A4) B4) A4))))
% 0.25/0.66 (assert (= tptp.ord_le929608341um_b_c (lambda ((B4 tptp.set_Su1783761653um_b_c) (A4 tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.sup_su1968964297um_b_c A4) B4) A4))))
% 0.25/0.66 (assert (forall ((B tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c B) (@ (@ tptp.sup_su1349021703um_c_c A) B))))
% 0.25/0.66 (assert (forall ((B tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c B) (@ (@ tptp.sup_su1968964297um_b_c A) B))))
% 0.25/0.66 (assert (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c A) (@ (@ tptp.sup_su1349021703um_c_c A) B))))
% 0.25/0.66 (assert (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c A) (@ (@ tptp.sup_su1968964297um_b_c A) B))))
% 0.25/0.66 (assert (= tptp.ord_le1772180283um_c_c (lambda ((B4 tptp.set_Sum_sum_c_c) (A4 tptp.set_Sum_sum_c_c)) (= A4 (@ (@ tptp.sup_su1349021703um_c_c A4) B4)))))
% 0.25/0.66 (assert (= tptp.ord_le929608341um_b_c (lambda ((B4 tptp.set_Su1783761653um_b_c) (A4 tptp.set_Su1783761653um_b_c)) (= A4 (@ (@ tptp.sup_su1968964297um_b_c A4) B4)))))
% 0.25/0.66 (assert (forall ((B tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c B) A) (=> (@ (@ tptp.ord_le1772180283um_c_c C) A) (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c B) C)) A)))))
% 0.25/0.66 (assert (forall ((B tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c B) A) (=> (@ (@ tptp.ord_le929608341um_b_c C) A) (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c B) C)) A)))))
% 0.25/0.66 (assert (forall ((B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c B) C)) A) (not (=> (@ (@ tptp.ord_le1772180283um_c_c B) A) (not (@ (@ tptp.ord_le1772180283um_c_c C) A)))))))
% 0.25/0.66 (assert (forall ((B tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c B) C)) A) (not (=> (@ (@ tptp.ord_le929608341um_b_c B) A) (not (@ (@ tptp.ord_le929608341um_b_c C) A)))))))
% 0.25/0.66 (assert (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X) Y) (= (@ (@ tptp.sup_su1349021703um_c_c X) Y) Y))))
% 0.25/0.66 (assert (forall ((X tptp.set_Su1783761653um_b_c) (Y tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X) Y) (= (@ (@ tptp.sup_su1968964297um_b_c X) Y) Y))))
% 0.25/0.66 (assert (forall ((Y tptp.set_Sum_sum_c_c) (X tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c Y) X) (= (@ (@ tptp.sup_su1349021703um_c_c X) Y) X))))
% 0.25/0.66 (assert (forall ((Y tptp.set_Su1783761653um_b_c) (X tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c Y) X) (= (@ (@ tptp.sup_su1968964297um_b_c X) Y) X))))
% 0.25/0.66 (assert (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A) B) (= (@ (@ tptp.sup_su1349021703um_c_c A) B) B))))
% 0.25/0.66 (assert (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A) B) (= (@ (@ tptp.sup_su1968964297um_b_c A) B) B))))
% 0.25/0.66 (assert (forall ((B tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c B) A) (= (@ (@ tptp.sup_su1349021703um_c_c A) B) A))))
% 0.25/0.66 (assert (forall ((B tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c B) A) (= (@ (@ tptp.sup_su1968964297um_b_c A) B) A))))
% 0.25/0.66 (assert (forall ((F (-> tptp.set_Sum_sum_c_c tptp.set_Sum_sum_c_c tptp.set_Sum_sum_c_c)) (X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c)) (=> (forall ((X2 tptp.set_Sum_sum_c_c) (Y4 tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c X2) (@ (@ F X2) Y4))) (=> (forall ((X2 tptp.set_Sum_sum_c_c) (Y4 tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c Y4) (@ (@ F X2) Y4))) (=> (forall ((X2 tptp.set_Sum_sum_c_c) (Y4 tptp.set_Sum_sum_c_c) (Z3 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c Y4) X2) (=> (@ (@ tptp.ord_le1772180283um_c_c Z3) X2) (@ (@ tptp.ord_le1772180283um_c_c (@ (@ F Y4) Z3)) X2)))) (= (@ (@ tptp.sup_su1349021703um_c_c X) Y) (@ (@ F X) Y)))))))
% 0.25/0.66 (assert (forall ((F (-> tptp.set_Su1783761653um_b_c tptp.set_Su1783761653um_b_c tptp.set_Su1783761653um_b_c)) (X tptp.set_Su1783761653um_b_c) (Y tptp.set_Su1783761653um_b_c)) (=> (forall ((X2 tptp.set_Su1783761653um_b_c) (Y4 tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c X2) (@ (@ F X2) Y4))) (=> (forall ((X2 tptp.set_Su1783761653um_b_c) (Y4 tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c Y4) (@ (@ F X2) Y4))) (=> (forall ((X2 tptp.set_Su1783761653um_b_c) (Y4 tptp.set_Su1783761653um_b_c) (Z3 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c Y4) X2) (=> (@ (@ tptp.ord_le929608341um_b_c Z3) X2) (@ (@ tptp.ord_le929608341um_b_c (@ (@ F Y4) Z3)) X2)))) (= (@ (@ tptp.sup_su1968964297um_b_c X) Y) (@ (@ F X) Y)))))))
% 0.25/0.66 (assert (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c)) (=> (= A (@ (@ tptp.sup_su1349021703um_c_c A) B)) (@ (@ tptp.ord_le1772180283um_c_c B) A))))
% 0.25/0.66 (assert (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c)) (=> (= A (@ (@ tptp.sup_su1968964297um_b_c A) B)) (@ (@ tptp.ord_le929608341um_b_c B) A))))
% 0.25/0.66 (assert (forall ((B tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c B) A) (= A (@ (@ tptp.sup_su1349021703um_c_c A) B)))))
% 0.25/0.66 (assert (forall ((B tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c B) A) (= A (@ (@ tptp.sup_su1968964297um_b_c A) B)))))
% 0.25/0.66 (assert (= tptp.ord_le1772180283um_c_c (lambda ((X3 tptp.set_Sum_sum_c_c) (Y5 tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.sup_su1349021703um_c_c X3) Y5) Y5))))
% 0.25/0.66 (assert (= tptp.ord_le929608341um_b_c (lambda ((X3 tptp.set_Su1783761653um_b_c) (Y5 tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.sup_su1968964297um_b_c X3) Y5) Y5))))
% 0.25/0.66 (assert (forall ((Y tptp.set_Sum_sum_c_c) (X tptp.set_Sum_sum_c_c) (Z tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c Y) X) (=> (@ (@ tptp.ord_le1772180283um_c_c Z) X) (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c Y) Z)) X)))))
% 0.25/0.66 (assert (forall ((Y tptp.set_Su1783761653um_b_c) (X tptp.set_Su1783761653um_b_c) (Z tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c Y) X) (=> (@ (@ tptp.ord_le929608341um_b_c Z) X) (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c Y) Z)) X)))))
% 0.25/0.66 (assert (forall ((A tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (D tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A) C) (=> (@ (@ tptp.ord_le1772180283um_c_c B) D) (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c A) B)) (@ (@ tptp.sup_su1349021703um_c_c C) D))))))
% 0.25/0.66 (assert (forall ((A tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (D tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A) C) (=> (@ (@ tptp.ord_le929608341um_b_c B) D) (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c A) B)) (@ (@ tptp.sup_su1968964297um_b_c C) D))))))
% 0.25/0.66 (assert (forall ((C tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c) (D tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c C) A) (=> (@ (@ tptp.ord_le1772180283um_c_c D) B) (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c C) D)) (@ (@ tptp.sup_su1349021703um_c_c A) B))))))
% 0.25/0.66 (assert (forall ((C tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c) (D tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c C) A) (=> (@ (@ tptp.ord_le929608341um_b_c D) B) (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c C) D)) (@ (@ tptp.sup_su1968964297um_b_c A) B))))))
% 0.25/0.66 (assert (forall ((X tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.ord_le1772180283um_c_c X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c A) B))))))
% 0.25/0.66 (assert (forall ((X tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.ord_le929608341um_b_c X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su1968964297um_b_c A) B))))))
% 0.25/0.66 (assert (forall ((X tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.ord_le1772180283um_c_c X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c A) B))))))
% 0.25/0.66 (assert (forall ((X tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.ord_le929608341um_b_c X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su1968964297um_b_c A) B))))))
% 0.25/0.66 (assert (forall ((Y tptp.set_Sum_sum_c_c) (X tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c Y) (@ (@ tptp.sup_su1349021703um_c_c X) Y))))
% 0.25/0.66 (assert (forall ((Y tptp.set_Su1783761653um_b_c) (X tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c Y) (@ (@ tptp.sup_su1968964297um_b_c X) Y))))
% 0.25/0.66 (assert (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c X) (@ (@ tptp.sup_su1349021703um_c_c X) Y))))
% 0.25/0.66 (assert (forall ((X tptp.set_Su1783761653um_b_c) (Y tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c X) (@ (@ tptp.sup_su1968964297um_b_c X) Y))))
% 0.25/0.66 (assert (forall ((A tptp.set_Sum_sum_c_c) (X tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A) X) (=> (@ (@ tptp.ord_le1772180283um_c_c B) X) (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c A) B)) X)))))
% 0.25/0.66 (assert (forall ((A tptp.set_Su1783761653um_b_c) (X tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A) X) (=> (@ (@ tptp.ord_le929608341um_b_c B) X) (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c A) B)) X)))))
% 0.25/0.66 (assert (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (X tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c A) B)) X) (not (=> (@ (@ tptp.ord_le1772180283um_c_c A) X) (not (@ (@ tptp.ord_le1772180283um_c_c B) X)))))))
% 0.25/0.66 (assert (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (X tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c A) B)) X) (not (=> (@ (@ tptp.ord_le929608341um_b_c A) X) (not (@ (@ tptp.ord_le929608341um_b_c B) X)))))))
% 0.25/0.66 (assert (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c X) (@ (@ tptp.sup_su1349021703um_c_c X) Y))))
% 0.25/0.66 (assert (forall ((X tptp.set_Su1783761653um_b_c) (Y tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c X) (@ (@ tptp.sup_su1968964297um_b_c X) Y))))
% 0.25/0.66 (assert (forall ((Y tptp.set_Sum_sum_c_c) (X tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c Y) (@ (@ tptp.sup_su1349021703um_c_c X) Y))))
% 0.25/0.66 (assert (forall ((Y tptp.set_Su1783761653um_b_c) (X tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c Y) (@ (@ tptp.sup_su1968964297um_b_c X) Y))))
% 0.25/0.66 (assert (= tptp.ord_le1772180283um_c_c (lambda ((A3 tptp.set_Sum_sum_c_c) (B3 tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.sup_su1349021703um_c_c A3) B3) B3))))
% 0.25/0.66 (assert (= tptp.ord_le929608341um_b_c (lambda ((A3 tptp.set_Su1783761653um_b_c) (B3 tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.sup_su1968964297um_b_c A3) B3) B3))))
% 0.25/0.66 (assert (forall ((C2 tptp.set_Sum_sum_c_c) (A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c C2) (@ (@ tptp.sup_su1349021703um_c_c A2) B2)) (not (forall ((A5 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A5) A2) (forall ((B5 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c B5) B2) (not (= C2 (@ (@ tptp.sup_su1349021703um_c_c A5) B5)))))))))))
% 0.25/0.66 (assert (forall ((C2 tptp.set_Su1783761653um_b_c) (A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c C2) (@ (@ tptp.sup_su1968964297um_b_c A2) B2)) (not (forall ((A5 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A5) A2) (forall ((B5 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c B5) B2) (not (= C2 (@ (@ tptp.sup_su1968964297um_b_c A5) B5)))))))))))
% 0.25/0.66 (assert (forall ((B2 tptp.set_Sum_sum_c_c) (A2 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c B2) A2) (= (@ (@ tptp.sup_su1349021703um_c_c A2) B2) A2))))
% 0.25/0.66 (assert (forall ((B2 tptp.set_Su1783761653um_b_c) (A2 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c B2) A2) (= (@ (@ tptp.sup_su1968964297um_b_c A2) B2) A2))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A2) B2) (= (@ (@ tptp.sup_su1349021703um_c_c A2) B2) B2))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A2) B2) (= (@ (@ tptp.sup_su1968964297um_b_c A2) B2) B2))))
% 0.25/0.66 (assert (forall ((B2 tptp.set_Sum_sum_c_c) (A2 tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c B2) (@ (@ tptp.sup_su1349021703um_c_c A2) B2))))
% 0.25/0.66 (assert (forall ((B2 tptp.set_Su1783761653um_b_c) (A2 tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c B2) (@ (@ tptp.sup_su1968964297um_b_c A2) B2))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c A2) (@ (@ tptp.sup_su1349021703um_c_c A2) B2))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c A2) (@ (@ tptp.sup_su1968964297um_b_c A2) B2))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Sum_sum_c_c) (C2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A2) C2) (=> (@ (@ tptp.ord_le1772180283um_c_c B2) C2) (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c A2) B2)) C2)))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Su1783761653um_b_c) (C2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A2) C2) (=> (@ (@ tptp.ord_le929608341um_b_c B2) C2) (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c A2) B2)) C2)))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Sum_sum_c_c) (C2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (D2 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A2) C2) (=> (@ (@ tptp.ord_le1772180283um_c_c B2) D2) (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c A2) B2)) (@ (@ tptp.sup_su1349021703um_c_c C2) D2))))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Su1783761653um_b_c) (C2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c) (D2 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A2) C2) (=> (@ (@ tptp.ord_le929608341um_b_c B2) D2) (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c A2) B2)) (@ (@ tptp.sup_su1968964297um_b_c C2) D2))))))
% 0.25/0.66 (assert (forall ((A tptp.hp_a_b_c) (B tptp.hp_a_b_c)) (=> (@ tptp.hpsafe_a_b_c A) (=> (@ tptp.hpsafe_a_b_c B) (@ tptp.hpsafe_a_b_c (@ (@ tptp.choice_a_b_c A) B))))))
% 0.25/0.66 (assert (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c) (Z tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c X))) (let ((_let_2 (@ tptp.sup_su1349021703um_c_c Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.25/0.66 (assert (forall ((B tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c B))) (let ((_let_2 (@ tptp.sup_su1349021703um_c_c A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.25/0.66 (assert (= tptp.sup_su1349021703um_c_c (lambda ((X3 tptp.set_Sum_sum_c_c) (Y5 tptp.set_Sum_sum_c_c)) (@ (@ tptp.sup_su1349021703um_c_c Y5) X3))))
% 0.25/0.66 (assert (= tptp.sup_su1349021703um_c_c (lambda ((A4 tptp.set_Sum_sum_c_c) (B4 tptp.set_Sum_sum_c_c)) (@ (@ tptp.sup_su1349021703um_c_c B4) A4))))
% 0.25/0.66 (assert (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c) (Z tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c X))) (= (@ (@ tptp.sup_su1349021703um_c_c (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c Y) Z))))))
% 0.25/0.66 (assert (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c A))) (= (@ (@ tptp.sup_su1349021703um_c_c (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c B) C))))))
% 0.25/0.66 (assert (forall ((B2 tptp.set_Sum_sum_c_c) (K tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c A))) (let ((_let_2 (@ tptp.sup_su1349021703um_c_c K))) (=> (= B2 (@ _let_2 B)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B))))))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Sum_sum_c_c) (K tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.sup_su1349021703um_c_c A2) B) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c A) B)))))))
% 0.25/0.66 (assert (= tptp.sup_su1349021703um_c_c (lambda ((X3 tptp.set_Sum_sum_c_c) (Y5 tptp.set_Sum_sum_c_c)) (@ (@ tptp.sup_su1349021703um_c_c Y5) X3))))
% 0.25/0.66 (assert (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c) (Z tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c X))) (= (@ (@ tptp.sup_su1349021703um_c_c (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c Y) Z))))))
% 0.25/0.66 (assert (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c) (Z tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c X))) (let ((_let_2 (@ tptp.sup_su1349021703um_c_c Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.25/0.66 (assert (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (C2 tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c A2))) (let ((_let_2 (@ tptp.sup_su1349021703um_c_c B2))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))))
% 0.25/0.66 (assert (= tptp.sup_su1349021703um_c_c (lambda ((A3 tptp.set_Sum_sum_c_c) (B3 tptp.set_Sum_sum_c_c)) (@ (@ tptp.sup_su1349021703um_c_c B3) A3))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.sup_su1349021703um_c_c A2) A2) A2)))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (C2 tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c A2))) (= (@ (@ tptp.sup_su1349021703um_c_c (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c B2) C2))))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (P (-> tptp.sum_sum_c_c Bool))) (= (forall ((X3 tptp.sum_sum_c_c)) (=> (@ (@ tptp.member_Sum_sum_c_c X3) (@ (@ tptp.sup_su1349021703um_c_c A2) B2)) (@ P X3))) (and (forall ((X3 tptp.sum_sum_c_c)) (=> (@ (@ tptp.member_Sum_sum_c_c X3) A2) (@ P X3))) (forall ((X3 tptp.sum_sum_c_c)) (=> (@ (@ tptp.member_Sum_sum_c_c X3) B2) (@ P X3)))))))
% 0.25/0.66 (assert (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (P (-> tptp.sum_sum_c_c Bool))) (= (exists ((X3 tptp.sum_sum_c_c)) (and (@ (@ tptp.member_Sum_sum_c_c X3) (@ (@ tptp.sup_su1349021703um_c_c A2) B2)) (@ P X3))) (or (exists ((X3 tptp.sum_sum_c_c)) (and (@ (@ tptp.member_Sum_sum_c_c X3) A2) (@ P X3))) (exists ((X3 tptp.sum_sum_c_c)) (and (@ (@ tptp.member_Sum_sum_c_c X3) B2) (@ P X3)))))))
% 0.25/0.66 (assert (forall ((C tptp.produc640052711real_c) (B2 tptp.set_Pr754230471real_c) (A2 tptp.set_Pr754230471real_c)) (let ((_let_1 (@ tptp.member346808080real_c C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_su588839579real_c A2) B2))))))
% 0.25/0.66 (assert (forall ((C tptp.sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (A2 tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.member_Sum_sum_c_c C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c A2) B2))))))
% 0.25/0.66 (assert (forall ((C tptp.produc640052711real_c) (A2 tptp.set_Pr754230471real_c) (B2 tptp.set_Pr754230471real_c)) (let ((_let_1 (@ tptp.member346808080real_c C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su588839579real_c A2) B2))))))
% 0.25/0.66 (assert (forall ((C tptp.sum_sum_c_c) (A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.member_Sum_sum_c_c C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c A2) B2))))))
% 0.25/0.66 (assert (forall ((C tptp.produc640052711real_c) (A2 tptp.set_Pr754230471real_c) (B2 tptp.set_Pr754230471real_c)) (let ((_let_1 (@ tptp.member346808080real_c C))) (=> (@ _let_1 (@ (@ tptp.sup_su588839579real_c A2) B2)) (=> (not (@ _let_1 A2)) (@ _let_1 B2))))))
