Vampire---5.0.1.THM-Ref.s

%------------------------------------------------------------------------------
% File     : Vampire---5.0.1
% Problem  : SCT230_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% Computer : n002.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 12:37:17 PM UTC 2026

% Result   : Theorem 2.68s 1.31s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   62 (  14 unt;   0 typ;   0 def)
%            Number of atoms       :  222 (  19 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  286 ( 126   ~; 140   |;   5   &)
%                                         (   6 <=>;   6  =>;   0  <=;   3 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-5 aty)
%            Number of functors    :   54 (  54 usr;  10 con; 0-7 aty)
%            Number of variables   :   90 (  87   !;   3   ?;  90   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    arrow_411405190le_alt: $tType ).

tff(type_def_6,type,
    arrow_159774573e_indi: $tType ).

tff(type_def_7,type,
    bool: $tType ).

tff(type_def_8,type,
    fun: ( $tType * $tType ) > $tType ).

tff(type_def_9,type,
    product_prod: ( $tType * $tType ) > $tType ).

tff(func_def_0,type,
    arrow_1985332922le_Lin: fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool) ).

tff(func_def_1,type,
    arrow_610318064e_Prof: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),bool) ).

tff(func_def_2,type,
    arrow_1158827142_above: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).

tff(func_def_3,type,
    arrow_319942042_below: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).

tff(func_def_4,type,
    arrow_276188178_mkbot: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).

tff(func_def_5,type,
    arrow_424895264_mktop: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).

tff(func_def_6,type,
    comp: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).

tff(func_def_7,type,
    product_Pair: 
      !>[X0: $tType,X1: $tType] : ( ( X0 * X1 ) > product_prod(X0,X1) ) ).

tff(func_def_8,type,
    product_curry: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X0,X1),X2) > fun(X0,fun(X1,X2)) ) ).

tff(func_def_9,type,
    produc1605651328_split: 
      !>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).

tff(func_def_10,type,
    product_prod_case: 
      !>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).

tff(func_def_11,type,
    product_prod_rec: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).

tff(func_def_12,type,
    id_on: 
      !>[X0: $tType] : ( fun(X0,bool) > fun(product_prod(X0,X0),bool) ) ).

tff(func_def_13,type,
    converse: 
      !>[X0: $tType,X1: $tType] : fun(fun(product_prod(X0,X1),bool),fun(product_prod(X1,X0),bool)) ).

tff(func_def_14,type,
    inv_image: 
      !>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(X1,X0) ) > fun(product_prod(X1,X1),bool) ) ).

tff(func_def_15,type,
    aa: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).

tff(func_def_16,type,
    fFalse: bool ).

tff(func_def_17,type,
    fTrue: bool ).

tff(func_def_18,type,
    f: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).

tff(func_def_19,type,
    p1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).

tff(func_def_20,type,
    p: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).

tff(func_def_21,type,
    a: arrow_411405190le_alt ).

tff(func_def_22,type,
    b: arrow_411405190le_alt ).

tff(func_def_23,type,
    c: arrow_411405190le_alt ).

tff(func_def_24,type,
    sK0: 
      !>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X1,X0),bool) * product_prod(X0,X1) ) > X1 ) ).

tff(func_def_25,type,
    sK1: 
      !>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X1,X0),bool) * product_prod(X0,X1) ) > X0 ) ).

tff(func_def_26,type,
    sK2: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).

tff(func_def_27,type,
    sK3: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).

tff(func_def_28,type,
    sK4: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).

tff(func_def_29,type,
    sK5: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).

tff(func_def_30,type,
    sK6: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).

tff(func_def_31,type,
    sK7: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).

tff(func_def_32,type,
    sK8: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).

tff(func_def_33,type,
    sK9: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).

tff(func_def_34,type,
    sK10: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).

tff(func_def_35,type,
    sK11: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).

tff(func_def_36,type,
    sK12: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).

tff(func_def_37,type,
    sK13: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X0 ) ).

tff(func_def_38,type,
    sK14: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X1 ) ).

tff(func_def_39,type,
    sK15: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X2 ) ).

tff(func_def_40,type,
    sK16: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X3 ) ).

tff(func_def_41,type,
    sK17: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X4 ) ).

tff(func_def_42,type,
    sK18: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X0 ) ).

tff(func_def_43,type,
    sK19: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X1 ) ).

