TSTP Solution File: ITP161^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP161^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n018.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 03:18:46 EDT 2023
% Result : Theorem 15.51s 15.81s
% Output : Proof 15.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.18 % Problem : ITP161^1 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.19 % Command : do_cvc5 %s %d
% 0.19/0.41 % Computer : n018.cluster.edu
% 0.19/0.41 % Model : x86_64 x86_64
% 0.19/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.41 % Memory : 8042.1875MB
% 0.19/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.41 % CPULimit : 300
% 0.19/0.41 % WCLimit : 300
% 0.19/0.41 % DateTime : Sun Aug 27 12:03:31 EDT 2023
% 0.19/0.41 % CPUTime :
% 0.27/0.60 %----Proving TH0
% 0.27/0.61 %------------------------------------------------------------------------------
% 0.27/0.61 % File : ITP161^1 : TPTP v8.1.2. Released v7.5.0.
% 0.27/0.61 % Domain : Interactive Theorem Proving
% 0.27/0.61 % Problem : Sledgehammer Refine_Basic problem prob_1708__3602512_1
% 0.27/0.61 % Version : Especial.
% 0.27/0.61 % English :
% 0.27/0.61
% 0.27/0.61 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.27/0.61 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.27/0.61 % Source : [Des21]
% 0.27/0.61 % Names : Refine_Basic/prob_1708__3602512_1 [Des21]
% 0.27/0.61
% 0.27/0.61 % Status : Theorem
% 0.27/0.61 % Rating : 0.31 v8.1.0, 0.36 v7.5.0
% 0.27/0.61 % Syntax : Number of formulae : 503 ( 146 unt; 144 typ; 0 def)
% 0.27/0.61 % Number of atoms : 1005 ( 266 equ; 0 cnn)
% 0.27/0.61 % Maximal formula atoms : 7 ( 2 avg)
% 0.27/0.61 % Number of connectives : 3105 ( 107 ~; 1 |; 29 &;2426 @)
% 0.27/0.61 % ( 0 <=>; 542 =>; 0 <=; 0 <~>)
% 0.27/0.61 % Maximal formula depth : 17 ( 7 avg)
% 0.27/0.61 % Number of types : 27 ( 26 usr)
% 0.27/0.61 % Number of type conns : 394 ( 394 >; 0 *; 0 +; 0 <<)
% 0.27/0.61 % Number of symbols : 121 ( 118 usr; 12 con; 0-4 aty)
% 0.27/0.61 % Number of variables : 1083 ( 62 ^;1002 !; 19 ?;1083 :)
% 0.27/0.61 % SPC : TH0_THM_EQU_NAR
% 0.27/0.61
% 0.27/0.61 % Comments : This file was generated by Sledgehammer 2021-02-23 15:36:00.723
% 0.27/0.61 %------------------------------------------------------------------------------
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% 0.27/0.61 % nres.inject
% 0.27/0.61 thf(fact_8_if__rule,axiom,
% 0.27/0.61 ! [B: $o,S1: refine787176636t_unit,Phi: product_unit > $o,S2: refine787176636t_unit] :
% 0.27/0.61 ( ( B
% 0.27/0.61 => ( ord_le1051254044t_unit @ S1 @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) ) )
% 0.27/0.61 => ( ( ~ B
% 0.27/0.61 => ( ord_le1051254044t_unit @ S2 @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) ) )
% 0.27/0.61 => ( ord_le1051254044t_unit @ ( if_Ref1369692790t_unit @ B @ S1 @ S2 ) @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % if_rule
% 0.27/0.61 thf(fact_9_if__rule,axiom,
% 0.27/0.61 ! [B: $o,S1: refine432681134nres_b,Phi: b > $o,S2: refine432681134nres_b] :
% 0.27/0.61 ( ( B
% 0.27/0.61 => ( ord_le527798542nres_b @ S1 @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) )
% 0.27/0.61 => ( ( ~ B
% 0.27/0.61 => ( ord_le527798542nres_b @ S2 @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) )
% 0.27/0.61 => ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ B @ S1 @ S2 ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % if_rule
% 0.27/0.61 thf(fact_10_if__rule,axiom,
% 0.27/0.61 ! [B: $o,S1: refine424419629nres_a,Phi: a > $o,S2: refine424419629nres_a] :
% 0.27/0.61 ( ( B
% 0.27/0.61 => ( ord_le519537037nres_a @ S1 @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) )
% 0.27/0.61 => ( ( ~ B
% 0.27/0.61 => ( ord_le519537037nres_a @ S2 @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) )
% 0.27/0.61 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ S1 @ S2 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % if_rule
% 0.27/0.61 thf(fact_11_RES__rule,axiom,
% 0.27/0.61 ! [S: set_Product_prod_a_a,Phi: product_prod_a_a > $o] :
% 0.27/0.61 ( ! [X3: product_prod_a_a] :
% 0.27/0.61 ( ( member449909584od_a_a @ X3 @ S )
% 0.27/0.61 => ( Phi @ X3 ) )
% 0.27/0.61 => ( ord_le915866422od_a_a @ ( refine622451633od_a_a @ S ) @ ( refine622451633od_a_a @ ( collec645855634od_a_a @ Phi ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % RES_rule
% 0.27/0.61 thf(fact_12_RES__rule,axiom,
% 0.27/0.61 ! [S: set_Product_prod_b_a,Phi: product_prod_b_a > $o] :
% 0.27/0.61 ( ! [X3: product_prod_b_a] :
% 0.27/0.61 ( ( member1277678991od_b_a @ X3 @ S )
% 0.27/0.61 => ( Phi @ X3 ) )
% 0.27/0.61 => ( ord_le1135777269od_b_a @ ( refine1450221040od_b_a @ S ) @ ( refine1450221040od_b_a @ ( collec1473625041od_b_a @ Phi ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % RES_rule
% 0.27/0.61 thf(fact_13_RES__rule,axiom,
% 0.27/0.61 ! [S: set_Product_prod_b_b,Phi: product_prod_b_b > $o] :
% 0.27/0.61 ( ! [X3: product_prod_b_b] :
% 0.27/0.61 ( ( member1285940496od_b_b @ X3 @ S )
% 0.27/0.61 => ( Phi @ X3 ) )
% 0.27/0.61 => ( ord_le127857910od_b_b @ ( refine1458482545od_b_b @ S ) @ ( refine1458482545od_b_b @ ( collec1481886546od_b_b @ Phi ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % RES_rule
% 0.27/0.61 thf(fact_14_RES__rule,axiom,
% 0.27/0.61 ! [S: set_Product_prod_a_b,Phi: product_prod_a_b > $o] :
% 0.27/0.61 ( ! [X3: product_prod_a_b] :
% 0.27/0.61 ( ( member458171089od_a_b @ X3 @ S )
% 0.27/0.61 => ( Phi @ X3 ) )
% 0.27/0.61 => ( ord_le2055430711od_a_b @ ( refine630713138od_a_b @ S ) @ ( refine630713138od_a_b @ ( collec654117139od_a_b @ Phi ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % RES_rule
% 0.27/0.61 thf(fact_15_RES__rule,axiom,
% 0.27/0.61 ! [S: set_Product_unit,Phi: product_unit > $o] :
% 0.27/0.61 ( ! [X3: product_unit] :
% 0.27/0.61 ( ( member_Product_unit @ X3 @ S )
% 0.27/0.61 => ( Phi @ X3 ) )
% 0.27/0.61 => ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ S ) @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % RES_rule
% 0.27/0.61 thf(fact_16_RES__rule,axiom,
% 0.27/0.61 ! [S: set_b,Phi: b > $o] :
% 0.27/0.61 ( ! [X3: b] :
% 0.27/0.61 ( ( member_b @ X3 @ S )
% 0.27/0.61 => ( Phi @ X3 ) )
% 0.27/0.61 => ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ S ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % RES_rule
% 0.27/0.61 thf(fact_17_RES__rule,axiom,
% 0.27/0.61 ! [S: set_a,Phi: a > $o] :
% 0.27/0.61 ( ! [X3: a] :
% 0.27/0.61 ( ( member_a @ X3 @ S )
% 0.27/0.61 => ( Phi @ X3 ) )
% 0.27/0.61 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ S ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % RES_rule
% 0.27/0.61 thf(fact_18_SPEC__rule,axiom,
% 0.27/0.61 ! [Phi: product_unit > $o,Phi2: product_unit > $o] :
% 0.27/0.61 ( ! [X3: product_unit] :
% 0.27/0.61 ( ( Phi @ X3 )
% 0.27/0.61 => ( Phi2 @ X3 ) )
% 0.27/0.61 => ( ord_le1051254044t_unit @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi2 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % SPEC_rule
% 0.27/0.61 thf(fact_19_SPEC__rule,axiom,
% 0.27/0.61 ! [Phi: b > $o,Phi2: b > $o] :
% 0.27/0.61 ( ! [X3: b] :
% 0.27/0.61 ( ( Phi @ X3 )
% 0.27/0.61 => ( Phi2 @ X3 ) )
% 0.27/0.61 => ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi2 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % SPEC_rule
% 0.27/0.61 thf(fact_20_SPEC__rule,axiom,
% 0.27/0.61 ! [Phi: a > $o,Phi2: a > $o] :
% 0.27/0.61 ( ! [X3: a] :
% 0.27/0.61 ( ( Phi @ X3 )
% 0.27/0.61 => ( Phi2 @ X3 ) )
% 0.27/0.61 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi2 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % SPEC_rule
% 0.27/0.61 thf(fact_21_SPEC__trans,axiom,
% 0.27/0.61 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit,Postcond: product_unit > $o] :
% 0.27/0.61 ( ( ord_le1051254044t_unit @ X4 @ Y3 )
% 0.27/0.61 => ( ( ord_le1051254044t_unit @ Y3 @ ( refine1777164439t_unit @ ( collect_Product_unit @ Postcond ) ) )
% 0.27/0.61 => ( ord_le1051254044t_unit @ X4 @ ( refine1777164439t_unit @ ( collect_Product_unit @ Postcond ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % SPEC_trans
% 0.27/0.61 thf(fact_22_SPEC__trans,axiom,
% 0.27/0.61 ! [X4: refine432681134nres_b,Y3: refine432681134nres_b,Postcond: b > $o] :
% 0.27/0.61 ( ( ord_le527798542nres_b @ X4 @ Y3 )
% 0.27/0.61 => ( ( ord_le527798542nres_b @ Y3 @ ( refine1198353289_RES_b @ ( collect_b @ Postcond ) ) )
% 0.27/0.61 => ( ord_le527798542nres_b @ X4 @ ( refine1198353289_RES_b @ ( collect_b @ Postcond ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % SPEC_trans
% 0.27/0.61 thf(fact_23_SPEC__trans,axiom,
% 0.27/0.61 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Postcond: a > $o] :
% 0.27/0.61 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 0.27/0.61 => ( ( ord_le519537037nres_a @ Y3 @ ( refine1198353288_RES_a @ ( collect_a @ Postcond ) ) )
% 0.27/0.61 => ( ord_le519537037nres_a @ X4 @ ( refine1198353288_RES_a @ ( collect_a @ Postcond ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % SPEC_trans
% 0.27/0.61 thf(fact_24_lhs__step__If,axiom,
% 0.27/0.61 ! [B: $o,T: set_b,M: set_b,E: set_b] :
% 0.27/0.61 ( ( B
% 0.27/0.61 => ( ord_less_eq_set_b @ T @ M ) )
% 0.27/0.61 => ( ( ~ B
% 0.27/0.61 => ( ord_less_eq_set_b @ E @ M ) )
% 0.27/0.61 => ( ord_less_eq_set_b @ ( if_set_b @ B @ T @ E ) @ M ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % lhs_step_If
% 0.27/0.61 thf(fact_25_lhs__step__If,axiom,
% 0.27/0.61 ! [B: $o,T: set_a,M: set_a,E: set_a] :
% 0.27/0.61 ( ( B
% 0.27/0.61 => ( ord_less_eq_set_a @ T @ M ) )
% 0.27/0.61 => ( ( ~ B
% 0.27/0.61 => ( ord_less_eq_set_a @ E @ M ) )
% 0.27/0.61 => ( ord_less_eq_set_a @ ( if_set_a @ B @ T @ E ) @ M ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % lhs_step_If
% 0.27/0.61 thf(fact_26_lhs__step__If,axiom,
% 0.27/0.61 ! [B: $o,T: $o > refine424419629nres_a,M: $o > refine424419629nres_a,E: $o > refine424419629nres_a] :
% 0.27/0.61 ( ( B
% 0.27/0.61 => ( ord_le516598614nres_a @ T @ M ) )
% 0.27/0.61 => ( ( ~ B
% 0.27/0.61 => ( ord_le516598614nres_a @ E @ M ) )
% 0.27/0.61 => ( ord_le516598614nres_a @ ( if_o_R1705037948nres_a @ B @ T @ E ) @ M ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % lhs_step_If
% 0.27/0.61 thf(fact_27_lhs__step__If,axiom,
% 0.27/0.61 ! [B: $o,T: $o > refine432681134nres_b,M: $o > refine432681134nres_b,E: $o > refine432681134nres_b] :
% 0.27/0.61 ( ( B
% 0.27/0.61 => ( ord_le1656162903nres_b @ T @ M ) )
% 0.27/0.61 => ( ( ~ B
% 0.27/0.61 => ( ord_le1656162903nres_b @ E @ M ) )
% 0.27/0.61 => ( ord_le1656162903nres_b @ ( if_o_R697118589nres_b @ B @ T @ E ) @ M ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % lhs_step_If
% 0.27/0.61 thf(fact_28_lhs__step__If,axiom,
% 0.27/0.61 ! [B: $o,T: refine787176636t_unit,M: refine787176636t_unit,E: refine787176636t_unit] :
% 0.27/0.61 ( ( B
% 0.27/0.61 => ( ord_le1051254044t_unit @ T @ M ) )
% 0.27/0.61 => ( ( ~ B
% 0.27/0.61 => ( ord_le1051254044t_unit @ E @ M ) )
% 0.27/0.61 => ( ord_le1051254044t_unit @ ( if_Ref1369692790t_unit @ B @ T @ E ) @ M ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % lhs_step_If
% 0.27/0.61 thf(fact_29_lhs__step__If,axiom,
% 0.27/0.61 ! [B: $o,T: refine424419629nres_a,M: refine424419629nres_a,E: refine424419629nres_a] :
% 0.27/0.61 ( ( B
% 0.27/0.61 => ( ord_le519537037nres_a @ T @ M ) )
% 0.27/0.61 => ( ( ~ B
% 0.27/0.61 => ( ord_le519537037nres_a @ E @ M ) )
% 0.27/0.61 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ T @ E ) @ M ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % lhs_step_If
% 0.27/0.61 thf(fact_30_lhs__step__If,axiom,
% 0.27/0.61 ! [B: $o,T: refine432681134nres_b,M: refine432681134nres_b,E: refine432681134nres_b] :
% 0.27/0.61 ( ( B
% 0.27/0.61 => ( ord_le527798542nres_b @ T @ M ) )
% 0.27/0.61 => ( ( ~ B
% 0.27/0.61 => ( ord_le527798542nres_b @ E @ M ) )
% 0.27/0.61 => ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ B @ T @ E ) @ M ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % lhs_step_If
% 0.27/0.61 thf(fact_31_SPEC__cons__rule,axiom,
% 0.27/0.61 ! [M: refine787176636t_unit,Phi: product_unit > $o,Psi: product_unit > $o] :
% 0.27/0.61 ( ( ord_le1051254044t_unit @ M @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) )
% 0.27/0.61 => ( ! [X3: product_unit] :
% 0.27/0.61 ( ( Phi @ X3 )
% 0.27/0.61 => ( Psi @ X3 ) )
% 0.27/0.61 => ( ord_le1051254044t_unit @ M @ ( refine1777164439t_unit @ ( collect_Product_unit @ Psi ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % SPEC_cons_rule
% 0.27/0.61 thf(fact_32_SPEC__cons__rule,axiom,
% 0.27/0.61 ! [M: refine424419629nres_a,Phi: a > $o,Psi: a > $o] :
% 0.27/0.61 ( ( ord_le519537037nres_a @ M @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) )
% 0.27/0.61 => ( ! [X3: a] :
% 0.27/0.61 ( ( Phi @ X3 )
% 0.27/0.61 => ( Psi @ X3 ) )
% 0.27/0.61 => ( ord_le519537037nres_a @ M @ ( refine1198353288_RES_a @ ( collect_a @ Psi ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % SPEC_cons_rule
% 0.27/0.61 thf(fact_33_SPEC__cons__rule,axiom,
% 0.27/0.61 ! [M: refine432681134nres_b,Phi: b > $o,Psi: b > $o] :
% 0.27/0.61 ( ( ord_le527798542nres_b @ M @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) )
% 0.27/0.61 => ( ! [X3: b] :
% 0.27/0.61 ( ( Phi @ X3 )
% 0.27/0.61 => ( Psi @ X3 ) )
% 0.27/0.61 => ( ord_le527798542nres_b @ M @ ( refine1198353289_RES_b @ ( collect_b @ Psi ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % SPEC_cons_rule
% 0.27/0.61 thf(fact_34_RES__bind__choose,axiom,
% 0.27/0.61 ! [X4: a,X: set_a,M: refine424419629nres_a,F: a > refine424419629nres_a] :
% 0.27/0.61 ( ( member_a @ X4 @ X )
% 0.27/0.61 => ( ( ord_le519537037nres_a @ M @ ( F @ X4 ) )
% 0.27/0.61 => ( ord_le519537037nres_a @ M @ ( refine436832838nd_a_a @ ( refine1198353288_RES_a @ X ) @ F ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % RES_bind_choose
% 0.27/0.61 thf(fact_35_RES__bind__choose,axiom,
% 0.27/0.61 ! [X4: a,X: set_a,M: refine432681134nres_b,F: a > refine432681134nres_b] :
% 0.27/0.61 ( ( member_a @ X4 @ X )
% 0.27/0.61 => ( ( ord_le527798542nres_b @ M @ ( F @ X4 ) )
% 0.27/0.61 => ( ord_le527798542nres_b @ M @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X ) @ F ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % RES_bind_choose
% 0.27/0.61 thf(fact_36_RES__bind__choose,axiom,
% 0.27/0.61 ! [X4: b,X: set_b,M: refine432681134nres_b,F: b > refine432681134nres_b] :
% 0.27/0.61 ( ( member_b @ X4 @ X )
% 0.27/0.61 => ( ( ord_le527798542nres_b @ M @ ( F @ X4 ) )
% 0.27/0.61 => ( ord_le527798542nres_b @ M @ ( refine1264602246nd_b_b @ ( refine1198353289_RES_b @ X ) @ F ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % RES_bind_choose
% 0.27/0.61 thf(fact_37_RES__bind__choose,axiom,
% 0.27/0.61 ! [X4: b,X: set_b,M: refine424419629nres_a,F: b > refine424419629nres_a] :
% 0.27/0.61 ( ( member_b @ X4 @ X )
% 0.27/0.61 => ( ( ord_le519537037nres_a @ M @ ( F @ X4 ) )
% 0.27/0.61 => ( ord_le519537037nres_a @ M @ ( refine1264602245nd_b_a @ ( refine1198353289_RES_b @ X ) @ F ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % RES_bind_choose
% 0.27/0.61 thf(fact_38_RES__bind__choose,axiom,
% 0.27/0.61 ! [X4: a,X: set_a,M: refine787176636t_unit,F: a > refine787176636t_unit] :
% 0.27/0.61 ( ( member_a @ X4 @ X )
% 0.27/0.61 => ( ( ord_le1051254044t_unit @ M @ ( F @ X4 ) )
% 0.27/0.61 => ( ord_le1051254044t_unit @ M @ ( refine96995669t_unit @ ( refine1198353288_RES_a @ X ) @ F ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % RES_bind_choose
% 0.27/0.61 thf(fact_39_RES__bind__choose,axiom,
% 0.27/0.61 ! [X4: b,X: set_b,M: refine787176636t_unit,F: b > refine787176636t_unit] :
% 0.27/0.61 ( ( member_b @ X4 @ X )
% 0.27/0.61 => ( ( ord_le1051254044t_unit @ M @ ( F @ X4 ) )
% 0.27/0.61 => ( ord_le1051254044t_unit @ M @ ( refine216248468t_unit @ ( refine1198353289_RES_b @ X ) @ F ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % RES_bind_choose
% 0.27/0.61 thf(fact_40_RES__bind__choose,axiom,
% 0.27/0.61 ! [X4: product_unit,X: set_Product_unit,M: refine432681134nres_b,F: product_unit > refine432681134nres_b] :
% 0.27/0.61 ( ( member_Product_unit @ X4 @ X )
% 0.27/0.61 => ( ( ord_le527798542nres_b @ M @ ( F @ X4 ) )
% 0.27/0.61 => ( ord_le527798542nres_b @ M @ ( refine119808504unit_b @ ( refine1777164439t_unit @ X ) @ F ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % RES_bind_choose
% 0.27/0.61 thf(fact_41_RES__bind__choose,axiom,
% 0.27/0.61 ! [X4: product_unit,X: set_Product_unit,M: refine424419629nres_a,F: product_unit > refine424419629nres_a] :
% 0.27/0.61 ( ( member_Product_unit @ X4 @ X )
% 0.27/0.61 => ( ( ord_le519537037nres_a @ M @ ( F @ X4 ) )
% 0.27/0.61 => ( ord_le519537037nres_a @ M @ ( refine119808503unit_a @ ( refine1777164439t_unit @ X ) @ F ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % RES_bind_choose
% 0.27/0.61 thf(fact_42_RES__bind__choose,axiom,
% 0.27/0.61 ! [X4: product_unit,X: set_Product_unit,M: refine787176636t_unit,F: product_unit > refine787176636t_unit] :
% 0.27/0.61 ( ( member_Product_unit @ X4 @ X )
% 0.27/0.61 => ( ( ord_le1051254044t_unit @ M @ ( F @ X4 ) )
% 0.27/0.61 => ( ord_le1051254044t_unit @ M @ ( refine681446406t_unit @ ( refine1777164439t_unit @ X ) @ F ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % RES_bind_choose
% 0.27/0.61 thf(fact_43_RES__bind__choose,axiom,
% 0.27/0.61 ! [X4: product_prod_a_a,X: set_Product_prod_a_a,M: refine432681134nres_b,F: product_prod_a_a > refine432681134nres_b] :
% 0.27/0.61 ( ( member449909584od_a_a @ X4 @ X )
% 0.27/0.61 => ( ( ord_le527798542nres_b @ M @ ( F @ X4 ) )
% 0.27/0.61 => ( ord_le527798542nres_b @ M @ ( refine988994910_a_a_b @ ( refine622451633od_a_a @ X ) @ F ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % RES_bind_choose
% 0.27/0.61 thf(fact_44_order__mono__setup_Orefl,axiom,
% 0.27/0.61 ! [X4: set_b] : ( ord_less_eq_set_b @ X4 @ X4 ) ).
% 0.27/0.61
% 0.27/0.61 % order_mono_setup.refl
% 0.27/0.61 thf(fact_45_order__mono__setup_Orefl,axiom,
% 0.27/0.61 ! [X4: set_a] : ( ord_less_eq_set_a @ X4 @ X4 ) ).
% 0.27/0.61
% 0.27/0.61 % order_mono_setup.refl
% 0.27/0.61 thf(fact_46_order__mono__setup_Orefl,axiom,
% 0.27/0.61 ! [X4: $o > refine424419629nres_a] : ( ord_le516598614nres_a @ X4 @ X4 ) ).
% 0.27/0.61
% 0.27/0.61 % order_mono_setup.refl
% 0.27/0.61 thf(fact_47_order__mono__setup_Orefl,axiom,
% 0.27/0.61 ! [X4: $o > refine432681134nres_b] : ( ord_le1656162903nres_b @ X4 @ X4 ) ).
% 0.27/0.61
% 0.27/0.61 % order_mono_setup.refl
% 0.27/0.61 thf(fact_48_order__mono__setup_Orefl,axiom,
% 0.27/0.61 ! [X4: refine787176636t_unit] : ( ord_le1051254044t_unit @ X4 @ X4 ) ).
% 0.27/0.61
% 0.27/0.61 % order_mono_setup.refl
% 0.27/0.61 thf(fact_49_order__mono__setup_Orefl,axiom,
% 0.27/0.61 ! [X4: refine432681134nres_b] : ( ord_le527798542nres_b @ X4 @ X4 ) ).
% 0.27/0.61
% 0.27/0.61 % order_mono_setup.refl
% 0.27/0.61 thf(fact_50_order__mono__setup_Orefl,axiom,
% 0.27/0.61 ! [X4: refine424419629nres_a] : ( ord_le519537037nres_a @ X4 @ X4 ) ).
% 0.27/0.61
% 0.27/0.61 % order_mono_setup.refl
% 0.27/0.61 thf(fact_51_the__RES_Osimps,axiom,
% 0.27/0.61 ! [X: set_Product_unit] :
% 0.27/0.61 ( ( refine1208325748t_unit @ ( refine1777164439t_unit @ X ) )
% 0.27/0.61 = X ) ).
% 0.27/0.61
% 0.27/0.61 % the_RES.simps
% 0.27/0.61 thf(fact_52_the__RES_Osimps,axiom,
% 0.27/0.61 ! [X: set_a] :
% 0.27/0.61 ( ( refine1822134885_RES_a @ ( refine1198353288_RES_a @ X ) )
% 0.27/0.61 = X ) ).
% 0.27/0.61
% 0.27/0.61 % the_RES.simps
% 0.27/0.61 thf(fact_53_the__RES_Osimps,axiom,
% 0.27/0.61 ! [X: set_b] :
% 0.27/0.61 ( ( refine1822134886_RES_b @ ( refine1198353289_RES_b @ X ) )
% 0.27/0.61 = X ) ).
% 0.27/0.61
% 0.27/0.61 % the_RES.simps
% 0.27/0.61 thf(fact_54_nf__inres__RES,axiom,
% 0.27/0.61 ! [X: set_Product_prod_a_a,X4: product_prod_a_a] :
% 0.27/0.61 ( ( refine378960780od_a_a @ ( refine622451633od_a_a @ X ) @ X4 )
% 0.27/0.61 = ( member449909584od_a_a @ X4 @ X ) ) ).
% 0.27/0.61
% 0.27/0.61 % nf_inres_RES
% 0.27/0.61 thf(fact_55_nf__inres__RES,axiom,
% 0.27/0.61 ! [X: set_Product_prod_b_a,X4: product_prod_b_a] :
% 0.27/0.61 ( ( refine1206730187od_b_a @ ( refine1450221040od_b_a @ X ) @ X4 )
% 0.27/0.61 = ( member1277678991od_b_a @ X4 @ X ) ) ).
% 0.27/0.61
% 0.27/0.61 % nf_inres_RES
% 0.27/0.61 thf(fact_56_nf__inres__RES,axiom,
% 0.27/0.61 ! [X: set_Product_prod_b_b,X4: product_prod_b_b] :
% 0.27/0.61 ( ( refine1214991692od_b_b @ ( refine1458482545od_b_b @ X ) @ X4 )
% 0.27/0.61 = ( member1285940496od_b_b @ X4 @ X ) ) ).
% 0.27/0.61
% 0.27/0.61 % nf_inres_RES
% 0.27/0.61 thf(fact_57_nf__inres__RES,axiom,
% 0.27/0.61 ! [X: set_Product_prod_a_b,X4: product_prod_a_b] :
% 0.27/0.61 ( ( refine387222285od_a_b @ ( refine630713138od_a_b @ X ) @ X4 )
% 0.27/0.61 = ( member458171089od_a_b @ X4 @ X ) ) ).
% 0.27/0.61
% 0.27/0.61 % nf_inres_RES
% 0.27/0.61 thf(fact_58_nf__inres__RES,axiom,
% 0.27/0.61 ! [X: set_Product_unit,X4: product_unit] :
% 0.27/0.61 ( ( refine983493746t_unit @ ( refine1777164439t_unit @ X ) @ X4 )
% 0.27/0.61 = ( member_Product_unit @ X4 @ X ) ) ).
% 0.27/0.61
% 0.27/0.61 % nf_inres_RES
% 0.27/0.61 thf(fact_59_nf__inres__RES,axiom,
% 0.27/0.61 ! [X: set_a,X4: a] :
% 0.27/0.61 ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ X ) @ X4 )
% 0.27/0.61 = ( member_a @ X4 @ X ) ) ).
% 0.27/0.61
% 0.27/0.61 % nf_inres_RES
% 0.27/0.61 thf(fact_60_nf__inres__RES,axiom,
% 0.27/0.61 ! [X: set_b,X4: b] :
% 0.27/0.61 ( ( refine1312857700nres_b @ ( refine1198353289_RES_b @ X ) @ X4 )
% 0.27/0.61 = ( member_b @ X4 @ X ) ) ).
% 0.27/0.61
% 0.27/0.61 % nf_inres_RES
% 0.27/0.61 thf(fact_61_nf__inres__SPEC,axiom,
% 0.27/0.61 ! [Phi: product_unit > $o,X4: product_unit] :
% 0.27/0.61 ( ( refine983493746t_unit @ ( refine1777164439t_unit @ ( collect_Product_unit @ Phi ) ) @ X4 )
% 0.27/0.61 = ( Phi @ X4 ) ) ).
% 0.27/0.61
% 0.27/0.61 % nf_inres_SPEC
% 0.27/0.61 thf(fact_62_nf__inres__SPEC,axiom,
% 0.27/0.61 ! [Phi: a > $o,X4: a] :
% 0.27/0.61 ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ X4 )
% 0.27/0.61 = ( Phi @ X4 ) ) ).
% 0.27/0.61
% 0.27/0.61 % nf_inres_SPEC
% 0.27/0.61 thf(fact_63_nf__inres__SPEC,axiom,
% 0.27/0.61 ! [Phi: b > $o,X4: b] :
% 0.27/0.61 ( ( refine1312857700nres_b @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) @ X4 )
% 0.27/0.61 = ( Phi @ X4 ) ) ).
% 0.27/0.61
% 0.27/0.61 % nf_inres_SPEC
% 0.27/0.61 thf(fact_64_le__funD,axiom,
% 0.27/0.61 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a,X4: $o] :
% 0.27/0.61 ( ( ord_le516598614nres_a @ F @ G )
% 0.27/0.61 => ( ord_le519537037nres_a @ ( F @ X4 ) @ ( G @ X4 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % le_funD
% 0.27/0.61 thf(fact_65_le__funD,axiom,
% 0.27/0.61 ! [F: $o > refine432681134nres_b,G: $o > refine432681134nres_b,X4: $o] :
% 0.27/0.61 ( ( ord_le1656162903nres_b @ F @ G )
% 0.27/0.61 => ( ord_le527798542nres_b @ ( F @ X4 ) @ ( G @ X4 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % le_funD
% 0.27/0.61 thf(fact_66_le__funE,axiom,
% 0.27/0.61 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a,X4: $o] :
% 0.27/0.61 ( ( ord_le516598614nres_a @ F @ G )
% 0.27/0.61 => ( ord_le519537037nres_a @ ( F @ X4 ) @ ( G @ X4 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % le_funE
% 0.27/0.61 thf(fact_67_le__funE,axiom,
% 0.27/0.61 ! [F: $o > refine432681134nres_b,G: $o > refine432681134nres_b,X4: $o] :
% 0.27/0.61 ( ( ord_le1656162903nres_b @ F @ G )
% 0.27/0.61 => ( ord_le527798542nres_b @ ( F @ X4 ) @ ( G @ X4 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % le_funE
% 0.27/0.61 thf(fact_68_le__funI,axiom,
% 0.27/0.61 ! [F: $o > refine424419629nres_a,G: $o > refine424419629nres_a] :
% 0.27/0.61 ( ! [X3: $o] : ( ord_le519537037nres_a @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.27/0.61 => ( ord_le516598614nres_a @ F @ G ) ) ).
% 0.27/0.61
% 0.27/0.61 % le_funI
% 0.27/0.61 thf(fact_69_Refine__Misc_Oif__mono,axiom,
% 0.27/0.61 ! [B: $o,M1: refine432681134nres_b,M12: refine432681134nres_b,M2: refine432681134nres_b,M22: refine432681134nres_b] :
% 0.27/0.61 ( ( B
% 0.27/0.61 => ( ord_le527798542nres_b @ M1 @ M12 ) )
% 0.27/0.61 => ( ( ~ B
% 0.27/0.61 => ( ord_le527798542nres_b @ M2 @ M22 ) )
% 0.27/0.61 => ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ B @ M1 @ M2 ) @ ( if_Ref1732808808nres_b @ B @ M12 @ M22 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % Refine_Misc.if_mono
% 0.27/0.61 thf(fact_70_Refine__Misc_Oif__mono,axiom,
% 0.27/0.61 ! [B: $o,M1: refine424419629nres_a,M12: refine424419629nres_a,M2: refine424419629nres_a,M22: refine424419629nres_a] :
% 0.27/0.61 ( ( B
% 0.27/0.61 => ( ord_le519537037nres_a @ M1 @ M12 ) )
% 0.27/0.61 => ( ( ~ B
% 0.27/0.61 => ( ord_le519537037nres_a @ M2 @ M22 ) )
% 0.27/0.61 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ M1 @ M2 ) @ ( if_Ref1724547303nres_a @ B @ M12 @ M22 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % Refine_Misc.if_mono
% 0.27/0.61 thf(fact_71_order__subst1,axiom,
% 0.27/0.61 ! [A: refine432681134nres_b,F: refine432681134nres_b > refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.27/0.61 ( ( ord_le527798542nres_b @ A @ ( F @ B ) )
% 0.27/0.61 => ( ( ord_le527798542nres_b @ B @ C )
% 0.27/0.61 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.27/0.61 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 0.27/0.61 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.27/0.61 => ( ord_le527798542nres_b @ A @ ( F @ C ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % order_subst1
% 0.27/0.61 thf(fact_72_order__subst1,axiom,
% 0.27/0.61 ! [A: refine432681134nres_b,F: refine424419629nres_a > refine432681134nres_b,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.27/0.61 ( ( ord_le527798542nres_b @ A @ ( F @ B ) )
% 0.27/0.61 => ( ( ord_le519537037nres_a @ B @ C )
% 0.27/0.61 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.27/0.61 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.27/0.61 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.27/0.61 => ( ord_le527798542nres_b @ A @ ( F @ C ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % order_subst1
% 0.27/0.61 thf(fact_73_order__subst1,axiom,
% 0.27/0.61 ! [A: refine424419629nres_a,F: refine432681134nres_b > refine424419629nres_a,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.27/0.61 ( ( ord_le519537037nres_a @ A @ ( F @ B ) )
% 0.27/0.61 => ( ( ord_le527798542nres_b @ B @ C )
% 0.27/0.61 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.27/0.61 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 0.27/0.61 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.27/0.61 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % order_subst1
% 0.27/0.61 thf(fact_74_order__subst1,axiom,
% 0.27/0.61 ! [A: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.27/0.61 ( ( ord_le519537037nres_a @ A @ ( F @ B ) )
% 0.27/0.61 => ( ( ord_le519537037nres_a @ B @ C )
% 0.27/0.61 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.27/0.61 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.27/0.61 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.27/0.61 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % order_subst1
% 0.27/0.61 thf(fact_75_less__eq__nres_Osimps_I2_J,axiom,
% 0.27/0.61 ! [A: set_a,B: set_a] :
% 0.27/0.61 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
% 0.27/0.61 = ( ord_less_eq_set_a @ A @ B ) ) ).
% 0.27/0.61
% 0.27/0.61 % less_eq_nres.simps(2)
% 0.27/0.61 thf(fact_76_less__eq__nres_Osimps_I2_J,axiom,
% 0.27/0.61 ! [A: set_b,B: set_b] :
% 0.27/0.61 ( ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ A ) @ ( refine1198353289_RES_b @ B ) )
% 0.27/0.61 = ( ord_less_eq_set_b @ A @ B ) ) ).
% 0.27/0.61
% 0.27/0.61 % less_eq_nres.simps(2)
% 0.27/0.61 thf(fact_77_nres__order__simps_I5_J,axiom,
% 0.27/0.61 ! [X: set_a,Y: set_a] :
% 0.27/0.61 ( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ X ) @ ( refine1198353288_RES_a @ Y ) )
% 0.27/0.61 = ( ord_less_eq_set_a @ X @ Y ) ) ).
% 0.27/0.61
% 0.27/0.61 % nres_order_simps(5)
% 0.27/0.61 thf(fact_78_nres__order__simps_I5_J,axiom,
% 0.27/0.61 ! [X: set_b,Y: set_b] :
% 0.27/0.61 ( ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ X ) @ ( refine1198353289_RES_b @ Y ) )
% 0.27/0.61 = ( ord_less_eq_set_b @ X @ Y ) ) ).
% 0.27/0.61
% 0.27/0.61 % nres_order_simps(5)
% 0.27/0.61 thf(fact_79_order__mono__setup_Omono__if,axiom,
% 0.27/0.61 ! [T: refine432681134nres_b,T2: refine432681134nres_b,E: refine432681134nres_b,E2: refine432681134nres_b,B: $o] :
% 0.27/0.61 ( ( ord_le527798542nres_b @ T @ T2 )
% 0.27/0.61 => ( ( ord_le527798542nres_b @ E @ E2 )
% 0.27/0.61 => ( ord_le527798542nres_b @ ( if_Ref1732808808nres_b @ B @ T @ E ) @ ( if_Ref1732808808nres_b @ B @ T2 @ E2 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % order_mono_setup.mono_if
% 0.27/0.61 thf(fact_80_order__mono__setup_Omono__if,axiom,
% 0.27/0.61 ! [T: refine424419629nres_a,T2: refine424419629nres_a,E: refine424419629nres_a,E2: refine424419629nres_a,B: $o] :
% 0.27/0.61 ( ( ord_le519537037nres_a @ T @ T2 )
% 0.27/0.61 => ( ( ord_le519537037nres_a @ E @ E2 )
% 0.27/0.61 => ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ B @ T @ E ) @ ( if_Ref1724547303nres_a @ B @ T2 @ E2 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % order_mono_setup.mono_if
% 0.27/0.61 thf(fact_81_dual__order_Oantisym,axiom,
% 0.27/0.61 ! [B: refine432681134nres_b,A: refine432681134nres_b] :
% 0.27/0.61 ( ( ord_le527798542nres_b @ B @ A )
% 0.27/0.61 => ( ( ord_le527798542nres_b @ A @ B )
% 0.27/0.61 => ( A = B ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % dual_order.antisym
% 0.27/0.61 thf(fact_82_dual__order_Oantisym,axiom,
% 0.27/0.61 ! [B: refine424419629nres_a,A: refine424419629nres_a] :
% 0.27/0.61 ( ( ord_le519537037nres_a @ B @ A )
% 0.27/0.61 => ( ( ord_le519537037nres_a @ A @ B )
% 0.27/0.62 => ( A = B ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.antisym
% 0.27/0.62 thf(fact_83_dual__order_Oeq__iff,axiom,
% 0.27/0.62 ( ( ^ [Y5: refine432681134nres_b,Z: refine432681134nres_b] : ( Y5 = Z ) )
% 0.27/0.62 = ( ^ [A2: refine432681134nres_b,B2: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ B2 @ A2 )
% 0.27/0.62 & ( ord_le527798542nres_b @ A2 @ B2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.eq_iff
% 0.27/0.62 thf(fact_84_dual__order_Oeq__iff,axiom,
% 0.27/0.62 ( ( ^ [Y5: refine424419629nres_a,Z: refine424419629nres_a] : ( Y5 = Z ) )
% 0.27/0.62 = ( ^ [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ B2 @ A2 )
% 0.27/0.62 & ( ord_le519537037nres_a @ A2 @ B2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.eq_iff
% 0.27/0.62 thf(fact_85_dual__order_Otrans,axiom,
% 0.27/0.62 ! [B: refine432681134nres_b,A: refine432681134nres_b,C: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ B @ A )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ C @ B )
% 0.27/0.62 => ( ord_le527798542nres_b @ C @ A ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.trans
% 0.27/0.62 thf(fact_86_dual__order_Otrans,axiom,
% 0.27/0.62 ! [B: refine424419629nres_a,A: refine424419629nres_a,C: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ B @ A )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ C @ B )
% 0.27/0.62 => ( ord_le519537037nres_a @ C @ A ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.trans
% 0.27/0.62 thf(fact_87_dual__order_Orefl,axiom,
% 0.27/0.62 ! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ A ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.refl
% 0.27/0.62 thf(fact_88_dual__order_Orefl,axiom,
% 0.27/0.62 ! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ) ).
% 0.27/0.62
% 0.27/0.62 % dual_order.refl
% 0.27/0.62 thf(fact_89_order__trans,axiom,
% 0.27/0.62 ! [X4: refine432681134nres_b,Y3: refine432681134nres_b,Z2: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ X4 @ Y3 )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ Y3 @ Z2 )
% 0.27/0.62 => ( ord_le527798542nres_b @ X4 @ Z2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_trans
% 0.27/0.62 thf(fact_90_order__trans,axiom,
% 0.27/0.62 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a,Z2: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ Y3 @ Z2 )
% 0.27/0.62 => ( ord_le519537037nres_a @ X4 @ Z2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_trans
% 0.27/0.62 thf(fact_91_order__class_Oorder_Oantisym,axiom,
% 0.27/0.62 ! [A: refine432681134nres_b,B: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ A @ B )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ B @ A )
% 0.27/0.62 => ( A = B ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_class.order.antisym
% 0.27/0.62 thf(fact_92_order__class_Oorder_Oantisym,axiom,
% 0.27/0.62 ! [A: refine424419629nres_a,B: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ A @ B )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ B @ A )
% 0.27/0.62 => ( A = B ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_class.order.antisym
% 0.27/0.62 thf(fact_93_ord__le__eq__trans,axiom,
% 0.27/0.62 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ A @ B )
% 0.27/0.62 => ( ( B = C )
% 0.27/0.62 => ( ord_le527798542nres_b @ A @ C ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_le_eq_trans
% 0.27/0.62 thf(fact_94_ord__le__eq__trans,axiom,
% 0.27/0.62 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ A @ B )
% 0.27/0.62 => ( ( B = C )
% 0.27/0.62 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_le_eq_trans
% 0.27/0.62 thf(fact_95_ord__eq__le__trans,axiom,
% 0.27/0.62 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.27/0.62 ( ( A = B )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ B @ C )
% 0.27/0.62 => ( ord_le527798542nres_b @ A @ C ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_eq_le_trans
% 0.27/0.62 thf(fact_96_ord__eq__le__trans,axiom,
% 0.27/0.62 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.27/0.62 ( ( A = B )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ B @ C )
% 0.27/0.62 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_eq_le_trans
% 0.27/0.62 thf(fact_97_order__class_Oorder_Oeq__iff,axiom,
% 0.27/0.62 ( ( ^ [Y5: refine432681134nres_b,Z: refine432681134nres_b] : ( Y5 = Z ) )
% 0.27/0.62 = ( ^ [A2: refine432681134nres_b,B2: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ A2 @ B2 )
% 0.27/0.62 & ( ord_le527798542nres_b @ B2 @ A2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_class.order.eq_iff
% 0.27/0.62 thf(fact_98_order__class_Oorder_Oeq__iff,axiom,
% 0.27/0.62 ( ( ^ [Y5: refine424419629nres_a,Z: refine424419629nres_a] : ( Y5 = Z ) )
% 0.27/0.62 = ( ^ [A2: refine424419629nres_a,B2: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ A2 @ B2 )
% 0.27/0.62 & ( ord_le519537037nres_a @ B2 @ A2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_class.order.eq_iff
% 0.27/0.62 thf(fact_99_antisym__conv,axiom,
% 0.27/0.62 ! [Y3: refine432681134nres_b,X4: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ Y3 @ X4 )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ X4 @ Y3 )
% 0.27/0.62 = ( X4 = Y3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % antisym_conv
% 0.27/0.62 thf(fact_100_antisym__conv,axiom,
% 0.27/0.62 ! [Y3: refine424419629nres_a,X4: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ Y3 @ X4 )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 0.27/0.62 = ( X4 = Y3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % antisym_conv
% 0.27/0.62 thf(fact_101_order_Otrans,axiom,
% 0.27/0.62 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ A @ B )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ B @ C )
% 0.27/0.62 => ( ord_le527798542nres_b @ A @ C ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order.trans
% 0.27/0.62 thf(fact_102_order_Otrans,axiom,
% 0.27/0.62 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ A @ B )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ B @ C )
% 0.27/0.62 => ( ord_le519537037nres_a @ A @ C ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order.trans
% 0.27/0.62 thf(fact_103_eq__refl,axiom,
% 0.27/0.62 ! [X4: refine432681134nres_b,Y3: refine432681134nres_b] :
% 0.27/0.62 ( ( X4 = Y3 )
% 0.27/0.62 => ( ord_le527798542nres_b @ X4 @ Y3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % eq_refl
% 0.27/0.62 thf(fact_104_eq__refl,axiom,
% 0.27/0.62 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.27/0.62 ( ( X4 = Y3 )
% 0.27/0.62 => ( ord_le519537037nres_a @ X4 @ Y3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % eq_refl
% 0.27/0.62 thf(fact_105_antisym,axiom,
% 0.27/0.62 ! [X4: refine432681134nres_b,Y3: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ X4 @ Y3 )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ Y3 @ X4 )
% 0.27/0.62 => ( X4 = Y3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % antisym
% 0.27/0.62 thf(fact_106_antisym,axiom,
% 0.27/0.62 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ X4 @ Y3 )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ Y3 @ X4 )
% 0.27/0.62 => ( X4 = Y3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % antisym
% 0.27/0.62 thf(fact_107_mem__Collect__eq,axiom,
% 0.27/0.62 ! [A: a,P: a > $o] :
% 0.27/0.62 ( ( member_a @ A @ ( collect_a @ P ) )
% 0.27/0.62 = ( P @ A ) ) ).
% 0.27/0.62
% 0.27/0.62 % mem_Collect_eq
% 0.27/0.62 thf(fact_108_mem__Collect__eq,axiom,
% 0.27/0.62 ! [A: b,P: b > $o] :
% 0.27/0.62 ( ( member_b @ A @ ( collect_b @ P ) )
% 0.27/0.62 = ( P @ A ) ) ).
% 0.27/0.62
% 0.27/0.62 % mem_Collect_eq
% 0.27/0.62 thf(fact_109_Collect__mem__eq,axiom,
% 0.27/0.62 ! [A3: set_a] :
% 0.27/0.62 ( ( collect_a
% 0.27/0.62 @ ^ [X5: a] : ( member_a @ X5 @ A3 ) )
% 0.27/0.62 = A3 ) ).
% 0.27/0.62
% 0.27/0.62 % Collect_mem_eq
% 0.27/0.62 thf(fact_110_Collect__mem__eq,axiom,
% 0.27/0.62 ! [A3: set_b] :
% 0.27/0.62 ( ( collect_b
% 0.27/0.62 @ ^ [X5: b] : ( member_b @ X5 @ A3 ) )
% 0.27/0.62 = A3 ) ).
% 0.27/0.62
% 0.27/0.62 % Collect_mem_eq
% 0.27/0.62 thf(fact_111_Collect__cong,axiom,
% 0.27/0.62 ! [P: a > $o,Q: a > $o] :
% 0.27/0.62 ( ! [X3: a] :
% 0.27/0.62 ( ( P @ X3 )
% 0.27/0.62 = ( Q @ X3 ) )
% 0.27/0.62 => ( ( collect_a @ P )
% 0.27/0.62 = ( collect_a @ Q ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Collect_cong
% 0.27/0.62 thf(fact_112_Collect__cong,axiom,
% 0.27/0.62 ! [P: b > $o,Q: b > $o] :
% 0.27/0.62 ( ! [X3: b] :
% 0.27/0.62 ( ( P @ X3 )
% 0.27/0.62 = ( Q @ X3 ) )
% 0.27/0.62 => ( ( collect_b @ P )
% 0.27/0.62 = ( collect_b @ Q ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Collect_cong
% 0.27/0.62 thf(fact_113_eq__iff,axiom,
% 0.27/0.62 ( ( ^ [Y5: refine432681134nres_b,Z: refine432681134nres_b] : ( Y5 = Z ) )
% 0.27/0.62 = ( ^ [X5: refine432681134nres_b,Y6: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ X5 @ Y6 )
% 0.27/0.62 & ( ord_le527798542nres_b @ Y6 @ X5 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % eq_iff
% 0.27/0.62 thf(fact_114_eq__iff,axiom,
% 0.27/0.62 ( ( ^ [Y5: refine424419629nres_a,Z: refine424419629nres_a] : ( Y5 = Z ) )
% 0.27/0.62 = ( ^ [X5: refine424419629nres_a,Y6: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ X5 @ Y6 )
% 0.27/0.62 & ( ord_le519537037nres_a @ Y6 @ X5 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % eq_iff
% 0.27/0.62 thf(fact_115_ord__le__eq__subst,axiom,
% 0.27/0.62 ! [A: refine432681134nres_b,B: refine432681134nres_b,F: refine432681134nres_b > refine432681134nres_b,C: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ A @ B )
% 0.27/0.62 => ( ( ( F @ B )
% 0.27/0.62 = C )
% 0.27/0.62 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( F @ A ) @ C ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_le_eq_subst
% 0.27/0.62 thf(fact_116_ord__le__eq__subst,axiom,
% 0.27/0.62 ! [A: refine432681134nres_b,B: refine432681134nres_b,F: refine432681134nres_b > refine424419629nres_a,C: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ A @ B )
% 0.27/0.62 => ( ( ( F @ B )
% 0.27/0.62 = C )
% 0.27/0.62 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_le_eq_subst
% 0.27/0.62 thf(fact_117_ord__le__eq__subst,axiom,
% 0.27/0.62 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine432681134nres_b,C: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ A @ B )
% 0.27/0.62 => ( ( ( F @ B )
% 0.27/0.62 = C )
% 0.27/0.62 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( F @ A ) @ C ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_le_eq_subst
% 0.27/0.62 thf(fact_118_ord__le__eq__subst,axiom,
% 0.27/0.62 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ A @ B )
% 0.27/0.62 => ( ( ( F @ B )
% 0.27/0.62 = C )
% 0.27/0.62 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_le_eq_subst
% 0.27/0.62 thf(fact_119_ord__eq__le__subst,axiom,
% 0.27/0.62 ! [A: refine432681134nres_b,F: refine432681134nres_b > refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.27/0.62 ( ( A
% 0.27/0.62 = ( F @ B ) )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ B @ C )
% 0.27/0.62 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ A @ ( F @ C ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_eq_le_subst
% 0.27/0.62 thf(fact_120_ord__eq__le__subst,axiom,
% 0.27/0.62 ! [A: refine424419629nres_a,F: refine432681134nres_b > refine424419629nres_a,B: refine432681134nres_b,C: refine432681134nres_b] :
% 0.27/0.62 ( ( A
% 0.27/0.62 = ( F @ B ) )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ B @ C )
% 0.27/0.62 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_eq_le_subst
% 0.27/0.62 thf(fact_121_ord__eq__le__subst,axiom,
% 0.27/0.62 ! [A: refine432681134nres_b,F: refine424419629nres_a > refine432681134nres_b,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.27/0.62 ( ( A
% 0.27/0.62 = ( F @ B ) )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ B @ C )
% 0.27/0.62 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ A @ ( F @ C ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_eq_le_subst
% 0.27/0.62 thf(fact_122_ord__eq__le__subst,axiom,
% 0.27/0.62 ! [A: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
% 0.27/0.62 ( ( A
% 0.27/0.62 = ( F @ B ) )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ B @ C )
% 0.27/0.62 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_eq_le_subst
% 0.27/0.62 thf(fact_123_order__subst2,axiom,
% 0.27/0.62 ! [A: refine432681134nres_b,B: refine432681134nres_b,F: refine432681134nres_b > refine432681134nres_b,C: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ A @ B )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ ( F @ B ) @ C )
% 0.27/0.62 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( F @ A ) @ C ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_subst2
% 0.27/0.62 thf(fact_124_order__subst2,axiom,
% 0.27/0.62 ! [A: refine432681134nres_b,B: refine432681134nres_b,F: refine432681134nres_b > refine424419629nres_a,C: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ A @ B )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ ( F @ B ) @ C )
% 0.27/0.62 => ( ! [X3: refine432681134nres_b,Y4: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ X3 @ Y4 )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_subst2
% 0.27/0.62 thf(fact_125_order__subst2,axiom,
% 0.27/0.62 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine432681134nres_b,C: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ A @ B )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ ( F @ B ) @ C )
% 0.27/0.62 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( F @ A ) @ C ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_subst2
% 0.27/0.62 thf(fact_126_order__subst2,axiom,
% 0.27/0.62 ! [A: refine424419629nres_a,B: refine424419629nres_a,F: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ A @ B )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ ( F @ B ) @ C )
% 0.27/0.62 => ( ! [X3: refine424419629nres_a,Y4: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ X3 @ Y4 )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % order_subst2
% 0.27/0.62 thf(fact_127_the__RES__inv,axiom,
% 0.27/0.62 ! [M: refine424419629nres_a] :
% 0.27/0.62 ( ( refine412683989fail_a @ M )
% 0.27/0.62 => ( ( refine1198353288_RES_a @ ( refine1822134885_RES_a @ M ) )
% 0.27/0.62 = M ) ) ).
% 0.27/0.62
% 0.27/0.62 % the_RES_inv
% 0.27/0.62 thf(fact_128_the__RES__inv,axiom,
% 0.27/0.62 ! [M: refine432681134nres_b] :
% 0.27/0.62 ( ( refine412683990fail_b @ M )
% 0.27/0.62 => ( ( refine1198353289_RES_b @ ( refine1822134886_RES_b @ M ) )
% 0.27/0.62 = M ) ) ).
% 0.27/0.62
% 0.27/0.62 % the_RES_inv
% 0.27/0.62 thf(fact_129_Greatest__equality,axiom,
% 0.27/0.62 ! [P: refine432681134nres_b > $o,X4: refine432681134nres_b] :
% 0.27/0.62 ( ( P @ X4 )
% 0.27/0.62 => ( ! [Y4: refine432681134nres_b] :
% 0.27/0.62 ( ( P @ Y4 )
% 0.27/0.62 => ( ord_le527798542nres_b @ Y4 @ X4 ) )
% 0.27/0.62 => ( ( order_1722590613nres_b @ P )
% 0.27/0.62 = X4 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Greatest_equality
% 0.27/0.62 thf(fact_130_Greatest__equality,axiom,
% 0.27/0.62 ! [P: refine424419629nres_a > $o,X4: refine424419629nres_a] :
% 0.27/0.62 ( ( P @ X4 )
% 0.27/0.62 => ( ! [Y4: refine424419629nres_a] :
% 0.27/0.62 ( ( P @ Y4 )
% 0.27/0.62 => ( ord_le519537037nres_a @ Y4 @ X4 ) )
% 0.27/0.62 => ( ( order_1714329108nres_a @ P )
% 0.27/0.62 = X4 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Greatest_equality
% 0.27/0.62 thf(fact_131_GreatestI2__order,axiom,
% 0.27/0.62 ! [P: refine432681134nres_b > $o,X4: refine432681134nres_b,Q: refine432681134nres_b > $o] :
% 0.27/0.62 ( ( P @ X4 )
% 0.27/0.62 => ( ! [Y4: refine432681134nres_b] :
% 0.27/0.62 ( ( P @ Y4 )
% 0.27/0.62 => ( ord_le527798542nres_b @ Y4 @ X4 ) )
% 0.27/0.62 => ( ! [X3: refine432681134nres_b] :
% 0.27/0.62 ( ( P @ X3 )
% 0.27/0.62 => ( ! [Y7: refine432681134nres_b] :
% 0.27/0.62 ( ( P @ Y7 )
% 0.27/0.62 => ( ord_le527798542nres_b @ Y7 @ X3 ) )
% 0.27/0.62 => ( Q @ X3 ) ) )
% 0.27/0.62 => ( Q @ ( order_1722590613nres_b @ P ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % GreatestI2_order
% 0.27/0.62 thf(fact_132_GreatestI2__order,axiom,
% 0.27/0.62 ! [P: refine424419629nres_a > $o,X4: refine424419629nres_a,Q: refine424419629nres_a > $o] :
% 0.27/0.62 ( ( P @ X4 )
% 0.27/0.62 => ( ! [Y4: refine424419629nres_a] :
% 0.27/0.62 ( ( P @ Y4 )
% 0.27/0.62 => ( ord_le519537037nres_a @ Y4 @ X4 ) )
% 0.27/0.62 => ( ! [X3: refine424419629nres_a] :
% 0.27/0.62 ( ( P @ X3 )
% 0.27/0.62 => ( ! [Y7: refine424419629nres_a] :
% 0.27/0.62 ( ( P @ Y7 )
% 0.27/0.62 => ( ord_le519537037nres_a @ Y7 @ X3 ) )
% 0.27/0.62 => ( Q @ X3 ) ) )
% 0.27/0.62 => ( Q @ ( order_1714329108nres_a @ P ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % GreatestI2_order
% 0.27/0.62 thf(fact_133_le__rel__bool__arg__iff,axiom,
% 0.27/0.62 ( ord_le1656162903nres_b
% 0.27/0.62 = ( ^ [X6: $o > refine432681134nres_b,Y8: $o > refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ ( X6 @ $false ) @ ( Y8 @ $false ) )
% 0.27/0.62 & ( ord_le527798542nres_b @ ( X6 @ $true ) @ ( Y8 @ $true ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % le_rel_bool_arg_iff
% 0.27/0.62 thf(fact_134_le__rel__bool__arg__iff,axiom,
% 0.27/0.62 ( ord_le516598614nres_a
% 0.27/0.62 = ( ^ [X6: $o > refine424419629nres_a,Y8: $o > refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ ( X6 @ $false ) @ ( Y8 @ $false ) )
% 0.27/0.62 & ( ord_le519537037nres_a @ ( X6 @ $true ) @ ( Y8 @ $true ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % le_rel_bool_arg_iff
% 0.27/0.62 thf(fact_135_ord__eq__le__eq__trans,axiom,
% 0.27/0.62 ! [A: refine432681134nres_b,B: refine432681134nres_b,C: refine432681134nres_b,D: refine432681134nres_b] :
% 0.27/0.62 ( ( A = B )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ B @ C )
% 0.27/0.62 => ( ( C = D )
% 0.27/0.62 => ( ord_le527798542nres_b @ A @ D ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_eq_le_eq_trans
% 0.27/0.62 thf(fact_136_ord__eq__le__eq__trans,axiom,
% 0.27/0.62 ! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
% 0.27/0.62 ( ( A = B )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ B @ C )
% 0.27/0.62 => ( ( C = D )
% 0.27/0.62 => ( ord_le519537037nres_a @ A @ D ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord_eq_le_eq_trans
% 0.27/0.62 thf(fact_137_nofail__simps_I2_J,axiom,
% 0.27/0.62 ! [X: set_a] : ( refine412683989fail_a @ ( refine1198353288_RES_a @ X ) ) ).
% 0.27/0.62
% 0.27/0.62 % nofail_simps(2)
% 0.27/0.62 thf(fact_138_nofail__simps_I2_J,axiom,
% 0.27/0.62 ! [X: set_b] : ( refine412683990fail_b @ ( refine1198353289_RES_b @ X ) ) ).
% 0.27/0.62
% 0.27/0.62 % nofail_simps(2)
% 0.27/0.62 thf(fact_139_subset__Collect__conv,axiom,
% 0.27/0.62 ! [S: set_a,P: a > $o] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ S @ ( collect_a @ P ) )
% 0.27/0.62 = ( ! [X5: a] :
% 0.27/0.62 ( ( member_a @ X5 @ S )
% 0.27/0.62 => ( P @ X5 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_Collect_conv
% 0.27/0.62 thf(fact_140_subset__Collect__conv,axiom,
% 0.27/0.62 ! [S: set_b,P: b > $o] :
% 0.27/0.62 ( ( ord_less_eq_set_b @ S @ ( collect_b @ P ) )
% 0.27/0.62 = ( ! [X5: b] :
% 0.27/0.62 ( ( member_b @ X5 @ S )
% 0.27/0.62 => ( P @ X5 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_Collect_conv
% 0.27/0.62 thf(fact_141_pwD1,axiom,
% 0.27/0.62 ! [S: refine432681134nres_b,S3: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ S @ S3 )
% 0.27/0.62 => ( ( refine412683990fail_b @ S3 )
% 0.27/0.62 => ( refine412683990fail_b @ S ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % pwD1
% 0.27/0.62 thf(fact_142_pwD1,axiom,
% 0.27/0.62 ! [S: refine424419629nres_a,S3: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ S @ S3 )
% 0.27/0.62 => ( ( refine412683989fail_a @ S3 )
% 0.27/0.62 => ( refine412683989fail_a @ S ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % pwD1
% 0.27/0.62 thf(fact_143_le__nofailI,axiom,
% 0.27/0.62 ! [M3: refine432681134nres_b,M4: refine432681134nres_b] :
% 0.27/0.62 ( ( ( refine412683990fail_b @ M3 )
% 0.27/0.62 => ( ord_le527798542nres_b @ M4 @ M3 ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ M4 @ M3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % le_nofailI
% 0.27/0.62 thf(fact_144_le__nofailI,axiom,
% 0.27/0.62 ! [M3: refine424419629nres_a,M4: refine424419629nres_a] :
% 0.27/0.62 ( ( ( refine412683989fail_a @ M3 )
% 0.27/0.62 => ( ord_le519537037nres_a @ M4 @ M3 ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ M4 @ M3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % le_nofailI
% 0.27/0.62 thf(fact_145_nofail__RES__conv,axiom,
% 0.27/0.62 ( refine412683989fail_a
% 0.27/0.62 = ( ^ [M5: refine424419629nres_a] :
% 0.27/0.62 ? [M6: set_a] :
% 0.27/0.62 ( M5
% 0.27/0.62 = ( refine1198353288_RES_a @ M6 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % nofail_RES_conv
% 0.27/0.62 thf(fact_146_nofail__RES__conv,axiom,
% 0.27/0.62 ( refine412683990fail_b
% 0.27/0.62 = ( ^ [M5: refine432681134nres_b] :
% 0.27/0.62 ? [M6: set_b] :
% 0.27/0.62 ( M5
% 0.27/0.62 = ( refine1198353289_RES_b @ M6 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % nofail_RES_conv
% 0.27/0.62 thf(fact_147_ref__two__step,axiom,
% 0.27/0.62 ! [A3: refine432681134nres_b,R: set_Product_prod_b_b,B3: refine432681134nres_b,C2: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ A3 @ ( refine122110613un_b_b @ R @ B3 ) )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ B3 @ C2 )
% 0.27/0.62 => ( ord_le527798542nres_b @ A3 @ ( refine122110613un_b_b @ R @ C2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ref_two_step
% 0.27/0.62 thf(fact_148_ref__two__step,axiom,
% 0.27/0.62 ! [A3: refine432681134nres_b,R: set_Product_prod_b_a,B3: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ A3 @ ( refine122110612un_b_a @ R @ B3 ) )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ B3 @ C2 )
% 0.27/0.62 => ( ord_le527798542nres_b @ A3 @ ( refine122110612un_b_a @ R @ C2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ref_two_step
% 0.27/0.62 thf(fact_149_ref__two__step,axiom,
% 0.27/0.62 ! [A3: refine424419629nres_a,R: set_Product_prod_a_b,B3: refine432681134nres_b,C2: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ A3 @ ( refine1441824854un_a_b @ R @ B3 ) )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ B3 @ C2 )
% 0.27/0.62 => ( ord_le519537037nres_a @ A3 @ ( refine1441824854un_a_b @ R @ C2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ref_two_step
% 0.27/0.62 thf(fact_150_ref__two__step,axiom,
% 0.27/0.62 ! [A3: refine424419629nres_a,R: set_Product_prod_a_a,B3: refine424419629nres_a,C2: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ A3 @ ( refine1441824853un_a_a @ R @ B3 ) )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ B3 @ C2 )
% 0.27/0.62 => ( ord_le519537037nres_a @ A3 @ ( refine1441824853un_a_a @ R @ C2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ref_two_step
% 0.27/0.62 thf(fact_151_le__RES__nofailI,axiom,
% 0.27/0.62 ! [A: refine424419629nres_a,X4: set_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ X4 ) )
% 0.27/0.62 => ( refine412683989fail_a @ A ) ) ).
% 0.27/0.62
% 0.27/0.62 % le_RES_nofailI
% 0.27/0.62 thf(fact_152_le__RES__nofailI,axiom,
% 0.27/0.62 ! [A: refine432681134nres_b,X4: set_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ A @ ( refine1198353289_RES_b @ X4 ) )
% 0.27/0.62 => ( refine412683990fail_b @ A ) ) ).