% 0.25/0.66 (assert (forall ((C tptp.sum_sum_c_c) (A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.member_Sum_sum_c_c C))) (=> (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c A2) B2)) (=> (not (@ _let_1 A2)) (@ _let_1 B2))))))
% 0.25/0.66 (assert (@ (@ (@ tptp.denota69106024_a_b_c tptp.i) tptp.j) (@ tptp.static_SIGP_a_b_c (@ (@ tptp.choice_a_b_c tptp.a) tptp.b))))
% 0.25/0.66 (assert (forall ((I tptp.denota231621370t_unit) (J tptp.denota231621370t_unit)) (and (forall ((Nu tptp.produc190496183real_c) (Nu2 tptp.produc190496183real_c) (Mu2 tptp.produc190496183real_c) (V tptp.set_Sum_sum_c_c)) (=> (@ (@ (@ tptp.denota69106024_a_b_c I) J) (@ tptp.static_SIGP_a_b_c tptp.a)) (=> (@ (@ (@ tptp.denota1997846518gree_c Nu) Nu2) V) (=> (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.static_FVP_a_b_c tptp.a)) V) (=> (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c Nu) Mu2)) (@ (@ tptp.denota904684656_a_b_c I) tptp.a)) (exists ((Mu3 tptp.produc190496183real_c)) (and (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c Nu2) Mu3)) (@ (@ tptp.denota904684656_a_b_c J) tptp.a)) (@ (@ (@ tptp.denota1997846518gree_c Mu2) Mu3) (@ (@ tptp.sup_su1349021703um_c_c (@ tptp.static_MBV_a_b_c tptp.a)) V))))))))) (@ (@ tptp.coinci772602909_a_b_c tptp.a) I))))
% 0.25/0.67 (assert (forall ((I tptp.denota231621370t_unit) (J tptp.denota231621370t_unit)) (and (forall ((Nu tptp.produc190496183real_c) (Nu2 tptp.produc190496183real_c) (Mu2 tptp.produc190496183real_c) (V tptp.set_Sum_sum_c_c)) (=> (@ (@ (@ tptp.denota69106024_a_b_c I) J) (@ tptp.static_SIGP_a_b_c tptp.b)) (=> (@ (@ (@ tptp.denota1997846518gree_c Nu) Nu2) V) (=> (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.static_FVP_a_b_c tptp.b)) V) (=> (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c Nu) Mu2)) (@ (@ tptp.denota904684656_a_b_c I) tptp.b)) (exists ((Mu3 tptp.produc190496183real_c)) (and (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c Nu2) Mu3)) (@ (@ tptp.denota904684656_a_b_c J) tptp.b)) (@ (@ (@ tptp.denota1997846518gree_c Mu2) Mu3) (@ (@ tptp.sup_su1349021703um_c_c (@ tptp.static_MBV_a_b_c tptp.b)) V))))))))) (@ (@ tptp.coinci772602909_a_b_c tptp.b) I))))
% 0.25/0.67 (assert (= tptp.coinci1852866155_a_b_c (lambda ((Alpha tptp.hp_a_b_c)) (forall ((I2 tptp.denota231621370t_unit) (J2 tptp.denota231621370t_unit)) (and (@ (@ (@ tptp.coinci354700372_a_b_c Alpha) I2) J2) (@ (@ tptp.coinci772602909_a_b_c Alpha) I2))))))
% 0.25/0.67 (assert (forall ((Alpha2 tptp.hp_a_b_c) (Beta tptp.hp_a_b_c)) (= (@ tptp.static_FVP_a_b_c (@ (@ tptp.choice_a_b_c Alpha2) Beta)) (@ (@ tptp.sup_su1349021703um_c_c (@ tptp.static_FVP_a_b_c Alpha2)) (@ tptp.static_FVP_a_b_c Beta)))))
% 0.25/0.67 (assert (forall ((B2 tptp.set_Sum_sum_c_c) (A2 tptp.set_Sum_sum_c_c) (Nu3 tptp.produc190496183real_c) (Nu4 tptp.produc190496183real_c)) (let ((_let_1 (@ (@ tptp.denota1997846518gree_c Nu3) Nu4))) (=> (@ (@ tptp.ord_le1772180283um_c_c B2) A2) (=> (@ _let_1 A2) (@ _let_1 B2))))))
% 0.25/0.67 (assert (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (Nu3 tptp.produc190496183real_c) (Omega tptp.produc190496183real_c)) (let ((_let_1 (@ (@ tptp.denota1997846518gree_c Nu3) Omega))) (=> (@ (@ tptp.ord_le1772180283um_c_c A2) B2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 0.25/0.67 (assert (forall ((A tptp.produc190496183real_c) (B tptp.produc190496183real_c) (A6 tptp.produc190496183real_c) (B6 tptp.produc190496183real_c)) (= (= (@ (@ tptp.produc1687028567real_c A) B) (@ (@ tptp.produc1687028567real_c A6) B6)) (and (= A A6) (= B B6)))))
% 0.25/0.67 (assert (forall ((A tptp.finite1398487019real_c) (B tptp.finite1398487019real_c) (A6 tptp.finite1398487019real_c) (B6 tptp.finite1398487019real_c)) (= (= (@ (@ tptp.produc394644079real_c A) B) (@ (@ tptp.produc394644079real_c A6) B6)) (and (= A A6) (= B B6)))))
% 0.25/0.67 (assert (forall ((X1 tptp.produc190496183real_c) (X22 tptp.produc190496183real_c) (Y1 tptp.produc190496183real_c) (Y22 tptp.produc190496183real_c)) (= (= (@ (@ tptp.produc1687028567real_c X1) X22) (@ (@ tptp.produc1687028567real_c Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 0.25/0.67 (assert (forall ((X1 tptp.finite1398487019real_c) (X22 tptp.finite1398487019real_c) (Y1 tptp.finite1398487019real_c) (Y22 tptp.finite1398487019real_c)) (= (= (@ (@ tptp.produc394644079real_c X1) X22) (@ (@ tptp.produc394644079real_c Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 0.25/0.67 (assert (forall ((X tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c X) X)))
% 0.25/0.67 (assert (forall ((X tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c X) X)))
% 0.25/0.67 (assert (@ (@ tptp.ord_le929608341um_b_c (@ tptp.static_SIGP_a_b_c tptp.b)) (@ tptp.static_SIGP_a_b_c (@ (@ tptp.choice_a_b_c tptp.a) tptp.b))))
% 0.25/0.67 (assert (@ (@ tptp.ord_le929608341um_b_c (@ tptp.static_SIGP_a_b_c tptp.a)) (@ tptp.static_SIGP_a_b_c (@ (@ tptp.choice_a_b_c tptp.a) tptp.b))))
% 0.25/0.67 (assert (@ (@ (@ tptp.denota69106024_a_b_c tptp.i) tptp.j) (@ tptp.static_SIGP_a_b_c tptp.b)))
% 0.25/0.67 (assert (@ (@ (@ tptp.denota69106024_a_b_c tptp.i) tptp.j) (@ tptp.static_SIGP_a_b_c tptp.a)))
% 0.25/0.67 (assert (= tptp.coinci354700372_a_b_c (lambda ((Alpha tptp.hp_a_b_c) (I2 tptp.denota231621370t_unit) (J2 tptp.denota231621370t_unit)) (forall ((Nu5 tptp.produc190496183real_c) (Nu6 tptp.produc190496183real_c) (Mu4 tptp.produc190496183real_c) (V2 tptp.set_Sum_sum_c_c)) (=> (@ (@ (@ tptp.denota69106024_a_b_c I2) J2) (@ tptp.static_SIGP_a_b_c Alpha)) (=> (@ (@ (@ tptp.denota1997846518gree_c Nu5) Nu6) V2) (=> (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.static_FVP_a_b_c Alpha)) V2) (=> (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c Nu5) Mu4)) (@ (@ tptp.denota904684656_a_b_c I2) Alpha)) (exists ((Mu5 tptp.produc190496183real_c)) (and (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c Nu6) Mu5)) (@ (@ tptp.denota904684656_a_b_c J2) Alpha)) (@ (@ (@ tptp.denota1997846518gree_c Mu4) Mu5) (@ (@ tptp.sup_su1349021703um_c_c (@ tptp.static_MBV_a_b_c Alpha)) V2))))))))))))
% 0.25/0.67 (assert (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c) (I3 tptp.denota231621370t_unit) (J3 tptp.denota231621370t_unit)) (let ((_let_1 (@ (@ tptp.denota69106024_a_b_c I3) J3))) (=> (@ (@ tptp.ord_le929608341um_b_c A2) B2) (=> (@ _let_1 B2) (@ _let_1 A2))))))
% 0.25/0.67 (assert (forall ((I3 tptp.denota231621370t_unit) (A2 tptp.set_Su1783761653um_b_c)) (@ (@ (@ tptp.denota69106024_a_b_c I3) I3) A2)))
% 0.25/0.67 (assert (forall ((A2 tptp.denota231621370t_unit) (B2 tptp.denota231621370t_unit) (V3 tptp.set_Su1783761653um_b_c)) (=> (@ (@ (@ tptp.denota69106024_a_b_c A2) B2) V3) (@ (@ (@ tptp.denota69106024_a_b_c B2) A2) V3))))
% 0.25/0.67 (assert (forall ((A tptp.hp_a_b_c) (B tptp.hp_a_b_c)) (= (@ tptp.static_SIGP_a_b_c (@ (@ tptp.choice_a_b_c A) B)) (@ (@ tptp.sup_su1968964297um_b_c (@ tptp.static_SIGP_a_b_c A)) (@ tptp.static_SIGP_a_b_c B)))))
% 0.25/0.67 (assert (forall ((B tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c B) A) (=> (@ (@ tptp.ord_le1772180283um_c_c A) B) (= A B)))))
% 0.25/0.67 (assert (forall ((B tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c B) A) (=> (@ (@ tptp.ord_le929608341um_b_c A) B) (= A B)))))
% 0.25/0.67 (assert (= (lambda ((Y2 tptp.set_Sum_sum_c_c) (Z2 tptp.set_Sum_sum_c_c)) (= Y2 Z2)) (lambda ((A4 tptp.set_Sum_sum_c_c) (B4 tptp.set_Sum_sum_c_c)) (and (@ (@ tptp.ord_le1772180283um_c_c B4) A4) (@ (@ tptp.ord_le1772180283um_c_c A4) B4)))))
% 0.25/0.67 (assert (= (lambda ((Y2 tptp.set_Su1783761653um_b_c) (Z2 tptp.set_Su1783761653um_b_c)) (= Y2 Z2)) (lambda ((A4 tptp.set_Su1783761653um_b_c) (B4 tptp.set_Su1783761653um_b_c)) (and (@ (@ tptp.ord_le929608341um_b_c B4) A4) (@ (@ tptp.ord_le929608341um_b_c A4) B4)))))
% 0.25/0.67 (assert (forall ((B tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.ord_le1772180283um_c_c C))) (=> (@ (@ tptp.ord_le1772180283um_c_c B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.25/0.67 (assert (forall ((B tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.ord_le929608341um_b_c C))) (=> (@ (@ tptp.ord_le929608341um_b_c B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.25/0.67 (assert (forall ((A tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c A) A)))
% 0.25/0.67 (assert (forall ((A tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c A) A)))
% 0.25/0.67 (assert (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c) (Z tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.ord_le1772180283um_c_c X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le1772180283um_c_c Y) Z) (@ _let_1 Z))))))
% 0.25/0.67 (assert (forall ((X tptp.set_Su1783761653um_b_c) (Y tptp.set_Su1783761653um_b_c) (Z tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.ord_le929608341um_b_c X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le929608341um_b_c Y) Z) (@ _let_1 Z))))))
% 0.25/0.67 (assert (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A) B) (=> (@ (@ tptp.ord_le1772180283um_c_c B) A) (= A B)))))
% 0.25/0.67 (assert (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A) B) (=> (@ (@ tptp.ord_le929608341um_b_c B) A) (= A B)))))
% 0.25/0.67 (assert (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.ord_le1772180283um_c_c A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.25/0.67 (assert (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.ord_le929608341um_b_c A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.25/0.67 (assert (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c)) (=> (= A B) (=> (@ (@ tptp.ord_le1772180283um_c_c B) C) (@ (@ tptp.ord_le1772180283um_c_c A) C)))))
% 0.25/0.67 (assert (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c)) (=> (= A B) (=> (@ (@ tptp.ord_le929608341um_b_c B) C) (@ (@ tptp.ord_le929608341um_b_c A) C)))))
% 0.25/0.67 (assert (= (lambda ((Y2 tptp.set_Sum_sum_c_c) (Z2 tptp.set_Sum_sum_c_c)) (= Y2 Z2)) (lambda ((A4 tptp.set_Sum_sum_c_c) (B4 tptp.set_Sum_sum_c_c)) (and (@ (@ tptp.ord_le1772180283um_c_c A4) B4) (@ (@ tptp.ord_le1772180283um_c_c B4) A4)))))
% 0.25/0.67 (assert (= (lambda ((Y2 tptp.set_Su1783761653um_b_c) (Z2 tptp.set_Su1783761653um_b_c)) (= Y2 Z2)) (lambda ((A4 tptp.set_Su1783761653um_b_c) (B4 tptp.set_Su1783761653um_b_c)) (and (@ (@ tptp.ord_le929608341um_b_c A4) B4) (@ (@ tptp.ord_le929608341um_b_c B4) A4)))))
% 0.25/0.67 (assert (forall ((Y tptp.set_Sum_sum_c_c) (X tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c Y) X) (= (@ (@ tptp.ord_le1772180283um_c_c X) Y) (= X Y)))))
% 0.25/0.67 (assert (forall ((Y tptp.set_Su1783761653um_b_c) (X tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c Y) X) (= (@ (@ tptp.ord_le929608341um_b_c X) Y) (= X Y)))))
% 0.25/0.67 (assert (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.ord_le1772180283um_c_c A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le1772180283um_c_c B) C) (@ _let_1 C))))))
% 0.25/0.67 (assert (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.ord_le929608341um_b_c A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le929608341um_b_c B) C) (@ _let_1 C))))))
% 0.25/0.67 (assert (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c)) (=> (= X Y) (@ (@ tptp.ord_le1772180283um_c_c X) Y))))
% 0.25/0.67 (assert (forall ((X tptp.set_Su1783761653um_b_c) (Y tptp.set_Su1783761653um_b_c)) (=> (= X Y) (@ (@ tptp.ord_le929608341um_b_c X) Y))))
% 0.25/0.67 (assert (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X) Y) (=> (@ (@ tptp.ord_le1772180283um_c_c Y) X) (= X Y)))))
% 0.25/0.67 (assert (forall ((X tptp.set_Su1783761653um_b_c) (Y tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X) Y) (=> (@ (@ tptp.ord_le929608341um_b_c Y) X) (= X Y)))))
% 0.25/0.67 (assert (= (lambda ((Y2 tptp.set_Sum_sum_c_c) (Z2 tptp.set_Sum_sum_c_c)) (= Y2 Z2)) (lambda ((X3 tptp.set_Sum_sum_c_c) (Y5 tptp.set_Sum_sum_c_c)) (and (@ (@ tptp.ord_le1772180283um_c_c X3) Y5) (@ (@ tptp.ord_le1772180283um_c_c Y5) X3)))))
% 0.25/0.67 (assert (= (lambda ((Y2 tptp.set_Su1783761653um_b_c) (Z2 tptp.set_Su1783761653um_b_c)) (= Y2 Z2)) (lambda ((X3 tptp.set_Su1783761653um_b_c) (Y5 tptp.set_Su1783761653um_b_c)) (and (@ (@ tptp.ord_le929608341um_b_c X3) Y5) (@ (@ tptp.ord_le929608341um_b_c Y5) X3)))))
% 0.25/0.67 (assert (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (F (-> tptp.set_Sum_sum_c_c tptp.set_Sum_sum_c_c)) (C tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A) B) (=> (= (@ F B) C) (=> (forall ((X2 tptp.set_Sum_sum_c_c) (Y4 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X2) Y4) (@ (@ tptp.ord_le1772180283um_c_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le1772180283um_c_c (@ F A)) C))))))
% 0.25/0.67 (assert (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (F (-> tptp.set_Sum_sum_c_c tptp.set_Su1783761653um_b_c)) (C tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A) B) (=> (= (@ F B) C) (=> (forall ((X2 tptp.set_Sum_sum_c_c) (Y4 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X2) Y4) (@ (@ tptp.ord_le929608341um_b_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le929608341um_b_c (@ F A)) C))))))
% 0.25/0.67 (assert (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (F (-> tptp.set_Su1783761653um_b_c tptp.set_Sum_sum_c_c)) (C tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A) B) (=> (= (@ F B) C) (=> (forall ((X2 tptp.set_Su1783761653um_b_c) (Y4 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X2) Y4) (@ (@ tptp.ord_le1772180283um_c_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le1772180283um_c_c (@ F A)) C))))))
% 0.25/0.67 (assert (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (F (-> tptp.set_Su1783761653um_b_c tptp.set_Su1783761653um_b_c)) (C tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A) B) (=> (= (@ F B) C) (=> (forall ((X2 tptp.set_Su1783761653um_b_c) (Y4 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X2) Y4) (@ (@ tptp.ord_le929608341um_b_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le929608341um_b_c (@ F A)) C))))))
% 0.25/0.67 (assert (forall ((A tptp.set_Sum_sum_c_c) (F (-> tptp.set_Sum_sum_c_c tptp.set_Sum_sum_c_c)) (B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le1772180283um_c_c B) C) (=> (forall ((X2 tptp.set_Sum_sum_c_c) (Y4 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X2) Y4) (@ (@ tptp.ord_le1772180283um_c_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le1772180283um_c_c A) (@ F C)))))))
% 0.25/0.67 (assert (forall ((A tptp.set_Su1783761653um_b_c) (F (-> tptp.set_Sum_sum_c_c tptp.set_Su1783761653um_b_c)) (B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le1772180283um_c_c B) C) (=> (forall ((X2 tptp.set_Sum_sum_c_c) (Y4 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X2) Y4) (@ (@ tptp.ord_le929608341um_b_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le929608341um_b_c A) (@ F C)))))))
% 0.25/0.67 (assert (forall ((A tptp.set_Sum_sum_c_c) (F (-> tptp.set_Su1783761653um_b_c tptp.set_Sum_sum_c_c)) (B tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le929608341um_b_c B) C) (=> (forall ((X2 tptp.set_Su1783761653um_b_c) (Y4 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X2) Y4) (@ (@ tptp.ord_le1772180283um_c_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le1772180283um_c_c A) (@ F C)))))))
% 0.25/0.67 (assert (forall ((A tptp.set_Su1783761653um_b_c) (F (-> tptp.set_Su1783761653um_b_c tptp.set_Su1783761653um_b_c)) (B tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le929608341um_b_c B) C) (=> (forall ((X2 tptp.set_Su1783761653um_b_c) (Y4 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X2) Y4) (@ (@ tptp.ord_le929608341um_b_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le929608341um_b_c A) (@ F C)))))))
% 0.25/0.67 (assert (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (F (-> tptp.set_Sum_sum_c_c tptp.set_Sum_sum_c_c)) (C tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A) B) (=> (@ (@ tptp.ord_le1772180283um_c_c (@ F B)) C) (=> (forall ((X2 tptp.set_Sum_sum_c_c) (Y4 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X2) Y4) (@ (@ tptp.ord_le1772180283um_c_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le1772180283um_c_c (@ F A)) C))))))
% 0.25/0.67 (assert (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (F (-> tptp.set_Sum_sum_c_c tptp.set_Su1783761653um_b_c)) (C tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A) B) (=> (@ (@ tptp.ord_le929608341um_b_c (@ F B)) C) (=> (forall ((X2 tptp.set_Sum_sum_c_c) (Y4 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X2) Y4) (@ (@ tptp.ord_le929608341um_b_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le929608341um_b_c (@ F A)) C))))))
% 0.25/0.67 (assert (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (F (-> tptp.set_Su1783761653um_b_c tptp.set_Sum_sum_c_c)) (C tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A) B) (=> (@ (@ tptp.ord_le1772180283um_c_c (@ F B)) C) (=> (forall ((X2 tptp.set_Su1783761653um_b_c) (Y4 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X2) Y4) (@ (@ tptp.ord_le1772180283um_c_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le1772180283um_c_c (@ F A)) C))))))
% 0.25/0.67 (assert (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (F (-> tptp.set_Su1783761653um_b_c tptp.set_Su1783761653um_b_c)) (C tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A) B) (=> (@ (@ tptp.ord_le929608341um_b_c (@ F B)) C) (=> (forall ((X2 tptp.set_Su1783761653um_b_c) (Y4 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X2) Y4) (@ (@ tptp.ord_le929608341um_b_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le929608341um_b_c (@ F A)) C))))))
% 0.25/0.67 (assert (forall ((A tptp.set_Sum_sum_c_c) (F (-> tptp.set_Sum_sum_c_c tptp.set_Sum_sum_c_c)) (B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.ord_le1772180283um_c_c A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le1772180283um_c_c B) C) (=> (forall ((X2 tptp.set_Sum_sum_c_c) (Y4 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X2) Y4) (@ (@ tptp.ord_le1772180283um_c_c (@ F X2)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 0.25/0.67 (assert (forall ((A tptp.set_Sum_sum_c_c) (F (-> tptp.set_Su1783761653um_b_c tptp.set_Sum_sum_c_c)) (B tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.ord_le1772180283um_c_c A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le929608341um_b_c B) C) (=> (forall ((X2 tptp.set_Su1783761653um_b_c) (Y4 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X2) Y4) (@ (@ tptp.ord_le1772180283um_c_c (@ F X2)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 0.25/0.67 (assert (forall ((A tptp.set_Su1783761653um_b_c) (F (-> tptp.set_Sum_sum_c_c tptp.set_Su1783761653um_b_c)) (B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.ord_le929608341um_b_c A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le1772180283um_c_c B) C) (=> (forall ((X2 tptp.set_Sum_sum_c_c) (Y4 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X2) Y4) (@ (@ tptp.ord_le929608341um_b_c (@ F X2)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 0.25/0.67 (assert (forall ((A tptp.set_Su1783761653um_b_c) (F (-> tptp.set_Su1783761653um_b_c tptp.set_Su1783761653um_b_c)) (B tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.ord_le929608341um_b_c A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le929608341um_b_c B) C) (=> (forall ((X2 tptp.set_Su1783761653um_b_c) (Y4 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X2) Y4) (@ (@ tptp.ord_le929608341um_b_c (@ F X2)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 0.25/0.67 (assert (forall ((P2 tptp.produc640052711real_c)) (exists ((X2 tptp.produc190496183real_c) (Y4 tptp.produc190496183real_c)) (= P2 (@ (@ tptp.produc1687028567real_c X2) Y4)))))