tff(func_def_44,type,
    sK20: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X2 ) ).

tff(func_def_45,type,
    sK21: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X3 ) ).

tff(func_def_46,type,
    sK22: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X4 ) ).

tff(func_def_47,type,
    sK23: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X5 ) ).

tff(func_def_48,type,
    sK24: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).

tff(func_def_49,type,
    sK25: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).

tff(func_def_50,type,
    sK26: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).

tff(func_def_51,type,
    sK27: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).

tff(pred_def_1,type,
    arrow_1958449194le_IIA: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > $o ).

tff(pred_def_2,type,
    arrow_987702531ctator: ( fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_159774573e_indi ) > $o ).

tff(pred_def_3,type,
    arrow_2069624013nimity: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > $o ).

tff(pred_def_4,type,
    in_rel: 
      !>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X1),bool) * X0 * X1 ) > $o ) ).

tff(pred_def_5,type,
    antisym: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).

tff(pred_def_6,type,
    irrefl: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).

tff(pred_def_7,type,
    total_on: 
      !>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) ) > $o ) ).

tff(pred_def_8,type,
    member: 
      !>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).

tff(pred_def_9,type,
    pp: bool > $o ).

tff(f3,axiom,
    a != b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_A_I1_J) ).

tff(f6,axiom,
    member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),p,arrow_610318064e_Prof),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_A_I4_J) ).

tff(f8,axiom,
    member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),arrow_610318064e_Prof),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_cP) ).

tff(f14,axiom,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ( X3 != X2 )
     => ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
       => ( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
         => ( ! [X4: arrow_159774573e_indi] :
                ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X4))
              <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X4)) )
           => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
            <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__C3_C) ).

tff(f18,axiom,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X0),bool),X3: X0,X4: X1] :
      ( member(product_prod(X1,X0),product_Pair(X1,X0,X4,X3),X2)
     => member(product_prod(X0,X1),product_Pair(X0,X1,X3,X4),aa(fun(product_prod(X1,X0),bool),fun(product_prod(X0,X1),bool),converse(X1,X0),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_converseI) ).

tff(f24,axiom,
    ! [X0: $tType,X1: $tType,X2: $tType,X3: fun(X2,X1),X4: fun(X1,X0),X5: X2] : ( aa(X2,X0,comp(X1,X0,X2,X4,X3),X5) = aa(X1,X0,X4,aa(X2,X1,X3,X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_o__def) ).

tff(f26,axiom,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X0),bool),X3: X1,X4: X0] :
      ( member(product_prod(X0,X1),product_Pair(X0,X1,X4,X3),aa(fun(product_prod(X1,X0),bool),fun(product_prod(X0,X1),bool),converse(X1,X0),X2))
     => member(product_prod(X1,X0),product_Pair(X1,X0,X3,X4),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_converseD) ).

tff(f101,conjecture,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p))
  <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(f102,negated_conjecture,
    ~ ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p))
    <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p))) ),
    inference(negated_conjecture,[status(cth)],[f101]) ).

tff(f103,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p))
  <~> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p))) ),
    inference(ennf_transformation,[],[f102]) ).

tff(f109,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X0),bool),X3: X1,X4: X0] :
      ( member(product_prod(X1,X0),product_Pair(X1,X0,X3,X4),X2)
      | ~ member(product_prod(X0,X1),product_Pair(X0,X1,X4,X3),aa(fun(product_prod(X1,X0),bool),fun(product_prod(X0,X1),bool),converse(X1,X0),X2)) ),
    inference(ennf_transformation,[],[f26]) ).

tff(f110,plain,
    ! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X0),bool),X3: X0,X4: X1] :
      ( member(product_prod(X0,X1),product_Pair(X0,X1,X3,X4),aa(fun(product_prod(X1,X0),bool),fun(product_prod(X0,X1),bool),converse(X1,X0),X2))
      | ~ member(product_prod(X1,X0),product_Pair(X1,X0,X4,X3),X2) ),
    inference(ennf_transformation,[],[f18]) ).

tff(f112,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) )
      | ? [X4: arrow_159774573e_indi] :
          ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X4))
        <~> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X4)) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X3 ) ),
    inference(ennf_transformation,[],[f14]) ).

tff(f113,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      <=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) )
      | ? [X4: arrow_159774573e_indi] :
          ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X4))
        <~> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X4)) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X3 ) ),
    inference(flattening,[],[f112]) ).

