TSTP Solution File: SWW469+5 by Otter---3.3

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SWW469+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n012.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 : Wed Jul 27 13:22:35 EDT 2022

% Result   : Theorem 2.24s 2.42s
% Output   : Refutation 2.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    3
% Syntax   : Number of clauses     :    5 (   4 unt;   0 nHn;   3 RR)
%            Number of literals    :    6 (   3 equ;   2 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :    2 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    ( ~ hBOOL(hoare_1883395792gleton)
    | ti(state,dollar_c2) != ti(state,dollar_c1) ),
    file('SWW469+5.p',unknown),
    [] ).

cnf(102,axiom,
    hBOOL(hoare_1883395792gleton),
    file('SWW469+5.p',unknown),
    [] ).

cnf(103,axiom,
    ti(state,A) = ti(state,dollar_c3),
    file('SWW469+5.p',unknown),
    [] ).

cnf(105,plain,
    ti(state,dollar_c3) = ti(state,A),
    inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[103])]),
    [iquote('copy,103,flip.1')] ).

cnf(106,plain,
    $false,
    inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[103,4]),102,105]),
    [iquote('para_from,103.1.1,4.2.1,unit_del,102,105')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SWW469+5 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.12  % Command  : otter-tptp-script %s
% 0.11/0.33  % Computer : n012.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Wed Jul 27 02:51:05 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 2.19/2.40  ----- Otter 3.3f, August 2004 -----
% 2.19/2.40  The process was started by sandbox on n012.cluster.edu,
% 2.19/2.40  Wed Jul 27 02:51:05 2022
% 2.19/2.40  The command was "./otter".  The process ID is 17926.
% 2.19/2.40  
% 2.19/2.40  set(prolog_style_variables).
% 2.19/2.40  set(auto).
% 2.19/2.40     dependent: set(auto1).
% 2.19/2.40     dependent: set(process_input).
% 2.19/2.40     dependent: clear(print_kept).
% 2.19/2.40     dependent: clear(print_new_demod).
% 2.19/2.40     dependent: clear(print_back_demod).
% 2.19/2.40     dependent: clear(print_back_sub).
% 2.19/2.40     dependent: set(control_memory).
% 2.19/2.40     dependent: assign(max_mem, 12000).
% 2.19/2.40     dependent: assign(pick_given_ratio, 4).
% 2.19/2.40     dependent: assign(stats_level, 1).
% 2.19/2.40     dependent: assign(max_seconds, 10800).
% 2.19/2.40  clear(print_given).
% 2.19/2.40  
% 2.19/2.40  formula_list(usable).
% 2.19/2.40  all A (A=A).
% 2.19/2.40  all X_a (cl_HOL_Oe_qual(X_a)->ti(fun(X_a,fun(X_a,bool)),e_qual_e_qual(X_a))=e_qual_e_qual(X_a)).
% 2.19/2.40  all X_a (ti(fun(X_a,fun(X_a,bool)),induct_e_qual(X_a))=induct_e_qual(X_a)).
% 2.19/2.40  ti(bool,induct_false)=induct_false.
% 2.19/2.40  ti(bool,induct_true)=induct_true.
% 2.19/2.40  all X_a (ti(X_a,undefined(X_a))=undefined(X_a)).
% 2.19/2.40  all X_a (ti(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a)),hoare_244953527triple(X_a))=hoare_244953527triple(X_a)).
% 2.19/2.40  all X_a (ti(fun(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_2037801986triple(X_a))=hoare_2037801986triple(X_a)).
% 2.19/2.40  ti(bool,hoare_1883395792gleton)=hoare_1883395792gleton.
% 2.19/2.40  all X_a (ti(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),hoare_1580379338ep_set(X_a))=hoare_1580379338ep_set(X_a)).
% 2.19/2.40  all X_a (ti(fun(fun(X_a,bool),fun(X_a,bool)),collect(X_a))=collect(X_a)).
% 2.19/2.40  all X_a X_b (ti(fun(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool))),type_definition(X_a,X_b))=type_definition(X_a,X_b)).
% 2.19/2.40  all X_a (ti(fun(X_a,fun(X_a,bool)),fe_qual(X_a))=fe_qual(X_a)).
% 2.19/2.40  all X_b X_a B_1 B_2 (hAPP(X_b,X_a,ti(fun(X_b,X_a),B_1),B_2)=hAPP(X_b,X_a,B_1,B_2)).
% 2.19/2.40  all X_b X_a B_1 B_2 (hAPP(X_b,X_a,B_1,ti(X_b,B_2))=hAPP(X_b,X_a,B_1,B_2)).
% 2.19/2.40  all X_a X_b B_1 B_2 (ti(X_a,hAPP(X_b,X_a,B_1,B_2))=hAPP(X_b,X_a,B_1,B_2)).
% 2.19/2.40  all B_1 (hBOOL(ti(bool,B_1))<->hBOOL(B_1)).
% 2.19/2.40  all X_b (ti(fun(X_b,fun(fun(X_b,bool),bool)),member(X_b))=member(X_b)).
% 2.19/2.40  hBOOL(hoare_1883395792gleton)<-> (exists S T (ti(state,S)!=ti(state,T))).
% 2.19/2.40  all X_a X_1 Y_1 (hBOOL(hAPP(hoare_509422987triple(X_a),bool,hAPP(hoare_509422987triple(X_a),fun(hoare_509422987triple(X_a),bool),e_qual_e_qual(hoare_509422987triple(X_a)),X_1),Y_1))<->X_1=Y_1).
% 2.19/2.40  all X_a X_1 Y_1 (hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),X_1)=hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),Y_1)<->X_1=Y_1).
% 2.19/2.40  all X_a (cl_HOL_Oe_qual(X_a)->e_qual_e_qual(X_a)=fe_qual(X_a)).
% 2.19/2.40  all X_a (cl_HOL_Oe_qual(X_a)-> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),e_qual_e_qual(X_a),X),X)))).
% 2.19/2.40  all X_a (cl_HOL_Oe_qual(X_a)-> (all X_1 Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),e_qual_e_qual(X_a),X_1),Y_1))<->ti(X_a,X_1)=ti(X_a,Y_1)))).
% 2.19/2.40  all X_a (cl_HOL_Oe_qual(X_a)->fe_qual(X_a)=e_qual_e_qual(X_a)).