% 0.25/0.67 (assert (forall ((P2 tptp.produc190496183real_c)) (exists ((X2 tptp.finite1398487019real_c) (Y4 tptp.finite1398487019real_c)) (= P2 (@ (@ tptp.produc394644079real_c X2) Y4)))))
% 0.25/0.67 (assert (forall ((P (-> tptp.produc640052711real_c Bool)) (P2 tptp.produc640052711real_c)) (=> (forall ((A7 tptp.produc190496183real_c) (B7 tptp.produc190496183real_c)) (@ P (@ (@ tptp.produc1687028567real_c A7) B7))) (@ P P2))))
% 0.25/0.67 (assert (forall ((P (-> tptp.produc190496183real_c Bool)) (P2 tptp.produc190496183real_c)) (=> (forall ((A7 tptp.finite1398487019real_c) (B7 tptp.finite1398487019real_c)) (@ P (@ (@ tptp.produc394644079real_c A7) B7))) (@ P P2))))
% 0.25/0.67 (assert (forall ((A tptp.produc190496183real_c) (B tptp.produc190496183real_c) (A6 tptp.produc190496183real_c) (B6 tptp.produc190496183real_c)) (=> (= (@ (@ tptp.produc1687028567real_c A) B) (@ (@ tptp.produc1687028567real_c A6) B6)) (not (=> (= A A6) (not (= B B6)))))))
% 0.25/0.67 (assert (forall ((A tptp.finite1398487019real_c) (B tptp.finite1398487019real_c) (A6 tptp.finite1398487019real_c) (B6 tptp.finite1398487019real_c)) (=> (= (@ (@ tptp.produc394644079real_c A) B) (@ (@ tptp.produc394644079real_c A6) B6)) (not (=> (= A A6) (not (= B B6)))))))
% 0.25/0.67 (assert (forall ((Y tptp.produc640052711real_c)) (not (forall ((A7 tptp.produc190496183real_c) (B7 tptp.produc190496183real_c)) (not (= Y (@ (@ tptp.produc1687028567real_c A7) B7)))))))
% 0.25/0.67 (assert (forall ((Y tptp.produc190496183real_c)) (not (forall ((A7 tptp.finite1398487019real_c) (B7 tptp.finite1398487019real_c)) (not (= Y (@ (@ tptp.produc394644079real_c A7) B7)))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.produc640052711real_c Bool)) (Prod tptp.produc640052711real_c)) (=> (forall ((A7 tptp.produc190496183real_c) (B7 tptp.produc190496183real_c)) (@ P (@ (@ tptp.produc1687028567real_c A7) B7))) (@ P Prod))))
% 0.25/0.67 (assert (forall ((P (-> tptp.produc190496183real_c Bool)) (Prod tptp.produc190496183real_c)) (=> (forall ((A7 tptp.finite1398487019real_c) (B7 tptp.finite1398487019real_c)) (@ P (@ (@ tptp.produc394644079real_c A7) B7))) (@ P Prod))))
% 0.25/0.67 (assert (forall ((A2 tptp.produc190496183real_c) (B2 tptp.produc190496183real_c) (V3 tptp.set_Sum_sum_c_c)) (=> (@ (@ (@ tptp.denota1997846518gree_c A2) B2) V3) (@ (@ (@ tptp.denota1997846518gree_c B2) A2) V3))))
% 0.25/0.67 (assert (forall ((Nu3 tptp.produc190496183real_c) (A2 tptp.set_Sum_sum_c_c)) (@ (@ (@ tptp.denota1997846518gree_c Nu3) Nu3) A2)))
% 0.25/0.67 (assert (forall ((Y tptp.produc640052711real_c)) (not (forall ((A7 tptp.produc190496183real_c) (B7 tptp.finite1398487019real_c) (C3 tptp.finite1398487019real_c)) (not (= Y (@ (@ tptp.produc1687028567real_c A7) (@ (@ tptp.produc394644079real_c B7) C3))))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.produc640052711real_c Bool)) (X tptp.produc640052711real_c)) (=> (forall ((A7 tptp.produc190496183real_c) (B7 tptp.finite1398487019real_c) (C3 tptp.finite1398487019real_c)) (@ P (@ (@ tptp.produc1687028567real_c A7) (@ (@ tptp.produc394644079real_c B7) C3)))) (@ P X))))
% 0.25/0.67 (assert (forall ((Nu3 tptp.produc190496183real_c) (Omega tptp.produc190496183real_c) (A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ (@ tptp.denota1997846518gree_c Nu3) Omega))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c A2) B2)))))))
% 0.25/0.67 (assert (forall ((I3 tptp.denota231621370t_unit) (Alpha2 tptp.hp_a_b_c) (Beta tptp.hp_a_b_c)) (let ((_let_1 (@ tptp.denota904684656_a_b_c I3))) (= (@ _let_1 (@ (@ tptp.choice_a_b_c Alpha2) Beta)) (@ (@ tptp.sup_su588839579real_c (@ _let_1 Alpha2)) (@ _let_1 Beta))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.produc190496183real_c Bool)) (X tptp.produc190496183real_c) (Y3 tptp.produc190496183real_c) (Y tptp.produc190496183real_c) (R (-> tptp.produc190496183real_c tptp.set_Pr754230471real_c))) (let ((_let_1 (@ tptp.produc1687028567real_c X))) (=> (@ P X) (=> (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c Y3) Y)) (@ R X)) (@ (@ tptp.member616151824real_c (@ (@ tptp.produc544496471real_c (@ _let_1 Y3)) (@ _let_1 Y))) (@ (@ tptp.same_f598810924real_c P) R)))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.finite1398487019real_c Bool)) (X tptp.finite1398487019real_c) (Y3 tptp.finite1398487019real_c) (Y tptp.finite1398487019real_c) (R (-> tptp.finite1398487019real_c tptp.set_Pr1389752855real_c))) (let ((_let_1 (@ tptp.produc394644079real_c X))) (=> (@ P X) (=> (@ (@ tptp.member1895684704real_c (@ (@ tptp.produc394644079real_c Y3) Y)) (@ R X)) (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c (@ _let_1 Y3)) (@ _let_1 Y))) (@ (@ tptp.same_f1974156740real_c P) R)))))))
% 0.25/0.67 (assert (= tptp.bNF_Ca1667803246um_c_c (lambda ((R2 tptp.set_Pr754230471real_c) (As (-> tptp.produc190496183real_c tptp.set_Sum_sum_c_c))) (forall ((I4 tptp.produc190496183real_c) (J4 tptp.produc190496183real_c)) (=> (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c I4) J4)) R2) (@ (@ tptp.ord_le1772180283um_c_c (@ As I4)) (@ As J4)))))))
% 0.25/0.67 (assert (= tptp.bNF_Ca1693016812um_c_c (lambda ((R2 tptp.set_Pr1389752855real_c) (As (-> tptp.finite1398487019real_c tptp.set_Sum_sum_c_c))) (forall ((I4 tptp.finite1398487019real_c) (J4 tptp.finite1398487019real_c)) (=> (@ (@ tptp.member1895684704real_c (@ (@ tptp.produc394644079real_c I4) J4)) R2) (@ (@ tptp.ord_le1772180283um_c_c (@ As I4)) (@ As J4)))))))
% 0.25/0.67 (assert (= tptp.bNF_Ca419199138um_b_c (lambda ((R2 tptp.set_Pr754230471real_c) (As (-> tptp.produc190496183real_c tptp.set_Su1783761653um_b_c))) (forall ((I4 tptp.produc190496183real_c) (J4 tptp.produc190496183real_c)) (=> (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c I4) J4)) R2) (@ (@ tptp.ord_le929608341um_b_c (@ As I4)) (@ As J4)))))))
% 0.25/0.67 (assert (= tptp.bNF_Ca318582436um_b_c (lambda ((R2 tptp.set_Pr1389752855real_c) (As (-> tptp.finite1398487019real_c tptp.set_Su1783761653um_b_c))) (forall ((I4 tptp.finite1398487019real_c) (J4 tptp.finite1398487019real_c)) (=> (@ (@ tptp.member1895684704real_c (@ (@ tptp.produc394644079real_c I4) J4)) R2) (@ (@ tptp.ord_le929608341um_b_c (@ As I4)) (@ As J4)))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.set_Sum_sum_c_c Bool)) (X tptp.set_Sum_sum_c_c) (Q (-> tptp.set_Sum_sum_c_c Bool))) (=> (@ P X) (=> (forall ((Y4 tptp.set_Sum_sum_c_c)) (=> (@ P Y4) (@ (@ tptp.ord_le1772180283um_c_c Y4) X))) (=> (forall ((X2 tptp.set_Sum_sum_c_c)) (=> (@ P X2) (=> (forall ((Y6 tptp.set_Sum_sum_c_c)) (=> (@ P Y6) (@ (@ tptp.ord_le1772180283um_c_c Y6) X2))) (@ Q X2)))) (@ Q (@ tptp.order_1776530114um_c_c P)))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.set_Su1783761653um_b_c Bool)) (X tptp.set_Su1783761653um_b_c) (Q (-> tptp.set_Su1783761653um_b_c Bool))) (=> (@ P X) (=> (forall ((Y4 tptp.set_Su1783761653um_b_c)) (=> (@ P Y4) (@ (@ tptp.ord_le929608341um_b_c Y4) X))) (=> (forall ((X2 tptp.set_Su1783761653um_b_c)) (=> (@ P X2) (=> (forall ((Y6 tptp.set_Su1783761653um_b_c)) (=> (@ P Y6) (@ (@ tptp.ord_le929608341um_b_c Y6) X2))) (@ Q X2)))) (@ Q (@ tptp.order_365181262um_b_c P)))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.set_Sum_sum_c_c Bool)) (X tptp.set_Sum_sum_c_c)) (=> (@ P X) (=> (forall ((Y4 tptp.set_Sum_sum_c_c)) (=> (@ P Y4) (@ (@ tptp.ord_le1772180283um_c_c Y4) X))) (= (@ tptp.order_1776530114um_c_c P) X)))))
% 0.25/0.67 (assert (forall ((P (-> tptp.set_Su1783761653um_b_c Bool)) (X tptp.set_Su1783761653um_b_c)) (=> (@ P X) (=> (forall ((Y4 tptp.set_Su1783761653um_b_c)) (=> (@ P Y4) (@ (@ tptp.ord_le929608341um_b_c Y4) X))) (= (@ tptp.order_365181262um_b_c P) X)))))
% 0.25/0.67 (assert (forall ((Prod tptp.produc640052711real_c)) (= (@ (@ tptp.produc1687028567real_c (@ tptp.produc876006723real_c Prod)) (@ tptp.produc415593093real_c Prod)) Prod)))
% 0.25/0.67 (assert (forall ((Prod tptp.produc190496183real_c)) (= (@ (@ tptp.produc394644079real_c (@ tptp.produc2010422875real_c Prod)) (@ tptp.produc314122909real_c Prod)) Prod)))
% 0.25/0.67 (assert (= tptp.ord_le684454199um_c_c (lambda ((X3 tptp.produc214722967um_c_c) (Y5 tptp.produc214722967um_c_c)) (and (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.produc1983230011um_c_c X3)) (@ tptp.produc1983230011um_c_c Y5)) (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.produc1132019837um_c_c X3)) (@ tptp.produc1132019837um_c_c Y5))))))
% 0.25/0.67 (assert (= tptp.ord_le542695343um_b_c (lambda ((X3 tptp.produc263671631um_b_c) (Y5 tptp.produc263671631um_b_c)) (and (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.produc1758795157um_b_c X3)) (@ tptp.produc1758795157um_b_c Y5)) (@ (@ tptp.ord_le929608341um_b_c (@ tptp.produc1193764051um_b_c X3)) (@ tptp.produc1193764051um_b_c Y5))))))
% 0.25/0.67 (assert (= tptp.ord_le1852514783um_c_c (lambda ((X3 tptp.produc1573491071um_c_c) (Y5 tptp.produc1573491071um_c_c)) (and (@ (@ tptp.ord_le929608341um_b_c (@ tptp.produc1455464333um_c_c X3)) (@ tptp.produc1455464333um_c_c Y5)) (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.produc890433227um_c_c X3)) (@ tptp.produc890433227um_c_c Y5))))))
% 0.25/0.67 (assert (= tptp.ord_le907560199um_b_c (lambda ((X3 tptp.produc1415638375um_b_c) (Y5 tptp.produc1415638375um_b_c)) (and (@ (@ tptp.ord_le929608341um_b_c (@ tptp.produc1961869763um_b_c X3)) (@ tptp.produc1961869763um_b_c Y5)) (@ (@ tptp.ord_le929608341um_b_c (@ tptp.produc932426501um_b_c X3)) (@ tptp.produc932426501um_b_c Y5))))))
% 0.25/0.67 (assert (= tptp.sup_su1399591867real_c (lambda ((X3 tptp.produc640052711real_c) (Y5 tptp.produc640052711real_c)) (@ (@ tptp.produc1687028567real_c (@ (@ tptp.sup_su1639086475real_c (@ tptp.produc876006723real_c X3)) (@ tptp.produc876006723real_c Y5))) (@ (@ tptp.sup_su1639086475real_c (@ tptp.produc415593093real_c X3)) (@ tptp.produc415593093real_c Y5))))))
% 0.25/0.67 (assert (= tptp.sup_su1639086475real_c (lambda ((X3 tptp.produc190496183real_c) (Y5 tptp.produc190496183real_c)) (@ (@ tptp.produc394644079real_c (@ (@ tptp.sup_su2141622551real_c (@ tptp.produc2010422875real_c X3)) (@ tptp.produc2010422875real_c Y5))) (@ (@ tptp.sup_su2141622551real_c (@ tptp.produc314122909real_c X3)) (@ tptp.produc314122909real_c Y5))))))
% 0.25/0.67 (assert (= tptp.sup_su1672617323um_c_c (lambda ((X3 tptp.produc214722967um_c_c) (Y5 tptp.produc214722967um_c_c)) (@ (@ tptp.produc1439061071um_c_c (@ (@ tptp.sup_su1349021703um_c_c (@ tptp.produc1983230011um_c_c X3)) (@ tptp.produc1983230011um_c_c Y5))) (@ (@ tptp.sup_su1349021703um_c_c (@ tptp.produc1132019837um_c_c X3)) (@ tptp.produc1132019837um_c_c Y5))))))
% 0.25/0.67 (assert (forall ((X1 tptp.produc190496183real_c) (X22 tptp.produc190496183real_c)) (= (@ tptp.produc876006723real_c (@ (@ tptp.produc1687028567real_c X1) X22)) X1)))
% 0.25/0.67 (assert (forall ((X1 tptp.finite1398487019real_c) (X22 tptp.finite1398487019real_c)) (= (@ tptp.produc2010422875real_c (@ (@ tptp.produc394644079real_c X1) X22)) X1)))
% 0.25/0.67 (assert (forall ((X tptp.produc190496183real_c) (Y tptp.produc190496183real_c) (A tptp.produc190496183real_c)) (=> (= (@ tptp.produc876006723real_c (@ (@ tptp.produc1687028567real_c X) Y)) A) (= X A))))
% 0.25/0.67 (assert (forall ((X tptp.finite1398487019real_c) (Y tptp.finite1398487019real_c) (A tptp.finite1398487019real_c)) (=> (= (@ tptp.produc2010422875real_c (@ (@ tptp.produc394644079real_c X) Y)) A) (= X A))))
% 0.25/0.67 (assert (forall ((X1 tptp.produc190496183real_c) (X22 tptp.produc190496183real_c)) (= (@ tptp.produc415593093real_c (@ (@ tptp.produc1687028567real_c X1) X22)) X22)))
% 0.25/0.67 (assert (forall ((X1 tptp.finite1398487019real_c) (X22 tptp.finite1398487019real_c)) (= (@ tptp.produc314122909real_c (@ (@ tptp.produc394644079real_c X1) X22)) X22)))
% 0.25/0.67 (assert (forall ((X tptp.produc190496183real_c) (Y tptp.produc190496183real_c) (A tptp.produc190496183real_c)) (=> (= (@ tptp.produc415593093real_c (@ (@ tptp.produc1687028567real_c X) Y)) A) (= Y A))))
% 0.25/0.67 (assert (forall ((X tptp.finite1398487019real_c) (Y tptp.finite1398487019real_c) (A tptp.finite1398487019real_c)) (=> (= (@ tptp.produc314122909real_c (@ (@ tptp.produc394644079real_c X) Y)) A) (= Y A))))
% 0.25/0.67 (assert (forall ((T2 tptp.produc640052711real_c)) (= T2 (@ (@ tptp.produc1687028567real_c (@ tptp.produc876006723real_c T2)) (@ tptp.produc415593093real_c T2)))))
% 0.25/0.67 (assert (forall ((T2 tptp.produc190496183real_c)) (= T2 (@ (@ tptp.produc394644079real_c (@ tptp.produc2010422875real_c T2)) (@ tptp.produc314122909real_c T2)))))
% 0.25/0.67 (assert (forall ((Prod tptp.produc640052711real_c)) (= Prod (@ (@ tptp.produc1687028567real_c (@ tptp.produc876006723real_c Prod)) (@ tptp.produc415593093real_c Prod)))))
% 0.25/0.67 (assert (forall ((Prod tptp.produc190496183real_c)) (= Prod (@ (@ tptp.produc394644079real_c (@ tptp.produc2010422875real_c Prod)) (@ tptp.produc314122909real_c Prod)))))
% 0.25/0.67 (assert (forall ((P (-> tptp.produc190496183real_c tptp.produc190496183real_c Bool)) (Y tptp.produc190496183real_c) (X tptp.produc190496183real_c)) (let ((_let_1 (@ (@ tptp.produc1687028567real_c X) Y))) (=> (@ (@ P Y) X) (@ (@ P (@ tptp.produc415593093real_c _let_1)) (@ tptp.produc876006723real_c _let_1))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.finite1398487019real_c tptp.finite1398487019real_c Bool)) (Y tptp.finite1398487019real_c) (X tptp.finite1398487019real_c)) (let ((_let_1 (@ (@ tptp.produc394644079real_c X) Y))) (=> (@ (@ P Y) X) (@ (@ P (@ tptp.produc314122909real_c _let_1)) (@ tptp.produc2010422875real_c _let_1))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.produc190496183real_c Bool)) (P2 tptp.produc190496183real_c) (Q (-> tptp.produc190496183real_c Bool)) (Q2 tptp.produc190496183real_c)) (let ((_let_1 (@ (@ tptp.produc1687028567real_c P2) Q2))) (=> (@ P P2) (=> (@ Q Q2) (and (@ P (@ tptp.produc876006723real_c _let_1)) (@ Q (@ tptp.produc415593093real_c _let_1))))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.finite1398487019real_c Bool)) (P2 tptp.finite1398487019real_c) (Q (-> tptp.finite1398487019real_c Bool)) (Q2 tptp.finite1398487019real_c)) (let ((_let_1 (@ (@ tptp.produc394644079real_c P2) Q2))) (=> (@ P P2) (=> (@ Q Q2) (and (@ P (@ tptp.produc2010422875real_c _let_1)) (@ Q (@ tptp.produc314122909real_c _let_1))))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.produc190496183real_c tptp.produc190496183real_c Bool)) (X tptp.produc190496183real_c) (Y tptp.produc190496183real_c) (A tptp.produc640052711real_c)) (=> (@ (@ P X) Y) (=> (= A (@ (@ tptp.produc1687028567real_c X) Y)) (@ (@ P (@ tptp.produc876006723real_c A)) (@ tptp.produc415593093real_c A))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.finite1398487019real_c tptp.finite1398487019real_c Bool)) (X tptp.finite1398487019real_c) (Y tptp.finite1398487019real_c) (A tptp.produc190496183real_c)) (=> (@ (@ P X) Y) (=> (= A (@ (@ tptp.produc394644079real_c X) Y)) (@ (@ P (@ tptp.produc2010422875real_c A)) (@ tptp.produc314122909real_c A))))))
% 0.25/0.67 (assert (forall ((X tptp.produc640052711real_c) (Y tptp.produc190496183real_c) (Z tptp.produc190496183real_c)) (=> (= X (@ (@ tptp.produc1687028567real_c Y) Z)) (= (@ tptp.produc415593093real_c X) Z))))
% 0.25/0.67 (assert (forall ((X tptp.produc190496183real_c) (Y tptp.finite1398487019real_c) (Z tptp.finite1398487019real_c)) (=> (= X (@ (@ tptp.produc394644079real_c Y) Z)) (= (@ tptp.produc314122909real_c X) Z))))
% 0.25/0.67 (assert (forall ((X tptp.produc640052711real_c) (Y tptp.produc190496183real_c) (Z tptp.produc190496183real_c)) (=> (= X (@ (@ tptp.produc1687028567real_c Y) Z)) (= (@ tptp.produc876006723real_c X) Y))))
% 0.25/0.67 (assert (forall ((X tptp.produc190496183real_c) (Y tptp.finite1398487019real_c) (Z tptp.finite1398487019real_c)) (=> (= X (@ (@ tptp.produc394644079real_c Y) Z)) (= (@ tptp.produc2010422875real_c X) Y))))
% 0.25/0.67 (assert (forall ((B tptp.produc190496183real_c) (P2 tptp.produc640052711real_c)) (= (= B (@ tptp.produc415593093real_c P2)) (exists ((A4 tptp.produc190496183real_c)) (= P2 (@ (@ tptp.produc1687028567real_c A4) B))))))
% 0.25/0.67 (assert (forall ((B tptp.finite1398487019real_c) (P2 tptp.produc190496183real_c)) (= (= B (@ tptp.produc314122909real_c P2)) (exists ((A4 tptp.finite1398487019real_c)) (= P2 (@ (@ tptp.produc394644079real_c A4) B))))))
% 0.25/0.67 (assert (forall ((A tptp.produc190496183real_c) (P2 tptp.produc640052711real_c)) (= (= A (@ tptp.produc876006723real_c P2)) (exists ((B4 tptp.produc190496183real_c)) (= P2 (@ (@ tptp.produc1687028567real_c A) B4))))))
% 0.25/0.67 (assert (forall ((A tptp.finite1398487019real_c) (P2 tptp.produc190496183real_c)) (= (= A (@ tptp.produc2010422875real_c P2)) (exists ((B4 tptp.finite1398487019real_c)) (= P2 (@ (@ tptp.produc394644079real_c A) B4))))))
% 0.25/0.67 (assert (= tptp.produc350724343real_c (lambda ((P3 tptp.produc640052711real_c)) (@ (@ tptp.produc1687028567real_c (@ tptp.produc415593093real_c P3)) (@ tptp.produc876006723real_c P3)))))
% 0.25/0.67 (assert (= tptp.produc704157711real_c (lambda ((P3 tptp.produc190496183real_c)) (@ (@ tptp.produc394644079real_c (@ tptp.produc314122909real_c P3)) (@ tptp.produc2010422875real_c P3)))))
% 0.25/0.67 (assert (forall ((X tptp.produc190496183real_c) (Y tptp.produc190496183real_c)) (= (@ tptp.produc350724343real_c (@ (@ tptp.produc1687028567real_c X) Y)) (@ (@ tptp.produc1687028567real_c Y) X))))
% 0.77/0.98 (assert (forall ((X tptp.finite1398487019real_c) (Y tptp.finite1398487019real_c)) (= (@ tptp.produc704157711real_c (@ (@ tptp.produc394644079real_c X) Y)) (@ (@ tptp.produc394644079real_c Y) X))))
% 0.77/0.98 (assert (not (exists ((Mu6 tptp.produc190496183real_c)) (let ((_let_1 (@ (@ tptp.choice_a_b_c tptp.a) tptp.b))) (and (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c (@ (@ tptp.produc394644079real_c tptp.nu_22) tptp.nu_2)) Mu6)) (@ (@ tptp.denota904684656_a_b_c tptp.j) _let_1)) (@ (@ (@ tptp.denota1997846518gree_c (@ (@ tptp.produc394644079real_c tptp.mu3) tptp.mu2)) Mu6) (@ (@ tptp.sup_su1349021703um_c_c (@ tptp.static_MBV_a_b_c _let_1)) tptp.v)))))))
% 0.77/0.98 (set-info :filename cvc5---1.0.5_22994)
% 0.77/0.98 (check-sat-assuming ( true ))
% 0.77/0.98 ------- get file name : TPTP file name is ITP036^1
% 0.77/0.98 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_22994.smt2...