% 0.27/0.62
% 0.27/0.62 % le_RES_nofailI
% 0.27/0.62 thf(fact_153_pw__RES__bind__choose_I1_J,axiom,
% 0.27/0.62 ! [X: set_a,F: a > refine432681134nres_b] :
% 0.27/0.62 ( ( refine412683990fail_b @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X ) @ F ) )
% 0.27/0.62 = ( ! [X5: a] :
% 0.27/0.62 ( ( member_a @ X5 @ X )
% 0.27/0.62 => ( refine412683990fail_b @ ( F @ X5 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % pw_RES_bind_choose(1)
% 0.27/0.62 thf(fact_154_rhs__step__bind__RES,axiom,
% 0.27/0.62 ! [X7: a,X8: set_a,M: refine432681134nres_b,R: set_Product_prod_b_b,F2: a > refine432681134nres_b] :
% 0.27/0.62 ( ( member_a @ X7 @ X8 )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ M @ ( refine122110613un_b_b @ R @ ( F2 @ X7 ) ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ M @ ( refine122110613un_b_b @ R @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X8 ) @ F2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rhs_step_bind_RES
% 0.27/0.62 thf(fact_155_rhs__step__bind__RES,axiom,
% 0.27/0.62 ! [X7: a,X8: set_a,M: refine424419629nres_a,R: set_Product_prod_a_b,F2: a > refine432681134nres_b] :
% 0.27/0.62 ( ( member_a @ X7 @ X8 )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ M @ ( refine1441824854un_a_b @ R @ ( F2 @ X7 ) ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ M @ ( refine1441824854un_a_b @ R @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X8 ) @ F2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rhs_step_bind_RES
% 0.27/0.62 thf(fact_156_rhs__step__bind__SPEC,axiom,
% 0.27/0.62 ! [Phi: a > $o,X7: a,M: refine432681134nres_b,R: set_Product_prod_b_b,F2: a > refine432681134nres_b] :
% 0.27/0.62 ( ( Phi @ X7 )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ M @ ( refine122110613un_b_b @ R @ ( F2 @ X7 ) ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ M @ ( refine122110613un_b_b @ R @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ F2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rhs_step_bind_SPEC
% 0.27/0.62 thf(fact_157_rhs__step__bind__SPEC,axiom,
% 0.27/0.62 ! [Phi: a > $o,X7: a,M: refine424419629nres_a,R: set_Product_prod_a_b,F2: a > refine432681134nres_b] :
% 0.27/0.62 ( ( Phi @ X7 )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ M @ ( refine1441824854un_a_b @ R @ ( F2 @ X7 ) ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ M @ ( refine1441824854un_a_b @ R @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) @ F2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rhs_step_bind_SPEC
% 0.27/0.62 thf(fact_158_subsetI,axiom,
% 0.27/0.62 ! [A3: set_a,B3: set_a] :
% 0.27/0.62 ( ! [X3: a] :
% 0.27/0.62 ( ( member_a @ X3 @ A3 )
% 0.27/0.62 => ( member_a @ X3 @ B3 ) )
% 0.27/0.62 => ( ord_less_eq_set_a @ A3 @ B3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % subsetI
% 0.27/0.62 thf(fact_159_subsetI,axiom,
% 0.27/0.62 ! [A3: set_b,B3: set_b] :
% 0.27/0.62 ( ! [X3: b] :
% 0.27/0.62 ( ( member_b @ X3 @ A3 )
% 0.27/0.62 => ( member_b @ X3 @ B3 ) )
% 0.27/0.62 => ( ord_less_eq_set_b @ A3 @ B3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % subsetI
% 0.27/0.62 thf(fact_160_bind__sim__select__rule,axiom,
% 0.27/0.62 ! [M: refine424419629nres_a,F2: a > refine424419629nres_a,Psi: a > $o,F: a > refine432681134nres_b,Phi: b > $o] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M @ F2 ) @ ( refine1198353288_RES_a @ ( collect_a @ Psi ) ) )
% 0.27/0.62 => ( ! [X3: a] :
% 0.27/0.62 ( ( refine412683989fail_a @ M )
% 0.27/0.62 => ( ( refine1001002027nres_a @ M @ X3 )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ ( F2 @ X3 ) @ ( refine1198353288_RES_a @ ( collect_a @ Psi ) ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M @ F ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % bind_sim_select_rule
% 0.27/0.62 thf(fact_161_bind__sim__select__rule,axiom,
% 0.27/0.62 ! [M: refine424419629nres_a,F2: a > refine432681134nres_b,Psi: b > $o,F: a > refine424419629nres_a,Phi: a > $o] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M @ F2 ) @ ( refine1198353289_RES_b @ ( collect_b @ Psi ) ) )
% 0.27/0.62 => ( ! [X3: a] :
% 0.27/0.62 ( ( refine412683989fail_a @ M )
% 0.27/0.62 => ( ( refine1001002027nres_a @ M @ X3 )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ ( F2 @ X3 ) @ ( refine1198353289_RES_b @ ( collect_b @ Psi ) ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M @ F ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % bind_sim_select_rule
% 0.27/0.62 thf(fact_162_bind__sim__select__rule,axiom,
% 0.27/0.62 ! [M: refine424419629nres_a,F2: a > refine432681134nres_b,Psi: b > $o,F: a > refine432681134nres_b,Phi: b > $o] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M @ F2 ) @ ( refine1198353289_RES_b @ ( collect_b @ Psi ) ) )
% 0.27/0.62 => ( ! [X3: a] :
% 0.27/0.62 ( ( refine412683989fail_a @ M )
% 0.27/0.62 => ( ( refine1001002027nres_a @ M @ X3 )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ ( F2 @ X3 ) @ ( refine1198353289_RES_b @ ( collect_b @ Psi ) ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M @ F ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % bind_sim_select_rule
% 0.27/0.62 thf(fact_163_in__mono,axiom,
% 0.27/0.62 ! [A3: set_a,B3: set_a,X4: a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.27/0.62 => ( ( member_a @ X4 @ A3 )
% 0.27/0.62 => ( member_a @ X4 @ B3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % in_mono
% 0.27/0.62 thf(fact_164_in__mono,axiom,
% 0.27/0.62 ! [A3: set_b,B3: set_b,X4: b] :
% 0.27/0.62 ( ( ord_less_eq_set_b @ A3 @ B3 )
% 0.27/0.62 => ( ( member_b @ X4 @ A3 )
% 0.27/0.62 => ( member_b @ X4 @ B3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % in_mono
% 0.27/0.62 thf(fact_165_subsetD,axiom,
% 0.27/0.62 ! [A3: set_a,B3: set_a,C: a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ A3 @ B3 )
% 0.27/0.62 => ( ( member_a @ C @ A3 )
% 0.27/0.62 => ( member_a @ C @ B3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subsetD
% 0.27/0.62 thf(fact_166_subsetD,axiom,
% 0.27/0.62 ! [A3: set_b,B3: set_b,C: b] :
% 0.27/0.62 ( ( ord_less_eq_set_b @ A3 @ B3 )
% 0.27/0.62 => ( ( member_b @ C @ A3 )
% 0.27/0.62 => ( member_b @ C @ B3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subsetD
% 0.27/0.62 thf(fact_167_inres__simps_I2_J,axiom,
% 0.27/0.62 ! [X: set_a] :
% 0.27/0.62 ( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ X ) )
% 0.27/0.62 = ( ^ [X5: a] : ( member_a @ X5 @ X ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % inres_simps(2)
% 0.27/0.62 thf(fact_168_inres__simps_I2_J,axiom,
% 0.27/0.62 ! [X: set_b] :
% 0.27/0.62 ( ( refine1001002028nres_b @ ( refine1198353289_RES_b @ X ) )
% 0.27/0.62 = ( ^ [X5: b] : ( member_b @ X5 @ X ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % inres_simps(2)
% 0.27/0.62 thf(fact_169_pwD2,axiom,
% 0.27/0.62 ! [S: refine432681134nres_b,S3: refine432681134nres_b,X4: b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ S @ S3 )
% 0.27/0.62 => ( ( refine1001002028nres_b @ S @ X4 )
% 0.27/0.62 => ( refine1001002028nres_b @ S3 @ X4 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % pwD2
% 0.27/0.62 thf(fact_170_pwD2,axiom,
% 0.27/0.62 ! [S: refine424419629nres_a,S3: refine424419629nres_a,X4: a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ S @ S3 )
% 0.27/0.62 => ( ( refine1001002027nres_a @ S @ X4 )
% 0.27/0.62 => ( refine1001002027nres_a @ S3 @ X4 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % pwD2
% 0.27/0.62 thf(fact_171_pw__RES__bind__choose_I2_J,axiom,
% 0.27/0.62 ! [X: set_a,F: a > refine432681134nres_b,Y3: b] :
% 0.27/0.62 ( ( refine1001002028nres_b @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X ) @ F ) @ Y3 )
% 0.27/0.62 = ( ? [X5: a] :
% 0.27/0.62 ( ( member_a @ X5 @ X )
% 0.27/0.62 & ( refine1001002028nres_b @ ( F @ X5 ) @ Y3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % pw_RES_bind_choose(2)
% 0.27/0.62 thf(fact_172_pw__leI,axiom,
% 0.27/0.62 ! [S3: refine432681134nres_b,S: refine432681134nres_b] :
% 0.27/0.62 ( ( ( refine412683990fail_b @ S3 )
% 0.27/0.62 => ( ( refine412683990fail_b @ S )
% 0.27/0.62 & ! [X3: b] :
% 0.27/0.62 ( ( refine1001002028nres_b @ S @ X3 )
% 0.27/0.62 => ( refine1001002028nres_b @ S3 @ X3 ) ) ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ S @ S3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % pw_leI
% 0.27/0.62 thf(fact_173_pw__leI,axiom,
% 0.27/0.62 ! [S3: refine424419629nres_a,S: refine424419629nres_a] :
% 0.27/0.62 ( ( ( refine412683989fail_a @ S3 )
% 0.27/0.62 => ( ( refine412683989fail_a @ S )
% 0.27/0.62 & ! [X3: a] :
% 0.27/0.62 ( ( refine1001002027nres_a @ S @ X3 )
% 0.27/0.62 => ( refine1001002027nres_a @ S3 @ X3 ) ) ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ S @ S3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % pw_leI
% 0.27/0.62 thf(fact_174_pw__leI_H,axiom,
% 0.27/0.62 ! [S3: refine432681134nres_b,S: refine432681134nres_b] :
% 0.27/0.62 ( ( ( refine412683990fail_b @ S3 )
% 0.27/0.62 => ( refine412683990fail_b @ S ) )
% 0.27/0.62 => ( ! [X3: b] :
% 0.27/0.62 ( ( refine412683990fail_b @ S3 )
% 0.27/0.62 => ( ( refine1001002028nres_b @ S @ X3 )
% 0.27/0.62 => ( refine1001002028nres_b @ S3 @ X3 ) ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ S @ S3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % pw_leI'
% 0.27/0.62 thf(fact_175_pw__leI_H,axiom,
% 0.27/0.62 ! [S3: refine424419629nres_a,S: refine424419629nres_a] :
% 0.27/0.62 ( ( ( refine412683989fail_a @ S3 )
% 0.27/0.62 => ( refine412683989fail_a @ S ) )
% 0.27/0.62 => ( ! [X3: a] :
% 0.27/0.62 ( ( refine412683989fail_a @ S3 )
% 0.27/0.62 => ( ( refine1001002027nres_a @ S @ X3 )
% 0.27/0.62 => ( refine1001002027nres_a @ S3 @ X3 ) ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ S @ S3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % pw_leI'
% 0.27/0.62 thf(fact_176_pw__le__iff,axiom,
% 0.27/0.62 ( ord_le527798542nres_b
% 0.27/0.62 = ( ^ [S4: refine432681134nres_b,S5: refine432681134nres_b] :
% 0.27/0.62 ( ( refine412683990fail_b @ S5 )
% 0.27/0.62 => ( ( refine412683990fail_b @ S4 )
% 0.27/0.62 & ! [X5: b] :
% 0.27/0.62 ( ( refine1001002028nres_b @ S4 @ X5 )
% 0.27/0.62 => ( refine1001002028nres_b @ S5 @ X5 ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % pw_le_iff
% 0.27/0.62 thf(fact_177_pw__le__iff,axiom,
% 0.27/0.62 ( ord_le519537037nres_a
% 0.27/0.62 = ( ^ [S4: refine424419629nres_a,S5: refine424419629nres_a] :
% 0.27/0.62 ( ( refine412683989fail_a @ S5 )
% 0.27/0.62 => ( ( refine412683989fail_a @ S4 )
% 0.27/0.62 & ! [X5: a] :
% 0.27/0.62 ( ( refine1001002027nres_a @ S4 @ X5 )
% 0.27/0.62 => ( refine1001002027nres_a @ S5 @ X5 ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % pw_le_iff
% 0.27/0.62 thf(fact_178_pw__bind__nofail,axiom,
% 0.27/0.62 ! [M4: refine424419629nres_a,F: a > refine432681134nres_b] :
% 0.27/0.62 ( ( refine412683990fail_b @ ( refine436832839nd_a_b @ M4 @ F ) )
% 0.27/0.62 = ( ( refine412683989fail_a @ M4 )
% 0.27/0.62 & ! [X5: a] :
% 0.27/0.62 ( ( refine1001002027nres_a @ M4 @ X5 )
% 0.27/0.62 => ( refine412683990fail_b @ ( F @ X5 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % pw_bind_nofail
% 0.27/0.62 thf(fact_179_pw__bind__le__iff,axiom,
% 0.27/0.62 ! [M4: refine424419629nres_a,F: a > refine432681134nres_b,S: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M4 @ F ) @ S )
% 0.27/0.62 = ( ( ( refine412683990fail_b @ S )
% 0.27/0.62 => ( refine412683989fail_a @ M4 ) )
% 0.27/0.62 & ! [X5: a] :
% 0.27/0.62 ( ( ( refine412683989fail_a @ M4 )
% 0.27/0.62 & ( refine1001002027nres_a @ M4 @ X5 ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( F @ X5 ) @ S ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % pw_bind_le_iff
% 0.27/0.62 thf(fact_180_pw__bind__leI,axiom,
% 0.27/0.62 ! [S: refine432681134nres_b,M4: refine424419629nres_a,F: a > refine432681134nres_b] :
% 0.27/0.62 ( ( ( refine412683990fail_b @ S )
% 0.27/0.62 => ( refine412683989fail_a @ M4 ) )
% 0.27/0.62 => ( ! [X3: a] :
% 0.27/0.62 ( ( refine412683989fail_a @ M4 )
% 0.27/0.62 => ( ( refine1001002027nres_a @ M4 @ X3 )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( F @ X3 ) @ S ) ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M4 @ F ) @ S ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % pw_bind_leI
% 0.27/0.62 thf(fact_181_Collect__mono__iff,axiom,
% 0.27/0.62 ! [P: a > $o,Q: a > $o] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) )
% 0.27/0.62 = ( ! [X5: a] :
% 0.27/0.62 ( ( P @ X5 )
% 0.27/0.62 => ( Q @ X5 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Collect_mono_iff
% 0.27/0.62 thf(fact_182_Collect__mono__iff,axiom,
% 0.27/0.62 ! [P: b > $o,Q: b > $o] :
% 0.27/0.62 ( ( ord_less_eq_set_b @ ( collect_b @ P ) @ ( collect_b @ Q ) )
% 0.27/0.62 = ( ! [X5: b] :
% 0.27/0.62 ( ( P @ X5 )
% 0.27/0.62 => ( Q @ X5 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Collect_mono_iff
% 0.27/0.62 thf(fact_183_Collect__mono,axiom,
% 0.27/0.62 ! [P: a > $o,Q: a > $o] :
% 0.27/0.62 ( ! [X3: a] :
% 0.27/0.62 ( ( P @ X3 )
% 0.27/0.62 => ( Q @ X3 ) )
% 0.27/0.62 => ( ord_less_eq_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Collect_mono
% 0.27/0.62 thf(fact_184_Collect__mono,axiom,
% 0.27/0.62 ! [P: b > $o,Q: b > $o] :
% 0.27/0.62 ( ! [X3: b] :
% 0.27/0.62 ( ( P @ X3 )
% 0.27/0.62 => ( Q @ X3 ) )
% 0.27/0.62 => ( ord_less_eq_set_b @ ( collect_b @ P ) @ ( collect_b @ Q ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Collect_mono
% 0.27/0.62 thf(fact_185_subset__iff,axiom,
% 0.27/0.62 ( ord_less_eq_set_a
% 0.27/0.62 = ( ^ [A4: set_a,B4: set_a] :
% 0.27/0.62 ! [T3: a] :
% 0.27/0.62 ( ( member_a @ T3 @ A4 )
% 0.27/0.62 => ( member_a @ T3 @ B4 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_iff
% 0.27/0.62 thf(fact_186_subset__iff,axiom,
% 0.27/0.62 ( ord_less_eq_set_b
% 0.27/0.62 = ( ^ [A4: set_b,B4: set_b] :
% 0.27/0.62 ! [T3: b] :
% 0.27/0.62 ( ( member_b @ T3 @ A4 )
% 0.27/0.62 => ( member_b @ T3 @ B4 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_iff
% 0.27/0.62 thf(fact_187_subset__eq,axiom,
% 0.27/0.62 ( ord_less_eq_set_a
% 0.27/0.62 = ( ^ [A4: set_a,B4: set_a] :
% 0.27/0.62 ! [X5: a] :
% 0.27/0.62 ( ( member_a @ X5 @ A4 )
% 0.27/0.62 => ( member_a @ X5 @ B4 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_eq
% 0.27/0.62 thf(fact_188_subset__eq,axiom,
% 0.27/0.62 ( ord_less_eq_set_b
% 0.27/0.62 = ( ^ [A4: set_b,B4: set_b] :
% 0.27/0.62 ! [X5: b] :
% 0.27/0.62 ( ( member_b @ X5 @ A4 )
% 0.27/0.62 => ( member_b @ X5 @ B4 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % subset_eq
% 0.27/0.62 thf(fact_189_rhs__step__bind,axiom,
% 0.27/0.62 ! [M: refine432681134nres_b,R: set_Product_prod_b_a,M7: refine424419629nres_a,X4: b,Lhs: refine432681134nres_b,S: set_Product_prod_b_b,F2: a > refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ M @ ( refine122110612un_b_a @ R @ M7 ) )
% 0.27/0.62 => ( ( refine1001002028nres_b @ M @ X4 )
% 0.27/0.62 => ( ! [X9: a] :
% 0.27/0.62 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ X4 @ X9 ) @ R )
% 0.27/0.62 => ( ord_le527798542nres_b @ Lhs @ ( refine122110613un_b_b @ S @ ( F2 @ X9 ) ) ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ Lhs @ ( refine122110613un_b_b @ S @ ( refine436832839nd_a_b @ M7 @ F2 ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rhs_step_bind
% 0.27/0.62 thf(fact_190_rhs__step__bind,axiom,
% 0.27/0.62 ! [M: refine432681134nres_b,R: set_Product_prod_b_a,M7: refine424419629nres_a,X4: b,Lhs: refine424419629nres_a,S: set_Product_prod_a_b,F2: a > refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ M @ ( refine122110612un_b_a @ R @ M7 ) )
% 0.27/0.62 => ( ( refine1001002028nres_b @ M @ X4 )
% 0.27/0.62 => ( ! [X9: a] :
% 0.27/0.62 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ X4 @ X9 ) @ R )
% 0.27/0.62 => ( ord_le519537037nres_a @ Lhs @ ( refine1441824854un_a_b @ S @ ( F2 @ X9 ) ) ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ Lhs @ ( refine1441824854un_a_b @ S @ ( refine436832839nd_a_b @ M7 @ F2 ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rhs_step_bind
% 0.27/0.62 thf(fact_191_rhs__step__bind,axiom,
% 0.27/0.62 ! [M: refine424419629nres_a,R: set_Product_prod_a_a,M7: refine424419629nres_a,X4: a,Lhs: refine432681134nres_b,S: set_Product_prod_b_b,F2: a > refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ M @ ( refine1441824853un_a_a @ R @ M7 ) )
% 0.27/0.62 => ( ( refine1001002027nres_a @ M @ X4 )
% 0.27/0.62 => ( ! [X9: a] :
% 0.27/0.62 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X9 ) @ R )
% 0.27/0.62 => ( ord_le527798542nres_b @ Lhs @ ( refine122110613un_b_b @ S @ ( F2 @ X9 ) ) ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ Lhs @ ( refine122110613un_b_b @ S @ ( refine436832839nd_a_b @ M7 @ F2 ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rhs_step_bind
% 0.27/0.62 thf(fact_192_rhs__step__bind,axiom,
% 0.27/0.62 ! [M: refine424419629nres_a,R: set_Product_prod_a_a,M7: refine424419629nres_a,X4: a,Lhs: refine424419629nres_a,S: set_Product_prod_a_b,F2: a > refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ M @ ( refine1441824853un_a_a @ R @ M7 ) )
% 0.27/0.62 => ( ( refine1001002027nres_a @ M @ X4 )
% 0.27/0.62 => ( ! [X9: a] :
% 0.27/0.62 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X9 ) @ R )
% 0.27/0.62 => ( ord_le519537037nres_a @ Lhs @ ( refine1441824854un_a_b @ S @ ( F2 @ X9 ) ) ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ Lhs @ ( refine1441824854un_a_b @ S @ ( refine436832839nd_a_b @ M7 @ F2 ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rhs_step_bind
% 0.27/0.62 thf(fact_193_RES__refine,axiom,
% 0.27/0.62 ! [S: set_a,S3: set_a,R: set_Product_prod_a_a] :
% 0.27/0.62 ( ! [S6: a] :
% 0.27/0.62 ( ( member_a @ S6 @ S )
% 0.27/0.62 => ? [X10: a] :
% 0.27/0.62 ( ( member_a @ X10 @ S3 )
% 0.27/0.62 & ( member449909584od_a_a @ ( product_Pair_a_a @ S6 @ X10 ) @ R ) ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ S ) @ ( refine1441824853un_a_a @ R @ ( refine1198353288_RES_a @ S3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % RES_refine
% 0.27/0.62 thf(fact_194_RES__refine,axiom,
% 0.27/0.62 ! [S: set_a,S3: set_b,R: set_Product_prod_a_b] :
% 0.27/0.62 ( ! [S6: a] :
% 0.27/0.62 ( ( member_a @ S6 @ S )
% 0.27/0.62 => ? [X10: b] :
% 0.27/0.62 ( ( member_b @ X10 @ S3 )
% 0.27/0.62 & ( member458171089od_a_b @ ( product_Pair_a_b @ S6 @ X10 ) @ R ) ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ S ) @ ( refine1441824854un_a_b @ R @ ( refine1198353289_RES_b @ S3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % RES_refine
% 0.27/0.62 thf(fact_195_RES__refine,axiom,
% 0.27/0.62 ! [S: set_b,S3: set_a,R: set_Product_prod_b_a] :
% 0.27/0.62 ( ! [S6: b] :
% 0.27/0.62 ( ( member_b @ S6 @ S )
% 0.27/0.62 => ? [X10: a] :
% 0.27/0.62 ( ( member_a @ X10 @ S3 )
% 0.27/0.62 & ( member1277678991od_b_a @ ( product_Pair_b_a @ S6 @ X10 ) @ R ) ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ S ) @ ( refine122110612un_b_a @ R @ ( refine1198353288_RES_a @ S3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % RES_refine
% 0.27/0.62 thf(fact_196_RES__refine,axiom,
% 0.27/0.62 ! [S: set_b,S3: set_b,R: set_Product_prod_b_b] :
% 0.27/0.62 ( ! [S6: b] :
% 0.27/0.62 ( ( member_b @ S6 @ S )
% 0.27/0.62 => ? [X10: b] :
% 0.27/0.62 ( ( member_b @ X10 @ S3 )
% 0.27/0.62 & ( member1285940496od_b_b @ ( product_Pair_b_b @ S6 @ X10 ) @ R ) ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ S ) @ ( refine122110613un_b_b @ R @ ( refine1198353289_RES_b @ S3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % RES_refine
% 0.27/0.62 thf(fact_197_less__eq__nres_Oelims_I1_J,axiom,
% 0.27/0.62 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a,Y3: $o] :
% 0.27/0.62 ( ( ( ord_le519537037nres_a @ X4 @ Xa )
% 0.27/0.62 = Y3 )
% 0.27/0.62 => ( ( ( Xa = refine464223677AILi_a )
% 0.27/0.62 => ~ Y3 )
% 0.27/0.62 => ( ! [A5: set_a] :
% 0.27/0.62 ( ( X4
% 0.27/0.62 = ( refine1198353288_RES_a @ A5 ) )
% 0.27/0.62 => ! [B5: set_a] :
% 0.27/0.62 ( ( Xa
% 0.27/0.62 = ( refine1198353288_RES_a @ B5 ) )
% 0.27/0.62 => ( Y3
% 0.27/0.62 = ( ~ ( ord_less_eq_set_a @ A5 @ B5 ) ) ) ) )
% 0.27/0.62 => ~ ( ( X4 = refine464223677AILi_a )
% 0.27/0.62 => ( ? [Uv: set_a] :
% 0.27/0.62 ( Xa
% 0.27/0.62 = ( refine1198353288_RES_a @ Uv ) )
% 0.27/0.62 => Y3 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % less_eq_nres.elims(1)
% 0.27/0.62 thf(fact_198_less__eq__nres_Oelims_I1_J,axiom,
% 0.27/0.62 ! [X4: refine432681134nres_b,Xa: refine432681134nres_b,Y3: $o] :
% 0.27/0.62 ( ( ( ord_le527798542nres_b @ X4 @ Xa )
% 0.27/0.62 = Y3 )
% 0.27/0.62 => ( ( ( Xa = refine464223678AILi_b )
% 0.27/0.62 => ~ Y3 )
% 0.27/0.62 => ( ! [A5: set_b] :
% 0.27/0.62 ( ( X4
% 0.27/0.62 = ( refine1198353289_RES_b @ A5 ) )
% 0.27/0.62 => ! [B5: set_b] :
% 0.27/0.62 ( ( Xa
% 0.27/0.62 = ( refine1198353289_RES_b @ B5 ) )
% 0.27/0.62 => ( Y3
% 0.27/0.62 = ( ~ ( ord_less_eq_set_b @ A5 @ B5 ) ) ) ) )
% 0.27/0.62 => ~ ( ( X4 = refine464223678AILi_b )
% 0.27/0.62 => ( ? [Uv: set_b] :
% 0.27/0.62 ( Xa
% 0.27/0.62 = ( refine1198353289_RES_b @ Uv ) )
% 0.27/0.62 => Y3 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % less_eq_nres.elims(1)
% 0.27/0.62 thf(fact_199_less__eq__nres_Oelims_I2_J,axiom,
% 0.27/0.62 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ X4 @ Xa )
% 0.27/0.62 => ( ( Xa != refine464223677AILi_a )
% 0.27/0.62 => ~ ! [A5: set_a] :
% 0.27/0.62 ( ( X4
% 0.27/0.62 = ( refine1198353288_RES_a @ A5 ) )
% 0.27/0.62 => ! [B5: set_a] :
% 0.27/0.62 ( ( Xa
% 0.27/0.62 = ( refine1198353288_RES_a @ B5 ) )
% 0.27/0.62 => ~ ( ord_less_eq_set_a @ A5 @ B5 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % less_eq_nres.elims(2)
% 0.27/0.62 thf(fact_200_less__eq__nres_Oelims_I2_J,axiom,
% 0.27/0.62 ! [X4: refine432681134nres_b,Xa: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ X4 @ Xa )
% 0.27/0.62 => ( ( Xa != refine464223678AILi_b )
% 0.27/0.62 => ~ ! [A5: set_b] :
% 0.27/0.62 ( ( X4
% 0.27/0.62 = ( refine1198353289_RES_b @ A5 ) )
% 0.27/0.62 => ! [B5: set_b] :
% 0.27/0.62 ( ( Xa
% 0.27/0.62 = ( refine1198353289_RES_b @ B5 ) )
% 0.27/0.62 => ~ ( ord_less_eq_set_b @ A5 @ B5 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % less_eq_nres.elims(2)
% 0.27/0.62 thf(fact_201_less__eq__nres_Ocases,axiom,
% 0.27/0.62 ! [X4: produc1609974940nres_a] :
% 0.27/0.62 ( ! [Uu: refine424419629nres_a] :
% 0.27/0.62 ( X4
% 0.27/0.62 != ( produc1136923598nres_a @ Uu @ refine464223677AILi_a ) )
% 0.27/0.62 => ( ! [A5: set_a,B5: set_a] :
% 0.27/0.62 ( X4
% 0.27/0.62 != ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) ) )
% 0.27/0.62 => ~ ! [Uv: set_a] :
% 0.27/0.62 ( X4
% 0.27/0.62 != ( produc1136923598nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % less_eq_nres.cases
% 0.27/0.62 thf(fact_202_less__eq__nres_Ocases,axiom,
% 0.27/0.62 ! [X4: produc1587512412nres_b] :
% 0.27/0.62 ( ! [Uu: refine432681134nres_b] :
% 0.27/0.62 ( X4
% 0.27/0.62 != ( produc2130641934nres_b @ Uu @ refine464223678AILi_b ) )
% 0.27/0.62 => ( ! [A5: set_b,B5: set_b] :
% 0.27/0.62 ( X4
% 0.27/0.62 != ( produc2130641934nres_b @ ( refine1198353289_RES_b @ A5 ) @ ( refine1198353289_RES_b @ B5 ) ) )
% 0.27/0.62 => ~ ! [Uv: set_b] :
% 0.27/0.62 ( X4
% 0.27/0.62 != ( produc2130641934nres_b @ refine464223678AILi_b @ ( refine1198353289_RES_b @ Uv ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % less_eq_nres.cases
% 0.27/0.62 thf(fact_203_less__nres_Ocases,axiom,
% 0.27/0.62 ! [X4: produc1609974940nres_a] :
% 0.27/0.62 ( ! [Uu: refine424419629nres_a] :
% 0.27/0.62 ( X4
% 0.27/0.62 != ( produc1136923598nres_a @ refine464223677AILi_a @ Uu ) )
% 0.27/0.62 => ( ! [Uv: set_a] :
% 0.27/0.62 ( X4
% 0.27/0.62 != ( produc1136923598nres_a @ ( refine1198353288_RES_a @ Uv ) @ refine464223677AILi_a ) )
% 0.27/0.62 => ~ ! [A5: set_a,B5: set_a] :
% 0.27/0.62 ( X4
% 0.27/0.62 != ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % less_nres.cases
% 0.27/0.62 thf(fact_204_less__nres_Ocases,axiom,
% 0.27/0.62 ! [X4: produc1587512412nres_b] :
% 0.27/0.62 ( ! [Uu: refine432681134nres_b] :
% 0.27/0.62 ( X4
% 0.27/0.62 != ( produc2130641934nres_b @ refine464223678AILi_b @ Uu ) )
% 0.27/0.62 => ( ! [Uv: set_b] :
% 0.27/0.62 ( X4
% 0.27/0.62 != ( produc2130641934nres_b @ ( refine1198353289_RES_b @ Uv ) @ refine464223678AILi_b ) )
% 0.27/0.62 => ~ ! [A5: set_b,B5: set_b] :
% 0.27/0.62 ( X4
% 0.27/0.62 != ( produc2130641934nres_b @ ( refine1198353289_RES_b @ A5 ) @ ( refine1198353289_RES_b @ B5 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % less_nres.cases
% 0.27/0.62 thf(fact_205_sup__nres_Ocases,axiom,
% 0.27/0.62 ! [X4: produc1609974940nres_a] :
% 0.27/0.62 ( ! [Uu: refine424419629nres_a] :
% 0.27/0.62 ( X4
% 0.27/0.62 != ( produc1136923598nres_a @ Uu @ refine464223677AILi_a ) )
% 0.27/0.62 => ( ! [V: set_a] :
% 0.27/0.62 ( X4
% 0.27/0.62 != ( produc1136923598nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ V ) ) )
% 0.27/0.62 => ~ ! [A5: set_a,B5: set_a] :
% 0.27/0.62 ( X4
% 0.27/0.62 != ( produc1136923598nres_a @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % sup_nres.cases
% 0.27/0.62 thf(fact_206_sup__nres_Ocases,axiom,
% 0.27/0.62 ! [X4: produc1587512412nres_b] :
% 0.27/0.62 ( ! [Uu: refine432681134nres_b] :
% 0.27/0.62 ( X4
% 0.27/0.62 != ( produc2130641934nres_b @ Uu @ refine464223678AILi_b ) )
% 0.27/0.62 => ( ! [V: set_b] :
% 0.27/0.62 ( X4
% 0.27/0.62 != ( produc2130641934nres_b @ refine464223678AILi_b @ ( refine1198353289_RES_b @ V ) ) )
% 0.27/0.62 => ~ ! [A5: set_b,B5: set_b] :
% 0.27/0.62 ( X4
% 0.27/0.62 != ( produc2130641934nres_b @ ( refine1198353289_RES_b @ A5 ) @ ( refine1198353289_RES_b @ B5 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % sup_nres.cases
% 0.27/0.62 thf(fact_207_less__eq__nres_Osimps_I1_J,axiom,
% 0.27/0.62 ! [Uu2: refine432681134nres_b] : ( ord_le527798542nres_b @ Uu2 @ refine464223678AILi_b ) ).
% 0.27/0.62
% 0.27/0.62 % less_eq_nres.simps(1)
% 0.27/0.62 thf(fact_208_less__eq__nres_Osimps_I1_J,axiom,
% 0.27/0.62 ! [Uu2: refine424419629nres_a] : ( ord_le519537037nres_a @ Uu2 @ refine464223677AILi_a ) ).
% 0.27/0.62
% 0.27/0.62 % less_eq_nres.simps(1)
% 0.27/0.62 thf(fact_209_nres_Odistinct_I1_J,axiom,
% 0.27/0.62 ! [X2: set_a] :
% 0.27/0.62 ( refine464223677AILi_a
% 0.27/0.62 != ( refine1198353288_RES_a @ X2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % nres.distinct(1)
% 0.27/0.62 thf(fact_210_nres_Odistinct_I1_J,axiom,
% 0.27/0.62 ! [X2: set_b] :
% 0.27/0.62 ( refine464223678AILi_b
% 0.27/0.62 != ( refine1198353289_RES_b @ X2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % nres.distinct(1)
% 0.27/0.62 thf(fact_211_nres_Oinduct,axiom,
% 0.27/0.62 ! [P: refine424419629nres_a > $o,Nres: refine424419629nres_a] :
% 0.27/0.62 ( ( P @ refine464223677AILi_a )
% 0.27/0.62 => ( ! [X3: set_a] : ( P @ ( refine1198353288_RES_a @ X3 ) )
% 0.27/0.62 => ( P @ Nres ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % nres.induct
% 0.27/0.62 thf(fact_212_nres_Oinduct,axiom,
% 0.27/0.62 ! [P: refine432681134nres_b > $o,Nres: refine432681134nres_b] :
% 0.27/0.62 ( ( P @ refine464223678AILi_b )
% 0.27/0.62 => ( ! [X3: set_b] : ( P @ ( refine1198353289_RES_b @ X3 ) )
% 0.27/0.62 => ( P @ Nres ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % nres.induct
% 0.27/0.62 thf(fact_213_nres_Oexhaust,axiom,
% 0.27/0.62 ! [Y3: refine424419629nres_a] :
% 0.27/0.62 ( ( Y3 != refine464223677AILi_a )
% 0.27/0.62 => ~ ! [X22: set_a] :
% 0.27/0.62 ( Y3
% 0.27/0.62 != ( refine1198353288_RES_a @ X22 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % nres.exhaust
% 0.27/0.62 thf(fact_214_nres_Oexhaust,axiom,
% 0.27/0.62 ! [Y3: refine432681134nres_b] :
% 0.27/0.62 ( ( Y3 != refine464223678AILi_b )
% 0.27/0.62 => ~ ! [X22: set_b] :
% 0.27/0.62 ( Y3
% 0.27/0.62 != ( refine1198353289_RES_b @ X22 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % nres.exhaust
% 0.27/0.62 thf(fact_215_sup__nres_Oinduct,axiom,
% 0.27/0.62 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 0.27/0.62 ( ! [Uu: refine424419629nres_a] : ( P @ Uu @ refine464223677AILi_a )
% 0.27/0.62 => ( ! [V: set_a] : ( P @ refine464223677AILi_a @ ( refine1198353288_RES_a @ V ) )
% 0.27/0.62 => ( ! [A5: set_a,B5: set_a] : ( P @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) )
% 0.27/0.62 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % sup_nres.induct
% 0.27/0.62 thf(fact_216_sup__nres_Oinduct,axiom,
% 0.27/0.62 ! [P: refine432681134nres_b > refine432681134nres_b > $o,A0: refine432681134nres_b,A1: refine432681134nres_b] :
% 0.27/0.62 ( ! [Uu: refine432681134nres_b] : ( P @ Uu @ refine464223678AILi_b )
% 0.27/0.62 => ( ! [V: set_b] : ( P @ refine464223678AILi_b @ ( refine1198353289_RES_b @ V ) )
% 0.27/0.62 => ( ! [A5: set_b,B5: set_b] : ( P @ ( refine1198353289_RES_b @ A5 ) @ ( refine1198353289_RES_b @ B5 ) )
% 0.27/0.62 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % sup_nres.induct
% 0.27/0.62 thf(fact_217_less__nres_Oinduct,axiom,
% 0.27/0.62 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 0.27/0.62 ( ! [X_1: refine424419629nres_a] : ( P @ refine464223677AILi_a @ X_1 )
% 0.27/0.62 => ( ! [Uv: set_a] : ( P @ ( refine1198353288_RES_a @ Uv ) @ refine464223677AILi_a )
% 0.27/0.62 => ( ! [A5: set_a,B5: set_a] : ( P @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) )
% 0.27/0.62 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % less_nres.induct
% 0.27/0.62 thf(fact_218_less__nres_Oinduct,axiom,
% 0.27/0.62 ! [P: refine432681134nres_b > refine432681134nres_b > $o,A0: refine432681134nres_b,A1: refine432681134nres_b] :
% 0.27/0.62 ( ! [X_1: refine432681134nres_b] : ( P @ refine464223678AILi_b @ X_1 )
% 0.27/0.62 => ( ! [Uv: set_b] : ( P @ ( refine1198353289_RES_b @ Uv ) @ refine464223678AILi_b )
% 0.27/0.62 => ( ! [A5: set_b,B5: set_b] : ( P @ ( refine1198353289_RES_b @ A5 ) @ ( refine1198353289_RES_b @ B5 ) )
% 0.27/0.62 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % less_nres.induct
% 0.27/0.62 thf(fact_219_less__eq__nres_Oinduct,axiom,
% 0.27/0.62 ! [P: refine424419629nres_a > refine424419629nres_a > $o,A0: refine424419629nres_a,A1: refine424419629nres_a] :
% 0.27/0.62 ( ! [Uu: refine424419629nres_a] : ( P @ Uu @ refine464223677AILi_a )
% 0.27/0.62 => ( ! [A5: set_a,B5: set_a] : ( P @ ( refine1198353288_RES_a @ A5 ) @ ( refine1198353288_RES_a @ B5 ) )
% 0.27/0.62 => ( ! [Uv: set_a] : ( P @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv ) )
% 0.27/0.62 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % less_eq_nres.induct
% 0.27/0.62 thf(fact_220_less__eq__nres_Oinduct,axiom,
% 0.27/0.62 ! [P: refine432681134nres_b > refine432681134nres_b > $o,A0: refine432681134nres_b,A1: refine432681134nres_b] :
% 0.27/0.62 ( ! [Uu: refine432681134nres_b] : ( P @ Uu @ refine464223678AILi_b )
% 0.27/0.62 => ( ! [A5: set_b,B5: set_b] : ( P @ ( refine1198353289_RES_b @ A5 ) @ ( refine1198353289_RES_b @ B5 ) )
% 0.27/0.62 => ( ! [Uv: set_b] : ( P @ refine464223678AILi_b @ ( refine1198353289_RES_b @ Uv ) )
% 0.27/0.62 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % less_eq_nres.induct
% 0.27/0.62 thf(fact_221_less__eq__nres_Osimps_I3_J,axiom,
% 0.27/0.62 ! [Uv2: set_a] :
% 0.27/0.62 ~ ( ord_le519537037nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ Uv2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % less_eq_nres.simps(3)
% 0.27/0.62 thf(fact_222_less__eq__nres_Osimps_I3_J,axiom,
% 0.27/0.62 ! [Uv2: set_b] :
% 0.27/0.62 ~ ( ord_le527798542nres_b @ refine464223678AILi_b @ ( refine1198353289_RES_b @ Uv2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % less_eq_nres.simps(3)
% 0.27/0.62 thf(fact_223_less__eq__nres_Oelims_I3_J,axiom,
% 0.27/0.62 ! [X4: refine424419629nres_a,Xa: refine424419629nres_a] :
% 0.27/0.62 ( ~ ( ord_le519537037nres_a @ X4 @ Xa )
% 0.27/0.62 => ( ! [A5: set_a] :
% 0.27/0.62 ( ( X4
% 0.27/0.62 = ( refine1198353288_RES_a @ A5 ) )
% 0.27/0.62 => ! [B5: set_a] :
% 0.27/0.62 ( ( Xa
% 0.27/0.62 = ( refine1198353288_RES_a @ B5 ) )
% 0.27/0.62 => ( ord_less_eq_set_a @ A5 @ B5 ) ) )
% 0.27/0.62 => ~ ( ( X4 = refine464223677AILi_a )
% 0.27/0.62 => ! [Uv: set_a] :
% 0.27/0.62 ( Xa
% 0.27/0.62 != ( refine1198353288_RES_a @ Uv ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % less_eq_nres.elims(3)
% 0.27/0.62 thf(fact_224_less__eq__nres_Oelims_I3_J,axiom,
% 0.27/0.62 ! [X4: refine432681134nres_b,Xa: refine432681134nres_b] :
% 0.27/0.62 ( ~ ( ord_le527798542nres_b @ X4 @ Xa )
% 0.27/0.62 => ( ! [A5: set_b] :
% 0.27/0.62 ( ( X4
% 0.27/0.62 = ( refine1198353289_RES_b @ A5 ) )
% 0.27/0.62 => ! [B5: set_b] :
% 0.27/0.62 ( ( Xa
% 0.27/0.62 = ( refine1198353289_RES_b @ B5 ) )
% 0.27/0.62 => ( ord_less_eq_set_b @ A5 @ B5 ) ) )
% 0.27/0.62 => ~ ( ( X4 = refine464223678AILi_b )
% 0.27/0.62 => ! [Uv: set_b] :
% 0.27/0.62 ( Xa
% 0.27/0.62 != ( refine1198353289_RES_b @ Uv ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % less_eq_nres.elims(3)
% 0.27/0.62 thf(fact_225_return__refine__prop__return,axiom,
% 0.27/0.62 ! [M: refine432681134nres_b,X4: b,R: set_Product_prod_b_b] :
% 0.27/0.62 ( ( refine412683990fail_b @ M )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X4 ) @ ( refine122110613un_b_b @ R @ M ) )
% 0.27/0.62 => ~ ! [X9: b] :
% 0.27/0.62 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X4 @ X9 ) @ R )
% 0.27/0.62 => ~ ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X9 ) @ M ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % return_refine_prop_return
% 0.27/0.62 thf(fact_226_return__refine__prop__return,axiom,
% 0.27/0.62 ! [M: refine424419629nres_a,X4: b,R: set_Product_prod_b_a] :
% 0.27/0.62 ( ( refine412683989fail_a @ M )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X4 ) @ ( refine122110612un_b_a @ R @ M ) )
% 0.27/0.62 => ~ ! [X9: a] :
% 0.27/0.62 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ X4 @ X9 ) @ R )
% 0.27/0.62 => ~ ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X9 ) @ M ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % return_refine_prop_return
% 0.27/0.62 thf(fact_227_return__refine__prop__return,axiom,
% 0.27/0.62 ! [M: refine432681134nres_b,X4: a,R: set_Product_prod_a_b] :
% 0.27/0.62 ( ( refine412683990fail_b @ M )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1441824854un_a_b @ R @ M ) )
% 0.27/0.62 => ~ ! [X9: b] :
% 0.27/0.62 ( ( member458171089od_a_b @ ( product_Pair_a_b @ X4 @ X9 ) @ R )
% 0.27/0.62 => ~ ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X9 ) @ M ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % return_refine_prop_return
% 0.27/0.62 thf(fact_228_return__refine__prop__return,axiom,
% 0.27/0.62 ! [M: refine424419629nres_a,X4: a,R: set_Product_prod_a_a] :
% 0.27/0.62 ( ( refine412683989fail_a @ M )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1441824853un_a_a @ R @ M ) )
% 0.27/0.62 => ~ ! [X9: a] :
% 0.27/0.62 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X9 ) @ R )
% 0.27/0.62 => ~ ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X9 ) @ M ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % return_refine_prop_return
% 0.27/0.62 thf(fact_229_ret__le__down__conv,axiom,
% 0.27/0.62 ! [M: refine432681134nres_b,C: b,R: set_Product_prod_b_b] :
% 0.27/0.62 ( ( refine412683990fail_b @ M )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ C ) @ ( refine122110613un_b_b @ R @ M ) )
% 0.27/0.62 = ( ? [A2: b] :
% 0.27/0.62 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ A2 ) @ R )
% 0.27/0.62 & ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A2 ) @ M ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ret_le_down_conv
% 0.27/0.62 thf(fact_230_ret__le__down__conv,axiom,
% 0.27/0.62 ! [M: refine424419629nres_a,C: b,R: set_Product_prod_b_a] :
% 0.27/0.62 ( ( refine412683989fail_a @ M )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ C ) @ ( refine122110612un_b_a @ R @ M ) )
% 0.27/0.62 = ( ? [A2: a] :
% 0.27/0.62 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ C @ A2 ) @ R )
% 0.27/0.62 & ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A2 ) @ M ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ret_le_down_conv
% 0.27/0.62 thf(fact_231_ret__le__down__conv,axiom,
% 0.27/0.62 ! [M: refine432681134nres_b,C: a,R: set_Product_prod_a_b] :
% 0.27/0.62 ( ( refine412683990fail_b @ M )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ C ) @ ( refine1441824854un_a_b @ R @ M ) )
% 0.27/0.62 = ( ? [A2: b] :
% 0.27/0.62 ( ( member458171089od_a_b @ ( product_Pair_a_b @ C @ A2 ) @ R )
% 0.27/0.62 & ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ A2 ) @ M ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ret_le_down_conv
% 0.27/0.62 thf(fact_232_ret__le__down__conv,axiom,
% 0.27/0.62 ! [M: refine424419629nres_a,C: a,R: set_Product_prod_a_a] :
% 0.27/0.62 ( ( refine412683989fail_a @ M )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ C ) @ ( refine1441824853un_a_a @ R @ M ) )
% 0.27/0.62 = ( ? [A2: a] :
% 0.27/0.62 ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A2 ) @ R )
% 0.27/0.62 & ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A2 ) @ M ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ret_le_down_conv
% 0.27/0.62 thf(fact_233_nres__order__simps_I20_J,axiom,
% 0.27/0.62 ! [X4: b,Y3: b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X4 ) @ ( refine2063221605TURN_b @ Y3 ) )
% 0.27/0.62 = ( X4 = Y3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % nres_order_simps(20)
% 0.27/0.62 thf(fact_234_nres__order__simps_I20_J,axiom,
% 0.27/0.62 ! [X4: a,Y3: a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine2063221604TURN_a @ Y3 ) )
% 0.27/0.62 = ( X4 = Y3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % nres_order_simps(20)
% 0.27/0.62 thf(fact_235_nres__monad1,axiom,
% 0.27/0.62 ! [X4: a,F: a > refine432681134nres_b] :
% 0.27/0.62 ( ( refine436832839nd_a_b @ ( refine2063221604TURN_a @ X4 ) @ F )
% 0.27/0.62 = ( F @ X4 ) ) ).
% 0.27/0.62
% 0.27/0.62 % nres_monad1
% 0.27/0.62 thf(fact_236_nres__order__simps_I21_J,axiom,
% 0.27/0.62 ! [X4: a,Y: set_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1198353288_RES_a @ Y ) )
% 0.27/0.62 = ( member_a @ X4 @ Y ) ) ).
% 0.27/0.62
% 0.27/0.62 % nres_order_simps(21)
% 0.27/0.62 thf(fact_237_nres__order__simps_I21_J,axiom,
% 0.27/0.62 ! [X4: b,Y: set_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X4 ) @ ( refine1198353289_RES_b @ Y ) )
% 0.27/0.62 = ( member_b @ X4 @ Y ) ) ).
% 0.27/0.62
% 0.27/0.62 % nres_order_simps(21)
% 0.27/0.62 thf(fact_238_SPEC__eq__is__RETURN_I1_J,axiom,
% 0.27/0.62 ! [X4: a] :
% 0.27/0.62 ( ( refine1198353288_RES_a
% 0.27/0.62 @ ( collect_a
% 0.27/0.62 @ ( ^ [Y5: a,Z: a] : ( Y5 = Z )
% 0.27/0.62 @ X4 ) ) )
% 0.27/0.62 = ( refine2063221604TURN_a @ X4 ) ) ).
% 0.27/0.62
% 0.27/0.62 % SPEC_eq_is_RETURN(1)
% 0.27/0.62 thf(fact_239_SPEC__eq__is__RETURN_I1_J,axiom,
% 0.27/0.62 ! [X4: b] :
% 0.27/0.62 ( ( refine1198353289_RES_b
% 0.27/0.62 @ ( collect_b
% 0.27/0.62 @ ( ^ [Y5: b,Z: b] : ( Y5 = Z )
% 0.27/0.62 @ X4 ) ) )
% 0.27/0.62 = ( refine2063221605TURN_b @ X4 ) ) ).
% 0.27/0.62
% 0.27/0.62 % SPEC_eq_is_RETURN(1)
% 0.27/0.62 thf(fact_240_RETURN__rule,axiom,
% 0.27/0.62 ! [Phi: a > $o,X4: a] :
% 0.27/0.62 ( ( Phi @ X4 )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % RETURN_rule
% 0.27/0.62 thf(fact_241_RETURN__rule,axiom,
% 0.27/0.62 ! [Phi: b > $o,X4: b] :
% 0.27/0.62 ( ( Phi @ X4 )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X4 ) @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % RETURN_rule
% 0.27/0.62 thf(fact_242_lhs__step__RES,axiom,
% 0.27/0.62 ! [X: set_a,M: refine424419629nres_a] :
% 0.27/0.62 ( ! [X3: a] :
% 0.27/0.62 ( ( member_a @ X3 @ X )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ X ) @ M ) ) ).
% 0.27/0.62
% 0.27/0.62 % lhs_step_RES
% 0.27/0.62 thf(fact_243_lhs__step__RES,axiom,
% 0.27/0.62 ! [X: set_b,M: refine432681134nres_b] :
% 0.27/0.62 ( ! [X3: b] :
% 0.27/0.62 ( ( member_b @ X3 @ X )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X3 ) @ M ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( refine1198353289_RES_b @ X ) @ M ) ) ).
% 0.27/0.62
% 0.27/0.62 % lhs_step_RES
% 0.27/0.62 thf(fact_244_RETURN__to__SPEC__rule,axiom,
% 0.27/0.62 ! [M: refine424419629nres_a,V2: a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ M
% 0.27/0.62 @ ( refine1198353288_RES_a
% 0.27/0.62 @ ( collect_a
% 0.27/0.62 @ ( ^ [Y5: a,Z: a] : ( Y5 = Z )
% 0.27/0.62 @ V2 ) ) ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ M @ ( refine2063221604TURN_a @ V2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % RETURN_to_SPEC_rule
% 0.27/0.62 thf(fact_245_RETURN__to__SPEC__rule,axiom,
% 0.27/0.62 ! [M: refine432681134nres_b,V2: b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ M
% 0.27/0.62 @ ( refine1198353289_RES_b
% 0.27/0.62 @ ( collect_b
% 0.27/0.62 @ ( ^ [Y5: b,Z: b] : ( Y5 = Z )
% 0.27/0.62 @ V2 ) ) ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ M @ ( refine2063221605TURN_b @ V2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % RETURN_to_SPEC_rule
% 0.27/0.62 thf(fact_246_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.27/0.62 ! [M4: refine432681134nres_b,M3: refine432681134nres_b,F: b > refine432681134nres_b,F2: b > refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ M4 @ M3 )
% 0.27/0.62 => ( ! [X3: b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X3 ) @ M4 )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F2 @ X3 ) ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( refine1264602246nd_b_b @ M4 @ F ) @ ( refine1264602246nd_b_b @ M3 @ F2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(1)
% 0.27/0.62 thf(fact_247_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.27/0.62 ! [M4: refine432681134nres_b,M3: refine432681134nres_b,F: b > refine424419629nres_a,F2: b > refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ M4 @ M3 )
% 0.27/0.62 => ( ! [X3: b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X3 ) @ M4 )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F2 @ X3 ) ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( refine1264602245nd_b_a @ M4 @ F ) @ ( refine1264602245nd_b_a @ M3 @ F2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(1)
% 0.27/0.62 thf(fact_248_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.27/0.62 ! [M4: refine424419629nres_a,M3: refine424419629nres_a,F: a > refine424419629nres_a,F2: a > refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ M4 @ M3 )
% 0.27/0.62 => ( ! [X3: a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M4 )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( F @ X3 ) @ ( F2 @ X3 ) ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ M4 @ F ) @ ( refine436832838nd_a_a @ M3 @ F2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(1)
% 0.27/0.62 thf(fact_249_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J,axiom,
% 0.27/0.62 ! [M4: refine424419629nres_a,M3: refine424419629nres_a,F: a > refine432681134nres_b,F2: a > refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ M4 @ M3 )
% 0.27/0.62 => ( ! [X3: a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M4 )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( F @ X3 ) @ ( F2 @ X3 ) ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( refine436832839nd_a_b @ M4 @ F ) @ ( refine436832839nd_a_b @ M3 @ F2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(1)
% 0.27/0.62 thf(fact_250_bind__cong,axiom,
% 0.27/0.62 ! [M: refine424419629nres_a,M7: refine424419629nres_a,F: a > refine432681134nres_b,F2: a > refine432681134nres_b] :
% 0.27/0.62 ( ( M = M7 )
% 0.27/0.62 => ( ! [X3: a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X3 ) @ M7 )
% 0.27/0.62 => ( ( F @ X3 )
% 0.27/0.62 = ( F2 @ X3 ) ) )
% 0.27/0.62 => ( ( refine436832839nd_a_b @ M @ F )
% 0.27/0.62 = ( refine436832839nd_a_b @ M7 @ F2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % bind_cong
% 0.27/0.62 thf(fact_251_inres__def,axiom,
% 0.27/0.62 ( refine1001002028nres_b
% 0.27/0.62 = ( ^ [S4: refine432681134nres_b,X5: b] : ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X5 ) @ S4 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % inres_def
% 0.27/0.62 thf(fact_252_inres__def,axiom,
% 0.27/0.62 ( refine1001002027nres_a
% 0.27/0.62 = ( ^ [S4: refine424419629nres_a,X5: a] : ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X5 ) @ S4 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % inres_def
% 0.27/0.62 thf(fact_253_RETURN__ref__SPECD,axiom,
% 0.27/0.62 ! [C: b,R: set_Product_prod_b_a,Phi: a > $o] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ C ) @ ( refine122110612un_b_a @ R @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) )
% 0.27/0.62 => ~ ! [A5: a] :
% 0.27/0.62 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ C @ A5 ) @ R )
% 0.27/0.62 => ~ ( Phi @ A5 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % RETURN_ref_SPECD
% 0.27/0.62 thf(fact_254_RETURN__ref__SPECD,axiom,
% 0.27/0.62 ! [C: a,R: set_Product_prod_a_a,Phi: a > $o] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ C ) @ ( refine1441824853un_a_a @ R @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) )
% 0.27/0.62 => ~ ! [A5: a] :
% 0.27/0.62 ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A5 ) @ R )
% 0.27/0.62 => ~ ( Phi @ A5 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % RETURN_ref_SPECD
% 0.27/0.62 thf(fact_255_RETURN__ref__SPECD,axiom,
% 0.27/0.62 ! [C: b,R: set_Product_prod_b_b,Phi: b > $o] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ C ) @ ( refine122110613un_b_b @ R @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) )
% 0.27/0.62 => ~ ! [A5: b] :
% 0.27/0.62 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ A5 ) @ R )
% 0.27/0.62 => ~ ( Phi @ A5 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % RETURN_ref_SPECD
% 0.27/0.62 thf(fact_256_RETURN__ref__SPECD,axiom,
% 0.27/0.62 ! [C: a,R: set_Product_prod_a_b,Phi: b > $o] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ C ) @ ( refine1441824854un_a_b @ R @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) )
% 0.27/0.62 => ~ ! [A5: b] :
% 0.27/0.62 ( ( member458171089od_a_b @ ( product_Pair_a_b @ C @ A5 ) @ R )
% 0.27/0.62 => ~ ( Phi @ A5 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % RETURN_ref_SPECD
% 0.27/0.62 thf(fact_257_RETURN__SPEC__refine,axiom,
% 0.27/0.62 ! [X4: b,R: set_Product_prod_b_a,Phi: a > $o] :
% 0.27/0.62 ( ? [X11: a] :
% 0.27/0.62 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ X4 @ X11 ) @ R )
% 0.27/0.62 & ( Phi @ X11 ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X4 ) @ ( refine122110612un_b_a @ R @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % RETURN_SPEC_refine
% 0.27/0.62 thf(fact_258_RETURN__SPEC__refine,axiom,
% 0.27/0.62 ! [X4: a,R: set_Product_prod_a_a,Phi: a > $o] :
% 0.27/0.62 ( ? [X11: a] :
% 0.27/0.62 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X11 ) @ R )
% 0.27/0.62 & ( Phi @ X11 ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1441824853un_a_a @ R @ ( refine1198353288_RES_a @ ( collect_a @ Phi ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % RETURN_SPEC_refine
% 0.27/0.62 thf(fact_259_RETURN__SPEC__refine,axiom,
% 0.27/0.62 ! [X4: b,R: set_Product_prod_b_b,Phi: b > $o] :
% 0.27/0.62 ( ? [X11: b] :
% 0.27/0.62 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X4 @ X11 ) @ R )
% 0.27/0.62 & ( Phi @ X11 ) )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( refine2063221605TURN_b @ X4 ) @ ( refine122110613un_b_b @ R @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % RETURN_SPEC_refine
% 0.27/0.62 thf(fact_260_RETURN__SPEC__refine,axiom,
% 0.27/0.62 ! [X4: a,R: set_Product_prod_a_b,Phi: b > $o] :
% 0.27/0.62 ( ? [X11: b] :
% 0.27/0.62 ( ( member458171089od_a_b @ ( product_Pair_a_b @ X4 @ X11 ) @ R )
% 0.27/0.62 & ( Phi @ X11 ) )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ X4 ) @ ( refine1441824854un_a_b @ R @ ( refine1198353289_RES_b @ ( collect_b @ Phi ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % RETURN_SPEC_refine
% 0.27/0.62 thf(fact_261_abs__trans__additional_I1_J,axiom,
% 0.27/0.62 ! [A3: refine432681134nres_b,B3: refine432681134nres_b,R: set_Product_prod_b_b,C2: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ A3 @ B3 )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ R @ B3 ) @ C2 )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( refine1964549110un_b_b @ R @ A3 ) @ C2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % abs_trans_additional(1)
% 0.27/0.62 thf(fact_262_abs__trans__additional_I1_J,axiom,
% 0.27/0.62 ! [A3: refine432681134nres_b,B3: refine432681134nres_b,R: set_Product_prod_b_a,C2: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ A3 @ B3 )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ ( refine1964549109un_b_a @ R @ B3 ) @ C2 )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( refine1964549109un_b_a @ R @ A3 ) @ C2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % abs_trans_additional(1)
% 0.27/0.62 thf(fact_263_abs__trans__additional_I1_J,axiom,
% 0.27/0.62 ! [A3: refine424419629nres_a,B3: refine424419629nres_a,R: set_Product_prod_a_b,C2: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ A3 @ B3 )
% 0.27/0.62 => ( ( ord_le527798542nres_b @ ( refine1136779703un_a_b @ R @ B3 ) @ C2 )
% 0.27/0.62 => ( ord_le527798542nres_b @ ( refine1136779703un_a_b @ R @ A3 ) @ C2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % abs_trans_additional(1)
% 0.27/0.62 thf(fact_264_abs__trans__additional_I1_J,axiom,
% 0.27/0.62 ! [A3: refine424419629nres_a,B3: refine424419629nres_a,R: set_Product_prod_a_a,C2: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ A3 @ B3 )
% 0.27/0.62 => ( ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ B3 ) @ C2 )
% 0.27/0.62 => ( ord_le519537037nres_a @ ( refine1136779702un_a_a @ R @ A3 ) @ C2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % abs_trans_additional(1)
% 0.27/0.62 thf(fact_265_abs__fun__simps_I3_J,axiom,
% 0.27/0.62 ! [X: set_a,R: set_Pr1628433942t_unit] :
% 0.27/0.62 ( ~ ( ord_less_eq_set_a @ X @ ( domain799550107t_unit @ R ) )
% 0.27/0.62 => ( ( refine341651653t_unit @ R @ ( refine1198353288_RES_a @ X ) )
% 0.27/0.62 = top_to177290092t_unit ) ) ).
% 0.27/0.62
% 0.27/0.62 % abs_fun_simps(3)
% 0.27/0.62 thf(fact_266_abs__fun__simps_I3_J,axiom,
% 0.27/0.62 ! [X: set_b,R: set_Pr1707992533t_unit] :
% 0.27/0.62 ( ~ ( ord_less_eq_set_b @ X @ ( domain918802906t_unit @ R ) )
% 0.27/0.62 => ( ( refine460904452t_unit @ R @ ( refine1198353289_RES_b @ X ) )
% 0.27/0.62 = top_to177290092t_unit ) ) ).
% 0.27/0.62
% 0.27/0.62 % abs_fun_simps(3)
% 0.27/0.62 thf(fact_267_abs__fun__simps_I2_J,axiom,
% 0.27/0.62 ! [X: set_a,R: set_Product_prod_a_a] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ X @ ( domain_a_a @ R ) )
% 0.27/0.62 => ( ( refine1136779702un_a_a @ R @ ( refine1198353288_RES_a @ X ) )
% 0.27/0.62 = ( refine1198353288_RES_a @ ( image_a_a @ R @ X ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % abs_fun_simps(2)
% 0.27/0.62 thf(fact_268_abs__fun__simps_I2_J,axiom,
% 0.27/0.62 ! [X: set_a,R: set_Product_prod_a_b] :
% 0.27/0.62 ( ( ord_less_eq_set_a @ X @ ( domain_a_b @ R ) )
% 0.27/0.62 => ( ( refine1136779703un_a_b @ R @ ( refine1198353288_RES_a @ X ) )
% 0.27/0.62 = ( refine1198353289_RES_b @ ( image_a_b @ R @ X ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % abs_fun_simps(2)
% 0.27/0.62 thf(fact_269_abs__fun__simps_I2_J,axiom,
% 0.27/0.62 ! [X: set_b,R: set_Product_prod_b_a] :
% 0.27/0.62 ( ( ord_less_eq_set_b @ X @ ( domain_b_a @ R ) )
% 0.27/0.62 => ( ( refine1964549109un_b_a @ R @ ( refine1198353289_RES_b @ X ) )
% 0.27/0.62 = ( refine1198353288_RES_a @ ( image_b_a @ R @ X ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % abs_fun_simps(2)
% 0.27/0.62 thf(fact_270_abs__fun__simps_I2_J,axiom,
% 0.27/0.62 ! [X: set_b,R: set_Product_prod_b_b] :
% 0.27/0.62 ( ( ord_less_eq_set_b @ X @ ( domain_b_b @ R ) )
% 0.27/0.62 => ( ( refine1964549110un_b_b @ R @ ( refine1198353289_RES_b @ X ) )
% 0.27/0.62 = ( refine1198353289_RES_b @ ( image_b_b @ R @ X ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % abs_fun_simps(2)
% 0.27/0.62 thf(fact_271_ImageI,axiom,
% 0.27/0.62 ! [A: a,B: a,R2: set_Product_prod_a_a,A3: set_a] :
% 0.27/0.62 ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ R2 )
% 0.27/0.62 => ( ( member_a @ A @ A3 )
% 0.27/0.62 => ( member_a @ B @ ( image_a_a @ R2 @ A3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ImageI
% 0.27/0.62 thf(fact_272_ImageI,axiom,
% 0.27/0.62 ! [A: a,B: b,R2: set_Product_prod_a_b,A3: set_a] :
% 0.27/0.62 ( ( member458171089od_a_b @ ( product_Pair_a_b @ A @ B ) @ R2 )
% 0.27/0.62 => ( ( member_a @ A @ A3 )
% 0.27/0.62 => ( member_b @ B @ ( image_a_b @ R2 @ A3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ImageI
% 0.27/0.62 thf(fact_273_ImageI,axiom,
% 0.27/0.62 ! [A: b,B: a,R2: set_Product_prod_b_a,A3: set_b] :
% 0.27/0.62 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ A @ B ) @ R2 )
% 0.27/0.62 => ( ( member_b @ A @ A3 )
% 0.27/0.62 => ( member_a @ B @ ( image_b_a @ R2 @ A3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ImageI
% 0.27/0.62 thf(fact_274_ImageI,axiom,
% 0.27/0.62 ! [A: b,B: b,R2: set_Product_prod_b_b,A3: set_b] :
% 0.27/0.62 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ R2 )
% 0.27/0.62 => ( ( member_b @ A @ A3 )
% 0.27/0.62 => ( member_b @ B @ ( image_b_b @ R2 @ A3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ImageI
% 0.27/0.62 thf(fact_275_nres__order__simps_I4_J,axiom,
% 0.27/0.62 ! [M4: refine787176636t_unit] :
% 0.27/0.62 ( ( ord_le1051254044t_unit @ top_to177290092t_unit @ M4 )
% 0.27/0.62 = ( M4 = top_to177290092t_unit ) ) ).
% 0.27/0.62
% 0.27/0.62 % nres_order_simps(4)
% 0.27/0.62 thf(fact_276_nres__order__simps_I4_J,axiom,
% 0.27/0.62 ! [M4: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ top_to240090974nres_b @ M4 )
% 0.27/0.62 = ( M4 = top_to240090974nres_b ) ) ).
% 0.27/0.62
% 0.27/0.62 % nres_order_simps(4)
% 0.27/0.62 thf(fact_277_nres__order__simps_I4_J,axiom,
% 0.27/0.62 ! [M4: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ M4 )
% 0.27/0.62 = ( M4 = top_to231829469nres_a ) ) ).
% 0.27/0.62
% 0.27/0.62 % nres_order_simps(4)
% 0.27/0.62 thf(fact_278_conc__fun__FAIL,axiom,
% 0.27/0.62 ! [R: set_Pr451126599t_unit] :
% 0.27/0.62 ( ( refine944483349t_unit @ R @ top_to177290092t_unit )
% 0.27/0.62 = top_to177290092t_unit ) ).
% 0.27/0.62
% 0.27/0.62 % conc_fun_FAIL
% 0.27/0.62 thf(fact_279_conc__fun__fail__iff_I1_J,axiom,
% 0.27/0.62 ! [R: set_Pr451126599t_unit,S: refine787176636t_unit] :
% 0.27/0.62 ( ( ( refine944483349t_unit @ R @ S )
% 0.27/0.62 = top_to177290092t_unit )
% 0.27/0.62 = ( S = top_to177290092t_unit ) ) ).
% 0.27/0.62
% 0.27/0.62 % conc_fun_fail_iff(1)
% 0.27/0.62 thf(fact_280_conc__fun__fail__iff_I2_J,axiom,
% 0.27/0.62 ! [R: set_Pr451126599t_unit,S: refine787176636t_unit] :
% 0.27/0.62 ( ( top_to177290092t_unit
% 0.27/0.62 = ( refine944483349t_unit @ R @ S ) )
% 0.27/0.62 = ( S = top_to177290092t_unit ) ) ).
% 0.27/0.62
% 0.27/0.62 % conc_fun_fail_iff(2)
% 0.27/0.62 thf(fact_281_bind__FAIL,axiom,
% 0.27/0.62 ! [F: product_unit > refine787176636t_unit] :
% 0.27/0.62 ( ( refine681446406t_unit @ top_to177290092t_unit @ F )
% 0.27/0.62 = top_to177290092t_unit ) ).
% 0.27/0.62
% 0.27/0.62 % bind_FAIL
% 0.27/0.62 thf(fact_282_bind__FAIL,axiom,
% 0.27/0.62 ! [F: a > refine432681134nres_b] :
% 0.27/0.62 ( ( refine436832839nd_a_b @ top_to231829469nres_a @ F )
% 0.27/0.62 = top_to240090974nres_b ) ).
% 0.27/0.62
% 0.27/0.62 % bind_FAIL
% 0.27/0.62 thf(fact_283_nofail__simps_I1_J,axiom,
% 0.27/0.62 ~ ( refine579265252t_unit @ top_to177290092t_unit ) ).
% 0.27/0.62
% 0.27/0.62 % nofail_simps(1)
% 0.27/0.62 thf(fact_284_inres__simps_I1_J,axiom,
% 0.27/0.62 ( ( refine558004794t_unit @ top_to177290092t_unit )
% 0.27/0.62 = ( ^ [Uu3: product_unit] : $true ) ) ).
% 0.27/0.62
% 0.27/0.62 % inres_simps(1)
% 0.27/0.62 thf(fact_285_nres__simp__internals_I2_J,axiom,
% 0.27/0.62 refine1607584204t_unit = top_to177290092t_unit ).
% 0.27/0.62
% 0.27/0.62 % nres_simp_internals(2)
% 0.27/0.62 thf(fact_286_abs__fun__simps_I1_J,axiom,
% 0.27/0.62 ! [R: set_Pr451126599t_unit] :
% 0.27/0.62 ( ( refine838861686t_unit @ R @ top_to177290092t_unit )
% 0.27/0.62 = top_to177290092t_unit ) ).
% 0.27/0.62
% 0.27/0.62 % abs_fun_simps(1)
% 0.27/0.62 thf(fact_287_FAIL__refine,axiom,
% 0.27/0.62 ! [X: refine432681134nres_b,R: set_Pr1707992533t_unit] : ( ord_le527798542nres_b @ X @ ( refine2140306339t_unit @ R @ top_to177290092t_unit ) ) ).
% 0.27/0.62
% 0.27/0.62 % FAIL_refine
% 0.27/0.62 thf(fact_288_FAIL__refine,axiom,
% 0.27/0.62 ! [X: refine424419629nres_a,R: set_Pr1628433942t_unit] : ( ord_le519537037nres_a @ X @ ( refine2021053540t_unit @ R @ top_to177290092t_unit ) ) ).
% 0.27/0.62
% 0.27/0.62 % FAIL_refine
% 0.27/0.62 thf(fact_289_rev__ImageI,axiom,
% 0.27/0.62 ! [A: a,A3: set_a,B: a,R2: set_Product_prod_a_a] :
% 0.27/0.62 ( ( member_a @ A @ A3 )
% 0.27/0.62 => ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ R2 )
% 0.27/0.62 => ( member_a @ B @ ( image_a_a @ R2 @ A3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_ImageI
% 0.27/0.62 thf(fact_290_rev__ImageI,axiom,
% 0.27/0.62 ! [A: a,A3: set_a,B: b,R2: set_Product_prod_a_b] :
% 0.27/0.62 ( ( member_a @ A @ A3 )
% 0.27/0.62 => ( ( member458171089od_a_b @ ( product_Pair_a_b @ A @ B ) @ R2 )
% 0.27/0.62 => ( member_b @ B @ ( image_a_b @ R2 @ A3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_ImageI
% 0.27/0.62 thf(fact_291_rev__ImageI,axiom,
% 0.27/0.62 ! [A: b,A3: set_b,B: a,R2: set_Product_prod_b_a] :
% 0.27/0.62 ( ( member_b @ A @ A3 )
% 0.27/0.62 => ( ( member1277678991od_b_a @ ( product_Pair_b_a @ A @ B ) @ R2 )
% 0.27/0.62 => ( member_a @ B @ ( image_b_a @ R2 @ A3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_ImageI
% 0.27/0.62 thf(fact_292_rev__ImageI,axiom,
% 0.27/0.62 ! [A: b,A3: set_b,B: b,R2: set_Product_prod_b_b] :
% 0.27/0.62 ( ( member_b @ A @ A3 )
% 0.27/0.62 => ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ R2 )
% 0.27/0.62 => ( member_b @ B @ ( image_b_b @ R2 @ A3 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_ImageI
% 0.27/0.62 thf(fact_293_ImageE,axiom,
% 0.27/0.62 ! [B: a,R2: set_Product_prod_a_a,A3: set_a] :
% 0.27/0.62 ( ( member_a @ B @ ( image_a_a @ R2 @ A3 ) )
% 0.27/0.62 => ~ ! [X3: a] :
% 0.27/0.62 ( ( member449909584od_a_a @ ( product_Pair_a_a @ X3 @ B ) @ R2 )
% 0.27/0.62 => ~ ( member_a @ X3 @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ImageE
% 0.27/0.62 thf(fact_294_ImageE,axiom,
% 0.27/0.62 ! [B: a,R2: set_Product_prod_b_a,A3: set_b] :
% 0.27/0.62 ( ( member_a @ B @ ( image_b_a @ R2 @ A3 ) )
% 0.27/0.62 => ~ ! [X3: b] :
% 0.27/0.62 ( ( member1277678991od_b_a @ ( product_Pair_b_a @ X3 @ B ) @ R2 )
% 0.27/0.62 => ~ ( member_b @ X3 @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ImageE
% 0.27/0.62 thf(fact_295_ImageE,axiom,
% 0.27/0.62 ! [B: b,R2: set_Product_prod_a_b,A3: set_a] :
% 0.27/0.62 ( ( member_b @ B @ ( image_a_b @ R2 @ A3 ) )
% 0.27/0.62 => ~ ! [X3: a] :
% 0.27/0.62 ( ( member458171089od_a_b @ ( product_Pair_a_b @ X3 @ B ) @ R2 )
% 0.27/0.62 => ~ ( member_a @ X3 @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ImageE
% 0.27/0.62 thf(fact_296_ImageE,axiom,
% 0.27/0.62 ! [B: b,R2: set_Product_prod_b_b,A3: set_b] :
% 0.27/0.62 ( ( member_b @ B @ ( image_b_b @ R2 @ A3 ) )
% 0.27/0.62 => ~ ! [X3: b] :
% 0.27/0.62 ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X3 @ B ) @ R2 )
% 0.27/0.62 => ~ ( member_b @ X3 @ A3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ImageE
% 0.27/0.62 thf(fact_297_nres__inequalities_I3_J,axiom,
% 0.27/0.62 ! [X4: product_unit] :
% 0.27/0.62 ( top_to177290092t_unit
% 0.27/0.62 != ( refine1420258419t_unit @ X4 ) ) ).