tff(f125,plain,
    ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) )
    & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ) ),
    inference(nnf_transformation,[],[f103]) ).

tff(f129,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1)) ) )
      | ? [X4: arrow_159774573e_indi] :
          ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X4))
            | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X4)) )
          & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X4))
            | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,X4)) ) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X3 ) ),
    inference(nnf_transformation,[],[f113]) ).

tff(f130,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
      ( ( ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1)) ) )
      | ( ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK3(X0,X1,X2,X3)))
          | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK3(X0,X1,X2,X3))) )
        & ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK3(X0,X1,X2,X3)))
          | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK3(X0,X1,X2,X3))) ) )
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X3 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X4,sK3(X0,X1,X2,X3))],[f129]) ).

tff(f143,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p)))
    | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ),
    inference(cnf_transformation,[],[f125]) ).

tff(f144,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p)))
    | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ),
    inference(cnf_transformation,[],[f125]) ).

tff(f147,plain,
    ! [X1: $tType,X0: $tType,X2: $tType,X3: fun(X2,X1),X4: fun(X1,X0),X5: X2] : ( aa(X2,X0,comp(X1,X0,X2,X4,X3),X5) = aa(X1,X0,X4,aa(X2,X1,X3,X5)) ),
    inference(cnf_transformation,[],[f24]) ).

tff(f154,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool),X3: X1,X4: X0] :
      ( ~ member(product_prod(X0,X1),product_Pair(X0,X1,X4,X3),aa(fun(product_prod(X1,X0),bool),fun(product_prod(X0,X1),bool),converse(X1,X0),X2))
      | member(product_prod(X1,X0),product_Pair(X1,X0,X3,X4),X2) ),
    inference(cnf_transformation,[],[f109]) ).

tff(f156,plain,
    ! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool),X3: X0,X4: X1] :
      ( member(product_prod(X0,X1),product_Pair(X0,X1,X3,X4),aa(fun(product_prod(X1,X0),bool),fun(product_prod(X0,X1),bool),converse(X1,X0),X2))
      | ~ member(product_prod(X1,X0),product_Pair(X1,X0,X4,X3),X2) ),
    inference(cnf_transformation,[],[f110]) ).

tff(f160,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK3(X0,X1,X2,X3)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK3(X0,X1,X2,X3)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X3 ) ),
    inference(cnf_transformation,[],[f130]) ).

tff(f161,plain,
    ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X1))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X2,X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK3(X0,X1,X2,X3)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,X3,X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X1,sK3(X0,X1,X2,X3)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1,arrow_610318064e_Prof)
      | ( X2 = X3 ) ),
    inference(cnf_transformation,[],[f130]) ).

tff(f170,plain,
    member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),arrow_610318064e_Prof),
    inference(cnf_transformation,[],[f8]) ).

tff(f171,plain,
    member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),p,arrow_610318064e_Prof),
    inference(cnf_transformation,[],[f6]) ).

tff(f172,plain,
    a != b,
    inference(cnf_transformation,[],[f3]) ).

tff(f437,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),X0,b,a)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),X0,b,a)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ( a = b )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ),
    inference(resolution,[],[f160,f144]) ).

tff(f443,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),X0,b,a)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),X0,b,a)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ( a = b )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ),
    inference(forward_subsumption_resolution,[],[f437,f170]) ).

tff(f445,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),X0,b,a)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),X0,b,a)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ),
    inference(forward_subsumption_resolution,[],[f443,f172]) ).

tff(f447,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),converse(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),X0,b,a))))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),X0,b,a)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ),
    inference(forward_demodulation,[],[f445,f147]) ).

tff(f453,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),X0,b,a)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),X0,b,a)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) ),
    inference(resolution,[],[f447,f154]) ).

tff(f456,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),X0,b,a)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),X0,b,a)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ( a = b )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ),
    inference(resolution,[],[f161,f144]) ).

tff(f462,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),X0,b,a)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),X0,b,a)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ( a = b )
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ),
    inference(forward_subsumption_resolution,[],[f456,f170]) ).

tff(f464,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),X0,b,a)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),X0,b,a)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ),
    inference(forward_subsumption_resolution,[],[f462,f172]) ).

tff(f466,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),converse(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),X0,b,a))))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),X0,b,a)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ),
    inference(forward_demodulation,[],[f464,f147]) ).