% 0.77/0.98 --- Run --ho-elim --full-saturate-quant at 10...
% 0.77/0.98 % SZS status Theorem for ITP036^1
% 0.77/0.98 % SZS output start Proof for ITP036^1
% 0.77/0.98 (
% 0.77/0.98 (let ((_let_1 (not (exists ((Mu6 tptp.produc190496183real_c)) (let ((_let_1 (@ (@ tptp.choice_a_b_c tptp.a) tptp.b))) (and (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c (@ (@ tptp.produc394644079real_c tptp.nu_22) tptp.nu_2)) Mu6)) (@ (@ tptp.denota904684656_a_b_c tptp.j) _let_1)) (@ (@ (@ tptp.denota1997846518gree_c (@ (@ tptp.produc394644079real_c tptp.mu3) tptp.mu2)) Mu6) (@ (@ tptp.sup_su1349021703um_c_c (@ tptp.static_MBV_a_b_c _let_1)) tptp.v)))))))) (let ((_let_2 (@ tptp.static_SIGP_a_b_c tptp.a))) (let ((_let_3 (@ (@ tptp.denota69106024_a_b_c tptp.i) tptp.j))) (let ((_let_4 (@ tptp.static_SIGP_a_b_c tptp.b))) (let ((_let_5 (@ (@ tptp.choice_a_b_c tptp.a) tptp.b))) (let ((_let_6 (@ tptp.static_SIGP_a_b_c _let_5))) (let ((_let_7 (@ tptp.denota904684656_a_b_c tptp.i))) (let ((_let_8 (@ (@ tptp.produc394644079real_c tptp.mu3) tptp.mu2))) (let ((_let_9 (@ (@ tptp.produc394644079real_c tptp.nu_12) tptp.nu_1))) (let ((_let_10 (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c _let_9) _let_8)))) (let ((_let_11 (@ _let_10 (@ _let_7 tptp.b)))) (let ((_let_12 (@ _let_10 (@ _let_7 tptp.a)))) (let ((_let_13 (@ (@ tptp.produc394644079real_c tptp.nu_22) tptp.nu_2))) (let ((_let_14 (@ (@ tptp.denota1997846518gree_c _let_8) tptp.mu))) (let ((_let_15 (@ tptp.denota904684656_a_b_c tptp.j))) (let ((_let_16 (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c _let_13) tptp.mu)))) (let ((_let_17 (@ _let_14 (@ (@ tptp.sup_su1349021703um_c_c (@ tptp.static_MBV_a_b_c _let_5)) tptp.v)))) (let ((_let_18 (@ _let_16 (@ _let_15 _let_5)))) (let ((_let_19 (forall ((Mu6 tptp.produc190496183real_c)) (let ((_let_1 (ho_118 (ho_117 k_116 tptp.a) tptp.b))) (or (not (ho_84 (ho_83 k_82 (ho_109 (ho_108 k_107 (ho_121 (ho_120 k_119 tptp.nu_22) tptp.nu_2)) Mu6)) (ho_106 (ho_105 k_104 tptp.j) _let_1))) (not (ho_47 (ho_103 (ho_102 k_101 (ho_121 (ho_120 k_119 tptp.mu3) tptp.mu2)) Mu6) (ho_61 (ho_60 k_62 (ho_100 k_99 _let_1)) tptp.v)))))))) (let ((_let_20 (ho_118 (ho_117 k_116 tptp.a) tptp.b))) (let ((_let_21 (ho_47 (ho_103 (ho_102 k_101 (ho_121 (ho_120 k_119 tptp.mu3) tptp.mu2)) tptp.mu) (ho_61 (ho_60 k_62 (ho_100 k_99 _let_20)) tptp.v)))) (let ((_let_22 (not _let_21))) (let ((_let_23 (ho_84 (ho_83 k_82 (ho_109 (ho_108 k_107 (ho_121 (ho_120 k_119 tptp.nu_22) tptp.nu_2)) tptp.mu)) (ho_106 (ho_105 k_104 tptp.j) _let_20)))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_22))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((Mu6 tptp.produc190496183real_c)) (let ((_let_1 (@ (@ tptp.choice_a_b_c tptp.a) tptp.b))) (or (not (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c (@ (@ tptp.produc394644079real_c tptp.nu_22) tptp.nu_2)) Mu6)) (@ (@ tptp.denota904684656_a_b_c tptp.j) _let_1))) (not (@ (@ (@ tptp.denota1997846518gree_c (@ (@ tptp.produc394644079real_c tptp.mu3) tptp.mu2)) Mu6) (@ (@ tptp.sup_su1349021703um_c_c (@ tptp.static_MBV_a_b_c _let_1)) tptp.v)))))) _let_19))))))) (let ((_let_27 (not _let_25))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (tptp.mu QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_19))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_24 _let_22 _let_27))) (EQ_RESOLVE (ASSUME :args (_let_18)) (PREPROCESS :args ((= _let_18 _let_23)))) (EQ_RESOLVE (ASSUME :args (_let_17)) (PREPROCESS :args ((= _let_17 _let_21)))) :args (_let_27 false _let_23 false _let_21)) _let_26 :args (false true _let_25 false _let_19)) :args ((@ tptp.coinci1852866155_a_b_c tptp.b) (@ tptp.coinci1852866155_a_b_c tptp.a) _let_18 _let_17 (@ _let_16 (@ _let_15 tptp.b)) (@ tptp.hpsafe_a_b_c tptp.b) (@ tptp.hpsafe_a_b_c tptp.a) (@ _let_14 (@ (@ tptp.sup_su1349021703um_c_c (@ tptp.static_MBV_a_b_c tptp.b)) tptp.v)) (not (forall ((Mu tptp.produc190496183real_c)) (=> (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c (@ (@ tptp.produc394644079real_c tptp.nu_22) tptp.nu_2)) Mu)) (@ (@ tptp.denota904684656_a_b_c tptp.j) tptp.b)) (not (@ (@ (@ tptp.denota1997846518gree_c (@ (@ tptp.produc394644079real_c tptp.mu3) tptp.mu2)) Mu) (@ (@ tptp.sup_su1349021703um_c_c (@ tptp.static_MBV_a_b_c tptp.b)) tptp.v)))))) (@ (@ (@ tptp.denota1997846518gree_c _let_9) _let_13) tptp.v) (forall ((A tptp.finite1398487019real_c) (B tptp.finite1398487019real_c) (C tptp.finite1398487019real_c) (D tptp.finite1398487019real_c)) (= (@ (@ tptp.sup_su1639086475real_c (@ (@ tptp.produc394644079real_c A) B)) (@ (@ tptp.produc394644079real_c C) D)) (@ (@ tptp.produc394644079real_c (@ (@ tptp.sup_su2141622551real_c A) C)) (@ (@ tptp.sup_su2141622551real_c B) D)))) (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c) (D tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.sup_su1672617323um_c_c (@ (@ tptp.produc1439061071um_c_c A) B)) (@ (@ tptp.produc1439061071um_c_c C) D)) (@ (@ tptp.produc1439061071um_c_c (@ (@ tptp.sup_su1349021703um_c_c A) C)) (@ (@ tptp.sup_su1349021703um_c_c B) D)))) (forall ((A tptp.produc190496183real_c) (B tptp.produc190496183real_c) (C tptp.produc190496183real_c) (D tptp.produc190496183real_c)) (= (@ (@ tptp.sup_su1399591867real_c (@ (@ tptp.produc1687028567real_c A) B)) (@ (@ tptp.produc1687028567real_c C) D)) (@ (@ tptp.produc1687028567real_c (@ (@ tptp.sup_su1639086475real_c A) C)) (@ (@ tptp.sup_su1639086475real_c B) D)))) (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Su1783761653um_b_c) (C tptp.set_Sum_sum_c_c) (D tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.sup_su421398139um_b_c (@ (@ tptp.produc919784577um_b_c A) B)) (@ (@ tptp.produc919784577um_b_c C) D)) (@ (@ tptp.produc919784577um_b_c (@ (@ tptp.sup_su1349021703um_c_c A) C)) (@ (@ tptp.sup_su1968964297um_b_c B) D)))) (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Sum_sum_c_c) (C tptp.set_Su1783761653um_b_c) (D tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.sup_su1731217579um_c_c (@ (@ tptp.produc616453753um_c_c A) B)) (@ (@ tptp.produc616453753um_c_c C) D)) (@ (@ tptp.produc616453753um_c_c (@ (@ tptp.sup_su1968964297um_b_c A) C)) (@ (@ tptp.sup_su1349021703um_c_c B) D)))) (forall ((A tptp.set_Sum_sum_c_c) (B tptp.produc190496183real_c) (C tptp.set_Sum_sum_c_c) (D tptp.produc190496183real_c)) (= (@ (@ tptp.sup_su2023888701real_c (@ (@ tptp.produc439851843real_c A) B)) (@ (@ tptp.produc439851843real_c C) D)) (@ (@ tptp.produc439851843real_c (@ (@ tptp.sup_su1349021703um_c_c A) C)) (@ (@ tptp.sup_su1639086475real_c B) D)))) (forall ((A tptp.produc190496183real_c) (B tptp.set_Sum_sum_c_c) (C tptp.produc190496183real_c) (D tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.sup_su1347303021um_c_c (@ (@ tptp.produc639456571um_c_c A) B)) (@ (@ tptp.produc639456571um_c_c C) D)) (@ (@ tptp.produc639456571um_c_c (@ (@ tptp.sup_su1639086475real_c A) C)) (@ (@ tptp.sup_su1349021703um_c_c B) D)))) (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c) (D tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.sup_su1580927803um_b_c (@ (@ tptp.produc754249687um_b_c A) B)) (@ (@ tptp.produc754249687um_b_c C) D)) (@ (@ tptp.produc754249687um_b_c (@ (@ tptp.sup_su1968964297um_b_c A) C)) (@ (@ tptp.sup_su1968964297um_b_c B) D)))) (forall ((A tptp.set_Sum_sum_c_c) (B tptp.produc214722967um_c_c) (C tptp.set_Sum_sum_c_c) (D tptp.produc214722967um_c_c)) (= (@ (@ tptp.sup_su505296157um_c_c (@ (@ tptp.produc1333497635um_c_c A) B)) (@ (@ tptp.produc1333497635um_c_c C) D)) (@ (@ tptp.produc1333497635um_c_c (@ (@ tptp.sup_su1349021703um_c_c A) C)) (@ (@ tptp.sup_su1672617323um_c_c B) D)))) (forall ((A tptp.produc190496183real_c) (B tptp.set_Su1783761653um_b_c) (C tptp.produc190496183real_c) (D tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.sup_su1009753337um_b_c (@ (@ tptp.produc2010919061um_b_c A) B)) (@ (@ tptp.produc2010919061um_b_c C) D)) (@ (@ tptp.produc2010919061um_b_c (@ (@ tptp.sup_su1639086475real_c A) C)) (@ (@ tptp.sup_su1968964297um_b_c B) D)))) (@ _let_10 (@ _let_7 _let_5)) (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.static_FVP_a_b_c _let_5)) tptp.v) (not _let_12) (forall ((X61 tptp.hp_a_b_c) (X62 tptp.hp_a_b_c) (Y61 tptp.hp_a_b_c) (Y62 tptp.hp_a_b_c)) (= (= (@ (@ tptp.choice_a_b_c X61) X62) (@ (@ tptp.choice_a_b_c Y61) Y62)) (and (= X61 Y61) (= X62 Y62)))) (forall ((C tptp.produc190496183real_c) (B2 tptp.set_Pr1389752855real_c) (A2 tptp.set_Pr1389752855real_c)) (let ((_let_1 (@ tptp.member1895684704real_c C))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A2)) (@ _let_1 (@ (@ tptp.sup_su1857314283real_c A2) B2))))) (forall ((C tptp.produc1037099239real_c) (B2 tptp.set_Pr242060487real_c) (A2 tptp.set_Pr242060487real_c)) (let ((_let_1 (@ tptp.member616151824real_c C))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A2)) (@ _let_1 (@ (@ tptp.sup_su880588443real_c A2) B2))))) (forall ((C tptp.sum_su737395349um_b_c) (B2 tptp.set_Su1783761653um_b_c) (A2 tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.member1893232190um_b_c C))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A2)) (@ _let_1 (@ (@ tptp.sup_su1968964297um_b_c A2) B2))))) (forall ((C tptp.produc640052711real_c) (B2 tptp.set_Pr754230471real_c) (A2 tptp.set_Pr754230471real_c)) (let ((_let_1 (@ tptp.member346808080real_c C))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A2)) (@ _let_1 (@ (@ tptp.sup_su588839579real_c A2) B2))))) (forall ((C tptp.sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (A2 tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.member_Sum_sum_c_c C))) (=> (=> (not (@ _let_1 B2)) (@ _let_1 A2)) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c A2) B2))))) (forall ((C tptp.produc190496183real_c) (A2 tptp.set_Pr1389752855real_c) (B2 tptp.set_Pr1389752855real_c)) (let ((_let_1 (@ tptp.member1895684704real_c C))) (= (@ _let_1 (@ (@ tptp.sup_su1857314283real_c A2) B2)) (or (@ _let_1 A2) (@ _let_1 B2))))) (forall ((C tptp.produc1037099239real_c) (A2 tptp.set_Pr242060487real_c) (B2 tptp.set_Pr242060487real_c)) (let ((_let_1 (@ tptp.member616151824real_c C))) (= (@ _let_1 (@ (@ tptp.sup_su880588443real_c A2) B2)) (or (@ _let_1 A2) (@ _let_1 B2))))) (forall ((C tptp.sum_su737395349um_b_c) (A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.member1893232190um_b_c C))) (= (@ _let_1 (@ (@ tptp.sup_su1968964297um_b_c A2) B2)) (or (@ _let_1 A2) (@ _let_1 B2))))) (forall ((C tptp.produc640052711real_c) (A2 tptp.set_Pr754230471real_c) (B2 tptp.set_Pr754230471real_c)) (let ((_let_1 (@ tptp.member346808080real_c C))) (= (@ _let_1 (@ (@ tptp.sup_su588839579real_c A2) B2)) (or (@ _let_1 A2) (@ _let_1 B2))))) (forall ((C tptp.sum_sum_c_c) (A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.member_Sum_sum_c_c C))) (= (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c A2) B2)) (or (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A tptp.produc190496183real_c)) (= (@ (@ tptp.sup_su1639086475real_c A) A) A)) (forall ((A tptp.produc640052711real_c)) (= (@ (@ tptp.sup_su1399591867real_c A) A) A)) (forall ((A tptp.produc214722967um_c_c)) (= (@ (@ tptp.sup_su1672617323um_c_c A) A) A)) (forall ((A tptp.set_Pr754230471real_c)) (= (@ (@ tptp.sup_su588839579real_c A) A) A)) (forall ((A tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.sup_su1968964297um_b_c A) A) A)) (forall ((A tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.sup_su1349021703um_c_c A) A) A)) (forall ((X tptp.produc190496183real_c)) (= (@ (@ tptp.sup_su1639086475real_c X) X) X)) (forall ((X tptp.produc640052711real_c)) (= (@ (@ tptp.sup_su1399591867real_c X) X) X)) (forall ((X tptp.produc214722967um_c_c)) (= (@ (@ tptp.sup_su1672617323um_c_c X) X) X)) (forall ((X tptp.set_Pr754230471real_c)) (= (@ (@ tptp.sup_su588839579real_c X) X) X)) (forall ((X tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.sup_su1968964297um_b_c X) X) X)) (forall ((X tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.sup_su1349021703um_c_c X) X) X)) (forall ((A tptp.produc190496183real_c) (B tptp.produc190496183real_c)) (let ((_let_1 (@ tptp.sup_su1639086475real_c A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.produc640052711real_c) (B tptp.produc640052711real_c)) (let ((_let_1 (@ tptp.sup_su1399591867real_c A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.produc214722967um_c_c) (B tptp.produc214722967um_c_c)) (let ((_let_1 (@ tptp.sup_su1672617323um_c_c A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.set_Pr754230471real_c) (B tptp.set_Pr754230471real_c)) (let ((_let_1 (@ tptp.sup_su588839579real_c A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.sup_su1968964297um_b_c A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A2 tptp.set_Pr1389752855real_c) (B2 tptp.set_Pr1389752855real_c)) (=> (forall ((X2 tptp.produc190496183real_c)) (let ((_let_1 (@ tptp.member1895684704real_c X2))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le977353143real_c A2) B2))) (forall ((A2 tptp.set_Pr242060487real_c) (B2 tptp.set_Pr242060487real_c)) (=> (forall ((X2 tptp.produc1037099239real_c)) (let ((_let_1 (@ tptp.member616151824real_c X2))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le100418663real_c A2) B2))) (forall ((A2 tptp.set_Pr754230471real_c) (B2 tptp.set_Pr754230471real_c)) (=> (forall ((X2 tptp.produc640052711real_c)) (let ((_let_1 (@ tptp.member346808080real_c X2))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le1988344935real_c A2) B2))) (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (=> (forall ((X2 tptp.sum_sum_c_c)) (let ((_let_1 (@ tptp.member_Sum_sum_c_c X2))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le1772180283um_c_c A2) B2))) (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c)) (=> (forall ((X2 tptp.sum_su737395349um_b_c)) (let ((_let_1 (@ tptp.member1893232190um_b_c X2))) (=> (@ _let_1 A2) (@ _let_1 B2)))) (@ (@ tptp.ord_le929608341um_b_c A2) B2))) (forall ((A2 tptp.set_Pr754230471real_c) (B2 tptp.set_Pr754230471real_c)) (=> (@ (@ tptp.ord_le1988344935real_c A2) B2) (=> (@ (@ tptp.ord_le1988344935real_c B2) A2) (= A2 B2)))) (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A2) B2) (=> (@ (@ tptp.ord_le1772180283um_c_c B2) A2) (= A2 B2)))) (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A2) B2) (=> (@ (@ tptp.ord_le929608341um_b_c B2) A2) (= A2 B2)))) (forall ((A tptp.produc190496183real_c) (B tptp.produc190496183real_c)) (let ((_let_1 (@ (@ tptp.sup_su1639086475real_c A) B))) (= (@ (@ tptp.sup_su1639086475real_c _let_1) B) _let_1))) (forall ((A tptp.produc640052711real_c) (B tptp.produc640052711real_c)) (let ((_let_1 (@ (@ tptp.sup_su1399591867real_c A) B))) (= (@ (@ tptp.sup_su1399591867real_c _let_1) B) _let_1))) (forall ((A tptp.produc214722967um_c_c) (B tptp.produc214722967um_c_c)) (let ((_let_1 (@ (@ tptp.sup_su1672617323um_c_c A) B))) (= (@ (@ tptp.sup_su1672617323um_c_c _let_1) B) _let_1))) (forall ((A tptp.set_Pr754230471real_c) (B tptp.set_Pr754230471real_c)) (let ((_let_1 (@ (@ tptp.sup_su588839579real_c A) B))) (= (@ (@ tptp.sup_su588839579real_c _let_1) B) _let_1))) (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ (@ tptp.sup_su1968964297um_b_c A) B))) (= (@ (@ tptp.sup_su1968964297um_b_c _let_1) B) _let_1))) (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ (@ tptp.sup_su1349021703um_c_c A) B))) (= (@ (@ tptp.sup_su1349021703um_c_c _let_1) B) _let_1))) (forall ((X tptp.produc190496183real_c) (Y tptp.produc190496183real_c)) (let ((_let_1 (@ tptp.sup_su1639086475real_c X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.produc640052711real_c) (Y tptp.produc640052711real_c)) (let ((_let_1 (@ tptp.sup_su1399591867real_c X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.produc214722967um_c_c) (Y tptp.produc214722967um_c_c)) (let ((_let_1 (@ tptp.sup_su1672617323um_c_c X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.set_Pr754230471real_c) (Y tptp.set_Pr754230471real_c)) (let ((_let_1 (@ tptp.sup_su588839579real_c X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.set_Su1783761653um_b_c) (Y tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.sup_su1968964297um_b_c X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.static_FVP_a_b_c tptp.b)) tptp.v) (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.static_FVP_a_b_c tptp.a)) tptp.v) (forall ((A tptp.produc190496183real_c) (B tptp.produc190496183real_c) (C tptp.produc190496183real_c) (D tptp.produc190496183real_c)) (= (@ (@ tptp.ord_le652477831real_c (@ (@ tptp.produc1687028567real_c A) B)) (@ (@ tptp.produc1687028567real_c C) D)) (and (@ (@ tptp.ord_le850691415real_c A) C) (@ (@ tptp.ord_le850691415real_c B) D)))) (forall ((A tptp.finite1398487019real_c) (B tptp.finite1398487019real_c) (C tptp.finite1398487019real_c) (D tptp.finite1398487019real_c)) (= (@ (@ tptp.ord_le850691415real_c (@ (@ tptp.produc394644079real_c A) B)) (@ (@ tptp.produc394644079real_c C) D)) (and (@ (@ tptp.ord_le775706699real_c A) C) (@ (@ tptp.ord_le775706699real_c B) D)))) (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c) (D tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.ord_le684454199um_c_c (@ (@ tptp.produc1439061071um_c_c A) B)) (@ (@ tptp.produc1439061071um_c_c C) D)) (and (@ (@ tptp.ord_le1772180283um_c_c A) C) (@ (@ tptp.ord_le1772180283um_c_c B) D)))) (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Su1783761653um_b_c) (C tptp.set_Sum_sum_c_c) (D tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.ord_le542695343um_b_c (@ (@ tptp.produc919784577um_b_c A) B)) (@ (@ tptp.produc919784577um_b_c C) D)) (and (@ (@ tptp.ord_le1772180283um_c_c A) C) (@ (@ tptp.ord_le929608341um_b_c B) D)))) (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Sum_sum_c_c) (C tptp.set_Su1783761653um_b_c) (D tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.ord_le1852514783um_c_c (@ (@ tptp.produc616453753um_c_c A) B)) (@ (@ tptp.produc616453753um_c_c C) D)) (and (@ (@ tptp.ord_le929608341um_b_c A) C) (@ (@ tptp.ord_le1772180283um_c_c B) D)))) (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c) (D tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.ord_le907560199um_b_c (@ (@ tptp.produc754249687um_b_c A) B)) (@ (@ tptp.produc754249687um_b_c C) D)) (and (@ (@ tptp.ord_le929608341um_b_c A) C) (@ (@ tptp.ord_le929608341um_b_c B) D)))) (forall ((B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c B) C)) A) (and (@ (@ tptp.ord_le1772180283um_c_c B) A) (@ (@ tptp.ord_le1772180283um_c_c C) A)))) (forall ((B tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c B) C)) A) (and (@ (@ tptp.ord_le929608341um_b_c B) A) (@ (@ tptp.ord_le929608341um_b_c C) A)))) (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c) (Z tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c X) Y)) Z) (and (@ (@ tptp.ord_le1772180283um_c_c X) Z) (@ (@ tptp.ord_le1772180283um_c_c Y) Z)))) (forall ((X tptp.set_Su1783761653um_b_c) (Y tptp.set_Su1783761653um_b_c) (Z tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c X) Y)) Z) (and (@ (@ tptp.ord_le929608341um_b_c X) Z) (@ (@ tptp.ord_le929608341um_b_c Y) Z)))) (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (C2 tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c A2) B2)) C2) (and (@ (@ tptp.ord_le1772180283um_c_c A2) C2) (@ (@ tptp.ord_le1772180283um_c_c B2) C2)))) (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c) (C2 tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c A2) B2)) C2) (and (@ (@ tptp.ord_le929608341um_b_c A2) C2) (@ (@ tptp.ord_le929608341um_b_c B2) C2)))) (forall ((A tptp.hp_a_b_c) (B tptp.hp_a_b_c)) (= (@ tptp.hpsafe_a_b_c (@ (@ tptp.choice_a_b_c A) B)) (and (@ tptp.hpsafe_a_b_c A) (@ tptp.hpsafe_a_b_c B)))) _let_11 (or _let_12 _let_11) (forall ((A2 tptp.set_Pr754230471real_c) (B2 tptp.set_Pr754230471real_c) (X tptp.produc640052711real_c)) (let ((_let_1 (@ tptp.member346808080real_c X))) (=> (@ (@ tptp.ord_le1988344935real_c A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (X tptp.sum_sum_c_c)) (let ((_let_1 (@ tptp.member_Sum_sum_c_c X))) (=> (@ (@ tptp.ord_le1772180283um_c_c A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c) (X tptp.sum_su737395349um_b_c)) (let ((_let_1 (@ tptp.member1893232190um_b_c X))) (=> (@ (@ tptp.ord_le929608341um_b_c A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_Pr754230471real_c) (B2 tptp.set_Pr754230471real_c) (C tptp.produc640052711real_c)) (let ((_let_1 (@ tptp.member346808080real_c C))) (=> (@ (@ tptp.ord_le1988344935real_c A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (C tptp.sum_sum_c_c)) (let ((_let_1 (@ tptp.member_Sum_sum_c_c C))) (=> (@ (@ tptp.ord_le1772180283um_c_c A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c) (C tptp.sum_su737395349um_b_c)) (let ((_let_1 (@ tptp.member1893232190um_b_c C))) (=> (@ (@ tptp.ord_le929608341um_b_c A2) B2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (=> (= A2 B2) (not (=> (@ (@ tptp.ord_le1772180283um_c_c A2) B2) (not (@ (@ tptp.ord_le1772180283um_c_c B2) A2)))))) (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c)) (=> (= A2 B2) (not (=> (@ (@ tptp.ord_le929608341um_b_c A2) B2) (not (@ (@ tptp.ord_le929608341um_b_c B2) A2)))))) (= tptp.ord_le1988344935real_c (lambda ((A3 tptp.set_Pr754230471real_c) (B3 tptp.set_Pr754230471real_c)) (forall ((X3 tptp.produc640052711real_c)) (let ((_let_1 (@ tptp.member346808080real_c X3))) (=> (@ _let_1 A3) (@ _let_1 B3)))))) (= tptp.ord_le1772180283um_c_c (lambda ((A3 tptp.set_Sum_sum_c_c) (B3 tptp.set_Sum_sum_c_c)) (forall ((X3 tptp.sum_sum_c_c)) (let ((_let_1 (@ tptp.member_Sum_sum_c_c X3))) (=> (@ _let_1 A3) (@ _let_1 B3)))))) (= tptp.ord_le929608341um_b_c (lambda ((A3 tptp.set_Su1783761653um_b_c) (B3 tptp.set_Su1783761653um_b_c)) (forall ((X3 tptp.sum_su737395349um_b_c)) (let ((_let_1 (@ tptp.member1893232190um_b_c X3))) (=> (@ _let_1 A3) (@ _let_1 B3)))))) (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (=> (= A2 B2) (@ (@ tptp.ord_le1772180283um_c_c A2) B2))) (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c)) (=> (= A2 B2) (@ (@ tptp.ord_le929608341um_b_c A2) B2))) (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (=> (= A2 B2) (@ (@ tptp.ord_le1772180283um_c_c B2) A2))) (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c)) (=> (= A2 B2) (@ (@ tptp.ord_le929608341um_b_c B2) A2))) (= tptp.ord_le1988344935real_c (lambda ((A3 tptp.set_Pr754230471real_c) (B3 tptp.set_Pr754230471real_c)) (forall ((T tptp.produc640052711real_c)) (let ((_let_1 (@ tptp.member346808080real_c T))) (=> (@ _let_1 A3) (@ _let_1 B3)))))) (= tptp.ord_le1772180283um_c_c (lambda ((A3 tptp.set_Sum_sum_c_c) (B3 tptp.set_Sum_sum_c_c)) (forall ((T tptp.sum_sum_c_c)) (let ((_let_1 (@ tptp.member_Sum_sum_c_c T))) (=> (@ _let_1 A3) (@ _let_1 B3)))))) (= tptp.ord_le929608341um_b_c (lambda ((A3 tptp.set_Su1783761653um_b_c) (B3 tptp.set_Su1783761653um_b_c)) (forall ((T tptp.sum_su737395349um_b_c)) (let ((_let_1 (@ tptp.member1893232190um_b_c T))) (=> (@ _let_1 A3) (@ _let_1 B3)))))) (forall ((A2 tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c A2) A2)) (forall ((A2 tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c A2) A2)) (forall ((P (-> tptp.sum_sum_c_c Bool)) (Q (-> tptp.sum_sum_c_c Bool))) (=> (forall ((X2 tptp.sum_sum_c_c)) (=> (@ P X2) (@ Q X2))) (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.collect_Sum_sum_c_c P)) (@ tptp.collect_Sum_sum_c_c Q)))) (forall ((P (-> tptp.sum_su737395349um_b_c Bool)) (Q (-> tptp.sum_su737395349um_b_c Bool))) (=> (forall ((X2 tptp.sum_su737395349um_b_c)) (=> (@ P X2) (@ Q X2))) (@ (@ tptp.ord_le929608341um_b_c (@ tptp.collec2086029184um_b_c P)) (@ tptp.collec2086029184um_b_c Q)))) (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (C2 tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.ord_le1772180283um_c_c A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le1772180283um_c_c B2) C2) (@ _let_1 C2))))) (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c) (C2 tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.ord_le929608341um_b_c A2))) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le929608341um_b_c B2) C2) (@ _let_1 C2))))) (= (lambda ((Y2 tptp.set_Sum_sum_c_c) (Z2 tptp.set_Sum_sum_c_c)) (= Y2 Z2)) (lambda ((A3 tptp.set_Sum_sum_c_c) (B3 tptp.set_Sum_sum_c_c)) (and (@ (@ tptp.ord_le1772180283um_c_c A3) B3) (@ (@ tptp.ord_le1772180283um_c_c B3) A3)))) (= (lambda ((Y2 tptp.set_Su1783761653um_b_c) (Z2 tptp.set_Su1783761653um_b_c)) (= Y2 Z2)) (lambda ((A3 tptp.set_Su1783761653um_b_c) (B3 tptp.set_Su1783761653um_b_c)) (and (@ (@ tptp.ord_le929608341um_b_c A3) B3) (@ (@ tptp.ord_le929608341um_b_c B3) A3)))) (forall ((A tptp.produc640052711real_c) (P (-> tptp.produc640052711real_c Bool))) (= (@ (@ tptp.member346808080real_c A) (@ tptp.collec1126017874real_c P)) (@ P A))) (forall ((A2 tptp.set_Pr754230471real_c)) (= (@ tptp.collec1126017874real_c (lambda ((X3 tptp.produc640052711real_c)) (@ (@ tptp.member346808080real_c X3) A2))) A2)) (forall ((P (-> tptp.sum_sum_c_c Bool)) (Q (-> tptp.sum_sum_c_c Bool))) (= (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.collect_Sum_sum_c_c P)) (@ tptp.collect_Sum_sum_c_c Q)) (forall ((X3 tptp.sum_sum_c_c)) (=> (@ P X3) (@ Q X3))))) (forall ((P (-> tptp.sum_su737395349um_b_c Bool)) (Q (-> tptp.sum_su737395349um_b_c Bool))) (= (@ (@ tptp.ord_le929608341um_b_c (@ tptp.collec2086029184um_b_c P)) (@ tptp.collec2086029184um_b_c Q)) (forall ((X3 tptp.sum_su737395349um_b_c)) (=> (@ P X3) (@ Q X3))))) (forall ((X tptp.produc190496183real_c) (X4 tptp.produc190496183real_c) (Y tptp.produc190496183real_c) (Y3 tptp.produc190496183real_c)) (=> (@ (@ tptp.ord_le850691415real_c X) X4) (=> (@ (@ tptp.ord_le850691415real_c Y) Y3) (@ (@ tptp.ord_le652477831real_c (@ (@ tptp.produc1687028567real_c X) Y)) (@ (@ tptp.produc1687028567real_c X4) Y3))))) (forall ((X tptp.finite1398487019real_c) (X4 tptp.finite1398487019real_c) (Y tptp.finite1398487019real_c) (Y3 tptp.finite1398487019real_c)) (=> (@ (@ tptp.ord_le775706699real_c X) X4) (=> (@ (@ tptp.ord_le775706699real_c Y) Y3) (@ (@ tptp.ord_le850691415real_c (@ (@ tptp.produc394644079real_c X) Y)) (@ (@ tptp.produc394644079real_c X4) Y3))))) (forall ((X tptp.set_Sum_sum_c_c) (X4 tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c) (Y3 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X) X4) (=> (@ (@ tptp.ord_le1772180283um_c_c Y) Y3) (@ (@ tptp.ord_le684454199um_c_c (@ (@ tptp.produc1439061071um_c_c X) Y)) (@ (@ tptp.produc1439061071um_c_c X4) Y3))))) (forall ((X tptp.set_Sum_sum_c_c) (X4 tptp.set_Sum_sum_c_c) (Y tptp.set_Su1783761653um_b_c) (Y3 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X) X4) (=> (@ (@ tptp.ord_le929608341um_b_c Y) Y3) (@ (@ tptp.ord_le542695343um_b_c (@ (@ tptp.produc919784577um_b_c X) Y)) (@ (@ tptp.produc919784577um_b_c X4) Y3))))) (forall ((X tptp.set_Su1783761653um_b_c) (X4 tptp.set_Su1783761653um_b_c) (Y tptp.set_Sum_sum_c_c) (Y3 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X) X4) (=> (@ (@ tptp.ord_le1772180283um_c_c Y) Y3) (@ (@ tptp.ord_le1852514783um_c_c (@ (@ tptp.produc616453753um_c_c X) Y)) (@ (@ tptp.produc616453753um_c_c X4) Y3))))) (forall ((X tptp.set_Su1783761653um_b_c) (X4 tptp.set_Su1783761653um_b_c) (Y tptp.set_Su1783761653um_b_c) (Y3 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X) X4) (=> (@ (@ tptp.ord_le929608341um_b_c Y) Y3) (@ (@ tptp.ord_le907560199um_b_c (@ (@ tptp.produc754249687um_b_c X) Y)) (@ (@ tptp.produc754249687um_b_c X4) Y3))))) (forall ((C tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.ord_le1772180283um_c_c C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c A) B))))) (forall ((C tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.ord_le929608341um_b_c C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su1968964297um_b_c A) B))))) (forall ((C tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.ord_le1772180283um_c_c C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c A) B))))) (forall ((C tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.ord_le929608341um_b_c C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su1968964297um_b_c A) B))))) (= tptp.ord_le1772180283um_c_c (lambda ((A4 tptp.set_Sum_sum_c_c) (B4 tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.sup_su1349021703um_c_c A4) B4) B4))) (= tptp.ord_le929608341um_b_c (lambda ((A4 tptp.set_Su1783761653um_b_c) (B4 tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.sup_su1968964297um_b_c A4) B4) B4))) (= tptp.ord_le1772180283um_c_c (lambda ((B4 tptp.set_Sum_sum_c_c) (A4 tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.sup_su1349021703um_c_c A4) B4) A4))) (= tptp.ord_le929608341um_b_c (lambda ((B4 tptp.set_Su1783761653um_b_c) (A4 tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.sup_su1968964297um_b_c A4) B4) A4))) (forall ((B tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c B) (@ (@ tptp.sup_su1349021703um_c_c A) B))) (forall ((B tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c B) (@ (@ tptp.sup_su1968964297um_b_c A) B))) (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c A) (@ (@ tptp.sup_su1349021703um_c_c A) B))) (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c A) (@ (@ tptp.sup_su1968964297um_b_c A) B))) (= tptp.ord_le1772180283um_c_c (lambda ((B4 tptp.set_Sum_sum_c_c) (A4 tptp.set_Sum_sum_c_c)) (= A4 (@ (@ tptp.sup_su1349021703um_c_c A4) B4)))) (= tptp.ord_le929608341um_b_c (lambda ((B4 tptp.set_Su1783761653um_b_c) (A4 tptp.set_Su1783761653um_b_c)) (= A4 (@ (@ tptp.sup_su1968964297um_b_c A4) B4)))) (forall ((B tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c B) A) (=> (@ (@ tptp.ord_le1772180283um_c_c C) A) (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c B) C)) A)))) (forall ((B tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c B) A) (=> (@ (@ tptp.ord_le929608341um_b_c C) A) (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c B) C)) A)))) (forall ((B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c B) C)) A) (not (=> (@ (@ tptp.ord_le1772180283um_c_c B) A) (not (@ (@ tptp.ord_le1772180283um_c_c C) A)))))) (forall ((B tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c B) C)) A) (not (=> (@ (@ tptp.ord_le929608341um_b_c B) A) (not (@ (@ tptp.ord_le929608341um_b_c C) A)))))) (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X) Y) (= (@ (@ tptp.sup_su1349021703um_c_c X) Y) Y))) (forall ((X tptp.set_Su1783761653um_b_c) (Y tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X) Y) (= (@ (@ tptp.sup_su1968964297um_b_c X) Y) Y))) (forall ((Y tptp.set_Sum_sum_c_c) (X tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c Y) X) (= (@ (@ tptp.sup_su1349021703um_c_c X) Y) X))) (forall ((Y tptp.set_Su1783761653um_b_c) (X tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c Y) X) (= (@ (@ tptp.sup_su1968964297um_b_c X) Y) X))) (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A) B) (= (@ (@ tptp.sup_su1349021703um_c_c A) B) B))) (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A) B) (= (@ (@ tptp.sup_su1968964297um_b_c A) B) B))) (forall ((B tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c B) A) (= (@ (@ tptp.sup_su1349021703um_c_c A) B) A))) (forall ((B tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c B) A) (= (@ (@ tptp.sup_su1968964297um_b_c A) B) A))) (forall ((F (-> tptp.set_Sum_sum_c_c tptp.set_Sum_sum_c_c tptp.set_Sum_sum_c_c)) (X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c)) (=> (forall ((X2 tptp.set_Sum_sum_c_c) (Y4 tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c X2) (@ (@ F X2) Y4))) (=> (forall ((X2 tptp.set_Sum_sum_c_c) (Y4 tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c Y4) (@ (@ F X2) Y4))) (=> (forall ((X2 tptp.set_Sum_sum_c_c) (Y4 tptp.set_Sum_sum_c_c) (Z3 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c Y4) X2) (=> (@ (@ tptp.ord_le1772180283um_c_c Z3) X2) (@ (@ tptp.ord_le1772180283um_c_c (@ (@ F Y4) Z3)) X2)))) (= (@ (@ tptp.sup_su1349021703um_c_c X) Y) (@ (@ F X) Y)))))) (forall ((F (-> tptp.set_Su1783761653um_b_c tptp.set_Su1783761653um_b_c tptp.set_Su1783761653um_b_c)) (X tptp.set_Su1783761653um_b_c) (Y