% 0.27/0.62
% 0.27/0.62 % nres_inequalities(3)
% 0.27/0.62 thf(fact_298_top__nres__def,axiom,
% 0.27/0.62 top_to177290092t_unit = refine1607584204t_unit ).
% 0.27/0.62
% 0.27/0.62 % top_nres_def
% 0.27/0.62 thf(fact_299_top__greatest,axiom,
% 0.27/0.62 ! [A: refine787176636t_unit] : ( ord_le1051254044t_unit @ A @ top_to177290092t_unit ) ).
% 0.27/0.62
% 0.27/0.62 % top_greatest
% 0.27/0.62 thf(fact_300_top__greatest,axiom,
% 0.27/0.62 ! [A: refine432681134nres_b] : ( ord_le527798542nres_b @ A @ top_to240090974nres_b ) ).
% 0.27/0.62
% 0.27/0.62 % top_greatest
% 0.27/0.62 thf(fact_301_top__greatest,axiom,
% 0.27/0.62 ! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ top_to231829469nres_a ) ).
% 0.27/0.62
% 0.27/0.62 % top_greatest
% 0.27/0.62 thf(fact_302_top_Oextremum__unique,axiom,
% 0.27/0.62 ! [A: refine787176636t_unit] :
% 0.27/0.62 ( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
% 0.27/0.62 = ( A = top_to177290092t_unit ) ) ).
% 0.27/0.62
% 0.27/0.62 % top.extremum_unique
% 0.27/0.62 thf(fact_303_top_Oextremum__unique,axiom,
% 0.27/0.62 ! [A: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ top_to240090974nres_b @ A )
% 0.27/0.62 = ( A = top_to240090974nres_b ) ) ).
% 0.27/0.62
% 0.27/0.62 % top.extremum_unique
% 0.27/0.62 thf(fact_304_top_Oextremum__unique,axiom,
% 0.27/0.62 ! [A: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
% 0.27/0.62 = ( A = top_to231829469nres_a ) ) ).
% 0.27/0.62
% 0.27/0.62 % top.extremum_unique
% 0.27/0.62 thf(fact_305_top_Oextremum__uniqueI,axiom,
% 0.27/0.62 ! [A: refine787176636t_unit] :
% 0.27/0.62 ( ( ord_le1051254044t_unit @ top_to177290092t_unit @ A )
% 0.27/0.62 => ( A = top_to177290092t_unit ) ) ).
% 0.27/0.62
% 0.27/0.62 % top.extremum_uniqueI
% 0.27/0.62 thf(fact_306_top_Oextremum__uniqueI,axiom,
% 0.27/0.62 ! [A: refine432681134nres_b] :
% 0.27/0.62 ( ( ord_le527798542nres_b @ top_to240090974nres_b @ A )
% 0.27/0.62 => ( A = top_to240090974nres_b ) ) ).
% 0.27/0.62
% 0.27/0.62 % top.extremum_uniqueI
% 0.27/0.62 thf(fact_307_top_Oextremum__uniqueI,axiom,
% 0.27/0.62 ! [A: refine424419629nres_a] :
% 0.27/0.62 ( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
% 0.27/0.62 => ( A = top_to231829469nres_a ) ) ).
% 0.27/0.62
% 0.27/0.62 % top.extremum_uniqueI
% 0.27/0.62 thf(fact_308_nres__order__simps_I3_J,axiom,
% 0.27/0.62 ! [M4: refine787176636t_unit] : ( ord_le1051254044t_unit @ M4 @ top_to177290092t_unit ) ).
% 0.27/0.62
% 0.27/0.62 % nres_order_simps(3)
% 0.27/0.62 thf(fact_309_nres__order__simps_I3_J,axiom,
% 0.27/0.62 ! [M4: refine432681134nres_b] : ( ord_le527798542nres_b @ M4 @ top_to240090974nres_b ) ).
% 0.27/0.62
% 0.27/0.62 % nres_order_simps(3)
% 0.27/0.62 thf(fact_310_nres__order__simps_I3_J,axiom,
% 0.27/0.62 ! [M4: refine424419629nres_a] : ( ord_le519537037nres_a @ M4 @ top_to231829469nres_a ) ).
% 0.27/0.62
% 0.27/0.62 % nres_order_simps(3)
% 0.27/0.62 thf(fact_311_nres__inequalities_I1_J,axiom,
% 0.27/0.62 ! [X: set_Product_unit] :
% 0.27/0.62 ( top_to177290092t_unit
% 0.27/0.62 != ( refine1777164439t_unit @ X ) ) ).
% 0.27/0.62
% 0.27/0.62 % nres_inequalities(1)
% 0.27/0.62 thf(fact_312_nres__inequalities_I1_J,axiom,
% 0.27/0.62 ! [X: set_a] :
% 0.27/0.62 ( top_to231829469nres_a
% 0.27/0.62 != ( refine1198353288_RES_a @ X ) ) ).
% 0.27/0.62
% 0.27/0.62 % nres_inequalities(1)
% 0.27/0.62 thf(fact_313_nres__inequalities_I1_J,axiom,
% 0.27/0.62 ! [X: set_b] :
% 0.27/0.62 ( top_to240090974nres_b
% 0.27/0.62 != ( refine1198353289_RES_b @ X ) ) ).
% 0.27/0.62
% 0.27/0.62 % nres_inequalities(1)
% 0.27/0.62 thf(fact_314_nres__cases,axiom,
% 0.27/0.62 ! [M4: refine787176636t_unit] :
% 0.27/0.62 ( ( M4 != top_to177290092t_unit )
% 0.27/0.62 => ~ ! [X12: set_Product_unit] :
% 0.27/0.62 ( M4
% 0.27/0.62 != ( refine1777164439t_unit @ X12 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % nres_cases
% 0.27/0.62 thf(fact_315_nres__cases,axiom,
% 0.27/0.62 ! [M4: refine424419629nres_a] :
% 0.27/0.62 ( ( M4 != top_to231829469nres_a )
% 0.27/0.62 => ~ ! [X12: set_a] :
% 0.27/0.62 ( M4
% 0.27/0.62 != ( refine1198353288_RES_a @ X12 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % nres_cases
% 0.27/0.62 thf(fact_316_nres__cases,axiom,
% 0.27/0.62 ! [M4: refine432681134nres_b] :
% 0.27/0.62 ( ( M4 != top_to240090974nres_b )
% 0.27/0.62 => ~ ! [X12: set_b] :
% 0.27/0.62 ( M4
% 0.27/0.62 != ( refine1198353289_RES_b @ X12 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % nres_cases
% 0.27/0.62 thf(fact_317_not__nofail__iff,axiom,
% 0.27/0.62 ! [S: refine787176636t_unit] :
% 0.27/0.62 ( ( ~ ( refine579265252t_unit @ S ) )
% 0.27/0.62 = ( S = top_to177290092t_unit ) ) ).
% 0.27/0.62
% 0.27/0.62 % not_nofail_iff
% 0.27/0.62 thf(fact_318_nofail__def,axiom,
% 0.27/0.62 ( refine579265252t_unit
% 0.27/0.62 = ( ^ [S4: refine787176636t_unit] : ( S4 != top_to177290092t_unit ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % nofail_def
% 0.27/0.62 thf(fact_319_intro__nofail_I2_J,axiom,
% 0.27/0.62 ! [S: refine787176636t_unit] :
% 0.27/0.62 ( ( top_to177290092t_unit != S )
% 0.27/0.62 = ( refine579265252t_unit @ S ) ) ).
% 0.27/0.62
% 0.27/0.62 % intro_nofail(2)
% 0.27/0.62 thf(fact_320_ibind__strict_I2_J,axiom,
% 0.27/0.62 ! [F: product_unit > refine787176636t_unit] :
% 0.27/0.62 ( ( refine681446406t_unit @ top_to177290092t_unit @ F )
% 0.27/0.62 = top_to177290092t_unit ) ).
% 0.27/0.62
% 0.27/0.62 % ibind_strict(2)
% 0.27/0.62 thf(fact_321_meta__le__everything__if__top,axiom,
% 0.27/0.62 ! [M: refine787176636t_unit,X4: refine787176636t_unit] :
% 0.27/0.62 ( ( M = top_to177290092t_unit )
% 0.27/0.62 => ( ord_le1051254044t_unit @ X4 @ M ) ) ).
% 0.27/0.62
% 0.27/0.62 % meta_le_everything_if_top
% 0.27/0.62 thf(fact_322_meta__le__everything__if__top,axiom,
% 0.27/0.62 ! [M: refine432681134nres_b,X4: refine432681134nres_b] :
% 0.27/0.62 ( ( M = top_to240090974nres_b )
% 0.27/0.62 => ( ord_le527798542nres_b @ X4 @ M ) ) ).
% 0.27/0.62
% 0.27/0.62 % meta_le_everything_if_top
% 0.27/0.62 thf(fact_323_meta__le__everything__if__top,axiom,
% 0.27/0.62 ! [M: refine424419629nres_a,X4: refine424419629nres_a] :
% 0.27/0.62 ( ( M = top_to231829469nres_a )
% 0.27/0.62 => ( ord_le519537037nres_a @ X4 @ M ) ) ).
% 0.27/0.62
% 0.27/0.62 % meta_le_everything_if_top
% 0.27/0.62 thf(fact_324_pw__flat__ge__iff,axiom,
% 0.27/0.62 ! [S: refine787176636t_unit,S3: refine787176636t_unit] :
% 0.27/0.62 ( ( partia1658438072t_unit @ top_to177290092t_unit @ S @ S3 )
% 0.27/0.62 = ( ( refine579265252t_unit @ S )
% 0.27/0.62 => ( ( refine579265252t_unit @ S3 )
% 0.27/0.62 & ! [X5: product_unit] :
% 0.27/0.62 ( ( refine558004794t_unit @ S @ X5 )
% 0.27/0.62 = ( refine558004794t_unit @ S3 @ X5 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % pw_flat_ge_iff
% 0.27/0.62 thf(fact_325_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J,axiom,
% 0.27/0.62 ! [M4: refine787176636t_unit,M3: refine787176636t_unit,F: product_unit > refine787176636t_unit,F2: product_unit > refine787176636t_unit] :
% 0.27/0.62 ( ( partia1658438072t_unit @ top_to177290092t_unit @ M4 @ M3 )
% 0.27/0.62 => ( ! [X3: product_unit] : ( partia1658438072t_unit @ top_to177290092t_unit @ ( F @ X3 ) @ ( F2 @ X3 ) )
% 0.27/0.62 => ( partia1658438072t_unit @ top_to177290092t_unit @ ( refine681446406t_unit @ M4 @ F ) @ ( refine681446406t_unit @ M3 @ F2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(2)
% 0.27/0.62 thf(fact_326_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I2_J,axiom,
% 0.27/0.62 ! [M4: refine424419629nres_a,M3: refine424419629nres_a,F: a > refine432681134nres_b,F2: a > refine432681134nres_b] :
% 0.27/0.62 ( ( partia906949161nres_a @ top_to231829469nres_a @ M4 @ M3 )
% 0.27/0.62 => ( ! [X3: a] : ( partia915210666nres_b @ top_to240090974nres_b @ ( F @ X3 ) @ ( F2 @ X3 ) )
% 0.27/0.62 => ( partia915210666nres_b @ top_to240090974nres_b @ ( refine436832839nd_a_b @ M4 @ F ) @ ( refine436832839nd_a_b @ M3 @ F2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Refine_Basic_Mirabelle_kwjuvthmas.bind_mono(2)
% 0.27/0.62 thf(fact_327_flat__ord__compat_I2_J,axiom,
% 0.27/0.62 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.27/0.62 ( ( partia1658438072t_unit @ top_to177290092t_unit @ X4 @ Y3 )
% 0.27/0.62 => ( ord_le1051254044t_unit @ Y3 @ X4 ) ) ).
% 0.27/0.62
% 0.27/0.62 % flat_ord_compat(2)
% 0.27/0.62 thf(fact_328_flat__ord__compat_I2_J,axiom,
% 0.27/0.62 ! [X4: refine432681134nres_b,Y3: refine432681134nres_b] :
% 0.27/0.62 ( ( partia915210666nres_b @ top_to240090974nres_b @ X4 @ Y3 )
% 0.27/0.62 => ( ord_le527798542nres_b @ Y3 @ X4 ) ) ).
% 0.27/0.62
% 0.27/0.62 % flat_ord_compat(2)
% 0.27/0.62 thf(fact_329_flat__ord__compat_I2_J,axiom,
% 0.27/0.62 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.27/0.62 ( ( partia906949161nres_a @ top_to231829469nres_a @ X4 @ Y3 )
% 0.27/0.62 => ( ord_le519537037nres_a @ Y3 @ X4 ) ) ).
% 0.27/0.62
% 0.27/0.62 % flat_ord_compat(2)
% 0.27/0.62 thf(fact_330_UNIV__I,axiom,
% 0.27/0.62 ! [X4: a] : ( member_a @ X4 @ top_top_set_a ) ).
% 0.27/0.62
% 0.27/0.62 % UNIV_I
% 0.27/0.62 thf(fact_331_UNIV__I,axiom,
% 0.27/0.62 ! [X4: b] : ( member_b @ X4 @ top_top_set_b ) ).
% 0.27/0.62
% 0.27/0.62 % UNIV_I
% 0.27/0.62 thf(fact_332_eq__UNIV__iff,axiom,
% 0.27/0.62 ! [S: set_a] :
% 0.27/0.62 ( ( S = top_top_set_a )
% 0.27/0.62 = ( ! [X5: a] : ( member_a @ X5 @ S ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % eq_UNIV_iff
% 0.27/0.62 thf(fact_333_eq__UNIV__iff,axiom,
% 0.27/0.62 ! [S: set_b] :
% 0.27/0.62 ( ( S = top_top_set_b )
% 0.27/0.62 = ( ! [X5: b] : ( member_b @ X5 @ S ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % eq_UNIV_iff
% 0.27/0.62 thf(fact_334_UNIV__witness,axiom,
% 0.27/0.62 ? [X3: a] : ( member_a @ X3 @ top_top_set_a ) ).
% 0.27/0.62
% 0.27/0.62 % UNIV_witness
% 0.27/0.62 thf(fact_335_UNIV__witness,axiom,
% 0.27/0.62 ? [X3: b] : ( member_b @ X3 @ top_top_set_b ) ).
% 0.27/0.62
% 0.27/0.62 % UNIV_witness
% 0.27/0.62 thf(fact_336_top__set__def,axiom,
% 0.27/0.62 ( top_top_set_a
% 0.27/0.62 = ( collect_a @ top_top_a_o ) ) ).
% 0.27/0.62
% 0.27/0.62 % top_set_def
% 0.27/0.62 thf(fact_337_top__set__def,axiom,
% 0.27/0.62 ( top_top_set_b
% 0.27/0.62 = ( collect_b @ top_top_b_o ) ) ).
% 0.27/0.62
% 0.27/0.62 % top_set_def
% 0.27/0.62 thf(fact_338_UNIV__eq__I,axiom,
% 0.27/0.62 ! [A3: set_a] :
% 0.27/0.62 ( ! [X3: a] : ( member_a @ X3 @ A3 )
% 0.27/0.62 => ( top_top_set_a = A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % UNIV_eq_I
% 0.27/0.62 thf(fact_339_UNIV__eq__I,axiom,
% 0.27/0.62 ! [A3: set_b] :
% 0.27/0.62 ( ! [X3: b] : ( member_b @ X3 @ A3 )
% 0.27/0.62 => ( top_top_set_b = A3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % UNIV_eq_I
% 0.27/0.62 thf(fact_340_top__empty__eq,axiom,
% 0.27/0.62 ( top_top_a_o
% 0.27/0.62 = ( ^ [X5: a] : ( member_a @ X5 @ top_top_set_a ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % top_empty_eq
% 0.27/0.62 thf(fact_341_top__empty__eq,axiom,
% 0.27/0.62 ( top_top_b_o
% 0.27/0.62 = ( ^ [X5: b] : ( member_b @ X5 @ top_top_set_b ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % top_empty_eq
% 0.27/0.62 thf(fact_342_ASSERT__simps_I2_J,axiom,
% 0.27/0.62 ( ( refine2039610767ASSERT @ $false )
% 0.27/0.62 = top_to177290092t_unit ) ).
% 0.27/0.62
% 0.27/0.62 % ASSERT_simps(2)
% 0.27/0.62
% 0.27/0.62 % Helper facts (15)
% 0.27/0.62 thf(help_If_2_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
% 0.27/0.62 ! [X4: set_a,Y3: set_a] :
% 0.27/0.62 ( ( if_set_a @ $false @ X4 @ Y3 )
% 0.27/0.62 = Y3 ) ).
% 0.27/0.62
% 0.27/0.62 thf(help_If_1_1_If_001t__Set__Oset_Itf__a_J_T,axiom,
% 0.27/0.62 ! [X4: set_a,Y3: set_a] :
% 0.27/0.62 ( ( if_set_a @ $true @ X4 @ Y3 )
% 0.27/0.62 = X4 ) ).
% 0.27/0.62
% 0.27/0.62 thf(help_If_2_1_If_001t__Set__Oset_Itf__b_J_T,axiom,
% 0.27/0.62 ! [X4: set_b,Y3: set_b] :
% 0.27/0.62 ( ( if_set_b @ $false @ X4 @ Y3 )
% 0.27/0.62 = Y3 ) ).
% 0.27/0.62
% 0.27/0.62 thf(help_If_1_1_If_001t__Set__Oset_Itf__b_J_T,axiom,
% 0.27/0.62 ! [X4: set_b,Y3: set_b] :
% 0.27/0.62 ( ( if_set_b @ $true @ X4 @ Y3 )
% 0.27/0.62 = X4 ) ).
% 0.27/0.62
% 0.27/0.62 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 0.27/0.62 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.27/0.62 ( ( if_Ref1724547303nres_a @ $false @ X4 @ Y3 )
% 0.27/0.62 = Y3 ) ).
% 0.27/0.62
% 0.27/0.62 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
% 0.27/0.62 ! [X4: refine424419629nres_a,Y3: refine424419629nres_a] :
% 0.27/0.62 ( ( if_Ref1724547303nres_a @ $true @ X4 @ Y3 )
% 0.27/0.62 = X4 ) ).
% 0.27/0.62
% 0.27/0.62 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_T,axiom,
% 0.27/0.62 ! [X4: refine432681134nres_b,Y3: refine432681134nres_b] :
% 0.27/0.62 ( ( if_Ref1732808808nres_b @ $false @ X4 @ Y3 )
% 0.27/0.62 = Y3 ) ).
% 0.27/0.62
% 0.27/0.62 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_T,axiom,
% 0.27/0.62 ! [X4: refine432681134nres_b,Y3: refine432681134nres_b] :
% 0.27/0.62 ( ( if_Ref1732808808nres_b @ $true @ X4 @ Y3 )
% 0.27/0.62 = X4 ) ).
% 0.27/0.62
% 0.27/0.62 thf(help_If_2_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T,axiom,
% 0.27/0.62 ! [X4: $o > refine424419629nres_a,Y3: $o > refine424419629nres_a] :
% 0.27/0.62 ( ( if_o_R1705037948nres_a @ $false @ X4 @ Y3 )
% 0.27/0.62 = Y3 ) ).
% 0.27/0.62
% 0.27/0.62 thf(help_If_1_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_J_T,axiom,
% 0.27/0.62 ! [X4: $o > refine424419629nres_a,Y3: $o > refine424419629nres_a] :
% 0.27/0.62 ( ( if_o_R1705037948nres_a @ $true @ X4 @ Y3 )
% 0.27/0.62 = X4 ) ).
% 0.27/0.62
% 0.27/0.62 thf(help_If_2_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J_T,axiom,
% 0.27/0.62 ! [X4: $o > refine432681134nres_b,Y3: $o > refine432681134nres_b] :
% 0.27/0.62 ( ( if_o_R697118589nres_b @ $false @ X4 @ Y3 )
% 0.27/0.62 = Y3 ) ).
% 0.27/0.62
% 0.27/0.62 thf(help_If_1_1_If_001_062_I_Eo_Mt__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__b_J_J_T,axiom,
% 0.27/0.71 ! [X4: $o > refine432681134nres_b,Y3: $o > refine432681134nres_b] :
% 0.27/0.71 ( ( if_o_R697118589nres_b @ $true @ X4 @ Y3 )
% 0.27/0.71 = X4 ) ).
% 0.27/0.71
% 0.27/0.71 thf(help_If_3_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T,axiom,
% 0.27/0.71 ! [P: $o] :
% 0.27/0.71 ( ( P = $true )
% 0.27/0.71 | ( P = $false ) ) ).
% 0.27/0.71
% 0.27/0.71 thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T,axiom,
% 0.27/0.71 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.27/0.71 ( ( if_Ref1369692790t_unit @ $false @ X4 @ Y3 )
% 0.27/0.71 = Y3 ) ).
% 0.27/0.71
% 0.27/0.71 thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_It__Product____Type__Ounit_J_T,axiom,
% 0.27/0.71 ! [X4: refine787176636t_unit,Y3: refine787176636t_unit] :
% 0.27/0.71 ( ( if_Ref1369692790t_unit @ $true @ X4 @ Y3 )
% 0.27/0.71 = X4 ) ).
% 0.27/0.71
% 0.27/0.71 % Conjectures (1)
% 0.27/0.71 thf(conj_0,conjecture,
% 0.27/0.71 ord_le527798542nres_b @ m @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ f ) ).
% 0.27/0.71
% 0.27/0.71 %------------------------------------------------------------------------------
% 0.27/0.71 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Om1wd6JRxK/cvc5---1.0.5_16958.p...
% 0.27/0.71 (declare-sort $$unsorted 0)
% 0.27/0.71 (declare-sort tptp.produc1587512412nres_b 0)
% 0.27/0.71 (declare-sort tptp.produc1609974940nres_a 0)
% 0.27/0.71 (declare-sort tptp.set_Pr451126599t_unit 0)
% 0.27/0.71 (declare-sort tptp.refine2031285398od_b_b 0)
% 0.27/0.71 (declare-sort tptp.refine891721109od_b_a 0)
% 0.27/0.71 (declare-sort tptp.refine1811374551od_a_b 0)
% 0.27/0.71 (declare-sort tptp.refine671810262od_a_a 0)
% 0.27/0.71 (declare-sort tptp.refine787176636t_unit 0)
% 0.27/0.71 (declare-sort tptp.set_Pr1707992533t_unit 0)
% 0.27/0.71 (declare-sort tptp.set_Pr1628433942t_unit 0)
% 0.27/0.71 (declare-sort tptp.refine432681134nres_b 0)
% 0.27/0.71 (declare-sort tptp.refine424419629nres_a 0)
% 0.27/0.71 (declare-sort tptp.set_Product_prod_b_b 0)
% 0.27/0.71 (declare-sort tptp.set_Product_prod_b_a 0)
% 0.27/0.71 (declare-sort tptp.set_Product_prod_a_b 0)
% 0.27/0.71 (declare-sort tptp.set_Product_prod_a_a 0)
% 0.27/0.71 (declare-sort tptp.set_Product_unit 0)
% 0.27/0.71 (declare-sort tptp.product_prod_b_b 0)
% 0.27/0.71 (declare-sort tptp.product_prod_b_a 0)
% 0.27/0.71 (declare-sort tptp.product_prod_a_b 0)
% 0.27/0.71 (declare-sort tptp.product_prod_a_a 0)
% 0.27/0.71 (declare-sort tptp.product_unit 0)
% 0.27/0.71 (declare-sort tptp.set_b 0)
% 0.27/0.71 (declare-sort tptp.set_a 0)
% 0.27/0.71 (declare-sort tptp.b 0)
% 0.27/0.71 (declare-sort tptp.a 0)
% 0.27/0.71 (declare-fun tptp.if_o_R1705037948nres_a (Bool (-> Bool tptp.refine424419629nres_a) (-> Bool tptp.refine424419629nres_a) Bool) tptp.refine424419629nres_a)
% 0.27/0.71 (declare-fun tptp.if_o_R697118589nres_b (Bool (-> Bool tptp.refine432681134nres_b) (-> Bool tptp.refine432681134nres_b) Bool) tptp.refine432681134nres_b)
% 0.27/0.71 (declare-fun tptp.if_Ref1369692790t_unit (Bool tptp.refine787176636t_unit tptp.refine787176636t_unit) tptp.refine787176636t_unit)
% 0.27/0.71 (declare-fun tptp.if_Ref1724547303nres_a (Bool tptp.refine424419629nres_a tptp.refine424419629nres_a) tptp.refine424419629nres_a)
% 0.27/0.71 (declare-fun tptp.if_Ref1732808808nres_b (Bool tptp.refine432681134nres_b tptp.refine432681134nres_b) tptp.refine432681134nres_b)
% 0.27/0.71 (declare-fun tptp.if_set_a (Bool tptp.set_a tptp.set_a) tptp.set_a)
% 0.27/0.71 (declare-fun tptp.if_set_b (Bool tptp.set_b tptp.set_b) tptp.set_b)
% 0.27/0.71 (declare-fun tptp.ord_le516598614nres_a ((-> Bool tptp.refine424419629nres_a) (-> Bool tptp.refine424419629nres_a)) Bool)
% 0.27/0.71 (declare-fun tptp.ord_le1656162903nres_b ((-> Bool tptp.refine432681134nres_b) (-> Bool tptp.refine432681134nres_b)) Bool)
% 0.27/0.71 (declare-fun tptp.ord_le915866422od_a_a (tptp.refine671810262od_a_a tptp.refine671810262od_a_a) Bool)
% 0.27/0.71 (declare-fun tptp.ord_le2055430711od_a_b (tptp.refine1811374551od_a_b tptp.refine1811374551od_a_b) Bool)
% 0.27/0.71 (declare-fun tptp.ord_le1135777269od_b_a (tptp.refine891721109od_b_a tptp.refine891721109od_b_a) Bool)
% 0.27/0.71 (declare-fun tptp.ord_le127857910od_b_b (tptp.refine2031285398od_b_b tptp.refine2031285398od_b_b) Bool)
% 0.27/0.71 (declare-fun tptp.ord_le1051254044t_unit (tptp.refine787176636t_unit tptp.refine787176636t_unit) Bool)
% 0.27/0.71 (declare-fun tptp.ord_le519537037nres_a (tptp.refine424419629nres_a tptp.refine424419629nres_a) Bool)
% 0.27/0.71 (declare-fun tptp.ord_le527798542nres_b (tptp.refine432681134nres_b tptp.refine432681134nres_b) Bool)
% 0.27/0.71 (declare-fun tptp.ord_less_eq_set_a (tptp.set_a tptp.set_a) Bool)
% 0.27/0.71 (declare-fun tptp.ord_less_eq_set_b (tptp.set_b tptp.set_b) Bool)
% 0.27/0.71 (declare-fun tptp.order_1714329108nres_a ((-> tptp.refine424419629nres_a Bool)) tptp.refine424419629nres_a)
% 0.27/0.71 (declare-fun tptp.order_1722590613nres_b ((-> tptp.refine432681134nres_b Bool)) tptp.refine432681134nres_b)
% 0.27/0.71 (declare-fun tptp.top_top_a_o (tptp.a) Bool)
% 0.27/0.71 (declare-fun tptp.top_top_b_o (tptp.b) Bool)
% 0.27/0.71 (declare-fun tptp.top_to177290092t_unit () tptp.refine787176636t_unit)
% 0.27/0.71 (declare-fun tptp.top_to231829469nres_a () tptp.refine424419629nres_a)
% 0.27/0.71 (declare-fun tptp.top_to240090974nres_b () tptp.refine432681134nres_b)
% 0.27/0.71 (declare-fun tptp.top_top_set_a () tptp.set_a)
% 0.27/0.71 (declare-fun tptp.top_top_set_b () tptp.set_b)
% 0.27/0.71 (declare-fun tptp.partia1658438072t_unit (tptp.refine787176636t_unit tptp.refine787176636t_unit tptp.refine787176636t_unit) Bool)
% 0.27/0.71 (declare-fun tptp.partia906949161nres_a (tptp.refine424419629nres_a tptp.refine424419629nres_a tptp.refine424419629nres_a) Bool)
% 0.27/0.71 (declare-fun tptp.partia915210666nres_b (tptp.refine432681134nres_b tptp.refine432681134nres_b tptp.refine432681134nres_b) Bool)
% 0.27/0.71 (declare-fun tptp.produc1136923598nres_a (tptp.refine424419629nres_a tptp.refine424419629nres_a) tptp.produc1609974940nres_a)
% 0.27/0.71 (declare-fun tptp.produc2130641934nres_b (tptp.refine432681134nres_b tptp.refine432681134nres_b) tptp.produc1587512412nres_b)
% 0.27/0.71 (declare-fun tptp.product_Pair_a_a (tptp.a tptp.a) tptp.product_prod_a_a)
% 0.27/0.71 (declare-fun tptp.product_Pair_a_b (tptp.a tptp.b) tptp.product_prod_a_b)
% 0.27/0.71 (declare-fun tptp.product_Pair_b_a (tptp.b tptp.a) tptp.product_prod_b_a)
% 0.27/0.71 (declare-fun tptp.product_Pair_b_b (tptp.b tptp.b) tptp.product_prod_b_b)
% 0.27/0.71 (declare-fun tptp.refine2039610767ASSERT (Bool) tptp.refine787176636t_unit)
% 0.27/0.71 (declare-fun tptp.refine1420258419t_unit (tptp.product_unit) tptp.refine787176636t_unit)
% 0.27/0.71 (declare-fun tptp.refine2063221604TURN_a (tptp.a) tptp.refine424419629nres_a)
% 0.27/0.71 (declare-fun tptp.refine2063221605TURN_b (tptp.b) tptp.refine432681134nres_b)
% 0.27/0.71 (declare-fun tptp.refine838861686t_unit (tptp.set_Pr451126599t_unit tptp.refine787176636t_unit) tptp.refine787176636t_unit)
% 0.27/0.71 (declare-fun tptp.refine341651653t_unit (tptp.set_Pr1628433942t_unit tptp.refine424419629nres_a) tptp.refine787176636t_unit)
% 0.27/0.71 (declare-fun tptp.refine1136779702un_a_a (tptp.set_Product_prod_a_a tptp.refine424419629nres_a) tptp.refine424419629nres_a)
% 0.27/0.71 (declare-fun tptp.refine1136779703un_a_b (tptp.set_Product_prod_a_b tptp.refine424419629nres_a) tptp.refine432681134nres_b)
% 0.27/0.71 (declare-fun tptp.refine460904452t_unit (tptp.set_Pr1707992533t_unit tptp.refine432681134nres_b) tptp.refine787176636t_unit)
% 0.27/0.71 (declare-fun tptp.refine1964549109un_b_a (tptp.set_Product_prod_b_a tptp.refine432681134nres_b) tptp.refine424419629nres_a)
% 0.27/0.71 (declare-fun tptp.refine1964549110un_b_b (tptp.set_Product_prod_b_b tptp.refine432681134nres_b) tptp.refine432681134nres_b)
% 0.27/0.71 (declare-fun tptp.refine988994910_a_a_b (tptp.refine671810262od_a_a (-> tptp.product_prod_a_a tptp.refine432681134nres_b)) tptp.refine432681134nres_b)
% 0.27/0.71 (declare-fun tptp.refine681446406t_unit (tptp.refine787176636t_unit (-> tptp.product_unit tptp.refine787176636t_unit)) tptp.refine787176636t_unit)
% 0.27/0.71 (declare-fun tptp.refine119808503unit_a (tptp.refine787176636t_unit (-> tptp.product_unit tptp.refine424419629nres_a)) tptp.refine424419629nres_a)
% 0.27/0.71 (declare-fun tptp.refine119808504unit_b (tptp.refine787176636t_unit (-> tptp.product_unit tptp.refine432681134nres_b)) tptp.refine432681134nres_b)
% 0.27/0.71 (declare-fun tptp.refine96995669t_unit (tptp.refine424419629nres_a (-> tptp.a tptp.refine787176636t_unit)) tptp.refine787176636t_unit)
% 0.27/0.71 (declare-fun tptp.refine436832838nd_a_a (tptp.refine424419629nres_a (-> tptp.a tptp.refine424419629nres_a)) tptp.refine424419629nres_a)
% 0.27/0.71 (declare-fun tptp.refine436832839nd_a_b (tptp.refine424419629nres_a (-> tptp.a tptp.refine432681134nres_b)) tptp.refine432681134nres_b)
% 0.27/0.71 (declare-fun tptp.refine216248468t_unit (tptp.refine432681134nres_b (-> tptp.b tptp.refine787176636t_unit)) tptp.refine787176636t_unit)
% 0.27/0.71 (declare-fun tptp.refine1264602245nd_b_a (tptp.refine432681134nres_b (-> tptp.b tptp.refine424419629nres_a)) tptp.refine424419629nres_a)
% 0.27/0.71 (declare-fun tptp.refine1264602246nd_b_b (tptp.refine432681134nres_b (-> tptp.b tptp.refine432681134nres_b)) tptp.refine432681134nres_b)
% 0.27/0.71 (declare-fun tptp.refine944483349t_unit (tptp.set_Pr451126599t_unit tptp.refine787176636t_unit) tptp.refine787176636t_unit)
% 0.27/0.71 (declare-fun tptp.refine2021053540t_unit (tptp.set_Pr1628433942t_unit tptp.refine787176636t_unit) tptp.refine424419629nres_a)
% 0.27/0.71 (declare-fun tptp.refine1441824853un_a_a (tptp.set_Product_prod_a_a tptp.refine424419629nres_a) tptp.refine424419629nres_a)
% 0.27/0.71 (declare-fun tptp.refine1441824854un_a_b (tptp.set_Product_prod_a_b tptp.refine432681134nres_b) tptp.refine424419629nres_a)
% 0.27/0.71 (declare-fun tptp.refine2140306339t_unit (tptp.set_Pr1707992533t_unit tptp.refine787176636t_unit) tptp.refine432681134nres_b)
% 0.27/0.71 (declare-fun tptp.refine122110612un_b_a (tptp.set_Product_prod_b_a tptp.refine424419629nres_a) tptp.refine432681134nres_b)
% 0.27/0.71 (declare-fun tptp.refine122110613un_b_b (tptp.set_Product_prod_b_b tptp.refine432681134nres_b) tptp.refine432681134nres_b)
% 0.27/0.71 (declare-fun tptp.refine558004794t_unit (tptp.refine787176636t_unit tptp.product_unit) Bool)
% 0.27/0.71 (declare-fun tptp.refine1001002027nres_a (tptp.refine424419629nres_a tptp.a) Bool)
% 0.27/0.71 (declare-fun tptp.refine1001002028nres_b (tptp.refine432681134nres_b tptp.b) Bool)
% 0.27/0.71 (declare-fun tptp.refine378960780od_a_a (tptp.refine671810262od_a_a tptp.product_prod_a_a) Bool)
% 0.27/0.71 (declare-fun tptp.refine387222285od_a_b (tptp.refine1811374551od_a_b tptp.product_prod_a_b) Bool)
% 0.27/0.71 (declare-fun tptp.refine1206730187od_b_a (tptp.refine891721109od_b_a tptp.product_prod_b_a) Bool)
% 0.27/0.71 (declare-fun tptp.refine1214991692od_b_b (tptp.refine2031285398od_b_b tptp.product_prod_b_b) Bool)
% 0.27/0.71 (declare-fun tptp.refine983493746t_unit (tptp.refine787176636t_unit tptp.product_unit) Bool)
% 0.27/0.71 (declare-fun tptp.refine1312857699nres_a (tptp.refine424419629nres_a tptp.a) Bool)
% 0.27/0.71 (declare-fun tptp.refine1312857700nres_b (tptp.refine432681134nres_b tptp.b) Bool)
% 0.27/0.71 (declare-fun tptp.refine579265252t_unit (tptp.refine787176636t_unit) Bool)
% 0.27/0.71 (declare-fun tptp.refine412683989fail_a (tptp.refine424419629nres_a) Bool)
% 0.27/0.71 (declare-fun tptp.refine412683990fail_b (tptp.refine432681134nres_b) Bool)
% 0.27/0.71 (declare-fun tptp.refine1607584204t_unit () tptp.refine787176636t_unit)
% 0.27/0.71 (declare-fun tptp.refine464223677AILi_a () tptp.refine424419629nres_a)
% 0.27/0.71 (declare-fun tptp.refine464223678AILi_b () tptp.refine432681134nres_b)
% 0.27/0.71 (declare-fun tptp.refine622451633od_a_a (tptp.set_Product_prod_a_a) tptp.refine671810262od_a_a)
% 0.27/0.71 (declare-fun tptp.refine630713138od_a_b (tptp.set_Product_prod_a_b) tptp.refine1811374551od_a_b)
% 0.27/0.71 (declare-fun tptp.refine1450221040od_b_a (tptp.set_Product_prod_b_a) tptp.refine891721109od_b_a)
% 0.27/0.71 (declare-fun tptp.refine1458482545od_b_b (tptp.set_Product_prod_b_b) tptp.refine2031285398od_b_b)
% 0.27/0.71 (declare-fun tptp.refine1777164439t_unit (tptp.set_Product_unit) tptp.refine787176636t_unit)
% 0.27/0.71 (declare-fun tptp.refine1198353288_RES_a (tptp.set_a) tptp.refine424419629nres_a)
% 0.27/0.71 (declare-fun tptp.refine1198353289_RES_b (tptp.set_b) tptp.refine432681134nres_b)
% 0.27/0.71 (declare-fun tptp.refine1208325748t_unit (tptp.refine787176636t_unit) tptp.set_Product_unit)
% 0.27/0.71 (declare-fun tptp.refine1822134885_RES_a (tptp.refine424419629nres_a) tptp.set_a)
% 0.27/0.71 (declare-fun tptp.refine1822134886_RES_b (tptp.refine432681134nres_b) tptp.set_b)
% 0.27/0.71 (declare-fun tptp.domain799550107t_unit (tptp.set_Pr1628433942t_unit) tptp.set_a)
% 0.27/0.71 (declare-fun tptp.domain_a_a (tptp.set_Product_prod_a_a) tptp.set_a)
% 0.27/0.71 (declare-fun tptp.domain_a_b (tptp.set_Product_prod_a_b) tptp.set_a)
% 0.27/0.71 (declare-fun tptp.domain918802906t_unit (tptp.set_Pr1707992533t_unit) tptp.set_b)
% 0.27/0.71 (declare-fun tptp.domain_b_a (tptp.set_Product_prod_b_a) tptp.set_b)
% 0.27/0.71 (declare-fun tptp.domain_b_b (tptp.set_Product_prod_b_b) tptp.set_b)
% 0.27/0.71 (declare-fun tptp.image_a_a (tptp.set_Product_prod_a_a tptp.set_a) tptp.set_a)
% 0.27/0.71 (declare-fun tptp.image_a_b (tptp.set_Product_prod_a_b tptp.set_a) tptp.set_b)
% 0.27/0.71 (declare-fun tptp.image_b_a (tptp.set_Product_prod_b_a tptp.set_b) tptp.set_a)
% 0.27/0.71 (declare-fun tptp.image_b_b (tptp.set_Product_prod_b_b tptp.set_b) tptp.set_b)
% 0.27/0.71 (declare-fun tptp.collec645855634od_a_a ((-> tptp.product_prod_a_a Bool)) tptp.set_Product_prod_a_a)
% 0.27/0.71 (declare-fun tptp.collec654117139od_a_b ((-> tptp.product_prod_a_b Bool)) tptp.set_Product_prod_a_b)
% 0.27/0.71 (declare-fun tptp.collec1473625041od_b_a ((-> tptp.product_prod_b_a Bool)) tptp.set_Product_prod_b_a)
% 0.27/0.71 (declare-fun tptp.collec1481886546od_b_b ((-> tptp.product_prod_b_b Bool)) tptp.set_Product_prod_b_b)
% 0.27/0.71 (declare-fun tptp.collect_Product_unit ((-> tptp.product_unit Bool)) tptp.set_Product_unit)
% 0.27/0.71 (declare-fun tptp.collect_a ((-> tptp.a Bool)) tptp.set_a)
% 0.27/0.71 (declare-fun tptp.collect_b ((-> tptp.b Bool)) tptp.set_b)
% 0.27/0.71 (declare-fun tptp.member449909584od_a_a (tptp.product_prod_a_a tptp.set_Product_prod_a_a) Bool)
% 0.27/0.71 (declare-fun tptp.member458171089od_a_b (tptp.product_prod_a_b tptp.set_Product_prod_a_b) Bool)
% 0.27/0.71 (declare-fun tptp.member1277678991od_b_a (tptp.product_prod_b_a tptp.set_Product_prod_b_a) Bool)
% 0.27/0.71 (declare-fun tptp.member1285940496od_b_b (tptp.product_prod_b_b tptp.set_Product_prod_b_b) Bool)
% 0.27/0.71 (declare-fun tptp.member_Product_unit (tptp.product_unit tptp.set_Product_unit) Bool)
% 0.27/0.71 (declare-fun tptp.member_a (tptp.a tptp.set_a) Bool)
% 0.27/0.71 (declare-fun tptp.member_b (tptp.b tptp.set_b) Bool)
% 0.27/0.71 (declare-fun tptp.phi (tptp.a) Bool)
% 0.27/0.71 (declare-fun tptp.f (tptp.a) tptp.refine432681134nres_b)
% 0.27/0.71 (declare-fun tptp.m () tptp.refine432681134nres_b)
% 0.27/0.71 (declare-fun tptp.x () tptp.a)
% 0.27/0.71 (assert (@ tptp.phi tptp.x))
% 0.27/0.71 (assert (@ (@ tptp.ord_le527798542nres_b tptp.m) (@ tptp.f tptp.x)))
% 0.27/0.71 (assert (forall ((X tptp.set_Product_unit) (Y tptp.set_Product_unit)) (= (= (@ tptp.refine1777164439t_unit X) (@ tptp.refine1777164439t_unit Y)) (= X Y))))
% 0.27/0.71 (assert (forall ((X tptp.set_b) (Y tptp.set_b)) (= (= (@ tptp.refine1198353289_RES_b X) (@ tptp.refine1198353289_RES_b Y)) (= X Y))))
% 0.27/0.71 (assert (forall ((X tptp.set_a) (Y tptp.set_a)) (= (= (@ tptp.refine1198353288_RES_a X) (@ tptp.refine1198353288_RES_a Y)) (= X Y))))
% 0.27/0.71 (assert (forall ((X2 tptp.set_Product_unit) (Y2 tptp.set_Product_unit)) (= (= (@ tptp.refine1777164439t_unit X2) (@ tptp.refine1777164439t_unit Y2)) (= X2 Y2))))
% 0.27/0.71 (assert (forall ((X2 tptp.set_b) (Y2 tptp.set_b)) (= (= (@ tptp.refine1198353289_RES_b X2) (@ tptp.refine1198353289_RES_b Y2)) (= X2 Y2))))
% 0.27/0.71 (assert (forall ((X2 tptp.set_a) (Y2 tptp.set_a)) (= (= (@ tptp.refine1198353288_RES_a X2) (@ tptp.refine1198353288_RES_a Y2)) (= X2 Y2))))
% 0.27/0.71 (assert (forall ((B Bool) (S1 tptp.refine787176636t_unit) (Phi (-> tptp.product_unit Bool)) (S2 tptp.refine787176636t_unit)) (let ((_let_1 (@ tptp.refine1777164439t_unit (@ tptp.collect_Product_unit Phi)))) (=> (=> B (@ (@ tptp.ord_le1051254044t_unit S1) _let_1)) (=> (=> (not B) (@ (@ tptp.ord_le1051254044t_unit S2) _let_1)) (@ (@ tptp.ord_le1051254044t_unit (@ (@ (@ tptp.if_Ref1369692790t_unit B) S1) S2)) _let_1))))))
% 0.27/0.71 (assert (forall ((B Bool) (S1 tptp.refine432681134nres_b) (Phi (-> tptp.b Bool)) (S2 tptp.refine432681134nres_b)) (let ((_let_1 (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi)))) (=> (=> B (@ (@ tptp.ord_le527798542nres_b S1) _let_1)) (=> (=> (not B) (@ (@ tptp.ord_le527798542nres_b S2) _let_1)) (@ (@ tptp.ord_le527798542nres_b (@ (@ (@ tptp.if_Ref1732808808nres_b B) S1) S2)) _let_1))))))
% 0.27/0.71 (assert (forall ((B Bool) (S1 tptp.refine424419629nres_a) (Phi (-> tptp.a Bool)) (S2 tptp.refine424419629nres_a)) (let ((_let_1 (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi)))) (=> (=> B (@ (@ tptp.ord_le519537037nres_a S1) _let_1)) (=> (=> (not B) (@ (@ tptp.ord_le519537037nres_a S2) _let_1)) (@ (@ tptp.ord_le519537037nres_a (@ (@ (@ tptp.if_Ref1724547303nres_a B) S1) S2)) _let_1))))))
% 0.27/0.71 (assert (forall ((S tptp.set_Product_prod_a_a) (Phi (-> tptp.product_prod_a_a Bool))) (=> (forall ((X3 tptp.product_prod_a_a)) (=> (@ (@ tptp.member449909584od_a_a X3) S) (@ Phi X3))) (@ (@ tptp.ord_le915866422od_a_a (@ tptp.refine622451633od_a_a S)) (@ tptp.refine622451633od_a_a (@ tptp.collec645855634od_a_a Phi))))))
% 0.27/0.71 (assert (forall ((S tptp.set_Product_prod_b_a) (Phi (-> tptp.product_prod_b_a Bool))) (=> (forall ((X3 tptp.product_prod_b_a)) (=> (@ (@ tptp.member1277678991od_b_a X3) S) (@ Phi X3))) (@ (@ tptp.ord_le1135777269od_b_a (@ tptp.refine1450221040od_b_a S)) (@ tptp.refine1450221040od_b_a (@ tptp.collec1473625041od_b_a Phi))))))
% 0.27/0.71 (assert (forall ((S tptp.set_Product_prod_b_b) (Phi (-> tptp.product_prod_b_b Bool))) (=> (forall ((X3 tptp.product_prod_b_b)) (=> (@ (@ tptp.member1285940496od_b_b X3) S) (@ Phi X3))) (@ (@ tptp.ord_le127857910od_b_b (@ tptp.refine1458482545od_b_b S)) (@ tptp.refine1458482545od_b_b (@ tptp.collec1481886546od_b_b Phi))))))
% 0.27/0.71 (assert (forall ((S tptp.set_Product_prod_a_b) (Phi (-> tptp.product_prod_a_b Bool))) (=> (forall ((X3 tptp.product_prod_a_b)) (=> (@ (@ tptp.member458171089od_a_b X3) S) (@ Phi X3))) (@ (@ tptp.ord_le2055430711od_a_b (@ tptp.refine630713138od_a_b S)) (@ tptp.refine630713138od_a_b (@ tptp.collec654117139od_a_b Phi))))))
% 0.27/0.71 (assert (forall ((S tptp.set_Product_unit) (Phi (-> tptp.product_unit Bool))) (=> (forall ((X3 tptp.product_unit)) (=> (@ (@ tptp.member_Product_unit X3) S) (@ Phi X3))) (@ (@ tptp.ord_le1051254044t_unit (@ tptp.refine1777164439t_unit S)) (@ tptp.refine1777164439t_unit (@ tptp.collect_Product_unit Phi))))))
% 0.27/0.71 (assert (forall ((S tptp.set_b) (Phi (-> tptp.b Bool))) (=> (forall ((X3 tptp.b)) (=> (@ (@ tptp.member_b X3) S) (@ Phi X3))) (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine1198353289_RES_b S)) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi))))))
% 0.27/0.71 (assert (forall ((S tptp.set_a) (Phi (-> tptp.a Bool))) (=> (forall ((X3 tptp.a)) (=> (@ (@ tptp.member_a X3) S) (@ Phi X3))) (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine1198353288_RES_a S)) (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi))))))
% 0.27/0.71 (assert (forall ((Phi (-> tptp.product_unit Bool)) (Phi2 (-> tptp.product_unit Bool))) (=> (forall ((X3 tptp.product_unit)) (=> (@ Phi X3) (@ Phi2 X3))) (@ (@ tptp.ord_le1051254044t_unit (@ tptp.refine1777164439t_unit (@ tptp.collect_Product_unit Phi))) (@ tptp.refine1777164439t_unit (@ tptp.collect_Product_unit Phi2))))))
% 0.27/0.71 (assert (forall ((Phi (-> tptp.b Bool)) (Phi2 (-> tptp.b Bool))) (=> (forall ((X3 tptp.b)) (=> (@ Phi X3) (@ Phi2 X3))) (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi))) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi2))))))
% 0.27/0.71 (assert (forall ((Phi (-> tptp.a Bool)) (Phi2 (-> tptp.a Bool))) (=> (forall ((X3 tptp.a)) (=> (@ Phi X3) (@ Phi2 X3))) (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi))) (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi2))))))
% 0.27/0.71 (assert (forall ((X4 tptp.refine787176636t_unit) (Y3 tptp.refine787176636t_unit) (Postcond (-> tptp.product_unit Bool))) (let ((_let_1 (@ tptp.refine1777164439t_unit (@ tptp.collect_Product_unit Postcond)))) (let ((_let_2 (@ tptp.ord_le1051254044t_unit X4))) (=> (@ _let_2 Y3) (=> (@ (@ tptp.ord_le1051254044t_unit Y3) _let_1) (@ _let_2 _let_1)))))))
% 0.27/0.71 (assert (forall ((X4 tptp.refine432681134nres_b) (Y3 tptp.refine432681134nres_b) (Postcond (-> tptp.b Bool))) (let ((_let_1 (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Postcond)))) (let ((_let_2 (@ tptp.ord_le527798542nres_b X4))) (=> (@ _let_2 Y3) (=> (@ (@ tptp.ord_le527798542nres_b Y3) _let_1) (@ _let_2 _let_1)))))))
% 0.27/0.71 (assert (forall ((X4 tptp.refine424419629nres_a) (Y3 tptp.refine424419629nres_a) (Postcond (-> tptp.a Bool))) (let ((_let_1 (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Postcond)))) (let ((_let_2 (@ tptp.ord_le519537037nres_a X4))) (=> (@ _let_2 Y3) (=> (@ (@ tptp.ord_le519537037nres_a Y3) _let_1) (@ _let_2 _let_1)))))))
% 0.27/0.71 (assert (forall ((B Bool) (T tptp.set_b) (M tptp.set_b) (E tptp.set_b)) (=> (=> B (@ (@ tptp.ord_less_eq_set_b T) M)) (=> (=> (not B) (@ (@ tptp.ord_less_eq_set_b E) M)) (@ (@ tptp.ord_less_eq_set_b (@ (@ (@ tptp.if_set_b B) T) E)) M)))))
% 0.27/0.71 (assert (forall ((B Bool) (T tptp.set_a) (M tptp.set_a) (E tptp.set_a)) (=> (=> B (@ (@ tptp.ord_less_eq_set_a T) M)) (=> (=> (not B) (@ (@ tptp.ord_less_eq_set_a E) M)) (@ (@ tptp.ord_less_eq_set_a (@ (@ (@ tptp.if_set_a B) T) E)) M)))))
% 0.27/0.71 (assert (forall ((B Bool) (T (-> Bool tptp.refine424419629nres_a)) (M (-> Bool tptp.refine424419629nres_a)) (E (-> Bool tptp.refine424419629nres_a))) (=> (=> B (@ (@ tptp.ord_le516598614nres_a T) M)) (=> (=> (not B) (@ (@ tptp.ord_le516598614nres_a E) M)) (@ (@ tptp.ord_le516598614nres_a (@ (@ (@ tptp.if_o_R1705037948nres_a B) T) E)) M)))))
% 0.27/0.71 (assert (forall ((B Bool) (T (-> Bool tptp.refine432681134nres_b)) (M (-> Bool tptp.refine432681134nres_b)) (E (-> Bool tptp.refine432681134nres_b))) (=> (=> B (@ (@ tptp.ord_le1656162903nres_b T) M)) (=> (=> (not B) (@ (@ tptp.ord_le1656162903nres_b E) M)) (@ (@ tptp.ord_le1656162903nres_b (@ (@ (@ tptp.if_o_R697118589nres_b B) T) E)) M)))))
% 0.27/0.71 (assert (forall ((B Bool) (T tptp.refine787176636t_unit) (M tptp.refine787176636t_unit) (E tptp.refine787176636t_unit)) (=> (=> B (@ (@ tptp.ord_le1051254044t_unit T) M)) (=> (=> (not B) (@ (@ tptp.ord_le1051254044t_unit E) M)) (@ (@ tptp.ord_le1051254044t_unit (@ (@ (@ tptp.if_Ref1369692790t_unit B) T) E)) M)))))
% 0.27/0.71 (assert (forall ((B Bool) (T tptp.refine424419629nres_a) (M tptp.refine424419629nres_a) (E tptp.refine424419629nres_a)) (=> (=> B (@ (@ tptp.ord_le519537037nres_a T) M)) (=> (=> (not B) (@ (@ tptp.ord_le519537037nres_a E) M)) (@ (@ tptp.ord_le519537037nres_a (@ (@ (@ tptp.if_Ref1724547303nres_a B) T) E)) M)))))
% 0.27/0.71 (assert (forall ((B Bool) (T tptp.refine432681134nres_b) (M tptp.refine432681134nres_b) (E tptp.refine432681134nres_b)) (=> (=> B (@ (@ tptp.ord_le527798542nres_b T) M)) (=> (=> (not B) (@ (@ tptp.ord_le527798542nres_b E) M)) (@ (@ tptp.ord_le527798542nres_b (@ (@ (@ tptp.if_Ref1732808808nres_b B) T) E)) M)))))
% 0.27/0.71 (assert (forall ((M tptp.refine787176636t_unit) (Phi (-> tptp.product_unit Bool)) (Psi (-> tptp.product_unit Bool))) (let ((_let_1 (@ tptp.ord_le1051254044t_unit M))) (=> (@ _let_1 (@ tptp.refine1777164439t_unit (@ tptp.collect_Product_unit Phi))) (=> (forall ((X3 tptp.product_unit)) (=> (@ Phi X3) (@ Psi X3))) (@ _let_1 (@ tptp.refine1777164439t_unit (@ tptp.collect_Product_unit Psi))))))))
% 0.27/0.71 (assert (forall ((M tptp.refine424419629nres_a) (Phi (-> tptp.a Bool)) (Psi (-> tptp.a Bool))) (let ((_let_1 (@ tptp.ord_le519537037nres_a M))) (=> (@ _let_1 (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi))) (=> (forall ((X3 tptp.a)) (=> (@ Phi X3) (@ Psi X3))) (@ _let_1 (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Psi))))))))
% 0.27/0.71 (assert (forall ((M tptp.refine432681134nres_b) (Phi (-> tptp.b Bool)) (Psi (-> tptp.b Bool))) (let ((_let_1 (@ tptp.ord_le527798542nres_b M))) (=> (@ _let_1 (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi))) (=> (forall ((X3 tptp.b)) (=> (@ Phi X3) (@ Psi X3))) (@ _let_1 (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Psi))))))))
% 0.27/0.71 (assert (forall ((X4 tptp.a) (X tptp.set_a) (M tptp.refine424419629nres_a) (F (-> tptp.a tptp.refine424419629nres_a))) (let ((_let_1 (@ tptp.ord_le519537037nres_a M))) (=> (@ (@ tptp.member_a X4) X) (=> (@ _let_1 (@ F X4)) (@ _let_1 (@ (@ tptp.refine436832838nd_a_a (@ tptp.refine1198353288_RES_a X)) F)))))))
% 0.27/0.71 (assert (forall ((X4 tptp.a) (X tptp.set_a) (M tptp.refine432681134nres_b) (F (-> tptp.a tptp.refine432681134nres_b))) (let ((_let_1 (@ tptp.ord_le527798542nres_b M))) (=> (@ (@ tptp.member_a X4) X) (=> (@ _let_1 (@ F X4)) (@ _let_1 (@ (@ tptp.refine436832839nd_a_b (@ tptp.refine1198353288_RES_a X)) F)))))))
% 0.27/0.71 (assert (forall ((X4 tptp.b) (X tptp.set_b) (M tptp.refine432681134nres_b) (F (-> tptp.b tptp.refine432681134nres_b))) (let ((_let_1 (@ tptp.ord_le527798542nres_b M))) (=> (@ (@ tptp.member_b X4) X) (=> (@ _let_1 (@ F X4)) (@ _let_1 (@ (@ tptp.refine1264602246nd_b_b (@ tptp.refine1198353289_RES_b X)) F)))))))
% 0.27/0.71 (assert (forall ((X4 tptp.b) (X tptp.set_b) (M tptp.refine424419629nres_a) (F (-> tptp.b tptp.refine424419629nres_a))) (let ((_let_1 (@ tptp.ord_le519537037nres_a M))) (=> (@ (@ tptp.member_b X4) X) (=> (@ _let_1 (@ F X4)) (@ _let_1 (@ (@ tptp.refine1264602245nd_b_a (@ tptp.refine1198353289_RES_b X)) F)))))))
% 0.27/0.71 (assert (forall ((X4 tptp.a) (X tptp.set_a) (M tptp.refine787176636t_unit) (F (-> tptp.a tptp.refine787176636t_unit))) (let ((_let_1 (@ tptp.ord_le1051254044t_unit M))) (=> (@ (@ tptp.member_a X4) X) (=> (@ _let_1 (@ F X4)) (@ _let_1 (@ (@ tptp.refine96995669t_unit (@ tptp.refine1198353288_RES_a X)) F)))))))
% 0.27/0.71 (assert (forall ((X4 tptp.b) (X tptp.set_b) (M tptp.refine787176636t_unit) (F (-> tptp.b tptp.refine787176636t_unit))) (let ((_let_1 (@ tptp.ord_le1051254044t_unit M))) (=> (@ (@ tptp.member_b X4) X) (=> (@ _let_1 (@ F X4)) (@ _let_1 (@ (@ tptp.refine216248468t_unit (@ tptp.refine1198353289_RES_b X)) F)))))))
% 0.27/0.71 (assert (forall ((X4 tptp.product_unit) (X tptp.set_Product_unit) (M tptp.refine432681134nres_b) (F (-> tptp.product_unit tptp.refine432681134nres_b))) (let ((_let_1 (@ tptp.ord_le527798542nres_b M))) (=> (@ (@ tptp.member_Product_unit X4) X) (=> (@ _let_1 (@ F X4)) (@ _let_1 (@ (@ tptp.refine119808504unit_b (@ tptp.refine1777164439t_unit X)) F)))))))
% 0.27/0.71 (assert (forall ((X4 tptp.product_unit) (X tptp.set_Product_unit) (M tptp.refine424419629nres_a) (F (-> tptp.product_unit tptp.refine424419629nres_a))) (let ((_let_1 (@ tptp.ord_le519537037nres_a M))) (=> (@ (@ tptp.member_Product_unit X4) X) (=> (@ _let_1 (@ F X4)) (@ _let_1 (@ (@ tptp.refine119808503unit_a (@ tptp.refine1777164439t_unit X)) F)))))))
% 0.27/0.71 (assert (forall ((X4 tptp.product_unit) (X tptp.set_Product_unit) (M tptp.refine787176636t_unit) (F (-> tptp.product_unit tptp.refine787176636t_unit))) (let ((_let_1 (@ tptp.ord_le1051254044t_unit M))) (=> (@ (@ tptp.member_Product_unit X4) X) (=> (@ _let_1 (@ F X4)) (@ _let_1 (@ (@ tptp.refine681446406t_unit (@ tptp.refine1777164439t_unit X)) F)))))))
% 0.27/0.71 (assert (forall ((X4 tptp.product_prod_a_a) (X tptp.set_Product_prod_a_a) (M tptp.refine432681134nres_b) (F (-> tptp.product_prod_a_a tptp.refine432681134nres_b))) (let ((_let_1 (@ tptp.ord_le527798542nres_b M))) (=> (@ (@ tptp.member449909584od_a_a X4) X) (=> (@ _let_1 (@ F X4)) (@ _let_1 (@ (@ tptp.refine988994910_a_a_b (@ tptp.refine622451633od_a_a X)) F)))))))
% 0.27/0.71 (assert (forall ((X4 tptp.set_b)) (@ (@ tptp.ord_less_eq_set_b X4) X4)))
% 0.27/0.71 (assert (forall ((X4 tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a X4) X4)))
% 0.27/0.71 (assert (forall ((X4 (-> Bool tptp.refine424419629nres_a))) (@ (@ tptp.ord_le516598614nres_a X4) X4)))
% 0.27/0.71 (assert (forall ((X4 (-> Bool tptp.refine432681134nres_b))) (@ (@ tptp.ord_le1656162903nres_b X4) X4)))
% 0.27/0.71 (assert (forall ((X4 tptp.refine787176636t_unit)) (@ (@ tptp.ord_le1051254044t_unit X4) X4)))
% 0.27/0.71 (assert (forall ((X4 tptp.refine432681134nres_b)) (@ (@ tptp.ord_le527798542nres_b X4) X4)))
% 0.27/0.71 (assert (forall ((X4 tptp.refine424419629nres_a)) (@ (@ tptp.ord_le519537037nres_a X4) X4)))
% 0.27/0.71 (assert (forall ((X tptp.set_Product_unit)) (= (@ tptp.refine1208325748t_unit (@ tptp.refine1777164439t_unit X)) X)))
% 0.27/0.71 (assert (forall ((X tptp.set_a)) (= (@ tptp.refine1822134885_RES_a (@ tptp.refine1198353288_RES_a X)) X)))
% 0.27/0.71 (assert (forall ((X tptp.set_b)) (= (@ tptp.refine1822134886_RES_b (@ tptp.refine1198353289_RES_b X)) X)))
% 0.27/0.71 (assert (forall ((X tptp.set_Product_prod_a_a) (X4 tptp.product_prod_a_a)) (= (@ (@ tptp.refine378960780od_a_a (@ tptp.refine622451633od_a_a X)) X4) (@ (@ tptp.member449909584od_a_a X4) X))))
% 0.27/0.71 (assert (forall ((X tptp.set_Product_prod_b_a) (X4 tptp.product_prod_b_a)) (= (@ (@ tptp.refine1206730187od_b_a (@ tptp.refine1450221040od_b_a X)) X4) (@ (@ tptp.member1277678991od_b_a X4) X))))
% 0.27/0.71 (assert (forall ((X tptp.set_Product_prod_b_b) (X4 tptp.product_prod_b_b)) (= (@ (@ tptp.refine1214991692od_b_b (@ tptp.refine1458482545od_b_b X)) X4) (@ (@ tptp.member1285940496od_b_b X4) X))))
% 0.27/0.71 (assert (forall ((X tptp.set_Product_prod_a_b) (X4 tptp.product_prod_a_b)) (= (@ (@ tptp.refine387222285od_a_b (@ tptp.refine630713138od_a_b X)) X4) (@ (@ tptp.member458171089od_a_b X4) X))))
% 0.27/0.71 (assert (forall ((X tptp.set_Product_unit) (X4 tptp.product_unit)) (= (@ (@ tptp.refine983493746t_unit (@ tptp.refine1777164439t_unit X)) X4) (@ (@ tptp.member_Product_unit X4) X))))
% 0.27/0.71 (assert (forall ((X tptp.set_a) (X4 tptp.a)) (= (@ (@ tptp.refine1312857699nres_a (@ tptp.refine1198353288_RES_a X)) X4) (@ (@ tptp.member_a X4) X))))
% 0.27/0.71 (assert (forall ((X tptp.set_b) (X4 tptp.b)) (= (@ (@ tptp.refine1312857700nres_b (@ tptp.refine1198353289_RES_b X)) X4) (@ (@ tptp.member_b X4) X))))
% 0.27/0.71 (assert (forall ((Phi (-> tptp.product_unit Bool)) (X4 tptp.product_unit)) (= (@ (@ tptp.refine983493746t_unit (@ tptp.refine1777164439t_unit (@ tptp.collect_Product_unit Phi))) X4) (@ Phi X4))))
% 0.27/0.71 (assert (forall ((Phi (-> tptp.a Bool)) (X4 tptp.a)) (= (@ (@ tptp.refine1312857699nres_a (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi))) X4) (@ Phi X4))))
% 0.27/0.71 (assert (forall ((Phi (-> tptp.b Bool)) (X4 tptp.b)) (= (@ (@ tptp.refine1312857700nres_b (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi))) X4) (@ Phi X4))))
% 0.27/0.71 (assert (forall ((F (-> Bool tptp.refine424419629nres_a)) (G (-> Bool tptp.refine424419629nres_a)) (X4 Bool)) (=> (@ (@ tptp.ord_le516598614nres_a F) G) (@ (@ tptp.ord_le519537037nres_a (@ F X4)) (@ G X4)))))
% 0.27/0.71 (assert (forall ((F (-> Bool tptp.refine432681134nres_b)) (G (-> Bool tptp.refine432681134nres_b)) (X4 Bool)) (=> (@ (@ tptp.ord_le1656162903nres_b F) G) (@ (@ tptp.ord_le527798542nres_b (@ F X4)) (@ G X4)))))
% 0.27/0.71 (assert (forall ((F (-> Bool tptp.refine424419629nres_a)) (G (-> Bool tptp.refine424419629nres_a)) (X4 Bool)) (=> (@ (@ tptp.ord_le516598614nres_a F) G) (@ (@ tptp.ord_le519537037nres_a (@ F X4)) (@ G X4)))))
% 0.27/0.71 (assert (forall ((F (-> Bool tptp.refine432681134nres_b)) (G (-> Bool tptp.refine432681134nres_b)) (X4 Bool)) (=> (@ (@ tptp.ord_le1656162903nres_b F) G) (@ (@ tptp.ord_le527798542nres_b (@ F X4)) (@ G X4)))))
% 0.27/0.71 (assert (forall ((F (-> Bool tptp.refine424419629nres_a)) (G (-> Bool tptp.refine424419629nres_a))) (=> (forall ((X3 Bool)) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ G X3))) (@ (@ tptp.ord_le516598614nres_a F) G))))
% 0.27/0.71 (assert (forall ((B Bool) (M1 tptp.refine432681134nres_b) (M12 tptp.refine432681134nres_b) (M2 tptp.refine432681134nres_b) (M22 tptp.refine432681134nres_b)) (let ((_let_1 (@ tptp.if_Ref1732808808nres_b B))) (=> (=> B (@ (@ tptp.ord_le527798542nres_b M1) M12)) (=> (=> (not B) (@ (@ tptp.ord_le527798542nres_b M2) M22)) (@ (@ tptp.ord_le527798542nres_b (@ (@ _let_1 M1) M2)) (@ (@ _let_1 M12) M22)))))))
% 0.27/0.71 (assert (forall ((B Bool) (M1 tptp.refine424419629nres_a) (M12 tptp.refine424419629nres_a) (M2 tptp.refine424419629nres_a) (M22 tptp.refine424419629nres_a)) (let ((_let_1 (@ tptp.if_Ref1724547303nres_a B))) (=> (=> B (@ (@ tptp.ord_le519537037nres_a M1) M12)) (=> (=> (not B) (@ (@ tptp.ord_le519537037nres_a M2) M22)) (@ (@ tptp.ord_le519537037nres_a (@ (@ _let_1 M1) M2)) (@ (@ _let_1 M12) M22)))))))
% 0.27/0.71 (assert (forall ((A tptp.refine432681134nres_b) (F (-> tptp.refine432681134nres_b tptp.refine432681134nres_b)) (B tptp.refine432681134nres_b) (C tptp.refine432681134nres_b)) (let ((_let_1 (@ tptp.ord_le527798542nres_b A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le527798542nres_b B) C) (=> (forall ((X3 tptp.refine432681134nres_b) (Y4 tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b X3) Y4) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 0.27/0.71 (assert (forall ((A tptp.refine432681134nres_b) (F (-> tptp.refine424419629nres_a tptp.refine432681134nres_b)) (B tptp.refine424419629nres_a) (C tptp.refine424419629nres_a)) (let ((_let_1 (@ tptp.ord_le527798542nres_b A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le519537037nres_a B) C) (=> (forall ((X3 tptp.refine424419629nres_a) (Y4 tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a X3) Y4) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 0.27/0.71 (assert (forall ((A tptp.refine424419629nres_a) (F (-> tptp.refine432681134nres_b tptp.refine424419629nres_a)) (B tptp.refine432681134nres_b) (C tptp.refine432681134nres_b)) (let ((_let_1 (@ tptp.ord_le519537037nres_a A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le527798542nres_b B) C) (=> (forall ((X3 tptp.refine432681134nres_b) (Y4 tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b X3) Y4) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 0.27/0.71 (assert (forall ((A tptp.refine424419629nres_a) (F (-> tptp.refine424419629nres_a tptp.refine424419629nres_a)) (B tptp.refine424419629nres_a) (C tptp.refine424419629nres_a)) (let ((_let_1 (@ tptp.ord_le519537037nres_a A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le519537037nres_a B) C) (=> (forall ((X3 tptp.refine424419629nres_a) (Y4 tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a X3) Y4) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))))
% 0.27/0.71 (assert (forall ((A tptp.set_a) (B tptp.set_a)) (= (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine1198353288_RES_a A)) (@ tptp.refine1198353288_RES_a B)) (@ (@ tptp.ord_less_eq_set_a A) B))))
% 0.27/0.71 (assert (forall ((A tptp.set_b) (B tptp.set_b)) (= (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine1198353289_RES_b A)) (@ tptp.refine1198353289_RES_b B)) (@ (@ tptp.ord_less_eq_set_b A) B))))
% 0.27/0.71 (assert (forall ((X tptp.set_a) (Y tptp.set_a)) (= (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine1198353288_RES_a X)) (@ tptp.refine1198353288_RES_a Y)) (@ (@ tptp.ord_less_eq_set_a X) Y))))
% 0.27/0.71 (assert (forall ((X tptp.set_b) (Y tptp.set_b)) (= (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine1198353289_RES_b X)) (@ tptp.refine1198353289_RES_b Y)) (@ (@ tptp.ord_less_eq_set_b X) Y))))
% 0.27/0.71 (assert (forall ((T tptp.refine432681134nres_b) (T2 tptp.refine432681134nres_b) (E tptp.refine432681134nres_b) (E2 tptp.refine432681134nres_b) (B Bool)) (let ((_let_1 (@ tptp.if_Ref1732808808nres_b B))) (=> (@ (@ tptp.ord_le527798542nres_b T) T2) (=> (@ (@ tptp.ord_le527798542nres_b E) E2) (@ (@ tptp.ord_le527798542nres_b (@ (@ _let_1 T) E)) (@ (@ _let_1 T2) E2)))))))
% 0.27/0.71 (assert (forall ((T tptp.refine424419629nres_a) (T2 tptp.refine424419629nres_a) (E tptp.refine424419629nres_a) (E2 tptp.refine424419629nres_a) (B Bool)) (let ((_let_1 (@ tptp.if_Ref1724547303nres_a B))) (=> (@ (@ tptp.ord_le519537037nres_a T) T2) (=> (@ (@ tptp.ord_le519537037nres_a E) E2) (@ (@ tptp.ord_le519537037nres_a (@ (@ _let_1 T) E)) (@ (@ _let_1 T2) E2)))))))
% 0.27/0.71 (assert (forall ((B tptp.refine432681134nres_b) (A tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b B) A) (=> (@ (@ tptp.ord_le527798542nres_b A) B) (= A B)))))
% 0.27/0.71 (assert (forall ((B tptp.refine424419629nres_a) (A tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a B) A) (=> (@ (@ tptp.ord_le519537037nres_a A) B) (= A B)))))
% 0.27/0.71 (assert (= (lambda ((Y5 tptp.refine432681134nres_b) (Z tptp.refine432681134nres_b)) (= Y5 Z)) (lambda ((A2 tptp.refine432681134nres_b) (B2 tptp.refine432681134nres_b)) (and (@ (@ tptp.ord_le527798542nres_b B2) A2) (@ (@ tptp.ord_le527798542nres_b A2) B2)))))
% 0.27/0.71 (assert (= (lambda ((Y5 tptp.refine424419629nres_a) (Z tptp.refine424419629nres_a)) (= Y5 Z)) (lambda ((A2 tptp.refine424419629nres_a) (B2 tptp.refine424419629nres_a)) (and (@ (@ tptp.ord_le519537037nres_a B2) A2) (@ (@ tptp.ord_le519537037nres_a A2) B2)))))