% 2.19/2.40  all X_a X_1 (hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),X_1))=X_1).
% 2.19/2.40  all X_a X_1 hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),X_1)),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a)))).
% 2.19/2.40  all X_a P Y_1 (hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_1),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))-> ((all X_2 hBOOL(hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool,P,hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),X_2))))->hBOOL(hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool,P,Y_1)))).
% 2.19/2.40  all X_a Y_1 (hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_1),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))-> -(all X_2 (Y_1!=hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),X_2)))).
% 2.19/2.40  all X_a Y_1 (hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_1),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))->hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),Y_1))=Y_1).
% 2.19/2.40  all X_a hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a)),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),hAPP(fun(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a)),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool)),type_definition(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_2037801986triple(X_a)),hoare_244953527triple(X_a)),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a)))).
% 2.19/2.40  all X_a Y_1 X_1 (hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),X_1),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))-> (hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_1),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))-> (hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),X_1)=hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),Y_1)<->X_1=Y_1))).
% 2.19/2.40  all X_a X_1 P ((all Y_2 (hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_2),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))->hBOOL(hAPP(hoare_509422987triple(X_a),bool,P,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),Y_2)))))->hBOOL(hAPP(hoare_509422987triple(X_a),bool,P,X_1))).
% 2.19/2.40  all X_a X_1 (-(all Y_2 (X_1=hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),Y_2)-> -hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_2),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))))).
% 2.19/2.40  all X_b X_a Y_1 X_1 Rep Abs A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_1))-> (hAPP(X_b,X_a,Abs,X_1)=hAPP(X_b,X_a,Abs,Y_1)<->ti(X_b,X_1)=ti(X_b,Y_1))))).
% 2.19/2.40  all X_b X_a Y_1 Rep Abs A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_1))->hAPP(X_a,X_b,Rep,hAPP(X_b,X_a,Abs,Y_1))=ti(X_b,Y_1))).
% 2.19/2.40  all X_b X_a X_1 Y_1 Rep Abs A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))-> (hAPP(X_a,X_b,Rep,X_1)=hAPP(X_a,X_b,Rep,Y_1)<->ti(X_a,X_1)=ti(X_a,Y_1))).
% 2.19/2.40  all X_b X_a X_1 Rep Abs A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))->hAPP(X_b,X_a,Abs,hAPP(X_a,X_b,Rep,X_1))=ti(X_a,X_1)).
% 2.19/2.40  all X_b X_a X_1 Rep Abs A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))->hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,Rep,X_1)),A_1))).
% 2.19/2.40  -hBOOL(induct_false).
% 2.19/2.40  all X_b X_a Y_1 Rep Abs A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_1))-> -(all X_2 (ti(X_b,Y_1)!=hAPP(X_a,X_b,Rep,X_2))))).
% 2.19/2.40  all X_b X_a X_1 Rep Abs A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))-> -(all Y_2 (ti(X_a,X_1)=hAPP(X_b,X_a,Abs,Y_2)-> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),A_1))))).
% 2.19/2.40  all X_b X_a X_1 P Rep Abs A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))-> ((all Y_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_2),A_1))->hBOOL(hAPP(X_a,bool,P,hAPP(X_b,X_a,Abs,Y_2)))))->hBOOL(hAPP(X_a,bool,P,X_1)))).
% 2.19/2.40  all X_b X_a P Y_1 Rep Abs A_1 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))-> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_1))-> ((all X_2 hBOOL(hAPP(X_b,bool,P,hAPP(X_a,X_b,Rep,X_2))))->hBOOL(hAPP(X_b,bool,P,Y_1))))).
% 2.19/2.40  hBOOL(induct_true).
% 2.19/2.40  hBOOL(induct_true).
% 2.19/2.40  all X_a X_1 Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),induct_e_qual(X_a),X_1),Y_1))<->ti(X_a,X_1)=ti(X_a,Y_1)).
% 2.19/2.40  all X_a X_b F G ((all X_2 (hAPP(X_a,X_b,F,X_2)=hAPP(X_a,X_b,G,X_2)))->ti(fun(X_a,X_b),F)=ti(fun(X_a,X_b),G)).
% 2.19/2.40  all X_a X_1 A_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))<->hBOOL(hAPP(X_a,bool,A_1,X_1))).
% 2.19/2.40  all X_a P (hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P)=ti(fun(X_a,bool),P)).
% 2.19/2.40  all T_2 T_1_1 (enum(T_1_1)&enum(T_2)->enum(sum_sum(T_2,T_1_1))).
% 2.19/2.40  enum(bool).
% 2.19/2.40  all T_2 T_1_1 (enum(T_1_1)&enum(T_2)->enum(fun(T_2,T_1_1))).
% 2.19/2.40  all T_2 T_1_1 (cl_HOL_Oe_qual(T_1_1)&enum(T_2)->cl_HOL_Oe_qual(fun(T_2,T_1_1))).
% 2.19/2.40  cl_HOL_Oe_qual(com).
% 2.19/2.40  cl_HOL_Oe_qual(bool).
% 2.19/2.40  cl_HOL_Oe_qual(state).
% 2.19/2.40  all T_2 T_1_1 cl_HOL_Oe_qual(sum_sum(T_2,T_1_1)).
% 2.19/2.40  all T_1_1 cl_HOL_Oe_qual(hoare_509422987triple(T_1_1)).
% 2.19/2.40  all T_1 A (ti(T_1,ti(T_1,A))=ti(T_1,A)).
% 2.19/2.40  all X_a X Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fe_qual(X_a),X),Y))|ti(X_a,X)=ti(X_a,Y)).
% 2.19/2.40  all X_a X Y (ti(X_a,X)!=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fe_qual(X_a),X),Y))).
% 2.19/2.40  hBOOL(hoare_1883395792gleton).
% 2.19/2.40  -(all T (-(all S (ti(state,S)=ti(state,T))))).
% 2.19/2.40  end_of_list.
% 2.19/2.40  
% 2.19/2.40  -------> usable clausifies to:
% 2.19/2.40  
% 2.19/2.40  list(usable).
% 2.19/2.40  0 [] A=A.
% 2.19/2.40  0 [] -cl_HOL_Oe_qual(X_a)|ti(fun(X_a,fun(X_a,bool)),e_qual_e_qual(X_a))=e_qual_e_qual(X_a).