tff(f473,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),X0,b,a)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),X0,b,a)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0)) ),
    inference(resolution,[],[f466,f156]) ).

tff(f492,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),p,b,a)))
    | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),p,arrow_610318064e_Prof)
    | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p))
    | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ),
    inference(factoring,[],[f473]) ).

tff(f493,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),p,b,a)))
    | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),p,arrow_610318064e_Prof)
    | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ),
    inference(duplicate_literal_removal,[],[f492]) ).

tff(f495,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),p,b,a)))
    | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ),
    inference(forward_subsumption_resolution,[],[f493,f171]) ).

tff(f512,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p))
    | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),p,b,a)))
    | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),p,arrow_610318064e_Prof)
    | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p))
    | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ),
    inference(resolution,[],[f495,f453]) ).

tff(f513,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p))
    | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),p,b,a)))
    | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),p,arrow_610318064e_Prof) ),
    inference(duplicate_literal_removal,[],[f512]) ).

tff(f514,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p))
    | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),p,arrow_610318064e_Prof) ),
    inference(forward_subsumption_resolution,[],[f513,f495]) ).

tff(f515,plain,
    ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)),
    inference(forward_subsumption_resolution,[],[f514,f171]) ).

tff(f518,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(p,X0,a,b)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK3(p,X0,a,b)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),p,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ( a = b ) ),
    inference(resolution,[],[f515,f161]) ).

tff(f519,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(p,X0,a,b)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK3(p,X0,a,b)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),p,arrow_610318064e_Prof)
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ( a = b ) ),
    inference(resolution,[],[f515,f160]) ).

tff(f520,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(p,X0,a,b)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK3(p,X0,a,b)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ( a = b ) ),
    inference(forward_subsumption_resolution,[],[f519,f171]) ).

tff(f521,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(p,X0,a,b)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK3(p,X0,a,b)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof)
      | ( a = b ) ),
    inference(forward_subsumption_resolution,[],[f518,f171]) ).

tff(f524,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(p,X0,a,b)))
      | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK3(p,X0,a,b)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof) ),
    inference(forward_subsumption_resolution,[],[f520,f172]) ).

tff(f525,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,X0))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(p,X0,a,b)))
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK3(p,X0,a,b)))
      | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X0,arrow_610318064e_Prof) ),
    inference(forward_subsumption_resolution,[],[f521,f172]) ).

tff(f540,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(p,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),a,b)))
    | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),sK3(p,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),a,b)))
    | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),arrow_610318064e_Prof)
    | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ),
    inference(resolution,[],[f524,f143]) ).

tff(f554,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(p,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),a,b)))
    | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),sK3(p,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),a,b)))
    | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ),
    inference(forward_subsumption_resolution,[],[f540,f170]) ).

tff(f555,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(p,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),a,b)))
    | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),sK3(p,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),a,b))) ),
    inference(forward_subsumption_resolution,[],[f554,f515]) ).

tff(f556,plain,
    ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),converse(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(p,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),a,b))))
    | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(p,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),a,b))) ),
    inference(forward_demodulation,[],[f555,f147]) ).

tff(f557,plain,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(p,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),a,b))),
    inference(forward_subsumption_resolution,[],[f556,f154]) ).

tff(f577,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(p,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),a,b)))
    | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),sK3(p,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),a,b)))
    | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),arrow_610318064e_Prof)
    | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ),
    inference(resolution,[],[f525,f143]) ).

tff(f594,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),sK3(p,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),a,b)))
    | ~ member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),arrow_610318064e_Prof)
    | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ),
    inference(forward_subsumption_resolution,[],[f577,f557]) ).

tff(f595,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),sK3(p,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),a,b)))
    | member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,p)) ),
    inference(forward_subsumption_resolution,[],[f594,f170]) ).

tff(f596,plain,
    ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),sK3(p,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),a,b))),
    inference(forward_subsumption_resolution,[],[f595,f515]) ).

tff(f597,plain,
    ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,b,a),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),converse(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(p,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),a,b)))),
    inference(forward_demodulation,[],[f596,f147]) ).

tff(f610,plain,
    ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt,a,b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK3(p,comp(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi,converse(arrow_411405190le_alt,arrow_411405190le_alt),p),a,b))),
    inference(resolution,[],[f597,f156]) ).