tptp.set_Su1783761653um_b_c)) (=> (forall ((X2 tptp.set_Su1783761653um_b_c) (Y4 tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c X2) (@ (@ F X2) Y4))) (=> (forall ((X2 tptp.set_Su1783761653um_b_c) (Y4 tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c Y4) (@ (@ F X2) Y4))) (=> (forall ((X2 tptp.set_Su1783761653um_b_c) (Y4 tptp.set_Su1783761653um_b_c) (Z3 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c Y4) X2) (=> (@ (@ tptp.ord_le929608341um_b_c Z3) X2) (@ (@ tptp.ord_le929608341um_b_c (@ (@ F Y4) Z3)) X2)))) (= (@ (@ tptp.sup_su1968964297um_b_c X) Y) (@ (@ F X) Y)))))) (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c)) (=> (= A (@ (@ tptp.sup_su1349021703um_c_c A) B)) (@ (@ tptp.ord_le1772180283um_c_c B) A))) (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c)) (=> (= A (@ (@ tptp.sup_su1968964297um_b_c A) B)) (@ (@ tptp.ord_le929608341um_b_c B) A))) (forall ((B tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c B) A) (= A (@ (@ tptp.sup_su1349021703um_c_c A) B)))) (forall ((B tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c B) A) (= A (@ (@ tptp.sup_su1968964297um_b_c A) B)))) (= tptp.ord_le1772180283um_c_c (lambda ((X3 tptp.set_Sum_sum_c_c) (Y5 tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.sup_su1349021703um_c_c X3) Y5) Y5))) (= tptp.ord_le929608341um_b_c (lambda ((X3 tptp.set_Su1783761653um_b_c) (Y5 tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.sup_su1968964297um_b_c X3) Y5) Y5))) (forall ((Y tptp.set_Sum_sum_c_c) (X tptp.set_Sum_sum_c_c) (Z tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c Y) X) (=> (@ (@ tptp.ord_le1772180283um_c_c Z) X) (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c Y) Z)) X)))) (forall ((Y tptp.set_Su1783761653um_b_c) (X tptp.set_Su1783761653um_b_c) (Z tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c Y) X) (=> (@ (@ tptp.ord_le929608341um_b_c Z) X) (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c Y) Z)) X)))) (forall ((A tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (D tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A) C) (=> (@ (@ tptp.ord_le1772180283um_c_c B) D) (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c A) B)) (@ (@ tptp.sup_su1349021703um_c_c C) D))))) (forall ((A tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (D tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A) C) (=> (@ (@ tptp.ord_le929608341um_b_c B) D) (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c A) B)) (@ (@ tptp.sup_su1968964297um_b_c C) D))))) (forall ((C tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c) (D tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c C) A) (=> (@ (@ tptp.ord_le1772180283um_c_c D) B) (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c C) D)) (@ (@ tptp.sup_su1349021703um_c_c A) B))))) (forall ((C tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c) (D tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c C) A) (=> (@ (@ tptp.ord_le929608341um_b_c D) B) (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c C) D)) (@ (@ tptp.sup_su1968964297um_b_c A) B))))) (forall ((X tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.ord_le1772180283um_c_c X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c A) B))))) (forall ((X tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.ord_le929608341um_b_c X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su1968964297um_b_c A) B))))) (forall ((X tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.ord_le1772180283um_c_c X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c A) B))))) (forall ((X tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.ord_le929608341um_b_c X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su1968964297um_b_c A) B))))) (forall ((Y tptp.set_Sum_sum_c_c) (X tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c Y) (@ (@ tptp.sup_su1349021703um_c_c X) Y))) (forall ((Y tptp.set_Su1783761653um_b_c) (X tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c Y) (@ (@ tptp.sup_su1968964297um_b_c X) Y))) (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c X) (@ (@ tptp.sup_su1349021703um_c_c X) Y))) (forall ((X tptp.set_Su1783761653um_b_c) (Y tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c X) (@ (@ tptp.sup_su1968964297um_b_c X) Y))) (forall ((A tptp.set_Sum_sum_c_c) (X tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A) X) (=> (@ (@ tptp.ord_le1772180283um_c_c B) X) (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c A) B)) X)))) (forall ((A tptp.set_Su1783761653um_b_c) (X tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A) X) (=> (@ (@ tptp.ord_le929608341um_b_c B) X) (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c A) B)) X)))) (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (X tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c A) B)) X) (not (=> (@ (@ tptp.ord_le1772180283um_c_c A) X) (not (@ (@ tptp.ord_le1772180283um_c_c B) X)))))) (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (X tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c A) B)) X) (not (=> (@ (@ tptp.ord_le929608341um_b_c A) X) (not (@ (@ tptp.ord_le929608341um_b_c B) X)))))) (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c X) (@ (@ tptp.sup_su1349021703um_c_c X) Y))) (forall ((X tptp.set_Su1783761653um_b_c) (Y tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c X) (@ (@ tptp.sup_su1968964297um_b_c X) Y))) (forall ((Y tptp.set_Sum_sum_c_c) (X tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c Y) (@ (@ tptp.sup_su1349021703um_c_c X) Y))) (forall ((Y tptp.set_Su1783761653um_b_c) (X tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c Y) (@ (@ tptp.sup_su1968964297um_b_c X) Y))) (= tptp.ord_le1772180283um_c_c (lambda ((A3 tptp.set_Sum_sum_c_c) (B3 tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.sup_su1349021703um_c_c A3) B3) B3))) (= tptp.ord_le929608341um_b_c (lambda ((A3 tptp.set_Su1783761653um_b_c) (B3 tptp.set_Su1783761653um_b_c)) (= (@ (@ tptp.sup_su1968964297um_b_c A3) B3) B3))) (forall ((C2 tptp.set_Sum_sum_c_c) (A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c C2) (@ (@ tptp.sup_su1349021703um_c_c A2) B2)) (not (forall ((A5 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A5) A2) (forall ((B5 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c B5) B2) (not (= C2 (@ (@ tptp.sup_su1349021703um_c_c A5) B5)))))))))) (forall ((C2 tptp.set_Su1783761653um_b_c) (A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c C2) (@ (@ tptp.sup_su1968964297um_b_c A2) B2)) (not (forall ((A5 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A5) A2) (forall ((B5 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c B5) B2) (not (= C2 (@ (@ tptp.sup_su1968964297um_b_c A5) B5)))))))))) (forall ((B2 tptp.set_Sum_sum_c_c) (A2 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c B2) A2) (= (@ (@ tptp.sup_su1349021703um_c_c A2) B2) A2))) (forall ((B2 tptp.set_Su1783761653um_b_c) (A2 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c B2) A2) (= (@ (@ tptp.sup_su1968964297um_b_c A2) B2) A2))) (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A2) B2) (= (@ (@ tptp.sup_su1349021703um_c_c A2) B2) B2))) (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A2) B2) (= (@ (@ tptp.sup_su1968964297um_b_c A2) B2) B2))) (forall ((B2 tptp.set_Sum_sum_c_c) (A2 tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c B2) (@ (@ tptp.sup_su1349021703um_c_c A2) B2))) (forall ((B2 tptp.set_Su1783761653um_b_c) (A2 tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c B2) (@ (@ tptp.sup_su1968964297um_b_c A2) B2))) (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c A2) (@ (@ tptp.sup_su1349021703um_c_c A2) B2))) (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c A2) (@ (@ tptp.sup_su1968964297um_b_c A2) B2))) (forall ((A2 tptp.set_Sum_sum_c_c) (C2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A2) C2) (=> (@ (@ tptp.ord_le1772180283um_c_c B2) C2) (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c A2) B2)) C2)))) (forall ((A2 tptp.set_Su1783761653um_b_c) (C2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A2) C2) (=> (@ (@ tptp.ord_le929608341um_b_c B2) C2) (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c A2) B2)) C2)))) (forall ((A2 tptp.set_Sum_sum_c_c) (C2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (D2 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A2) C2) (=> (@ (@ tptp.ord_le1772180283um_c_c B2) D2) (@ (@ tptp.ord_le1772180283um_c_c (@ (@ tptp.sup_su1349021703um_c_c A2) B2)) (@ (@ tptp.sup_su1349021703um_c_c C2) D2))))) (forall ((A2 tptp.set_Su1783761653um_b_c) (C2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c) (D2 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A2) C2) (=> (@ (@ tptp.ord_le929608341um_b_c B2) D2) (@ (@ tptp.ord_le929608341um_b_c (@ (@ tptp.sup_su1968964297um_b_c A2) B2)) (@ (@ tptp.sup_su1968964297um_b_c C2) D2))))) (forall ((A tptp.hp_a_b_c) (B tptp.hp_a_b_c)) (=> (@ tptp.hpsafe_a_b_c A) (=> (@ tptp.hpsafe_a_b_c B) (@ tptp.hpsafe_a_b_c (@ (@ tptp.choice_a_b_c A) B))))) (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c) (Z tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c X))) (let ((_let_2 (@ tptp.sup_su1349021703um_c_c Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((B tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c B))) (let ((_let_2 (@ tptp.sup_su1349021703um_c_c A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (= tptp.sup_su1349021703um_c_c (lambda ((X3 tptp.set_Sum_sum_c_c) (Y5 tptp.set_Sum_sum_c_c)) (@ (@ tptp.sup_su1349021703um_c_c Y5) X3))) (= tptp.sup_su1349021703um_c_c (lambda ((A4 tptp.set_Sum_sum_c_c) (B4 tptp.set_Sum_sum_c_c)) (@ (@ tptp.sup_su1349021703um_c_c B4) A4))) (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c) (Z tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c X))) (= (@ (@ tptp.sup_su1349021703um_c_c (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c Y) Z))))) (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c A))) (= (@ (@ tptp.sup_su1349021703um_c_c (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c B) C))))) (forall ((B2 tptp.set_Sum_sum_c_c) (K tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c A))) (let ((_let_2 (@ tptp.sup_su1349021703um_c_c K))) (=> (= B2 (@ _let_2 B)) (= (@ _let_1 B2) (@ _let_2 (@ _let_1 B))))))) (forall ((A2 tptp.set_Sum_sum_c_c) (K tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.sup_su1349021703um_c_c A2) B) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c A) B)))))) (= tptp.sup_su1349021703um_c_c (lambda ((X3 tptp.set_Sum_sum_c_c) (Y5 tptp.set_Sum_sum_c_c)) (@ (@ tptp.sup_su1349021703um_c_c Y5) X3))) (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c) (Z tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c X))) (= (@ (@ tptp.sup_su1349021703um_c_c (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c Y) Z))))) (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c) (Z tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c X))) (let ((_let_2 (@ tptp.sup_su1349021703um_c_c Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (C2 tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c A2))) (let ((_let_2 (@ tptp.sup_su1349021703um_c_c B2))) (= (@ _let_1 (@ _let_2 C2)) (@ _let_2 (@ _let_1 C2)))))) (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c A2))) (let ((_let_2 (@ _let_1 B2))) (= (@ _let_1 _let_2) _let_2)))) (= tptp.sup_su1349021703um_c_c (lambda ((A3 tptp.set_Sum_sum_c_c) (B3 tptp.set_Sum_sum_c_c)) (@ (@ tptp.sup_su1349021703um_c_c B3) A3))) (forall ((A2 tptp.set_Sum_sum_c_c)) (= (@ (@ tptp.sup_su1349021703um_c_c A2) A2) A2)) (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (C2 tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.sup_su1349021703um_c_c A2))) (= (@ (@ tptp.sup_su1349021703um_c_c (@ _let_1 B2)) C2) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c B2) C2))))) (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (P (-> tptp.sum_sum_c_c Bool))) (= (forall ((X3 tptp.sum_sum_c_c)) (=> (@ (@ tptp.member_Sum_sum_c_c X3) (@ (@ tptp.sup_su1349021703um_c_c A2) B2)) (@ P X3))) (and (forall ((X3 tptp.sum_sum_c_c)) (=> (@ (@ tptp.member_Sum_sum_c_c X3) A2) (@ P X3))) (forall ((X3 tptp.sum_sum_c_c)) (=> (@ (@ tptp.member_Sum_sum_c_c X3) B2) (@ P X3)))))) (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (P (-> tptp.sum_sum_c_c Bool))) (= (exists ((X3 tptp.sum_sum_c_c)) (and (@ (@ tptp.member_Sum_sum_c_c X3) (@ (@ tptp.sup_su1349021703um_c_c A2) B2)) (@ P X3))) (or (exists ((X3 tptp.sum_sum_c_c)) (and (@ (@ tptp.member_Sum_sum_c_c X3) A2) (@ P X3))) (exists ((X3 tptp.sum_sum_c_c)) (and (@ (@ tptp.member_Sum_sum_c_c X3) B2) (@ P X3)))))) (forall ((C tptp.produc640052711real_c) (B2 tptp.set_Pr754230471real_c) (A2 tptp.set_Pr754230471real_c)) (let ((_let_1 (@ tptp.member346808080real_c C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_su588839579real_c A2) B2))))) (forall ((C tptp.sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (A2 tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.member_Sum_sum_c_c C))) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c A2) B2))))) (forall ((C tptp.produc640052711real_c) (A2 tptp.set_Pr754230471real_c) (B2 tptp.set_Pr754230471real_c)) (let ((_let_1 (@ tptp.member346808080real_c C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su588839579real_c A2) B2))))) (forall ((C tptp.sum_sum_c_c) (A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.member_Sum_sum_c_c C))) (=> (@ _let_1 A2) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c A2) B2))))) (forall ((C tptp.produc640052711real_c) (A2 tptp.set_Pr754230471real_c) (B2 tptp.set_Pr754230471real_c)) (let ((_let_1 (@ tptp.member346808080real_c C))) (=> (@ _let_1 (@ (@ tptp.sup_su588839579real_c A2) B2)) (=> (not (@ _let_1 A2)) (@ _let_1 B2))))) (forall ((C tptp.sum_sum_c_c) (A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.member_Sum_sum_c_c C))) (=> (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c A2) B2)) (=> (not (@ _let_1 A2)) (@ _let_1 B2))))) (@ _let_3 _let_6) (forall ((I tptp.denota231621370t_unit) (J tptp.denota231621370t_unit)) (and (forall ((Nu tptp.produc190496183real_c) (Nu2 tptp.produc190496183real_c) (Mu2 tptp.produc190496183real_c) (V tptp.set_Sum_sum_c_c)) (=> (@ (@ (@ tptp.denota69106024_a_b_c I) J) (@ tptp.static_SIGP_a_b_c tptp.a)) (=> (@ (@ (@ tptp.denota1997846518gree_c Nu) Nu2) V) (=> (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.static_FVP_a_b_c tptp.a)) V) (=> (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c Nu) Mu2)) (@ (@ tptp.denota904684656_a_b_c I) tptp.a)) (exists ((Mu3 tptp.produc190496183real_c)) (and (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c Nu2) Mu3)) (@ (@ tptp.denota904684656_a_b_c J) tptp.a)) (@ (@ (@ tptp.denota1997846518gree_c Mu2) Mu3) (@ (@ tptp.sup_su1349021703um_c_c (@ tptp.static_MBV_a_b_c tptp.a)) V))))))))) (@ (@ tptp.coinci772602909_a_b_c tptp.a) I))) (forall ((I tptp.denota231621370t_unit) (J tptp.denota231621370t_unit)) (and (forall ((Nu tptp.produc190496183real_c) (Nu2 tptp.produc190496183real_c) (Mu2 tptp.produc190496183real_c) (V tptp.set_Sum_sum_c_c)) (=> (@ (@ (@ tptp.denota69106024_a_b_c I) J) (@ tptp.static_SIGP_a_b_c tptp.b)) (=> (@ (@ (@ tptp.denota1997846518gree_c Nu) Nu2) V) (=> (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.static_FVP_a_b_c tptp.b)) V) (=> (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c Nu) Mu2)) (@ (@ tptp.denota904684656_a_b_c I) tptp.b)) (exists ((Mu3 tptp.produc190496183real_c)) (and (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c Nu2) Mu3)) (@ (@ tptp.denota904684656_a_b_c J) tptp.b)) (@ (@ (@ tptp.denota1997846518gree_c Mu2) Mu3) (@ (@ tptp.sup_su1349021703um_c_c (@ tptp.static_MBV_a_b_c tptp.b)) V))))))))) (@ (@ tptp.coinci772602909_a_b_c tptp.b) I))) (= tptp.coinci1852866155_a_b_c (lambda ((Alpha tptp.hp_a_b_c)) (forall ((I2 tptp.denota231621370t_unit) (J2 tptp.denota231621370t_unit)) (and (@ (@ (@ tptp.coinci354700372_a_b_c Alpha) I2) J2) (@ (@ tptp.coinci772602909_a_b_c