% 2.19/2.40  0 [] ti(fun(X_a,fun(X_a,bool)),induct_e_qual(X_a))=induct_e_qual(X_a).
% 2.19/2.40  0 [] ti(bool,induct_false)=induct_false.
% 2.19/2.40  0 [] ti(bool,induct_true)=induct_true.
% 2.19/2.40  0 [] ti(X_a,undefined(X_a))=undefined(X_a).
% 2.19/2.40  0 [] ti(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a)),hoare_244953527triple(X_a))=hoare_244953527triple(X_a).
% 2.19/2.40  0 [] ti(fun(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_2037801986triple(X_a))=hoare_2037801986triple(X_a).
% 2.19/2.40  0 [] ti(bool,hoare_1883395792gleton)=hoare_1883395792gleton.
% 2.19/2.40  0 [] ti(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),hoare_1580379338ep_set(X_a))=hoare_1580379338ep_set(X_a).
% 2.19/2.40  0 [] ti(fun(fun(X_a,bool),fun(X_a,bool)),collect(X_a))=collect(X_a).
% 2.19/2.40  0 [] ti(fun(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool))),type_definition(X_a,X_b))=type_definition(X_a,X_b).
% 2.19/2.40  0 [] ti(fun(X_a,fun(X_a,bool)),fe_qual(X_a))=fe_qual(X_a).
% 2.19/2.40  0 [] hAPP(X_b,X_a,ti(fun(X_b,X_a),B_1),B_2)=hAPP(X_b,X_a,B_1,B_2).
% 2.19/2.40  0 [] hAPP(X_b,X_a,B_1,ti(X_b,B_2))=hAPP(X_b,X_a,B_1,B_2).
% 2.19/2.40  0 [] ti(X_a,hAPP(X_b,X_a,B_1,B_2))=hAPP(X_b,X_a,B_1,B_2).
% 2.19/2.40  0 [] -hBOOL(ti(bool,B_1))|hBOOL(B_1).
% 2.19/2.40  0 [] hBOOL(ti(bool,B_1))| -hBOOL(B_1).
% 2.19/2.40  0 [] ti(fun(X_b,fun(fun(X_b,bool),bool)),member(X_b))=member(X_b).
% 2.19/2.40  0 [] -hBOOL(hoare_1883395792gleton)|ti(state,$c2)!=ti(state,$c1).
% 2.19/2.40  0 [] hBOOL(hoare_1883395792gleton)|ti(state,S)=ti(state,T).
% 2.19/2.40  0 [] -hBOOL(hAPP(hoare_509422987triple(X_a),bool,hAPP(hoare_509422987triple(X_a),fun(hoare_509422987triple(X_a),bool),e_qual_e_qual(hoare_509422987triple(X_a)),X_1),Y_1))|X_1=Y_1.
% 2.19/2.40  0 [] hBOOL(hAPP(hoare_509422987triple(X_a),bool,hAPP(hoare_509422987triple(X_a),fun(hoare_509422987triple(X_a),bool),e_qual_e_qual(hoare_509422987triple(X_a)),X_1),Y_1))|X_1!=Y_1.
% 2.19/2.40  0 [] hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),X_1)!=hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),Y_1)|X_1=Y_1.
% 2.19/2.40  0 [] hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),X_1)=hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),Y_1)|X_1!=Y_1.
% 2.19/2.40  0 [] -cl_HOL_Oe_qual(X_a)|e_qual_e_qual(X_a)=fe_qual(X_a).
% 2.19/2.40  0 [] -cl_HOL_Oe_qual(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),e_qual_e_qual(X_a),X),X)).
% 2.19/2.40  0 [] -cl_HOL_Oe_qual(X_a)| -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),e_qual_e_qual(X_a),X_1),Y_1))|ti(X_a,X_1)=ti(X_a,Y_1).
% 2.19/2.40  0 [] -cl_HOL_Oe_qual(X_a)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),e_qual_e_qual(X_a),X_1),Y_1))|ti(X_a,X_1)!=ti(X_a,Y_1).
% 2.19/2.40  0 [] -cl_HOL_Oe_qual(X_a)|fe_qual(X_a)=e_qual_e_qual(X_a).
% 2.19/2.40  0 [] hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),X_1))=X_1.
% 2.19/2.40  0 [] hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),X_1)),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a)))).
% 2.19/2.40  0 [] -hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_1),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))| -hBOOL(hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool,P,hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),$f1(X_a,P,Y_1))))|hBOOL(hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool,P,Y_1)).
% 2.19/2.40  0 [] -hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_1),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))|Y_1=hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),$f2(X_a,Y_1)).
% 2.19/2.40  0 [] -hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_1),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))|hAPP(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_2037801986triple(X_a),hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),Y_1))=Y_1.
% 2.19/2.40  0 [] hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a)),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),hAPP(fun(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a)),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool)),type_definition(hoare_509422987triple(X_a),fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_2037801986triple(X_a)),hoare_244953527triple(X_a)),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a)))).
% 2.19/2.40  0 [] -hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),X_1),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))| -hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_1),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))|hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),X_1)!=hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),Y_1)|X_1=Y_1.
% 2.24/2.41  0 [] -hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),X_1),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))| -hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),Y_1),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))|hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),X_1)=hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),Y_1)|X_1!=Y_1.
% 2.24/2.41  0 [] hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),$f3(X_a,X_1,P)),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a))))|hBOOL(hAPP(hoare_509422987triple(X_a),bool,P,X_1)).
% 2.24/2.41  0 [] -hBOOL(hAPP(hoare_509422987triple(X_a),bool,P,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),$f3(X_a,X_1,P))))|hBOOL(hAPP(hoare_509422987triple(X_a),bool,P,X_1)).
% 2.24/2.41  0 [] X_1=hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),hoare_509422987triple(X_a),hoare_244953527triple(X_a),$f4(X_a,X_1)).
% 2.24/2.41  0 [] hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),fun(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),bool),member(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),$f4(X_a,X_1)),hAPP(fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),fun(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool),bool),collect(fun(node(sum_sum(com,fun(X_a,fun(state,bool))),sum_sum(state,X_a)),bool)),hoare_1580379338ep_set(X_a)))).
% 2.24/2.41  0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_1))|hAPP(X_b,X_a,Abs,X_1)!=hAPP(X_b,X_a,Abs,Y_1)|ti(X_b,X_1)=ti(X_b,Y_1).