tff(f611,plain,
    $false,
    inference(forward_subsumption_resolution,[],[f610,f557]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SCT230_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37  % Computer : n002.cluster.edu
% 0.11/0.37  % Model    : x86_64 x86_64
% 0.11/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37  % Memory   : 8046.5625MB
% 0.11/0.37  % OS       : Linux 6.8.0-71-generic
% 0.11/0.37  % CPULimit : 300
% 0.11/0.37  % WCLimit  : 300
% 0.11/0.37  % DateTime : Mon Sep 28 00:03:22 UTC 2026
% 0.11/0.38  % CPUTime  : 
% 0.11/0.38  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41  Running first-order theorem proving
% 0.11/0.41  Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.68/1.31  % (4027156)Detected formulas, will run a generic FOF schedule.
% 2.68/1.31  % (4027161)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=548533816:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.31  % (4027166)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2481983290:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.31  % (4027164)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2873411333:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.31  % (4027167)dis-21_1_sil=8000:lcm=predicate:random_seed=2670195617:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.68/1.31  % (4027163)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4279075024:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.31  % (4027162)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2012434725:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.31  % (4027165)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3263666326:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.31  % (4027164)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.68/1.31  % (4027163)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.68/1.31  % (4027164)Refutation not found, incomplete strategy
% 2.68/1.31  % (4027164)------------------------------
% 2.68/1.31  % (4027164)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.31  % (4027164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.31  % (4027164)CaDiCaL version: 2.1.3
% 2.68/1.31  % (4027164)Termination reason: Refutation not found, incomplete strategy
% 2.68/1.31  % (4027164)Time elapsed: 0.009 s
% 2.68/1.31  % (4027164)Peak memory usage: 89 MB
% 2.68/1.31  % (4027164)Instructions burned: 13 (million)
% 2.68/1.31  % (4027165)First to succeed.
% 2.68/1.31  % (4027165)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4027156"
% 2.68/1.31  % (4027167)Instruction limit reached! 
% 2.68/1.31  % (4027167)------------------------------
% 2.68/1.31  % (4027167)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.31  % (4027167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.31  % (4027167)CaDiCaL version: 2.1.3
% 2.68/1.31  % (4027167)Termination reason: Instruction limit
% 2.68/1.31  % (4027167)Termination phase: Saturation
% 2.68/1.31  % (4027167)Time elapsed: 0.075 s
% 2.68/1.31  % (4027167)Peak memory usage: 89 MB
% 2.68/1.31  % (4027167)Instructions burned: 129 (million)
% 2.68/1.31  % (4027166)Instruction limit reached! 
% 2.68/1.31  % (4027166)------------------------------
% 2.68/1.31  % (4027166)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.31  % (4027166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.31  % (4027166)CaDiCaL version: 2.1.3
% 2.68/1.31  % (4027166)Termination reason: Instruction limit
% 2.68/1.31  % (4027166)Termination phase: Saturation
% 2.68/1.31  % (4027166)Time elapsed: 0.094 s
% 2.68/1.31  % (4027166)Peak memory usage: 90 MB
% 2.68/1.31  % (4027166)Instructions burned: 140 (million)
% 2.68/1.31  % Exception at run slice level
% 2.68/1.31  User error: GNN currently only supports monomorphic FOL.
% 2.68/1.31  % (4027175)lrs+10_1_sil=8000:sp=occurrence:random_seed=863128416:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.68/1.31  % (4027164)------------------------------
% 2.68/1.31  % (4027164)------------------------------
% 2.68/1.31  % (4027176)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2974583920:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.68/1.31  % (4027165)Refutation found. Thanks to Tanya!
% 2.68/1.31  % SZS status Theorem for theBenchmark
% 2.68/1.31  % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50  % (4027165)------------------------------
% 0.17/1.50  % (4027165)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50  % (4027165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50  % (4027165)CaDiCaL version: 2.1.3
% 0.17/1.50  % (4027165)Termination reason: Refutation
% 0.17/1.50  % (4027165)Time elapsed: 0.032 s
% 0.17/1.50  % (4027165)Peak memory usage: 89 MB
% 0.17/1.50  % (4027165)Instructions burned: 53 (million)
% 0.17/1.50  % (4027165)------------------------------
% 0.17/1.50  % (4027165)------------------------------
% 0.17/1.50  % (4027156)Success in time 0.461 s
% 0.17/1.50  % Vampire exiting
%------------------------------------------------------------------------------