Alpha) I2))))) (forall ((Alpha2 tptp.hp_a_b_c) (Beta tptp.hp_a_b_c)) (= (@ tptp.static_FVP_a_b_c (@ (@ tptp.choice_a_b_c Alpha2) Beta)) (@ (@ tptp.sup_su1349021703um_c_c (@ tptp.static_FVP_a_b_c Alpha2)) (@ tptp.static_FVP_a_b_c Beta)))) (forall ((B2 tptp.set_Sum_sum_c_c) (A2 tptp.set_Sum_sum_c_c) (Nu3 tptp.produc190496183real_c) (Nu4 tptp.produc190496183real_c)) (let ((_let_1 (@ (@ tptp.denota1997846518gree_c Nu3) Nu4))) (=> (@ (@ tptp.ord_le1772180283um_c_c B2) A2) (=> (@ _let_1 A2) (@ _let_1 B2))))) (forall ((A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c) (Nu3 tptp.produc190496183real_c) (Omega tptp.produc190496183real_c)) (let ((_let_1 (@ (@ tptp.denota1997846518gree_c Nu3) Omega))) (=> (@ (@ tptp.ord_le1772180283um_c_c A2) B2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((A tptp.produc190496183real_c) (B tptp.produc190496183real_c) (A6 tptp.produc190496183real_c) (B6 tptp.produc190496183real_c)) (= (= (@ (@ tptp.produc1687028567real_c A) B) (@ (@ tptp.produc1687028567real_c A6) B6)) (and (= A A6) (= B B6)))) (forall ((A tptp.finite1398487019real_c) (B tptp.finite1398487019real_c) (A6 tptp.finite1398487019real_c) (B6 tptp.finite1398487019real_c)) (= (= (@ (@ tptp.produc394644079real_c A) B) (@ (@ tptp.produc394644079real_c A6) B6)) (and (= A A6) (= B B6)))) (forall ((X1 tptp.produc190496183real_c) (X22 tptp.produc190496183real_c) (Y1 tptp.produc190496183real_c) (Y22 tptp.produc190496183real_c)) (= (= (@ (@ tptp.produc1687028567real_c X1) X22) (@ (@ tptp.produc1687028567real_c Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X1 tptp.finite1398487019real_c) (X22 tptp.finite1398487019real_c) (Y1 tptp.finite1398487019real_c) (Y22 tptp.finite1398487019real_c)) (= (= (@ (@ tptp.produc394644079real_c X1) X22) (@ (@ tptp.produc394644079real_c Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c X) X)) (forall ((X tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c X) X)) (@ (@ tptp.ord_le929608341um_b_c _let_4) _let_6) (@ (@ tptp.ord_le929608341um_b_c _let_2) _let_6) (@ _let_3 _let_4) (@ _let_3 _let_2) (= tptp.coinci354700372_a_b_c (lambda ((Alpha tptp.hp_a_b_c) (I2 tptp.denota231621370t_unit) (J2 tptp.denota231621370t_unit)) (forall ((Nu5 tptp.produc190496183real_c) (Nu6 tptp.produc190496183real_c) (Mu4 tptp.produc190496183real_c) (V2 tptp.set_Sum_sum_c_c)) (=> (@ (@ (@ tptp.denota69106024_a_b_c I2) J2) (@ tptp.static_SIGP_a_b_c Alpha)) (=> (@ (@ (@ tptp.denota1997846518gree_c Nu5) Nu6) V2) (=> (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.static_FVP_a_b_c Alpha)) V2) (=> (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c Nu5) Mu4)) (@ (@ tptp.denota904684656_a_b_c I2) Alpha)) (exists ((Mu5 tptp.produc190496183real_c)) (and (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c Nu6) Mu5)) (@ (@ tptp.denota904684656_a_b_c J2) Alpha)) (@ (@ (@ tptp.denota1997846518gree_c Mu4) Mu5) (@ (@ tptp.sup_su1349021703um_c_c (@ tptp.static_MBV_a_b_c Alpha)) V2))))))))))) (forall ((A2 tptp.set_Su1783761653um_b_c) (B2 tptp.set_Su1783761653um_b_c) (I3 tptp.denota231621370t_unit) (J3 tptp.denota231621370t_unit)) (let ((_let_1 (@ (@ tptp.denota69106024_a_b_c I3) J3))) (=> (@ (@ tptp.ord_le929608341um_b_c A2) B2) (=> (@ _let_1 B2) (@ _let_1 A2))))) (forall ((I3 tptp.denota231621370t_unit) (A2 tptp.set_Su1783761653um_b_c)) (@ (@ (@ tptp.denota69106024_a_b_c I3) I3) A2)) (forall ((A2 tptp.denota231621370t_unit) (B2 tptp.denota231621370t_unit) (V3 tptp.set_Su1783761653um_b_c)) (=> (@ (@ (@ tptp.denota69106024_a_b_c A2) B2) V3) (@ (@ (@ tptp.denota69106024_a_b_c B2) A2) V3))) (forall ((A tptp.hp_a_b_c) (B tptp.hp_a_b_c)) (= (@ tptp.static_SIGP_a_b_c (@ (@ tptp.choice_a_b_c A) B)) (@ (@ tptp.sup_su1968964297um_b_c (@ tptp.static_SIGP_a_b_c A)) (@ tptp.static_SIGP_a_b_c B)))) (forall ((B tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c B) A) (=> (@ (@ tptp.ord_le1772180283um_c_c A) B) (= A B)))) (forall ((B tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c B) A) (=> (@ (@ tptp.ord_le929608341um_b_c A) B) (= A B)))) (= (lambda ((Y2 tptp.set_Sum_sum_c_c) (Z2 tptp.set_Sum_sum_c_c)) (= Y2 Z2)) (lambda ((A4 tptp.set_Sum_sum_c_c) (B4 tptp.set_Sum_sum_c_c)) (and (@ (@ tptp.ord_le1772180283um_c_c B4) A4) (@ (@ tptp.ord_le1772180283um_c_c A4) B4)))) (= (lambda ((Y2 tptp.set_Su1783761653um_b_c) (Z2 tptp.set_Su1783761653um_b_c)) (= Y2 Z2)) (lambda ((A4 tptp.set_Su1783761653um_b_c) (B4 tptp.set_Su1783761653um_b_c)) (and (@ (@ tptp.ord_le929608341um_b_c B4) A4) (@ (@ tptp.ord_le929608341um_b_c A4) B4)))) (forall ((B tptp.set_Sum_sum_c_c) (A tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.ord_le1772180283um_c_c C))) (=> (@ (@ tptp.ord_le1772180283um_c_c B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.set_Su1783761653um_b_c) (A tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.ord_le929608341um_b_c C))) (=> (@ (@ tptp.ord_le929608341um_b_c B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((A tptp.set_Sum_sum_c_c)) (@ (@ tptp.ord_le1772180283um_c_c A) A)) (forall ((A tptp.set_Su1783761653um_b_c)) (@ (@ tptp.ord_le929608341um_b_c A) A)) (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c) (Z tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.ord_le1772180283um_c_c X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le1772180283um_c_c Y) Z) (@ _let_1 Z))))) (forall ((X tptp.set_Su1783761653um_b_c) (Y tptp.set_Su1783761653um_b_c) (Z tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.ord_le929608341um_b_c X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_le929608341um_b_c Y) Z) (@ _let_1 Z))))) (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A) B) (=> (@ (@ tptp.ord_le1772180283um_c_c B) A) (= A B)))) (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A) B) (=> (@ (@ tptp.ord_le929608341um_b_c B) A) (= A B)))) (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.ord_le1772180283um_c_c A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.ord_le929608341um_b_c A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c)) (=> (= A B) (=> (@ (@ tptp.ord_le1772180283um_c_c B) C) (@ (@ tptp.ord_le1772180283um_c_c A) C)))) (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c)) (=> (= A B) (=> (@ (@ tptp.ord_le929608341um_b_c B) C) (@ (@ tptp.ord_le929608341um_b_c A) C)))) (= (lambda ((Y2 tptp.set_Sum_sum_c_c) (Z2 tptp.set_Sum_sum_c_c)) (= Y2 Z2)) (lambda ((A4 tptp.set_Sum_sum_c_c) (B4 tptp.set_Sum_sum_c_c)) (and (@ (@ tptp.ord_le1772180283um_c_c A4) B4) (@ (@ tptp.ord_le1772180283um_c_c B4) A4)))) (= (lambda ((Y2 tptp.set_Su1783761653um_b_c) (Z2 tptp.set_Su1783761653um_b_c)) (= Y2 Z2)) (lambda ((A4 tptp.set_Su1783761653um_b_c) (B4 tptp.set_Su1783761653um_b_c)) (and (@ (@ tptp.ord_le929608341um_b_c A4) B4) (@ (@ tptp.ord_le929608341um_b_c B4) A4)))) (forall ((Y tptp.set_Sum_sum_c_c) (X tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c Y) X) (= (@ (@ tptp.ord_le1772180283um_c_c X) Y) (= X Y)))) (forall ((Y tptp.set_Su1783761653um_b_c) (X tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c Y) X) (= (@ (@ tptp.ord_le929608341um_b_c X) Y) (= X Y)))) (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.ord_le1772180283um_c_c A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le1772180283um_c_c B) C) (@ _let_1 C))))) (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.ord_le929608341um_b_c A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le929608341um_b_c B) C) (@ _let_1 C))))) (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c)) (=> (= X Y) (@ (@ tptp.ord_le1772180283um_c_c X) Y))) (forall ((X tptp.set_Su1783761653um_b_c) (Y tptp.set_Su1783761653um_b_c)) (=> (= X Y) (@ (@ tptp.ord_le929608341um_b_c X) Y))) (forall ((X tptp.set_Sum_sum_c_c) (Y tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X) Y) (=> (@ (@ tptp.ord_le1772180283um_c_c Y) X) (= X Y)))) (forall ((X tptp.set_Su1783761653um_b_c) (Y tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X) Y) (=> (@ (@ tptp.ord_le929608341um_b_c Y) X) (= X Y)))) (= (lambda ((Y2 tptp.set_Sum_sum_c_c) (Z2 tptp.set_Sum_sum_c_c)) (= Y2 Z2)) (lambda ((X3 tptp.set_Sum_sum_c_c) (Y5 tptp.set_Sum_sum_c_c)) (and (@ (@ tptp.ord_le1772180283um_c_c X3) Y5) (@ (@ tptp.ord_le1772180283um_c_c Y5) X3)))) (= (lambda ((Y2 tptp.set_Su1783761653um_b_c) (Z2 tptp.set_Su1783761653um_b_c)) (= Y2 Z2)) (lambda ((X3 tptp.set_Su1783761653um_b_c) (Y5 tptp.set_Su1783761653um_b_c)) (and (@ (@ tptp.ord_le929608341um_b_c X3) Y5) (@ (@ tptp.ord_le929608341um_b_c Y5) X3)))) (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (F (-> tptp.set_Sum_sum_c_c tptp.set_Sum_sum_c_c)) (C tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A) B) (=> (= (@ F B) C) (=> (forall ((X2 tptp.set_Sum_sum_c_c) (Y4 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X2) Y4) (@ (@ tptp.ord_le1772180283um_c_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le1772180283um_c_c (@ F A)) C))))) (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (F (-> tptp.set_Sum_sum_c_c tptp.set_Su1783761653um_b_c)) (C tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A) B) (=> (= (@ F B) C) (=> (forall ((X2 tptp.set_Sum_sum_c_c) (Y4 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X2) Y4) (@ (@ tptp.ord_le929608341um_b_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le929608341um_b_c (@ F A)) C))))) (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (F (-> tptp.set_Su1783761653um_b_c tptp.set_Sum_sum_c_c)) (C tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A) B) (=> (= (@ F B) C) (=> (forall ((X2 tptp.set_Su1783761653um_b_c) (Y4 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X2) Y4) (@ (@ tptp.ord_le1772180283um_c_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le1772180283um_c_c (@ F A)) C))))) (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (F (-> tptp.set_Su1783761653um_b_c tptp.set_Su1783761653um_b_c)) (C tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A) B) (=> (= (@ F B) C) (=> (forall ((X2 tptp.set_Su1783761653um_b_c) (Y4 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X2) Y4) (@ (@ tptp.ord_le929608341um_b_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le929608341um_b_c (@ F A)) C))))) (forall ((A tptp.set_Sum_sum_c_c) (F (-> tptp.set_Sum_sum_c_c tptp.set_Sum_sum_c_c)) (B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le1772180283um_c_c B) C) (=> (forall ((X2 tptp.set_Sum_sum_c_c) (Y4 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X2) Y4) (@ (@ tptp.ord_le1772180283um_c_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le1772180283um_c_c A) (@ F C)))))) (forall ((A tptp.set_Su1783761653um_b_c) (F (-> tptp.set_Sum_sum_c_c tptp.set_Su1783761653um_b_c)) (B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le1772180283um_c_c B) C) (=> (forall ((X2 tptp.set_Sum_sum_c_c) (Y4 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X2) Y4) (@ (@ tptp.ord_le929608341um_b_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le929608341um_b_c A) (@ F C)))))) (forall ((A tptp.set_Sum_sum_c_c) (F (-> tptp.set_Su1783761653um_b_c tptp.set_Sum_sum_c_c)) (B tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le929608341um_b_c B) C) (=> (forall ((X2 tptp.set_Su1783761653um_b_c) (Y4 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X2) Y4) (@ (@ tptp.ord_le1772180283um_c_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le1772180283um_c_c A) (@ F C)))))) (forall ((A tptp.set_Su1783761653um_b_c) (F (-> tptp.set_Su1783761653um_b_c tptp.set_Su1783761653um_b_c)) (B tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le929608341um_b_c B) C) (=> (forall ((X2 tptp.set_Su1783761653um_b_c) (Y4 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X2) Y4) (@ (@ tptp.ord_le929608341um_b_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le929608341um_b_c A) (@ F C)))))) (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (F (-> tptp.set_Sum_sum_c_c tptp.set_Sum_sum_c_c)) (C tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A) B) (=> (@ (@ tptp.ord_le1772180283um_c_c (@ F B)) C) (=> (forall ((X2 tptp.set_Sum_sum_c_c) (Y4 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X2) Y4) (@ (@ tptp.ord_le1772180283um_c_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le1772180283um_c_c (@ F A)) C))))) (forall ((A tptp.set_Sum_sum_c_c) (B tptp.set_Sum_sum_c_c) (F (-> tptp.set_Sum_sum_c_c tptp.set_Su1783761653um_b_c)) (C tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c A) B) (=> (@ (@ tptp.ord_le929608341um_b_c (@ F B)) C) (=> (forall ((X2 tptp.set_Sum_sum_c_c) (Y4 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X2) Y4) (@ (@ tptp.ord_le929608341um_b_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le929608341um_b_c (@ F A)) C))))) (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (F (-> tptp.set_Su1783761653um_b_c tptp.set_Sum_sum_c_c)) (C tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A) B) (=> (@ (@ tptp.ord_le1772180283um_c_c (@ F B)) C) (=> (forall ((X2 tptp.set_Su1783761653um_b_c) (Y4 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X2) Y4) (@ (@ tptp.ord_le1772180283um_c_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le1772180283um_c_c (@ F A)) C))))) (forall ((A tptp.set_Su1783761653um_b_c) (B tptp.set_Su1783761653um_b_c) (F (-> tptp.set_Su1783761653um_b_c tptp.set_Su1783761653um_b_c)) (C tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c A) B) (=> (@ (@ tptp.ord_le929608341um_b_c (@ F B)) C) (=> (forall ((X2 tptp.set_Su1783761653um_b_c) (Y4 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X2) Y4) (@ (@ tptp.ord_le929608341um_b_c (@ F X2)) (@ F Y4)))) (@ (@ tptp.ord_le929608341um_b_c (@ F A)) C))))) (forall ((A tptp.set_Sum_sum_c_c) (F (-> tptp.set_Sum_sum_c_c tptp.set_Sum_sum_c_c)) (B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.ord_le1772180283um_c_c A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le1772180283um_c_c B) C) (=> (forall ((X2 tptp.set_Sum_sum_c_c) (Y4 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X2) Y4) (@ (@ tptp.ord_le1772180283um_c_c (@ F X2)) (@ F Y4)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.set_Sum_sum_c_c) (F (-> tptp.set_Su1783761653um_b_c tptp.set_Sum_sum_c_c)) (B tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.ord_le1772180283um_c_c A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le929608341um_b_c B) C) (=> (forall ((X2 tptp.set_Su1783761653um_b_c) (Y4 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X2) Y4) (@ (@ tptp.ord_le1772180283um_c_c (@ F X2)) (@ F Y4)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.set_Su1783761653um_b_c) (F (-> tptp.set_Sum_sum_c_c tptp.set_Su1783761653um_b_c)) (B tptp.set_Sum_sum_c_c) (C tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ tptp.ord_le929608341um_b_c A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le1772180283um_c_c B) C) (=> (forall ((X2 tptp.set_Sum_sum_c_c) (Y4 tptp.set_Sum_sum_c_c)) (=> (@ (@ tptp.ord_le1772180283um_c_c X2) Y4) (@ (@ tptp.ord_le929608341um_b_c (@ F X2)) (@ F Y4)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.set_Su1783761653um_b_c) (F (-> tptp.set_Su1783761653um_b_c tptp.set_Su1783761653um_b_c)) (B tptp.set_Su1783761653um_b_c) (C tptp.set_Su1783761653um_b_c)) (let ((_let_1 (@ tptp.ord_le929608341um_b_c A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le929608341um_b_c B) C) (=> (forall ((X2 tptp.set_Su1783761653um_b_c) (Y4 tptp.set_Su1783761653um_b_c)) (=> (@ (@ tptp.ord_le929608341um_b_c X2) Y4) (@ (@ tptp.ord_le929608341um_b_c (@ F X2)) (@ F Y4)))) (@ _let_1 (@ F C))))))) (forall ((P2 tptp.produc640052711real_c)) (exists ((X2 tptp.produc190496183real_c) (Y4 tptp.produc190496183real_c)) (= P2 (@ (@ tptp.produc1687028567real_c X2) Y4)))) (forall ((P2 tptp.produc190496183real_c)) (exists ((X2 tptp.finite1398487019real_c) (Y4 tptp.finite1398487019real_c)) (= P2 (@ (@ tptp.produc394644079real_c X2) Y4)))) (forall ((P (-> tptp.produc640052711real_c Bool)) (P2 tptp.produc640052711real_c)) (=> (forall ((A7 tptp.produc190496183real_c) (B7 tptp.produc190496183real_c)) (@ P (@ (@ tptp.produc1687028567real_c A7) B7))) (@ P P2))) (forall ((P (-> tptp.produc190496183real_c Bool)) (P2 tptp.produc190496183real_c)) (=> (forall ((A7 tptp.finite1398487019real_c) (B7 tptp.finite1398487019real_c)) (@ P (@ (@ tptp.produc394644079real_c A7) B7))) (@ P P2))) (forall ((A tptp.produc190496183real_c) (B tptp.produc190496183real_c) (A6 tptp.produc190496183real_c) (B6 tptp.produc190496183real_c)) (=> (= (@ (@ tptp.produc1687028567real_c A) B) (@ (@ tptp.produc1687028567real_c A6) B6)) (not (=> (= A A6) (not (= B B6)))))) (forall ((A tptp.finite1398487019real_c) (B tptp.finite1398487019real_c) (A6 tptp.finite1398487019real_c) (B6 tptp.finite1398487019real_c)) (=> (= (@ (@ tptp.produc394644079real_c A) B) (@ (@ tptp.produc394644079real_c A6) B6)) (not (=> (= A A6) (not (= B B6)))))) (forall ((Y tptp.produc640052711real_c)) (not (forall ((A7 tptp.produc190496183real_c) (B7 tptp.produc190496183real_c)) (not (= Y (@ (@ tptp.produc1687028567real_c A7) B7)))))) (forall ((Y tptp.produc190496183real_c)) (not (forall ((A7 tptp.finite1398487019real_c) (B7 tptp.finite1398487019real_c)) (not (= Y (@ (@ tptp.produc394644079real_c A7) B7)))))) (forall ((P (-> tptp.produc640052711real_c Bool)) (Prod tptp.produc640052711real_c)) (=> (forall ((A7 tptp.produc190496183real_c) (B7 tptp.produc190496183real_c)) (@ P (@ (@ tptp.produc1687028567real_c A7) B7))) (@ P Prod))) (forall ((P (-> tptp.produc190496183real_c Bool)) (Prod tptp.produc190496183real_c)) (=> (forall ((A7 tptp.finite1398487019real_c) (B7 tptp.finite1398487019real_c)) (@ P (@ (@ tptp.produc394644079real_c A7) B7))) (@ P Prod))) (forall ((A2 tptp.produc190496183real_c) (B2 tptp.produc190496183real_c) (V3 tptp.set_Sum_sum_c_c)) (=> (@ (@ (@ tptp.denota1997846518gree_c A2) B2) V3) (@ (@ (@ tptp.denota1997846518gree_c B2) A2) V3))) (forall ((Nu3 tptp.produc190496183real_c) (A2 tptp.set_Sum_sum_c_c)) (@ (@ (@ tptp.denota1997846518gree_c Nu3) Nu3) A2)) (forall ((Y tptp.produc640052711real_c)) (not (forall ((A7 tptp.produc190496183real_c) (B7 tptp.finite1398487019real_c) (C3 tptp.finite1398487019real_c)) (not (= Y (@ (@ tptp.produc1687028567real_c A7) (@ (@ tptp.produc394644079real_c B7) C3))))))) (forall ((P (-> tptp.produc640052711real_c Bool)) (X tptp.produc640052711real_c)) (=> (forall ((A7 tptp.produc190496183real_c) (B7 tptp.finite1398487019real_c) (C3 tptp.finite1398487019real_c)) (@ P (@ (@ tptp.produc1687028567real_c A7) (@ (@ tptp.produc394644079real_c B7) C3)))) (@ P X))) (forall ((Nu3 tptp.produc190496183real_c) (Omega tptp.produc190496183real_c) (A2 tptp.set_Sum_sum_c_c) (B2 tptp.set_Sum_sum_c_c)) (let ((_let_1 (@ (@ tptp.denota1997846518gree_c Nu3) Omega))) (=> (@ _let_1 A2) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.sup_su1349021703um_c_c A2) B2)))))) (forall ((I3 tptp.denota231621370t_unit) (Alpha2 tptp.hp_a_b_c) (Beta tptp.hp_a_b_c)) (let ((_let_1 (@ tptp.denota904684656_a_b_c I3))) (= (@ _let_1 (@ (@ tptp.choice_a_b_c Alpha2) Beta)) (@ (@ tptp.sup_su588839579real_c (@ _let_1 Alpha2)) (@ _let_1 Beta))))) (forall ((P (-> tptp.produc190496183real_c Bool)) (X tptp.produc190496183real_c) (Y3 tptp.produc190496183real_c) (Y tptp.produc190496183real_c) (R (-> tptp.produc190496183real_c tptp.set_Pr754230471real_c))) (let ((_let_1 (@ tptp.produc1687028567real_c X))) (=> (@ P X) (=> (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c Y3) Y)) (@ R X)) (@ (@ tptp.member616151824real_c (@ (@ tptp.produc544496471real_c (@ _let_1 Y3)) (@ _let_1 Y))) (@ (@ tptp.same_f598810924real_c P) R)))))) (forall ((P (-> tptp.finite1398487019real_c Bool)) (X tptp.finite1398487019real_c) (Y3 tptp.finite1398487019real_c) (Y tptp.finite1398487019real_c) (R (-> tptp.finite1398487019real_c tptp.set_Pr1389752855real_c))) (let ((_let_1 (@ tptp.produc394644079real_c X))) (=> (@ P X) (=> (@ (@ tptp.member1895684704real_c (@ (@ tptp.produc394644079real_c Y3) Y)) (@ R X)) (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c (@ _let_1 Y3)) (@ _let_1 Y))) (@ (@ tptp.same_f1974156740real_c P) R)))))) (= tptp.bNF_Ca1667803246um_c_c (lambda ((R2 tptp.set_Pr754230471real_c) (As (-> tptp.produc190496183real_c tptp.set_Sum_sum_c_c))) (forall ((I4 tptp.produc190496183real_c) (J4 tptp.produc190496183real_c)) (=> (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c I4) J4)) R2) (@ (@ tptp.ord_le1772180283um_c_c (@ As I4)) (@ As J4)))))) (= tptp.bNF_Ca1693016812um_c_c (lambda ((R2 tptp.set_Pr1389752855real_c) (As (-> tptp.finite1398487019real_c tptp.set_Sum_sum_c_c))) (forall ((I4 tptp.finite1398487019real_c) (J4 tptp.finite1398487019real_c)) (=> (@ (@ tptp.member1895684704real_c (@ (@ tptp.produc394644079real_c I4) J4)) R2) (@ (@ tptp.ord_le1772180283um_c_c (@ As I4)) (@ As J4)))))) (= tptp.bNF_Ca419199138um_b_c (lambda ((R2 tptp.set_Pr754230471real_c) (As (-> tptp.produc190496183real_c tptp.set_Su1783761653um_b_c))) (forall ((I4 tptp.produc190496183real_c) (J4 tptp.produc190496183real_c)) (=> (@ (@ tptp.member346808080real_c (@ (@ tptp.produc1687028567real_c I4) J4)) R2) (@ (@ tptp.ord_le929608341um_b_c (@ As I4)) (@ As J4)))))) (= tptp.bNF_Ca318582436um_b_c (lambda ((R2 tptp.set_Pr1389752855real_c) (As (-> tptp.finite1398487019real_c tptp.set_Su1783761653um_b_c))) (forall ((I4 tptp.finite1398487019real_c) (J4 tptp.finite1398487019real_c)) (=> (@ (@ tptp.member1895684704real_c (@ (@ tptp.produc394644079real_c I4) J4)) R2) (@ (@ tptp.ord_le929608341um_b_c (@ As I4)) (@ As J4)))))) (forall ((P (-> tptp.set_Sum_sum_c_c Bool)) (X tptp.set_Sum_sum_c_c) (Q (-> tptp.set_Sum_sum_c_c Bool))) (=> (@ P X) (=> (forall ((Y4 tptp.set_Sum_sum_c_c)) (=> (@ P Y4) (@ (@ tptp.ord_le1772180283um_c_c Y4) X))) (=> (forall ((X2 tptp.set_Sum_sum_c_c)) (=> (@ P X2) (=> (forall ((Y6 tptp.set_Sum_sum_c_c)) (=> (@ P Y6) (@ (@ tptp.ord_le1772180283um_c_c Y6) X2))) (@ Q X2)))) (@ Q (@ tptp.order_1776530114um_c_c P)))))) (forall ((P (-> tptp.set_Su1783761653um_b_c Bool)) (X tptp.set_Su1783761653um_b_c) (Q (-> tptp.set_Su1783761653um_b_c Bool))) (=> (@ P X) (=> (forall ((Y4 tptp.set_Su1783761653um_b_c)) (=> (@ P Y4) (@ (@ tptp.ord_le929608341um_b_c Y4) X))) (=> (forall ((X2 tptp.set_Su1783761653um_b_c)) (=> (@ P X2) (=> (forall ((Y6 tptp.set_Su1783761653um_b_c)) (=> (@ P Y6) (@ (@ tptp.ord_le929608341um_b_c Y6) X2))) (@ Q X2)))) (@ Q (@ tptp.order_365181262um_b_c P)))))) (forall ((P (-> tptp.set_Sum_sum_c_c Bool)) (X tptp.set_Sum_sum_c_c)) (=> (@ P X) (=> (forall ((Y4 tptp.set_Sum_sum_c_c)) (=> (@ P Y4) (@ (@ tptp.ord_le1772180283um_c_c Y4) X))) (= (@ tptp.order_1776530114um_c_c P) X)))) (forall ((P (-> tptp.set_Su1783761653um_b_c Bool)) (X tptp.set_Su1783761653um_b_c)) (=> (@ P X) (=> (forall ((Y4 tptp.set_Su1783761653um_b_c)) (=> (@ P Y4) (@ (@ tptp.ord_le929608341um_b_c Y4) X))) (= (@ tptp.order_365181262um_b_c P) X)))) (forall ((Prod tptp.produc640052711real_c)) (= (@ (@ tptp.produc1687028567real_c (@ tptp.produc876006723real_c Prod)) (@ tptp.produc415593093real_c Prod)) Prod)) (forall ((Prod tptp.produc190496183real_c)) (= (@ (@ tptp.produc394644079real_c (@ tptp.produc2010422875real_c Prod)) (@ tptp.produc314122909real_c Prod)) Prod)) (= tptp.ord_le684454199um_c_c (lambda ((X3 tptp.produc214722967um_c_c) (Y5 tptp.produc214722967um_c_c)) (and (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.produc1983230011um_c_c X3)) (@ tptp.produc1983230011um_c_c Y5)) (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.produc1132019837um_c_c X3)) (@ tptp.produc1132019837um_c_c Y5))))) (= tptp.ord_le542695343um_b_c (lambda ((X3 tptp.produc263671631um_b_c) (Y5 tptp.produc263671631um_b_c)) (and (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.produc1758795157um_b_c X3)) (@ tptp.produc1758795157um_b_c Y5)) (@ (@ tptp.ord_le929608341um_b_c (@ tptp.produc1193764051um_b_c X3)) (@ tptp.produc1193764051um_b_c Y5))))) (= tptp.ord_le1852514783um_c_c (lambda ((X3 tptp.produc1573491071um_c_c) (Y5 tptp.produc1573491071um_c_c)) (and (@ (@ tptp.ord_le929608341um_b_c (@ tptp.produc1455464333um_c_c X3)) (@ tptp.produc1455464333um_c_c Y5)) (@ (@ tptp.ord_le1772180283um_c_c (@ tptp.produc890433227um_c_c X3)) (@ tptp.produc890433227um_c_c Y5))))) (= tptp.ord_le907560199um_b_c (lambda ((X3 tptp.produc1415638375um_b_c) (Y5 tptp.produc1415638375um_b_c)) (and (@ (@ tptp.ord_le929608341um_b_c (@ tptp.produc1961869763um_b_c X3)) (@ tptp.produc1961869763um_b_c Y5)) (@ (@ tptp.ord_le929608341um_b_c (@ tptp.produc932426501um_b_c X3)) (@ tptp.produc932426501um_b_c Y5))))) (= tptp.sup_su1399591867real_c (lambda ((X3 tptp.produc640052711real_c) (Y5 tptp.produc640052711real_c)) (@ (@ tptp.produc1687028567real_c (@ (@ tptp.sup_su1639086475real_c (@ tptp.produc876006723real_c X3)) (@ tptp.produc876006723real_c Y5))) (@ (@ tptp.sup_su1639086475real_c (@ tptp.produc415593093real_c X3)) (@ tptp.produc415593093real_c Y5))))) (= tptp.sup_su1639086475real_c (lambda ((X3 tptp.produc190496183real_c) (Y5 tptp.produc190496183real_c)) (@ (@ tptp.produc394644079real_c (@ (@ tptp.sup_su2141622551real_c (@ tptp.produc2010422875real_c X3)) (@ tptp.produc2010422875real_c Y5))) (@ (@ tptp.sup_su2141622551real_c (@ tptp.produc314122909real_c X3)) (@ tptp.produc314122909real_c Y5))))) (= tptp.sup_su1672617323um_c_c (lambda ((X3 tptp.produc214722967um_c_c) (Y5 tptp.produc214722967um_c_c)) (@ (@ tptp.produc1439061071um_c_c (@ (@ tptp.sup_su1349021703um_c_c (@ tptp.produc1983230011um_c_c X3)) (@ tptp.produc1983230011um_c_c Y5))) (@ (@ tptp.sup_su1349021703um_c_c (@ tptp.produc1132019837um_c_c X3)) (@ tptp.produc1132019837um_c_c Y5))))) (forall ((X1 tptp.produc190496183real_c) (X22 tptp.produc190496183real_c)) (= (@ tptp.produc876006723real_c (@ (@ tptp.produc1687028567real_c X1) X22)) X1)) (forall ((X1 tptp.finite1398487019real_c) (X22 tptp.finite1398487019real_c)) (= (@ tptp.produc2010422875real_c (@ (@ tptp.produc394644079real_c X1) X22)) X1)) (forall ((X tptp.produc190496183real_c) (Y tptp.produc190496183real_c) (A tptp.produc190496183real_c)) (=> (= (@ tptp.produc876006723real_c (@ (@ tptp.produc1687028567real_c X) Y)) A) (= X A))) (forall ((X tptp.finite1398487019real_c) (Y tptp.finite1398487019real_c) (A tptp.finite1398487019real_c)) (=> (= (@ tptp.produc2010422875real_c (@ (@ tptp.produc394644079real_c X) Y)) A) (= X A))) (forall ((X1 tptp.produc190496183real_c) (X22 tptp.produc190496183real_c)) (= (@ tptp.produc415593093real_c (@ (@ tptp.produc1687028567real_c X1) X22)) X22)) (forall ((X1 tptp.finite1398487019real_c) (X22 tptp.finite1398487019real_c)) (= (@ tptp.produc314122909real_c (@ (@ tptp.produc394644079real_c X1) X22)) X22)) (forall ((X tptp.produc190496183real_c) (Y tptp.produc190496183real_c) (A tptp.produc190496183real_c)) (=> (= (@ tptp.produc415593093real_c (@ (@ tptp.produc1687028567real_c X) Y)) A) (= Y A))) (forall ((X tptp.finite1398487019real_c) (Y tptp.finite1398487019real_c) (A tptp.finite1398487019real_c)) (=> (= (@ tptp.produc314122909real_c (@ (@ tptp.produc394644079real_c X) Y)) A) (= Y A))) (forall ((T2 tptp.produc640052711real_c)) (= T2 (@ (@ tptp.produc1687028567real_c (@ tptp.produc876006723real_c T2)) (@ tptp.produc415593093real_c T2)))) (forall ((T2 tptp.produc190496183real_c)) (= T2 (@ (@ tptp.produc394644079real_c (@ tptp.produc2010422875real_c T2)) (@ tptp.produc314122909real_c T2)))) (forall ((Prod tptp.produc640052711real_c)) (= Prod (@ (@ tptp.produc1687028567real_c (@ tptp.produc876006723real_c Prod)) (@ tptp.produc415593093real_c Prod)))) (forall ((Prod tptp.produc190496183real_c)) (= Prod (@ (@ tptp.produc394644079real_c (@ tptp.produc2010422875real_c Prod)) (@ tptp.produc314122909real_c Prod)))) (forall ((P (-> tptp.produc190496183real_c tptp.produc190496183real_c Bool)) (Y tptp.produc190496183real_c) (X tptp.produc190496183real_c)) (let ((_let_1 (@ (@ tptp.produc1687028567real_c X) Y))) (=> (@ (@ P Y) X) (@ (@ P (@ tptp.produc415593093real_c _let_1)) (@ tptp.produc876006723real_c _let_1))))) (forall ((P (-> tptp.finite1398487019real_c tptp.finite1398487019real_c Bool)) (Y tptp.finite1398487019real_c) (X tptp.finite1398487019real_c)) (let ((_let_1 (@ (@ tptp.produc394644079real_c X) Y))) (=> (@ (@ P Y) X) (@ (@ P (@ tptp.produc314122909real_c _let_1)) (@ tptp.produc2010422875real_c _let_1))))) (forall ((P (-> tptp.produc190496183real_c Bool)) (P2 tptp.produc190496183real_c) (Q (-> tptp.produc190496183real_c Bool)) (Q2 tptp.produc190496183real_c)) (let ((_let_1 (@ (@ tptp.produc1687028567real_c P2) Q2))) (=> (@ P P2) (=> (@ Q Q2) (and (@ P (@ tptp.produc876006723real_c _let_1)) (@ Q (@ tptp.produc415593093real_c _let_1))))))) (forall ((P (-> tptp.finite1398487019real_c Bool)) (P2 tptp.finite1398487019real_c) (Q (-> tptp.finite1398487019real_c Bool)) (Q2 tptp.finite1398487019real_c)) (let ((_let_1 (@ (@ tptp.produc394644079real_c P2) Q2))) (=> (@ P P2) (=> (@ Q Q2) (and (@ P (@ tptp.produc2010422875real_c _let_1)) (@ Q (@ tptp.produc314122909real_c _let_1))))))) (forall ((P (-> tptp.produc190496183real_c tptp.produc190496183real_c Bool)) (X tptp.produc190496183real_c) (Y tptp.produc190496183real_c) (A tptp.produc640052711real_c)) (=> (@ (@ P X) Y) (=> (= A (@ (@ tptp.produc1687028567real_c X) Y)) (@ (@ P (@ tptp.produc876006723real_c A)) (@ tptp.produc415593093real_c A))))) (forall ((P (-> tptp.finite1398487019real_c tptp.finite1398487019real_c Bool)) (X tptp.finite1398487019real_c) (Y tptp.finite1398487019real_c) (A tptp.produc190496183real_c)) (=> (@ (@ P X) Y) (=> (= A (@ (@ tptp.produc394644079real_c X) Y)) (@ (@ P (@ tptp.produc2010422875real_c A)) (@ tptp.produc314122909real_c A))))) (forall ((X tptp.produc640052711real_c) (Y tptp.produc190496183real_c) (Z tptp.produc190496183real_c)) (=> (= X (@ (@ tptp.produc1687028567real_c Y) Z)) (= (@ tptp.produc415593093real_c X) Z))) (forall ((X tptp.produc190496183real_c) (Y tptp.finite1398487019real_c) (Z tptp.finite1398487019real_c)) (=> (= X (@ (@ tptp.produc394644079real_c Y) Z)) (= (@ tptp.produc314122909real_c X) Z))) (forall ((X tptp.produc640052711real_c) (Y tptp.produc190496183real_c) (Z tptp.produc190496183real_c)) (=> (= X (@ (@ tptp.produc1687028567real_c Y) Z)) (= (@ tptp.produc876006723real_c X) Y))) (forall ((X tptp.produc190496183real_c) (Y tptp.finite1398487019real_c) (Z tptp.finite1398487019real_c)) (=> (= X (@ (@ tptp.produc394644079real_c Y) Z)) (= (@ tptp.produc2010422875real_c X) Y))) (forall ((B tptp.produc190496183real_c) (P2 tptp.produc640052711real_c)) (= (= B (@ tptp.produc415593093real_c P2)) (exists ((A4 tptp.produc190496183real_c)) (= P2 (@ (@ tptp.produc1687028567real_c A4) B))))) (forall ((B tptp.finite1398487019real_c) (P2 tptp.produc190496183real_c)) (= (= B (@ tptp.produc314122909real_c P2)) (exists ((A4 tptp.finite1398487019real_c)) (= P2 (@ (@ tptp.produc394644079real_c A4) B))))) (forall ((A tptp.produc190496183real_c) (P2 tptp.produc640052711real_c)) (= (= A (@ tptp.produc876006723real_c P2)) (exists ((B4 tptp.produc190496183real_c)) (= P2 (@ (@ tptp.produc1687028567real_c A) B4))))) (forall ((A tptp.finite1398487019real_c) (P2 tptp.produc190496183real_c)) (= (= A (@ tptp.produc2010422875real_c P2)) (exists ((B4 tptp.finite1398487019real_c)) (= P2 (@ (@ tptp.produc394644079real_c A) B4))))) (= tptp.produc350724343real_c (lambda ((P3 tptp.produc640052711real_c)) (@ (@ tptp.produc1687028567real_c (@ tptp.produc415593093real_c P3)) (@ tptp.produc876006723real_c P3)))) (= tptp.produc704157711real_c (lambda ((P3 tptp.produc190496183real_c)) (@ (@ tptp.produc394644079real_c (@ tptp.produc314122909real_c P3)) (@ tptp.produc2010422875real_c P3)))) (forall ((X tptp.produc190496183real_c) (Y tptp.produc190496183real_c)) (= (@ tptp.produc350724343real_c (@ (@ tptp.produc1687028567real_c X) Y)) (@ (@ tptp.produc1687028567real_c Y) X))) (forall ((X tptp.finite1398487019real_c) (Y tptp.finite1398487019real_c)) (= (@ tptp.produc704157711real_c (@ (@ tptp.produc394644079real_c X) Y)) (@ (@ tptp.produc394644079real_c Y) X))) _let_1 true))))))))))))))))))))))))))))))
% 0.77/0.99 )
% 0.77/0.99 % SZS output end Proof for ITP036^1
% 0.77/0.99 % cvc5---1.0.5 exiting
% 0.77/0.99 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------