% 2.24/2.41  0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_1))|hAPP(X_b,X_a,Abs,X_1)=hAPP(X_b,X_a,Abs,Y_1)|ti(X_b,X_1)!=ti(X_b,Y_1).
% 2.24/2.41  0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_1))|hAPP(X_a,X_b,Rep,hAPP(X_b,X_a,Abs,Y_1))=ti(X_b,Y_1).
% 2.24/2.41  0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))|hAPP(X_a,X_b,Rep,X_1)!=hAPP(X_a,X_b,Rep,Y_1)|ti(X_a,X_1)=ti(X_a,Y_1).
% 2.24/2.41  0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))|hAPP(X_a,X_b,Rep,X_1)=hAPP(X_a,X_b,Rep,Y_1)|ti(X_a,X_1)!=ti(X_a,Y_1).
% 2.24/2.41  0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))|hAPP(X_b,X_a,Abs,hAPP(X_a,X_b,Rep,X_1))=ti(X_a,X_1).
% 2.24/2.41  0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,Rep,X_1)),A_1)).
% 2.24/2.41  0 [] -hBOOL(induct_false).
% 2.24/2.41  0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_1))|ti(X_b,Y_1)=hAPP(X_a,X_b,Rep,$f5(X_b,X_a,Y_1,Rep,Abs,A_1)).
% 2.24/2.41  0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))|ti(X_a,X_1)=hAPP(X_b,X_a,Abs,$f6(X_b,X_a,X_1,Rep,Abs,A_1)).
% 2.24/2.41  0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f6(X_b,X_a,X_1,Rep,Abs,A_1)),A_1)).
% 2.24/2.41  0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))|hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),$f7(X_b,X_a,X_1,P,Rep,Abs,A_1)),A_1))|hBOOL(hAPP(X_a,bool,P,X_1)).
% 2.24/2.41  0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))| -hBOOL(hAPP(X_a,bool,P,hAPP(X_b,X_a,Abs,$f7(X_b,X_a,X_1,P,Rep,Abs,A_1))))|hBOOL(hAPP(X_a,bool,P,X_1)).
% 2.24/2.41  0 [] -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),bool),hAPP(fun(X_a,X_b),fun(fun(X_b,X_a),fun(fun(X_b,bool),bool)),type_definition(X_a,X_b),Rep),Abs),A_1))| -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),Y_1),A_1))| -hBOOL(hAPP(X_b,bool,P,hAPP(X_a,X_b,Rep,$f8(X_b,X_a,P,Y_1,Rep,Abs,A_1))))|hBOOL(hAPP(X_b,bool,P,Y_1)).
% 2.24/2.41  0 [] hBOOL(induct_true).
% 2.24/2.41  0 [] hBOOL(induct_true).
% 2.24/2.41  0 [] -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),induct_e_qual(X_a),X_1),Y_1))|ti(X_a,X_1)=ti(X_a,Y_1).
% 2.24/2.41  0 [] hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),induct_e_qual(X_a),X_1),Y_1))|ti(X_a,X_1)!=ti(X_a,Y_1).
% 2.24/2.41  0 [] hAPP(X_a,X_b,F,$f9(X_a,X_b,F,G))!=hAPP(X_a,X_b,G,$f9(X_a,X_b,F,G))|ti(fun(X_a,X_b),F)=ti(fun(X_a,X_b),G).
% 2.24/2.41  0 [] -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))|hBOOL(hAPP(X_a,bool,A_1,X_1)).
% 2.24/2.41  0 [] hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))| -hBOOL(hAPP(X_a,bool,A_1,X_1)).
% 2.24/2.41  0 [] hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P)=ti(fun(X_a,bool),P).
% 2.24/2.41  0 [] -enum(T_1_1)| -enum(T_2)|enum(sum_sum(T_2,T_1_1)).
% 2.24/2.41  0 [] enum(bool).
% 2.24/2.41  0 [] -enum(T_1_1)| -enum(T_2)|enum(fun(T_2,T_1_1)).
% 2.24/2.41  0 [] -cl_HOL_Oe_qual(T_1_1)| -enum(T_2)|cl_HOL_Oe_qual(fun(T_2,T_1_1)).
% 2.24/2.41  0 [] cl_HOL_Oe_qual(com).
% 2.24/2.41  0 [] cl_HOL_Oe_qual(bool).
% 2.24/2.41  0 [] cl_HOL_Oe_qual(state).
% 2.24/2.41  0 [] cl_HOL_Oe_qual(sum_sum(T_2,T_1_1)).
% 2.24/2.41  0 [] cl_HOL_Oe_qual(hoare_509422987triple(T_1_1)).
% 2.24/2.41  0 [] ti(T_1,ti(T_1,A))=ti(T_1,A).
% 2.24/2.41  0 [] -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fe_qual(X_a),X),Y))|ti(X_a,X)=ti(X_a,Y).
% 2.24/2.41  0 [] ti(X_a,X)!=ti(X_a,Y)|hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fe_qual(X_a),X),Y)).
% 2.24/2.41  0 [] hBOOL(hoare_1883395792gleton).
% 2.24/2.41  0 [] ti(state,S)=ti(state,$c3).
% 2.24/2.41  end_of_list.
% 2.24/2.41  
% 2.24/2.41  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 2.24/2.41  
% 2.24/2.41  This ia a non-Horn set with equality.  The strategy will be
% 2.24/2.41  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.24/2.41  deletion, with positive clauses in sos and nonpositive
% 2.24/2.41  clauses in usable.
% 2.24/2.41  
% 2.24/2.41     dependent: set(knuth_bendix).
% 2.24/2.41     dependent: set(anl_eq).
% 2.24/2.41     dependent: set(para_from).
% 2.24/2.41     dependent: set(para_into).
% 2.24/2.41     dependent: clear(para_from_right).
% 2.24/2.41     dependent: clear(para_into_right).
% 2.24/2.41     dependent: set(para_from_vars).
% 2.24/2.41     dependent: set(eq_units_both_ways).
% 2.24/2.41     dependent: set(dynamic_demod_all).
% 2.24/2.41     dependent: set(dynamic_demod).
% 2.24/2.41     dependent: set(order_eq).
% 2.24/2.41     dependent: set(back_demod).
% 2.24/2.41     dependent: set(lrpo).
% 2.24/2.41     dependent: set(hyper_res).