% 0.27/0.71 (assert (forall ((B tptp.refine432681134nres_b) (A tptp.refine432681134nres_b) (C tptp.refine432681134nres_b)) (let ((_let_1 (@ tptp.ord_le527798542nres_b C))) (=> (@ (@ tptp.ord_le527798542nres_b B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.27/0.71 (assert (forall ((B tptp.refine424419629nres_a) (A tptp.refine424419629nres_a) (C tptp.refine424419629nres_a)) (let ((_let_1 (@ tptp.ord_le519537037nres_a C))) (=> (@ (@ tptp.ord_le519537037nres_a B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.27/0.71 (assert (forall ((A tptp.refine432681134nres_b)) (@ (@ tptp.ord_le527798542nres_b A) A)))
% 0.27/0.71 (assert (forall ((A tptp.refine424419629nres_a)) (@ (@ tptp.ord_le519537037nres_a A) A)))
% 0.27/0.71 (assert (forall ((X4 tptp.refine432681134nres_b) (Y3 tptp.refine432681134nres_b) (Z2 tptp.refine432681134nres_b)) (let ((_let_1 (@ tptp.ord_le527798542nres_b X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_le527798542nres_b Y3) Z2) (@ _let_1 Z2))))))
% 0.27/0.71 (assert (forall ((X4 tptp.refine424419629nres_a) (Y3 tptp.refine424419629nres_a) (Z2 tptp.refine424419629nres_a)) (let ((_let_1 (@ tptp.ord_le519537037nres_a X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_le519537037nres_a Y3) Z2) (@ _let_1 Z2))))))
% 0.27/0.71 (assert (forall ((A tptp.refine432681134nres_b) (B tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b A) B) (=> (@ (@ tptp.ord_le527798542nres_b B) A) (= A B)))))
% 0.27/0.71 (assert (forall ((A tptp.refine424419629nres_a) (B tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a A) B) (=> (@ (@ tptp.ord_le519537037nres_a B) A) (= A B)))))
% 0.27/0.71 (assert (forall ((A tptp.refine432681134nres_b) (B tptp.refine432681134nres_b) (C tptp.refine432681134nres_b)) (let ((_let_1 (@ tptp.ord_le527798542nres_b A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.27/0.71 (assert (forall ((A tptp.refine424419629nres_a) (B tptp.refine424419629nres_a) (C tptp.refine424419629nres_a)) (let ((_let_1 (@ tptp.ord_le519537037nres_a A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.27/0.71 (assert (forall ((A tptp.refine432681134nres_b) (B tptp.refine432681134nres_b) (C tptp.refine432681134nres_b)) (=> (= A B) (=> (@ (@ tptp.ord_le527798542nres_b B) C) (@ (@ tptp.ord_le527798542nres_b A) C)))))
% 0.27/0.71 (assert (forall ((A tptp.refine424419629nres_a) (B tptp.refine424419629nres_a) (C tptp.refine424419629nres_a)) (=> (= A B) (=> (@ (@ tptp.ord_le519537037nres_a B) C) (@ (@ tptp.ord_le519537037nres_a A) C)))))
% 0.27/0.71 (assert (= (lambda ((Y5 tptp.refine432681134nres_b) (Z tptp.refine432681134nres_b)) (= Y5 Z)) (lambda ((A2 tptp.refine432681134nres_b) (B2 tptp.refine432681134nres_b)) (and (@ (@ tptp.ord_le527798542nres_b A2) B2) (@ (@ tptp.ord_le527798542nres_b B2) A2)))))
% 0.27/0.71 (assert (= (lambda ((Y5 tptp.refine424419629nres_a) (Z tptp.refine424419629nres_a)) (= Y5 Z)) (lambda ((A2 tptp.refine424419629nres_a) (B2 tptp.refine424419629nres_a)) (and (@ (@ tptp.ord_le519537037nres_a A2) B2) (@ (@ tptp.ord_le519537037nres_a B2) A2)))))
% 0.27/0.71 (assert (forall ((Y3 tptp.refine432681134nres_b) (X4 tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b Y3) X4) (= (@ (@ tptp.ord_le527798542nres_b X4) Y3) (= X4 Y3)))))
% 0.27/0.71 (assert (forall ((Y3 tptp.refine424419629nres_a) (X4 tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a Y3) X4) (= (@ (@ tptp.ord_le519537037nres_a X4) Y3) (= X4 Y3)))))
% 0.27/0.71 (assert (forall ((A tptp.refine432681134nres_b) (B tptp.refine432681134nres_b) (C tptp.refine432681134nres_b)) (let ((_let_1 (@ tptp.ord_le527798542nres_b A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le527798542nres_b B) C) (@ _let_1 C))))))
% 0.27/0.71 (assert (forall ((A tptp.refine424419629nres_a) (B tptp.refine424419629nres_a) (C tptp.refine424419629nres_a)) (let ((_let_1 (@ tptp.ord_le519537037nres_a A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le519537037nres_a B) C) (@ _let_1 C))))))
% 0.27/0.71 (assert (forall ((X4 tptp.refine432681134nres_b) (Y3 tptp.refine432681134nres_b)) (=> (= X4 Y3) (@ (@ tptp.ord_le527798542nres_b X4) Y3))))
% 0.27/0.71 (assert (forall ((X4 tptp.refine424419629nres_a) (Y3 tptp.refine424419629nres_a)) (=> (= X4 Y3) (@ (@ tptp.ord_le519537037nres_a X4) Y3))))
% 0.27/0.71 (assert (forall ((X4 tptp.refine432681134nres_b) (Y3 tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b X4) Y3) (=> (@ (@ tptp.ord_le527798542nres_b Y3) X4) (= X4 Y3)))))
% 0.27/0.71 (assert (forall ((X4 tptp.refine424419629nres_a) (Y3 tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a X4) Y3) (=> (@ (@ tptp.ord_le519537037nres_a Y3) X4) (= X4 Y3)))))
% 0.27/0.71 (assert (forall ((A tptp.a) (P (-> tptp.a Bool))) (= (@ (@ tptp.member_a A) (@ tptp.collect_a P)) (@ P A))))
% 0.27/0.71 (assert (forall ((A tptp.b) (P (-> tptp.b Bool))) (= (@ (@ tptp.member_b A) (@ tptp.collect_b P)) (@ P A))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_a)) (= (@ tptp.collect_a (lambda ((X5 tptp.a)) (@ (@ tptp.member_a X5) A3))) A3)))
% 0.27/0.71 (assert (forall ((A3 tptp.set_b)) (= (@ tptp.collect_b (lambda ((X5 tptp.b)) (@ (@ tptp.member_b X5) A3))) A3)))
% 0.27/0.71 (assert (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (=> (forall ((X3 tptp.a)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_a P) (@ tptp.collect_a Q)))))
% 0.27/0.71 (assert (forall ((P (-> tptp.b Bool)) (Q (-> tptp.b Bool))) (=> (forall ((X3 tptp.b)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_b P) (@ tptp.collect_b Q)))))
% 0.27/0.71 (assert (= (lambda ((Y5 tptp.refine432681134nres_b) (Z tptp.refine432681134nres_b)) (= Y5 Z)) (lambda ((X5 tptp.refine432681134nres_b) (Y6 tptp.refine432681134nres_b)) (and (@ (@ tptp.ord_le527798542nres_b X5) Y6) (@ (@ tptp.ord_le527798542nres_b Y6) X5)))))
% 0.27/0.71 (assert (= (lambda ((Y5 tptp.refine424419629nres_a) (Z tptp.refine424419629nres_a)) (= Y5 Z)) (lambda ((X5 tptp.refine424419629nres_a) (Y6 tptp.refine424419629nres_a)) (and (@ (@ tptp.ord_le519537037nres_a X5) Y6) (@ (@ tptp.ord_le519537037nres_a Y6) X5)))))
% 0.27/0.71 (assert (forall ((A tptp.refine432681134nres_b) (B tptp.refine432681134nres_b) (F (-> tptp.refine432681134nres_b tptp.refine432681134nres_b)) (C tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.refine432681134nres_b) (Y4 tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b X3) Y4) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le527798542nres_b (@ F A)) C))))))
% 0.27/0.71 (assert (forall ((A tptp.refine432681134nres_b) (B tptp.refine432681134nres_b) (F (-> tptp.refine432681134nres_b tptp.refine424419629nres_a)) (C tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le527798542nres_b A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.refine432681134nres_b) (Y4 tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b X3) Y4) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le519537037nres_a (@ F A)) C))))))
% 0.27/0.71 (assert (forall ((A tptp.refine424419629nres_a) (B tptp.refine424419629nres_a) (F (-> tptp.refine424419629nres_a tptp.refine432681134nres_b)) (C tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le519537037nres_a A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.refine424419629nres_a) (Y4 tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a X3) Y4) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le527798542nres_b (@ F A)) C))))))
% 0.27/0.71 (assert (forall ((A tptp.refine424419629nres_a) (B tptp.refine424419629nres_a) (F (-> tptp.refine424419629nres_a tptp.refine424419629nres_a)) (C tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.refine424419629nres_a) (Y4 tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a X3) Y4) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le519537037nres_a (@ F A)) C))))))
% 0.27/0.71 (assert (forall ((A tptp.refine432681134nres_b) (F (-> tptp.refine432681134nres_b tptp.refine432681134nres_b)) (B tptp.refine432681134nres_b) (C tptp.refine432681134nres_b)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le527798542nres_b B) C) (=> (forall ((X3 tptp.refine432681134nres_b) (Y4 tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b X3) Y4) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le527798542nres_b A) (@ F C)))))))
% 0.27/0.71 (assert (forall ((A tptp.refine424419629nres_a) (F (-> tptp.refine432681134nres_b tptp.refine424419629nres_a)) (B tptp.refine432681134nres_b) (C tptp.refine432681134nres_b)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le527798542nres_b B) C) (=> (forall ((X3 tptp.refine432681134nres_b) (Y4 tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b X3) Y4) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le519537037nres_a A) (@ F C)))))))
% 0.27/0.71 (assert (forall ((A tptp.refine432681134nres_b) (F (-> tptp.refine424419629nres_a tptp.refine432681134nres_b)) (B tptp.refine424419629nres_a) (C tptp.refine424419629nres_a)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le519537037nres_a B) C) (=> (forall ((X3 tptp.refine424419629nres_a) (Y4 tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a X3) Y4) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le527798542nres_b A) (@ F C)))))))
% 0.27/0.71 (assert (forall ((A tptp.refine424419629nres_a) (F (-> tptp.refine424419629nres_a tptp.refine424419629nres_a)) (B tptp.refine424419629nres_a) (C tptp.refine424419629nres_a)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le519537037nres_a B) C) (=> (forall ((X3 tptp.refine424419629nres_a) (Y4 tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a X3) Y4) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le519537037nres_a A) (@ F C)))))))
% 0.27/0.71 (assert (forall ((A tptp.refine432681134nres_b) (B tptp.refine432681134nres_b) (F (-> tptp.refine432681134nres_b tptp.refine432681134nres_b)) (C tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b A) B) (=> (@ (@ tptp.ord_le527798542nres_b (@ F B)) C) (=> (forall ((X3 tptp.refine432681134nres_b) (Y4 tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b X3) Y4) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le527798542nres_b (@ F A)) C))))))
% 0.27/0.71 (assert (forall ((A tptp.refine432681134nres_b) (B tptp.refine432681134nres_b) (F (-> tptp.refine432681134nres_b tptp.refine424419629nres_a)) (C tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le527798542nres_b A) B) (=> (@ (@ tptp.ord_le519537037nres_a (@ F B)) C) (=> (forall ((X3 tptp.refine432681134nres_b) (Y4 tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b X3) Y4) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le519537037nres_a (@ F A)) C))))))
% 0.27/0.71 (assert (forall ((A tptp.refine424419629nres_a) (B tptp.refine424419629nres_a) (F (-> tptp.refine424419629nres_a tptp.refine432681134nres_b)) (C tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le519537037nres_a A) B) (=> (@ (@ tptp.ord_le527798542nres_b (@ F B)) C) (=> (forall ((X3 tptp.refine424419629nres_a) (Y4 tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a X3) Y4) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le527798542nres_b (@ F A)) C))))))
% 0.27/0.71 (assert (forall ((A tptp.refine424419629nres_a) (B tptp.refine424419629nres_a) (F (-> tptp.refine424419629nres_a tptp.refine424419629nres_a)) (C tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a A) B) (=> (@ (@ tptp.ord_le519537037nres_a (@ F B)) C) (=> (forall ((X3 tptp.refine424419629nres_a) (Y4 tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a X3) Y4) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le519537037nres_a (@ F A)) C))))))
% 0.27/0.71 (assert (forall ((M tptp.refine424419629nres_a)) (=> (@ tptp.refine412683989fail_a M) (= (@ tptp.refine1198353288_RES_a (@ tptp.refine1822134885_RES_a M)) M))))
% 0.27/0.71 (assert (forall ((M tptp.refine432681134nres_b)) (=> (@ tptp.refine412683990fail_b M) (= (@ tptp.refine1198353289_RES_b (@ tptp.refine1822134886_RES_b M)) M))))
% 0.27/0.71 (assert (forall ((P (-> tptp.refine432681134nres_b Bool)) (X4 tptp.refine432681134nres_b)) (=> (@ P X4) (=> (forall ((Y4 tptp.refine432681134nres_b)) (=> (@ P Y4) (@ (@ tptp.ord_le527798542nres_b Y4) X4))) (= (@ tptp.order_1722590613nres_b P) X4)))))
% 0.27/0.71 (assert (forall ((P (-> tptp.refine424419629nres_a Bool)) (X4 tptp.refine424419629nres_a)) (=> (@ P X4) (=> (forall ((Y4 tptp.refine424419629nres_a)) (=> (@ P Y4) (@ (@ tptp.ord_le519537037nres_a Y4) X4))) (= (@ tptp.order_1714329108nres_a P) X4)))))
% 0.27/0.71 (assert (forall ((P (-> tptp.refine432681134nres_b Bool)) (X4 tptp.refine432681134nres_b) (Q (-> tptp.refine432681134nres_b Bool))) (=> (@ P X4) (=> (forall ((Y4 tptp.refine432681134nres_b)) (=> (@ P Y4) (@ (@ tptp.ord_le527798542nres_b Y4) X4))) (=> (forall ((X3 tptp.refine432681134nres_b)) (=> (@ P X3) (=> (forall ((Y7 tptp.refine432681134nres_b)) (=> (@ P Y7) (@ (@ tptp.ord_le527798542nres_b Y7) X3))) (@ Q X3)))) (@ Q (@ tptp.order_1722590613nres_b P)))))))
% 0.27/0.71 (assert (forall ((P (-> tptp.refine424419629nres_a Bool)) (X4 tptp.refine424419629nres_a) (Q (-> tptp.refine424419629nres_a Bool))) (=> (@ P X4) (=> (forall ((Y4 tptp.refine424419629nres_a)) (=> (@ P Y4) (@ (@ tptp.ord_le519537037nres_a Y4) X4))) (=> (forall ((X3 tptp.refine424419629nres_a)) (=> (@ P X3) (=> (forall ((Y7 tptp.refine424419629nres_a)) (=> (@ P Y7) (@ (@ tptp.ord_le519537037nres_a Y7) X3))) (@ Q X3)))) (@ Q (@ tptp.order_1714329108nres_a P)))))))
% 0.27/0.71 (assert (= tptp.ord_le1656162903nres_b (lambda ((X6 (-> Bool tptp.refine432681134nres_b)) (Y8 (-> Bool tptp.refine432681134nres_b))) (and (@ (@ tptp.ord_le527798542nres_b (@ X6 false)) (@ Y8 false)) (@ (@ tptp.ord_le527798542nres_b (@ X6 true)) (@ Y8 true))))))
% 0.27/0.71 (assert (= tptp.ord_le516598614nres_a (lambda ((X6 (-> Bool tptp.refine424419629nres_a)) (Y8 (-> Bool tptp.refine424419629nres_a))) (and (@ (@ tptp.ord_le519537037nres_a (@ X6 false)) (@ Y8 false)) (@ (@ tptp.ord_le519537037nres_a (@ X6 true)) (@ Y8 true))))))
% 0.27/0.71 (assert (forall ((A tptp.refine432681134nres_b) (B tptp.refine432681134nres_b) (C tptp.refine432681134nres_b) (D tptp.refine432681134nres_b)) (=> (= A B) (=> (@ (@ tptp.ord_le527798542nres_b B) C) (=> (= C D) (@ (@ tptp.ord_le527798542nres_b A) D))))))
% 0.27/0.71 (assert (forall ((A tptp.refine424419629nres_a) (B tptp.refine424419629nres_a) (C tptp.refine424419629nres_a) (D tptp.refine424419629nres_a)) (=> (= A B) (=> (@ (@ tptp.ord_le519537037nres_a B) C) (=> (= C D) (@ (@ tptp.ord_le519537037nres_a A) D))))))
% 0.27/0.71 (assert (forall ((X tptp.set_a)) (@ tptp.refine412683989fail_a (@ tptp.refine1198353288_RES_a X))))
% 0.27/0.71 (assert (forall ((X tptp.set_b)) (@ tptp.refine412683990fail_b (@ tptp.refine1198353289_RES_b X))))
% 0.27/0.71 (assert (forall ((S tptp.set_a) (P (-> tptp.a Bool))) (= (@ (@ tptp.ord_less_eq_set_a S) (@ tptp.collect_a P)) (forall ((X5 tptp.a)) (=> (@ (@ tptp.member_a X5) S) (@ P X5))))))
% 0.27/0.71 (assert (forall ((S tptp.set_b) (P (-> tptp.b Bool))) (= (@ (@ tptp.ord_less_eq_set_b S) (@ tptp.collect_b P)) (forall ((X5 tptp.b)) (=> (@ (@ tptp.member_b X5) S) (@ P X5))))))
% 0.27/0.71 (assert (forall ((S tptp.refine432681134nres_b) (S3 tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b S) S3) (=> (@ tptp.refine412683990fail_b S3) (@ tptp.refine412683990fail_b S)))))
% 0.27/0.71 (assert (forall ((S tptp.refine424419629nres_a) (S3 tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a S) S3) (=> (@ tptp.refine412683989fail_a S3) (@ tptp.refine412683989fail_a S)))))
% 0.27/0.71 (assert (forall ((M3 tptp.refine432681134nres_b) (M4 tptp.refine432681134nres_b)) (let ((_let_1 (@ (@ tptp.ord_le527798542nres_b M4) M3))) (=> (=> (@ tptp.refine412683990fail_b M3) _let_1) _let_1))))
% 0.27/0.71 (assert (forall ((M3 tptp.refine424419629nres_a) (M4 tptp.refine424419629nres_a)) (let ((_let_1 (@ (@ tptp.ord_le519537037nres_a M4) M3))) (=> (=> (@ tptp.refine412683989fail_a M3) _let_1) _let_1))))
% 0.27/0.71 (assert (= tptp.refine412683989fail_a (lambda ((M5 tptp.refine424419629nres_a)) (exists ((M6 tptp.set_a)) (= M5 (@ tptp.refine1198353288_RES_a M6))))))
% 0.27/0.71 (assert (= tptp.refine412683990fail_b (lambda ((M5 tptp.refine432681134nres_b)) (exists ((M6 tptp.set_b)) (= M5 (@ tptp.refine1198353289_RES_b M6))))))
% 0.27/0.71 (assert (forall ((A3 tptp.refine432681134nres_b) (R tptp.set_Product_prod_b_b) (B3 tptp.refine432681134nres_b) (C2 tptp.refine432681134nres_b)) (let ((_let_1 (@ tptp.refine122110613un_b_b R))) (let ((_let_2 (@ tptp.ord_le527798542nres_b A3))) (=> (@ _let_2 (@ _let_1 B3)) (=> (@ (@ tptp.ord_le527798542nres_b B3) C2) (@ _let_2 (@ _let_1 C2))))))))
% 0.27/0.71 (assert (forall ((A3 tptp.refine432681134nres_b) (R tptp.set_Product_prod_b_a) (B3 tptp.refine424419629nres_a) (C2 tptp.refine424419629nres_a)) (let ((_let_1 (@ tptp.refine122110612un_b_a R))) (let ((_let_2 (@ tptp.ord_le527798542nres_b A3))) (=> (@ _let_2 (@ _let_1 B3)) (=> (@ (@ tptp.ord_le519537037nres_a B3) C2) (@ _let_2 (@ _let_1 C2))))))))
% 0.27/0.71 (assert (forall ((A3 tptp.refine424419629nres_a) (R tptp.set_Product_prod_a_b) (B3 tptp.refine432681134nres_b) (C2 tptp.refine432681134nres_b)) (let ((_let_1 (@ tptp.refine1441824854un_a_b R))) (let ((_let_2 (@ tptp.ord_le519537037nres_a A3))) (=> (@ _let_2 (@ _let_1 B3)) (=> (@ (@ tptp.ord_le527798542nres_b B3) C2) (@ _let_2 (@ _let_1 C2))))))))
% 0.27/0.71 (assert (forall ((A3 tptp.refine424419629nres_a) (R tptp.set_Product_prod_a_a) (B3 tptp.refine424419629nres_a) (C2 tptp.refine424419629nres_a)) (let ((_let_1 (@ tptp.refine1441824853un_a_a R))) (let ((_let_2 (@ tptp.ord_le519537037nres_a A3))) (=> (@ _let_2 (@ _let_1 B3)) (=> (@ (@ tptp.ord_le519537037nres_a B3) C2) (@ _let_2 (@ _let_1 C2))))))))
% 0.27/0.71 (assert (forall ((A tptp.refine424419629nres_a) (X4 tptp.set_a)) (=> (@ (@ tptp.ord_le519537037nres_a A) (@ tptp.refine1198353288_RES_a X4)) (@ tptp.refine412683989fail_a A))))
% 0.27/0.71 (assert (forall ((A tptp.refine432681134nres_b) (X4 tptp.set_b)) (=> (@ (@ tptp.ord_le527798542nres_b A) (@ tptp.refine1198353289_RES_b X4)) (@ tptp.refine412683990fail_b A))))
% 0.27/0.71 (assert (forall ((X tptp.set_a) (F (-> tptp.a tptp.refine432681134nres_b))) (= (@ tptp.refine412683990fail_b (@ (@ tptp.refine436832839nd_a_b (@ tptp.refine1198353288_RES_a X)) F)) (forall ((X5 tptp.a)) (=> (@ (@ tptp.member_a X5) X) (@ tptp.refine412683990fail_b (@ F X5)))))))
% 0.27/0.71 (assert (forall ((X7 tptp.a) (X8 tptp.set_a) (M tptp.refine432681134nres_b) (R tptp.set_Product_prod_b_b) (F2 (-> tptp.a tptp.refine432681134nres_b))) (let ((_let_1 (@ tptp.refine122110613un_b_b R))) (let ((_let_2 (@ tptp.ord_le527798542nres_b M))) (=> (@ (@ tptp.member_a X7) X8) (=> (@ _let_2 (@ _let_1 (@ F2 X7))) (@ _let_2 (@ _let_1 (@ (@ tptp.refine436832839nd_a_b (@ tptp.refine1198353288_RES_a X8)) F2)))))))))
% 0.27/0.71 (assert (forall ((X7 tptp.a) (X8 tptp.set_a) (M tptp.refine424419629nres_a) (R tptp.set_Product_prod_a_b) (F2 (-> tptp.a tptp.refine432681134nres_b))) (let ((_let_1 (@ tptp.refine1441824854un_a_b R))) (let ((_let_2 (@ tptp.ord_le519537037nres_a M))) (=> (@ (@ tptp.member_a X7) X8) (=> (@ _let_2 (@ _let_1 (@ F2 X7))) (@ _let_2 (@ _let_1 (@ (@ tptp.refine436832839nd_a_b (@ tptp.refine1198353288_RES_a X8)) F2)))))))))
% 0.27/0.71 (assert (forall ((Phi (-> tptp.a Bool)) (X7 tptp.a) (M tptp.refine432681134nres_b) (R tptp.set_Product_prod_b_b) (F2 (-> tptp.a tptp.refine432681134nres_b))) (let ((_let_1 (@ tptp.refine122110613un_b_b R))) (let ((_let_2 (@ tptp.ord_le527798542nres_b M))) (=> (@ Phi X7) (=> (@ _let_2 (@ _let_1 (@ F2 X7))) (@ _let_2 (@ _let_1 (@ (@ tptp.refine436832839nd_a_b (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi))) F2)))))))))
% 0.27/0.71 (assert (forall ((Phi (-> tptp.a Bool)) (X7 tptp.a) (M tptp.refine424419629nres_a) (R tptp.set_Product_prod_a_b) (F2 (-> tptp.a tptp.refine432681134nres_b))) (let ((_let_1 (@ tptp.refine1441824854un_a_b R))) (let ((_let_2 (@ tptp.ord_le519537037nres_a M))) (=> (@ Phi X7) (=> (@ _let_2 (@ _let_1 (@ F2 X7))) (@ _let_2 (@ _let_1 (@ (@ tptp.refine436832839nd_a_b (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi))) F2)))))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_a) (B3 tptp.set_a)) (=> (forall ((X3 tptp.a)) (let ((_let_1 (@ tptp.member_a X3))) (=> (@ _let_1 A3) (@ _let_1 B3)))) (@ (@ tptp.ord_less_eq_set_a A3) B3))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_b) (B3 tptp.set_b)) (=> (forall ((X3 tptp.b)) (let ((_let_1 (@ tptp.member_b X3))) (=> (@ _let_1 A3) (@ _let_1 B3)))) (@ (@ tptp.ord_less_eq_set_b A3) B3))))
% 0.27/0.71 (assert (forall ((M tptp.refine424419629nres_a) (F2 (-> tptp.a tptp.refine424419629nres_a)) (Psi (-> tptp.a Bool)) (F (-> tptp.a tptp.refine432681134nres_b)) (Phi (-> tptp.b Bool))) (=> (@ (@ tptp.ord_le519537037nres_a (@ (@ tptp.refine436832838nd_a_a M) F2)) (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Psi))) (=> (forall ((X3 tptp.a)) (=> (@ tptp.refine412683989fail_a M) (=> (@ (@ tptp.refine1001002027nres_a M) X3) (=> (@ (@ tptp.ord_le519537037nres_a (@ F2 X3)) (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Psi))) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi))))))) (@ (@ tptp.ord_le527798542nres_b (@ (@ tptp.refine436832839nd_a_b M) F)) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi)))))))
% 0.27/0.71 (assert (forall ((M tptp.refine424419629nres_a) (F2 (-> tptp.a tptp.refine432681134nres_b)) (Psi (-> tptp.b Bool)) (F (-> tptp.a tptp.refine424419629nres_a)) (Phi (-> tptp.a Bool))) (=> (@ (@ tptp.ord_le527798542nres_b (@ (@ tptp.refine436832839nd_a_b M) F2)) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Psi))) (=> (forall ((X3 tptp.a)) (=> (@ tptp.refine412683989fail_a M) (=> (@ (@ tptp.refine1001002027nres_a M) X3) (=> (@ (@ tptp.ord_le527798542nres_b (@ F2 X3)) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Psi))) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi))))))) (@ (@ tptp.ord_le519537037nres_a (@ (@ tptp.refine436832838nd_a_a M) F)) (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi)))))))
% 0.27/0.71 (assert (forall ((M tptp.refine424419629nres_a) (F2 (-> tptp.a tptp.refine432681134nres_b)) (Psi (-> tptp.b Bool)) (F (-> tptp.a tptp.refine432681134nres_b)) (Phi (-> tptp.b Bool))) (let ((_let_1 (@ tptp.refine436832839nd_a_b M))) (=> (@ (@ tptp.ord_le527798542nres_b (@ _let_1 F2)) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Psi))) (=> (forall ((X3 tptp.a)) (=> (@ tptp.refine412683989fail_a M) (=> (@ (@ tptp.refine1001002027nres_a M) X3) (=> (@ (@ tptp.ord_le527798542nres_b (@ F2 X3)) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Psi))) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi))))))) (@ (@ tptp.ord_le527798542nres_b (@ _let_1 F)) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi))))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_a) (B3 tptp.set_a) (X4 tptp.a)) (let ((_let_1 (@ tptp.member_a X4))) (=> (@ (@ tptp.ord_less_eq_set_a A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_b) (B3 tptp.set_b) (X4 tptp.b)) (let ((_let_1 (@ tptp.member_b X4))) (=> (@ (@ tptp.ord_less_eq_set_b A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_a) (B3 tptp.set_a) (C tptp.a)) (let ((_let_1 (@ tptp.member_a C))) (=> (@ (@ tptp.ord_less_eq_set_a A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_b) (B3 tptp.set_b) (C tptp.b)) (let ((_let_1 (@ tptp.member_b C))) (=> (@ (@ tptp.ord_less_eq_set_b A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))))
% 0.27/0.71 (assert (forall ((X tptp.set_a)) (= (@ tptp.refine1001002027nres_a (@ tptp.refine1198353288_RES_a X)) (lambda ((X5 tptp.a)) (@ (@ tptp.member_a X5) X)))))
% 0.27/0.71 (assert (forall ((X tptp.set_b)) (= (@ tptp.refine1001002028nres_b (@ tptp.refine1198353289_RES_b X)) (lambda ((X5 tptp.b)) (@ (@ tptp.member_b X5) X)))))
% 0.27/0.71 (assert (forall ((S tptp.refine432681134nres_b) (S3 tptp.refine432681134nres_b) (X4 tptp.b)) (=> (@ (@ tptp.ord_le527798542nres_b S) S3) (=> (@ (@ tptp.refine1001002028nres_b S) X4) (@ (@ tptp.refine1001002028nres_b S3) X4)))))
% 0.27/0.71 (assert (forall ((S tptp.refine424419629nres_a) (S3 tptp.refine424419629nres_a) (X4 tptp.a)) (=> (@ (@ tptp.ord_le519537037nres_a S) S3) (=> (@ (@ tptp.refine1001002027nres_a S) X4) (@ (@ tptp.refine1001002027nres_a S3) X4)))))
% 0.27/0.71 (assert (forall ((X tptp.set_a) (F (-> tptp.a tptp.refine432681134nres_b)) (Y3 tptp.b)) (= (@ (@ tptp.refine1001002028nres_b (@ (@ tptp.refine436832839nd_a_b (@ tptp.refine1198353288_RES_a X)) F)) Y3) (exists ((X5 tptp.a)) (and (@ (@ tptp.member_a X5) X) (@ (@ tptp.refine1001002028nres_b (@ F X5)) Y3))))))
% 0.27/0.71 (assert (forall ((S3 tptp.refine432681134nres_b) (S tptp.refine432681134nres_b)) (=> (=> (@ tptp.refine412683990fail_b S3) (and (@ tptp.refine412683990fail_b S) (forall ((X3 tptp.b)) (=> (@ (@ tptp.refine1001002028nres_b S) X3) (@ (@ tptp.refine1001002028nres_b S3) X3))))) (@ (@ tptp.ord_le527798542nres_b S) S3))))
% 0.27/0.71 (assert (forall ((S3 tptp.refine424419629nres_a) (S tptp.refine424419629nres_a)) (=> (=> (@ tptp.refine412683989fail_a S3) (and (@ tptp.refine412683989fail_a S) (forall ((X3 tptp.a)) (=> (@ (@ tptp.refine1001002027nres_a S) X3) (@ (@ tptp.refine1001002027nres_a S3) X3))))) (@ (@ tptp.ord_le519537037nres_a S) S3))))
% 0.27/0.71 (assert (forall ((S3 tptp.refine432681134nres_b) (S tptp.refine432681134nres_b)) (=> (=> (@ tptp.refine412683990fail_b S3) (@ tptp.refine412683990fail_b S)) (=> (forall ((X3 tptp.b)) (=> (@ tptp.refine412683990fail_b S3) (=> (@ (@ tptp.refine1001002028nres_b S) X3) (@ (@ tptp.refine1001002028nres_b S3) X3)))) (@ (@ tptp.ord_le527798542nres_b S) S3)))))
% 0.27/0.71 (assert (forall ((S3 tptp.refine424419629nres_a) (S tptp.refine424419629nres_a)) (=> (=> (@ tptp.refine412683989fail_a S3) (@ tptp.refine412683989fail_a S)) (=> (forall ((X3 tptp.a)) (=> (@ tptp.refine412683989fail_a S3) (=> (@ (@ tptp.refine1001002027nres_a S) X3) (@ (@ tptp.refine1001002027nres_a S3) X3)))) (@ (@ tptp.ord_le519537037nres_a S) S3)))))
% 0.27/0.71 (assert (= tptp.ord_le527798542nres_b (lambda ((S4 tptp.refine432681134nres_b) (S5 tptp.refine432681134nres_b)) (=> (@ tptp.refine412683990fail_b S5) (and (@ tptp.refine412683990fail_b S4) (forall ((X5 tptp.b)) (=> (@ (@ tptp.refine1001002028nres_b S4) X5) (@ (@ tptp.refine1001002028nres_b S5) X5))))))))
% 0.27/0.71 (assert (= tptp.ord_le519537037nres_a (lambda ((S4 tptp.refine424419629nres_a) (S5 tptp.refine424419629nres_a)) (=> (@ tptp.refine412683989fail_a S5) (and (@ tptp.refine412683989fail_a S4) (forall ((X5 tptp.a)) (=> (@ (@ tptp.refine1001002027nres_a S4) X5) (@ (@ tptp.refine1001002027nres_a S5) X5))))))))
% 0.27/0.71 (assert (forall ((M4 tptp.refine424419629nres_a) (F (-> tptp.a tptp.refine432681134nres_b))) (= (@ tptp.refine412683990fail_b (@ (@ tptp.refine436832839nd_a_b M4) F)) (and (@ tptp.refine412683989fail_a M4) (forall ((X5 tptp.a)) (=> (@ (@ tptp.refine1001002027nres_a M4) X5) (@ tptp.refine412683990fail_b (@ F X5))))))))
% 0.27/0.71 (assert (forall ((M4 tptp.refine424419629nres_a) (F (-> tptp.a tptp.refine432681134nres_b)) (S tptp.refine432681134nres_b)) (= (@ (@ tptp.ord_le527798542nres_b (@ (@ tptp.refine436832839nd_a_b M4) F)) S) (and (=> (@ tptp.refine412683990fail_b S) (@ tptp.refine412683989fail_a M4)) (forall ((X5 tptp.a)) (=> (and (@ tptp.refine412683989fail_a M4) (@ (@ tptp.refine1001002027nres_a M4) X5)) (@ (@ tptp.ord_le527798542nres_b (@ F X5)) S)))))))
% 0.27/0.71 (assert (forall ((S tptp.refine432681134nres_b) (M4 tptp.refine424419629nres_a) (F (-> tptp.a tptp.refine432681134nres_b))) (=> (=> (@ tptp.refine412683990fail_b S) (@ tptp.refine412683989fail_a M4)) (=> (forall ((X3 tptp.a)) (=> (@ tptp.refine412683989fail_a M4) (=> (@ (@ tptp.refine1001002027nres_a M4) X3) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) S)))) (@ (@ tptp.ord_le527798542nres_b (@ (@ tptp.refine436832839nd_a_b M4) F)) S)))))
% 0.27/0.71 (assert (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (= (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a P)) (@ tptp.collect_a Q)) (forall ((X5 tptp.a)) (=> (@ P X5) (@ Q X5))))))
% 0.27/0.71 (assert (forall ((P (-> tptp.b Bool)) (Q (-> tptp.b Bool))) (= (@ (@ tptp.ord_less_eq_set_b (@ tptp.collect_b P)) (@ tptp.collect_b Q)) (forall ((X5 tptp.b)) (=> (@ P X5) (@ Q X5))))))
% 0.27/0.71 (assert (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (=> (forall ((X3 tptp.a)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a P)) (@ tptp.collect_a Q)))))
% 0.27/0.71 (assert (forall ((P (-> tptp.b Bool)) (Q (-> tptp.b Bool))) (=> (forall ((X3 tptp.b)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_less_eq_set_b (@ tptp.collect_b P)) (@ tptp.collect_b Q)))))
% 0.27/0.71 (assert (= tptp.ord_less_eq_set_a (lambda ((A4 tptp.set_a) (B4 tptp.set_a)) (forall ((T3 tptp.a)) (let ((_let_1 (@ tptp.member_a T3))) (=> (@ _let_1 A4) (@ _let_1 B4)))))))
% 0.27/0.71 (assert (= tptp.ord_less_eq_set_b (lambda ((A4 tptp.set_b) (B4 tptp.set_b)) (forall ((T3 tptp.b)) (let ((_let_1 (@ tptp.member_b T3))) (=> (@ _let_1 A4) (@ _let_1 B4)))))))
% 0.27/0.71 (assert (= tptp.ord_less_eq_set_a (lambda ((A4 tptp.set_a) (B4 tptp.set_a)) (forall ((X5 tptp.a)) (let ((_let_1 (@ tptp.member_a X5))) (=> (@ _let_1 A4) (@ _let_1 B4)))))))
% 0.27/0.71 (assert (= tptp.ord_less_eq_set_b (lambda ((A4 tptp.set_b) (B4 tptp.set_b)) (forall ((X5 tptp.b)) (let ((_let_1 (@ tptp.member_b X5))) (=> (@ _let_1 A4) (@ _let_1 B4)))))))
% 0.27/0.71 (assert (forall ((M tptp.refine432681134nres_b) (R tptp.set_Product_prod_b_a) (M7 tptp.refine424419629nres_a) (X4 tptp.b) (Lhs tptp.refine432681134nres_b) (S tptp.set_Product_prod_b_b) (F2 (-> tptp.a tptp.refine432681134nres_b))) (=> (@ (@ tptp.ord_le527798542nres_b M) (@ (@ tptp.refine122110612un_b_a R) M7)) (=> (@ (@ tptp.refine1001002028nres_b M) X4) (=> (forall ((X9 tptp.a)) (=> (@ (@ tptp.member1277678991od_b_a (@ (@ tptp.product_Pair_b_a X4) X9)) R) (@ (@ tptp.ord_le527798542nres_b Lhs) (@ (@ tptp.refine122110613un_b_b S) (@ F2 X9))))) (@ (@ tptp.ord_le527798542nres_b Lhs) (@ (@ tptp.refine122110613un_b_b S) (@ (@ tptp.refine436832839nd_a_b M7) F2))))))))
% 0.27/0.71 (assert (forall ((M tptp.refine432681134nres_b) (R tptp.set_Product_prod_b_a) (M7 tptp.refine424419629nres_a) (X4 tptp.b) (Lhs tptp.refine424419629nres_a) (S tptp.set_Product_prod_a_b) (F2 (-> tptp.a tptp.refine432681134nres_b))) (=> (@ (@ tptp.ord_le527798542nres_b M) (@ (@ tptp.refine122110612un_b_a R) M7)) (=> (@ (@ tptp.refine1001002028nres_b M) X4) (=> (forall ((X9 tptp.a)) (=> (@ (@ tptp.member1277678991od_b_a (@ (@ tptp.product_Pair_b_a X4) X9)) R) (@ (@ tptp.ord_le519537037nres_a Lhs) (@ (@ tptp.refine1441824854un_a_b S) (@ F2 X9))))) (@ (@ tptp.ord_le519537037nres_a Lhs) (@ (@ tptp.refine1441824854un_a_b S) (@ (@ tptp.refine436832839nd_a_b M7) F2))))))))
% 0.27/0.71 (assert (forall ((M tptp.refine424419629nres_a) (R tptp.set_Product_prod_a_a) (M7 tptp.refine424419629nres_a) (X4 tptp.a) (Lhs tptp.refine432681134nres_b) (S tptp.set_Product_prod_b_b) (F2 (-> tptp.a tptp.refine432681134nres_b))) (=> (@ (@ tptp.ord_le519537037nres_a M) (@ (@ tptp.refine1441824853un_a_a R) M7)) (=> (@ (@ tptp.refine1001002027nres_a M) X4) (=> (forall ((X9 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) X9)) R) (@ (@ tptp.ord_le527798542nres_b Lhs) (@ (@ tptp.refine122110613un_b_b S) (@ F2 X9))))) (@ (@ tptp.ord_le527798542nres_b Lhs) (@ (@ tptp.refine122110613un_b_b S) (@ (@ tptp.refine436832839nd_a_b M7) F2))))))))
% 0.27/0.71 (assert (forall ((M tptp.refine424419629nres_a) (R tptp.set_Product_prod_a_a) (M7 tptp.refine424419629nres_a) (X4 tptp.a) (Lhs tptp.refine424419629nres_a) (S tptp.set_Product_prod_a_b) (F2 (-> tptp.a tptp.refine432681134nres_b))) (=> (@ (@ tptp.ord_le519537037nres_a M) (@ (@ tptp.refine1441824853un_a_a R) M7)) (=> (@ (@ tptp.refine1001002027nres_a M) X4) (=> (forall ((X9 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) X9)) R) (@ (@ tptp.ord_le519537037nres_a Lhs) (@ (@ tptp.refine1441824854un_a_b S) (@ F2 X9))))) (@ (@ tptp.ord_le519537037nres_a Lhs) (@ (@ tptp.refine1441824854un_a_b S) (@ (@ tptp.refine436832839nd_a_b M7) F2))))))))
% 0.27/0.71 (assert (forall ((S tptp.set_a) (S3 tptp.set_a) (R tptp.set_Product_prod_a_a)) (=> (forall ((S6 tptp.a)) (=> (@ (@ tptp.member_a S6) S) (exists ((X10 tptp.a)) (and (@ (@ tptp.member_a X10) S3) (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a S6) X10)) R))))) (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine1198353288_RES_a S)) (@ (@ tptp.refine1441824853un_a_a R) (@ tptp.refine1198353288_RES_a S3))))))
% 0.27/0.71 (assert (forall ((S tptp.set_a) (S3 tptp.set_b) (R tptp.set_Product_prod_a_b)) (=> (forall ((S6 tptp.a)) (=> (@ (@ tptp.member_a S6) S) (exists ((X10 tptp.b)) (and (@ (@ tptp.member_b X10) S3) (@ (@ tptp.member458171089od_a_b (@ (@ tptp.product_Pair_a_b S6) X10)) R))))) (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine1198353288_RES_a S)) (@ (@ tptp.refine1441824854un_a_b R) (@ tptp.refine1198353289_RES_b S3))))))
% 0.27/0.71 (assert (forall ((S tptp.set_b) (S3 tptp.set_a) (R tptp.set_Product_prod_b_a)) (=> (forall ((S6 tptp.b)) (=> (@ (@ tptp.member_b S6) S) (exists ((X10 tptp.a)) (and (@ (@ tptp.member_a X10) S3) (@ (@ tptp.member1277678991od_b_a (@ (@ tptp.product_Pair_b_a S6) X10)) R))))) (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine1198353289_RES_b S)) (@ (@ tptp.refine122110612un_b_a R) (@ tptp.refine1198353288_RES_a S3))))))
% 0.27/0.71 (assert (forall ((S tptp.set_b) (S3 tptp.set_b) (R tptp.set_Product_prod_b_b)) (=> (forall ((S6 tptp.b)) (=> (@ (@ tptp.member_b S6) S) (exists ((X10 tptp.b)) (and (@ (@ tptp.member_b X10) S3) (@ (@ tptp.member1285940496od_b_b (@ (@ tptp.product_Pair_b_b S6) X10)) R))))) (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine1198353289_RES_b S)) (@ (@ tptp.refine122110613un_b_b R) (@ tptp.refine1198353289_RES_b S3))))))
% 0.27/0.71 (assert (forall ((X4 tptp.refine424419629nres_a) (Xa tptp.refine424419629nres_a) (Y3 Bool)) (=> (= (@ (@ tptp.ord_le519537037nres_a X4) Xa) Y3) (=> (=> (= Xa tptp.refine464223677AILi_a) (not Y3)) (=> (forall ((A5 tptp.set_a)) (=> (= X4 (@ tptp.refine1198353288_RES_a A5)) (forall ((B5 tptp.set_a)) (=> (= Xa (@ tptp.refine1198353288_RES_a B5)) (= Y3 (not (@ (@ tptp.ord_less_eq_set_a A5) B5))))))) (not (=> (= X4 tptp.refine464223677AILi_a) (=> (exists ((Uv tptp.set_a)) (= Xa (@ tptp.refine1198353288_RES_a Uv))) Y3))))))))
% 0.27/0.71 (assert (forall ((X4 tptp.refine432681134nres_b) (Xa tptp.refine432681134nres_b) (Y3 Bool)) (=> (= (@ (@ tptp.ord_le527798542nres_b X4) Xa) Y3) (=> (=> (= Xa tptp.refine464223678AILi_b) (not Y3)) (=> (forall ((A5 tptp.set_b)) (=> (= X4 (@ tptp.refine1198353289_RES_b A5)) (forall ((B5 tptp.set_b)) (=> (= Xa (@ tptp.refine1198353289_RES_b B5)) (= Y3 (not (@ (@ tptp.ord_less_eq_set_b A5) B5))))))) (not (=> (= X4 tptp.refine464223678AILi_b) (=> (exists ((Uv tptp.set_b)) (= Xa (@ tptp.refine1198353289_RES_b Uv))) Y3))))))))
% 0.27/0.71 (assert (forall ((X4 tptp.refine424419629nres_a) (Xa tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a X4) Xa) (=> (not (= Xa tptp.refine464223677AILi_a)) (not (forall ((A5 tptp.set_a)) (=> (= X4 (@ tptp.refine1198353288_RES_a A5)) (forall ((B5 tptp.set_a)) (=> (= Xa (@ tptp.refine1198353288_RES_a B5)) (not (@ (@ tptp.ord_less_eq_set_a A5) B5)))))))))))
% 0.27/0.71 (assert (forall ((X4 tptp.refine432681134nres_b) (Xa tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b X4) Xa) (=> (not (= Xa tptp.refine464223678AILi_b)) (not (forall ((A5 tptp.set_b)) (=> (= X4 (@ tptp.refine1198353289_RES_b A5)) (forall ((B5 tptp.set_b)) (=> (= Xa (@ tptp.refine1198353289_RES_b B5)) (not (@ (@ tptp.ord_less_eq_set_b A5) B5)))))))))))
% 0.27/0.71 (assert (forall ((X4 tptp.produc1609974940nres_a)) (=> (forall ((Uu tptp.refine424419629nres_a)) (not (= X4 (@ (@ tptp.produc1136923598nres_a Uu) tptp.refine464223677AILi_a)))) (=> (forall ((A5 tptp.set_a) (B5 tptp.set_a)) (not (= X4 (@ (@ tptp.produc1136923598nres_a (@ tptp.refine1198353288_RES_a A5)) (@ tptp.refine1198353288_RES_a B5))))) (not (forall ((Uv tptp.set_a)) (not (= X4 (@ (@ tptp.produc1136923598nres_a tptp.refine464223677AILi_a) (@ tptp.refine1198353288_RES_a Uv))))))))))
% 0.27/0.71 (assert (forall ((X4 tptp.produc1587512412nres_b)) (=> (forall ((Uu tptp.refine432681134nres_b)) (not (= X4 (@ (@ tptp.produc2130641934nres_b Uu) tptp.refine464223678AILi_b)))) (=> (forall ((A5 tptp.set_b) (B5 tptp.set_b)) (not (= X4 (@ (@ tptp.produc2130641934nres_b (@ tptp.refine1198353289_RES_b A5)) (@ tptp.refine1198353289_RES_b B5))))) (not (forall ((Uv tptp.set_b)) (not (= X4 (@ (@ tptp.produc2130641934nres_b tptp.refine464223678AILi_b) (@ tptp.refine1198353289_RES_b Uv))))))))))
% 0.27/0.71 (assert (forall ((X4 tptp.produc1609974940nres_a)) (=> (forall ((Uu tptp.refine424419629nres_a)) (not (= X4 (@ (@ tptp.produc1136923598nres_a tptp.refine464223677AILi_a) Uu)))) (=> (forall ((Uv tptp.set_a)) (not (= X4 (@ (@ tptp.produc1136923598nres_a (@ tptp.refine1198353288_RES_a Uv)) tptp.refine464223677AILi_a)))) (not (forall ((A5 tptp.set_a) (B5 tptp.set_a)) (not (= X4 (@ (@ tptp.produc1136923598nres_a (@ tptp.refine1198353288_RES_a A5)) (@ tptp.refine1198353288_RES_a B5))))))))))
% 0.27/0.71 (assert (forall ((X4 tptp.produc1587512412nres_b)) (=> (forall ((Uu tptp.refine432681134nres_b)) (not (= X4 (@ (@ tptp.produc2130641934nres_b tptp.refine464223678AILi_b) Uu)))) (=> (forall ((Uv tptp.set_b)) (not (= X4 (@ (@ tptp.produc2130641934nres_b (@ tptp.refine1198353289_RES_b Uv)) tptp.refine464223678AILi_b)))) (not (forall ((A5 tptp.set_b) (B5 tptp.set_b)) (not (= X4 (@ (@ tptp.produc2130641934nres_b (@ tptp.refine1198353289_RES_b A5)) (@ tptp.refine1198353289_RES_b B5))))))))))
% 0.27/0.71 (assert (forall ((X4 tptp.produc1609974940nres_a)) (=> (forall ((Uu tptp.refine424419629nres_a)) (not (= X4 (@ (@ tptp.produc1136923598nres_a Uu) tptp.refine464223677AILi_a)))) (=> (forall ((V tptp.set_a)) (not (= X4 (@ (@ tptp.produc1136923598nres_a tptp.refine464223677AILi_a) (@ tptp.refine1198353288_RES_a V))))) (not (forall ((A5 tptp.set_a) (B5 tptp.set_a)) (not (= X4 (@ (@ tptp.produc1136923598nres_a (@ tptp.refine1198353288_RES_a A5)) (@ tptp.refine1198353288_RES_a B5))))))))))
% 0.27/0.71 (assert (forall ((X4 tptp.produc1587512412nres_b)) (=> (forall ((Uu tptp.refine432681134nres_b)) (not (= X4 (@ (@ tptp.produc2130641934nres_b Uu) tptp.refine464223678AILi_b)))) (=> (forall ((V tptp.set_b)) (not (= X4 (@ (@ tptp.produc2130641934nres_b tptp.refine464223678AILi_b) (@ tptp.refine1198353289_RES_b V))))) (not (forall ((A5 tptp.set_b) (B5 tptp.set_b)) (not (= X4 (@ (@ tptp.produc2130641934nres_b (@ tptp.refine1198353289_RES_b A5)) (@ tptp.refine1198353289_RES_b B5))))))))))
% 0.27/0.71 (assert (forall ((Uu2 tptp.refine432681134nres_b)) (@ (@ tptp.ord_le527798542nres_b Uu2) tptp.refine464223678AILi_b)))
% 0.27/0.71 (assert (forall ((Uu2 tptp.refine424419629nres_a)) (@ (@ tptp.ord_le519537037nres_a Uu2) tptp.refine464223677AILi_a)))
% 0.27/0.71 (assert (forall ((X2 tptp.set_a)) (not (= tptp.refine464223677AILi_a (@ tptp.refine1198353288_RES_a X2)))))
% 0.27/0.71 (assert (forall ((X2 tptp.set_b)) (not (= tptp.refine464223678AILi_b (@ tptp.refine1198353289_RES_b X2)))))
% 0.27/0.71 (assert (forall ((P (-> tptp.refine424419629nres_a Bool)) (Nres tptp.refine424419629nres_a)) (=> (@ P tptp.refine464223677AILi_a) (=> (forall ((X3 tptp.set_a)) (@ P (@ tptp.refine1198353288_RES_a X3))) (@ P Nres)))))
% 0.27/0.71 (assert (forall ((P (-> tptp.refine432681134nres_b Bool)) (Nres tptp.refine432681134nres_b)) (=> (@ P tptp.refine464223678AILi_b) (=> (forall ((X3 tptp.set_b)) (@ P (@ tptp.refine1198353289_RES_b X3))) (@ P Nres)))))
% 0.27/0.71 (assert (forall ((Y3 tptp.refine424419629nres_a)) (=> (not (= Y3 tptp.refine464223677AILi_a)) (not (forall ((X22 tptp.set_a)) (not (= Y3 (@ tptp.refine1198353288_RES_a X22))))))))
% 0.27/0.71 (assert (forall ((Y3 tptp.refine432681134nres_b)) (=> (not (= Y3 tptp.refine464223678AILi_b)) (not (forall ((X22 tptp.set_b)) (not (= Y3 (@ tptp.refine1198353289_RES_b X22))))))))
% 0.27/0.71 (assert (forall ((P (-> tptp.refine424419629nres_a tptp.refine424419629nres_a Bool)) (A0 tptp.refine424419629nres_a) (A1 tptp.refine424419629nres_a)) (=> (forall ((Uu tptp.refine424419629nres_a)) (@ (@ P Uu) tptp.refine464223677AILi_a)) (=> (forall ((V tptp.set_a)) (@ (@ P tptp.refine464223677AILi_a) (@ tptp.refine1198353288_RES_a V))) (=> (forall ((A5 tptp.set_a) (B5 tptp.set_a)) (@ (@ P (@ tptp.refine1198353288_RES_a A5)) (@ tptp.refine1198353288_RES_a B5))) (@ (@ P A0) A1))))))
% 0.27/0.71 (assert (forall ((P (-> tptp.refine432681134nres_b tptp.refine432681134nres_b Bool)) (A0 tptp.refine432681134nres_b) (A1 tptp.refine432681134nres_b)) (=> (forall ((Uu tptp.refine432681134nres_b)) (@ (@ P Uu) tptp.refine464223678AILi_b)) (=> (forall ((V tptp.set_b)) (@ (@ P tptp.refine464223678AILi_b) (@ tptp.refine1198353289_RES_b V))) (=> (forall ((A5 tptp.set_b) (B5 tptp.set_b)) (@ (@ P (@ tptp.refine1198353289_RES_b A5)) (@ tptp.refine1198353289_RES_b B5))) (@ (@ P A0) A1))))))
% 0.27/0.71 (assert (forall ((P (-> tptp.refine424419629nres_a tptp.refine424419629nres_a Bool)) (A0 tptp.refine424419629nres_a) (A1 tptp.refine424419629nres_a)) (=> (forall ((X_1 tptp.refine424419629nres_a)) (@ (@ P tptp.refine464223677AILi_a) X_1)) (=> (forall ((Uv tptp.set_a)) (@ (@ P (@ tptp.refine1198353288_RES_a Uv)) tptp.refine464223677AILi_a)) (=> (forall ((A5 tptp.set_a) (B5 tptp.set_a)) (@ (@ P (@ tptp.refine1198353288_RES_a A5)) (@ tptp.refine1198353288_RES_a B5))) (@ (@ P A0) A1))))))
% 0.27/0.71 (assert (forall ((P (-> tptp.refine432681134nres_b tptp.refine432681134nres_b Bool)) (A0 tptp.refine432681134nres_b) (A1 tptp.refine432681134nres_b)) (=> (forall ((X_1 tptp.refine432681134nres_b)) (@ (@ P tptp.refine464223678AILi_b) X_1)) (=> (forall ((Uv tptp.set_b)) (@ (@ P (@ tptp.refine1198353289_RES_b Uv)) tptp.refine464223678AILi_b)) (=> (forall ((A5 tptp.set_b) (B5 tptp.set_b)) (@ (@ P (@ tptp.refine1198353289_RES_b A5)) (@ tptp.refine1198353289_RES_b B5))) (@ (@ P A0) A1))))))
% 0.27/0.71 (assert (forall ((P (-> tptp.refine424419629nres_a tptp.refine424419629nres_a Bool)) (A0 tptp.refine424419629nres_a) (A1 tptp.refine424419629nres_a)) (=> (forall ((Uu tptp.refine424419629nres_a)) (@ (@ P Uu) tptp.refine464223677AILi_a)) (=> (forall ((A5 tptp.set_a) (B5 tptp.set_a)) (@ (@ P (@ tptp.refine1198353288_RES_a A5)) (@ tptp.refine1198353288_RES_a B5))) (=> (forall ((Uv tptp.set_a)) (@ (@ P tptp.refine464223677AILi_a) (@ tptp.refine1198353288_RES_a Uv))) (@ (@ P A0) A1))))))
% 0.27/0.71 (assert (forall ((P (-> tptp.refine432681134nres_b tptp.refine432681134nres_b Bool)) (A0 tptp.refine432681134nres_b) (A1 tptp.refine432681134nres_b)) (=> (forall ((Uu tptp.refine432681134nres_b)) (@ (@ P Uu) tptp.refine464223678AILi_b)) (=> (forall ((A5 tptp.set_b) (B5 tptp.set_b)) (@ (@ P (@ tptp.refine1198353289_RES_b A5)) (@ tptp.refine1198353289_RES_b B5))) (=> (forall ((Uv tptp.set_b)) (@ (@ P tptp.refine464223678AILi_b) (@ tptp.refine1198353289_RES_b Uv))) (@ (@ P A0) A1))))))
% 0.27/0.71 (assert (forall ((Uv2 tptp.set_a)) (not (@ (@ tptp.ord_le519537037nres_a tptp.refine464223677AILi_a) (@ tptp.refine1198353288_RES_a Uv2)))))
% 0.27/0.71 (assert (forall ((Uv2 tptp.set_b)) (not (@ (@ tptp.ord_le527798542nres_b tptp.refine464223678AILi_b) (@ tptp.refine1198353289_RES_b Uv2)))))
% 0.27/0.71 (assert (forall ((X4 tptp.refine424419629nres_a) (Xa tptp.refine424419629nres_a)) (=> (not (@ (@ tptp.ord_le519537037nres_a X4) Xa)) (=> (forall ((A5 tptp.set_a)) (=> (= X4 (@ tptp.refine1198353288_RES_a A5)) (forall ((B5 tptp.set_a)) (=> (= Xa (@ tptp.refine1198353288_RES_a B5)) (@ (@ tptp.ord_less_eq_set_a A5) B5))))) (not (=> (= X4 tptp.refine464223677AILi_a) (forall ((Uv tptp.set_a)) (not (= Xa (@ tptp.refine1198353288_RES_a Uv))))))))))
% 0.27/0.71 (assert (forall ((X4 tptp.refine432681134nres_b) (Xa tptp.refine432681134nres_b)) (=> (not (@ (@ tptp.ord_le527798542nres_b X4) Xa)) (=> (forall ((A5 tptp.set_b)) (=> (= X4 (@ tptp.refine1198353289_RES_b A5)) (forall ((B5 tptp.set_b)) (=> (= Xa (@ tptp.refine1198353289_RES_b B5)) (@ (@ tptp.ord_less_eq_set_b A5) B5))))) (not (=> (= X4 tptp.refine464223678AILi_b) (forall ((Uv tptp.set_b)) (not (= Xa (@ tptp.refine1198353289_RES_b Uv))))))))))
% 0.27/0.71 (assert (forall ((M tptp.refine432681134nres_b) (X4 tptp.b) (R tptp.set_Product_prod_b_b)) (=> (@ tptp.refine412683990fail_b M) (=> (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b X4)) (@ (@ tptp.refine122110613un_b_b R) M)) (not (forall ((X9 tptp.b)) (=> (@ (@ tptp.member1285940496od_b_b (@ (@ tptp.product_Pair_b_b X4) X9)) R) (not (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b X9)) M)))))))))
% 0.27/0.71 (assert (forall ((M tptp.refine424419629nres_a) (X4 tptp.b) (R tptp.set_Product_prod_b_a)) (=> (@ tptp.refine412683989fail_a M) (=> (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b X4)) (@ (@ tptp.refine122110612un_b_a R) M)) (not (forall ((X9 tptp.a)) (=> (@ (@ tptp.member1277678991od_b_a (@ (@ tptp.product_Pair_b_a X4) X9)) R) (not (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X9)) M)))))))))
% 0.27/0.71 (assert (forall ((M tptp.refine432681134nres_b) (X4 tptp.a) (R tptp.set_Product_prod_a_b)) (=> (@ tptp.refine412683990fail_b M) (=> (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X4)) (@ (@ tptp.refine1441824854un_a_b R) M)) (not (forall ((X9 tptp.b)) (=> (@ (@ tptp.member458171089od_a_b (@ (@ tptp.product_Pair_a_b X4) X9)) R) (not (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b X9)) M)))))))))
% 0.27/0.71 (assert (forall ((M tptp.refine424419629nres_a) (X4 tptp.a) (R tptp.set_Product_prod_a_a)) (=> (@ tptp.refine412683989fail_a M) (=> (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X4)) (@ (@ tptp.refine1441824853un_a_a R) M)) (not (forall ((X9 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) X9)) R) (not (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X9)) M)))))))))
% 0.27/0.71 (assert (forall ((M tptp.refine432681134nres_b) (C tptp.b) (R tptp.set_Product_prod_b_b)) (=> (@ tptp.refine412683990fail_b M) (= (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b C)) (@ (@ tptp.refine122110613un_b_b R) M)) (exists ((A2 tptp.b)) (and (@ (@ tptp.member1285940496od_b_b (@ (@ tptp.product_Pair_b_b C) A2)) R) (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b A2)) M)))))))
% 0.27/0.71 (assert (forall ((M tptp.refine424419629nres_a) (C tptp.b) (R tptp.set_Product_prod_b_a)) (=> (@ tptp.refine412683989fail_a M) (= (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b C)) (@ (@ tptp.refine122110612un_b_a R) M)) (exists ((A2 tptp.a)) (and (@ (@ tptp.member1277678991od_b_a (@ (@ tptp.product_Pair_b_a C) A2)) R) (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a A2)) M)))))))
% 0.27/0.71 (assert (forall ((M tptp.refine432681134nres_b) (C tptp.a) (R tptp.set_Product_prod_a_b)) (=> (@ tptp.refine412683990fail_b M) (= (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a C)) (@ (@ tptp.refine1441824854un_a_b R) M)) (exists ((A2 tptp.b)) (and (@ (@ tptp.member458171089od_a_b (@ (@ tptp.product_Pair_a_b C) A2)) R) (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b A2)) M)))))))
% 0.27/0.71 (assert (forall ((M tptp.refine424419629nres_a) (C tptp.a) (R tptp.set_Product_prod_a_a)) (=> (@ tptp.refine412683989fail_a M) (= (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a C)) (@ (@ tptp.refine1441824853un_a_a R) M)) (exists ((A2 tptp.a)) (and (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a C) A2)) R) (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a A2)) M)))))))
% 0.27/0.71 (assert (forall ((X4 tptp.b) (Y3 tptp.b)) (= (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b X4)) (@ tptp.refine2063221605TURN_b Y3)) (= X4 Y3))))
% 0.27/0.71 (assert (forall ((X4 tptp.a) (Y3 tptp.a)) (= (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X4)) (@ tptp.refine2063221604TURN_a Y3)) (= X4 Y3))))
% 0.27/0.71 (assert (forall ((X4 tptp.a) (F (-> tptp.a tptp.refine432681134nres_b))) (= (@ (@ tptp.refine436832839nd_a_b (@ tptp.refine2063221604TURN_a X4)) F) (@ F X4))))
% 0.27/0.71 (assert (forall ((X4 tptp.a) (Y tptp.set_a)) (= (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X4)) (@ tptp.refine1198353288_RES_a Y)) (@ (@ tptp.member_a X4) Y))))
% 0.27/0.71 (assert (forall ((X4 tptp.b) (Y tptp.set_b)) (= (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b X4)) (@ tptp.refine1198353289_RES_b Y)) (@ (@ tptp.member_b X4) Y))))
% 0.27/0.71 (assert (forall ((X4 tptp.a)) (= (@ tptp.refine1198353288_RES_a (@ tptp.collect_a (@ (lambda ((Y5 tptp.a) (Z tptp.a)) (= Y5 Z)) X4))) (@ tptp.refine2063221604TURN_a X4))))
% 0.27/0.71 (assert (forall ((X4 tptp.b)) (= (@ tptp.refine1198353289_RES_b (@ tptp.collect_b (@ (lambda ((Y5 tptp.b) (Z tptp.b)) (= Y5 Z)) X4))) (@ tptp.refine2063221605TURN_b X4))))
% 0.27/0.71 (assert (forall ((Phi (-> tptp.a Bool)) (X4 tptp.a)) (=> (@ Phi X4) (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X4)) (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi))))))
% 0.27/0.71 (assert (forall ((Phi (-> tptp.b Bool)) (X4 tptp.b)) (=> (@ Phi X4) (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b X4)) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi))))))
% 0.27/0.71 (assert (forall ((X tptp.set_a) (M tptp.refine424419629nres_a)) (=> (forall ((X3 tptp.a)) (=> (@ (@ tptp.member_a X3) X) (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X3)) M))) (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine1198353288_RES_a X)) M))))
% 0.27/0.71 (assert (forall ((X tptp.set_b) (M tptp.refine432681134nres_b)) (=> (forall ((X3 tptp.b)) (=> (@ (@ tptp.member_b X3) X) (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b X3)) M))) (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine1198353289_RES_b X)) M))))
% 0.27/0.71 (assert (forall ((M tptp.refine424419629nres_a) (V2 tptp.a)) (let ((_let_1 (@ tptp.ord_le519537037nres_a M))) (=> (@ _let_1 (@ tptp.refine1198353288_RES_a (@ tptp.collect_a (@ (lambda ((Y5 tptp.a) (Z tptp.a)) (= Y5 Z)) V2)))) (@ _let_1 (@ tptp.refine2063221604TURN_a V2))))))
% 0.27/0.71 (assert (forall ((M tptp.refine432681134nres_b) (V2 tptp.b)) (let ((_let_1 (@ tptp.ord_le527798542nres_b M))) (=> (@ _let_1 (@ tptp.refine1198353289_RES_b (@ tptp.collect_b (@ (lambda ((Y5 tptp.b) (Z tptp.b)) (= Y5 Z)) V2)))) (@ _let_1 (@ tptp.refine2063221605TURN_b V2))))))
% 0.27/0.71 (assert (forall ((M4 tptp.refine432681134nres_b) (M3 tptp.refine432681134nres_b) (F (-> tptp.b tptp.refine432681134nres_b)) (F2 (-> tptp.b tptp.refine432681134nres_b))) (=> (@ (@ tptp.ord_le527798542nres_b M4) M3) (=> (forall ((X3 tptp.b)) (=> (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b X3)) M4) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ F2 X3)))) (@ (@ tptp.ord_le527798542nres_b (@ (@ tptp.refine1264602246nd_b_b M4) F)) (@ (@ tptp.refine1264602246nd_b_b M3) F2))))))
% 0.27/0.71 (assert (forall ((M4 tptp.refine432681134nres_b) (M3 tptp.refine432681134nres_b) (F (-> tptp.b tptp.refine424419629nres_a)) (F2 (-> tptp.b tptp.refine424419629nres_a))) (=> (@ (@ tptp.ord_le527798542nres_b M4) M3) (=> (forall ((X3 tptp.b)) (=> (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b X3)) M4) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ F2 X3)))) (@ (@ tptp.ord_le519537037nres_a (@ (@ tptp.refine1264602245nd_b_a M4) F)) (@ (@ tptp.refine1264602245nd_b_a M3) F2))))))
% 0.27/0.71 (assert (forall ((M4 tptp.refine424419629nres_a) (M3 tptp.refine424419629nres_a) (F (-> tptp.a tptp.refine424419629nres_a)) (F2 (-> tptp.a tptp.refine424419629nres_a))) (=> (@ (@ tptp.ord_le519537037nres_a M4) M3) (=> (forall ((X3 tptp.a)) (=> (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X3)) M4) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ F2 X3)))) (@ (@ tptp.ord_le519537037nres_a (@ (@ tptp.refine436832838nd_a_a M4) F)) (@ (@ tptp.refine436832838nd_a_a M3) F2))))))
% 0.27/0.71 (assert (forall ((M4 tptp.refine424419629nres_a) (M3 tptp.refine424419629nres_a) (F (-> tptp.a tptp.refine432681134nres_b)) (F2 (-> tptp.a tptp.refine432681134nres_b))) (=> (@ (@ tptp.ord_le519537037nres_a M4) M3) (=> (forall ((X3 tptp.a)) (=> (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X3)) M4) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ F2 X3)))) (@ (@ tptp.ord_le527798542nres_b (@ (@ tptp.refine436832839nd_a_b M4) F)) (@ (@ tptp.refine436832839nd_a_b M3) F2))))))