% 2.24/2.41     dependent: set(unit_deletion).
% 2.24/2.41     dependent: set(factor).
% 2.24/2.41  
% 2.24/2.41  ------------> process usable:
% 2.24/2.41  ** KEPT (pick-wt=13): 1 [] -cl_HOL_Oe_qual(A)|ti(fun(A,fun(A,bool)),e_qual_e_qual(A))=e_qual_e_qual(A).
% 2.24/2.41  ** KEPT (pick-wt=6): 2 [] -hBOOL(ti(bool,A))|hBOOL(A).
% 2.24/2.41  ** KEPT (pick-wt=6): 3 [] hBOOL(ti(bool,A))| -hBOOL(A).
% 2.24/2.41  ** KEPT (pick-wt=9): 4 [] -hBOOL(hoare_1883395792gleton)|ti(state,$c2)!=ti(state,$c1).
% 2.24/2.41  ** KEPT (pick-wt=20): 5 [] -hBOOL(hAPP(hoare_509422987triple(A),bool,hAPP(hoare_509422987triple(A),fun(hoare_509422987triple(A),bool),e_qual_e_qual(hoare_509422987triple(A)),B),C))|B=C.
% 2.24/2.41  ** KEPT (pick-wt=20): 6 [] hBOOL(hAPP(hoare_509422987triple(A),bool,hAPP(hoare_509422987triple(A),fun(hoare_509422987triple(A),bool),e_qual_e_qual(hoare_509422987triple(A)),B),C))|B!=C.
% 2.24/2.41  ** KEPT (pick-wt=42): 7 [] hAPP(hoare_509422987triple(A),fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_2037801986triple(A),B)!=hAPP(hoare_509422987triple(A),fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_2037801986triple(A),C)|B=C.
% 2.24/2.41  ** KEPT (pick-wt=42): 8 [] hAPP(hoare_509422987triple(A),fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_2037801986triple(A),B)=hAPP(hoare_509422987triple(A),fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_2037801986triple(A),C)|B!=C.
% 2.24/2.41  ** KEPT (pick-wt=7): 10 [copy,9,flip.2] -cl_HOL_Oe_qual(A)|fe_qual(A)=e_qual_e_qual(A).
% 2.24/2.41  ** KEPT (pick-wt=15): 11 [] -cl_HOL_Oe_qual(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),e_qual_e_qual(A),B),B)).
% 2.24/2.41  ** KEPT (pick-wt=22): 12 [] -cl_HOL_Oe_qual(A)| -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),e_qual_e_qual(A),B),C))|ti(A,B)=ti(A,C).
% 2.24/2.41  ** KEPT (pick-wt=22): 13 [] -cl_HOL_Oe_qual(A)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),e_qual_e_qual(A),B),C))|ti(A,B)!=ti(A,C).
% 2.24/2.41    Following clause subsumed by 10 during input processing: 0 [] -cl_HOL_Oe_qual(A)|fe_qual(A)=e_qual_e_qual(A).
% 2.24/2.41  ** KEPT (pick-wt=168): 14 [] -hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),fun(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool),member(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),B),hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),collect(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),hoare_1580379338ep_set(A))))| -hBOOL(hAPP(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool,C,hAPP(hoare_509422987triple(A),fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_2037801986triple(A),$f1(A,C,B))))|hBOOL(hAPP(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool,C,B)).
% 2.24/2.41  ** KEPT (pick-wt=134): 16 [copy,15,flip.2] -hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),fun(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool),member(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),B),hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),collect(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),hoare_1580379338ep_set(A))))|hAPP(hoare_509422987triple(A),fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_2037801986triple(A),$f2(A,B))=B.
% 2.24/2.41  ** KEPT (pick-wt=150): 17 [] -hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),fun(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool),member(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),B),hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),collect(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),hoare_1580379338ep_set(A))))|hAPP(hoare_509422987triple(A),fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_2037801986triple(A),hAPP(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_509422987triple(A),hoare_244953527triple(A),B))=B.
% 2.24/2.41  ** KEPT (pick-wt=264): 18 [] -hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),fun(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool),member(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),B),hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),collect(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),hoare_1580379338ep_set(A))))| -hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),fun(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool),member(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),C),hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),collect(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),hoare_1580379338ep_set(A))))|hAPP(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_509422987triple(A),hoare_244953527triple(A),B)!=hAPP(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_509422987triple(A),hoare_244953527triple(A),C)|B=C.
% 2.24/2.41  ** KEPT (pick-wt=264): 19 [] -hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),fun(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool),member(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),B),hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),collect(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),hoare_1580379338ep_set(A))))| -hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),fun(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool),member(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),C),hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),collect(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),hoare_1580379338ep_set(A))))|hAPP(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_509422987triple(A),hoare_244953527triple(A),B)=hAPP(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_509422987triple(A),hoare_244953527triple(A),C)|B!=C.
% 2.24/2.41  ** KEPT (pick-wt=35): 20 [] -hBOOL(hAPP(hoare_509422987triple(A),bool,B,hAPP(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_509422987triple(A),hoare_244953527triple(A),$f3(A,C,B))))|hBOOL(hAPP(hoare_509422987triple(A),bool,B,C)).
% 2.24/2.41  ** KEPT (pick-wt=86): 21 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,B),fun(fun(A,bool),bool),hAPP(fun(B,A),fun(fun(A,B),fun(fun(A,bool),bool)),type_definition(B,A),C),D),E))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),F),E))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),G),E))|hAPP(A,B,D,F)!=hAPP(A,B,D,G)|ti(A,F)=ti(A,G).
% 2.24/2.41  ** KEPT (pick-wt=86): 22 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,B),fun(fun(A,bool),bool),hAPP(fun(B,A),fun(fun(A,B),fun(fun(A,bool),bool)),type_definition(B,A),C),D),E))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),F),E))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),G),E))|hAPP(A,B,D,F)=hAPP(A,B,D,G)|ti(A,F)!=ti(A,G).
% 2.24/2.41  ** KEPT (pick-wt=64): 23 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,B),fun(fun(A,bool),bool),hAPP(fun(B,A),fun(fun(A,B),fun(fun(A,bool),bool)),type_definition(B,A),C),D),E))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),F),E))|hAPP(B,A,C,hAPP(A,B,D,F))=ti(A,F).
% 2.24/2.41  ** KEPT (pick-wt=52): 24 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,B),fun(fun(A,bool),bool),hAPP(fun(B,A),fun(fun(A,B),fun(fun(A,bool),bool)),type_definition(B,A),C),D),E))|hAPP(B,A,C,F)!=hAPP(B,A,C,G)|ti(B,F)=ti(B,G).
% 2.24/2.41  ** KEPT (pick-wt=52): 25 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,B),fun(fun(A,bool),bool),hAPP(fun(B,A),fun(fun(A,B),fun(fun(A,bool),bool)),type_definition(B,A),C),D),E))|hAPP(B,A,C,F)=hAPP(B,A,C,G)|ti(B,F)!=ti(B,G).
% 2.24/2.41  ** KEPT (pick-wt=47): 26 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,B),fun(fun(A,bool),bool),hAPP(fun(B,A),fun(fun(A,B),fun(fun(A,bool),bool)),type_definition(B,A),C),D),E))|hAPP(A,B,D,hAPP(B,A,C,F))=ti(B,F).
% 2.24/2.41  ** KEPT (pick-wt=55): 27 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,B),fun(fun(A,bool),bool),hAPP(fun(B,A),fun(fun(A,B),fun(fun(A,bool),bool)),type_definition(B,A),C),D),E))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(B,A,C,F)),E)).
% 2.24/2.41  ** KEPT (pick-wt=2): 28 [] -hBOOL(induct_false).
% 2.24/2.41  ** KEPT (pick-wt=66): 29 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,B),fun(fun(A,bool),bool),hAPP(fun(B,A),fun(fun(A,B),fun(fun(A,bool),bool)),type_definition(B,A),C),D),E))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),F),E))|ti(A,F)=hAPP(B,A,C,$f5(A,B,F,C,D,E)).
% 2.24/2.41  ** KEPT (pick-wt=49): 30 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,B),fun(fun(A,bool),bool),hAPP(fun(B,A),fun(fun(A,B),fun(fun(A,bool),bool)),type_definition(B,A),C),D),E))|ti(B,F)=hAPP(A,B,D,$f6(A,B,F,C,D,E)).
% 2.24/2.41  ** KEPT (pick-wt=57): 31 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,B),fun(fun(A,bool),bool),hAPP(fun(B,A),fun(fun(A,B),fun(fun(A,bool),bool)),type_definition(B,A),C),D),E))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),$f6(A,B,F,C,D,E)),E)).
% 2.24/2.41  ** KEPT (pick-wt=64): 32 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,B),fun(fun(A,bool),bool),hAPP(fun(B,A),fun(fun(A,B),fun(fun(A,bool),bool)),type_definition(B,A),C),D),E))|hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),$f7(A,B,F,G,C,D,E)),E))|hBOOL(hAPP(B,bool,G,F)).
% 2.24/2.41  ** KEPT (pick-wt=57): 33 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,B),fun(fun(A,bool),bool),hAPP(fun(B,A),fun(fun(A,B),fun(fun(A,bool),bool)),type_definition(B,A),C),D),E))| -hBOOL(hAPP(B,bool,F,hAPP(A,B,D,$f7(A,B,G,F,C,D,E))))|hBOOL(hAPP(B,bool,F,G)).
% 2.24/2.41  ** KEPT (pick-wt=74): 34 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,B),fun(fun(A,bool),bool),hAPP(fun(B,A),fun(fun(A,B),fun(fun(A,bool),bool)),type_definition(B,A),C),D),E))| -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),F),E))| -hBOOL(hAPP(A,bool,G,hAPP(B,A,C,$f8(A,B,G,F,C,D,E))))|hBOOL(hAPP(A,bool,G,F)).
% 2.24/2.41  ** KEPT (pick-wt=20): 35 [] -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),induct_e_qual(A),B),C))|ti(A,B)=ti(A,C).
% 2.24/2.41  ** KEPT (pick-wt=20): 36 [] hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),induct_e_qual(A),B),C))|ti(A,B)!=ti(A,C).
% 2.24/2.41  ** KEPT (pick-wt=30): 37 [] hAPP(A,B,C,$f9(A,B,C,D))!=hAPP(A,B,D,$f9(A,B,C,D))|ti(fun(A,B),C)=ti(fun(A,B),D).
% 2.24/2.41  ** KEPT (pick-wt=23): 38 [] -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))|hBOOL(hAPP(A,bool,C,B)).
% 2.24/2.41  ** KEPT (pick-wt=23): 39 [] hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),C))| -hBOOL(hAPP(A,bool,C,B)).
% 2.24/2.41  ** KEPT (pick-wt=8): 40 [] -enum(A)| -enum(B)|enum(sum_sum(B,A)).
% 2.24/2.41  ** KEPT (pick-wt=8): 41 [] -enum(A)| -enum(B)|enum(fun(B,A)).
% 2.24/2.41  ** KEPT (pick-wt=8): 42 [] -cl_HOL_Oe_qual(A)| -enum(B)|cl_HOL_Oe_qual(fun(B,A)).
% 2.24/2.41  ** KEPT (pick-wt=20): 43 [] -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),fe_qual(A),B),C))|ti(A,B)=ti(A,C).
% 2.24/2.41  ** KEPT (pick-wt=20): 44 [] ti(A,B)!=ti(A,C)|hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),fe_qual(A),B),C)).
% 2.24/2.41  
% 2.24/2.41  ------------> process sos:
% 2.24/2.41  ** KEPT (pick-wt=3): 51 [] A=A.
% 2.24/2.41  ** KEPT (pick-wt=11): 52 [] ti(fun(A,fun(A,bool)),induct_e_qual(A))=induct_e_qual(A).
% 2.24/2.41  ---> New Demodulator: 53 [new_demod,52] ti(fun(A,fun(A,bool)),induct_e_qual(A))=induct_e_qual(A).
% 2.24/2.41  ** KEPT (pick-wt=5): 54 [] ti(bool,induct_false)=induct_false.
% 2.24/2.41  ---> New Demodulator: 55 [new_demod,54] ti(bool,induct_false)=induct_false.
% 2.24/2.41  ** KEPT (pick-wt=5): 56 [] ti(bool,induct_true)=induct_true.
% 2.24/2.41  ---> New Demodulator: 57 [new_demod,56] ti(bool,induct_true)=induct_true.