% 0.27/0.71 (assert (forall ((M tptp.refine424419629nres_a) (M7 tptp.refine424419629nres_a) (F (-> tptp.a tptp.refine432681134nres_b)) (F2 (-> tptp.a tptp.refine432681134nres_b))) (=> (= M M7) (=> (forall ((X3 tptp.a)) (=> (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X3)) M7) (= (@ F X3) (@ F2 X3)))) (= (@ (@ tptp.refine436832839nd_a_b M) F) (@ (@ tptp.refine436832839nd_a_b M7) F2))))))
% 0.27/0.71 (assert (= tptp.refine1001002028nres_b (lambda ((S4 tptp.refine432681134nres_b) (X5 tptp.b)) (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b X5)) S4))))
% 0.27/0.71 (assert (= tptp.refine1001002027nres_a (lambda ((S4 tptp.refine424419629nres_a) (X5 tptp.a)) (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X5)) S4))))
% 0.27/0.71 (assert (forall ((C tptp.b) (R tptp.set_Product_prod_b_a) (Phi (-> tptp.a Bool))) (=> (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b C)) (@ (@ tptp.refine122110612un_b_a R) (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi)))) (not (forall ((A5 tptp.a)) (=> (@ (@ tptp.member1277678991od_b_a (@ (@ tptp.product_Pair_b_a C) A5)) R) (not (@ Phi A5))))))))
% 0.27/0.71 (assert (forall ((C tptp.a) (R tptp.set_Product_prod_a_a) (Phi (-> tptp.a Bool))) (=> (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a C)) (@ (@ tptp.refine1441824853un_a_a R) (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi)))) (not (forall ((A5 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a C) A5)) R) (not (@ Phi A5))))))))
% 0.27/0.71 (assert (forall ((C tptp.b) (R tptp.set_Product_prod_b_b) (Phi (-> tptp.b Bool))) (=> (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b C)) (@ (@ tptp.refine122110613un_b_b R) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi)))) (not (forall ((A5 tptp.b)) (=> (@ (@ tptp.member1285940496od_b_b (@ (@ tptp.product_Pair_b_b C) A5)) R) (not (@ Phi A5))))))))
% 0.27/0.71 (assert (forall ((C tptp.a) (R tptp.set_Product_prod_a_b) (Phi (-> tptp.b Bool))) (=> (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a C)) (@ (@ tptp.refine1441824854un_a_b R) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi)))) (not (forall ((A5 tptp.b)) (=> (@ (@ tptp.member458171089od_a_b (@ (@ tptp.product_Pair_a_b C) A5)) R) (not (@ Phi A5))))))))
% 0.27/0.71 (assert (forall ((X4 tptp.b) (R tptp.set_Product_prod_b_a) (Phi (-> tptp.a Bool))) (=> (exists ((X11 tptp.a)) (and (@ (@ tptp.member1277678991od_b_a (@ (@ tptp.product_Pair_b_a X4) X11)) R) (@ Phi X11))) (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b X4)) (@ (@ tptp.refine122110612un_b_a R) (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi)))))))
% 0.27/0.71 (assert (forall ((X4 tptp.a) (R tptp.set_Product_prod_a_a) (Phi (-> tptp.a Bool))) (=> (exists ((X11 tptp.a)) (and (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) X11)) R) (@ Phi X11))) (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X4)) (@ (@ tptp.refine1441824853un_a_a R) (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi)))))))
% 0.27/0.71 (assert (forall ((X4 tptp.b) (R tptp.set_Product_prod_b_b) (Phi (-> tptp.b Bool))) (=> (exists ((X11 tptp.b)) (and (@ (@ tptp.member1285940496od_b_b (@ (@ tptp.product_Pair_b_b X4) X11)) R) (@ Phi X11))) (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b X4)) (@ (@ tptp.refine122110613un_b_b R) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi)))))))
% 0.27/0.71 (assert (forall ((X4 tptp.a) (R tptp.set_Product_prod_a_b) (Phi (-> tptp.b Bool))) (=> (exists ((X11 tptp.b)) (and (@ (@ tptp.member458171089od_a_b (@ (@ tptp.product_Pair_a_b X4) X11)) R) (@ Phi X11))) (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X4)) (@ (@ tptp.refine1441824854un_a_b R) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi)))))))
% 0.27/0.71 (assert (forall ((A3 tptp.refine432681134nres_b) (B3 tptp.refine432681134nres_b) (R tptp.set_Product_prod_b_b) (C2 tptp.refine432681134nres_b)) (let ((_let_1 (@ tptp.refine1964549110un_b_b R))) (=> (@ (@ tptp.ord_le527798542nres_b A3) B3) (=> (@ (@ tptp.ord_le527798542nres_b (@ _let_1 B3)) C2) (@ (@ tptp.ord_le527798542nres_b (@ _let_1 A3)) C2))))))
% 0.27/0.71 (assert (forall ((A3 tptp.refine432681134nres_b) (B3 tptp.refine432681134nres_b) (R tptp.set_Product_prod_b_a) (C2 tptp.refine424419629nres_a)) (let ((_let_1 (@ tptp.refine1964549109un_b_a R))) (=> (@ (@ tptp.ord_le527798542nres_b A3) B3) (=> (@ (@ tptp.ord_le519537037nres_a (@ _let_1 B3)) C2) (@ (@ tptp.ord_le519537037nres_a (@ _let_1 A3)) C2))))))
% 0.27/0.71 (assert (forall ((A3 tptp.refine424419629nres_a) (B3 tptp.refine424419629nres_a) (R tptp.set_Product_prod_a_b) (C2 tptp.refine432681134nres_b)) (let ((_let_1 (@ tptp.refine1136779703un_a_b R))) (=> (@ (@ tptp.ord_le519537037nres_a A3) B3) (=> (@ (@ tptp.ord_le527798542nres_b (@ _let_1 B3)) C2) (@ (@ tptp.ord_le527798542nres_b (@ _let_1 A3)) C2))))))
% 0.27/0.71 (assert (forall ((A3 tptp.refine424419629nres_a) (B3 tptp.refine424419629nres_a) (R tptp.set_Product_prod_a_a) (C2 tptp.refine424419629nres_a)) (let ((_let_1 (@ tptp.refine1136779702un_a_a R))) (=> (@ (@ tptp.ord_le519537037nres_a A3) B3) (=> (@ (@ tptp.ord_le519537037nres_a (@ _let_1 B3)) C2) (@ (@ tptp.ord_le519537037nres_a (@ _let_1 A3)) C2))))))
% 0.27/0.71 (assert (forall ((X tptp.set_a) (R tptp.set_Pr1628433942t_unit)) (=> (not (@ (@ tptp.ord_less_eq_set_a X) (@ tptp.domain799550107t_unit R))) (= (@ (@ tptp.refine341651653t_unit R) (@ tptp.refine1198353288_RES_a X)) tptp.top_to177290092t_unit))))
% 0.27/0.71 (assert (forall ((X tptp.set_b) (R tptp.set_Pr1707992533t_unit)) (=> (not (@ (@ tptp.ord_less_eq_set_b X) (@ tptp.domain918802906t_unit R))) (= (@ (@ tptp.refine460904452t_unit R) (@ tptp.refine1198353289_RES_b X)) tptp.top_to177290092t_unit))))
% 0.27/0.71 (assert (forall ((X tptp.set_a) (R tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.ord_less_eq_set_a X) (@ tptp.domain_a_a R)) (= (@ (@ tptp.refine1136779702un_a_a R) (@ tptp.refine1198353288_RES_a X)) (@ tptp.refine1198353288_RES_a (@ (@ tptp.image_a_a R) X))))))
% 0.27/0.71 (assert (forall ((X tptp.set_a) (R tptp.set_Product_prod_a_b)) (=> (@ (@ tptp.ord_less_eq_set_a X) (@ tptp.domain_a_b R)) (= (@ (@ tptp.refine1136779703un_a_b R) (@ tptp.refine1198353288_RES_a X)) (@ tptp.refine1198353289_RES_b (@ (@ tptp.image_a_b R) X))))))
% 0.27/0.71 (assert (forall ((X tptp.set_b) (R tptp.set_Product_prod_b_a)) (=> (@ (@ tptp.ord_less_eq_set_b X) (@ tptp.domain_b_a R)) (= (@ (@ tptp.refine1964549109un_b_a R) (@ tptp.refine1198353289_RES_b X)) (@ tptp.refine1198353288_RES_a (@ (@ tptp.image_b_a R) X))))))
% 0.27/0.71 (assert (forall ((X tptp.set_b) (R tptp.set_Product_prod_b_b)) (=> (@ (@ tptp.ord_less_eq_set_b X) (@ tptp.domain_b_b R)) (= (@ (@ tptp.refine1964549110un_b_b R) (@ tptp.refine1198353289_RES_b X)) (@ tptp.refine1198353289_RES_b (@ (@ tptp.image_b_b R) X))))))
% 0.27/0.71 (assert (forall ((A tptp.a) (B tptp.a) (R2 tptp.set_Product_prod_a_a) (A3 tptp.set_a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A) B)) R2) (=> (@ (@ tptp.member_a A) A3) (@ (@ tptp.member_a B) (@ (@ tptp.image_a_a R2) A3))))))
% 0.27/0.71 (assert (forall ((A tptp.a) (B tptp.b) (R2 tptp.set_Product_prod_a_b) (A3 tptp.set_a)) (=> (@ (@ tptp.member458171089od_a_b (@ (@ tptp.product_Pair_a_b A) B)) R2) (=> (@ (@ tptp.member_a A) A3) (@ (@ tptp.member_b B) (@ (@ tptp.image_a_b R2) A3))))))
% 0.27/0.71 (assert (forall ((A tptp.b) (B tptp.a) (R2 tptp.set_Product_prod_b_a) (A3 tptp.set_b)) (=> (@ (@ tptp.member1277678991od_b_a (@ (@ tptp.product_Pair_b_a A) B)) R2) (=> (@ (@ tptp.member_b A) A3) (@ (@ tptp.member_a B) (@ (@ tptp.image_b_a R2) A3))))))
% 0.27/0.71 (assert (forall ((A tptp.b) (B tptp.b) (R2 tptp.set_Product_prod_b_b) (A3 tptp.set_b)) (=> (@ (@ tptp.member1285940496od_b_b (@ (@ tptp.product_Pair_b_b A) B)) R2) (=> (@ (@ tptp.member_b A) A3) (@ (@ tptp.member_b B) (@ (@ tptp.image_b_b R2) A3))))))
% 0.27/0.71 (assert (forall ((M4 tptp.refine787176636t_unit)) (= (@ (@ tptp.ord_le1051254044t_unit tptp.top_to177290092t_unit) M4) (= M4 tptp.top_to177290092t_unit))))
% 0.27/0.71 (assert (forall ((M4 tptp.refine432681134nres_b)) (= (@ (@ tptp.ord_le527798542nres_b tptp.top_to240090974nres_b) M4) (= M4 tptp.top_to240090974nres_b))))
% 0.27/0.71 (assert (forall ((M4 tptp.refine424419629nres_a)) (= (@ (@ tptp.ord_le519537037nres_a tptp.top_to231829469nres_a) M4) (= M4 tptp.top_to231829469nres_a))))
% 0.27/0.71 (assert (forall ((R tptp.set_Pr451126599t_unit)) (= (@ (@ tptp.refine944483349t_unit R) tptp.top_to177290092t_unit) tptp.top_to177290092t_unit)))
% 0.27/0.71 (assert (forall ((R tptp.set_Pr451126599t_unit) (S tptp.refine787176636t_unit)) (= (= (@ (@ tptp.refine944483349t_unit R) S) tptp.top_to177290092t_unit) (= S tptp.top_to177290092t_unit))))
% 0.27/0.71 (assert (forall ((R tptp.set_Pr451126599t_unit) (S tptp.refine787176636t_unit)) (= (= tptp.top_to177290092t_unit (@ (@ tptp.refine944483349t_unit R) S)) (= S tptp.top_to177290092t_unit))))
% 0.27/0.71 (assert (forall ((F (-> tptp.product_unit tptp.refine787176636t_unit))) (= (@ (@ tptp.refine681446406t_unit tptp.top_to177290092t_unit) F) tptp.top_to177290092t_unit)))
% 0.27/0.71 (assert (forall ((F (-> tptp.a tptp.refine432681134nres_b))) (= (@ (@ tptp.refine436832839nd_a_b tptp.top_to231829469nres_a) F) tptp.top_to240090974nres_b)))
% 0.27/0.71 (assert (not (@ tptp.refine579265252t_unit tptp.top_to177290092t_unit)))
% 0.27/0.71 (assert (= (@ tptp.refine558004794t_unit tptp.top_to177290092t_unit) (lambda ((Uu3 tptp.product_unit)) true)))
% 0.27/0.71 (assert (= tptp.refine1607584204t_unit tptp.top_to177290092t_unit))
% 0.27/0.71 (assert (forall ((R tptp.set_Pr451126599t_unit)) (= (@ (@ tptp.refine838861686t_unit R) tptp.top_to177290092t_unit) tptp.top_to177290092t_unit)))
% 0.27/0.71 (assert (forall ((X tptp.refine432681134nres_b) (R tptp.set_Pr1707992533t_unit)) (@ (@ tptp.ord_le527798542nres_b X) (@ (@ tptp.refine2140306339t_unit R) tptp.top_to177290092t_unit))))
% 0.27/0.71 (assert (forall ((X tptp.refine424419629nres_a) (R tptp.set_Pr1628433942t_unit)) (@ (@ tptp.ord_le519537037nres_a X) (@ (@ tptp.refine2021053540t_unit R) tptp.top_to177290092t_unit))))
% 0.27/0.71 (assert (forall ((A tptp.a) (A3 tptp.set_a) (B tptp.a) (R2 tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member_a A) A3) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A) B)) R2) (@ (@ tptp.member_a B) (@ (@ tptp.image_a_a R2) A3))))))
% 0.27/0.71 (assert (forall ((A tptp.a) (A3 tptp.set_a) (B tptp.b) (R2 tptp.set_Product_prod_a_b)) (=> (@ (@ tptp.member_a A) A3) (=> (@ (@ tptp.member458171089od_a_b (@ (@ tptp.product_Pair_a_b A) B)) R2) (@ (@ tptp.member_b B) (@ (@ tptp.image_a_b R2) A3))))))
% 0.27/0.71 (assert (forall ((A tptp.b) (A3 tptp.set_b) (B tptp.a) (R2 tptp.set_Product_prod_b_a)) (=> (@ (@ tptp.member_b A) A3) (=> (@ (@ tptp.member1277678991od_b_a (@ (@ tptp.product_Pair_b_a A) B)) R2) (@ (@ tptp.member_a B) (@ (@ tptp.image_b_a R2) A3))))))
% 0.27/0.71 (assert (forall ((A tptp.b) (A3 tptp.set_b) (B tptp.b) (R2 tptp.set_Product_prod_b_b)) (=> (@ (@ tptp.member_b A) A3) (=> (@ (@ tptp.member1285940496od_b_b (@ (@ tptp.product_Pair_b_b A) B)) R2) (@ (@ tptp.member_b B) (@ (@ tptp.image_b_b R2) A3))))))
% 0.27/0.71 (assert (forall ((B tptp.a) (R2 tptp.set_Product_prod_a_a) (A3 tptp.set_a)) (=> (@ (@ tptp.member_a B) (@ (@ tptp.image_a_a R2) A3)) (not (forall ((X3 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) B)) R2) (not (@ (@ tptp.member_a X3) A3))))))))
% 0.27/0.71 (assert (forall ((B tptp.a) (R2 tptp.set_Product_prod_b_a) (A3 tptp.set_b)) (=> (@ (@ tptp.member_a B) (@ (@ tptp.image_b_a R2) A3)) (not (forall ((X3 tptp.b)) (=> (@ (@ tptp.member1277678991od_b_a (@ (@ tptp.product_Pair_b_a X3) B)) R2) (not (@ (@ tptp.member_b X3) A3))))))))
% 0.27/0.71 (assert (forall ((B tptp.b) (R2 tptp.set_Product_prod_a_b) (A3 tptp.set_a)) (=> (@ (@ tptp.member_b B) (@ (@ tptp.image_a_b R2) A3)) (not (forall ((X3 tptp.a)) (=> (@ (@ tptp.member458171089od_a_b (@ (@ tptp.product_Pair_a_b X3) B)) R2) (not (@ (@ tptp.member_a X3) A3))))))))
% 0.27/0.71 (assert (forall ((B tptp.b) (R2 tptp.set_Product_prod_b_b) (A3 tptp.set_b)) (=> (@ (@ tptp.member_b B) (@ (@ tptp.image_b_b R2) A3)) (not (forall ((X3 tptp.b)) (=> (@ (@ tptp.member1285940496od_b_b (@ (@ tptp.product_Pair_b_b X3) B)) R2) (not (@ (@ tptp.member_b X3) A3))))))))
% 0.27/0.71 (assert (forall ((X4 tptp.product_unit)) (not (= tptp.top_to177290092t_unit (@ tptp.refine1420258419t_unit X4)))))
% 0.27/0.71 (assert (= tptp.top_to177290092t_unit tptp.refine1607584204t_unit))
% 0.27/0.71 (assert (forall ((A tptp.refine787176636t_unit)) (@ (@ tptp.ord_le1051254044t_unit A) tptp.top_to177290092t_unit)))
% 0.27/0.71 (assert (forall ((A tptp.refine432681134nres_b)) (@ (@ tptp.ord_le527798542nres_b A) tptp.top_to240090974nres_b)))
% 0.27/0.71 (assert (forall ((A tptp.refine424419629nres_a)) (@ (@ tptp.ord_le519537037nres_a A) tptp.top_to231829469nres_a)))
% 0.27/0.71 (assert (forall ((A tptp.refine787176636t_unit)) (= (@ (@ tptp.ord_le1051254044t_unit tptp.top_to177290092t_unit) A) (= A tptp.top_to177290092t_unit))))
% 0.27/0.71 (assert (forall ((A tptp.refine432681134nres_b)) (= (@ (@ tptp.ord_le527798542nres_b tptp.top_to240090974nres_b) A) (= A tptp.top_to240090974nres_b))))
% 0.27/0.71 (assert (forall ((A tptp.refine424419629nres_a)) (= (@ (@ tptp.ord_le519537037nres_a tptp.top_to231829469nres_a) A) (= A tptp.top_to231829469nres_a))))
% 0.27/0.71 (assert (forall ((A tptp.refine787176636t_unit)) (=> (@ (@ tptp.ord_le1051254044t_unit tptp.top_to177290092t_unit) A) (= A tptp.top_to177290092t_unit))))
% 0.27/0.71 (assert (forall ((A tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b tptp.top_to240090974nres_b) A) (= A tptp.top_to240090974nres_b))))
% 0.27/0.71 (assert (forall ((A tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a tptp.top_to231829469nres_a) A) (= A tptp.top_to231829469nres_a))))
% 0.27/0.71 (assert (forall ((M4 tptp.refine787176636t_unit)) (@ (@ tptp.ord_le1051254044t_unit M4) tptp.top_to177290092t_unit)))
% 0.27/0.71 (assert (forall ((M4 tptp.refine432681134nres_b)) (@ (@ tptp.ord_le527798542nres_b M4) tptp.top_to240090974nres_b)))
% 0.27/0.71 (assert (forall ((M4 tptp.refine424419629nres_a)) (@ (@ tptp.ord_le519537037nres_a M4) tptp.top_to231829469nres_a)))
% 0.27/0.71 (assert (forall ((X tptp.set_Product_unit)) (not (= tptp.top_to177290092t_unit (@ tptp.refine1777164439t_unit X)))))
% 0.27/0.71 (assert (forall ((X tptp.set_a)) (not (= tptp.top_to231829469nres_a (@ tptp.refine1198353288_RES_a X)))))
% 0.27/0.71 (assert (forall ((X tptp.set_b)) (not (= tptp.top_to240090974nres_b (@ tptp.refine1198353289_RES_b X)))))
% 0.27/0.71 (assert (forall ((M4 tptp.refine787176636t_unit)) (=> (not (= M4 tptp.top_to177290092t_unit)) (not (forall ((X12 tptp.set_Product_unit)) (not (= M4 (@ tptp.refine1777164439t_unit X12))))))))
% 0.27/0.71 (assert (forall ((M4 tptp.refine424419629nres_a)) (=> (not (= M4 tptp.top_to231829469nres_a)) (not (forall ((X12 tptp.set_a)) (not (= M4 (@ tptp.refine1198353288_RES_a X12))))))))
% 0.27/0.71 (assert (forall ((M4 tptp.refine432681134nres_b)) (=> (not (= M4 tptp.top_to240090974nres_b)) (not (forall ((X12 tptp.set_b)) (not (= M4 (@ tptp.refine1198353289_RES_b X12))))))))
% 0.27/0.71 (assert (forall ((S tptp.refine787176636t_unit)) (= (not (@ tptp.refine579265252t_unit S)) (= S tptp.top_to177290092t_unit))))
% 0.27/0.71 (assert (= tptp.refine579265252t_unit (lambda ((S4 tptp.refine787176636t_unit)) (not (= S4 tptp.top_to177290092t_unit)))))
% 0.27/0.71 (assert (forall ((S tptp.refine787176636t_unit)) (= (not (= tptp.top_to177290092t_unit S)) (@ tptp.refine579265252t_unit S))))
% 0.27/0.71 (assert (forall ((F (-> tptp.product_unit tptp.refine787176636t_unit))) (= (@ (@ tptp.refine681446406t_unit tptp.top_to177290092t_unit) F) tptp.top_to177290092t_unit)))
% 0.27/0.71 (assert (forall ((M tptp.refine787176636t_unit) (X4 tptp.refine787176636t_unit)) (=> (= M tptp.top_to177290092t_unit) (@ (@ tptp.ord_le1051254044t_unit X4) M))))
% 0.27/0.71 (assert (forall ((M tptp.refine432681134nres_b) (X4 tptp.refine432681134nres_b)) (=> (= M tptp.top_to240090974nres_b) (@ (@ tptp.ord_le527798542nres_b X4) M))))
% 0.27/0.71 (assert (forall ((M tptp.refine424419629nres_a) (X4 tptp.refine424419629nres_a)) (=> (= M tptp.top_to231829469nres_a) (@ (@ tptp.ord_le519537037nres_a X4) M))))
% 0.27/0.71 (assert (forall ((S tptp.refine787176636t_unit) (S3 tptp.refine787176636t_unit)) (= (@ (@ (@ tptp.partia1658438072t_unit tptp.top_to177290092t_unit) S) S3) (=> (@ tptp.refine579265252t_unit S) (and (@ tptp.refine579265252t_unit S3) (forall ((X5 tptp.product_unit)) (= (@ (@ tptp.refine558004794t_unit S) X5) (@ (@ tptp.refine558004794t_unit S3) X5))))))))
% 0.27/0.71 (assert (forall ((M4 tptp.refine787176636t_unit) (M3 tptp.refine787176636t_unit) (F (-> tptp.product_unit tptp.refine787176636t_unit)) (F2 (-> tptp.product_unit tptp.refine787176636t_unit))) (let ((_let_1 (@ tptp.partia1658438072t_unit tptp.top_to177290092t_unit))) (=> (@ (@ _let_1 M4) M3) (=> (forall ((X3 tptp.product_unit)) (@ (@ (@ tptp.partia1658438072t_unit tptp.top_to177290092t_unit) (@ F X3)) (@ F2 X3))) (@ (@ _let_1 (@ (@ tptp.refine681446406t_unit M4) F)) (@ (@ tptp.refine681446406t_unit M3) F2)))))))
% 0.27/0.71 (assert (forall ((M4 tptp.refine424419629nres_a) (M3 tptp.refine424419629nres_a) (F (-> tptp.a tptp.refine432681134nres_b)) (F2 (-> tptp.a tptp.refine432681134nres_b))) (=> (@ (@ (@ tptp.partia906949161nres_a tptp.top_to231829469nres_a) M4) M3) (=> (forall ((X3 tptp.a)) (@ (@ (@ tptp.partia915210666nres_b tptp.top_to240090974nres_b) (@ F X3)) (@ F2 X3))) (@ (@ (@ tptp.partia915210666nres_b tptp.top_to240090974nres_b) (@ (@ tptp.refine436832839nd_a_b M4) F)) (@ (@ tptp.refine436832839nd_a_b M3) F2))))))
% 0.27/0.71 (assert (forall ((X4 tptp.refine787176636t_unit) (Y3 tptp.refine787176636t_unit)) (=> (@ (@ (@ tptp.partia1658438072t_unit tptp.top_to177290092t_unit) X4) Y3) (@ (@ tptp.ord_le1051254044t_unit Y3) X4))))
% 0.27/0.71 (assert (forall ((X4 tptp.refine432681134nres_b) (Y3 tptp.refine432681134nres_b)) (=> (@ (@ (@ tptp.partia915210666nres_b tptp.top_to240090974nres_b) X4) Y3) (@ (@ tptp.ord_le527798542nres_b Y3) X4))))
% 0.27/0.71 (assert (forall ((X4 tptp.refine424419629nres_a) (Y3 tptp.refine424419629nres_a)) (=> (@ (@ (@ tptp.partia906949161nres_a tptp.top_to231829469nres_a) X4) Y3) (@ (@ tptp.ord_le519537037nres_a Y3) X4))))
% 0.27/0.71 (assert (forall ((X4 tptp.a)) (@ (@ tptp.member_a X4) tptp.top_top_set_a)))
% 0.27/0.71 (assert (forall ((X4 tptp.b)) (@ (@ tptp.member_b X4) tptp.top_top_set_b)))
% 0.27/0.71 (assert (forall ((S tptp.set_a)) (= (= S tptp.top_top_set_a) (forall ((X5 tptp.a)) (@ (@ tptp.member_a X5) S)))))
% 0.27/0.71 (assert (forall ((S tptp.set_b)) (= (= S tptp.top_top_set_b) (forall ((X5 tptp.b)) (@ (@ tptp.member_b X5) S)))))
% 0.27/0.71 (assert (exists ((X3 tptp.a)) (@ (@ tptp.member_a X3) tptp.top_top_set_a)))
% 0.27/0.71 (assert (exists ((X3 tptp.b)) (@ (@ tptp.member_b X3) tptp.top_top_set_b)))
% 0.27/0.71 (assert (= tptp.top_top_set_a (@ tptp.collect_a tptp.top_top_a_o)))
% 0.27/0.71 (assert (= tptp.top_top_set_b (@ tptp.collect_b tptp.top_top_b_o)))
% 0.27/0.71 (assert (forall ((A3 tptp.set_a)) (=> (forall ((X3 tptp.a)) (@ (@ tptp.member_a X3) A3)) (= tptp.top_top_set_a A3))))
% 0.27/0.71 (assert (forall ((A3 tptp.set_b)) (=> (forall ((X3 tptp.b)) (@ (@ tptp.member_b X3) A3)) (= tptp.top_top_set_b A3))))
% 0.27/0.71 (assert (= tptp.top_top_a_o (lambda ((X5 tptp.a)) (@ (@ tptp.member_a X5) tptp.top_top_set_a))))
% 0.27/0.71 (assert (= tptp.top_top_b_o (lambda ((X5 tptp.b)) (@ (@ tptp.member_b X5) tptp.top_top_set_b))))
% 0.27/0.71 (assert (= (@ tptp.refine2039610767ASSERT false) tptp.top_to177290092t_unit))
% 0.27/0.71 (assert (forall ((X4 tptp.set_a) (Y3 tptp.set_a)) (= (@ (@ (@ tptp.if_set_a false) X4) Y3) Y3)))
% 0.27/0.71 (assert (forall ((X4 tptp.set_a) (Y3 tptp.set_a)) (= (@ (@ (@ tptp.if_set_a true) X4) Y3) X4)))
% 0.27/0.71 (assert (forall ((X4 tptp.set_b) (Y3 tptp.set_b)) (= (@ (@ (@ tptp.if_set_b false) X4) Y3) Y3)))
% 0.27/0.71 (assert (forall ((X4 tptp.set_b) (Y3 tptp.set_b)) (= (@ (@ (@ tptp.if_set_b true) X4) Y3) X4)))
% 0.27/0.71 (assert (forall ((X4 tptp.refine424419629nres_a) (Y3 tptp.refine424419629nres_a)) (= (@ (@ (@ tptp.if_Ref1724547303nres_a false) X4) Y3) Y3)))
% 0.27/0.71 (assert (forall ((X4 tptp.refine424419629nres_a) (Y3 tptp.refine424419629nres_a)) (= (@ (@ (@ tptp.if_Ref1724547303nres_a true) X4) Y3) X4)))
% 0.27/0.71 (assert (forall ((X4 tptp.refine432681134nres_b) (Y3 tptp.refine432681134nres_b)) (= (@ (@ (@ tptp.if_Ref1732808808nres_b false) X4) Y3) Y3)))
% 0.27/0.71 (assert (forall ((X4 tptp.refine432681134nres_b) (Y3 tptp.refine432681134nres_b)) (= (@ (@ (@ tptp.if_Ref1732808808nres_b true) X4) Y3) X4)))
% 0.27/0.71 (assert (forall ((X4 (-> Bool tptp.refine424419629nres_a)) (Y3 (-> Bool tptp.refine424419629nres_a))) (= (@ (@ (@ tptp.if_o_R1705037948nres_a false) X4) Y3) Y3)))
% 0.27/0.71 (assert (forall ((X4 (-> Bool tptp.refine424419629nres_a)) (Y3 (-> Bool tptp.refine424419629nres_a))) (= (@ (@ (@ tptp.if_o_R1705037948nres_a true) X4) Y3) X4)))
% 0.27/0.71 (assert (forall ((X4 (-> Bool tptp.refine432681134nres_b)) (Y3 (-> Bool tptp.refine432681134nres_b))) (= (@ (@ (@ tptp.if_o_R697118589nres_b false) X4) Y3) Y3)))
% 0.27/0.71 (assert (forall ((X4 (-> Bool tptp.refine432681134nres_b)) (Y3 (-> Bool tptp.refine432681134nres_b))) (= (@ (@ (@ tptp.if_o_R697118589nres_b true) X4) Y3) X4)))
% 0.27/0.71 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 15.51/15.81 (assert (forall ((X4 tptp.refine787176636t_unit) (Y3 tptp.refine787176636t_unit)) (= (@ (@ (@ tptp.if_Ref1369692790t_unit false) X4) Y3) Y3)))
% 15.51/15.81 (assert (forall ((X4 tptp.refine787176636t_unit) (Y3 tptp.refine787176636t_unit)) (= (@ (@ (@ tptp.if_Ref1369692790t_unit true) X4) Y3) X4)))
% 15.51/15.81 (assert (not (@ (@ tptp.ord_le527798542nres_b tptp.m) (@ (@ tptp.refine436832839nd_a_b (@ tptp.refine1198353288_RES_a (@ tptp.collect_a tptp.phi))) tptp.f))))
% 15.51/15.81 (set-info :filename cvc5---1.0.5_16958)
% 15.51/15.81 (check-sat-assuming ( true ))
% 15.51/15.81 ------- get file name : TPTP file name is ITP161^1
% 15.51/15.81 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_16958.smt2...
% 15.51/15.81 --- Run --ho-elim --full-saturate-quant at 10...
% 15.51/15.81 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 15.51/15.81 % SZS status Theorem for ITP161^1
% 15.51/15.81 % SZS output start Proof for ITP161^1
% 15.51/15.81 (
% 15.51/15.81 (let ((_let_1 (@ tptp.ord_le527798542nres_b tptp.m))) (let ((_let_2 (not (@ _let_1 (@ (@ tptp.refine436832839nd_a_b (@ tptp.refine1198353288_RES_a (@ tptp.collect_a tptp.phi))) tptp.f))))) (let ((_let_3 (@ tptp.refine2039610767ASSERT false))) (let ((_let_4 (= _let_3 tptp.top_to177290092t_unit))) (let ((_let_5 (= tptp.top_top_set_b (@ tptp.collect_b tptp.top_top_b_o)))) (let ((_let_6 (= tptp.top_top_set_a (@ tptp.collect_a tptp.top_top_a_o)))) (let ((_let_7 (= tptp.refine579265252t_unit (lambda ((S4 tptp.refine787176636t_unit)) (not (= S4 tptp.top_to177290092t_unit)))))) (let ((_let_8 (= tptp.top_to177290092t_unit tptp.refine1607584204t_unit))) (let ((_let_9 (= tptp.ord_less_eq_set_b (lambda ((A4 tptp.set_b) (B4 tptp.set_b)) (forall ((T3 tptp.b)) (let ((_let_1 (@ tptp.member_b T3))) (=> (@ _let_1 A4) (@ _let_1 B4)))))))) (let ((_let_10 (= tptp.ord_less_eq_set_a (lambda ((A4 tptp.set_a) (B4 tptp.set_a)) (forall ((T3 tptp.a)) (let ((_let_1 (@ tptp.member_a T3))) (=> (@ _let_1 A4) (@ _let_1 B4)))))))) (let ((_let_11 (forall ((M4 tptp.refine424419629nres_a) (F (-> tptp.a tptp.refine432681134nres_b))) (= (@ tptp.refine412683990fail_b (@ (@ tptp.refine436832839nd_a_b M4) F)) (and (@ tptp.refine412683989fail_a M4) (forall ((X5 tptp.a)) (=> (@ (@ tptp.refine1001002027nres_a M4) X5) (@ tptp.refine412683990fail_b (@ F X5))))))))) (let ((_let_12 (= tptp.ord_le519537037nres_a (lambda ((S4 tptp.refine424419629nres_a) (S5 tptp.refine424419629nres_a)) (=> (@ tptp.refine412683989fail_a S5) (and (@ tptp.refine412683989fail_a S4) (forall ((X5 tptp.a)) (=> (@ (@ tptp.refine1001002027nres_a S4) X5) (@ (@ tptp.refine1001002027nres_a S5) X5))))))))) (let ((_let_13 (= tptp.ord_le527798542nres_b (lambda ((S4 tptp.refine432681134nres_b) (S5 tptp.refine432681134nres_b)) (=> (@ tptp.refine412683990fail_b S5) (and (@ tptp.refine412683990fail_b S4) (forall ((X5 tptp.b)) (=> (@ (@ tptp.refine1001002028nres_b S4) X5) (@ (@ tptp.refine1001002028nres_b S5) X5))))))))) (let ((_let_14 (forall ((X tptp.set_a) (F (-> tptp.a tptp.refine432681134nres_b)) (Y3 tptp.b)) (= (@ (@ tptp.refine1001002028nres_b (@ (@ tptp.refine436832839nd_a_b (@ tptp.refine1198353288_RES_a X)) F)) Y3) (exists ((X5 tptp.a)) (and (@ (@ tptp.member_a X5) X) (@ (@ tptp.refine1001002028nres_b (@ F X5)) Y3))))))) (let ((_let_15 (forall ((X tptp.set_a)) (= (@ tptp.refine1001002027nres_a (@ tptp.refine1198353288_RES_a X)) (lambda ((X5 tptp.a)) (@ (@ tptp.member_a X5) X)))))) (let ((_let_16 (= tptp.refine412683990fail_b (lambda ((M5 tptp.refine432681134nres_b)) (exists ((M6 tptp.set_b)) (= M5 (@ tptp.refine1198353289_RES_b M6))))))) (let ((_let_17 (= tptp.refine412683989fail_a (lambda ((M5 tptp.refine424419629nres_a)) (exists ((M6 tptp.set_a)) (= M5 (@ tptp.refine1198353288_RES_a M6))))))) (let ((_let_18 (= tptp.ord_le516598614nres_a (lambda ((X6 (-> Bool tptp.refine424419629nres_a)) (Y8 (-> Bool tptp.refine424419629nres_a))) (and (@ (@ tptp.ord_le519537037nres_a (@ X6 false)) (@ Y8 false)) (@ (@ tptp.ord_le519537037nres_a (@ X6 true)) (@ Y8 true))))))) (let ((_let_19 (= tptp.ord_le1656162903nres_b (lambda ((X6 (-> Bool tptp.refine432681134nres_b)) (Y8 (-> Bool tptp.refine432681134nres_b))) (and (@ (@ tptp.ord_le527798542nres_b (@ X6 false)) (@ Y8 false)) (@ (@ tptp.ord_le527798542nres_b (@ X6 true)) (@ Y8 true))))))) (let ((_let_20 (forall ((A tptp.a) (P (-> tptp.a Bool))) (= (@ (@ tptp.member_a A) (@ tptp.collect_a P)) (@ P A))))) (let ((_let_21 (@ _let_1 (@ tptp.f tptp.x)))) (let ((_let_22 (@ tptp.phi tptp.x))) (let ((_let_23 (forall ((X5 tptp.b)) (or (not (ho_32 (ho_57 k_56 tptp.m) X5)) (ho_32 (ho_57 k_56 (ho_99 k_98 tptp.x)) X5))))) (let ((_let_24 (ho_32 (ho_57 k_56 (ho_99 k_98 tptp.x)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2302))) (let ((_let_25 (ho_32 (ho_57 k_56 tptp.m) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2302))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_26 _let_24))) (let ((_let_28 (forall ((M6 tptp.set_b)) (not (= tptp.m (ho_61 k_60 M6)))))) (let ((_let_29 (not _let_28))) (let ((_let_30 (and _let_29 _let_23))) (let ((_let_31 (forall ((M6 tptp.set_b)) (not (= (ho_61 k_60 M6) (ho_99 k_98 tptp.x)))))) (let ((_let_32 (not _let_31))) (let ((_let_33 (ho_43 k_42 k_97))) (let ((_let_34 (ho_54 k_53 _let_33))) (let ((_let_35 (ho_50 k_49 _let_34))) (let ((_let_36 (ho_40 _let_35 tptp.x))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_32))) (let ((_let_39 (forall ((X5 tptp.a)) (or (not (ho_40 (ho_50 k_49 (ho_54 k_53 (ho_43 k_42 k_97))) X5)) (not (forall ((M6 tptp.set_b)) (not (= (ho_61 k_60 M6) (ho_99 k_98 X5))))))))) (let ((_let_40 (and (not (forall ((M6 tptp.set_a)) (not (= (ho_54 k_53 M6) (ho_54 k_53 (ho_43 k_42 k_97)))))) _let_39))) (let ((_let_41 (forall ((M6 tptp.set_b)) (not (= (ho_61 k_60 M6) (ho_189 (ho_188 k_187 (ho_54 k_53 (ho_43 k_42 k_97))) k_98)))))) (let ((_let_42 (not _let_41))) (let ((_let_43 (= _let_42 _let_40))) (let ((_let_44 (forall ((M4 tptp.refine424419629nres_a) (BOUND_VARIABLE_38022 |u_(-> tptp.a tptp.refine432681134nres_b)|)) (= (not (forall ((M6 tptp.set_b)) (not (= (ho_61 k_60 M6) (ho_189 (ho_188 k_187 M4) BOUND_VARIABLE_38022))))) (and (not (forall ((M6 tptp.set_a)) (not (= M4 (ho_54 k_53 M6))))) (forall ((X5 tptp.a)) (or (not (ho_40 (ho_50 k_49 M4) X5)) (not (forall ((M6 tptp.set_b)) (not (= (ho_61 k_60 M6) (ho_99 BOUND_VARIABLE_38022 X5)))))))))))) (let ((_let_45 (ASSUME :args (_let_19)))) (let ((_let_46 (ASSUME :args (_let_18)))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_48 _let_47 _let_46 _let_45) :args ((= tptp.ord_le527798542nres_b (lambda ((S4 tptp.refine432681134nres_b) (S5 tptp.refine432681134nres_b)) (=> (@ tptp.refine412683990fail_b S5) (and (@ tptp.refine412683990fail_b S4) (forall ((X5 tptp.b)) (or (not (@ (@ tptp.refine1001002028nres_b S4) X5)) (@ (@ tptp.refine1001002028nres_b S5) X5))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_49 _let_48 _let_47 _let_46 _let_45) :args ((= tptp.ord_le519537037nres_a (lambda ((S4 tptp.refine424419629nres_a) (S5 tptp.refine424419629nres_a)) (=> (@ tptp.refine412683989fail_a S5) (and (@ tptp.refine412683989fail_a S4) (forall ((X5 tptp.a)) (or (not (@ (@ tptp.refine1001002027nres_a S4) X5)) (@ (@ tptp.refine1001002027nres_a S5) X5))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_11)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args ((forall ((M4 tptp.refine424419629nres_a) (F (-> tptp.a tptp.refine432681134nres_b))) (= (@ tptp.refine412683990fail_b (@ (@ tptp.refine436832839nd_a_b M4) F)) (and (@ tptp.refine412683989fail_a M4) (forall ((X5 tptp.a)) (or (not (@ (@ tptp.refine1001002027nres_a M4) X5)) (@ tptp.refine412683990fail_b (@ F X5))))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((M4 tptp.refine424419629nres_a) (F (-> tptp.a tptp.refine432681134nres_b))) (= (and (not (forall ((M6 tptp.set_a)) (not (= (@ tptp.refine1198353288_RES_a M6) M4)))) (forall ((X5 tptp.a)) (or (not (@ (@ tptp.refine1001002027nres_a M4) X5)) (not (forall ((M6 tptp.set_b)) (not (= (@ tptp.refine1198353289_RES_b M6) (@ F X5)))))))) (not (forall ((M6 tptp.set_b)) (not (= (@ tptp.refine1198353289_RES_b M6) (@ (@ tptp.refine436832839nd_a_b M4) F))))))) _let_44))))))) (let ((_let_52 (forall ((X5 tptp.b)) (or (not (ho_32 (ho_57 k_56 tptp.m) X5)) (ho_32 (ho_57 k_56 (ho_189 (ho_188 k_187 (ho_54 k_53 (ho_43 k_42 k_97))) k_98)) X5))))) (let ((_let_53 (not (forall ((M6 tptp.set_b)) (not (= tptp.m (@ tptp.refine1198353289_RES_b M6))))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (ASSUME :args (_let_8)))) (let ((_let_57 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_56 _let_55 _let_54 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args ((= tptp.refine579265252t_unit (lambda ((S4 tptp.refine787176636t_unit)) (not (= tptp.top_to177290092t_unit S4)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_58 (ASSUME :args (_let_6)))) (let ((_let_59 (ASSUME :args (_let_5)))) (let ((_let_60 (AND_INTRO (EQ_RESOLVE (SYMM (ASSUME :args (_let_4))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45) :args ((= tptp.top_to177290092t_unit _let_3) SB_DEFAULT SBA_FIXPOINT))) _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_2)) (TRANS (MACRO_SR_EQ_INTRO _let_60 :args (_let_2 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (=> (not (forall ((M6 tptp.set_b)) (not (= (@ tptp.refine1198353289_RES_b M6) (@ (@ tptp.refine436832839nd_a_b (@ tptp.refine1198353288_RES_a (@ tptp.collect_a tptp.phi))) tptp.f))))) (and _let_53 (forall ((X5 tptp.b)) (or (not (@ (@ tptp.refine1001002028nres_b tptp.m) X5)) (@ (@ tptp.refine1001002028nres_b (@ (@ tptp.refine436832839nd_a_b (@ tptp.refine1198353288_RES_a (@ tptp.collect_a tptp.phi))) tptp.f)) X5)))))) (not (=> _let_42 (and _let_29 _let_52)))))))))) (let ((_let_62 (not _let_43))) (let ((_let_63 (or))) (let ((_let_64 (_let_39))) (let ((_let_65 (tptp.x QUANTIFIERS_INST_ENUM))) (let ((_let_66 (ho_78 k_77 _let_33))) (let ((_let_67 (= _let_35 _let_66))) (let ((_let_68 (ho_40 _let_66 tptp.x))) (let ((_let_69 (forall ((X tptp.set_a)) (= (ho_78 k_77 X) (ho_50 k_49 (ho_54 k_53 X)))))) (let ((_let_70 (forall ((X tptp.set_a)) (= (@ tptp.refine1001002027nres_a (@ tptp.refine1198353288_RES_a X)) (@ ll_16 X))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_15)) (TRANS (PREPROCESS :args ((= _let_15 _let_70))) (PREPROCESS :args ((= _let_70 _let_69))))))) (let ((_let_72 (ho_46 (ho_45 k_44 tptp.x) _let_33))) (let ((_let_73 (= _let_72 _let_68))) (let ((_let_74 (forall ((BOUND_VARIABLE_30582 tptp.set_a) (BOUND_VARIABLE_30583 tptp.a)) (= (ho_40 (ho_78 k_77 BOUND_VARIABLE_30582) BOUND_VARIABLE_30583) (ho_46 (ho_45 k_44 BOUND_VARIABLE_30583) BOUND_VARIABLE_30582))))) (let ((_let_75 (forall ((u |u_(-> _u_(-> tptp.refine424419629nres_a Bool)_ tptp.refine424419629nres_a)|) (e tptp.refine424419629nres_a) (i |u_(-> tptp.refine424419629nres_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.refine424419629nres_a Bool)_ tptp.refine424419629nres_a)|)) (not (forall ((ii |u_(-> tptp.refine424419629nres_a Bool)|)) (= (ho_244 v ii) (ite (= i ii) e (ho_244 u ii)))))))))) (let ((_let_76 (forall ((x |u_(-> _u_(-> tptp.refine424419629nres_a Bool)_ tptp.refine424419629nres_a)|) (y |u_(-> _u_(-> tptp.refine424419629nres_a Bool)_ tptp.refine424419629nres_a)|)) (or (not (forall ((z |u_(-> tptp.refine424419629nres_a Bool)|)) (= (ho_244 x z) (ho_244 y z)))) (= x y))))) (let ((_let_77 (forall ((u |u_(-> tptp.refine432681134nres_b tptp.refine424419629nres_a)|) (e tptp.refine424419629nres_a) (i tptp.refine432681134nres_b)) (not (forall ((v |u_(-> tptp.refine432681134nres_b tptp.refine424419629nres_a)|)) (not (forall ((ii tptp.refine432681134nres_b)) (= (ho_240 v ii) (ite (= i ii) e (ho_240 u ii)))))))))) (let ((_let_78 (forall ((x |u_(-> tptp.refine432681134nres_b tptp.refine424419629nres_a)|) (y |u_(-> tptp.refine432681134nres_b tptp.refine424419629nres_a)|)) (or (not (forall ((z tptp.refine432681134nres_b)) (= (ho_240 x z) (ho_240 y z)))) (= x y))))) (let ((_let_79 (forall ((u |u_(-> _u_(-> tptp.refine432681134nres_b Bool)_ tptp.refine432681134nres_b)|) (e tptp.refine432681134nres_b) (i |u_(-> tptp.refine432681134nres_b Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.refine432681134nres_b Bool)_ tptp.refine432681134nres_b)|)) (not (forall ((ii |u_(-> tptp.refine432681134nres_b Bool)|)) (= (ho_242 v ii) (ite (= i ii) e (ho_242 u ii)))))))))) (let ((_let_80 (forall ((x |u_(-> _u_(-> tptp.refine432681134nres_b Bool)_ tptp.refine432681134nres_b)|) (y |u_(-> _u_(-> tptp.refine432681134nres_b Bool)_ tptp.refine432681134nres_b)|)) (or (not (forall ((z |u_(-> tptp.refine432681134nres_b Bool)|)) (= (ho_242 x z) (ho_242 y z)))) (= x y))))) (let ((_let_81 (forall ((u |u_(-> tptp.refine787176636t_unit tptp.set_Product_unit)|) (e tptp.set_Product_unit) (i tptp.refine787176636t_unit)) (not (forall ((v |u_(-> tptp.refine787176636t_unit tptp.set_Product_unit)|)) (not (forall ((ii tptp.refine787176636t_unit)) (= (ho_222 v ii) (ite (= i ii) e (ho_222 u ii)))))))))) (let ((_let_82 (forall ((x |u_(-> tptp.refine787176636t_unit tptp.set_Product_unit)|) (y |u_(-> tptp.refine787176636t_unit tptp.set_Product_unit)|)) (or (not (forall ((z tptp.refine787176636t_unit)) (= (ho_222 x z) (ho_222 y z)))) (= x y))))) (let ((_let_83 (forall ((u |u_(-> tptp.b tptp.b Bool)|) (e |u_(-> tptp.b Bool)|) (i tptp.b)) (not (forall ((v |u_(-> tptp.b tptp.b Bool)|)) (not (forall ((ii tptp.b)) (= (ho_64 v ii) (ite (= i ii) e (ho_64 u ii)))))))))) (let ((_let_84 (forall ((x |u_(-> tptp.b tptp.b Bool)|) (y |u_(-> tptp.b tptp.b Bool)|)) (or (not (forall ((z tptp.b)) (= (ho_64 x z) (ho_64 y z)))) (= x y))))) (let ((_let_85 (forall ((u |u_(-> tptp.refine671810262od_a_a _u_(-> tptp.product_prod_a_a tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|) (e |u_(-> _u_(-> tptp.product_prod_a_a tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|) (i tptp.refine671810262od_a_a)) (not (forall ((v |u_(-> tptp.refine671810262od_a_a _u_(-> tptp.product_prod_a_a tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|)) (not (forall ((ii tptp.refine671810262od_a_a)) (= (ho_219 v ii) (ite (= i ii) e (ho_219 u ii)))))))))) (let ((_let_86 (forall ((x |u_(-> tptp.refine671810262od_a_a _u_(-> tptp.product_prod_a_a tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|) (y |u_(-> tptp.refine671810262od_a_a _u_(-> tptp.product_prod_a_a tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|)) (or (not (forall ((z tptp.refine671810262od_a_a)) (= (ho_219 x z) (ho_219 y z)))) (= x y))))) (let ((_let_87 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|) (e tptp.refine432681134nres_b) (i |u_(-> tptp.product_prod_a_a tptp.refine432681134nres_b)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a tptp.refine432681134nres_b)|)) (= (ho_220 v ii) (ite (= i ii) e (ho_220 u ii)))))))))) (let ((_let_88 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|) (y |u_(-> _u_(-> tptp.product_prod_a_a tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a tptp.refine432681134nres_b)|)) (= (ho_220 x z) (ho_220 y z)))) (= x y))))) (let ((_let_89 (forall ((u |u_(-> tptp.set_Product_prod_a_b tptp.set_a)|) (e tptp.set_a) (i tptp.set_Product_prod_a_b)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_b tptp.set_a)|)) (not (forall ((ii tptp.set_Product_prod_a_b)) (= (ho_297 v ii) (ite (= i ii) e (ho_297 u ii)))))))))) (let ((_let_90 (forall ((x |u_(-> tptp.set_Product_prod_a_b tptp.set_a)|) (y |u_(-> tptp.set_Product_prod_a_b tptp.set_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_b)) (= (ho_297 x z) (ho_297 y z)))) (= x y))))) (let ((_let_91 (forall ((u |u_(-> tptp.product_unit tptp.refine787176636t_unit)|) (e tptp.refine787176636t_unit) (i tptp.product_unit)) (not (forall ((v |u_(-> tptp.product_unit tptp.refine787176636t_unit)|)) (not (forall ((ii tptp.product_unit)) (= (ho_213 v ii) (ite (= i ii) e (ho_213 u ii)))))))))) (let ((_let_92 (forall ((x |u_(-> tptp.product_unit tptp.refine787176636t_unit)|) (y |u_(-> tptp.product_unit tptp.refine787176636t_unit)|)) (or (not (forall ((z tptp.product_unit)) (= (ho_213 x z) (ho_213 y z)))) (= x y))))) (let ((_let_93 (forall ((u |u_(-> tptp.refine787176636t_unit _u_(-> tptp.product_unit tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|) (e |u_(-> _u_(-> tptp.product_unit tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|) (i tptp.refine787176636t_unit)) (not (forall ((v |u_(-> tptp.refine787176636t_unit _u_(-> tptp.product_unit tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|)) (not (forall ((ii tptp.refine787176636t_unit)) (= (ho_207 v ii) (ite (= i ii) e (ho_207 u ii)))))))))) (let ((_let_94 (forall ((x |u_(-> tptp.refine787176636t_unit _u_(-> tptp.product_unit tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|) (y |u_(-> tptp.refine787176636t_unit _u_(-> tptp.product_unit tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|)) (or (not (forall ((z tptp.refine787176636t_unit)) (= (ho_207 x z) (ho_207 y z)))) (= x y))))) (let ((_let_95 (forall ((u |u_(-> tptp.refine432681134nres_b _u_(-> tptp.b tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|) (e |u_(-> _u_(-> tptp.b tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|) (i tptp.refine432681134nres_b)) (not (forall ((v |u_(-> tptp.refine432681134nres_b _u_(-> tptp.b tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|)) (not (forall ((ii tptp.refine432681134nres_b)) (= (ho_203 v ii) (ite (= i ii) e (ho_203 u ii)))))))))) (let ((_let_96 (forall ((x |u_(-> tptp.refine432681134nres_b _u_(-> tptp.b tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|) (y |u_(-> tptp.refine432681134nres_b _u_(-> tptp.b tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|)) (or (not (forall ((z tptp.refine432681134nres_b)) (= (ho_203 x z) (ho_203 y z)))) (= x y))))) (let ((_let_97 (forall ((u |u_(-> tptp.b tptp.refine787176636t_unit)|) (e tptp.refine787176636t_unit) (i tptp.b)) (not (forall ((v |u_(-> tptp.b tptp.refine787176636t_unit)|)) (not (forall ((ii tptp.b)) (= (ho_201 v ii) (ite (= i ii) e (ho_201 u ii)))))))))) (let ((_let_98 (forall ((x |u_(-> tptp.b tptp.refine787176636t_unit)|) (y |u_(-> tptp.b tptp.refine787176636t_unit)|)) (or (not (forall ((z tptp.b)) (= (ho_201 x z) (ho_201 y z)))) (= x y))))) (let ((_let_99 (forall ((u |u_(-> _u_(-> Bool tptp.refine424419629nres_a)_ Bool tptp.refine424419629nres_a)|) (e |u_(-> Bool tptp.refine424419629nres_a)|) (i |u_(-> Bool tptp.refine424419629nres_a)|)) (not (forall ((v |u_(-> _u_(-> Bool tptp.refine424419629nres_a)_ Bool tptp.refine424419629nres_a)|)) (not (forall ((ii |u_(-> Bool tptp.refine424419629nres_a)|)) (= (ho_178 v ii) (ite (= i ii) e (ho_178 u ii)))))))))) (let ((_let_100 (forall ((x |u_(-> _u_(-> Bool tptp.refine424419629nres_a)_ Bool tptp.refine424419629nres_a)|) (y |u_(-> _u_(-> Bool tptp.refine424419629nres_a)_ Bool tptp.refine424419629nres_a)|)) (or (not (forall ((z |u_(-> Bool tptp.refine424419629nres_a)|)) (= (ho_178 x z) (ho_178 y z)))) (= x y))))) (let ((_let_101 (forall ((u |u_(-> tptp.product_unit tptp.refine432681134nres_b)|) (e tptp.refine432681134nres_b) (i tptp.product_unit)) (not (forall ((v |u_(-> tptp.product_unit tptp.refine432681134nres_b)|)) (not (forall ((ii tptp.product_unit)) (= (ho_205 v ii) (ite (= i ii) e (ho_205 u ii)))))))))) (let ((_let_102 (forall ((x |u_(-> tptp.product_unit tptp.refine432681134nres_b)|) (y |u_(-> tptp.product_unit tptp.refine432681134nres_b)|)) (or (not (forall ((z tptp.product_unit)) (= (ho_205 x z) (ho_205 y z)))) (= x y))))) (let ((_let_103 (forall ((u |u_(-> _u_(-> tptp.a tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|) (e tptp.refine787176636t_unit) (i |u_(-> tptp.a tptp.refine787176636t_unit)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|)) (not (forall ((ii |u_(-> tptp.a tptp.refine787176636t_unit)|)) (= (ho_200 v ii) (ite (= i ii) e (ho_200 u ii)))))))))) (let ((_let_104 (forall ((x |u_(-> _u_(-> tptp.a tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|) (y |u_(-> _u_(-> tptp.a tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|)) (or (not (forall ((z |u_(-> tptp.a tptp.refine787176636t_unit)|)) (= (ho_200 x z) (ho_200 y z)))) (= x y))))) (let ((_let_105 (forall ((u |u_(-> tptp.set_a tptp.set_a)|) (e tptp.set_a) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.set_a)|)) (not (forall ((ii tptp.set_a)) (= (ho_173 v ii) (ite (= i ii) e (ho_173 u ii)))))))))) (let ((_let_106 (forall ((x |u_(-> tptp.set_a tptp.set_a)|) (y |u_(-> tptp.set_a tptp.set_a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_173 x z) (ho_173 y z)))) (= x y))))) (let ((_let_107 (forall ((u |u_(-> tptp.set_Product_prod_b_a tptp.refine432681134nres_b tptp.refine424419629nres_a)|) (e |u_(-> tptp.refine432681134nres_b tptp.refine424419629nres_a)|) (i tptp.set_Product_prod_b_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_b_a tptp.refine432681134nres_b tptp.refine424419629nres_a)|)) (not (forall ((ii tptp.set_Product_prod_b_a)) (= (ho_273 v ii) (ite (= i ii) e (ho_273 u ii)))))))))) (let ((_let_108 (forall ((x |u_(-> tptp.set_Product_prod_b_a tptp.refine432681134nres_b tptp.refine424419629nres_a)|) (y |u_(-> tptp.set_Product_prod_b_a tptp.refine432681134nres_b tptp.refine424419629nres_a)|)) (or (not (forall ((z tptp.set_Product_prod_b_a)) (= (ho_273 x z) (ho_273 y z)))) (= x y))))) (let ((_let_109 (forall ((u |u_(-> tptp.refine424419629nres_a tptp.refine432681134nres_b)|) (e tptp.refine432681134nres_b) (i tptp.refine424419629nres_a)) (not (forall ((v |u_(-> tptp.refine424419629nres_a tptp.refine432681134nres_b)|)) (not (forall ((ii tptp.refine424419629nres_a)) (= (ho_239 v ii) (ite (= i ii) e (ho_239 u ii)))))))))) (let ((_let_110 (forall ((x |u_(-> tptp.refine424419629nres_a tptp.refine432681134nres_b)|) (y |u_(-> tptp.refine424419629nres_a tptp.refine432681134nres_b)|)) (or (not (forall ((z tptp.refine424419629nres_a)) (= (ho_239 x z) (ho_239 y z)))) (= x y))))) (let ((_let_111 (forall ((u |u_(-> tptp.product_prod_a_b tptp.set_Product_prod_a_b Bool)|) (e |u_(-> tptp.set_Product_prod_a_b Bool)|) (i tptp.product_prod_a_b)) (not (forall ((v |u_(-> tptp.product_prod_a_b tptp.set_Product_prod_a_b Bool)|)) (not (forall ((ii tptp.product_prod_a_b)) (= (ho_161 v ii) (ite (= i ii) e (ho_161 u ii)))))))))) (let ((_let_112 (forall ((x |u_(-> tptp.product_prod_a_b tptp.set_Product_prod_a_b Bool)|) (y |u_(-> tptp.product_prod_a_b tptp.set_Product_prod_a_b Bool)|)) (or (not (forall ((z tptp.product_prod_a_b)) (= (ho_161 x z) (ho_161 y z)))) (= x y))))) (let ((_let_113 (forall ((u |u_(-> tptp.a tptp.refine787176636t_unit)|) (e tptp.refine787176636t_unit) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.refine787176636t_unit)|)) (not (forall ((ii tptp.a)) (= (ho_197 v ii) (ite (= i ii) e (ho_197 u ii)))))))))) (let ((_let_114 (forall ((x |u_(-> tptp.a tptp.refine787176636t_unit)|) (y |u_(-> tptp.a tptp.refine787176636t_unit)|)) (or (not (forall ((z tptp.a)) (= (ho_197 x z) (ho_197 y z)))) (= x y))))) (let ((_let_115 (forall ((u |u_(-> tptp.refine432681134nres_b _u_(-> tptp.b tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|) (e |u_(-> _u_(-> tptp.b tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|) (i tptp.refine432681134nres_b)) (not (forall ((v |u_(-> tptp.refine432681134nres_b _u_(-> tptp.b tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|)) (not (forall ((ii tptp.refine432681134nres_b)) (= (ho_195 v ii) (ite (= i ii) e (ho_195 u ii)))))))))) (let ((_let_116 (forall ((x |u_(-> tptp.refine432681134nres_b _u_(-> tptp.b tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|) (y |u_(-> tptp.refine432681134nres_b _u_(-> tptp.b tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|)) (or (not (forall ((z tptp.refine432681134nres_b)) (= (ho_195 x z) (ho_195 y z)))) (= x y))))) (let ((_let_117 (forall ((u |u_(-> tptp.b tptp.refine424419629nres_a)|) (e tptp.refine424419629nres_a) (i tptp.b)) (not (forall ((v |u_(-> tptp.b tptp.refine424419629nres_a)|)) (not (forall ((ii tptp.b)) (= (ho_193 v ii) (ite (= i ii) e (ho_193 u ii)))))))))) (let ((_let_118 (forall ((x |u_(-> tptp.b tptp.refine424419629nres_a)|) (y |u_(-> tptp.b tptp.refine424419629nres_a)|)) (or (not (forall ((z tptp.b)) (= (ho_193 x z) (ho_193 y z)))) (= x y))))) (let ((_let_119 (forall ((u |u_(-> tptp.refine432681134nres_b _u_(-> tptp.b tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|) (e |u_(-> _u_(-> tptp.b tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|) (i tptp.refine432681134nres_b)) (not (forall ((v |u_(-> tptp.refine432681134nres_b _u_(-> tptp.b tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|)) (not (forall ((ii tptp.refine432681134nres_b)) (= (ho_191 v ii) (ite (= i ii) e (ho_191 u ii)))))))))) (let ((_let_120 (forall ((x |u_(-> tptp.refine432681134nres_b _u_(-> tptp.b tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|) (y |u_(-> tptp.refine432681134nres_b _u_(-> tptp.b tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|)) (or (not (forall ((z tptp.refine432681134nres_b)) (= (ho_191 x z) (ho_191 y z)))) (= x y))))) (let ((_let_121 (forall ((u |u_(-> tptp.refine891721109od_b_a Bool)|) (e Bool) (i tptp.refine891721109od_b_a)) (not (forall ((v |u_(-> tptp.refine891721109od_b_a Bool)|)) (not (forall ((ii tptp.refine891721109od_b_a)) (= (ho_137 v ii) (ite (= i ii) e (ho_137 u ii)))))))))) (let ((_let_122 (forall ((x |u_(-> tptp.refine891721109od_b_a Bool)|) (y |u_(-> tptp.refine891721109od_b_a Bool)|)) (or (not (forall ((z tptp.refine891721109od_b_a)) (= (ho_137 x z) (ho_137 y z)))) (= x y))))) (let ((_let_123 (forall ((u |u_(-> tptp.refine424419629nres_a _u_(-> tptp.a tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|) (e |u_(-> _u_(-> tptp.a tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|) (i tptp.refine424419629nres_a)) (not (forall ((v |u_(-> tptp.refine424419629nres_a _u_(-> tptp.a tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|)) (not (forall ((ii tptp.refine424419629nres_a)) (= (ho_188 v ii) (ite (= i ii) e (ho_188 u ii)))))))))) (let ((_let_124 (forall ((x |u_(-> tptp.refine424419629nres_a _u_(-> tptp.a tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|) (y |u_(-> tptp.refine424419629nres_a _u_(-> tptp.a tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|)) (or (not (forall ((z tptp.refine424419629nres_a)) (= (ho_188 x z) (ho_188 y z)))) (= x y))))) (let ((_let_125 (forall ((u |u_(-> _u_(-> Bool tptp.refine424419629nres_a)_ _u_(-> Bool tptp.refine424419629nres_a)_ Bool tptp.refine424419629nres_a)|) (e |u_(-> _u_(-> Bool tptp.refine424419629nres_a)_ Bool tptp.refine424419629nres_a)|) (i |u_(-> Bool tptp.refine424419629nres_a)|)) (not (forall ((v |u_(-> _u_(-> Bool tptp.refine424419629nres_a)_ _u_(-> Bool tptp.refine424419629nres_a)_ Bool tptp.refine424419629nres_a)|)) (not (forall ((ii |u_(-> Bool tptp.refine424419629nres_a)|)) (= (ho_177 v ii) (ite (= i ii) e (ho_177 u ii)))))))))) (let ((_let_126 (forall ((x |u_(-> _u_(-> Bool tptp.refine424419629nres_a)_ _u_(-> Bool tptp.refine424419629nres_a)_ Bool tptp.refine424419629nres_a)|) (y |u_(-> _u_(-> Bool tptp.refine424419629nres_a)_ _u_(-> Bool tptp.refine424419629nres_a)_ Bool tptp.refine424419629nres_a)|)) (or (not (forall ((z |u_(-> Bool tptp.refine424419629nres_a)|)) (= (ho_177 x z) (ho_177 y z)))) (= x y))))) (let ((_let_127 (forall ((u |u_(-> tptp.refine424419629nres_a _u_(-> tptp.a tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|) (e |u_(-> _u_(-> tptp.a tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|) (i tptp.refine424419629nres_a)) (not (forall ((v |u_(-> tptp.refine424419629nres_a _u_(-> tptp.a tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|)) (not (forall ((ii tptp.refine424419629nres_a)) (= (ho_185 v ii) (ite (= i ii) e (ho_185 u ii)))))))))) (let ((_let_128 (forall ((x |u_(-> tptp.refine424419629nres_a _u_(-> tptp.a tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|) (y |u_(-> tptp.refine424419629nres_a _u_(-> tptp.a tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|)) (or (not (forall ((z tptp.refine424419629nres_a)) (= (ho_185 x z) (ho_185 y z)))) (= x y))))) (let ((_let_129 (forall ((u |u_(-> _u_(-> tptp.b tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|) (e tptp.refine787176636t_unit) (i |u_(-> tptp.b tptp.refine787176636t_unit)|)) (not (forall ((v |u_(-> _u_(-> tptp.b tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|)) (not (forall ((ii |u_(-> tptp.b tptp.refine787176636t_unit)|)) (= (ho_204 v ii) (ite (= i ii) e (ho_204 u ii)))))))))) (let ((_let_130 (forall ((x |u_(-> _u_(-> tptp.b tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|) (y |u_(-> _u_(-> tptp.b tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|)) (or (not (forall ((z |u_(-> tptp.b tptp.refine787176636t_unit)|)) (= (ho_204 x z) (ho_204 y z)))) (= x y))))) (let ((_let_131 (forall ((u |u_(-> _u_(-> tptp.a tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|) (e tptp.refine424419629nres_a) (i |u_(-> tptp.a tptp.refine424419629nres_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.refine424419629nres_a)|)) (= (ho_186 v ii) (ite (= i ii) e (ho_186 u ii)))))))))) (let ((_let_132 (forall ((x |u_(-> _u_(-> tptp.a tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|) (y |u_(-> _u_(-> tptp.a tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.refine424419629nres_a)|)) (= (ho_186 x z) (ho_186 y z)))) (= x y))))) (let ((_let_133 (forall ((u |u_(-> _u_(-> Bool tptp.refine432681134nres_b)_ Bool tptp.refine432681134nres_b)|) (e |u_(-> Bool tptp.refine432681134nres_b)|) (i |u_(-> Bool tptp.refine432681134nres_b)|)) (not (forall ((v |u_(-> _u_(-> Bool tptp.refine432681134nres_b)_ Bool tptp.refine432681134nres_b)|)) (not (forall ((ii |u_(-> Bool tptp.refine432681134nres_b)|)) (= (ho_183 v ii) (ite (= i ii) e (ho_183 u ii)))))))))) (let ((_let_134 (forall ((x |u_(-> _u_(-> Bool tptp.refine432681134nres_b)_ Bool tptp.refine432681134nres_b)|) (y |u_(-> _u_(-> Bool tptp.refine432681134nres_b)_ Bool tptp.refine432681134nres_b)|)) (or (not (forall ((z |u_(-> Bool tptp.refine432681134nres_b)|)) (= (ho_183 x z) (ho_183 y z)))) (= x y))))) (let ((_let_135 (forall ((u |u_(-> tptp.refine432681134nres_b tptp.b Bool)|) (e |u_(-> tptp.b Bool)|) (i tptp.refine432681134nres_b)) (not (forall ((v |u_(-> tptp.refine432681134nres_b tptp.b Bool)|)) (not (forall ((ii tptp.refine432681134nres_b)) (= (ho_57 v ii) (ite (= i ii) e (ho_57 u ii)))))))))) (let ((_let_136 (forall ((x |u_(-> tptp.refine432681134nres_b tptp.b Bool)|) (y |u_(-> tptp.refine432681134nres_b tptp.b Bool)|)) (or (not (forall ((z tptp.refine432681134nres_b)) (= (ho_57 x z) (ho_57 y z)))) (= x