% 2.24/2.41  ** KEPT (pick-wt=7): 58 [] ti(A,undefined(A))=undefined(A).
% 2.24/2.41  ---> New Demodulator: 59 [new_demod,58] ti(A,undefined(A))=undefined(A).
% 2.24/2.41  ** KEPT (pick-wt=22): 60 [] ti(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_509422987triple(A)),hoare_244953527triple(A))=hoare_244953527triple(A).
% 2.24/2.41  ---> New Demodulator: 61 [new_demod,60] ti(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_509422987triple(A)),hoare_244953527triple(A))=hoare_244953527triple(A).
% 2.24/2.41  ** KEPT (pick-wt=22): 62 [] ti(fun(hoare_509422987triple(A),fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),hoare_2037801986triple(A))=hoare_2037801986triple(A).
% 2.24/2.41  ---> New Demodulator: 63 [new_demod,62] ti(fun(hoare_509422987triple(A),fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),hoare_2037801986triple(A))=hoare_2037801986triple(A).
% 2.24/2.41  ** KEPT (pick-wt=5): 64 [] ti(bool,hoare_1883395792gleton)=hoare_1883395792gleton.
% 2.24/2.41  ---> New Demodulator: 65 [new_demod,64] ti(bool,hoare_1883395792gleton)=hoare_1883395792gleton.
% 2.24/2.41  ** KEPT (pick-wt=21): 66 [] ti(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),hoare_1580379338ep_set(A))=hoare_1580379338ep_set(A).
% 2.24/2.41  ---> New Demodulator: 67 [new_demod,66] ti(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),hoare_1580379338ep_set(A))=hoare_1580379338ep_set(A).
% 2.24/2.41  ** KEPT (pick-wt=13): 68 [] ti(fun(fun(A,bool),fun(A,bool)),collect(A))=collect(A).
% 2.24/2.41  ---> New Demodulator: 69 [new_demod,68] ti(fun(fun(A,bool),fun(A,bool)),collect(A))=collect(A).
% 2.24/2.41  ** KEPT (pick-wt=21): 70 [] ti(fun(fun(A,B),fun(fun(B,A),fun(fun(B,bool),bool))),type_definition(A,B))=type_definition(A,B).
% 2.24/2.42  ---> New Demodulator: 71 [new_demod,70] ti(fun(fun(A,B),fun(fun(B,A),fun(fun(B,bool),bool))),type_definition(A,B))=type_definition(A,B).
% 2.24/2.42  ** KEPT (pick-wt=11): 72 [] ti(fun(A,fun(A,bool)),fe_qual(A))=fe_qual(A).
% 2.24/2.42  ---> New Demodulator: 73 [new_demod,72] ti(fun(A,fun(A,bool)),fe_qual(A))=fe_qual(A).
% 2.24/2.42  ** KEPT (pick-wt=15): 74 [] hAPP(A,B,ti(fun(A,B),C),D)=hAPP(A,B,C,D).
% 2.24/2.42  ---> New Demodulator: 75 [new_demod,74] hAPP(A,B,ti(fun(A,B),C),D)=hAPP(A,B,C,D).
% 2.24/2.42  ** KEPT (pick-wt=13): 76 [] hAPP(A,B,C,ti(A,D))=hAPP(A,B,C,D).
% 2.24/2.42  ---> New Demodulator: 77 [new_demod,76] hAPP(A,B,C,ti(A,D))=hAPP(A,B,C,D).
% 2.24/2.42  ** KEPT (pick-wt=13): 78 [] ti(A,hAPP(B,A,C,D))=hAPP(B,A,C,D).
% 2.24/2.42  ---> New Demodulator: 79 [new_demod,78] ti(A,hAPP(B,A,C,D))=hAPP(B,A,C,D).
% 2.24/2.42  ** KEPT (pick-wt=13): 80 [] ti(fun(A,fun(fun(A,bool),bool)),member(A))=member(A).
% 2.24/2.42  ---> New Demodulator: 81 [new_demod,80] ti(fun(A,fun(fun(A,bool),bool)),member(A))=member(A).
% 2.24/2.42  ** KEPT (pick-wt=9): 82 [] hBOOL(hoare_1883395792gleton)|ti(state,A)=ti(state,B).
% 2.24/2.42  ** KEPT (pick-wt=39): 83 [] hAPP(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_509422987triple(A),hoare_244953527triple(A),hAPP(hoare_509422987triple(A),fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_2037801986triple(A),B))=B.
% 2.24/2.42  ---> New Demodulator: 84 [new_demod,83] hAPP(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_509422987triple(A),hoare_244953527triple(A),hAPP(hoare_509422987triple(A),fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_2037801986triple(A),B))=B.
% 2.24/2.42  ** KEPT (pick-wt=129): 85 [] hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),fun(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool),member(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),hAPP(hoare_509422987triple(A),fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_2037801986triple(A),B)),hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),collect(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),hoare_1580379338ep_set(A)))).
% 2.24/2.42  ** KEPT (pick-wt=170): 86 [] hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool,hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_509422987triple(A)),fun(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool),hAPP(fun(hoare_509422987triple(A),fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),fun(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_509422987triple(A)),fun(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool)),type_definition(hoare_509422987triple(A),fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),hoare_2037801986triple(A)),hoare_244953527triple(A)),hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),collect(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),hoare_1580379338ep_set(A)))).
% 2.24/2.42  ** KEPT (pick-wt=121): 87 [] hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),fun(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool),member(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),$f3(A,B,C)),hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),collect(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),hoare_1580379338ep_set(A))))|hBOOL(hAPP(hoare_509422987triple(A),bool,C,B)).
% 2.24/2.42  ** KEPT (pick-wt=23): 89 [copy,88,flip.1] hAPP(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_509422987triple(A),hoare_244953527triple(A),$f4(A,B))=B.
% 2.24/2.42  ---> New Demodulator: 90 [new_demod,89] hAPP(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),hoare_509422987triple(A),hoare_244953527triple(A),$f4(A,B))=B.
% 2.24/2.42  ** KEPT (pick-wt=113): 91 [] hBOOL(hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool,hAPP(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),fun(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),bool),member(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),$f4(A,B)),hAPP(fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),fun(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool),bool),collect(fun(node(sum_sum(com,fun(A,fun(state,bool))),sum_sum(state,A)),bool)),hoare_1580379338ep_set(A)))).