y))))) (let ((_let_137 (forall ((u |u_(-> Bool tptp.refine432681134nres_b)|) (e tptp.refine432681134nres_b) (i Bool)) (not (forall ((v |u_(-> Bool tptp.refine432681134nres_b)|)) (not (forall ((ii Bool)) (= (ho_179 v ii) (ite (= i ii) e (ho_179 u ii)))))))))) (let ((_let_138 (forall ((x |u_(-> Bool tptp.refine432681134nres_b)|) (y |u_(-> Bool tptp.refine432681134nres_b)|)) (or (not (forall ((z Bool)) (= (ho_179 x z) (ho_179 y z)))) (= x y))))) (let ((_let_139 (forall ((u |u_(-> tptp.set_Product_prod_b_a tptp.refine424419629nres_a tptp.refine432681134nres_b)|) (e |u_(-> tptp.refine424419629nres_a tptp.refine432681134nres_b)|) (i tptp.set_Product_prod_b_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_b_a tptp.refine424419629nres_a tptp.refine432681134nres_b)|)) (not (forall ((ii tptp.set_Product_prod_b_a)) (= (ho_248 v ii) (ite (= i ii) e (ho_248 u ii)))))))))) (let ((_let_140 (forall ((x |u_(-> tptp.set_Product_prod_b_a tptp.refine424419629nres_a tptp.refine432681134nres_b)|) (y |u_(-> tptp.set_Product_prod_b_a tptp.refine424419629nres_a tptp.refine432681134nres_b)|)) (or (not (forall ((z tptp.set_Product_prod_b_a)) (= (ho_248 x z) (ho_248 y z)))) (= x y))))) (let ((_let_141 (forall ((u |u_(-> Bool _u_(-> Bool tptp.refine424419629nres_a)_ _u_(-> Bool tptp.refine424419629nres_a)_ Bool tptp.refine424419629nres_a)|) (e |u_(-> _u_(-> Bool tptp.refine424419629nres_a)_ _u_(-> Bool tptp.refine424419629nres_a)_ Bool tptp.refine424419629nres_a)|) (i Bool)) (not (forall ((v |u_(-> Bool _u_(-> Bool tptp.refine424419629nres_a)_ _u_(-> Bool tptp.refine424419629nres_a)_ Bool tptp.refine424419629nres_a)|)) (not (forall ((ii Bool)) (= (ho_176 v ii) (ite (= i ii) e (ho_176 u ii)))))))))) (let ((_let_142 (forall ((x |u_(-> Bool _u_(-> Bool tptp.refine424419629nres_a)_ _u_(-> Bool tptp.refine424419629nres_a)_ Bool tptp.refine424419629nres_a)|) (y |u_(-> Bool _u_(-> Bool tptp.refine424419629nres_a)_ _u_(-> Bool tptp.refine424419629nres_a)_ Bool tptp.refine424419629nres_a)|)) (or (not (forall ((z Bool)) (= (ho_176 x z) (ho_176 y z)))) (= x y))))) (let ((_let_143 (forall ((u |u_(-> Bool tptp.refine424419629nres_a)|) (e tptp.refine424419629nres_a) (i Bool)) (not (forall ((v |u_(-> Bool tptp.refine424419629nres_a)|)) (not (forall ((ii Bool)) (= (ho_174 v ii) (ite (= i ii) e (ho_174 u ii)))))))))) (let ((_let_144 (forall ((x |u_(-> Bool tptp.refine424419629nres_a)|) (y |u_(-> Bool tptp.refine424419629nres_a)|)) (or (not (forall ((z Bool)) (= (ho_174 x z) (ho_174 y z)))) (= x y))))) (let ((_let_145 (forall ((u |u_(-> tptp.refine1811374551od_a_b tptp.product_prod_a_b Bool)|) (e |u_(-> tptp.product_prod_a_b Bool)|) (i tptp.refine1811374551od_a_b)) (not (forall ((v |u_(-> tptp.refine1811374551od_a_b tptp.product_prod_a_b Bool)|)) (not (forall ((ii tptp.refine1811374551od_a_b)) (= (ho_234 v ii) (ite (= i ii) e (ho_234 u ii)))))))))) (let ((_let_146 (forall ((x |u_(-> tptp.refine1811374551od_a_b tptp.product_prod_a_b Bool)|) (y |u_(-> tptp.refine1811374551od_a_b tptp.product_prod_a_b Bool)|)) (or (not (forall ((z tptp.refine1811374551od_a_b)) (= (ho_234 x z) (ho_234 y z)))) (= x y))))) (let ((_let_147 (forall ((u |u_(-> Bool tptp.set_a tptp.set_a tptp.set_a)|) (e |u_(-> tptp.set_a tptp.set_a tptp.set_a)|) (i Bool)) (not (forall ((v |u_(-> Bool tptp.set_a tptp.set_a tptp.set_a)|)) (not (forall ((ii Bool)) (= (ho_171 v ii) (ite (= i ii) e (ho_171 u ii)))))))))) (let ((_let_148 (forall ((x |u_(-> Bool tptp.set_a tptp.set_a tptp.set_a)|) (y |u_(-> Bool tptp.set_a tptp.set_a tptp.set_a)|)) (or (not (forall ((z Bool)) (= (ho_171 x z) (ho_171 y z)))) (= x y))))) (let ((_let_149 (forall ((u |u_(-> tptp.b tptp.product_prod_b_b)|) (e tptp.product_prod_b_b) (i tptp.b)) (not (forall ((v |u_(-> tptp.b tptp.product_prod_b_b)|)) (not (forall ((ii tptp.b)) (= (ho_264 v ii) (ite (= i ii) e (ho_264 u ii)))))))))) (let ((_let_150 (forall ((x |u_(-> tptp.b tptp.product_prod_b_b)|) (y |u_(-> tptp.b tptp.product_prod_b_b)|)) (or (not (forall ((z tptp.b)) (= (ho_264 x z) (ho_264 y z)))) (= x y))))) (let ((_let_151 (forall ((u |u_(-> tptp.refine787176636t_unit _u_(-> tptp.product_unit tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|) (e |u_(-> _u_(-> tptp.product_unit tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|) (i tptp.refine787176636t_unit)) (not (forall ((v |u_(-> tptp.refine787176636t_unit _u_(-> tptp.product_unit tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|)) (not (forall ((ii tptp.refine787176636t_unit)) (= (ho_215 v ii) (ite (= i ii) e (ho_215 u ii)))))))))) (let ((_let_152 (forall ((x |u_(-> tptp.refine787176636t_unit _u_(-> tptp.product_unit tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|) (y |u_(-> tptp.refine787176636t_unit _u_(-> tptp.product_unit tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|)) (or (not (forall ((z tptp.refine787176636t_unit)) (= (ho_215 x z) (ho_215 y z)))) (= x y))))) (let ((_let_153 (forall ((u |u_(-> tptp.set_a tptp.set_a tptp.set_a)|) (e |u_(-> tptp.set_a tptp.set_a)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.set_a tptp.set_a)|)) (not (forall ((ii tptp.set_a)) (= (ho_172 v ii) (ite (= i ii) e (ho_172 u ii)))))))))) (let ((_let_154 (forall ((x |u_(-> tptp.set_a tptp.set_a tptp.set_a)|) (y |u_(-> tptp.set_a tptp.set_a tptp.set_a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_172 x z) (ho_172 y z)))) (= x y))))) (let ((_let_155 (forall ((u |u_(-> tptp.set_Pr1707992533t_unit tptp.refine432681134nres_b tptp.refine787176636t_unit)|) (e |u_(-> tptp.refine432681134nres_b tptp.refine787176636t_unit)|) (i tptp.set_Pr1707992533t_unit)) (not (forall ((v |u_(-> tptp.set_Pr1707992533t_unit tptp.refine432681134nres_b tptp.refine787176636t_unit)|)) (not (forall ((ii tptp.set_Pr1707992533t_unit)) (= (ho_287 v ii) (ite (= i ii) e (ho_287 u ii)))))))))) (let ((_let_156 (forall ((x |u_(-> tptp.set_Pr1707992533t_unit tptp.refine432681134nres_b tptp.refine787176636t_unit)|) (y |u_(-> tptp.set_Pr1707992533t_unit tptp.refine432681134nres_b tptp.refine787176636t_unit)|)) (or (not (forall ((z tptp.set_Pr1707992533t_unit)) (= (ho_287 x z) (ho_287 y z)))) (= x y))))) (let ((_let_157 (forall ((u |u_(-> tptp.refine891721109od_b_a tptp.product_prod_b_a Bool)|) (e |u_(-> tptp.product_prod_b_a Bool)|) (i tptp.refine891721109od_b_a)) (not (forall ((v |u_(-> tptp.refine891721109od_b_a tptp.product_prod_b_a Bool)|)) (not (forall ((ii tptp.refine891721109od_b_a)) (= (ho_230 v ii) (ite (= i ii) e (ho_230 u ii)))))))))) (let ((_let_158 (forall ((x |u_(-> tptp.refine891721109od_b_a tptp.product_prod_b_a Bool)|) (y |u_(-> tptp.refine891721109od_b_a tptp.product_prod_b_a Bool)|)) (or (not (forall ((z tptp.refine891721109od_b_a)) (= (ho_230 x z) (ho_230 y z)))) (= x y))))) (let ((_let_159 (forall ((u |u_(-> Bool tptp.set_b tptp.set_b tptp.set_b)|) (e |u_(-> tptp.set_b tptp.set_b tptp.set_b)|) (i Bool)) (not (forall ((v |u_(-> Bool tptp.set_b tptp.set_b tptp.set_b)|)) (not (forall ((ii Bool)) (= (ho_167 v ii) (ite (= i ii) e (ho_167 u ii)))))))))) (let ((_let_160 (forall ((x |u_(-> Bool tptp.set_b tptp.set_b tptp.set_b)|) (y |u_(-> Bool tptp.set_b tptp.set_b tptp.set_b)|)) (or (not (forall ((z Bool)) (= (ho_167 x z) (ho_167 y z)))) (= x y))))) (let ((_let_161 (forall ((u |u_(-> tptp.set_b tptp.set_b)|) (e tptp.set_b) (i tptp.set_b)) (not (forall ((v |u_(-> tptp.set_b tptp.set_b)|)) (not (forall ((ii tptp.set_b)) (= (ho_169 v ii) (ite (= i ii) e (ho_169 u ii)))))))))) (let ((_let_162 (forall ((x |u_(-> tptp.set_b tptp.set_b)|) (y |u_(-> tptp.set_b tptp.set_b)|)) (or (not (forall ((z tptp.set_b)) (= (ho_169 x z) (ho_169 y z)))) (= x y))))) (let ((_let_163 (forall ((u |u_(-> tptp.b tptp.a tptp.product_prod_b_a)|) (e |u_(-> tptp.a tptp.product_prod_b_a)|) (i tptp.b)) (not (forall ((v |u_(-> tptp.b tptp.a tptp.product_prod_b_a)|)) (not (forall ((ii tptp.b)) (= (ho_254 v ii) (ite (= i ii) e (ho_254 u ii)))))))))) (let ((_let_164 (forall ((x |u_(-> tptp.b tptp.a tptp.product_prod_b_a)|) (y |u_(-> tptp.b tptp.a tptp.product_prod_b_a)|)) (or (not (forall ((z tptp.b)) (= (ho_254 x z) (ho_254 y z)))) (= x y))))) (let ((_let_165 (forall ((u |u_(-> tptp.product_unit tptp.set_Product_unit Bool)|) (e |u_(-> tptp.set_Product_unit Bool)|) (i tptp.product_unit)) (not (forall ((v |u_(-> tptp.product_unit tptp.set_Product_unit Bool)|)) (not (forall ((ii tptp.product_unit)) (= (ho_164 v ii) (ite (= i ii) e (ho_164 u ii)))))))))) (let ((_let_166 (forall ((x |u_(-> tptp.product_unit tptp.set_Product_unit Bool)|) (y |u_(-> tptp.product_unit tptp.set_Product_unit Bool)|)) (or (not (forall ((z tptp.product_unit)) (= (ho_164 x z) (ho_164 y z)))) (= x y))))) (let ((_let_167 (forall ((u |u_(-> _u_(-> tptp.a tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|) (e tptp.refine432681134nres_b) (i |u_(-> tptp.a tptp.refine432681134nres_b)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|)) (not (forall ((ii |u_(-> tptp.a tptp.refine432681134nres_b)|)) (= (ho_189 v ii) (ite (= i ii) e (ho_189 u ii)))))))))) (let ((_let_168 (forall ((x |u_(-> _u_(-> tptp.a tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|) (y |u_(-> _u_(-> tptp.a tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|)) (or (not (forall ((z |u_(-> tptp.a tptp.refine432681134nres_b)|)) (= (ho_189 x z) (ho_189 y z)))) (= x y))))) (let ((_let_169 (forall ((u |u_(-> tptp.set_Product_unit Bool)|) (e Bool) (i tptp.set_Product_unit)) (not (forall ((v |u_(-> tptp.set_Product_unit Bool)|)) (not (forall ((ii tptp.set_Product_unit)) (= (ho_165 v ii) (ite (= i ii) e (ho_165 u ii)))))))))) (let ((_let_170 (forall ((x |u_(-> tptp.set_Product_unit Bool)|) (y |u_(-> tptp.set_Product_unit Bool)|)) (or (not (forall ((z tptp.set_Product_unit)) (= (ho_165 x z) (ho_165 y z)))) (= x y))))) (let ((_let_171 (forall ((u |u_(-> tptp.refine1811374551od_a_b tptp.refine1811374551od_a_b Bool)|) (e |u_(-> tptp.refine1811374551od_a_b Bool)|) (i tptp.refine1811374551od_a_b)) (not (forall ((v |u_(-> tptp.refine1811374551od_a_b tptp.refine1811374551od_a_b Bool)|)) (not (forall ((ii tptp.refine1811374551od_a_b)) (= (ho_158 v ii) (ite (= i ii) e (ho_158 u ii)))))))))) (let ((_let_172 (forall ((x |u_(-> tptp.refine1811374551od_a_b tptp.refine1811374551od_a_b Bool)|) (y |u_(-> tptp.refine1811374551od_a_b tptp.refine1811374551od_a_b Bool)|)) (or (not (forall ((z tptp.refine1811374551od_a_b)) (= (ho_158 x z) (ho_158 y z)))) (= x y))))) (let ((_let_173 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_b Bool)_ tptp.set_Product_prod_a_b)|) (e tptp.set_Product_prod_a_b) (i |u_(-> tptp.product_prod_a_b Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_b Bool)_ tptp.set_Product_prod_a_b)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_b Bool)|)) (= (ho_154 v ii) (ite (= i ii) e (ho_154 u ii)))))))))) (let ((_let_174 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_b Bool)_ tptp.set_Product_prod_a_b)|) (y |u_(-> _u_(-> tptp.product_prod_a_b Bool)_ tptp.set_Product_prod_a_b)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_b Bool)|)) (= (ho_154 x z) (ho_154 y z)))) (= x y))))) (let ((_let_175 (forall ((u |u_(-> tptp.product_prod_a_b Bool)|) (e Bool) (i tptp.product_prod_a_b)) (not (forall ((v |u_(-> tptp.product_prod_a_b Bool)|)) (not (forall ((ii tptp.product_prod_a_b)) (= (ho_152 v ii) (ite (= i ii) e (ho_152 u ii)))))))))) (let ((_let_176 (forall ((x |u_(-> tptp.product_prod_a_b Bool)|) (y |u_(-> tptp.product_prod_a_b Bool)|)) (or (not (forall ((z tptp.product_prod_a_b)) (= (ho_152 x z) (ho_152 y z)))) (= x y))))) (let ((_let_177 (forall ((u |u_(-> tptp.refine787176636t_unit Bool)|) (e Bool) (i tptp.refine787176636t_unit)) (not (forall ((v |u_(-> tptp.refine787176636t_unit Bool)|)) (not (forall ((ii tptp.refine787176636t_unit)) (= (ho_110 v ii) (ite (= i ii) e (ho_110 u ii)))))))))) (let ((_let_178 (forall ((x |u_(-> tptp.refine787176636t_unit Bool)|) (y |u_(-> tptp.refine787176636t_unit Bool)|)) (or (not (forall ((z tptp.refine787176636t_unit)) (= (ho_110 x z) (ho_110 y z)))) (= x y))))) (let ((_let_179 (forall ((u |u_(-> tptp.set_Product_prod_a_b tptp.refine1811374551od_a_b)|) (e tptp.refine1811374551od_a_b) (i tptp.set_Product_prod_a_b)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_b tptp.refine1811374551od_a_b)|)) (not (forall ((ii tptp.set_Product_prod_a_b)) (= (ho_156 v ii) (ite (= i ii) e (ho_156 u ii)))))))))) (let ((_let_180 (forall ((x |u_(-> tptp.set_Product_prod_a_b tptp.refine1811374551od_a_b)|) (y |u_(-> tptp.set_Product_prod_a_b tptp.refine1811374551od_a_b)|)) (or (not (forall ((z tptp.set_Product_prod_a_b)) (= (ho_156 x z) (ho_156 y z)))) (= x y))))) (let ((_let_181 (forall ((u |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a Bool)|) (e |u_(-> tptp.refine424419629nres_a Bool)|) (i tptp.refine424419629nres_a)) (not (forall ((v |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a Bool)|)) (not (forall ((ii tptp.refine424419629nres_a)) (= (ho_80 v ii) (ite (= i ii) e (ho_80 u ii)))))))))) (let ((_let_182 (forall ((x |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a Bool)|) (y |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a Bool)|)) (or (not (forall ((z tptp.refine424419629nres_a)) (= (ho_80 x z) (ho_80 y z)))) (= x y))))) (let ((_let_183 (forall ((u |u_(-> tptp.product_unit Bool)|) (e Bool) (i tptp.product_unit)) (not (forall ((v |u_(-> tptp.product_unit Bool)|)) (not (forall ((ii tptp.product_unit)) (= (ho_48 v ii) (ite (= i ii) e (ho_48 u ii)))))))))) (let ((_let_184 (forall ((x |u_(-> tptp.product_unit Bool)|) (y |u_(-> tptp.product_unit Bool)|)) (or (not (forall ((z tptp.product_unit)) (= (ho_48 x z) (ho_48 y z)))) (= x y))))) (let ((_let_185 (forall ((u |u_(-> tptp.refine432681134nres_b Bool)|) (e Bool) (i tptp.refine432681134nres_b)) (not (forall ((v |u_(-> tptp.refine432681134nres_b Bool)|)) (not (forall ((ii tptp.refine432681134nres_b)) (= (ho_85 v ii) (ite (= i ii) e (ho_85 u ii)))))))))) (let ((_let_186 (forall ((x |u_(-> tptp.refine432681134nres_b Bool)|) (y |u_(-> tptp.refine432681134nres_b Bool)|)) (or (not (forall ((z tptp.refine432681134nres_b)) (= (ho_85 x z) (ho_85 y z)))) (= x y))))) (let ((_let_187 (forall ((u |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b Bool)|) (e |u_(-> tptp.refine432681134nres_b Bool)|) (i tptp.refine432681134nres_b)) (not (forall ((v |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b Bool)|)) (not (forall ((ii tptp.refine432681134nres_b)) (= (ho_84 v ii) (ite (= i ii) e (ho_84 u ii)))))))))) (let ((_let_188 (forall ((x |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b Bool)|) (y |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b Bool)|)) (or (not (forall ((z tptp.refine432681134nres_b)) (= (ho_84 x z) (ho_84 y z)))) (= x y))))) (let ((_let_189 (forall ((u |u_(-> tptp.set_Product_prod_b_a tptp.refine891721109od_b_a)|) (e tptp.refine891721109od_b_a) (i tptp.set_Product_prod_b_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_b_a tptp.refine891721109od_b_a)|)) (not (forall ((ii tptp.set_Product_prod_b_a)) (= (ho_134 v ii) (ite (= i ii) e (ho_134 u ii)))))))))) (let ((_let_190 (forall ((x |u_(-> tptp.set_Product_prod_b_a tptp.refine891721109od_b_a)|) (y |u_(-> tptp.set_Product_prod_b_a tptp.refine891721109od_b_a)|)) (or (not (forall ((z tptp.set_Product_prod_b_a)) (= (ho_134 x z) (ho_134 y z)))) (= x y))))) (let ((_let_191 (forall ((u |u_(-> tptp.set_Product_prod_b_b tptp.refine432681134nres_b tptp.refine432681134nres_b)|) (e |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b)|) (i tptp.set_Product_prod_b_b)) (not (forall ((v |u_(-> tptp.set_Product_prod_b_b tptp.refine432681134nres_b tptp.refine432681134nres_b)|)) (not (forall ((ii tptp.set_Product_prod_b_b)) (= (ho_246 v ii) (ite (= i ii) e (ho_246 u ii)))))))))) (let ((_let_192 (forall ((x |u_(-> tptp.set_Product_prod_b_b tptp.refine432681134nres_b tptp.refine432681134nres_b)|) (y |u_(-> tptp.set_Product_prod_b_b tptp.refine432681134nres_b tptp.refine432681134nres_b)|)) (or (not (forall ((z tptp.set_Product_prod_b_b)) (= (ho_246 x z) (ho_246 y z)))) (= x y))))) (let ((_let_193 (forall ((u |u_(-> tptp.product_prod_b_a tptp.set_Product_prod_b_a Bool)|) (e |u_(-> tptp.set_Product_prod_b_a Bool)|) (i tptp.product_prod_b_a)) (not (forall ((v |u_(-> tptp.product_prod_b_a tptp.set_Product_prod_b_a Bool)|)) (not (forall ((ii tptp.product_prod_b_a)) (= (ho_139 v ii) (ite (= i ii) e (ho_139 u ii)))))))))) (let ((_let_194 (forall ((x |u_(-> tptp.product_prod_b_a tptp.set_Product_prod_b_a Bool)|) (y |u_(-> tptp.product_prod_b_a tptp.set_Product_prod_b_a Bool)|)) (or (not (forall ((z tptp.product_prod_b_a)) (= (ho_139 x z) (ho_139 y z)))) (= x y))))) (let ((_let_195 (forall ((u |u_(-> tptp.refine787176636t_unit tptp.product_unit Bool)|) (e |u_(-> tptp.product_unit Bool)|) (i tptp.refine787176636t_unit)) (not (forall ((v |u_(-> tptp.refine787176636t_unit tptp.product_unit Bool)|)) (not (forall ((ii tptp.refine787176636t_unit)) (= (ho_236 v ii) (ite (= i ii) e (ho_236 u ii)))))))))) (let ((_let_196 (forall ((x |u_(-> tptp.refine787176636t_unit tptp.product_unit Bool)|) (y |u_(-> tptp.refine787176636t_unit tptp.product_unit Bool)|)) (or (not (forall ((z tptp.refine787176636t_unit)) (= (ho_236 x z) (ho_236 y z)))) (= x y))))) (let ((_let_197 (forall ((u |u_(-> Bool _u_(-> Bool tptp.refine432681134nres_b)_ _u_(-> Bool tptp.refine432681134nres_b)_ Bool tptp.refine432681134nres_b)|) (e |u_(-> _u_(-> Bool tptp.refine432681134nres_b)_ _u_(-> Bool tptp.refine432681134nres_b)_ Bool tptp.refine432681134nres_b)|) (i Bool)) (not (forall ((v |u_(-> Bool _u_(-> Bool tptp.refine432681134nres_b)_ _u_(-> Bool tptp.refine432681134nres_b)_ Bool tptp.refine432681134nres_b)|)) (not (forall ((ii Bool)) (= (ho_181 v ii) (ite (= i ii) e (ho_181 u ii)))))))))) (let ((_let_198 (forall ((x |u_(-> Bool _u_(-> Bool tptp.refine432681134nres_b)_ _u_(-> Bool tptp.refine432681134nres_b)_ Bool tptp.refine432681134nres_b)|) (y |u_(-> Bool _u_(-> Bool tptp.refine432681134nres_b)_ _u_(-> Bool tptp.refine432681134nres_b)_ Bool tptp.refine432681134nres_b)|)) (or (not (forall ((z Bool)) (= (ho_181 x z) (ho_181 y z)))) (= x y))))) (let ((_let_199 (forall ((u |u_(-> tptp.set_a tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_78 v ii) (ite (= i ii) e (ho_78 u ii)))))))))) (let ((_let_200 (forall ((x |u_(-> tptp.set_a tptp.a Bool)|) (y |u_(-> tptp.set_a tptp.a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_78 x z) (ho_78 y z)))) (= x y))))) (let ((_let_201 (forall ((u |u_(-> tptp.product_prod_a_a tptp.refine432681134nres_b)|) (e tptp.refine432681134nres_b) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.refine432681134nres_b)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_217 v ii) (ite (= i ii) e (ho_217 u ii)))))))))) (let ((_let_202 (forall ((x |u_(-> tptp.product_prod_a_a tptp.refine432681134nres_b)|) (y |u_(-> tptp.product_prod_a_a tptp.refine432681134nres_b)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_217 x z) (ho_217 y z)))) (= x y))))) (let ((_let_203 (forall ((u |u_(-> tptp.product_prod_b_b tptp.set_Product_prod_b_b Bool)|) (e |u_(-> tptp.set_Product_prod_b_b Bool)|) (i tptp.product_prod_b_b)) (not (forall ((v |u_(-> tptp.product_prod_b_b tptp.set_Product_prod_b_b Bool)|)) (not (forall ((ii tptp.product_prod_b_b)) (= (ho_150 v ii) (ite (= i ii) e (ho_150 u ii)))))))))) (let ((_let_204 (forall ((x |u_(-> tptp.product_prod_b_b tptp.set_Product_prod_b_b Bool)|) (y |u_(-> tptp.product_prod_b_b tptp.set_Product_prod_b_b Bool)|)) (or (not (forall ((z tptp.product_prod_b_b)) (= (ho_150 x z) (ho_150 y z)))) (= x y))))) (let ((_let_205 (forall ((u |u_(-> tptp.set_Product_prod_b_b Bool)|) (e Bool) (i tptp.set_Product_prod_b_b)) (not (forall ((v |u_(-> tptp.set_Product_prod_b_b Bool)|)) (not (forall ((ii tptp.set_Product_prod_b_b)) (= (ho_151 v ii) (ite (= i ii) e (ho_151 u ii)))))))))) (let ((_let_206 (forall ((x |u_(-> tptp.set_Product_prod_b_b Bool)|) (y |u_(-> tptp.set_Product_prod_b_b Bool)|)) (or (not (forall ((z tptp.set_Product_prod_b_b)) (= (ho_151 x z) (ho_151 y z)))) (= x y))))) (let ((_let_207 (forall ((u |u_(-> _u_(-> tptp.product_unit Bool)_ tptp.set_Product_unit)|) (e tptp.set_Product_unit) (i |u_(-> tptp.product_unit Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_unit Bool)_ tptp.set_Product_unit)|)) (not (forall ((ii |u_(-> tptp.product_unit Bool)|)) (= (ho_103 v ii) (ite (= i ii) e (ho_103 u ii)))))))))) (let ((_let_208 (forall ((x |u_(-> _u_(-> tptp.product_unit Bool)_ tptp.set_Product_unit)|) (y |u_(-> _u_(-> tptp.product_unit Bool)_ tptp.set_Product_unit)|)) (or (not (forall ((z |u_(-> tptp.product_unit Bool)|)) (= (ho_103 x z) (ho_103 y z)))) (= x y))))) (let ((_let_209 (forall ((u |u_(-> tptp.a tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_66 v ii) (ite (= i ii) e (ho_66 u ii)))))))))) (let ((_let_210 (forall ((x |u_(-> tptp.a tptp.a Bool)|) (y |u_(-> tptp.a tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_66 x z) (ho_66 y z)))) (= x y))))) (let ((_let_211 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.refine671810262od_a_a)|) (e tptp.refine671810262od_a_a) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.refine671810262od_a_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_123 v ii) (ite (= i ii) e (ho_123 u ii)))))))))) (let ((_let_212 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.refine671810262od_a_a)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.refine671810262od_a_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_123 x z) (ho_123 y z)))) (= x y))))) (let ((_let_213 (forall ((u |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b)|) (e tptp.refine432681134nres_b) (i tptp.refine432681134nres_b)) (not (forall ((v |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b)|)) (not (forall ((ii tptp.refine432681134nres_b)) (= (ho_114 v ii) (ite (= i ii) e (ho_114 u ii)))))))))) (let ((_let_214 (forall ((x |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b)|) (y |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b)|)) (or (not (forall ((z tptp.refine432681134nres_b)) (= (ho_114 x z) (ho_114 y z)))) (= x y))))) (let ((_let_215 (forall ((u |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a tptp.refine424419629nres_a Bool)|) (e |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a Bool)|) (i tptp.refine424419629nres_a)) (not (forall ((v |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a tptp.refine424419629nres_a Bool)|)) (not (forall ((ii tptp.refine424419629nres_a)) (= (ho_323 v ii) (ite (= i ii) e (ho_323 u ii)))))))))) (let ((_let_216 (forall ((x |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a tptp.refine424419629nres_a Bool)|) (y |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a tptp.refine424419629nres_a Bool)|)) (or (not (forall ((z tptp.refine424419629nres_a)) (= (ho_323 x z) (ho_323 y z)))) (= x y))))) (let ((_let_217 (forall ((u |u_(-> tptp.set_Product_prod_b_a Bool)|) (e Bool) (i tptp.set_Product_prod_b_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_b_a Bool)|)) (not (forall ((ii tptp.set_Product_prod_b_a)) (= (ho_140 v ii) (ite (= i ii) e (ho_140 u ii)))))))))) (let ((_let_218 (forall ((x |u_(-> tptp.set_Product_prod_b_a Bool)|) (y |u_(-> tptp.set_Product_prod_b_a Bool)|)) (or (not (forall ((z tptp.set_Product_prod_b_a)) (= (ho_140 x z) (ho_140 y z)))) (= x y))))) (let ((_let_219 (forall ((u |u_(-> tptp.refine787176636t_unit _u_(-> tptp.product_unit tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|) (e |u_(-> _u_(-> tptp.product_unit tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|) (i tptp.refine787176636t_unit)) (not (forall ((v |u_(-> tptp.refine787176636t_unit _u_(-> tptp.product_unit tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|)) (not (forall ((ii tptp.refine787176636t_unit)) (= (ho_211 v ii) (ite (= i ii) e (ho_211 u ii)))))))))) (let ((_let_220 (forall ((x |u_(-> tptp.refine787176636t_unit _u_(-> tptp.product_unit tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|) (y |u_(-> tptp.refine787176636t_unit _u_(-> tptp.product_unit tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|)) (or (not (forall ((z tptp.refine787176636t_unit)) (= (ho_211 x z) (ho_211 y z)))) (= x y))))) (let ((_let_221 (forall ((u |u_(-> tptp.refine671810262od_a_a Bool)|) (e Bool) (i tptp.refine671810262od_a_a)) (not (forall ((v |u_(-> tptp.refine671810262od_a_a Bool)|)) (not (forall ((ii tptp.refine671810262od_a_a)) (= (ho_126 v ii) (ite (= i ii) e (ho_126 u ii)))))))))) (let ((_let_222 (forall ((x |u_(-> tptp.refine671810262od_a_a Bool)|) (y |u_(-> tptp.refine671810262od_a_a Bool)|)) (or (not (forall ((z tptp.refine671810262od_a_a)) (= (ho_126 x z) (ho_126 y z)))) (= x y))))) (let ((_let_223 (forall ((u |u_(-> tptp.b tptp.set_b Bool)|) (e |u_(-> tptp.set_b Bool)|) (i tptp.b)) (not (forall ((v |u_(-> tptp.b tptp.set_b Bool)|)) (not (forall ((ii tptp.b)) (= (ho_37 v ii) (ite (= i ii) e (ho_37 u ii)))))))))) (let ((_let_224 (forall ((x |u_(-> tptp.b tptp.set_b Bool)|) (y |u_(-> tptp.b tptp.set_b Bool)|)) (or (not (forall ((z tptp.b)) (= (ho_37 x z) (ho_37 y z)))) (= x y))))) (let ((_let_225 (forall ((u |u_(-> tptp.set_b tptp.refine432681134nres_b)|) (e tptp.refine432681134nres_b) (i tptp.set_b)) (not (forall ((v |u_(-> tptp.set_b tptp.refine432681134nres_b)|)) (not (forall ((ii tptp.set_b)) (= (ho_61 v ii) (ite (= i ii) e (ho_61 u ii)))))))))) (let ((_let_226 (forall ((x |u_(-> tptp.set_b tptp.refine432681134nres_b)|) (y |u_(-> tptp.set_b tptp.refine432681134nres_b)|)) (or (not (forall ((z tptp.set_b)) (= (ho_61 x z) (ho_61 y z)))) (= x y))))) (let ((_let_227 (forall ((u |u_(-> tptp.refine424419629nres_a tptp.set_a)|) (e tptp.set_a) (i tptp.refine424419629nres_a)) (not (forall ((v |u_(-> tptp.refine424419629nres_a tptp.set_a)|)) (not (forall ((ii tptp.refine424419629nres_a)) (= (ho_224 v ii) (ite (= i ii) e (ho_224 u ii)))))))))) (let ((_let_228 (forall ((x |u_(-> tptp.refine424419629nres_a tptp.set_a)|) (y |u_(-> tptp.refine424419629nres_a tptp.set_a)|)) (or (not (forall ((z tptp.refine424419629nres_a)) (= (ho_224 x z) (ho_224 y z)))) (= x y))))) (let ((_let_229 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_40 v ii) (ite (= i ii) e (ho_40 u ii)))))))))) (let ((_let_230 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_40 x z) (ho_40 y z)))) (= x y))))) (let ((_let_231 (forall ((u |u_(-> _u_(-> Bool tptp.refine432681134nres_b)_ _u_(-> Bool tptp.refine432681134nres_b)_ Bool tptp.refine432681134nres_b)|) (e |u_(-> _u_(-> Bool tptp.refine432681134nres_b)_ Bool tptp.refine432681134nres_b)|) (i |u_(-> Bool tptp.refine432681134nres_b)|)) (not (forall ((v |u_(-> _u_(-> Bool tptp.refine432681134nres_b)_ _u_(-> Bool tptp.refine432681134nres_b)_ Bool tptp.refine432681134nres_b)|)) (not (forall ((ii |u_(-> Bool tptp.refine432681134nres_b)|)) (= (ho_182 v ii) (ite (= i ii) e (ho_182 u ii)))))))))) (let ((_let_232 (forall ((x |u_(-> _u_(-> Bool tptp.refine432681134nres_b)_ _u_(-> Bool tptp.refine432681134nres_b)_ Bool tptp.refine432681134nres_b)|) (y |u_(-> _u_(-> Bool tptp.refine432681134nres_b)_ _u_(-> Bool tptp.refine432681134nres_b)_ Bool tptp.refine432681134nres_b)|)) (or (not (forall ((z |u_(-> Bool tptp.refine432681134nres_b)|)) (= (ho_182 x z) (ho_182 y z)))) (= x y))))) (let ((_let_233 (forall ((u |u_(-> tptp.refine424419629nres_a tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i tptp.refine424419629nres_a)) (not (forall ((v |u_(-> tptp.refine424419629nres_a tptp.a Bool)|)) (not (forall ((ii tptp.refine424419629nres_a)) (= (ho_50 v ii) (ite (= i ii) e (ho_50 u ii)))))))))) (let ((_let_234 (forall ((x |u_(-> tptp.refine424419629nres_a tptp.a Bool)|) (y |u_(-> tptp.refine424419629nres_a tptp.a Bool)|)) (or (not (forall ((z tptp.refine424419629nres_a)) (= (ho_50 x z) (ho_50 y z)))) (= x y))))) (let ((_let_235 (forall ((u |u_(-> tptp.refine787176636t_unit tptp.refine432681134nres_b)|) (e tptp.refine432681134nres_b) (i tptp.refine787176636t_unit)) (not (forall ((v |u_(-> tptp.refine787176636t_unit tptp.refine432681134nres_b)|)) (not (forall ((ii tptp.refine787176636t_unit)) (= (ho_313 v ii) (ite (= i ii) e (ho_313 u ii)))))))))) (let ((_let_236 (forall ((x |u_(-> tptp.refine787176636t_unit tptp.refine432681134nres_b)|) (y |u_(-> tptp.refine787176636t_unit tptp.refine432681134nres_b)|)) (or (not (forall ((z tptp.refine787176636t_unit)) (= (ho_313 x z) (ho_313 y z)))) (= x y))))) (let ((_let_237 (forall ((u |u_(-> tptp.set_b tptp.b Bool)|) (e |u_(-> tptp.b Bool)|) (i tptp.set_b)) (not (forall ((v |u_(-> tptp.set_b tptp.b Bool)|)) (not (forall ((ii tptp.set_b)) (= (ho_76 v ii) (ite (= i ii) e (ho_76 u ii)))))))))) (let ((_let_238 (forall ((x |u_(-> tptp.set_b tptp.b Bool)|) (y |u_(-> tptp.set_b tptp.b Bool)|)) (or (not (forall ((z tptp.set_b)) (= (ho_76 x z) (ho_76 y z)))) (= x y))))) (let ((_let_239 (forall ((u |u_(-> tptp.product_prod_a_a Bool)|) (e Bool) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a Bool)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_119 v ii) (ite (= i ii) e (ho_119 u ii)))))))))) (let ((_let_240 (forall ((x |u_(-> tptp.product_prod_a_a Bool)|) (y |u_(-> tptp.product_prod_a_a Bool)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_119 x z) (ho_119 y z)))) (= x y))))) (let ((_let_241 (forall ((u |u_(-> tptp.refine432681134nres_b tptp.produc1587512412nres_b)|) (e tptp.produc1587512412nres_b) (i tptp.refine432681134nres_b)) (not (forall ((v |u_(-> tptp.refine432681134nres_b tptp.produc1587512412nres_b)|)) (not (forall ((ii tptp.refine432681134nres_b)) (= (ho_270 v ii) (ite (= i ii) e (ho_270 u ii)))))))))) (let ((_let_242 (forall ((x |u_(-> tptp.refine432681134nres_b tptp.produc1587512412nres_b)|) (y |u_(-> tptp.refine432681134nres_b tptp.produc1587512412nres_b)|)) (or (not (forall ((z tptp.refine432681134nres_b)) (= (ho_270 x z) (ho_270 y z)))) (= x y))))) (let ((_let_243 (forall ((u |u_(-> tptp.set_Product_unit tptp.refine787176636t_unit)|) (e tptp.refine787176636t_unit) (i tptp.set_Product_unit)) (not (forall ((v |u_(-> tptp.set_Product_unit tptp.refine787176636t_unit)|)) (not (forall ((ii tptp.set_Product_unit)) (= (ho_101 v ii) (ite (= i ii) e (ho_101 u ii)))))))))) (let ((_let_244 (forall ((x |u_(-> tptp.set_Product_unit tptp.refine787176636t_unit)|) (y |u_(-> tptp.set_Product_unit tptp.refine787176636t_unit)|)) (or (not (forall ((z tptp.set_Product_unit)) (= (ho_101 x z) (ho_101 y z)))) (= x y))))) (let ((_let_245 (forall ((u |u_(-> tptp.refine424419629nres_a tptp.produc1609974940nres_a)|) (e tptp.produc1609974940nres_a) (i tptp.refine424419629nres_a)) (not (forall ((v |u_(-> tptp.refine424419629nres_a tptp.produc1609974940nres_a)|)) (not (forall ((ii tptp.refine424419629nres_a)) (= (ho_267 v ii) (ite (= i ii) e (ho_267 u ii)))))))))) (let ((_let_246 (forall ((x |u_(-> tptp.refine424419629nres_a tptp.produc1609974940nres_a)|) (y |u_(-> tptp.refine424419629nres_a tptp.produc1609974940nres_a)|)) (or (not (forall ((z tptp.refine424419629nres_a)) (= (ho_267 x z) (ho_267 y z)))) (= x y))))) (let ((_let_247 (forall ((u |u_(-> tptp.set_b tptp.set_b Bool)|) (e |u_(-> tptp.set_b Bool)|) (i tptp.set_b)) (not (forall ((v |u_(-> tptp.set_b tptp.set_b Bool)|)) (not (forall ((ii tptp.set_b)) (= (ho_70 v ii) (ite (= i ii) e (ho_70 u ii)))))))))) (let ((_let_248 (forall ((x |u_(-> tptp.set_b tptp.set_b Bool)|) (y |u_(-> tptp.set_b tptp.set_b Bool)|)) (or (not (forall ((z tptp.set_b)) (= (ho_70 x z) (ho_70 y z)))) (= x y))))) (let ((_let_249 (forall ((u |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b tptp.refine432681134nres_b)|) (e |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b)|) (i tptp.refine432681134nres_b)) (not (forall ((v |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b tptp.refine432681134nres_b)|)) (not (forall ((ii tptp.refine432681134nres_b)) (= (ho_113 v ii) (ite (= i ii) e (ho_113 u ii)))))))))) (let ((_let_250 (forall ((x |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b tptp.refine432681134nres_b)|) (y |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b tptp.refine432681134nres_b)|)) (or (not (forall ((z tptp.refine432681134nres_b)) (= (ho_113 x z) (ho_113 y z)))) (= x y))))) (let ((_let_251 (forall ((u |u_(-> _u_(-> tptp.b tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|) (e tptp.refine432681134nres_b) (i |u_(-> tptp.b tptp.refine432681134nres_b)|)) (not (forall ((v |u_(-> _u_(-> tptp.b tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|)) (not (forall ((ii |u_(-> tptp.b tptp.refine432681134nres_b)|)) (= (ho_192 v ii) (ite (= i ii) e (ho_192 u ii)))))))))) (let ((_let_252 (forall ((x |u_(-> _u_(-> tptp.b tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|) (y |u_(-> _u_(-> tptp.b tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|)) (or (not (forall ((z |u_(-> tptp.b tptp.refine432681134nres_b)|)) (= (ho_192 x z) (ho_192 y z)))) (= x y))))) (let ((_let_253 (forall ((u |u_(-> tptp.refine787176636t_unit tptp.refine787176636t_unit tptp.refine787176636t_unit Bool)|) (e |u_(-> tptp.refine787176636t_unit tptp.refine787176636t_unit Bool)|) (i tptp.refine787176636t_unit)) (not (forall ((v |u_(-> tptp.refine787176636t_unit tptp.refine787176636t_unit tptp.refine787176636t_unit Bool)|)) (not (forall ((ii tptp.refine787176636t_unit)) (= (ho_319 v ii) (ite (= i ii) e (ho_319 u ii)))))))))) (let ((_let_254 (forall ((x |u_(-> tptp.refine787176636t_unit tptp.refine787176636t_unit tptp.refine787176636t_unit Bool)|) (y |u_(-> tptp.refine787176636t_unit tptp.refine787176636t_unit tptp.refine787176636t_unit Bool)|)) (or (not (forall ((z tptp.refine787176636t_unit)) (= (ho_319 x z) (ho_319 y z)))) (= x y))))) (let ((_let_255 (forall ((u |u_(-> tptp.a tptp.refine432681134nres_b)|) (e tptp.refine432681134nres_b) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.refine432681134nres_b)|)) (not (forall ((ii tptp.a)) (= (ho_99 v ii) (ite (= i ii) e (ho_99 u ii)))))))))) (let ((_let_256 (forall ((x |u_(-> tptp.a tptp.refine432681134nres_b)|) (y |u_(-> tptp.a tptp.refine432681134nres_b)|)) (or (not (forall ((z tptp.a)) (= (ho_99 x z) (ho_99 y z)))) (= x y))))) (let ((_let_257 (forall ((u |u_(-> tptp.refine671810262od_a_a tptp.product_prod_a_a Bool)|) (e |u_(-> tptp.product_prod_a_a Bool)|) (i tptp.refine671810262od_a_a)) (not (forall ((v |u_(-> tptp.refine671810262od_a_a tptp.product_prod_a_a Bool)|)) (not (forall ((ii tptp.refine671810262od_a_a)) (= (ho_228 v ii) (ite (= i ii) e (ho_228 u ii)))))))))) (let ((_let_258 (forall ((x |u_(-> tptp.refine671810262od_a_a tptp.product_prod_a_a Bool)|) (y |u_(-> tptp.refine671810262od_a_a tptp.product_prod_a_a Bool)|)) (or (not (forall ((z tptp.refine671810262od_a_a)) (= (ho_228 x z) (ho_228 y z)))) (= x y))))) (let ((_let_259 (forall ((u |u_(-> tptp.refine2031285398od_b_b Bool)|) (e Bool) (i tptp.refine2031285398od_b_b)) (not (forall ((v |u_(-> tptp.refine2031285398od_b_b Bool)|)) (not (forall ((ii tptp.refine2031285398od_b_b)) (= (ho_148 v ii) (ite (= i ii) e (ho_148 u ii)))))))))) (let ((_let_260 (forall ((x |u_(-> tptp.refine2031285398od_b_b Bool)|) (y |u_(-> tptp.refine2031285398od_b_b Bool)|)) (or (not (forall ((z tptp.refine2031285398od_b_b)) (= (ho_148 x z) (ho_148 y z)))) (= x y))))) (let ((_let_261 (forall ((u |u_(-> _u_(-> tptp.product_unit tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|) (e tptp.refine432681134nres_b) (i |u_(-> tptp.product_unit tptp.refine432681134nres_b)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_unit tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|)) (not (forall ((ii |u_(-> tptp.product_unit tptp.refine432681134nres_b)|)) (= (ho_208 v ii) (ite (= i ii) e (ho_208 u ii)))))))))) (let ((_let_262 (forall ((x |u_(-> _u_(-> tptp.product_unit tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|) (y |u_(-> _u_(-> tptp.product_unit tptp.refine432681134nres_b)_ tptp.refine432681134nres_b)|)) (or (not (forall ((z |u_(-> tptp.product_unit tptp.refine432681134nres_b)|)) (= (ho_208 x z) (ho_208 y z)))) (= x y))))) (let ((_let_263 (forall ((u |u_(-> Bool tptp.refine432681134nres_b tptp.refine432681134nres_b tptp.refine432681134nres_b)|) (e |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b tptp.refine432681134nres_b)|) (i Bool)) (not (forall ((v |u_(-> Bool tptp.refine432681134nres_b tptp.refine432681134nres_b tptp.refine432681134nres_b)|)) (not (forall ((ii Bool)) (= (ho_112 v ii) (ite (= i ii) e (ho_112 u ii)))))))))) (let ((_let_264 (forall ((x |u_(-> Bool tptp.refine432681134nres_b tptp.refine432681134nres_b tptp.refine432681134nres_b)|) (y |u_(-> Bool tptp.refine432681134nres_b tptp.refine432681134nres_b tptp.refine432681134nres_b)|)) (or (not (forall ((z Bool)) (= (ho_112 x z) (ho_112 y z)))) (= x y))))) (let ((_let_265 (forall ((u |u_(-> tptp.a tptp.set_a Bool)|) (e |u_(-> tptp.set_a Bool)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.set_a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_45 v ii) (ite (= i ii) e (ho_45 u ii)))))))))) (let ((_let_266 (forall ((x |u_(-> tptp.a tptp.set_a Bool)|) (y |u_(-> tptp.a tptp.set_a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_45 x z) (ho_45 y z)))) (= x y))))) (let ((_let_267 (forall ((u |u_(-> tptp.refine424419629nres_a Bool)|) (e Bool) (i tptp.refine424419629nres_a)) (not (forall ((v |u_(-> tptp.refine424419629nres_a Bool)|)) (not (forall ((ii tptp.refine424419629nres_a)) (= (ho_81 v ii) (ite (= i ii) e (ho_81 u ii)))))))))) (let ((_let_268 (forall ((x |u_(-> tptp.refine424419629nres_a Bool)|) (y |u_(-> tptp.refine424419629nres_a Bool)|)) (or (not (forall ((z tptp.refine424419629nres_a)) (= (ho_81 x z) (ho_81 y z)))) (= x y))))) (let ((_let_269 (forall ((u |u_(-> tptp.set_a tptp.refine424419629nres_a)|) (e tptp.refine424419629nres_a) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.refine424419629nres_a)|)) (not (forall ((ii tptp.set_a)) (= (ho_54 v ii) (ite (= i ii) e (ho_54 u ii)))))))))) (let ((_let_270 (forall ((x |u_(-> tptp.set_a tptp.refine424419629nres_a)|) (y |u_(-> tptp.set_a tptp.refine424419629nres_a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_54 x z) (ho_54 y z)))) (= x y))))) (let ((_let_271 (forall ((u |u_(-> tptp.set_b Bool)|) (e Bool) (i tptp.set_b)) (not (forall ((v |u_(-> tptp.set_b Bool)|)) (not (forall ((ii tptp.set_b)) (= (ho_38 v ii) (ite (= i ii) e (ho_38 u ii)))))))))) (let ((_let_272 (forall ((x |u_(-> tptp.set_b Bool)|) (y |u_(-> tptp.set_b Bool)|)) (or (not (forall ((z tptp.set_b)) (= (ho_38 x z) (ho_38 y z)))) (= x y))))) (let ((_let_273 (forall ((u |u_(-> tptp.refine432681134nres_b tptp.set_b)|) (e tptp.set_b) (i tptp.refine432681134nres_b)) (not (forall ((v |u_(-> tptp.refine432681134nres_b tptp.set_b)|)) (not (forall ((ii tptp.refine432681134nres_b)) (= (ho_226 v ii) (ite (= i ii) e (ho_226 u ii)))))))))) (let ((_let_274 (forall ((x |u_(-> tptp.refine432681134nres_b tptp.set_b)|) (y |u_(-> tptp.refine432681134nres_b tptp.set_b)|)) (or (not (forall ((z tptp.refine432681134nres_b)) (= (ho_226 x z) (ho_226 y z)))) (= x y))))) (let ((_let_275 (forall ((u |u_(-> _u_(-> tptp.product_unit tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|) (e tptp.refine787176636t_unit) (i |u_(-> tptp.product_unit tptp.refine787176636t_unit)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_unit tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|)) (not (forall ((ii |u_(-> tptp.product_unit tptp.refine787176636t_unit)|)) (= (ho_216 v ii) (ite (= i ii) e (ho_216 u ii)))))))))) (let ((_let_276 (forall ((x |u_(-> _u_(-> tptp.product_unit tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|) (y |u_(-> _u_(-> tptp.product_unit tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|)) (or (not (forall ((z |u_(-> tptp.product_unit tptp.refine787176636t_unit)|)) (= (ho_216 x z) (ho_216 y z)))) (= x y))))) (let ((_let_277 (forall ((u |u_(-> tptp.set_Product_prod_b_b tptp.refine2031285398od_b_b)|) (e tptp.refine2031285398od_b_b) (i tptp.set_Product_prod_b_b)) (not (forall ((v |u_(-> tptp.set_Product_prod_b_b tptp.refine2031285398od_b_b)|)) (not (forall ((ii tptp.set_Product_prod_b_b)) (= (ho_145 v ii) (ite (= i ii) e (ho_145 u ii)))))))))) (let ((_let_278 (forall ((x |u_(-> tptp.set_Product_prod_b_b tptp.refine2031285398od_b_b)|) (y |u_(-> tptp.set_Product_prod_b_b tptp.refine2031285398od_b_b)|)) (or (not (forall ((z tptp.set_Product_prod_b_b)) (= (ho_145 x z) (ho_145 y z)))) (= x y))))) (let ((_let_279 (forall ((u |u_(-> tptp.b Bool)|) (e Bool) (i tptp.b)) (not (forall ((v |u_(-> tptp.b Bool)|)) (not (forall ((ii tptp.b)) (= (ho_32 v ii) (ite (= i ii) e (ho_32 u ii)))))))))) (let ((_let_280 (forall ((x |u_(-> tptp.b Bool)|) (y |u_(-> tptp.b Bool)|)) (or (not (forall ((z tptp.b)) (= (ho_32 x z) (ho_32 y z)))) (= x y))))) (let ((_let_281 (forall ((u |u_(-> tptp.a tptp.product_prod_b_a)|) (e tptp.product_prod_b_a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.product_prod_b_a)|)) (not (forall ((ii tptp.a)) (= (ho_255 v ii) (ite (= i ii) e (ho_255 u ii)))))))))) (let ((_let_282 (forall ((x |u_(-> tptp.a tptp.product_prod_b_a)|) (y |u_(-> tptp.a tptp.product_prod_b_a)|)) (or (not (forall ((z tptp.a)) (= (ho_255 x z) (ho_255 y z)))) (= x y))))) (let ((_let_283 (forall ((u |u_(-> Bool tptp.refine787176636t_unit tptp.refine787176636t_unit tptp.refine787176636t_unit)|) (e |u_(-> tptp.refine787176636t_unit tptp.refine787176636t_unit tptp.refine787176636t_unit)|) (i Bool)) (not (forall ((v |u_(-> Bool tptp.refine787176636t_unit tptp.refine787176636t_unit tptp.refine787176636t_unit)|)) (not (forall ((ii Bool)) (= (ho_105 v ii) (ite (= i ii) e (ho_105 u ii)))))))))) (let ((_let_284 (forall ((x |u_(-> Bool tptp.refine787176636t_unit tptp.refine787176636t_unit tptp.refine787176636t_unit)|) (y |u_(-> Bool tptp.refine787176636t_unit tptp.refine787176636t_unit tptp.refine787176636t_unit)|)) (or (not (forall ((z Bool)) (= (ho_105 x z) (ho_105 y z)))) (= x y))))) (let ((_let_285 (forall ((u |u_(-> tptp.product_unit tptp.refine424419629nres_a)|) (e tptp.refine424419629nres_a) (i tptp.product_unit)) (not (forall ((v |u_(-> tptp.product_unit tptp.refine424419629nres_a)|)) (not (forall ((ii tptp.product_unit)) (= (ho_209 v ii) (ite (= i ii) e (ho_209 u ii)))))))))) (let ((_let_286 (forall ((x |u_(-> tptp.product_unit tptp.refine424419629nres_a)|) (y |u_(-> tptp.product_unit tptp.refine424419629nres_a)|)) (or (not (forall ((z tptp.product_unit)) (= (ho_209 x z) (ho_209 y z)))) (= x y))))) (let ((_let_287 (forall ((u |u_(-> tptp.set_Product_prod_a_a Bool)|) (e Bool) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a Bool)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_129 v ii) (ite (= i ii) e (ho_129 u ii)))))))))) (let ((_let_288 (forall ((x |u_(-> tptp.set_Product_prod_a_a Bool)|) (y |u_(-> tptp.set_Product_prod_a_a Bool)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_129 x z) (ho_129 y z)))) (= x y))))) (let ((_let_289 (forall ((u |u_(-> tptp.refine787176636t_unit tptp.refine787176636t_unit)|) (e tptp.refine787176636t_unit) (i tptp.refine787176636t_unit)) (not (forall ((v |u_(-> tptp.refine787176636t_unit tptp.refine787176636t_unit)|)) (not (forall ((ii tptp.refine787176636t_unit)) (= (ho_107 v ii) (ite (= i ii) e (ho_107 u ii)))))))))) (let ((_let_290 (forall ((x |u_(-> tptp.refine787176636t_unit tptp.refine787176636t_unit)|) (y |u_(-> tptp.refine787176636t_unit tptp.refine787176636t_unit)|)) (or (not (forall ((z tptp.refine787176636t_unit)) (= (ho_107 x z) (ho_107 y z)))) (= x y))))) (let ((_let_291 (forall ((u |u_(-> tptp.refine1811374551od_a_b Bool)|) (e Bool) (i tptp.refine1811374551od_a_b)) (not (forall ((v |u_(-> tptp.refine1811374551od_a_b Bool)|)) (not (forall ((ii tptp.refine1811374551od_a_b)) (= (ho_159 v ii) (ite (= i ii) e (ho_159 u ii)))))))))) (let ((_let_292 (forall ((x |u_(-> tptp.refine1811374551od_a_b Bool)|) (y |u_(-> tptp.refine1811374551od_a_b Bool)|)) (or (not (forall ((z tptp.refine1811374551od_a_b)) (= (ho_159 x z) (ho_159 y z)))) (= x y))))) (let ((_let_293 (forall ((u |u_(-> tptp.refine787176636t_unit tptp.refine787176636t_unit tptp.refine787176636t_unit)|) (e |u_(-> tptp.refine787176636t_unit tptp.refine787176636t_unit)|) (i tptp.refine787176636t_unit)) (not (forall ((v |u_(-> tptp.refine787176636t_unit tptp.refine787176636t_unit tptp.refine787176636t_unit)|)) (not (forall ((ii tptp.refine787176636t_unit)) (= (ho_106 v ii) (ite (= i ii) e (ho_106 u ii)))))))))) (let ((_let_294 (forall ((x |u_(-> tptp.refine787176636t_unit tptp.refine787176636t_unit tptp.refine787176636t_unit)|) (y |u_(-> tptp.refine787176636t_unit tptp.refine787176636t_unit tptp.refine787176636t_unit)|)) (or (not (forall ((z tptp.refine787176636t_unit)) (= (ho_106 x z) (ho_106 y z)))) (= x y))))) (let ((_let_295 (forall ((u |u_(-> _u_(-> tptp.product_prod_b_b Bool)_ tptp.set_Product_prod_b_b)|) (e tptp.set_Product_prod_b_b) (i |u_(-> tptp.product_prod_b_b Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_b_b Bool)_ tptp.set_Product_prod_b_b)|)) (not (forall ((ii |u_(-> tptp.product_prod_b_b Bool)|)) (= (ho_143 v ii) (ite (= i ii) e (ho_143 u ii)))))))))) (let ((_let_296 (forall ((x |u_(-> _u_(-> tptp.product_prod_b_b Bool)_ tptp.set_Product_prod_b_b)|) (y |u_(-> _u_(-> tptp.product_prod_b_b Bool)_ tptp.set_Product_prod_b_b)|)) (or (not (forall ((z |u_(-> tptp.product_prod_b_b Bool)|)) (= (ho_143 x z) (ho_143 y z)))) (= x y))))) (let ((_let_297 (forall ((u |u_(-> tptp.set_a tptp.set_b)|) (e tptp.set_b) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.set_b)|)) (not (forall ((ii tptp.set_a)) (= (ho_295 v ii) (ite (= i ii) e (ho_295 u ii)))))))))) (let ((_let_298 (forall ((x |u_(-> tptp.set_a tptp.set_b)|) (y |u_(-> tptp.set_a tptp.set_b)|)) (or (not (forall ((z tptp.set_a)) (= (ho_295 x z) (ho_295 y z)))) (= x y))))) (let ((_let_299 (forall ((u |u_(-> _u_(-> tptp.b Bool)_ tptp.set_b)|) (e tptp.set_b) (i |u_(-> tptp.b Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.b Bool)_ tptp.set_b)|)) (not (forall ((ii |u_(-> tptp.b Bool)|)) (= (ho_35 v ii) (ite (= i ii) e (ho_35 u ii)))))))))) (let ((_let_300 (forall ((x |u_(-> _u_(-> tptp.b Bool)_ tptp.set_b)|) (y |u_(-> _u_(-> tptp.b Bool)_ tptp.set_b)|)) (or (not (forall ((z |u_(-> tptp.b Bool)|)) (= (ho_35 x z) (ho_35 y z)))) (= x y))))) (let ((_let_301 (forall ((u |u_(-> tptp.b tptp.product_prod_a_b)|) (e tptp.product_prod_a_b) (i tptp.b)) (not (forall ((v |u_(-> tptp.b tptp.product_prod_a_b)|)) (not (forall ((ii tptp.b)) (= (ho_261 v ii) (ite (= i ii) e (ho_261 u ii)))))))))) (let ((_let_302 (forall ((x |u_(-> tptp.b tptp.product_prod_a_b)|) (y |u_(-> tptp.b tptp.product_prod_a_b)|)) (or (not (forall ((z tptp.b)) (= (ho_261 x z) (ho_261 y z)))) (= x y))))) (let ((_let_303 (forall ((u |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a)|) (e tptp.refine424419629nres_a) (i tptp.refine424419629nres_a)) (not (forall ((v |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a)|)) (not (forall ((ii tptp.refine424419629nres_a)) (= (ho_118 v ii) (ite (= i ii) e (ho_118 u ii)))))))))) (let ((_let_304 (forall ((x |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a)|) (y |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a)|)) (or (not (forall ((z tptp.refine424419629nres_a)) (= (ho_118 x z) (ho_118 y z)))) (= x y))))) (let ((_let_305 (forall ((u |u_(-> tptp.set_Pr451126599t_unit tptp.refine787176636t_unit tptp.refine787176636t_unit)|) (e |u_(-> tptp.refine787176636t_unit tptp.refine787176636t_unit)|) (i tptp.set_Pr451126599t_unit)) (not (forall ((v |u_(-> tptp.set_Pr451126599t_unit tptp.refine787176636t_unit tptp.refine787176636t_unit)|)) (not (forall ((ii tptp.set_Pr451126599t_unit)) (= (ho_308 v ii) (ite (= i ii) e (ho_308 u ii)))))))))) (let ((_let_306 (forall ((x |u_(-> tptp.set_Pr451126599t_unit tptp.refine787176636t_unit tptp.refine787176636t_unit)|) (y |u_(-> tptp.set_Pr451126599t_unit tptp.refine787176636t_unit tptp.refine787176636t_unit)|)) (or (not (forall ((z tptp.set_Pr451126599t_unit)) (= (ho_308 x z) (ho_308 y z)))) (= x y))))) (let ((_let_307 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.refine424419629nres_a tptp.refine424419629nres_a)|) (e |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.refine424419629nres_a tptp.refine424419629nres_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_252 v ii) (ite (= i ii) e (ho_252 u ii)))))))))) (let ((_let_308 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.refine424419629nres_a tptp.refine424419629nres_a)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.refine424419629nres_a tptp.refine424419629nres_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_252 x z) (ho_252 y z)))) (= x y))))) (let ((_let_309 (forall ((u |u_(-> _u_(-> tptp.b tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|) (e tptp.refine424419629nres_a) (i |u_(-> tptp.b tptp.refine424419629nres_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.b tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|)) (not (forall ((ii |u_(-> tptp.b tptp.refine424419629nres_a)|)) (= (ho_196 v ii) (ite (= i ii) e (ho_196 u ii)))))))))) (let ((_let_310 (forall ((x |u_(-> _u_(-> tptp.b tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|) (y |u_(-> _u_(-> tptp.b tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|)) (or (not (forall ((z |u_(-> tptp.b tptp.refine424419629nres_a)|)) (= (ho_196 x z) (ho_196 y z)))) (= x y))))) (let ((_let_311 (forall ((u |u_(-> Bool tptp.refine787176636t_unit)|) (e tptp.refine787176636t_unit) (i Bool)) (not (forall ((v |u_(-> Bool tptp.refine787176636t_unit)|)) (not (forall ((ii Bool)) (= (ho_280 v ii) (ite (= i ii) e (ho_280 u ii)))))))))) (let ((_let_312 (forall ((x |u_(-> Bool tptp.refine787176636t_unit)|) (y |u_(-> Bool tptp.refine787176636t_unit)|)) (or (not (forall ((z Bool)) (= (ho_280 x z) (ho_280 y z)))) (= x y))))) (let ((_let_313 (forall ((u |u_(-> _u_(-> tptp.a Bool)_ tptp.set_a)|) (e tptp.set_a) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ tptp.set_a)|)) (not (forall ((ii |u_(-> tptp.a Bool)|)) (= (ho_43 v ii) (ite (= i ii) e (ho_43 u ii)))))))))) (let ((_let_314 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ tptp.set_a)|) (y |u_(-> _u_(-> tptp.a Bool)_ tptp.set_a)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_43 x z) (ho_43 y z)))) (= x y))))) (let ((_let_315 (forall ((u |u_(-> tptp.set_a Bool)|) (e Bool) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_46 v ii) (ite (= i ii) e (ho_46 u ii)))))))))) (let ((_let_316 (forall ((x |u_(-> tptp.set_a Bool)|) (y |u_(-> tptp.set_a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_46 x z) (ho_46 y z)))) (= x y))))) (let ((_let_317 (forall ((u |u_(-> tptp.product_prod_b_b Bool)|) (e Bool) (i tptp.product_prod_b_b)) (not (forall ((v |u_(-> tptp.product_prod_b_b Bool)|)) (not (forall ((ii tptp.product_prod_b_b)) (= (ho_141 v ii) (ite (= i ii) e (ho_141 u ii)))))))))) (let ((_let_318 (forall ((x |u_(-> tptp.product_prod_b_b Bool)|) (y |u_(-> tptp.product_prod_b_b Bool)|)) (or (not (forall ((z tptp.product_prod_b_b)) (= (ho_141 x z) (ho_141 y z)))) (= x y))))) (let ((_let_319 (forall ((u |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a tptp.refine424419629nres_a)|) (e |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a)|) (i tptp.refine424419629nres_a)) (not (forall ((v |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a tptp.refine424419629nres_a)|)) (not (forall ((ii tptp.refine424419629nres_a)) (= (ho_117 v ii) (ite (= i ii) e (ho_117 u ii)))))))))) (let ((_let_320 (forall ((x |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a tptp.refine424419629nres_a)|) (y |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a tptp.refine424419629nres_a)|)) (or (not (forall ((z tptp.refine424419629nres_a)) (= (ho_117 x z) (ho_117 y z)))) (= x y))))) (let ((_let_321 (forall ((u |u_(-> tptp.b tptp.refine432681134nres_b)|) (e tptp.refine432681134nres_b) (i tptp.b)) (not (forall ((v |u_(-> tptp.b tptp.refine432681134nres_b)|)) (not (forall ((ii tptp.b)) (= (ho_59 v ii) (ite (= i ii) e (ho_59 u ii)))))))))) (let ((_let_322 (forall ((x |u_(-> tptp.b tptp.refine432681134nres_b)|) (y |u_(-> tptp.b tptp.refine432681134nres_b)|)) (or (not (forall ((z tptp.b)) (= (ho_59 x z) (ho_59 y z)))) (= x y))))) (let ((_let_323 (forall ((u |u_(-> Bool tptp.refine424419629nres_a tptp.refine424419629nres_a