% 2.24/2.42  ** KEPT (pick-wt=2): 92 [] hBOOL(induct_true).
% 2.24/2.42    Following clause subsumed by 92 during input processing: 0 [] hBOOL(induct_true).
% 2.24/2.42  ** KEPT (pick-wt=16): 93 [] hAPP(fun(A,bool),fun(A,bool),collect(A),B)=ti(fun(A,bool),B).
% 2.24/2.42  ** KEPT (pick-wt=2): 94 [] enum(bool).
% 2.24/2.42  ** KEPT (pick-wt=2): 95 [] cl_HOL_Oe_qual(com).
% 2.24/2.42  ** KEPT (pick-wt=2): 96 [] cl_HOL_Oe_qual(bool).
% 2.24/2.42  ** KEPT (pick-wt=2): 97 [] cl_HOL_Oe_qual(state).
% 2.24/2.42  ** KEPT (pick-wt=4): 98 [] cl_HOL_Oe_qual(sum_sum(A,B)).
% 2.24/2.42  ** KEPT (pick-wt=3): 99 [] cl_HOL_Oe_qual(hoare_509422987triple(A)).
% 2.24/2.42  ** KEPT (pick-wt=9): 100 [] ti(A,ti(A,B))=ti(A,B).
% 2.24/2.42  ---> New Demodulator: 101 [new_demod,100] ti(A,ti(A,B))=ti(A,B).
% 2.24/2.42  ** KEPT (pick-wt=2): 102 [] hBOOL(hoare_1883395792gleton).
% 2.24/2.42  ** KEPT (pick-wt=7): 103 [] ti(state,A)=ti(state,$c3).
% 2.24/2.42    Following clause subsumed by 51 during input processing: 0 [copy,51,flip.1] A=A.
% 2.24/2.42  51 back subsumes 48.
% 2.24/2.42  51 back subsumes 47.
% 2.24/2.42  51 back subsumes 46.
% 2.24/2.42  51 back subsumes 45.
% 2.24/2.42  >>>> Starting back demodulation with 53.
% 2.24/2.42  >>>> Starting back demodulation with 55.
% 2.24/2.42  >>>> Starting back demodulation with 57.
% 2.24/2.42  >>>> Starting back demodulation with 59.
% 2.24/2.42  >>>> Starting back demodulation with 61.
% 2.24/2.42  >>>> Starting back demodulation with 63.
% 2.24/2.42  >>>> Starting back demodulation with 65.
% 2.24/2.42  >>>> Starting back demodulation with 67.
% 2.24/2.42  >>>> Starting back demodulation with 69.
% 2.24/2.42  >>>> Starting back demodulation with 71.
% 2.24/2.42  >>>> Starting back demodulation with 73.
% 2.24/2.42  >>>> Starting back demodulation with 75.
% 2.24/2.42  >>>> Starting back demodulation with 77.
% 2.24/2.42  >>>> Starting back demodulation with 79.
% 2.24/2.42  >>>> Starting back demodulation with 81.
% 2.24/2.42  >>>> Starting back demodulation with 84.
% 2.24/2.42  >>>> Starting back demodulation with 90.
% 2.24/2.42  ** KEPT (pick-wt=16): 104 [copy,93,flip.1] ti(fun(A,bool),B)=hAPP(fun(A,bool),fun(A,bool),collect(A),B).
% 2.24/2.42  >>>> Starting back demodulation with 101.
% 2.24/2.42  102 back subsumes 82.
% 2.24/2.42  ** KEPT (pick-wt=7): 105 [copy,103,flip.1] ti(state,$c3)=ti(state,A).
% 2.24/2.42    Following clause subsumed by 93 during input processing: 0 [copy,104,flip.1] hAPP(fun(A,bool),fun(A,bool),collect(A),B)=ti(fun(A,bool),B).
% 2.24/2.42    Following clause subsumed by 103 during input processing: 0 [copy,105,flip.1] ti(state,A)=ti(state,$c3).
% 2.24/2.42  
% 2.24/2.42  ======= end of input processing =======
% 2.24/2.42  
% 2.24/2.42  =========== start of search ===========
% 2.24/2.42  
% 2.24/2.42  
% 2.24/2.42  Resetting weight limit to 2.
% 2.24/2.42  
% 2.24/2.42  
% 2.24/2.42  Resetting weight limit to 2.
% 2.24/2.42  
% 2.24/2.42  sos_size=34
% 2.24/2.42  
% 2.24/2.42  -------- PROOF -------- 
% 2.24/2.42  
% 2.24/2.42  -----> EMPTY CLAUSE at   0.03 sec ----> 106 [para_from,103.1.1,4.2.1,unit_del,102,105] $F.
% 2.24/2.42  
% 2.24/2.42  Length of proof is 1.  Level of proof is 1.
% 2.24/2.42  
% 2.24/2.42  ---------------- PROOF ----------------
% 2.24/2.42  % SZS status Theorem
% 2.24/2.42  % SZS output start Refutation
% See solution above
% 2.24/2.42  ------------ end of proof -------------
% 2.24/2.42  
% 2.24/2.42  
% 2.24/2.42  Search stopped by max_proofs option.
% 2.24/2.42  
% 2.24/2.42  
% 2.24/2.42  Search stopped by max_proofs option.
% 2.24/2.42  
% 2.24/2.42  ============ end of search ============
% 2.24/2.42  
% 2.24/2.42  -------------- statistics -------------
% 2.24/2.42  clauses given                 15
% 2.24/2.42  clauses generated            279
% 2.24/2.42  clauses kept                  84
% 2.24/2.42  clauses forward subsumed      13
% 2.24/2.42  clauses back subsumed          5
% 2.24/2.42  Kbytes malloced             5859
% 2.24/2.42  
% 2.24/2.42  ----------- times (seconds) -----------
% 2.24/2.42  user CPU time          0.03          (0 hr, 0 min, 0 sec)
% 2.24/2.42  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 2.24/2.42  wall-clock time        2             (0 hr, 0 min, 2 sec)
% 2.24/2.42  
% 2.24/2.42  That finishes the proof of the theorem.
% 2.24/2.42  
% 2.24/2.42  Process 17926 finished Wed Jul 27 02:51:07 2022
% 2.24/2.42  Otter interrupted
% 2.24/2.42  PROOF FOUND
%------------------------------------------------------------------------------