tptp.refine424419629nres_a)|) (e |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a tptp.refine424419629nres_a)|) (i Bool)) (not (forall ((v |u_(-> Bool tptp.refine424419629nres_a tptp.refine424419629nres_a tptp.refine424419629nres_a)|)) (not (forall ((ii Bool)) (= (ho_116 v ii) (ite (= i ii) e (ho_116 u ii)))))))))) (let ((_let_324 (forall ((x |u_(-> Bool tptp.refine424419629nres_a tptp.refine424419629nres_a tptp.refine424419629nres_a)|) (y |u_(-> Bool tptp.refine424419629nres_a tptp.refine424419629nres_a tptp.refine424419629nres_a)|)) (or (not (forall ((z Bool)) (= (ho_116 x z) (ho_116 y z)))) (= x y))))) (let ((_let_325 (forall ((u |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.set_Product_prod_a_a)|) (e tptp.set_Product_prod_a_a) (i |u_(-> tptp.product_prod_a_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.set_Product_prod_a_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_121 v ii) (ite (= i ii) e (ho_121 u ii)))))))))) (let ((_let_326 (forall ((x |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.set_Product_prod_a_a)|) (y |u_(-> _u_(-> tptp.product_prod_a_a Bool)_ tptp.set_Product_prod_a_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_a_a Bool)|)) (= (ho_121 x z) (ho_121 y z)))) (= x y))))) (let ((_let_327 (forall ((u |u_(-> _u_(-> tptp.product_unit tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|) (e tptp.refine424419629nres_a) (i |u_(-> tptp.product_unit tptp.refine424419629nres_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_unit tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|)) (not (forall ((ii |u_(-> tptp.product_unit tptp.refine424419629nres_a)|)) (= (ho_212 v ii) (ite (= i ii) e (ho_212 u ii)))))))))) (let ((_let_328 (forall ((x |u_(-> _u_(-> tptp.product_unit tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|) (y |u_(-> _u_(-> tptp.product_unit tptp.refine424419629nres_a)_ tptp.refine424419629nres_a)|)) (or (not (forall ((z |u_(-> tptp.product_unit tptp.refine424419629nres_a)|)) (= (ho_212 x z) (ho_212 y z)))) (= x y))))) (let ((_let_329 (forall ((u |u_(-> tptp.refine2031285398od_b_b tptp.product_prod_b_b Bool)|) (e |u_(-> tptp.product_prod_b_b Bool)|) (i tptp.refine2031285398od_b_b)) (not (forall ((v |u_(-> tptp.refine2031285398od_b_b tptp.product_prod_b_b Bool)|)) (not (forall ((ii tptp.refine2031285398od_b_b)) (= (ho_232 v ii) (ite (= i ii) e (ho_232 u ii)))))))))) (let ((_let_330 (forall ((x |u_(-> tptp.refine2031285398od_b_b tptp.product_prod_b_b Bool)|) (y |u_(-> tptp.refine2031285398od_b_b tptp.product_prod_b_b Bool)|)) (or (not (forall ((z tptp.refine2031285398od_b_b)) (= (ho_232 x z) (ho_232 y z)))) (= x y))))) (let ((_let_331 (forall ((u |u_(-> tptp.set_Product_prod_a_b Bool)|) (e Bool) (i tptp.set_Product_prod_a_b)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_b Bool)|)) (not (forall ((ii tptp.set_Product_prod_a_b)) (= (ho_162 v ii) (ite (= i ii) e (ho_162 u ii)))))))))) (let ((_let_332 (forall ((x |u_(-> tptp.set_Product_prod_a_b Bool)|) (y |u_(-> tptp.set_Product_prod_a_b Bool)|)) (or (not (forall ((z tptp.set_Product_prod_a_b)) (= (ho_162 x z) (ho_162 y z)))) (= x y))))) (let ((_let_333 (forall ((u |u_(-> tptp.refine787176636t_unit tptp.refine787176636t_unit Bool)|) (e |u_(-> tptp.refine787176636t_unit Bool)|) (i tptp.refine787176636t_unit)) (not (forall ((v |u_(-> tptp.refine787176636t_unit tptp.refine787176636t_unit Bool)|)) (not (forall ((ii tptp.refine787176636t_unit)) (= (ho_109 v ii) (ite (= i ii) e (ho_109 u ii)))))))))) (let ((_let_334 (forall ((x |u_(-> tptp.refine787176636t_unit tptp.refine787176636t_unit Bool)|) (y |u_(-> tptp.refine787176636t_unit tptp.refine787176636t_unit Bool)|)) (or (not (forall ((z tptp.refine787176636t_unit)) (= (ho_109 x z) (ho_109 y z)))) (= x y))))) (let ((_let_335 (forall ((u |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a Bool)|) (e |u_(-> tptp.set_Product_prod_a_a Bool)|) (i tptp.product_prod_a_a)) (not (forall ((v |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a Bool)|)) (not (forall ((ii tptp.product_prod_a_a)) (= (ho_128 v ii) (ite (= i ii) e (ho_128 u ii)))))))))) (let ((_let_336 (forall ((x |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a Bool)|) (y |u_(-> tptp.product_prod_a_a tptp.set_Product_prod_a_a Bool)|)) (or (not (forall ((z tptp.product_prod_a_a)) (= (ho_128 x z) (ho_128 y z)))) (= x y))))) (let ((_let_337 (forall ((u |u_(-> tptp.refine424419629nres_a _u_(-> tptp.a tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|) (e |u_(-> _u_(-> tptp.a tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|) (i tptp.refine424419629nres_a)) (not (forall ((v |u_(-> tptp.refine424419629nres_a _u_(-> tptp.a tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|)) (not (forall ((ii tptp.refine424419629nres_a)) (= (ho_199 v ii) (ite (= i ii) e (ho_199 u ii)))))))))) (let ((_let_338 (forall ((x |u_(-> tptp.refine424419629nres_a _u_(-> tptp.a tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|) (y |u_(-> tptp.refine424419629nres_a _u_(-> tptp.a tptp.refine787176636t_unit)_ tptp.refine787176636t_unit)|)) (or (not (forall ((z tptp.refine424419629nres_a)) (= (ho_199 x z) (ho_199 y z)))) (= x y))))) (let ((_let_339 (forall ((u |u_(-> tptp.refine671810262od_a_a tptp.refine671810262od_a_a Bool)|) (e |u_(-> tptp.refine671810262od_a_a Bool)|) (i tptp.refine671810262od_a_a)) (not (forall ((v |u_(-> tptp.refine671810262od_a_a tptp.refine671810262od_a_a Bool)|)) (not (forall ((ii tptp.refine671810262od_a_a)) (= (ho_125 v ii) (ite (= i ii) e (ho_125 u ii)))))))))) (let ((_let_340 (forall ((x |u_(-> tptp.refine671810262od_a_a tptp.refine671810262od_a_a Bool)|) (y |u_(-> tptp.refine671810262od_a_a tptp.refine671810262od_a_a Bool)|)) (or (not (forall ((z tptp.refine671810262od_a_a)) (= (ho_125 x z) (ho_125 y z)))) (= x y))))) (let ((_let_341 (forall ((u |u_(-> tptp.set_b tptp.set_b tptp.set_b)|) (e |u_(-> tptp.set_b tptp.set_b)|) (i tptp.set_b)) (not (forall ((v |u_(-> tptp.set_b tptp.set_b tptp.set_b)|)) (not (forall ((ii tptp.set_b)) (= (ho_168 v ii) (ite (= i ii) e (ho_168 u ii)))))))))) (let ((_let_342 (forall ((x |u_(-> tptp.set_b tptp.set_b tptp.set_b)|) (y |u_(-> tptp.set_b tptp.set_b tptp.set_b)|)) (or (not (forall ((z tptp.set_b)) (= (ho_168 x z) (ho_168 y z)))) (= x y))))) (let ((_let_343 (forall ((u |u_(-> tptp.a tptp.b tptp.product_prod_a_b)|) (e |u_(-> tptp.b tptp.product_prod_a_b)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.b tptp.product_prod_a_b)|)) (not (forall ((ii tptp.a)) (= (ho_260 v ii) (ite (= i ii) e (ho_260 u ii)))))))))) (let ((_let_344 (forall ((x |u_(-> tptp.a tptp.b tptp.product_prod_a_b)|) (y |u_(-> tptp.a tptp.b tptp.product_prod_a_b)|)) (or (not (forall ((z tptp.a)) (= (ho_260 x z) (ho_260 y z)))) (= x y))))) (let ((_let_345 (forall ((u |u_(-> tptp.product_prod_b_a Bool)|) (e Bool) (i tptp.product_prod_b_a)) (not (forall ((v |u_(-> tptp.product_prod_b_a Bool)|)) (not (forall ((ii tptp.product_prod_b_a)) (= (ho_130 v ii) (ite (= i ii) e (ho_130 u ii)))))))))) (let ((_let_346 (forall ((x |u_(-> tptp.product_prod_b_a Bool)|) (y |u_(-> tptp.product_prod_b_a Bool)|)) (or (not (forall ((z tptp.product_prod_b_a)) (= (ho_130 x z) (ho_130 y z)))) (= x y))))) (let ((_let_347 (forall ((u |u_(-> tptp.refine891721109od_b_a tptp.refine891721109od_b_a Bool)|) (e |u_(-> tptp.refine891721109od_b_a Bool)|) (i tptp.refine891721109od_b_a)) (not (forall ((v |u_(-> tptp.refine891721109od_b_a tptp.refine891721109od_b_a Bool)|)) (not (forall ((ii tptp.refine891721109od_b_a)) (= (ho_136 v ii) (ite (= i ii) e (ho_136 u ii)))))))))) (let ((_let_348 (forall ((x |u_(-> tptp.refine891721109od_b_a tptp.refine891721109od_b_a Bool)|) (y |u_(-> tptp.refine891721109od_b_a tptp.refine891721109od_b_a Bool)|)) (or (not (forall ((z tptp.refine891721109od_b_a)) (= (ho_136 x z) (ho_136 y z)))) (= x y))))) (let ((_let_349 (forall ((u |u_(-> tptp.a tptp.refine424419629nres_a)|) (e tptp.refine424419629nres_a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.refine424419629nres_a)|)) (not (forall ((ii tptp.a)) (= (ho_52 v ii) (ite (= i ii) e (ho_52 u ii)))))))))) (let ((_let_350 (forall ((x |u_(-> tptp.a tptp.refine424419629nres_a)|) (y |u_(-> tptp.a tptp.refine424419629nres_a)|)) (or (not (forall ((z tptp.a)) (= (ho_52 x z) (ho_52 y z)))) (= x y))))) (let ((_let_351 (forall ((u |u_(-> _u_(-> tptp.product_prod_b_a Bool)_ tptp.set_Product_prod_b_a)|) (e tptp.set_Product_prod_b_a) (i |u_(-> tptp.product_prod_b_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.product_prod_b_a Bool)_ tptp.set_Product_prod_b_a)|)) (not (forall ((ii |u_(-> tptp.product_prod_b_a Bool)|)) (= (ho_132 v ii) (ite (= i ii) e (ho_132 u ii)))))))))) (let ((_let_352 (forall ((x |u_(-> _u_(-> tptp.product_prod_b_a Bool)_ tptp.set_Product_prod_b_a)|) (y |u_(-> _u_(-> tptp.product_prod_b_a Bool)_ tptp.set_Product_prod_b_a)|)) (or (not (forall ((z |u_(-> tptp.product_prod_b_a Bool)|)) (= (ho_132 x z) (ho_132 y z)))) (= x y))))) (let ((_let_353 (forall ((u |u_(-> tptp.set_Product_prod_a_b tptp.refine432681134nres_b tptp.refine424419629nres_a)|) (e |u_(-> tptp.refine432681134nres_b tptp.refine424419629nres_a)|) (i tptp.set_Product_prod_a_b)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_b tptp.refine432681134nres_b tptp.refine424419629nres_a)|)) (not (forall ((ii tptp.set_Product_prod_a_b)) (= (ho_250 v ii) (ite (= i ii) e (ho_250 u ii)))))))))) (let ((_let_354 (forall ((x |u_(-> tptp.set_Product_prod_a_b tptp.refine432681134nres_b tptp.refine424419629nres_a)|) (y |u_(-> tptp.set_Product_prod_a_b tptp.refine432681134nres_b tptp.refine424419629nres_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_b)) (= (ho_250 x z) (ho_250 y z)))) (= x y))))) (let ((_let_355 (forall ((u |u_(-> tptp.set_a tptp.set_a Bool)|) (e |u_(-> tptp.set_a Bool)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.set_a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_73 v ii) (ite (= i ii) e (ho_73 u ii)))))))))) (let ((_let_356 (forall ((x |u_(-> tptp.set_a tptp.set_a Bool)|) (y |u_(-> tptp.set_a tptp.set_a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_73 x z) (ho_73 y z)))) (= x y))))) (let ((_let_357 (forall ((u |u_(-> tptp.refine2031285398od_b_b tptp.refine2031285398od_b_b Bool)|) (e |u_(-> tptp.refine2031285398od_b_b Bool)|) (i tptp.refine2031285398od_b_b)) (not (forall ((v |u_(-> tptp.refine2031285398od_b_b tptp.refine2031285398od_b_b Bool)|)) (not (forall ((ii tptp.refine2031285398od_b_b)) (= (ho_147 v ii) (ite (= i ii) e (ho_147 u ii)))))))))) (let ((_let_358 (forall ((x |u_(-> tptp.refine2031285398od_b_b tptp.refine2031285398od_b_b Bool)|) (y |u_(-> tptp.refine2031285398od_b_b tptp.refine2031285398od_b_b Bool)|)) (or (not (forall ((z tptp.refine2031285398od_b_b)) (= (ho_147 x z) (ho_147 y z)))) (= x y))))) (let ((_let_359 (forall ((u |u_(-> tptp.a tptp.product_prod_a_a)|) (e tptp.product_prod_a_a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.product_prod_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_258 v ii) (ite (= i ii) e (ho_258 u ii)))))))))) (let ((_let_360 (forall ((x |u_(-> tptp.a tptp.product_prod_a_a)|) (y |u_(-> tptp.a tptp.product_prod_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_258 x z) (ho_258 y z)))) (= x y))))) (let ((_let_361 (forall ((u |u_(-> tptp.a tptp.a tptp.product_prod_a_a)|) (e |u_(-> tptp.a tptp.product_prod_a_a)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a tptp.product_prod_a_a)|)) (not (forall ((ii tptp.a)) (= (ho_257 v ii) (ite (= i ii) e (ho_257 u ii)))))))))) (let ((_let_362 (forall ((x |u_(-> tptp.a tptp.a tptp.product_prod_a_a)|) (y |u_(-> tptp.a tptp.a tptp.product_prod_a_a)|)) (or (not (forall ((z tptp.a)) (= (ho_257 x z) (ho_257 y z)))) (= x y))))) (let ((_let_363 (forall ((u |u_(-> tptp.b tptp.b tptp.product_prod_b_b)|) (e |u_(-> tptp.b tptp.product_prod_b_b)|) (i tptp.b)) (not (forall ((v |u_(-> tptp.b tptp.b tptp.product_prod_b_b)|)) (not (forall ((ii tptp.b)) (= (ho_263 v ii) (ite (= i ii) e (ho_263 u ii)))))))))) (let ((_let_364 (forall ((x |u_(-> tptp.b tptp.b tptp.product_prod_b_b)|) (y |u_(-> tptp.b tptp.b tptp.product_prod_b_b)|)) (or (not (forall ((z tptp.b)) (= (ho_263 x z) (ho_263 y z)))) (= x y))))) (let ((_let_365 (forall ((u |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a tptp.produc1609974940nres_a)|) (e |u_(-> tptp.refine424419629nres_a tptp.produc1609974940nres_a)|) (i tptp.refine424419629nres_a)) (not (forall ((v |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a tptp.produc1609974940nres_a)|)) (not (forall ((ii tptp.refine424419629nres_a)) (= (ho_266 v ii) (ite (= i ii) e (ho_266 u ii)))))))))) (let ((_let_366 (forall ((x |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a tptp.produc1609974940nres_a)|) (y |u_(-> tptp.refine424419629nres_a tptp.refine424419629nres_a tptp.produc1609974940nres_a)|)) (or (not (forall ((z tptp.refine424419629nres_a)) (= (ho_266 x z) (ho_266 y z)))) (= x y))))) (let ((_let_367 (forall ((u |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b tptp.produc1587512412nres_b)|) (e |u_(-> tptp.refine432681134nres_b tptp.produc1587512412nres_b)|) (i tptp.refine432681134nres_b)) (not (forall ((v |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b tptp.produc1587512412nres_b)|)) (not (forall ((ii tptp.refine432681134nres_b)) (= (ho_269 v ii) (ite (= i ii) e (ho_269 u ii)))))))))) (let ((_let_368 (forall ((x |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b tptp.produc1587512412nres_b)|) (y |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b tptp.produc1587512412nres_b)|)) (or (not (forall ((z tptp.refine432681134nres_b)) (= (ho_269 x z) (ho_269 y z)))) (= x y))))) (let ((_let_369 (forall ((u |u_(-> tptp.set_Product_prod_a_b tptp.refine424419629nres_a tptp.refine432681134nres_b)|) (e |u_(-> tptp.refine424419629nres_a tptp.refine432681134nres_b)|) (i tptp.set_Product_prod_a_b)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_b tptp.refine424419629nres_a tptp.refine432681134nres_b)|)) (not (forall ((ii tptp.set_Product_prod_a_b)) (= (ho_275 v ii) (ite (= i ii) e (ho_275 u ii)))))))))) (let ((_let_370 (forall ((x |u_(-> tptp.set_Product_prod_a_b tptp.refine424419629nres_a tptp.refine432681134nres_b)|) (y |u_(-> tptp.set_Product_prod_a_b tptp.refine424419629nres_a tptp.refine432681134nres_b)|)) (or (not (forall ((z tptp.set_Product_prod_a_b)) (= (ho_275 x z) (ho_275 y z)))) (= x y))))) (let ((_let_371 (forall ((u |u_(-> tptp.set_Pr1628433942t_unit tptp.set_a)|) (e tptp.set_a) (i tptp.set_Pr1628433942t_unit)) (not (forall ((v |u_(-> tptp.set_Pr1628433942t_unit tptp.set_a)|)) (not (forall ((ii tptp.set_Pr1628433942t_unit)) (= (ho_278 v ii) (ite (= i ii) e (ho_278 u ii)))))))))) (let ((_let_372 (forall ((x |u_(-> tptp.set_Pr1628433942t_unit tptp.set_a)|) (y |u_(-> tptp.set_Pr1628433942t_unit tptp.set_a)|)) (or (not (forall ((z tptp.set_Pr1628433942t_unit)) (= (ho_278 x z) (ho_278 y z)))) (= x y))))) (let ((_let_373 (forall ((u |u_(-> tptp.refine424419629nres_a tptp.refine787176636t_unit)|) (e tptp.refine787176636t_unit) (i tptp.refine424419629nres_a)) (not (forall ((v |u_(-> tptp.refine424419629nres_a tptp.refine787176636t_unit)|)) (not (forall ((ii tptp.refine424419629nres_a)) (= (ho_283 v ii) (ite (= i ii) e (ho_283 u ii)))))))))) (let ((_let_374 (forall ((x |u_(-> tptp.refine424419629nres_a tptp.refine787176636t_unit)|) (y |u_(-> tptp.refine424419629nres_a tptp.refine787176636t_unit)|)) (or (not (forall ((z tptp.refine424419629nres_a)) (= (ho_283 x z) (ho_283 y z)))) (= x y))))) (let ((_let_375 (forall ((u |u_(-> tptp.set_Pr1628433942t_unit tptp.refine424419629nres_a tptp.refine787176636t_unit)|) (e |u_(-> tptp.refine424419629nres_a tptp.refine787176636t_unit)|) (i tptp.set_Pr1628433942t_unit)) (not (forall ((v |u_(-> tptp.set_Pr1628433942t_unit tptp.refine424419629nres_a tptp.refine787176636t_unit)|)) (not (forall ((ii tptp.set_Pr1628433942t_unit)) (= (ho_282 v ii) (ite (= i ii) e (ho_282 u ii)))))))))) (let ((_let_376 (forall ((x |u_(-> tptp.set_Pr1628433942t_unit tptp.refine424419629nres_a tptp.refine787176636t_unit)|) (y |u_(-> tptp.set_Pr1628433942t_unit tptp.refine424419629nres_a tptp.refine787176636t_unit)|)) (or (not (forall ((z tptp.set_Pr1628433942t_unit)) (= (ho_282 x z) (ho_282 y z)))) (= x y))))) (let ((_let_377 (forall ((u |u_(-> tptp.set_Pr1707992533t_unit tptp.set_b)|) (e tptp.set_b) (i tptp.set_Pr1707992533t_unit)) (not (forall ((v |u_(-> tptp.set_Pr1707992533t_unit tptp.set_b)|)) (not (forall ((ii tptp.set_Pr1707992533t_unit)) (= (ho_285 v ii) (ite (= i ii) e (ho_285 u ii)))))))))) (let ((_let_378 (forall ((x |u_(-> tptp.set_Pr1707992533t_unit tptp.set_b)|) (y |u_(-> tptp.set_Pr1707992533t_unit tptp.set_b)|)) (or (not (forall ((z tptp.set_Pr1707992533t_unit)) (= (ho_285 x z) (ho_285 y z)))) (= x y))))) (let ((_let_379 (forall ((u |u_(-> tptp.refine432681134nres_b tptp.refine787176636t_unit)|) (e tptp.refine787176636t_unit) (i tptp.refine432681134nres_b)) (not (forall ((v |u_(-> tptp.refine432681134nres_b tptp.refine787176636t_unit)|)) (not (forall ((ii tptp.refine432681134nres_b)) (= (ho_288 v ii) (ite (= i ii) e (ho_288 u ii)))))))))) (let ((_let_380 (forall ((x |u_(-> tptp.refine432681134nres_b tptp.refine787176636t_unit)|) (y |u_(-> tptp.refine432681134nres_b tptp.refine787176636t_unit)|)) (or (not (forall ((z tptp.refine432681134nres_b)) (= (ho_288 x z) (ho_288 y z)))) (= x y))))) (let ((_let_381 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.set_a tptp.set_a)|) (e |u_(-> tptp.set_a tptp.set_a)|) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.set_a tptp.set_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_290 v ii) (ite (= i ii) e (ho_290 u ii)))))))))) (let ((_let_382 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.set_a tptp.set_a)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.set_a tptp.set_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_290 x z) (ho_290 y z)))) (= x y))))) (let ((_let_383 (forall ((u |u_(-> tptp.set_Product_prod_a_a tptp.set_a)|) (e tptp.set_a) (i tptp.set_Product_prod_a_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_a tptp.set_a)|)) (not (forall ((ii tptp.set_Product_prod_a_a)) (= (ho_292 v ii) (ite (= i ii) e (ho_292 u ii)))))))))) (let ((_let_384 (forall ((x |u_(-> tptp.set_Product_prod_a_a tptp.set_a)|) (y |u_(-> tptp.set_Product_prod_a_a tptp.set_a)|)) (or (not (forall ((z tptp.set_Product_prod_a_a)) (= (ho_292 x z) (ho_292 y z)))) (= x y))))) (let ((_let_385 (forall ((u |u_(-> tptp.set_Product_prod_a_b tptp.set_a tptp.set_b)|) (e |u_(-> tptp.set_a tptp.set_b)|) (i tptp.set_Product_prod_a_b)) (not (forall ((v |u_(-> tptp.set_Product_prod_a_b tptp.set_a tptp.set_b)|)) (not (forall ((ii tptp.set_Product_prod_a_b)) (= (ho_294 v ii) (ite (= i ii) e (ho_294 u ii)))))))))) (let ((_let_386 (forall ((x |u_(-> tptp.set_Product_prod_a_b tptp.set_a tptp.set_b)|) (y |u_(-> tptp.set_Product_prod_a_b tptp.set_a tptp.set_b)|)) (or (not (forall ((z tptp.set_Product_prod_a_b)) (= (ho_294 x z) (ho_294 y z)))) (= x y))))) (let ((_let_387 (forall ((u |u_(-> tptp.set_b tptp.set_a)|) (e tptp.set_a) (i tptp.set_b)) (not (forall ((v |u_(-> tptp.set_b tptp.set_a)|)) (not (forall ((ii tptp.set_b)) (= (ho_300 v ii) (ite (= i ii) e (ho_300 u ii)))))))))) (let ((_let_388 (forall ((x |u_(-> tptp.set_b tptp.set_a)|) (y |u_(-> tptp.set_b tptp.set_a)|)) (or (not (forall ((z tptp.set_b)) (= (ho_300 x z) (ho_300 y z)))) (= x y))))) (let ((_let_389 (forall ((u |u_(-> tptp.set_Product_prod_b_a tptp.set_b tptp.set_a)|) (e |u_(-> tptp.set_b tptp.set_a)|) (i tptp.set_Product_prod_b_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_b_a tptp.set_b tptp.set_a)|)) (not (forall ((ii tptp.set_Product_prod_b_a)) (= (ho_299 v ii) (ite (= i ii) e (ho_299 u ii)))))))))) (let ((_let_390 (forall ((x |u_(-> tptp.set_Product_prod_b_a tptp.set_b tptp.set_a)|) (y |u_(-> tptp.set_Product_prod_b_a tptp.set_b tptp.set_a)|)) (or (not (forall ((z tptp.set_Product_prod_b_a)) (= (ho_299 x z) (ho_299 y z)))) (= x y))))) (let ((_let_391 (forall ((u |u_(-> tptp.set_Product_prod_b_a tptp.set_b)|) (e tptp.set_b) (i tptp.set_Product_prod_b_a)) (not (forall ((v |u_(-> tptp.set_Product_prod_b_a tptp.set_b)|)) (not (forall ((ii tptp.set_Product_prod_b_a)) (= (ho_302 v ii) (ite (= i ii) e (ho_302 u ii)))))))))) (let ((_let_392 (forall ((x |u_(-> tptp.set_Product_prod_b_a tptp.set_b)|) (y |u_(-> tptp.set_Product_prod_b_a tptp.set_b)|)) (or (not (forall ((z tptp.set_Product_prod_b_a)) (= (ho_302 x z) (ho_302 y z)))) (= x y))))) (let ((_let_393 (forall ((u |u_(-> tptp.set_Product_prod_b_b tptp.set_b tptp.set_b)|) (e |u_(-> tptp.set_b tptp.set_b)|) (i tptp.set_Product_prod_b_b)) (not (forall ((v |u_(-> tptp.set_Product_prod_b_b tptp.set_b tptp.set_b)|)) (not (forall ((ii tptp.set_Product_prod_b_b)) (= (ho_304 v ii) (ite (= i ii) e (ho_304 u ii)))))))))) (let ((_let_394 (forall ((x |u_(-> tptp.set_Product_prod_b_b tptp.set_b tptp.set_b)|) (y |u_(-> tptp.set_Product_prod_b_b tptp.set_b tptp.set_b)|)) (or (not (forall ((z tptp.set_Product_prod_b_b)) (= (ho_304 x z) (ho_304 y z)))) (= x y))))) (let ((_let_395 (forall ((u |u_(-> tptp.set_Product_prod_b_b tptp.set_b)|) (e tptp.set_b) (i tptp.set_Product_prod_b_b)) (not (forall ((v |u_(-> tptp.set_Product_prod_b_b tptp.set_b)|)) (not (forall ((ii tptp.set_Product_prod_b_b)) (= (ho_306 v ii) (ite (= i ii) e (ho_306 u ii)))))))))) (let ((_let_396 (forall ((x |u_(-> tptp.set_Product_prod_b_b tptp.set_b)|) (y |u_(-> tptp.set_Product_prod_b_b tptp.set_b)|)) (or (not (forall ((z tptp.set_Product_prod_b_b)) (= (ho_306 x z) (ho_306 y z)))) (= x y))))) (let ((_let_397 (forall ((u |u_(-> tptp.set_Pr1707992533t_unit tptp.refine787176636t_unit tptp.refine432681134nres_b)|) (e |u_(-> tptp.refine787176636t_unit tptp.refine432681134nres_b)|) (i tptp.set_Pr1707992533t_unit)) (not (forall ((v |u_(-> tptp.set_Pr1707992533t_unit tptp.refine787176636t_unit tptp.refine432681134nres_b)|)) (not (forall ((ii tptp.set_Pr1707992533t_unit)) (= (ho_312 v ii) (ite (= i ii) e (ho_312 u ii)))))))))) (let ((_let_398 (forall ((x |u_(-> tptp.set_Pr1707992533t_unit tptp.refine787176636t_unit tptp.refine432681134nres_b)|) (y |u_(-> tptp.set_Pr1707992533t_unit tptp.refine787176636t_unit tptp.refine432681134nres_b)|)) (or (not (forall ((z tptp.set_Pr1707992533t_unit)) (= (ho_312 x z) (ho_312 y z)))) (= x y))))) (let ((_let_399 (forall ((u |u_(-> tptp.refine787176636t_unit tptp.refine424419629nres_a)|) (e tptp.refine424419629nres_a) (i tptp.refine787176636t_unit)) (not (forall ((v |u_(-> tptp.refine787176636t_unit tptp.refine424419629nres_a)|)) (not (forall ((ii tptp.refine787176636t_unit)) (= (ho_316 v ii) (ite (= i ii) e (ho_316 u ii)))))))))) (let ((_let_400 (forall ((x |u_(-> tptp.refine787176636t_unit tptp.refine424419629nres_a)|) (y |u_(-> tptp.refine787176636t_unit tptp.refine424419629nres_a)|)) (or (not (forall ((z tptp.refine787176636t_unit)) (= (ho_316 x z) (ho_316 y z)))) (= x y))))) (let ((_let_401 (forall ((u |u_(-> tptp.set_Pr1628433942t_unit tptp.refine787176636t_unit tptp.refine424419629nres_a)|) (e |u_(-> tptp.refine787176636t_unit tptp.refine424419629nres_a)|) (i tptp.set_Pr1628433942t_unit)) (not (forall ((v |u_(-> tptp.set_Pr1628433942t_unit tptp.refine787176636t_unit tptp.refine424419629nres_a)|)) (not (forall ((ii tptp.set_Pr1628433942t_unit)) (= (ho_315 v ii) (ite (= i ii) e (ho_315 u ii)))))))))) (let ((_let_402 (forall ((x |u_(-> tptp.set_Pr1628433942t_unit tptp.refine787176636t_unit tptp.refine424419629nres_a)|) (y |u_(-> tptp.set_Pr1628433942t_unit tptp.refine787176636t_unit tptp.refine424419629nres_a)|)) (or (not (forall ((z tptp.set_Pr1628433942t_unit)) (= (ho_315 x z) (ho_315 y z)))) (= x y))))) (let ((_let_403 (forall ((u |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b tptp.refine432681134nres_b Bool)|) (e |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b Bool)|) (i tptp.refine432681134nres_b)) (not (forall ((v |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b tptp.refine432681134nres_b Bool)|)) (not (forall ((ii tptp.refine432681134nres_b)) (= (ho_321 v ii) (ite (= i ii) e (ho_321 u ii)))))))))) (let ((_let_404 (forall ((x |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b tptp.refine432681134nres_b Bool)|) (y |u_(-> tptp.refine432681134nres_b tptp.refine432681134nres_b tptp.refine432681134nres_b Bool)|)) (or (not (forall ((z tptp.refine432681134nres_b)) (= (ho_321 x z) (ho_321 y z)))) (= x y))))) (let ((_let_405 (forall ((BOUND_VARIABLE_30730 tptp.b)) (= (ho_32 k_31 BOUND_VARIABLE_30730) (ho_38 (ho_37 k_36 BOUND_VARIABLE_30730) (ho_35 k_34 k_33)))))) (let ((_let_406 (forall ((BOUND_VARIABLE_30723 tptp.a)) (= (ho_40 k_39 BOUND_VARIABLE_30723) (ho_46 (ho_45 k_44 BOUND_VARIABLE_30723) (ho_43 k_42 k_41)))))) (let ((_let_407 (forall ((BOUND_VARIABLE_30718 tptp.product_unit)) (ho_48 k_47 BOUND_VARIABLE_30718)))) (let ((_let_408 (forall ((BOUND_VARIABLE_30694 tptp.refine424419629nres_a) (BOUND_VARIABLE_30695 tptp.a)) (= (ho_40 (ho_50 k_55 BOUND_VARIABLE_30694) BOUND_VARIABLE_30695) (or (forall ((M6 tptp.set_a)) (not (= BOUND_VARIABLE_30694 (ho_54 k_53 M6)))) (and (not (forall ((M6 tptp.set_a)) (not (= (ho_52 k_51 BOUND_VARIABLE_30695) (ho_54 k_53 M6))))) (forall ((X5 tptp.a)) (or (not (ho_40 (ho_50 k_49 (ho_52 k_51 BOUND_VARIABLE_30695)) X5)) (ho_40 (ho_50 k_49 BOUND_VARIABLE_30694) X5))))))))) (let ((_let_409 (forall ((BOUND_VARIABLE_30670 tptp.refine432681134nres_b) (BOUND_VARIABLE_30671 tptp.b)) (= (ho_32 (ho_57 k_62 BOUND_VARIABLE_30670) BOUND_VARIABLE_30671) (or (forall ((M6 tptp.set_b)) (not (= BOUND_VARIABLE_30670 (ho_61 k_60 M6)))) (and (not (forall ((M6 tptp.set_b)) (not (= (ho_59 k_58 BOUND_VARIABLE_30671) (ho_61 k_60 M6))))) (forall ((X5 tptp.b)) (or (not (ho_32 (ho_57 k_56 (ho_59 k_58 BOUND_VARIABLE_30671)) X5)) (ho_32 (ho_57 k_56 BOUND_VARIABLE_30670) X5))))))))) (let ((_let_410 (forall ((BOUND_VARIABLE_30663 tptp.b) (BOUND_VARIABLE_30664 tptp.b)) (= (= BOUND_VARIABLE_30663 BOUND_VARIABLE_30664) (ho_32 (ho_64 k_63 BOUND_VARIABLE_30663) BOUND_VARIABLE_30664))))) (let ((_let_411 (forall ((BOUND_VARIABLE_30656 tptp.a) (BOUND_VARIABLE_30657 tptp.a)) (= (= BOUND_VARIABLE_30656 BOUND_VARIABLE_30657) (ho_40 (ho_66 k_65 BOUND_VARIABLE_30656) BOUND_VARIABLE_30657))))) (let ((_let_412 (forall ((BOUND_VARIABLE_30649 tptp.b) (BOUND_VARIABLE_30650 tptp.b)) (= (= BOUND_VARIABLE_30649 BOUND_VARIABLE_30650) (ho_32 (ho_64 k_67 BOUND_VARIABLE_30649) BOUND_VARIABLE_30650))))) (let ((_let_413 (forall ((BOUND_VARIABLE_30642 tptp.a) (BOUND_VARIABLE_30643 tptp.a)) (= (= BOUND_VARIABLE_30642 BOUND_VARIABLE_30643) (ho_40 (ho_66 k_68 BOUND_VARIABLE_30642) BOUND_VARIABLE_30643))))) (let ((_let_414 (forall ((BOUND_VARIABLE_30631 tptp.set_b) (BOUND_VARIABLE_30632 tptp.set_b)) (= (ho_38 (ho_70 k_69 BOUND_VARIABLE_30631) BOUND_VARIABLE_30632) (forall ((T3 tptp.b)) (let ((_let_1 (ho_37 k_36 T3))) (or (not (ho_38 _let_1 BOUND_VARIABLE_30631)) (ho_38 _let_1 BOUND_VARIABLE_30632)))))))) (let ((_let_415 (forall ((BOUND_VARIABLE_30620 tptp.set_b) (BOUND_VARIABLE_30621 tptp.set_b)) (= (ho_38 (ho_70 k_71 BOUND_VARIABLE_30620) BOUND_VARIABLE_30621) (forall ((X5 tptp.b)) (let ((_let_1 (ho_37 k_36 X5))) (or (not (ho_38 _let_1 BOUND_VARIABLE_30620)) (ho_38 _let_1 BOUND_VARIABLE_30621)))))))) (let ((_let_416 (forall ((BOUND_VARIABLE_30609 tptp.set_a) (BOUND_VARIABLE_30610 tptp.set_a)) (= (ho_46 (ho_73 k_72 BOUND_VARIABLE_30609) BOUND_VARIABLE_30610) (forall ((T3 tptp.a)) (let ((_let_1 (ho_45 k_44 T3))) (or (not (ho_46 _let_1 BOUND_VARIABLE_30609)) (ho_46 _let_1 BOUND_VARIABLE_30610)))))))) (let ((_let_417 (forall ((BOUND_VARIABLE_30598 tptp.set_a) (BOUND_VARIABLE_30599 tptp.set_a)) (= (ho_46 (ho_73 k_74 BOUND_VARIABLE_30598) BOUND_VARIABLE_30599) (forall ((X5 tptp.a)) (let ((_let_1 (ho_45 k_44 X5))) (or (not (ho_46 _let_1 BOUND_VARIABLE_30598)) (ho_46 _let_1 BOUND_VARIABLE_30599)))))))) (let ((_let_418 (forall ((BOUND_VARIABLE_30590 tptp.set_b) (BOUND_VARIABLE_30591 tptp.b)) (= (ho_32 (ho_76 k_75 BOUND_VARIABLE_30590) BOUND_VARIABLE_30591) (ho_38 (ho_37 k_36 BOUND_VARIABLE_30591) BOUND_VARIABLE_30590))))) (let ((_let_419 (forall ((BOUND_VARIABLE_30575 tptp.refine424419629nres_a) (BOUND_VARIABLE_30576 tptp.refine424419629nres_a)) (= (= BOUND_VARIABLE_30575 BOUND_VARIABLE_30576) (ho_81 (ho_80 k_79 BOUND_VARIABLE_30575) BOUND_VARIABLE_30576))))) (let ((_let_420 (forall ((BOUND_VARIABLE_30546 tptp.refine424419629nres_a) (BOUND_VARIABLE_30547 tptp.refine424419629nres_a)) (let ((_let_1 (forall ((M6 tptp.set_a)) (not (= BOUND_VARIABLE_30547 (ho_54 k_53 M6)))))) (let ((_let_2 (forall ((M6 tptp.set_a)) (not (= BOUND_VARIABLE_30546 (ho_54 k_53 M6)))))) (= (ho_81 (ho_80 k_82 BOUND_VARIABLE_30546) BOUND_VARIABLE_30547) (and (or _let_1 (and (not _let_2) (forall ((X5 tptp.a)) (or (not (ho_40 (ho_50 k_49 BOUND_VARIABLE_30546) X5)) (ho_40 (ho_50 k_49 BOUND_VARIABLE_30547) X5))))) (or _let_2 (and (not _let_1) (forall ((X5 tptp.a)) (or (not (ho_40 (ho_50 k_49 BOUND_VARIABLE_30547) X5)) (ho_40 (ho_50 k_49 BOUND_VARIABLE_30546) X5)))))))))))) (let ((_let_421 (forall ((BOUND_VARIABLE_30539 tptp.refine432681134nres_b) (BOUND_VARIABLE_30540 tptp.refine432681134nres_b)) (= (= BOUND_VARIABLE_30539 BOUND_VARIABLE_30540) (ho_85 (ho_84 k_83 BOUND_VARIABLE_30539) BOUND_VARIABLE_30540))))) (let ((_let_422 (forall ((BOUND_VARIABLE_30510 tptp.refine432681134nres_b) (BOUND_VARIABLE_30511 tptp.refine432681134nres_b)) (let ((_let_1 (forall ((M6 tptp.set_b)) (not (= BOUND_VARIABLE_30511 (ho_61 k_60 M6)))))) (let ((_let_2 (forall ((M6 tptp.set_b)) (not (= BOUND_VARIABLE_30510 (ho_61 k_60 M6)))))) (= (ho_85 (ho_84 k_86 BOUND_VARIABLE_30510) BOUND_VARIABLE_30511) (and (or _let_1 (and (not _let_2) (forall ((X5 tptp.b)) (or (not (ho_32 (ho_57 k_56 BOUND_VARIABLE_30510) X5)) (ho_32 (ho_57 k_56 BOUND_VARIABLE_30511) X5))))) (or _let_2 (and (not _let_1) (forall ((X5 tptp.b)) (or (not (ho_32 (ho_57 k_56 BOUND_VARIABLE_30511) X5)) (ho_32 (ho_57 k_56 BOUND_VARIABLE_30510) X5)))))))))))) (let ((_let_423 (forall ((BOUND_VARIABLE_30502 tptp.set_b) (BOUND_VARIABLE_30503 tptp.b)) (= (ho_32 (ho_76 k_87 BOUND_VARIABLE_30502) BOUND_VARIABLE_30503) (ho_38 (ho_37 k_36 BOUND_VARIABLE_30503) BOUND_VARIABLE_30502))))) (let ((_let_424 (forall ((BOUND_VARIABLE_30494 tptp.set_a) (BOUND_VARIABLE_30495 tptp.a)) (= (ho_40 (ho_78 k_88 BOUND_VARIABLE_30494) BOUND_VARIABLE_30495) (ho_46 (ho_45 k_44 BOUND_VARIABLE_30495) BOUND_VARIABLE_30494))))) (let ((_let_425 (forall ((BOUND_VARIABLE_30487 tptp.refine424419629nres_a) (BOUND_VARIABLE_30488 tptp.refine424419629nres_a)) (= (= BOUND_VARIABLE_30487 BOUND_VARIABLE_30488) (ho_81 (ho_80 k_89 BOUND_VARIABLE_30487) BOUND_VARIABLE_30488))))) (let ((_let_426 (forall ((BOUND_VARIABLE_30458 tptp.refine424419629nres_a) (BOUND_VARIABLE_30459 tptp.refine424419629nres_a)) (let ((_let_1 (forall ((M6 tptp.set_a)) (not (= BOUND_VARIABLE_30459 (ho_54 k_53 M6)))))) (let ((_let_2 (forall ((M6 tptp.set_a)) (not (= BOUND_VARIABLE_30458 (ho_54 k_53 M6)))))) (= (ho_81 (ho_80 k_90 BOUND_VARIABLE_30458) BOUND_VARIABLE_30459) (and (or _let_1 (and (not _let_2) (forall ((X5 tptp.a)) (or (not (ho_40 (ho_50 k_49 BOUND_VARIABLE_30458) X5)) (ho_40 (ho_50 k_49 BOUND_VARIABLE_30459) X5))))) (or _let_2 (and (not _let_1) (forall ((X5 tptp.a)) (or (not (ho_40 (ho_50 k_49 BOUND_VARIABLE_30459) X5)) (ho_40 (ho_50 k_49 BOUND_VARIABLE_30458) X5)))))))))))) (let ((_let_427 (forall ((BOUND_VARIABLE_30451 tptp.refine432681134nres_b) (BOUND_VARIABLE_30452 tptp.refine432681134nres_b)) (= (= BOUND_VARIABLE_30451 BOUND_VARIABLE_30452) (ho_85 (ho_84 k_91 BOUND_VARIABLE_30451) BOUND_VARIABLE_30452))))) (let ((_let_428 (forall ((BOUND_VARIABLE_30422 tptp.refine432681134nres_b) (BOUND_VARIABLE_30423 tptp.refine432681134nres_b)) (let ((_let_1 (forall ((M6 tptp.set_b)) (not (= BOUND_VARIABLE_30423 (ho_61 k_60 M6)))))) (let ((_let_2 (forall ((M6 tptp.set_b)) (not (= BOUND_VARIABLE_30422 (ho_61 k_60 M6)))))) (= (ho_85 (ho_84 k_92 BOUND_VARIABLE_30422) BOUND_VARIABLE_30423) (and (or _let_1 (and (not _let_2) (forall ((X5 tptp.b)) (or (not (ho_32 (ho_57 k_56 BOUND_VARIABLE_30422) X5)) (ho_32 (ho_57 k_56 BOUND_VARIABLE_30423) X5))))) (or _let_2 (and (not _let_1) (forall ((X5 tptp.b)) (or (not (ho_32 (ho_57 k_56 BOUND_VARIABLE_30423) X5)) (ho_32 (ho_57 k_56 BOUND_VARIABLE_30422) X5)))))))))))) (let ((_let_429 (forall ((BOUND_VARIABLE_30415 tptp.refine424419629nres_a) (BOUND_VARIABLE_30416 tptp.refine424419629nres_a)) (= (= BOUND_VARIABLE_30415 BOUND_VARIABLE_30416) (ho_81 (ho_80 k_93 BOUND_VARIABLE_30415) BOUND_VARIABLE_30416))))) (let ((_let_430 (forall ((BOUND_VARIABLE_30386 tptp.refine424419629nres_a) (BOUND_VARIABLE_30387 tptp.refine424419629nres_a)) (let ((_let_1 (forall ((M6 tptp.set_a)) (not (= BOUND_VARIABLE_30386 (ho_54 k_53 M6)))))) (let ((_let_2 (forall ((M6 tptp.set_a)) (not (= BOUND_VARIABLE_30387 (ho_54 k_53 M6)))))) (= (ho_81 (ho_80 k_94 BOUND_VARIABLE_30386) BOUND_VARIABLE_30387) (and (or _let_1 (and (not _let_2) (forall ((X5 tptp.a)) (or (not (ho_40 (ho_50 k_49 BOUND_VARIABLE_30387) X5)) (ho_40 (ho_50 k_49 BOUND_VARIABLE_30386) X5))))) (or _let_2 (and (not _let_1) (forall ((X5 tptp.a)) (or (not (ho_40 (ho_50 k_49 BOUND_VARIABLE_30386) X5)) (ho_40 (ho_50 k_49 BOUND_VARIABLE_30387) X5)))))))))))) (let ((_let_431 (forall ((BOUND_VARIABLE_30379 tptp.refine432681134nres_b) (BOUND_VARIABLE_30380 tptp.refine432681134nres_b)) (= (= BOUND_VARIABLE_30379 BOUND_VARIABLE_30380) (ho_85 (ho_84 k_95 BOUND_VARIABLE_30379) BOUND_VARIABLE_30380))))) (let ((_let_432 (forall ((BOUND_VARIABLE_30350 tptp.refine432681134nres_b) (BOUND_VARIABLE_30351 tptp.refine432681134nres_b)) (let ((_let_1 (forall ((M6 tptp.set_b)) (not (= BOUND_VARIABLE_30350 (ho_61 k_60 M6)))))) (let ((_let_2 (forall ((M6 tptp.set_b)) (not (= BOUND_VARIABLE_30351 (ho_61 k_60 M6)))))) (= (ho_85 (ho_84 k_96 BOUND_VARIABLE_30350) BOUND_VARIABLE_30351) (and (or _let_1 (and (not _let_2) (forall ((X5 tptp.b)) (or (not (ho_32 (ho_57 k_56 BOUND_VARIABLE_30351) X5)) (ho_32 (ho_57 k_56 BOUND_VARIABLE_30350) X5))))) (or _let_2 (and (not _let_1) (forall ((X5 tptp.b)) (or (not (ho_32 (ho_57 k_56 BOUND_VARIABLE_30350) X5)) (ho_32 (ho_57 k_56 BOUND_VARIABLE_30351) X5)))))))))))) (let ((_let_433 (ho_40 k_97 tptp.x))) (let ((_let_434 (forall ((BOUND_VARIABLE_30730 tptp.b)) (= (@ (@ tptp.member_b BOUND_VARIABLE_30730) (@ tptp.collect_b tptp.top_top_b_o)) (ll_30 BOUND_VARIABLE_30730))))) (let ((_let_435 (forall ((BOUND_VARIABLE_30723 tptp.a)) (= (@ (@ tptp.member_a BOUND_VARIABLE_30723) (@ tptp.collect_a tptp.top_top_a_o)) (ll_29 BOUND_VARIABLE_30723))))) (let ((_let_436 (forall ((BOUND_VARIABLE_30718 tptp.product_unit)) (ll_28 BOUND_VARIABLE_30718)))) (let ((_let_437 (forall ((BOUND_VARIABLE_30694 tptp.refine424419629nres_a) (BOUND_VARIABLE_30695 tptp.a)) (= (ll_27 BOUND_VARIABLE_30694 BOUND_VARIABLE_30695) (or (forall ((M6 tptp.set_a)) (not (= (@ tptp.refine1198353288_RES_a M6) BOUND_VARIABLE_30694))) (and (not (forall ((M6 tptp.set_a)) (not (= (@ tptp.refine1198353288_RES_a M6) (@ tptp.refine2063221604TURN_a BOUND_VARIABLE_30695))))) (forall ((X5 tptp.a)) (or (not (@ (@ tptp.refine1001002027nres_a (@ tptp.refine2063221604TURN_a BOUND_VARIABLE_30695)) X5)) (@ (@ tptp.refine1001002027nres_a BOUND_VARIABLE_30694) X5))))))))) (let ((_let_438 (forall ((BOUND_VARIABLE_30670 tptp.refine432681134nres_b) (BOUND_VARIABLE_30671 tptp.b)) (= (ll_26 BOUND_VARIABLE_30670 BOUND_VARIABLE_30671) (or (forall ((M6 tptp.set_b)) (not (= (@ tptp.refine1198353289_RES_b M6) BOUND_VARIABLE_30670))) (and (not (forall ((M6 tptp.set_b)) (not (= (@ tptp.refine1198353289_RES_b M6) (@ tptp.refine2063221605TURN_b BOUND_VARIABLE_30671))))) (forall ((X5 tptp.b)) (or (not (@ (@ tptp.refine1001002028nres_b (@ tptp.refine2063221605TURN_b BOUND_VARIABLE_30671)) X5)) (@ (@ tptp.refine1001002028nres_b BOUND_VARIABLE_30670) X5))))))))) (let ((_let_439 (forall ((BOUND_VARIABLE_30663 tptp.b) (BOUND_VARIABLE_30664 tptp.b)) (= (= BOUND_VARIABLE_30663 BOUND_VARIABLE_30664) (ll_25 BOUND_VARIABLE_30663 BOUND_VARIABLE_30664))))) (let ((_let_440 (forall ((BOUND_VARIABLE_30656 tptp.a) (BOUND_VARIABLE_30657 tptp.a)) (= (= BOUND_VARIABLE_30656 BOUND_VARIABLE_30657) (ll_24 BOUND_VARIABLE_30656 BOUND_VARIABLE_30657))))) (let ((_let_441 (forall ((BOUND_VARIABLE_30649 tptp.b) (BOUND_VARIABLE_30650 tptp.b)) (= (= BOUND_VARIABLE_30649 BOUND_VARIABLE_30650) (ll_23 BOUND_VARIABLE_30649 BOUND_VARIABLE_30650))))) (let ((_let_442 (forall ((BOUND_VARIABLE_30642 tptp.a) (BOUND_VARIABLE_30643 tptp.a)) (= (= BOUND_VARIABLE_30642 BOUND_VARIABLE_30643) (ll_22 BOUND_VARIABLE_30642 BOUND_VARIABLE_30643))))) (let ((_let_443 (forall ((BOUND_VARIABLE_30631 tptp.set_b) (BOUND_VARIABLE_30632 tptp.set_b)) (= (forall ((T3 tptp.b)) (let ((_let_1 (@ tptp.member_b T3))) (or (not (@ _let_1 BOUND_VARIABLE_30631)) (@ _let_1 BOUND_VARIABLE_30632)))) (ll_21 BOUND_VARIABLE_30631 BOUND_VARIABLE_30632))))) (let ((_let_444 (forall ((BOUND_VARIABLE_30620 tptp.set_b) (BOUND_VARIABLE_30621 tptp.set_b)) (= (forall ((X5 tptp.b)) (let ((_let_1 (@ tptp.member_b X5))) (or (not (@ _let_1 BOUND_VARIABLE_30620)) (@ _let_1 BOUND_VARIABLE_30621)))) (ll_20 BOUND_VARIABLE_30620 BOUND_VARIABLE_30621))))) (let ((_let_445 (forall ((BOUND_VARIABLE_30609 tptp.set_a) (BOUND_VARIABLE_30610 tptp.set_a)) (= (forall ((T3 tptp.a)) (let ((_let_1 (@ tptp.member_a T3))) (or (not (@ _let_1 BOUND_VARIABLE_30609)) (@ _let_1 BOUND_VARIABLE_30610)))) (ll_19 BOUND_VARIABLE_30609 BOUND_VARIABLE_30610))))) (let ((_let_446 (forall ((BOUND_VARIABLE_30598 tptp.set_a) (BOUND_VARIABLE_30599 tptp.set_a)) (= (forall ((X5 tptp.a)) (let ((_let_1 (@ tptp.member_a X5))) (or (not (@ _let_1 BOUND_VARIABLE_30598)) (@ _let_1 BOUND_VARIABLE_30599)))) (ll_18 BOUND_VARIABLE_30598 BOUND_VARIABLE_30599))))) (let ((_let_447 (forall ((BOUND_VARIABLE_30590 tptp.set_b) (BOUND_VARIABLE_30591 tptp.b)) (= (@ (@ tptp.member_b BOUND_VARIABLE_30591) BOUND_VARIABLE_30590) (ll_17 BOUND_VARIABLE_30590 BOUND_VARIABLE_30591))))) (let ((_let_448 (forall ((BOUND_VARIABLE_30582 tptp.set_a) (BOUND_VARIABLE_30583 tptp.a)) (= (@ (@ tptp.member_a BOUND_VARIABLE_30583) BOUND_VARIABLE_30582) (ll_16 BOUND_VARIABLE_30582 BOUND_VARIABLE_30583))))) (let ((_let_449 (forall ((BOUND_VARIABLE_30575 tptp.refine424419629nres_a) (BOUND_VARIABLE_30576 tptp.refine424419629nres_a)) (= (= BOUND_VARIABLE_30575 BOUND_VARIABLE_30576) (ll_15 BOUND_VARIABLE_30575 BOUND_VARIABLE_30576))))) (let ((_let_450 (forall ((BOUND_VARIABLE_30546 tptp.refine424419629nres_a) (BOUND_VARIABLE_30547 tptp.refine424419629nres_a)) (let ((_let_1 (forall ((M6 tptp.set_a)) (not (= (@ tptp.refine1198353288_RES_a M6) BOUND_VARIABLE_30547))))) (let ((_let_2 (forall ((M6 tptp.set_a)) (not (= (@ tptp.refine1198353288_RES_a M6) BOUND_VARIABLE_30546))))) (= (ll_14 BOUND_VARIABLE_30546 BOUND_VARIABLE_30547) (and (or _let_1 (and (not _let_2) (forall ((X5 tptp.a)) (or (not (@ (@ tptp.refine1001002027nres_a BOUND_VARIABLE_30546) X5)) (@ (@ tptp.refine1001002027nres_a BOUND_VARIABLE_30547) X5))))) (or _let_2 (and (not _let_1) (forall ((X5 tptp.a)) (or (not (@ (@ tptp.refine1001002027nres_a BOUND_VARIABLE_30547) X5)) (@ (@ tptp.refine1001002027nres_a BOUND_VARIABLE_30546) X5)))))))))))) (let ((_let_451 (forall ((BOUND_VARIABLE_30539 tptp.refine432681134nres_b) (BOUND_VARIABLE_30540 tptp.refine432681134nres_b)) (= (= BOUND_VARIABLE_30539 BOUND_VARIABLE_30540) (ll_13 BOUND_VARIABLE_30539 BOUND_VARIABLE_30540))))) (let ((_let_452 (forall ((BOUND_VARIABLE_30510 tptp.refine432681134nres_b) (BOUND_VARIABLE_30511 tptp.refine432681134nres_b)) (let ((_let_1 (forall ((M6 tptp.set_b)) (not (= (@ tptp.refine1198353289_RES_b M6) BOUND_VARIABLE_30511))))) (let ((_let_2 (forall ((M6 tptp.set_b)) (not (= (@ tptp.refine1198353289_RES_b M6) BOUND_VARIABLE_30510))))) (= (ll_12 BOUND_VARIABLE_30510 BOUND_VARIABLE_30511) (and (or _let_1 (and (not _let_2) (forall ((X5 tptp.b)) (or (not (@ (@ tptp.refine1001002028nres_b BOUND_VARIABLE_30510) X5)) (@ (@ tptp.refine1001002028nres_b BOUND_VARIABLE_30511) X5))))) (or _let_2 (and (not _let_1) (forall ((X5 tptp.b)) (or (not (@ (@ tptp.refine1001002028nres_b BOUND_VARIABLE_30511) X5)) (@ (@ tptp.refine1001002028nres_b BOUND_VARIABLE_30510) X5)))))))))))) (let ((_let_453 (forall ((BOUND_VARIABLE_30502 tptp.set_b) (BOUND_VARIABLE_30503 tptp.b)) (= (@ (@ tptp.member_b BOUND_VARIABLE_30503) BOUND_VARIABLE_30502) (ll_11 BOUND_VARIABLE_30502 BOUND_VARIABLE_30503))))) (let ((_let_454 (forall ((BOUND_VARIABLE_30494 tptp.set_a) (BOUND_VARIABLE_30495 tptp.a)) (= (@ (@ tptp.member_a BOUND_VARIABLE_30495) BOUND_VARIABLE_30494) (ll_10 BOUND_VARIABLE_30494 BOUND_VARIABLE_30495))))) (let ((_let_455 (forall ((BOUND_VARIABLE_30487 tptp.refine424419629nres_a) (BOUND_VARIABLE_30488 tptp.refine424419629nres_a)) (= (= BOUND_VARIABLE_30487 BOUND_VARIABLE_30488) (ll_9 BOUND_VARIABLE_30487 BOUND_VARIABLE_30488))))) (let ((_let_456 (forall ((BOUND_VARIABLE_30458 tptp.refine424419629nres_a) (BOUND_VARIABLE_30459 tptp.refine424419629nres_a)) (let ((_let_1 (forall ((M6 tptp.set_a)) (not (= (@ tptp.refine1198353288_RES_a M6) BOUND_VARIABLE_30459))))) (let ((_let_2 (forall ((M6 tptp.set_a)) (not (= (@ tptp.refine1198353288_RES_a M6) BOUND_VARIABLE_30458))))) (= (ll_8 BOUND_VARIABLE_30458 BOUND_VARIABLE_30459) (and (or _let_1 (and (not _let_2) (forall ((X5 tptp.a)) (or (not (@ (@ tptp.refine1001002027nres_a BOUND_VARIABLE_30458) X5)) (@ (@ tptp.refine1001002027nres_a BOUND_VARIABLE_30459) X5))))) (or _let_2 (and (not _let_1) (forall ((X5 tptp.a)) (or (not (@ (@ tptp.refine1001002027nres_a BOUND_VARIABLE_30459) X5)) (@ (@ tptp.refine1001002027nres_a BOUND_VARIABLE_30458) X5)))))))))))) (let ((_let_457 (forall ((BOUND_VARIABLE_30451 tptp.refine432681134nres_b) (BOUND_VARIABLE_30452 tptp.refine432681134nres_b)) (= (= BOUND_VARIABLE_30451 BOUND_VARIABLE_30452) (ll_7 BOUND_VARIABLE_30451 BOUND_VARIABLE_30452))))) (let ((_let_458 (forall ((BOUND_VARIABLE_30422 tptp.refine432681134nres_b) (BOUND_VARIABLE_30423 tptp.refine432681134nres_b)) (let ((_let_1 (forall ((M6 tptp.set_b)) (not (= (@ tptp.refine1198353289_RES_b M6) BOUND_VARIABLE_30423))))) (let ((_let_2 (forall ((M6 tptp.set_b)) (not (= (@ tptp.refine1198353289_RES_b M6) BOUND_VARIABLE_30422))))) (= (ll_6 BOUND_VARIABLE_30422 BOUND_VARIABLE_30423) (and (or _let_1 (and (not _let_2) (forall ((X5 tptp.b)) (or (not (@ (@ tptp.refine1001002028nres_b BOUND_VARIABLE_30422) X5)) (@ (@ tptp.refine1001002028nres_b BOUND_VARIABLE_30423) X5))))) (or _let_2 (and (not _let_1) (forall ((X5 tptp.b)) (or (not (@ (@ tptp.refine1001002028nres_b BOUND_VARIABLE_30423) X5)) (@ (@ tptp.refine1001002028nres_b BOUND_VARIABLE_30422) X5)))))))))))) (let ((_let_459 (forall ((BOUND_VARIABLE_30415 tptp.refine424419629nres_a) (BOUND_VARIABLE_30416 tptp.refine424419629nres_a)) (= (= BOUND_VARIABLE_30415 BOUND_VARIABLE_30416) (ll_5 BOUND_VARIABLE_30415 BOUND_VARIABLE_30416))))) (let ((_let_460 (forall ((BOUND_VARIABLE_30386 tptp.refine424419629nres_a) (BOUND_VARIABLE_30387 tptp.refine424419629nres_a)) (let ((_let_1 (forall ((M6 tptp.set_a)) (not (= (@ tptp.refine1198353288_RES_a M6) BOUND_VARIABLE_30386))))) (let ((_let_2 (forall ((M6 tptp.set_a)) (not (= (@ tptp.refine1198353288_RES_a M6) BOUND_VARIABLE_30387))))) (= (ll_4 BOUND_VARIABLE_30386 BOUND_VARIABLE_30387) (and (or _let_1 (and (not _let_2) (forall ((X5 tptp.a)) (or (not (@ (@ tptp.refine1001002027nres_a BOUND_VARIABLE_30387) X5)) (@ (@ tptp.refine1001002027nres_a BOUND_VARIABLE_30386) X5))))) (or _let_2 (and (not _let_1) (forall ((X5 tptp.a)) (or (not (@ (@ tptp.refine1001002027nres_a BOUND_VARIABLE_30386) X5)) (@ (@ tptp.refine1001002027nres_a BOUND_VARIABLE_30387) X5)))))))))))) (let ((_let_461 (forall ((BOUND_VARIABLE_30379 tptp.refine432681134nres_b) (BOUND_VARIABLE_30380 tptp.refine432681134nres_b)) (= (= BOUND_VARIABLE_30379 BOUND_VARIABLE_30380) (ll_3 BOUND_VARIABLE_30379 BOUND_VARIABLE_30380))))) (let ((_let_462 (forall ((BOUND_VARIABLE_30350 tptp.refine432681134nres_b) (BOUND_VARIABLE_30351 tptp.refine432681134nres_b)) (let ((_let_1 (forall ((M6 tptp.set_b)) (not (= (@ tptp.refine1198353289_RES_b M6) BOUND_VARIABLE_30350))))) (let ((_let_2 (forall ((M6 tptp.set_b)) (not (= (@ tptp.refine1198353289_RES_b M6) BOUND_VARIABLE_30351))))) (= (ll_2 BOUND_VARIABLE_30350 BOUND_VARIABLE_30351) (and (or _let_1 (and (not _let_2) (forall ((X5 tptp.b)) (or (not (@ (@ tptp.refine1001002028nres_b BOUND_VARIABLE_30351) X5)) (@ (@ tptp.refine1001002028nres_b BOUND_VARIABLE_30350) X5))))) (or _let_2 (and (not _let_1) (forall ((X5 tptp.b)) (or (not (@ (@ tptp.refine1001002028nres_b BOUND_VARIABLE_30350) X5)) (@ (@ tptp.refine1001002028nres_b BOUND_VARIABLE_30351) X5)))))))))))) (let ((_let_463 (and _let_22 _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434))) (let ((_let_464 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (ASSUME :args (_let_22)) (PREPROCESS :args ((and _let_462 _let_461 _let_460 _let_459 _let_458 _let_457 _let_456 _let_455 _let_454 _let_453 _let_452 _let_451 _let_450 _let_449 _let_448 _let_447 _let_446 _let_445 _let_444 _let_443 _let_442 _let_441 _let_440 _let_439 _let_438 _let_437 _let_436 _let_435 _let_434)))) :args (_let_463)) (PREPROCESS :args ((= _let_463 (and _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_74 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405))))) (PREPROCESS :args ((and _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75)))) :args ((and _let_433 _let_432 _let_431 _let_430 _let_429 _let_428 _let_427 _let_426 _let_425 _let_424 _let_423 _let_422 _let_421 _let_420 _let_419 _let_74 _let_418 _let_417 _let_416 _let_415 _let_414 _let_413 _let_412 _let_411 _let_410 _let_409 _let_408 _let_407 _let_406 _let_405 _let_404 _let_403 _let_402 _let_401 _let_400 _let_399 _let_398 _let_397 _let_396 _let_395 _let_394 _let_393 _let_392 _let_391 _let_390 _let_389 _let_388 _let_387 _let_386 _let_385 _let_384 _let_383 _let_382 _let_381 _let_380 _let_379 _let_378 _let_377 _let_376 _let_375 _let_374 _let_373 _let_372 _let_371 _let_370 _let_369 _let_368 _let_367 _let_366 _let_365 _let_364 _let_363 _let_362 _let_361 _let_360 _let_359 _let_358 _let_357 _let_356 _let_355 _let_354 _let_353 _let_352 _let_351 _let_350 _let_349 _let_348 _let_347 _let_346 _let_345 _let_344 _let_343 _let_342 _let_341 _let_340 _let_339 _let_338 _let_337 _let_336 _let_335 _let_334 _let_333 _let_332 _let_331 _let_330 _let_329 _let_328 _let_327 _let_326 _let_325 _let_324 _let_323 _let_322 _let_321 _let_320 _let_319 _let_318 _let_317 _let_316 _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165 _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75))))) (let ((_let_465 (_let_74))) (let ((_let_466 (= _let_433 _let_72))) (let ((_let_467 (forall ((A tptp.a) (BOUND_VARIABLE_35277 |u_(-> tptp.a Bool)|)) (= (ho_40 BOUND_VARIABLE_35277 A) (ho_46 (ho_45 k_44 A) (ho_43 k_42 BOUND_VARIABLE_35277)))))) (let ((_let_468 (EQ_RESOLVE (ASSUME :args (_let_20)) (PREPROCESS :args ((= _let_20 _let_467)))))) (let ((_let_469 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_466)) :args ((or (not _let_433) _let_72 (not _let_466)))) (AND_ELIM _let_464 :args (0)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_468 :args (tptp.x k_97 QUANTIFIERS_INST_ENUM)) :args (_let_467))) _let_468 :args (_let_466 false _let_467)) :args (_let_72 false _let_433 false _let_466)))) (let ((_let_470 (not _let_72))) (let ((_let_471 (and _let_68 _let_67))) (let ((_let_472 (ASSUME :args (_let_68)))) (let ((_let_473 (ASSUME :args (_let_67)))) (let ((_let_474 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_21)) (TRANS (MACRO_SR_EQ_INTRO _let_60 :args (_let_21 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (=> (not (forall ((M6 tptp.set_b)) (not (= (@ tptp.f tptp.x) (@ tptp.refine1198353289_RES_b M6))))) (and _let_53 (forall ((X5 tptp.b)) (or (not (@ (@ tptp.refine1001002028nres_b tptp.m) X5)) (@ (@ tptp.refine1001002028nres_b (@ tptp.f tptp.x)) X5))))) (=> _let_32 _let_30))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) (REFL :args (_let_30)) :args _let_63)) :args ((or _let_30 _let_31))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_32 _let_37 (not _let_38)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args 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tptp.ord_less_eq_set_b X4) X4)) (forall ((X4 tptp.set_a)) (@ (@ tptp.ord_less_eq_set_a X4) X4)) (forall ((X4 (-> Bool tptp.refine424419629nres_a))) (@ (@ tptp.ord_le516598614nres_a X4) X4)) (forall ((X4 (-> Bool tptp.refine432681134nres_b))) (@ (@ tptp.ord_le1656162903nres_b X4) X4)) (forall ((X4 tptp.refine787176636t_unit)) (@ (@ tptp.ord_le1051254044t_unit X4) X4)) (forall ((X4 tptp.refine432681134nres_b)) (@ (@ tptp.ord_le527798542nres_b X4) X4)) (forall ((X4 tptp.refine424419629nres_a)) (@ (@ tptp.ord_le519537037nres_a X4) X4)) (forall ((X tptp.set_Product_unit)) (= (@ tptp.refine1208325748t_unit (@ tptp.refine1777164439t_unit X)) X)) (forall ((X tptp.set_a)) (= (@ tptp.refine1822134885_RES_a (@ tptp.refine1198353288_RES_a X)) X)) (forall ((X tptp.set_b)) (= (@ tptp.refine1822134886_RES_b (@ tptp.refine1198353289_RES_b X)) X)) (forall ((X tptp.set_Product_prod_a_a) (X4 tptp.product_prod_a_a)) (= (@ (@ tptp.refine378960780od_a_a (@ tptp.refine622451633od_a_a X)) X4) (@ (@ tptp.member449909584od_a_a X4) X))) (forall ((X tptp.set_Product_prod_b_a) (X4 tptp.product_prod_b_a)) (= (@ (@ tptp.refine1206730187od_b_a (@ tptp.refine1450221040od_b_a X)) X4) (@ (@ tptp.member1277678991od_b_a X4) X))) (forall ((X tptp.set_Product_prod_b_b) (X4 tptp.product_prod_b_b)) (= (@ (@ tptp.refine1214991692od_b_b (@ tptp.refine1458482545od_b_b X)) X4) (@ (@ tptp.member1285940496od_b_b X4) X))) (forall ((X tptp.set_Product_prod_a_b) (X4 tptp.product_prod_a_b)) (= (@ (@ tptp.refine387222285od_a_b (@ tptp.refine630713138od_a_b X)) X4) (@ (@ tptp.member458171089od_a_b X4) X))) (forall ((X tptp.set_Product_unit) (X4 tptp.product_unit)) (= (@ (@ tptp.refine983493746t_unit (@ tptp.refine1777164439t_unit X)) X4) (@ (@ tptp.member_Product_unit X4) X))) (forall ((X tptp.set_a) (X4 tptp.a)) (= (@ (@ tptp.refine1312857699nres_a (@ tptp.refine1198353288_RES_a X)) X4) (@ (@ tptp.member_a X4) X))) (forall ((X tptp.set_b) (X4 tptp.b)) (= (@ (@ tptp.refine1312857700nres_b (@ tptp.refine1198353289_RES_b X)) X4) (@ (@ tptp.member_b X4) X))) (forall ((Phi (-> tptp.product_unit Bool)) (X4 tptp.product_unit)) (= (@ (@ tptp.refine983493746t_unit (@ tptp.refine1777164439t_unit (@ tptp.collect_Product_unit Phi))) X4) (@ Phi X4))) (forall ((Phi (-> tptp.a Bool)) (X4 tptp.a)) (= (@ (@ tptp.refine1312857699nres_a (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi))) X4) (@ Phi X4))) (forall ((Phi (-> tptp.b Bool)) (X4 tptp.b)) (= (@ (@ tptp.refine1312857700nres_b (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi))) X4) (@ Phi X4))) (forall ((F (-> Bool tptp.refine424419629nres_a)) (G (-> Bool tptp.refine424419629nres_a)) (X4 Bool)) (=> (@ (@ tptp.ord_le516598614nres_a F) G) (@ (@ tptp.ord_le519537037nres_a (@ F X4)) (@ G X4)))) (forall ((F (-> Bool tptp.refine432681134nres_b)) (G (-> Bool tptp.refine432681134nres_b)) (X4 Bool)) (=> (@ (@ tptp.ord_le1656162903nres_b F) G) (@ (@ tptp.ord_le527798542nres_b (@ F X4)) (@ G X4)))) (forall ((F (-> Bool 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Bool) (M1 tptp.refine424419629nres_a) (M12 tptp.refine424419629nres_a) (M2 tptp.refine424419629nres_a) (M22 tptp.refine424419629nres_a)) (let ((_let_1 (@ tptp.if_Ref1724547303nres_a B))) (=> (=> B (@ (@ tptp.ord_le519537037nres_a M1) M12)) (=> (=> (not B) (@ (@ tptp.ord_le519537037nres_a M2) M22)) (@ (@ tptp.ord_le519537037nres_a (@ (@ _let_1 M1) M2)) (@ (@ _let_1 M12) M22)))))) (forall ((A tptp.refine432681134nres_b) (F (-> tptp.refine432681134nres_b tptp.refine432681134nres_b)) (B tptp.refine432681134nres_b) (C tptp.refine432681134nres_b)) (let ((_let_1 (@ tptp.ord_le527798542nres_b A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le527798542nres_b B) C) (=> (forall ((X3 tptp.refine432681134nres_b) (Y4 tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b X3) Y4) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.refine432681134nres_b) (F (-> tptp.refine424419629nres_a tptp.refine432681134nres_b)) (B tptp.refine424419629nres_a) (C tptp.refine424419629nres_a)) (let ((_let_1 (@ tptp.ord_le527798542nres_b A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le519537037nres_a B) C) (=> (forall ((X3 tptp.refine424419629nres_a) (Y4 tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a X3) Y4) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.refine424419629nres_a) (F (-> tptp.refine432681134nres_b tptp.refine424419629nres_a)) (B tptp.refine432681134nres_b) (C tptp.refine432681134nres_b)) (let ((_let_1 (@ tptp.ord_le519537037nres_a A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le527798542nres_b B) C) (=> (forall ((X3 tptp.refine432681134nres_b) (Y4 tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b X3) Y4) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.refine424419629nres_a) (F (-> tptp.refine424419629nres_a tptp.refine424419629nres_a)) (B tptp.refine424419629nres_a) (C tptp.refine424419629nres_a)) (let ((_let_1 (@ tptp.ord_le519537037nres_a A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_le519537037nres_a B) C) (=> (forall ((X3 tptp.refine424419629nres_a) (Y4 tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a X3) Y4) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ F Y4)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.set_a) (B tptp.set_a)) (= (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine1198353288_RES_a A)) (@ tptp.refine1198353288_RES_a B)) (@ (@ tptp.ord_less_eq_set_a A) B))) (forall ((A tptp.set_b) (B tptp.set_b)) (= (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine1198353289_RES_b A)) (@ tptp.refine1198353289_RES_b B)) (@ (@ tptp.ord_less_eq_set_b A) B))) (forall ((X tptp.set_a) (Y tptp.set_a)) (= (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine1198353288_RES_a X)) (@ tptp.refine1198353288_RES_a Y)) (@ (@ tptp.ord_less_eq_set_a X) Y))) (forall ((X tptp.set_b) (Y tptp.set_b)) (= (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine1198353289_RES_b X)) (@ tptp.refine1198353289_RES_b Y)) (@ (@ tptp.ord_less_eq_set_b X) Y))) (forall ((T tptp.refine432681134nres_b) (T2 tptp.refine432681134nres_b) (E tptp.refine432681134nres_b) (E2 tptp.refine432681134nres_b) (B Bool)) (let ((_let_1 (@ tptp.if_Ref1732808808nres_b B))) (=> (@ (@ tptp.ord_le527798542nres_b T) T2) (=> (@ (@ tptp.ord_le527798542nres_b E) E2) (@ (@ tptp.ord_le527798542nres_b (@ (@ _let_1 T) E)) (@ (@ _let_1 T2) E2)))))) (forall ((T tptp.refine424419629nres_a) (T2 tptp.refine424419629nres_a) (E tptp.refine424419629nres_a) (E2 tptp.refine424419629nres_a) (B Bool)) (let ((_let_1 (@ tptp.if_Ref1724547303nres_a B))) (=> (@ (@ tptp.ord_le519537037nres_a T) T2) (=> (@ (@ tptp.ord_le519537037nres_a E) E2) (@ (@ tptp.ord_le519537037nres_a (@ (@ _let_1 T) E)) (@ (@ _let_1 T2) E2)))))) (forall ((B tptp.refine432681134nres_b) (A tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b B) A) (=> (@ (@ tptp.ord_le527798542nres_b A) B) (= A B)))) (forall ((B tptp.refine424419629nres_a) (A tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a B) A) (=> (@ (@ tptp.ord_le519537037nres_a A) B) (= A B)))) (= (lambda ((Y5 tptp.refine432681134nres_b) (Z tptp.refine432681134nres_b)) (= Y5 Z)) (lambda ((A2 tptp.refine432681134nres_b) (B2 tptp.refine432681134nres_b)) (and (@ (@ tptp.ord_le527798542nres_b B2) A2) (@ (@ tptp.ord_le527798542nres_b A2) B2)))) (= (lambda ((Y5 tptp.refine424419629nres_a) (Z tptp.refine424419629nres_a)) (= Y5 Z)) (lambda ((A2 tptp.refine424419629nres_a) (B2 tptp.refine424419629nres_a)) (and (@ (@ tptp.ord_le519537037nres_a B2) A2) (@ (@ tptp.ord_le519537037nres_a A2) B2)))) (forall ((B tptp.refine432681134nres_b) (A tptp.refine432681134nres_b) (C tptp.refine432681134nres_b)) (let ((_let_1 (@ tptp.ord_le527798542nres_b C))) (=> (@ (@ tptp.ord_le527798542nres_b B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((B tptp.refine424419629nres_a) (A tptp.refine424419629nres_a) (C tptp.refine424419629nres_a)) (let ((_let_1 (@ tptp.ord_le519537037nres_a C))) (=> (@ (@ tptp.ord_le519537037nres_a B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((A tptp.refine432681134nres_b)) (@ (@ tptp.ord_le527798542nres_b A) A)) (forall ((A tptp.refine424419629nres_a)) (@ (@ tptp.ord_le519537037nres_a A) A)) (forall ((X4 tptp.refine432681134nres_b) (Y3 tptp.refine432681134nres_b) (Z2 tptp.refine432681134nres_b)) (let ((_let_1 (@ tptp.ord_le527798542nres_b X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_le527798542nres_b Y3) Z2) (@ _let_1 Z2))))) (forall ((X4 tptp.refine424419629nres_a) (Y3 tptp.refine424419629nres_a) (Z2 tptp.refine424419629nres_a)) (let ((_let_1 (@ tptp.ord_le519537037nres_a X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_le519537037nres_a Y3) Z2) (@ _let_1 Z2))))) (forall ((A tptp.refine432681134nres_b) (B tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b A) B) (=> (@ (@ tptp.ord_le527798542nres_b B) A) (= A B)))) (forall ((A tptp.refine424419629nres_a) (B tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a A) B) (=> (@ (@ tptp.ord_le519537037nres_a B) A) (= A B)))) (forall ((A tptp.refine432681134nres_b) (B tptp.refine432681134nres_b) (C tptp.refine432681134nres_b)) (let ((_let_1 (@ tptp.ord_le527798542nres_b A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((A tptp.refine424419629nres_a) (B tptp.refine424419629nres_a) (C tptp.refine424419629nres_a)) (let ((_let_1 (@ tptp.ord_le519537037nres_a A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((A tptp.refine432681134nres_b) (B tptp.refine432681134nres_b) (C tptp.refine432681134nres_b)) (=> (= A B) (=> (@ (@ tptp.ord_le527798542nres_b B) C) (@ (@ tptp.ord_le527798542nres_b A) C)))) (forall ((A tptp.refine424419629nres_a) (B tptp.refine424419629nres_a) (C tptp.refine424419629nres_a)) (=> (= A B) (=> (@ (@ tptp.ord_le519537037nres_a B) C) (@ (@ tptp.ord_le519537037nres_a A) C)))) (= (lambda ((Y5 tptp.refine432681134nres_b) (Z tptp.refine432681134nres_b)) (= Y5 Z)) (lambda ((A2 tptp.refine432681134nres_b) (B2 tptp.refine432681134nres_b)) (and (@ (@ tptp.ord_le527798542nres_b A2) B2) (@ (@ tptp.ord_le527798542nres_b B2) A2)))) (= (lambda ((Y5 tptp.refine424419629nres_a) (Z tptp.refine424419629nres_a)) (= Y5 Z)) (lambda ((A2 tptp.refine424419629nres_a) (B2 tptp.refine424419629nres_a)) (and (@ (@ tptp.ord_le519537037nres_a A2) B2) (@ (@ tptp.ord_le519537037nres_a B2) A2)))) (forall ((Y3 tptp.refine432681134nres_b) (X4 tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b Y3) X4) (= (@ (@ tptp.ord_le527798542nres_b X4) Y3) (= X4 Y3)))) (forall ((Y3 tptp.refine424419629nres_a) (X4 tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a Y3) X4) (= (@ (@ tptp.ord_le519537037nres_a X4) Y3) (= X4 Y3)))) (forall ((A tptp.refine432681134nres_b) (B tptp.refine432681134nres_b) (C tptp.refine432681134nres_b)) (let ((_let_1 (@ tptp.ord_le527798542nres_b A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le527798542nres_b B) C) (@ _let_1 C))))) (forall ((A tptp.refine424419629nres_a) (B tptp.refine424419629nres_a) (C tptp.refine424419629nres_a)) (let ((_let_1 (@ tptp.ord_le519537037nres_a A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le519537037nres_a B) C) (@ _let_1 C))))) (forall ((X4 tptp.refine432681134nres_b) (Y3 tptp.refine432681134nres_b)) (=> (= X4 Y3) (@ (@ tptp.ord_le527798542nres_b X4) Y3))) (forall ((X4 tptp.refine424419629nres_a) (Y3 tptp.refine424419629nres_a)) (=> (= X4 Y3) (@ (@ tptp.ord_le519537037nres_a X4) Y3))) (forall ((X4 tptp.refine432681134nres_b) (Y3 tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b X4) Y3) (=> (@ (@ tptp.ord_le527798542nres_b Y3) X4) (= X4 Y3)))) (forall ((X4 tptp.refine424419629nres_a) (Y3 tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a X4) Y3) (=> (@ (@ tptp.ord_le519537037nres_a Y3) X4) (= X4 Y3)))) _let_20 (forall ((A tptp.b) (P (-> tptp.b Bool))) (= (@ (@ tptp.member_b A) (@ tptp.collect_b P)) (@ P A))) (forall ((A3 tptp.set_a)) (= (@ tptp.collect_a (lambda ((X5 tptp.a)) (@ (@ tptp.member_a X5) A3))) A3)) (forall ((A3 tptp.set_b)) (= (@ tptp.collect_b (lambda ((X5 tptp.b)) (@ (@ tptp.member_b X5) A3))) A3)) (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (=> (forall ((X3 tptp.a)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_a P) (@ tptp.collect_a Q)))) (forall ((P (-> tptp.b Bool)) (Q (-> tptp.b Bool))) (=> (forall ((X3 tptp.b)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_b P) (@ tptp.collect_b Q)))) (= (lambda ((Y5 tptp.refine432681134nres_b) (Z tptp.refine432681134nres_b)) (= Y5 Z)) (lambda ((X5 tptp.refine432681134nres_b) (Y6 tptp.refine432681134nres_b)) (and (@ (@ tptp.ord_le527798542nres_b X5) Y6) (@ (@ tptp.ord_le527798542nres_b Y6) X5)))) (= (lambda ((Y5 tptp.refine424419629nres_a) (Z tptp.refine424419629nres_a)) (= Y5 Z)) (lambda ((X5 tptp.refine424419629nres_a) (Y6 tptp.refine424419629nres_a)) (and (@ (@ tptp.ord_le519537037nres_a X5) Y6) (@ (@ tptp.ord_le519537037nres_a Y6) X5)))) (forall ((A tptp.refine432681134nres_b) (B tptp.refine432681134nres_b) (F (-> tptp.refine432681134nres_b tptp.refine432681134nres_b)) (C tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.refine432681134nres_b) (Y4 tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b X3) Y4) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le527798542nres_b (@ F A)) C))))) (forall ((A tptp.refine432681134nres_b) (B tptp.refine432681134nres_b) (F (-> tptp.refine432681134nres_b tptp.refine424419629nres_a)) (C tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le527798542nres_b A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.refine432681134nres_b) (Y4 tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b X3) Y4) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le519537037nres_a (@ F A)) C))))) (forall ((A tptp.refine424419629nres_a) (B tptp.refine424419629nres_a) (F (-> tptp.refine424419629nres_a tptp.refine432681134nres_b)) (C tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le519537037nres_a A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.refine424419629nres_a) (Y4 tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a X3) Y4) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le527798542nres_b (@ F A)) C))))) (forall ((A tptp.refine424419629nres_a) (B tptp.refine424419629nres_a) (F (-> tptp.refine424419629nres_a tptp.refine424419629nres_a)) (C tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.refine424419629nres_a) (Y4 tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a X3) Y4) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le519537037nres_a (@ F A)) C))))) (forall ((A tptp.refine432681134nres_b) (F (-> tptp.refine432681134nres_b tptp.refine432681134nres_b)) (B tptp.refine432681134nres_b) (C tptp.refine432681134nres_b)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le527798542nres_b B) C) (=> (forall ((X3 tptp.refine432681134nres_b) (Y4 tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b X3) Y4) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le527798542nres_b A) (@ F C)))))) (forall ((A tptp.refine424419629nres_a) (F (-> tptp.refine432681134nres_b tptp.refine424419629nres_a)) (B tptp.refine432681134nres_b) (C tptp.refine432681134nres_b)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le527798542nres_b B) C) (=> (forall ((X3 tptp.refine432681134nres_b) (Y4 tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b X3) Y4) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le519537037nres_a A) (@ F C)))))) (forall ((A tptp.refine432681134nres_b) (F (-> tptp.refine424419629nres_a tptp.refine432681134nres_b)) (B tptp.refine424419629nres_a) (C tptp.refine424419629nres_a)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le519537037nres_a B) C) (=> (forall ((X3 tptp.refine424419629nres_a) (Y4 tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a X3) Y4) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le527798542nres_b A) (@ F C)))))) (forall ((A tptp.refine424419629nres_a) (F (-> tptp.refine424419629nres_a tptp.refine424419629nres_a)) (B tptp.refine424419629nres_a) (C tptp.refine424419629nres_a)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_le519537037nres_a B) C) (=> (forall ((X3 tptp.refine424419629nres_a) (Y4 tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a X3) Y4) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le519537037nres_a A) (@ F C)))))) (forall ((A tptp.refine432681134nres_b) (B tptp.refine432681134nres_b) (F (-> tptp.refine432681134nres_b tptp.refine432681134nres_b)) (C tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b A) B) (=> (@ (@ tptp.ord_le527798542nres_b (@ F B)) C) (=> (forall ((X3 tptp.refine432681134nres_b) (Y4 tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b X3) Y4) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le527798542nres_b (@ F A)) C))))) (forall ((A tptp.refine432681134nres_b) (B tptp.refine432681134nres_b) (F (-> tptp.refine432681134nres_b tptp.refine424419629nres_a)) (C tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le527798542nres_b A) B) (=> (@ (@ tptp.ord_le519537037nres_a (@ F B)) C) (=> (forall ((X3 tptp.refine432681134nres_b) (Y4 tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b X3) Y4) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le519537037nres_a (@ F A)) C))))) (forall ((A tptp.refine424419629nres_a) (B tptp.refine424419629nres_a) (F (-> tptp.refine424419629nres_a tptp.refine432681134nres_b)) (C tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le519537037nres_a A) B) (=> (@ (@ tptp.ord_le527798542nres_b (@ F B)) C) (=> (forall ((X3 tptp.refine424419629nres_a) (Y4 tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a X3) Y4) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le527798542nres_b (@ F A)) C))))) (forall ((A tptp.refine424419629nres_a) (B tptp.refine424419629nres_a) (F (-> tptp.refine424419629nres_a tptp.refine424419629nres_a)) (C tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a A) B) (=> (@ (@ tptp.ord_le519537037nres_a (@ F B)) C) (=> (forall ((X3 tptp.refine424419629nres_a) (Y4 tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a X3) Y4) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ F Y4)))) (@ (@ tptp.ord_le519537037nres_a (@ F A)) C))))) (forall ((M tptp.refine424419629nres_a)) (=> (@ tptp.refine412683989fail_a M) (= (@ tptp.refine1198353288_RES_a (@ tptp.refine1822134885_RES_a M)) M))) (forall ((M tptp.refine432681134nres_b)) (=> (@ tptp.refine412683990fail_b M) (= (@ tptp.refine1198353289_RES_b (@ tptp.refine1822134886_RES_b M)) M))) (forall ((P (-> tptp.refine432681134nres_b Bool)) (X4 tptp.refine432681134nres_b)) (=> (@ P X4) (=> (forall ((Y4 tptp.refine432681134nres_b)) (=> (@ P Y4) (@ (@ tptp.ord_le527798542nres_b Y4) X4))) (= (@ tptp.order_1722590613nres_b P) X4)))) (forall ((P (-> tptp.refine424419629nres_a Bool)) (X4 tptp.refine424419629nres_a)) (=> (@ P X4) (=> (forall ((Y4 tptp.refine424419629nres_a)) (=> (@ P Y4) (@ (@ tptp.ord_le519537037nres_a Y4) X4))) (= (@ tptp.order_1714329108nres_a P) X4)))) (forall ((P (-> tptp.refine432681134nres_b Bool)) (X4 tptp.refine432681134nres_b) (Q (-> tptp.refine432681134nres_b Bool))) (=> (@ P X4) (=> (forall ((Y4 tptp.refine432681134nres_b)) (=> (@ P Y4) (@ (@ tptp.ord_le527798542nres_b Y4) X4))) (=> (forall ((X3 tptp.refine432681134nres_b)) (=> (@ P X3) (=> (forall ((Y7 tptp.refine432681134nres_b)) (=> (@ P Y7) (@ (@ tptp.ord_le527798542nres_b Y7) X3))) (@ Q X3)))) (@ Q (@ tptp.order_1722590613nres_b P)))))) (forall ((P (-> tptp.refine424419629nres_a Bool)) (X4 tptp.refine424419629nres_a) (Q (-> tptp.refine424419629nres_a Bool))) (=> (@ P X4) (=> (forall ((Y4 tptp.refine424419629nres_a)) (=> (@ P Y4) (@ (@ tptp.ord_le519537037nres_a Y4) X4))) (=> (forall ((X3 tptp.refine424419629nres_a)) (=> (@ P X3) (=> (forall ((Y7 tptp.refine424419629nres_a)) (=> (@ P Y7) (@ (@ tptp.ord_le519537037nres_a Y7) X3))) (@ Q X3)))) (@ Q (@ tptp.order_1714329108nres_a P)))))) _let_19 _let_18 (forall ((A tptp.refine432681134nres_b) (B tptp.refine432681134nres_b) (C tptp.refine432681134nres_b) (D tptp.refine432681134nres_b)) (=> (= A B) (=> (@ (@ tptp.ord_le527798542nres_b B) C) (=> (= C D) (@ (@ tptp.ord_le527798542nres_b A) D))))) (forall ((A tptp.refine424419629nres_a) (B tptp.refine424419629nres_a) (C tptp.refine424419629nres_a) (D tptp.refine424419629nres_a)) (=> (= A B) (=> (@ (@ tptp.ord_le519537037nres_a B) C) (=> (= C D) (@ (@ tptp.ord_le519537037nres_a A) D))))) (forall ((X tptp.set_a)) (@ tptp.refine412683989fail_a (@ tptp.refine1198353288_RES_a X))) (forall ((X tptp.set_b)) (@ tptp.refine412683990fail_b (@ tptp.refine1198353289_RES_b X))) (forall ((S tptp.set_a) (P (-> tptp.a Bool))) (= (@ (@ tptp.ord_less_eq_set_a S) (@ tptp.collect_a P)) (forall ((X5 tptp.a)) (=> (@ (@ tptp.member_a X5) S) (@ P X5))))) (forall ((S tptp.set_b) (P (-> tptp.b Bool))) (= (@ (@ tptp.ord_less_eq_set_b S) (@ tptp.collect_b P)) (forall ((X5 tptp.b)) (=> (@ (@ tptp.member_b X5) S) (@ P X5))))) (forall ((S tptp.refine432681134nres_b) (S3 tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b S) S3) (=> (@ tptp.refine412683990fail_b S3) (@ tptp.refine412683990fail_b S)))) (forall ((S tptp.refine424419629nres_a) (S3 tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a S) S3) (=> (@ tptp.refine412683989fail_a S3) (@ tptp.refine412683989fail_a S)))) (forall ((M3 tptp.refine432681134nres_b) (M4 tptp.refine432681134nres_b)) (let ((_let_1 (@ (@ tptp.ord_le527798542nres_b M4) M3))) (=> (=> (@ tptp.refine412683990fail_b M3) _let_1) _let_1))) (forall ((M3 tptp.refine424419629nres_a) (M4 tptp.refine424419629nres_a)) (let ((_let_1 (@ (@ tptp.ord_le519537037nres_a M4) M3))) (=> (=> (@ tptp.refine412683989fail_a M3) _let_1) _let_1))) _let_17 _let_16 (forall ((A3 tptp.refine432681134nres_b) (R tptp.set_Product_prod_b_b) (B3 tptp.refine432681134nres_b) (C2 tptp.refine432681134nres_b)) (let ((_let_1 (@ tptp.refine122110613un_b_b R))) (let ((_let_2 (@ tptp.ord_le527798542nres_b A3))) (=> (@ _let_2 (@ _let_1 B3)) (=> (@ (@ tptp.ord_le527798542nres_b B3) C2) (@ _let_2 (@ _let_1 C2))))))) (forall ((A3 tptp.refine432681134nres_b) (R tptp.set_Product_prod_b_a) (B3 tptp.refine424419629nres_a) (C2 tptp.refine424419629nres_a)) (let ((_let_1 (@ tptp.refine122110612un_b_a R))) (let ((_let_2 (@ tptp.ord_le527798542nres_b A3))) (=> (@ _let_2 (@ _let_1 B3)) (=> (@ (@ tptp.ord_le519537037nres_a B3) C2) (@ _let_2 (@ _let_1 C2))))))) (forall ((A3 tptp.refine424419629nres_a) (R tptp.set_Product_prod_a_b) (B3 tptp.refine432681134nres_b) (C2 tptp.refine432681134nres_b)) (let ((_let_1 (@ tptp.refine1441824854un_a_b R))) (let ((_let_2 (@ tptp.ord_le519537037nres_a A3))) (=> (@ _let_2 (@ 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tptp.refine432681134nres_b))) (let ((_let_1 (@ tptp.refine122110613un_b_b R))) (let ((_let_2 (@ tptp.ord_le527798542nres_b M))) (=> (@ Phi X7) (=> (@ _let_2 (@ _let_1 (@ F2 X7))) (@ _let_2 (@ _let_1 (@ (@ tptp.refine436832839nd_a_b (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi))) F2)))))))) (forall ((Phi (-> tptp.a Bool)) (X7 tptp.a) (M tptp.refine424419629nres_a) (R tptp.set_Product_prod_a_b) (F2 (-> tptp.a tptp.refine432681134nres_b))) (let ((_let_1 (@ tptp.refine1441824854un_a_b R))) (let ((_let_2 (@ tptp.ord_le519537037nres_a M))) (=> (@ Phi X7) (=> (@ _let_2 (@ _let_1 (@ F2 X7))) (@ _let_2 (@ _let_1 (@ (@ tptp.refine436832839nd_a_b (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi))) F2)))))))) (forall ((A3 tptp.set_a) (B3 tptp.set_a)) (=> (forall ((X3 tptp.a)) (let ((_let_1 (@ tptp.member_a X3))) (=> (@ _let_1 A3) (@ _let_1 B3)))) (@ (@ tptp.ord_less_eq_set_a A3) B3))) (forall ((A3 tptp.set_b) (B3 tptp.set_b)) (=> (forall ((X3 tptp.b)) (let ((_let_1 (@ tptp.member_b X3))) (=> (@ _let_1 A3) (@ _let_1 B3)))) (@ (@ tptp.ord_less_eq_set_b A3) B3))) (forall ((M tptp.refine424419629nres_a) (F2 (-> tptp.a tptp.refine424419629nres_a)) (Psi (-> tptp.a Bool)) (F (-> tptp.a tptp.refine432681134nres_b)) (Phi (-> tptp.b Bool))) (=> (@ (@ tptp.ord_le519537037nres_a (@ (@ tptp.refine436832838nd_a_a M) F2)) (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Psi))) (=> (forall ((X3 tptp.a)) (=> (@ tptp.refine412683989fail_a M) (=> (@ (@ tptp.refine1001002027nres_a M) X3) (=> (@ (@ tptp.ord_le519537037nres_a (@ F2 X3)) (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Psi))) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi))))))) (@ (@ tptp.ord_le527798542nres_b (@ (@ tptp.refine436832839nd_a_b M) F)) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi)))))) (forall ((M tptp.refine424419629nres_a) (F2 (-> tptp.a tptp.refine432681134nres_b)) (Psi (-> tptp.b Bool)) (F (-> tptp.a tptp.refine424419629nres_a)) (Phi (-> tptp.a Bool))) (=> (@ (@ tptp.ord_le527798542nres_b (@ (@ tptp.refine436832839nd_a_b M) F2)) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Psi))) (=> (forall ((X3 tptp.a)) (=> (@ tptp.refine412683989fail_a M) (=> (@ (@ tptp.refine1001002027nres_a M) X3) (=> (@ (@ tptp.ord_le527798542nres_b (@ F2 X3)) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Psi))) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi))))))) (@ (@ tptp.ord_le519537037nres_a (@ (@ tptp.refine436832838nd_a_a M) F)) (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi)))))) (forall ((M tptp.refine424419629nres_a) (F2 (-> tptp.a tptp.refine432681134nres_b)) (Psi (-> tptp.b Bool)) (F (-> tptp.a tptp.refine432681134nres_b)) (Phi (-> tptp.b Bool))) (let ((_let_1 (@ tptp.refine436832839nd_a_b M))) (=> (@ (@ tptp.ord_le527798542nres_b (@ _let_1 F2)) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Psi))) (=> (forall ((X3 tptp.a)) (=> (@ tptp.refine412683989fail_a M) (=> (@ (@ tptp.refine1001002027nres_a M) X3) (=> (@ (@ tptp.ord_le527798542nres_b (@ F2 X3)) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Psi))) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi))))))) (@ (@ tptp.ord_le527798542nres_b (@ _let_1 F)) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi))))))) (forall ((A3 tptp.set_a) (B3 tptp.set_a) (X4 tptp.a)) (let ((_let_1 (@ tptp.member_a X4))) (=> (@ (@ tptp.ord_less_eq_set_a A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))) (forall ((A3 tptp.set_b) (B3 tptp.set_b) (X4 tptp.b)) (let ((_let_1 (@ tptp.member_b X4))) (=> (@ (@ tptp.ord_less_eq_set_b A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))) (forall ((A3 tptp.set_a) (B3 tptp.set_a) (C tptp.a)) (let ((_let_1 (@ tptp.member_a C))) (=> (@ (@ tptp.ord_less_eq_set_a A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))) (forall ((A3 tptp.set_b) (B3 tptp.set_b) (C tptp.b)) (let ((_let_1 (@ tptp.member_b C))) (=> (@ (@ tptp.ord_less_eq_set_b A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))) _let_15 (forall ((X tptp.set_b)) (= (@ tptp.refine1001002028nres_b (@ tptp.refine1198353289_RES_b X)) (lambda ((X5 tptp.b)) (@ (@ tptp.member_b X5) X)))) (forall ((S tptp.refine432681134nres_b) (S3 tptp.refine432681134nres_b) (X4 tptp.b)) (=> (@ (@ tptp.ord_le527798542nres_b S) S3) (=> (@ (@ tptp.refine1001002028nres_b S) X4) (@ (@ tptp.refine1001002028nres_b S3) X4)))) (forall ((S tptp.refine424419629nres_a) (S3 tptp.refine424419629nres_a) (X4 tptp.a)) (=> (@ (@ tptp.ord_le519537037nres_a S) S3) (=> (@ (@ tptp.refine1001002027nres_a S) X4) (@ (@ tptp.refine1001002027nres_a S3) X4)))) _let_14 (forall ((S3 tptp.refine432681134nres_b) (S tptp.refine432681134nres_b)) (=> (=> (@ tptp.refine412683990fail_b S3) (and (@ tptp.refine412683990fail_b S) (forall ((X3 tptp.b)) (=> (@ (@ tptp.refine1001002028nres_b S) X3) (@ (@ tptp.refine1001002028nres_b S3) X3))))) (@ (@ tptp.ord_le527798542nres_b S) S3))) (forall ((S3 tptp.refine424419629nres_a) (S tptp.refine424419629nres_a)) (=> (=> (@ tptp.refine412683989fail_a S3) (and (@ tptp.refine412683989fail_a S) (forall ((X3 tptp.a)) (=> (@ (@ tptp.refine1001002027nres_a S) X3) (@ (@ tptp.refine1001002027nres_a S3) X3))))) (@ (@ tptp.ord_le519537037nres_a S) S3))) (forall ((S3 tptp.refine432681134nres_b) (S tptp.refine432681134nres_b)) (=> (=> (@ tptp.refine412683990fail_b S3) (@ tptp.refine412683990fail_b S)) (=> (forall ((X3 tptp.b)) (=> (@ tptp.refine412683990fail_b S3) (=> (@ (@ tptp.refine1001002028nres_b S) X3) (@ (@ tptp.refine1001002028nres_b S3) X3)))) (@ (@ tptp.ord_le527798542nres_b S) S3)))) (forall ((S3 tptp.refine424419629nres_a) (S tptp.refine424419629nres_a)) (=> (=> (@ tptp.refine412683989fail_a S3) (@ tptp.refine412683989fail_a S)) (=> (forall ((X3 tptp.a)) (=> (@ tptp.refine412683989fail_a S3) (=> (@ (@ tptp.refine1001002027nres_a S) X3) (@ (@ tptp.refine1001002027nres_a S3) X3)))) (@ (@ tptp.ord_le519537037nres_a S) S3)))) _let_13 _let_12 _let_11 (forall ((M4 tptp.refine424419629nres_a) (F (-> tptp.a tptp.refine432681134nres_b)) (S tptp.refine432681134nres_b)) (= (@ (@ tptp.ord_le527798542nres_b (@ (@ tptp.refine436832839nd_a_b M4) F)) S) (and (=> (@ tptp.refine412683990fail_b S) (@ tptp.refine412683989fail_a M4)) (forall ((X5 tptp.a)) (=> (and (@ tptp.refine412683989fail_a M4) (@ (@ tptp.refine1001002027nres_a M4) X5)) (@ (@ tptp.ord_le527798542nres_b (@ F X5)) S)))))) (forall ((S tptp.refine432681134nres_b) (M4 tptp.refine424419629nres_a) (F (-> tptp.a tptp.refine432681134nres_b))) (=> (=> (@ tptp.refine412683990fail_b S) (@ tptp.refine412683989fail_a M4)) (=> (forall ((X3 tptp.a)) (=> (@ tptp.refine412683989fail_a M4) (=> (@ (@ tptp.refine1001002027nres_a M4) X3) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) S)))) (@ (@ tptp.ord_le527798542nres_b (@ (@ tptp.refine436832839nd_a_b M4) F)) S)))) (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (= (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a P)) (@ tptp.collect_a Q)) (forall ((X5 tptp.a)) (=> (@ P X5) (@ Q X5))))) (forall ((P (-> tptp.b Bool)) (Q (-> tptp.b Bool))) (= (@ (@ tptp.ord_less_eq_set_b (@ tptp.collect_b P)) (@ tptp.collect_b Q)) (forall ((X5 tptp.b)) (=> (@ P X5) (@ Q X5))))) (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (=> (forall ((X3 tptp.a)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_less_eq_set_a (@ tptp.collect_a P)) (@ tptp.collect_a Q)))) (forall ((P (-> tptp.b Bool)) (Q (-> tptp.b Bool))) (=> (forall ((X3 tptp.b)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_less_eq_set_b (@ tptp.collect_b P)) (@ tptp.collect_b Q)))) _let_10 _let_9 (= tptp.ord_less_eq_set_a (lambda ((A4 tptp.set_a) (B4 tptp.set_a)) (forall ((X5 tptp.a)) (let ((_let_1 (@ tptp.member_a X5))) (=> (@ _let_1 A4) (@ _let_1 B4)))))) (= tptp.ord_less_eq_set_b (lambda ((A4 tptp.set_b) (B4 tptp.set_b)) (forall ((X5 tptp.b)) (let ((_let_1 (@ tptp.member_b X5))) (=> (@ _let_1 A4) (@ _let_1 B4)))))) (forall ((M tptp.refine432681134nres_b) (R tptp.set_Product_prod_b_a) (M7 tptp.refine424419629nres_a) (X4 tptp.b) (Lhs tptp.refine432681134nres_b) (S tptp.set_Product_prod_b_b) (F2 (-> tptp.a tptp.refine432681134nres_b))) (=> (@ (@ tptp.ord_le527798542nres_b M) (@ (@ tptp.refine122110612un_b_a R) M7)) (=> (@ (@ tptp.refine1001002028nres_b M) X4) (=> (forall ((X9 tptp.a)) (=> (@ (@ tptp.member1277678991od_b_a (@ (@ tptp.product_Pair_b_a X4) X9)) R) (@ (@ tptp.ord_le527798542nres_b Lhs) (@ (@ tptp.refine122110613un_b_b S) (@ F2 X9))))) (@ (@ tptp.ord_le527798542nres_b Lhs) (@ (@ tptp.refine122110613un_b_b S) (@ (@ tptp.refine436832839nd_a_b M7) F2))))))) (forall ((M tptp.refine432681134nres_b) (R tptp.set_Product_prod_b_a) (M7 tptp.refine424419629nres_a) (X4 tptp.b) (Lhs tptp.refine424419629nres_a) (S tptp.set_Product_prod_a_b) (F2 (-> tptp.a tptp.refine432681134nres_b))) (=> (@ (@ tptp.ord_le527798542nres_b M) (@ (@ tptp.refine122110612un_b_a R) M7)) (=> (@ (@ tptp.refine1001002028nres_b M) X4) (=> (forall ((X9 tptp.a)) (=> (@ (@ tptp.member1277678991od_b_a (@ (@ tptp.product_Pair_b_a X4) X9)) R) (@ (@ tptp.ord_le519537037nres_a Lhs) (@ (@ tptp.refine1441824854un_a_b S) (@ F2 X9))))) (@ (@ tptp.ord_le519537037nres_a Lhs) (@ (@ tptp.refine1441824854un_a_b S) (@ (@ tptp.refine436832839nd_a_b M7) F2))))))) (forall ((M tptp.refine424419629nres_a) (R tptp.set_Product_prod_a_a) (M7 tptp.refine424419629nres_a) (X4 tptp.a) (Lhs tptp.refine432681134nres_b) (S tptp.set_Product_prod_b_b) (F2 (-> tptp.a tptp.refine432681134nres_b))) (=> (@ (@ tptp.ord_le519537037nres_a M) (@ (@ tptp.refine1441824853un_a_a R) M7)) (=> (@ (@ tptp.refine1001002027nres_a M) X4) (=> (forall ((X9 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) X9)) R) (@ (@ tptp.ord_le527798542nres_b Lhs) (@ (@ tptp.refine122110613un_b_b S) (@ F2 X9))))) (@ (@ tptp.ord_le527798542nres_b Lhs) (@ (@ tptp.refine122110613un_b_b S) (@ (@ tptp.refine436832839nd_a_b M7) F2))))))) (forall ((M tptp.refine424419629nres_a) (R tptp.set_Product_prod_a_a) (M7 tptp.refine424419629nres_a) (X4 tptp.a) (Lhs 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tptp.set_Product_prod_a_b)) (=> (forall ((S6 tptp.a)) (=> (@ (@ tptp.member_a S6) S) (exists ((X10 tptp.b)) (and (@ (@ tptp.member_b X10) S3) (@ (@ tptp.member458171089od_a_b (@ (@ tptp.product_Pair_a_b S6) X10)) R))))) (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine1198353288_RES_a S)) (@ (@ tptp.refine1441824854un_a_b R) (@ tptp.refine1198353289_RES_b S3))))) (forall ((S tptp.set_b) (S3 tptp.set_a) (R tptp.set_Product_prod_b_a)) (=> (forall ((S6 tptp.b)) (=> (@ (@ tptp.member_b S6) S) (exists ((X10 tptp.a)) (and (@ (@ tptp.member_a X10) S3) (@ (@ tptp.member1277678991od_b_a (@ (@ tptp.product_Pair_b_a S6) X10)) R))))) (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine1198353289_RES_b S)) (@ (@ tptp.refine122110612un_b_a R) (@ tptp.refine1198353288_RES_a S3))))) (forall ((S tptp.set_b) (S3 tptp.set_b) (R tptp.set_Product_prod_b_b)) (=> (forall ((S6 tptp.b)) (=> (@ (@ tptp.member_b S6) S) (exists ((X10 tptp.b)) (and (@ (@ tptp.member_b X10) S3) (@ (@ tptp.member1285940496od_b_b (@ (@ 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(=> (@ tptp.refine412683990fail_b M) (=> (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X4)) (@ (@ tptp.refine1441824854un_a_b R) M)) (not (forall ((X9 tptp.b)) (=> (@ (@ tptp.member458171089od_a_b (@ (@ tptp.product_Pair_a_b X4) X9)) R) (not (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b X9)) M)))))))) (forall ((M tptp.refine424419629nres_a) (X4 tptp.a) (R tptp.set_Product_prod_a_a)) (=> (@ tptp.refine412683989fail_a M) (=> (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X4)) (@ (@ tptp.refine1441824853un_a_a R) M)) (not (forall ((X9 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) X9)) R) (not (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X9)) M)))))))) (forall ((M tptp.refine432681134nres_b) (C tptp.b) (R tptp.set_Product_prod_b_b)) (=> (@ tptp.refine412683990fail_b M) (= (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b C)) (@ (@ tptp.refine122110613un_b_b R) M)) (exists 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tptp.refine432681134nres_b) (M3 tptp.refine432681134nres_b) (F (-> tptp.b tptp.refine432681134nres_b)) (F2 (-> tptp.b tptp.refine432681134nres_b))) (=> (@ (@ tptp.ord_le527798542nres_b M4) M3) (=> (forall ((X3 tptp.b)) (=> (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b X3)) M4) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ F2 X3)))) (@ (@ tptp.ord_le527798542nres_b (@ (@ tptp.refine1264602246nd_b_b M4) F)) (@ (@ tptp.refine1264602246nd_b_b M3) F2))))) (forall ((M4 tptp.refine432681134nres_b) (M3 tptp.refine432681134nres_b) (F (-> tptp.b tptp.refine424419629nres_a)) (F2 (-> tptp.b tptp.refine424419629nres_a))) (=> (@ (@ tptp.ord_le527798542nres_b M4) M3) (=> (forall ((X3 tptp.b)) (=> (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b X3)) M4) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ F2 X3)))) (@ (@ tptp.ord_le519537037nres_a (@ (@ tptp.refine1264602245nd_b_a M4) F)) (@ (@ tptp.refine1264602245nd_b_a M3) F2))))) (forall ((M4 tptp.refine424419629nres_a) (M3 tptp.refine424419629nres_a) (F (-> tptp.a tptp.refine424419629nres_a)) (F2 (-> tptp.a tptp.refine424419629nres_a))) (=> (@ (@ tptp.ord_le519537037nres_a M4) M3) (=> (forall ((X3 tptp.a)) (=> (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X3)) M4) (@ (@ tptp.ord_le519537037nres_a (@ F X3)) (@ F2 X3)))) (@ (@ tptp.ord_le519537037nres_a (@ (@ tptp.refine436832838nd_a_a M4) F)) (@ (@ tptp.refine436832838nd_a_a M3) F2))))) (forall ((M4 tptp.refine424419629nres_a) (M3 tptp.refine424419629nres_a) (F (-> tptp.a tptp.refine432681134nres_b)) (F2 (-> tptp.a tptp.refine432681134nres_b))) (=> (@ (@ tptp.ord_le519537037nres_a M4) M3) (=> (forall ((X3 tptp.a)) (=> (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X3)) M4) (@ (@ tptp.ord_le527798542nres_b (@ F X3)) (@ F2 X3)))) (@ (@ tptp.ord_le527798542nres_b (@ (@ tptp.refine436832839nd_a_b M4) F)) (@ (@ tptp.refine436832839nd_a_b M3) F2))))) (forall ((M tptp.refine424419629nres_a) (M7 tptp.refine424419629nres_a) (F (-> tptp.a tptp.refine432681134nres_b)) (F2 (-> tptp.a tptp.refine432681134nres_b))) (=> (= M M7) (=> (forall ((X3 tptp.a)) (=> (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X3)) M7) (= (@ F X3) (@ F2 X3)))) (= (@ (@ tptp.refine436832839nd_a_b M) F) (@ (@ tptp.refine436832839nd_a_b M7) F2))))) (= tptp.refine1001002028nres_b (lambda ((S4 tptp.refine432681134nres_b) (X5 tptp.b)) (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b X5)) S4))) (= tptp.refine1001002027nres_a (lambda ((S4 tptp.refine424419629nres_a) (X5 tptp.a)) (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X5)) S4))) (forall ((C tptp.b) (R tptp.set_Product_prod_b_a) (Phi (-> tptp.a Bool))) (=> (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b C)) (@ (@ tptp.refine122110612un_b_a R) (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi)))) (not (forall ((A5 tptp.a)) (=> (@ (@ tptp.member1277678991od_b_a (@ (@ tptp.product_Pair_b_a C) A5)) R) (not (@ Phi A5))))))) (forall ((C tptp.a) (R tptp.set_Product_prod_a_a) (Phi (-> tptp.a Bool))) (=> (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a C)) (@ (@ tptp.refine1441824853un_a_a R) (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi)))) (not (forall ((A5 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a C) A5)) R) (not (@ Phi A5))))))) (forall ((C tptp.b) (R tptp.set_Product_prod_b_b) (Phi (-> tptp.b Bool))) (=> (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b C)) (@ (@ tptp.refine122110613un_b_b R) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi)))) (not (forall ((A5 tptp.b)) (=> (@ (@ tptp.member1285940496od_b_b (@ (@ tptp.product_Pair_b_b C) A5)) R) (not (@ Phi A5))))))) (forall ((C tptp.a) (R tptp.set_Product_prod_a_b) (Phi (-> tptp.b Bool))) (=> (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a C)) (@ (@ tptp.refine1441824854un_a_b R) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi)))) (not (forall ((A5 tptp.b)) (=> (@ (@ tptp.member458171089od_a_b (@ (@ tptp.product_Pair_a_b C) A5)) R) (not (@ Phi A5))))))) (forall ((X4 tptp.b) (R tptp.set_Product_prod_b_a) (Phi (-> tptp.a Bool))) (=> (exists ((X11 tptp.a)) (and (@ (@ tptp.member1277678991od_b_a (@ (@ tptp.product_Pair_b_a X4) X11)) R) (@ Phi X11))) (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b X4)) (@ (@ tptp.refine122110612un_b_a R) (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi)))))) (forall ((X4 tptp.a) (R tptp.set_Product_prod_a_a) (Phi (-> tptp.a Bool))) (=> (exists ((X11 tptp.a)) (and (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X4) X11)) R) (@ Phi X11))) (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X4)) (@ (@ tptp.refine1441824853un_a_a R) (@ tptp.refine1198353288_RES_a (@ tptp.collect_a Phi)))))) (forall ((X4 tptp.b) (R tptp.set_Product_prod_b_b) (Phi (-> tptp.b Bool))) (=> (exists ((X11 tptp.b)) (and (@ (@ tptp.member1285940496od_b_b (@ (@ tptp.product_Pair_b_b X4) X11)) R) (@ Phi X11))) (@ (@ tptp.ord_le527798542nres_b (@ tptp.refine2063221605TURN_b X4)) (@ (@ tptp.refine122110613un_b_b R) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi)))))) (forall ((X4 tptp.a) (R tptp.set_Product_prod_a_b) (Phi (-> tptp.b Bool))) (=> (exists ((X11 tptp.b)) (and (@ (@ tptp.member458171089od_a_b (@ (@ tptp.product_Pair_a_b X4) X11)) R) (@ Phi X11))) (@ (@ tptp.ord_le519537037nres_a (@ tptp.refine2063221604TURN_a X4)) (@ (@ tptp.refine1441824854un_a_b R) (@ tptp.refine1198353289_RES_b (@ tptp.collect_b Phi)))))) (forall ((A3 tptp.refine432681134nres_b) (B3 tptp.refine432681134nres_b) (R tptp.set_Product_prod_b_b) (C2 tptp.refine432681134nres_b)) (let ((_let_1 (@ tptp.refine1964549110un_b_b R))) (=> (@ (@ tptp.ord_le527798542nres_b A3) B3) (=> (@ (@ tptp.ord_le527798542nres_b (@ _let_1 B3)) C2) (@ (@ tptp.ord_le527798542nres_b (@ _let_1 A3)) C2))))) (forall ((A3 tptp.refine432681134nres_b) (B3 tptp.refine432681134nres_b) (R tptp.set_Product_prod_b_a) (C2 tptp.refine424419629nres_a)) (let ((_let_1 (@ tptp.refine1964549109un_b_a R))) (=> (@ (@ tptp.ord_le527798542nres_b A3) B3) (=> (@ (@ tptp.ord_le519537037nres_a (@ _let_1 B3)) C2) (@ (@ tptp.ord_le519537037nres_a (@ _let_1 A3)) C2))))) (forall ((A3 tptp.refine424419629nres_a) (B3 tptp.refine424419629nres_a) (R tptp.set_Product_prod_a_b) (C2 tptp.refine432681134nres_b)) (let ((_let_1 (@ tptp.refine1136779703un_a_b R))) (=> (@ (@ tptp.ord_le519537037nres_a A3) B3) (=> (@ (@ tptp.ord_le527798542nres_b (@ _let_1 B3)) C2) (@ (@ tptp.ord_le527798542nres_b (@ _let_1 A3)) C2))))) (forall ((A3 tptp.refine424419629nres_a) (B3 tptp.refine424419629nres_a) (R tptp.set_Product_prod_a_a) (C2 tptp.refine424419629nres_a)) (let ((_let_1 (@ tptp.refine1136779702un_a_a R))) (=> (@ (@ tptp.ord_le519537037nres_a A3) B3) (=> (@ (@ tptp.ord_le519537037nres_a (@ _let_1 B3)) C2) (@ (@ tptp.ord_le519537037nres_a (@ _let_1 A3)) C2))))) (forall ((X tptp.set_a) (R tptp.set_Pr1628433942t_unit)) (=> (not (@ (@ tptp.ord_less_eq_set_a X) (@ tptp.domain799550107t_unit R))) (= (@ (@ tptp.refine341651653t_unit R) (@ tptp.refine1198353288_RES_a X)) tptp.top_to177290092t_unit))) (forall ((X tptp.set_b) (R tptp.set_Pr1707992533t_unit)) (=> (not (@ (@ tptp.ord_less_eq_set_b X) (@ tptp.domain918802906t_unit R))) (= (@ (@ tptp.refine460904452t_unit R) (@ tptp.refine1198353289_RES_b X)) tptp.top_to177290092t_unit))) (forall ((X tptp.set_a) (R tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.ord_less_eq_set_a X) (@ tptp.domain_a_a R)) (= (@ (@ tptp.refine1136779702un_a_a R) (@ tptp.refine1198353288_RES_a X)) (@ tptp.refine1198353288_RES_a (@ (@ tptp.image_a_a R) X))))) (forall ((X tptp.set_a) (R tptp.set_Product_prod_a_b)) (=> (@ (@ tptp.ord_less_eq_set_a X) (@ tptp.domain_a_b R)) (= (@ (@ tptp.refine1136779703un_a_b R) (@ tptp.refine1198353288_RES_a X)) (@ tptp.refine1198353289_RES_b (@ (@ tptp.image_a_b R) X))))) (forall ((X tptp.set_b) (R tptp.set_Product_prod_b_a)) (=> (@ (@ tptp.ord_less_eq_set_b X) (@ tptp.domain_b_a R)) (= (@ (@ tptp.refine1964549109un_b_a R) (@ tptp.refine1198353289_RES_b X)) (@ tptp.refine1198353288_RES_a (@ (@ tptp.image_b_a R) X))))) (forall ((X tptp.set_b) (R tptp.set_Product_prod_b_b)) (=> (@ (@ tptp.ord_less_eq_set_b X) (@ tptp.domain_b_b R)) (= (@ (@ tptp.refine1964549110un_b_b R) (@ tptp.refine1198353289_RES_b X)) (@ tptp.refine1198353289_RES_b (@ (@ tptp.image_b_b R) X))))) (forall ((A tptp.a) (B tptp.a) (R2 tptp.set_Product_prod_a_a) (A3 tptp.set_a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A) B)) R2) (=> (@ (@ tptp.member_a A) A3) (@ (@ tptp.member_a B) (@ (@ tptp.image_a_a R2) A3))))) (forall ((A tptp.a) (B tptp.b) (R2 tptp.set_Product_prod_a_b) (A3 tptp.set_a)) (=> (@ (@ tptp.member458171089od_a_b (@ (@ tptp.product_Pair_a_b A) B)) R2) (=> (@ (@ tptp.member_a A) A3) (@ (@ tptp.member_b B) (@ (@ tptp.image_a_b R2) A3))))) (forall ((A tptp.b) (B tptp.a) (R2 tptp.set_Product_prod_b_a) (A3 tptp.set_b)) (=> (@ (@ tptp.member1277678991od_b_a (@ (@ tptp.product_Pair_b_a A) B)) R2) (=> (@ (@ tptp.member_b A) A3) (@ (@ tptp.member_a B) (@ (@ tptp.image_b_a R2) A3))))) (forall ((A tptp.b) (B tptp.b) (R2 tptp.set_Product_prod_b_b) (A3 tptp.set_b)) (=> (@ (@ tptp.member1285940496od_b_b (@ (@ tptp.product_Pair_b_b A) B)) R2) (=> (@ (@ tptp.member_b A) A3) (@ (@ tptp.member_b B) (@ (@ tptp.image_b_b R2) A3))))) (forall ((M4 tptp.refine787176636t_unit)) (= (@ (@ tptp.ord_le1051254044t_unit tptp.top_to177290092t_unit) M4) (= M4 tptp.top_to177290092t_unit))) (forall ((M4 tptp.refine432681134nres_b)) (= (@ (@ tptp.ord_le527798542nres_b tptp.top_to240090974nres_b) M4) (= M4 tptp.top_to240090974nres_b))) (forall ((M4 tptp.refine424419629nres_a)) (= (@ (@ tptp.ord_le519537037nres_a tptp.top_to231829469nres_a) M4) (= M4 tptp.top_to231829469nres_a))) (forall ((R tptp.set_Pr451126599t_unit)) (= (@ (@ tptp.refine944483349t_unit R) tptp.top_to177290092t_unit) tptp.top_to177290092t_unit)) (forall ((R tptp.set_Pr451126599t_unit) (S tptp.refine787176636t_unit)) (= (= (@ (@ tptp.refine944483349t_unit R) S) tptp.top_to177290092t_unit) (= S tptp.top_to177290092t_unit))) (forall ((R tptp.set_Pr451126599t_unit) (S tptp.refine787176636t_unit)) (= (= tptp.top_to177290092t_unit (@ (@ tptp.refine944483349t_unit R) S)) (= S tptp.top_to177290092t_unit))) (forall ((F (-> tptp.product_unit tptp.refine787176636t_unit))) (= (@ (@ tptp.refine681446406t_unit tptp.top_to177290092t_unit) F) tptp.top_to177290092t_unit)) (forall ((F (-> tptp.a tptp.refine432681134nres_b))) (= (@ (@ tptp.refine436832839nd_a_b tptp.top_to231829469nres_a) F) tptp.top_to240090974nres_b)) (not (@ tptp.refine579265252t_unit tptp.top_to177290092t_unit)) (= (@ tptp.refine558004794t_unit tptp.top_to177290092t_unit) (lambda ((Uu3 tptp.product_unit)) true)) (= tptp.refine1607584204t_unit tptp.top_to177290092t_unit) (forall ((R tptp.set_Pr451126599t_unit)) (= (@ (@ tptp.refine838861686t_unit R) tptp.top_to177290092t_unit) tptp.top_to177290092t_unit)) (forall ((X tptp.refine432681134nres_b) (R tptp.set_Pr1707992533t_unit)) (@ (@ tptp.ord_le527798542nres_b X) (@ (@ tptp.refine2140306339t_unit R) tptp.top_to177290092t_unit))) (forall ((X tptp.refine424419629nres_a) (R tptp.set_Pr1628433942t_unit)) (@ (@ tptp.ord_le519537037nres_a X) (@ (@ tptp.refine2021053540t_unit R) tptp.top_to177290092t_unit))) (forall ((A tptp.a) (A3 tptp.set_a) (B tptp.a) (R2 tptp.set_Product_prod_a_a)) (=> (@ (@ tptp.member_a A) A3) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a A) B)) R2) (@ (@ tptp.member_a B) (@ (@ tptp.image_a_a R2) A3))))) (forall ((A tptp.a) (A3 tptp.set_a) (B tptp.b) (R2 tptp.set_Product_prod_a_b)) (=> (@ (@ tptp.member_a A) A3) (=> (@ (@ tptp.member458171089od_a_b (@ (@ tptp.product_Pair_a_b A) B)) R2) (@ (@ tptp.member_b B) (@ (@ tptp.image_a_b R2) A3))))) (forall ((A tptp.b) (A3 tptp.set_b) (B tptp.a) (R2 tptp.set_Product_prod_b_a)) (=> (@ (@ tptp.member_b A) A3) (=> (@ (@ tptp.member1277678991od_b_a (@ (@ tptp.product_Pair_b_a A) B)) R2) (@ (@ tptp.member_a B) (@ (@ tptp.image_b_a R2) A3))))) (forall ((A tptp.b) (A3 tptp.set_b) (B tptp.b) (R2 tptp.set_Product_prod_b_b)) (=> (@ (@ tptp.member_b A) A3) (=> (@ (@ tptp.member1285940496od_b_b (@ (@ tptp.product_Pair_b_b A) B)) R2) (@ (@ tptp.member_b B) (@ (@ tptp.image_b_b R2) A3))))) (forall ((B tptp.a) (R2 tptp.set_Product_prod_a_a) (A3 tptp.set_a)) (=> (@ (@ tptp.member_a B) (@ (@ tptp.image_a_a R2) A3)) (not (forall ((X3 tptp.a)) (=> (@ (@ tptp.member449909584od_a_a (@ (@ tptp.product_Pair_a_a X3) B)) R2) (not (@ (@ tptp.member_a X3) A3))))))) (forall ((B tptp.a) (R2 tptp.set_Product_prod_b_a) (A3 tptp.set_b)) (=> (@ (@ tptp.member_a B) (@ (@ tptp.image_b_a R2) A3)) (not (forall ((X3 tptp.b)) (=> (@ (@ tptp.member1277678991od_b_a (@ (@ tptp.product_Pair_b_a X3) B)) R2) (not (@ (@ tptp.member_b X3) A3))))))) (forall ((B tptp.b) (R2 tptp.set_Product_prod_a_b) (A3 tptp.set_a)) (=> (@ (@ tptp.member_b B) (@ (@ tptp.image_a_b R2) A3)) (not (forall ((X3 tptp.a)) (=> (@ (@ tptp.member458171089od_a_b (@ (@ tptp.product_Pair_a_b X3) B)) R2) (not (@ (@ tptp.member_a X3) A3))))))) (forall ((B tptp.b) (R2 tptp.set_Product_prod_b_b) (A3 tptp.set_b)) (=> (@ (@ tptp.member_b B) (@ (@ tptp.image_b_b R2) A3)) (not (forall ((X3 tptp.b)) (=> (@ (@ tptp.member1285940496od_b_b (@ (@ tptp.product_Pair_b_b X3) B)) R2) (not (@ (@ tptp.member_b X3) A3))))))) (forall ((X4 tptp.product_unit)) (not (= tptp.top_to177290092t_unit (@ tptp.refine1420258419t_unit X4)))) _let_8 (forall ((A tptp.refine787176636t_unit)) (@ (@ tptp.ord_le1051254044t_unit A) tptp.top_to177290092t_unit)) (forall ((A tptp.refine432681134nres_b)) (@ (@ tptp.ord_le527798542nres_b A) tptp.top_to240090974nres_b)) (forall ((A tptp.refine424419629nres_a)) (@ (@ tptp.ord_le519537037nres_a A) tptp.top_to231829469nres_a)) (forall ((A tptp.refine787176636t_unit)) (= (@ (@ tptp.ord_le1051254044t_unit tptp.top_to177290092t_unit) A) (= A tptp.top_to177290092t_unit))) (forall ((A tptp.refine432681134nres_b)) (= (@ (@ tptp.ord_le527798542nres_b tptp.top_to240090974nres_b) A) (= A tptp.top_to240090974nres_b))) (forall ((A tptp.refine424419629nres_a)) (= (@ (@ tptp.ord_le519537037nres_a tptp.top_to231829469nres_a) A) (= A tptp.top_to231829469nres_a))) (forall ((A tptp.refine787176636t_unit)) (=> (@ (@ tptp.ord_le1051254044t_unit tptp.top_to177290092t_unit) A) (= A tptp.top_to177290092t_unit))) (forall ((A tptp.refine432681134nres_b)) (=> (@ (@ tptp.ord_le527798542nres_b tptp.top_to240090974nres_b) A) (= A tptp.top_to240090974nres_b))) (forall ((A tptp.refine424419629nres_a)) (=> (@ (@ tptp.ord_le519537037nres_a tptp.top_to231829469nres_a) A) (= A tptp.top_to231829469nres_a))) (forall ((M4 tptp.refine787176636t_unit)) (@ (@ tptp.ord_le1051254044t_unit M4) tptp.top_to177290092t_unit)) (forall ((M4 tptp.refine432681134nres_b)) (@ (@ tptp.ord_le527798542nres_b M4) tptp.top_to240090974nres_b)) (forall ((M4 tptp.refine424419629nres_a)) (@ (@ tptp.ord_le519537037nres_a M4) tptp.top_to231829469nres_a)) (forall ((X tptp.set_Product_unit)) (not (= tptp.top_to177290092t_unit (@ tptp.refine1777164439t_unit X)))) (forall ((X tptp.set_a)) (not (= tptp.top_to231829469nres_a (@ tptp.refine1198353288_RES_a X)))) (forall ((X tptp.set_b)) (not (= tptp.top_to240090974nres_b (@ tptp.refine1198353289_RES_b X)))) (forall ((M4 tptp.refine787176636t_unit)) (=> (not (= M4 tptp.top_to177290092t_unit)) (not (forall ((X12 tptp.set_Product_unit)) (not (= M4 (@ tptp.refine1777164439t_unit X12))))))) (forall ((M4 tptp.refine424419629nres_a)) (=> (not (= M4 tptp.top_to231829469nres_a)) (not (forall ((X12 tptp.set_a)) (not (= M4 (@ tptp.refine1198353288_RES_a X12))))))) (forall ((M4 tptp.refine432681134nres_b)) (=> (not (= M4 tptp.top_to240090974nres_b)) (not (forall ((X12 tptp.set_b)) (not (= M4 (@ tptp.refine1198353289_RES_b X12))))))) (forall ((S tptp.refine787176636t_unit)) (= (not (@ tptp.refine579265252t_unit S)) (= S tptp.top_to177290092t_unit))) _let_7 (forall ((S tptp.refine787176636t_unit)) (= (not (= tptp.top_to177290092t_unit S)) (@ tptp.refine579265252t_unit S))) (forall ((F (-> tptp.product_unit tptp.refine787176636t_unit))) (= (@ (@ tptp.refine681446406t_unit tptp.top_to177290092t_unit) F) tptp.top_to177290092t_unit)) (forall ((M tptp.refine787176636t_unit) (X4 tptp.refine787176636t_unit)) (=> (= M tptp.top_to177290092t_unit) (@ (@ tptp.ord_le1051254044t_unit X4) M))) (forall ((M tptp.refine432681134nres_b) (X4 tptp.refine432681134nres_b)) (=> (= M tptp.top_to240090974nres_b) (@ (@ tptp.ord_le527798542nres_b X4) M))) (forall ((M tptp.refine424419629nres_a) (X4 tptp.refine424419629nres_a)) (=> (= M tptp.top_to231829469nres_a) (@ (@ tptp.ord_le519537037nres_a X4) M))) (forall ((S tptp.refine787176636t_unit) (S3 tptp.refine787176636t_unit)) (= (@ (@ (@ tptp.partia1658438072t_unit tptp.top_to177290092t_unit) S) S3) (=> (@ tptp.refine579265252t_unit S) (and (@ tptp.refine579265252t_unit S3) (forall ((X5 tptp.product_unit)) (= (@ (@ tptp.refine558004794t_unit S) X5) (@ (@ tptp.refine558004794t_unit S3) X5))))))) (forall ((M4 tptp.refine787176636t_unit) (M3 tptp.refine787176636t_unit) (F (-> tptp.product_unit tptp.refine787176636t_unit)) (F2 (-> tptp.product_unit tptp.refine787176636t_unit))) (let ((_let_1 (@ tptp.partia1658438072t_unit tptp.top_to177290092t_unit))) (=> (@ (@ _let_1 M4) M3) (=> (forall ((X3 tptp.product_unit)) (@ (@ (@ tptp.partia1658438072t_unit tptp.top_to177290092t_unit) (@ F X3)) (@ F2 X3))) (@ (@ _let_1 (@ (@ tptp.refine681446406t_unit M4) F)) (@ (@ tptp.refine681446406t_unit M3) F2)))))) (forall ((M4 tptp.refine424419629nres_a) (M3 tptp.refine424419629nres_a) (F (-> tptp.a tptp.refine432681134nres_b)) (F2 (-> tptp.a tptp.refine432681134nres_b))) (=> (@ (@ (@ tptp.partia906949161nres_a tptp.top_to231829469nres_a) M4) M3) (=> (forall ((X3 tptp.a)) (@ (@ (@ tptp.partia915210666nres_b tptp.top_to240090974nres_b) (@ F X3)) (@ F2 X3))) (@ (@ (@ tptp.partia915210666nres_b tptp.top_to240090974nres_b) (@ (@ tptp.refine436832839nd_a_b M4) F)) (@ (@ tptp.refine436832839nd_a_b M3) F2))))) (forall ((X4 tptp.refine787176636t_unit) (Y3 tptp.refine787176636t_unit)) (=> (@ (@ (@ tptp.partia1658438072t_unit tptp.top_to177290092t_unit) X4) Y3) (@ (@ tptp.ord_le1051254044t_unit Y3) X4))) (forall ((X4 tptp.refine432681134nres_b) (Y3 tptp.refine432681134nres_b)) (=> (@ (@ (@ tptp.partia915210666nres_b tptp.top_to240090974nres_b) X4) Y3) (@ (@ tptp.ord_le527798542nres_b Y3) X4))) (forall ((X4 tptp.refine424419629nres_a) (Y3 tptp.refine424419629nres_a)) (=> (@ (@ (@ tptp.partia906949161nres_a tptp.top_to231829469nres_a) X4) Y3) (@ (@ tptp.ord_le519537037nres_a Y3) X4))) (forall ((X4 tptp.a)) (@ (@ tptp.member_a X4) tptp.top_top_set_a)) (forall ((X4 tptp.b)) (@ (@ tptp.member_b X4) tptp.top_top_set_b)) (forall ((S tptp.set_a)) (= (= S tptp.top_top_set_a) (forall ((X5 tptp.a)) (@ (@ tptp.member_a X5) S)))) (forall ((S tptp.set_b)) (= (= S tptp.top_top_set_b) (forall ((X5 tptp.b)) (@ (@ tptp.member_b X5) S)))) (exists ((X3 tptp.a)) (@ (@ tptp.member_a X3) tptp.top_top_set_a)) (exists ((X3 tptp.b)) (@ (@ tptp.member_b X3) tptp.top_top_set_b)) _let_6 _let_5 (forall ((A3 tptp.set_a)) (=> (forall ((X3 tptp.a)) (@ (@ tptp.member_a X3) A3)) (= tptp.top_top_set_a A3))) (forall ((A3 tptp.set_b)) (=> (forall ((X3 tptp.b)) (@ (@ tptp.member_b X3) A3)) (= tptp.top_top_set_b A3))) (= tptp.top_top_a_o (lambda ((X5 tptp.a)) (@ (@ tptp.member_a X5) tptp.top_top_set_a))) (= tptp.top_top_b_o (lambda ((X5 tptp.b)) (@ (@ tptp.member_b X5) tptp.top_top_set_b))) _let_4 (forall ((X4 tptp.set_a) (Y3 tptp.set_a)) (= (@ (@ (@ tptp.if_set_a false) X4) Y3) Y3)) (forall ((X4 tptp.set_a) (Y3 tptp.set_a)) (= (@ (@ (@ tptp.if_set_a true) X4) Y3) X4)) (forall ((X4 tptp.set_b) (Y3 tptp.set_b)) (= (@ (@ (@ tptp.if_set_b false) X4) Y3) Y3)) (forall ((X4 tptp.set_b) (Y3 tptp.set_b)) (= (@ (@ (@ tptp.if_set_b true) X4) Y3) X4)) (forall ((X4 tptp.refine424419629nres_a) (Y3 tptp.refine424419629nres_a)) (= (@ (@ (@ tptp.if_Ref1724547303nres_a false) X4) Y3) Y3)) (forall ((X4 tptp.refine424419629nres_a) (Y3 tptp.refine424419629nres_a)) (= (@ (@ (@ tptp.if_Ref1724547303nres_a true) X4) Y3) X4)) (forall ((X4 tptp.refine432681134nres_b) (Y3 tptp.refine432681134nres_b)) (= (@ (@ (@ tptp.if_Ref1732808808nres_b false) X4) Y3) Y3)) (forall ((X4 tptp.refine432681134nres_b) (Y3 tptp.refine432681134nres_b)) (= (@ (@ (@ tptp.if_Ref1732808808nres_b true) X4) Y3) X4)) (forall ((X4 (-> Bool tptp.refine424419629nres_a)) (Y3 (-> Bool tptp.refine424419629nres_a))) (= (@ (@ (@ tptp.if_o_R1705037948nres_a false) X4) Y3) Y3)) (forall ((X4 (-> Bool tptp.refine424419629nres_a)) (Y3 (-> Bool tptp.refine424419629nres_a))) (= (@ (@ (@ tptp.if_o_R1705037948nres_a true) X4) Y3) X4)) (forall ((X4 (-> Bool tptp.refine432681134nres_b)) (Y3 (-> Bool tptp.refine432681134nres_b))) (= (@ (@ (@ tptp.if_o_R697118589nres_b false) X4) Y3) Y3)) (forall ((X4 (-> Bool tptp.refine432681134nres_b)) (Y3 (-> Bool tptp.refine432681134nres_b))) (= (@ (@ (@ tptp.if_o_R697118589nres_b true) X4) Y3) X4)) (forall ((P Bool)) (or (= P true) (= P false))) (forall ((X4 tptp.refine787176636t_unit) (Y3 tptp.refine787176636t_unit)) (= (@ (@ (@ tptp.if_Ref1369692790t_unit false) X4) Y3) Y3)) (forall ((X4 tptp.refine787176636t_unit) (Y3 tptp.refine787176636t_unit)) (= (@ (@ (@ tptp.if_Ref1369692790t_unit true) X4) Y3) X4)) _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 15.51/15.82 )
% 15.51/15.82 % SZS output end Proof for ITP161^1
% 15.51/15.82 % cvc5---1.0.5 exiting
% 15.51/15.82 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------